Aristotle - Metaphysics, Volume 2 (Ross).pdf

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TE 1rapaKOAov8ELV luaxw~ TaL~ KaT'I'/yop(aL~ Ital I-'~ EfvaL fV l-''I'/aEI-'Lff (ofov oiir' fV Tp T( furLV oiir' fV Tp 1rOLOV, ciAA' ., t rt ~ ¥) \ ~ \ ~8 Ol-' OLWS "'XEL ooU1rEp Tu uV KaL Tit 1-''1'/ 1rpOUltaT'I'/yopELU at b 28 OOX1 E 29 ro] T' TO EJr AI. Xpo,lM' om. AI • •rra JTr i et ut vid. AI.: .l AbE 31 roiiTo ••• 32 ¢orros seel. 32 3'] yap fOTt. AI. 33 rlll6)11 codd. r AI.: r",o,lI Christ Jaeger 35 ~"U(6)S Ab 1054.2 tPt»lIqfll ~ rTVP.tPt»I'OIl (ort, AI. 6 III om. E '"] III rfi J 7 ;11] 1111 Ab 8 awo Ab et fort. Al.: aWoii EJr: awo Ilwoii i 10 &'II'a."., AbAl.o: '11'0.".1 EJ 12 oiJulall p.lOIl EJr et ut vid. AI.: owlll p.la Ab 'YP' E awo EJ AI. : awo rr Ab 13 ro &,,] &11 1<:J 14-15 ,,, '''~ fecit £ : '" P.~~f~ ~II (plap expunctum) J IS ri om. A 16 r'ii p.q] 0\1 rljl AI. 'YP' E

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Aas, Kal Tciiv Ka6' tKaCITov' frl'/ yap c1v, p.~ lip.a, 0 ain-os 35 AfVKOS Kal plAas' Ka(ToI fVavT(OV TO AfVKOV T!fl p./AaVI)· dMa Tciiv fvavrlwv TO. P.Ev KaTa CTVP.{3f{3I'/KOS 117rapXfl fVtOlS, OLOV Kal Ta VVV flpl'/plva Kal c1AAa '7I'OAAa, TO. at(Osg& aMvaTov, ~v fClTl Kal TO rp6apTov Kal TO c1rp6apTov' ouat-v yap fCTn rp6apTov KaTa CTVP.{3f{3I'/KOS· TO p.'tv yap CTVP.{3f{3l'/KOS ~Va/xfTal p.~ 1l'71'apXfw, TO a't rp6ap'l"ov Tciiv U avaYKI'/S hapxovrwv ~CITtV OLS 11'71'apXH' ~ ICITal TO aUTO Kal tv rp6ap5 TOV Kal c1rp6apTov, d fvaixnal p.~ 11'71'apXflV aUT!fl TO rp6apTov. ~ T~V oUCTlav c1pa ~ ~V Til OUCT(q. avaYKI'/ 11'71'apXfW TO rp6apTov fKaCITIfI TIdV rp6ap'l"ciiv. 0 a' ain-os AOYOS Kal '7I'fpl TOV arp6apTov' Tciiv yap ff avaYKI'/S v'7I'apxovrwv c1p.rpw. c1pa Kal Ka6' & '7I'PIdTOV TO p.t-v rp6aoTov TO a' c1rp6apTov, 10 lXH avrl6fCTlv, clSClTf avaYKI'/ YfVH tnpa fival. rpavfpov Tolvvv {)n OUK fvalxnal fival ftal'/ TOlavTa oLa AlyovCT( nVH' ICTTa! yap Kal c1v6pw'7l'os 0 P.EV rp6apTos 0 a' c1rp6apTos. Ka(ToI T!fl fraH TaVTa AiYfTal fival TO. dal'/ TO&S nCTl Kat oux op.6wvp.a· Ta at- ylvfl tnpa '7I'Af&OV allCTTI'/Kfv ~ TO. fiaH.

n

15

K "On p.t-v 1j CTorp(a '7I'fpl apXas f'7l'lCTT1IP.1'/ Tls fCTn, a~AOV EK Tciiv '7I'p0TWV fV o's all'/'7I'0pI'/Ta! '7I'pOS Ta V'7I'O Tciiv c1Mwv ~o flpl'/p.tva '7I'fpl Tciiv apxciiv' a'7l'OprlCTflf a' c1v TIS '7I'OTfPOV p.(av V'7I'OAa{3f&V Eival af& T~V CTorp(av f'7l'lcrn7P.I'/V ~ '7I'oMas' El p.'fv yap p.lav, p.la y' ECTTlv afl Tciiv fva~'T(wv, a1 a' apxal OUK fvavr(al' El at- p.~ p.(a, '7I'o(as af& 6fwal TavTas; In TaS a'7l'OaHKnKaS apXas 6fwp~CTal p.w.s ~ '7I'AfWVWV; fl p.'tv yap 25 p.w.s, T( p.O.AAOV TaVTI1S ~ O'7l'OlaCToVV; d a'f '7I'AflOVWV, '7I'o(as af& TaVTas Tl6lval; In '7I'onpov '7I'!4CTciiv Tciiv OUCTlldV ~ oV; d p.'tv yap p.~ '7I'aCTIdV, '7I'olwv XaAf'7l'OV a'7l'OaoiJval' fl a't '7I'a1059" 2
1059" 4 Ka, om. Ab 7 .; a{,TOS II. Ab 9 q Ab KaO' 3 Bonitz: KaOo codd. U 'Ka, om. EJr 13 TOis Tlul om. r 14 fiafl] filln i$TI IIi ~ !Torpia 7Tfpi apxas 17T'CTT~"" Ab 18 I7TlUT~"'''S r T'S Ab AI.: om. EJr 22 y'] /I' EJl' 23 ,.'011 ri 26 TlOflla, Ab AI. : Of'''O' EJ

O'WII p,la, c1aT/>,oll 'II'W~ illalXETaL 'II'>'ELOIIII)l' ",'.' a~n)l' l'll'L11' ~ '£as IJ.OVOV ' II:TL 'II'OTf.POII 'II'EpL, Ta~ OVO' 1/~ KaL, TO, tTVp,{3E{3T/KOTa [4'11'OaE&(t~ lITTIII] j d ytlp 'II'Ept yE 1'4 tTVp,{3E{3T/- 30 KOTa 4'11'OaE&(ls ilTTw, 'II'Epl T4S o~O'las O~K IITTw' d a' lTfpa, --1. ~ u. "P,T/II EWaL.

Tls lKaTIpa Kal 'II'oTIpa O'ot/>laj " p,'fv Y4P 4'11'OaELKnK~, 0'0t/>la ~ 'II'Epl 1'4 O'Vp,{3E{3T/KOTa' p ~~ 'II'Ep2 1'4 'II'pWTa, ~ TWV O~O'LWV. 4).>.' ooa'f 'II'Ept TaS iv TOL'S t/>VO'LKOL'S dpT/p.fvas aiTlas ",V i'll'L(T/TOVp.fVT/V i'll'LO'n7p,T/V 6ETIov' O~E yap 'II'Epl TO OU (VEKEV 35 (TOLMOV Y4P TO 4ya60v,ToWO a'ill TOL'S 'II'paKTo,s iI'II'apXEL Ka2 TOL'S OOO'LII iv KW~a-f.L· Ka2 ToVTO 'II'PWTOV K"'E~TOLoVTOV yap 1'6 ~ '"'' ~ ~ . "EITTIII ltV 1 ~, , )"~ l'lAOS-TO vII: 'II'P",TOV KLVT/a-av OVK TOLS OKWT/TOLS' OA"'S ~' 4'11'Oplav IXEL 'II'OTEpOV 'II'0Tf. 'II'Epl T4S Ola-~TaS ooa-las ilTTu' ~ (T/TOVp.fVT/ WV i'll'~P,T/ ~ 011, 'II'Epl al Twas fTIpas. El Y4P I059b 'II'Ep2 IDas, ~ 'II'Ep2 Ttl E~T/ EfT/ &V ~ 'II'Epl 1'4 p,aBr,p.anKa. Ta p.fV ovv EtaT/ 8n O~K IITTL, ~~>.ov (8p.&Js a'f 4'11'oplav IXEL, K&V Elval TLS awa 6p, aLa Tl '11'01" O~ C,a-'II'EP E'II'2 TWII p.a6T/p,anKWV, oih-",s IXEL Ka2 i'll'l TWV ID",v ~V IlTTLV daT/' 5 >.IY&J a' lIn Ta ~p.aTLKa p.fV p.ETafU TE TWV ElM)v n61aa-L Ka2 TWV ala-~Twv otov TplTa nV4 'II'apa 1'4 E~T/ TE Kal 1'4 aEVpO, TplTOS ~. c1v6p"''II'os O~K IITTLV o~' r'll"ll'o~ 'II'ap' awov Tf. Kat TO~S Ka6' (Kaa-TOV' d~' av p,~ 100TW cds >.IYOV(rL, 'II'Ept 'II'o,a 6ETfov 'II'payp,aTEVEa-6aL TOil p.a~p.anKOVj O~ y4p 10 a~ 'II'Ept 1'4 ~EVpO' TOVT",V yap ovelv la-nv otov at p,a~p,anKa2 (T/TOWL TWV i'll'LIrTl'/p,wv)' oo~'f p,~v 'II'Ep2 1'4 p,06T/p.aTLKa ~ (T/TOVp.fVT/ WV ElTTl.V i'll'La-n/p,T/ (XWPLITTOV yap awwII ovefv)' au' O~E TWV ala-~T;;'v o~O'Lidv' t/>6apTat yap. 8>.w~~' 4'11'0p~a-E" ns &v 'II'olas ilTTl.v i'll'LITT~P,T/S TO aLa'll'O~a-aL 'II'EPI. rij~ 1;\

a 28 IIWrjll in margo E 30 o,..cSaf&~'r ifl'f'&" EJr AI.: om. Ab .,. om. EJ 32 i Luthe (d. 996b 10): ~ codd. r AI. aMflla mcl. Christ }3 .; om Ab AI. J Luthe: ~ codd. r AI. 34 o~~' ... 38 OK&"'I"O,," susp. Bonitz 35 i,..&C'I"0v,"""" Ab AI.: CFJf'OVlAi""" EJ oll.,.. codd. AI.: oMf d. Bonitz "a d '''fK'''] f'OV '/lflti" ",/lOr Ab: "a ' ..KO ,.&POr AI.: ,.a ;"f':''' ,.[lIor Eucken 36 trpa,mKoir Ab 37 m1 ••• K&lIfi in margo b loll, ,,"i trfp1 r 2 ft" all q ••• 3 fill" om. J, 4 A" .; ••• "a" in margo habet: qd lor trfpl "a f'G8"f'G"'''o' ,.a p.f" 'Yap fta" r 3 a,o,.& Ab ~ ...r Ab 6 ,.f om. EJ 9 'KllfI'f'lI EI 11-12 C"f'Oia&ll1l1 f'Gs"p.IIf"Ka1 Ab 15 &11 om. El

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TnN META TA 4l"l':EIKA K TWV p..lihJp.aTLlcwv i$A71s, 01lTf yap TijS CPVIT&KijS, ala TO 7rfP' Ta lxoVTa ~V am-o!:s apx~v KUI~lTfWS Kal IJ"TaUfWS ~v Toli cpvu&Koli 7rliuav d'va& 7rpayp.aTf(av, o-baf p.~v TijS UK07rOVU7JS 7rfP~ a7rQafC,f0S Tf Ka~ ~7r&u~p.r/S" 7rfpl yap a~o TOVrO TO 30 ylvos ~V (~T7JUW 7rO&f!:Ta&, Af(7rfTa& TO{VVV T~V 7rpoKnp.IV7Jv cpt>..ouocp(av 7rfpl a-bTwv T~V uKb/lw 7r0&f!:u8a&, a&a7r0p~UfU a' I1v ns fl af!: 8f'iva& T~V (71TOVP./v71V ~7r&~P.71V 7rfpl TaS apX4S, TO. KaAOvp.fva inr& nvwv UTO&Xf!:a' TaVra af 7raVTfS ~VV7rapXOVTa TO'iS uvv81T0&s n81auw, p./iUov a' av M~f&f 35 TWV Ka8&Aov af!:V flva& T~V (71TOVp.lV7JV ~7r&~P.71V' 7rlis yap A&YOS Kal 7rliua ~7r&~P.71 TWV Ka8&Aov Kal oll TWV ~uxaTw", ,zO"T' fC71. av o~w TWV 7rp0TWV YfVWV, TaVra af y(YVO&T' T& Tf av Kal TO lv' TaVra yap p.&>..&UT' av v7roA."cp8f{." 7rfPUXfW Ta 6J1Ta 7raJITa Kal p.&A&UTa apxa'is ~o&Klva& ala 30 TO flva& 7rpC»Ta Ttl CPVUf&' cp8ap'JlTwv yap awwv uvvava&pf!:Ta& Kal TO. AO&7ra' 7rliv yap av Kal tv, aE TaS a&a,/,.' ,~ ~ 1 , IJ' " .J ."opas aVTWV avaYK71 P.fTfXflV f l l1''1Uf& ns aVTa y~V7J, a&acpopa a' oU}fp.(a Toli ylvovs P.fT'Xf&, Tath-ll a' O-bK av MCf&f af'iv awa T&81va& ylV7J o-ba' apXas, In a' fl p./iAAoV 35 apx~ TO lt7rAOVUTfPOV Toli ~TTOV TO&OVTOV, TO. a' luxaTa TWV ~K Toli y'vovs lt7rAOVUTfpa TWV YfVWV (I1TOp.a yap, TO. y'V7J a' fls ffa." 7rAfCw Kal a&aq.'poVTa a&a&pf'iTa&), p./iAAoV av apx~ M,f&fV flva& Ta ft'a71 TWV YfVWV, ri aE uvVaVa&pf'iTa& TO!:S y'VfU& Ta ffa.", TO. y'V7J Ta'is apxa'is 10&Kf p./iAAOJl" 1060& apx~ yap TO lTVVaVa&povv, TO. JJ.fV OUV ~V a7r0p{av lxoJITa TaVra Kal TO&aVr' ~O"Tlv ITfpa. "En 7r&TfPOV af'i n8fVa& n 7rapa TO. Ka8' (KaO"Ta ~ o1J, II d.AAa Toth-wv ~ (."TOVp.lV7J ~7r&U~JJ."'; MAO. TaliTa hf&pa' 5 Ta yf p.~v 7rapa TO. Ka8' IKal1Ta Y/V71 ~ fCa71 ~O"T(v, au' o-bafT'poV TOth-WV ~ (."TOVP.'V7J vvv ~7r&~JJ."" awn yap aMvaTOV TOVrO, fCP7JTa&, Kal yap /JAWS a7rOp{av lXf& 7r&TfPOV

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af' TWa lnroXa{3E'ill o/udav flvaL XWPLITT7,V 1Tapa Tas alerB."TQS over£as Kal TaS afVpO, ~ oil, IDd TavT' flvaL Ta ol'Ta Kai 1Tfpl Tawa ",V eroq,Cav v1TapXfw. (f/TfW P.fV yap folKap.fll 10 &XXf/V nva, Kal TO 1TPOKfCP.fVOV TOW' lernv ~p.'v, Xlyw af TO laf'V ff n XWPLITTOV Ka6' aVro Kal p.f/afvl TctlV alerB."Tctlv VtrapXov. ITL a' d 1Tapa TaS alerB."TaS overlas lerTL TLS ~Tlpa oVerCa, 1Tapd 1To£as TctlV alerB."Tctlv af' TL6lvaL TaVTf/V flvaL; T£ yap ,MlXXOV 1Tapa TOllS aV6p01TOVS ~ TOVS r1T1TOVS ~ TctlV 15 4Axwv (';wv 6~erfL ns avn,v ~ Kal TctlV a#xwv {)XWS; TO yf p.~v feras Ta,s alerB."Ta's Kal q,6aprais overLaLS arMovs fTlpas KaTaerKfva(fLv flCTOS TctlV fVXOYWV M[HfV av 1T£1TTfW. fl af p.~ XWPLITT7, TctlV erwp.aTwv ~ (f/TOVP.tVl1 VVV apX~' TLva &v ns &uf/V 6ftf/ ,MlUov T~S ~Xf/s; a~ yf p.~V 30 lVfPYf{q. P.fv OVK IITTL, aVvaILH a' IITTW. ,MlUov T' av apx', ICVpLwTlpa Ta6r."s M[mv flval TO flaOS Kal ~ p.opq,~. TOWO a'f q,6apTov, lJJer6' {)Xws OVK IlTTw ataloS oVerCa XWPLITT7, Kal Ka6' a~v. ahX' &T01TOV' 10LKf yap Kal (17Tf'TaL erXfMv V1TO TctlV xapLflTTaTWV &Is avera TLS apx~ Kal over£a TOLa6r.,,· 35 1TctlS yap lerTaL Ta[LS p.~ nvos OJITOS a;;acov Kal XWPLITTOV Kal p,fVOVTOS; In a' ff1TfP IITTL ns overCa Kal apX~ TOLaVrf/ T~II q,verw orav IJVV VlTOVp.fV, Kal a~ p.Ca 1TavTwv Kal ~ avn, TctlV a;;a£wv Tf Kal q,6aprctlv, a1TOp£av IXfL aLa T£ 1TOTf ~r a~s apx~s oilCTf/S TO. p.lv llTTLV ataLa TctlV V1TO T~V apx~v 30 TO. a' OVK atdLa (TOWO yap &T01TOV)' d a' 4AXf/ p.lv llTTuJ apx~ TctlV ¢6apTctlv &AXf/ af TctlV a;;Mwv, fl P.fV ataLoS Kal ~ TctlV q,6aprctlv, dp.oCws a1To~erop.fV (aLa T{ yap oIIK a;;alov ~S apx~s oiierf/s Kal TO. V7rO ~V apX~V ataLa;)· q,6ap~s a' oiierf/s &Uf/ ns apx~ y£yz'fTaL Ta6r."s KaKf£v17s fTlpa, Ital 36 TOW' fls &1TfLpOV 1TpOHerw. d a' av ns TaS aOKoveras P.aAl.OT' apXas aKL~TOVS flvaL, TO Tf bv Kal TO tv, ~erfL, 1TPWTOV P.fV d p.~ TOaf n Kal over£av ~KaTfpov aVTctlV CTf/p.a£VfL, 1Tctlf Io6ob leroJlTaL xwpLlTTal Kal Ka6' aVras; TOLaVras af (17TOVP.fV Tar 10601' 27-36, lOO2b II

cC. 1000'- S - 1001& 3

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F

l060b 19-23, cf. 1003& 5-17 28-30, cr. 999b 24 - l000a 4

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1062'" 19-23. cf. l006b 28-34 23-30, cr. loo7 b 18 - 1008'" 2 31-35. cr. lOOSb 23-26 36 - b 7. d. 1008'" 4-7

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1066" 26-34, cf. 202" 13-21 3S - b 7, cf. 204" 3-14 204" 17-19 8-11, cf. 204" 14-17

b

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c;

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20-23,

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cr.

~

,,~

b 1-9. cr. Pltys. v. cr. 224b 28-30

,~,

224& 21 _ b I 14 - 106gb

ai EJrot: b 2 flab""/I EIJr 5 T' «al &atTd frpGJrO/l EJr 6 T' om. iot 7 a; pro Abot: ,..'" EJr 8 U alt. om. E IT' ,,, ¥ EJrot: I" T'/I' Ab 9 IS XJIO/IOS iot: XpO/IOS Christ TO alt. Ab Simpl. Them.: om. EJ 16 4 ou" ... 18 3. VwOlC.i,.../IO/I EJrot: om. Ab &

28 IT""" alIT8'ITd/l Abot: alIT8'1ri", IT.,,.,.a EJr 35 Tei alt. om. Ab 36 xpowp r

a; a" Ab

32

TON META TA

cIl'Y'~IKA

K

G>rrr' av&ylC7/ TPf'~ fweu I-'fTa~oAa~' ~ yap E, oVx V'7fO/Cf&I-'lvov d~ I-'~ WO/cfCl-'fVOV oll/C lITTl I-'fTa~oA~' ~f yap fvavTCa mn-f bTCc/>aCTC~ EITTW, 8Tl oll/C bTC8fCTl~, ~,uv oW oll/C f' WO/Cf&~VOV fl~ VTrO/cfCl-'fVOV /CaT' bTCc/>aCTW ylvfCTC~ EITTW, ~ . I-''(v c\1I'A6i~ c\1I'A7j, ~ a'( TWO~ T{~' ~ a' i, wO/Cf&1J.lvov d~ I-'~ wO/cfllJ.fvOV c/>80p4, ~ ,uv c\1I'A6i~ c\wA7j, ~ a'( TWO~ 25 TC~, d a~ TO I-'~ av AIYfTal 1I'Afovax6i~, /Cal I-'~f TO /CaTa crUv8fCTW ~ alalpfCTW EvalXfTal /clVf,CT8al I-'~f TO /CaTa Mval-'W TO T~ c\wA6i~ 8UTl bTl/cfll-'fVOV (TO yap I-'~ Aft//Cov ~ I-'~ clya80v 81Jl»~ ivalXfTal /cwf,CT8al /CaTa ITVI-'~f~"'/CO~, ft." yap 4v8pw1l'0~ TO I-'~ Aft//Cov' TO a' c\1I'A.6i~ 30 I-'~ TOaf o~al-'6i~), clMvaTov TO I-'~ av /cwf,CT8al (d a'( ToVrO, /Cal ~v ylvfCTlv /Ctvr,CTW flval' yCYVfTal yap TO I-'~ 8v' d yap /Cal 8Tl l-'d.\lCTTa /CaTa ITVI-'~f~"'/CO~ y[YVfTal, clll' 81Jl»~ clA..,,8,(~ fl1l'f'V ;n.l wapXfl TO I-'~ av /CaTa 10

av

ToV YlYVO~VOV c\1I'A6i~)' dl-'olw~ a'( /Cal TO ~pflJ.fiv, TailT& 35 Tf a~ ITV~alvf& aVCTXfp7l, /Cal d 'IIiv TO /CwoVIJ.fVOV fV TOwCP, TO a'( I-'~ av oll/C ICTTW EV T01l'CP' fr." yap 11'0'6, O~'( a~ ~

av

c/>80pa /C{Jlf/CTl~' EVClVTlov yap /C~CTfl /Clv"'CTl~ ~ ~pfl-'la, 1068& c/>80pa a'( YfvlCTfl, f1l'd a'( 'IIiCTa /c{V"'CTl~ I-'fTa~oA~ Tl~, I-'fTa~oAal a'( TPfi~ al flp.,,~val, ToWWV a' al /CaTa ylvfITW /Cal c/>80pav oV /CW~CTfl~, awa, a' dCTlv al /CaT' bTlc/>aCTW, clvay/C." ~v E, wO/Cf&l-'lvov tl~ V1I'0/Cfll-'fVOV /Ctvr,CTW flval 5,u$Jlf/V, Ta a' WO/cft,uva ~ EVCIVTCa ~ I-'fTa~ (/Cal yap ~ rrrlp."CT'~ /CfCCT8w EVClUTlov), /Cal a."AoVra, /CaTac/>aCTf&, otov TO yvl-'JlOV /Cal vwaGv /Call-'lAav, El cWv al /CaTf/YopCa, alpP71UTa, OllCTl" 1I'0lOTf/Tl, T01l'CP, III T. 1I'0lf'V ~ 1I'aCTXfW,' T. 1I'pO~ Tl, T. 1I'0CT., clvaylC7/ TPf'~ Ie flva, /cl~CTf&~, 1I'0'OV 1I'0CToV TOwOV' /CaT' oVCTCav a' 00, ala TO 1-'.,,8,(v fwal owl, EVCIJIT{OV, oll8,( ToV 1I'pO~ T' (lrrrl yap 8aTIpov

J068 b 2

II. Io67bI9-12. J.l,ETa{3&J...AOVTO~ J.I,~

1tA7j8EVEU8al 8anpov J.l,7jafV J.l,ETa{3aAAOV, &SUTE ICaTa U1JJ.I,{3E{37jICO~ ~ IC{V7jUl~ aWedv), O~aE 'II'OlOVvTOr ICa~ 'II'aaxoVTO~, ~ ICWoVVTor ICal IClVOV,uVOV, ifn ollIC IUTl ICW7/UEW~ IC{V7jUl~

O~af

YEvluEw~ ylvEul~, 0~3' ifAW~ J.l,ETa-

J5

{30Aij~ J.l,ETa{3oA7/. alXed~ yap fvalXETal IClv7/O'EW~ Etval IC{V7juw, ~ ~~ 1nrOICEl,uVOV (orov Ii t&v8pw'II'0~ ICwE'i:Tal ifn tIC

AWICOV El~ ,uAav J.l,ETa{3aAAEl, &Sun otn-w ICa~ ~ IC{V7jUl~ ~ ' ~ ~ 8EpJ.l,alVETal 11.. "H~ 'I""XETal 11 TO'll'OV al\AaTTEl 11 aV~ETa,' TOtITO af aMvaTov' O~ yap TedV tJ'II'OICEl,uVWV n ~ J.l,ETa{3oA7/), ~ lO Tef) tTEPOV n tJ'II'OICE{J.I,EVOV tIC J.l,fTa{3oAij~ J.l,ETa{3aAAElv El~ t&AAo ElaO~, orov 4v8pw'll'ov tIC VOUOV El~ iry{Elav. ItAA' O~af TOVTO aVvaTov 'II'A~v ICaTa U1JJ.I,{3E{37jICO~. 'II'aO'a yap IC{V7jU'~ tf 4ll0v El~ <1AAo tUT~ J.l,ETa{3oA7/. ICaL ylvEO'l~ ICal t/J80pa ~uaww~' 'II'A~V at J.l,fV El~ lunUElJ.l,EVa ~al, ~ a' ~a{, ~ IC{V7jU'~. l5 11J.ta ouv J.l,ETa{3illE' tf tJYlE{a~ El~ vouov, ICa~ f! a~~ TaVT7j~ rij~ J.l,ETa{3oAij~ fl~ 4AAl1V. aijAOV a~ ifT' &v VOu7/up, J.l,ETa{3E{3Al1lCo~ IUTal El~ li'll'OLaVOVV (tv31XETal yap ~PEJ.I,E'i:V) ICal In d~ J.I,~ n)v TVxowav aE{' lCaICE[V7j IIC nvo~ d~ n 4110 IUTal' //Ju8' ~ 4vTlICElJ.l,lV7j IUTal, tJy{avu,~, ItAAa 30 Tef) U1JJ.I,{3E{311ICIval, orov I! aVaJ.l,V7/UEW~ d~ A7/87jv J.l,ETa{3illEl ifn ,; 1nrapXEl fICf'i:VO J.l,ETa{3illEl, IiTf J.l,W d~ f'll',UT7/J.I,l1V liTE af d~ 4YVOLav.-IT' El~ 4'11'E'POV {3aa'E'.,.a" El IUTa, J.l,ETa{3oAij~ J.l,ETa{3oA~ ICa~ YEvluEw~ ylvEO"~. avdYIC7j a~ ICal ~v 'II'poTIpav, d ~ tJUTIpa' orov El ~ l1.'II'Aij ylvEu,~ 35 lylyvETo 'II'OTE, ICaL TO y'YV0J.l,fVOV ly[yvETo' //JUTE oV'II'W I068b ~V TO YlYVOJ.l,EVOV &'II'Aed~. MAa T' YlYVOJ.l,EVOV [~] y,yv0J.l,EVOV ..,

,-, ,

,

.."

• 12 l'f7'a{:laXXovror I'~ ut vid. AI. Them., Schwegler: l'ua{Jd>..XOJOr'Of I'"B• ., Ab: 1''1{JiIlI"Ta{:lQXXovror EJr: I"Ta{:jciXXo"Tor iea Simpl. : l'f7'a{:lQ~Xovror 1''1«'T' ci. Christ l''1a." EJN: p.'1a. Ab 14 «al pro EJN: ~ Ab 15 fl"'a{:loXijr I"Ta{:loX;, Abr Simp1.o : I'na{:loX~ 1lf7'a{:loXijr EJ ea 16 .l"a, «lll'lu,,, EJrea: «lll'lu,,, ~rllG' Ab 23 /&rau, Ab yop) -yop q Ab 25 'E Rvr'«fI""'61" Jr q If ;"al Ab Simpl.: q ;"a, EJr Phil. eaEI: om. eaFHI q «l"'11T,r AbeaE Simpl.: ~ 3. «{lIJ]tlIS' .H: rj ai lCi"!JfT&f oilx. op.olmf c1JFI : oll 1('''~O'f&r EJr 27 a' EJr "oaij, El 28 ./11 Otro'90V" r an olJ« ,,,a'X'Ta,? 30 lUTa, alt. om. E1J 33 .!'}'I'C!'OII Smith, legerunt ut vid. Phil. Simpl.: lJ-ylnall codd. rea 35 -yl"'IT" 'yly,,",el EJI'<): .yfIlfTO Ab b 1 'y~Y"'TO EJ.N: Ii",X"r 'yt'Y."no Ab 2 TO ••• 3 ~a,,1 qa'l AI.: qa'l dXXa y,II6I'0'o" ~" y""'I""o" qa'l yp. AI.: 1',,61"110' d",~Glr d~M T' y,,,6I""o,, qa'l eaH yp. AI. Yjl. Simpl• .,.0 om. EJ T' Y'"1"ol""o" :y,y"0l""o" Bonitz: T' Y''Y''elllf''O'' ij yool"IIO" E: T' Y'"1"01'~1I01l d",XGlr ij y,"elI"II011 Jr: T' Y'Y"0I""OI «al y'y,,6,,~IfO" eaFI : Y'"1"':1""0" T' q 1'"ell'.1I01l Ab : 1'y!f61"IfOIITO eaE : y,II61",oll ci. Asp.

TON META TA

'Y'~IKA

K, A

~~'I. lCal 7'OW' iy{YVfTO '11'07'(, tlSOT' ,w1C ~v 'II'W 7'07'( y,yvoIUvov. l'll'd a, 7'6IV o.'II'f(pWV oillC la'7" 7'L 'II'p6ITOV, ,w1C 5 IOTa, 7'0 'II'p6I7'OV, tlSOT' oil~f TO l)(0IUVOV. mE ytYVfa'641. oVV mf ICwfi'0"8a' oUv Tf mf ILf7'a/3&.u.fW OO~'V. ITL TOV awoo 1CUn,a"S ~ lV4VT'la lCal ~P'IL'Ia"S, lCal Y'Vfa"S lCal. t/>60pd, tlSOTf TO Y'YV&ILfIlOIl, gTav yfl'flTa, Y'YV&ILfVOV, TM-f t/>6fCPf7'41.. 01)7'( yap flI6vs Y'YV&ILfIlOV 01)6' ~OTfpOII· fWa, yap afi' 10 7'0 t/>6npoILwov. In afi' lA'I1I wfi'va, T" y,yvoILlv't lCal. ILfTa/3dllovn. T{S ovv IOTa, tlSa''II'fP TO O,).,).,O'WTOV a'6Ip.4 ~ Vrox~ - O~W Tt TO Y'YV&ILfIlOV IC{V'Ia"S ~ ylvfa"S; lCa, IT, T{ Els & ICWOVV7'a,; afi' yap ftlla, ",II 7'OOOf llC TOV~f fls TOaf ICUn,O"'V ~ ylvfa'w. 'II'6IS ovv; 00 yap IOTa, JMi6f1a"s rijs IS ~a'fWS, tlSOT' ,waf yillfa"s Yfll'a'fWS. l'll'd a' m' owlas mf 7'06 'II'pOs T'L OiiT"f TOO 'II'O'f'V lCal 'II'a.UXf'lI, AfC'II'fTa, lCaTa 7'0 '11'0'0" lCal. 'II'oO"clv lCal. 7'O'll'OV 1CUn,a'W ftva, (TOVrWII yap llC&OTCfI lvaV7'~O"'s la'TLv), Alyw af TO 'II'O'OV oil TO lv Tp olla'{" (lCal yap ~ awt/>opa '11'0'(11) o')")"a TO 'II'a6'1T,lCov, lCa6' .& 30 A/YfTa, 'II'a.a'XfW ~ Q'II'a6fs ftva,. TO af QIC{I'fITOV TO Tf SAws Q~WaTOV 1CLVf18~va, lCal. TO p.OA,S lv xpovCfI 'II'oAAcfI ~ /3po.a/ws 4PXOILfVOV, lCal TO 'II'ft/>VICOS IL'II ICwf'a'6a, lCal ~VV&ILWOV (p.~ ICWOVILfIlOV) ~f gTf 'II'lt/>vlCf lCal oV lCal tlSs· & lCaA6I -~PfILfi'V T6I11 QIC'~TWV ".oVOII· lll4V7'tov yap ~PEILla IS 1C~a'f', tlSOTE OTlP'1a"S tiv If'l TOV afICT'ICOV. l068b 15-20,

cr.

226& 23-29

20-25,

d. 226b 10-16

b 3 fB" Ab+: .z B'; EJr rdTf EJN: 'IN"" Ab an "I,-pd,.."o" 'Y'''I''d,.fllOlI? 4 .,., om. EJ Simpl. 4-5 oll/C IITT'O' TO ffpOoTO" EJN: om. Ab Simpl. 5-6 o~" (I~ro, oln EI 7 ylWI1U EJN : 9 'Yf"ffTif Ab 9 J,-pd,.'1I01I EJ.: "If11dP..IIOIl Abr: an "I'-pdl"1I01l 'Y'''I..o,..IIO''? 12 Oliroo om. J r{ JAb+F Simpl.: n r-: T' (sed erasum) /Cal E: 3;' .1 /C{"'1lTef EJr.: 9/c{II'Il1uAb /CIl19Yf"'11'If Jr I.,., om. EJr: 71'0).'11. 13 r.j~] rIT';" EJr. 14 4yf".alll .E'HI AI. Simpl.: ,..; /C{"'Ia,,, codd. r "Ip. Al: /Coi p.'; /C{""a,,, .E': ,..; /c{""ITIII ~ y(IIfa,,,.F: ,..j /C{"'1alll &rr).ciIf Lasson rqf l'OiJq(1'fOlf, &a,I 0;'3." 'Y'''fa,r 'Yp. J: om. J Tijf l'O(J,jafOlf] 9 rqf ,.oiJ;,a-ft»f "If"faU Ab. IS "I",fUfCllf "f"fa'f .EFI Simpl.o Phil.: r9f "Ifllfau••f Ab 17 /Cal pr.] /Coi .,.0 At. Simpl. TO 71'.." Jr. 19 YO-P Jr. ; p ,,01 E: om. Ab 9 aaof/>op;, EJr.: rfi aaof/oow Ali 1m 6.: /CoiJo codd. 21 ~r Ab q Ab Simpl. Them.: om. EJr. 22 .,.0] &n J /Cal ••• 23 B•• : ,.;, B"""I"lIo, B. codd. r 23 rrf~lI/cf Ab+: om. EJr

/a

12. 1068b

3 ---

I. 1069& 20

"Ap.a. KaT« T07l'OV ifcra ~V ~vl T07l'ftJ 71'p0TftJ, Kal Xt.IlpLS' ifcra iv 4AAftJ· 1171'Tfcr8a, a~ c:iv T« (.&!Cpa l1p.a· P.fT~ ~' flS' & 71'/4>VKf 71'POTfPOV a4>'Kvflcr8a, TO p.fTa/34U.ov ~ tlS' & 'crxaTov p.fTa/3OAAn KaTa 4>vcrw TO CTVVfXfdS' p.fTa/34U.OV. ~lIaVT'OIl KaTa T07l'OV TO KaT' fV8flall a7l'/Xoll 71'Afl- 30 CTTOV· ~~S' ~~ ov P.ETa T~II apX~v 6VTOS', 8Ecrn ~ ffan ~ 4.\At.IlS' 71't.IlS' a4>opw8/VTOS', p.1J8~1I P.fT~ iCTT' TWV iv Taw, y/vn 'Cal oV ~4>f~S' iCTTw, otov ypap.p.a.~ ypap.p.~S' ~ p.CJva~fS' p.ovdaoS' ~ OlKlaS' olKla (&Uo a' oV8~v Kt.IlAVn P.fT~ fTva,). TO yap ~,ijS' nvoS' i4>E~S' Kal fCTTfPOV T'· ov yap TO 35 b ~'~S' Tfdll Mo ova' ~ lIovp.1Jvla ~S' afVT/paS'. ~XOp.EVOV 1069& a~ & av ~~S' I1v 1171'T1JTa,. i7l'El aE 71'acra p.fTa/3oA~ ill TOlS' &VT'KE'P./VO'S', TaVTa a~ TO. ivaVTla KaL aVTl4>acr,S', aVT'4>acrft.llS' a' ova~v cWa p.fcrov, aijAOV WS' iv TOlS' ivaVTlo,S' TO P.fT~. TO aE CTVVfXES' if7l'fP ~X0p.EVoV no A'yt.ll ~E CTVVEXES' 5 ifTaI1 Tawo y'""TaL Kal b TO ~KaT/pov 71'/paS' otS' 1171'TOVTCU Kal CTVV/XOVTa" tZCTTf a~AOV 8n TO CTVVfXfS' ~V ToWO" i, c:ill Iv n 71'/4>VKf ylYVfcr8a, KaTa ~V crVlla"'w. leal (h-, 71'pWTOV TO ~4>f'~S', ~~AOII (TO yap ~4>f~S' oVx. 1171'TfTCU, TOVTO a' ~4>f~S'· KaL fl CTVVfX'S', 1171'TETaL, fl a' 1171'TfTaL, 10 MOO CTVVfX'S'· ~v otS' aE p.~ ICTTw l1.4>~, ov" ICTT' crVp.4>VcrLS' ~v TOm-O'S')· tZCTT' OVK ICTT' CTT'yP.~ p.CJv&a& Tawov· Ta&S' p.~v yap wapXE£ TO 1171'Tfcr8a" TalS' a' O~, au« TO ~4>f~S'· KaL TWf p.~v P.ET~ T& TWV a' O~. 15

A llfP' ~S' uVulaS' ~ 8ft.llpla· TWV yap ovcrLfdV al apxa, Ka, TO. afna (l1TovVTaL. Ka, yap fl ~S' ifAOV n TO 71'all, ~ ovcrla 71'PWTOV p./poS'. KaL tl T, ~4>E~S', KaV Oln-t.IlS' 71'PWTOV 26-30, cf. 226b :u-25

30 - 1069& 14,

cr.

226b 32 - 227& 31

B.

b 26 f"EJx-.: om. Abo II'prM-tjlEJrSimpI.: lI'pf#roIJAb 27 Elx-.: om. Ab 29" om. EJ. 33 o~ EJr.: 6 Ab fcf>f~ijr A .: iEijr EJ 35 ,.,lIOr] ,."" Ab. 1069& 2 6" 1J7IT'l"a, EJr.FI Them.: &..a.,.'l"IU Ab fll'fl ••. 5 ,,.,.oE" ante ",f'I"aE" 1068b27 interp. Them., ante fllOlJ'I"loIJ 1068b 30 ponenda d. Prantl 3 ,.ei E1J.E: ,.,j,.' E"FHI : om. Ab 5 ,.,. 'AfyoJ EJx-.: ,., q d".,.cSf'(I'OIJ. 'Ai,..,.o, Ab 9 f¢f~ijr alt. et 10 fcf>.~ijr Ab.: IEijr EJ 13" alt. A~ : II'pOf'l"~ EJr 20 ,." EJI' AI.o: "0 Ab "a,,] mi EJ

30

TON MET A T A TIIKA A ~ oVITCa,

ETTa TO 'II'Oll)lI, ETTa TO '11'011'011. I1JLa at ova' ollTa ~s El'll'E'1I A'II'A~S' TaiJTa, dA.\a 'II'OLOT7JTES' Ka~ KLII1/ITELS', ~ Ka~ TO OV AEVKOII Kal TO OVK EVe.;· AlyoJLEII yoiiv ETllaL Ka~ TaiJTa, OtOIl IlTnll oil AWKOII. In OVatll T~II ~AAt.IllI Xt.llPLITTOII. ~:. p.aPTVpoV(1'L at Kat 01 dPXa'OL IpyCf" rijS' yap OVlTlas i'~TOVII dPXaS' Kal ITToLXE,a Kal arna. 01 JLtll OVII vVlI Ta Ka60Aov oVITCaS' p.O.,\AOII n61aITLII (Ta yap y/ll." Ka60AOV, 11 alTw ~, t • ~" 1>' TO " AOyLKt.IlS' ~ I': ~) u.pxas KaL" OVITIaS' ELllaL p.a1V\01l uLa \,."TEW· 01 at 'II'4A.aL Ta Ka6' lKalTTa, otOIl '!I'f1p Kal y7}1I, d.A.\' OV TO 30 KOWOII, 1T~p.a. OVITCaL at TPE'S', JLCa JLtll allTB.,,~ - ~S' ~ JLtll dtaLOS' ~ af 8a~, ~II 'II'aIlTES' 6JLoAoyoVITLII, OtOIl Ta 4>wa Kal Ta ~ [~ a' ataLOS'] - ~S' dllay"" Ta ITTOLXE&a Aa/3E'II, dTE ~II Ern 'II'oA.\a· 4,\A7J af aKlJl'lToS', Kal TavT7111 aITC TLIIES' ETllaL Xt.IlPL~II, 01 JLfll ElS' Mo aLaLpOVIITE~, 35 01 af ElS' JLCav VITLII n6111TES' Ta Era." Kal Ta p.a6."p.aTLKa, 01 ~ Ta JLa67JJLanKa JLOIIOII TOWt.IllI. iKELllaL,..,E1I a~ VI069b ITLK~S' (p,ETa KunllTEt.IlS yap), a~ af lTlpaS', El JL."aEJLla allTo,S' dPX~ KOLII1/' 001171') d.A.\' iK TOV illallTCov, dllaYK7J iI'II'E'lIaC n TO p.ETa/34A.AolI Els T~II illaJITCwITLII' OV yap Ta illallTCa JLETa/34AAEL. ITL TO JLfll iI'II'Op,fIlEL, TO a' II illaJJTlOII OVX iI'II'OJLIIIEL' IlTnll 4.pa n TpCTOII 'II'apa Ta illavTCa, ~ ~A7J. El a~ at JLETa/3oAal TirrapES', ~ KaTa TO T{ 10 ~ KaTa TO '11'0'011 ~ '11'011'011 ~ 'II'OV, Kal yfIlEITLS' JLfll ~ b.'II'A~ KaL 60pa ~ KaTa (TO)' TOaE, ailffJlTLS' at Kal. 6lITLS' ~ KaTa TO '11'011'611, d.,\AO't.Il/TLS' at ~ KaTa TO 'II'46oS', opa af ~ &:U ,lTo 'TO alt. Ab AI. : ~ EJr 22 d"')''''r fitl"l" Abr 'Towa EJr AI.o: 'T/IX>.o Ab yp. E Them. d)'M codd. ret ut vid. Them.: olm, AL .~ J Al.o: ~ EAbr Them. 23 'TO alt. Ab AI.: om. EJ 23-24 yoii" «al 'TOWO ,1,,01 Ab 29 1«0IT'T0 Ab AI.o : l«ufTToII EJ 30 ~r ••• 31 OI'O).OYOiifTIII] ~"",&",U' ol'o).or,iifTIJI, ~r , ',#,./J AI'" ~ '\. .. ! "~ r '''''8 • 'I "'" '1"'0pT'7 .: 'I" tl'aJI'Tfr OptJAOYOl'fTI", 'Ir '7 1"" RlOIOr '7 f.." lJP'Tf/ Them. 32 q 4' dtalor codd. r AI., yp. AI. apud Averroem: om. Them. AI. apud Averroem 33 «01 Ab AI. : om. EJr 34 Tallir ,lllot 4>aul A Ii 35 1'lI8'1I'l1T1«a 01 3i 'TO A br AI. : 1'lI8'1I'OTI«0 01 4i in margo J : om. E 36 1'08'tjT.«a J b 3 ~ alt.] 4;' E'JI S yap «al ~ Essen 7 "'TO~).fI/I El 9 'TO sup. lin. F; II rj om. EJ Al.e 10 adieci 12 'TO pro sup. lin. E rp80pa EJI I

f

av

tVQVTU.}O"fiS flEV Ta~ ICa8' t«aaTov a1 411aYK17 a~ p.fTa~aUfw T~II f5A7111 avvap.fllrjll 4p.t/Jw· i1l'd af alTTOII TO 811, p.fTa~4Ufl 1I'all i/C Toil av- IS lIap.fl OIlTOS fls TO illfPYflfl 811 (oroll i/C AfV/Coil avvap.fl fls 1 '\ ' J I ~, l' '(;' \ "'(J' TO\ ellfP)'flfl n.fV/COII, OP.OlWS Of /Cal\ e1l' aV~71UfWS /Cal .." lUfWS),
T07fO"', Elr

p.fTa~oAal.

b 2 1 'A"ol'"m,Bpr'v LUtze 0" Jackson fj.'>.'rlO" ••• "";JI1'a sed. Karsten "lap om. "IP. E 22 «al' A"aEnycS~1I LUtze: fort. am. AL 23 0/loii 'YP' E: ';/li" EJAbr 25 a>.>.' i'rip"" post !/loft I. 26, omisso dA).' I. 26, Goebel f'r.pn f'r'~n" ci. Bonitz yep'rrr(i A 26 ye"P'1'rlj" Ab 31 «al EJ AI.: am. A r 32 IJ~] & Schwegler 33 nl am. JAb 34 'rc\ all ••• v).., am. p 1070" 1 'r'l TI lenl ;~o~ Ab &] o~ J 4 Bi Goebel S olia-ia EJ AI.: ., olia-ia Ab

TUN META TA

T~IKA

A

apx~ lv aw¥ (/1vBpoo7foS yap livBpw7foV YfVVq), al a~ Aonral alTla, UTfP~UI!&S TO~TooV. ovu,a, aE TPfis, ~ ILEV l$A7j 10 To3f n ovua Tefl t/laevfuBa, (~ua yap dt/lfj /Cal IL~ ITVILt/lVUf', ~A7j /Cal WO""ClLfVOV), ~ aE t/lvu,s TOaf n /Cal tf,s ns fls iiv' In TpCT7j ~ llC TOWooV ~ /CaB' t/C4UTa, otov ~oo/CpaT7jS ~ KaUlas. l7fl IL~V ovv TW~V TO TOaf n ov/C IUT' 7fapa T~V ITVvB~v ovulav, otov ol/CCas TO ftaOS, d 15 IL~ ~ Tlxv7j (oU' IUT& ytVfU&S lCa, ~Bopa ToWooV, MA' etA· AOv TP07fOV flul /Cal oV/C fZulll ol/Cla Tf ~ c1vEV ~A7jS /Cal Vyel!&a /Cal 7fQV TO /CaTa TlXJlf/v), MA' fr7ffp, l7fl T~V t/lvUf&' a&O a~ ov /Ca/C~s nAaTOOV It/l,, ~n fra7j IUT'v d7foua t/lVUI!&, fr7ffp IUT&V da7j I1Ua TOWooV *otov rip uapf /cft/laA~' 3~ l17fallTa yap 1$A7j lUTe, /Cal rijs ",aA&UT' oou(as ~ uAEVTala*. Ta ILEV ovv /C,voilllTa arna ~s 1I'POYfYfV7jILIva OllTa, TO: .a' ~s d AOYOS l1p.a. ;;U yap Vy&aCVI!& d I1vBpw7fos, TOU /Cal ~ ~y[I!&a IUT&v, /Cal TO ux~p.a rijs XaA~S u~a(pas 11.p.a /Cal ~ XaA~ ut/la'lpa (d af /Cal 1$UTfpOV T& WOp.fVf', (T/(f7fTloV' 35 f7f' lvlwv yap OVafV /CooAVf', otov d ~ +vX~ TO'OilTOV, IL~ 7fQua MA' 0 vails' 7fQuav yap aMvaTov !uoos). t/lavfpOV a~ ~T& O,UfV afi a&& )If TailT' ftva, TaS la/as' livBpw7fos yap ltvBpoo7foV YfVVq, 0 /CaB' t/CaUTov TOV TWa- dp.o(oos af /Cal l1l'l T~V Tl!XV~v' ~ yap laTp&~ TIXJIf/ d Myos rijs Vy&fta.s 30 lUT(V.

Ta a' arna /Cal al apxal 4AAa ltlloov IUTw &Ss, lUT& 4 a' ~s, &V /CaBOAov A/yy T&S /Cal /CaT' O,vaAoyla.v, TaWa 7faIlTOOv. a7fopt}Ul!&f yap ltv T&S 7fOTfPOV tTfpa& ~ at awal ..1_" ......,... ,... , .."xa, /Ca& UTO'Xf," TOOV OVU&WV /Cal TooV 1I'pOS T', /Cal /Cal7 ,~

& 8 a~T. recc. r: a{,r; EJ : ;a~ A b ll"sfH''lror ••• ~II"; ad I. S pertinere censuit AI.: an ex 11. 27, 28 inserta? 10 ow'" Jr a yap E1J A1. : yap '1T'f'''' EIAbr II cpUITIr ml ,,0& Ab 01 ••• 12 qll i et fort. AI.: .lr ~II KIll ;~'f !"If codd. r AI.a: O~ITIJ «Ill ZEcr "If Bullinger 12 ;, alt.) ~ lCal Ab -13 '"' om. EJr 16 ". om. EJ 18 aq om. Ab UAa,.6111 Irj.>" EJ AI.: cI U).a,.6111 lep" Ab: 01 "0""" ",8il""01 lepllfTRII AI. apud Averroem et ut vid. Them. 19 .nAil A bIr AI.: dAAQ EAbl AI. apud Averroem : llA).oll J : dAAa "I' all Christ Olall ••• 20 ".A.wow post ('lTolCdl"""" I. II ponenda vidit AI. 19-20 IC,cp..A;'. &lI'o",.a ~"AI. apud Averroem 23 et 2S .; om. Ab 28 K118i1C1I1T'f'0f Ab 29 cI om. Ab AI. 30 'UTili EJr AI. : om. Ab 31 "0 a') lOT' a. "0 Ab .tAAal Ab AI.l IITn. C,f om. Ab 32 Afyol Ati 33 'lro""." EJr AI.: lI'a",.a Ab yap) a' Jr

E/CaUT7/V a~ T"V /CaT'T/yopL"V 01A-0LWS. aAA' c1T01l'OV EL TaWel 35 1I'4VTWV' l/C T"V aliT"v yap l(1'TaL Ta 1I'pOS TL /Cat at oliuLaL. TL O~V TOW' l(1'TaLj 1I'apel yelp T~V oliuLav /Cal T4lla Ta /CaTy/- I070b YOpOVIA-EVa ooolv l(1'TL /COWOV, 1I'pOTEPOV af TO (1'TOLXEi'oV ~ ~V ITTOLXEWV' alla IA-~V olia' ~ oliuLa uToLXEi'oV T"V 1I'pOS TL, olJaf TOVrWV OliafV T~S oliu(as. ITL 1I'''S lVaEXETaL 1I'4VTWV EwaL TaWa (1'TOLXEiaj OliafV yap olov T' ElvaL T"V (1'TOLXE(WV 5 T!fI E/C ITTOLXELwV ITVY/cfLIA-EV,!, TO awo, olov T!fI BA T-O B ~ A (Oliaf a~ T"V VO'T/T"V (1'TOLXEi'oV l(1'Tw, olov TO ~V ~ TO ~V' 1nr4PXEL yap Tawa l/C4UT'!' /Cal. T"V ITVVOETWV). OliafV c1p' IlTTaL aw"v OW' oliULa OWE 1I'pOS TL' aAA' avay/Cai'ov. ov/C I(1'TW c1pa 1I'4VTWV TalJra (1'TOLXELa.-~ aVELa' t/>"s U/cOTOS a~p, l/C 3f roVrwv ~IA-Epa /Cal. WC. 11l'El. af ov IA-0VOV rel lvv1I'apxovra afTLa, aua /Cal. r"v I/cTos -olov TO /CLVOVv, a~AOV l$n lrEpov apX~ /Cal. (1'TOLXEi'oV, afTLa a' c1IA-t/>w, /Cal. Els rawa aLaLpEi'raL ~ apx~) ro a' ~s /CWoVV ~ lurclv apx~ TLS /Cal. ovula, 11 laTI TO Elr 6 I" A b AI.e: f" TAlII EJ fj] TO J A] ill£t/>oJ J 7 an ov3flll ITTO'X,lOlIl EJr AI. fUT'. om.EJrAI.l 'II~ToS.,EJr: &VlCol.,.o;.,AI.l 12 ~A'IAbAI.: ~ vA'I EJ 13 owl" r 14 8,pp.ou "UI ,yuXpnu EJr AI. : tuxpou ""l 8,p/,ou Ab IS ;T'POJl •.• 16 ')',"&/".,011 post T' L 9 ponenda d. AI. 16 TflUTR Er 17 TO Ab 18 ,fft'o"JI Ab 20 XpOl,.au, A b 21 ICaI om. EJ 25 llTTAlJI A bAl. "al owl,,] O~ITR EJr: "..I olTia ci. Ilonitz /,'11 om. J 26 OfT'O Ab 27 ft'pAlTO.,] ft'O''IT'''OJl d, Bonitz taTl'S

H

TUN META T A

«I»T~IKA

A

TOuWC. 1rAW80,' TO 'UVOVV ol/Coo0IJ.''''' [/Cal dr Tawa auu· pfiTa, ~ clpX~]' ~1rfl a~ TO /CWoVV ~V IJ.EV Toir t/>VfT,/Co,r clv81*1r" &v8ptJ)1ror. ~V aE Toir cln a~vo£cu TO fl&or ~ TO ~vaVTlov. Tp01rOV TW4 Tpla arT~ av ff'l. wal aE TlTTapa. Vylf~ yap 1rGlr ~ laTp'"", /Cal ol/C&a.r f~or ~ ol/CooolJ.'/c~' /Cal &v8pc')1ror &V8PtJ)1rOV YfVViJ' IT, 1rap4 Tawa TO wr 35 1rpIi»TOV nVTo)u /C,voW 1raVTa. 'E1r" a' ~fTTl T4 IJ.fV Xo)PWT4 T4 a' ov xO)pWTa. oVfTUU 5 1071& ~/cfiva. /Cal a~ TOWO 1rclVTo)V afT~ Tawa. ~, TIi»V oVfT~V &vfV OV/C IITT' Tci 1raer, /Cal al /c~fTnr. 11rnTa IITTa, Tawa .1_. ' ~ ~ ! t: ~ II ,,"X'" tfTO)r /Ca,\ fTO)lJ.a. .".. vovr /Ca,\ !opE
5 yf~

/Cal BVvaIJ.,r· clAAa /Cal Tawa &AAa Tf flAAo,r /Cal 4AAO)r. ~v ~vlo,r IJ.fV yap TO awo m-E IJ.EV fVfPYfltf IITTW m-~ aE avvdlJ.n, olav owor ~ fTapf ~ &v8ptJ)1ror (1r'1rW aE /Cal Tawa dr TO dp'llJ.lva arT~' ~VfPYf'q ~v yaD TO flaor. fav 'P Xo)P&fTTOV. /Cal TO ~f alJ.t/>oiv ITTlp."fTU al, olav 10 fT/Cc1ror ~ /CalJ.vov, avvcilJ.n aE ~ fA.,,' ToWO yap ~ITT' TO 3vvd,uvov y'yvffT8a, &1J.t/>0)! 4MO)r 3' IVfP'YfCtf /Cal 3vvdlJ.n 3,at/>lpn WV 1J.1,lITTW ~

avn,

fA..". WV (~vw)u) OV/C IITT' TO

awo ftaor clAA' ITfpov, OSfT1rfP clv8p~1rov afT'OV Tel Tf ITTO'Xfia. rip /Cal y7i wr SA." /Cal TO 13,0v ftaor. /Cal In T' 15 &lio If0) olov d 1ran1P. /Cal 1rapa. Tawa d IiAwr /Cal d Ao~r IW/cAor, oWf SA." oVTa o1'ir' ftaor oWf ITTlP"1fT,r ollTf dlJ.Of&BEr 4AAa /cwoVVTa. In BE opav Bfi ~, TO ~V /Ca80AoV IITTw d1rfiv, T4 a' 011. 1rclvTo)V a~ 1rpimA' clpxal TO b 29 d1 ••• 30 dpXI/ om. Ab AI. /Cal a,',zt J 31 d..sp,..

a.

IMJpOJrror Zeller: d..splMrmr d"sl*1for E AI. : ll"spawor h8pt1t'1fOt et d~fMIIIJf'" WfHIfI'op E marg.: IlPIJp.llrtlr JAbr 32 om. Jl 33 by.la J 34 T'c\.r ci. Bonitz: .lit ri caddo 36 "/P. E 1071& I l/CfWa EIAb AI.!: law.. EIJr d1 EJr AI. : om. Ab mwo d. Christ: T'aWe codd. r AI. 2 IOTa,] laT" AI. 3 ~ ••• om.]I: ~ •.• a.",., ~ &lNt" /Cal a.",. fort. AI. 4 al om. E l",~," 6 1lA)..r 1ft margo EI S 1l~).O"'f .tumr AI. Them. 8 lpf~l, E AV: 1";PY',aJAbr AI. 9 11 EJr AI.e: J T'c\ Ab /COl] ~ 'YP. E Them. OTfpr,.:rlr ••• 10 leel"pop damnavit Christ: a ... a. om. Them. II tJ' codd. rAI.: a' ~ Trendelenburg 12 ... 1"[,.,,, scripsi: 1111 codd. rAI.: /COl 1111 'YP' E Them.: ~ oW Zeller 13 c,cnrfe ••• 17 lelJ/oiiJlm ~st "awa I070b 3S ponenda ci. Christ 14 '''''l.l EJI' 17 3f EJI' Al.l: 18 "all'l".JI •.• 19 3u".i"" post lOT'" I. 20 ponenda d. om. All Christ 31 Al.e

_La

fT.r

'p.,.",

...

fllfPYfC'I 'ltpiiJTOV 1'001. Kal. 4,u0 & 3vvd".f&. iKfWa ".EI' O;V TO. Ka60Aov OVK Ia'TtV· apX~ yap TO Ka8' 'KauTOII TiiJII:lO KaB' 'Kaa'T'OV' 4118pol'ltor ".EV yap 1l»8p$'ltov KaBoAov, aM' OVK Ia'T'W aUfCr, aMa n'lAEVr 'AxtUlQ)r a'OV aE IS 'ltanlP, Kaf Toa1 TO B 1'0031 TOV BA, 3AQ)r aE TO B TOO 4'1tA&lr BA. l'ltftTa, El a~ 1'4 T&lV oW"'v, 4AAa 3E 4AACliv afTta Kal. a'T'O&Xfia, 1JJa''ltfP iAIXB1!, T&lV ".~ ill Taw, yl- JS 11ft, XPQ)".dTQ)V t0ti'Q)V oVa'&&l1I 'ltOa'~Tor, 'ltA~1I 1', avdAoyov' Kal. T&lV iv Taw, d3f& 'TEpa, oVK ff3f& aM' 81'& T&lV Ka8' 'Kaa'T'OIl 4AA0, ij Tf ~ fA'I Ka~ TO ftaor Ka~ TO K&vi;. a'av Ka& ~ i".~, 7', Ka8oAov 3E AcSy, TaVTd. 7'0 3E ('lTfiv 1'''''' apXal. ~ a'T'o&Xfia T&lV OVa'&&l1I Ka~ 'ltpOr 1'& Ka~ 'itO "'", 30 'ltOrfPOV a1 awal. ~ fl"fpa&, aijAov /W& 'ltoMaxir yf AfYO,,",110111 la'T'w lKda'T'ov, ata&pf81VT'Q)v 3E ov Taw4 aAA' 'Tfpa, 'ltA~v ~1 Kal. 'ltQ".,.Q)v, ~31 ".Ell TaWa ~ 7'0 alldAoyolI, 31'& J;A'I, ftaor, a'T'lp'la'&r, TO KtVoVv, Kal. &131 1'4 Till OVu&iiJv afTta ~r afTta 'ltcUn-Q)v, 31'& alla&PfiTa& ll»a&pov,,",vQ)v' 11'& a5 TO 'ltpiTOII iVT'fAfXf''1' &131 aE tTEpa. 'ltpiTa 3a'a TO. fVaVTla &. "'~f &lr yllI'I AIYfTa& "'~TE 'lto,uaxir AIYf. Ta&' Ka~ 11'& a1 ~Aa&. TlvEr ".Ev OOV al Ilpxa1 Till ala'B1!T&l1I I07Ib Kal. 'ltoa'a&, Ka~ 'ltir al awa1 Kal. 'ltir 'TEpa&, ffP'1Ta&. 6 'E'ltf1 3' ~a'aJI TpEir oVa'Ca&, avo ".0 al t/Jva'&Kal ".la 3' ~ aKWr,Tor, 'ltfp& TaVn,r AfKTlolI 31'& Il»dYK'I fWa& M3wv Twa oVa'lav aKCII'lTOV. af Tf yap oVa'la& 'ltpiiJTa& Till 8VT'Q)II, 5 Kal fl fta'a& .,,8apraC, 'ltdVT'a .,,8apTd· aM' aaVvaTov K""'ITW ~ Yfvla'8a& ~ .,,8apijVat (ad yap ~II), aUE xpdvOII. oV yap otov Tf TO 'ltpOTfPOV Kal J;a'T'fPOV fllla& ".~ 8VT'or xpd1I0V' Kal. ~ KUn,a'&r 4pa afrQ) ITVllfx~r 1JJa''ltfP Kal. IS xpdvor' ~ yo.p TO aVTO ~ K~a'f~r 1'& 'lt480r. K(II'1a''' a' OVK 10 1a'T'& a'Vllfx~r aM' ~ ~ KaTa TO'ltOV, Kal. TaVn,f ~ KVM,.

TOa1 EJr AI.: n; .ra., Ab: rc\.&&, recc. 20 1'4 EJ AI. : 20-21 1'''' J ,,",aTOll EJ'r AI.: om. AbJl 23 Tc\ alt. om. EJ 24 .l a.j Rolfes: .ra., JIAb AI.: fa., EJ1r: ,.Q .ra., Christ II.] an ,.. ? 28 1'..,] 11 et fecit E: ,.0 Jl Tc\ IrlllijcrCIII Ira! rc\ f:aoe Ab 29 ,.c\ a.j E Al.r 31 y. Christ: ,.. cocld. • 19

om. Ab

T'CII

33 ,ull] a. Ab

, om. Fb Bonitz Tc\ scripsi: T. cocld. 34 .al] b 1 al alt. om. EJ :z 11:01 ,..WOI bis E ,..." alt. om. Ab 3-4 11:01 /Ala ~ J1r: !Cal p.la a' ~ JI 4-5 TllIOdtalOlI Ab 9 &pa]"op yp. E II dU" r recc.: GAA' EJAb: .tAA'I , ut vid. AI.

&rl e Them. ci. nODitz

T.nN META TA

cIir~IKA

A

,AUa II-qll fi laT& K&II,,1'&KOII ~ nO&"1'&KOII, II-~ fllfpyoVII 31 1'&, OOK laTa, KWr,tnr' ill3lXfTa, yap 1'0 3vllall-'II 'xoll II-~ illfpyi'". 008fll 4pa 8"'fA.or oU' iall ootTtar nO'~tTO)I'fll ai-' 15 3loor, OStTnfp 01 1'4 ff3", fi I'~ 1'&r 3vuQfAf"" illlaTa& apX~ I'f1'a/34AA,,"' 00 1'O{uvll 003' aiST" lK~, 003' 4U" owla. napa 1'0. d3,,· fi yap I'~ illfpntTf&, OOK ltT1'tU Kl""tT&r. h& aU' fi illfpntTf&, q 3' owla alrriir' 3vllal'&r' 00 yap laTa& K"'"tT,r clt3wr' ill3lXfTa& yap 1'0 aVII41''' &, II-~ fTlla&. 3fi 30 4pa fTlla, apX~II 1'O&aVn,II ~r q OOtTla illlpYf&a. 11'& 1'olllVll 1'awar a,i 1'ar olltTtar tTlla& 411fV 'A."r· clL3lovr yap 3fi, dnEp yf Kal 4Uo 1'& clt3,oll. illlpye&a 4pa. Kal1'o& clnopta· 30Kfi yap 1'0 ~ illfPYoOu rill avllatT8ai 1'0 3f 3VII4I'fllOll oil rill illfPYfW, OSaTf npOTfpoII fWa& ~II 3Vllall-&II. 25 clUa II-~II d 1'oilT'o, 006111 laTa& 1'&ill 811T'0)II' ill3lXfT'tU yap avllatT6a& ,"II fWa& lI-~nO) 3' fWII&. KaC1'O' d ~r A.fyootT&II 01 6foA.Oyo& 01 iK IIVK1'Or Yfllll&illT'fr, ~ ~r 01 "'VtT&Kol 6".00 n411T'a XPJ11'111'4 .,,11(1'&, 1'0 allT'o clavllll1'Oll. n&ir yap K&II"",tTfT'II&, d II-~ laTa& illfpYfC, 1'& af1'&oll; oil yap if yf 30 i$A." It&ptftTf& a~ la~II, clUa 1'fKT'Oll&q, oo3f 1'a in,I'~II&a oVa' q yii, clUa 1'0. tTnlpl'll1'a Kal q yo~. 3&cl IIIw& no&o1icr&II cltl illlpYf&all, otoll AfVK&'IMI'Or KIll nA.41'o)II· clfl yap fwaC F& K""'tT&II. clUa 3&4 1'C KIll 1''''11 00 A.fYOVtT&II, ol.o3', (d) ~3l (.) ~3C, 1'~II ai1'tau. ovafll yap ~r 35 lnxf K&IIfi1'II&, clUa afi 1'& clfl VrrdPXf&ll, l/J(J'1ffP rill ."VtTf& ,"II ~3l, fJl, af ~ ~no 1100 4 ctuoo ~3l. (ET1'a nola. n,*T'f/; 3&a."lpt& yap clf.&~xCllloII 3tTOII). clA.A.a II-~II 003f nM1'o)II' J07a" yf oroll 1'f A.ly,," 411 off1'a& illCon clPX~II fwa" 1'0 allT'o ICIVT'o K&IIoW' 'tTT'fPOII yap Kill 41'11 1'rp ollpurp ~ 1frox~, ~r "'"tT"'. 1'0 I'W 3~ 3VIICIf.&&II offtT6a& illfpyfla.r npotEpoII laT& I'W ~r KCIA.&ir laT& 3' ~r oV (Efp,,1'a& 3f n&ir)' tfr& 3' b I~ .1 om. JI tan AbAl•• : 'f7'I'OI Jr et fecit E ~ frO'",.'''.;., om. JI 13 'errlll Jr AI.: If7'I'l EAb 16 owq Abr 17 Ab 'f7'I'OI EJr Af•• : 'f7'I'l Ab 18 d et ~ om. r 21 ,.,}r et 2~ 'yt EJ AI •• : oat. Ab 22 ''''pyno Ab AI.: 'P'P"td, Er : lal 'YP' EJ ~7 ~r Ab 'Yp. EI'I': om. EJI 01 om. yp. E 28 opoii] ifp 0/M'v IIAbr cl3.iNt'OI'l of,.lo.. ut vide AI. ~9 "."sip Ab n om. A\ 34 oM', II ~& ~ t.al, fort. AI., Diels: ~ tW1 oM. codd. r 35 ,., _1 EJr AL: ald n Ab : .rl _1 af",o.. Usener: n alIi ,.1 Jackson: an "'.,' _11 37 &0t/>f,.1P Ab Iluo.. om. Ab ,..~I;""'I'.1 Ab 1072& 1 4.. om. Ab

'IItmIT'I

' ' flYl

fv'PYEta lrPOTEPOV, I-'aprvpEL 'Avafayopas (0 yap voils fvlp- 5 YEta) KcU 'EI-'lrEaoKA71s cptA{av Kal TO VELKOS, Kal ot aEl AIYOUTES K{V7Icnv Elvat, /JJUlrEP AEVKt'lr'lrOS' /JJfTT' OilK ~V &lrEtpOV • )(POVOV Xaos ~ vVt, cL\Ad. TaWd. aEt ~ lrEPt~'f> ~ c'l'\,\WS, EflrEP lrptYrEPOV fvlpYEta avveil-'EWS. El a~ TO awo aEt lrEptOa'f>, aEL n aEt I-"VEtV cduaVTws fVEPYOVP. El a, 10 ,""MEt yIVEUtS Kal CP80pd. EWat, &'\'\0 aEi Elvat ad fVEPyovv &,\,\WS Kat &,\,\WS. aveiYKl'/ ltpa cdal I-'tV Ka8' awo fVEPYELV cdat at KaT' &'\'\0' 11TOt c'lpa Ka8' ITEPOV ~ KaTa TO lrpWTOV. dV4YKl'/ a~ KaTa TOWO' lr4.\w yap fKEivo awcfi TE afTtOV KdKE{V'f>. OVKOVV f3''\nov TO lrPWTOV' KcU 15 yap afTwv ~v fKELVO TOV dd cduaVTws' TOV a' &'\'\wr lTEpov, TOV a' dEl c'lUwr 41-'cpw al'/'\ovon. OilKoVV O;n.Wi' Kal lxovutv at KW7JUE'S. T{ o~v c'lUas aEi (l'/TEiv dpxqs; 7 'ElrEl a' o;n.w 1" fVa'XETat, Kal d p.~ otlTwS, fK vvKTOS IfTTa, Kat Ol-'OV 1r4UTWV Kat fK I-'~ OUTOS, '\VO'T' av 3~ Tawa, Kat IfTT' 1" dd KWoVI-'EVOV K{Vl'/UtV &lravfTTOV, a~ a' ~ K6KA'f> (Kal ToVTO oil '\&y'f> ,...oVOV cL\A' lpy'f> aii,\ov), /JJfTT' dtator av dl'/ 0 lrpli)T9s oilpavos. IfTT' TO{VVV .,..t KaL & KWEi. flrEl a, TO KtVOVI-'EVOV Kal KWOVv [Kat] I-"UOV, f.,..o{vvvt IUTt n & oil KWOVI-'EVOV KWEL, dtatov Kat oouCa Kal fv'pYE,a 35 ooua. KWEL a, ~aE TO dPEKTOV Kat TO VOl'/TOV' KWEi oil KWOV#-'Eva. TOVTWV 1'4 lrpWTa TO. awei. flrtevl-'l'/TOV I-"V yap TO cpaW0l-'EVOV Ka'\ov, {30V'\71TOV a, lrPWTOV TO ~V Ka,\OV' dPEyO#-'E8a a, aWTt aOKEL p.ii,\,\ov ~ aOKEL atOT' dpEY0l-'E8a' dpx~ yap ~ v&71u,s. VoVS a, wo TOV V07JTOV KWELTa" V07J~ aE 30 ~ ITIpa fTVfTTO'Xla Ka8' a~v' Kal TaW71r ~ oVU&a lrPctJT'71, Kal Tav.,..."s ~ Alr,\71 Kal KaT' fV'PYE&aV (IITT' aE TO tv Kat • 5 ;"'pyt,a alt. Tr AI.: ;1Ifp"/'U} EJAb 6 T~ om. Ab ."ICOS J ol.id] ola ol J 8 XpcS.,ou Ali 10 Mom. JI II ,l",a, ~ei t'1I.P'Y0iill] ;lIfpyoii" .l"a, EJr 15 a~ r AI.: "irri> codd. ICaIC""".

.n>.o Lasson

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~i, a,i J 10 ulCorrov".'"olJs Diels 11 ouai,,] I" A /linD" ••• 12 cpall'PO" sic interpunxit Diels : alTuS" 'Unll, ~s "..IITa. ffOIOiiUI, cpa"'po" AI. ~s Ab AI.: ',,,illO Jr Syr.1: om. E 12 ,~

ai, E:

codd. r Syr.: III AI. leaj et UUUTOIXias om. E 13 lUfile's lUll" AI.e Syr.1 ret fecit J : luap'O".o" E: fao" Ab 14 at . .• aPIO".;;", secl. Diels lCa, at Jar Syr.1 ;:'Ptl J 'rOltluaf J 18 T;'] TO fecit Ab 21 Xpo'! E 22 ap".oll'O»" fort. AI.

TUN META TA

«I>T~lKA

N

clU~AWV 01 fero, E~E" ICal ya.p al p.ov&.au)' cZlTTE 3w. yE TailTa d3'l 011 'lTO''lnOV, TO. p.'fv OVV crvp.{3aiuoVTa TaVrci 25 TE ICav IT, 'lTAELW crvvax8E('l' 1o 'ICE 3'f TEICP.~P'OV Elva, TO 'lToMa. ICaICo'ITa8E'i:v 'lTEpl ",V YEvEerw aVTii>v leal p.'l3EVa TPO'lTOV 3vvaer8a, crvvELpa, Toil p.~ xwp,erT4 Elva, TO. p.a8'lp.aT'ICa. T;;'V aler~T;;'v. c:.s lvLO, AEYOVtJ'L. p.'l3'f TaVTas Elva, Ta.S uPXas,

b23 ala om. E 24 .,olJ.,/t ~:a'l E firm"", I' 27 O'uHipOI] aula"" E

BOOK

z

SUBSTANCE (chs. I, 2). Who/';s' ;n the primary sense ;s substance (ch. 1). 10118& 10. While' is 'has the various senses distinguished in ~. 7, what' is' in the primary sense is substance (i. e. 'what a thing is'e.g. man, god, as opposed to 'good', 'three cubits high '-or a' this '). 18. Other things are said to ' be' by virtue of being quantities, "c., of this. 110. Hence one might doubt whether' walking' and the like are existent; no such thing can exist apart from substance. 114. 'That which walks' more truly is, because it has an individual substance as substratum. 30. Substance is primary in definition, in knowledge, and in time; in time because it alone among the categories can exist apart; in definition because the definition of a substance is involved in the definition of anything else; in knowledge because we know a thing better when we know' what it is' than when we know its quality, "c.; we know even a quantity or a quality only when we know what it is. b II. The eternal question 'what is being' really means 'what is substance' (it is substance that was said by various thinkers to be one or many, and if many, finite or infinite in number), and so this is our chief and first and practically our only subject.

10118" 10. Kdciftp &~E~U"'EeU 1rPOTEPOV, ~. 7. II. T£ lem Kul T6&E T~. The two phrases indicate the two sides there are to Aristotle's doctrine of substance. A TtIOT& is the TtIOT& of something, the answer to the queslion ' what is it?'; and whether this something be an individual or a universal, its essence can only be stated as a universal or a combination of universals. Tt IOT& in fact points to the distinction between essential and accidental predication. A roBE T& on the other hand is not the To8£ T& of anything; it is simply an individual; the term TO& T& points not to the distinction of essential from acccidental but to that of substance from attribute. The fact is that abatu means initially for Aristotle nothing more definite than' that which most truly or fully is'. He sometimes thinks of it as that

160

COMMENTARY

in things which most truly is-Tl €I1TL or essence; and sometime~ as that which most truly is because it is not in anything but exists by itself-T08E TL or the individual. The same ambiguity occurs in the Categories, where 1rpw"J ow-la answers to To8E T& and 8EVTipa ow-la. to , TL EI1TI.. 16. Aristotle's ohject being to distinguish quality from substance, not from the other categories, Tpl1r7J)(V ~ is irrelevant, and was suspected by Bz. It was, however, read by Alexander, and apparently by Asclepius, and Aristotle is not incapable of such irrelevancies, especially in a clause which like the PIV clause here is unemphasized. Cf. 0. 1047& 10 n. 19. I have restored from Ab AI. the grammatically correct1rOO'~Ei, 1rOL0"JTEi, instead of the accusatives. III. Ab's reading '"I"o.(m seems to be required, instead of ~ p~ OV, to explain the grammar of (KaI1TOV alrrwv. 'Whether the words" to walk", &Ce., imply that each of these things is existent' cr. L. and S. CTTJp.alvw III. I. 114. Aristotle does not mean that TO {3a8l(.ov unlike TO {3a8[(.Elv can exist apart from substance, but that TO {3a8[(.ov, since it is a substance (though referred to only as the possessor of an activity), can exist apart, while TO {3a8l(.ELv, since it is only an activity (though it implies a substance as the possessor of the activity), cannot exist apart. 116-117. SLOTL ••• ':'pLu"lvov. I.e., when we say TO {3a8[(.ov, we think of some definite man or animal that is walking; when we say TO {3a8{(.ELv we imply that there is a subject but do not think of any definite one. 118. i"t....ETO'L ••• TOLo.UTt!, • is plainly implied in the use of such a designation'. 30. TO 'lrpWT"''' &.. 1I00L oil TL &.. cn,~' &.. 4'1r~w", ' that which is primarilr, i.e. not in a qualified sense, but without qualification '. 311. 1I00L My,!, 1I00L Y"WUEL 1I00L xpo ..,:,. Alexander takes TWV •. poVfl II. 33, 34 to be explanatory of XJJOV':'. Substance is prior to the attributes it successively possesses, as a jar is prior to the wines that successively fill it. What Aristotle sars, however, is ' for none of the other categories can exist apart; substance alone can '. Priority in this sense is elsewhere distinguished from priority in time (Cal. I
.

z.

I. 10288. 16 -

1028b

5

161

already mentioned. It seems best to suppose with Alexander that the next words (II. 33 f.) are meant to explain )(pIJ",!,. That which can exist without other things while they cannot exist without it may naturally be said to exist before other things. Priority AOy,!, and priority '}'l'Wufl are not elsewhere distinguished. In loaSb 27 we have priority AOy,!" XJ>O"'I'I 10'(IT"; in 0. I049 b II N>j'IfI, oW{!l-, XJ>O"'!'; in Phys. 265& 22 ~wn, M')''!'. ')(poVtf!. In~. IOISb 31 priority "ClTa. TO" AOyo" is one form of priority 'rii '}'l'Wun; in 0. I049 b 16 f. the two are identified. But here they seem to be distinguished from each other; as "Ill before XJ>O"'!' means 'and', it is difficult to suppose that "Ill before '}'l'Wun means • i.e.' Alexander is probably , right in supposing that II. 34-36 refer to AOyId and II. 36-b 2 to '}'l'(dfT€&' 34. Arislotle here says that substance is 7rPw-ro" ~ as compared with the other categories. In M. I077b 6 he says TO AR"O" is prior in AOyOi to ~ AR"Oi IJ.v8PW7rOi
.

17- 2 7.

b 4. ot I'~" lv, the schools of Miletus and Elea. 5. ot I'~v 1r€1n!puc1l'lvCl, the Pythagoreans, and Empedocles and his followers; ot &i cl1r€&PCl, Anaxagoras and the atomists.

---------

Various opinions as 10 lire deno/alio" of mbslonce (ch. 2). 10118" 8. (I) Substance is thought to belong most evidently to bodies-animals and plants and their parts, the elements and their

COMMENT ARY

162

parts and what is composed of them, e. g. the physical universe and the stars. 16. (3) Some think the limits of body-surface, line, point, and unit-are more truly substances. Ig. (3) Some think there are eternal things more numerous and more real than the sensibles, e. g. (a) Plato thinks Forms and mathematical objects are two other kinds of substance. III. (b) Speusippus thinks there are many kinds of substance, each with its own first principles-numbers, spatial magnitudes, soul, &cc. 114. (c) Some think that Forms and numbers are of the same kind, but that there are other kinds dependent on this-lines, planes, &cc., ending with the class of sensibles. 117. These views we must examine, after first outlining the nature of substance. IOll8b II. KCll TWI' TOLOdTWI' 'KCIVTOI'. For the probable meaning cf. H. 1042& 8 n. 111-13. ~ I'oP£"'1' ••• Cl6TOU. The physical universe (for this sense of ollpav6e cf. Bz. Index 541b 56-542& '7) is composed of the totality of naturel bodies or elements (De Catlo 378h 21); its parts are composed of parts of this totality. Hz. conjectures TLVWv or lv{wv for ,..aP£"'I'. But this suggestion is not, as be supposes, supported by Alexander, who evidently read p.op{wv (462. 6). 14. I have inserted here, from T, ~ TodT",1' TLI'~I ~ KCll cU),ClL. F.J Asc. have; TOWWV TLVle ; lCo.~ dUwv, Ab ; TO~V TLVIe lCa~ tLUwv, where tLUwv (sc. Ttvl~) would be difficult to defend. With; lCo.~ tLUo., ; ToWWV T'VI~ ; lCo.~ cIAMu ; TOVTWV before them, it is natural that the writers of the inferior manuscripts should have passed from the first &AM' to the second, instead of the first, ~ TOW",V. The possibilities stated by Aristotle are that the complete list of substances should blclude(I) only those already named, 2) those and others, 3) only some of those already named, 4) some of those already named and some others (; KCll tLUa,), 5) only certain others. 16. TLITL, sc. Pythagoreans. The Platonic view is given as distinct from this in l. 19. The Pythagorean belief that planes, lines, points, and units are substances contained in bodies is distinguished from the Platonic view that there are substances apart from bodies. For the B. 1003& 4. former v:ew 18. ot 1'4", the pre-Socratics, cf. B. 1002& 8. Ig. ot SI . • . AiSLe&. rAI{'" may mean (I) more numerous tban sensible substances (cf. A. 990b 4) or (2) of more than one kind. Again we may translate (I) 'eternal entities more in number ami more

!

cr.

Z. 2. 1028 b 11-31

real', or (2), with a comma after p.«Uov, 'entities more in number and more truly substances, being eternal'. The first alternative in each case seems preferable. p.O.Uov must not be taken with d.t8la, for etemality is not a matter of degree. III. Speusippus' doctrine is referred to in M. 1076& 21, 1080b 14, loB5& 31, N. 1091& 34. It is this doctrine that makes the nature of things' episodic, like a bad tragedy' (A. 1076& I, N. 1090b 19)' The d.PXa{ of numbers were unity and plurality (M. 1085 b 5, 1087 b 6, B, 27, 30, N. I091b 31, 1092& 35); the d.pXa{ of magnitudes were the point and' a matter akin to plurality but distinct from it' (M. loB5 a 32). E. Frank, in Plato u.d. sogenannten Pylhagoreer, 245-251, holds that Speusippus recognized ten stages in the structure of the universe, vi?. (I) absolute unity, (2) absolute plurality, (3) number, (4) spatial magnitudes, (5) perceptible bodies, (6) the soul, (7) reason, (B) desire, (9) movement, (10) the good. This view is, however, largely conjectural. ~4. lVLOL Sl. This is the school of Xenocrates (so Asc.); for the evidence of this cf. M. 1076& 20 n. Other references to the view are found in A. 1069& 35, M. 1080b 22, 28, loB6& 5, N. 1090b 2B, 31 j it is in M. 1083b 2 called the worst of the Platonic views about numbers. ~6-~7. I'lxpL ••• Cltri')TC£. Theophr. fro xii. 12 gives Xenocrates credit for carrying out his explanation of the universe more thoroughly than Plato and Speusippus; O~TO~ yAp «I7raVTa 7r1ll~ 7r~PLT{~CTL 7r~pl T~V KrXrP.OV, ;'p.o{~ alcr~TA Kal v07p'A Kal p.a~p.aTlKA Kal ITL 8.q TA 8(ia. According to Sextus Empiricus (Adv. il'Iath. vii. 147) he distinguished \. aLCTv,{, -tl--l. J I ''"IV (" \ '"IV 'IV OVCTlav (VTO~ OvpaVOV , '"IV v07JTTJl' TIIlV ~KT~ ovpavov , JI

" CTVVI7€TOV Il '("'"IV KaL,~~ oo~aCTTTJv '"IV aVTOV

"')'

'(

....

' \

II

.... )

-OvpaVOV . -) • TOV

~8-31. The question whether there are any substances 7rapA T~~ alCT81JTa~ is distinguished from the question whether there is a XWPLCTTT, oVU'La 7rap;,. TA~ alU'~Ta~. The first is the question whether there are

any substances besides sensible substances-e. g. forms of sensible substances j the second is the question whether there is any substance capable oj' separate existence besides the sensible substances, i. e. any pure substantial form.

SUBSTANCE AS SUBSTRATUM

lo~8b

(ch. 3).

33. At least four things are said to be substance: (A) essence, (B) the universal, (C) the genus, (D) the substratum. 36. (D) The substratum is that which is subject of everything else, never predicate; it is thought to be, most of all things, substance.

16 4

COMMENT ARY

losa9& sa. In one sense matter, in another sense form, in another sense their compound, is said to be the substratum. 5. If form is prior to matter, it is prior to their compound. 7. Our account of substance as that which is always subject is inadequate; for it would follow that matter is substance, since it is what persists when all attributes are taken away. sao. By matter I mean that which in itself is not any particular thing nor of any quantity nor otherwise determined. The other attributes are predicated of substance, and substance of matter. sa7. But substance must be capable of separate existence and be a ' this " so that form, and the compound of form and malter, are more truly substance than matter is. 30. The compound we defer, as posterior in nature and familiar; we will study form, the most difficult of the three. We look for it first in certain generally recognized sensible substances. b 3. For the order of learning is from the less intelligible by nature and more intelligible to us to the more intelligible by nature. --sa8 b 34-36. TlI TC ~v Etvcu is examined in chs. 4-6, 10-12; n K"ecS~OU in chs. 13, 14; TlI ~1I'OKlC"'IVOV in ch. 3. TlI y4vos is nowhere separately examined in Z. At the beginning of ch. 13 Aristotle says that, as he has enmined the essence and the substratum, it remains to examine the claim of the universal to be substance. From this it appears that the genus has dropped out of view. But in fact chs. 13, 14 serve as an examination of genus as well as of the universal. Every genus is a universal (though the converse is not true, differentiae and properties being also included among universals), and if the universal cannot be substance, genus cannot be so. 10sagB- 1-'.18. The two characteristics of substance here signalized as primary-that of being ultimate subject of predication and that of having separate individual existence-are the same two that are mentioned in .1. 1017 b 23-26. sa. The treatmen t of Tli {nrOKE{P.OIOII as ambiguous, meaning ( I ) matter and (2) the concrete unity of matter and form, is natural, and common enough in Aristotle (matter underlies actuality or form, the concrete individual underlies its affections or accidents, I. 113, cf. i038b 5): but it is surprising to find (3) form put forward as one of its meanings. The same suggestion, however, occurs in H. 1042& 28. Aristotle's meaning js that the form or essence, instead of the concrete individual, may be thought to be what underlies properties and accidents; cf. the description of the soul as the {nrOK£{P.(JIOII of life, .1. 1022& 32. The reference to form, then, is not as Bz. suggests a slip due to the constant association of matter, form, and the unity of the two, in Aristotle's thought. Nor is the fact that form is discussed under the head of T{ ;V ETv"" not of {nrOK({p.01011 (Bz. 301) a real objection to its

z.

3.

1028b

34 -

102 9& 29

presence here. Substratum and essence present themselves with the universal and genus as rival candidates for the position of substance. If essence turns out to be a kind of substratum, the original division into four turns out to be a cross-division; but we already know from the case of TO KaiJOMv and TO 1ill0'; that that is so. The original fourfold division is merely aprimafacie one. 3. ~ fIoOP~. p.o~~ is often identified with .t8o~ and Tl ~II .lllCl', but means primarily sensible shape; cf. TO ux7IJU' "11; l8ial; 1. 4, Tilll III ~ alu6Tri ~ I033 b 6. 6. Ka.l TaU 4f'+oill. The evidence is pretty equally divided between Toli and TO, but the former gives a better sense. If A is prior to B it is clear that it is prior to A + B, but it is not so clear that A + B is prior to B, which is what TO would imply. Further, while it is true that in 1. 29 Aristotle says the concrete unity is substance more truly than matter, he says nothing of its logical priority; but in 1. 31 he says that form is prior to the concrete unity; this again confirms Toli. 10. a..na ••• ToiiTO, i. e. the vague statement (Tlhr't' in 1. 8 f. ISI-16. Aristotle divides the process of' stripping off' (7f'.p''''POV,uIlWII) into two stages. Tel. rua., the elements in the nature of a sensible thing other than length, breadth, and depth (i.e. the secondary qualities), are mere affections, actions, and powers of bodies. But secondly, length, breadth, and depth are themselves not substances but qualities and may be ' stripped away' in thought. SlSI-Sl3. .; Ta Etl/G.L • • • iKdaTn. The being of matter is different from that of any of the categories, because, while matter is not predicated of anything, substance is predicated of matter and the other categories are predicated of substance. It is noteworthy that even in working out the line of thought from which it might be inferred that matter is substance, Aristotle implies (in aim, 8~ "1~ iJA"1!1) that substance is something other than matter, something not entirely stripped of attributes but including certain attributes. SIS. o"8~ ~ a.t 41I'o+claEL!I, , nor will the ultimate subject per se be the negations of these " i. e. o~ T~ o~ 7f'OCTOII, &tc. This is difficult; one would suppose that it was just the essence of matter, a'l Aristotle conceives it, to be not Tt, not 7f'OCTOII, &tc. But he seems ~re to feel that to say even this of it is to assign it a character, while its character is to have no character. Sl7. Aristotle does not criticize the line of thought according to which matter is substance, precisely in the way which might seem most natural, by pointing out that the effort to find the truest reality in that of which attributes are predicated has left us with that of which nothing can be predicated. He puts the case differently. Matter lacks two of the characteristic marks of substance. It is not capable of separate existence, and it is not individual. It fails in both respects, we may say, because it is characterless. Slg. In what sense are separate existence and individuality more characteristic of form than of matter (that they are more characteristic of the concrete individual than of matter is intelligible enough)?

.e

.r,n,,-a,)

166

COMMENT ARY

A similar remark about form occurs in A. 1017 b 25, and the note on that passage may be referred to. 81. ~C1Tipa, cf. l. 6 n. 3~. ~).'1, 'obvious to sense'. +al'lpA Si 'II''''~ Kat ~ ").'1, i. e. rfi d••a.>..oyly. q,aVEpa, as Alexander ~ays. Cf. Phys. 191& 7-1 I ~ 0 {)7roKELp.lv." q,VuL~ l7rL~ KaT' dva.>..oylav. W~ 'Yap 'II'p(l~ civ8pU£VTa xaAK6~ ••• o1lT(J)~ allT." 'II'p(l~ ooo-tav IXEL. 33-34. Bonitz translates 'Es wird nun aber aIlgemein anerkannt, dass es gewisse Wesenheiten der sinnlichen Dinge giebt '. But it seems more likely that of"nwv should be understood with TWV alo-9-qTWV, to account for the feminine TLVI~, and that ooo-laL is predicate. b 3-I~. Bz. has pointed out that (I) II. I, 2 do not naturally lead up to II. 3-12, since the Tl ~v ElvaL is far from being 'Y"6JPLp.GV ~p.'iv, and (2) II. 3-12 do not naturally lead up to II. 13 If., since then there is nothing in what immediately precedes Ka, 7rpWTOV KTA. l. 13 for awov to refer to. It plainly refers to the Tl ~v ElvaL, which has not been mentioned since I. 2. His suggestion that 3 'II'p(l lpyov ••• 12 awwv should be placed after & 34 7rpWToV meets both these difficulties. This section is meant to justify the treatment of form as it exists in sensible things (a 34) before passing to pure self-existent form. Jaeger suggests with much probability (Art'sl. 205 n.) that the whole section, with the preceding sentence, was a note added later by Aristotle; the first sentence of the note was written between the lines of Aristotle's manu~cript and therefore appears in its proper place, but the remainder of the note had to be written on a separate sheet and has therefore been misplaced. Jaeger holds that the section belongs to a later period, when Aristotle first began to view the discussion of sensible substance in Z as preliminary to the discussion of insensible substance in A. Cf. 1037& 10-20 n. 5. .:scnrlp.1' TaL, 'II'pC£~lcn. The passage is to some extent explained by E. N. II 29 b 5, where we learn that we should choose what is good for us (i.e. what aids us towards the good life) and pray that what is good in itself (i.e. external goods) may be good for us. Here he simply says' make' instead of ' pray'. Originally, owing to some defect in us, what is good in itself may not be good for us; but we must (starting by choosing the things that are good for us) transform ourselves till this is no longer so. So too what is intelligible in itself is originally not intelligible to us; but we must clarify our minds until it ;s intelligible to us, by starting with the apprehension of what is already intelligible to us. SUBSTANCE AS ESSENCE

Jrhallhitzgs hat'e 10~9b 1.

(chs. 4-6).

fSSettfe;

(ch. 4).

(A) We proceed to study essence, 13. (I) in the abstract. The essence of a thing is what it is said to be per se (e. g. (a) your elisence i~ not to-be-musical).

z.

3.

102 98.

31 -

1029b

5

167

16. But not all of this; e.g. (6) the essence of surface is not whiteness; nor (c) to be a white surface, for here ' surface' itself is added improperly in the definition. The account of the essence of a thing is the account that states its nature but does not use its name. u. (d) There are compounds of substance and another category; is there an account of the essence of each such compound? Have they an essence? ~7. E. g. has ' white man' an essence? It might be objected that • essence of white man' is not a thing that exists per se. But a proposed definition can be • not ptr se ' to its subject only (i) because of an improper addition (thus whiteness must not be defined by giving the account of I white man '), 33. or (ii) because the subject has a qualification which is omitted in the definition (e. g. • white man' must not be defined by giving the account of whiteness). 1030a a. But is 'being a white man' an essence at all? No, fol' an essence is 'just what something is', but where one thing is asserted of another, as in • white man " this is not' just what something is " since it is not a substance. Only those things have an essence whose account is a definition. 7. It is not a definition if we merely have an account which means the same as a name (for then all accounts would be definitions, since any might have a name put to it), but only if it is the account of a primary real, i. e. of olle which does not imply the assertion of something about something else. II. Thus only a species has an essetlt"t or definition (for in a species, and only in a species, one element does not belong to the other by mere participation or by accident); but there can be an auounlof the meaning of any name (saying that' this belongs to that '), or an accurate account can be given instead of a vague one. 17. Or perhaps definition has more than one sense, just as I what a thing is' means now substance, now one of the other categories. 'What a thing is', like I is' itself, belongs primarily to substance, secondarily to the others. a3. For we may ask even ·of a quality what it is; just as not-being is, in so far as it is not-being, so quality is in a sense a • what it is '. ~7. (2) Since the proper way of using the term essence is now clear, we may say that in fact essence belongs (a) primarily to substance, (6) secondarily to the other categories, being in their case • the essence of a quality', &c. 3a. The other categories are said to ' be' by an equivocation or with a qualification j or rathe9', they' are' neither in the same sense ali

COMMENTARY

168

substance nor in a merely equivocal sense, but just as various things are ' medical ' by virtue of relation to a single end. b 4. Definition and essence, then, are primarily of substance, secondly of the other categories. 7. But there is definition only if there is a name meaning the same as an account which is one in one of the senses of ' one' answering to the senses of' being', viz. to the categories. lSI. Hence (c) there is a definition of' white man', but in a different sense of definition from that in which there is one of 'white' or of a substance. IOSlgb I. l"

dpxii,

1028 b 33.

13. }.oy~Kw~ sug~ests

plausibility rather than truth (Top. 162 b 27), dialectic or sophistic as opposed to science (An. Posi. 93& 15, and cf. r. 1005b 22, N. 1087 b 20 with De Inl. I7& 36), a reference to abstract considerations (AOYOt) rather than to the precise nature of the facts in question [)(cpVUtKw~, dVaAVTtKW~, lK TWV OlKE{WV dpxwv, Phys. 204b4, 10, De Gen. el Corr. 3161\11, G.A. 747b28, 748&8, and cr. A. 1069& 28 with lv TO'~ AOyOt~ A. 987b 3 I, ®. 1050b 35]. Usually its sense is depreciatory, but where abstract arguments are those that are required Aoytl(O~ may = dKPtf3~~, M. 1080& 10. It probably always refers to linguistic inquiries or considerations, cf. AOytKW~ here and in 1030& 25 with 1030& 27-28 n. It is in 1030& 28 that the real as opposed to the verbal inquiry begins. 14. There is no other case in Aristotle of the accusative with Tl ~v Elvat (in ~. 10161\ 34 Tl ~v Elvat is probably a gloss, cf. n. ad loc.), so that the manuscript reading (KaUTOV II AEYETat will not stand (unless, which is unlikely, the meaning is 'the TI. ~v ETvat is each thing, viz. what it is said per St to be " or 'the T[ ~v Elvat is what each thing is said per St to be '). £KUUTOV &AEYETat is palaeographically better than Bz.'s £KUUT'(J 8 AEYETat. For the genitive cr. 1032& 3, b 2. 16. O~8E 8~ TOUTO 'lrei... Aristotle rules out, as not the Tl EO'Tt of A, a term B which is Ka()' aUTO to A in the seco1td sense recognized in A,l. Posi. (731\ 37), viz. that (I) it lV1l1l'UpX" in A, is an attribute of A, and (2) A lVV1rUPX" in the definition of it. For this sense and the instance cf. ~. 1022& 30. He thus in effect implies that the Tl ~v Elvat of A is that which is Ka()' aUTO to it in the firsl sense (73& 34), viz. that it is present in the TlluTt and definition of A. 19. OT~ 'lrpOII'Ecrr~" a~TcS, i. e. such a statement of the essence of surface as 'to be a white surface' is wrong because it is tautologous. SlI-SllI. /lxn' Et ••• l .., , so that jf to be a white surface is to be a ~.mooth surface, then, though we are not told the essence of surface, it is implied that" to be white" and" to be smooth" are identical '. Aristotle is thinking of Democritus, who identified them (De StIIstt Hll b II, Theophr. De Smsu 13, cr. De Gm. eI Corr. 316& I).

112-23. bel S' 'aTL . . • cnl,,8eTA. There are uVvliETa or uVvoXa, not only within the category of substance (8 5, ~. 1023& 31) but also corresponding to the other categories, i.e. not only combinations of matter and form but also (more complicated) combinations of substance and accidental attribute. In fact every term in any category other than substance presupposes an underlying substance in which it inheres. 115. Tyj KWiJO'CL. The mention of this among the categories is unusual, but cf. E. E. I217L 29, where Ktvliuliat, KtVEtV occur as categories. KLVT/Utt; is a synonym for 1I"OtELV and 'll'cUrX€tv (cf. Top. 120b 26); it occurs in less formal lists of categories in I. 1054" 6, A. 1071" 2. More strictly, K{VT/Utt; is said to occur in the categories of substance, quality, quantity, place (PhJ's, 261& 27-36, De Gen. el Corr. 315& 28 sqq.). 117. The omission of Elvat with T£ ~" is unparalleled in Aristotle, and it is probable that the bracketed words are a gloss. 118. For a similar use of i,...dnov cf. H. 1045& 26, De b,l. 18& 19. cl>J..a ""~,, oGS. TW" Ka8' A~TO ).Eyoflt"",,, oGS. ToiiTo. Aristotle here ,anticipates an objection. Some one may say' it is no use asking what TO ipn.TL't! Elvat is. The thing denoted is not Ka()' am-o XEyop.EVov-white is not Kali' am-o to man-and therefore cannot be the essence of 'white man'. The objection assumes, arbitrarily enough, that only what is internally Kali' am-o can be a Ka()' am-o predicate to something else. But Aristolle takes it seriously and shows that' white man' may have something said of it which is not of! Kali' a{,To in either of the senses in which a definition should not be of! Kali' a{,To to its subject. 30. TO S. oJ. 'The other errs not by addition', which is idiomatically equivalent to saring that it errs by omission; cf. Bz. Index 539& 14-47· 31-33. Tii Alho cU.)'" "'POO'KEiriAL . . . Tii cU.).o AGT~. The antithesis is mis;"adingly stated. ReaIly the error arises in one case because in the definition the definiendum is added to something else; in the other because in the definiendum something else is conjoined with what is stated in the definition. 'll'POUKELuliat in I. 31 refers, as 'll'pouliiuEwt; does in I. 30, to the addition in Ihoughl of a qualification j the 'll'pouKEWliat which has to be understood in I. 33 refers to the conjunction of a qualification in facl. Alexander's understanding of 8ELV 'll'POuKELUliat in this line, which would remove the ambiguity, is indefensible. 34. To define is not opt'EtV but opt,Euliat (Bz. Ittde_",' 524b 8). JAb's reading c\p£toLTO ifldTLO" must therefore be right. Alexander (470. 18) read either this or opt,OtTO TO iP.o.TtOV (so W). 10308 I-II. It seems necessary to insert TO before Ti ~"dvaL. ' But its essence is not to be white '. For the omission of TO before XEUKW Elvat d. ~. JOl4 b 6 n., Att. Pro 67 b 12, 13, PI. Cral. 385 B 2, 10, 408 A 5, l'heael. 176 B 3. II. In pointing out the relevant senses of 0;" Kali' am-o Aristotle has IITS·I

M

COMMENTARY shown that the essence of' white man' is not' to be white '. But is being white man an essence at all, he now asks, and answers that it is not, though for a different reason from that suggested in 1029 b 28 and subsequently set aside. An essence is Ow-EP TI, 'just what a particular thing is', and a term like 'white man', in which an attribute is assigned to a subject distinct from itself (&rail ruG KaT' ruov Aiyrrral), is not 67rEP TOSE 'Tt (= Ow-EP T!), since thisness belongs only to substance and' white man' is not a substance but a substance + an accidental attribule. The editions before Bz. place the full slOp after the second instead of the first Ellla! in this line; the sense makes the change quite necessary. 3. 3'R'EP yap T£, the reading of Ab yp. E, gives a good sense, and it is not necessary to read with Bz. 67rEp yap (TOSE) T!. For T! = TOSE 'Tt cf. 1029& 20, 24. OTo.l' S' &).).0 Ko.T· &).).ou )'lYTJTo.~. It might be said that a term like , man " of which Aristotle thinks there is an essence, implies the predication of one term of another (' rational' of ' animal'). Aristotle would reply that these are not a>..Aa to one another since • rational' exists only as an attribute of' animal' and has no separate existence. Cf. Z. 12, H. 6. On the other hand a man need not be white, nor a white thing a man. 6. OCTIIII' 6 Myo~ tln11' 6p~CTI'~' Any 01101£0. (like ip.aTtOII) can have a AOyOS or combination of words, and any>"oyos (like t white man ') can have a AOYOS d.Kp!/3lCT'TEPOS, which means the same as it; but that >"oyos is not a definition, unless that which is thus explained is a 7rpw-rOll, a primary or simple real which is not the union of a subject with an irrelevant attribute. 9. Ab and apparently Alexander (47 1.28, 29) have My,!, where our other authorities have >..Oy'fl Tawoll. The shorter reading is supported by An. Post. 92b 31 El." yap ~II 01101£0. (Uu8a! b1rOt'flOw AOy'fl. WerrE Ko.l '" ·I).~a~ 6p~CTJAO~ Eno.~, i. e. the poem, being a combination of words, would be a definition of the word • Iliad'. The Iliad is a typical instance of the things that are only uvvSlup.'fl (II, Z. 1030b 9, H. 1045 8 13, An. Post. 93 b 36, Poet. 1457& 29. II-I4. Only ylvovs ElS." have an essence, i. e. genuine species as opposed both to Platonic ElS." (cf. A. 991& 31 n.) and to collocations of !>ubstance + accident like • white man'. Platonic Forms KaTa p.ETOX""" >"lyETa!-' participation I is one of Plato's favourite ways of expressing the relation of particulars to the Form. Again, the Platonic Form need not express the innermost nature or-its particulars, but is any universal under which they happen to fall, and may be a mere 7ro.8os or UVp./3E/3."KOS of them. In' white man' the relation between the two elements is of the same external and accidental character. On the other hand, the genus which is implied in the name of a species does not' share' in the differentia; the differentia is not a mere' affection' or' concomitant' of it, but is its proper differt'ntia. That KaTCt p.ETOxV" is to be interpreted as above seems to be shown by 1037 b 18, where

z. 4.

1030& 3-35

also Aristotle is speaking of the unity of a species as opposed to a term like' white man', and says lvrav6a 8' (in the species) OU p.f.TlX" 6aTlpov 6';'TEPOV' TO yap ylvo<; OU 8oICE& P.ETlXEW Taw 81acpopWv. No important distinction seems to be intended here between lCaTa P.ETOX~V, lCaTa m1.60<;, and ill<; rroP.{3E{3'r/ICO<;. ~~. T\i "lv, to substance. ~5. ).OY'K~, i.e. that which is not cannot be said to 'be' in the plain sense of that word, but speaking '\OYIICW<;, with reference to linguistic usage (0' '\oyol-cf. 1rw<; 8E& ,\€yEIV, l. 27), we may say that it is, since we can say it is non-existent. Cf. A. 1069& 21. For '\oytICw<; cf. 1029b 13 n. So too a qualitative term is never the answer to the question T{ lUTI in its primary sense, i. e. what is such and such a thing, but is an answer to the question what is such and such a quality. 'A colour' is the answer to the question' what is white? '. Cf. 1028b I, B. 996b 18-22, Top. 103b 27 ff. ~6. T'V£~ is perhaps a reference to Plato j cf. Soph. 237, 256 ff. ~7-~8. 8EL ,,~v 'XEL, i. e. such linguistic inquiries as Aristotle has been conducting since 1029b 13 ('\OYIICW<;) and has referred to in I. 25 are important enough, but it is still more important to study the facts themselves. The mode of using the term T{ ~v Elval being now plain, Aristotle proceeds to draw the conclusion about the facts with regard to the T{ ~v Elval, viz. that non-substances have in a qualified sense a T{ ~v Elval, not an essence simply, but' the essence of a quality',

...

&c.

(1.31).

~9.

6/'0£111$ is explained by ffxnrEP I
r.

1003b I).

Terms which are neither bp.wvvp.a nor rrovwvvp.a are, as here, said to be 1rpo,> (V in r. 1003" 33, K. 1061" 11. In E. N. I096b 27 Aristotle

COMMENTARY

1711

offers d.c/l' lvOr and KaT' dvaAoy&a.v as alternatives to 7rpOr a.., and seems to prefer, at least in the case of the various goods, KaT'dllaAoy&a.lI. Ii 4. 1111'OTipwr, i.e. whelher we say that various categories' are' in the same sense but with qualifications or deductions (a 33) or that they • are", not in the same sense (Ka6' a..) but 7rpOr III (a 35-b 3). lrrrvrlpwr can hardly refer to the alternatives stated in a 31, 33, for Aristotle would not regard it as immaterial whether 011 is a mere lJp.!fwvp.oll, applied to the various • beings' by a mere play upon words. 8-10. TOUTo 8~ ••• I", 'i.e. with a Ao-yol: which.is the Ao-yor of something that is one, not by continuilY •.. , but in one. of the senses of " one" which answer to the essential senses of" being" '. 6craXWt UynclU ,.0 I" is to be interpreted in the light of II. 10-12. For the correspondence of the senses of' one' to the categories cf. r. 100 jI 33, A. 1018& 35, I. 1053b liS, De An. .plb 8. UI. Since unity in some sense can be found ill any of the categories, • white man' (which is a union of terms from two categories) has a cerlain unity and can have a definition, though not in the same sense in which • white' has one, while this again has a definition in a different sense from that in which a substance has one. It is clear that the chapter does not do what it set out to do, viz. to discover whether essence is substance. It only tells us that it is substances alone that in the primary sense have essence. But this may be found to be a step towards the answering of the original question.

Have c(lupled terms an essence or definition; (ch. 5). I030b 14. With regard to (d) a coupled term like • snubness', whicIl per se belongs to the nose, not as • white' belongs to Callias or to man but as • male' belongs to animal, (i) how can such a term be defined, if definition must not involve an improper addition? a3. Per se attributes are those in whose definition the account or the name of the subject must be present. If lhey have an essence, it must be in a sense different from the strict sense. 118. (ii) There is another difficulty about these. If snub nose = hollow nose, snub hollow; but if this cannot be so because we cannot say • snub' \\'ithout implying the nose, • snub nose' is tautohollow nose nose '. Thus, if such terms had an logical, being essence, an infinite regress would be involved. I031a I. Only substance, then, is definable, for definition of anything else would involve an improper addition; • odd' cannot be defined apart from number. 5. Therefore (e) if the terms are coupled, as in 'odd number',

=

=·

such combinations cannot be defined, any more than terms like' odd', or can be defined only in another sense of' definition '. II. Substance, then, is the only or the primary subject of definition. In this chapter Aristotle raises two problems about ,.a o~X d.7I'Aa cnw8£811fJ.up.llllJ., terms which stand for an atlribute which is coupled with a subject (ro8( III 'T,8£ I. IS) not accidentally but in virtue of the very nature of the attribute; the attribute being KIJ.8' IJ.~O to the subject in the sense that it cannot be defined without either naming or defining the subject (I. 23), i. e. in the second of the senses recognized in the Pos/trior Analy/ies (73& 37-b 3). 'T4!TVII8t:811fJ.!Tp.lv1J. are in fact propria (e. g. snUb) or unions of subject and proprium (e. g. snub nose), which are initially distinguished from (a) substances, (6) terms in other categories, and (e) combinations of substance and accident (e. g. white man), all of which have been shown in ch, 4 to be definable, though (a) are definable in a more proper sense than (6), and (6) than (e). But ultimately all terms in categories other than substance are shown to be in principle of the same type as' snub', in that the' definition' of them must be lK 7I'pou8lufElJ)f;, must involve a reference to the substance to which they belong (1031& 2-5). The question whether' the snub' bas a definition is significant for Aristotle because 7I'ilJI'T1J. 'To. f/>V(nK4 ;,p.otwl 'T, 11""" AlyoJI'TIJ.' (E. 102S b 34). But there is an important difference between ,.0 U,p.OII and natural substances; cf. n. ad loc. The conclusion drawn from the first problem (1030b 14-IS) is that such terms cannot be defined, or can be defined only in a secondary sense, Kddwep _£I»'1KIIII"" The reference here is to &17-b 13, but Aristotle does not mean that he has already mentioned this particular sense (for the !TVv8fEBvlJ.up.ivlJ. are a different class of terms-cf. b Ie-from terms like' white man', which he was there referring to), but that he has said there are secondary kinds of definition. There cannot be a proper definition of 'T4 !TVv8fEBvIJ.!Tp.llllJ. because the account of them must be lK 7I'pou8lufEliil, and this prevents it from being a proper definition (1019 b 30). The cnw8fEBvIJ.!Tp.ivoil is a quality; yet you cannot give an account of it without mentioning its subject as well as it. 'The equal' is 'a quantity which is equal'; 'the male' is • an animal which is male'. Thus you define X as XY and break the rule against 7I'p/xr8(U'I. The second problem of the chapter is stated in 1030b IS10 3 1 & I: If 'snub nose' = 'hollow nose', 'snub' = ' hollow'. But' snub' is not hollow', since 'snub' implies a reference to the nose while 'hollow' does not • • • . ' Snub nose' is not 'hollow nose' • . . . If we say' snub nose' at all, we are saying what is = not to 'hollow nose' but rather to ' nose which is a nose-which-is-hollow'. Such terms cannot have an essence, since this would involve an in-

rua

='

=

COMMENTARY finite regress; 'nose which is a nose-which-is-snub • will involve' nose' once more. By I such terms' (I 030b 34) Aristotle seems to mean such terms as , snub', since this is the class of terms which he is throughout the earlier part of the chapter trying to prove indefinable (he advances to 'snub nose' only in 1031& 5). But he is evidently assuming that' snub' is equivalent to 'snub nose' (which is what is implied in saying that the account of it must be lK 7rpou(JlcT(w'i); for it is only by applying this equation that he reaches the term' snub nose nose' in 1. 35. He had previously (1. 33) reduced 'snub nose' to 'hollow nose nose', which leads to no infinite regress, but now, substituting for 'snub' its equivalent' snub nose " he gets the form' snub nose nose', and has no difficulty in showing that if the same substitution be repeated we are landed in an infinite regress. I take d 8( p.~ 1. 35 as = El 81 Tt'i >..I'1£t OTt lUTat Kal. Iv TOWot'i TO Ti ~v £ww Kal.~pUT~ (AI. 478.15). Alternatively, we might treat 8tO ••• £tvw ll. 34, 35 as parenthetical, and interpret' otherwise-i.e. if it be denied that the snub-nose is a hollow-nose-nose-we shall be committed to a process ad injinitum. For (since the snub is the nose Ihal is snub, the snub nose will be the snub-nose nose: and) the snub-nose nose will contain yet another nose (and so on ad injinitum) '. This may well be right. In any case Bz. is wrong in supposing that the introduction of Pl.'i Pl.'i Utp.~ in 1. 35 is a mere slip. To this' infinite regress' argument for the indefinability of 'snub' Aristotle himself in effect supplies the answer in Soph. El. 182& 4. 'The snub' = 'a snub nose " but it does not follow that in 'snub nose' we can substitute' snub nose' for' snub', and so ad znjim"lum. For in 'snub nose' 'snub' does not mean 'the snub', i. e. 'that which is snub', but a quality of the nose (i)Lvo'i To8t, otov 7ra(Jo'i), so that 'snub nose' is analysed not into' snub nose nose' but into' nose having the kind of hollowness proper to a nose " in which no infinite regress is involved (IllUT' oMtv 4T07rOV, El .q Pl.'i.q Utp.7J pi'i lUTtv lxovua KOtA6T7}Ta PtvO'i). 1. e. the Sophislici Elenchi draws the distinction which Aristotle fails to draw here between TO Utp.ov in the sense of , snub' and TO Utp.Ov in the sense of • that which is snub '. The corresponding distinction between the two senses of TO ~ruKOV is drawn in 1031b 23. The main upshot of the discussion of both problems is that TO Utp.Ov is not strictly definable because the account of it must be lK 7rpou(Jlu£w'i. The two problems bring out the two aspects in the notion of IK 7rpou(Jlu£wt>. The first shows that the account of such a term must introduce something other than the term, viz. the underlying substance (1030b 23-26); the second, that it must involve a tautology ( 103 1 & 4). IOSOb 24. o~

27. K48cbrtp

=

TO~OV o~.

ttP~K4".tl', a I 7-b 13.

IOSIa I. Aristotle now concludes that in general only substance is definable. If there be a non-substance X, there is always a subject Y which it presupposes, and it could only be defined as XV, i. e. IK

z. 7rpouOlu(w<;.

5.

9

175

Therefore it cannot be defined at all.

To this also the

I03 0b 24 -

I03 1&

Sophislici EIQlch,' evidently provides the answer. 3. 1fO'OU can hardly be right, but neither Bz.'s d.pTlov nor Goebel's 7rOUOV is convincing. 8-g. ~TO' ••• TlI T( ~v (tv!n. I. e. either such terms can be properly defined in some way which does not involve the addition of the subject (which Aristotle does not admit that they can), or we must distinguish improper from proper definition and say they can only be defined in an improper sense of ' define'. 8-g. Ku9el1f.p ... TlI T( ~v (tvu,. The construction is due to a fusion of two possible constructions, l(aO&'7r(p lMXOTJ, Ml"ly(uOa, T~V /'pwpiJv, &c., and l(aO&'7r€p l>"lxB-r, 7ro>..>..axw.. >"ly€uOa, oopwpiJ<;. &c .• OVTW vVv >"(l
Is a Ihing Ihe same as ils essencel (ch. 6). 1031& 15. Is a thing the same as its essence? This bears on the study of substance. for a thing seems to be = its substance, and its substance to be = its essence. Ig. (I) An accidental unity like' white man' would seem not to be = its own essence. For else essence of man = essence of white man, since man = white man. ~4. But perhaps it does not follow from white man being = essence of white man that the essence of accidental unities is the same as that of the simple terms (essence of white man = e~sence of man); for the extreme terms of the syllogism are not identical in the same way with the middle term. It might. however, seem at least to follow that the accidental extremes (e. g. essence of white and essence of musical) are the same j but they are not. ~8. (2) Is a per se term necessarily the same as its essence? Take (a) primary terms like the Ideas? If the Good Itself is to be different from the essence of good. (i) there will be substances prior to the Ideas, if essenc::e is substance. b 3. (ii) If the Ideas are separated from their essences, (a) they will not be known, and (ft) the essences will not be existent. For (a) we know a thing only when we know its essence. and 7. (p) if the essence of good is not good. the essence of being will not be, and since all essences are on the same footing, no essence will be.

COMMENTARY II. (iii) That to which 'being good' wiII not attach (IC. the Good Itself) wiII not be good. Therefore all terms (whether Ideas or not) which are self-subsistent must be the same as their essences. (15. If the Ideas are such as the Platonists suppose, it will not be substratum that is substance, since they are substances which do not imply a substratum.) 18. (b) That a thing is the same as its essence is also clear from this, that to know a thing is to know its essence. (I&SI. If we consider an accidental term like' the white', the essence of white will not be the same as that which is white (the white man), but it will be the same as the quality white.) 1&8. (c) The absurdity of separating a thing and its essence is further seen if we put a name to each essence, for then it will have another essence of its own; it is better to recognize at once that some things = their essences. 351. The definition of a thing, also, = the definition of its essence; for it is not per accidms that e. g. unity and its essence are one. To separate them would produce an infinite regress. 1032&4. F..ach simple per se term, then, is the same as its essence. 6. The sophistical objections are to be met in the same way as the question whether Socrates = being Socrates.

Aristotle's doctrine in this chapter is that TO. AryOp.wo. ICIlTo.

uvp.p.-

p'1JIC&r (i. e. terms denoting- a union of a subject with an accident) are not, and TO. ICIl(f 1lW4 AEY&/MVII (terms denoting a self-subsistent

unity, i. e. either a summum genus or a species, either in the category of substance or in some other, 1031b 2'1,28) are, identical with their essence. E. g. I to be a man' sums up the whole substantial, permanent nature of each individual man and is' identical with each and every man j 'to be a sitting man' does not express the permanent nature of any man, and ' to be a white man' expresses the permanent nature of some men but not of others. Aristotle first discusses accidental terms (1031a 19-28) and puts forward a proof of their non-identity with their essences. If (I) a white man = the essence of white man, then, since (2) a man a white man, • '. a man = the essence of white man. Now, if (I) is true, similarly (3) the essence of man = a man, ••• the essence of man = the essence of white man. But this is evidently not true. Therefore a white man is not the essence of white man. This reduclio ad absurdum, however, Aristotle points out in I. 24, fails. It does not follow that the essence of accidental combinations

=

=

Z.

6.

103 la 29 -

103 I b 10

is identical, sc. with that of the corresponding simple terms. For the extremes are not identical in the same way, sc. with the middle term. In the first syllogism the major term is absolutely identified with the middle, while the minor is identical with the middle only per accidens j in the second syllogism the converse is true. Aristotle next puts forward (I. 25 dU' lu(j)~ KTA.) an alternative reductio ad absurdum. If the fallacy of the above reductio be detected, it might at any rate seem to follow from the identification of an accidental term with its essence that the accidental extremes, essence of white and essence of musical, are identical. But evidently they are not. Therefore accidental terms are not identical with their essence!'. The argument here implied is: The musical man = the essence of musical man. The man = the musical man. The white man = the man. The essence of white man the white man . . . . The essence of white man = the essence of musical man • . . . The essence of white = the essence of musical. This conclusion might seem to follow, because here musical man and white man are both identical with the middle term man in the same way, i. e. per accidens. The argument is, of course, unsound; but Aristotle does not commit himself to its accuracy-he merely says

=

&Senw &v (TlJp.{Ja{vElv. 103Ia !lg. It is not obvious why Aristotle should have chosen as his illustration of the identity of a Ka8' a{/TIl term with its essence a class of Ka()' am-o terms which he does not believe in, the Ideas. The reason doubtless is that the argument in a 29-b I I conveys a covert criticism of the ideal theory. Plato, so Aristotle thinks, believes in a separate good which is neither a particular good thing nor' being good' (or the essence of good). But the separation of the good itself from the essence of good leads to insuperable difficulties and is therefore condemned. Instead of Ideas we should believe simply in essences or universals. 3!l. t~II, sc. am-o TO ''iiov. T~ (III, sc. am-o TO ~v. b 3-11. These arguments only show that the Idea and the essence must not be thought of as existing independently of one another (t.broAEAvp.£va.I, I. 3). But Aristotle uses them to show that Idea and essence are identical and cannot even be logically distinguished. One might hold that they are distinguishable but not independent, as is the case with any pair of correlatives. p.£v in Ei p.f.V (I. 3) looks as if Aristotle had noticed this point and meant to add another argument to show that if they are thus distinguished, but not treated as d1TOAEAvp.f.Val, other difficulties follow. But if this was his intention, he has not carried it out. 3. ,.wll 1'111, the Ideas. That they will not be knowable is proved in II. 6, 7. 4. Tel S', the essences. That they will not exist is proved in II. 7-10. 10. B1.. objects that Aristotle has no right to say that if the essence

COMMENTARY of being is not, no other essence will be. The corresponding result for the other essences would be that the essence of good is not good, and so on. But the argument seems sound enough. The reason for believing in essences holds of all terms alike. If the essence of being does not exist, there is no reason for supposing that any other essence exists. II. To his two main arguments against the separation of the Ideas from their essences (11. 1-10) Aristotle now adds a third, that if the essence does not belong to the Idea or thing-itself, the ' good-itself' will not be good, which is absurd. Alexander takes this sentence as proving that the essence of good is not good. But this has already been stated in 11. 6, 8, so that ITL would be unexplained. Besides, it would be tautologous to say' that to which being good does not belong is not good '. There is more point in saying' that to which being-good (the essence of good) does not belong is not good'. Aristotle has already said (1. 5) that being-good will not belong to the Good-itself'; he now draws the inference that the Good-itself will not be good. tlya6'ii ETvaL is used = TO tlya6«ii fTvaL, cf. 1030& 1-2 n. 13. The question Aristotle stated in & 28 was the general one whether self-subsistent entities are identical with their essences. He has discussed it in connexion with one class of alleged self-subsistent entities, the Ideas, but he now applies his conclusion to all self-subsistent or primary entities. These include not only substances (like horse,1. 30) but also terms like' white' (I. 27) and' one' (10321\ 2), in fact presumably all terms except compounds of terms in two categories (1029 b 23) like' white man' (1031& 20). Things are identical with their essences if they are self.subsistent, even if they are not Ideas, or rather (Aristotle contemptuously adds), even if they are Ideas. 15-18. The reference to Ideas suggests to Aristotle a parenthetical remark about them. 'If the Ideas are separate entities, it will not be substratum that is substance; for they are substances which involve no substratum, since if they were predicable of a substratum they would exist merely by being participated in by the substratum.' 16. OI1K EaTen TO ~'II"OKe("evov ol1er(a. Thus the belief in Ideas conflicts with a well-founded view about the nature of substance (1029& I). 18. KaTB ,uhl,v seems to mean not' in the sense that they partici.

pate in the substratum', but' in the sense that they are participated in by the substratum', i. e. immanent in it; so AI. 483. 37. For the passive sense of "0.1'4 p.I6E~tV cf. Top. 132b 35-133" II. The Ideas according to Plato are participated in by the particulars, but he would not admit that they exist only by being participated in. ~I. ~e Kal KaTB rill' EdeerLl' dvuYK'I EV TL etvaL 41'+101. On the meaning of 1,,6fcTL<;, IICTL61vaL, IICTt6ECT6ac cf. A. 992b 10 n. Bz. interprets here si (juis seorsim ponere susceperil rem eI eius "IE, is inMligel, ul poss,'/ ommi,o fsse scienlia, ulru1I1'ltie poliuS' idem aebert esse. But "0.1'4 n,v l,,6fCTLV would be a rather odd way of expressing the meaning here indicated. Schwegler translates aer gegebenen Enlwicklung sufi/ge,

Z.

6.

1031b I I - - 1032& 10

179

which clearly will not do. In his commentary he suggests alternatively that KtU KaTa ~v lK6(O'w may mean' even from the standpoint of the Platonic separation of the Idea from particulars '. What Aristotle says, however, is: 'that each thing and its essence are per se one and the same follows both from these arguments (those directed above against the Platonists), and from the fact that to know each thing is to know its essence, so that according to ~ lK6(0',.., also, both are necessarily identical '. lK6(u,.. seems therefore to be a way of proving, without reference to the ideal theory, that a thing and its essence are one. Alexander paraphrases lK6(u,.. here by l7rayw"YTI. and this seems to be substantially right. lK6(u,.. here is lK6(u,.. in the first of the technical senses explained in the note on A. 99Zb lo-proof by means of instances. Take anything you please, and you will find that to know it is to know its essence. ~7. 'The essence of white is not identical with the man (se. who is white) or with the white man, but it is identical with the quality white.' The reading Tc? JLEV • • • Ka2 T.j) clearly gives a better sen8e than Alexander's and Bz.'s TO JLfv ••• Ka2 TO. 30. Bz.'s excision of the second t7Ml"1[l seems necess:lry. 31. KahoL TC Kw).d.L KT).. 'Why should we not, to avoid stich a duplication of essences, identify some things straight off with their essences?' 103~a 4. i'll"' iuC"w", 'in the case of terms like" essence of unity" '. As we got one of the original terms by asking what was the essence of the other, we shall get a third by asking what is the essence of that essence, and so on. Ka2 bro' IK£lvwv might be taken to mean 'in the case of unity and essence of unity, as in the case of horse and essence of horse' (103rb 28-30). But then we should expect TOVrWV, not lK£lvwv. 7. 9EIT'" is used not in the technical sense defined in An. Posi. 72& 15, but = thesis. Cpo Bz.lndex 327b 29-41. 8. The sophistical difficulties about Socrates and' being Socrates' were probably, as Alexander says,. of the following type: If Socrates and being Socrates are different, Socrates will be different from himself. If they are the same, and Socrates is white, being Socrates will be the same as being white Socrates, a substance the same as its accident. The fact that Aristotle treats the question whether Socrates and being Socrates are the same, as different from, though allied to, the question he has been discussing throughout the chapter, indicates that the latter is a question about universals. Regarding universals we should agree that they should not be distinguished from essences, but if Aristotle means that we should answer that Socrates and being Socrates are the same, as the universal of a group of substances is the same as their essence, it seems that he is either using Socrates in the sense of the form or soul of Socrates, or including matter in the essence of Socrates. He would answer the question about Socrates by saying (cf. 1037" 7) that if by Socrates you mean his soul, that is the same as his essence; if you mean the union of soul and body, that is not. 9-10. o~S~" •.• l'll"LTilXOL, i.e. the basis of both problems is a confusion

COMMENTARY

180

between substance and accident: the basis of the answer to both is the clearing up of the confusion:

THE IMPLICATIONS OF BECOIlfING (chs. 7-9)'

Conditions

0/ Iht 1}arious kinds 0/ becoming (ch.

7).

Things that come to be do so (I) by nature, (2) by art, or (;;) spontaneously. Genesis is by something, from something, of something; the • things' may be in any category IS. (I) Natural genesis is that in which the agent and the resultant are natural beings such as man or plant; the' from which', here as in artistic production, is matter, i. e. the power of being or not being. !I!I. That from which and that according to which natural genesis takes place are both nature; so is that by which it is produced, viz. the specifically identical nature in the parent. !l6. (2) All other genesis is called making; it proceeds from art, faculty, or thought. Some artificial products, like some natural products, can also be produced spontaneously. 3!1. Artistic production presupposes the presence of the form of the product in the soul of the artist. Contraries have in a sense the same form; disease is just the absence of health, and health is the definition in the physician's soul and is the art of medicine. b6. Health is produced (a) by thinking of the conditions of health and the conditions of those conditions, till we come to something that it is in our power to produce. (b) When the thought is complete, the making begins. II. Thus in a sense health comes from health, house from house (the material from the immaterial); for medical science is the form of health. IS. The genesis, then, has two stages, thinking and making. Each intermediate stage in the production is produced similarly. !II. While the agent in artistic production is the form in the soul, the agent in (3) spontaneous production is that which starts the malting in artistic production, e. g. the heat in the body, which is either a part or followed by a part of health. This, viz. tht which produces a part of health, is the minimum necessary basis of health, as stones are of a house. 30. Thus some part of the product must pre-exist, viz. the matter. Is matter also an element in the definition of the thing? Yes; in defining a bronze circle we state both its matter and its form. I03!1a I!I.

z. 7.

1032& 12

181

1033a 5. Some things are described by a name derived from the name of that from which they come, like 'wooden'; 1 but a healthy man is not so described. The reason is that while genesis presupposes both a privation and a substratum, it is said to proceed from the privation, 'sick " rather than from the substratum, , man' (so that the healthy are not said to be sick but to be men); 13. but when the privation has no name, e. g. the privation-of-theshape-of-a-house in wood, the house is thought to come from the wood as the healthy was said to come from the sick, so that as the healthy man was not said to be sick, the house is not said to be wood, but wooden j 19. though strictly it does not come from wood, since the' from which' must change and not persist. 10311a III. Aristotle's object, says Alexander, is to prove that form is not generated. This will help him to show whether natural forms can exist without matter, as Plato maintained that they could. To show that form is not generated Aristotle shows that generation always presupposes a given substratum, whether it takes place (I) by nature, (2) by art, or (3) spontaneously. From this it follows that if form were generated, it would be generated from a substratum, and an infinite regress would be involved. The summaries in II. 1037 a 21-b 7 and in H. I. I042a 4-22 contain no reference to chs. 7-9, and confirm the view which the chapters themselves suggest, that they originally formed a separate treatise. They are, however, referred to in 15. 1039 b 26. Natorp considers that Z. is a combination of two treatises, viz. (I) chs. 1-6, 10-14 (with the addition of 16. I041a 3-5, which refers to 13. 1038b 8, 35, 1039a 3, 16). (2) Chs. 17, 7-9, 15, 16. Ch. 17, he thinks, contains the transition from the first to the second treatise; cf. the first words of the chapter, in which Aristotle speaks of starting the inquiry from a fresh standpoint. The transition is from discussing the cause of being to discussing the cause of becoming (cf. 17. 1041& 31). Chs. 15, 16 conclude the whole inquiry by saying what substance is not. Natorp is right in regarding chs. 1-6,10-12 as forming a continuous treatise which is interrupted by chs. 7-9' But chs. 15, 16 (though the former refers to the doctrine of chs: 7-9), in the main continues the line of thought of chs. 13, 14 (cr. 1041& 3-5 with I039a 15-17); nor does ch. 17 form a natural transition from the main thought of the book to the doctrine of 'Ylv(u,,~ in chs. 7-9. Rather the new attempt in ch. 17 to say what substance is follows naturally on the statement in chs. 13-16 of what it is not. 1 I use this instance instead of translating Ai91110S, because we cannot speak of a • stOIlY statue '. The instance of wood oc.:url t.elow, 11. '5-ao.

182

COMMENTARY

IlI-la. Ta. p.'v . .• mtlTop.uTOU. The triple division rpVUtS, T(X'I'T/, TaliTorecurs only in A. 1070a 6, but cf. Tafu-op.tJ.ToII, TVx:rI, vovs, rpVUtS Phj·s. 19811 10, K. 1065 b 3. 14. Ka9" lKclanJV KaTtJyop£av. This is not exact. Change takes place, according to Aristotle, in respect of the four categories here named,and cannot take place with respect to any other (Phys. 225 b 10226a 26). Sometimes all four kinds of change are included under Klllf1uts (Phys. 261 a 27-36, De Gm. eI Corr. 315a 28); sometimes only three are included under Kllll1UtS, and change KaT' ofJulall is called Y(V(UIS in distinction from them (P~s. 192b 14, 22Sa 26, 32, b 7, 226 a 24, 243" 6, 260a 26, De Caelo 310a 23, K. 1067L 31, 36, 1068a 9, b 16). All are included under IJ.(TafJo>"~ (A. 1069b 9, H. 1042a 32, De Gm. eI Corr. 319b 31); or else all except ylll(uts (Meteor. 465 b 30). 16. aL p.lv is resumed by ov".w P-lv o~v in I. 25, and the antithesis to it comes in I. 26. go. The (~ o~ of natural generation having been said in I. 17 to be matter, Aristotle here breaks off to say that the (~ o~ of all generation is matter. In I. 22 he returns to his main point, and sums up what he has said in II. 17-19 by saying that in natural generation U o~, KaO' 0, and ~rp' o~ are alike nature. gg. For the description of the U o~ or matter as rpvut.. cr. ~. 1014 b 26-35, Bz. Index 839 11 1-12. Kill. Ka9" 3 +u(n~. KaO' 0 corresponds to T£ in II. 14, 18, i. e. that which a thing becomes is identified with the form which it acquires and itl virtue ofwhit:h it is what it is after the change. For this sense of KaO' 0 cr. ~. 1022 a 14. ga. T~ ya.p ••• +UCl'LV, 'for that which comes to be has a nature', u. in virtue of which it is what it is. g4. The vrp' o~ of change is strictly not the parent considered as· a unity of form and matter, but its nature in the sense of its form, which is the same in species with the form acquired by the offspring, for it is only a man that can beget a man. Aristotle holds that the form comes from the father, the matter from the mother, G.A. Hob I, 10. g7..g8. " cl'll'~ TlXV1J~ ••. S~llvo'a~, cf. E. 1025 b 22 n. gg. Kal cl'll'~ Ta~op.UTOU Kal. cl'll'~ TUX"~' The first Kat means 'also', so that the distinction between T~ afu-op.tJ.Tov and TVXl1 is not stressed. The former includes the latter (Plzys. 197 a 36). Only those beings can act d7T~ TVXl1<; which can act deliberately (i. e. adult human beings, 197 b 7); TVX11 is alTlo. KaTu (T1JP.fJ(fJl1K~ lv Toi~ KaTa. 'II'poa£p(~v TWV lvEKc1 TOU (1971\ S). l. e. chance is found when an action incidentally and exceptionally produces a result which might naturally have been the object of deliberate action. Since one such result may be produced incidentally by a variety of actions, chance is of the nature of the indefinite (197& 9), and since the result could not have been foreseen, chance is ' a cause obscure to human thought' (196b 6). ro afu-op.tJ.TOIIJ on the other hand, occurs' in events that normally happen for an end, whenever something whose cause is l'~:lernal happens not for the sake of the result which actually follow",' (197 b 18), e. g. when a horse p.tJ.TOII

z. 7.

1032& 12 -

I032b 15

(sc. being pursued by thieves) is saved by going to a certain place, but did not go in order to be saved (197 b 15), or when a stone (It'. being pushed) falls and hits some one without having been meant to do so {197 b 30). But besides the cases in which something moved by an txltrnal torce achieves· an unintended result, TO a.(".Op.a.TOV also occurs when an in/mlal cause, i. e. nature, produces an exceptional result (197 b 33), e. g. when an illness cures itself(H. A. 604b 9). A specially important instance of the latter kind of spontaneity is 'spontaneous generation' of plants or animals from rotting earth, dew, mud, excrements, wood, etc., (or which cr. Bz. I1Ifux U4 b 3-30. In general, then, chance simulates the action or art or, more generally, or thought, while in spontaneity (the more general term) (I) the action of thought is simulated, or (2) the normal action of nature is simulated by nature producing in an exceptional way (e. g. /J.VEV cnrlpp.a.Tos, J 03 2& 31) what it normally produces otherwise (e. g. II( cnr'rp.a.TOS). Thus chance is more appropriate to ToWlIIV Twls. 'makings , and !'pontaneity to TO. d.1I'0 t/JVITfIllS "I''Y''0P.Eva.. 80-81. 11I'a. yAp ••• clllfu cnripl'a.TOt, e. g. eels (H. A. 570a 7). fishes (569-11), testaceans (547 b 18, G. A. 761b 23), insects (539- 2-1-, G. A. 732b 12). 8S. TOUTWII, I. e. TIIIV a.1I'O Ta.VTOP.a.TOV I(a., 1111'0 TVX{!S. ilC1TlPOII incrKE'lM'ioll, cf. b 23-30, 1034& 9-21 , 4-7. b S. ,",II "'P''"III 04crlGII, i. e. the O-flUtll /J.VEV J)"7JS (I. 14', matter being only in a secondary way part of the substance of the concrete product. s-4. KGl yAp • • • 1I0000U. Aristotle has said that 'by art are produced those things whose form is in the soul'. But, he re8ects, disease can be produced by medical art no less than health, yet the doctor i;!as not in his soul the form of disease; disease has no (orm but is merely a privation. To meet this objection he now adds that the form is in a sense the form of the privation (only' in a sense, because it is not by its presence but by its absence that it produces the privation). Thus if the doctor knows the (orm of health, he can produce either health or disease. 4. For i".l"ll yc\p bouerlG ~ IICScros. the reading of Ab, cf. r. J004& 104. 6-10. This account of production may be compared with the account of moral deliberation and action, in which TO 'axllTOV Iv rD d.va.AVan is said 1I'PDl'rOV Elva., Iv rfj "Ialan (E. N. 1I12 b 23). Still nearer is E. E. IU7b 28-33. 7. otOIl c\p.a.).&nJTG, .t 8~ TOiiTO, 8,p".o'"lTa.. Heat produces 11'",,". by which different elements in the body (i. e. portions with unequal temperature or unequal humidity) are chemically changed into a: homo1.1, ' , -\' ., i. ~ . , (J h I {1I'~'I"S geneous woe (ITT, TIfI\(I.CIJIT'S V1I'0 TOV~ 'P"U&I(OV I(a.', O'I(EWV (PP.OV~ il( TWV d.VT'I(f:&P.EvIllV Tl'a.9r,r'I(WV, Meteor. 379~ 18, cf. 381& 20). 14. Uylll ~ .•••tlla." 'when I speak 9f substance without malter (I. 12) I mean the essence '. 15> There is much probability in Bywater's conjecture of "'" &\ for TWV 81. &7 would naturally introduce the summing up of the account given ill II. 6-14. .~

•

"'.'

I

,

,

I

\

,

CO!\IMENT ARY 17. TWI' 4}'}'",I' TWI' JIotTB~U, i. e. the things that have to be done before the final object is achieved. ~4. TOU 'II'OLt'I' is emphatic, being opposed to TO l'oEil'; cf. 1. 15. For 4pXEL cf. 1034& II. ~6. The heat in the body is (I) an element in health, or (2) is followed (a) directly, or (b) indirectly (~ul 7TAEtOVWV) by an element in health. Thus, if once heat is present, health may be produced without the action of a doctor just M it is produced ~ his action. The' making' iF the same; only the thought is missing. ~7. TL • • • TOLOUTOI', something of the same kind, e. g. uniformity

(11·7, 19)·

~8-30. I follow here the reading of Ab, which seems to have been that of Alexander. with the unimportant exception that Alexander may not have read the (un after EUXa.TOV. Alexander's words are (492. II) TO ~€ TOUTO &' EC1)(.cnOl' TO 'II'OLOUI' (add. TO JIoEPO' rij, llyLELa.S LF) TOI.OVrOV &1' Ei:TI, OTL ~ Tpil/lL' ~ 7Tol.Oiiua. TO ""'P~ T~' VyIEia., (UxaTTJ (UT~ ICa.~ ~, BEPJLOTTJT~ ICa.~ ~, Op.a.A&TTJTo, ICa.~ TWV AOL7TWV. Aristotle's meaning is • and this, viz. that which produces the part of health, is the limiting point, or minimal necessary basis, and there is similarly a necessary basis for a house (sc. the stones) and for every other product '. It would be also possible (I) to put a comma after JL(po' and make ~, vYLEia.sdepend on (UXa.TOV; and(2 a)to read ICa.~ TO oVrw, JL(po' for TO JLl~ (following EJ except that (UTi is omitted) and translate' that which produces health and is in that sense a part of it'; or (2 b) to read TO 7TOLC;iiv TO JL(P~ ICa.~ TO oVrws JLlpo" 'that which produces the part of health and in that sense is a part of it '. ICa.~ ~, oiICia., (oroI' ot MBoL) ICa.~ TWV cL\Awv is tacked on very loosely, like ICa.1. TO 1I'iip in 1034& 17. It is difficult, however, to regard the relation of heat (or rubbing) t~ health as analogous to that of stones to the house that is made of them. In the generalization which follows, Aristotle regards himself as having shown that the matter of that which is produced must exist before the production takes place (1. 31); and stones evidently are the matter of a house. But the heat in the body is naturally conceived not as the material but as the efficient cause of health, and so it seems to be conceived in 1. 21. Aristotle has got into difficulties through taking as parallel two things that are not parallel-health and a house (I. II). That which is to the doctor as a house is to the builder is not health but a healthy body. Having stated the product abstractly Aristotle also states the cause abstractly, not as 'a body having heat' but as , heat in the body'; and thus he gets something not really parallel Lo the stones-which are the material cause of a house-and not really a material cause. There is, however, in his view a real difference between the two cases (1034& 9). Stones are inert, at least so far as grouping themselves into a house is concerned, and are therefore simply tlA7J. But a body with heat in it has an innate power of transforming itself into a healthy state. It is thus both a material and an efficient cause; it is ~ VA7J ~ ¥xouua.~, YEV(UfWS (1034& ll). So, too, here it

z. 7.

I032b

17 -

IO.13 a I

is first spoken of as an efficient (1. 2I) and then as a material cause

(1·32). Shute suggests that heat is the material cause of health as the genus is the material of its species (A. 1024b 8, Z. IOa8& 6), since heat has to be specifically qualified in order to become health. But even so its relation to health is not a very close analogue to the relation of the stones to the house. 30. Kcdcbrcp UyeTGL, • as we (in general) maintain', not referring to any particular passage. Cf., however, A. I069 b 6, Phys. i. 6-10. 38. +Gvcp6." ~ yap t».1J ".ipOi. It has been expressly remarked with regard to natural generation that it presupposes a pre-existing matter (a 17), and the same has been implied in the account of artistic and fortuitous production. 1033& I. Y£YIlETGL,not 'comes into being' but' comes to be something'. 1-5. It is most natural to take dA}.' c1PG KT}., as answering to c1rL JI-'Ev o~v ICTA. The whole section will then mean 'It is evident then that a part of the product must necessarily pre-exist; for the matter is a part, since it is already present in the thing and undergoes genesis. But does some element in the definition also pre-exist? Well, we state in two ways what bronze circles are, naming both their matterbronze, and their form-such and such a shape; and shape is the proximate genus in which the circle is placed. The bronze circle therefore has its material (or generic) element in its definition (as well as matter in the more ordinary sense-viz. sensible matter, bronze-in its concrete wholeness. And this must pre-exist as well as the sensible matter; the bronze which is given a circular figure must already have figure of some kind) '. The section, on this view, refers to the doctrine that genus is related to differentia as matter to form, and thus is in a sense matter (A. 1024b 8). The objections to this interpretation are: (I) the ellipticalness of the expression. The section concludes not, as would be expected on this interpretation, by saying' thus part of the form must pre-exist, as well as of the matter', but by saying I the bronze circle, then, has its matter in its definition'. (2) The question of the pre-existence of form is raised in the next chapter as a IllW question, while the pre-existence of matter is assumed to have been proved in ch. 7. (3) In the discussion of the pre-existence of form, Aristotle expressly sets aside the notion that part of the form pre-exists while the ,.est supervenes (b 11-16). For these reasons I am inclined to think that Alexander and Bz. are wrong in finding here a reference to the doctrine that genus is UA'I' What answers to c1rL JI-'Ev OW, then, is not elM' J.pa but l~ o~ al ICTA. 1. 5. The words to be supplied with elM' J.pa lCal TWV IV Ttfi AUy",; are; UA'I p,epos (from 1032 b 32), as is shown by the conclusion 0 a~ XmAKOVS KVKAoS 'X" IV Ttfi ~ ~v UA'/V. The passage simply points out that the bronze circle is a AOyos IWADS (De A". 403a 2S), that bronze is present not only in its concrete wholeness but ill its definition. 1&712

N

COMMENTARY

186

The main difficulty for this interpretation is KC1~ TOVT" (!TTl ,.0 y&o
le

Form does not come to be, any more than maller, but only the combination of the two (ch. 8).

IOaaa 114. What comes to be comes to be by something and from something (let us take this to be not the privation, but the matter) and comes to be something, e.g. a sphere. The sphere is not made, any

z.

7.

1033& 2 -

8.

1033 b 1

more than the bronze, which is the matter; save per accidens, since the bronze sphere is a sphere and is made. 31. For to make a 'this' is to make it out of the substratum, in the full sense (i. e. out of a given form as well as a given matter). If the substratum were made, it would be made out of something else, and so ad infinitum. b 5. Evidently, then, the form is not made; the concrete thing is made by putting the form into the matter; if the form were made it would have to be divisible into matter and form. 19. Is there a sphere apart from the particular spheres, a house apart from the bricks? Surely there would never have come into being a ' this' at all if that were so. The form is a' such " not a • this'; in making, a • this such' is made out of a ' this '. The whole 'this " e. g. Callias, is analogous to 'this bronze sphere', man to 'bronze sphere'. :a6. The Forms, if there are any Forms apart from particulars, do nothing to explain be comings or substances, and are not, on that account at least, to be viewed as self-subsistent substances. 29. In some cases it is obvious that the producer is something one in kind with the product, i. e. in natural generation, except in abnormal cases such as the production of a mule by a horse, and even there the class that comprises both parents presumably has the characteristics ot both, and is something like a mule. 1034a 2. Thus we need not posit a Platonic Form as pattern, for living things are what are most truly substances, and there would be a Form here if anywhere. The begetter is adequate to the putting of the form into the matter. The individual is 'such a form in this matter', matter being what differentiates individuals identical in form. 1033&26. ~S'I yo.p SU.sPICM'IU, in 10 32& 17. 31. l" TOU iI~lIIs ~'II'OKE~".t.,ou, • from the substratum in the full sense of the word', including form as well as matter (1029& 2). So AI.

495· 9· 32. For the absence of the article before ,-0., xu~"o., CM'poyyu>'o., 'II'O~Ei., cr. ~. 1014b6 n., Kuhner ii. 2. §472 A. A good example is found in PI. Rep. 493 C ~ ~v T(;W 71'oAMiv • •• "mv Ku1 ~Bova!; KaTaV(V07fK(VIlI. CTot/l{av ~OVJLEVO!;.

34. It is doubtful whether we should not insert a comma after TOVTO and translate' but is to make one of two different elements--e.g. this form, viz. sphericity-in another'. This is attractive, but the combination fTfpoV Tt lv ~ does not seem very likely; we should expect ToB, tv T~' or T1 tv Twl. b I. TOUTO yAp ~1fJ"uTo, ' for this was assumed' (a 25).

COMMENTARY

188

3. TOUTO seems to refer to TO;; &~ ~oICnpivov & 3 I, the intervening passage being parenthetical. 5-6. ollS~ ,.a .1801 • • • Y£Y'CTcn. Aristotle does not necessarily mean that form is eternal. Sometimes he says that it comes into being and passes out of being instantaneously. Cf. I039b 26, H. 10Hb 21. In one passage (H. lo.a b 14) he gives both alternative~ clt&ov cWcu ; t/l8a.phJv civEv TOV t/l(JClpEUfJru ICcd yeyOVEvo.L ciVR TO;; ylYVEU(Ja.L. He apparently means these two alternatives to apply to different kinds of form. Pure forms which exist untrammelled by any conjunction with matter-God, the intelligences that move the spheres, the human reason-are eternal. Among the forms the acquisition of which by matter constitutes becoming or change, a distinction must be drawn. Where what is produced is a new substance, its form must have pre-existed in another individual; where what is produced is a substance with a new quality, quantity, etc., the quality, quantity, etc., need not have pre-existed actually; it may have existed only potentially (I034b 18). IJ.v(Jponro .. civ6ponrov YEWq., but there is no corresponding pl'inciple ARICov ARICov y~. I. e. in the former case the form is eternal; in the latter it comes into being instantaneously; it supervenes in a moment on a change which has taken time. 6. For the superfluous oil cf. & 16, 21. 7. ollS~ TO T£ ~, IEtJla.L. In these words Aristotle simply brings out another aspect of what has already been called TO El8o.. and ; w T4i a.lO'~ viz. that it is what is stated in a definition. S. t/lu".L.. as opposed to TE)(I'71 and 8wa.p.L" is d.pxJIw a.~ as against lv ciM", (A. 1070& 7, De Catlo 30lb 17). For the difference between TE)(1'''1 and 8Wa.p.&" cf. E. 102Sb 22 n. 14-15. TO ".i" the genus, which is to the differentia as ilA"I to cl8o.. (cf. ~. I024b 3, 8). TO S', the differentia. TO Si, the specific form. 16. oto, here introduces not an example but a comparison. The specific form, as composed of genus and differentia, answers to the concrete thing, as composed of matter and form. For this use of olov cr. Bz. Index 50lb 55-60. 17. It is possible that the manuscript reading rrVvo80 .. might mean 'the coalescence of matter and form '. But such a meaning for the word would be without parallel in Aristotle or, as far as I know, elsewhere, and Jaeger is almost certainly right in reading rrWoAo'i. For; rrWoAOI ( = ; rrVvoAo'i olxrla.) cf. 1037& 26, 30. The same confusion has occurred in manuscripts in both those passages; ~ and A are easily interchanged. 19. YIEJlJlw".l,«t', the reading of EJ, is supported by YEWfj., 1. 23 (cr. I. 30). TOSE ••• riSIE, sc. ilA"I ••• cl80'0, cr. 1. 13. 'll"OTfPOJl KT).. Aristotle passes I.OW to consider a doctrine which might seem to follow from his denial of the creation of form, viz. the Platonic doctrine that Forms exist eternally and independently. To this Aristotle answers that form is never a substance, always a characteristic; never a T08c, always a TOc.Ov8c. Before it existed as the for111 of the offspring it existed as tbe form of the parent.

p.om,

z.

8. I033b.3 -

10348. 3

T89

SI. ~ o.)S' 4" . . . T~. Since one substance cannot contain another actually existing substance (1039& 3), it follows that if the form were a substance there could never come into being an individual substance containing it as an element. So AI. Bz. But quite probably we should omit the comma after ~v, and translate' Perhaps the answer is that if the form were an individual subsistent in this manner, coming-to-be would never take place at all'. s4. Ku)J.(u~, cf. A. 981& 8 n. sS. 11 TW" .t8w" uMu, ' the cause which consists of the Forms '. s8. lI'pO! yE TA~ yEJIi(m~, the reading of Ab, is clearly an improvement on the vulgate lI'po.. T( Ta~ y(JII(T(t~. 33. Aristotle's account is that the form of the mule is not the same as that of its sire, the horse, since this has failed to master the opposition offered by the material element coming from the dam. the ass; but it is identical with the generic form of the sire, since this is also the generic form of the dam and thus has no opposition to conquer. Thus the mule is a sort of abstract universal, with the generic qualities common to horse and ass but without (or at least not having all) the specific qualities of either. 1034& I. O.)K c:.vO"CWTu~. Aristotle himself uses the word AOf/lovpov, 'bushy-tailed creature' (e. g. in H. A. 491& I). 3· TOdTOL~, sc. Ta f/lVULIC&' (1033b 32), living things.

The conditions 0/ spontaneous production answering (a) to arlz'stic (b) 10 lla/tlral prodtlction. The conditions 0/production in categories other than substance (ch. 9). 1034& g. (I) (a) Why are some things (e. g. health) produced spontaneously as well as by art, and others not (e. g. a house)? The reason is that in some cases the matter which begins the production is such as to be moved by itself, in some not; sometimes again it can move itself in the particular way required, sometimes not. 18. Accordingly the product will or will not need the artist for its production; in the latter case it can be set in motion by what has not the art but can be moved either by something else that has not the art or by a movement starting from an already existing part of the product. SI. Thus all artifacta are produced from something else with the same name as themselves, as living things are produced, or from a part which is of the same name (e.g. a house from a house, since the art of building is identical with the formal element in a house) or from what contains a part-unless the production be merely incidental. ss. For the cause of direct per St production is a part of the

COMMENTARY

190

product; the heat in the rubbing produces heat i!l the body, which i!l or is followed by health or a part of health; whence it is said to produce health, since it produces that on which health follows. 30. Thus production, like syllogism, starts from the substance or essence. 33. (6) Natural production is like artificial; (i) the seed operates like the things which work by art; the source of the seed is something which has the same name, in a sense, as the offspring (only in a sense, for woman is produced from man)--unless the offspring is an abnormality (which is why the parent of a mule is not a mule). b 4. (ii) Spontaneous production, as before, occurs when the matter can give itself the movement which normally the seed gives to it; when it cannot, generation by parents is necessary. 7. (2) As the form of a substance is not produced, so too with other categories. 14. It is not the quality or quantity but the wood of that quality or quantity that is produced; but another individual of the same kind need not pre-exist actually as in the case of substance; it is enough if the quality, &c., pre-exist potentially. In A 9-32 Aristotle discusses the conditions under which spontaneity mimics art, in II 33-b 1 those under which it mimics nature. In b 1-19 he discusses the genesis of qualities, quantities, &c., as distinct from that of substances. 1034I1n-13. TWJI ".~" " .n." ... " ".~" TOLCl~. As Bz. observes, the insertion of the explanatory words ~ I1.pxovua., &c., has caused Aristotle to forget the original structure of the ~entence. The anacolouthon is a natural one. n. " .n." " 4pXOUCTCl rlj~ yE"lCTE"'~. The phrase might seem peculiar, in view of the passivity commonly ascribed to matter by Aristotle. The explanation is that it is only prime matter that is entirely pas!live ; other matter has some quality of its own and can thus initiate movement. Cf. 1032b 28-30 n. 12. TL ".lpo~ TOG 'II'pC£y"'ClTO~. The notion that a part of the result must he pre-existent has been already expounded in 1032b 26103311

I.

13-18. Aristotle divides maltt'r thus: (I) some matter can initiate motion, (2) some cannot. Of (I), (a) some can initiate motion of the particular sort required to produce a certain result; (b) some can initiate motion of some kind but not of the kind required; e. g. stones of themselves can fall but cannot arrange themselves into a house, fire can rise but cannot move so as to heat bronze. Two mistakes seem to be involved in this classification. (i) Aristotle assumes wrongly that the elements have a natural motion in certain

z.

9.

1034& 11-21

directions, earth downwards, fire upwards. (ii) This once assumed, it is hard to see what is the matter he describes as having no power of starting motion on its own account. Apelt suggests that great masses of rock may be meant, and this is possible, though, as he says, inkon-

sequent genug.

,17. For r:,Sl ".IVTOL vo.£ cf. Top. 17 I II 20 IOTL p.w W~ ov, IOTL 8' W~ 18-19. TG ,"V, those products whose matter is of type (I b) (e. g. a house), TG SI, those whose matter is of type (I a) (e. g. health):

vat..

19. It seems clear that KW,,~aETo.L is used in a peculiar sense. The subject of the sentence is 'the products which can come into existence without the agency of an artist', and K'VT/6~o"(Tfl' m ....>t mean • the motion which produces them will be started', very much as if we had had 'YEv~u£TaL (cr. iJ.p..pw ICLn/U£t, 0. I046b 21). The sentence then means 'the motion leading to such products will be originated by these things (the things which have some power of originating the required motion, cf. l. 14), which have not the art in question but can themselves be moved either by other things which have not the art, or with a motion that starts from a part of the product which already exists in the things themselves '. Thus Aristotle recognizes three modes of production of, e. g., health; it may be produced (I) purposely, by the physician, (2) spontaneously, (a) by some action of a non-physician (or a material object) on the sick body, (b) by a motion starting from ~ome element of health (e.g. heat) present in the sick body. 20-21. KLvEia9cn ••• TEX"'IV, There is no trace of these words in Alexander (498. 29), and they are decidedly suspicious; the p.ivof EJ in I. 20 looks hke a piece of patchwork inserted in view of an intrusive Si clause following. Christ conjectured very reasonably (Studia, 45) that ICWELU6flL SVVflp.EVWV fl~WV (loosely used for ICW£tu6fl! ~, , ') was a g Ioss on K!VT/v"U£TflL, Il.!. • • WV\wv "'" . .EXOJ'TWV , ovvap.EVa flVTll an d V7T OVK 1'1]v TiXVT/v a variant of {mo TOVTWV TWV oliK IX6VTwv 1'1]v TiMv, 21. lK "EPOU~ is difficult, but a comparison with 1032b 26-1033" I, 1034& 12, 24-30 shows what is meant. Asc. gives a good instance of Aristotle's meaning, TOV lp..pwov 6EPp.oV 'JI'A£OVaUflVT~ ICa2 ICflTf1O'PiuflVTO~ 1'1]v 1/roxp4V SVUICpaU{flV (407. 6). Not improbably, however, ~ lK p.ipov~ has been wrongly inserted here, as in I. 24, from the margin. 21-26. The section II 9-32 is concerned with the conditions under which products normally produced by art are occasionally produced spontaneously. It is not till II 33 that Aristotle passes to consider natural products and the conditions under which spontaneity mimics the work of nature. 'JI'aVTa, then, means' all arlifada', i.e. things of the type of arlifoda, whether actually produced by art or spontaneously. The reference to natural products (ifxnrf.p TO. .pVUE!) is by way of comparison-just as orlifada are referred to by way of comparison in the account of natural products (11 34, b 4). 'All or1ifo(la are produced from a thing having the same name as themselves, as are natural products, or (more exactly) from an element in themselves

COMMENTARY which has the same name as themselves (e. g. a house is produced from a house, inasmuch as it is vroduced by reason, for the art of building is identical with the formal element in a house), qr from something involving an element in them (and having the same name as it) '. One is tempted to punctuate SQ as to take ~e ol,cla~, IK P.(pov<; (S(. bp.wvUp.ov) ~ lXWT~ T' p.ipo<; as stating for the case of the house the alternatives stated generally as ~e bp.wwp.ov, IK p.ipov<; bp.wvUp.ov. But a house cannot be produced ~K p.ipov<; in the sense in which IK p.ipov<; is used in l. 21 and presumably thererore in l. 24. For ~K p.ipov<; is used in l. 2 I to indicate the way in which spontaneous production takes place, anrl a house is never produced spontaneously (I. 10). The sentence is evidently corrupt; the repetition ~ IK p.ipov<; bp.wwp.ov ••• ~ (,e p1pov~ can hardly stand. Bonitz detected corruption but offered no cure. Christ bracketed ~ IK p1pov~ bp.wvUp.ov in I. 23 and read ~ IK P.(pov<; bp.wwp.ov in I. 24, assuming that Alexander read ~ I" P.(pov<; CTVVWvUp.oV (or bp.wvUp.ov) there (AI. 499. 20). But Alexander seems to have had this phrase in l. 23 (499. 12), and perhaps only there; and the same is true of Asclepius (410. 3). It seems probable that ~ I" p.(pov<;, having at some early date been displaced from I. 23, was added in the margin and later inserted in I. 24. Cf. previous note. SS. l~ c\fU"VIl"ou. Td f/l..JU(l are actually produced I" CTUI/WvUp.oV (A. 1070& 5), from that which shares their nature as well as their name, but Aristotle occasionally ignores the distinction between bp.mp.ov and CTVVWVVp.oV, which did not exist in ordinary Greek usage; cf. A. 987b 9 n., De Gen. e/ Corr. 328b 21. 114. 611'0 IIOG. This emendation, which had occurred to me independently, has been proposed by L. Robin in Archiv f. Gesclz. d. Plu7. xxiii. 3. The manuscript reading ~ {mb vov is not impossible, but a justification of ~e oi,,{a<; rather than an alternative to it seems to be required. V would easily be corrupted into ~ by the influence of the other ~ in the sentence. t\ lxo~ T~ "ipot. For the absence of the article with lXOVT~ cf. ~. 1022& 6. s5-s6. lml/ ••• jl-ipot. Aristotle notes here that what he has said in II. 21-25 of the implications of production applies only to production which is not merely incidental. That by virtue of which A produces B directly per se is a part of B. TOV 7TOI.(W 7Tp/lYrOV /CaO' a{n-O, 'of its producing the result directly per se '. Incidental production may be illustrated by the case of the builder's producing not a house simply (which he produces directly) but a house which is agreeable or injurious to its inmates (E. 1026b 6-10). s8. "tlKO).OUeEi. Jaeger supposes Vto have been corrupted into ~ as in I. 24. But Alexander read ~ (499. 27, 30, 35); cf. also 103 2b '27· s9-30. 8~1I ••• [e.p"cS'M)"]' The manuscript reading if kept would have to be translated' that is why the rubbing (cf. 1032b 26) is said to produce health, because that of which health is a consequence produces

n

193

health, viz. heat '. But a far better sense is got by treating (with Jaeger) r1jv Vy{nav and (J(pp.6rq,> as glosses on 8tO Kal 'A.ly(Tat 1I"0t(W aQd iJn ~K(LVO 1I"0t(L respectively. The sense then is 'and this is why the heat in the rubbing is said to produce health, viz. because it produces that on which health follows '. Alexander understood the passage rightly (499. 36-5 00• 6), though Ai.o has 1I"0tfi r1jv {,y{(t(Lv. 30-3s. In syllogism, i.e. in the scientific syllogism, a property is shown to belong to a subject in virtue of the subject's essence or definition (An. Posi. 90b 31). So too in generation the product springs from its own essence. This applies to all three kinds of production described in II. 21-30. (I) In natural production it is the specific essence of the father (which is identical ,vith that of the offspring) that produces the offspring. (2) In artistic production the essence of the product, conceived by the artist, is the cause. (3) In spontaneous production heat, for example, which is the cause of the production of health, is the inner essence of which health is the manifestation. 33-34, TO I'~V yc\p cnrlpl'a. • • • Tlxv",>, 'for the seed is productive in the same way as the things that work by art '. b 3-4. lc\v •• . -ifl'LOJlOU. These clauses as traditionally arranged can be made intelligible only by reading IlU' U.v and punctuating as foI,1I"aVTa ' • Joe • ll' • II , , Iows: ou.yap OVTIII 0(1. ..71T€W III'> (10 aVupIII1I"0V avupw1l"0'>-Kat yap -yvvq U dv8p& .. • 8w ~p.lovo,> OllK le ~p.u;vov-cLU· lo.v p..q m7PWp.a.y. But this is excessively awkward. 8to •.• ~p.u;vov does not follow naturally on the previous clause. Alexander (500. 13, 35) and Asclepius (,p I. 7) as weIl as Ab read Uv simply, and dAM is pretty evidently a piece of later patchwork; and not a successful one, since IlU' lo.v ••• V has to be taken rather unnaturaIly as = 'but only if it is not a m7plllp.a '. Alexander interprets fo.V • •• V as coming before 8to • • • ~p.r.Ovov, and may have had the clauses before him in that order, The sense gained by the transposition is quite satisfactory; oll yo.p ••• dv8pO'> is interposed parenthetically to explain the cautious 11"111'> in i. I, and then the exception to ((TTl 11"111'> ~p.wvvp.ov is stated in lo.v p.~ m7pwp.a .y (cr. the position or lo.v p..q KaTu UVP.{3({371KO'> y{yvrtT'at in &25), and illustrated. cr. &v p.~ n 1I"apo. f/lvuw ylvrJTat, orav i1T1TO'> ~p.lovov 1033b 33. 4. &Wlp lKEL, i. e. in the field of nature as in the already (11 9-32) discussed field of art. For' spontaneous generation' cr. Bz. Index I24b 3-26. 7-19. Christ thinks this passage belongs properly to ch. 8. It is, more exactly, an appendix to the whole subject discussed in chs. 7-9. 7. a.I'ITG"" 'from the parent animals themselves '. Cf. Schwegler, Excursus III, on the pregnant use or allTo... 9. TG", 1I'plli1'lllv. For this as a name for the categories cf. TO. KOWo. 1I"pima An. Post. 96b 20, TO. 1I"pWTa TWV y(VWV B. 998b 15. II. Ka.ll1l'l XMKOii, Et Y£Y"ITa.L, 'and as bronze, if it is generated, implies a form and a matter that are not generated at the same time as it '. 13. The coming into being of a bronze sphere is the imposition of a new shape (which is a kind of quality, Cal. 10~ II) on an existing ~

le

~

~

,~.

'94

COMMENTARY

substance; the coming into being of bronze is the generation of a new Aristotle now generalizes and says' so is it, sc. generalIy, both in the case of substance and in that of quality', &c. 16-lg. Cf. 1033b 5-6 n. subslance.

ESSENCE AND DEFINITION

(chs. 10-12).

( I) Should Ihe accounl of a whole conlatit Ihal of Ihe paris? ( 2) Whal paris areprior/o Ihe whole? (ch. 10). 1034bSO. (I) Must the definition of a whole contain that of the parts? The definition of the circle does not contain that of the segments, but the definition of the syllable contains that of the letters; why is this? sS. (2) If the parts are prior to the whole, the acute angle should be prior to the right angle, the finger to the man. Yet the wholes arl" prior both in definition and in power of independent existence. 3s. (I) Really I part' is equivocal. The parts of substance are matter and form, but in a sense only the elements of the form are parts of the thing. 1035& 4. E. g. flesh is a part of snubness but not of hollowness; bronze is a part of the whole statue but not of it as form (a name, like 'statue', may be applied to the form or to the thing as having form, but never to the bare matter). g. This is why the case of the circle differs from that of the syllable (cf. I034b 24). The letters are parts of the form of the syUable; the segments of the circle are matter on which form supervenes, though. nearer the form than the bronze in a bronze circle is. 14. In a sense not all the letters are present in the definition of the syllable; the letters in wax or in the air are only the sensible matter of the syllable. For the parts into which a whole is dissolved may be parts of the concrete whole but not of the form, and therefore not present in the definition. s5. Hence things which are composed of form and matter (e. g. the !>nub, the bronze circle) can be dissolved into their material parts; immaterial things cannot be so dissolved. 31. Thus the clay statue is dissolved into clay, and even the circle into its segments-i. e. the individual circle, not the circle in the abstract. I, 3. (2) To restate the matter, (a) parts which are parts of the definition and into which the definition is analysed are, at any rate some of them, prior to the whole definition; but the definition of the

z.

9. I034 b 16-19

195

right angle is not analysed into that of the acute but vice versa, for the acute angle is defined :l.S ' less than a right angle'. g. So too with the circle and the semicircle, the man and his finger. The parts which are matter are posterior to the whole; the parts of the substance as defined are prior, at least some of them. 14. (a) Since the soul is the substance as defined (or form) of ·such and such a body (at least no part of the body can be properly defined apart from its function, which involves perception), so that (b) the parts of the soul are (all or some) prior to the concrete animal, while the body and its parts are posterior to the soul and are the constituents not of it but of the concrete whole, ~~. therefore (c), while the bodily parts are prior in a sense to tbe concrete whole, in a sense they are not (for the finger in the proper sense cannot exist apart from the animal); while some bodily parts are neither prior nor posterior, viz. the supreme parts in which the essence immediately resides, e. g. the heart or the brain. ~7. Things which are predicated universally of particulars (e.g. man) are not substance but a compound of this definition and this matter taken universally, while the itldividual comprises an ultimate individual portion of matter. 31. (I) (Return to the first problem.) There are parts of the form, parts of the concrete thing, and parts of the matter; only the first are parts of the definition, which is of the universal. 1036a~. The concrete individual, whether sensible like a bronze circle or intelligible like a mathematical circle, is not definable but knowable by the aid of intuition or perception; when the circles have passed from actuality, it is 110t clear whether they exist or not, but they are described by the universal definition. S. Their matter itself is unknowable. Matter is sensible and changeable, or else intelligible-viz. the matter which exists in sensibles not qua sensible, i. e. mathematical figures. 1~. We have now treated of whole and part, priority and posteriority; we must next answer question (2) (return to the second problem), whether the right angle, the circle, the animal, or their parts are prior. We answer by a distinction : 16. If' animal' may mean the soul, 'the circle' circularity, the right angle' right-angleness, then while the whole in a sense is posterior to the parts in a sense, i. e. the bronze right angle or the right angle formed by particular lines is posterior to the parts in the definition and to the parts of the particular right angle, the immaterial right angle is posterior to the parts in the definition but prior to those of the particular ;

196

COMMENTARY

114. but if the soul cannot be said to be the animal, even so some wholes are prior to their parts, others not, as has been said In this chapter Aristotle returns from the digression on generation which has occupied chs. 7-9, to continue, in effect, the discussion of es~encewhichoccupied chs. 4-6. The chapter raises two main questions: (I) Should the definition of a whole contain the definitions of the parts (1034b 20-28)? (2) Are the parts prior to the whole (b 28-32)? The treatment of the two questions is interwoven: (I) is discussed in b 32-103Sb 3, 103Sb 31-1°36& 12, (2) in 103S b 3-31, 1036 & 13-2 5. 1034b 110. 'II'as 8~ Myos ,..ip1J eXfL. A Myol must contain at least two words (De Int. 16b 26); it must mention a genus and at least one differentia. 31. The subject of UYOI'Ta.L is • the parts', though in the next clause , the wholes' are again the subject. Schwegler's proposal to read o~ &K" in I. 30 does not mend matters, since then there is a change of subject in Klil T'ii ,tv", 8~ ctVfV ru.qAIIIV 7rpOTfpa., and further lIC,{vlllv will not refer to the same thinis as lIC"VIi. (Schwegler is wrong in thinking that Alexander read o~ BOK". At 502. 16 Alexander is paraphrasing the rense.) For a similar construction cf. M. 10n b 3 n. KAl on; ItVIiL 8~ II'IU 4l.l.~l.1II1' 'II'pOT'Pa.. What Aristotle says is true enough of the finger; the body can exist without it, while it cannot exist without the body-it ceases to be a finger, except in name. But he is careless in assuming that the position of the acute angle is similar; it is not true that the right angle can exist without the acute angle and not the acute angle witho~t the right angle. Take a finger away from a living body and you leave it still a living body; take an acute angle away from a right angle and it ceases to be a right angle. Aristotle distinguishes the two cases clearly enough ill .1. 27. His other point, that the definition of the acute angle presupposes that of the right angle and not vice versa, is of course correct. 33. Its ~I' ••• '11'-01'. For this TpWOI cr. .1. 1023 b 15. 1035& 7. 'For the form or the thing as having form may be spoken of as the so-and-so (lICIicr.TOV), but the material element by itself should never be said to be the so-and-so.' This is probably intended by Aristotle to justify him in speaking (in 11. 6, 7) of the form alone (as well as the concrete whole) as 'the statue', while he refuses to call the matter alone a ' statue '. II. Alexander is no doubt right in taking TOU l.6you as dependent on p.iptJ, not on O'TOLX,im (504. 5-8). For TOV Myov TOO ,Z80VI cf. I. 4. Ill. i." ~s. With the manuscript reading l4>' ofI, we have, very awkwardly, to suppose a comma afta- VA.". Jaeger is no doubt right in supposing ofl to have come in by itacism (cf. apparatus crilicus to r. 1004& 20, .1. 1024& 23, Z. 1030b 35). 14>' ~I is sufficiently confirmed by 1035& S. 1036& 3t, b 6. 18-14. lYYUTipw ..• lyyil'1JTa.L. In a bronze circle there are two

Z. 10. I034b 20 -

103S a 20

197

grades of matter, one more essential than the other. Strip off the sensible matter (bronze) and you are still left with intelligible matter (the spatial parts of the circle). Aristotle's remark here anticipates the doctrine stated in IOa6&9. 16. Tc\ l" Trt 4ipl, letters spoken and propagated through the air; cf. De Sensu H6b 6. !ZO. TO (1'VvOAoV is not to be identified either with the sensible or with the individual. It is applicable (I) to the intelligible individual (loa6& a), (2) to the universal answering to a set of sensible individuals (loa5b 29), (a) to the sensible individual; in fact to anything that contains matter either universal or particular, either intelligible or sensible. One would suppose that, as the universal of a set of sensible individuals contains the universal of their sensible matters (IOa5b 29), the universal of a set of intelligible individuals would contain the universal of their intelligible matters and would thus be a fourth kind of uUVOAOV. But Aristotle does not draw this inference, and treats 'the circle' not as corresponding to 'man' and differing from it only by containing intelligible instead of sensible matter, but rather as corresponding to 'soul', which he identifies with' being a soul', i. e. with the pure form of vitality (loa61\ I). The main importance of the chapter lies in the recognition of (I) the intelligible indi\'idual, and (2) the materiate universal or Abyos lvvAo~(De An. 40a& 25), as intermediates between the sensible individual and the pure form or, as we may call it, M-yos a:VAor. A consideration of, say, the circle leads to the recognition of live entities: (a) the relation stated in the equation to the circle, (b) this relation spatialized (the circle in general), (c) this relation exemplified in a particular space---(I) above, (d) this relation embodied in a certain type of matter-(2) above, (e) this relation embodied in a particular portion of matter(a) above. Aristotle in effect here ignores (b) or identifies it with (a). And in loa6b 7-20 he rejects the Platonic conception that the form of line is something non-spatial-the number 2. This goes with his insistence (in the Posterior AnalYtics) on a complete ~pparation between arithmetic and geometry. It is evident that Aristotle's intelligible individuals answer to Tc\ p.(Ta.~ of the Platonists (for which cf. A. 987b 14 n.). He attacks these (A. 991b 29, B. 997 b 14, K. 1059 b 6, M. 1077 a I, N. 1090b a6) without hinting ~hat he himself held a similar doctrine. There is, however, an essential difference, in his opinion, between the two doctrines. He thinks, rightly or wrongly, that the Platonists regarded the intermediates as separately existing entities, while he himself thinks of them as existing in sensible things and separable only by definition (loa6& II, M. 2, a); his objection to Tc\ p.(Ta.~ is the same as his fundamental objection to the Ideas. But it is noteworthy that he also attacks a doctrine of intermediates which, like his own, conceived of them as existing ifl sensible things (B. 998& 7). This doctrine too, he

COMMENTARY would doubtless say, ~gards the intermediates as substances, while he regards them merely as characters of substances. 111-113. Neither the text of EJ nor that of Ab in these lines can be accepted, and an early corruption is clearly indicated. The singular Vin I. 23 indicates that Myos has been spoken of in the singular, and T~ P.fv ••• T~ 8' was probably the original reading. This was corrupted into TWV P.fv • •• TWV 8', and the reading of Ab implies an attempt to amend the whole reading thus produced. 113. av f'~ ToG auveL).1J".".lvou. Jaeger (anticipated by Christ) thinks this a gloss, (I) because in his view, whether we understand these words as meaning' unless the parts are parts of the concrete thing' or 'unless the definition is the definition of the concrete thing', they destroy the sense, and (2) because he thinks TO UVJI(f).:qp.p.lvov could not be thus used without any explanation. not having occurred before in Z. The words occur, however, in all the manuscripts and in Alexander and are defensible, though not necessary. (I) They state the condition under which the parts should not be mentioned in the definition of the whole. 'But in another kind of definiLion the definition of such parts bhould not be present, viz. if the definition is not the definition of the concrete whole.' (2) UVJI(t).:qp.p.l~ov P.(T~ n7~ ~A"1f has occurred already in E. I025 b 32; further, CTVv(tA71P.p.lvov is explained presently, in 1. 25. IIg. ~ 3),,,,, ~ OllTOL OllT'" ye. Forms are not destroyed by dismemberment but are eternal or else cease instantaneously to be (H. IO.ab 14). For these two alternatives cf. I033b 5-6 n. 311. Bz.'s addition of XaArOl between,., and cr+IILpIl is not necessary. The bronze circle has been mentioned already (I033a 30 ff.), so that XaArOl can easily be supplied in thought. 33. 6 KII).).(~, cr. A. 98 la 8 n. b II. 6 KII" IKCl.l7TCI, cr. B. 999 a 26 n. 5. ~ 'II'ciVTII ~ 'VLII. The last differentia of a species is logically neither prior nor posterior to it (1038& 19); all the other elements in the species are prior to it. 7. The insertion of 6 seems necessary. 14. ~ 'II'ciVTII ~ 'VLII, cr. I. 5 n. 14~7. This is to be treated as one sentence, the apodosis beginning not with i/xrr( (I. 18) but, as often in a long sentence, with p.~v ow (I. 22). 18. 3 04X 4'11'dpeeL aVlu IItaf~cre"", sc. ' and therefore involves soul '. Ig. ~ nVTII ~ 'VLII, cf. I. 5 n. The clements of the form other than the last differentia are prior to the materiate universal, as they are to the form; the last differentia is ' simultaneous' with both. KilL Kllr IKCl.l7TOV S~ 6".0("". AI. 508. 8 interprets this as meaning • and as with animals, so with other concrete wholes'. Aristotle's way of expressing this would probably be op.o{w~ 8~ ICall1TL Tidv lliwv. The meaning is 'and as the parts of the soul are prior to the concrete animal as such, the parts of Socrates' and Callias' souls are prior to Socrates and Callias, the concrete individuals '. 113. 'nLv~, 'nL S' oil. The parts of the body are prior to the

n

r:..

Z. 10. I03Sa 2 1 - 1036a 10

199

concrete whole of form and matter as the element is prior to the compound, but not prior in the sense that they can exist apart from it. When they are separated from it they remain the same only in name. ~5. EVla. S~ &I'li. These supreme parts are of course prior to the concrete whole in the sense in which a finger is so (cf. previous note), but in the sense in which the finger is posterior to the concrete whole these are neither prior nor posterior to it; they cannot exist without it nor it without them. Cf. a. 1024& 23-28. !36. KlipSLIi ~ lyKl+Ii}.o~, cr. a: 1013& 5 n. !39. ollK EI7TlI' 01l17(a.. This may be compared with the view of the Calegon'es that these things are 8cOTfpa.L oOO-LaL. 30. ~ KliecS}.OU goes, I think, with T711T8~ rij~ ~>"T/~, T711T8~ rij~ ~>"T/~ c:,~ Ka8o>..ov being opposed to rij~ (ITX';'T71'> v>"~. 33. Bz.'s addition of a second Klil rij~ u>"1J~ is required to account for alorij'>. But it is hard to see how Aristotle could distinguish parts of the matter from parts of the concrete thing; the third alternative is probably added simply for the sake of naming all the logical possibilities. 103& 4. 0101' = 'i. e.' TOU~ I'a.81JI'a.TlK06~, i. e. the plurality of circles which many geometrical propositions imply, different on the one hand from 'the circle' or circularity, on the other from material approximate circles. 5. I'ETa. 1'cn117EWIl ~ a.tae~I7EWS, not exclusively by rational intuition or by perception, but by discursive thought with the aid of them. cr. Plato's description of sensibles as apprehended 8o~ /LET' alIT8~ITEIJJ~ (11m. 52 A). 6. lK rijs ll'n}.E)(((a.~, the activity of intuition (V"T/ vmrn1 occurs, in Aristotle's works, only here and in 1037& 4, H. 1045& 34, 36. Prima fade it has different meanings in the two books. In Z it is something which exists in individuals (1037& I, 2)-in non-sensible individuals (I036b 35) or in sensible individuals not considered as sensible (1036& 1 J). and the only instances given of these individuals are mathematical figures (1036& 4, 12, 1037& 2). It seems to be equivalent to ~ TWV /La~/LaTLKwV v>"T/ of K. 1059 b 15. Alexander accordingly identifies it with extension (510. 3, 5 1 4. 27), and as far as Z goes this interpretation would be satisfactory. But in H it is the generic element in a definition, and therefore (I) is present in the natule of a species (there is no reference here to individuals), and (2) has no limitation to mathematical objects. It is not likely, however, that Aristotle would have used the phrase in two quite unconnected semes, and it is noteworthy that

200

COMMENTARY

the instance of it gh'en in H is a mathematical one; • plane figure' is the JAT/ v07l'"1 of the circle. It would seem, then, that either the wider conception was already in his mind when he wrote Z, and extension is merely given as an instance of JAT/ v07l'"1' or (which seems more probable) he generalized the notion when he came to write H. If we are right in connecting the two uses, JAT/ v07l'"1 in its widest conception is the thinkable generic element which is involved both in species and in individuals, and of which they are specifications and individualizations. It is evident from J. I I that in Aristotle's view everything that has sensible matter has intelligible matter, while the converse is not the case. Similarly everything that has JAT/ "YWIIT/~ /Cal ~Oaprt, has JAT/ T01TunI and the matter involved in growth and in alteration (H. 10.pb 3), whereas JAT/ T07l't/c~, at any rate, can exist without JAT/ Y'w7I'"1 (10.2 b ., 10Hb 7, e. 1050b 17, A. 1069b 25). So also can the matter involved in alteration (e. 1050b 17). It is further stated that JAT/ T07l't~ implies none of the others (H. 10H b 7, e. 1050b 21, Phys. 260& 28). Further, alteration presupposes local movement (260 b 4), and growth presupposes alteration (260& 29)-and therefore local movement (H. 10.2 b • n.). Cal. 14, which asserts the independence of the different kinds of change, is probably not by Aristotle. We thusget a scale of matters, each of which implies all that precede it: (I) JAT/ v07l'"1, (2) JAT/ aw8-qr-q, (a) /Ctv7l'"1 (T01Tt/c~), (6) lliOUlI'T11, (c) alJ~ /Cal ~(h~, (d) Y'~ /Cal ~Oaprt" which is JAT/ P.OAIUTo. /Co., /Cvptw .. (De Gm. eI Corr. 320" 2). II. ~ ill TO'~ o.tcr&1JTO'~ il1rdpxoucro. ".~ ti o.tcr&1JTct For Aristotle's view of the mode of existence of TO. p.aOT/p.aTt/Ca. cf. M. 2, 3. 16. 3Tl ollx c111').w~, • that neither can be said without qualification to be prior'. 17. tioll f\ '".+UXOII should be read, with the best manuscripts. • If (not only the concrete whole, but) even the soul may be said to be the animal or (to put it more widely so as to include plants) the living thing.' I9-~3. Aristotle's answer to the question of priority is as follows: (I) Some wholes are posterior to some parts; viz., the particular or materiate right angle (whether its matter be sensible or intelligible) is posterior (a) to the elements in the definition, and (6) to the parts of a particular right angle (whether sensible or intelligible). But (2) the immateriate right angle, while (a) posterior to the parts of the definition, is (6) prior to the parts of the particular right angle. According to this interpretation TWV (V Tee AO)'CtJ /Cai. TtV~" /'pfJ.ij .. answers to T'~" in I. 19, and /Cal yap . .. TaL.. /CaO' (/CaUTa answers to 1't I take /Cal TIVO" /'pfJ.ij .. as = /Cal TWV TW~ /'pfJ.ij... But this is very doubtful Greek, and TWV should perhaps be inserted.

Z. 10. 1036a 11-23

:a01

~ "I'" Tijs ~1JS, ~ xabij c\p~ is a perceptible right angle with perceptible matter (cf. 11 • .J, 10); ~ ... TaLs VPCIf'I'mis Tais real 'reClOTm is an intelligible right angle with intelligible matter (cr. 11. 3, II).

Whkh paris are paris of llu form, which of Ihe concrete whole; (ch. II).

103& 86. Which parts are parts of the form, which only of the concrete thing? Until we know this we cannot define anything, for definition is of the form. 31. When the form supervenes on specifically different materials (e. g. the circle on bronze, stone, wood), the materials are evidently no part of the form; but when this is not so, it is hard to eliminate the matter in thought. b 3. E. g. the form of man is always found in flesh, bone, etc.; are these, then, parts of the form, or parts of the matter but difficult to eliminate because the form never supervenes on other materials? 7. Some have suggested that lines are to the circle as flesh to man; they reduce all mathematical objects to numbers and say the definition of the line is the definition of • two'. 18. Some Platonists say two is the line itself; others say it is the Form of the line, holding that, while two is the same as its Form, the line is not the same as its Form. 17. It would follow that (I) there is one Form of many things which evidently have different forms; (:a) at this rate there may be one supreme }<'orm, the others not being Forms at all j but thus all things will be one. SI. We have stated the difficulty about definitions, and its reason. It follows that it is a mistake thus to eliminate matter: some things are essential1y 'this form in this matter' or 'these things in this state'. s4- The comparison of ' animal ' to 'circle' used by Socrates the younger is misleading; it implies that man can exist without his parts as the circle can without bronze j but the animal is a sensible object and cannot be defined apart from movement, i. e. apart from its parts, and these in a certain state; for it is only the hand which can do its work, i. e. which is alive, that is a part of a man. 8s. Why is not the definition of the semicircles included in that of the circle? Not because they are sensible objects, for they are not. But in truth some non-sensible things have matter; every individual thing has matter, intelligible if not sensible. The semicircles are not parts of the universal circle, though they are of particular circles. llYN

0

202

COMMENT ARY

1037& 5. Soul is the primary substance; the body is matter; man is the unity of the two taken universally. Socrates may perhaps be identified either with his soul or with the concrete unity; but if only with the latter, the particular (Socrates) answers to the universal (man). 10. Whether there is another matter apart from the matter of such substances, and another substance, must be considered later. It is with a view to this that we are examining sensible substances, which belong in a sense rather to physics, since physics must study the substance as defined, even more than it studies matter. 17. How the elements in the definition are parts of it, and what constitutes the unity of definition, must be examined later. The thing evidently is one, but what makes it so ? III. We have stated generally (I) what essence is and in what sense it is self-subsistent, (2) why the definition of some things contains the parts of the things while that of others does not, 84. (3) that the material parts are not present in the definition (for they are not parts of the substance as defined but of the concrete substance, which in its union with matter cannot be defined but can only be defined according to its primary substance, the indwelling form, e. g. hollowness as opposed to snubness); but in the concrete substance (e. g. the snub nose) there is matter; 33. ( .. ) that primary substances (i. e. those which do not imply the presence of something in something else which is its substratum), e. g. crookedness, are the same as their essence, while concrete things involving matter, and unities of substance with an accident, e. g. Socrates + musical, are not the same as their essences. 1036b 3. li+EAEiv TOUTOV, cf. d.q,atpEiv T7Jv iJAT/V, 1. 23. 8. Ibropoucr( TLI'ES. Pythagoreans, says Alexander; and Aristotle's expression d.vayoVO't 71'aVTII d~ TOW d.pt9p.a6s (1. 12) (coupled with the distinction between these thinkers and the Platonists, 1. 13) shows that he is right. Cf. Scholia on Euclid, p. 78. 19 Heiberg, ol 8~ TIv911YoPEtOt TO p.& CT'rlp.Eiov d.VaAoyov IAap.!3l1vov p.olla8t, 8va8t 8~ T7JII YPIIJLp.~II. The representation of the point by I, of the line by 2, of the triangle by 3, and of the tetrahedron by", goes back to Philolaus (Tluol. Ar. p. 62. 17-22). Alexander's note (5u. 20-513. 3) preserves some information about the Pythagorean theory which he probably derived from Aristotle's lost work On lhe Pylhagortans. The number 2 was, according to them, TO 71'pw-rOll 8taCTTIITOII, the first product of the diremption of the unit, and, quantity being no part of the essence of the line but the mailer in which it is embodied, the line should be defined not as 71'00"011 lq,' til 8tauTaToII, quantity dirempted in one dimension, but as TO 71'pw-rOll 8taCTTaToII.

13-17. Il seems clear that TO d80s T~S ypu",,,,~s is opposed not (as .Alexander, Asclepius, and Bz. take it) to r1JII SveHlu but to ufrrOypap.p.~II, and that {llta p.f.II yap, etc., explains the position of those who said that 2 is the form of the line but not the' line itself'. The distinction between aVrcrypap.p.~ and TO €rSO~ Ti1~ ypap.p.TJ<; is doubtless peculiar to one of the later forms of Platonism; 01 1££11 probably indudes Plato himself. The two views are put neatly in H. 1043" 33; the question is whether the line is 8va.~ III p.~KEt or Sva~. 18. O'lr€P Kul TOLS nu9uyope(oLS (J'uvlliuwEil. Thus for instance they identified .. both with friendship and with justice and with many other things. Cf. A. 987& 27. 19. Whether we print a~T6(tSo~ or a~To €rSO~, a~T6 probably goes with €rSO~ in the sense of 'Form-itself' or supreme Form. 'lr4VTIIIV = 'of all Forms '. ~O. KU(TOL OUTWS b 'lr4VTU lCJ'Tut, since the nature of things depends, for the Platonists, on their Form. ~4. ~ 'lrupulio}.~ ~ tl'lrl TOU t~u, i. e. the comparison of the relation of flesh and bones to humanity with that of bronze to circularity (II. 5-7). ~5. IWKP4T'1)S c\ VEWTEPOS, a Socratic and a contemporary of Theaetetus, mentioned in Theac/. 147 D, Soph. 218 B, Epp. 358 D. He is one of the interlocutors in the Po/i#cus. 30. lXGVTWV 'lrWS is really irrelevant. Aristotle is insisting that the definition of man must mention the parts of the body. This reminds him, however, that it is not enough to mention the parts of the body; it must be specified that they are in a certain condition, i. e. alive. We must not forget the matter; but we must equally not forget the form, I/rox~ or vitality. 31. cl}'}"~. For the usage cf. 1038& 14 n. 3~-1037a 5. Alexander thinks this section may have originally gone with the previous discussion on the difference between the relation of the circle to its semicircles and that of the syIlable to its letters (I034b 24-1035" 17), and have been separated by Eudemus; and Bz. also thinks it out of place. But it seems to be quite appropriately placed. Aristotle has just rejected the comparison of sensible things like 'the animal' to intelligible things like the circle (I. 24), and has insisted that in the definition of ' animal' its sensible materials must be mentioned, while in that of the circle its sensible materials (bronze, etc.) must not be mentioned, !>ince they are accidental to it. This naturally leads to the further question about the circle, why are its parts in another sense, the semicircles, not mentioned in its definition. The reason is not that these are sensible materials and therefore irrelevant to the circle, which is an intelligible. They are not sensible. But they contain material none the less-intelligible material, and therefore are not parts of the universal' circle '. From this Aristotle, naturally enough, returns to the case of' the animal " in 1037" 5. The reasoning, however, is inconsequent. If' animal', though a universal, cannot be defined without the mention of its necessary material, the circle cannot be defined without the mention of ils

20 4

COMMENTARY

nec.::ssary material, though the material is in this case not sensible but intelligible. Aristotle is right in saying that the semicircles are not mentioned in defining the circle, but the reason is not that they are matter but that the definition would be circula~. The circle cannot, in fact, be properly defined without referring to its' material', viz. space. 35. len4L yAp U>.'1 M",,, K4l ".~ 4taf1)T&i". For i$A7J v07JT7l cf. n. I03? I-Q. The fuller form given by Ab runs rather more naturally than the shorter form given by the other manuscripts, and I have accordingly kept it, though it is quite possible that Ab's reading may be, as Bz. suggests, merely derived from Alexander's interpretation. 7. KOPLCI'KOS, cf• .1. 1015 b 17 n. d ,utI K41 -It +ux~ I"'KpuT1)s. The insertion of 1.WKpa.TTJ~, with Ab, makes the meaning clearer. As Aristotle had suggested ( 1036& 17) that' animal' may be identified with its form, soul, he here suggests that Socrates may perhaps be identified with his form, his soul. If he may be identified with his soul alone, as an alternative to being identified with his soul + his body, then 'Socrates' is 8L'M'OV, an ambiguous term. For the general sense cf. 1036& 16-25, H. 1043 b 2-4. g. It seems necessary to insert TO, which is read by the Aldine edition, though probably only ex conieclura. Wtrlp TO KdcSl.ou [TI] K41 TO Kd'IKBaTO", 'as is the universal (man), so will be the individual', i. e. a unity of form and matter (cf. I. 6). There is some probability in Apelt's suggestion that T' has arisen from an abbreviation of oww. The sentence would read rather more naturally with oVrw, but cf. 1038b 2 f. T' in any case must be wrong. Christ is perhaps right in reading a comma after &.1I"AcQ~. wrnr.p ... IK4CTTOV then means' the individual corresponding to the universal '. Io-~O. Jaeger regards this (AnSI. 206 n.) as a section added later by Aristotle, when he began to view the discussion of sensible substance in Bk. Z as preliminary to the discussion of insensible substance in A. Cf. 102gb 3-12 n. II. TLS 4l.l.'1, i.e. a quasi-material principle (such as the great-andsmall) present in incorporal things. It seems impossible to supply ooo-Ca, as one is tempted to do, as the substantive understood with TLI dM7J. I~. Cl'Kl'IrTlo" ilenlpo". The reference is to Bks. M N. 13-14. TOVrou yAp ••• 8LOp"I'". For other indications that the treatment of sensible substance is preliminary to the true business of metaphysics cr. 1029& 33, b 3-12. 16. oil yap ".15"0,, 'lrlpl Tijs U>.'1S KTl.. Cf. De An. i. I. 17. Tijs K4TA TO" l.cSyo", sc. o/Jcr{al. i'lr' may be defended by a comparison with the passages referred to in Bz. Indtx 268. 31-44, but Brandis's conjecture .TL is very likely right. ~O. Cl'KI'lrTlo" ilenlpo", H. 6. !l1-!l~. TL ••• e'lP'lT4L answers to ch. 4, ~S-33. lILA TL ••• U>.'1 to chs. 10, I I (11. 30-32 to ch. 5), 33. aTL ••• b 7 to ch. 6. This summary contains no reference to chs. 7-9, and confil ms the view that these belong originally to a distinct treatise. Cf. 1032" 12 n.

&"

Z.

I

I. I036b 3S -

I037 b S

20 5

~7. !,ETA !,E" ya.p rij~ w.,,~ OGK EO'T'''. Yet Aristotle has said (1036 b 29) that the definition of man must mention his material parts. Of

course a definition must not mention prime matter, since that is d.&PWTov, i. e. nothing definite can be said about it j but in certain

cases the proximate matter must be mentioned. 31. &1~ yAp i" TO.lTO'~ ~'I\'c£peEL "p(~. These words appear quite irrelevant in this context, and seem to be due to a copyist who had 1030b 32 in his mind. b 5. The simplest emendation of o~8l is oW d. I Nor is a thing the same as its essence if the thing be a compound of a subject with an accid!;ntal attribute.' Cf. 103 la 19-28.

What constitutes lite unity oj' a subjeel oj'definilzon r (ch. 12). I037b 8. Let us discuss definition in so far as it has not been discussed in the Ana{Ylics. The question there stated is of use to our inquiries about substance, viz. the question why that, the account of which is a definition, is one. 13. Why is I two-footed animal' one and not two? ' Man' and , white' are two when the one does not belong to the other, one when it does j 18. but in ' two-footed animal' one element does not share in the other j the genus does not share in the differentiae, else it would share in contraries at the same time. Even if it does share in its differentiae, the same difficulty occurs, since the differentiae of man are more than one-possessed of feet, two-footed, wingless. Why are these one? Not because they are present in one genus, for then all the differentiae that belong to a genus will form a unity. 1014. But the elements in definition must be one, since substance, the subject of definition, is a unity, a ' this'. 1017. Let us examine, first, definition reached by division. There is nothing in definition but the first genus (e. g. animal) and the differentiae j the lower genera are the first genus + the differentiae (e. g. two-footed animal). 33. The number of the elements of the definition makes no difference j let us reduce them to the genus and one differentia. 1038a 5. Now (I) the genus does not exist apart from the species, or, if it does, exists only as matter; therefore definition is the account consisting of the differentiae. 9. But (2) we must at each stage divide by the differentia of the previous differentia j we must divide ' possessed of feet' into I clovenfooted' and I whole-footed', not into I winged' and ' wingless '.

206

COMMENTARY

15. We must proceed so till we come to the indivisible species. There will th!!n be as many kinds of foot, and of footed animals, as there are differentiae. The last differentia will be the substance and definition of the thing. ~O. If we mention the earlier differentiae as well, we shall repeat ourselves. ~5. If, then, we take a differentia of a differentia, one differentiathe last-will be the form; but if each differentia is accidental to the previous one, there will be as many differentiae as there are steps in the division. Definition, then, properly consists of the last differentia. 30. If we change the order of the definition, putting' two-footed' before 'possessed of feet', the latter is evidently superfluous; but there is no order in substance (therefore 'possessed of feet' must be superfluous even when it stands first). So much for definition by the method of division. The unity of a definition, and of its subject, according to Aristotle, lies in the fact that the genus and the differentiae have no existence apart from one another, nor have the successive differentiae. The genus is merely the ' matter' of the definition, and each differentia the 'matter' of the next. He accordingly condemns definitions in which any of the differentiae are accidental to the genus or to one another. The discussion is carried further in H. 6. 1037b 8. For the discussion of definition in the Ana!J'lics cf~ A1,. Posi. ii. 3-10, 13. g. lv lKElIIOLS, An. Posi. 92a 29. The d.7f'opta is there raised but not answered. II. o~ T~II ).6yoll 6pLO'JIoOV Etllo.l +uJIoEII. The distinction between AOyo~ and bpLCTp&~ has been drawn in 10308 [4. 14-~I. The obvious intention of this argument is (I) to show how man and white form a unity, when they do so (11. 14-18) and (2) to point out that genus and differentia cannot form a miity in this way (11. 18-21). Bz. argues that the mode of unity referred to in the first section (KaTu, 7f'0.90'» is not the same as that referred to in the second (KaTu, pi9£tLV). He thinks therefore that Aristotle is arguing that genus and differentia are not one either KaTo. 7f'0.90,> or KaTo. pl9£tw, and that it is merely by carelessness that he frames the sentence in a way which suggests that these modes are the same. But in 1030813 P£TOx-1 is used in this connexion as synonymous with 7f'0.90~. If P(TlX£LV be so used here, the argument can have its natural meaning. In 14-18 Aristotle describes a unity KaTo. P£TO~V Kal 7f'0.90~, and in 18-21 he shows that the definition is not a unity of that sort. It is true that in the Topics (121 all and elsewhere) TO p£Tixnv is defined differently, but that account of it does not seem to be in Aris otle's mind here; he is using P(TiX£LV in the Platonic sense alluded to in H. 10451\ 14-20, b 7-9' The argument of 11. I.~-2 1 may be put thus. A unity KaTu.

20

7

p.l8fe,V is one which may exist between A and B and between A and

not B, but not between both at once; but the relation of genus A to differentia B is one which A has at once to B and to not-B. Therefore genus and differentia do not form a unity KaT~ P.€8fe,V. 1011. Et S~ Kal !'€TEXEL. 'Even if the genus could partake of the differentia, this would not explain how a genus + several differentiae form a unity.' ~. O~IJI !'~v yap ••• Iv. ' For at that rate a genus and all its differentiae would form a unity.' 1OI7-1OI9. Aristotle says the question must first be considered with regard to definitions by division (cf. 1038& 34), but he never gets to any other kind. The other kind is that ~K TWV ~VV7I'apx6VTWv (B. 998b 13, H. 1043a 20). 1038a 5-9. Since the genus does not exist apart from the species

or exists only as their matter, it offers no obstacle to the unity of the definition, and accordingly the definition may be considered as if it consisted only of differentiae. This is the first step in the explanation of the unity of the definition. The next step is to show that the differentiae in a definition may be reduced to one. 5. Ta ~ YEVOUS E'lS", cr. A. 991& 31 n. 7. Ta dSYJ Kal Ta aToLXELa, 'the species, i. e. the letters '. 9-10. Tij .•• SLa+Opq;, Prof. Joachim's emendation of ~v • •• 8,atPopav, seems to be required by the sense. 14. AXX' ~ KTX., '(and in general we can divide" animal with feet" into nothing) except" with divided feet" and "with undivided feet" '. dAA' 11 in effect = 'but only'. Cf. 1036b 31, r. 1005& 12, H. A. 563b 22, 580a 20, Pol. I257b 2 I. The idiom is explained by Cook Wilson in Class. Quart. iii. 12 1-124. 17-18. TOTE S' ••• SLa+opaLS, i. e. there will be as many infimae species of foot or of animal with feet as there are ultimate differentiae. Ig. " TEXEuTaCa SLa+Opa " ollaCa TOU 1I'pC£y!,aTo<; laTaL, since it will presuppose all the previous differentiae and finally the genus. From another point of view Aristotle can say (To/>. 139& 29, 142b 27, 143& 18) that the genus is the element in the definition most expressive of the essence; it is so because all the other elements presuppose it. 30. KaTC£ yE ,.0 6p8ov, i. e. according to the method in which each differentia is a differentia of the previou'l one. 33. TC£eLS S' OllK laTW Iv Tfi olla£~, se. and therefore what is seen by a p.fTtiTae,,. 10 be superfluous must have been superfluous before. 35. ,",V 1I'pll'lTYJv, 'at the first attempt', cf. 1037 b 27 n. For the idiom (in which some such word as ~86v was originally understood) cr. Ar. 1'hesm. 662, Dem. 01. iii. 2, Hdt. iii. 134, i. 153 (the last passage has ~v 1I'pwTTJV fIvaL). Pol. 1286 a 5 is not a parallel, for dt/lf{a8w ~v 1I'pwTTJV seems to mean dt/lE{u8w ~v 1I'pWTTJV p.ovapx{av , ~

f1l"UK07TELV.

COMMENTARY

z08

No

UNIVERSAL IS SUBSTANCE; NO SUBSTANCE CONSISTS OF SliBSTANCES

(chs.

13-16).

The universal is not substance (ch.

13)'

1038b 1 (B) (cf. 1028b 33). We have discllssed two things that are held to be substance-the essence, and the substratum (which we showed to 'underlie' in two ways, as the' this' underlies the accidents, and as the matter underlies the actuality). 6. We now proceed to discuss the universal, which some think to be the truest cause. But it seems that no universal can be a substance, for g. (I) If it be suggested that the universal is the substance of a thing, we answer: (a) The substance of a thing is that which is peculiar to it, but the universal is common to many. It must be the substance of all or of none. But it cannot be the substance of all i and if it be the substance of one, this one will be the others, for things whose substance or essence is one are one. 15. (b) It is that which is not predicated of a subject that is substance, but the universal is predicated of a subject. 16. (2) If it be suggested that the universal is not substance in the sense of essence, but is included in the essence, e. g. ' animal' in man, then (a) evidently it is definable (and so there will be an infinite regress). Ig. But (b) even if not all elements in substance are definable, the universal will be the substance of something; as ' man' is the substance of the man in whom it is present, 'animal' will be the substance of that in which it is present and to which it is confined. (Thus sugge~tion (2) turns into (I).) g3. Further, (c) a ' this' or substance, if it is composite, must consist not of qualities but of substances. Otherwise non-substance wiII be prior to substance; but this is impossible; for affections are not prior to substance in definition, in time, or in generation, else they would be capable of existing apart. gg. Further, (d) in Socrates a substance (animal) will be present as an element, and will therefore be the substance of two things (the class of animals and Socrates). 30. (e) In general, if infimae species are substances, none of the elements in their definition is the substance of anything or can exist apart from its particular instances or in anything else. 34. (3) No common predicate indicates a 'this', but only a 'such '. Otherwise we get the 'third man' and other difficulties.

Z. 13. I03 8b 2-7 I03ga 3. (4) A substance cannot consist of other substances existing actually; for what is actually two is not actually one (e. g. a line which is double another consists only potentially of two halves, for their actualization separates them). g. Democritus puts our point well when he says that one cannot be produced out of two nor 'lzce versa; he refers to atoms, which he regards as the only substances. Similarly, if number is, as some say, a synthesis of units, the number two is not one, or else contains no units actually. 14. Our result involves a difficulty. If no substance can consist of universals (because they indicate a 'such', not a 'this '), nor of substances actually existing, all substance will be uncompounded and therefore indefinable. Ig. But it is universally agreed that substance is the only or the chief object of definition. Either, then, all things are indefinable or they are definable in one sense though not in another. Our meaning will appear more clearly later.

Chs. 13-16 form a separate section of the inquiry into substance, the main upshot of which is summed up in 1041a 3-5: 'no universal is substance, and no substance contains substances as its parts '. The section begins (ch. 13) by discussing and rejecting the claim of the third claimant to the title of substance-the universal, and implicitly also that of the fourth claimant-the genus. From this follows (ch. 14) the rejection of the claim of the Ideas to be substance. Further it is argued (ch. 15) that the individual is indefinable. This is argued partly on the ground that the individual is subject to destruction and change; but the connecting link with ch. 13 lies in the other argument, that since the universal is never a substance, never a 'this', always a 'such' (13. 1039 a 15, 16), definition, which is an enumeration of universal marks, can never adequately express the nature of an individual. Next a corollary is inferred from the principle which was made the basis of one of the proofs in ch. 13 (1039a 3, 16), viz. that substance cannot be composed of actual substances; it is argued that the material parts of substances are not actually substances (16. 104 0b 516). And finally a further attack is made on the Platonic tendency to identify substance with the universal (1040b 16-104 1a 5). I038 b !J, 3. This is a reminiscence of 1028b 34; genus, however, is now omitted (as coming under the universal), and TO (K TOVTWV, the concrete individual, is added. 4. 1fEpl TOU TL ~v ElV(IoL, chs. 4-6, 10-12; KGl TOU ~1fOKEL"€VOU, ch. 3. 5. OTL 8LXW~ ~1fcSl
210

CO!l;TMENT ARY

10. I have adopted here the reading which sense and idiom seem to require; it accounts well for the various readings found in the manuscri pts and the commentators. IS-15. The argument is not clear but may be interpreted as follows: 'What wiII the universal be substance of? Either of all its particulars or of none (for there is no reason why it should be substance of one any more than of the others); but it cannot be substance of all (since, as we have just seen, I. 10, the substance of a thing is something peculiar to it. It follows, then, that it is the substance of none of its particulars). Ifwe try to avoid this conclusion and treat it as the substance of one of them, then (since (the universal will be no less the substance of its other particulars, and) things that have the same substance are identical) this one will be the others; which is absurd.' 18-!JS. In answer to the suggestion now put forward, that the universal is not the substance of things in the sense of essence, but is a substance because it is an element present in their essence, Aristotle replies that the universal can be defined, and seems to have meant to add that in that case it will itself contain a generic or unh'ersal element, and so substance will be contained in substance, ad ,'ljinilunz. But, he observes, we need not make this assumption, that everything that is part of the substance of something can be defined. Quite apart from this assumption, the universal will be the substance of something, as ' man' is of the man in whom it is present; so that the new view that the unh'ersal is a substance presml in the essence of its particulars turns into the old one which has already (9-16) been refuted, that the universal is essence. For the universal, e. g. animal, will be the substance, not indeed of man but of that in which it is present as something peculiar to it; i. e. of the class including all animals. This interpretation enables us to treat II. 19-23, 23-29, 29-30 as giving three distinct arguments (as IT! in II. 23, 29 shows that they do), not (as Bz. does) as giving parts of one argument. !J!J. Bz.'s suspicions of olJCTla in this line are amply confirmed by its absence in Ab and in Asc.c. The \'ulgate reading is due to the conflation of alternative readings, olJCTla lKEIII01I and lK£lI/OV olJCTla. !JS-!Jg. The argument seems to be as follows: Universals having been shown not to be substances (II. 9-16), they must not be regarded as constitutive elements of substance (as the view under consideration regards them, 16-18), since then non-substance would be prior to substance. !J7-!J8. OUTE My,!, yAp OUTE Xpov'!' oun YEviaEL ••• 'lrpOTEpa.. Aristotle nowhere else distinguishes between ')(pOlice 7rpo-npoll and ')'fII€CT£I 7rpO. T£POII, nor is any possible distinction apparent. Prof. A. R. Lord has suggested ')'IIWCT£! for ')'fII€CT£!, and this derives some support from 1028& 32. But (I) the Greek commentaries as well as the manuscripts read ')'fII€CT£L, and (2) ')(p6l1ce would not be likely to be put b;!tween Af,yce and ')'IIWCT£I, which are at least very near one another in sense (in @. 10491> 17 they seem to be identified). It is better there-

Z. 13. I038b IO-I039a 22

211

fore, to keep ')I(viu(! and to suppose that it is added as a synonym of }(POv~.

~9. Alexander has Tct lflJKpcJ.T£! o~ulq. OVTL EII11II'apefL owla. The meaning is: 'In Socrates there will be substance present in substance, and this will therefore be the substance of two things' (st. of the class of animals and also of Socrates). 30 \\ ci..ePlll1fOI, i.e. the individual man, Alexander thinks. But, as Hz. observes, we should in that case expect something like Ii Tt~ dIl8pfIJ""o~; and we should expect in l. 33 Tllla dv8pw7roV 1fa";" Toil~ T!Va~. It seems, therefore, that Aristotle means the infima species, which according to one of his lines of thought he regards as substance; cr. P.A ..6441\23. It is the substantiality not of man but of animal that he has been attacking in II. 16-30; the infima species is at any rate more substantial than the genus. 3~. lv A>'" not, as Alexander interprets it, 'in the Idea'. The words are quite general. 33. TA TWcl, 'the particular species or animal '. 34. CK TE ••• TO~TIIIV is answered by Kat 0." (' and because '). 10391\~. \\ TPLTOI ciVeplll1fOI, cr. A. 990b 17 n. 6. ~ Sur>'QaLo.. sc. ')Ipa/Lp.~, says Asc., doubtless rightly. We may d. ~ £M(ia, ~ 7ro8!ala, and Il. 101988 n., 0. 1048& 33 n. 8. The editions have a comma or colon after lvu1fapxoucrwv, but Kat KaT« TOVTOII T()II TP07rOIl appears to go closely with ElI11II'apxOVuwv and to mean Kat EIITfA(X({q. lllv7rapxovuwv. Possibly we should print a colon after Tpo.".OIl and read 8 with T. 10-11. TA yAp ••• trOL(L, 'for he identifies substances with the atoms', from whose atomic nature it follows that one atom cannot contain two atoms. cr. De Caelo 303& 6, De Gen. e/ Corr. 3 25& 35· I~. \\ clpLel'~1 cr~veE(JLS I'OVclSIIIV. This is practically the same as the earliest recorded Greek definition of number, /Lolla8wlI uVCTT'J]/La., which Thales is said to have borrowed from the Egyptians (Iambl. in Nicom. AI'. In/rod. p. 10.8). Cf. Il. 1020&13 n. 15-16. I't\TE ••• a'IJI'o.LVELv, cf. 1038b 23-29; 16-17. I'~T' le O"crLWV ••• crU..eETOV, cf. 1039"3-11. 19. l>'lXe'IJ II'cl>'o.L, 1031& 12. ~~. T~IV UCl'TEPOV, Z. 15, H. 6. Aristotle is not ver' successful in solving the problem.

Tile Ideas are no/ substance (ch. 14). I039&~4. Observe the consequences for thoSE who say the Ideas are separately existing substances, and at the same time resolve the species into genus and differentiae. ' Animal' will be either the same

212

COMMENTARY

or different in ' man' and in ' horse'-i. e. numerically; in definition it is clearly the same. If man is a separate • this', animal must be so too. 33. (I) If 'animal' be supposed the same in horse and in man, (a) how can it be the same in things that exist apart? Will it not be divided from itself? b g. Further, (6) if it shares in 'two-footed' and in 'many-footed " it, though one individual, will have contrary attributes; if it does not, in what sense can it be two-footed? It is absurd to say' by composition', i. e. by contact or by mixture. 7. (2) If 'animal' is different in each species, (a) there will be practically an infinity of things whose substance is ' animal '. Further, (b) each of several things will be 'animal itself'. For (i) the' animal' in each species will be the substance of that species, for it is that and not anything else that each species is called after; otherwise that other would be the genus of man; and (ii) all the elements in the essence of man will be Ideas; and therefore, since what is the substance of one thing cannot be the Idea of another, the .mimal' in each species of animal will be 'animal itself '. 14. Further, (c) from what will the' animal' in each species be derived? how can it be derived from 'animal itself'? How can the 'animal', whose essence is just to be animal, exist apart from , animal itself'? 16. (3) These and even greater difficulties arise if we consider the relation of Ideas to sensible things. Evidently, then, there are not Forms of sensible things such as some suppose.

1039- g6-b 19 is very similar to PI. Parnl. 131 A-E, and in particular the language in b J recalls that in 131 B tv iI.pa ~v Krt Tawov lv 71'OAAOtl1 Kat Xlllpls O&-IV oAoy J.p.a. lvirrra" Kat OWIIIS awa awov XlllptS &v (Z7]. Siebeck thinks this confirms his notion that the Par11lenides is directed against the Metaphysics, but more probably Aristotle is pressing the difficulties raised by Parmenides in the dialogue. 33. c:\crre Ka.l TO t~v might easily have been dispensed with, but is read by Asclepius as well as by the manuscripts, and need not be excised as Christ proposed. It ".~v o3v TO a.~. The other alternative comes in b 7. b I-sa. Ka.l liLt). T( ••• TOUTO; 'If the Idea is present in separate things, does not this amount to separating it from itself? ' 7-8. HKOUV • • • a..eplll'll'~. The argument, as :T' in I. 9 indicates, is meant to be complete in itself. The conclusion 471'('pG. WS 17l'os .l7l'(ty Irrr(U ~v ~ owEa ~~Y is absurd, because things whose substance is one are one (I038b 14).

ct'lrELpA " 'WQ! El••Lv is an exaggeration, since for Aristotle the number of species in a genus is limited. 9-14. The argument is very obscure, but may perhaps be expanded as follows: 'Further, each of several things will be the Idea of animal. For (i) the •• animal" in each species of animal will be the sUNlan" of that species j for it is after that and nothing else that the species is called (i. e. when we want to say what e. g. man essentially is, we say he is an animal, not an anything else); else that other would be the generic element in man. And (ii) each element in man, and therefore among others the element" animal", is on the Platonic theory an Idea. We may infer that the" animal" in man is not the Idea of one thing and the subslan" of another. Therefore the " animal" in the various species of animal, which as we have seen is the subs",,"e of each of these species, will be the Idea of animal.' For the force of KaT' elMo >"EyETaL 1. 10 cf. A. 987b 9. 14-16. ITL • • • Further, from what does this "animal .. in each species spring? How is it derived from animal-itself? Or, if not derived from it, how can this "animal ", whose very substance is animality, exist apart from animal-itself (the Idea of animal)?' 15- mi, "-'TOU '¥ou; seems to be correctly explained by Alexander, 7rWs /K TOV TOLOVrov aw~c;ov 111TlU TO lv 1i awoa"opt/nr't aw~p ; The reading and punctuation suggested by Bz. and given in the text is a great improvement on the traditional form ,,0 (p 3 of,a-Ua, TOVTO afrrO 7rOP' awo, and derives some support from AL 5 2 9. 17. 16, 17. The difficulties raised in & 26-b 16 have referred to the relation of genus to species; Aristotle now says that even greater difficulties for the ideal theory attend the relation of species to sensible individuals.

,,01'; ·

ie

Individuals, and therefore Ideas, are indeji"able (ch. IS). 1039b 80. Concrete things are generable and therefore destructible; ferms are never in course of being destroyed any more than of being created; they are or are not, without generation or destruction. 87. This is why (I) particular sensible substances are not subjects of definition or of demonstration, viz. because they have matter capable ofbeing and of not being. If knowledge can never become ignorance, there cannot be demonstration or definition of the contingent, but only opinion. 104011 8. For perishable things are no longer known ·whell they have passed out of our perception, and, though the formula in the solll remains the same, there is then no longer definition or demonstration j thus it is always possible to overthrow a definition of a particular, (or it cannOI really be defined.

COMMENTARY 8. (2) Therefore an Idea, also, cannot be defined, for (a) it is said to be a separate particular. Its definition would have to consist of words, but new-coined words would not be understood, while old ones are common to all things of a class. 14. If it be said that, while the marks used in the definition separately belong to many things, together they may belong only to one, we answer (i) that they will also belong to both elements in the definition, e. g. ' two-footed animal' to ' animal' and to ' the two-footed' (where the elements are eternal, this musl be so, since they are prior to the compound and, further, separately existent, because, if' man' is to exist apart from its particulars, so must' animal', and if 'animal', then also' the two-footed '); further, (ii) that the elements are prior to the whole, and therefore are not removed when the whole is removed. ~~. (b) Again, if the elements of Ideas are Ideas (as they must be, elements being simpler than the compounds1 the el~ments, e.g. 'animal' and 'two-footed', will be predicable of many subjects. Otherwise how could they be recognized? All Ideas are thought to be shared in by a plurality of subjects. ~7. In the case of eternal things, especially if they are unique, like the sun, people do not realize the impossibility of definition. Definition may err not only by adding irrelevant attributes such as 'going round the earth ' (the sun would still be a sun if it did not do this, for 'sun ' means a certain sUbstance) ; 33. but also by naming attributes which can belong to another subject. Such a definition will be common, while the sun was supposed to be an individual.-Why does not some Platonist produce the definition of an Idea? The truth of our remarks would become apparent. Hz. thinks that as in chs. 13, J 4 Aristotle has proved that universals are not substances, he now proves that individuals are not substances. But (I) that is not Aristotle's view, and (2) Bz. can arrive at it only by piecing together the conclusion of this chapter, that individuals are indefinable, with the conclusion of ch. 4, that substances are the sUblect of definition. If Aristotle had meant his readers to draw Bz.'s conclusion, he could hardly have failed to call attention to it. The interest of the chapter is silllply in the problem of definition. Aristotle has al>ked in ch. 13 (103911 14-22) whether anything can be defined, and begins his answer here by pointing out that at any rate individuals cannot. While chs. 10-14 ha\'e continued the line of thought of chs. 1-6 and contained no reference to chs. '-9, ch. 15 has such a reference (I039b 26). But it also continues the line of thought of chs. 1-6, 10-

z.

15 1039 b 2 2 - 1040& 15

21 5

14, and in particular the problem of the possibility of definition, which was raised in ch. 13. 103gb !z!z. 1\ My~ 3).111$, 'the definition in its full extent', 110t bound up with any particular matter. Bz.'s suspicion of OAro~ seems unjustified; in the Ittdex he quotes a phrase which is a good parallel, TO Ilt dlltatp£T()I' OAro~ (De Gen. el Corr. 326a 28). Cf. also 1029 b 6, I033b 26. !Z4. otiTIIIi Ware +8elpEa8a.L, 'in the sense that it is ever in course of being destroyed '. Cf. I033b 5-6 n., E. 1027~ 29 n. !Z6 8~eLKTa.L, in ch. 8. !ZS. Tiiiv Ka.8· lKa.aTa., cf. B. 999& 26 n.

OUTE chro8ELeL$ (aTLV, 'nor can there be demonstration aboul such substances " i. e. demonstration of their attributes. 30-31. 8LO +8a.PTa. ••• a.~Tiiiv. Aristotle shows no knowledge here of the distinction drawn in A. 1069& 30 between two kinds of sensible substance, the eternal (the heavenly bodies) and the perishable. Ta. Ka.8· lKa.aTa., cf. B. 999& 26 n. 31. Ka.l 1\ I\PLal'0S l1fLaTIJ!'OVLKOV, sc. ' and therefore TWV dva.YKa{wv'. 1.040& !Z-4. c181JM Te ya.p ... c11fEUn, cr. 1036& 6. 6. Bz. interprets Tiiiv 1fPOs 3pov as meaning quod ad dejinili(menz allznd. Parallels to such a use of Ta rpo~ oPOl' may be found in Top. 102 b 27, 120b 13 (tern Il( Tawa CTTOtX(ta TWV rpOs TOV~ opov~), but the genitive is very difficult. It seems better to suppose with Alexander that the phrase means TWV rpO~ opov Ttvo~ 7rpaYJ14Twop.(.,roV. But corruption may be suspected. S. Tiiiv ••• Ko.r lKa.aTOV ,., t8~a., 'the Idea is an individual'. II. 1faaLV, 'to all the members of the class denoted by the name '. 14-15. It 8E TLS ••• 61fCipXELV. The definition of an Idea might be defended against the attack just made, on the ground that, though each of the marks separately belongs to more than one subject, taken together they belong only to.the Idea in question. Aristotle proceeds in 1. 15 to object to this defence, bUl, as Bz. observes, he himself gives a similar account of definition in An. Posi. 96& 33 lKaCTTov p.(., (r~ rA(tov vrap~(t, c1raVTa Ilt p., lr~ rAfol'. The objection, then, must derive its force, if it has any, from the peculiar nature of the Ideas-from the fact that they are individuals and exist separately (I. 9). . The first objection is stated in n. 15-17. 'Two-footed animal' will belong both to 'animal' and to ' the two-footed'. Bz. thinks that fnrap· XftV is here used (by an illegitimate change of meaning) not in the sense of' be predicable of', which it has in 1. 15, but in the sense of ' be contained in the extension of'; but for this sense he offers no parallel. Wra.pXf.tV has, in fact, its ordinary sense. Aristotle means that 'twofooted animal' is predicable (I) of 'animal' (not universally, but in certain cases), and (2) of ' the two-footed' (universally, since tworootedness belongs only to animals, as a differentia should belong only to its genus, Top. 143& 30). This objection would not apply to an ordinary definition, since that does not imply the existence of genus and differentia apart 'from the species. But according to the Platonists

216

COMMENTARY

, animal " 'the two-footed " and C man' are separately existing Ideas; and 'two-footed animal' is predicable of all three, and therefore not a proper definition of man_ The difference between the Idea and the ordinary subject of definition is brought out in the next words (17-1I). ' This applicability of the proposed definition to more subjects than that for which it is proposed must exist in the case of the eternal entities (the Ideas), since the genus and the differentia are prior to and parts of the compound, the species, and since further they exist separately. They must exist separately, if the species does; for the genus is described as existing apart from the species, and if the genus does so the differentia must do so too.' 18. 1fPOTCPC£ i IIna. Ita.ll'ip'l is a loose accusative absolute, for which cr. KUhner ii. 2. § .S7. 3b• al. Bz. objects to de' {which purports to introduce a new argument} on the ground that the priority of genus and differentia to species has already been used in the previous argument (I. IS). But Alexander affords no support to Bz.'s suggestion 8w.q,opa.lUTa." on, except that he seems not to have read (lO'. Bz.'s objection is removed if we treat Ka.l. TOVTO ... 8uJ.fpopO. (17-21) as parenthetical, and (l(l OT', &c., as answering to 7rpliYrov p.lv, 1. 15. The second argument then is: Genus and differentia are prior in being to species, and what is prior to another is not destroyed by its destruction and therefore cannot be its· definition. aa. clna.va.Lp«LTa.L. Aristotle has IlVTavaip€uts in a somewhat similar sense (Top. 15Sb 33), but his usual word for this relation is ITVVa.va.,pliv (e. g. K. I059b 3S), Alexander had In instead of 11fCLTa. (or l7rnTa 8l) cl, and treats 'T-I. ••• ~v (\. 23) as a separate argument. But so taken it is excessively obscure, while, if we read (l, this clause offers a suitable protasis to what follows. ' Again, if the elements of Ideas are Ideas (as they must be, elements being simpler than their compounds), it will follow further that they must be predicable of more than one subject: Asc. seems to imply such a connexion (Ilv&y'"l o~v Ka."tTfYOP€i,uOa., KTA., H3. 12). The history of Alexander's reading is doubtless as follows. The first part of ANTANAIPEITAIEII EITAEI was read as ANTANAIPEITAIETI, and the last part omitted by haplography. aa--7. The argument is: 'Genus and differentia must be predicable of more than one subject. (.'. They cannot form the definition of a single subject.)' How, Aristotle asks, can genus and diflerentia merely by combination with one another lose this character of C commonness'1 as. 'lfWS yv"pLoftlaETa.L; se., the Ideas being usually apprehended by generalization from several particulars. The Idea is for Plato what answers to a common name (Rep. 596 A 6). a7-b a. lv Tois cli8LOLS goes (as Asc. sees) not with ll~vvaTov op{ua.CTOQ.L but with Aa.v6av€t. It is not impossible to define eternal individuals any more than other .individuals, but the impossibility is less obvious, since the objection arising from the fact of perishability {I039b 27~

,e

Z. 15. 1040& 18 -

1040b

3

21

7

1040a 7) is not present in their case. Again, Ta p.ollaxo., things which are the only instances of their kinds, are not specially impossible to define, but the impossibility is specially hard to detect. Definitions may be (I) unduly narrow (29-33) or (2) unduly wide (33-b 2). (I) In the definition of A as BC, B or C may be irrelevant. If there are several instances of A, probably there will be some in which B or C is absent and the badness of the definition will be noticed. But where there is one instance only, the badness may easily escape notice (cf. I036b 6). (2) If you define an individual A as BC, then if there are like individuals the definition will apply to them also and will be seen to be a bad definition of A. But if, like the sun, A is unique, and there are no other things to which BC is applicable, you may easily not realize that there might 6e other such things, and that you have defined not • the sun' but only • sun '. Definition of the individual is inevitably liable to both the errors here described. (1) You may be sure that certain attributes are not essential, but since you do not know the whole history of the individual you cannot be sure whether certain others are essential or not. (2) No series of marks will exhaust the nature of the individual, since every series of marks marks off not an individual but a kind. Thus the individual is indefinable, and if Ideas are individuals, they are indefinable. rl7. ,;sImIP 03" ItP1JTCU. Aristotle has not made the remark in question before, but he has treated the impossibility of definition as less obvious in the case of eternal entities, since he has given several arguments to prove it (8-27) over and above the general arguments against the definition of individuals (1039b 27-1040a7). Cf. esp, 1040• 17. 31. "UKT~KPU+~S, apparently a coinage of Aristotle's on the analogy of Parmenides' VVKT,4>a,ES tPWs for the moon (fr. 14). 3rl. 4ft may very well be understood without being actually inserted. Asc. has it in his interpretation. but there is no reason to suppose that he read it. b I-rl. elM' ~" ..• I"'Kp'~. I. e. the sun though unique is as much an individual member of a class of suns as Cleon is a member of the class of men. rl-3. l'lrll S~m T£ •.• tSc!a.s j is tacked on loosely. • If the definition of the individual (and therefore of the Idea) is not open to these objections, why do the Platonists never produce a definition of an Idea? '

"+avn.

Two wro1lg 7)leWS about substallce (ch. 16). I040 b 5. (I) Most so-called,substances are potentialities-the parts of animals (which do not exist separately, and even when 5Cparated mM

P

118

COMMENTARY

are merely matter) and the elements; they are not unities but merely aggregates till they are fused into one. 10. One might suppose that the parts of living things and the corresponding parts of the soul are both, existing both actually and potentially, because living things have sources of movement in their joints so that some animals live when divided. Yet they exist only potentially when they are united by nature-not by force or by adhesion, which is a malformation. 16. (II) Since the meaning of' one' answers to that of' being', and the substance of what is one is one, and things whose substance is one are one, unity or being cannot be the substance of things, any more than being an element or principle can be so; we have still to ask what the principle is. 81. 'Being' and 'unity' are more substantial than 'principle' or 'element' or 'cause', but are not substance, becauE'e (a) they are common, while substance belongs only to itself and to that which has it. Further (0), one thing cannot be in many places at once, while what is common can. No universal, then, exists separately from particulars. . 87. The believers in Forms are right in saying the Forms exist apart if they are substances, but wrong in saying that the one in many is a Form. Because they cannot say what the eternal substances are that exist apart from sensible particulars, they make them the same in kind as the perishable things which we do know, merely adding 'itself',-' the horse itself', &c. 34. But, even if we had never seen the stars, they would have been eternal substances apart from the things we knew; and so, even if we do not know what eternal substances there are, yet there must be some. 1041& a. No universal, then, is a substance, and no substance is compounded out of substances. In this chapter Aristotle abandons his own fourfold list of the things that might be considered to be substance (ch. 3 ad "nil.), and returns to criticize the popular views about substance expressed in ch. II according to which the parts of living things, and the four elements, are among the things that have the most obvious claim to be substanc~s.

I040b 6. au"'".e" eterC, are not actual substances but components capable of contributing to the life of the whole body. 6-8. 'For none of them is sepaTately existent; and when they are separated from the living body, then too they are existent, all oflhem, only as maller.' The band while it is in the body is 110t separately

Z. 16. I040b 6-13

21 9

existent, and therefore not a substance but simply a material constituent, isolable in thought, of a substance. And when removed from the body, then too it is not a substance, with an activity of its own, but a mere collection of bP.O/OP.~pr" skin, bone, and flesh. Cf. 1035 b I7, G.A. 726b 22. 8. Kal yij Kul'lfup Kul 4~p. Alexander and Bz. take these words closely with Il>~ 11A"I, but a comparison with 1028 b 9, 10 shows that they are co-ordinate with Ttf T~ papla TWV {.ewv. Bz. has to suppose that T~ is answered by p.&>..urra S' (I. 10). 8-10. ol'lS~v yAp •.• lv, i. e. a part of an animal body, e. g. a hand, is unified into a genuine whole only by the form of the living body to which it belongs-otherwise it is simply a collection of diverse materials, cf. De Gen. el Corr. 3ub 31 S/O Kat T((JV~WTO~ p.allov I1v SQt(lW ~rval ETt CTa.~ Kat OCTTOVV ~ x~l.p Kat {JpaX{rov. g. a",p~, which is much better attested than b oppO~, is Aristotle's regular example of that which has not organic unity (IO.pb 12, H. 10H& 4, 1045& 9, M. 1084 b 22), while &pp6~ does not seem to be used in this way. The latter reading is no doubt due to 71'~"'fJ.O, but both the plural a~Twv and the usage of 71'plv show that 71'pl.v fj KTA. goes with OMfV 'Yap a~wv tv (CTTLV, not with olov CTrop6~. 71'ETT~tV, a regular Aristotelian term for maturing or working up (cf. Bz. bldex 590& 61591& I), is applicable both to the elements {cf. A. 989& 16) and to the parts of the body. II. 'lfApeyyus 41'+w y£yveriuL. Alexander's interpretation p.&>..ICTTa Sf 1nroAtf{JOI I1v Tt~ Ta. TWV f.p.lf!Vxrov p.oPLa, ••• bp.olro~ Sf Kat rij~ ';vx:ij'>, 71'tfp"Y'f1J'i TOV Kat f.v~P'Y~ly. P.ETa. TOV OAOV OVTa olJCTla~ a~a. AEY(lV Kat SvvtfP.EL (535. 27), interprets 71'a.p€'Y'YV~ in an impossible way. So does Bz.'s 'Yl-YVEcrfJal CTXESOV oVTa d.P.rpOTEpro~ Kat (VTEAEXEU[. Kat llvvap.(I (the comma being omitted). 71'&.pry-yv~ does not mean CTXESOV. Like O"livry-yv~, it is used adjectivally rather than adverbially, and (where it does not mean 'near' in place or time) means 'closely related' (Top. 167& 5, G.A. 769b 27, Pol. 127Ib 20). Probably the best translation is' above all one might suppose the parts of animate things and the parts of the soul nearly related to them to turn out to be both, i. e. existent both actually and potentially'. An alternative translation is: 'One might be specially tempted to suppose that the parts of the animals come-to-be more or less on the same level of being (7I'UPE'Y'YV'» as the parts of the soul, thus possessing, both taken together, a being which is actual as well as a being which is potential'. Ill. OVTG KllllVTe}.Exe£q. Kill SUVA".", i. e. existing actually, since they can initiate movement by themselves, and potentially, since they are absorbed in the life of the whole soul and the whole body. 111-13. T~ 4pXAs .•. KIl!,1fOLS. For the ball and socket joint as the bodily instrument of motion cf. De An. 433 b 19-27, M. A. 698& 16-1> 7. 13. SL~ lVLu t4iu SLIlLpou".evu tn, i. e. some insects and many other animals oCTa p.~ {fJJTIKa. Alllv (wi, e. g. tortoises, as well as some plants (De A,1. 4111> 19, 413b16, P.N. 467a18, 468&25, 479"3, P.A. 682& 5, b 30, I. A. 707b 2, G. A. 731& 21).

:uo

COMMENTARY

15. cru,,+UCr«L. Aristotle's use of this word is rather puzzling. Sometimes it means complete normal organic union (Phys. Zl3&9, 227& 23, .1. 101.b 22, K. 1069& 12, A. 1070& I I); sometimes as here it is applied to abnormal unions (e. g. atresiae, G. A. 773& I., 16, 25, • Siamese twins', ib .•, S). Insects are one CTVp.q,vun (De Iuv . • 68b 9) ; the parts may be said to exist actually just because the whole is not fully one. 16. ,.0 Iv }.iyncn .:'Jcnrcp Ko.l TO 01', i. e. these are the widest of all universals, common to all things whatsover, B. 99Sb 2 I. They cannot be the substance of things, for then all things would be one. IU-IIII. "auo.. ~v ••• Cl"T~OV. One of the reasons which Alexander gives for this (536. 35) is doubtless what Aristotle had in mind-that being and unity belong to a thing in itself, while it is a principle, element, or cause only in relation to something else. 115-117. 'T~ TO Iv .•. xwp£~. 'Further, that which is truly one cannot be in many places at once, while that which is common (like being or unity) is in many places at once. No universal, then, can be an individual existing apart from its particulars: 38. TClUTCl~. as if Aristotle had said TaL~ q,(JaprQL~ in the previous clause. 34. .ni"Q has here the wider sense of' word' (cf. Top. qSb 36, De Aud. SO.b 30, M. AI. I202 b IS), not its regular Aristotelian sense of 'verb '. 1041& I. av .•• ~crClV, 'they would have been '. Aristotle's argument is: There may be eternal entities of which we do not know. The Platonists, then, were wrong in saying' there must be eternal substances (se. to explain the sensible world and the fact of knowledge), but we cannot think of any save such as are akin to sensible substances; the eternal substances therefore are of this nature'. Aristotle usually attacks the Ideas on the ground of their transcendence. Here he admits that there are eternal, non-sensible, transcendent substances, and objects that they should not be hastily identified with the universal characters in sensible things. But the two criticisms are not inconsistent. They are two ways of putting the same point, that the Ideas are held to combine characteristics that are incompatible, immanence and transcendence. There are immanent intelligiblesthe universals in the particulars; and there are transcendent. intelligibles-God and the beings that move the planetary spheres (A.l073&33)i but those that are immanent must not be confounded with those that are transcendent. 3. T£"C~ eter£.. must mean 'what the non-sensible (IO.ob 31, 32) eternal entities (as distinct from the stars) are '. 3-S. 3n "t" 03..... o..,Siv o"'cr£o. sums up IO.O b 16-10.1& 3 i olIT' ... o"'crwv sums up 10.ob 5-16. Schwegler tries to find a connexion between the two parts of the chapter in the fact that universals, like the parts of a substance, exist only 8wa.p.c& (e. 1051& 2 i cr. the conception of genus as ~>"7J)' But Aristotle would have pointed out this connexion if it had been in his mind.

"'V

au At the same time these words sum up the general conclusions of chs. 13-16, which are evidently thought of as forming a single section of the inquiry into substance. Cf. r 3. 1°39.' 4-17.

The true view oj'substance; substance isform (ch. 17). 1041 • 6. Let us approach afresh the question of the nature of substance; we may thus learn about the substance that exists apart from sensible things. We start with the fact that substance is an originative source and cause. 10. • Why?' always means 'Why does A belong to B ?' , Why is the musical man a musical man?' means either ' Why is the man musical? ' or something different from this. 14. Now' Why is a thing itself? ' is meaningless; for before we ask , Why?', the facl must be evident, and the fact that a thing is itself already answers the question why the man i"l man or the musical musical-unless one prefers to answer 'because a thing is indivisible from itself'; but this is a stock and concise answer to all such questions. :ao. The real question is, Why is man an animal of such and such a kind? i.e. Why,is A true of B? Why does it thunder? = Why is noise produced in the clouds? :a7. Evidently we are seeking the cause, i. e. (speaking abstractly) the essence, which in some cases is an end (e. g. in the case of a house), in some a first mover. The latter is looked for only in cases of becoming and perishing, the former also in that of being. a:a. The object of inquiry escapes notice most when subject and attribute are not distinguished, e. g. in the question' What is man? ' We must make the question articulate; otherwise it is hardly a real question. b 4. One really asks, 'Why is this material a certain thing?' 'Why are these things a house?' Because the essence of house is present in them. Thus we are looking for the cause by reason of which the matter is something, i.e. the form; and this is substance. Evidently, then, the method of inquiry into simple entities is one different from that described above. II. The syllable is not identical with its letters, nor flesh with fire and earth (for after the dissolution of the elements the whole will not exist though the elements will); they involve something else as well. Ig. Now (I) if this is an element, flesh will consist of fire and earth and this element + something else, and so ad injini/u",; (a) if it is

222

COMMENTARY

a compound, it mUFt have more than one element, and the same difficulty will arise as in the original case of flesh or the syllable. 1.15. Yet this • other' is something. not an element, and is the reason why this is flesh and that is a syllable. This is the mbslancf of things (for it is the primary cause of their being). Since all substances are held together according to nature and by nature, this' nature " which is not a material element but a principle, seems to be substance; the eiemm/s, on the other hand, are the material constituents of things. Of the four claimants to the title of substance (lo28 b 33) Aristotle has now discussed substratum, and shown that it in its most obvious sense (viz. matter) is not substance (ch. 3). He has discussed essence from many points of view, but without reaching any very de6nite conclusion as to whether it is substance (chs .•-12). He has discussed the universal (and implicitly the fourth claimant, the genus), and shown that it is not substance, and has shown further that substance cannot contain actual substances as its parts (chs. 13-16). He now makes a fresh start and essays to show that essence is substance, using as his guide the principle that substance must be causal, something that answers the question • Why? ' 1041a 6. Tl ••• Kal 6_itS., TL, • what, i. e. what kind of thing '. The two expressions do not seem to stand here, as they sometimes do, fer genus and differentia respectively. 11-1.14. This difficult passage may be paraphrased thus:-The question' Why is the musical man a musical man?' is either (I) of the type just mentioned (I. II), viz.' Why is the man musical?', or (2) it is different from this. In this second case, it is of the type 'Why is a thing itself?' and it is no question at all. For when we ask w~ a thing is so, we must already know Ihal it is so. But that a thing is itself is already sufficient answer to any question of the type' Why is a man a man? '; in such a case the question • Why? ' is not really a further question at all. • Because a thing is itself' is the only answer, unless one prefers to put it in the form • because each thing is indivisible from itself, and this is what being one means' But this is an answer which meets all such cases and is a • short and easy way' with them, and its existence does not show the parlimiar question of the type • Why is man man? ' to be a sensible one. But the question • Why is man such and such a kind of animal? ' ;s one which may fairly be asked. It is of the type mentioned in I. J I ; it asks 'Why does A belong to B?', and assumes that it does belong. I. e. of the two alternatives stated as to the meaning of the question' Why is A A ? I Aristotle rejects the second and adopts the first, that it really is of the form • Why is B A ? ' Christ treats Sti yc\p (I. J 5) ... 6 l'0uaLK~i l'ouaLKcSi (\. 18) as parenthetical and connects 7r>...;p, El TL~ KT>". with ofJ8iv lOTL '7lTliv. But it can hardly be right to disconnect ih-, ci8uuPETOV 1TPO~ ain-o lKaOTov thus from aw;" OTt aw6, for which it is an aiternath·e and fuller

z.

17. I04Ia

6-33

expression. The paraphrase above indicates sufficiently how 1I"A~JI should be taken. 13. Bz. thought with Alexander that TO etp'I..,lIvov t'lTeiv must be TO {"1ni:JI IlLA Tt IOTLJI and therefore proposed in this line IltA Tt ~ tJ.J16(JW1T0'; p.01Juuco<; tJ.Jl8pw7f'0'; p.oVULKO<; lOTW. But this is bad grammar, and further TO dp7Jp.wOJl {7JT(tJl means just the opposite of what he supposes. It refers to I. 1 I, and means asking why B is A, not why A is A. It is possible, however, that we should read with Prof. Joachim IlLA Tt b p.OVULKO<; C1J18(JW1T0'; p.01Juuco<; d.Jl8(JW1T0<; lOTW, in which case TO (lfnlp.(JIOJI refers to 1. 1 z. The sentence then, as Prof. Joachim admits, becomes rather pointless; but he cites An. Post. 93& 3-6 as a parallel. 15. BIL yap TO aTL Kul TO etvuL .)W«PXIIV ~}.u se. when the IlLA Tt is being inquired into. Cf. An. Post. ii. I, 2. !Z4. Aristotle means that BLa T[ I3poVT~; resolves itself into IltA Tt "'oq,o<; ,,/lyvlTaL lJl TOtO; JI(q,(UW ; !Z8. TOUTO B' 1O"T1 ,.0 T( ~v ItVUI, 41<; dWILV }.0YIKW<;. Alexander believed these words to be spurious, and a premature anticipation of the doctrine stated in b 6 If. The suspicion is unnecessary. The doctrine is that the cause of the inherence of a 11"0.80<; in a substratum (e. g. of noise in clouds) or of a quality in certain materials (e. g. of the shape characteristic of a house in bricks and timber) is always-to state the matter abstractly (AOYLK(d<;)-the Tt ~JI (IJlaL or definition of the union of substratum and 11"0.80<;, or of materials and quality. But ill some cases this definition expresses the final cause-e. g. a house is defined as a shelter for living things and goods (H. 1043& 16, 33); in other cases the definition expresses the efficient cause-e. g. thunder is a noise in clouds due to, i. e. produced by, the quenching of fire (Al1. Post. 93 b 8, 94& 3). In other words the formal cause is not a distinct cause over and above the final or efficient, but is either of those when considered as forming the definition of the thing in question. Similarly in An. Post. ii. I I the formal cause is identified with the efficient (94 b 18-21) and even with the material (there treated as = the sum of the necessary conditions of a conclusion) (94" 34). 3I-8!Z. TO ..,iv TOIOUTOV aLnov, the efficient cause; 8«Tlpov BII, the final. It is when we are inquiring why has so-and-so come into being, or ceased to be, that we look for the d.pxJI KLV1]u(II)<;, the origin of the movement which brought the thing into being or destroyed it. On the other hand we may ask not only for what purpose has so-and-so come into being or ceased to be, but also for what purpose it exists. It would be possible to take TO p.~JI TOWVTOJI alnoJl to refer to the final and efficient causes, 80.T€po!I III to the formal, but the Greek does not so naturally suggest this. 33. The vulgate reading is p.~ KaTaAA~Aw<;. KaTdll7JAo<;, KaTaAA~Aw<; are not found in the genuine works of Aristotle, and when they occur (in later Greek) they mean' corresponding', 'correspondingly', which does not suit the sense here. lJl Toi:<; p.~ KaT' d..U.~AwJl A(,,/Op.("OL<; gives the right sense, ' where one term is not predicated of another '. For

awo

awo,

aVTa,

COMMENTARY ICa.T' ru~Mw

= ' one of another', not' of one another', cf.Inr-' 8A)':'1M.,

Cat.

Ib 16. b I. The

general line of thought in the chapter is as follows: Substance is a cause (8 g). Therefore, if we can find out what in general is the cause of things, the answer to the question 'Why?', we shall have found what substance is. Now' Why?' always means 'Why is B A?' We have therefore only to find the general nature of the answer to this question. In general it is a statement of form or essence. Form or essence, then, is substance. It has been thought, therefore, that a reference here to the question , Wlzat is man?' is irrelevant. Alexander interprets Tl in this line as meaning &A Tl, which it cannot mean; Bz. with greater probability f!roposes to read 8,A Tl, which occurs as a marginal reading in E {but has probably made its way there from Alexander's commentary). It seems, however, that Aristotle's meaning is as follows: The object of our search, the fact that it is the formal cause we are looking for, is concealed when we use a simple expression, un analysed into subject and attribute, like' man '. We then ask' Wlzat is man?' But if we analyse our question, we find that it means, 'By reason of what is this combination of bones, sinews, &c., a man?' (8LA Tl T48c ,.oaf). And the answer is, 'Because it is informed by the form of man, the human soul '. Until we have performed such an analysis, our question • shares the character of a genuine and of a meaningless inquiry' (II. 3, 4); i. e. it is not yet clear whether we are asking a genuine question. For the reduction of the question' What?' to the question ' Why?' cr. An. Post. 8g b 39-9081, 90814-21. But in that work it is only the definition of attributes that is reduced to the question ' Why do they occur?', whereas here the definition of man seems to be similarly reduced. 4. 8fi EX.LV, 'one must know'. Cf. Bz. Index 305b 46. 5. Christ's 8,1\ TC TC is a better emendation of 8LA Tl than Bz.'s Ta.81 8LA Tl, and seems to answer belter to Alexander's interpretation (541. 31). Cf. ~ T{ lf7T'LV, I. 8. Prof. Joachim thinks the manuscript reading may be retained and translated 'why the matter is there-what it exists for'; and suggests alternatively 8LA Tl (-roBl). 5-7. 'E. g. Why do these materials form a house? Because what it was to be a house (the essence of house) is present in them. Similarly this matter, or rather this matter having this form, is a man: It does not seem necessary to read &181 l}(Ov with Bz. for To81 lxov. The form of man is To8. lv Tcji8. (1030b 18), and the body can therefore be said lXILVT'o8l, to contain the form (cr. .:1. 1023" 11-13. 23-25). 7, 8. What Aristotle has been illustrating in II. 4-7 is not the cause of the matter but the reason why such and such matter constitutes such and such things. ,.0 a.lnov ~ ;;>"v; must therefore not be taken alone, but with ~ Tl lf7T'LV, 'the cause whereby the matter is some definite thing '. To get this result it is not necessary, with Christ, to regard -rWro • • • .l8o~ as spurious; it is enough to treat it as parenthetical.

9-10. +uvrp~v ••• TOL06TIIIV. Since' Why? ' always means' Why is B A?', we cannot ask the question' Why A is' if A is a pure form, not a complex of form and matter; such entities must be understood in some other way, sc. by that intuition which is ' like touching'. For this cf. 0. 1051b 17-1052& 4 nn., De An. 430& 26, b 26-31. • 10. 'TfPOS Tp&1I'OS rijl t,,~O'rflll, 'another method of inquiry than that described above '. II-!&7. In this sentence not even the clause beginning with lre{ is ever completed; the parenthesis 1j 8~ tTVUa.p~ /(TA. is so long that the original construction is quite forgotten. 17. For the description of the syllable as 'Trp&v TL apart from the etters cf. Pl. Theael. 203 K. 19-515. rt TOtvuV ••• crullu"~I. 'Let us suppose that this principle of union must be either an element or a complex of elements. If it is the first, this leads to an infinite regress (ll. 20-22), and so too if it is the second (ll. 22-25). Therefore it is neither.' •• For iIC crTOLxetou (singular) cf. H. 1043b 12. 513. " IKrLvo u.na 'eFTUL, ' or else (if it were composed of only one~ that one would be the thing itself'. For ~ = el & p.~ cr. E. N. 1170

17,0. 1050& 14 (1). 519. &crAL o4O'(uL (dut), KUTm +6O'LV Kul +60''' cruve~KAcrL.

For Aristotle's tendency to restrict sensible substance to natural as opposed to arlificial things cf. H. 1043& 4, b 21. On the other side cf. A. 1070& 5. The reason for the restriclion is that art does not make new substances but merely imposes new qualities, quantities, etc., on sub· stances. The statue retains the substantial or essential nature of wood, house, etc. And qua wooden it is a natural substance; it is only qua having such and such a shape that it is artificial, and in this respect it is not a substance. 30. [lCul] au.,.q ~ ,pVfTLr. Ab reads ML, EJr TLcrL, both of which are impossible. Probably ML is an emblema due to Alexander's paraphrase ,pavqXJv ML, and TLcrL and /Cal are attempts to emend ML. 30-31. u~ ~ +dcrLl ••• ~ leFTLV 04 crTO~xeLov c1).}.' c1px~. i. e. the t/JwLr described not'in .:1. 1014b 27 but in ib. 36, that which is not matter but form. For the difference between O'TOLXfiov and. clpX~ cf. .:1. I, 3.

COMMENTARY

226

BOOK

II

Sensible substances; mailer (ch. I). I04Aa 3. We proceed to sum up what has been said and to bring our inquiry to its conclusion. We have said that (I) the causes of substances are the object of our search. 6. (2) Some substances are generally recognized, i. e. the physical, viz. the elements, plants and animals and their parts, the physical universe and its parts j while certain thinkers treat the Forms and the objects of mathematics as substances. IA. (3) Other substances are established by argument-the essence, the substratum I the genus, the universal; with the two latter are connected the Ideas. 17. (4) Since the essence is substance, we had to discuss definition and therefore also what parts are parts of the substance, and whether these are also parts of the definition. m:. (5) Neither the universal nor the genus is substance; the Ideas and the objects of mathematics must be considered later. Sl4. We must now discuss the acknowledged substances, viz. those that are sensible, all of which have matter. The substratum is substance, and this is (I) in one sense the matter (which is potentially a 'this '), (2) in another the definition or shape (which is a • this' and is separable in definition), (3) in another the union of these, which alone is subject to generation and destruction and is separable in the full sense (while only some of the substances in the sense of definable essences are separable). 3Sl. Of these three, even (I) mailer is substance, for in all change there is something that underlies the change, whether it be change of place, of size, of quality, or in respect of substance {generation and destruction}. b 3. The last kind of change involves all the others, but either one or two of the others do not involve it; a thing need not have matter for generation and destruction if it has the matter or potentiality for local change.

The

chapt~r

IO.pa 4-6

"

,. "

" "

opens with a summary of the contents of Book Z. refers, roughly, to Z. 1,

6-12" 12-1;' 17,18 18-21 21,22

"

t,2,

"

" " " "

"

"

"

"

"

"

3. I028 b 33-36,

4-6,

12,

15,

10, I I, 13, 16. 1040 b 16-104 1&

5.

It is noteworthy that the summary makes no reference to Z. 7-9, which we have already seen reason to regard as not belonging to the original plan of Z. The doctrine of those chapters is, however, referred to below in I. 30. 104G& 3. cru).).0yLcrucreCU seems to have its original meaning of 'reckoning up'. 'We must reckon up the results of what has been said and compute the sum of them.' Cf. E, N. 1101& 34 0p4v.

S. Tt1).).CI TA c111'M aWp.ClTa, cf. 4. 1017 b II, Z. 102Bb II. What simple bodies other than the four elements can Aristotle mean? The answer is given by De Catlo 26Bb 27 AfyIlJ 8' cl.7rM ••• otov.,rop Ka2 yiiv Ka~ T4 TOWIIJV ~r87] K& T4 uvyym} TOWOt~. 1. e. Trua is the various species of fire, air, water, and earth (T4 uvyym) TOWOt~ = air and water, cf. Meteor. 339& 2B). 10. c\ 04paveS" 'the physical universe', as in Z. 102Bb 12. SI. Christ is right in dispensing with the comma after TaW4, Tawa = T4 ~~ olJCT{a~ plp7]. Christ's emendation of ITL to (eTTL is unnecessary. For (TL TO{VW cf. A. 1071b 20. sa. ilCTTEpOV CTKE'll'Tc!OV, in MN. sS. cU).IIJS S' c\ ).cSyos Kal " P.op+tj, cf. Z. 1029& 2 n. 29. For the description of form as TcSSE TL cf. 4. 101 7b 25 n. 30. o~ Yc!VECTLS p.cSvou Kal .80pc( ICTTL, cr. Z. B. 31. at p.~v at S' oil. The only form that is XlIJpteTTOV cl1l'>'w~ is vov~. cr. A. 7. 9, De An. 413b 24. 429b 5,430& 22. Reason exists in God, in the spirits of the spheres, and in man. 32-b 3. Aristotle's classification of change into four kinds is partly anticipated in Theaet. IB I D, where Plato distinguishes d.llolIlJCTt~ and 4>0p4. b !I-3. vOl' P.EV ••• CTTc!P'lCTLV.

vvv p.iv refers to the time when a substance is being destroyed, 1I'&.\.tV 8' to the time when it is being produced. What underlies or undergoes destruction is matter qualified by a positive form, i. e. a T08E Tt; what underlies generation is matter qualified by a privation. 4. f\ P.L~ f\ Suo~v. Aristotle leaves it open whether ;;>'7] dUown/, as well as ;;>'7] T01l'tKJ/, does not imply;;>'7] YEVI'1I'"1; in 0. 1050b 17 he says definitely that it does not. His words here ·suggest that ;;>.7] alJ~ implies ;;>'7] y~, and this is confirmed by De Gm. tI Corr. i. 5 (e. g. 322& 6, 7). On the relations between the various ~>'aL cf. Z. 10 36& 9 n. 5-6. o~ yAp ... 'XELV. The stars have i1A7] T01I'LK~ but not i1>'7] y~, 10H b 7, A. 1069b 26. 6. iJ).'Iv", TO'll'LKtlV. The phrase is a ltapax lego1llmon in Aristotle, cr. i1>'7] KaT4 TWOV KtV11"1, IOH b 7, i1>'7] 11'08& 1I'0l, A. 1069 b 26.

but

a>.'Iv, .• YEVVTjTtjV, not matter that can be generated (matter is eternal) but matter which can take on a new substantial form. 7. TO p..q cl1l'>'W~ y{"(JIcCT8aL is applicable to the three kinds of change other than generation or destruction, viz. 4>0p4, a;;t,crL~, d.llO{IIJCTL~,

228

COMMENTARY

in which a thing does not come to be, simply, but changes its place, size, or quality. The distinction in De Gm. el Corr. i. 3 between c171'A1j 'Ylv£(Tt~ and 'YlV£(T{~ 'TL~ within the category of substance does not seem to be in Aristotle's mind here. 8. lv TOLS +ucnKoLS dp1JTClL, Phys. 225 a 12-20, De Gen. eI Corr. 317a 17-31. For the citation of other works than the Physics under the title 'To. t/JVULKa. cr. Bz. Index I02 b 9.

FORM OR ACTUALITY (chs. 2, 3). The van'ous {JIles

of differenlia

or consliluliveform (ch. 2).

I04!Zb g. Since substance as matter, i. e. the substance that is substance potentiaJly, is generally recognized, we next (2) discuss the substance, as aclualt'{JI, of sensible things. Democritus seems to think there are three differentiae-shape, position, order. 15. But there are many; things are characterized by composition (e. g. by being mixed), by being tied, glued, nailed; by position, time, place i by the sensible qualities such as hardness and softness, some by some, some by aJl of these, and in general by excess and defect. !Z5. 'Is' must therefore have just as many meanings; for a threshold , being' means being so situated, for ice it means being so solidified; the being of some things, e. g. a hand, will be defined by all these characteristics. al. We must grasp the kinds of differentia, for they will be principles of being; e.g. excess and defect, straightness and crookedness, mixture. I04aa !Z. Since substance is the cause of a thing's being, it will depend on these differentiae what kind of being the thing in question has. None of them is substance even when coupled with matter, yet they are analogous to substance; as in the definition of substancell what is predicated or the matter is the actuality, in other definitions it is what most resembles actuality. 7. E. g. to define 'threshold' we say 'wood or stone in such a position' (adding sometimes the final cause). I!Z. To different matter there answers a different actuality or definition-composition, mixture, &c. Those who define a house as ' stones, bricks, and timbers' are stating the potential house; those who say 'a covering for animals and goods' state the actuality; those who combine both statements give the concrete substance.

H.

I.

I042b8-2. 10438.14

229

lU. Of the last kind were the definitions approved by Archytas, e. g. , still weather is absence of motion in a large extent of air'. !l6. Sensible substance, then, is (I) matter, (2) form and actuality, (3) the union of the two.

1042b n-15, cf. A. 985b 13-19 nn. 16. It is curious to find ICpO.CTtt; treated as a kind of CTvv8€CTtt;. Elsewhere the two are opposed as one might oppose chemical com· bination to mechanical composition (De Gen. eI Corr. 328B 8, N. 1092B 24,26, and cf. 1042b 29 n. with 1043B13). But cr. De A,l. 407b 30 T"ijv dpp.ov[av ICpacTtv ICa~ uVV8€CTW fl,all'T[wv €Tvat. uVV8€CTtS may in fact be used as the genus induding ICpaCTtS, though usually it means a species opposed to it. !l4. T4 ".~v lV£OLS TOUTWV T4 S~ 1I"&en TOUTOLS. All physical bodies are characterized, according to Aristotle, by dryness or wetness (which form one of the 7f'pWTat lvall'Tto.n7T€s), and presumably also by density or rarity. Every WptCTplVOV CTWp.a, i. e. every actual sensible body as distinguished from the pure elements, is characterized as well by hardness or softness (llft/eor. 382B 8). Kul iI~ws T4 ".IV ~1I"Epoxii T4 St l~~E£"'El. This applies only to TO. Tois TWV alu8-rrrwv 7f'Ii8€CTW (I.

2 1 ).

!l7. We should perhaps read ICPVCTTOA>"'I! with one manuscript of Alexander, but KpUC7Ta.~~OV is not impossible. 29. T4 ".IV ".ifl'x9a.l, TO. S~ KEKp&ageu. ICpaCTts is properly a kind of pUtt;, the pi~ts of liquids (Top. 122 b 26-31). pUtS is probably here used in a narrower sense = the chemical mixture of solids. 33. T4 TI{j ".&~~ov, i. e. those that are characterized by degree, the 7f'a.8'YJ TWV a.lCT8TfTwv, cf. 21-25. 1043B!I. " OllC7£U utT£u TOU EtVUL, cr. Z. 17. 4-5. OllC7£U ".IV o3v ••• iKOC7TIt'. I. e. none of these differentiae is substance either (I) when taken by itself or (2) when coupled with matter; but it is what is analogous to substance in each case. The differentiae mentioned are in categories other than substances-in that of txnv (uV;·8€UtS, 8(CTpOS, IColl'YJ, ')'op,pos), of IC(iu8aL, of 7f'OT€, of 7f'OV, or of 7f'OtoV (TO. TWV a.iCT8-rrrWV 7f'a.8'YJ)' They indicate not the inmost nature of that to which they belong but a mode of arrangement or other characteristic which may be only temporary. Therefore the things characterized by them-( I) artefacta, (2) states of a substance (ICpVUTa.llov, and perhaps 7f'V(vp.a, cr. Meleor. ii. 4), (3) parts of living things-are not substances but only analogous to substances in that they contain elements answering to matter and form. For the exclusion of (I) from the dignity of substance cr. b 21, Z. 1041b 29, and for the exclusion of (3) cr. Z. 1040b 6. The reason for the exclusion of (3) is stated there. 7. ",O~LC7TU. I. e. it is more truly lv€p')'Eta. than anything else in such definitions is. 13-14. TWV ".IV yAp •.• ELPTJ".lvwv. Cf. 1042b 16n., 29 n.

33 0

COMMENTARY

!Z1. Archytas, one of the most famous members of the Pythagorean school, and a contemporary of Plato. We have· no further light than that which this passage offers on his doctrine of definition. The type of definition he approved is identical with Aristotle's nominal definition of attributes per genus et subieclum, the bpwp.o'O which is crvp.7r(paup.&. Tt d7ro8({~(IJl" (An. Post. 75 b 32, cr. 93& 22, 94& 7). !ZS. For the corruption of Ko.L into OTt cr. N. 1089b 35 n.

DistincHon between concrele substance and actuality or form. The former is generated and destroyed, the laller not. Analogy befu)een form or definition and number (ch. 3). . 1043& !Zg. Sometimes it is not clear whether a word means the concrete substance or the actuality, e. g. 'house', 'line', 'animal' a6. The two meanings have a common reference, if not a common definition. The question of the two meanings does not affect the investigation of sensible substance; for the essence pla.inly attaches to theform. For' soul' and' to be soul' are the same, while' man' and • to be man' are different, unless the soul can be calIed man. b 4. The syllable does not consist of the letters + composition; for the composition is not derived from the things compounded. The position is not derived from the threshold, but vice verla. 10. Man is not animal + two-footed; if these are the matter of man, there must be something apart from these-neither an element nor a compound but the substance. Those who describe man as animal + two-footed are omitting this, and stating the matter. If, then, this is the cause of man's being, and that is the 'substance of man, they will not be stating man's very substance. (14. This is either eternal, or perishable and generable without ever being in process of perishing or becoming. It is not the form but the concrete thing that is generated. Evidently the substances of some perishable things cannot exist separately, viz. those that cannot exist apart from the particular instances, e. g. house. Perhaps these, and indeed all things that are not formed by nature, are not substances; the nature in natural objects is the only substance in perishable things.) !Z3. Thus there is some point in Antisthenes' problem; he said you cannot define what a thing is (definition being simply circumlocution), but can teach what sort of thing it is (e. g. that silver is like tin), laS. so that composite substance, whether sensible or intelligible, can be defined, but its elements cannot, since definition predicates one thing (form) of another (matter).

H. 2. I043a 21 -

3. I043 b I I

311. If numbers are substances, it is in this way and not as assemblages of units; for (I) definition is a sort of number, being divisible. and divisible into indivisibles. 36. (a) Definition, like number, loses its identity if anything be subtracted from or added to it. 1044& II. (3) A number must be something by virtue of which it is one-else it is a mere aggregate; a definition also is one; but the principle of unity in both is commonly missed. This is natural, for substance has the sort of unity that a number, not a unit, has; it is an actuality and a definite nature. 9. (4) Formal substance, like number, does not admit of degree; if any substance does so, it is concrete substance. We have shown, then, in what sense generation and destruction of so-called substances is possible, and have dealt with the reduction of substance to number. This chapter is a collection of ill-connected remarks on various topics relating to essence and definition. 1043& 119-b 4 is a note on the ambiguity of words like 'house', 'line', &c. At b 4 Aristotle returns to the main subject. 88. 'lrOTEPOV SU4s lv I'tlKE' f\ [3T'] Suds. Cf. Z. 1036b 13-17 n. 34. OTt, I10S Bywater pointed out, is doubtless an emblema from ll. 31, 33. For the intrusion of OTt cf. Z. 1041b 30 (Ab), N. 1089& 7, Prob!. 96a& a and possibly @. 1050& 14, 1051& 30. 87. ~s 'lrpas lv, cf. r. 1003& 33 n. b II. +ux~ ,"v yap Kill +uxti Etvll' TllaTOV. Aristotle has tried to prove this in Z. 6. 4. T'vll'~v Twl S' oil. 1. e. 'being man' will be the same as man in the sense of 'the human soul', but not as man in the sense of 'the complex of soul and body'. 4-8. The reasoning is inconsecutive. 'The syllable does not consist of the letters + their composition. This is natural because the composition does not consist of the letters.' The second sentence contains a suggestion which is quite different from that contained in the first, and yo.p is unjustifiable. Aristotle rejects both suggestions; the form is O~TE UTOtXEioJl ow' lK UTOLXE{OV (1. 12). Bz. takes lK TOWwJl (1. 7) to mean 'one of the things', but the use of lK in two quite different senses is most improbable. 9. Et 6 ol1Sas flaE', cf. 104ab 19. 9-10. OI1K lK TOU ol1Sou ••• lKE{II1JS. ' The position is not made up out of the threshold' (i. e. out of the material parts of the threshold, cf.1. 7 ~K TOW"'JI ~JllUTl aVv8Eo"'~), 'but rather the threshold is constituted by the position '. II. Usually the genus is described as matter, the differentia as form, cf. A. 10Z4 b 8, Z. 1038& 6, 19. To treat genus and differentia

23 2

COMMENT ARY

as ir they existed side by side like material elements and required a third thing to unite them is un-Aristotelian. Cf. Z. 12, H. 6, where Aristotle makes the unity of essence depend on the fact that genus has no existence apart from differentia. Dittenberger therefore would omit oli8£ ••• 8i7l'ovv as an interpolation due to a misunderstanding of ch. 6, and treat bp.otw<; ••• lK({VTJ<; (8-10) as parenthetical. He has, however, misunderstood what Aristotle says. 'Man is not '~ov+8{7I'OVV but '~ov 8{7I'ovv (Z. 1037 b 12-14). To describe him as '~ov+8{7I'ovv is to treat these as the materials of which he consists, and if these are mere materials, then there must be something else which is neither an element nor composed of elements but the substance; this they omit, and mention only the matter, if they describe man as ,ljiov + 8{7I'ovv.' 12. l~(UPOUI'TES, according to AI. 553. 7, governs 'I'1]v v~:'1v. Cf. Z. 1036b 23 tl,paLp(I.V 'I'1]v v).:'1v, 'Which people name when they eliminate the matter.' What people? Alexander suggests the Platonists. But a reference to them is out of place. Aristotle is dealing in this chapter with the common tendency to describe a whole as a sum of parts or materials, omitting the principle of unity; cf. 1044 a 3, 6. Lines 10-14 form a much more consecutive piece of reasoning if lear.povVT(<; be taken to govern J. Cf. (in a similar context) De Gm. el Corr. 335ll 35 UaLpovuL "I?p TO T{ ~V (lVaL Ka~ 'I'1]V p.oprp~v. 13. Bz.'s Ka~ ollu{a<;, TOVTO a~v KTA., though it derives some support from AI. 553. I I, is not really needed. The reading of E1Jr gives a good argument: The principle of union is the cause of being. This (the cause of being) is substance (cf. a 2) . .'. In omitting the principle of union and naming only the matter they will not be naming the substance itself. 14. The omission of oll in A b AI. is due to the misunderstanding of l:) UaLpovl'T(<; 'I'1]v VA7JV AEYOVULV (\. I 2). 14-16. ~ tltSLOI' ••• ylYI'£aeCu. Cf. E. 1027" 29 n., Z. 1033b 5-6 n. 16. Iv &~~OLS, Z. 8. 17. 'lrOL£LT(U TOSE, YlYVETCU S~ TO lK TO~TIIIV is pleonastic, and there is a good deal to be said for Bz.'s 7I'OUI. £i<; -r08E. Cf. Z. 1033b 10. 18. TO~TIIIV, i. e. matter and form, cf. II. II, 12. 18-19. Et S' £tal ••. S~~ov. In the long run it appears that for Aristotle reason is the only XWPLUTOV (l80<;. Every other form iii the form of a certain kind of matter and inseparable from it. 19-21. 'Ir~~1' ••• UKEUOS. Cf. Z. 1033 b 19-21. 21-22. OUTE TL ••. auvlaTt)K£V. cr. a 4-5 n.~ Z. 104 I b 29 n. 23-25. t:luTE ~ cbropla ... lXEL TWa. K(UPOI'. Aristotle has said (II. 10-14) that if the genus and differentia are treated as the matter of the thing defined, the definition must miss the essence of the thing defined. , Thus', he continues, ' there is a certain timeliness in the Antisthenean doctrine that definition is impossible, that any definition must miss the essence of its object.' Lines 14-23 must be regarded as a digression. la4. ot 'AI'TLaelv£LOL Kul ot OUTIIIS tl'lrCl(S(UTOL, cr. ~. 1024b 32-34 n. The view of the Antistheneans seem!; to be that which is referred to

H. 3. I043b 1 2 - I044a 2

233

in PI. Theael. 201 E-202 c, viz. that simple entities cannot be defined but only named, and that complex entities can only be defined to the extent of naming their simple elements, i. e. by a definition which contains indefinables. Definition is an cSvofta'TWV CT1Jp:lrAoK~. It explains its subject only by reference to elements themselves a>..oya. Ka.l dyvWOTa., and is thus but a AO-YOi fta.KpOi, a diffuse and evasive answer to a question. (For >..6YOi ftaKpOi cf. N. 1091n 7 n.) Hence simple entities (of which silver is taken as an example) cannot be defined at all, but only described as like certain other simple entities. 29. T~t; C7uv8lTOu. Uv TE a.LC78YJrlJ lBV TE V01JrlJ What is definable must in any case be a universal. The definable senszoie composite will be a term like 'man', which is analysable into a certain form and a certain kind of sensible matter (Z. 1035b 29). The definable tnlellzgzole composite will be a term like' line " which is analysable into the form 'two' and the intelligible matter' length' (Z. 1036b 13-17. cf. 1035&

n.

20n.).

The analysis of' man' into' two-footed and' animal " also, would be an analysis into form and' intelligible matter', in another sense of that term ( 10 45" 34). lBV TE a.ta&YJrlJ lBV TE vOYJrlJ It is certain that Antisthenes, who was an out-and-out sensationalist, meant by a complex a thing which could be divided into senslole parts or elements. Cf. Theael. 201 E 'Ta 7rpilYra. O~OV7f'EPElIT'TOLXE'ia., Ie ~V ~ftE'ii 'TE CTVYKE{ftE()a. Ka.l 'TaAAa.. Aristotle interprets him in the light of his own doctrine of ~A7J v~. 31-3l1. TO ".lv, the genus; TO Sl, the differentia. Cf.~. 1024 b 8, I

n.

Z. 1038&6, 19.

32-1°448 14. This is a section, not closely connected with what precedes, in which Aristotle, while pointing out that substances are not numbers in the way in which he thinks the Platonists supposed them to be so, shows that there are certain analogies between substances and numbers. They are, he thinks, mere analogies, but they account for the attractiveness, to some minds, of the reduction of substance to number. 33. OUTwt; ELC7£ KT~., i. e. they are not simply aggregates of units but have a principle of unity which keeps their parts together. 34. t:lt; TLVEt; ~lyouC7L, se. the Pythagoreans and Platonists. Cf. M. 6, 7. Aristotle seems rather confused about the view he is attacking. He here describes it as the view that substance is like an aggregate of units; in 1044& 8 he describes it as the view that substance is a sort of unit (unless indeed he is there referring to the view of some other thinkers, perhaps a different set of Platonists). It is rather hard on the Platonists to attack them for treating the essential substllnce of things as an aggregate, if (as seems to be the case) the doctrine of inaddible numbers was meant just to avoid this implication. But Aristotle does not seem to understand the' inaddible numbers '. Cf. M. 6, 7 nn. 1044. 2. Ka.l TOV dPL8".ov BEL EtVa.£ TL ~ Eft;. Bz. proposes T~ dpL()ftcf for TOV dpL(),wV, but Aristotle means not thaI number must hat'e, but that it 2678-2


234

COMMENTARY

must be, a principle of unity, just as in general he identifies substance with the unifying principle. S-g. cl).).' o~X ... iKQC1T1J' cr. 1043 b 34 n. Aristotle here opposes his view of essence as an ' actuality and nature' which holds together material parts to the view that it is a mere indivisible'unit. g-IO. IZC71rEP o~8c 6 clpLe".OS ••• ~TTOV. 1. e. a number cannot be more or less a particular number; it either definitely is it or definitely is not it. II. dU' d1l'EP, " ".ETQ Tijs .1).1Is. In Cat. 3b 33-4a 9 Aristotle implies that not even ~ JL(Ta '"is v>':YJs, the concrete individual, can be more or less the substance it is. II-Ia. 1I'£pl ".cv o3v YEvlaEws ••• clSUVUTOV refers to 1043 b 14-23, 1I'Epl TijS EtS TOV clpLS".OV clvuywyijs to 1043 b 32-1044a II. These, then, are for Aristotle the main sections of the chapter.

The 'lJarious causes of generable natural substances, eternal natural substances, and natural events (ch. 4). 1044& IS. Even if all things have the same ultimate matter, they have different proximate matter. ~O. The same thing has more than one matter. Phlegm comes (I) (a) from what is fat, directly, (b) from the sweet, because the fat comes from the sweet, (2) from bile, by the resolution of bile into prime matter. ~S. From the same matter different moving causes can sometimes produce different things; in other cases different things involve different matter. If the same thing can come from different matters, the moving cause must be the same. a~. When we look for the cause of a thing, we must state all the causes we can-material, efficient, formal, final (the last two being perhaps the same), taking care to get the proximate cause. b a, So much for generable natural substances. The case of eternal natural substances is different; some things presumably have no matter, or only the matter which qualifies things for spatial movement. S. In natural things that are not substances there is no matter; the substance is their substratum. There is no matter of eclipse; the moon is what suffers it; the efficient cause is the earth; there is presumably no final cause. The formal cause is the definition, but this is obscure unless it states the efficient cause, as does the definition , deprivation of light by the interposition of the earth '. 15. The importance of getting the proximate cause may be illustrated by the causes of sleep.

1044& 16. lK TOU u~u 'II'civru 'II'p'rou, i. e. from prime matter j ~ T.,V u6~v

IlII 1fP'TIIIV, i. e. from the four elements. rO ~L1fUpaV lK TOU y~udol, cf. De A". 4ub 12, De Smsle HZ& 17, 23· 33-34. 'II'UUI ••• T&I MiEXO!,ivul utTCul, i. e. all the causes we can state. 35. &pu rc\ KUTU!,~"'U; Cf. G. A. 727b 31, 729& 30. &pu TlI cnripl"'; Cf. 729& 28. b I. tcrtoll &i TUUT" 41'+111 TlI u"rO. Cf. De Gm. el Corr. 335b 6. 6. ~r +uo'LK"v ~ .. 4iSClllv &~ o"erL.,v, i. e. the celestial spheres and the stars. 9. O"K lerTL rodrOLI KT~. What underlies an accident, as matter underlies substance, is not matter but substance. Cf. Z. 1038b 5. Ill. rO S' 03 IVEKu terlill O"K lerrLv. This is a serious admission, in view of Aristotle's identification in 1. I of the formal with the final cause. His teleology is in fact not complete. There is not always a final cause. But where there is, it is the formal cause as well. In the absence of a final cause, the thing is defined by reference to its efficient cause, as in 11. 14, 15. Eclipse is for Adstotle an example of T"lmJp.O:ro". The sun's motion is no doubt Q,EKo. TOU and so is that of the moon, but the two acting together may produce a result which is not Q,EKo. TOU. 16. m' TlI t¥ov; vue, 4~~d KT~. is very like 1. 19 &T' d.K'lI1JfTlo. TOUJ.8l j' JfGl, ru' K'f'A. The first ruo. is natural enough in introducing a suggested answer. cr. L. and S. s. V. II. I, KOhner ii. 2. § S89. 9. The manuscript reading ru' &rL is therefore preferable to Bz.'s conjecture /1).).0 T' (' Is it anything other than the animal? '), a phrase which does not seem to occur in Aristotle. 17. KUP"'" Sleep is a nOol TOU KUploU rid" cLUCIW 11'0.",""" ula-(J.qrqplou(De Somno 455& 20-26, 33, blO, 458& 28}, which is the heart (456&4) or, in bloodless animals, what is analogous to it {456& I I}. Elsewhere Aristotle connects sleep especially with the brain (Po A. 653& 10). A definition quoted thus by way of illustration is not necessarily his own; e. g. in similar contexts (An. Posi. 93 b 8, 94& 4) he cites Anaxagoras' definition of thunder, though his own was different (Meleor. 369& 10-370& 33). Cf. 0. 1049& 2 n. 1111•• t

n"

an

Only things subject to gmeration a"d change have mailer. The relations belwem mailer and ils conlrary slates {ch. 5}. I044b III. Since points, and in general forms, are and are not, without generation and destruction (for white does not come to be but wood comes to be white), not all contraries come to be out of one another (pale man from dark man but not pale from dark) j nor have all things maUu, but only the things liable to generation and reciprocal transformation.

COMMENTARY lIg. How is matter related to its contrary states? Is a body potentially diseased as well as potentially healthy, water potentially vinegar as well as potentially wine? It is the matter of the one in virtue of a positive state or form, of the other in virtue of the privation of the form. 34. Again, why is not wine 'potentially vinegar " the living man 'potentially dead'? These corruptions are incidental; the matter of the living man is by force of corruption potentially a dead man, and water (the matter of wine) potentially vinegar. Where, as here, opposites change into one another, the negative (e. g. dead body, vinegar) must be resolved into its matter before it can change into its positive. I044b lII. EV~U &V(U y(vla(~ Kul .eop&~ EaT~ Kal O~K EaTLV, cf.

E. 1027& 29 n., Z. 1033 b 5-6 n. lIlI. olov ut aT~y".a', cf. B. 1002832, E. N. II74 b 12. (t'll'£P ELa', 'if they may be said to exist '. The Pythagoreans and Platonists thought they existed as substances, but Aristotle insists that they are merely Top.a{, 8LaLplCT£t<;, 7f'lpaTa of lines (K. 1060b I2 If., N. 109 0b 5 If.). liS. dU.' lTlp",~ KT}.. A black thing (I) can become a white thing, and (2) does so by a process, by one part after another becoming white (Phys. vi. 4). But (I) black does not become white-all that we can say is that there was black and there is white; and (2) white succeeds black instantaneously. When Aristotle says that contraries do not change into one another (A. 1069b 6), he is using ;'vaVT{ov in only one (the more fundamental) of the two senses here referred to, i. e. of the contrary qualities, not of the things characterized by thme qualities. In the work II£pl. ;'vaVT{wv (fr. J 19 Rose) he distinguished the two kinds of contraries as TO. Ka(J' aVTa. I.vavTla and TO. T!fJ p.£TlX£lV ;'vaVT{wv;'vaVT{a. Cf. I. 1057 b 6. 34. d'll'op'u Sl n~ EaT~. Aristotle's answer to the question is that wine is not the matter of vinegar but the normal product of the same matter of which vinegar is the abnormal product. In such a case there is no direct transition from the normal to the abnormal product nor vice versa; the given product must first be reduced to its constituent matter. This is stated explicitly of the change from the abnormal to the normal product (104511. 4-6), and implied with regard to the converse change (10H b 34-1045& 2). 36. KUTB au".I3EI3'1)KO~ ut +8opu', i. e. the degeneration into vinegar does not attach to the wine directly, but to the water of which the wine is a particular form. Thus the chapter indicates three ways in which A may change into B : (I) Ka(J' €ew Kat KaTa. TO (180<;, as water into wine, (2) KaTa. CTTlpYJCTtV Kat CP(Jopa.v T1JV 7rhpa. CPVCTLV, as water into vinegar,

H.

5.

1044b 21 -

1045&

3

23i

(3) KaT4 rrvp.{3'/lqK6s, as wine into vinegar, or vinegar into wine. U oivov. As wine and vinegar have a common matter, water, so day and night have a common substratum, air (A. 1070b 21). 1045" 3. lK TOUTII"', Ie. lK ''I!ov,

The uni!JI of definition (ch. 6). 1045&7. We return to the question (cr. 1044& 3) what makes a definition or a number one. All wholes as opposed to mere aggregates must have a cause of unity, which in bodies is contact, viscidity,

&c. III. A definition is one not by external union but by being the definition of one object. What, then, makes man one, not animal + two-footed? In particular, if there are Ideas of animal and twofooted, why do not men exist by participation in these two rather than in one Idea? 110. The usual modes of definition afford no answer to the question, but the distinction of form and matter does. 115. The difficulty is the same as that of the unity of ' round bronze', if this be the definition of some term. It is one simply because bronze is matter and round is form. There is no cause of the actual coming to be of what was potentially, save the efficient cause, in the case of things subject to becoming. It is the essence of the potential sphere to become actual, of the actual to have been potential. 33. Malter may be either sensible, or intelligible; in a definition there is always an element of matter as well as one of actuality (e. g. 'plane figure' in the definition of circle). 36. Things that have not matter of either kind, i. e. the categories, are directly and essentially some kind of one as they are some kind of being; hence their existence and their oneness are not stated in their definitions. Their essence is directly a one as it is an existent; hence there is no other cause of their unity or of their existence; for each is directly an existent and a one, though being and unity are not their genera and do not exist apart from the particular kinds of being and unity. b 7. Some solve the problem of unity by 'participation', which they cannot explain or define; others by 'intercourse' (so Lycophron). 'composition', 'connexion '-formulae that can be applied to anything whatever. 16. Their mistake is that they look for a difference between, and a unifying formula for, potentiality and actuality, while really the proxi-

COMMENTARY mate matter and the form are one, the first being potentially what the second is actually, so that there is no reason of their unity except that which causes the movement from potentiality to actuality; while immaterial things are without qualification and essentially unities. 1045& 7. Tijl etP'll'l"ll, Z. 12, H. 1044& 2-6. 8. KAl mpl TO~ 4p~8p.odt. The chapter in fact discusses only the unity of definitions. 115. ICM'~ ymp Aa,"! ..., c1'1ropCA KT)., The problem is that of the unity of genus or VA't/ "0fIT'I with differentia. Aristotle illustrates it by the more familiar notion of the unity of form with VA't/ AWfhrrq in e. g. a bronze ball, and then in 1. 33 returns to the case of genus and differentia, and points out that genus is to differentia as sensible matter to form and may therefore be called intelligible matter. 116. For Ip.J.T&w taken thus arbitrarily cf. De Inl. 18& 19, Z. 1029b 28. 33. iKa.np't' may mean (I) C for the potential ball and for the potential man' (1. 18) (this is Alexander's second interpretation, 562. 10); or (2) C it was the essence of the potential ball to become an actual ball, and of the actual ball to be produced from a potential ball '. This is the more probable interpretation; the reference to the case of man occurs too far back to be referred to here as Alexander suggests. 34. VA't/ If07JT"1 means here the generic element in a species. For this use of VA't/ (without the adjective) cf.1. 23, 11. 1024b 9, Z. 1038& 6, I. 1058& 23. VA't/ 1'07Jn1 occurs in (apparently) a different sense in Z. 1036& 9, where see note. 35. axijl'a. ''lr£'lrESov. The interest here being in matter, Aristotle states only the material or generic element in the definition of circle. 36-b 7. Aristotle has shown that a species is unified by the fact that its genus exists only as the matter of its differentia, and its differentia only as the form of its genus. This explanation does not apply to summa genera (i. e. categories), which have no matter either intelligible or sensible. The unity of these, however, needs no explanation; they are by their own nature instances of unity (MrEP lv Ti), as they are instances of being. Because unity and being are inevitably predicable of them, unity and being are not mentioned in their definitions {really, of course, they have no definitions but can merely be described, Alexander 563. 17). The section contains a certain amount of repetition, but this is for the sake of emphasis. The rearrangements of the text by Alexander and Schwegler are not necessary and do not help matters; the justification of 8uS in b 2, which was the point that troubled them, lies in E{,8t$~ (& 36). Since any summum genus must from its very nature be a one and an existent, 'one' and • existent' need not be inserted in the definition of any summum genus. b 6-7. ~-WI ••• 'lra.pm Tm Ka.e' 'KACM'G. is evidently directed against the Platonists.

H. 6. 104S& 7 -

104S b 19

139

6. o~x" . . . M. Aristotle holds that being and unity are not genera, for reasons given in B. 998b II ff. Each of them is one T
Ab. 1lICM'!! 3p.o~ov itT).. • So that it is like asking what in general is the cause of unity and of a thing's being one '-which is an obviously absurd question.

BOOK e POTENCY

(chs. 1-5).

Potency in Ike slnel mISt, ,: e. power 10 produce motion (ch. I). 104Sb fill. We have treated of primary being, to which all the other categories imply a reference, viz. substance; since being is divided according as it means potency or complete reality as well as according to the categories, we must discuss potency and complete reality. 35. First we will discuss potency in the strict sense, which, bowever, is not the most sUitable to our present purpose. Later, in our discussion of actuality, we will explain the other senses of potency.

CO:\fl\fF.NTARY 1046" 4. We may set aside the potencies that are so called by equivocation (i. e. potencies or powers in geometry). g. Potencies in the proper sense are originative sources, and are called potencies by reference to a primary kind (a), that which is a source of change in another thing or in the thing itself qua other. The derivative kinds are (b) the potency of being acted on, of being changed by another or by the thing itself qua other, and (c) insusceptibility to change for the worse by the agency of another thing or of the thing itself qua other. 16. Again, these are potencies of acting or being acted on simply, or of acting or being acted on well; the definition of the former is implied in that of the latter. Ig. In a sense the potency of acting is one with that of being acted on; in a sense it is different. The one is in the patient (it is because even the matter is a motive principle that things can be acted on, different things by different things); the other is in the agent. Thus so far as a thing is an organic unity it cannot be acted on by itself, for it contains no distinction of agent and patient. !ag. To every potency there answers a privation of potency, an incapacity to do that same thing in that same relation. We say a thing is 'deprived' of an attribute (I) when it has not it, (2) when it might naturally have it but has not it-has not it (a) at any time or (b) when it might have it, and again (a) has not it in a particular way (e. g. completely) or ({3) has not it at all. Again, we sometimes mean that it is prevented by force from having what it would naturally have. 1045h !as. ELP'ITIU. The reference is to ZH in general. 3!a. EL'II'Ol'EV lv TOLs 'II'~TOLS MYOLS. The point has been made both in r. 1003" 33 and in Z. I. As it is doubtful whether r was originally part of the same treatise as 0, Z seems likely to be meant here. 3!a-34. t!'II'El S( ... lpyov. For the full list of meanings of ov cf. E. 1026" 33-h 2. 35-1046a 4. The two senses of 8vvaJL'<; which Aristotle wants to distinguish may be indicated by the words 'power' and ' potentiality' respectively. He proposes to treat first of power, and then, in discussing actuality, to treat incidentally of potentiality (1046& 2-4). Power he explains as primarily a power in A to produce a change in n, or in A, considered in one respect, to produce change in itself ill another respect (1046" II). Potentiality on the other hand is a potentiality in A of passing into some new state or engaging in some new activity (1048& 32). This activity may be the production of a change in B but the notion of a B to be acted on is not necessarily implied in the

notion of potentiality, as it is in that of power. The notion of power is obscure enough, but it is certainly familiar and it is easily distinguished from that of potentiality. But Aristotle proceeds to treat a~ subsidiary to the notion of power as distinct from potentiality, of ~ KaTa. K{VTJUtV ilwap.t .. (1046a 2), (a) the power in A of being changed by B and (b) the power in A of not being changed for the worse by B (I 1-15). In these 'powers' part of the distinctive nature of power as against potentiality is still present-viz. the distinct implication of two things A and B; but the other part of its distinctive nature i~ gone-viz. the implication of positive force, for in (a) weakness rather than force, and in (b) inertial resistance rather than force is implied as being present in A. That Aristotle does not successfully preserve the distinction between power and potentiality is further indicated by the facts noticed by Bz., that in the discussion of power he introduces (I) a definition of ilVVaTOY which clearly refers to potentiality rather than to power (t047a 24), and (2) a lengthy section which also refers to potentiality rather than to power (10471. 3-30). 1046a lI. ~hr6vTE~ 'II'~pl TBUT1J~, in chs. 1-5. 3. lv TOL~ 'II'Epl Tij~ lv~py(£B~ SLOPLal'0io;, chs. 6-10. The precise reference is to 1048a 27. 5. lv 4lloLo;, A. 12. 7. KB84'11'EP lv YE"'I'ETpC,. Cf. A. 1019 b 33 n. 8. Schwegler puts a comma after YEWP.ETp{1!- and takes Kal ilvvaTu I(T,\. as referring to the senses of ilVVaTOY and dilvvaTov expounded in A. 1019 b 21-33, but the run of the sentence forbids this. 13. 4'11'a8(£BO; Tijo; l1l'1 T? XEipov is used elliptically for d1rafh{a<; IUTa{30A~<; ~<; l1rl TO XEtPOV, and cp()opii<; depends, like the 'understood' p.ETa{3oA~", on d1ra()({a ... 17. TOU before 1rafUiv seems pretty certainly to have been in~erted hy a copyist who did not see the point. I9-lIO. lan I'tv ••• 'II'4axELV. In saying that the power of acting and that of being acted on are in a sense one Aristotle does not, as Bz. supposes, make use of an ambiguity in the phrase dpx.TI/J.(TB{3oA~<; lv dH't' (I. I I), by which lv c1AA't' can 'he taken either with dpX~ or with p.ETa{3oA~<;. The whole context shows that lv dH't' goes only with p.(Ta{3oA~<;; it is in virtue of this that dpx.TI p.ETa{3oA~<; lv dAA't' can be opposed to dpX~ p.ETa~oA~<; V1r' !THou (I. 12). Rather the unity, in some sense, of the active and the passive 8vvap.t<; is based on this, that the single fact that A can change B leads us to ascribe both an active power to A and a passive power to B. The active and the passive power are thus the complementary aspects of a single fact. Cf. De AlI. 42ijb 25-426330. lI4. T? }.L'II'BP?V I'll' yap KQUaTcv. I. e. that which suffers burning must ha\'e a matter which lends itself to burning; it must be fat. 28. aUI''II'l+uKEV. cf. Z. 1040" 15 n. 31. '" SE aTlp'laLO; }'lYETBL 'II'o}.).BXliio;, cf. A. 22.

CO:\J:\IENT ARY

Rational and l1on-ra/iol1al po/mCits (ch. 2). 1046a 36. Some potencies are irrational, others rational; thus the arts are potencies. b 4. Rational potencies are of contraries, irrational of one result only; the hot can only heat, but the medical art can cause either disease or health, because knowledge is a rational accoUllt and the same account explains both a thing and its privation; 9. but it explains the one essentially, the other incidentally by the absence of the first. 15. Thus the scientific man, starting from the single principle of movement which he has in his soul, can produce contrary results, linking both movements syllogistically with the same rational account. !Z4. The power of doing a thing well (or being acted on well) implies the power of doing it (or being acted on~ but not vice versa. 1046b 3. ut 1I'oL1)nKull1l'Lcrnj,...uL = a1 T'XVat. Kal is explicative. cr. A. 1075& I. 4. ut ,...£v ,...nll Myou 1I'CicrUL Tiiiv lVUIIT(lIIv ut ullTut Aristotle is not asserting contingency in the sphere of rational powers-asserting that precisely the same cause can produce opposite results. Opposite results may supervene on the presence of a single AOyO!1, but it has not been their sole cause; llU£vota alm, O~8Ev KtV€'i (E. N. I I 39& 35); desi re or choice turns the scale (1048& 10). The AOyO!1 has been accompanied in the one case by the desire, say, to cure, in the other by the desire to kill, and this accounts for the difference in the result. 14. "yap C7TJp1)crL~ "1I'pwT1) ,.0 lvulIT(ov. lvallTlfIKTt.. proper is CTT'fYTIUt.. T€Adu (I. 1055& 34); if a subject which might have a certain attribute completely fails to have it, this state is 'contrary' to the state of having the attribute completely. 15. l1I'd S~ Tc\ lvulIT(u ollK lyy'yvnuL lv Tell ullT'i. This gives the reason for TO p.£v rymvov. • • tfroXPfrrrlTa, while .q Il' i'1rtcrn1P.'" • • • dp)(f/v gives the reason for b Il' l7rtcrn1p.wv /1.p.tJ>w; and it is on b Il' l'Irtcrn1p.wv o.p.tJ>w and the reason for it that the stress falls. 'While the wholesome produces only health because its power qua wholesome, being an irrational power, is a power only to produce health and the law of contradiction forbids its having also the contrary power, on the other hand since knowledge .•. , the man who has knowledge can produce both.' 110. ~oyo~ yo.p ••• ".Jv. 'For it (the MyO!1 mentioned in I. 17) is a AOyO!1 of both the contrary results.' III. ~ 'XeL. Jaeger prefers V'X.t, but Alexander read ~ IX€L (570. 6). The AOyO!1 is not present in a soul in virtue of the soul's having an dpX; of movement, but is present in a soul which in fact has such an dpX;, and it is this coincidence that leads to action. III-lIIi. Alexander explains both Tij~ allrij~ BpX~~ and Tdro as TO

AOYUTTuc6v. That T~~ at,~~ dpx7i~ means lJ A6yO~ is shown by I. 24, and Talrr6 probably means this also. The soul will initiate either of two contrary movements all a result of the same originative source, the account it has framed for itself of the object, and it will have linked both movements with the same thing, i. e. deduced them from this account as the movements necessary to bring the object into existence or to prevent its coming into existence. For O'Vva1TT(W used of syllogistic 'linking up' cr. An. Pro 41B I, 12, 19, 65 b 33,69& 18, '9. !I!a-!l4. A thing which has a rational power can produce the contraries of the two results which two things having irrational powers respectively produce. Wholesome food produces only health, unwholesome food only disease; a doctor can produce both. Toi~ aV(11 AOyOI1 8l1VaToi~ is, however, rather pointless, and may be a mistaken gloss on TdvaVT{a.

Potency defended against allack (ch. 3).

I046b !l9. There are some who say, as the Megaric school does, that there is potency only when there is actuality. This leads to manifest paradoxes: 33. (I) A man will not be a builder if he is not building, for to be a builder is to be able to build. Now if one cannot have an art without having learnt it, or, later, be without it without having lost it (i. e. by forgetfulness, disease, or lapse of time, for the ob/eel of art cannot be destroyed), are we to suppose that the moment he stops building he has lost the art j if, then. he starts building again immediately, how will he have recovered the art? 1047& 4. Again, nothing will be cold or hot when it is not being perceived (so that they are really maintaining the theory of Protagoras), nor will anything have perception if it is not perceiving; people will be blind and deaf many times a day. 10. (2) That which is not happening will be incapable of happening, and then we must never say that it will be, so that change is done away with; what stands will always stand, what sits will always sit. 17. To avoid these consequences we must distinguish potency and actuality. !l4. A thing is ' capable' of something if there is nothing impossible in its having the actuality of that of which it is said to have the potency. 30. The word' actuality', which we connect with' complete reality', refers originally to movement; hence we do not ascribe movement to non-existent things, though we assign to them prt'dicates like' thinkable' because they will sometime actual1y exist.

COMMENTARY Chapter 3 defends the notion of the possible in distinction from the actual; chapter 4 defends the notion of the impossible. 1046b ~9. otov ot Mf)'UpLKOt Apart from this passage we have no information about l\Iegaric views on possibility earlier than those of Diodorus Cronus (ob. 307 B. c.). Diodorus in his famous IOIpLWWV AOyo~ used the principles lhal • everything that is past is necessarily true' (an Aristotelian dictum, E. N. 1139b 7-9, Rlzel. 1418a 3-5) and that' on what is possible nothing impossible follows' (the criterion of the possible stated in this chapter, 1047 a 24-26) to tlisprove a thttd principle' that may be possible which neither is, nor will be true' and to prove instead that 'nothing is possible which neither is nor will be true '. In this he gives up (presumably in view of Aristotle's arguments in this chapter) the original Megarian position that' nothing is possible which is not true'. Maier maintains (Archiv f. Gesch. d. Phil. xiii. 31) that Diodorus' own position is directed against Aristotle's statement (1047b 8) oMf.v KWAV(L 8vvaTov T! t.v ETva! ~ ywlu()a! p.~ ETva! p.f/8' (UEu()a!. But this cannot be so. These words are not Aristotle's own statement but occur in his account of his adversary's position. His own statement is the direct opposite and is identical with that of Diodorus·-o~K lv8IX£Ta! c1Af/()f.~ ETva! Ta d7TEtV OT! 8VVaTaV p.f.V To8l, O~K

IUTa! 8E (I047b 4). Diodorus, with Aristotle, must have been attacking thinkers who interpreted the possible so widely that the impossible disappeared ( 1047 b 5). On Diodorus cf. also Ritter and Preller § 295, Zeller ii.4 I. 269. The Megarian paradox was probably reached by a very simple pit'ce of reasoning, natural for followers of Parmenides, 'A thing is what it is, and therefore cannot be-what-it-is-not'. The answer is equally simple. A thing cannot be what it is not, but it can become what it is not now. 'Can' refers always to the future, and it is no contradiction to say that what a thing ig not now it can be in' the future. ' Can' means that some of the conditions of the event are now present, and that if certain others are added the event will take place. Aristotle's answer, however, is more elaborate. His method is to point out the disastrous consequences of the Megarian doctrine. 34. For oilT' answered by 61'0(111'1 Sl cf. Dc An. 410b 18, 21. 1047& lI. TOU ••• 1I'pc£YI'UTO'l must be the form which is the object of the art in question, not as Alexander thinks the matter of the art; e. g. the form of house, not the stones of which it is made. 3-4. ISTuv ••• l-.ulJwv; The question is contained in 7TW~ Aa/Nov; it is not necessary to supply 7TW~ before OTav as Bz.. suggests. 6. T~V npIIITUYOPOU }.Oyov, cf. r. 5, 6. 9. KUl. iTL a", which has been suspected, is undoubtedly right. cr. An. Post. 74 b 32 (T! £Z T!~ p.~ oT8E VVV lxwv Tal' AOyov KUl. CJ'IIItOl'EVo'l. uw'op.ivov

TOV

7Tpa.yp.aTO<;, p.~ l7Tu..fAf/up.lvo~, o~8f. 7TpOTEPOV

118f!

(a

reminiscence of PI. Theael. 163 n). 10. KUl. Kw+OL is, of course, an afterthought; the words need not be

suspected, as they are by Bz. For a similar afterthought cr. Z. 1028& 16 n. 10-129. In this whole section Aristotle passes from the word 8vvauOat to the more colourless word 8vvaTol', He is using the notion of potentiality, not that of power, and thus confusing the two senses of 8vvap.ts which he proposed to keep distinct. Cf. l045b 35-1046& 4 n. II. The reading of Ab and AI., yt~V.sI'EVOV, accords better than the vulgate 'YEv6p.EVOV with the principle oTav lVEpyji p.Ovov 8vvauOat. 18. TOUTO, that which neither is nor will be. 128-124. Kull'~'" /3uS~tEW. The manuscript reading must be wrong, since it says the same as has already been said in 8VVaTI/I' {Ja8,'nv ~v p.~ {Ja8a;nv. The reading adopted is that proposed by Prof. Joachim. The other emendations which involve less change are in themselves less natural. Once {Ja8,'nv got corrupted into {JaU,ov, the corruption of ov into ETvat would naturally follow. 124-126. Considered as a definition of 8vvaTov, this statement would evidently be circular and therefore worthless. But it does not claim to be a definition. It only amounts to saying that before you can pronounce anything to be possible, you should satisfy yourself that none of its consequences is impossible. It is a criterion for the determination of possibility in doubtful cases. 126. Suvu,.ov Ku9~a&ut Kul lVSEXETUt KU~a&Ut. Maier rightly points out (S)!ll. d. Ar. i. 194) that Waitz's distinction between 8vvaTov and Ev8EX0P.EVOV as indicating respectively physical and logical possibility is inconsistent with the objectivity of Aristotle's thought. Aristotle gives the same criterion of the Ev8EX0P.EVOV in An. Pro 32" 18, P4Jls. 243" I, as he here gives for the 8vvaTov, and in such passages as An. Pro 19& 10, 13, 15, 2 I, A n. Post. 74 b 38 the two words are used as synonyms. The only difference is that 8VVU,TOV brings out more clearly than lv8EXOP.EVOV that the possibility is rooted in a real 8vvap.ts; the passages cited by Wailz as indicating a difference between the two notions (@. 1047" 20, 1049b 13, 1050b 13, N. 1088 b 19, An. Pro 31b 8, De Caelo 274 b 13, G. A. 736b 7) imply no more difference than this. 80. ~ 'II'pOIl ~v lVTEAEXEtUV O'uVTt9EI'EV'IJ' From 1050" 2 2 Tovvop.a lvip'Yna A€-yETat KaTe,. TO EP'YOV Kat UVVTE,vn 7rpOS T~V lVTEAiXEtav, it appears that strictly speaking lvip-yna means activity or actualization while EVTEAExna means the resulting actuality or perfection. Yet lVEp-yna is not a movement towards something other than itself; this is the difference between it and K'IIT1UtS. For the most part Aristotle uses the words as exact synonyms. Cf. Bz. Index 253 b 46-254" 12. Yet in A.6, 7, where God is viewed as the prime mover of the universe, He is called lVEp-yEta, activity, but in 8. 10740. 36, where the immateriality and perfection of His being is insisted on, He is described as EVTEA€Xna.. One would expect lVTEAEXEta to be derived from an adjective lVTEAEX~' as VOVVEXEta is from VOVVEX~S. But the existence of the word lVTEAEX~s in the time of Aristotle is doubtful. In PI. Legg. 905 E 3 the manuscripts read EVTEAEXWS, but Stobaeus gives lv8EAEXWs, which suits the context much better. In De Gm. el Corr. 336" 17,

COMMENTARY b 3 2 i ...nAEXws, i ...nAExl1, though read by some manuscripts, give no suitable sense. In Theophr. C. P. ii. 11. 10, V. I. 10 iVrEAEXES is unsuitable and Wimmer reads i ...8EAEXES. iVTEAEX~S seems to occur first in Philo 2. 587 l\Iangey. Hirzel, in Rhein. 1Jlus. 1884. 169208, put forward the view that Aristotle in one of his dialogues ascribed to the soul, as Plato had done, i ...8EAiXEta, continuous movement, and that he later invented the word iVTEAExna by a modification of E...8EAEXEta in order to express the change in his view about the soul. Diels, ill Zei/schr.fur Vergl. Phllol. xlvii. 200-3, successfully controverts this view, and shows that lVTEAEX~S is a correctly formed equivalent to TO EVTEA€S lXI!)If, 'having perfection '. iVTEA~s, though not found at all in Plato, and only once in Aristotle, is not uncommon in Greek of the period. It is not necessary to suppose, as Diels seems to do, that the word i ...T£AEXl1S existed in Aristotle's time; he may have formed the abstract noun directly from TO EVTEA€S lxo", or possibly from EVTEAws lXo.... The only other compound of EVTEA~s seems to be EVTEAOpow80s, [Dem.] 1212. 12, 'receiving pay in full '. 81. eJUl'Tt9El'iv". Diels feels a difficulty about the word, and proposes CTtJVTEWOpoi"'7J, citing 1050& 23 as a parallel. But it is only in the active voice that Aristotle uses CTtJVTELVnV in this sense. CTtJVTt8EPOEV7J implies that Aristotle was in the habit of connecting the words EVEPYEta and EVTEAiXEta together in his lectures, and such phrases as Els Ta~Tov {3autAEa Kal nipawov CTVVE8EPOEV (PI. Po/z"t. 276 E, cr. 259 D) form a close enough parallel. KILl .,..t Til. .v.XIL. The IDa are not as Alexander says TO. TEXV7JTrJ., for EVEpyna has 110 original reference to natural as opposed to artistic activities. III fact 8wapots, with which it is correlative, is apx.TI poETa{3oAl1S EV ID't' ~ V IDo (1046& II), which means art rather than nature. brl Tn IDa refers to the non-kinetic meaning of EVEP),na, which is best expressed in the sentence A€),ETat EVEPYELq. • • • Tn po€V ~s KLV"T/UtS 7I"POS 8vvapotv Til. S' Ills ollcr~IL ,..p6s TWIL OX"V I 048b 6-9 ; Evip)'Eta in this sense is not movement as opposed to the power to produce movement, but actuality as opposed to potentiality. Cf. E. N. II54 b 27 EvlpyEta aKtV7JULas. 3a. SOKEl, 'is commonly thought '. Aristotle's own view is that the divine EvipyEta aKtV7JULaS is EVEpyEta in the truest sense. 34. KILT1JYOPLILS, 'predicates', not' categories'. 35. TOUTO Si ••• lcrOVTILt .VEPYE~~. We refuse to say that they are

moved, because they do not exist actually; we say that they are objects of thought or desire, because they wt'll exist actually.

Possib,l,tyfttr/her considered (ch. 4).

1047 b 3. It cannot be true to say 'this is capable of being but will not be' (this would imply that nothing is incapable of being). 9. For it follows from our defiuitiou that if we sup!Josc that to

be which is not but is capable of being, nothing impossible is involved. On the view we are attacking something imp08sible is involved. The impossible is not the same as the false. 14. It is also clear that if, supposing A is, B must be, then if A is pos~ible, B must be possible; for ctherwise there is nothing to prevent its being impossible. Ltt A be possible. Then (we agreed) nothing impossible is involved in supposing A actually to be; but if so, B must be. But (cr. l. 17) it was supposed impossible. Let it, then, be impossible. If, then, B is impossible, A is impossible. But B was supposed impossible, therefore A is so. lf A is possible, then, B must be possible, if they were so related that if A is, B must be. gS. And if, supposing A is possible, B must be possible, then if A is, B must be.

V

I047 b 8. The traditional text d 8' IUT~ TO dp1fp.€vov 8vvaTov aKoAov(M can only mean 'if what we have described is possible in so far as the two things are conveltible' (with V aKoAov(M; may be compared VbrETat An. Post. 73 b 22); it is quite impossible to underbtand, as Alexander and Bz. do, TO IVEp~uat as the subject of aKOAOV6EL. There is much to be said for Zeller's El8' IUTt, TO EiP1fP.(VOV, 8vvaTov <~ a8VvaTov) P.~ aKoAov6EL. ~ a8vvaTol' P.~ dKOAoV6EL would be a good summary of TO EiP1fP.(VOV, i. e. of the criterion of 8vvaTov given ill & 24.

(Alternatively we might omit Zeller's commas and interpret' assuming that the 8vvaTov about which we have been speaking is that', &c.) This reading delives some support from the phrase in the KVptEVIIIV of D odorus Cronus (cf. I046b 29 n.) 8vVaTtfJ a8vvaTov P.~ dKoAov6ELV. A comparison of J047b 9 with the phrase in the KVptEVIIIV, 8vvaTov Elvat S oih' EUTtV aA1f6E~ Ol)T' EUTat suggebts that Diodorus was borrowing Aristotle's language. There ill, however, no absolute need to depart from the wellatte~ted reading given in the text, which derives some support from An. Pro 32& 24 .;;rot TawtiluTtv ~ aKoAov6EL dAA~AOt~. 5. WVrE • • • StU+EUYEtV. 'So that the things that are incapable of being would on this showing escape us.' if we can truly say a thing is possible but will never be, an) thing may at this rate be possible and there will be nothing impossible. 7. a JIo~ }"oyttOJloEVOi TO cl.SUVUTOV EtVUt may mean either 'i. e. the so; t of man who does not take account of that which is incapable of being' (L. and S. s. v. Aoyi'op.a.t iI. I), or 'i. e. the sort of man who does not consider the impossible to exist' (L. and S. iI. 2). In either case there is a reference to C:;UTE Ttl a8VVUTU Elvut TUlni1 8taq,EVyftV. The Greek would be somewhat more natural without ~, but the word is well attested. In any case the clause is parenthetical, and OTt oMi" KTA. gives the reason for 8vvaTov ••• P.ETP1f6~u(u6a,.

CO:\Il\lENT AR Y 10. TWV KELJIoEVWV, what we have laid down in a 24-26, b 3. II. O'UJIof31JO'ETCU Scf yE, se. d.IlVVClTOV TI. 14-26. The same point is proved in a not dissimilar \Vely in All.

Pro

.14" 5- 12 • 15. The reading of EJAb, SUVIlTOU ill'Tos dVIlL TOU· A, clearly ought to be restored here. 19. TO Scf yE B cl.VQYKT) EtVIlL KT>'., 'but ex hypothesi (cf. n. 14, IS) if A is, 13 must be. But it was assumed, on the view we are attacking, that though A was possible B might be impossible '. 21. cl.VQYKT) is an emblema from 1. 20. Kill TO A E(VIlL, se. d.IlVVClTOV. 24. OUTW; lXOVTWV TWV A B, 'A and B being so related (as they have been shown to be) that if the reality of A implies the reality of B, the possibility of A implies the possibility of B '. 25. OUTWS, sc. if A is possible. 26. ws IT£Iht, i. e. so related that the reality of A does imply the reality of B.

How potency is acquired, and aclualised (ch. 5). 104i' 81. The potencies that come by practice or learning are acquired by previous exercise; those that are innate or are passive are not. 35. Irrational potencies must result in action and being acted on when the agent and the patient meet in the way appropriate to their potency. 10488 7. RaHonal potencies need not so result; since they ar~ potencies for contrary results, if they were actualized necessarily they would produce contrary results at the same time, which is impossible. There must be something else that detelmines which result is to tuke place; this will be desire 01' will. Whichever action the agent decisively desires, that it will do, when it meets the patient in the appropriate way. 15. Its potency is conditional on the patient's being present and in a certain state. (We need not add ' and on the absence of external hindrance'; that is impJied by the positive conditions of the potency.) 21. The possibility of doing contraries at the same time is excluded, even if one simultaneously wants to do them both. 1047 b 31. Aristotle begins the chapter with a threefold classification of Ilvvup.uc;, into those that are inborn, those acquired by habit, and those acquired by learning. The latter two are then (1. 34) coupled together and opposed to the first. Aristotle then (104sa 2)

reverts to the distinction stated in ch. 2 (chs. 3 and 4 on the Megarian heresy have been something of a digression) between rational and irrational powers. It is clear that he means to identify the inborn powers with the irrational and to include Quat lOn as well as Quat AOy't' under the rational. This implies that IOo~ includes a certain amount of AOyo~, or the possession of a plan of action, as indeed it does, whether it be a comparatively mechanical dexterity such as that of TO a~AELv (I. 32) or a moral character (E. N. ii. I) that is being acquired by habituation. 33. Tall ".~V 4VC£YK'I) 'II'poEvfpY'laavTall lXf'v. This apparent paradox is explained in E.N. lIo5a 17-b 18. (I) To become ypo.p.p.aTtKOi you must have done ypap.p.anKov TI, but you need not have done it ypap.p.anKw~, i. e. with knowledge. (2) In the moral sphere there is a still greater difference between the activity that precedes the Ut~ and that which flows from it. In the latter the agent must act (a) with knowledge, (b) choosing the action, and for its own sake, (c) being in a firm and unchangeable condition of mind. The activities which establish the Ut~ have not any of these characteristics. Aristotle does not, however, show how actions done in ignorance and not from the right motive can establish a lel~ of acting with knowledge and from the right motive; he simply takes it from common experience that they do. A more abstract explanation of the paradox is given in I049b 35-I050a z. It is characteristic of all yEVfUt~ that of what is coming into being ~ome part must have already come to be. Therefore he who is learning must already have some of the knowledge in question; knowledge expands out of given knowledge. 34. Tall ".~ To,aUTall Kat Tall i'll'L TOU 'II'C£axE~V. Alexander has T;"~ 8' !lVEV AOYOV 8vvap.n~ Ern TOV €VfPYfLV Ein Ka, TOV 7f'auXnv, and Bz. conjectures that Alexander had a different reading from that in our text. But his words seem to be a paraphrase. T;"~ ciVEV AOYOV 8vvaP.ft~ Tali EVfP'YELV is a paraphrase of Ta.~ p.~ TotaVTa~ and refers to inborn irrational active powers, like the senses, already referred to in l. 32. Ta~ avfV A6yov 8vvap.n~ Toli 7f'auxnv is a paraphrase of Ta~ €7f" Tali 7f'auxnv and refers to inborn irrational passive powers like (to take Alexander's example) the power of wood to be cut. Kat is not, as might be liupposed, epexegetic, for the senses are not, in Aristotle's view, purely passive. 35. Talli'll'L TOU 'II'MXfLV. Cf. A. IOl9 B 26 n. 1048& g. waTE il".a 'II'o,~an Ta lvaVT~a, sc. if the power must necessarily act whenever agent and patient meet. 16. 'II'O'fLV is clearly an emblema from l. 15. • I!,-~U. TO yap ••• lv,a is parenthetical; 8tO oM' I. 2 I connects with

s,

(J)~ EX" I. 14. 20. It seems

better to take TaUTa (with Alexander) as object rather than (with Bz.) as subject of &,cpatpELTaL. With the latter interpretation rlcpatpoLT' av would be rather more natural than &,cpatpELTat. 24. O~TIoI\l, sc. ~~ loon 8vvap.L~.

COMMENT ARY

ACTUALITY

(chs.

6-9).

A.c/uab{y distingmsned/rompotmC)' alld/rom motion (ch. 6). 1048& 25. We now pass from the potency relative to movement, to actuality i we shall at the same time discover another kind of potency, which has really been the object of our search. 30. Actuality means the presence of a thing not potentially like that of the Hermes in the block of wood, or of the half-line in the whole, or of knowledge in the man who is not contemplating truth. 35. Our meaning can be seen by induction and analogy; definition must not be always demanded. Actuality is to potency as the waking to the sleeping, &lc. b 6. It is related either as movement to potency or as substance to matter. g. Potency and actuality are different in the case of the infinite, the void, and similar entities from what the,v are in the case of the seeing, the walking, &lc. The infinite does not exist potentially in the sense that it will ever actually have separate existence; it exists potentially only for knowledge. The fact that division does not cease implies that the activity of division exists potentially, but not that the infinite exists separately. 18. Since all actions which have a limit are means, not ends, they are not really actions, or not complete ones; that in which the end is present is an action. 23. Thus at the same time one is seeing and has seen, is thinking and has thought, is knowing and has known, but it is not true that one at the same time is learning and has learnt, is being cured and has been cured. 28. The latter al e movements, the former activities or actualities. Every movement is incomplete. 35. We have now explained the nature of actuality. 1048& 26. £tpYJTcn, sc. in chs. 1-5.

cr.

26-27. Tl Ti IanI' ... Kul 'II'OLOI' n, Z. 10,p& 6 n. 2g. f\ A'II'Mis f\ TPO'll'OV nvd, i. e. whether we admit all cases of move-

ment or restrict power to cases of movement towards the better (~. 1019& 22) or of good or successful movement (1019& 23, 1046& 17). 33. Tji 3>'n, sr. ypa.p.p:o, cr. ~. 1019'" 8 n. Alexander's Tji 8tap.iTP'l! is probably his interpretation of Tji o>..?), not a variant reading. 35. TO S~ lVEPYEl~. This, the reading of most manuscripts, is a highly elliptical txprelSsioll for' the opposite implied in (ach of these

cases (Sf. the Hermes when carved out of the wood, the half-line when the whole has been bisected, the man of science when actually thinking) exists, we say, actually'. Editors have been, not unnaturally, offended by the ellipse, and various conjectures have been made. (I) Schwegler proposes to treat eIll1~ov ••• uvvopav as parenthetical and omit (;Tt in 1. 37 with Ab, so that the main clause runs TO ell' (V(Py(Lq. Wi TO olKoellop.ovv KT~. (2) Bullinger agrees, except that he reads (; Tt for ~t. The parenthesis beginning wilh eIll1AOV, however, is awkward, and so is (as Cook Wilson points out) the separation of TO av&Aoyov from what is naturally the exegesis of it, viz. Wi TO olKoellop.ovv KT~. (3) Bz. proposes to read TO ell' (V(Py(lq. ~~ov continuously, omitting eIlt after eIll1~ov. (4) It has occurred to me that possibly we might read 6(wpl1uat Toell( (v(py(lq. with AbI' Ald. Cf. '& 6(wp(i lJ ypap.p.aTtKOi, TOell( TO t'1A.pa t'1A.pa M. 1087& 20, lJ ell' ~eIl1J 6(wpwv lvT(~(X(lq. !:'v KUl. KVplwi £1rtUTa.p.£VOi TOcIl( TO A De An. 417& 28. Finding none of these suggestions thoroughly convincing, I have preferred to keep the vulgate reading TO ell, £V(PY(Lq., which by no means Cf. for goes beyond the limits of Aristotle's love of compression. example De Gen. el Corr. 319b 33 (;Tav ell, p.7JeIl'v wop.Wo ot 6a.npov 1ra.60i ~ UVP.{J({J1JKOi (;~Wi, ytv(Uti, TO ell, .p6op&.. 36. o~ 8e~ 1rUI'T~ opo" t1JTEL". A science should at the OUlset define all its terms (An. Posi. 76" 32), but the same is not true of philosophy. For definition must be by genus and differentia, but philosophy deals with temlS that are not included within anyone genus but are common to all being as such. Potency or actuality, like being, unity, and good, is one only KaT' aVMoylav, and we must be content to grasp the analogy and see the nature of the universal term by studying the instances of it. It is beside the mark to criticize Aristotle for not succeeding in defining terms like potentiality and actuality, or for bringing out the nature of each by referring to the other. b ,. Wli TOUTO i" TOUT,\, answers to Wi ofJulu 1rpOi Twa v~1JV 1. 9; Wli TOiiTo ••• 1rp~ TOUTO to Wi KlV1Juti 1rpOi eIlvvap.w. 8. Ta ".i" yap Ws K'''1J17tS 1rpOS 8u"u".",. At one time Aristotle in· cludes £vEpyna in KLV1JUti (Rhel. 14 I2" 9); at another he includes Klv1JUti in (vEpynu (Phys. 20l b 31, De All. 431& 6, E. N. I 154 b 27); at another he speaks of the two as mutually exclusive (1048b 28). K{V1JUti is said to be an (vtpynu but aT(~~i (Phys. 20l b 31), or to differ from £vEpyna because it is aT(~~i (I048b 29). The variations of language need not disturb us. KlV1Juti and £VEPYEtU are species of something wider for which Aristotle has no name, and for which he uses now the name of one species, now that of the other. The difference is brought out as well in II. 18-35 as anywhere in Aristotle. To the test of an (vipynu as against a KlV1Juti which he there offers, viz. that of an activity we may say that we are doing it and have done it at the same time, he adds in the Eth,cS another, that we cannot be said £v(pyEiv quickly or slowly, though we may be quick or slow in passing into the state of ivtpyna (II73 b 2). Cf. also K. 1065 b 14-1066& 7, 1066& 17-26 and notes.

CO!'l1:MENTARY

9-17. On the infinite cr. P4fs. iii. 4-8, esp. 6-8, on the void Php. iv.6-9· Aristotle's views about the infinite are briefly as follows: Extension is not infinite except in the sense that it is inexhaustible, and it is not inexhaustible except in the sense that it is inexhaustible by one particular method, that of division. If you take half of it, then a fourth, and so on, or in general ~of it, then!.. of it, and so on, you will never n

exhaust it.

nl

But the same can be said of any finite part of space.

If

~ again, and n n so on, you will exhaust it if you go on long enough. Space is thus a.1f"Etpov KaTIt 8LalpEuLV but not KaTu, 1f"pOU6EULV, infinitely divisible but not infinite (206 b 7-13). Number on the other hand is a.1f"ELPOV KaTu, 1f"p6u6EuLV-not in the sense that an infinite number exists actually, but in the sense that a number larger than any hitherto thought of can be thought of; but it is not a.1tELpov KaTu, 8LalpEuLV, for in dividing it we come ultimately to the unit, which limits number in the downward direction. And its infinity does not persist but is always coming into being. Time is infinite both KaTu, 8LalpEuLV and KaTG. 1f"POU6EULV, both infinitely divisible and infinite. But its infinity, like that of number, does not persist but is always coming to be. Aristotle does not in the Physics explicitly make out any parallelism between the infinite and the void. But his doctrine about the void (Phys. 2171\ 21-b 28) is akin to his doctrine about the infinite; itis that though we can suppose matter rarer than any assigned matter, there is no space in which there is no matter at all. Cf. his conception of the dense and rare as stated in De Gen. eI Corr. 326b 31-327.1 (taken with what precedes). There are no atoms and interspaces, no pores, only a stuff varying intensively. Aristotle's view of matter in this respect has been compared by Prof. Joachim (ed. of De Gen. et Corr. 124) to Kant's view of' das Reale' in the' Anticipations of Perception '. 9-Ila. a~~",s • • . 6p", ... iv~. The construction of the sentence is hardly possible as it stands in the manuscripts, and it may be that after 8Wap.EL Kal. lVEpyElf!- something like ~ tJ1f"apXEL TO 8wap.EL Kal.lvEpyEu[' may have dropped out i perhaps, h(lwever, it is sufficient to insert '1 and treat the following datives as ethical datives used loosely as in the instances quoted in Bz. Index 166 b 26-38, viz. An. Pro Hb 29, An. Post. 82 b 21, De Res}. 476& 18, G. A. 755 b 12. For a somewhat similar change of construction cf. A. 102." 8, 9. 15-17. A comparison of this with the previous sentence would suggest that the subject is TO EWaL 8vva.p.EL Ta-.J.rvr T7}V lVEpyELaV. 'The infinite does not exist potentially in the sense that it will actually exist as an independent (or objective) entity, but in the sense that it exists potentially for knowledge. For the potential existence of this actuality ensures that the process of division never comes to an end, but not that the infinite exists independently.' TO p.~ tJ1f"OAEi1f"ELV n)v 8LalpEULV on the other hand you take

!. of the whole of space, then

n,v

would then answer to 'Y"cOO-"I, ,.0 ..tval 8vv&p."1 Tattrqv lvlP'Y..ta,' to ,.0 i1.7I'(ljJOv 8vv&"" lCTT&V, TO xlllpl{(u6a& to W~ lv"P'Y(lq,lcrOJU1'Ov XIllP&CTTOv. But a comparison with Phys. 203b 23-25 810. ;,.,roA({7I't"&V Ka~

yap

TO Iv Tji vm7u" p,;'

dpI6pln 80K(i 471'(1jJO~ ..Tval Ka~ TO. p,a6-qp.aTIKo' p''Yl6-q Ka2 TO l~ TOV olJpavov shows that ,.0 p,;' W-OA({7I'''&V ~v 81alp(u&v is 6

viewed as the given fact which yields one conclusion (d7l'08l8I1J(1'I) but not another. Alexander is therefore right in taking TO ".;, W-OA({7f'(&V ~v 81alp(u&v as the subject of both clauses; apart from the previous sentence this gives rather a more natural meaning. In any case it seems better to read ,.0 8£ Xlllpl{(ria., with Alexander than Tk 8£ X"'Pl{..u6al with the manuscripts. The sentence may be rendered thus: • For the fact that the process of dividing never comes to an end ensures that this activity (the activity of dividing without end) always exists potentially, but not that the infinite exists as a finished given fact '. 18-35. This passage occurs in most of the manuscripts (including Ab), and a paraphrase of it occurs in a good manuscript of Alexander (F). It is omitted by EJTr and Bessarion, and is very corrupt in the other manuscripts. But it contains sound Aristotelian doctrine and terminology, and is quite appropriate to the context, and there is no apparent motive for its introduction if it were spurious, so that on the whole it seems safe to treat it as genuine. The text has been vastly improved by Bz. On the distinction between K{II'r/!TI~ and IvlP'Yt"&a. proper cf. I. 8 n., K. 1065b 1,.-1066& 7 n. IS-sal. lnt 8. "wI' 'II'pdeclIIl' • • • O"K 'CIT' TaUTa 'II'pael.l. 7I'pii~I~ is first used in a general sense = K{V7IUI~, then in its stricter sense of K{V'1(TI
'aT, 'II'~pas is best explained by 18EI 4V 7I'OT( 7I'av(u6al, I. 26. Aristotle is speaking of actions which have a limit set to them by the fact that they aim at an end other than themselves, with the attainment 9f which they come to a stop. 19. otOI' TO Wxl'aCml' 4\ laxl'aaCa. The manuscript reading olov Toli i.uX".a{v..&v .q laxvau{a alJTo cannot stand. alJTO cannot be interpreted (as by Bz.) as TlA~. Nor is it enough to excise awO (with Christ) as due to dittography; for luXVfUT{a is not the end of TO iuxva{VE&V but the same thing. It is named among the Kun]u(l~ dT"AEi~ in I. 29' The end of,.o luX,Va.{VE&V is luXV~~ or, more remotely, ~yl(la (A. 1013" I, PhYS.194 h 36). I therefore follow Bywater's suggestion and read oTlw ,

TO

• , • , IUX,Va.&VE&V '1,., luxvaula

a,,-ra

(

Ie.

ov•

'\

•

,

TEAO~ EITT&V

.J\. \"

"'"

aAAa TIIIV

'\) 7I'Epi" TO TEAO~ •

8i chal' laxl'aC"!I, • the parts of the body themselves, when one is reducing their bulk'. alJT& is curious, and some corruption may be suspected. laO-lil. oaTIIIS ••• KCII'IJCI"S, • are in movement in this way, viz. not being already that for the sake of which the movement is'. The construction of I17I'J.pXOVTa. is very awkward, and perhaps we should with Fonseca read ~7I'apx.6VT_. IIIV would drop out easily by homoioteleuton. lila, laa. Bz.'s emendation lKC'1I'IJ ii, and his omission of~, are neces!'ary. la3. Bz. has emended this line successfully by the aid of De Smsu lIO.

COMMENTARY H6 b 2 Kal d lI'II'al' 1Ip.a .lKOun Kal clK~KOE Kal i.l>'w~ alcr8J.vlTa.L Kal iju8-qraL, and Sopko El. 178- 9 &P' lv81.XlTaL Ta awe} 3.p.a '11'0"", TE Kal'll'E'II'oL"1KlvaL ; oV. .lUo. p..ql' Apal' 11. TL 1Ip.a Kal IwpaKlvaL Ta awa Kal KaTo. Tawa lv8I.XlTaL. The manuscripts give APi- 4UQ. Kal r/JPOI'Et Kall'oEt KalI'EI'cn,KEI'. Bz. writes bpij. 3.p.a Kal IwpaKE, Kat r/JPOl'Et Kal 'II'Er/JPOvr,KE, Kall'oEt Kal Vwcn,KEI'. Fonseca bad already conjectured IwpaKE for r/Jpol'li, but that is much less probable. Bywater, while accepting IIp.a, thinks that the one perfect tense I'EI'O"1KEI' is enough and that the others are • understood J. But in the rest of the section Aristotle is careful to supply all the perfects; and in so corrupt a passage we may allow a greater freedom of emendation than usual. I therefore follow Bz. 38,33. It seems best to follow EJAb in reading IUI'E~TA' KAl KEK''''ITA' ••• KWEi KAl KEK{"'IKEII, and to put a comma after erEpOI'. 'It is not the case that a thing at the same time is being moved and has been moved; that which has been moved is different from that which is being moved, and that which has moved from that which is moving.' erEpOI' is easily understood as the subject of KLl'Et Kal KEKl""1KEI'. 35. T{ TI. len" KA1'lfOioll, cf. Z. IO.p- 6 n.

Wken is one tking tke potency of another J (ch. i). I048 b 37. When does a thing exist potentially? Earth is not potentially a man tiII it has become seed, and perhaps not then, just as not everything is capable of being healed, but only the potentially healthy. 1049& 5. (I) In artistic production one thing is said to be potentially another if (a) when the artist wishes, the actualization takes place if nothing external hinders, and if (6) nothing in the patient hinders; that is potentially a house, in which there is nothing to prevent its becoming a house, and which needs no addition, subtraction, or change; and so in all cases where the source of the actualization is external. 13. (2) Where the source of the actualization is internal, one thing is potentially another if when nothing external hinders, the actualization takes place by the thing's own nature. The seed is not yet potentially a man; for It must first fall into a certain material and be changed, as earth must become bronze in order to be potentially a statue. 18. When we say a thing is ' of' something else-as the casket is of wood or wooden, and the wood is earthen, and the earth is perhaps 'of' something else-that which it is • of' is potentially (in the unqualified sense) it; thus wood, not earth, is potentially a casket, is the matter of a casket.

255

114. If there is something that is not' of' anything else, it is prime matter, not being a 'this '. Subjects or substrata differ by being or not being , thises ' ; 119. (I) what underlies accidental attributes like' musical' is a substance like 'man I (and he is called not music but musical, as the casket is called wooden); 34. but (2) where the predicate is a form or ' this', the ultimate substratum is matter. 36. It is natural that the' of' or derivative form should be used with reference both to matter and to accidental attributes. for both are indefinite. Bz. argues that the insistence in this chapter on the fact that that which is potentially X is the sum of the proximate, not of the remote conditions of X, marks a difference between Bvvap.,~ and v>..'rJ. v>..'rJ is primarily applicable to 7f'pWrq v>..'rJ, the remote and absolutely unformed matter; BvvaJL!~ to the proximate conditions. This distinction does not, however, seem to be intended by Aristotle, for in his discussion of matter he has similarly insisted on the importance of finding the proximate matter of a thing (H. 10H b I). v>..'rJ and Bvvap.L~ are constantly used without any trace of such a distinction (e. g. 1049" 23, 1050815, b 27, A. 1071& 10, N. I088 b I. 109283). 1049& II. 3TUI' ;jS" yiV1JTU' cnrip"u. Aristotle is using CT7f'€Pp.a in what is for him its proper sense, that of the spermatozoon or male element in question, as opposed to TO. KUTap.Vv,a, the ova or female element; lor I. 14 TO CT7r€pp.a OV7rW (B,;: yo.p Iv lliftl (7f"CT';:V) Kal. P.'TU/3a.>..>"fLV) must refer to the entrance of the male element into the womb. But he is not taking account of his own view that the CT7r€pp.a forms no part of the matter of the offspring but is its formal and efficient cause; he writes as if he accepted the popular view which treated the male and female elements as uniting to form the matter of the offspring. He is merely illustrating a general principle; and in such cases he often writes from the point of view of a common theory not his own. Cf. H. 10Hb 17 n. o.,Si TOTt til'"" is explained in II. 14, 15. 3-5. Wcnr.p o~1' ... SUI"".,. It would be possible to treat this as the beginning of a long sentence, with the principal clause beginning (irregularly) with Ka~ Ocrwv BV in I. 13. Aristotle would then be illustrating natural production (11.1-3. 13-17) by artificial (11.3-12). But iJ,crTrfP occurs several times elliptically without any principal verb, a principal clause like oiJ.rw~ lXfL Ka~ Iv TOVroI~ being understood. Cf. B. 1000" I n. It seems best to take it so here. 5-18. Aristotle first states the o~ in the case of artistic produc"1~ YfV€CTf.IIIt. Then in 1. 13 he tion, cf. I. 12 OCTWV Uw(J", ; ,. ..,. • ( , passes t 0 nat uraI prod uc t 5, KaL OCTWV 071 'v aVTftI TftI 'XOVTI se. 'f'7JI' Y€V'CTLV). which are opposed to TO &7f'O BLavola~. The two types of pro-

ow

d.pm

~

~.

COMMENTARY duction, natural and artificial, have already been indicated in II. 1-3, 3-5. Aristotle is evidently trying to determine the ~onditions under which A may be said to be potentially B. In arlislti: production A, the matter, has to be acted on by C, the artist, before it can become B, the product. Thus the ;Spo'> in this case is as follows: A is potentially B when. if C wishes it and nothing external hinders, A becomes B, and when, further, nothing in A hinders (II. 5-8). This he illustrates in detail in the case of the question' What is potentially a house? ' (II. 8-II), and finishes by saying that the same formulation applies to all cases of artistic production (II. II, I2). In natural production there is no artist involved; nature is an d.pX~ KtV'l/ITEW,> (V a~ce V a(IT(). Thus here the ;Spo'> is simply that A is potentially B when, if nothing external hinders, A will of itself become B (II. 13. 14). Thus the male seed is not potentially a human being, for it has first to enter the womb and be transformed; but the ~p.a thus produced is potentially a human being, g. TO!STIt' Kal "1i tThn. Kat is clearly explicative. 10. For oliBi where p:qBi would be expected cf. I. 1053 b 18 n. l ., aUTIt' • ~ Tit'~"EXOVTL (SC. TaVTa ~.., \' .) 13. KaL\ .oaill., "l. 0" ovva/LEt "EYETat ELvat , caa KT).. 14-15. SE' yap ••• I'ETafld).).ELV. Alexander says 8E;: yap ttUce .. 'll'EITE;:V Kal/LETa/J&'uELv. 'll'EITEtV may be simply Alexander's interpretation, but it is difficult to suppose that some such verb can be 'understood' with Iv ttUce, and accordingly 'll'EITEW or some similar word should he inserted in the text. Cf. T71" /LYrrpa,. 'll'p(!" &'ll't'II'TEt TO IT'II'ip/LO, H. A. 583& 22. Alexander takes TO IT'II'ipp.a to be the seed of plants, but from II. 1-3 it appears that Aristotle has in view the male element in animal generation. 18-~~. Aristotle now proceeds to give a linguistic test of the potential matter of a thing. If we say y is x-m, x is the proximate matter ofy. The parenthetical example oroI' .•• IKEtvtVOV disturbs the construction of t!le sentence, so that we get as subject (KE'iVO, which does not refer to the same thing as ;S, and we have (ITTtV instead of ETvat, Ig. luiv"'DV, cf. Z. 1033& 5-23. ~O-~I. 'II'd).LV •.. lKEivLVOV. The construction is loose but intelligible. 'Again, earth will illustrate our point if it is similarly not something else but o/something else (not x but x·en).' ~4-~7. This is the nearest approach in Aristotle to the use of'll'pw", VA7J In the sense of entirely formless matter. But even here it ooes not mean that, but matter with the minimum of form. If there is no material, x, out of which fire is made, so that it can be called X-t1I. then fire is first matter, but it will still have the definite character of fire. Cf.~. 1015 a 8 n. ~7. o~ TeSSE TL o4aa. The sentence must be interpreted in the light of what follows in II. 27-36. Aristotle there distinguishes the case in which the substratum is a 'this' from that in which it is not. The substratum of a 'II',U}O,. is a . this' or substance; the substratum of

w

~-.

-·)1

a substance is matter. An opposition is therefore wanted between nUl and TOO, TL or of!uta, and we should read of! TOO, TL otua or of! TOO( TL

,

.

,

Kat OVULa.

lZ8. Apeh must be right in reading Ka.6' o~.

Alexander, who reads

KaOo>"ov, has no reawnable explanation to give of it, and Bz. says 'TO KaOO>..ov cur h. I. comparetur cum sub~trato, equidem non intelligo '. With KaO' o~ we get a good sense-' the subject or substratum (Kut ex-

plicative) differs in different cases by being or not being

:1.

this '.

For

otaq,ipn in this sense with a singular subject cf. .:l. 1016" 24, ll1e/(or. 341b 24. KaOo>..ov was probably introduced by a copyist who thought that 'the subject and the substratum differ' must mean that they differ from one another (which would be absurd). But Aristotle would almost certainly have expressed that by oLaq,€pn TOU {;7f'oKnp.ivolI. I have .found only two instances in Aristotle of the things which are said to differ being coupled by Kat (A11. Pro 57'" 33, All. Post. 77 3 14). The distinction which is drawn in 11. 29-36 occurs also in Z. 103 8b 5, H. 1044 b 9, and is there expressed as a difference not between the ~ubstratum and something else but between two kinds of substratum. What precedes Kat TO VrrOK({P.CVOV, then, must be a synonym of TO {;7f'OK,tP.CVOV, and TO KaO' o~ is exactly" h:lt we want. The s:lme error has been made by the manuscripts in r. Iooia J4 and in Sex!. Emp. 72 I. 2 (Bekker). The difference which Aristotle here points out is tha.t between two levels at which the cleavage between substratum and attributes may he made. You may distinguish accidental attributes from their subject, and in this case the subject is a substratum cont:lining certain essential characteristics; or ag"'r/' and C, 7f'a.~, are both indefinite. Aristotle often, as here, says that we describe things 7f'apwvvp.w~ by words derived from the names of qualities. Cf. Cal. la 12, 61> [.1, IOa28, Top. IIla33-b4. He can hardly ha\'e thought that the word >"WKOV was derived from the word >"(vKOT'r/~. What he means Tathel is that when we say a man is white we are not saying that he is a certain entity, but that he is qualified by the posses~,ion of a certain entity, whiteness. ' White', though linguistically simvler and earlier tlUIl , whiteness " stands for a more complex meaning, viz. 'qualified by whiteness " just as ' wooden' stauds for a more complex meaning than 'wood'. b I. What is the meaning of ~aying that both v>"l1 and mW-q are indefinite? Matter is TO dOpLaTOV 7f'plv ;'Ptu(j~l'at Kat P.CTUU)(fiv (is,'t,~

CO:\1:MENT ARY TLVO~

(A. 989b 18); it is indefinite in the sense that it has (relatively to that whose matter it is) no form or character. 1rafir} (such as whiteness) are indefinite not in the sense of having no character but in the sense of being 'floating universals', not in themselves fixed down to anyone substance but capable of belonging to anyone out of many. Now since substances on the one hand have a character and on the other hand are definite individuals, no substance can be said to be its matter (e. g. 'wood ') or its 7raBo,> (e. g. 'whiteness') but only to be made of its matter (' wooden ') or characterized by its 7raBo,. (' white ').

Aclualt'{y prior 10 potency (ch. 8).

104gb 4. Actuality is prior to potency, not only to that which is a principle of change in another thing or in the thing itself qua other, but to any principle of change or rest. Nature is a principle of change, but in the thing itself qua itself. 10. Actuality is prior to any such principle in definition and in substance, and in a sense in time; (I) in definition, for what is , capable' is so by being able to be active; thus knowledge of the potency presupposes knowledge of the actuality. 17. (2) In time an actual member of a species precedes any potential member, though the individual is potential before it is actual; !Z4. the potential is actualized by another individual which exists actually-man by man, musician by musician. !Zg. Hence it is thought that one cannot be a builder if one has built nothing, whence arises the sophistic objection that a learner without having an art has to do that which it is the business of the art to do. 35. The answer is that since, of that which is coming to be, something must have already come to be, the learner must already partially have the art. 1050& 4. (3) In substance actuality is prior, (a) because what is posterior in genesis is prior in substance, since it already possesses its form, 7. and because everything that comes to be moves towards an origin, i. e. an end, and activity is the end of potency; animals have sight in order that they may see, they do not see in order that they may have sight. 15. Further, matter exists potentially just because it can come to its form; when it exists actually it is in its form. The same is true where the end is a movement; teachers think they have attained their end when they exhibit their pupils at work; and so it is too

~59

with nature. The work is the end, and the actuality is the work; thus lvipy€l.a. (actuality), which is derived from lpyov (work), comes to mean much the same as lvnAiX(1.Q. (complete reality). gS. In fome cases the exercise is the ultimate thing (e. g. sight), while in others there is a separate result (e. g. a house as well as the act of building results from the building art); the actuality is in the first case the end, in the second at any rate more of an end than the potency. so. Where there is a separate result, the actuality is in the thing made (the act of building is in the thing built); where there is not, it is in the agent (seeing is in the man who sees). b g. Thus substance or form is actuality, and therefore actuality is prior in substance to potency; and we have seen (I049b"l7-29) that in time actuality presupposes actuality right back to that of the prime mover. 6. (6) Actuality is prior in substance in a stricter sense of 'prior in substance'. For eternal things are prior to perishable, and no eternal thing exists potentially. Everything that is capable of being is also capable of not being, and therefore perishable, 14. either absolutely in respect of its substance, or in some respect, i. e. capable of changing its place, quantity, or quality. What is not in the absolute sense perishable cannot • exist potentially' in the absolute sense (though it may in a qualified sense). go. Nor can eternal movement so exist, nor an eternal moved object, if there are such things. Thus there is no fear that the sun, stars, and heavens will ever come to rest, nor do they tire of movement; for it is only matter and the capacity for the opposite (i. e. for resting) that can make movement laborious. gS. Even the things which are in continual transformation, like earth and fire, imitate the imperishable things, for they have eternal movement by their own nature. so. All other potencies are potencies for contradictories. Rational potencies are capable of opposite actualizations, and irrational potencies produce opposites according as they are present or absent. S4. It may be objected to the Ideas that since 'science itself' is a potency, there must be an actuality which is more scientific than it; and so in other cases. 1049b 4. 8LwpLC1Tcn, .:1. I I. 8. The false reading in EJ has arisen, as Bz. points out, from a dittography of lv Ta.~ yiv(1 and a subsequent attempt to make sense of the result by emendation.

CO:'lJ:'IfF.NT ARY 13. TlI 'll'PWTWS 8UI'UTOl', cr. 8VJ1UP.EIIl~ ~ >"€YETal p.u.>"uTTa /(Vpllll~, 1045 b 35. Aristotle means 8Vvap.l~ in the sense not of potentiality but of power in relation to movement, the sense discussed in chs. 1-5. 18. TlI Ttii £18.1 T~ allT~ ll'Epyoul' 'll'POTEPOI', 'the aClual which is identical in species is prior'. I. e. prior to the potential member of a species (e. g. to a seed of corn) there must be an actual member of the species. SlI. .,. '»''1 answers to Tali d.v()p6nrOV, TlI cnripI''' to Tali ulrov, ft 6pATIICOI' to Tali ;,po,JITOi. CT'Jr€PJ£I& is frequently used of the male element in animal generation, but that is not the matter or potentiality of the offspring, but its formal and efficient cause, so that mpJ£I& here probably means (as it often does in Aristotle) the seed of a plant. I n a r -3, r 4, 15 Aristotle writes without reference to his doctrine of the parts played by the male and female elements in generation, but he has it in view in 11. 24-26 below, and it is better to interpret here in accordance with it. Sl4-Sl5. 4t!1 yAp ••• 1l1'T0I does not prove Aristotle's point. He has said that there must be an actual member of the species prior to the potential member of the species. This is not proved by pointing out that :\11 actual member is needed in order to transform the potential member into an actual member. He would have proved his point (as regards animal generation) if he had referred not to the male parent which (on his theory) transforms the matter, but to the female parent which provides the matter. The internal logic of ll. 23-25 would be right if we could suppose ToVTIIlV ill I. 23 to refer to ;;'v6ptmrOfl 1(0.1 O'tTO~ /(0.2 ;'po,v, but it must refer to ~ iJ>..." 1(0.1 Ta CT7f'€PJ£I& 1(0.2 ~ OpaTll(OV or it would not illustrate the main thesis that actuality is prior to potentiality. !as. otOI' 4vtplll'll'Os le 41'8pw'II'Ou. U is used loosely, since what Aristotle means to exemplify is not II( Tali 8vvO.p.EI OVTQC but wa lvEpYEll!- 3vToc. Sl6. /'OUcrllClIs 6'11'1I p.oucrLICl'U, i. e. the musical faculty in A can be actualized only by the teaching of B who is already a musician. S117. Etp'lTaL 8~ ll' TOLS 'll'Ep1 '"is o"crCas AcSyOLS. Z. 7, 8. SIIg-I050B 3. Aristotle here pas8cs to a second proof of the priority of actuality to potentiality in time. It must be prior because one cannot have the potentiality of building (for example) without having engaged in the actuality. This is said (I. 29) to be a corollary of the principle to which Aristotle has been referring in 11. 17-27, that a potential A can be made into an actual A only hy a member of the same species. This principle might be applied in either of two ways; it might be said (I) that a potential builder can be transformed into an-actual builder only by the teaching of another actual builder, or (2) that a potency of building can be transformed into an actuality of building only by another actuality of building, i.e. that by means of imperfect and inartistic acts of building (cf. what the Ethics calls, in a similar discussion, doing ypap.p.aTII(OV TI but not -ypaP.J£I&TII(bv;, 11(\5" 24) the potentiality of building conies to be actualized in

261

perfect and artistic acts of building. Now (I) is irrelevant to what Aristotle says in b 29-32, and even (2) does not exactly correspond to it. For (2) could only show that the potentiality needs, for its aclualt'salt'rJtl, another actuality, whereas what Aristotle claims in II. 29-32 is that it presupposes, as a condition of its e.,,(tslmce, another actuality. At first sight it looks as if there were the same confusion as seems to exist at I. 24. But Aristotle's meaning is that though a bare 8vvaJLL~ of building may exist in a man before he has done any building, such a man is not an OlKO&>p.o~. Being an OlKO&>p.o~ is not a bare 8vVaJLL~ but a leL~, and this presupposes lvtpyua. 35. 4~M introduces Aristotle's answer to the sophistical objection, and should, as Bz. saw, have a full stop before it. 36. iv Toi, 1I'Epl KLV1jcrC"". For this as a mode of reference to the last half of the Pqyszes, De Cado 27 2a 30, 275 il 2 1,299" 10, De Gell. d Carr. 318a 3, De Sensu 445 il 19. The particular reference here is to vi. 6. The proof there is as follows: 'That which moves must move in every part of the time which is the immediate or proper time of the movement. For if it moved only in some part of the time, that part would be the immediate or proper time of the movement. Now if a thing has moved a certain distance in a certain time, a thing which began to move at the same time and moved at the same speed must have moved half the distance in half the time. Therefore the original thing must have moved half the distance in half the time. Therefore that which is moving must have moved. Further (an alternath'e proof, 237" 3-11) it must have moved in each part of the tIme during which it has been moving. Therefore, since time is infinitely divisible, everything that is changing must have ullllergolle an infinite number of changes. Further (an alternative proof, 237 a 11-17) that which changes continuously must either change or have changed Iv bTI{'OVV (237 8 q : one must not say' in each part of the time', for the moment, which Aristotle proceeds to speak about, is not a part but a section (TOJL~) of the time). Now it cannot change in a moment. Therefore it must have changed at each moment, and must therefore have undergone an infinite number of changes, since there is an infinite number of moments in any time'. So far Aristotle has said that the thing which is moving must have moved, not, what he says in the present passage, that a part of it mUlit have moved. But he goes on to draw this distinction in the case of y(V(TL~, though not of K{VTJ(TL~ gellerally (237" 1 I; the passage 237" I 7- b 9 may be omitted). 'A house which is coming into being has not already come into being; but its foundations have.' The distinction drawn ill th\: PhYSI£'S seems to be due to an ambiguity in th.: word Y£YOVE. It would be abslIrd to say that \I h,1t is coming into being mus. have come into being; allll Arbtotle therefore contents I,i'llsclf wilh saying that a part of it mllst have come into being. But what rcally answers to the phrase 'what is moving must have moveJ' is 'what is (;oming into being must have beell L'01mi'C into being' (for . hal; ,'()/Ilt: into being' implies a (;omplction

cr.

COMMENT ARY which 'has moved' does not), and here no distinction between part and whole need be introduced. Aristotle in the present passage unnecessarily introduces in the case of movement the distinction which in the P4J!sics is drawn only in the case of becoming. Aristotle's application here of the thesis established in the PhJ'stcs is as follows: It will follow that if an ~Trt(Tn,p.'YJ is coming into being, part of it must have already come into being. Thus the sophistical objection, that if the Svvap.w; p.€Ta AOyov are acquired by (vlP'Yna a man who has not yet acquired an art must yet be supposed capable of acting artistically, is met by the answer that he has the art to some extent. In other words the faculty is not produced by actuality but transformed into actuality by it. This brings the fact in question under the general principle ~K Toli Svv&.p.n oVTor;; ytyvETat TO (VEP'YEtf!- ~V {J7rc, ~V€P'Y€{f!- OVTor;; (I. 24), but it really gives up what Aristotle is trying to prove, that actuality precedes potentiality in time. There is the same confusion which we have observed in the note on II. 24-25. 1050& 4-b 2. What Aristotle uies to prove in this section is that actuality is prior to potentiality in substance, i. e. is more real or more substantial. The general principle on which he bases his proof is that what is posterior in generation is prior in form and reality. More definitely, actuality is prior in reality because the actually existent has reached its form while the potentially existent has not. The potentially existent or undeveloped has features unintelligible in themselves, which can be understood only as the prophecy of attributes which wiII be found in it when developed. It still lacks part of its nature; it is matter without form, and therefore not primary substance. 4. At first sight it seems inconsistent to maintain (I) that actuality is prior to potentiality in genesis (I. 3), (2) that it is prior in substance because it is posterior in genesis (I. 4). But with the qualifications with which Aristotle makes these statements (in the whole context) they are quite compatible. 7-10. The reasoning is somewhat complicated: (I) The TlAO" of a ytyv6p.£vov is its &pX~' its origin (that this is the underlying meaning of (Tr' &Px!lV (JaSt'n ••• Kat TlAor;;, 'moves to an ~PX~ which is its TlAor;;', is shown by the fact that Aristotle subjoins a proof that the TtAor;; is the &.PX~' viz. : The o~ €V€Ka is the &pX~. The TtAor;; is the o~ €V€Ka). ( 2) The (vtP'Yna is the Tf.Aor;;. Therefore (3) the ~v(pyna is the &pX~' and therefore prior to the Svvap.tr;;. 14. 4\ 3T1

O~8EI' 8loI'TUL 8EWPELI' is excessively difficult, and one would be tempted to regard it as a gloss (so Diels, according to the editor of Bz.'s translation), if one saw what the gloss meant. Alexander's interpretation implies that he had these words, except OTt, of which his interpretation (as distinct from the lemma) has no trace. This being so,

e. 8.

105011.4-19

it is possible (I) that we should omit OTt as an intruder which has come in from the next line, and take ~ as equivalent to d 8, JL~ (cf. Z. 10.pb 23, E. N. II70b 17). For the intrusion of OTt cf. H. 1043& 34 n., Prob!. 962& 2. 'They are not speculating, except in a qualified sense of that word' (speculating in the proper sense means speculating for the sake of doing so, or of reaching the truth (cf. a. 993 b 20, Pol. 1325b 20»; 'otherwise (if they are speculating ill the proper sense) they have no need to speculate' (sc. for the sake of acquiring (hwP1/Tt~, because in that case they must already have it). (2) Alternatively we might read with E ol>X V(ol>Xl has replaced ol>X Vin good manuscripts in An. Posi. 84 b 8, E. N. 1161& I) and interpret' and these are said to speculate in order to get the speculative faculty, not in so far as they speculate but only in 80 far as they do so in a particular way, or because they have no craving to speculate (for its own sake) '. Or (3) we might, besides reading ol>X V. read 0 Tt or OT( for OTt. 'And these speculate in order to get the speCUlative faculty, not in so far as they speculate, but only in so far as they speculate in a particular way, or about subjects about which' (or' at a time at which ') 'they have no craving to speculate.' Apelt's d).)..' ~ w8l, OTt ol> 8vvaJITat (hwp(tv is not very probable. 16-17. 6,...0(1115 8~ ..• TJAOS. 'And so too in all other cases, even those in which the end is a movement'. Aristotle has said that matter exists potentially just because in certain circumstances it will proceed into its formed state «(18o~). But, he now says, the principle that potentiality exists only in relation to a possible realization is equally true when there is no matter to be impressed with a form, no material object to be produced, but the end is a movement. The distinction between these two cases (7f'ol'¥J(J'L~ and 7f'paeL~) runs through the whole passage & 15-b 2. 18. lVEPYOUVTCI., sc. TOV JLaffrJ~v. 19. KCl.l ", +uaLS 6,...0(IIIs. Aristotle is thinking of such things as

sight (I. 24). Nature is content not when it has produced creatures capable of sight but when it has exhibited them in full exercise of the activity. 6 nCl.ualllv~ InCl.L 'Ep,...ijs. Alexander tells us that Pauson made a Hermes about which it was hard to say whether it was carved in the ordinary way on the surface of a stone, or enclosed in a transparent substance. 'How could it be "without", when the surface looked perfectly smooth like that of a mirror, or " within ", when the surface showed no trace of joinings? ' This account is, however, certainly wrong. In the first place Pauson was not a sculptor but a painter, and in the second place the kind of sculpture Alexander mentions is not known and is most improbable. Pauson was apparently addicted to trick pictures. cr. the story told by Ps.-Luc. (Demoslh. ElIcom. 24), Aelian (Var. Hisl. xiv. 15). and Plutarch (de Pylhzae Orac. 5. 396 E) of his picture of a horse running, which by being turned upside down was made to represent a horse rolling on its back. Professor Percy Gardnet suggests that the Hermes may have been

CO?lIMENT AR Y a tricky painting, which deceived the eye somewhat in the manner of those in the Wiertz Gallery at Brussels, which stand out, apparently, in high relief from the canvas. ~O. draw f\ lew, i. e. whether the knowledge has been absorbed by the pupil or has remained' outside' him. ~!iII-!iII3. 8LO ••• lllTE).iXELul'. Because the lfTYOl' is the T(Aoi (I. 21), the word ll'(PYEI.O., which is derived from lpyOJl, tends to mean the same as Mt:A(Xt:I.O.. Cf. 1047330 n. !i117. lvell I'il' refers to cases like seeing, l..ell 8i to cases like building. !i118-~9. ,., yAp otK0861''1aLI ••• OtKLIf gives the justification for 11'84 S, p.a.>.Aov TIAOIl "ill SWaP.EWIl laTIV. The actuality is more of an end than the potentiality, for it resides in the lp"Yol', and comes into being, and exists, simultaneously with the lp"Yol', which is the end in the strict sense; while the potentiality does not reside in the lpyOJl, exists before the lp-yov, and can exist after the lpyov has perished. ,., yAp otK0861''1aLI ll' Trt otK080l'ouI'i"'t'. The point of lv in this and the following lines is this: an activity like building, or like seeing, is evidently not a wo/C({p.t:vov, but lv WO/cElp1V'f!; it requires a substratum. Now a 7rO{TJO'IIl like building is the actuality both of the builder and of the house (PhYI. 202& 13-16), and resides, in a sense, in both. But that in which it most properly and directly resides is that which exactly answers to it, which comes into being with it and exists simultaneously with it. This is obviously the house rather than the builrier. In the case of a 7rpO.tlll like seeing, on the other hand (I. 34), there is no separate lpyov, and the actualily must be said to reside in the lvt:fTYOvv itself. b J. The reference to EUa'p.oV{a is a digression. Aristotle points out, as against a materialistic view, that happiness is in the soul, is an acti\"ity of it, and therefore does not depend primarily on the goods of the body, nor on external goods (d. E. N. 109Sb 12-22~ !i11-3. WaTE +"I'IPOI' ••• lll'TLl'. This follows not from what directly precedes but from the whole section & 4-b 2. For the language cf. a 15, 16. 4. WI11fEP It'll'O"..I', 1049b 17-29. That passage, however, contained no explicit reference to the pri1llum 1Il0Vml. For the doctrine cf. A. 6, 7. 6. 4)')'A I'~I' Kill KupLwTlplIII, Ie. ""pCyrepov Tjj ooo-~ lvlpyE&4 Bvvo.p.t:CIl!l (I. 3). The new argument is:The eternal is prior in substance to the perishable (assumed here, but cf. B. 999 b 5, Z. 1032b 30, A. 6, 7). . Eternal things exist actually, perishable things potentially (proved in II. 8-18; I. IS-1051& 2 state corollaries of this, which form a digression). Therefore the actual is prior to the potential. Therefore (on the principle that what belongs to the better is better than what belongs to the worse, Top. II6 b 12) activity is prior to potentiality.

e. 8. IOSoa 20 -

IOSOb 30

It is not obvious why this is priority rii olJutq. in a more proper sense (KVpLWTifX'l~) than those already mentioned. But in A. 1019" II Aristotle has said that all the senses of prior and posterior may be reduced to that which is stated in 1019" 2; 'those things are prior in nature and substance which can exist without others while the others canno~ exist without them '. Now the eternal can exist without the perishable and the perishable cannot exist without the eternal, and though Aristotle does not explicitly put the matter in this way (except incidentally in 1. 19), it seems that this is the 'stricter' sense 01 'plior in substance' which he has in mind. ,. EUTL S' ouGEv SUl'nfloEL cltSLOV. The most obvious rendering would be ' nothing is potentially eternal', but from 1. 16 it appears that di8wv goes closel" with oMiv, 'nothing eternal exists potentially'. So AI. 591. 20. 8. lI'&O'a S.lvafloL~ Ilfloa Tij~ cl"'TL+nO'Ew~ iUTLI'. It is the peculiarity of rational faculties to be able to produce either of two contraries (I046b 5); a knowledge of medicine enables a man either to cure or to kill. But all potentialities are potentialities for either of two contradictory results. That which can under certain circumstances become or do something can also, if those circumstances be absent, net become or do it. g-II. T~ floEI' ••• 04GEVL is merely preparatory; ro SuvaT~v ••• iVEPyEll' is the emphatic clause. II. On the difference between SuvaTov and €V8EX6P.EI·OV cf. 1047" 26 n. 14. +GapTOI', tj 411'},.W~ tj ToiiTo a4T~ 8 }'JYETaL ivSJXEa8al fIo~ EtvaL. , Perishable either in the unqualified sense or in that precise respect in which t is said to be capable of not being.' A thing is 'perishable' if it can lose Its essence; 'localIy perishable' if it can change its place; • quantitatively perishable' if it can change its size; 'qualitatively perishable' if it can change its quality. Ig. KaLTOL TaUTa lI'PWTa is the minor premise of the syllogism: Things existing of necessity do not exist potentially. The primary things are the things that exist of necessity. (Therefore the primary things do not exist potentially. Therefore actuality is prior to potentiality.) 21. 04K EUTL ••• 1I'0L. 1. e. it is necessarily moved, but while moving from A to B it may be capable of moving from 13 to C. 23. 8 +of3oUI'TaL OL lI'Epl +.lO'E"'~. Alexander says the reference is to EmpedocJes, and this is confirmed by De Cado 284" 24 ovn 81j TOVrov TOV Tpmrov v7ro>':rprTiov, OVTE 8L~ 8tV1luLV 8aTTOv~ TlI)'xavoVTa (TOV

"JV

ovpavov) cpopU.~ ~s olKEta~ IjoTrijs ETL uW'Eu8aL TOUOVTOV xrOvov, Ka8a7rEp ·EP.7rE8oK'\~S cplJU'{v. Aristotle compares EmpedocJes' view to the

traditional belief in the necessity of an Atlas to hold up the heavens. There is nothing about this in the remaining fragments of Empedodes. 30. Ka8' alhC\ ••• KLV1)O'LI'. It is doubtful whether this refers to the natural movement of fire upwards, and of earth dowr.wards, or to the IG?S.I

S

266

COl\ll\lENTARY

constant tendency of the elements to change into one another, by vii tue of which Aristotle says (De Gen. el Corr. 33'.1-') they imitate the circular movement of the heavenly bodies. 30-33. Aristotle repeats here the general statement (cr. I. 8) that all potentialities are potentialities for either of two contra(iictories. He then subdivides. (I) Things which in virtue of a AOyoi can act ill one way can also act in the contrary way (JL~ w8t = 'to move not thus', not 'not to move thus '). (2) Irrational potentialities are potentialities for either of two contradictories according as they are present or not. Thus under (2) Aristotle is not referring to the sense explained above (11. 8-12) in which potentialities are potentialities for either of two contradictories according as certain conditions are present or not (Alexander interprets it so, but the Greek will not bear this interpretation), but is saying that they are potentialities for either of two contradictory results according as they themselves are present or not. This at first sight seems pointless. But in Pkys. 251a 31 Aristotle says that there is something in physical things akin to the contrary actualizations of a 'rational power', T~ "'lap I/roXP~If (J~pp.a.ilfEL CM'pm4tl., lI'Wi Ka, c17T(A661f. That which is cold is capable of becoming hot, and then of heating other things. This seems to be the meaning here. 30. al 8. cl).).cu 8Wo.JLfLi' because Aristotle has been speaking of things which are in some respect tainted with 8VlfaJLLi, e. g. in respect of their position in space (cf. 11. I', 18), though in other respects existing in actuality. 31· le~., SLWPLCM'CU. The statement is a general one about at ruaL SwaJL£Li 7raUaL, so that the reference is probably not to the distinction of J"ational from irrational powers as being Tc7w WalfTtwIf at aVra.l (1046b 4, 1048a 8), but to the discussion of potentialities in 1050b 8-12. 35. OL l., Toii )'cSYOLi, 'the people who occupy themselves with verbal discussions '. Cf. A. 98,b 31 n. 36-10518 II. a",-O ill'L~""1J is the faculty of knowledge itself, apart from particular manifestations, and as such inferior to the activity of knowledge. 1051" 3. KA1 SU"Ap.EWS KA111'clcnJi dpX~s ""ETAI3).1JTLK~i, cr. 1049 b 6.

lI/isrellaneous r~marks about polmcy alld artlla/i(y (ch. 9)'

I051R 4. A good actuality is better than the good potency. For capacity for one thing is always capacity for the opposite, and is so at the same time (though the opposites cannot exist at the same time), and therefore is both good and bad, or neither.

15. Similarly a bad actuality is worse than the potency, and posterior to it, and therefore evil cannot be an actual substance existing apart from bad things. Therefore among eternal things there is nothing evil. 1011. Geometrical relations are discovered by actualization, i. e. by dividing the given figures by lines that before existed potentially. Cf. the proof that the angles of a triangle = two right angles, or that the angle in a semicircle is a right angle. What exists potentially is discovered by being actualized. The reason is that the geometer's thinking is an actuality. Thus potency comes from actuality (and therefore the knowledge comes by action), though the actuality is later in genesis than its own potency. I051 1L 5. QUIl yap KUTa TO S&VIla8IlL )'IYETIlL, TUUTOV IUTL SUVIlTOV TdAristotle's strict doctrine seems to be that while rational ovvap.£ts can produce contrary results, irrational ovvap.£ts are only ovvap.£ts of contradictories, (I) in the sense that they may either be actualized or not (1050b 8 n.), and (2) in the sense that their presence leads to one result and their absence to the contradictory result (I050b 33 and note on 1050b 30-33). He here says all ovvap.£ts are ovvap.ELs of confrarz'es. The apparent contradiction between the present passage and 1046b 5, 10481L 8 is due to the fact that in the former passages he was thinking of ovvap.£ts KaTa r1JV K{V'Y/CTLV, positive powers or forces, while here he is thinking of mere potentialities. For the difference 1045 b 35-1046a 4 n. That which can produce health (e. g. wholesome food) cannot produce sickness, but that which can be healLhy can also be sick. 7. Bz.'s conjecture in the Observalz'o1Zes, Kill TO VOUELV (sc. OvvaCT8aL ~Ey6p.EVOV), is obviously better than his aCLUal reading, Kat VOCTE;:V. II, 1101. 'But contraries cannot belong to a thing at the same time, and (therefore) the actualizations also cannot belong to it at the same time.' 13-15. 'n' dvnYK1J .•• fiE).T£WV. The reasoning is not very clearly expressed but seems to be as follows: 'To be capable of A is to be also capable of its contrary B. Therefore, while what is good (ill the sphere of a particular OVVIlP.LS and the corresponding EVEpynaL) must be one of the contrary EVEpYELaL, thc ovvap.Ls must be said either to be both good and bad or to be ncither; therefore the good actuality must be beller than the ovvap.Ls '. 'TOVTWV 8aTfpov ETvaL Taya86v is in sense subordinate; TO ovvaCT8aL KT~. is what follows from the protasis. Bz. complains that Aristotle suggests that of any two contraries one must be good, and thus introduces good and evil into regions where they are inappropriate. But Aristotle does not make this mistake. He takes only the ovvap.ns which would be called good (I. 4), and shows that they are really neutral, and are called good only because we forget the bad actualizations of which they are capable; and that VIlVT£Il.

cr.

268

COMMENT AR Y

therefore the good actualization is better than the potentiality. His only mistake is in calling one thing better than another when the other is strictly speaking not good at all but neutral. 17-!u. oM' in I. 19 shows that Aristotle means to draw two distinct conclusions :-( I) that evil does not exist apart from individual evil things, (2) that there is no evil among the original and eternal principles of the universe. The former contention is directed against the Platonic belief in an Idea of evil (Rep. 476 A, cf. 402 c, Theael. 176 x). The latter contention is directed against the Platonic beliefthat the first principles of the universe, the one and the indefinite dyad, are good and bad respectively (A. 988&14, A. 1075&35. N. 109Ib31); Aristotle may have the bad world-soul of the Laws (896 H, 898 c) especially in mind. The reasoning implied in II. 17-19 seems to be as follows: What exists apart from its particular manifestations must exist actually. Actuality is prior in nature to potentiality. Potentiality is prior to the bad. Therefore what exists apart from its particular manifestations is prior to the bad. Therefore the bad does not exist apart from its particular manifestations. From the fact that the bad is posterior to potentiality it also follows (Aristotle adds in II. 19-2 I) that there is nothing bad among the original and eternal entities. If we placed a full stop after 1rpa:yp.a:ra and a colon after 8vvap.(ws we might sl1ppose aUK /lpa ••• 8Lfcp8a.pp.lvav to be a repetition in other words of 811Aov ••• 1rpD.yp.aTa (which Bz. apparently takes it to be); but this hardly does justice to aMi. The reasoning in II. 17-19 involves, as Hz. shows, a fallacy of equivocation. For actuality is prior to potentiality, according to Aristotle's view, in reality or substantiality (this was what was argued in 1050& 41051& 3), while potentiality is prior to the bad in worth (this was what was argued in 105111 15-17). When the bad is shown to be posterior to the potentiality (in worth), it is treated as one of the contrary actualizations of the potentiality. But then it must be prior to the potentiality in reality, according to the argument of 1050& 4- 105 1 &3. ~1-33. In the attempt to interpret this difficult passage lowe much to the late Professor Cook Wilson, who discussed it with me. The passage is evidently out of place. It belongs in principle to the argument for the temporal priority of actuality to potentiality ( I0 49 b 17-1050a 3)· ~~. 8La.ypOl'I'a.Ta. is taken by Hz. to mean 'geometrical proofs " and the word sometimes occurs in this sense, cf. B. 998& 25 n. But d 0 ~v 8L7IP'YJp.iva, cpavfpa ~v ~v' vvv o· ~VV1ra.PX(L 8vvap.(L seems to show that the word has its ordinary meaning of 'geometrical constructions '. (To make the construction intelligently, however, is to see the proof, and Aristotle at once passes to this (8~AOV 8La Tl, I. 26).} What he says, then, is that' geometrical constructions are dis-

covered by an activity; for we find them by dividing '. The activit}' is later (I. 30) described as V07/U,,", and this may seem inconsistent with the description of it as division. But it is not really so, for division here does not mean the drawing of lines with chalk or pen but the apprehension that the geometrical figures with which we are dealing are divisible in certain ways. The geometer is dealing with figures which are voy/Ta (Z. I036a 3). and his essential activity is v07/u,,>, not the construction of anything alu(}7/T'ov; the latter is merely all aid to the former. ~4-~6. The proposition is Euc. i. 32. The given figurl'! is

A

c

B

We have only to 'divide' (in this case to divide the space surrounding the triangle) in order to see the reason why the interior angles of the triangle must be equal to two right angles.

A I

I I

,

I

I

I

I

I

I

,

I

I I

I

~--------------------------~~--------------------

B

D

Produce BC to D and draw CE upwards (dl'~KTO) parallel to BA. Then the angle CAB ACE anti ABC ECD (Euc. i. 29).

=

=

CO:\IMENT ARY Therefore DCA+CAD+ADC= DCA +ACE+ECD, which DCA +ACD, which = two right angles (i. 13). Therefore the interior angles of the triangle two right angles. Of the two supplementary lines which had to be drawn, Aristotle mentions only CEo In Euclid this theorem is the second part of a proposition of which the first part is that' in every triangle, if one of the sides be produced, the external angle is equal to the two interior and opposite angles', so that CD is supposed to be already drawn; and Aristotle probably knew the proposition in its Euclidean form. 25. £t o3v c!.vijKTO ti lI'upci -M]v lI'}.Eupciv (sc. ypap.p.~). The use of tlvaY£Lv for the drawing of a line is 110t recognized in L. and S., and Bz. gives only one other instance of it, viz. 111e1eor. 376& I. Aristotle seems not to be using technical language (cf. II. 27-29 n.). He uses civayftv in the natural sense of ' draw upwards'; the parallel line must be drawn on the same side of the base as the triangle. 26, 27. The vulgate reading is B,u. Tl ~v .qP.tKvKAl'l! &p8~ Ka80Aov; Bton (Mil KTA.). The best manuscripts read B,u. Tt ~v .qP.tICVKAllJ,! &p~ Ka80Aov BtU. Tl. Alexander says (596. 21) 1TaAtV f.PWTWP.fVOt 01" B,u. Tl (V .qP.'KVK>..tlJ,! &p8~ f...ov BUI T{ .q (II .qP.tKVKA{'l! &p8~", from which it would appear that his text read Btu.T{ f.V .qP.tKVKAtlJ,! &p8~ ; Ku80>..ov BtU. Tl; BtoTt, the reading of the inferior manuscripts in I. 27, cannot be right; the angle in a semicircle i!> not right because it is clear to people who know certain facts that it is so. We should either read and punctuate as in the text, or follow Alex· ander's text. For BtU. Tt at the end of the sentence cf. H. IOH b 17 c!.AAa 1'0;;"0 KUTU. T{; Bz.'s addition of.q seems to be unnecessary; for the form of the proposition cf. An. Post. 94& 33 1'6 ~v .qP.tKVKAUf &p~v (lvat. 27-29. The proposition is Euc. iii. 3 I. The construction contemplated seems to be as follows:

=

=

B

BA C is an angle in a semicircle. From the centre D draw DE perpendicular to BC (~ lK p.Euov l1TtCTTafhiua &pfJ~) and meeting the semicircle at E. Join BE, CEo Then DE = DB. Therefore the angle DEB = DEE. DE = DC. Therefore DEC = nCE. Therefore DEB + DEC = DBE+DCE, i.e. BEC CBE+

=

BCE.

But BEC+ CBE+BCE = two right angles (i. 32) Therefore BEC is a right angle. But BAC = BEC (iii. 21). Therefore BA C is a right angle. There are two difficulties here: (I) The triangle BEC is superfluous. If AD had been joined, BAC could have been proved to be a right angle just as BEC has been proved to be so. Euclid dispenses with BEC. (2) tJp~ is commonly applied not to lines but to angles. Christ proposes to remedy these difficulties by reading lay ••• lll'UTTafJEiua, tJpfJ~ (' the angle is a right angle '). 186VTI 87, 8i1~ov KT~. But this loses the correspondence with 1. 26, where the apodosis is 180VTI &v ~v E{,(JVi 81j~ov 810. Tl. Mr. Cannan (reading in 1. 27 KafJo~ov 810. T{ j) proposed lav. • • E1TtCTTafJE'iua, tJp(J7, 8LC\ T(; 81j~ov, which would get over the difficulties; but the corruption is not a very probable one. n it be supposed to have occurred, it would seem better to punctuate EaV. • • ElI'lCTTafJE'iua, tJpfJ~. 81a TL 81j~ov (as in 1. 2 6 81j~ov aLa Tt). Alexander has the traditional text, whIch is (I think) quite sound; as regards the difficulties stated above we may say that (I) it would be natural enough for Aristotle by an oversight to think that the angle could more easily be proved to be right in the symmetrical case in which it is the sum of two half right angles. In any case Aristotle's proofis not the same as Euclid's, for he dispenses with the production of BA ; that he does so is clear from A 11. Posi. 71 &19, 94& 28-34. Similarly his proof of Euc. i 5 (An. Pro 41b 13-22) is quite different from Euclid's. (2) Aristotle is not using technical language (cf. liv1]KTO 1. 25); tJpfJ~ is used in its ordinary sense of' upright '. The translation is ' the line set upright on the base from the middle of the base '. ~8. 18cSIITL &;j).Ol' Tcii lKELI'O d8cSTL. 'The proof is evident, when he sees the figure, to him who knows the former proposition.' What is , the former proposition'? (a) Alexander says it is ' that if the three straight lines are equal, the angle in the semicircle will be proved to be right '. But this would amount to saying I if L is M, then that N is P is clear to him who knows that if L is M, N is P', which is an improbably clumsy way of stating a very simple thought. (b) lKEivo may be simply ;;"'1 iuaL TPEii, ~ Tf paULi Ilvo KaL ~ lK p.EUOV f.7rLCTTafJEiua dpfJ~. But (c) lKfivo would naLUrally refer to something more remote. It refers in fact to the proposition stated in ll. 2-1--26, that the angles of a triangle = two right angles. Cf. An. Posi. 7 I" 19 OTt p.f.V yap 1rQV Tplywvov Ix" IlvuLV tJpfJa'ii iuai, lI'pOyj8E'· OTt Ilf. ToilE TO lv T'il ~P.LKVKAt'l! Tplywvov lCTTLV, ilp.a f.7rayop.Evo<; I.YVWP'UfV. ~9-33.

The interpretation of this passage is complicated by two

CO\\DTF.NTARY qnestions of reading. (1) In I. 30 F. J and apparently Alexander (cIywv 597.14, cIY(TaL 597. 16) read ayoJL(va where the other manuscripts have avayoJLrva. Now a pllliosopher might be said TO. 8VVaJL£L c)VTa €i.. EvipY€lav ava-Y£Lv (' refer hack ') when he shows as Aristotle does here that the actuality is the prius of the potentiality. Cf. E. N. I I 70a 16 TO 8E '~V Opl'ovTaL TOL~ ,ceOL.. 8VVaJL£L alu(}~uEWS, av(}pW7roL~ 8' alu(}~u(w.. ~ V~U(w,,· .q 8E ilVVaJLL" €i.. n,v EvipY£Lav avaY(TaL, TO 8E KVPWV EV rii EVEPY(LCf' lOLK( 8~ TO '1jv (TVaL KVPLW" TO alu(}uV(u(}aL ~ VOELV. 1I13 a 5 7TavETaL yap EKaUTo~ 'Y/T;;w 7T;;'" 7Tpuf£L, oTav €i.. aUrov avaya'Y?1 n,v apx~v. b 19 (l 8E TaVra cpaLVETaL Kat JL~ lXOJLEV El.. tilla .. apx" .. avayaYELV 7Tapa TO. .. (V .qJLLV, fuV Kat III a( Xat EV .qJLLV, Kat aUra Ecp' .qJLLV Kat (KOVULa. But the operation here described is that of the mathematician; the sense required is ' the constructions which exist potentially are discovered by being actualized' (perducla ad aclum polenfl'a, Bz.), and this sense demands ayOJLEva. Cf. E. N. I 153 a 12 TWV €i.. n,v T(AELWULV ayoJLivwv T1j.. CPVU(W". (2) The manuscript reading aiTwv 8E OTL VO'r/UL" .q EvipYELa is difficult. 'The potentially existing constructions are discovered by being brought into actuality j the reason is that the actuality is an act of thought.' This identifies the actuality of the figure wilh the actuality of thought, while II. 32, 33 seem to distinguish them. Aristotle has committed himself to the view that VO'r/UL" actualizes the figures, but it is doubtful whether he would identify the actuality of the figures with the v0"7UL'" True, TO VOOVJLEVOV and 0 vov.. are identical in the case of oua JL~ 1$A'r/V lX£L (A. I075a 3, cf. De An. 430" 3). But mathematical objects do contain 1$A'I'/, even if it be vO'r/n, VA'I'/ (Z. I036a II, b 35, K. 1059 b IS). They are not the pure forms which alone Aristotle identifies with the apprehension of them. Nor does the manuscript reading seem to be that of Alexander, though it is impossible to say exactly what lies behind his words: cpavEpov cIpa oTt 8vvdJL€l c)VTa Kat lVEpy~ua.. 7TEpt aUra 0 VOV .. WpLuKfTaL' aVro" yap EUTLV 0 aiTw .. 0 cIywv aUra €i.. Evlpy£Lav. VO'l'/UL.. .q I.VipyELa may have arisen from .q VO'l]UL .. EvlpyELa (cf. A. 1072b 16), which goes well with what precedes and what follows: 'the potentially existing constructions are discovered by being actualized; and the explanation is that the geometer's thinking is an actuality, so that the potentiality proceeds from an actuality, and therefore it is by doing that people come to know' (or 'by making constructions that people come to know them'). Aristotle, then, brings the case under his general rule EK TOV 8vvdJL€l c)VTO" YLYV(TaL TO EVEPYElq. ~V lJ.,ro EV(PYElq. OVTO" (I 049 b 24); the potential constructions are actualized by the actuality of thought. And as, before, Aristotle drew from the necessity of an actuality for the actualization of a potentiality the inference that actuality is prior to potentiality (1049b 23), so he does here in the words WUT' (f (V(pyELa .. • ~, (I· , , . th . I d WpLUKfTaL. ., 'I] ovva.JLt.. un eSB a.LTLOV ••• (V(PY€la. IS paren etlca an not ylYV(Ta.L. is to be understood with (~ (VEPY(la. .. .q 8vvaJLL"). a.iTwv 8llUTL VO'l'/UL .. .q EV(PYELCf may also be ~uggested; this comes nearer to

273

on

Alexander's paraphrase. For confusion between lUTI and due to tachygraphy cf. Bast 810. 3!1-33. Aristotle has said that potentiality comes from actuality; he now guards against misinterpretation. • But it is only in a sense that actuality is prior to potentiality, for the individual actuality is posterior in generation to the corresponding individual potentiality.' Cf. 1049 b 19. In his view, the potentiality of the construction presupposes the activity of thought but precedes the actuality of the construction. For a similar elliptical use of yap cf. T(lp. 119" 7, 122 b 39, De A,t. 407" 23, 409" 24. The emendation of I. 30 gives point to this clause, which Bz. found unintelligible. We are now in a position to see the object of the whole passage II. 21-33. Aristotle's purpose is to enforce his doctrine of the priority of actuality by two considerations with regard to Ta P.afJ."P.aTlKa. (I) It is only by being actualized that they are known. In their case therefore, as in all others (1049b 17), actuality is prior to potentiality TV yvwun. And (2), as in all other cases (10 .. 9b 17-10,,)0" 3), though their potentiality precedes their actuality in time, it presupposes another actuality, that of apprehension. The passage is of great importance because it emphasizes the significance of the intuition of the construction for the underctanding of the proof (l86VTt 8~AOV, 11. 26, 28). It thus corrects Aristotle'::; tendency in the Orgallon to treat mathematical proof as if it were simply a process of deducing conclusions syllogistically from definitions and ~7TOfJ'U(tl., and anticipates Kant's doctrine of the synthet:c nature of mathematical procedure. But it cannot be said that Ari~totle \I orks this out clearly. The Italure q/irlllh (ch. 10). 1051" 34- • Being' and • not being' are used wi th reference (I) to the categories, (2) to potency and actuality, (3) to truth and falsity. Truth means thinking that to be divided or united which is divided or united, respectively; error means being in a state contrary to the facts. b 5. When is truth present? You are not white because we truly think you are, but vice 1lerSfl. 9. (I) Some things are always united, others always divided, others may be either. Being is being-united; not being is not-being-united. About things which may be either united or divided the same opinion is at different times false and true; not so with regard to things that must be as they are. 17. (2) In the case of incomposites what is being and truth? For them, being is not being-united, and truth cannot be what it was in the case of composites.

COMMENTARY ~~. (a) Truth in this case is contact and assertion (as distinct from affirmation). Ignorance can only mean in this case non-contact; error is not possible (except per accidens) regarding what a thing is or an incomposite substance. Such substances all exist actually, not potentially; otherwise they would have come into being and perished, but there is nothing out of which being itself can have come to be. 30. About all things that are essences and actualities, then, we cannot err; either we know them or we do not. But we may inquire what they are, whether they are such-and-such. 33. (b) The being which answers to truth does not in this case mean being united; if the thing exists at all it exists in a certain way. Truth means knowing such objects; no error about them is possible, but only ignorance-not, however, ignorance analogous to blindness, which would be a complete absence of the knowing faculty. 105~& 4. (Return to (I». Regarding the unchangeable, if we believe it to be unchangeable, we cannot mistakenly suppose that it sometimes has a certain attribute and sometimes not; but we may suppose one member of a class to have an attribute and another not. About a single member we cannot make even this mistake; whether we are right or wrong, it is implied that the facts are eternal.

This chapter, dealing with truth and falsity, has little to do with the rest of book 0, which treats of potency and actuality. Schwegler and Christ therefore treat it as the work. of an editor. Bz. and Bullinger point out that in view of the enumeration of the senses of ' being' in .:l. 1 it is only natural that after discussing the chief category, substance, and the distinction of potency and actuality, Aristotle should go on to discuss truth and falsity j and that the chapter is specially in place here because ch. 8 has introduced us to the simple and eternal substances which are lvipy(LQt I1VEll Bvv&'p.(wr;, and are now described as the objects with which one kind of truth is concerned (1051b 21). Jaeger thinks that the chapter is by Aristotle, but was inserted here simply because there was some room at the end of the roll on which Z-0. 9 was written. Between this view and that of Bz. it is difficult to decide; that the chapter is the work of Aristotle there is no reason to doubt; E. 1021 b 28 has prepared us to find such a discussion in the Melap~sics. 1051& 34-b~. For the classification cf. A. 1, E. 1026& 33-b 2. 85. TO S~ KGTa SIlVGI'LV ~ lvlpVELGV TollTWV ~ Tc\VGVT(G, i. e. being or not-being may be divided not only according as it is the being (or notbeing) of (I) a substance, (2) a quality, (3) a quantity, &c., but also may be further subdivided according as it is the being (or not-being) (a) potentially or (b) actually of a substance, quality, &c. b I. TO ~~ LKUPLWTGTG &v] c\~1Je~\; ~ "'EUSO\;. Being as truth and not-

being as falsitv are elsewhere treated as emphatically not the primary or strictest senses of being and not-being (,.0 8' WrCIJi &v &.pov &v Tii)V ICV"u.,i, E. 1027b 31), but as being due merely to ~ 8&4VolaH' .".J.fJoi (ib. 34) and presupposing being in its primary sense, that in which it is subdivided into the categories (; yap ,.0 T{ lcTTtv .q OT' 7I'O,ov.q OT' 7I'OO"OV ~ T' ~o CTIIV&7I'Tft ; 8t.a.'P';:'; 8t&VOt.a., ib. 31). Jaeger suggests that Aristotle may mean merely that the copulative' is' of the judgement is the commonest usage of the verb ' to be " but it is improbable that ICVpmaTfJ. l$v should mean this. The words are probably a gloss, or should go after pill in a 34. It will be seen that there is a good deal of divergence among the manuscripts at this point. If retained, ICVP'WTaTa l$v must go with cU:'16" .q y,.vOOi, 'that which is true or false in the most proper sense of those terms " in contrast to truth and falsity 7I'.pl TO. cluVv6fTfJ., which Aristotle treats of later (I. 17-1052a4). But it is highly unnatural to sever ICVpWwaTa l$v from TO 81. II. 1'OiiTo S' .71'1 TWII 'lrpGYI'GTWIl laTl T'ii avylteiafcn ~ Slnpijcrfcn, ' and this depends, in the things' (i. e. so far as the objects are concerned), 'on their being united or divided'. The implied opposition is between T4 7I'pUypaTa and ~ Uta (I. 14). 11-13. TlI ,"II ••••tllal. This passage makes no use of the distinction drawn at the beginning of the sentence between things always united, things always divided, and things capable of being either united or divided. That distinction is first used in what follows, 7I',p~ p& o~v • •• y,fV8.ij (13-1 7~ Bessarion and Christ therefore treat TO plv ••.•Tva, as parenthetical, while Bz. (following what may have been Alexander's reading) inserts /Cal before T~ plv. It seems probable, however, that grammatically TO plv • •.•Tva, is the apodosis, though logically it only prepares the way for what follows. 17-10511a 4. There is much Obscurity in Aristotle's references to truth and falsity with regard to TO. dmJv6fTa., TO. d7l".\ci, ,.0 d&a.lPfTOv. In E. 4 and De An. iii. 6, as well as here, it is contrasted with truth and falsity with regard to composites, which is clearly truth and falsity of propositions. Aristotle seems to reason as follows. What is true in the ordinary sense is a judgement in which two things (a subject and an attribute) are thought to be united which are united in reality, or two things to be separated which are separated in reality. But if we think of two things as united, must we not first think of each thing by itself, and in this thinking is there not a possibility of truth and of error? Aristotle's strict theory is that there is not (I. 2, E. 1027b 19, Cal. 2a 8, De An. 430.26) j that the only alternatives are, to apprehend them or not to apprehend them. He says in this chapter clearly enough that there can be no falsity with regard to them (I. 25), but he does not say as clearly as he might that there can be no truth dther. That which could not possibly be false cannot without tautology, and therefore absurdity, be said to be true, just as 'true knowledge' is an absurd expression because there could not be false knowledge. But instead of saying this he says that truth t;Z anolher

COMMENTARY tha1l the ordi11(11Y Se1lse is possibl'~ with regard to incomposites (I. 24).

The fault, however, is only in the expression; the distinction is probably clear enough in his mind. But what he means by d.cn$,,(iETU and the analogous expressions is not equally clear. In the De Am·ma, instead of discussing terms in general as distinct from propositions, he discusses three kinds of object which are d.~LU{pETU in quite another sense. (I) Tb KUTG. Tb 7rOO'bv d.~Lu{pnov EVEfYYEu,. (430b 7-14), i. e. things like lines, which though quantitatively divisible are not quantitatively divided. (2) Tb ft." ...' (Ob ) t he 11'.J.ma ° .G ° ( ' KUTU " TO T'l' (Lon UOLULP£TOV I . 14-20, stuus. 3 )TO 7rOITl,V d~LU{p€TOV 8vvcfp.n (430b 20-26), that which is quantitatively indivisible, like points (or. we might add, moments). Of these three only the second is relevant to the discussion of the present passage, and unfortunately the few lines devoted to it are so obscure and the text so doubtful that they need illumination rather than afford it. In the present passage Aristotle seems for the most part to be reasoning from the bare notion of an 'incomposite' as opposed to a 'composite', without asking himself very definitely what he means by an ' incomposite'. From the very fact that it is simple, it follows that there cannot be truth or f~\lsity about it of the same kind as truth or falsity about composites. His primary meaning seems to be that if you say A is B you must attach a definite meaning to your terms; you must know about A, and about B, 'what it is' (I. 25 f.). The alternative to knowing what it is is not having a false opinion about what it is, but simply not being 'in touch' with it at all. But from this general position about the terms of any judgement Aristotle pa!:~s to a point which he distinguishes from this ([,p.o{w<; 8~ Kai KTA., I. 26). The terms of a judgement are, so far as their function in the judgement goes, simple, but they may be in themselves complex terms, and again they need not be substances, and if substances, they need not be simple substances. '\Vhite',' incommensurate', 'diagonal ' are not substances; 'wood' is a substance concrete of form and matter. What has been said of all terms with reference to their place in judgement may be said without qualification of 'incomposite substances', the things which are free from any admixture of potentiality and therefore eternal, which are pure forms (' just what it is to be something ') (11. 26-31), i. e. God and the intelligences which move the spheres. !ZO. Bywater proposed T~ ~EUK~I' (Tb) ~d~ol', 'the proposition that the wood is white', so as to get a phrase 01 the same form as Tb d.cn$p.p.£Tpov TlJV 8&rI.p.£TPOV, and the addition seems to be necessary. !Z3. ~ "'~I' cU.,,8~1l fj ",'USOIl is answered by Tb 8~ .rVUL in 1. 33. Truth and falsity as states of mind are discussed in 11. 23-33; 'being in the sense of being true' and' not-being in the sense of being false " i. e. the objective counterparts of truth and falsity as states of mind, are discussed in 1. 33-1052& I. T~ dJ.:'18Ir is explained in 11. 24, 25 ; instead of explaining what Tb .pEv80r is in the case of incomposites,

Aristotle points out that there is no y,t:V&.. or &'7I"a"1 with regard to them but only Q')'JIOUl (I. 25). "4. e~YEil'. The metaphor of contact in the description of simple apprehension recurs in A. I072b 21. Its implications are (I) the absence of any possibility of error, which characterizes the apprehension of the l:8Ul ulu8-qTa (cf. De An. 430b 29), (2) the apparent (though on Aristotle's view only apparent, De A". i. II) absence of a medium in the case of touch. TO 6c'Y,iv means an apprehension which is infallible and direct. +dva.~ does not seem to be used elsewhere by Aristotle as meaniug anything other than ICUTUcpavat, but cpaut.. in the sense of the term. as opposed to the proposition occurs in De Int. 16b 27, 17& 17. "5. c171"a.T1Je~l'cU yap 7I"Epl ,.0 T~ lcm.1' ollK ECn'll' c1AA.' ~ Ka.T« au".IIEII'IKOt. Alexander and Bz. interpret this as meaning that one cannot be deceived about the T{ llTT' unless by an abuse of the word 1171"a"1 nescience be called d7l"un}. This does not seem a possible meaning for ICUTa. uvp.{3,{37JKO". The words must be interpreted in connexion with l. 32 cL\Aa. TO T{ €ITT' {7JT,iTU' 7I"'pl awwv, d TO'UWa llTTtv 7i p.~. Both statements are extremely difficult, but may be interpreted as follows:-Aristotle has, as we have seen, passed from the antithesis between terms and propositions to that between forms and complexes of form-and-matter. Now in our thought of a form considered as a term in a proposition there is no room for error, since error comes in only when we think two terms to be connected in a certain way. But the form or term, though IIcnSv8£TOvas compared with the proposition, is (unless it is a SU71l11111111 gmus) not absolutely incomposite. It contains a genus and a differentia, and the attempt may be made to ascertain what they are (TO T{ €ITT' {7JT'wu, 7I"t:pl uwwv--about the forms-whether they are such and such or not). Thus, while about the term considered as a simple term there can be no error, there can be error about it incidentally, viz. in view of the fact that it is not merely an element in the complex of the proposition, but also itself a complex of genus and differentia. Or, to put the matter otherwise, if some one says that A is B, we cannot properly attack his thought of A alone or of B alone, but only his thought that B is an attribute of A; but on the other hand if he tries to analyse the A he is thinking about he may say it is an X which is Y, and we may point out that all X's are Y or that no X's are Y, or that from other things which he says about A it is clear that the A he is thinking about is not an X which is Y. .De A". 430b 16, 17 may be meant similarly to point to the fact that in one aspect TO cl8'cUp£TOV T.fj ,t8" is (KUTa. uvp.{3,{37JKo..) 8'ULpETOJl, but the reading and the interpretation are vcry doubtful. It might be thought that TO T{ €ITT' {7JTt:iTU' 7I"€pi ul
COMMENTARY asking whether they are' such-like' or not. But it is doubtful whether this can be read into TOUlVTa. Bz. conjectures that Of!K should be added before Ei TOtaVTa, and Alexander (600. 34) may have read this. The meaning then would be ' but inquiry about the "what" of simple entities does not take the form of asking whether they are of such and such a nature or not '. This might be held to derive some support from Z. I04Ib g-II. But it is difficult to see what other form the inquiry into their' what' could take. If an of! is to be inserted, it would be better to insert it before CT/TEiTat. But on the whole the traditional text seems to agree with the suggestion conveyed by ill' ~ KaT~ CJ1)JL{1E{171KO.., and should be kept. ~9. TO 61' m~TcS, i. e. the pure form. o~ y~yvETmL o~S~ +eE~pETCU, cf. z. 1033 b 17. 3~-33. cl}'M TO T~ lcm • " . tj ,...~, cf. 1. 25 n. 83. Aristotle has said (1. 22) that both truth and being (truth of apprehension, being of the object of apprehension) have a different meaning in the case of incomposites from that which they have in the case of composites. He has explained the different sense of truth, and now passes to the different sense of being which answers to the different sense of truth (T;' Elvat 00" T;' d.A71(Ji.. ). But first (II. 34, 35) he repeats in brief his account of the mode of being which answers to the other mode of truth. Being, for a composite, means being compounded j not-being, not being compounded. 34-35. For II' I'll' ... TO S~ tv cf. Pol. I285b 38-I286a 1 ~v JLEv • •• ~v

8l.

35-36. 'The other, if it is existent, exists so j if it does not exist so, it does not exist at all.' I. e. as on the subjective side the only alternatives here are apprehension and non-apprehension, so on the objecti\'e side the only alternatives are being and not-being. We have not now to do with the question whether A is thu3, i. e. conjoined with E, or otherwise, but simply with the question whether A is (in which case it can only be A) or is not. This interpretation is much to be preferred to that of Bz., who deletes the comma after 01' in 1. 35 and supposes the transition to incomposites not to occur till 1052" 1 £i SE JL~ oliTw... Christ's EZ7rEP t,v OVTI1I<;, lCTTW gives no good sense. Aristotle's carelessness of language has made his meaning seem more obscure than it really is. In 11. 22, 23' he distinguishes the two modes of being (se. of composites and of incomposites) from the corresponding two senses in which apprehension of them may be said to be true or false. He has treated the question of truth in II. 23-33, and in 33-I052a 4 he is treating the question of being. But instead of saying 'the being of the object which answers to the truth of the apprehension' he says (1. 33) 'the being in the sense of truth J; and instead of saying that the composite is, if it is compounded, and is not, if it is not compounded, he says (II. 34, 35) that it is true if it is compounded and false if it is not, and then complicates matters still

further by recurring in 1052& 1-4 to the question of the apprehension of incomposites, which has already been treated in 1051 b 23-33' It would be easy to argue for a double recension, but Aristotle seems to be often so careless of form that that hypothesis is not necessary. 10511& 1-4. With regard to incomposites there is not error but only nescience, but Aristotle points out that it is not a nescience comparable to blindness, which necessarily shuts oft' the blind man from knowledge of a whole set of facts. What would answer to this would be a complete absence of the power of apprehending essences, but what we have to do with here is simply failure to apprehend certain particular essences. 4-11. From the treatment of cluVv9ETI1 Aristotle now recurs to certain uW9ETI1, viz. TO. clK{vrrrll, the things which if they ever have an attribute have it always (i. e. those which cl,l aVyKfLTI1L Kill cl8vvIlTa 8LIlt.p,9ijVIl" 105Ib9). About TO. cluVv9ETa there can be no cl"'4nH about those cr6v9ETIl which are clK{vrrrll one form of cl"'4T71 is impossible, provided that we realize that they are clKtvrrra. If we realize that a triangle is clK{vrrrOV we cannot err by supposing that it sometimes has and sometimes has not its angles = two right angles. It may, however, be the case that some members of a class of clK{Vrrrll have a certain attribute and others have not, so that one might suppose either (wrongly) that no even number is prime, or (rightly) that one (the number two) is prime and the others are not. If we are thinking not of a class of dKlvrrra but of a single dKlllflTOv even this source of error is removed; whether we be right or wrong, we shall make our judgement on the understanding that the facts are always so. g. Aple".'i S~ 'II'Epllva "'Epl 8' d.pLfJp.ov WIl d.pL9p.~ 'about a single number '. It is not impossible, however, that WIl, TW4, TW4 are neuter plural. For ~Vll plural cf. I. 1056b 21, M. 10831& 25, Phys.

=

201b 1. 10. oil yAp lTl TwA ".~v TWcl S' 00 ot~C7ETal. I have restored the emphatic oil from oll of Ab yp. E. Cf. L. and S. s. v. oll, B.

BOOK The meanillg

1

of tinily (ch. I).

10ssa& IS. There are four main senses of unity--excluding accidental unity. The' one' is (I) the continuous, especially what is continuous by nature, not by mere contact or colIigation, and more especially that whose motion is indivisible and simple.

280

CO:\DIENTARY

~~. UllIty belongs even more to (2) wholes which have a definite form, especially to natural wholes which have in themselves the cause of their continuity, i. e. which have a motion indivisible in place and time. Thus that which naturally moves with the 'primary kind of movement, i. e. circular locomotion, is a single magnitude in the primary sense. fig. Further, those things are one the definition or thought of which is one, i. e. which are indivisible (3) in number (viz. individuals) or (4) in form (i. e. for knowledge)-that which gives substances unity. Thus • the one' means' the naturally continuous', 'the whole', 'the individual " or • the universal'. All of these are one either because their motion is one or because the thought or definition of them is one. b I. The questions' What sorts of things are said to be one?' and 'What is it to be one?' are different. Each of the things we have named is one, bUl to be one, while it sometimes means to be one of thebe things, sometimes means something else which is the more literal meaning, though these others express better the significance of the term. 7. Similarly we must distinguish the questions' What is the ultimate physical element?' and' What is it to be an element? ' 14. To be one is to be indivisible, being essentially a this and separate in place, in form, or in thought, or to' be whole and indivisible, but above all to be the first measure of a class, and especially of quantity, from which it has been extended to the other cases. flO. A measure is that by which quantity is known; this is either'a unit or a number, and a number is known by means of a unit, so that all quantity is known by means of a unit; hence the unit is the startingpoint of number as number. !Z4. Hence in other cases also that by which a thing is primarily known is a measure, and the measure of everything is a unit-in length, breadth, depth, weight, speed (the last two terms applying to what is light or slow as well as to what is heavy or fast). 31. In all these cases there is a measure and IItarting-point which is something one and indivisible in quality or in quantity. 35. An accurate measure is one which cannot be laken from or added to; hence the measure of number is most accurate, for the unit is in every way indivisible. In other cases, since a large quantity can be added to or taken from without detection, men choose as measure the first thing which cannot be added to or taken from "ithout detection. 1053" 8. l\Iotion is meat;ured by the quickest simple motion (i. e., in

a81

astronomy, the motion of the heavens); similarly the quarter-tone is the measure in music, the letter in speech. 14. Sometimes there are more than one measure, e. g. in music, in speech, in incommensurate magnitudes. 18. The one is the measure in the sense that we learn what the essence of a thing consists of by dividing it either in quantity or in kind. The unit is indivisible either in all respects (like the numerical unit) or to sense (like the foot). 114. The measure is always akin to that which it measures; e. g. the measure of units is a unit; we must not say that the measure of numbers is a number; that would be like saying that the measure of units is units, for a number is a plurality of units. 81. We call knowledge and sensation the measure of things because we become acquainted with things by them, but really they are measured rather than measure. It is as if we learned our height by some one else measuring us. Protagoras says man is measure of all things, meaning • the man who knows' or • the man who perceives' ; there is nothing remarkable in what he says. b 4. Thus' one', if we define it literally, means a measure, primarily of quantity, secondly of quality; i. e. what is indivisible in quantity or in quality. I0511a IS. iv TOi:~ 'lrEpl TOU 'lroO'o;xw~, A. 6. The classification of the senses of ' one' there given is as follows: (1) TO KaTa. CJ1)P.{Jf{JlIKO,., e. g. the unity of • Coriscus and musical',

&c.

(2) TO Ka8'

a~TO

(V,

(a) T~ CJ1)VEX£" (tvat (e. g. a bundle), (6) Tiji TO ~7rOK({P.(VOV Tcf) (i8EL Etvat d.8uicpopov (e. g. all wine is one) or J,v TO YCvO'> ~V 8tacpipov Tai:,. aVTLK(Lp.£vo;t,. 8taq,opai:,. (e. g. horse, man, dog are all one), \ -' \ ' .~, , f.tI\,I\.OV '" \ TOV ' (C) OUIIlV 0 ""yo,. 0 TO Tt lIV (Lvat ",(Ylllv aotWpfTo,. 7rpo" ~AoVVTa [T{ ~v Etvat] TO 7rpo.yp.a (e. g. that which increases and diminishes is still one if its definition does not change). (These three senses are summed up in IOI6 b 9 p.la V CJ1)V(X({~ V(i8" VA!Yylfl, d. IOI7 a 3-6). (d) The essence of' one' is d.pxfi T"" tlpdJp.ov (lvat. 17. TlTTo;pE~. These are given in 1. 34-'7"0 CJ1)V(Xii, TO oMV, TO Ka8' (KaUTOV, TO Ka(JoAOIJ. The first answers to (2 a) above, the third to (2 c), the fourth to (26). The second appears as a species of (2 a), the continuous which has a single form, e. g. a shoe as opposed to the same materials when not arranged to serve a purpose (IOI6 b 11-17). (I) is expressly excluded in this chapter (I052a 18); (2 d) is introduced as the primary meaning in I052b 18. 117. d Tt ••• 'lrpwT'lJv. Grammar requires us to translate • if anything

. .

tG13.2

.,'..

..

T

COMMENTARY by nature has a principle of movement which is the primary principle of the primary movement '. But it is hard to assign any definite meaning to 'the primary principle'. It seems clear that ~s 'If'pWrqs is explained by ¢opas and points to the fact that locomotion is the primary kind of movement, and that ~v 'If'p~V is explained by KVK>..o¢op{av and points to the fact that circular motion is the primary kind of locomotion. I. e. ~i 'If'P~i and ~v 'If'ptfmw are used in the sense which they would properly have if K{VT/UW, not KL~UEWS dpX~v, had preceded. Tijs 'II'pWT1Js. Locomotion is prior to the other kinds of changechange of size, of quality, of substance (generation and destruction), since a subject can have it without having the others (P!!),s. 260a 20261 a 26). Cf. Z. 1036a 9 n. 1'1)1' 'II'pWT1Jv. Circular motion is prior to other kinds of motion because (on Aristotle's view) it does not involve change of direction. This is equally true of motion in a straight line, but the latter is exposed to the objection that if it is to go on it ultimately requires infinite space (which Aristotle does not believe in); circular motion returns on itself and does not need infinite space (Phys. viii. 7). ~8. TOUTO 'II'PWTOV ,...lYE6os EV, i. e. a celestial sphere is the best instance of what is one by continuity. ~9. Just as the continuous and the whole are akin, so are the other two main kinds of unity, TO KaO' (KauToV and TO Ka06>..ov j they are introduced as subdivisions of TO. ~v ilv b >"o-yos Efs V. The first two are one because their movement is indivisible, the last two because the thought of them is indivisible (I. 36). 33. TO TGLS oGaiaL~ GinoI' TOU lvcI~, i. e. the essence. 35. It is rather surprising to find the fourth kind of unity described as TO KaOo>..ov; what Aristotle has said about it (\. 31) suggests only the infima species, the least universal of universals. A genus is one object of thought in the sense that it has a single definite nature; it is not one in the sense that it is logically indivisible, and Aristotle seems here rather to confuse the two things. But he is right in recognizing the unity of a universal, whether genus or species, as one kind of unity. b I. Aristotle now introduces' the distinction expressed in modem logic as that between extension and intension, or denotation and connotation. He has named four kinds of thing that are one; he now proposes to state the single connotation of the word 'one '. This is 'nearer to the word', while the others are 'nearer to its application' (I. 6). The connotation of' one' is 'indivisible' (\. 16), or • whole and indivisible' (I. 17), or 'first measure of a class, and primarily of quantity' (1. 18). 7. Tfi SUVC£,...EL S' lKELva. Alexander takes this to mean 'but the others are only potentially one'. It seems clear, however, that pJiAAov EyyVS is to be understood and that the meaning is 'while they are nearer to the force (or application) of the word '. For this meaning of 8vvap.Ls cf. Lys. 10. 7, PI. Grat. 394 B 3.

10. T~ ihmpov, Anaximander's 'indeterminate '. W]. KOLVOV lv Toi~ .vaVTLoL~, i. e. each of the terms is common to each

of two contraries. 1053& I~. 8LEaL~, cf. Il. IOl6 b 22 n. IS. at liLlaEL~ Suo. There can be little doubt that this refers to the

two distinguished by Aristotle's pupil Aristoxenus (i. 2I), the enharmonic, which was a quarter-tone, and the chromatic, which was onethird of a tone. Aristotle ignores the hemiolian atECTte;, mentioned in Aristox. ii. 51, which was three-eighths of a tone. Bz. thinks that the two aLecme; were the major semitone (d1l'0TOP.~) and the minor semitone (>I.EIP.p.a) recognized by Philolaus. But PhiIolaus seems to have used 8tEuLe; simply in the sense of 'minor semiLone' (Boethius, Insl. Mus. iii. 5, 8, pp. 277, 278 FriedL). 17. at +wval'll'A.ELou~ at~ IJ.ETPOUI'EV, i. e. there is no one letter which is the measure of speech more than the others. A, e, z', 0, u, and again b, c, d, &c., are equally units of speech and not necessarily of equal length. Kal "" SLBI'ETPO~ Sua1l'ETpEiTcu Kal "" 'II'A.EupB. It is difficult in view of the order of the words to translate this' the diagonal and the side of the square are measured by two different measures '. It may be that the diagonal itself is said to be measured by two measures, i. e. that it is conceived as consisting of two parts, a part equal to the side, and a part which represents its excess over the side, and that these parts being incommensurate are said to be measured by different units.

Cf. Il. 102 1& 3 TO a' fJ1I'EpexOV 1I'poe; TO V1I'EPEXOP.EVOV o~we; dOPLCTTOV KaT' dPLO,...ov· ~ yo.p dptO,...oe; uvp.p.ETpoe;, KaTo. p.~ (]'1Jp.p.&pov 8E dpLOp.oe; 011 ~tyETaL, TO a~ fJ1I'EpexOV 1I'poe; TO VrEPEX0P.EVOV TOCTOVrOV Te iUTL Kat lTL, TOVrO a' dOpLUTOV. If this interpretation be right, Kat ~ 1I'~EVpa is the gloss of an over-zealous copyist. 18. Kal Tc\ I'Eyl8tJ 'II'BVTa. Bz. takes this to refer to quite a different point, that the areas of all plane figures are me.lsured by multiplying together two numbers which express the length of the sides of a rectangle equal to the given figure. But (I) it is difficult to interpret TO. P.E-ye071 1I'aVTa as referring only to plane figures. P.Eye071 covers all lines, surfaces, and solids. (2) The two factors of the area are not at all analogous to the two aduELe;, the various letters of the alphabet, the two different units required for the measurement of incommensurate lines. They are not two units used to measure different things; both .\ are used to measure anyone plane figure. No suitable meaning for TO. P.E-yE071 7TaVTa presents itself, unless it be the rather vague one 'and in "l.Il kinds of spatial magnitudes similar incommensurabilities can be found '. There is something to be said for Ab' S reading ~ 8Lap.ETpoe; ••• Kat ~ 7T~EVprl, P.EY'071 TWO. ClVTa. al1~ov 8~, which seems to have been read by Alexander (610. 6, 7). In that case OTL should be inserted after a~. But p.Eye~ TWO. ClVTa appears pointless. Goebel's Kat P.Eye071 TWa. oroI' TO 1l~~LOV. oVrw is more ingenious than convincing. ~3. 8ETlov is Profesllor E. S. Forster's conjecture. For TLO'vaL de;

CO:\Il\IENTARY , to class among', d. Phys. 201 iJ 24, .E. N. 1156& 3'0, &c. Ab's (JlAn represents the first stage in the corruption. This emendation gives a better sentence than Bz.'s Elva! d,8UUP£TOV (for £l~ cl8u1lpETa), in which the position of Elval is unnatural. WCMrEp ELP1JTa~ ~S1J, 1. 5. 30. 6 S' clp~el'0~ 'Ir).~eo~ l'ovciSwv, cr. Z. 1039& 12 n. 3g. l'lrEL I'ETpOUVTcn I'&).).ov ~ I'ETpoua~v, 'although really they are measured rather than measure '. The scope and variety of reality is not measured by knowledge and perception, since there are real things which we do not know or perceive; but the scope of our knowledge and perception is measured by the things we know or perceive, as, when something of known length (e.g. a cubit-rule) is affixed to our body, o:u body is measured by the cubit-rule and not the cubit-rule by our body. On the priority of the object of knowledge (or perception) to knowledge (or perception) cf. 1057& 7-12, r. 1010b 30-IOU& 2, Il. 1021& 29- b 2,0. 105Ib6-9. 35. l'lrl TGaOUTOV. It seems difficult to take this as = TOITaVTaK!~ as Alexander does, and probably the reading bri TOUOVTOV ~P.{j)V1 'over such and such a fraction of ourselves', is preferable to Ab Al.'s TOITOVTOV

br,

~p.tv.

lTm"(y 1101 a substance but a predicate

coe~;letlsive

with being (ch. 2).

1053b 9. Is the one a substance, as the Pythagoreans and Plato say, or does some nature underlie it, e. g. (as the natural philosophers say) friendship, air, or the indefinite? 16. (I) If, as we have said, no universal is a substance, and being is not an independent substance but a predicate merely, the same is true of the one; being and unity are the most universal of all predicated terms. Thus genera are not separately existing substances, and unity is not a genus, any more than being or substance is so. g4. (2) Since in qualities and in quantities' one' is the attribute of something that underlies it, we must similarly in all the categories ask what the one is; it is never the whole nature of a thing to be or to be one. In colour the one is a colour (e. g. white), so that if the world consisted of colours, it would be a number, indeed, but a number of colours, and the one would be one something. 34. So too if the world consisted of tunes, articulate sounds, or rectilinear figures, it would be a number of quarter-tones, letters, or figures, and the one would be the quarter-tone, the vowel, or the triangle. 1054" 4. If this is true of the other categories, it must be true of substam;e; the one itself must be one substance.

13. That unity in a sense means the same as being is clear (I) because it is found in aU the categories; (2) because it adds nothing to the meaning of a term, any more than' existing' does; (3) because for a thing to be one is to be the particular thing it is. 10531'10.

iv TOLi SLCl'll"Op~"a.ow, B. 1001&4-b25.

'll"Wi SEt yvwpll'wTlpWi ).E)(9~VClL should not he answered at the same moment that it is asked, by the worrls Ka~ JLu.AAOV 6JIT1rEP KTA. In view of this, and of Alexander's apa 6J(T1rEp 01 1I"EP~ q,vuEwr;, he proposes ~ JLaAAov (interrogative) for KaL JLallov. But this does 110t remove aU difficulties: 1I"wr; 8EL YVWptJLWTEpwr; AEx/h1val remains a very curious phrase. The order is much against Schwegler's 1I"wr; for 1I"Wr;. The best solution is to excise 1I"0,r; as an emblema from KaL 1I"wr; 8EL, I. I I. 15-16. I\l'lv ni, Empedoclesj 1\ S', Anaximenes; 1\ Sl, Anaximander. 17. iv TOLi 'll"Ept o~a(Cli, Z. 13. 18. The tradition'll reading makes o~S' Cl~TO TOUTO KT).. dependent on El, and 01l8E after El is irregular. The irregularity may be removed by reading with Bywater OTt olIO', depending on EtpYJTat. For omissions of OTt in the manuscripts cf. 0. 1048& 37, Top. 1221> 10, 156 b I r, Soplz. El. 182333. Alternatively the irregularity might be removed by punctuating after instead of before 8;jAov ~r; in I. 20; for 8~AOV ~r; at the end of a clause cf. 811Aov OTt in De Caelo 282& 12, De Gen. eI Corr. 316b II, De All. 411B 22, Pol. 1333326. But oME is not surprising in view of the facts that El here = (1I"E{ and that a clause has intervened. Cf. 0. 104939, 10, where there is not even an intervening clause, and Cope's ed. of Rlzel. vol. i. 301-303. awo TOWO refers to TO i$v (1I"EP~ Toli i$vror;, J. 17). aw;' TOWO is subject, ollu{av predicate; this is preferable to making aw;' TOwo, ollu{av, subject, as Bz. does. 113. For the reason why being and unity cannot be genern cf. B. 998b 23. 114-118. 'The question whether unity is self-subsistent or requires a subject must be answered for all the categories alike. Now in the category of quality unity is the attribute of some subject or other (e g. a colour); therefore it must be so in aU the categories.' 119. ian TO Iv Xpwl'u, Alexander (613. 12) seems to have read (CTTl T! TO ~v, and Bz. thinks the right reading is that of EJr, (CTTl T! TO ~v ](pwJLa, 'the one is some colour'. But the order is strange; either T! or XpWJLa is probably an excrescence, and it seems better to read ](pWp.a with all the manuscripts and to omit T! with Ab. Tt has come in by dittography or by the influence of J. 26. 119. The true reading seems to have been preserved by JT, who have EITa. AI.'s commentary (6 I 3. 13) suggests ETTa rather than El, which has no doubt been produced by haplography. 31-311. TOUTO ••• +wT6s. Jaeger is probably right in treating this as

14. Bz. sees that the quegtion

286

COMMENTARY

a gloss; for glosses somewhat of this form cf. A. 984b II, r. 1009& 26, A. 1073& 33. 1054& 13-19. For the argument cf. r. Io03b 22-34', Z. I030b 10-12, K. 1061& 18.

Unity and plurality " identity,. likeness " otherness " difference " contrariety (ch. 3).

1054& go. The one and the many are opposed in several senses-in one of them as the indivisible or undivided to the divisible or divided. The opposition is that of contrariety (involving as it does privation), not of contradiction nor of relation. g6. Unity is explained by reference to plurality, the indivisible by reference to the divisible, because the latter are more manifest to sense. gg. To the one belong the terms same, like, equal; to plurality the terms other, unlike, unequal. The same means (I) the same in number, (2) one both in definition and in number (in this sense you are the same with yourselt), (3) one in definition (in this sense equal straight lines are the same-here equality is unity). b 3. Things are like, (I) if, not being absolutely the same (i. e. without difference in their composite substance), they are the same in form (e.g. the larger square is like the smaller), (2) if they have the same form and do not differ in degree, (3) if they have the same attribute in different degrees, (4) if they have more attributes, or more of the obvious attributes, the same than different. 13. Other and unlike have a similar variety of meaning. Other is (I) opposed to the same, so that everything is either the same as or other than everything else. It is used (2) if the matter and the definition are not both one, and (3) as in mathematics. 18. Other is not the contradictory of the same j things which are not are neither the same nor other, but simply' not the same'; things that are are either the same or other. ga. Difference is different from otherness. The other need not be other in any particular respect, but the different must be different in some respect, so that there must be some identical thing in which the different things differ, i. e. either genus or species. Things differ in genus if they have not a common matter and do not pass into each other (i. e. things that belong to different categories); in species, if they belong to the same genus. 31. Contraries are different, and contrariety is a kind of difference.

All contraries differ; they are not only other but some are other in genus, while others are in the same category and therefore in the same genus. We have distinguished elsewhere which things are the same or other in genus. 10548 23. at clvTL9iO'(L, TETpaxw,.

The four kinds of opposite are (a. 1018& 20, cf. Cal.

clVT{.patTL~, TclvaVT{a, To.1I'PO~ TL, UTEI"IITL~ Ka~ leL~

17). 24. Bz.'s adoption of O~T( (Ab) for TOUTIIIV gives an impossible sense, unless his suggested rearrangement of I. 25, O~T( ~~ clVT{.patTL<- O~T( ~~ TO. 11'p6~ TL AEYO"A.(Va, (VaVT{a ~v (i"1, be adopted also. Alexander says t', • LJ , ". ,. , (6 15. 2 ) ! e1l'EI' oe aL aVTLU(IT('~ TETpaxw~, TO (V KaL Ta 1I'ol\l\a w~ Ta (VaVTta lIb

~

~,~'"

clVT{KEtTat, Ka2 O~E ~~ Tel 11'p6~ Tt O~E ~~ let~ Ka~ UTEl"IlTt~ O~( ~~ KaTa.patTt~ Ka2 cl1l'o.palTt~. It is impossible to say exactly what he read; he may be merely interpreting freely. It seems better to keep the reading TOVTWV, which gives a fair sense. I Since one of the terms "divisible" and "indivisible" is privative, they must be contraries and not contradictory or relative terms.' Aristotle should have said, in accordance with his fourfold division of opposites, I since they are not privative. nor contradictory, nor relative, they must be contrary'; but privation and contrariety are not mutually exclusive. Contrariety is the extreme form of privation, the form in which the attribute present in the one term is entz'refy absent in the other (1055b I.J, 26, r. 1004b 27, 10IIb 18). As·Bz. remarks, a clause indicating that the privation is of the extreme type has to be supplied in sense after 6aT(pov, 26. UYETaL points to the fact that cl8ta{pETov is derived from 8tatp(TOV. ~Ao1iTat points to the fact that the meaning of "one' or indivisible' is explained by reference to (many' or I divisible '. 30. ivTij8LaLpiO'EL TWV ivaVT~wv, cf. r. 1004& 2 n. 32. Other passages on the various senses of I the same I are ~. 9, Top. i. 7, v. 4. I33 b 15sqq. 33-34. Iva I'tV ••• a~6. Since this is opposed to unity of both definition and number (absolute identity, II. 34, 35) and to unity of definition (the unity of the members of a species, II. 35-h 3), Alexander must be right in explaining this first kind of unity as accidental unity, which is e¥pounded at length in a. IOl5 b 17-34. b 2. Bz. was right in omitting TO. before to'oywvLa; the word is actually omitted by Ab as well as by Alexander. T!Tpclywva. This word in Aristotle usually means I square' but here 'quadrilateral' (cf. De An. 414b31(?). PI. Tim. 55B, Crit. 1I8c). Euclid distinguishes the two as T(TpaywVOV and T(Tpa1l'Aropov respectively. 3-13. On the meanings of 'like' cf. a. 1018& 15-18. 13. ).(uK6v. There is no trace in Alexander of the manuscript reading ~ XPVlTit, which is in itself highly improbable. The balance of the sentence would lead one to expect something like VA(VKUV, and I

n

C01Il\fF.NT ARY

288

Alexander prohably read this; his words are b 8~ KaTT{npo'ii Tei» J.PyufJfJl KaTa TO '1f'pOX(l.POV, olov TO A€VKOV. xpvuei» doubtless came in by dittography. 14-1313. On the meanings of 'other' cf. A. 1018&9-11. 14-IS. Aristotle offers apparently three senses of' other', but really the first clause gives a quite general statement of its meaning, and the other two give varieties of this. 15. &wGV 'II'p~ &wnv \l TGUTO \l ci}.}.o. Aristotle's remarks in n. 19-22 show that with this is to be understood the reservation oo-a MYETa! ~ Ka2 Jv. 'Other' is the privative, not the contradictory, of' the same', and there are pairs of things (viz. p.~ JVTa) of which neither is predicable. 17. .:" Tel. lv TOL' fl48'1I'GTLKOL'. This is to be understood as opposed to the sense of' the same' given in I. I. IS. 8Lel. TOUTO, i. e. because 'other' is the oPpoliite of 'the same' (I. 15). Apelt (Bli/rage, p. 220) thinks it refers forwards to I. 19 o-tJ yap QVT{q,au{'ii IUT! TOV Tawov, but this is less probable. Christ's view that oLa TOVro is spurious is quite unjustified. 1313. Something like Apelt's '1f'£q,VK( OUG (cf. I. 19) appears to be wanted instead of 7r(q,VKO'ii. I have printed the elided form, for which cf. PI. Ph,l. 35 c 3 1TVp.{3l{3Y1X· ~p.i.v, Dem. 21. T 20 oMv. W'ii lOtK' t~8LKW,

&c.

133-31. On the meanings of' different' cf. A. 1018R 12-15. 136. clvclyK'I Tn~"s TL ElVGL ~ 8LG+lpouaLv. Aristotle means that if A and B are different, there must be a single statable respect in which they differ. If A differs from B in genus, B also differs from A in genus; if in species, then in species. He does not mean that they must have an attribute in common; this is not true in the extreme case, ouwv l1.>..Ao u~p.a. "l'ii KaTY/Yop{a'ii. 2S. The remark about Y£VO'ii and Y£V(U!'ii is an interesting inaication of the influence of biology on Aristotle's logic. cr. the account of Y£VO'ii in A. 28. !3g. otov 3awv ciUo crx~I'G~' KGT'JYOpCG'. In view of 1. 35 (note) it seems that olov == 'i. e:, not' e. g:. Aristotle seems in this context to restrict the name 'genus' to the categories. cr. A. 10 16 b 33 n. 31-32. Tel. 8' lVGVTLG ••• TL'. Bz. points out that these words are out of place, since Aristotle is dealing in this chapter only with oLaq,opa. and comes to IvaVTL~'ii only in the next. The objection is sound, but with this sentence belongs the next. For 7ravTa yap Ow.q,£poVTa (or 8Laq,lpoVTo. n) q,a{V(TaL is meaningless if the subject be TO. O!aq,£poVTa, but significant if it be TO. IvaVT{a. It seems better to treat 10Mb 311055& 2 as a discussion of contraries which ought to have been superseded by the fuller discussion in chapter 4 but was retained by the excessive zeal of the original editor. For the meanings of' contrary' cr. A. 1018& 25-35. 34. If we read Ttl 8Laq,lpovTa for Ow.q,£poVTa with Alexander, or oLaq,ipoVTa T2 q,a{vETaL, only the one sentence TO. o· lvaVT{a KTA. need be regarded as out of place. But it seems better to retain the manuscript

reading. Alexander's reading 'll"aVTa yO.p TA 8r.ar/JlpoVTa r/Ja1veraL /Cal. Ta~a is excluded by the fact that some things which are' different " viz. those that are different in category, are in no respect Ta~a. The point which Aristotle makes above and in 1. 35 is not that things that differ must be the same in some respect, but that there must be some one thing in which they differ. 'll"aVTa yO.p 8Lar/J1poVTa Tl. r/JalveraL /Cal. oli p.Ovov l'np4 OVTa would be a preferable departure from the manuscripts (though Aristotle would probably have said Twl rather than Tl, cr. I. 26); but 110 departure 8ee.ms necessary. 35. i" Tjj GIlT'!i Cl'UCrTCILXC, Tij'J KGT1JyopCal, cf. A. 986a 23 n. Here contraries (or differents) which are in the same' line of predication' are said to be in the same genus. In 1058& 13 (the only other passage in which CTVfTTOLxla '"ill /CaTTfYoplall is found) contraries in the same genus are said to be in the same • line of predication'. Thus' genus' and 'line of predication' are coextensive terms. Now it seems natural to identify the 'line of predication' here with the • figure of predication' six lines earlier. It is surprising to find genus identified with category, but the identification is vouched for by .:1. IOl6 b 33 (where see note), 1024b 12. Aristotle doubtless calls many classes which are not categories genera, but in the strict sense the categories are the only genera, since they are the only classes that are not species. Thus Bz.'s suggestion that CTVfTTOLxla '"ill /CaTTl"'loplall means one of the main divisions of a category, within which the same sort of predicate is found (thUS the various predicates of number might be thought of as forming a ' column' under the main predicates odd and even) falls to the ground. CTVCI'TOLXla is used (infer alia) of a series of terms of which each is wider than that which comes under it (An. POll. 66 b 27, 35, 79 b 7, 8, Sob 27, Sla 21, 87 b 6, 14), and each category is one CTVCI'TOLXla Tqll /CGTTfYOplall in the sense that it forms a 'Porphyry's tree' of which the apex is the name of the category. 105S&sa. i" tn}.OLI, .:1. 1024b 9-16.

Contrarzety (ch. 4). 10SSa 3. Contrariety is maximum difference. This is clear; for, while things that differ in genus cannot pass into each other at all, contraries are the starting-points and extremes in the passage into each other of things differing in spmes, and have the greatest interval between them. Now what is greatest in each class is complete (since there is no going beyond it), so that contrariety is complete difference, the meaning of ' complete' varying with the meaning of ' contrary'. 19. One thing cannot have more than one contrary, since (I) nothing can be more extreme than the extreme, nor can there be more than two extremes to the same interval, (2) contrariety is a difference, and difference is between two things.

CO:\J:\JF.NT ARY 23. The truth of the other definitions of contrariety follows: (I) the complete difference is the greatest difference, for (a) there is no difference between a thing and others outside its genus, and (h) the complete difference is the greatest difference between a thing and others ins/de its genus. (2) T he things that differ most in the same genus are contraries; so too are (3) the things that differ most in the same receptive material, and (4) the things faJling under the same capacity that differ most. 33. Positive state and privation are the first contrariety-but only when the privation is complete. Other contraries are so called because they possess, produce, tend to produce, or are acquisitions or losses of these or of other contraries. 38. The kinds of opposition are contradiction, privation, contrariety, relation. (I) Contradiction is not the same as contrariety since it does not admit of a mean while contrariety does. (2) Privation is a kind of contradiction, an incapacity which is determinate or involves the same subject which is capable of having the positive state. Hence, while contradiction has no mean, privation sometimes has; everything is equal or 1/0/ equal, but only that which could be equal must be either equal or unequal. b II. Since generation is from contrary to contrary, and is either from form or from privation, all contrariety is privation, though not aU privation is contrariety since there are various forms of privation; contraries are the extremes from which change starts. 17. This can be proved by induction. Every contrariety has a pri\'ation as one of its terms, but there are various kinds of privation; it sometimes means mere privation, sometimes privation at a particular time or in a particular part, or complete privation. Some of these kinds admit of a mean (a man need not be either good or bad), others do not (a number must be either odd or even). Again, some have a det~rminate subject, others have not. 26. Thus it is clear that one of two contraries is always privative. It ill enough to show this of the sU11l11la gmera of contraries, e. g. of one and many; the rest are reducible to these.

IOSsa 17-19. 1ro~~ax~ 8~ ... IIlho'L$ is explained by II. 24-33. Contraries may be defined as Ta 71'A€LO'TOV 8r.acplpovTa, as Ta lv Tai'1'
rarely found unless the protasis has been so long that the structure of the sentence has been to some extent forgotten. It is better to take !lAw.. 1"( d laTW ICTAo as subordinate to r/Jav£p/Jv (laTw). • And, to put the matter generally, this (that one thing has not more than one contrary) is evident if contrariety is difference, and difference-and therefore complete difference-is between two things.' ~3-33. The kinds of contrary mentioned in.:1. 1018& 25-35 are: ( I) Te\; p.~ 8vVaTQ up.a Tcil awcil 7rap£ivaL TWV 8mr/J£pOVTfI)v KaTe\; yivo'>, (z) Te\; 7rA£iUTOV 8Lar/JipOVTa TWV (V Tcil alm(i Yfvn (= 1055& 27), (3) Te\; 7rA£iaTOV 8Lar/JipoVTa TWV lv TallTl{j 8£ICTLKcil ( 1055& 29), {4} TQ 7rA£iaTOV 8mr/JipoVTa TWV fnriJ ~v a~ 8wap.w { ... 10551\ 3 1 }. I agrees with .:1 in the last three kinds, but excludes the first (1055a 26). In I the genus is conceived as a summum genus (1054b 29). Nothing can pass from one genus to another (1054b 29, 1057& 26); naturally therefore there cannot be contrary genera or contraries in different genera. In.:1 and elsewhere genus is treated more loosely, and virtue and vice can be treated as contrary genera (Top. 123b 14-16). ~6-~7. 8~ELKTCU yap ••• I'EYlcrnJ. ' For it has been shown that in relation to things outside its genus a thing has no difference, while with regard to things within one genus the complete difference is the greatest.' It is impos~ible to make consistent Aristotle's various statements in these chapters about difference. In chapter 3 difference in genus was freely rl'cogllized, and in its extremest form, viz. difference of category (1054 h 29, 35). So too in this chapter {1055a 6}. Yet here he says that there is no such thing as difference between a thing and something else outside its genus. Two explanations might be offered. (I) Aristotle may mean that if X and Y are in different genera they should not be said to have a difference, but the genera should. If this had been his meaning, however, he would probably have taken the trouhle to state it clearly. (2) It may be that while he uses 8Lar/JipELv, 8u;'r/Jnpov in a sense almost (not quite, cr. 1054 b 25) as wide as their everyday sense, he uses 8Lar/JopO. in the technical sense which it bears in his logic, viz. = a differentiation of a genus. This seems more likely. It is not clear where the proof referred to in 8i8ELICTO.L has been given. Presumably in I. 6. Things in different genera may be called 8Lar/JipoVTa, but since there is no passage from one to the other there is no definite measurable interval, no 8mr/Jopa, between them. h 3. Privation, we are told by Aristotle, is a kind of contradiction, and contrariety is a kind of privation. Zeller objects that when the conception of privation i!l cleared up it is seen to fall either under contradiction or under contrariety. This objection I have dealt with in notes on .:1. 1022" 22-24, 24-31. A 11. Posi. 73" 21, to which he refers, in no way proves his point; it rather suggests that contrariety reduces itself either to privation or to contradiction. The general position is this: Contradiction is the relation between two proposi-

=

CO:\J:\IF.NT.At. RY

tions of the type' A is B', 'A is not B'. Privation is the condition of a subject capable of being B (let us call it Ah) when it in any degree fails to be B. Contrariety is the relation between two conditions of Ab, that in which it is fully B and that in which it is not B at all. Thus contradiction includes privation as a particular case, and privation includes contrariety as a particular case. 4. ~ yap ,.a 48dvIIoTOV II}."" Ix,€LV. The application of a privative term to.a subject which is quite incapable of having the positive predicate is improper. In such a case it is only the contradictory term that should be applied. Strictly therefore Aristotle should not have included this as a case of privation (as he does both here and in ~. lou b 23), since privation is CTvvfLlI;qpo,u1'71 Ttf) 8fKTLKtf), i.e. implies that the subject could have the positive predicate, and is 8LOPLCT6lw-a., i. e. limited to such a subject. Aristotle is here taking account of the fact that terms like' blind " though properly applicable only to animals, are in ordinary language sometimes applied to other things. 7. lv.tUoL'J, A. U. g. CTT€P~cr€"''J 84 TLVOS 'CTTLV, i. e. in the case of all proper privations, as distinguished from the improper cases referred to in 1. 4 (note). For the possibility of an intermediate between leL~ and C1Tlp7JUL~ cf. Cal. 13 a 3 (seeing and blind), K. 106Ja 2I (just and unjust). 1111. ~ 1'f\i KUp£'tJ, • or in the dominant part '. Alexander aptly illustrates this by saying that a man might be called il.XfLP if he had no righl hand. 115. Bz. argues that the fact that some positive terms (like odd and even) have a determinate subject to which they are appropriate, while others (like good and bad) have none but may be applied in any category, is the reason why the former do not admit of a middle while the latter do. He therefore reads 0.,., for the manuscript In. Alexander gives the same general interpretation, and probably also read on (624. 12). But it seems clear that this is not the reason why good and bad' admit of a middle. Take Aristotle's favourite instance of privation, , blind', which has a determinate suhject, viz. animals j there are intermediates between • seeing' in the full sense and • blind' in the full sense. Distinctions such as are suggested by ~ rOT~ ~ Iv TWL, ofov &1' b .q.\&K4t TW~ ~ Ttf) /roplff!' ~ raJIT'[} are applicable to good and bad but not to odd and even, and this is the reason why the former admit of a middle and the latter do not. In T4 poll' KTA. raises a fresh point, the point of the proper application of privative terms, already mentioned in 1.4.

Tlte opposili01I

of' equal' 10 'grealer' and' less' (ch. 5).

I055 b 30. If one thing has only one contrary, how is one opposed to many, or equal to greater and smaller i I Whether' always implies opposition; we ask' whether it is white or black', 'whether it is white

293

or not white', but not' whether it is a man or white '. When we state alternatives between which there is no apparent opposition, as in 'whether Cleon came, or Socrates't we imply that they are incompatible; if they are compatible the question would be absurd and another opposition would take its place, 'whether both came, or only one of the two'. loS6& 3. Now we ask' whether it is greater, lesll, or equal'; what is the implied opposition of equal to the other terms? It is not contrary either to one or to both, for (I) it is not contrary to one any more than to the other; (2) it is contrary to unequal, so that it would have more than one contrary. If unequal is equivalent to greater and smaller together, equal would be opposed to both, but it would still have two contraries, which is impossible. (3) Equal is between great and small,. but a contrariety cannot be intermediate, or it would not be complete. IS. The opposition must therefore be either cOlltradiction or privation. ' Equal' is not the contradiction or privation of either extreme more than of the other; therefore it is the privative contradiction of both. Hence it is never stated as alternative to one of them alone. !:IO. It is not a necessary privation, for not everything that is neither greater nor less is equal, but only that which could be greater or less. It is the privative contradiction of both, and therefore intermediate between them. l34. What is neither good nor bad is opposed to both but has no name, since the terms are ambiguous and have no one appropriate subject-matter. Even what is neither white nor black has no one name, though the colours of which' neither white nor black' is predicated are limited. 30. Therefore it is not fair to object that if what is neither good nor bad is between the two, there will always be an intermediate between two terms, e. g. what is neither a shoe nor a hand will be between the two. The one is a joint contradiction of opposites between which there is an intermediate and an interval; between the other two terms there is no difference since they belong to different genera. 10SSb 34. l~ ~1I'OelCTEWS, i. e. on the as~umptioll that the person who came must have been either Cleon or Socrates. 36. c1).).' O~K ••• ylv,,~ TOUTO, i. e. this is not the necessary disjunction of any class. d>..>..a Kut TOUTO luie"v l>"~>"ue"v, 'but E~ven the use of" whether" in such a question as " whether Cleon or Socrates came" is derhoed from its proper use in which the alternatives stated are opvo~ite '.

294

CO:\I:\IE~TARY

1056" 1-8. It S,. •.. 4.".l81aLV, 'but if they could be true together, even so the question falls none the less into an antithesis '. 8-11. ' If "the unequal" means the same as both (the greater and the less), then the equal would be opposed to both, but this means (in spite ot the fact that we have now one word " unequal" to denote both) that one thing is contral'Y to two others, which is impossible.' 10. TOLl +daKouaL Til &.,wo., Suc£8« It.,«L, the Platonists, cf. N. 1087b 7. IS. Having shown that the opposition is 1I0t that of contrariety, Aristotle infers that it is eilher conlradiclioll (lr privalion (the fourth kind of opposition, that of relation, it evidently cannot bt", since the equal is in that sense opposed not to the unequal but to the equal). It is disconcerting to find him, immediately after, saying that it is/ri'l'alive co"lradiclion. But in truth contradiction and privation are not mutually exclusive. Equal and greater-or-smaller are not strictly con· tradictory, for neither is true of non-quanta. But they are privatively contradictory, i. e. contradictory (so that both cannot be true and one must be true) when predicated of any subject in a certain genus, the genus of quanta. d.7T#afTL<; fTT(p7JTLK~ amounts to the same thing as fTTlP71fTL<;. Cf. 1055b 3 n. 86. nUIIoXwIl yAp UylTIIL lK.iTlp0." the good and the bad are found in every category, E. N. 1096& 19. 35. The best sense is got by translating' for the one is a joint negation of opposites'. fTVIIfl7rOt/>auL<; is predicate, and ~ is attracted to its gender. TW., S' O~K 'aTL SLIIo+opa. according to the account of difference in 1054" 23-1055& 2.

"I.

The o/>posilir)1l of' olle'

10 • 111m!>,'

(eh. 6).

1056" 3. A similar question may be asked about one and many. If many is opposed to one absolutely, difficulties follow: (I) One will be few, because many is opposed to ft:\\'; (2) two will bc many and therefore one will be few, since it can only be in opposition to one that two is many; (3) 7TO.\U and ::Aiyov are in plurality what long and ~hort are in length, and what is much is many and what is many is much (unless fluids are an exception), so that the few will be a plurality, and therefore one will be a plurality. 14. The truth is that the many are also 'callcd mUl:h, but the meaning of the two terms is different; water may be much but is not many. But many is applicable to all things that are discrete, and means (I) a plurality which is absolutely or relatively superior, as opposed to few, but also (2) number, as opposed to one. The oppositi;)11 of one to mar:y is like that of one to ones or of white thing to

white things; each number is many because it com,ists of ones and is measured by one, and as opposed to one, not to few. 115. In this sense two is many; it is not many in the sense of being a plurality which is superior either relatively or absolutely. It is few absolutely, since it is the first inferior plurality (hence Anaxagoras was wrong in saying' all things were together, infinite in multitude and in smallness-by which he meant fewness-, for they were not infinite in fewness), since fewness is constituted not by one but by two. 311. One and many in numbers are opposed, then, as measure to the measurable, and these are opposed as things that are per Qcddclll relative. A may be relative to B (I) ,\S being its contrary, or (2) because B is relative to A (in which indirect sense • knowledge' is relative to ' knowable '). 10578 I. One may be fewer than some other things; it does not follow that it is few. II. Plurality is the genus of number; number is plurality measurable by one. One and number are opposed not as contraries but as some relative terms have been said to be opposed, viz. as measure to measurable; hence not everything that is one is a number. 7. Knowledge might be thought to be related to the knowable as measure to the measured, but in fact, while all knowledge is knowable, not everything knowable is knowledge; in a sense knowledge is measured by the knowable. III. Plurality is contrary neither to few (many being contrary to few as superior to inferior plurality), nor in every way to one. In one way it is contrary to one, because it is divisible while the one is indivisible; in another it is merely relative to it, as knowledge is to the knowable, if many means number and one the me~sure of number. 1056h 5. 6Myo.. fj 6)'lYII.

This does not mean 'little or few'.

dAlyov means 'few' as well as (~)..{ya, and is used only because of the

awkwardness of using the plural as a predicate of TO IV. On the other hand 7I"OAv and 7I"OllU are used with a distinction of meaning, 'much' and 'many', I. 12. II. Kill S a.. ii 1I'0).~ Kill 11'0).).«, Kill TO. 11'0).).6 1I'oM. This clause is introduced to confirm the premise ju~t st,tted, that 7I"oAv and o)..{yov are varieties of plurality; Arbtotle cOllfinm; this by remarking that (apal t from the case or fluids) what is 7I"oAV is 7I"OAAU, in which the plural case shows that a plurality is in q\le~tilJn. III. Et ,.nj TL • • • E~oplC1T~, • unless indeed there is a difference in an easily moulded contmuum', viz. a flui~, to which' much' but not , many' is applicable. Alexander reads dO/llO'T't, and takes this to refer to liquid; this is possible, since fluid is referred to in Dc Gm. eI

CO:\iMENT ARY

Corr. 329b 30 as TO c10PUTTOV OlK€L'I! 6p'l!, €VOPLOTOV 6V (what has no definite boundary of its own, and readily takes the shape of its reo ceptacle), but not probable, since fluid is often referred to as €MpLOTOV simpliciler (De Cado 313b 8, De Gen. eI Corr. 328b 17, Meteor. 360& 23, 3 81b 29). ' 14. AU· tcrws KT).. Aristotle begins here his discussion of the difficulties stated in 11. 5-14. The vital point in his solution of the difficulties is the distinction (II. 16-20) between two senses of 'many' -the sense of 'superior plurality', in which it is opposed to 'few', and the sense of 'number', in which it is opposed to 'one', and opposed not as its contrary but as its correlative. Thus (I) the first difficulty (II. 5, 6) disappears. Though many is opposed to one and to few, it does not follow that one is few, for it is many in different senses that is opposed to one and to few. (2) The second difficulty (11.6-10) disappears. We cannot say 'two is many and therefore one is few', for two is not many in the sense in which many is opposed to few (i. e. in the sense that there is a plurality which is smaller and which may be called few), but only in the sense in which many is opposed to one. (3) The third difficulty (II. 10-14) disappears. For one of the premises of the argument, viz. that one is few, has now been shown to be untrue. gl, g:l. Jaeger is no doubt right in treating Kal TO I'np'I)TcSl' as a gloss on Ka.l TO. I'EI'ETP'I)I'il'a., suggested by P.£TPTJTO<; in 1. 23. Besides this he reads a colon after AEVKa, inserts iJJrnr£p before TA P.£P.£TprJp.tva, and a comma after P.tTPOV. This produces a neat sentence, but is (1 think) an unnecessary departure from the evidence. It is just possible to retain Ka~ TO P.€TpTJTOV if we abolish the full stop after it. 'For we say one or many as though one said one and ones or white thing and white things; and things measured-in relation to their measure-and the measurable and multiples are spoken of in the same way.' :15. 1I').ij8os EX01' ~1I'EPOX~1' ~ 1I'pcSS n ~ A1rMit, a plurality greater than some olher, or than any other. g6. A)')'o' 1I'PWTOI', se. 1I'M,6o<; lOTW. gS. A1I'iaT'l) , 'ieft the subject',cf. Top. 107 b 9,Phys. 191bIO,E.N. I I 65& 35. 30. l8EL ••• "Kill 6).LycST'I)n" makes specific the criticism stated generally in the previous clause. 'Anaxagoras should not have been content to say " all things were together, infinite both in multitude and in smallness"; he ought to have said "and in fewness",' oll yap iI1f'€Lpa is then added somewhat elliptically. ' And thus the error of his view becomes apparent; for things cannot be infinite in fewness.' Aristotle thinks that when Anaxagoras said Ka~ 1I'A116o<; Ka~ up.LKp/rrrJTa (fr. I) he meant to be mentioning opposites; and the opposite of multitude is not smallness but fewness. Anaxagoras meant, as a matter of fact, what he said, that things were infinitely many a.nd infinitely small, in the sense that everything however small included yet smaller parts. If he had meant that they were infinitely few, Aristotle's objection

29'1

(all yap d.1r€tpa) that things cannot be infinitely few, since there is an absolute few, viz., two, would have been sound. After OllK lipOw,> d.1r€UTfJ we might have expected d.U· lon, but for similar instances of O€ cf. K. 1061& 23, De All: 409b 28, Pol. 1326& 12. , The meaning of the passage has been well brought out by Prof. A. A. Bowman in Class. Rev. xxx. 42-44. 31-32. l1l'Et T~ 6~LyOV ••• Suo evidently refers back to I. 2'1 &)..{ya 0' a1r)..w,> TO. Ova KT)... Christ is right in treating the intervening words as parenthetical, but his excision of aUK in I. 28 is indefensible. 35. lv &~~o~s,~. 1021& 26-b 3. There, however, TO. 1rpO'> Tt, oo-a p.~ KaO' aUTO. .TWV 1rpO.. Tt are opposed not to TO. 1rp6.. TL .:,'> EvaVT{a (for which cf. 1057& 37), but to the other kinds of 1rpO" Tt, (a) TO. .:,.. OL7l'M(noV 1rPO'> ~p.urv, (b) TO. .:,'> TO O(pp.aVTtKOV 1rpO" TO O(pp.aVTOV. These two kinds are here inaccurately summed up as To.1rp6,> TL':',> (VaVT{a. The point of distinction is that while' double', 'half', 'heating', 'heated' are all essentially relative terms, 'the measured', 'the known " , the object of thought' are relative terms only because something else, 'the measure', 'knowledge', 'thought', is relative to them. The relativity is one-sided, not mutual as in the other two cases (1021& 31). There is a further difficulty in the present passage. Knowledge is said (I. 36) to be relative to the known in the sense that something else (the known) is relative to it. But in ~. 1020b 30-32 the known was said to be relative to knowledge in this sense; cr. 1057"7-12. There the known, here knowledge, is made the term which is really absolute and only incidentally relative. The two statements are to be reconciled as follows: The term' knowledge' is prior to the term , knowable', since knowable possible object of knowledge. But the thing which is knowable is prior to the knowledge of it, since there can be a knowable which is not known but there cannot be knowledge which is not of something knowable. 1057& 3. run yAp 4p,e..,bs 1I'~~eos M P.ETp'IJTOV, cf. ~. 1020" 13 n. 8. For d1l'oSLSlllcr~V, 'turns out', cf. Afl. Post. 99& 30, Meteor. 363" II, H. A. 585b 32, 586& 2, G. A. 72288. 9-12. The sentence is difficult; the alleged fact (uvp.pa{vn 8£) is surprising in itself, and does not stand in a proper antithesis to what 'one might suppose' (oo~(L( p.£v yap av). The expression is loose, but the point (if the reading be right) seems to be this: Knowledge might be thought to be the measure of the knowable (a free rendering of Protagoras' maxim), but in point of fact, while all knowledge must be knowable, not all that is knowable is actually known or knowledge. The point is stated more accurately in Cal. 7b 22-35, where as here the relation of the knowable to knowledge is distinguished from the relation of a genuine 1rpO'> TL term to its correlative. Cf. 1053831-35. The doctrine of the identity of knowledge with its object (De An. 430& 4, &c.), to which Alexander and Bz. refer, does not seem to be relevant. I suspect, however, that we should read brurT1Jp.fJv p.€V 1racrav 11l"· UT'lJTOU (Ivat TO 8E £1rtCTT1JTOV p.~ 1raV 1I'pOS E1rlcrrqP.71V, 'that all knowledge is

=

U

CO:\I:\lENTARY of a knowable, but not all the knowable is relative to actual knowledge '. T his agrees better with Cal. 7b 29 l1rl.CTTrJTou p,€v yap /L~ ;;VTO~ ollK EITTW 17rtlTT~P,YJ (oM(JI~~ yap ElTTat l7rLCTrr}P,YJ), l1rLCTn,P,YJ~ 8f p,~ OV EiyE EITTW l1rtlTTYJTov, l1rLCTrr}P,YJ P,EV allTou ollK EITTW oMi1rlll, allT~~ 8f l1rwT't}Tov llTTw. 14-17. From one point of view number is contrary to the one, because they have contrary attributes, being respectively divisible and indivisible; but from another point of view they are related not as contraries but with the sort of relation that knowledge has to the knowable, being respectively number (i. e. the measurable) and measure. The distinction drawn in I056b 35 between waVT{a and the other kind of 7rpO~ Tt thus reappears in this sentence; the meaning is brought out better by deleting the comma after Tt in I. 16. It seems clear that the subject of V (I. 16) is not as Alexander and Bz. suppose ~ E1rtun,P,YJ but TO 7rA-ij8o'>, and that TO 8' ~v p.iTpov, not TO 8' ~v Kal p,iTPOV, is to be read.

Tht! 11alure of 111lermedialcs (ch. 7).

1057& 18. Intermediates must be compounded out 01 contraries; for (I) they are always in the same genus as the extremes, since (a) they are that into which things must change before they reach the e~ tremes, and (b) it is not possible to change from one genus into another except per aaidens, e. g. from a colour to a shape. 30. But (2) (a) all intermediates are between opposites (for it is only between these, per St, that change can take place); and (b), of opposites, (i) conlradzelories admit of no mean (contradiction being between opposites one of which must be true of every subject); while (ii) relalive terms that are not contrary have no mean because they are not in the same genus. Intermediates must therefore be between contraries. b 2. (3) They must therefore be composed of these contraries. For the contraries must either fall within one genus or not. (a) If they do, so that there is sometl:ing prior to the contraries, the differentiae that make the contrary species will be prior contraries; for the c;pecies consist of the genus + the differentiae. I2. The intermediates will be composed of the genus + certain differentiae, which will not be the first contraries (otherwise every colour would be either white or black), but are intermediate between them. 19. Thus we have to consider first, of witat are composed the intermediates between (b) contraries that are 1101 in the same genus; for the things in the same genus must be composed of terms that do not

299

involve the genus as an element in them, or else be incomposite. Contraries are not compounded of olle another, and are therefore starting-points; of the intermediates ail or 1l0lle are compounded out of the contraries. Now frolll the contraries there arises sOllltlllillg such that change reaches it before it reaches the contraries (for there must be something that is less than the one and more than the other). Therefore all the other intermedhltes also are composite; for that \\'hich has a quality in a higher degree than A and ill a lower degree than B must be compounded of A and B. ~g. But since there is nothing homogeneous with the contraries and prior to them, all intermediates must be compounded of the contraries, and therefore the lower terms, whether contraries or intermediates, will be compounded of the first contraries. Clearly, then, all intermediates are (I) in the same genus, (2) between contraries, and (3) compounded out of the contraries. Chapters 7-10 arc for some unknown reason not commented on by Alexander. ]057" 18. KaL lVLWV EO'TlV, i. e. in the great majority of cases; there arp. sOllie contraries, however, like odd and even, straight and crooked, which admit of no mean (105fib 24). Ig_h 34. That the intermediates arc compounder\ out of contraries is proved (cf. IJ 2-4) by three premises, (I) that all intermediates are in the same genus as their extremes (I. 19) (which is itself proved by two premises, (11) that intermediates lie on the path of change between extremes (I. 21), (t) that change from one genus to another is impossihle (I. 26)}; (2) that all intermediates are between contraries (\\'hich is proved by t\\'o premises, (a) that intermediates are between opposites (I. 30), (b) that they cannot be between an)' kind of opposites except contraries (I. .13-" (3) Intermediates between contraries in the same genus, i. e. hetween contrary species, presuppose intermediatcs betwcen contraries not in the same genus, i. e. between contrary differentiac (" 4-22); and sincc there is an intermediate differentia compounded Ollt of the contrary diffelentiae, and if any of the intermediates is compositc they all must be, allmusl be compounded out of the contraries (1122-32). ~7. KaTa. O'U,...fJEfJ1JKO", otov lK Xpw,...aTO'i Et.. O'xij,...a. A red thing may become round, but it does so not 'lltl' red but 'lila having some ligure other than the round. 33-11 I. Of the four kinds of oppositl'~, viz. contradictories, rclatil'es, privativl.'s, contraries, Aristotle sholl'S that the /irst two cannot have intcrmeuiatcs, and he infers that intermediates must be between contraries. He says nothing of privativt's, for contrariety is the extreme form of privation (1055" 35, 0. 104()h 14). so that any privation short of complete privation falls between contraries.

J».

300

COl\I:\IENT ARY

37. TWI' 8£ 11'pO~ n 00''' I'~ EI'''IfTL'', cf. 10561> 35. b 7. c'l81J ~ yl.I'OU~, i. e. €i&, in the sense of species- of a genus, not in the sense of Platonic Forms, cf. A. 991& 31 n. 8. ,.0 ""~I' 8~"KP~T~KlII' xpwl''', Plato's definition of white, Tim. 67 E TO p.~ 814KptTtKOV TTj~ 6"'€W~ An/Kav. Fine particles penetrate and dilate the visual stream, large particles compress it, and this produces white and black colour respectively (67 n). II. mc\ p.~I' Tel yc .I'''IfTL~ 8~U+l.pOrT" ,...auOl' .I'''rT£'' is very difficult. Bz. takes it to mean • but the contrary differentiae must be more contrary than the contrary species', since they are what make the latter contrary (cf. ". 993 b 24). But (I) Tel (vaYTCw~ 814cplpoYTa is a strange way of expressing 'the contrary differentiae', and (2) this would be a mere repetition of the previous clause. Tel (ya"TCw~ 8,acpEpoYTa would more naturally mean the species that differ by having contrary differentiae, and Aristotle's point may be that though the differentiae are in some sense prior contraries, the species are more properly called contraries. Cf. Cal. 6& 17 TO. 'lrA€iO'TOV dll~Awv 8wrT71KOTa TedV EV T'iJ aw'iJ yEV" (we may illustrate this by white and black as opposed to 8,aKp'T'Kav and ITV"fKp!T'KaV, which are p.~ (V YEV", 1. 20) IvaYTCa ;'pl{oYTa" and De Gen. eI Corr. 324& 2. Even this interpretation, however, is not very satisfactory. 12. Tc\ ).0~11'c\ KAt Tc\ P.ETA~d, 'the others, i.e. the intermediate speties'. 20-22. 'For the contraries which are in the same genus must be compounded out of (the genus and) the differentiae which are not themselves compounded with the genus (Le. in which the genus is not an element as it is in the species),-or else be uncompounded (which is incompatible with their nature as species).' 26. P.ETA~U UPA IO'TA~ KAt TOUTO TWI' .I'''I'T£'''I', , wherefore this differentia also comes between the contrary differentiae, as the intermediate species come between the contrary species'. 31-32. .:inc ... 1000rT"~. This seems to say that each extreme species as well as each intermediate species is compounded out of both the extreme differentiae. E. g. white would have to be to some extent , compressing' as well as 'dilating '. But this is not in itself a likely doctrine, and it can hardly be said to be proved in the present passage; the meaning probably is that each extreme species contains one of the extreme differentiae as a logical element (the other element being the geilUs), while each intermediate species contains both the differentiae.

Olmrness in spedes (ch. 8).

1057b

35. That which is other in species is different from something and this must belong to both the terms that are other than one another. They must therefore be in the same genus, for a genus is that which each of two things differing per se is said to be. in sonlflhz'ng,

I. j. 1057& 37 -

8. 1058& 8

301

loS8a II. For not only musl something common belong to both, but it must be different for each of them. The differentia must be an otherness of the genus; for a differentia of a genus is an otherness that makes the genus itself olher. 8. This otherness must be contrariety. For all division is by opposites, and contraries are in the same genus, since contrariety is complete difference and difference in species is always difference from somelhing in respect oC something and this something is identical and is the genus that embraces both terms. Hence all contraries that differ in species and not in genus are in the same category, and have the utmost difference and are incompatible. 17. To be other in species, then, is to be in the same genus, contrary, and indivisible (and to be the same in species is to be indivisible and have no contrariety)-for there are also contrarieties in the intermediate stages of division before we come to the indivisibles. III. Therefore no species is either the same in species as or other in species than its genus (for matter is made known by negation, and the genus is matter oC its species), nor with things not in the same genus; it differs in genus from them, in species from things in the same genus. For the difference must be a contrariety to that Crom which the given species differs in species, and contrariety exists only within a genus. 1057b 35. From 1058a 12 it would seem that T£ is • accusative of respect' j 'other in some respect'. The same meaning is sometimes conveyed by the dative, cr. 1054 b 25 ,.0 8f 8ul.f/Jopov TWOIO TW~ 8ul.f/Jopov. 38. I'fJ KUM aul'jJEjJ1)KOt Ixo ... 8LU+opd.... Cf. the rule that a genus must be divided according to its OlKE{U 8,alpE'nlO (Z. 12, I. loS8 a 37). loS8a I. EtTE ~ 1Th" il.... cf• .1. 1024 b 8. 4. 'TEpO... clU~>"fII"', 'different for one from what it is for the other '. 8. lVUI'TWuLt TO£ ...U... 'nuL uD-.,.,. That the differentiation of a genus must be by contraries is by no means proved by what has gone before; nor does what follows bear any resemblance to an bruy"'Y11' It seems better there Core to take 81jAov 8f K~ IK rijlO 17ru~1O as parenthetical (cf. Phys. 18Sa 13, 224 b 30, De Caelo 276a 14), and what follows as justiCying IvuVTtwu,1O TO{VVV 11TTll' o-Urq. Even so the juslification is far from complete. Aristotle merely points out that all division is by opposites, and that contraries are in the same genus. He does not show that they are the only opposites which are in the same genus (which alone would prove that all differentiation is by contraries). Yet he could almost prove this. For contradictories are not in the same genus, since they together embrace the whole universe; nor are relative terms necessarily in the same genus (1057.38). Privatives and contraries alone remain, and these are very closely bound up together (1057a 33 b In.).

("cnnIDn.\RY

3 02

Though Aristotle sa) s that differentiation is by contraries, he does not in practice confine himself to division by dichotomy j e. g. in Cal. 14 h 37 he divides animals into ;:'Tl'}VUV, 7r('OV, iVl'SpoV, II. SISElKTal, ch. 4. ~v, 105,jn 16. ~ S~ SIa+opa. ~

('iSEI 'll"a.cra TWOS TL, 'specific ditl"ercnce is always from something in something '. 13-14. Tti a,hii crucrTOLXLq. ••. '"is KaT1)yopLas, cr. 1054b 35 n., .1. 101li b 33 n. 17-lg. Both indivisible species and individual~ may be called dTOp.a. (Bz. Jlldi'.\" 120· 58, .8). But the ~Top.a which are said to be the same in species must be individuals, since two species are not the same in species. If, then, there is to be a proper opposition between the ddinitions of Enpa T~ (ZSn and Ta{,Ta. T~ (rS(L, dTop.a in I. 18 as in 1. 19 must refer to individuals. But since in II. 21-26, it is species thai are descrihed as different in species from other species, dTop.a in I. .8 probably refers to indh'isible species as well as individuals. . 18-lg. TaUT« ••• ClVTa is parenthetical. The next words justify the insertion or the previous q,Top.a (iVTa; in dividing a genus, we find contrarieties even in the previous stages (Kul. lv Tois p.ETatv), i. e. between dasses higher than the infimae species, but these constitute otherness in genus rather than in species; it is only hetween lhol'a (io7] that there is otherness in species. gl. TO Ka~OUI'EvOV ylvo<;, cf. .::l. 1014 b 9 Tc'J. KaAovp.(Va yEVl'}. The technical meaning 01 ylvos and Er8o~ is not quite familiar, and KaAOVP.EVOV introduces it with some diffidence. In chapter 10 we shall find yEVO~ and ElSo~ lIsed quite untechnically. Bz.'s conjectural emendations here are unnecessary. gg. WS ylvous. d. A. 9911\ 31 n. Christ was right in reading 'll"POInJKOVTWI. It is the reading of A b as well as of E. g4. I'~ Wi TO TWV 'HpaK~EL8wv, cr. .::l. (024" 32. d.~~' W!l TO Iv -rfi +ucrn, 'but in the sense of the genus which is an element in the nature of a thing'. Cf..::l. 1024 b 4 I} )"lYETaL lVT~ Tt , , EITTL, TOl'TO yEVO~.

-

g7.

o~ 8La+lpEL

= 1rPO~ TOVTO ot 8LaCPEPEL TL.

Whal cOIl/rani'lii's rOlls'//"le ollu'rIlt'Ss ill s/,ert't's (eh. 9).

10580 gg. Why does not the female differ from the male in species, when female and male are contrary and the differentia is a difl'erentia of animal as such? 34. This is much the same as the question why one contrariety(e.g. possession of feet and of wings) makes things other in species, and another (e.g. whiteness and blackness) does not. The reason is that

I.

S. 105sa

I I -

9. 105Sb

2

only the former are affections proper to the genus. Contrarieties in the definition make a difference in species, those in the concrete whole do not. b 3. Hence whiteness does not make a differentiation of man; for colour belongs to man on his material side, and matter does not make a differentia. Individual men are not species of man, though their flesh and bones are different; the concrete whole is other, but not other in species because there is no contrariety in the definition. Man is the last, indivisible species; Ca\lias is definition + matter, and so too i!l 'the white man', since' the man' is only white per accidens because Callias is white. I~. Hence a bronze and a wooden circle are not other in species; and a bronze triangle and a wooden circle are other in species not because of their matter but becausIl there is a contrariety in their definition. 15. But perhaps where the matter is other in a particular way it makes the things other in species in a sense. Why is this horse other in species than this man, though their definitions involve matter? Because there is a contrariety in their definitions. A white man and a black horse are other in species not qua white and black, for they would have been so even if they had both been white. ~I. Male and female are affections proper to animal, but not in virtue of its essence but in its matter (and hence the same seed can become male or female). This chapter implies a division into three kinds of the attributes which belong to some members of a genus and not to others. There are (I) 01K(ia 1f'a~ TOV Y(V01J'> (a 37, b 22), which belong to the genus KaU aw6 (a 32), i.e. are peculiar to it. These are subdivided into (0) those which are lv T~ Aery'fl (b I), which belong to the essential nature of the genus. i. e. differentiae like 'footed' and 'winged' in the genu!! 'animal' (a 36). and (b) those which are lv T~ uW£lAYJJLJL€v'fl rii vA'!l (b 2), which arise from the association of the essential nature with two or more kinds of matter. Thus a male animal is produced by the association of the U1r(PJLa or male element, in which the form of the species is transmitted, with one female or material element, and a female animal is produced by its association with a different female element (b 23). The attributes under this head are properties of the genus; every animal must be maleor-female. and nothing but an animal can be either. There are (2) attributes which are not olK(La 1f'ol}'1l TOV ylvov<; (a 37). like white and black, which belong to animals not qua animals but qua havina surfaces. These attributes are accidmts. <> I058b~. TijlO'u""~).1J,...,...i... 't' TfJ U).n. cf. E. I025 b 32.

CO:\f:\TENTA RY

5. ~s Wo.'1 yap II uv8pw1I'os, 'for when we distinguish the white man from the black man we are considering man on his material side '. 9. TOUTO S' iUTl TO EuxaTOV liTol'OV, , and this-that in whose definition no contrarieties are included-is the ultimate indivisible species '. For aTO/LOV cr. a 17-19 n. Il-12. Kalll ~EUKOS .•. uv8pw1I'os. 'The white man, then, is also definition + matter, for it is the individual Callias that is white; man, then, is white only incidentally (or per accidens).' 13. The substitution of a colon for a comma before oM' does away with any need for Bz.'s emendation, ~.\LVOV Tp{ywvov for ~V.\LVO~. 'The bronze circle and the wooden circle, then, do not differ in kind; nor do the bronze triangle and the wooden circle differ in kind because of their matter, but because of the contrariety in their definitions', i. e. between triangle and circle. 17. TOv8, d.v8pw1roV would (I think) be unparalleled in Aristotle, and the addition of TOV is necessary.

The perisllable and Ihe imperzshable differ I'n Itlnd (ch. 10).

1058b 26. Contraries are other in form, and the perishable and the imperishable are contraries. They must therefore be other in kind. But so far we have spoken only of the universal terms, so that it would not follow that every imperishable thing is different in kind from every perishable, any more than every white thing is from every black. The same thing may be both white and black, and, if it is a universal, may be both at the same time. 36. But while some contraries such as white and black belong t6 certain subjects per accidens, perishable and imperishable do not. Nothing is perishable per accidens; if it could be so, the same thing might be both perishable and imperishable. Perishableness is either the essence, or included in the essence, of all perishables. So too with imperishableness. Therefore the essential natures in virtue of which things are perishable and imperishable are opposed, and therefore are other in kind. 1059& 10. Therefore there cannot be Forms such as some thinkers maintain, for if there were there would be a perishable and an imperishable man. The Forms are said to be the same in species as the particulars, but things other in genus are further apart even than things olher in species. 1058b iJ7. I7TEP'lI7~S yAp ci8uI'al'£Cl 8~"'P~I7I'E"'I' ' Perishable' and imperishable' are contraries, not contradictories, for a privative term

l.

9. 1058b 5 -

10. 10590.

12

like 'imperishable' is not applicable to any and every thing that does not perish, but is limited to the class of things that might conceivably perish (cf. 1055 b 8). !Z8. ylm. The premises only warrant the conclusion that the perishable and the imperishable are different in species, and therefore Bz. reads Er8Et. But this does not remove the difficulty, for in 1059a 10 it is again stated, without any fresh grounds, that they differ 'I(VEt. It seems plain that Er8n and 'If.vEt are not here used in their technical sense. They may be translated 'form' and 'kind'. In I059a 14 on the other hand the technical distinction is found, and it seems probable that while the rest of the chapter was written before Aristotle had begun to use the words in their technical sense, 11. 10-14 were added later under the supposition that generic as opposed to specific difference between the perishable and the imperishable had been proved. These lines have the air of an afterthought; they use for the purpose of anti-Platonic polemic a result which in the rest of the chapter was established without any polemical motive. For other instances of the non-technical use of the words cr. A. 1071a 25 with 27, Cal. 8 b 27 with 9& 14, Atl. Post. 97 b 24 with 34, H. A. 490b 16 with 17, 31 with 34, 557 a 4 with 24, Pol. 1290h 33 with 36. In Plato the words are often used indifferently. 1059& I!Z. 6 "lv, the sensible individual; 6 S', man-himself or the Idea of man.

BOOK

K

Book K consists of two velY different parts, (1) 1059 a 18-1065& 26. a shorter version of the contents of BI'E, (2) 1065" 26-1069 a 4, a series of extracts from P~l's. II, III, V. The two parts are ingeniously connected together by a transition from a discussion of the accidental to a discussion of chance. Jaeger has given (AnsI. 216 If.) strong reasons for holding that the first part is earlier than BI'E, and was written when Aristotle was still much under the influence of Platonic presuppositions. (I) While E has a section pointing forward to the discussion of substance and activity in ZH@ (1026 a 33-h 2), this is lacking in K (1064 b (5). I.e., while E has been worked up into a form which served to connect the original introduction ABI'E. 1 with the later discussion of substance, ZH@, there is no trace of this in K. (2) In K. 1059a 39 Aristotle asks whether 'the science we are looking for' is concerned with sensible substances or with others. In the corresponding passage, B. 997 a 34, he a~ks whether we must maintain the existence cof sensible substances only or also of others.

306

CO:\TMENTARY

Jaeger argues (unsuccessrully, I think) that K here represents a more . Platonic point of view. (3) In K. J060 a 7-13 the object of inquiry is said to be EZ T' xwpurroll Kafl a~To Kal. p.YJ8E11l. TWII alu~wlI wapxoll. In B. 999 a 2432 the language is much less strongly Platonic. K. 1060a 21-27, b 1-3 reveal the same search for a transcendent object of knowledge. (4) In K. 1063a 10-17 Aristotle appeals from the changeableness of terrestrial things to the permanence of the celestial; in r. 1010a 15 ff., the appeal is to the permanent elements in the terrestrial world, and only incidentally (ib. 25-32) to the constancy of the heavens. (5) The problem about the tiAYJ TWII p.atJ.r,p.aT'KwlI is peculiar to K. J059b 14-21. It is discussed in N. 1088 b 14 ff., and N can on other grounds be shown to belong to the earliest drart of the Metaphysics. The prohlem springs naturally out of Plato's doctrine of the great-and-small. (6) The one problem which is found in B (1002 11 32-1003a 5) and not in K is the question whether the elements exist potentially or actually-a question closely related to the contents of ZH@. (7) K. 1059 b 3 presupposes the refutation of the ideal theory in A. 9; B. 997 b 3 does not do this, and evidently belongs to the later period in which the attack on the ideal theory was removed from A and relegated to M. 4, 5. Rerapittllalioll of lhe problems .rlaled in B. 2, 3 (ch. I). I059n 18. That wisdom is a science of first principles is clear from our examination of earlier thinkers, but the following questions arise : !Zo. (I) Is wisdom one science or more than one? If one, it should be of contraries, but the first principles are not contrary; if more than one, which are these sciences? !Z3. (2) Is it the business of one science to study the axioms? If of one, why of this more than of any other; if of more than one, which are these sciences? !Z6 (3) Does it study all substances? If not all, then which; if all, how can one science study more than one subject? :19. (4) Does it study attributes as well as substances? If it is a demonstration of attributes, it is not about substances; if a different science studies attributes, what is each and which is wisdom? Qua demonstrative, the science of attributes would be wisdom i qua aoout primaries, the science of substances. 34. The science we are looking for does not deal with the four causes; it cannot deal with the final cause, i. e. the good, which is the first mover and is not presupposed by unmovable things.

S8. (5) Generally, is this science concerned with sensible substances or with others? If with others, then either with Forms or with mathematical objects. (a) The Forms do not exist; but, if we suppose them to exist, why is there not a third man, &c., just as r" athematical objects are a tertium quid between Forms and sensible things; on the other hand, if this terh'um quid does not exist, what is mathematics about? Not about sensible things, which have not the required properties. b Ill. (b) Nor is the science we are looking for about mathematical objects, which have no separate existence, nor (c) about sensibles, which are perishable. 14. Which science should investigate the matter of mathematical objects? Not physics, which is occupied with things having a principle of motion and of rest in themselves; nor logic, which is absorbed in the study of knowledge. This must therefore be a task for metaphysics. b 81. (6) Does metaphysics study the elements present in composite objects? It might seem to be rather concerned with universals (since all knowledge is of universals) and therefore with the summa gmera, being and unity. These might seem most like first principles because if they are destroyed everything else perishes with them; everything is existent and one. SI. On the other hand, it would seem that these cannot be genera or first principles, because the differentiae must share in them, but no differentia shares in its genus. Further, what is simpler is more of a first principle than the less simple, and t'nji11lae species are simpler than their genera, being indivisible. But inasmuch as the destruction of the genus involves the destruction of its species, the genera are more like first principles. K. I, 2 covers the whole ground of B except the d:lropla ~tated in 996310, II and discussed in 1002 h 32-1003" 5. 10591\ 19-1l0. lK TWV 1I'PWTWV •.• 1I'tpl TWV clpxwv, i. e. A. 3-10. llo-~3. This &:lI'op{a is that which is stated in B. 995 11 5, 6 and discussed in 996& I8- h 26. The objection here urged against saying there is a single science of the dpXal. is the objection ~tated first in B (996& 20, 21). The question here stated to arise if there be said to be more than one science of dpXal is different from that stated in B. 99611 1-24. The SeC01ld objection stated in B (996& 21_11 I) against the first alternative is omitted here. The same point is made in 10593 34-38, but in a different connexion. llll. cd 8' 4pXa1 O~K lvaVTLaL. By the dpXa{ are meant, as is evident from B. 996& 21_11 I, the four causes, which are evidently not contraries. llS. ".La. We should perhaps follow r in reading ILi.uv, which gives the proper correspondence with (1 ILfV yup IL{uv, I. 2 I.

COMMENT ARY 'll'OCIl! 8Et 8ELI'IlL TlldTIl!; I what sort of sciences is it that must be held to make up CToq,{a? ' :&3-:&6. This problem answers to the problem stated in B. 995 b 610 and discussed in 996b 26-997· J 5. but is not identical with it. The question there was whether the science which studies the d.PXal of substance should also study the d.PXa{ of demonstration; here it is whether it is one or more than one science that studies the d.PXa{ of demonstration. The objection here stated to the first alternative answers, mutahs mutandIs, to that in 996b 33-997. 2. That to the second alternative answers to that in 997· 14, 15. The second argument against the first alternative (99732-11) and the first against the second alternative (997& 11-13) are here omitted. !IS. TC ,..&).).01' Tlld,",! \l 611'OLClaOUI'; i. e. since the demonstrative d.PXa{ are the d.PXal of all the sciences. how can it be the business of one and only one science to study them? The argument is purely dialectical. !l6-l19 answers to the problem stated in B. 995 h 10-13 and discussed in 997· 15-25. !l6. ITL wdupol' 'll'acrGIV,.w1' 0311'1/;'1' \l o{;; SC. {J7roAafNiv Elval 8ii -r7Jv CTOq,f.aV br~p'1Jv (I. 21). !Z9-34 answers to the problem stated in 995 b 18-27 and discussed in 997· 25-34· 80. A comparison with the corresponding passage in B shows that d.1I'68ELf{s ICTTLV is an intrusion from the next line. The question is whether CTOq,f.a is concerned with substances only or also with attributes; the reference to demonstration comes in only by way of showing the difficulty of supposing that it is concerned with both. 3!1-33. Christ has rightly found ~ d.'II'08EL1(,TL/(~ CTOq,f.a impossible, and therefore brackets CTOq,{a., but Luthe's Vp,£v ••• VU for ~ P,& •.. ~ 8£ is manifestly a better alteration of the text. Qua demonstrative, the knowledge of properties might be thought to be CToq,{a (since knowledge is often identified with demonstration); but qua dealing with TO. 1I'pGyra, the knowledge of substances might seem to be so. Luthe's reading is established by the parallel in 996b 9-14 T{va ~ /(aAELV TWV I.1I'LCTTTJ-

V

p,wv CTOq,f.aV EXEL .\6yov ~/(aCTTT}v 'll'pouayopWELV' p,£v yap d.pXI/(WTaTT} ••• ~ TOU TIAovs /(a~ Tclya80v TOlaVTT} • • •• 8£ TWV 1I'ptMWV alT{wv ••• ~ rijs ollCT{as AI'

V

ETT}

TOlavTT}'

34-38. This passage differs from the rest of the chapter in not propounding a problem but simply stating a fact about CTo#a. In a sense the passage connects with the first problem stated above, in II. 20-23. viz. whether one science can study all the clpxal; and the corresponding passage in B (996& 21- b I) occurs in the discussion of the first problem. On the other hand it seems impossible to remove the passag-e from its present position, for O\·,.,.E yap I. 35 is taken up by JAws fj I. 38, and the passage thus connected with the following problem. We may suppose that the notes on which this passage is based were in some confusion and have not been properly sorted out.

34. T4S ~II TOLs +UCrlKOLS ELp"".lllo.S o.LT(o.S, the four causes, Phys. ii. 3. 85. oiIT.. Bz. conjectures o~8i, but it seems more likely that oiST, is resumed irregularly (as often) by oAw!O 8' in I. 38. 38. TO S~ . . • clKLII1}TOLS, 'but a something that moved them first does not exist in the case of unchangeable things'. 38-b I4 answers to the problem stated in 995 b 13-18 and discussed in 997& 34-998&19. The question, however, is not the same. There it is whether there are substances other than the sensible; here it is whether it is the business of uoq,{a. to discuss the sensible substances or some others. b 3. S~XOII, sc. from A. 9. 8. It is to be noted that' third man' has not here the technical sense in which it occurs in A. 990b 17, Z. 1039& 2, M. 1079& 13; the absence of the definite article in the present passage is significant. The phrase seems to have become a catchword which was used in various senses other than the original one. cr. A. 990b 17 n. 14-21. This discussion of the question what science studies the matter of mathematical objects has no parallel in B. The question is not, what science studies mathematical objects (the answer to which is obviously' mathematics '), but what science studies the VA,,! that underlies mathematical objects. Thus the conclusion (I. 20) that metaphysics is the study in question does not contradict the statement in I. 12 that metaphysics does not study mathematical objects. 15. T~S TWII ".o.lhJ".o.TLKWil lTh"s practically = space. It is the VA,,! vo"IT~ of which Aristotle has spoken in Z. 1036& 9, where cr. n. 19. o.lho ToiiTo TO ylllos, i. e. ,hT08E!~L!O and bTLIT'T1/II."!' 21-1060& I. Aristotle begins with the query raised in 995 b 27-29 and discussed in 9981\ 20-b 14, whether the constituent elements or the universals are the &.PXa.f. studied by metaphysics, but he soon (1. 27) passes to the query raised in 995 b 29-31 and discussed in 998b 14-9991\ 23, whether sUlIlma genera or inftlllae species are the apxa.{·

23. Tel. Ko.XOU".Ello. ll1l'o TLIIWII CTTOLXELo.. Diels, Elemenlu1Il, 17 ff., shows that the word is found (not before 370) ill a tentatively metaphorical sense in Isocrates, Xenophon, and Plato (Theael., Soph.,

Ttin.). To.UTo. St 1I'UIITES lllU1I'UpXOlITo. TOLs crU..elTOLS TL9la.crLII, sc. while uoq,{a. deals with immaterial entities (1. 14). 30, 38. For the notion of the CTVVa.Va.CpoVv cf. Top. iv. 2, vi. 4. 33. SLo.+opel S' 048.".(0. TOU ylilous ".ETlXEL. The genus is predicated not of the differentia but of the species, Top. 144& 32. To.UTtI S', Christ conjectures 'Y' for 8', but 8' is sufficiently confirmed by the passages cited in Bz. Index 167& 7-12, cr. B. 999& 27 n. 35. Tel S' icrxo.To. TWII ~K TOU ylllou5, i. e. the itifimae species (as 1. 38 shows), not the individuals. For IJ.TOp.a. used of inftmae species ct. I. 10581\ 18.

CO:'lDIENTARY

3 10

Recapilulall'oll

of Ihe problems slaled in

B. 4-6 (ch. 2).

1060& 3. (7) Is there anything apart from individual things? These are infinite in number, but on the other hand the knowledge we are looking for cannot be of genera or species, which are the things that might be supposed to exist apart from individuals. Yet we seem to be looking for something independent which is not an attribute of any sensible thing. 13. If there is such a substance, which sensible substances does it exist alongside of? Why of some more than others? Yet it would be absurd to suppose eternal substances as numerous as the sensible and perishable. 19. But if the principle we are looking for is ,.of apart from bodies, matter might seem to have a strong claim j yet it exists only potentially. Form has a stronger claim, but it is perishable, so that apparently there is Ito eternal independent substance. Yet the best minds have always sought such a principle; indeed, without it how could there be any order? ~7. (8) If there is such a principle C01n1Jl011 to eternal and perishable things, why are some eternal and others not? If the principles are different, then (a) if the principle of perishables is eternal, why are they not eternal? (b) if it is perishable, it presupposes another principle, and so ad 11ifim·lltm. 36. (9) If we posit the principles that seem most unchangeable, being and unity, (a) if they are nol individual substances, how can they exist apart, as first principles must j if they are, all things will be substances, since being is predicable of all i but plainly not all things are substances. b 6. (b) Those who make unity the first principle and a substance, and generate number from it and from matter and make number a substance, cannot be right j for how can you think of two or any number as one? I~. (c) Lines, planes, &Cc., cannot be first pnnciples, since they are mere dh.:isions and limits and therefore cannot exist apart. 17. (d) The unit or the point cannot be a substance, since there is no generation of it. 19. (10) All knowledge is of universals, but substance is not universal but individual j if there is knowledge of the first principles, how can substance be the first principle? ~3. (11) If there is nothing apart from the concrete whole, such wholes are all perishable j if there is ~olllething, it must be form; now

K.

2.

lo6oa 3 -

lo6oh 13

in which cases will this exist apart? In some cases, e. g. that of a house, it evidently cannot. laS. (I2) Are the first principles the same in form or in number? if in number, all things will be the same.

1060& 3-!l7 states the problem raised in H. 99S b 31-36 and discussed in 999& 24-b 24. There is first the question whether there is anything apart from individual things (3-13, 999& 24-32); then the question whith sensible substances have a corresponding separate substance (13-18, 999& 32- b S, "17-20); the question whether, if the apX11 we are in search of is not separate, matter or form is more truly the apx~ (19-24) is peculiar to K, and the arguments in 999 b 5I 6 are peculiar to B. 3. TG Ka.8' lKa.OTa., cf. H. 999& 26 n. 7. dP1JTa.L. The reference seems to be to IOS9 b 31-38. 15-16. The change of construction is awkward though natural. 'Why should one suppose this other substance apart from men or horses any more than a substance distinct from the other animals', &c. lala. ToiiTo 8E +8a.PTOV. Aristotle believes that an ll'l'Aol' (r8o~ (like the soul of an animal, or of a man in so far as he is irrational) is q,()aprOl', though inueed it is q,()aPT0l' lil'€V TOV q,()({p(u()aL (H. 1043b IS n., cf. 1044" 22, A. 1°70" 15). cr. the distinction in Dc Caelo i. 9 between pure form and (r8o~ vAU P-(P-LYp-€I'Ol'; and Z. 1039" 20-23. laS. For o! xapdCTTaToL = 'the most cultivated, refine:': people', cf. A. 1075& 26, De Resp. 480 b 29, &c. !l7-a6 states the problem raised in 996" 2-4 and discussed in 1000& 5-1001" 3. K omits the historical discussion contained in 1000" 9-b 20. 36-" 19 slates the two problems raised in 996" 4-9, 12-15, and discussed in 1001" 4-b 21S, b 26-1002 b I I i the two problems are connected together by 1060" 6-12. h 4. Bz.'s conjecture lCTTaL is not necessary but is probable enough, and is confirmed by AI. 639.37, 640. 1. 5. Ka.T' lVLWV 81 Ka.l TO II'. Really fZJt!l:ylhlilg that is is one (1061" 18); (I'{WI' is used by way of caution. Alexander explains (I'{WI' as meaning all things but numbers, but this is unlikely. 6-9. TOL' ••• +aaKouaw dVa.L, the Pytbagoreans (A. 9878 18, B. 1001& 10) and Plato (A. 987" 21,992& 9, H. 1001& 9). 8. TOV clpL8".ov y(VVWaL 'II'PWTOV, sc. and subsequently Ta Y(Wp-(Tpuca. Cf. I. 12, B. 1001" 17-25. 10. TWv ••• cl.pL8,...wv TWV auv8ETwv, not in the ordinary sense of composite as opposed to prime numbcrs. The other nurnbels made out of the One and matter are meant. 13. l'll'L+GVCLa., TG. 1TpWTa.., i. e. intelligible as opposed to sensible surfaces. For the sense of 7rpWTO. cr. De All. 404h 20. TdiiTci y'. J records the variant i', which was conjectured independently by Bz. 8' and yap seem to be both corruptions of this,

3 12

CO:\DIENT ARY

18. OUCrLUS fIo(V yap WeiC1'lS yivEC1LS E«TTL, C1TLYflo~S S' O~K E«TTLV. It cannot be meant that all substances are subject to generation; for what then of God? The meaning is given better in B. 1002& 28-b 1 I. If a substance at one time is not and later is, it comes into being by a process of generation, while points, lines, and planes come into being instantaneously by the division of lines, planes, and solids. IQ-!Z3 states the problem raised in 996& 9, 10 and discussed in loo3a 5-17, especially in 11. 13-17. !Z3-!Z8 recurs to the problem discussed in & 3-27. !Z7-!Z8. lw' Mil/V yap ••• otKLcr.1I. The meaning is that there are evidently no separate universals of negations (A. 990b 13), of relations (990b 16), or of manufactured objects (991 b 6, A. 1070& 14). !Z8-30 states the problem raised in 996& 1, 2 and discussed in 999 h 24- 100011 4.

The sub/eel ofpllllosophl"al study (ch. 3).

1060 10 31. Philosophy is concerned with being as such universally, but being has more than one meaning. If it is merely ambiguous it cannot be dealt with by one science; if there is some common meaning, it can. 36. It is like the terms 'medical' and 'healthy', all of whose meanings have some reference to the medical art and to health respectively. So too everything that is is an affection, state, disposition, motion, &c., of being as such. 10611L 10. Since all that is is referable to some one thing, all contrarieties are referable to the primary differences of being-plurality and unity, likeness and unlikeness, &c. It matters not whether the reduction.be to being or to unity, for the two are at any rate convertible. IS. All contraries are objects of the same science, and each of them implies privation. (How can terms admitting of a mean, like just and unjust, involve privation? The privation must be said to be not of the whole definition but of the infima species. If the just man is ' one who by virtue of a state of will is obedient to the laws " the unjust man need not be the very reverse of this but may be "one who is in some respect deficient in obedience to the law~'; in this respect he suffers from a privation of justice.) !ZS. The mathematician abstracts from all sensible qualities and studies simply what is quantitative and continuous in one, two, or three dimensions, and its essential attributes. b 3. Similarly the study of the properties and contrarieties of being

K. 2. lo6ob 18 -

3.

I061 b

5

31 3

as such is the task of no science but philosophy; not of physics, which studies things not qua being but qua sharing in motion, nor of dialectic or sophistic, which study the attributes of things that are, but not qua being. II. Since all that is is so called by virtue of some one COIDDlon character, and things so related can fall under one science, we have solved our problem, how there can be one science of many things which differ in genus. This chapter answers to r. I, 2, the substance of which it states in a much briefer form. In the first part of the chapter, 1060b 31-1061& 28, the question raised in 1059& 20-23 is incidentally answered, and in the second part, 1061" 28-b II, that raised in 1059& 29-34, though at the end (1061 b 15) it is only claimed that the first of the two problems has been solved. 1061" 15. lG'Tfllau yAp A3TClL TEe.fllp","IIAL, cf. r. 1004& 2 n. Alexander here again refers to the De Bono. so-SIS. The question is how contraries that admit of a middle ACyITa.L I..6yov suggests the splitting up of the definition into genus and differentiae. Sl4. It laTLI' 6 "KALal Kae- I~LI' TLI'a. 'II'.LeApXLK~1 TOLl vOfIoOLI. This is the just man in the wider sense of justice, explained in E. N. I 129b 11-113°" 13· s5. 6 4&LKOI is here used of the person who is in any degree unjust, i. e. of;, !ivA p.luov, though in I. 22 TOU elllll
unjust man. 33. ,-wv ".~v i.' lv, i. e.

TWV p.f.V

cr.

TO ll/l- ~v fT1IV(X(~'

b 5. Ta.l lIlAVTL~a.LI A.)TOii, B. 995 b 20-27 n • • L).oao+lAI. I/I"'-oaol/lla in the sense of 'II'ptfyrq l/lLAorrol/lla. is rare, but l/lLAwO.pOfi occurs ill the corresponding sense in I003 b 19, 10041\ 34, ~I7S·2

X

COl\e\IENT ARY b 16, 1005& 21, b 6, II, and the ~&Ao~la. is implied in the

same narrowing down of the scope of distinction drawn between it and mathematics in A. 992& 33, A. 1073b 4.

------_._P Izilosop/gl dish"nguislztd from lIlatlzt1llalics and plzysics (ch. 4). Io61 b 17. Since even the mathematician uses the axioms only in

a special form, it is the task of first philosophy to study them.

That if equals be taken from equals equals remain is common to all quantities, but mathematics studies the several parts of its subject-matter (lines, angles, numbers, &c.), not qlla being but qua continuous; while philosophy studies particular things only in so far as they have being. A7. Physics is like mathematics; it studies the properties and principles of things qua moving, not fjlla being, while the first science studies the attributes of being as being. Hence physics and mathematics are oniy parts of wisdom. This chapter corresponds to r. 10051\ 19-b 2, and answers the question raised in 10591\ 23-26. lo61b 18. TOis Ko,jiois, i. e. the d.tufJp.o.Ta, cf. B. 997& 10. TGUT"'I', i. e. ,.rov p.o.8-qp.o.T&KWv. AO. KOLW.I' 1"1' lCTrLV l'll'l 'll'An",1' ,wI' 'll'o.,wl', i. e. this proposition is neither a common principle of all sciences nor peculiar to one; it is common to all the sciences of quantity. It thus belongs to a type not recognized in Aristotle's classification of d.pxai, An. Post. 76& 38. This axiom is similarly treated as a KOL"&V, though really common only to the sciences of quantity, in A,l. Post. 77& 30, 31. AI. 4'11'OlAjIoiiaA, • cutting a part off for separate consideration '. Cf. Potl. 1459& 35 and the use of d.-rrOT£p.v£a(JaL, r. 1003& 24. AS. ~ &~ +,locro+iA, cf. I. 5 n. g6-f1.7. 'll'Epl TO al' • . . e."'PEL. The construction seems to be, • but speculates about that which is, in so far as each particular thing is' (W &v TWV TOLOVrIllV lKaaTOV is opposed to fI avv£X" a~v lKaOTov, l. 24)-which is a brachylogy for • but speculates about that which is, and about particular things only in so far as each of them is '. 3A. TAU,",I' apparently refers to .q ~VULK~; the clause answers to r. 1005" I CaTL 8~ O'o~{a TL~ Kal .q ~VULK~. n,v 8"TP~V ... IT£POV TI mOst therefore be treated as parenthetical. The point of connexion between 8LO, &c., and what precedes is not very clear. Alexander supplies a reason for the conclusion that physics and mathematics are branches of wisdom, viz. 1'll'£L8~ d.7To8£LKvVOVUL Kal c\ p.a8-qp.u.TLK~ Ka2 A ~VO'LKO~, Ka2 oMi'll'OT( ';ai80JlT'aL, but this cannot properly be read into the text. It seems more likely that p.£fY'I is to be stressed. Because mathematics and physics do not study their objects 'lila being but qua continuous or '1'M moving, they are merely branches of wisrlom; wisdom proper is

K.

4.

I06l b

18-33

the more comprehens;ve science which studies being as such. This answers to the corresponding statement in r. [OOSb I laT' 8~ CTOf/J.a. T'~ /c111 .q ~1IfTuc.q, ill' 00 fI'~. aa. For this wide sense of CTO~f.a. in which it includes mathematics and physics as well as philosophy cf. A. 981" 27, r. [OOSb I, and E. N. vi. 'I, where it includes the study of U cliv ;, ,",CTp.o~ CT1JJICC1T7l/C(V, the constituents of the physical universe (1141 b I).

Defence ofl"e law of cOlllradidion (ch. S). 106lb a4. There is a principle about which it is impossible to be deceived-that the same thing cannot at the same time be and not be. Such truths cannot be proved absolutely because there is no more certain premise from which they can be inferred. 106m· 5. But they can be proved to a particular person, viz. to anyone who makes contradictory assertions; the method is to assume something that is identical with the truth in question but does not seem so to our opponent. II. People who are to discuss together must to some extent understand each other; therefore each of their words must mean something, and if it is ambiguous the intended meaning must be indicated. Now (I) he who says' A is and is not B' is saying that the word B does not mean what it does mean, and since this is impossible the law of contradiction is proved. Ig. (2) If the word means something and this meaning is truly asserted of a SUbject, the subject must necessarily have this character, and therefore can never not have it; so that the opposite statements cannot be trae of the same subject. ga. (3) If the affirmation is 110 more true than the negation, 'A is a man' is no truer than 'A is not a man', and therefore a flrliori no truer than • A is not a horse', and therefore (if contradictions are both true) no truer than • A is a horse'; so that the same object is a man, a horse, &c. al. If one had argued thus with Heraclitus he might have abandoned his view; he adopted it without realizing what he was saying. I f his dictum were true, even it itself would not be true. For if' A is B ' is no truer than' A is not B " 'A is both B and not B' is no truer than , A is neither B 110r not B '. b 7. Further, if l:othing can be truly affirmed it is false to say that no affirmation is true; while if something can be truly affirmed the dictum of these destroyers of all discussion is upset.

COMMENTARY

3 16

The chapter covers the ground of r. 3. I005b 8-end and of r. 4, with the exception of (I) the argument that if the law of contradiction be denied, substance is denied and everything reduced to accident (1007& 20_b 18). (2) the group of arguments in 1008& 7-b 12, (3) the argument that the opponents of the law of contradiction themselves act upon it (1008 b 12-1009& 5). For this cr. K. 1063& 28-35· Io61 b 34-I06~a ~ answers to Io05b 8-34. 36-I06~B~. Two kinds of contradictory proposition are here referred to, (I) , A is' and ' A is not', (2) • A is B' and • A is not B ' (TcL\Aa TO. TOVTOV a{,,-OL~ aJITLKE{pO'a TOV Tpmrov). Of these the second is the more general, since the first may be exhibited as a species of it, , A is existent' and •A is not existent '. lo6~a ~-5 answers to 1006& 5-18. 5-19 answers to 1006a 18-1007" 20. 6. 8'OT' +,u80<>. As Bz. points out, an argunlmlu11l ad hominem does not point out the reason of the opponent's mistake but only its existence. Thus BLOTt must be used in the sense of ' that'. Cf.lttdex 200b 39-45. I~. a.llTldV = dAA"Awv. Cf. L. and S. s. V. III. 16-19. In view of 106 Ib 36-1062& 2 (where see n.) the meaning seems to be ' He, then, who says that A is B and that it is not B denies what he asserts, so that what the word B means he says it does not mean; but this is impossible, so that if "being B " means something' (or 'if any word means" being something" '), ' the contradictory of it cannot be truly asserted of the same SUbject '. 17. Toilvo/,a., sc. TO ElvaL, says Bz., but the reference is to any predicate, d. TWV dVOp.O.TWV (KaUTOV, I. 13. In 1006& 30, to which Bz. refers, it is not clear whether TO Elvat ~ p~ ElvaL is as he supposes explicative of TO 6VOp.a, or TO ElvaL ~ p~ ElvaL TaB{ is the object of uT/pa{vEL, so that TO Jvap.a would be quite general. 18. ELlI'EP CMJ/,a.LVU T' TO Elva., To8E. TL may be either subject or object of UT/p.a{JIEL. 19-~3 answers to 1006 b 28-34. The meaning is expressed more clearly in r. ava-YKTI TO{VVV, Ei TL ~UTW aAT/8E~ Ei,ULV 6TL iJ.v8pw11'o~,

p,

• ~, (,. , , LJ )' ..}''t'av EWa.L OLlI'OVV TOVTO yap T/V 0~ EU71p.aWE TO' . a.vupwll'ar;· It TOVTO, aVK (v8(X'Ta.L ,fVa.L (TOTE) TO aVTO 'ciX>v B{lI'ovv.

'"

0

, , avaYKT/

answers to 1007 b 18-1008& 2. 31-35 answers to 1005 b 23-26. 36-b 7 answers to 1008 B4-7. The point is, however, different. Aristotle is there showing that if the law of contradiction is denied, the law of excluded middle must be denied too (avK avaYKT/ ~ ,pavat ~ all'o.pava.L). If it is true that A is a man and not a man, it will (or may) also be true that he is neither a man nor not a man. Here the point which is proved is that if the law of contradiction is denied, the denial of it must be denied too. If it is true that A is a man and not a man, then this proposition itself is no more true thall its opposite. ~3-30

b 6. OMEv p.o.Uov ~ d:'r~acTL" ~ T() o~ov ~..

(V KaTaq,acm TdUp.(vov

d.~':'18aJC1'(Ta,

gives just the opposite of the right sense. The simplest emendation is to transpose 11 to before ~, where it would easily have dropped out. A less probable alternative is to read ~ov for p.a>..~ov. 7-9 answers to rou b 13-18.

Inadequacy

of the grou1/ds .for denyrlrg the law of rOlrtradictioll (ch. 6).

I06~b I~. Protagoras' saying, 'man is measure of all things', is similar to the views we have been discussing. He means that what seems to each man is so; then since things seem different to different people, the same thing will be and not be. ~o. The problem will be solved if we consider the origin of this belief. (I) With some, it arose from the doctrine of the physicists; (2) with others, from observing that people have different impressions about the same thing. ~4. (I) That nothing can come into being from not-being but everything from being is a view common to most of the physicist!:. Therefore, since a thing does not become white if it was perfectly white, the white must come from what is not white; so that according to them it must come from not-being, unless the same thing was white and not white. The difficulty is easily removed; we have stated in the P4;Jsics in what sense things come to be from being and in what sense from not.being. 33. (2) (a) It is foolish to attend equally to opposite opinions. The same thing never seems sweet and sour to two people unless the sense·organ of the one has been injured; in that case only the other man is a measure. So too with good and bad, &c. We might just as well claim that the object which seems to be two when you press your eye must be two. 1063& 10. (b) We ought to judge of the nature of things not from the changes in the things around us but from the changelessness of the heavenly bodies. 17. (c) Again, if there is motion, there is a moving thing, which moves from something and into something; and wl'en it is in thp. one it is not in the other. ~~. (d) Even if things in this world were always changing in quantity-and the observation of such changes is one of the chief motives of the theory-they need not be always changing in quality, and essence depends on quality, which is determinate, not on quantity, which is indeterminate.

:,,8

CO:\I:i\IENT ARY

!lB. (t) Again, the fact that people act on the doctor's orders shows that they think things have a determinate nature which is not always changing. 35. (f) If we are always changing, the changes in our perceptions do not show the objects to be changing; if we are not changing, then there is somtthing that is at rest. b 7. It is not easy to meet those who feel these difficulties on dialectical grounds, for if they wi11 not posit something and no longer demand a reason for it, they make discussion impossible; those, on the other hand, who are puzzled by the traditional difficulties may be answered as we have shown. 15. Contradictory statements, then, cannot both be true; nor can contraries, because contrariety involves privation, as may be seen by analysing the definitions of ('ontraries. 19. Nor can an intermediate be predicated of the same subject of which one of the extremes is asserted. If A is white we cannot truly say it is neither black nor white, for we shall be saying that it is both white and not white. 84. Therefore neither the view of Heraclitus is right, nor that of Anaxagoras that there is a portion of everything in everything; if everything is present actuallY in everything, contraries are true of the same thing. 30. Similarly a\1 statements cannot be false, nor a\1 true-for this reason in addition to others, that if all are false this statement itself is false, and if all are true it wi11 be true that a1\ are false. This chapter covers almost the whole ground covered in r. 5-8, the main sections omitted being (I) the references to earlier views in 1009& 38-1010& 22, (2) the arguments in 1010b 26-101la 2, 10lla 17-b 12.

1068b 18-84 answers to 1009& 6-16, 22-30. 81-84. Of the two reasons for the Protagorean theory, the first is discussed in 24-33, the second in 33-1063 h 7. 84-33 answers to 1009a 30-36, though not closely. 86-30. • Since, then, white does not come to be if the perfeclly

white and in no wise not white existed before, that which becomell white must come from that which is not while; so that it will come from what is not, according to them, unless the same thing was white and not white.' In the first clause the general sense shows that ou goes with ylyvCTfl.&, not with A(VICOV, and the use of ov, not p..q, confirms this interpretation. vW 8, Y'YO'"fJp.lvov p.~ A(VICOV is not only unmeaning in ilself, but spoils the structure of the sentence, since the apodosis should begin with ylYVOtT' rIv. iflCTT( but rarely introduces an apodosis except after a parenthesis. Bz. is therefore right in suggesting that viiv •••

should be excised. These words look like a gloss by a coprist who took o~ A(VKOV together in I. 26. TIz. is also right in suggesting the excision of pI, after 'YL')'I'oP&ov. An alternative would be to insert pI, before A(VKOV, where it is read by E (in marg.) r; but there seems to be no reason why the case of the not-white coming from the notnot-white should be substituted for the simpler case of the white coming from the not-white. The argument then is : Nothing can come to be from what is not. The white comes to be from the not-white. Therefore the not-white must also have been white. 31. ill TOLl +uCI'LKOLI, Ph)'s, i. 1-9, De Gen. eI Corr. 311h I4-3 19 h 5. Aristotle's answer is that an A which is TI comes out of an A which i!l but is not B, or which is B potentially but not actually. 33-1063" 10 answers to IOIOb 1-26, 101 I" 31-34. 1063" 6-10, The illusion referred to is produced by pressing the finger against the under part of the eyeball, when a single object is seen as two. The same illusion is referred to in De SOIlI1l. 461U 30, Probl. 958" 24. • To expect this is just like expecting the thing;: which appear to people who put their finger under their eye and make the things appear two instead of one, to be both two because they appear to be two, and again one.' 9. The unintelligible vulgate reading 8vo 8' (TVaL has been produced by haplography from the correct avo 8(;:v £TvaL preserved in Jr. TU. qxuvop&a ••• 8vo 8(;:v (lVaL is the object of ~~LOVV understood. 10. KLlloucn refers not to movement of the ere but to interference with it. 10-17 answers to 1010" 25-32. 15. Tel KaTel T(III KcSUI'0ll, the heavenly bodies. 17-IZI answers to 1010" 35-h I, though only in a very general war. 17-19. There seems to be no parallel in Aristotle for apa i1t a/,odosi except after a long protasis (all the instances quoted by TIz., D,' jill. 19318 , De Gm. fI Corr. 333 h 29, 331" 24, De Al1. 425" 9, P. A. 6421\ 13, E. N. 1134" 6 are of this kind); so that Christ is right in putting a comma after llTTL I. I R and treating Kal. KLVOl:P£VOV TL as apodosis. 19, ~O. TIz. thinks that Aristotle could not have said • the movin~ thing must be in that <,u t of which it is to move, and not be in it " without indicating that it is at different times that it wiII be in it and not in it. He therefore supposes aUT~ to mean that lit!o which the moving thing moves. It seems impossible, howevl·r, to suppose that aUTe;; refers to anything different from what f.K({V,!! refers to; and R7.:s difllculty is an unreal one. The passage means, as a whole, that motion implies that contradictory predicates can be asserted of the changing thing at different times, but not at the same time. /T1'vaA7J()wfu()aL (I. 21), the reading of Ah Al., brings out the point better than the common reading rlA7J()Wf(T()UL. A(VKOV

~I. TO ••• KaTel ,",II clIlTL+aULII

=

TU.t; rlVTLKfLpEval

tPuuw;.

COMMENTARY

3 20

ss-aS answers to 10lot' 22-25. s3 Ka.lftp oilK a'IJe~t 3.,. Aristotle tries to show in Phys. 253 b 1323 that growth or diminution cannot go on continuously but proceeds by jumps. s7. 'Ii 8' oilala. Ka.Tc\ TO 1rO~cS." in the sense of 71'0101' explained in A.I020"33· s8. TO 8. 'lroaO., '"it tlopCIJ'TOU, the size of things is not definite and unchangeable as some of their qualities are. s8-35 answers to 1008 b 12-27. 3s. Christ's reading TOV 7I'pouG.X()lVTof, which in a note he describes as spurious, is a misprint. 35-h 7 answers to 100911 38-b 33, but with the references to other philosophers omitted. h7-16 answers to 100911 16-22, 1011113-16. 8. lK Uyou, 'on dialectical grounds '. Cf. 100911 20 Jerol Myov XaplV AJyOVCTI, 1011 11 4 nil' TOV~ Myov~ ToVro~ p.Ovov AeyOVTIIl", ib. 15 011" T-ii AO'/'tl

nw Pia." /Lo"o" ~7JTOVVT~.

14- lK Tiii., dP'IJl'i.""." sc. in 1062" 20-1063 b 7. 17-19 answers to 10llb 17-22. 19-s4 answers, though not closely, to r. 7. 10Ilb 23-101211 24. That chapter proves that there cannot be a middle between contradictories; here the poiJ;lt is that a middle between contraries cannot be asserted of one and the same thing (I. 20), sc. of which one of the contraries is asserted. The proof is: If the same thing is white and neither white nor black, it is white and not white; which breaks the law of contradiction. This is a point not made in r, though there is a general correspondence with r. 7. 1014-35 answers to 101211 24-b 18. s4-s5. Ka.r 'HpdK~e~TO" ••• ~~oVTa.t is to be understood by reference to 106211 31-b 2 (cf. 101211 25, 35). s5. Ka.T' 'A~a.ycSpa..,. The view referred to is indicated in II. 26-30 (cf. 101211 27).

Dish'ncl;on oflhtologyfi'om malhemalics and physics (ch. 7).

I06ab 36. Every science' marks out some genus for itself and studies this, but not guo being; they leave that for another science. These sciences get the essence of their SUbject by perception or by hypothesis, and try to prove the attributes; it is evident from a review of them that there is no proof of the essence. 106411 10. The science of nature is not a produch've science, for in such a science the principle of motion is in the producer and not in the product, being an art or other faclJlty; nor a praclical science, since here the motion ill in the doer, not in what is done, while physics is

concerned with things that have a principle of motion in themselves. It is Iluorelical, therefore. Ig. Since each science must know the essence of its subjects, we must note how the physicist should define. Should he define as one defines' snub' or as one defines 'hollow I, i. e. with or without refer. ence to matter? Flesh, eye, &c., must be defined with reference to their matter. !28. Is the science of being as being and as capable of separate existence the same as physics? Physics studies things having a principle of change in themselves; mathematics studies things unchanging but without separate existence. If, then, as we shall try to show, there is a separate unchanging substance, the science of il is different from physics and mathematics. If there is such a substance, here is the divine, and the first and most authoritative principle. b I. There are, then, three kinds of theoretical science, physics, mathematics, theology. Theoretical science is the best kind of science, and of its species the last·named is best, being about the best object. 6. Is the science of being as such universal? There is a universal mathematics as well as the various branches. If physical substanccs are the primary entities, physics is the first science; but if there i~ a substance which is separate and unchangeable, the knowledge of it is prior to physics, and universal because prior. This chapter answers to E. 1 much more closely than the preceding chapters answer to Band r. It answers the question raised in 1059" 26-2 9. 1064& ,. ,,1 fJo(II SL' "to'8~O'E"'~ ,,1 S' ':''II'on8IfJoEII''L, cf. E. 1025 h l i n . 36. O'll'EP 'll'ELp"O'cSfJoE8" SELKIIUIIGL, cf. A. 6, 7. But see vol. I, xxvii. f. h g. ~ S( KG8cS).ou KOL~ 'll'Ept 'll'an",", cf. E. 1026" 25 n. 13. KG8cS)'ou T~ 'll'poTlp"", cf. E. 1026" 23-32 n.

Accidenlal being and beiflg as lrulll; chmlCl (ch. 8). 1064b 15. (I) Let us first examine being in one of its senses-the accidental. The accidental is not studied by any of the traditional sciences; the builder does not ask what wiII happen to the people who use his house, but studies his own proper end. 23. Nor does any science reason that 'the musical man who becomes grammatical will be both at the same time, not having been so before; but what is, without always having been, must have come to be ; so that he must have become at the same time musical and gram-

COMMENTARY matical '. It is only sophistic that studies this; it is the only science of the accidental, and Plato was not far wrong in saying that the sophist spends his time on not-being. 30. That a science of the accidental is not even possible will be clear if we ask what the accidental if!. Everything that is is either always and of necessity (logical necessity, not compulsion), or for the most part, or' as it happens' (e.g. cold in the dog-days). The accidental is what happens, but not always nor for the most part, and for that reason there can be no knowledge of it. 1065& 6. There are no causes of the accidental such as there are of the essential; for then everything would be of necessity. If A is when B is, and B is when C is, and C is of necessity, all the effects down to the last will be necessary, and contingency will have been abolished. 14. Similarly, if the cause be not a being but an event, all events will be necessary; to-morrow's eclipse will follow necessarily from something now existent. SI. (2) Being as truth depends on a com bination in thought, and therefore we pass it by and fix our attention on independently existing being; being as accident is indeterminate and has indeterminate causes. s6. (3) Teleology is found in things happening by nature or as a result of thought. It is chance when some such event happens by accident; chance is an accidental cause of teleological events of the purposive kind. Hence chance and thought are concerned with the same objects; for purpose implies thought. The causes of chance events are indeterminate, and therefore chance is obscure to human reasoning and is a cause only per accidens. It is good luck or bad luck when it turns out well or ill; prosperity and adversity are good and bad luck on a large scale. Since nothing acci:lental is prior to the essential, if chance is a cause of the universe reason and nature are prior causes. 1064b IS-106Sa s6 answers roughly to E. 2-4, omitting (I) the account of the various senses of' being' in E. I026a 34-b 2, (2\ the statement that acddents are neither generated nor destroyed, 1026b 22-24. 3! the examples given in I026 b 35-1027a 5. 102'& 23-26. 4 the reference of the cause of accidents to matter, I027 a 13-15. 5 the discussion of being as truth in E. 4 (just touched on in Ic6Sa 21- 24).

!

83. It seems be~ to excise o"S~ I'0UCI'LltaV Itul ypcr.I'I'cr.TLIt&V, which is omitted in Alexander and was probably inserted by a reader who wished to indicate briefly the sophistical question mentioned in the corresponding passage of E-rOT€po" &€pO" ~ TUlWo" p.G1XTLICO" ICal ypa.p.p.aTLICOV (E. 1026 b 16, where see n.). O~8E p.o1XTLICO" ICU~ ypo.P.p.aT&ICO" will not stand by itself, and if these words be retained we must introduce after oMl either d with Bz., TO with Christ, or (best) €l TO with Bullinger. 83-86. o"S~ Tal' KIlTer. .•• YPUl'I'UTLltcSs. The sophistical argument here given is somewhat different from that in E. 1026b IS-20. The argu· ment is: A man who being musical becomes grammatical will be both at once, not having been so before. But that which is, but has not always been, must have come to be. Therefore such a man at the same time came to be musical and grammatical,-which ex Izypotlzesi he did not. The fallacy evidently lies in the supposition that because he must have come to be simultaneously' musical and grammatical', he must have simultaneously come to be musical and come to be grammatical; /I.p.a is • conjoined' with a word to which it does not really belong. The compiler has thus replaced the fallacy in E. 1026b IS20 by an instance of the familiar fallacy of crV,,6€u&s (Soplz. EI. 166:1 23-32). 86. Bz. brackets Si, and as an alternative suggests But 81 is justified by the passages quoted in Bz. Index 167- 24-34. 89-30. nu_v .. . SLuTp£II."" Soplz. 237 A, 254 A. 34. xp wl'.8cr. lv Toi, Itcr.TA Tc\s 4'1rOSE£~'L', i.e. ;" Alyop.€" Tcjj p.~ 1,,8lX€u6uL rulllS, E. 1026b 29. 1065- 81. ft S' &, 4).'I8~, 51' ltulltuTc\ Cl'uI'II'II'IIt&'. The insertion of p., after ICUt in most of the manuscripts and Alexander is doubtless due to the previous corruption of &).:,,61s into d.\'16Ws. p., ICUTa uvp./3€/3'1ICOS would be a proper synonym for the la~ter. Strict grammar would require TO ICUTa UVp./3E/3'1ICOs, but for the omission of the article cf. Pol. I2Sob 15,Poet. 1459 b 2, 37, &cc. There is no reason to suspect, wilh Bz., that the true reading is TO 8' c:,s d.\'16ES nIl ICul p.', ICu1 TO ICU,u uvp./3€/3'1ICOs• 84. IE",. Cf. E. 1028-:1 n. 86-b 4. The excerptor now supplements the account of the accidental in the preceding part of the chapter by an account of chance derived from PIzys. ii. 5, 6. 88. Toll_I', i. e. TW" l,,€ICa. TOV. It is hard til see how something that is for a purpose can happen by accident or incidentally. The context ill the Physics shows that Aristotle means by something lv€ICa. TOU something that might naturally result from the unconsciously teleological action of nature or from the consciously teleological action of ' 8' EV€ICU ' L ' TOO OCl' • U T€ U7rU , '8&U"O&US ' aI' 'II'pcr.x8n'l ' ICU&, .uuu U7rU " man (IUT& f/tvU€CIII, 196b 2 I); i. e. something that fulfils an aClual or possible purpose, whether it happens for a purpose or not. Cf. TOV ICopitruu6u&

8,.

n

COMMENTARY EVEKD. in 196" 35, where actual purpose is expressly excluded, and the use of 'TiAO<; in 19731 of what would naturally be an end of action. Where a result is produced accidentally that would normally be produced by purposive action, it is said to be a1l"0 roXl1S; where a result is produced accidentally that would normally be produced by nature, it is said to be a1l"0 TD.frrop.aTov. To say that A produces B KD.'To. UVP./1E/111K6to means (I) that A has a concomitant C which produces B, or (2) that A produces C which has a concomitant B. But KD.To. UVP./1E{311KO<; must be understood also in the light of the explanation of it given above in I. I; to say that A produces B accidentally is to imply that it produces it rarely. Torstrik (Hermes ix. 425-470) has tried to show that Aristotle represents chance results not as those which might naturally be produced by purposive action, but as those which are actually though incidentally so produced. But the evidence to the contrary in the Physics is too strong. Cf. 196b 22 &1' 7rpD.xfMl1 (cf. 197& 35, 198& 6), 19 6b 33197& 5, 197 b 21 (where TWV 1I"poatpETWV must mean' natural objects of choice', not 'things acquired as the result of choice '), b 30-32. Torstrik has to have recourse to emendation to prove his point; he has to read 7rpaxBii in 196b 22 and to excise TOV KOP.{UD.U(JD.t tvEKD. ib. 35. 31-31Z. 8,0 .•. 8,dI'0",. This serves to distinguish roX11 from 'TD.frroP.D.TOV. roXl1 is to purposive thought as TD.frrOP.D.TOV is to the unconscious purposiveness of nature. b IZ-4. l'll'El 8' •.• +da,<;. TO KD.'To. UVP./1E/111K6to is always an indirect relation of A to n which implies direct relations of A to C and of C to B. roX11 is just the production, by reason, of effects concomitant with its intended effects, and To.frrOp.aTOV is the production, by nature, of effects concomitant with those which it constantly tends to produce. Thus roXl1 presupposes reason, and TD.frrOP.D.TOV presupposes nature. Aristotle's attack here appears to be directed mainly against the Atomists. Cf. Phys. 196& 24. Simpl. 331. 16. Torstrik has grammatical correctness on his side in inserting TWV after o~elv. But probably KD.To. UVP./1E/111Kos is used practically as an adjective. 3. Et 4po. TdX1J \j TO a~cS"aTov atnov Toii o~po.voii. This is a clear indication that the latter part of K is an excerpt from the Physics, not notes preliminary to it. The excerptor is plainly referring to a previous passage of the Physics which does not occur in K, viz. Elu~ 8i TtVE<; ot

Kat TOVpaVOV Tov8E Ka~ TWV KOUP.WV 7rav'TWV alTtWVTat 'TO afrrop.D.TOV KTA.

(196& 24-35).

The reference is apparently to Democritus.

Po/mcy, aclualt'zaJion, movement (ch. 9).

lo6Sb 5. A thing may be, either actually or potentially or both actually and potentially, a substance, a quantity, or in one of the other categories.

7. There is no motion apart from things; for it is with respect to the categories that change occurs, and there is nothing common over these. In substance there are form and privation, in quality white and black, in quantity complete and incomplete, in place up and down, so that there are as many kinds of change as of being. 14. The distinction of potentiality and actualization exists in each class of things, and motion is the actualization of the potential as such; e.g. when the buildable as such actually exists, it is being built, and this is the process of building. Motion takes place when the actualization itself exists, and neither before nor after. !al. Thus the actualization of that which is potentially, when it exists actually, not as itself but as movable, is motion. The bronze is potentially a statue, but the actualization of the bronze as bronze is not motion, for it is not the same thing to be bronze and to be a certain potentiality. !as. This can be seen from tht' case of contraries; to be capable of health and of disease is not the same thing (if it were, health and disease would be the same thing), but the substratum of health and of disease is the same. 3!a. Motion, then, is the actualization of the potential qua potential. That motion is what we have defined it as being, and exists only when the actualization itself exists, is clear. For the actualization of the buildable as such must be either the act of building or the house; but when the house exists it is no longer buildable; on the other hand it is the buildable that is the object of the act of build/1Zg. Therefore the actualization of the buildable is the act of building; and this is a movement. 1066& ,. That we are right is shown by what others say about motion, and by the difficulty of defining it otherwise. It cannot be placed in any other genus; others say it is otherness, inequality, or not-being, but none of these need be moved, nor are they the terminus or startin3-point of motion any more than their opposites. 13. These thinkers define motion thus because it is thought to be indeterminate and the principles in one of the two columns are indeterminate because they are privative; none of them is in anyone of the categories. 17. l\lotion is thought to be indeterminate because it cannot be classed either with potentiality or with actualization, since neither that which can be, nor that which is, of a certain size need be moved. !\fotion is thought to be actualization, but incomplete, because that whose actualization it is is incomplete. It is difficult to grasp the nature of motion because it cannot be classed either as privation, as

COMMENTARY potentiality, or as unqualified actualization. It must, then, be actualization, and the actualization we have defined; it is difficult to grasp but capable of existing. l26. Clearly motion is in the movable; for it is the actualization of this by that which has the capacity \0 set in motion. And the actualization of the latter is none other; it must be the complete reality of both. The mover is movent by virtue of its capacity, but moves by virtue of its activity, and it is on the movable that it has the power of acting, so that the actualization of both is one, as the interval from one to two and that from two to one, or the uphill and the downhill slope, are one, their being not being one.

The excerptor now passes to the discussion of movement, and gives extracts on it from Phys. iii. 1-3. Aristotle begins his account of movement by referring (1065 b 5-7) to the distinction of potentiality and actuality, which is implied in the definition of movement he is about to give. After pointing out (ll. 7-14) that movement is always in respect of one or other of four categories-substance, quality, quantity, or place-and is movement between the opposite poles, so to say, which exist in the several categories, he formulates (I. 16) his definition-movement is the actuality or actualization of that which exists potentially, in so far as it exists potentially. I. e. movement is not the actualization of the whole character of that which is moved. Building is not the actualization of the buildable qua bricks and stones; the buildable is actually brickli and stones before the building process begins. Building is the actualization of the buildable qua buildable, and in general of the movable qua movable. I. e. part of the character of the bricks and stones is their capacity of being arranged into the form of a house, and the process or movement of building is the actualization of this capacity (II. 23-33). That it is so is confirmed (ll. 20-21, 341066 a 7) by the fact that the building process exists just when the actualization exists. Prima facie either the building process or the house might be regarded as the actualization of the buildable. But when the house has come into being, the buildable has ceased to be; on the other hand the buildable exists throughout the building process, since this implies at each moment that there is still something buildable. and not yet built, some material that has not yet received the last touch from the builder's hand. The process, therefore, rather than the product, is the actualization of the buildable, and what is true in this case is true ill all cases. Movement is always the actualization of a latent capacity (I 066 a 2-7). 1065b 5. TO p.~v lV£PY£LIf p..svov, i. e. pure intelligences; TO S~ Suvdp.u, i. e. such things as the infinite and the void, cf. @. 1048 b 9; TO Si Suvdp.u Kill iVEPy£LIf. i. e. physical objects comprising both matter and form ;

qua having form they are already actually something, qua having matter they are potentially something which they are not yet. 6. TO ".tv 31'. For Jv in the sense of substance cf. Phys. 191& IZ, De Gm. eI Corr. 317b 38. 7. ".ETo."d>'>'CL yap 4El Ko.Ta TaS TOU 3VTOS Ko.'MJYOP'o.s, i. e. change is KaT' ol!u{av, the generation or destruction of a substance; KaT« 1I'0UOV, growth or diminution; KaTa. 11'0101', alteration; or KaTa. T01l'0V, locomotion. 14. TOO'uuT" EIS" 30'u TOU 3I1TQS. This is not strictly true, since there is (according to Aristotle) p.f.Taf3oA~ in respect ot only four categories (substance, quality, quantity, place) and K{V7/UI'> in respect of only three (quality, quantity, place); cf. 1068& 9. 14-1066& 7. An aggregate of bricks, stones, &c., may be regarded (I) as so many bricks, stones, &c., (2) as potentially a house, (3) as The potentially being in course of being fashioned into a house. movement of building is the realization not (I) of the materials as those materials (they are, previously to the building, already actually these materials), nor yet (2) of their potentiality of being a house (the house is the realization of that), but (3) of their potentiality of being fashioned into a house (V olK080p.'l'JTOV). Similarly every movement is a realization-of-a-potentiality which implies a further potentiality and only exists while the further potentiality is not yet realized. Hence it is d.T(A~,> (1066& 2I) and, though in a sense an f.vlpyna, is distinct from an f.vlpyno. in the narrower sense in which f.lIlpyEla implies that no element of 8tivap.I'> is present at all. 16. ti TOLOUTOV ian.., i. e. 'in that respect in which it exists potentially'. Cf. ~ TOV 8vvaTOV Kat V8vvaTOv f.vTEAlxna, I. 33. 19. Kat KtiALCTI'> (Ab) is awkward, the other words in the list not being joined by Kat. These two words, which are not found in EJTr, seem to be a late importation from the Physics, where Ka{ occurs throughout the list. lZlZ. It seems quite possible to understand f.VTEAlxna after JVTO'>, and we therefqre need not read it (with Bz.), against all the manuscripts both of the Physics and of the Metaphysics. lZlZ. Of the variant readings, ~ 0.&0 ~ a..u.~ introduces an irrelevar.t distinction, that between self-moving things and things which move others. That the true reading is o~X ii o.~TO 4>'>" ii KL"'IJTOII is shown by the explanation of Vwhich follows in 23-33. lZ8-S!I. The distinction between the substratum (e.g. bronze) and the capacity (e. g. the capacity for being shaped into a statue) is here brought out by pointing to the fact that a single substratum combines opposite capacities in itself. The capacity for health is obviously not the same as the: capacity for disease, but one and the same substratum has both. 31••Ie' ~ypOT"S .Ie' ut".o.. The first view is that of Hippocrates, the founder of the humour-pathology, and of Plato in the Ttillaeus (81 E-86 A), the second probably that of Empedocles (cf. Diels3 i. 205· 9, 223. 38).

n.

CO:\Il\IENTARY 3la.

WcnrEp O~SE XPWI'U TUlhov Kul lIpUTOV.

Cf. De An.

41 8 b 2 8U)7I'EP

ofiX OPUTOV dVEV CPWTO~, &Ua 'II'iiv TO (KaUTOV ')(pwp.a (V CPWTL OpuTOV. It is ')(pwp.a that is visible, but it needs a further condition, viz. light,

before it becomes visible. 1. e. visibility is a CTlJP.f3Ef37JKO~ which under a certain condition belongs to the subject colour. 34. on I'EV is answered by OTL 8£, 1066 a 7. lo66a 3. Simplicius interprets TOUTO as TO OlK08op.7JTOv, i. e. the raw materials of a house, but this is plainly wrong. The alternatives, as the following lines show, are the act of building and the house. The most probable reading is that given in the text. 'The actuality is either this which has just been mentioned, viz. the act of building, or the house.' Bz.'s TOVTOV for TOVrO is improbable. 8. 'II'Epl u~rij~, i. e. about movement, referring back to 1065 b 33. g. There seems to be no clause responding to OilTE yd.p KT>'. Neither;; TE K{V7JUL~ KTA., I. 20, nor KaL 8La TOVro KTA., I. 22, will quite serve the purpose. The parenthesis proving that movement cannot be classed as anything but an (VEP'Yna seems to have made Aristotle forget what the second main member of the sentence was to have been. What logic would require as the second member would be 'nor, if movement is an (VEpyna, can it be any (VEP'Yna other than that of the 8vvaTov as such'. II. ot I'EV yap ••• TO I'~ i)v. Til~ 8' (TEPU~ CTlJUToLx{a~ KTA., I. 14, indicates that the Pythagoreans are referred to; cf. A. 986a 25, where movement occurs in the CTlJUTOLxia of the indefinite. But the reference to the other, the unequal, the non-existent suggests ratiwr the Platonic view. We may compare such passages as Soph. 256 D, Tim. 57 Elf. Simplicius is doubtless right in supposing that both the Pythagoreans and Plato are referred to. 11-13. If movement be identified with otherness, inequality, or notbeing, this can only (Aristotle argues) be a loose way of saying either that these are the subjects of movement or that they are the termini of movement. But (I) it would be untrue (or rather it would be nonsense) to say that they are necessarily moved, and (2) if they are termini of movement, then since movement is between contraries, their contra I ies are equally termini of movement, and have as much claim to be mentioned in the definition of movement. Ig-lao. OilTE yap ••• 'II'OCTOV. That which has the potentiality of attaining a certain size does not necessarily undergo the change to that size, so that KtV7JUL~ cannot be identified with 8vvap.L~. Nor, again, does that which actually has a certain size change to that size, so that K{V7JUL~ cannot be identified with (VEpYELa. laO. ~ TE K(VYJCJ'L~ ~VEPYELU I'EV EtVUL SOKEL TL~, CbE>'~~ Sl, cf. 0. 1048b 18-36• laS. The reading Kul IVEpYELuv Kul ~VlpyELUV ~v EtP1JI'EVYJV, 'both an actuality and the kind of actuality we have described', answers to the text of the Physics (202 a I), (VEpYELaV p.EV TLva Elva.., TOLaVT7JV 8' (VEP'YELav oiav (~7I'op.(v. EJr read KaL p.~ (VEP'YELaV in place of the second KaL (VEP'Ynav; but movement has been described 110t as p.~ (VEP'YELa but as

K. 9. 106S b 32 -

1066& 34

iVEpyELa dTEA~~, and further the reading we have adopted accounts better for Ab's reading simply Ka~ ivEpYELav -rqv £lp7J/LEv7JV' ~7. Iv TW KL"'ITW, sc. OflK Iv TW KtV7JTtKW. ~8. ~ T~ii KL"'I;LKOii lvipYELCI' O~K &~~~ llTTev, i. e. the actual moving of the one thing and the actual being moved of the other are inseparable aspects of the same event, as the same interval looked at in one way is the interval from I to 2 and looked at in another way the interval from 2 to I. ~9. BEL "EV yap EtVClL lVTE~iXELClv a,,+o'Lv, 'for it must be the complete reality of both '. The KtV'l'JTLKOV must have an actuality, viz. TO KtVEtV, and in this very act it actualizes the KLV7JTOV, so that one and the same event is on the one hand the actualization of the KLV7JTLKOV and on the other the aClualization of the KLV7JTOV. "iv in 8Et /La. yap KTA. seems to point forward to ;xEt fl' d7rop{av, which follows in the Physics (202 a 21) but not in the Melaphysicsanother indication that this part of K is not notes preparatory to the Physics but excerpts from it. 31-34. ll"oewt; ... WITIrEP ... lll'Oewt; is a goorl instance of Riddell's 'binary structure' (Apology of Plato, 198, § 209). Cf. A. 983b 16 n.

Non-existence

of an actual infinite (ch.

10).

106& 35. The infinite is either that which cannot be traversed because it is nOL its nature to be traversed, or that which is traversed with difficulty, or that which cannot be traversed though it is its nature to be traversed; again, it is infinite by addition or by subtraction or in both ways. (A) A separate entity it cannot be; for (I) if it is neither a magnitude nor a multitude but infinity is its whole nature, it is indivisible, and if so it is not infinite except in the sense in which the voice is invisible, which is not the sense in question. b 7. (2) How can infinity exist per se if number and spatial magnitude, whose attribute it is, do not so exist? 8. (3) If on the other hand it exists per accidens, it is not qua infinite an element in things, any more than the invisible is of speech, though the voice is invisible. II. (4) That it cannot exist actually is clear. For any part of it must be infinite (since the infinite and infiniteness are the same thing, if the infinite is a substance), so that it must be either indivisible or divisible into infinites; but the same thing cannot be many infinites, so that it must be indivisible. But that which is actually infinite cannot be indivisible, for it must have a certain quantity. The infinite must therefore exist only per accidens, and therefore not it but that of which it is an attribute wiII be the first principle. 2073·2

Y

330

COMMENTARY

SI. The above discussion is general; (B) that the infinite does not exist in sms;6lt th;ngs follows from the facts (I) that ir the definition of body is I that which is limited by planes', there can be no infinite body whether sensible or intelligible, and (2) that since number is numerable, there can be no separately existing infinite number. s6. The same fact is clear from the following physical considerations: (a) the infinite cannot (a) be composite, since the elements are limited in number; for ont of the elements cannot be infinite, the other finite, else the former would destroy the latter, and all cannot be infinite, since an infinite body must be infinite in all directions. 34. Nor (6) can the infinite be a simple body, either (i) as something distinct from the elements from which the physicists generate the world (for there is no such body apart f.om the elements; if there were such an element in things, they would be seen to be dissolved into it); or (ii) as one of the elements; for apart from the difficulty of supposing one of them infinite, the universe, e,'en if it is finite, cannot be or become anyone of the elements. The same argument applies as in case (i); everything actually changes from contrary into con• trary. 1061'7. (4) The sensible body is somewhere, and whole and part have the same proper place, so that if (a) the infinite body is homogeneous, i~ will be unmoving or else always moving, but this is impossible; for why should it rest or move in one place rather than another? Where will any part of it move or rest? The place of the cognate body is infinite; wiII it, then, occupy the whole place? How could it? It will either rest everywhere and nowhere be in motion, or move everywhere and nowhere be at rest. 15. If on the other hand (6) the all is not like throughout, the places will be unlike and (i) the body of the all will not be one save by contact; (ii) the parts wiIl be either finite or infinite in the number of their kinds. 18. (a) Finite they cannot be, for if the all is infinite, some parts will be infinite in size and wiII destroy the finite parts; while (f3) if they are infinite and simple, the places will be infinite and there will be an infinite number of elements. If this is impossible and the places must be finite, the all also must be finite. sa. (s) In general, it is impossible that there should be an infinite body and at the same time a place for bodies; for if every sen~ible body is either heavy or light it will move either towards the centre or upwards, but neither the whole nor the half of an infinite body can behave thus; for how can you divide it 1

K. 10. 1066&

35 -

I066b 26

33 1

la8. (6) Every sensible body is in a place, and there are six varieties of place; but these cannot exist in an infinite body. And generally, if there cannot be an infinite place there cannot be an infinite body; for what is in place is up or down, .tc., and each of these is a boundary. 33. The infinite is not the same thing in magnitude, motion, and time; motion, if it is infinite, is infinite in virtue of the distance traversed, and time is infinite in virtue of the motion that occupies it.

This chapter consists of extracts from P4Jrs. iii. 4, 5, 7 on the infinite. 1066& 3S-b I. Tc\ S' ihmpov ... 1f~Pa.'i. On the various meanings of a privative cf. .:1. I022 b 32. b I. ITL 1fpOae~a€L ~ cl+a.Lp~a€L ~ 4/'41111. The infinite may be infinite in the sense that it may be added to indefinitely (the sense in which number is infinite, according to Aristotle), or in the sense that it can be subtracted from (or divided-Btalp£ut'i is more usual than acpalp£ut'i in this connexion, cf. Phys. 204& 7) indefinitely (the sense in which space is infinite, on Aristotle's view), or in both senses (as time is, according to Aristotle). 4,,+111, i. e. 7rpou(Nu£t T£ 11.7r£tpoV Kat acpatp(u£t 11.7r£tpoV. XIIIPLaTc\V ,,~V ~ a.~TcS TL ilv. Aristotle considers first the view of the infinite held by the Pythagoreans and Plato (cf. Phys. 203& 4). In the vulgate reading, X,uptUT()V JLfv ~ am-o Tt av, aiu8.".rov 8' oliX T' €Ivat, the words aw-87JTov 8' are irrelevant to the argument, since the question whether the infinite can exist as an object of perception is not discussed until I. 22. Christ's emendation aiu87JTov T' does not remove this difficulty, and it seems better to regard the words as an unintelligent gloss. The alternative is to read aiu8'rJToV 8' o~, which would be a fair enough paraphrase of the reading of the P4Jrsics xwptITTOV TWV aw-~wv. • That the infinite should exist as a thing separate and existent by itself but not perceptible, is impossible.' The sort of infinite treated of in the argument in II. 2-2 I, which is JL7rr€ JL('I£8o'> JL7rr£ 7rA1j8o-., is in fact an insensible infinite. 8. That number and extension do not exist apart from actual concrete things has already been argued in A. 99 yb 9 ff. 18. cl).xa 4Sdva.TOV yc\ lv·nX€x€Cq. &v 41f€LPOV, sc. aJLiptITTov Kat a8talp€TOV £Ivat. laO. €tP'lTa.L, I. 9. lal. Tc\V tlipa.. The allusion is to Anaximenes and to Diogenes of Apollonia. Tc\ 4pTLOV alludes to the Pythagoreans (cf. 203& 10). laS-la6. 4pLe"",YC\V yap ... 4pLe"cSV. 'For number, or that which has number, is numerable '-and therefore not infinite. la6. +uaLKW'i, i. e. taldng account of the physical nature of the infinite body, viz. the question whether it is simple or compound, as opposed to the purely abstract consideration in II. 22-26.

orov

CO:\IMENTARY lZ8. EL 1I'E1I'EPIlVTIlL TIji 1I'A~9EL T3 C7TOLXE~Il. This has been proved in Phys. i. 6. 33. 1I'UVTn IC7TIlL Q1I'ELpOV, SC. and therefore there cab be no second body alongside of it. 34. For O.)SE lv Sl cf. De An. 427b II, E. N. II20 a 31. 85. ~ AEyoUC7~ TLV(~. The reference is to Anaximander. 87-lo67a I. 0.) +llrVETIlL • • • C7Wl'IlTIJ, • we do not see things resolved into anything beyond, more ultimate than, the four elements '. lo67a lZ-4. cl8uVIlTOV Tc\ il1l'IlV ••• f\ EtvllL f\ ylYVEC79IlL Iv TL Il.)Tii",. The reason seems to be given in 1. 6 1I'av 'Yap p.cTa/3clUn waVTwv. It is said to follow from this that there cannot be (I) an ultimate element other than the four, or (2) an ultimate element which is one of the four. Aristotle takes it as self-evident that (I) an element like that of Anaximander cannot be contrary to all the four a1l'Aa u.fJp.aTa, and (2) that none of these can be contrary to the other three. Further, anyone who represents x as the element of all things, without drawing Aristotle's distinction between matter and privation, thinks confusedly of x as something that persists in the compounds (which is implied in calling it their element) and yet as something that is left behind when they come into existence. 4. il1l'llVTIl y~yvEu9llr 1I'OT( 1I'Up. C( Heraclitus, frr. 30, 64, 66, 90. Zeller i.6 867 translates this .' all things will sometime become fire " and uses it as indicating Heraclitus' belief in a series of universal conflagrations. Professor Burnet corrects the mistranslation (E. G.P. § 78) and shows that Aristotle refers only to the Heraclitean doctrine of • the upward and downward path '. The evidence for a Heraclitean doctrine of a general conflagration is late and untrustworthy; cr. Burnet, §§", 78. Aristotle does not say that there is a time at which all things together become fire, but that there is nothing which does not sometime become fire. 5-6. 6 S' Il.)Tc\~ ••• +UC7LKO~, • the same argument applies to this one if the four elements which is the element of all the others, as applied to the one apart from the four elements which the physicists (Anaximander) posited '-for which cf. lo66 b 35-106711 I. 8. 6 Il~c\~ T611'O~ 1:Aou Kill I'0P~ou. Aristotle does not mean that the place (i.e. TO Tal) 1I'Cpt(XOVTo"1I'Epa.., the inner limit of that which contains the thing, Phys. 212 a 20) of a whole is identically the same as that of any of its parts, but that the region of the universe proper to a whole is also the region proper to each of its parts. A clod of earth tenos to fall towards the region proper to the earth, i. e. the part of the universe next the centre. The argument against an infinite body based on difficulties about its place discusses it under two alternative hypotheses, (a) that it is homogeneous throughout (11,9-15), (0) that it contains parts of different nature (11. 15-23). OtOIl rij~ yij~. Bz. would add Ka2 /3.fJAoV p.ta ..! rom the PhysIcs. But the Physit"S has an altogether fuller text, for it reads not only these

ie

K. 10. 1066b 28 -

1067a 10

333

words but further Kat 1nIpO<; Kat CT1TLV(J~po<;. olov T~C; ~<; is intelligible enough by itself. 8-15. The argument to show that there cannot be :1 homogeneous infinite body is difficult. Aristotle first states the genual position, and then (II-IS) illustrates it by taking a particular (''!se. The general argument is : (A) If the infinite body is homogeneous, it wiJJ be Immovable or else always in motion. (B) This is impossible. (C) For why should it rest, or move, down, or up, or anywhere in particular, rather than anywhere else? (Therefore (D) there cannot be a homogeneous infinite body.) Here each of the first three propositions is difficult. (I) The justification for (A) seems to be as follows: Since the whole is homogeneous, there is no part of its place which is more appropriate to one part of the whole than to another. The natural conclusion then is that each part, and therefore the whole, should remain where it is. But if the whole should move, then since no part of its place is a more appropriate resting-place for any part of the whole than for any other, it will never cease moving. (2) (B) and (C) (TOVrO 8€ &8vvaTov' Tl yap p'auov KaTw ~ avw ~ ~7I'OVOVV ;) look as if they referred only to the second alternative consequent (&(t olu87Ju(Tat). But if that be so, the first alternative is never shown to be false, and the antecedent «(1 ~p.o(t8(<;) is never refuted. TOVTO 8€ d8vvaTov must be taken to set aside both alternatives. This it will do if Tl yap p'auov KaTw ~ avw ~ ~7I'OVOW be taken to mean 'why should any part of the whole be resting unmoved, or be moving, in the downward or the upward or any particular region?' The question is grounded on the fact that, the whole being homogeneous, every part of its region is equally proper to every part of the whole. KaTw, avw, ~7I'OVOVV must refer to the place of rest, or motion, of the parts of the infinite whole; as applied to the whole itself they would be unmeaning. Accordingly Aristotle proceeds to illustrate his argument by the case of a clod of earth. g. Simplicius points out that the opposition of ~p.o(t8(c; to dvaP.O!OV is not identical with that of a7l'AOW to uVV(J(TOV (Io66 b 26). A uVV(J(TOV is ~p.o(t8(c; if its elements so thoroughly coalesce as to lose their own nature, as happens in p.i.ftc; as Aristotle conceives it. 10-15. Aristotle now comes to the particular case, that of a clod of earth. He considers and rejects various alternatives that present themselves. (I) Will the single clod occupy the whole region of earth? Obviously not. (2) How else can it rest, or mo\'e? (a) Suppose it to rest somewhere. it will equally well rest everywhere (all parts of the region of earth being alike to it), and so will never move. (b) Suppose it to move in one place, it will equally move everywhere, and so will never rest. That it should never move, and that it should never rest, Aristotle treats as alike absurd, in view of his experience of the fact that earth sometimes moves, viz. when it is not as near the centre

334

COMMENTARY

of the universe as it can get, and sometimes rests, viz. when it is as near as it can get: I~. It is best to follow most manuscripts of the Physics in reading TOU auyy.I'ou§ 1l.)T'!i aWfIollTQ§ instead of almjc; TOV UVYY€Vovc; UtiJp4TOc;. The order in the latter reading is very improbable, and Aristotle seems always to use the dative with UVYY(JI~c; except when it is used as a noun. 17. TIlUT" the parts of the infinite body. 18. 'lrE'I\'Epllaflo.I'1l fIo~I' O~I' o.)x oteSI' TE. Light is thrown on the argument by I066 b 28-34. A finite number of kinds cannot make an infinite whole, because some of them (i. e. at least one) would have to be infinite in quantity in order to make up an infinite whole, and these (or this one) would swamp and destroy the others, and prevent the whole from having the variety it is supposed to have. Aristotle tacitly assumes that all the kinds could not be infinite in quantity; they are. limited by each other and thus cannot all be infinite. ~O. Kill c1'1rM, • and if the parts which differ in species are themselves simple '. This is important with a view to both the conclusions that are drawn in I. 21. ~I. .t 8i TOUT' d8dI'llTO", sc. that there should be an infinite number of elements. This has been proved impossible in Pllys. i. 6. ~~. 01 TcS1ro~ 'Ir''Ir,pllaflo.llo~, i.e. there are only six regions, up and down, before and behind, right and left (Phys. 20Sb 31). Kill TO 'Ira.. cllldYK'I 'Ir''Ir.pcl..eIl~, i.e. the universe must contain a finite number of kinds of part, and therefore (in view of the argument in II. 18-20) be itself finite. ~4. .t 'lrall a'WfIoll Iltrirtrol' ~ Pclpo§ IXE~ ~ KOU+eST'lJTIl. The heavenly spheres have neither; but they are not ai.u87JTa. ~9. TeS'I\'OU 8i .'L8tJ Ie, cf. I. 22 n. 35-37. OtOIl K£lI'IJa~§ KIlTc\ TO fIoiy.eQ§ ••• XpeSI'O§ 8E 8~c\ ",I' K£lI'IJa~I', cf. ~. I020 a 28. Time is d.pt8,wc; Kt~U(CIIc;, Phys. 2 I;b I.

Change and movement (ch. I I).

lo67 b I. That which changes may change (I) per acddms; or (2) because a part of it changes; or (3) directly per se. That which moves another may be similarly divided. There is something that moves directly, something that is moved, a time in which it is moved, something from which and something into which it is moved. 9. The forms, affections, and places which are the termini of motion are themselves unmoved. Change per se does not take place between all things, but between contraries and their intermediates, and between contradictories.

335 14. Change must be from A to B, from not-A to not-B, from A to not-A, or from not-A to A (A and B standing for the positive terms), so that there are three kinds of change, since the process from not-A to not-B is not change, these terms being neither contrary nor contradictory. SlI. Change from not-A to A is generation, simple or qualified; that from A to not-A is destruction, simple or qualified. SIS. If neither that which is-not in the sense that it is a false proposition, nor that which is-not in the sense that it is only potentially, can be moved (that which is not white may be moved per accidens, since the not-white may be a man; but that which simply is not a particular thing cannot in any sense be moved), that which is not cannot be moved (and therefore generation is not motion, for that which is generated is not, and therefore that which is not is--per acctilens-generated); nor can it be at rest. 34. A further difficulty is that that which is moved is in a place but that which is not is not in a place. 36. Nor, again, is destruction motion; for the contrary of motion is motion or rest, but the contrary of destruction is generation. 1068a I. Of the three kinds of change, generation and destruction (the changes from not-A to A and from A to not-A) are not Illotion; motion must be the change from A to B. The termini are either contrary or intermediate (privative terms may be treated as contrary), and are indicated by positive terms such as 'naked '. Chapters II, 12 contain a series of extracts from Phys. v. 1-3 on the nature of change and on the definition of certain general physical relations. 1067b 6. Bz. is certainly right in omitting n, with Bessarion and the PhJ1sics. TL is due to the influence of :
COMMENTARY SI. Bz. would place OT~ 061C 4VTte.cn! before oilT( I. 20, and this would give a reading corresponding more closely to that of Phys. 225& 10

Vyap ofJ/e U lJ'Jf'O/((LP.EvOV dll p.~ Uzro/(({P.O'ov

oil/( IOTL p.ua{3oATj

8Ld. ,.0 p.~ ,lva~ /(aT' d.VT[()(UW· oilT( yap EVftVT[a OUT( d.VT{~au{1l EOTtV. That order is the preferable one, but the order given in the manuscripts yields a fair sense. ' There cannot he change from non-A to non-B because they are not related as the terms of a change must be, as contraries or contradictories; they cannot be either, since they are not opposed at all.' SS. ICAT' 4VTt+_W. I. e., the relation of the terminus a quo to the terminus ad quem is in this case (as opposed to that of change ~7l'o/((Lp.lvov ';11 Uzro/(({P.O'Ov) one of contradiction, not of contrariety. s3. '1\ I'~" 4'11'~iiI! A'II'Mi, '1\ 8f T~vO! T~. E.g. when a man is produced from what was not a man but a seed, this is d.7l'ATj ylv,uLIl; when a particular kind of man (a man with a particular quality, of a particular size, in a particular place) becomes a man with a different quality, size, or position, this is ylv(ulll TLIl (Phys. 186& 14, 225& 14, 15). Any d.>..>..oWULIl, aiJ~uLIl or ~(){ULIl, or ~op4 is ylv(u{1l TLIl, and can equally well be called ~()op4 TLIl (I. 24). Thus all the kinds of change recognized by Aristotle are included under the headings of change oil/( Ie lJ'ff'O/(fLp.lVOV dll lJ'ff'O/(({P.O'ov and U Uzro/((Lp.EvOV (til p.Tj Uzro/('{P.O'ov. Nothing is left for the third kind, change Ie Uzro/((Lp.lvov dll ~'Jf'O/(({P.O'ov (1. IS), and in fact Aristotle mentions it no more except very briefly in 1068a 4. The fact is that change of quality, size, or place may be regarded under either of two aspects. Take for instance change of quality. Aristotle first intends to bring it under the head of change Ie Uzro/(ILp.lvov dll Uzro/(({P.O'ov. It is change from X which is A to X which is B, where A and B are positive and contrary qualities. He meant to treat only generation as change oil/( Ie lJ'ff'O/((Lp.lvov .Ill Uzro/(£{P.O'ov, but by an after-thought brings qualitative change also under this heading. It may be described not only as it has been above, but also as change from X which is not B to X which is B. Or again it may equally well be described as ~()op4 T'Il, the destruction of X which is A. s5. ~ ICATel. ad.,e.a~" 'I 8~~p.a~". This is what is in N. 1089& 28 (cf. 11. 1017& 31, E. 1026& 35, e. 10SIb I) called ,.0 ~Il I{Iw8o!l p.~ c3v. ,.0 p.Tj &v ,.0 /(aTa uVV()(ULV is an untrue affirmative, ,.0 p.Tj &v TO IC4Ta 8L4lptuw an untrue negative proposition. Untrue propositions might be thought to change (Aristotle remarks) when they become true, but they do not really themselves change; they become true by a change in the facts (Cal. 4& 23 If.). s6-s7. I'~T' Tli ICATel. 8d"AI"" ••• 4VT~lCItl"lIO". ,.0 /(aTd. 8vvap.Lv p.Tj c3v, that which is not, in the sense that it is potentially but not actually so-and-so, is subdivided into (I) that which is opposed to TO d7l'Awt; c3v, and which is d.7l'AWIl p.~ T08, (I. 29), i. e. the p.Tj c3v of which' not-man' is an instance, and <2) that which is opposed to TO T2 c3v, i. e. the p.Tj c3v of which 'not-white is an instance (1. 27). These two, with the p.Tj c3v as I{I£v&Il' are the three kinds of not-being here recognized.

le

337 In N. 1089 a 26 we get a different threefold division of not· being, " , , ,,, II " - i l ' ( 2 ) 'TO, w~ • Ka'Ta 'Ta~ 7r'TWU£L~, e. g. 'TO PO"! aVllpW7rO~, 'TO PO"! £VIlV, "'£vBo~, (3) 'TO Ka'Ta Bvvap,w, e. g. 'TO PO~ avOpw7ro~ Bvvapo£L BE av(}pw7ro~, 'TO po~ AWKOV Bvvapo£L 8E AWKOV: and the last is said to be the starLingpoint of becoming. This division agrees with that in E. 1026 a 34, @. 1051a 34, if not-being in the sense of accidental not-being be left out of account. In A. 1069 b 27 Aristotle speaks of three senses of notbeing, but without specifying them, except by saying that one of them . t ( )'TO ' mOl

tUTt Bvvapo£L.

30. The common reading t1Bvva'Tov yap 'T6 po~ ~v KLv£LUOat leaves the sentence without a principal clause, and further does not agree with its general meaning. Aristotle has said that 'TO po~ ov has several senses, and that in two of. its senses it cannot be moved while in the third it can be moved but only per accide1ZS. That that which is not cannot be moved is evidently not the reason for any of the previous statements but is the summing up of what results from them. yap should therefore be omitted, with JT and Christ. This is confirmed by Themistius' words (in Pf!ys. 169. 18) t1BvvaTov TO'VUV 'To. oVrw po~ oV'Ta Kw£WOat.

3lZ. d yap Kul (In "ciA-LUTU KUTA au"fJt:~"Klis YlYV£TUL, i. e. even if it is only in virtue of the matter that accompanies it that the privation can be said to be the terminus a quo of generation. 34. li"OlWS 8£ Kul Tli ~P£,,€i:v, i.e. op,o{w't t1BvvaTov Kat ~P(P,(LV 'T~ po~ OV (cf. I. 30), the words in II. 30-34 being parenthetical. Rest, being the privation of movement, is equally inappropriate to that which is not. 34-35. TUUTci ••• Suax£p1j. M. 108s h 6, De Caelo 3041\ 22 lend support to Jaeger's emendation, hut the sense is rather against it. 35-36. €l ••• ok £l here practically = (BvuX(pE~ uvpo{3aivEt) OTt, so that OllK is not irregular. Cf. Kiihner ii. § 51 I. 4 by. 1068a lZ. ut €lPIJ"lvUL, sc. in 1067 h 19. 4. Kiv,,!ut~ is sometimes used as synonymous with po£Ta{3oA~, including all four kinds of change (cf. 1065 h 14), more often as including the three kinds of change other than generation and destruction, as here. 5-7. The terms between which movement (as opposed to generation and destruction) takes place are not contradictories but contraries or intermediates between contraries. Privative terms, though not strictly contraries (since only the extrcme degree of privation is contrariety, @. 1046b 14, I. 1055" 35), may be classed with contraries since they stand not for thc mere absence of a quality but for its absence from a subject which is in some degree qualified to have it. The termini of movement are, unlike the terllli1lus a quo of generation and the lel'mi1lus ad quem of destruction, expressed by a positive word (B,,!AoVTat KaTaauH), such as 'naked " 'toothless', • black '. , Naked' and' toothless' are typical privative terms, but 'black' is for Aristotle a typical contrary. KILt Bl1AOVTaL KILTaaUH, olov TO yvpoVOV KaL vwBOv KaL p,EAav therefore follows in sense not on KaL yap ~
COMMENTARY 7. Bz. in Arisl. Stud. i. 37 points out that Aristotle display!! great constancy in his choice of examples, and that he nowhere else cites yu"..,&., as an instance of a privative term. He thinks either TVcpAov (cf. Cal. 10 passim, .1. I022 b 26) or I/roxpov (cf. Cal. I2b 34, De Cae/o 286& 26, De Gen. et Corr. 3 I 8 h I7) preferable. But YV/LVOV is quite appropriate, and it would be a mistake to emend it when the evidence of all the manuscripts both of Physics and of Metaphysics, and of SimpJicius and Themistius, is in its favour.

Denial if change

if change (ch. 12).

1068& 8. There are three kinds of movement-Of quality, quantity, and place; not of substance, because substance has no contrary; nor of relation, for change of relation is accidental to the terms that undergo it; nor of agent and patient, since there is no movement of movement, nor generation of generation, nor, in general, change of change. 16. For (A) change of change would imply (I) that change is a subject of change, which it clearly is not; or (2) that some other subject changes from change into some other mode of existence. 1212. But this could only be per accidens. For change is from opposite to opposite. Hen(:e the subject would be changing at the same time from health to disease and from this change to another, i. e. into the opposite change, convalescence; but this can only be per accidens, just as there is a change from recollecting to forgetting only because the subject changes into a state of knowledge and then into a state of ignorance. 33. (.B) There will be an infinite regress if there is to be change of change. If coming to be was sometime coming to be, that which comes to be something was itself sometime coming to be, so that there was not yet that which simply" comes to be something, but there was already something coming to be coming to be something. But this was sometime itself coming to be, so that it was not yet coming to be something else. Now in an infinite series there is no first and therefore no subsequent term, so that there would be no change at all. b 6. (C) Generation and destruction belong to the same subject, so that that which comes to be is being destroyed when it has come to be coming to be; it must be then that it is being destroyed, for it cannot be before or after. 10. (D) What can be the nature of the underlying matter of change

K.

12.

106880

7-8

339

or becoming, and what can it be that they change into? The change must be change of something from something into something. 15. Since there is no change of substance, of relation, or of action and passivity, change must be in respect of quality, quantity, or place, each of which contains a contrariety; quality meaning not that which is included in the essence but that which is a mere affection of its subject. 80. The unchangeable means (I) in general, that which cannot change; (2) that which changes with difficulty or slowly; (S) that which is capable of changing but does not change when, where, and as it might; this alone of unchanging things is said to be at rest, rest being the contrary of motion and therefore presupposing the same subject.

Sundry definitions. 86. Those things are loge/her in place which are in the same proximate place; those things loucR whose extremities are together; those things are 6elwtm at which that which continuously changes arrives before it arrives at the extremes. Those things are contrary in place which are at the greatest distance in a straight line; that is successive to another which comes after the beginning and has nothing of the same kind between it and that which it succeeds. That is contiguous which is successive and touches. 106g& sa. Since all change is between opposites, i. e. between either contraries or contradictories, and the latter have no intermediates, what is between must be between contraries. 5. The conh"nuous is a species of the contiguous; it is found when the boundaries of the touching things are one. 8. 'Successive' is evidently the first of these terms; for what touches must be successive but not vice versa, and the continuous must touch but not vice versa. Therefore the point is not the same as the unit i for points have contact but units only successiveness, and points have intermediates but units have not. 1068& 8. In this list of categories 7f'OTE, /«(w()o,t, and IX£Lv are omitted The omission of the latter two is regular; they occur only in Cal. I b 27. 2& 2 f., Top. JOSb 2S. It seems probable that Aristotle had come to regard them not as categories but as sub-categories-perhaps (as Mr. Collingwood has suggested to me) merging them respectively in ~,&8((TL" and Itt", two of the sub-forms of 7f'Otov (Cal. 8b 26-9& IS). 7r'OT1 occurs in the common text of the corresponding passage in

340

COMMENTARY

the Ph;'ni:s (u5b 6), but is omitted by EH and by Simplicius (and in the summary in 226& 23), and its absence is required by the logic of the sentence. Aristotle shows that there are four categories in which there is no movement, and concludes that there are only three in which there is movement. He must, then, have a list of only seven in his mind. Such a list occurs nowhere else in his writings. Simplicius quotes a discussion by Alexander of the question why there is no movement in the category of time, and discusses the subject himself (829. 29-832. 25). The reason for Aristotle's omission of time here is probably that he saw that time, having the peculiar relation to a movement of being its number (Phys. 219b I), could not also be related to it as either subject or terminus. 10. KUT' O~O"UII S' oll. There is change (p.£Ta/3oA~) in respect of substance, but it is not movement (I({VI]ULi) but generation and destruction, being between contradictories, not between contraries. Cf. 1067 b 21, 1068a '5. 8lc\ TA ".",eill EtllUl O~O'lq. IllCllITlolI, cf. Cal. 3b 24. II. o~S~ TOU 'II'p6s n. There is no movement of, i. e. in respect of, relation, because A may change in respect of its relation to B when A itself does not change at all but only B. Then the movement of A in respect of relation is only incidental to a change of B in some other respect-in size, quality, or place. 12. Schwegler's emendation f/oETU/3Q}..}..OIlTOS I'ti is required by the sense and is strongly confirmed by Alexander (as quoted by Simpl. 834. 27- 835. 2) and by Them. 170.21-24, as well as by N. 1088a 34. 13. o~8€ 'II'OlOUIITOS Kul 'II'QO')(OllTos. I.e. there is not, besides movemem in size, quality, and place, another kind of movement in respect of action or passivity. Movement from one activity to another or from one passivity to another or from activity to passivity or vice versa is, as Aristotle will try to show in II. 22-33, merely incidental to alteration, increase or diminution, or locomotion. It is true that acceleration or retardation, or change of direction of movement, is incidental to locomotion, but that is no reason why these should not be viewed as belonging to a distinct class of movements, i.e. movements from one movement to another. 14. KlllOUIITOS Kul KLVOUf/oivou, variant names for the categories of 7I'OLE(V and 7I'UUX£!v. Cf. Z. 1029 h 25. 16. There might be supposed to be 'change of change', says Aristotle, in either of two senses. (I) Change might be thought of as a subject that changes from one state into another. But this is absurd. (2) (I. 20 if.). Some other subject migllt be supposed to change from a state of change into another mode of being. Simpl. and Phil. interpret Eii ~TEPOV E!OO~ in Ph)'s. 225 b 22 (answering to EtS ci}..}..o ET8os, 1068& 21) as 'into another kind of change'. But that is not a natural interpretation of II( p.ETa/3oA~i Eli aAAo E!OOi. It is true that in II. 26, 27 Aristotle says p.ETa/3uUn ••. ;t alJ~~ TaVT1}~ T~i

K. 12. 1068& 10-28 fJ-(Ta{3oA~i (1i

CI.>.A"/V, sc. fJ-(Ta{3oA~v, but that comes after he has recalled the fact that change is between opposites (1. 25). Here he expresses himself more generally in the vague phrase (1i 3.>..>..0

(laoi.

SllZ. olo.. a ..epIII'lfo" lK vOuou Et~ tlylElU". oloV must introduce an instance, not an analogy (the use of olov comparalioni signijicandae illustrated in Bz. Index 50 I b 55-502a I offers no parallel to the present use). It is surprising, however, to find the change from disease to health offered as an instance of change from change to another mode of being; in 1. 26 it is offered as an instance of the change from one slale to another which is accompanied by a change from one change to another. One must therefore suppose Aristotle to be here using VOuoi and Vy{£La loosely for' falling ill' and 'becoming well' j in 1. 26 they have their proper sense. lZ3-lZ5. This sentence is preliminary to the proof that when change takes place from one change to another, this is per accidens, incidental to change from one slale to another. In this sentence Aristotle merely lays down the general principle that all change is from one thing to another, and more precisely from opposite to opposite. He will presently apply this principle to change from change to change. Sl5. There is here a great variety in the readings of the manuscripts and of the Greek commentators; the best reading seems to be that of Ab and Simplicius, 7rA~V ai fJ-€V £1i aVTL/C({fJ-EVa w8l, ~ 8' Wlll, ~ /ClvT/cTL<;, • except that generation and destruction are changes into what are opposites in one sense (sc. contradictories, e.g. from not-man to man or vice versa), while the other, movement, is change into what are opposites in another sense ($C. contraries, e. g. from up to down, from small to large, from white to black),. For this distinction between generation-and-destruction and the other kinds of change cf. 1067 b 21 and note, Phys. 235 b 13, 261 b S. The readings of most of the manuscripts of the Physics~ 8€ /cLV7JULi (H), ~ 8€ /Clv7JULi ovX Op.o{Wi (FI}-seem to be attempts to get an antithesis to ai fJ-EV (1i aVTL/cf{fJ-(Va. w8{ after ~ 8' WU had been lost by haplography. The reading of E]r, ov /cLV~U£Li, seems to have been introduced from 1. 3. lZ6. Aristotle now proceeds to illustrate what he has referred to in 1. 23-a change from one change to another, incidental to a change from one slale to another. t1fJ-a at first sight seems questionable j it would seem that the change from change A to change B must succeed change A. But, as Simplicius points out, of that which is changing into something else some part must still have something of its former quality (r. 1010" IS). Change A must partly exist while it is changing into change B. lZ7. 6. .. VOcn1ut1, • if it has fallen iII'. lZS. Ets 61fOUJVOU .., sc. fJ-£Ta{3oA~v, • into whatever may be the other change concerned " M)lXETU~ yap ~p'JIo.i .. is difficult. It is, on the face of it, inconsistent

COMMENTARY

34 2

with the immediately preceding statement that the subject must have changed into some state of change. Phil. and Simpl. take Aristotle to be referring to the fact that after falling ill one may rest in the state of illness, and rejecting that fact as irrelevant to the case considered. 'In the case supposed, viz. that of change from one change to another, that which has changed from health to disease has also changed from falling ill to recovering (though we must remember that in fact it may rest in the state of disease) '. One is tempted to read OiJK €V8'XETaL, and to suppose OiJK to have fallen out by haplography after 07l"OLavoVv. 'For it is not possible, in the case we are considering, that the subject should be at rest.' 29. KAl ITL ••• dEl, 'and further the change from one change must not be, in any case, into any other change at random, but into the opposite change'. 30. The sense requires a comma after the second (UTaL. ' So that it will be the opposite change, viz. recovery of health.' 32: liTE tt, ill'Lcrrlt"1JV lITE liE Et, CLYVOLAV. ayvoLav is Prof. J. A. Smith's emendation of Vytnav. One would expect this clause to refer solely to the case last mentioned, the change from remembering to forgetting, while Vyt(LaV introduces a reference to the remoter case of change from falling ill to recovering. Further, bTt ••• bTl refers naturally not to different cases but to successive stages in the same case. Again, ~yt(La in the one case does not answer to €7I"L(T~P.71 in the olher. The corresponding pairs of terms are as follows: There is primarily a change from health to illness, or from ignorance to knowledge, and incidentally a change from falling ill to recovering, from recollecting to forgetting. Thus the corresponding term to €7I"~P.71 is VOCTO~. Finally, the change from recollecting to for!tetting is incidental not merely to the change from ignorance to knowledge but also to a subsequent change from knowledge to ignorance. On all these grounds, ayvoLav seems to be a necessaty emendation; it is confirmed by the interpretations of Simplicius (842. 18, 24, 26-843. I) and Philoponus (853. 3 2 , 854· 3)' 34- dvdYK1J Ii~ KAl ~v lI'poTipAV, se. Y€v(CTLV ytYV(CTOaL. Aristotle takes up the particular case of y(V'CT(W~ Y(V(CTL~ rather than the more general one of p.£Taf3oA~.. p.ETaf3oA~. If a generation is generated, its generation must have been generated, and so ad infim~um. 35. c1l1'Mj yiVECTL' has not here its technical meaning of generation as opposed to change in size, quality, or place (cf. lo67 b 22 f.)-a meaning which would be pointless here. It means the original, simple coming to be as opposed to the 'coming to be coming to be' which has just been mentioned in a 34 and will be mentioned again in b 2. b 1-3. In the extraordinary variety of readings recorded here by the manuscripts and the Greek commentators it is hard to choose that which Aristotle is most likely to have written. There would be little profit in discussing the readings in detail, but the following rc:marks may be made:

".v

K. 12. 1068& 29 -

1068b 10

343

(I) The balance of evidence is in favour of omitting·d".Mi~ in I. I, and the sense is not seriously affected by this. (:a) Bz.'s T' 'Y,rvOp.fVOII 'Y'Y"0p.fVOII in I. 2 is what the sense requires, and is confirmed by Mew 'Y-VflTtu 'Y''Y''0p.fVOII, I. 8. (3) There is good evidence for the omission of TO in I. 2, but ,.0 'Y''Y''0P.(JIOII seems to be needed rather than 'Y''Y''0P.(JIOII, as the antithesis to T' 'Y,yvOp.fVOII 'Y,yvOP.WOII. (4) The balance of evidence is strongly in favour of ~8"1 as against fl 8" in I. 3. The sentence which Bz. gets by reading d 8", viz. It 81J ICed TOW' ly''Y''ETO ".WI, i1xrr' OlJlC ~II "'11/ mf 'Y''Y''0p.fVOII, is a more violent instance of i1xrrf in apodosi than any in Aristotle, more violent even thanPhys. 232& 12-14, with which he compares it (Arirt. Sludien II. III. 109)' I-A. ICcU TlI y,y..o,...vov ••• y'yvcSI"vov [4\] y'yvcSl'lVOV, 'that which comes to be something (by the simple 'Y-I'fu,~) was itself at one time coming to be, so that there was not yet that which simply comes to be something, but there was already something coming to be coming to be something'. a. ICcU TOUT' ",CYVI"s 'I\'On, 1Mrr' oalC ~V '11'11/ "sTI y'yvcSl'll'Ov. There is the same ambiguity in 'Y''Y"lu()a, here as in ro 'Y''Y''0JUl'O" ly''Y''ETO in I. I. • And this was at one time itSelf coming to be, so that it was not yet at that time coming to be something else', i. e. coming to be coming to be something, which it was described in I. 2 as being. Cf. I. 9, where Y''Y''0P.(JIOII must from the context be interpreted as meaning 'Y''Y''0P.(JIOII y,yvOp.fVOII. 6-7. IT, ... +80pcl • Further, what is capable of one movement is capable of the contrary movement, and of resting, and what is capable of being generated is capable of being destroyed.' Philoponus understands ; lvallTla with "'plp."1O't~ as well as with 1
344

CO:\IMENT ARY

II. T', O~V ~I7Ta.L ciJl711'EP ••• oihw T' KT~. is an instance of Riddell's 'binary structure' (Apology of Plato, 198, § 209). 14. The reading of the manuscripts, p.~ K{VT/ULV, is unsatisfactory. The words will hardly bear Bz.'s rendering 'Denn Bewegung muss Bewegung sein aus diesem bestimmten Etwas in dies bestimmte Etwas, nicht blosse Bewegung '. To get this meaning, one would have with Lasson to insert a"'Aw~ after p.~ K{VT/ULV, and this might easily have dropped out before "'w~. But it is better to adopt the reading which Alexander preferred (Simp\. 854. 21) and which is found in most manuscripts of the Physics, ~ ylvf.I7LV. 'For it must be the movement or becoming of something from something to something.' 18-19. ~lyw 8. TO 'II'OLOV o~ TO Iv Tij O~I7'q. ••• dUC\ TO 1I'a.B1JTLKOV, cf. ~. 1020& 33, b 8. Change with respect to a "'OLOV which is EV Tj ofJu{q. would be not K{VT/UL~ but 'Y'Vf.UL~ 01' ¢8opO.. lUI. Bz. seems to be right in preferring the reading of the Physics (confirmed by Simp\. and Them.) Ka.l 8UVC£I'EVOV I'~ KLVOUI'f.VOV 81 to that of the manuscripts of the ilIeiaphysics, p.~ 8vvap.€vov 8'. The essential, in the meaning of a privative word, is not that the subject cannot, but that it does not, have the positive attribute when it might be expected to have it. Cf. Cal. u& 29, ~. 1022 b 27, @. 1046& 32. 25. The stress is on TOU 8EKTLKOii. Rest is privation of movement in that which is capable of movement, and therefore not in things which are rather non-movable than immovable (ro JAW~ d8vvaTov

KLV€'iu8aL ). 26-1069& 14. The terms whose relations Aristotle is mainly interested in working out are o."'T€U8aL, :t~~, EX0P.€VOV, UVV€X,~, o.p.a is introduced as implied in the definition of contact, IJ.€TatV as implied in the definition of U~~, and EvaVT{ov KaTa TO"'OV as connected with the definition of p.€Ta~v. The relations between the four main terms are not altogether clear. Aristotle begins by defining contact (a7I'Top.€vov) and succession (Ui7~) quite independently of one another, and says that both attributes must be united to make an EX0P.(VOV (1069& I). Thus, to take Simplicius' examples, two successive numbers are not Exop.€Va because they are not in contact; and a coat in contact with the body is not EX0P.(VOV to it because it is not successive to it, not being of the same kind (cf. the definition of succession, 1068 b 31); but two successive houses which touch are Ex0p.(Va. Later, however, Ari.stotle implies (10691\ 9) that €~~~ is a wider term including U7I'Top.€Vov. TO 'Yap U~~ ofJX /l7I'T(TaL (' is not necessarily in contact '), TOVrO 8' €~~. If this be so, if the a7I'Top.€vov be necessarily Uij~, then EX0P.(VOV is a mere synonym of a7rTop.€VOV and n. I, 2 are misleading. Finally, the continuous is described indifferently as a species of the EX0P.€VOV (1. 5), or of the a7I'Top.(VOV (1. 10). It is the species in which the extremities are not merely together but are one.

K. 12. 1068b I 1 - 1069& 5

345

Thus there is a confusion between two arrangements of the conceptions, which may be represented thus:

I

d,mp.Evov

II

I

+ltii~

£X°P.EVOV

I

I

d,7M'OP.EVOV

=

£X0P.EVOV

I

The latter is the prevalent classification in Aristotle. In no passage other than the present is there any attempt to distinguish £X0P.EVOV from d,7M'OP.EVOV. !l6. 3cru l., M TCS'II''t' 'II'pIflT't'. 'You are lv T'iJ O(,pall'iJ because you are III ~ dlpl, EV T'iJ d.lpt because you are lv Tj ¥ii, lv Tj rD. because you are in this place which contains nothing but you' {PRyS. 20 9& 33b I}. The last is your T07l"O~ r8w~, lv ~ 'II'~ (ib. & 33), in which you • are directly or proximately. It is evident, then, that two things cannot be 1J.p.a l(a1'4 TOrov, for the place which includes nothing but A cannot include nothing but B. Yet Aristotle evidently means that in some sense two things can be iJ.p.a l(aTa. T07l"OV. Two suggestions may be made as to his meaning. (I) He may mean that two things are lJ.p.a if they are in one place which includes nothing but the two, i. e. where there is nothing between them. Or (2) he might mean that one thing, occupying one place, may be two things in the sense that it discharges two functions. E. g. the ends of two lines which meet may be said to be 1J.p.a, but this only means that one point serves as the end of both lines. But, since 1J.p.a is used in the definition not of continuity but of the less close relation of contact (1. 27), and in the Physics the unity of the I1Kpa is expressly dislinguished from their being J.p.a (u7& u), it is evident that the former is Aristotle's meaning. aa. oto., ypG".".a;1 YPG"'rijt, 'e. g. lines between the given line and the first line of the series • 1069& II-S. "..fteu. This section seems to be out of place in the manuscripts both of the Metaphysics and of the Physics.

.,...1 . . .

2;)13·2

z

COMMENT ARY The most appropriate place for it would be before lvaVTlov in 106Sb 30, where Prant! proposed to place it In Themistius' paraphrase it comes before p.eratv in 106S b 27 (Plzys. 226b 23), and 106Sb 2627 ttp.a. ••• 4pa (PAys. 226 b 21-23) are omitted. This position is, however, less appropriate; it is more likely that the sentence was originally a note appended to the mention of ro peratv, which has been inserted at the wrong point in the text. I1-I~. i" ots S~ ... TOdTOLS. This repeats in another form what has been alreadl expressed by d !T11VEXl'i' tt'II'Tera&. I~. ..,. O~K Icm Cl'nyl'~ f'O"ciSL TG~,.o". Aristotle is probably attacking the view of Zeno, of whom we a,re told that n,v UT&yp.~V c:,'i TO ~ Aey" (Simpl. 99. 10). Or it may be, as Philoponus says, the Pythagoreans that Aristotfe has in mind, cf. M. 10Sob 19, IOS3 b 14· TGis I'~" yAp (se. UT&YP.Gt'i) tl'll'cipXEL TO l1'II'TEcr8GL. This is inconsistent with the definition of contact in 106Sb 27, 4'II'TEUOa& 0V Td. I1.Kpa. 4p.a, $C. KaTd. MOV (cf. I. 26). Points have no I1.Kpa.; and they have no TD7rO'i, since they do not occupy space and therefore have no 7rEp&txov. 13- KGt,.&i" I'~" I'ITG~d TL TW" S' olJ. P1!Ys. 227& 30 states this more fully: Ka, TWV p.w IYBlxera& Etvai T& P.ETatv ('II'ciua y?tp ypa.p.p.~ p.ETa~V A), TWV A 0~. OVI( • avaYKf/' • , '~" ~\ ~,~ ,~-If UT&YPWV OVOEV yap p.era,.., oOOOO'i Ka&, p.ovafJO'ii. there is to be any proper opposition between lv8lXera& and OI1K &VuYKf/, lv8lxera& must mean clVC£YK7] Iv8lXEuOa&, 'it is always possible', and OI1K clvaYKf/ must mean OI1K clvaYKf/ Iv8lXEuOa&. Now every line is betwe"en points, and therefore there is sometimes a p.ero;tV between points; but if points ever touched, as Aristotle has (I. 12) said they can, there would be no p.eratv between them. And on the other hand, though successive units have not a p.eratv, n6n-successive units have. Thus the opposition is ill thought-out.

BOOK

A

Jaeger (Art'sl. 229 fr.) has various arguments in favour of an early date for A. (I) Metaphysics is here restricted to the study of non-sensible substance; the study of sensible substance in chs. 1-5 is merely preliminary (1069& S6-b 2). But Z contains equally explicit statements of this view, and 'Izis argument appears to have no force. (2) A. 1071b 6 expresses like K (1060& 22) the view that if there were nothing apart from sensible things there would be no permanence in the world. Contrast this with the more guarded statements of Z. 103Sh 5, H. 1043b 15. Like K (1060& 12), A (r071b 20, 1073& 4) treats the object of metaphysics as being that which is present in no sensible thing. (S) There is a very close connexion between A and the early book N. 107 2b 30-1073- 3 is based on 1092& 9-1 7, 107Sb 37-1076& 4 on

K. 12 1069",11-13

34'7

109 0b 13-20, 10'75& 25-33 on 1087& 29-b 6, 1075& 34-36 on 10913 35-37, 30-3 2• But the astronomical theory of Callippus mentioned in ch. 8 belongs to the period 330-325, quite near the end of Aristotle's life (Jaeger, Artsl. 365-36'7, Heath, Artslarchus of Samos, 19'7, 198, 212). Jaeger points to the difference between the sketchy style of the other chapters, with its series of terse arguments introduced by such words or phrases as P.(To. Tawa OTt, lTt, Kat, /lp.a 8t, bp.o{w,> 8i, ~ Kai (1069 b 35, 10'70& 4, 10'74 b 21,25,36,38, 1075& 5, 6, 34, b 14, 16,28,34), and the ample style of ch. 8. The astronomical detail of this chapter breaks harshly into the continuity of the speculative theology of chs. '7, 9. Aristotle seems originally, in the II(p~ iPr.Aouocp{a~, to have replaced Plato's notion of a world-soul by that of a separate first mover, but to have retained the notion that each star or planet is moved by a single star-soul. The doctrine of ch. 8 is due to the influence exerted on this early mode of thought by Eudoxus' analysis of each planetary orbit into several distinct rotatory movements. But the two lines of thought are not satisfactorily combined; there remain inconsistencies which were already pointed out by Plotinus (Enn. v. I. 9). In particular the section 10'74& 31-38 is a fragment (in the curt style characteristic of A apart from ch. 8) representing the older doctrine, and inconsistent with the later doctrine of the' intelligences '. There is in this section nothing to which o~o, in b 3 can refer, but with this section removed o~o, is seen to refer to O({wv UWp.&.TWV in 3 30. Ch. 8 then seems to represent a late venture of Aristotle's in a field in which he was not really at home. He deserts here the path of metaphysical speculation and enters on that of astronomical observation and mathematical reasoning; and his prentice hand betrays itself in the arithmetical mistake of 10'74& 13.

Freudenthal's careful study of the quotations made by Averroes, in his commentary on this book, from the commentary of Alexander has established the fact that Averroes had before him the genuine commentary of Alexander (or rather an Arabic translation of a Syriac version of it), while the commentary which passes under the name of Alexander is not genuine. He argues with great probability that the latter work is to be dated somewhere between A. D. 450 and 600. The same judgement must probably be passed on the commentary on Books E-K, M, N, which have long been thought to stand on a different footing from the admittedly genuine commentary on A-~. The fact that Averroes was dealing with a translation of a translation greatly diminishes the value of his citations from Alexander, but some important

COMMENTARY hints are to be got from him. Similarly the value of Themistius' commentary is greatly diminished by the fact that we possess it only in a Hebrew translation of an Arabic translation; but here again something may be learnt of the text which Themistius had before him.

The /"ree !linds of substance . Change implies mailer as well as form and privation (chs. I, 2). 106g8 18. Our subject is substance. For (I) if the universe is a whole, substance is its first part, and (2) if it is only a series, substance is prior to the other categories. Further, these others have not being in the unqualified sense, or we shall have to say that things like 'the not-white' have it also. Further, none of the other categories can exist apart. It was of substance, too, that the ancient thinkers investigated the cal1ses. Modern thinkers owing to their abstract method make universals substances, but the ancients identified substance with some particular body such as fire. 30. There are three kinds of substance : (A) the sensible, including (A I) the eternal, and (A 2) the perishable (which is recognized by all)-e. g. plants and animals, (B) the unchangeable, to which some thinkers assign separate existence, (a) distinguishing Forms and mathematical objects, (b) identifying them, or (c) recognizing mathematical objects alone. (A) is discussed by physics, (B) by metaphysics. b 3. Since change is from one contrary or the middle state to the other contrary, there must be a substratum which changes (for the contraries do not change), and which remains when the contrary does not remain; and this something is matter. 9. There are four kinds of change(I) in respect of the 'what'-generation and destruction, (2) in respect of quality-alteration, (3) in respect of quantity-growth and diminution, (4) in respect of place-locomotion. 14. The matter which changes must be capable of both states. All change is from the potential to the actual, from that which is not (actually), but also is (potentially). !30. Anaxagoras, Empedocles, Anaximander, and Democritus all pointed to matter in their view of the original state of the universe. ~4. Different things have different kinds of matter; things that are

349 not capable of being generated have matter for locomotion. We must not say with Anaxagoras • all things were together', for if they had not differed in matter they would not have come to be different, the reason which was at work on them being admittedly uniform. 32. Thus there are three principles, form, privation, matter. 1069" 19-21. Aristotle states here two alternative ways in which the universe may be regarded, (I) as o>..ov Tt, (2) as TIj) It/J(~~, i. e. as being a universe by virtue merely of forming a series. Bz. explains the meaning of O>"OVTt in opposition to this by reference to I. 1052" 22 T~ JAOV Kal lx.0V TIVa. p.opcfJ~v Ka2 (r8o~,~. 10 16 b I 2 ~V p.~ Tt O>..OV V, TOWO 8, ~v p.~ TO (r80~ lX1/ (V (cf. H. 1045" 10, M. 1077" 28, 1084 b 30). One may regard the universe as being a unity of form and matter, as every individual substance (except those which are pure forms) is, and in this case, Aristotle says, substance, i.e. substance as form, is evidently the primary element in it. Cf. Z. 1029" 5 T~ (t8o~ nj~ JA1J~ 7f'p6T£POV Ka2 pJi>..>..ov av. If on the other hand we regard the universe as consisting merely of the categories arranged in a series, substance is evidently the first member of the series. Bz.'s explanation is, however, not satisfactory. Substance is here contrasted not with matter but with the other categories. The substance which is the subject of study in these chapters (1-5) is not specially substance as form but substance in all the senses enumerated in ~. 8, Z. 2, including substance as matter (1069" 2;), 1070R 9), as form (1070" II), and as individual thing (1070" I2). The contrast is simply that between the view of the unh'erse as a genuine unity, in which substance is the primary clement, and the view of it as forming a loosely connected series (the view, in fact, of Speusippus, which is referred to in this book, 10751> 37)-in which case substance is at any rate the first member. 22. It is doubtful whether we should read &A>..a with the manuscripts or oroI' with Alexander and Bz. The latter is the eagier reading; the former compels us to take 7f'OLO"lT(~ in a wider sense than 7f'ouh·, and to suppose that all the categories other than substance are summed up und ... r the two headings 7f'Ot~T(~ and KlVliO'u~. Evidently it would be impossible to bring the categories of relation, time, and place under either heading; but at any rate quality and quantity might he grouped under 7f'Ot6T1JT(~' and 7f'OtE!:V and 7f'aO'x.uv under KU'qO'Et~, and Aristotle may have meant the mention of 7f'O'~TE~ and Kt~O'Et~ to he suggestive rather than exhaustive. It would be hard to explain the origin of the vulgate reading T.l>..>..a &>..>..& from an original Tawa orov, while Tawa &AA& makes thc corruption natural enough. Themistius seems (1.21-23) to confirm &>..>..&. 23. ~lY0I'EV youI' dven Ka.L TauTa., oIov lanv oG ~EUKOV. (H', An'Kol' is evidently regarded here a!' the subject of E(TTU" Arbtotlc treats • a notwhite exists' as necessarily implied in the fact tll,1I, e. g., a man who happens not to be white exists (cf. ..l. 1017" 18).

350

COMMENTARY

~6. ot ... ,ii" evidently the Platonists. Alexander unjustifiably considers the doctrine referred to non-Platonic, but cannot suggest any other definite school which could be meant. ~8. SLA TlI XOYLKWi t"TEi,. For the use of AoYLKiiii cf. 1'. 100Sb 22, Z. 1029 b 13, and for similar expressions referring to Socrates, Plato, and the Platonists cr. A. 987b 3,0. 1050b 35, N. 1087 b 21. !Zg. m' 03 ro KOW.s" crwp.u. There is no KOWOV criiiJLO. (De Gen. el Corr. 320b 23), i.e. no kind of body which is the basis of all the elements. It is better therefore to place a comma after KOW6v and interpret • but not that which is common to them, viz. body'. 30-3~. There is considerable divergence here between the various readings. ~ JL& dtSwi ~ 8£ cpOufJT'17 • • • ~ F! dtSLOi, the reading of all the manuscripts, cannot stand, and the i?est solution is to omit ~ S' dtSwi with Themistius, and with Ale~ander as quoted by Averroes. Probably ~ JL& dtSLOi ~ S£ cpOafJT'17 was first corrupted by haplography into ~ JL& cpOafJT'l7, and two attempts were made to correct this, one by mentioning the dtSLOi olxrta before the cpOafJT'l7, and the other by mentioning it later, which attempts both found their way into the traditional text. The subdivision of perceptible substance into the eternal and the perishable, ~i ~ JL& ••• '~a, is doubtless parenthetical, and ~i dV4YK1/ Til crTOLX£iu Aa{3£iv refers to alO'O~ olJcriu in general. Aristotle proceeds to this general discussion of perceptible substance in I 069 b3-107 I b 2. Bz. thinks ~v 71'4VT£i OJLOAOYovcrw must refer to bOlh kinds 0f perceptible substance, and proposes to read JLia JLf.V alcr01/T~, ~v 71'4VT£i OJLOAOYovcrw, ~i ~ JLf.V cpOafJT'17 ••• ~ S' dtSwi, following Alexander and in part Themistius. The eternal perceptible subs lance (that of the heavenly bodies) is included among the generally recognized (OJLOAoyoVJL£VaL) substances in H. 1042& 10, cf. Z. 1028b 12. But the eternity ofthe heavenly bodies was not universally admitted, and ~v 71'4VT£i OJLOAoyoVcrw might well here be said only of terrestrial bodies; Bz.'s proposal is unnecessary. 34-36. TWES, Plato and his school. OL p.i" Plato, cf. Z. 1028 b 19; ot Si,' Xenocrates, cf. Z. 1028 b 24 n. ot Si, Speusippus, cr. M. 1076& 20-21 n. b I. uilT'! SE iTipus. Aristotle discusses unchangeable substance in chs.6-10. 5. 01'1 XEUKlI, yap '" i.e. voice is an opposite, in one sense, of • white '. Being not white it is contradictorily opposed to white. Yet there is no change from voice to white or vice versa. Hence change is not between contradictories but between contraries, which belong to the same genus as one another (I. 7). 6. 01'1 yAp TA l'UVTIU p.ETullc£XXEL, cr. H. 1044 b 25 n. 18. KUTA crup.IlEIl"ds l,SiXETuL YlY'Ecr6uL lK p.~ iSVTQS, i. e. a thing comes to be out of what incidentally, or in virtue of a concomitant, is not. Y comes out of an X of which not-Y can incidentally be predicated. !zo-!Z3. The traditional punctuation is "U~ TOW' (crTL TO 'Avatay6pov • ({3"EI\TWV yo,P.1/.oJLov~ 71'aVTa , ) KUL"EJL7I'£OOKI\EOVi .., , ,~ , 'A V~L_I: £v TO JLLYJLO. KaL p.4vSpov, Ka~ Wi t11/JL6KPLT6i rp1/crw, ~V OJLOV 71'4VTa SVV4JL£L, lVEP')'£tfl- S' o~. This reading, as Prof. Jackson has pointed out (J. of P. xxix. 139 f.),

tw""

presents the following difficulties. (a) Why does Aristotle, who in A. 989b 17 identifies Anaxagoras' vov~ with 'TO lv in the Platonic sense of that term, and his 71'av(T7l"€pp.la with (Ja'T€pov, here assert that lv is a better description of the 71'avU7I'£pp.la than &p.ov 71'av-ra? (b) By what right does Aristotle use p.;:yp.a to describe the material principle of Anaximander, who was a monist? (c) What does Aristotle mean by ascribing to Democritus the doctrine that ~v &p.ov 71'av-ra 8vvap.n, lv£py(lq. 8' oil? (d) Is not the addition of 8vvap.€t, lv(pydq. 0' oil just what ought to reconcile Aristotle to Anaxagoras' theory of the material cause? To find the material principle of Anaxagoras described as 'TO EV and that of Anaximander as TO p.i:yp.a is certainly somewhat surprising, and LUtze proposed accordingly to transpose 'Ava~ay&pov and 'AVa~tp.av­ opov. He also renewed Karsten's proposal to excise {1£ATtOV ya.p ~ &JI-Ov 71'clv-ra. This, however, is an unnecessary tampering with the text. Jackson adopts the less violent remedy of reading l$v for EV and altering the punctuation so that the sentence reads Kat TOVT' (OTt TO 'Ava~a, " I J '\ ," e , ( ' 'E ~- \.' YOpov OV· ,..(II.TWV 'Yap T/ op.av.... 71'av-ra Kat P.7I'(OOKII.€OV~, TO,... p.typ.a, Kat, {A va..l:'~ A' 'A. ... , ~, tp.avopov, Kat, .W~ ""T/P.OKPtTO~ 'f'T/(J'tV) T/v op.ov~ 71'av-ra ovvap.£t lv£py£lq. 8' oil. On his interpretation (I) the subject of {1tA'TWV yap ~ &p.o1o , ...... , ~, , ,~,." ( ) 'EP.7I'£OOKII.(OV~ ~ \' 71'av-ra IS T/v op.ov~ 71'av-ra ovvap.n (v£pynq. 0 ov , 2 an d 'Av~tp.cf.vopov depend on TO l$v, and TO p.i:yp.a. is parenthetical and refers . to Empedocles alone, (3) the words Kat 'EP.7I'(OOKA£ov~ ... CPT/(J'tV indicate that the doctrines of Empedodes, Anaximander, and Democritus should, like that of Anaxagoras, be amended by the admission that the material principle in its elemental state is only potentially existent. For the phrase Kat W~ dT/P.&KPtT&~ CPT/CTtV he compares A. 1071 b 26, De Gen. eI Corr. 3298 13, b I, and for the order of the words {11..hwv ya.p ~ &p.ov 71'clv-ra . . . ~v &p.ov 71'clv-ra 8vvap.(t lv£py(lf/ 8' oil he compares De AlI. 435" 5 810 Kat 71'~Pt aVaKAclCT(W~, {1I.ATWV ~ T~V l$tf!tV l~WVCTav avaKAiiu(Jat, TOV Ul.pa 71'4uX€tv {'7I'0 'TOV CTx~p.aTO~ Kat xpwp.aTo~ , 1". P.(Xpt 71'(P ov"'''av n~ 11' The first and the third point of Jackson's interpretation seem to be right, but in two respects a view different from his seems preferable. ( I) TO 'Ava~ay&pov EV can be defended. It is true that TO EV does not seem to have been used by Anaxagoras as a technical name for his material principle. But that principle is called a p.i.yp.a (Phys. 1878 23, d. 1012",28), and TO p.i.yp.a. ~v {1o~A(Tat (lvat (De Sensu 447 b 10), so that TO EV is not an inappropriate name for it, and in Phys. I 87 B 2 I it is actually called EV. It is true that in contrast with I'O~ it may be opposed to' the one', but in contrast with the various substances that come out of it it is properly called one. (2) It is not necessary to take 'Ep.7I'€8oKA'OV~TO p.i.yp.a. Kat' Ava~tp.a.v8pov in the awkward way in which Jackson takes it. It has commonly been thought necessary to apologize for, or explain away, the description of Anaximander's a7l'upov as a p.i:yp.a. Thus Zeller supposes that it is by an • easy zeugma' that p.i.yp.a., which is strictly applicable to Empedodes, is applied to Anaximander (i. G 279 n. I), and Prof. Burnet at one time (E. G. P.2 59) regarded Kat 'Ep.7I'(8oKAl.ov~ TO p.i.yp.a as an

COMMENTARY afterthought and held that 'AII~,p.&.1I8pov depended on Tb ~ (he now, ed. 3, p. 56, takes 'AIla.e,p.4118pov to depend on Tb p.'L-yp.a.). Zeller has little difficulty in refuting (i.1 277-283} Ritter's view that Anaximander's lJ.7r€r.pOIl was a mechanical compound in which the elements were actually present, and he therefore thinks it can only loosely be called a p.i:yp.a.. But the fact is that in Aristotle's terminology the word p.'''Ip.G. (a complete fusion) is more appropriate to Anaximander's lJ.7r€r.pD1I in which the elements were only potentially present than to the original matter of Empedocles and Anaxagoras in which they were actually present. The latter is a mechanical uVII8uoII rather than a genuine p.'''Ip.a.. It is true that Aristotle nowhere else calls Anaximander's lJ.7rftPOII a Jii"lp.a.. But then he mentions Anaximander by name only five times; and further he may have avoided the expression elsewhere because Anaximander himself had not used it, while he uses it of Empedocles probably because Empedocles used it himself, in a natural though non-Aristotelian sense. 115. Bz.'s conjectural insertion of lnpa. appears not to be necessary. Schwegler's parallels for d,ll' lTlpa.lI, A. 991b 10, H. 1044· 30, I. 1058b 15, are not sound, but the use of IDo for ruo IDov in 10711\ 28 seems to be a good parallel. 116. cln' 01'1 yE"lnrll 4).U 'll"oeill 7roC, i.e. not the matter presupposed by generation but that presupposed by spatial motion, the • local matter' of H. 1042b 6. 116-118. cl'll'Op~CI'EU S' 411 ••• 311 refers to lIC p.~ OllTO~ I. 20, the historical discussion being parenthetical. 117. TpLXiiit yAp,.a ,..~ 311. The three senses are given in N. 1089a 26 (in a similar context): (I) TO ICa.T4 T4~ 7rTWUEti (the categories), i.e. that which is not a man, that which is not white, Bec. (2) TO Wi "'Ev8oi, i.e. false propositions. (3) TO ICaT4 8UIla.P.LII, i.e. that which is not a man but is potentially a man, Bec. The same list is found in@>. 1°51.34. Aristotle answers explicitly in N, as he does implicitly here (d 8~ T' IUTL 8wa.p.(t, I. 281 that it is from the third kind of not-being that generation proceeds. Alexander gives a similar account of the three senses, except that for the first he substitutes TO p.f/8a.p.fj P.f/8aP.Wi Oil, that which ill no sense is. He is here doubtless following the suggestion ofK. 1067 b 2530, but inaccurately, for we have there (I) TO ICa.T4 a"W8€ULII V8uzlpEUtll ~-) ( ' ICaTa.'~'" a7rAlIli .\...OllTt a.lITtIC€tP.EIIOII , , (TO, Wi ", 't"EVOO~, 2 )TO owa.p.tII, ( a }TO' T'I' (Tb d7rAWi p.~ ,-68E), (b) Tb p.~ A(1IIColI V p.~ d"la8oll. K, however, does not offer a list of three senses of not-being so definitely as does N, nor is the context so similar to the present passage, so that N is doubtless to be followed here. 118. It ~ TL lCI'TL SUIIA,..n, 4).).' 311-"" oil TOU TUXcSIITO!, • if a thing exists by virtue of a potentiality, still it is not by virtue of a potentiality for anything and everything '. IIg. IIfIoOu 'II'AIITa. and 31. II ••• IIOU! show that Aristotle is thinking primarily of Anaxagoras, but his remarks apply also to the other thinkers mentioned in II. 21, 22. 311. luillo, i. e. lIC€'"0 P.OllOll.

.

.

.

353 o~ is explicable in the same way as TaU TVXOVTO~, I. 28, so that Schwegler's conjecture 0 is unnecessary. 32-34. TP£/I S~ ..• '»'1J. For this list of the implications of change cf. Phys. i. 6, 7. In view of the stress laid on fTTiP1Jut<; A stands closer to the P/v'SICS than to Z, which works for the most part with the simple opposition of 1)A71 and (1Bo<;.

Generalion considered. Individual, ills 106g b 35.

1/form

el'er eXlsls apart from the concrtie

In the case of natural objects (ch. 3).

Neither proximate matter nor proximate form is generated. For in all change something (matter) is changed by something (proximate mover) into something (form). If not only the bronze came to be round but also the round or the bronze came to be, this would involve an infinite regress. 10701' 4. Every substance comes from another of the same kind, (A) by art (where the principle of becoming is in something else). (B) by nature (where the principle of becoming is in the thing itself), (C) by luck (which means the absence of art), or (D) by spontaneity (which means the absence of natural process). g. There are three kindg of substance(A) matter, which is apparml/y an individual something but coheres merely by contact, not organically, (B) the individual nature and positive state of a thing, (C) the resulting individual. 13. In the case of the products of art, the individual form does not exist apart from the concrete result, except in so far as the arl is the form; nor do the forms of such things come into being or pass out of being; if the form ever exists apart, it is in the case of natural objects. Plato was not far wrong when he said that there are Forms of natural objects, if there are Forms distinct from sensible things. * Such as fire, flesh, head, which form a series of materials progressively approaching the complete substance * (these words should probably be transferred to I. II). 21. Motive causes precede, formal causes are simultaneous with, the thing they produce. It is a further question whether the form ever survives the thing. E.g. the reasonable part of the soul may survive the body. 26. So far, there is no need for Ideas. The individual produces the individual of the same class, and each specific art is the cause of its specific result.

354

COMMENT ARY

106gh as. "En TUUTU 3T', 'next we must observe that '. This phrase (repeated 1070& 4) is one of the clearest indications of the fact, apparent throughout chs. 1-5. that Aristotle is jotting down notes for a treatise (or lecture), not writing a treatise in its finished form; cf. 1071& 2 n. Alexander remarks on the 'confused and disordered' form of the book (673.34). a6. Uy", 8~ Ta. eoxuTu. Alexander takes Aristotle to mean the ultimate matter, that which is farthest from the individual 'YtyvOP.(JIOII, and the proximate form, that which is nearest to it (. Socrates' as opposed to 'flesh '). But it is impossible that luXaT'O'l should have opposite meanings in the two cases. If the lUX4rq uA:q is dllEl8E~ uA:q the lUXaTOil E~ should be diiAOII E~, and this is what ,.a lUXaTa means in Meteoy. 3go& 5. The instances Aristotle gives, however, are roundness and bronze (1070&3), which are instances of the proximate matter and form, those immediately involved in the 'YillEUt,", and it is of these that in Z. 8 Aristotle has shown that they are not generated «(033& 29), i. e. are not generated in the process of generating the bronze sphere. The bronze has been generated by previous processes, but that is beside the question. In saying MyliJ Ilt T4 luxaTa Aristotle does not mean that ultimate matter and form are generated, but merely that he is not speaking of them. For luXaTo," in the sense of ' proximate' cf. Bz. Indu: 2891' 55-2go &2. Cf. also TEA(1JTala uA." 1070& 20. 1070& I. 'II'pWTou also must mean' immediate' or • proximate '. For this sense of'll'pOrroll '''voVv d. Phys. 24311 3, 14, 245& 8, 25, b I. It is awkward that while (UXaTOII means • last, counting from the original state of things', 71'pidroll means • first, counting from the 'YLyvOP.EVOII', but Aristotle is indifferent to such inconsistencies. 4. "ETa. TUUTU 3TL, cf. 106g b 35 n. iKclcrnJ lK crUI'foIII.s"OU Y£Y"ETUL o4cr£u. lIC here refers not to origin but to agency. It is the agent of production, not the material, that is UVII6JIIVP.Oll with the product. 5. Ta. ya., +.scrE' O~cr£UL KUt Ta. 4)')'u, a note to show that substance is being taken to include not only natural substances such as the word primarily suggests (cf. b.. 1017bI0,Z. I028 b g, H. 1042&7 bp.oAoyovp.EVat P.tll at r/lvutICal), but also products of art, chance, or spontaneity. 6-g. Aristotle holds that, in natural and artistic production alike, A produces an actual B out of a potential B by virtue of the fact that A has the form of B in it. The male parent produces the offspring out of the matter contributed by the female parent, by impressing on the matter the form which is the form alike of the male parent and of the offspring. The artist produces the work of art out of tIie raw material by impressing on the latter the form of the product, which he • has' by virtue of knowing the art in question. The difference is that in the first case the producer • has' the form in the same sense in which the offspring will have it, and is therefore cal1~d by the same name, while in the second case the producer • has' the form only in the sense of knowing it, and is therefore not caIled by the same name. Thus a house is not produced by a house but by the ' form of house' in the

355

builder's mind, and is therefore not produced strictly lK CTVVWVV/LOV (or le b/LwwP-Ov, used loosely in Z. 10341\ 22 in the sense of lK CTVVWvV/LOV) but IK /Llpov,> bp.wvV/Lov, from a part of itself which shares its name (Z. 1034& 23). The difference stated in I. 7 between art as an d.pX~ K'II1/ lv .tUft' and nature as an d.pxTI (V aw;e is Aristotle's usual distinction between them. It is appropriate to most natural processes, where a living being produces changes in itself, but is not appropriate to generation, where the change produced is (V c1llft'. The definition of nature really breaks down in the case of generation, but Aristotle would presumably seek to justify it by saying that in some sense the parent and the offspring, being members of the same species, are the same, or that in some sense the offspring is a part of the parent (cf. E. N. II 34 b II, I I6 I b 18). 8. ilv8pw1I'os yap ilv8pw1I'ov YEVV'. This is, as we have seen, not a good illustration of nature as an d.pX~ £V aflTC~, and Alexander supposes that these words go with (K&'CTT7J (K CTVVWvV/LOV y{yvera, oliu{a (I. 5). But if placed after these words they would break very awkwardly the connexion between these words and Ta yap cpvun oliuuu Ka~ Ta llio.. It seems better to suppose (I) that Aristotle wrote them carelessly as an illustration of the d.pxTI €v awlj), or (2) that a copyist borrowed them from I. 27 below. The fact that the words already existed in their present place in the time of Alexander (cr. Alexander apud Averroem 82. 3) makes one hesitate to adopt this otherwise attractive supposition. ~ "Q'TLClL , (,sc. TVX7J , , ) CTnp"CTE'S J. ' Ql SI!' 1\0'1I'Q' Ka'" TaVTop.aTov TOUTWV. Taw6p.aTov is strictly the generic term, including all cases in which (I) something that is normally produced directly by the unconscious teleology of nature is produced as a merely incidental result of a natural process, or (2) something that is normally produced directly by purposive human agency (here rather narrowly described as TlX.V7J) is produced as a merely incidental result of a purposive act (Phys. 197 b 18, &36); while TVX7J is confined to the second type of case (Phys. 197& 36, b 2, 20). Sometimes, however, TVX7J and Taw6/LaTOV are used without distinction ill the general sense, and sometimes (as here) Taw6/LaTov tends to be confined to the first type of case, TVX7J being the CTT(P7JCTL<; T(XV7J'> and Taw6p.aTov the CTTlP7Ju,,> cpvu~w'>. Aristotle has said that all substances are produced (K CTVVWW/LOV, and that some are produced by TVX7J or Taw6p.aTov. But he does not mean that these are produced (K CTVVWW/LOV; spontaneously produced animals are produced OliK d.1TO CT1I"fY~V;;li' (H. A. 539& 22), and in chance events the art which is ' synonymous' with its product is lacking. He views chance and spontaneity, which are the negations of art and nature, as the exceptions that prove the rule'. The words' chance' and 'spontaneity', being meant merely to indicate the absence, in certain cases, of artistic or natural action, indicate that such action, with the' synonymity' which it implies, is the normal thing. 9. oUCTLa, Sf TpEi,. rf. 7.. 1C29a 2.

CO;\YJ\TENT ARY 10. TOSE TL O~CI'U T~ +ULVEaeUL. None of the attempts at emending this phrase seems at all successful. It is possible to make something of it as it stands. Ps.-Alexander interprets Tqi c/Ju{vEu(Jat as KaTtt .puvTuu{av, and Bz. follows him in supposing that the meaning is that matter is a 'this' to the eye of imagination, since it .has the power of becoming a 'this '. This interpretation of Tqi c/JalvEu(JUt, however, seems impossible, and it is better to adopt the simpler interpretation which, with others, is given by Alexander as quoted by Averroes, viz. 'which is a "this" in appearance '. 1. e. to outward appearance the material parts of a whole as they lie side by side look liKe an individual thing, but if the organic unity is not there the appearance is deceptive (Jua "YttP d#j Ka2 fL~ CTVfLc/Jvun, VAfJ Ku2 ~1f'OKElfLEVOV). Cf. Z. 1040b 5 TWV &KOV
ri Ku2.,n,p Ku2 d.~p.

It must be admitted, however, that this interpretation of o&--a Tqi c/JalvEu(Jat as = c/Jawo,uVYJ Elvat is not altogether satisfactory. 10. For Cl'UI'+IlCl'EL cf. Z. 1040b 15 n. II. The vulgate reading 'ri 8( c/JVUt~ TO& Tt d5 ~v Ku2 Ut5 Tt5 is intolerably harsh, and it seems best to read, as Alexander apparently did (676. 30), 'ri 8( c/JVUt5 To8E Tt (se. o&--a from I. 10) Ka2 t~t5 TL5 d~ ~v (se. 'ri "y£VEU{5 iUTW). For the description of the form all a ' this' cf. ~. J017 b2 5 n. 13. TO To8E TL, 'the individual character', i. e. the form, which has already been called To8E TI in I. I I. 14. Et I'~ 'iJ TiXVl), i. e. the form of the house has no existence separate from the house except as the art of house-building; cf. Z. 1034& 24 'ri "yap TfxVYJ TO E1805. 15. 0.,8' ECI'TL yiVECI'L' KUL +90pA TollTWV KT>'. Aristotle is not referring to the general fact that forms come into being not by a process but instantaneously (Z. 1033 b 5), but to some mode of 'being and not being without generation and destl'Uction' which is peculiar to the forms of arlifacta. This can only be the artist's instantaneously thinking of them and ceasing to think of them. So Alexander interprets the words. 17. Ii}.}.' EL1fEP, l1fL TWV +UCI'EL. This goes back in sense to (1f'2 fL€V o~v TtVWV KTA. (I. 13), ll. 15-17 being parenthetical. Aristotle cloes not think that the form of living things (Td c/Jvun), i. e. their soul, is in general capable of separate existence. Cf. Phys. 1931• 4, De A". 4°3" 16. It is only reason that can exist apart (De An. 4J3b 26, 430317, G. A. 737· 9, .E. S. II78" 22). Here he simply says that at any rate the forms of lifeless things eannol exist apart. 18. For Plato's limitation (though not in the dialogues) of the Ideas to natural objects cf. A. 99lh 6 n. It is noteworthy that the doctrine is ascribed to Plato himself and not merely to the' believers in Ideas '. But Alexander as recorded by Averroes read 01 T~ Er8YJ Tt(J'fLEIIOt Zc/Jacmv. and Themistius seems to have had the same reading (8. 13). 19. EL1fEP ECl'TLV E'l81J ct}.}.u TollTwv gives a good sense, 'if there are

A.

3.

107011. 10-21

357

Forms distinct from the things here on earth' (T<7W OEVPO Kat. alcr8vrwv Al.). Tawa does not seem to be used in this sense elsewhere by Aristot'e, but it is by Plato (Parm. 133 D 3, Phil. 58 E 5, 62 A 9). If we adopt this reading we must suppose with Alexander that olov ••• TEAElITala (ll. 19-20) is out of place, and is really a note to Jcm. • {)1rOKELILEVOV (II. 10-1 I). Bz:s interpretation, • if there are Forms other than these things, i. e. than fire,' &c. gives an unnatural sense. H we read d.AA' oll TOVrwV, we should have to interpret TOVrwV as referring forward and as explained by olov 1rVP crApe KE4>aA~. But (I) TOtlTWV olov in this sense is very unnatural, and (2) the denial of Forms of fire, flesh, or head does not agree with what we know of Plato's theory. olov ••• TEAEVTaLa would come in much more naturally in I. II, and it must be remembered that the first five chapters of A present, more perhaps than any other part of the Melapltysia, the appearance of a rather hastily put together series of notes, in which misplacements are likely to have occurred. Cf. note on 1069 b 35. 19-20. Fire, being a a1rAOVV crwILa, is the sort of material out of which flesh, a oILOtOILEpir;, is made. Flesh is the sort of material out of which the head, an d.voILOtOILEpi<;, is made. The head is the sort of material out of which a living body, which is a substance in the full sense, is made. cr. C. A. 715"9-11, Z. 1040b 5-10. 21-26. This passage has been used by Brentano as one of the main arguments for his view that the human reason, though imperishable, is not pre-existent from eternity, but is created by God at some point in the development of the embryo. This view is opposed not only to the explicit statement that reason is eternal (De An. 430" 23), but to the principle that what cannot perish cannot have been generated (De Cae/o 282 a 31, 283"29, b 19). Aristotle's assertion that the formal cause is simultaneous with its effect (1. 22) implies, no doubt, that it not only is when its effect is, but comes into being when its effect comes into being (An. Posi. 95& 22). But that of which Aristotle says that it may persist after the effect (the living body) has perished (11. 2426) is not the same thing which is described as coming into being when the living body does. The soul as a whole comes into being with the body and (I. 26) perishes with it; but something (n I. 24), i. e. some element of the soul, may persist, viz. the reason, or more definitely the VOVr; 1rOLfJTLKor; (De An. 430& 17); and this Aristotle certainly conceives as existing before birth no less than after death. The soul is both generated and perishable, but there is TL Tijr; I/roxijr; whkh is neither. The reference to the eternity of reason is parenthetical; the main point of the passage is to set aside the Platonic notion (cf. 1. 18) that Forms exist apart from and independently of the things whose Forms they are. Rather, they exist only when the concrete things do so, and only as elements in them. Further (II. 26-30), separate Forms are not necessary in order to explain generation i in natural production the cause is an individual parent, in artistic production it is the art, which must be plesenl in the mind of an individual arli~t.

COMMENTARY For the uselessness of the Forms in explaining generation cr. z. I033b 26. , EIf '" ~ • ( SC. atTLa ." ) 'illS ,..pOyEyEV'I ....I. I'll OVTII. • 21. T ...... OUIf KLVOUVTIIIILTLII faTLY

In what sense all things have the same cattses (chs. 4, 5).

1070& 31. (A) The causes of different things are different, but (B) analogically all are the same. 35. (A) (I) What could be the common cause of relations and substances? There is nothing common to the several categories and prior to them; nor can substance be an element in relations, nor vIce versa. b4. (2) No element can be the same as the complex whichinc1udes it (nor, therefore, can any of the intelligibles such as being or unity be the common element, for these are predicable of concrete things). Therefore no element is either substance or relation; but there is nothing else it can be. 10. (B) But (I) all sensible bodies have a form (e. g. heat), a privation (e. g. cold), and a matter. All things have by analogy the same elements, in that they all have form, privation, and matter; but these are different in detail for each different class of things. 22. Besides the internal causes or elements there is an external moving cause. There are three clements but four causes. The immediate moving cause, like the other immediate causes, is different for each different thing. 30. In nature the moving cause is a similar individual, and in art it is the form (or its contrary), so that as the efficient cause = the formal, we may say either that there are three or that there are four causes. Besides these there is the first mover, which is common to all things. 36. (2) Things which can exist apart are substances; the causes of all things are the same because affections and movements cannot exist without substances. These causes are, perhaps, soul and body (or l'eason, desire, and body). 1071& 3. (3) In another sense all things have the same principles analogically-viz. potentiality and actuality-though these are different in different cases, and apply in different ways. 6. They apply in different ways; for (a) in some cases the same thing is at one time actual, at another potential. This distinction can be brought into line with the previously named causes; the

359 form (if it is separable) and that which includes both elements but is a privation exist actually, the matter potentially. II. (b) The distinction of potentiality and actuality takes a different shape where cause and effect have not the same matter (the form also in some cases being different). The causes of a man are not only (as in (a» (0 his matter (fire and earth) and his peculiar form, but also (ii) his peculiar external cause (his father), and (iii) the sun and the ecliptic, which are neither the matter of the man nor his form nor the privation of his form nor identical in form with him, but the efficient causes. 17. Some causes can be stated universally, others cannot. The primary causes are the individual moving cause and the matter. The universals do not exist. Man is the cause of man, but there is no universal man. It is Achilles that exists, and his cause is Peleus. :a4. If the causes of substances are causes of all things, yet things in different kinds have different causes, which are only analogically the same; and things in the same kind have causes the same in kind but numerically different. :ag. The causes of things in different categories are the same or analogous (i. e. they are always matter, form, privation, mover); and the causes of substances are the causes of all things in the sense that with their destruction all things are destroyed. Further, the primum »lo'vms is the same for all things. But there are as many different causes as there are pairs of individual contraries, and the matters of different things are also different. I070b a. Ti;w 1fPOS TL. The category of relation, which is that farthest removed from substance (N. lo88 a 23), is here taken as typical of all the categories other than substance. Substance cannot be the elementary constituent of relations, !iince what consists of substances must itself be substance. Nor can a relation be the elementary constituent of a substance, since substance is prior to the other categories and elements are prior Lo their compounds (I. 2); cr. Z. I038b 23· 7-8. o~S~ ... auv9lTWv is clearly parenthetical, for atJTwv I. 9 refers not to TWV VOf/TWV nor to TWV (TlJV8ETWV but to TWV CTTOlXElwv, I. 6. The meaning must be 'nor is any of the intelligibles, therefore, e. g. unity or being, an element in things; for these terms are predicable even of each of the composite things' (and therefore cannot be their elements, on the principle stated in II. 5, 6). The use of the partitive genitive as subject (TWV vOfJTwv = TWV VOfJTWV n) is rare, but cr. I. 22, ~. I021 a 21 n.

CO:\Il\IENTARY For a similar argument, showing that unity and being cannot be the genera of things, cf. B. 9981> 22. Unity and being are called' intelligibles' in distinction from' sensibles', because they are the most universal predicates, those farthest removed from sense-particulars (cf. B. 998b 15-21). 10. .:lcnrep )'lyol'el', cf. a 31. I!a. ,.a 8ul'dl'e, TUUTU 'll'pml' KUe' u61'6, I that which directly, in virtue of itself (and not of a concomitant), potentially has these attributes '. 7f'pGrrov distinguishes the proximate matter from the remote, and ICU' uwo distinguishes the matter, which as such becomes, for example, cold, from 'the white', which becomes cold in virtue of the matter whose concomitant it is. la-IS. Aristotle distinguishes here three kinds of substance: (I) TUVTCI, i.e. matter, form, privation. (2) ,.a ,I( TOVn..V, i. e. substances which include (a) prime matter, (5) a certain form, e. g. heat, and which presuppose, as that which Ihey had before they had the form, (c) the privation of the form, e. g. cold. T4 II( TOWillI' are in fact the four elements, two of which Aristotle supposes to be characterized by heat and two by cold. (3) e% T& II( 6epp.ov I(ul tfroxpov ylYVeTCI& lv, olav CT4pt ~ dO'Tow, i. e. compounds of two oppositely qualified substances of class (2); in other words, binary compounds of the elements, or op.owJUp1J. Aristotle might have gone on to add the dvop.owlL€p1J and the living bodies which they make up (cf. a 19-20 n.). But since these are ultimately formed from the elements, they come under the general description el T& II( 6epp.ov I(ul tfroxpov (Aristotle take!> two of the 7f'pOJTU& lVClVT&tdCTe&S as typical of all four) ylYVeTCI& lv. Aristotle's doctrine has been explained above as not implying that privation must be actually present as well as form in every concrete substance, that every body which is hot must be partially cold; I have supposed him to mean that the form of each thing presupposes a previous privation. It is in this sense that matter, form, and privation are arrived at as the three d.pxJ in P~s. i. 6, ,. and it is this sense that is relevant in 1069b 32-34. But it is rather surprising to find privation which is merely presupposed as previously existing, described as lvvtr;.pxov (I. 22); it is rather'll'poV7f';.pXov. It may be, therefore, that Aristotle has in mind his doctrine that no actual instance of any of the four elements is pure. Fire, though in the main characterized by the ,tBOS heat, contains some of the fTTlpqCT&s cold, and so in other cases (De Gen. eleo". 330b 21, Meleor. 359b 32). Then ,l T& ll( 6'PlLov I(ul tfroXfJOv ylYVeTu& lv will refer to Ap.oUJIL'p1J compounded out of a substance that is in the main hot (e.g. actual fire) and one that is in the main cold (e. g. actual water). But on the whole the former interpretation of the passage seems preferable. 15-16. ITepol' ... yevcSl'tI'ov. Alexander thinks these words should be placed after 'If'pOs TL, \. 9. But they may stand in their present position. They are meant to justify the assumption just made (\. 13 olxrla,8£ "'ClVT~ n I(UL TIL II( TOVTWV), that compounds must be different from

their elements, or the assumption that a compound of hot and cold must be different from what is merely hot or merely cold. 16-18. Bz. prefers the reading TauTa in I. 16 on the ground that TOIJTWV Tawa, lliwv cL\Aa, 1TaVTwv T~ tlvaAoyov Tawa gives the most symmetrical form to the statement. But where does he get the Tawa which he supplies with T~ tlvaAoyov? It presupposes Tawa in I. 16. The meaning is: 'these things, then (sc. sensible substances), have the same elements and principles-sc. heat, cold, matter (though specifically different things have specifically different elements); but we cannot say that all things (i. e. non-sensible substances and things in other categories, as well as sensible substances) have the same elements in this sense, but only by virtue of an analogy'; the elements of all are form, privation, matter, which are analogically the same wherever they occur. ~~. For the construction of Te", lKTlls olov Tll KLVOUV cr. I. 7,11. 1021 a 21

n.

~3. ITl!pov clpx~ Kal C7T0LX~LOV,

d. 11. 1013 a 4,7, 1014 a 26. ~4. KaL ELS TauTa SLaLp~LTaL ~ clpXti is in EJI' repeated in I. 29, and

Christ brackets it here. But it is better to follow the authority of A b AI. and omit it in 1. 29. Here it makes quite good senseI principles are divided into two kinds, the (VU1I'apxov and the flCT6,,'; cf. 11. 1013a 4, 7. ~6. This list of four causes differs from Aristotle's ordinary list by the subdivision of form into form and privation (cf. Z. 1032b 2, Ph)'s. 193 b 19), and by the omission of the final cause (due doubtless to its identity with the formal cause, H. 1044 b I). Aristotle here identifies the proximate efficient cause with the formal (II. 30-32, cf. Phys. 198" 26), but distinguishes the uttilllate efficient cause from it (1. 34). ~7. Tll 1fPWTOV aLTLOV WS KLVOUV, the proximate moving cause. Bz. thinks this difficult in view of I. 34, where TO W" 1TpidrOV 1TaVTWV KWOUV 1I'aVTa means the utltillate moving cause; he therefore here proposes 1I'ou7T1K6v for 1TpWTOV. But Aristotle is careless in matters of this sort (cf... 1 n.), and further TO W" 1TpidrOV 1fUVTIIIV KWOUV 1fC£VTU is different enough from TO 1TPWTOV aiTtov w<; KLVOUV to remove any misumlerstanding. ~9-30. KaL ••• clpxti, cr. I. 24 n. 30. lv I'~v TOLS +UO'LKOLS clv8p~1f't' QV8plal1fOS. In view of Aristotle's frequent formula I1.vJpw1To<; I1.V()pW1TOV y~vvfj., and of the awkwardness of CPVrTLKOIS tlV()pW1TOL" if the two words do not go together, I have adopted Zeller's emendation. The corruption is evidently due to the influence of CPVrTLKO'i". 3~. Tp(a aLTLa S.v eL'I, i. e. matter, form, privation. 34. Bz.'s conjecture, Tll Wi for w<; T6, is required by the sense. The first moving cause, to which Aristotle comes only now, is to be the subject of the second half of the book, to which chs. 1-5 are preliminary. 1071" I. Christ's Ta~TC£ is preferable to the traditional Tai.,.«, since TUVTU in I. 2, which refers back to this word, must mean not 'subAa

COMMENTARY stances' but 'the causes of substances '. It is not substances but their causes that Aristotle views as the causes of aU things; cf. l. 34. Because all other things are dependent on substance, the causes of all things are the same, viz. the causes of substance. TWV ollenwv Ivcu. This is apparently the only passage in Aristotle in which dvt:v comes after the word it governs, that word not being a relative. The order is characteristic of later writers, and would in itself suggest a late date for A. "3. '1fCLTG ••• ",cfLI KGl crW"G. Aristotle concentrates his attention on living things, which are in the strict sense the only substances (Z. 1040b 5-10, H. 1043b 21-23), and indicates their material and formal causes, (I) uWp4 and (:I) I/tvx~ (subdivided, in the special case of man, into vo~ Kcd IJpt:e,r). Alexander seems to have read ~ lJpe:e,r Kat uOJp4 (the elements of irrational animals) arter ~ voVr Kal lJpt:e,r Kat uOJp4, and it is not unlikely that these words have dropped out by haplography. But it may be that this is an addition of Alexander's own. sa. '1ft:LTG comes in peculiarly here. Probably, like p.ero. TaVTa (1069 b 35 n., 1070.4) it means' next we shall point out that' &tc., and indicates the hypomnematic character of the first half of A. Cf. I. 24. lerren. If it be accepted that the causes of substances are the causes of all things, we shall perhaps find these universal causes to be soul and body, &tc. This seems to be the meaning of the future ZUTat. 3-17. Aristotle has in ch. 4 shown that matter, form, and privation are principles present in all things j he now proceeds to show that potency and actuality are present in all things. Not only, however, are the potency and the actuality of one thing different from those of another (cLUa cIllo,r, J. 5), but potency and actuality belong to things in different ways (Ka2 ciMlIIr, sc. lJ7T4pXt:L). Lines 6-17 explain what Aristotle means by ruwr. In some cases (0. lllunr plv, L 6) the antithesis of potency and actuality means that the same thing exists first potentially and then actually. But the distinction of potentiality and actuality is present in another way (cLUCdr 8l, l. II) where one thing acts on another. I take the two modes of presence of potency and actuality to answer to the two senses of potency distinguished in 0. The kind that is mentioned second here is 8wap.,r in the sense of , power', that which is p.erapoA~r 0. cLU'l' ~ .g cillo (1046& II), .q KaTo. K{IITJCT'" Aeyop.l1l7J (10488 25). 8wap.tr in this sense is the power in one thing to produce a change in another thing, and lvlpyt:l.a is the change produced. The kind of 8-Jvap.tr that is mentioned first here is 8Vvap.tr in the sense of potentiality which is followed by the corresponding actuality in the same individual (,.0 GtlTO 6T~ ~ lve:pyt:u,. IUT'" cW~ 8~ 8Vv4P.t:'; contrast lv~, 1046& II). lvlpyt:ta and 8v..ap.tr in this sense are opposed c:..r o~la 7TpOr Twa vA'Iv; in the other sense they are opposed Cdr K{lITJCTlr 7TpOr 8wap.w (1048b 8). 7. olol' otllOl, i.e. the same matter is at one time potentially wine and later actually wine. 1f£1fTCL 8~ KGl TGUTG cll TU t:l''I"ivG GtTLG, s,·. form, privation, matter

d."m

II). ."t7rTn El~, 'are divisible among'; for the phrase cf. r. 1005& 2, ~. 1013 b 17, Phys. 195& IS, 243 b 16, P. A. 675& 25. 9. lav X"'pLCM'6v. On the separate existence of the form in certain cases cf. 1070& 13-19. TO (~ &".+OLV, 'that which contains both form and matter '. The mention of the concrete individual is not really relevant, since it was not one of the causes recognized in I070b IT-13. The mention of it is due to Aristotle's habitual distinction of three senses of' substance'-matter, form, and the complex of the two. CM'ip'IaLS TE (vulg. 8£) olov aK6TOS ~ Kci".vov. The traditional reading is open to three objections: (I) If privation is being brought under the heading of actuality (as it must, since 8vvap,EL comes only in the next clause), the clause should be introduced not by O'T(P'l'JCTL" 8( but by KaL ~ CTTEP'l'JCTL". (2) The adducing of inbtances, darkness and disease, is peculiar, when form, concrete substance, and matter are left unillustrated. (3) Kap,vov is an instance not of privation but of the union of privation with matter; the privation in question is VOCTO" (cf. 10701• 28). Themistius apparently did not read O'TEp'l'JCTL" U, and Christ condemns the whole clause. But the manuscripts and Alexander agree in having it, and some mention of privation is wanted in order to account for ap,cpw in I. I I. I have endeavoured to remove the first objection by reading T£ for 8E. TE in this usage is rare in Aristotle, but cf. r. 1004 b lof, E. N. I 158b 10, 13. For confusion of TE and 8( in manuscripts cf. for instance E.N. I 153b 7. The second objection is not very important, and as regards the third, the confusion is one which Aristotle makes elsewhere. The adjective or participle in the neuter with the definite article may always stand for an attribute as well as for a concrete thing. Cf. TO p,tv 8EPP,OV KaTTrtOpta n .. Kat ElOo~, ~ 8£ ",v)('poT'l'J" O'T(P'l'JCTL~ De Gm. eI Corr. 3181> 16. Or, in the highly abbreviated mode of expression which is used in chs. 1-5, KaL TO if ap.cpo'iv (ilA'l'J" ' ) • .~ • ,j, "') KaL, O'TEp'l'JCTEW" , answermg to TO, E~ ap,,,,oLv (~\ V"'l'J" KaL' .ELOOV" , may be meant to he supplied in thought. CTKOTO" is an in~tance of CTT(P'l'JCTL", Kap,vov of TO (~ ap,cpo'iv. II. 'qualified by the form and by the privation', cf. 1070b 12, 13. It is implied that the privation no less than the form is a mode of realization of the matter, so that Alexander is wrong in supposing that Aristotle reckons privation to the side of potentialilY (682. 34). Privation is in fact a kind of form (Phys. 193 b 19). Bz. accepts Trendelenburg's emendation aUw~ 8' (~) €VEP'YE~ Kal 8vvap,EL 8Lacp(pEL ~v. But this ignores the evident correspondence between lliw" here and aUw~ in I. 6, and the opposition between lliw" 8' here and (V (ViOL" P,EV in I. 6. Aristotle has said that the distinction of 8vvap,L~ and (V(P'YELa belongs to different things in different ways. He has stated one way in II. 6-1 I; he now has to state the other. • The distinction in vii tue of actuality and potency is present in another sense in things which', &c. 1~-13. cr.v .. • U}.'h cr.v ... lTlpo~. It is to be noted that the negative in

(IOjOb

n

&""""

COMMENT ARY the first clause is p.~, in the second ollK. The two clauses are therefore not of the same nature. The first gives the essc!ntial nature of a certain class; the second states an additional fact about it; ollK in fact shows that the second wv might be replaced by Ka~ TOVrWV. This prevents us from interpreting the two clauses as meaning 'things which have neither the same matter nor the same form' (Alexander, Trendelenburg), or 'things which have not the same form differ from things which have not the same matter' (Bz.). The meaning of these clauses may be ascertained by observing what Aristotle goes on to say. He proceeds to distinguish the following causes of a man: (I) the elements present in him, i. e. (a) fire and earth, the matter of which he is made, and (6) his peculiar form, (2) an external (proximate efficient) cause, his father, (3) an external (remote efficient) cause (the sun and the ecliptic) 'which is neither (I a) matter nor (16) form (nor privation, which is included in form above), nor (2) of the same species as the product '. Aristotle has shown above (I. 6) that the existence iVfpyf~of a thing may be contrasted with its own previous existence SwaP.€t. He seems to be now saying (though the expression is very Obscure) that Svvap.ts and lvipyna may be applied to different individual things, in the sense that one has the power to produce the other, i. e. Svvap.ts may be applied to the father and to the sun, ivipyf.to. to the child which together they produce. Now both the father and the sun have a different matter from the child, and the sun has also a different form (ovn bP.OftSis, 1. 16). In view of the whole context, it seems that we must insert iVLwV after the second wv, and translate as follows: 'The distinction in respect of potency and actuality is present in a different sense in the case of causes which have not the same matter as their effects, some of them indeed not having the same form either '. If we emphasize LSLOV €l&s (I. 14) we may say that even the father has a different (ind;vidual) form from the child, and then lv{wv will be unnecessary. But the distinction between the relation of the father, and that of the sun, to the child, is emphasized, and is expressed by saying that the latter, unlike the former, is not bp.o€w£s with the child, so that TO awo €lSos probably means the same specific form or kind (as in I. 27). and this would involve lv{wv. The addition of this word does a good deal to diminish the harshness of the two juxtaposed wv clauses. In view of the similarity to TJ of one of the abbreviations of iv in manuscripts (Bast 762) vATJWVWLWV would not unnaturally become vATJWV by haplography. There is no great probability in Christ's conjecture that wrrrrcp ••• K&voma (ll. 13-17) should be placed after 7/'aJf1'o. in I07 0b 35. ~ ••• (T€poV would then be as difficult as ever. 14. The UTOLXfia (or (VV7Tc&PX0Jf1'o.) are evidently being distinguished from the external causes (iTL TL llMo Uw). Form, then, is included

amollg the O"TOLXfiu, as in 10iOh II, 25. The comma usually printed after iJA"1 must therefore be removed. 15. II ~).~O\l Kul II )'0~1I\l KUK).O\l. Aristotle's meaning appears from De Gen. d Corr. 336& 31, where he says that it is not the primary movement (the diurnal apparent mO\'ement) of the sun that is the cause of generation and decay, but ~ KaTa TOV AO~OV KVKAOV. If the sun had but one movement, this might explain generation or decay, but net both. The inclination of the 'oblique circle' to the equator brings the sun nearer to us at one time (se. when he is in that part of the' oblique circle' which is north of the equator, i. e. in the summer), and removes him farther away at another (when he is south of the equator, i. e. in winter), and generation and decay take place accordingly (336b6, 17). Cf. 1072& 10-12. II ).o~O\l KUK).O\l. The expression is a frequent one for the ecliptic, otherwise called 0 1M P.EO"WV TWV ''e8lwv KVKAO~ (1073b 19). It seems to have been first called 0 EKAEt7ITtKO~ by Hipparchus about 150 B. c. The discovery of the obliquity of the zodiacal belt or of the ecliptic to the equator is probably due to Oenopides, an older contemporary of Philolaus (Eudemus as quoted by Theo Smyrnaeus, Dielso s I. 1 I. 17). In 1073 b 2p we learn that Eudoxu8, whom Aristotle follows, believed the sun to move not in the direction of the zodiacal belt but at an angle to it (KaTa TOV AfAO~WP.EVOV EV TcfJ 1I'AaTEt TWV ''e8lwv), but the obliquity referred to in the phrase AO~O~ KVKAO~ is that of the sun's !lupposed path not to the zodiacal belt but to the equator. 17. Ta. I'EV K(96).ou laTLv dWELV, ' some causes may be stated universally (se. the causes of certain types of product), while othert' cannot (seo those of particular products) '. The cause of man is man, but the cause of Achilles is Peleus (I. 21). I8-~o. Christ suggests with some probability that these two clauses shourd he transposed, and that 8E should be read for 8~ (so ALe). Then 8E would answer to p.Ev o~v, which otherwise must be taken as marking a transition to a new point, as in H. A. 60Sb 19, Pod. 1460& II. 18. TO lVEpyE£~ WPWTOV ToSl Kul &).).0 S SUVdl'EI, i. e. the individual actually existing efficient cause, and the potentially existing matter. Cf. dEL EK TOV 8wap.Et OVTO~ ylYVETat TO EVEpyElff tv ~'lrO EVEPYE~ OVTO~, 0 1049 b 24. TO lVEpyf£~ WPWTOV TOS£ seems to mean' the" this" which is first in actuality 't i. e. which is not only prior to the product but (in Aristotle's view) prior also to the potentially existent matter. For this view cf.0. 1049 b 24-25 n. 19. lKELVU ••• Ta. K(96).ou, the universal causes referred to in I. 17. EKfiva may also suggest' the famous universals of the Platonists'; cf. KUhner ii. I. 650. 13. For the non-existence (more properly the lack of independent existence) of universals cf. Z. 13. 16. ~4. The manuscript reading ('irEtTa E,[8"1 (or ~8"1) Ta TWV o~O"twv does not give a satisfactory sense. If f,[8"1 be kept, it is at least necessary to insert Ta before it, with Christ. In that case we may (I) understand,

COMMENTARY with Bz., bpav B~i from l. 17, so that the general sense would be 'that we may judge rightly whether all things have the same causes (cf.l. 29 T~ BE {1fTEiv ICTA.) we must attend to the different species of things as well as to the different individuals ',-for which v. II. 20-24. But the ellipse of bpav BEi after such an interval is difficult.· Or (2) we may with Alexander understand alTL4 EaTL, taking '1fELTCl leTA. to be opposed to 7r4VTWV ~ 1fpWTClL dpXa{, l. 18; but this also is not very satisfactory. The right solution seems to be provided hy Rolfes's reading d a~, though in other respects his interpretation is questionable. If d B~ be read, a comma instead of a colon must be read after ollenwv. Then the sense is: 'Further, if the causes of substances are (as Aristotle has shown in 1070b 36-1°71" 2) the causes of all things, yet different things have different causes and elements '. For Bl adversative in the apodosis of a conditional sentence cf. Phys. 2Isb IS, Pol. n87b 13, B. 999& 27 n. 25. r:\Cl1rEP lUXfw). 10'1 ob 1'1. TWV ,...~ lv TClllni yiVEL is contrasted with TWV EV Taw~ ElBEL I. 27, so that ylvoll and ~l8oll do not mean genus and species but are used indifferently for' kind'. For the promiscuous use of the two words er. Bz. Index 151& 57-b 56, and I. 1058b 28 n. lIS. For &>'>'0 where cLUov cLUo might be expected cf. 1069 b 25 lTIpav

=

lTEpa IT£pav.

29. Ta ••. t'lTELv is a nominalivus pendens; the sentence does not end as it was meant to end. For a similar anacoluthon cf. Phys. 222b I I T~ BE "IALov cp4Vat 118v laAWK£Vat oll A£y0P.€V' 31. 1fO>'>'ClX&i!; yE >'Eyo,...il'C&lv 'CTTlI'lKdCTTOU, i.e. 7roUaxW!l y~ A£yOP.tvwV TWV OTOLXE{WV Taw4 EOTt TO. OTOtXEia lK4OTOV. So long as the names of the elements are used ambiguously, i. e. so long as we say 'matter, form, privation, mover' without specifying the particular matter, &c., we may say everything has the same elements. In view of the frequent confusion of yE and TE in manuscripts (cf. E. N. 1099& 22,1101& 8, I I 13 b 17, 1124& 9, 1178b 18, Pol. I29I& 17, 1339& 29, and Bast 710 )we need not hesitate to accept Christ's yE for TE. 33. eliSe, in the senses mentioned in ll. 33-36, i.e. (I) the causes are the same or analogous because matter, form, privation, and mover are causes of all things, (2) the causes of substances are causes of all things, (3) the first mover is the cause of all things. The sense requires TaWo. ~ TO dvdAoyov; cf. N. 1089 b 3 T~ allT~ Kal. T~ dvdAoyov. Tc(l dvdAoyov has come in from 1. 26. 33. ClTL 1Th'l' Etsos, CTTip'ICTLs, Ta KLVOUV, cf. 1070b 18, 22. 34. KCll elISl Td TWV OIlCTLWV ClLTtCl. Bz. thinks that we should perhaps read (In for flJBl, as Them. (13. 5) may have done. But flJBl is quite right, being explained by tiTt dVCUpEtTaL dvatpovp.£vwv. Themistius paraphrases the passage very briefly, and it cannot be said with any certainty that he read (lTL. Tc). TWV OIlCTLWV ClLTLCl ells GLTLCl1fdVT"'V, cf. 1070b 36-1071& 2. 35. ells ClITtCl 1faVT"'V. The superfluous ~ is difficult. Perhaps A£-

ymu is to be understood, in which case the phrase would be parallel to &ra A',),lTat ~ 8&xpva, Meleor. 388b 19, cf. Plzys. 200& 31, Meltor. 379b 26. m clv"tp~iTC" clv"lpou,..iv...v, • because when substances are removed all the other categories are removed'. 36-b I. ':'Sl Se ... 3~c". • But in the following respect there are different first causes, i. e. there are first causes as numerous as the contraries which are neither generic nor ambiguous terms; and further the matters are different for different things.' 'II'PWT" here means • proximate', while 'll'pWTOV earlier in the Hne meant • ultimate '. In using the word in the latter sense, Aristotle seems to have been reminded that it has also the former, and forthwith points this out. For the inconsistent use of 'll'pWTOi in a single context cf. 1070b 27, 35. H. 1044& 16, 18. Aristotle has just said (\. 34) that matter, form, privation, and moving cause are causes common to all things. He presently points out (b I) that nevertheless different things have different matters. Probably therefore in O(1'a Ta lvavna ••.• 'll'OA>..a.XW~ A'Y(Tat he is saying as in 1070b '9 that different things have different forms and different privations, the difference of the moving cause being omitted for the moment though it has been pointed out in 1070b 27, 1071& 28. 37. a ,..t\n ~, yi"" Uyn'''l ,..t\TI 'II'o~~"XW' ~iy~TGl. Aristotle indicates that he does not mean (I) contraries stated generically, e. g. white and black, which are the contraries involved in the whole genus of colour (107ob 20), nor (2) contraries stated still more widely, even ambiguously, i.e. form and privation, which are the contraries involved in all sensible things alike (1070b 17, 1071& 31-34). He must mean, then, the individual form and the individual privation which are different for each individual thing, cf. 11. 27-29. Kal ITt al ~>..a.t then will mean not that different kinds of thing have different kincls of matter but that different individual things have different individual matters (cf. a 28).

There musl be an eternal prime mover (ch. 6). I071b 3. We must now speak of the unchangeable substance which is distinct from the two natural substances. There must be an eternal substance, for if all substances are perishable, all things are perishable; but motion or time cannot be generable or perishable. For there cannot be a before or after where there is not time, and time is either = motion or an attribute of it, so that motion must be continuous as time is, and if so it must be local motion, and in a circle. 1111. That which is capable of moving things but does not actually do so will not account for motion. It is no use positing eternal substances (e. g. Forms) if we do not give them a principle of change. Nor will it do if the principle is active but its essence is potentiality,

:-lu8

CO:\J:\JF.~TA RY

for then motion wilInot be dernal. Therefore thert: must he a principle whose being is actuality. And these substances mu~t be without matter, for they must be eternal. Therefore they are actuality. SS. There is a difficulty. Everything actual has potentiality but.not e\'erything that is potential has actuality, so that potentiality seems prior. But if this were so, all that is might not be (i.e. not yet have been). s6. The same difficulty is involved if the world be generated from night or from 'all things together'. Matter cannot set itself in motion. Hence Leucippus and Plato say there is always motion-but do not specify it or its cause, or the cause of the motion's being of the particular kind it is. Nothing is moved at random; everYLhing has its own proper motion, and its motion under compulsion, etc. Further, what kind of motion is first? Further, Plato could not tell what he means by describing the self-moving as a first principle, for the soul is latercoeval with the heavens. It is in a sense right to take potentiality as prior to actuality, but in another sense wrong. Anaxagoras testifies that actuality is first; so do Empedocles and Leucippus. 107s· 7. Therefore chaos or night did not last an indefinite time. The same things existed always either in a cycle or in some other way, for actuality is prior to potentiality. If there is C)'C/it' change, something must remain always active in the saTlle way. If there is to be change at all, there must be something else whose acth'ity varies. This must act in one way per Sf, in another way hy virtue of something else, and this something else must be that which acts always in the same way. This is the cause of uniformity, the other the cause of variety, both together the cause of uniform variety,. Accordingly these are the movements that actually exist. What need, then, to seek other principles? 107lb 3. ~crAII, cr. 1069" 30. 5. AL TE yap O.)cr'A' 1rpWTa, TWII SIIT"'". Aristotle has tried La prort' this in 10691\ 19-26. 6-10. tlU,' 4SIlIIATOII ••• 1re£Soi. The argument is: If all substances are perishable, everything else is perishable (~iIlce everything else is posterior to and depends on substance). But movement and time are not perishable. Therefore not all substances are perishable. For the eternity of movement cf. PI!),s. viii. 1-3' 8. 0.) yAp ••• XpOIIOU. The argument is: If you say time comes into being, you imply that before that there was no time; but the very word 'before' implies time. But does not Aristotle's view that space is finite contain the same difficulty?

9. Having used the eternity of movement to prove that there must be an eternal substance, Aristotle now draws from it a further inference, that movement must be continuous, and from this he develops his whole astronomical theory. 10. f\ KLVYjaEW5 TL '11"4805, cf. Phys. 251b 28. In Phys. 219b I time is defined more precisely as d.ptOp.or; Ktvr/ KaTd TO 7rpOTEPOV Ka~ lJUTEPOV. It is further said to be d.ptOp.o,. ollX ~ d.ptOP.oVP.EV d.U' b d.ptOP.OVP.EVOS (nob 8), i. e. not abstract number, but the aspect in respect of which movement is numerable. 10-11. KCV1JaL5 S' ••• Kdd"tI. Aristotle's proof that local movement is the only change that can be continuous is given in Plzys. 261 a 3 I_b 26, and his proof that circular movement is the only one that can be continuous in 261 b 27-263" 3, 264& 7-265a 12. The reason for the first dictum is that all other changes are between opposites, and that, since a thing cannot have opposite movements at the same time, it must rest at the opposites which form the limits of its mo\!ement. The reason for the second dictum is that all other changes of place are from opposite to opposite, and therefore (like non-local changes) cannot be continuous. 13. O~K 'UTuL KCV1JaL5, 'there need not be (always) movement '. For this use of the future cf. Bz. Index 7M b 5-12. 15. Et I'~ TL5 SUVGI'EV1J iVEUTGL clpX~ I'ETGIi~~EW. Aristotle has argued in A. 98Sb 2 that there is no such d.pX'1 in the Ideas. 16. oW il~~"/) o~aCa 'll"apG TG €'LS"/), e.g. the mathematical objects which Plato supposes to be independent substances, Z. 1028 b 20. Robin suggests that the reference is to the Platonic world-soul (cf. 1072& I). But, since this is thought of as essentially active, the objection El P.V lVEpyr1u(l., OllK lUTat K{VT/ lXEt c:,,. ACyOV
oflX c:,r; 'EP.7r(lloKA~r; KUt ETEpot AfyOV
....~,

COMMENTARY 27. ot eEo~oyoL, cf. A. 983h 29 n. ot lK VUKT~ yEVVWI'TE~, cf. N. I09Ib 5, and Orpheus fro 12 Diels, l\fusaeus fr. 14, Epimenides fro 5. Acusilaus fro I, 3, Hesiod, Op. eI D. 17, Theog. I 16 ff., Aristoph. Av. 693. ot +UO"LKoC, i. e. in particular Anaxagoras, fro I, but his view is in this respect like those of Anaximander, EmpedocIes, Democritus, and others; cf. I069 b 20-23. 30. oelS~ TI\ lll'L"~VLU oelS' ~ yij, doUc\ Tc\ O'1I'ipP.UTU Kul ~ yo~, i. e. 'Y0v~ is needed to transform the l7l',p.~vl4, which are potentially the young animal, into the actual offspring, while lT7ripp.a.TU are needed to transform the earth, which is potentially the young plant, into the actual plant. 'Y0~ is properly used only of the male element in the sexual generation of animals (G. A. 724b 12), while IT7rlpp.a.Ta may be used with reference to plants as well, which have not the distinction of male and female (7I5b 19, 73Ib 10), but have something akin to it (715b 20, 732" 12), though the two elements are united in the same plant (731" I, 21,28, HIli 3, 759 b 30, 763b 24). 31. SL~ 'VLOL 'II'OLOUO'Ll' doEl lvipyllLUV, olov AE.sKL'II'1I'~. Cf. De Cado 300h 8. 32. Kul nMTfoW, cf. Tim. 30A. 33. a~~c\ SLc\ TC Kul TCVU oel ~iyOUO'LV. Cf. A. g85 b 19, De Caelo 300b 10, 16, and (on Democritus) 313& 21. The objection is not fair, as regards Plato; he makes the world-soul the cause of the movement, cf.. 1072& I. 34. Diels's reading, oelS', Et rlISl f\ IlISC, is much the best emendation of the unmeaning o~S~ IlIS~ o~8l of the manuscripts, and derives support from Alexander 690. 35. Schwegler's o~S~ TOV IlISland Zeller's o~S' d IlISl are less probable. 35. Prof. Jackson thinks that the readings of Ab (SEi alEl TL) and of E (SEi TL dEl) point to an original SEi TL SUI T[. But the two readings are merely an instance of the constant tendency of the two manuscript groups to vary the order of words, and the required sense 'there must be a cause' may be got out of the traditional reading. 'There must in every case be something present', se. to account for the particular movement. The simplest emendation would be SEi TW' (se. alTla.v) dE~ wdpXELv. 36. f\ •.• ~ Alexander takes to mean' either ••. or', Themistius (probably rightly) to mean "or •.. or '. ilUou, e.g. rill: cpaVTaula.1: (Alexander). 1072& I. apX~V, se. KL~UEWI:. 2. iJO'TEPOV, st. rill: ICL~UEWI:, not TOV o~paVOV as Bz. supposes. Aristotle seems to be reasoning from the late point at which the formation of the soul appears in the Timaeus (34 B). He argues that Plato makes soul coeval with the heavens, which are later than the original disordered movement of Tim. 30 A, and that soul therefore cannot be the cause of this movement. Plato no doubt describes the soul as the principle of all movement and as eternal (Phaedr. 245 C-246 A, cf. Laws 894 C-896 R). Further, he describes

it as /Co.2 "talan /cID d.pnii 7f'poTlpa.II /Co.2 7f'fKa{JVTlpa.II awp.a.TOt; (Tim. 34 c), and explains that it is only in the order of his exposition that it is later (34 B} But he at any rate describes it as made by God (34 c), while movement is found by God as something pre-existing (30 A). Something must be allowed for the mythical and conjectural character of the Timaeus, but it does not seem that, as Zeller maintains in Plaloniscne Sludien, Plato had a perfectly consistent theory. 4. ~tP1JTGL S~ wfiis. It is not very clear whether this refers to 10 7 1b 22-26 or to @. S. Bz. contends that when Aristotle refers in one book of the Metaphysics to another, the reference i!'! always fuller in form than this. H. 10421\ 3 and N. 1090.15 hardly form exceptions to this rule, since ZH and MN so clearly belong together respectively. The only genuine exception is K. 1064& 36, which seems to refer to A. 6, 7. In the other works the only instances I have noted of very vague references in one work 10 another are De Gen. tI Corr. 336& 15, De Catlo 2711\ 21, De Resp. 477 b 12, De Smsu 436. I, G. A. 715& I. On the whole Bz. seems justified in inferring that the reference here is to 1071b 22-26. That passage does not definitely say in what sense potency and in what sense actuality is prior, but indicate~ obscurely that though each individual potency is prior to the corresponding actuality, there must be some actuality prior to all potency. 5. Alexander seems to have read lvipYELG {691. 33}, and so do Tr Ald. This reading is preferable to that of EJAb. 6. ·EI''lrESou.'ijs +L>'£GV KGt ,.0 V~LKOS, sc. 'AqfJJII from 'Al"tollTtt. For the arbitrary insertion of ro cf. the passages referred to by Vahlen on

Poel. 1449&1-@. 1049b II, M. IOSI&34, Sopll. El. 173&9, De Resp. 47Sb 2S, Rllel. 1361& 24, 1363b 3, 1369b 5, 1390& 16, 1407b 31, 1414b 13·

ot Act ).iyOVT~S K£V1JO'LV ~tVGL, cf. 1071 b 32. S. TGIlTA Act ~ "'IPLO~ ~ cU..>'fJJS. 7f'IPuS~ refers to Empedocles' doc· trine of cycles (De Caelo 27gb 14, PlJys. 250b 26). rufJJS refers to any view which, without committing itself 10 cycles, holds that the main characteristics of the universe remain the same. In the next sentence Aristotle concentrates on the belief in cycles, though what he says of its implications would apply also to the alternative view referred to in ctUfJJS. It is not necessary with Schwegler to treat 7f'Ip'O~ in I. 10 as a gloss. 9-17. The general upshot of this passage is that the motion of the sphere of the fixed stars, which is parallel to the equator and therefore unchanging relatively to the earth, is the cause of the permanence in the history of the world, while the ecliptic motion of the sun, which brings it now nearer to and now farther from u!:, causes the alternation of hirth anel death. Cf. 1071· 15, De GI'1I. tt Corr. 336b 15. 10. Sti TL a~t fiiVELV 1lI00cWnJs lVEPYOUV. From De Gen. et C(lrr. 336" 23 fT. it is clear that the reference is to the sphere of the fixed stars, while the lllqryoUv dllfJJt; /cID dllfJJt; is the sun, which moves in one way {clJ8l)-i. e. has its yearly motion along the ecliptic- /Ca.D' al'Tu, and

COMMF.NT ARY moves in another way-i.e. has its daily motion paraIlel to the equator 11.>..M. The question then arises whether this I1.>..M is TO 7f'pCrrOV, i. e. the sphere of the fixed stars, or something else (e. g. the sphere of Saturn, says Alexander). But if we suppose something else to be the cause, then in tum the sphere of the fixed stars causes both the sun's motion and that of the supposed other. 15. u4Tl{j. The editors since Brandis read a{,r~ and take the clause to mean that the sphere of the fixed stars will cause both its own motion and that of the supposed other. But in Aristotle's view the motion of the sphere of the fixed stars is not self-caused; it is caused by God. It is therefore better to read aw~ with Alexander and take it to refer to the sun. Since we cannot suppose the motions, parallel to the equator, (a) of the fixed stars and (b) of .iiaturn and the sun, to be unconnected, we should have to suppose the motion of the fixed stars to be the cause of the motion of Saturn and therefore, indirectly, of the motion of the sun. 15-16. o~Koiiv ~Dmov Tc\ 'II'PWTOV • • • !lIO'UdTW!i. The principle is : If B causes C, but A causes B, A is more truly than B the cause of C. Cf. a. 994 a II. There is a further advantage in regarding the sphere of the fixed stars as the cause of the sun's daily motion; it has already been shown to be the cause of the uniformity in the universe (ICru 'Yap ai'TLOv ~v ICTA.), so that if we assign to it also the causation of the sun's daily motion we shaIl be practising economy in explanation. 17. o~Koiiv OilTW!i Kul'xouO'LV ut KLV~O'ElS. Theory requires the account given in II. 9-17, and accordingly the actual motions are found to be such as have been described. 18. illlu!i •.. dpXci!i, se. like the Platonic Ideas, cf. I071b 14.

-KaT'

Nature al1d modI' of operation of the first

11107'('1'

(ch. 7).

I07l1a 19. There must, then, be something that is in incessant, and therefore in circular, motion, and this is actuaIly ob{lerved to be the case. The first heaven, then, must be eternal. Therefore there must also be something that moves it. Since that which is moved and moves is a middle term, there must be an extreme which moves without being moved, being eternal, substance, and actuality. lI6. The object of desire and that of thought move thus. And in their primary forms they are identical. The object of desire is the good or the apparent good. Now desire depends on thought rather than thought on desire. And thought is moved by its object, and the terms in the column of positives are per se objects of thought, and

373 in this column substance, and among substance that which is simple and actual, comes first. But the good and desirable belongs to the same column, and the first term in this column must be most good. b I. A final cause in the sense of that whose good is aimed at cannot be found among unchangeable things, but a final cause in the sense of the good aimed at can; it moves by being loved, while all other things that move do so by being moved. 4. That which is moved is capable of being otherwise than as it is. so that if its activity is the primary (i. e. circular) motion, it has contingency in this sense-liability to spatial motion, though not to change of substance. The unmoved mover, on the other hand, has no contingency; it is not subject even to the minimal change (motion in a circle), since this is what it originates. It exists therefore of necessity; its being is therefore good, and it is in this way that it is a principle of motion. (The necessary in the sense of the non-contingent must be distinguished from the necessary in the sense of what is contrary to natural impulse, and from the necessary in the sense of the sine qua non). 13. On such a principle, then, the physical universe depends. It is a life which is always such as ours is at its best. Its very activity is pleasure-just as waking, perceiving, thinking are most pleasant because they are activities. 18. Thought which is independent of lower faculties must be thought of the best object. Now thought does think itself, because it shares in the intelligibility of its object. It becomes intelligible by contact with the intelligible, so that thought and object of thought are one. !Z!Z. Activity rather than potentiality is the divine thing in thoughtactual contemplation the pleasantest and best of all things. If God is always in that good state which we sometimes reach, this must move our wonder; and if his state is even better, this must move our wonder yet more. !Z6. God must also have life, for the actuality of thought is life and God is that actuality. God therefore has, or rather is, life continuous and eternal. 30. Those who, like the Pythagoreans and Speusippus, think the good is not a first principle because the developed living thing is better than the germ from which it comes, are wrong, for the germ comes from prior developed beings. 1073& 3. It is clear, then, that' there is a substance eternal, immovable, separate from I>cnsible things. We have shown that it

37.

COMMENTARY

must be without magnitude; it cannot have finite magnitude, for then it could not have the infinite power which it displays by causing motion eternally, and it cannot have infinite magnitude because there is no such thing. It must also be free from change of quality, for the other sorts of change presuppose locomotion. I07~" 19.

iK VUKTOI IOTen, cf. 1071 b 27.

~O. KuliK "iJ OI'TOl, cf. 1069b 19. ~I. uiInJ S' '" KdK).¥, cf. 1071 b 10-II n.

~3. 1\ 'll'pcin-ot o~puv6i, the sphere of the fixed stars, cf. De Caelo 28S" 15, 292b 22. This is 'first', counting from the outer edge of the universe. IOT~ TO~VUV T~ KUI. & K~VEi. From the existence of a KWOVP-EVOV there cannot be inferred the existence of something which it moves, but only the existence of something that moves it. 0 therefore is subject of KLV" as in I. 2 5. ~4. The traditional reading l7l'El S, TO KWOVl'fVOV Kal. KWOVV, Kal. I'(UOV Tolvvv EcrTl TL gives an unsatisfactory sense; the unmoved mover is not a I'(uov. Nor does it mend matters if we punctuate after I'(UOV instead of after KWOVV. (crTL Sf KuI. TO KWOVl'fVOV p.6v~ cannot as Alexander suggests be understood, and TO{VVV cannot begin a clause, nor is Kul p.€uov intelligible. Kal must in any case be excised; we may then read for Tolvvv EOT{ either IOTL TO{VVV or KWOW (crTL or simply (crTL. The argument then is as follows: Aristotle has just remarked that there must be something that moves the elEI. KLVOVI'EVOV of I. 2 I. This KWOVV may be (a) KWOVI'fVOV or (b) oll KLVOVl'fVOV. But a KWOVl'fVOV Kal. KWOVV is something intermediate, which presupposes TL & oll KWOVP-EVov KLVE" For the description of the KLVoVl'fVOV /Cal. KLVOW as a I'(UOV cr. M. A. 703& 5, and for the argument cr. Phys. 256b 20 If. Professor Jackson proposes mEl. S, TO KLVOVI'fVOV Kal. KWOVV Kal. I'~' t,v TO{VVV ,crT{ TL KTA., 'since there are two sorts of /cLVOVI'fV0V, a KWOVI'fVOV which is KLVOW and a /cWOVl'fVOV which is I'~ KLVOW, there is also, to complete the series, something existent which is KLVOW and I'~ KWOVI'EVOV '. But (1) Aristotle has not established the existence of a /cLVOVl'fVOV /Cal. KLVOVV and that of a /CWoVl'fVOV /Cal. I'~ /cwow, but only that of a /cLVOVP-EVOV (I. 21) and that of a /CLVOW (I. 23). (2) &1' TO{VVV ,crT{ TL is not a very natural mode of expression. Professor Jackson quotes De An. 433 b 13 in support of his view, but there we have not what his view implies, a division of TO KWOVI'EVOV into two kinds, but what our interpretation above implies, a division of TO KWOW into two kinds. ~6. K~VEi Se ~SE TO 6pEKTOV KGt TO V01JTOV' KlVEl o~ K~vod"EVU. In general, according to Aristotle, there is no /cWE'V without cl.vTLlCLVfiuSaL (G. A. 768b IS); the action of an object of desire is the only exception to this rule. On the dPEKTOV or aya.Sov as the motive power in the world of nature cf. PhJ's. 192& 16, De Gen. el Corr. 336b 27,

375

De Vita 4698 28, P. A. 687& J 5,1. A. 704b J 5. The doctrine becomes very prominent in Theophrastus; cr. his fragment on l\Ietaphysics, 309. 26, 310. JI, 311. 8, 312. 4, 315. 15, 321. 20. The doctrine that the motions of the stars were due to the desire to imitate the perfection of the divine nature lasted long. There was much discussion among theologians of the question whether the stars are conscious. St. Thomas (S. T. 1&. quo 70) sums up by saying that Origen and Jerome held them to be conscious, Basil and John of Damascus denied them consciousness, and Augustine was neutral. He himself concludes that corpora coelestia non sunt ani1llalia eo 1II0do quo plantae et a1li1llalia, sed aequivoce, i. e. the consciousness to which the motion of a star is due is not its OWIl form but the intelligence to which it is subject. Cf. Webb, Studies ill Ihe Hisl. of Nal. Tluol. 273 f. Kepler argued against the Ptolemaic theory on the ground, among others, that it implied that the planets know mathematics; but he himself thought that the SUIl apprehends the harmonies of number which regulate the planetary orbits. The colon after V07]Tov gives a better sense than B~kker's full stop after ~8( or Bz.'s comma after dPEICTOV (with ICLl'Otip.cvov for ICWOVP.CVa.). For ~8E referring backwards cf. b 26, KUhner i, p. 646. Aristotle is not here expressing the view that OPClL'i and vow are independent sources of acliotl or local movement, the view stated provisionally in De An. 433& J 3 and set aside in 433& 2 I in favour of the view that OpElL'i is the only direct principle of action. Line 30 here indicates that his meaning with regard to ,.0 VO'7Tov is that it stimulates 'hough' without being itself stimulated. S7-b I. The argument for the identity of the 7rpWTOV dpcl(rov and the 7rpWTOIf vo~v is as follows: The actual object of desire is either the apparent or the real ICaAOV, so that the primary object of desire- is evidently the ICQAOV. (Aristotle next observes that the desire of it presupposes the recognition of it as ICaAOV. This remark makes the transition from desire to thought but is not meant to prove the identity of their primary objects j the proof of that comes in what follows.) Now the proper object of vow is the assemblage of positive entities (~ n-(pa. avoTOLXla.), negatives being known only as the opposites of positive entities (cf. e. 1046b II). Substances are the first members of this assemblage, prior to positive qualilies, and simple immaterial substance is prior to substance which includes matter as well as form. Hence immaterial substance is the 7rp/:JTOIf VO'lTOV. But TO ICaAOV, which was shown to be the 7rpWTov dpEKTOV, is something positive and therefore also belongs to the positive assemblage. This Aristotle takes to imply that the positive assemblage is the assemblage of ICaM. And if so, immaterial substance, which is the first member of the assemblage, and therefore contains in the highest degree the character of all members of the assemblage (a.. 993b 24), must be the /l.pI.fTTOV or 7rpWTov dpEICTOV, while it has already been shown to he the 7rpWToV vo~v. S7. TOUT"'., Ta. 'II'PWTA Ta. a.I'ITG. Alexander points out that SOllIe

COMMENTARY dpEl(To' ,u\: nOl V"'1Tu, e. g. a loaf, ami some vO'1TU are not dp(ICTo', e. g. evil things. Sl7-:z8. .1rl'UtL1JTCW •.. &11 lta).tSlI. Aristotle establishes that the 7f'pWro" dp(KTOV is the l(cW)v by considering the species of opEets. There are in all three species~7f'''Jvp.la, 6vp,Oi, {Jov).:rp'ts (De An• •P4b 2, M. A. 700b 22); but Aristotle has also a tendency to divide 0pEetS simply into that which is rational ({Jov).:qcm) and that which is against reason (l7rt6vp.la.) (De An. 433& 22-26), and these two he is satisfied to mention here. 31. ~ l.T4pa. aUaTOLxlG, cf. A. 986& 23 n., K. 1066& 15, Pl!J1s. 201 b 25. Not only is averrotxla. used of the Pythagorean list of opposites, but Aristotle himself recognizes a positive averrotxla. or column including such terms as being, unity, substance, and a negative avcrrotXla including not-being, plurality, not-substance (r. 1004b 27, De Gm. e/ Corr. 319& 15, De Sensu 447 b 30,448& 16, P. A. 670b 21 ). In each case the negative is known not per se but as the negation of the positive term. 3S1-34. Alexander thinks this note on the difference between • one' and • simple' is meant to meet the objection that if the primary unmoveable substance is simple it must be one, whereas Aristotle believes ill a plurality of such substances (the beings that move the spheres, 1074& 15). Rather, Aristotle seems to be intent on explaining what he means by • simple', without any further motive. 3a. TO tL~1I yap III I'iTPOII U1JI'GC"L, cf• .1. 1016 b 18. TO Si A'II').oulI hS 'XOII G"ft. • One' denotes that a thing is the measure of some/hirlg, the unit used in counting an assemblage; • simple' denotes that a thing is ;/se!! in a certain condition, i. e. unmixed. b I. ItGl 'aTLII . . • 'II'P;:"'OIl. The first term in a series is the best term, if this description of it is appropriate {as it is in this case, since. TO l(cW)v is in the series} j or if it is not, then the first term may be said to be • analogous to the best'. Thus circular movement may by analogy be called the best movement, to take Alexander's example. b 1-3. aTL 5' ian ... 0"1t 'aTL. It might be thought (cf. B. 996& 22, K. 1059& 35) that the teleological view implied in calling immatelial substance (God) the 7f'pWTOV dp(ICTOV is incompatible with the unchanging, eternal nature of immaterial substance (& 25). Aristotle therefore proceeds to point out that TO o~ lV(I(a, the object of purposive action, may in one sense of these words be found in the realm of eternal, unchangeable entities. I. e., when we speak of the o~ lVEI(G of a ttring we may mean (I) that the thing is good Ttvl, lor seme conscious being, or (2) that it is good T"'OS (lv(I(a.), for the sake of some end. The latter exists in the sphere of unchangeables (Ierrt, 1. 3 = lerr", lv TOLS cll(~l17jTOts), while the former does not, since the altainment of good involves change in that which attains it. Christ's addition of 1(112 T"'Os (Ttv6r Ab) after lV(I(a. (1. 2) is amply justified by De A,l. •P5 b 2 TO 8' o~ iV(I(G 8tTTOV, TO p.~ o~ TO 8~ ~ {cf. ib. 20, Ph;'s. 194" 35}. G. A. 742& 22, which Christ quotes, is not

as-

377 a paralIel, for the true reading there is not TO 00 (VlKa but TO TOVrOV £VEKa. 2. -I, 8la'p1CTlS 8'1Xoi.

Cf. (V rU 8r.alpEUEi. TWV (VaVT{wv I. 1054& 30, 100482. Phys. 194& 36 says the distinction Eiprrrai. (V TOtS 7f'EPl. CPlAOO"oCPw.s, i. e. in Aristotle's early work of that name. Alexander thinks the reference is to the dialogue De BOliO, but elsewhere he refers to a separate 'EK>"0'Y~ TWV (VaVT{wv (cf. 250. 19, 262. 18, 23, 615. 14, 643. 2, 695. 26). The distinction here, however, is not a distinction of contraries, and it seems improbable that here V 8la{pEulS refers to a book at all. It probably means simply 'the welI-known distinction '. 3. The subject of KIVEi is the o~ (VEKa in the sense of TlVOS, the objective end. 4. KlVOJI'EVQ 8E Trua KIVEi. The manuscript reading KIVOVP,(V'I!, ' and by something moved it moves alI other things', is hardly possible Greek, and KIVOVp,EVOV, 'while the other (the 7f'PWTOS ovpavos) being moved moves all other things', is little better. KlVovp,Eva gives the right sense, 'it moves as being loved (se. without itself being moved), while all other things move by being moved', i. e. simply transmit the motion impressed on them. a and ware often confused in manuscripts (Bast 183, &c.). 5. Alexander's commentary here says €a.v (UTII' V (V(P'YElU TOV ovpavov V7f'pWrq cpop&., which leaves it doubtful what he read, except that there is no trace of the Kat which the manuscripts have before (v(P'YEea. I have adc.;>ted a reading which may have been that of Alexander, and which gives better sense than those of the manuscripts and, I think, than those of previous editors (El cpopa. V7f'pWT71 W(P'YEe&' (UTIV, V KIVELTal Bz., El Vcpopa. V7f'pWT71 (V(nEe';' lUTIV V KIVEiTal Christ). Taking V KIVElTal with what folIows, and reading TaVry 'YE, which the sense requires, we get the folIowing meaning for the sentence. Aristotle has said, with the heavenly spheres in mind, 'the other things move only by being moved. Now if a thing is moved, it is capable of being otherwise than as it is '. He now continues 'so that if its actual mode of existence is the primary kind of local movement (se. circular movement). then in so far as it is subject to change, in this respect it is capable of being otherwise, i. e. in respect of place even if not in respect of substance', i. e. even if it is not subject to gener.ation or destruction. The words d p,£v o~v ••• ovu{av (11. 4-7) are preparatory to the second part of the sentence, in which Aristotle points out that the 7f'pWTOV Kivovv, in contrast to the 7f'PWTOV KIVOVp,EVOV, is in 110 respect subject to contingency. Jaeger reads EZ cpopa. V 7f'PWT71 Kal. (V(P'YEe';' (UTII' V KIVEtTal, TaVry 8' (valXETal ruws (XEIV KaTci TWOI', and interprets ' thus if locomotion is the primary kind of movement and if it has activity only in so far as it is moved (i. e. realIy occurs), yet just for that reason it can be otherwise in respect of place'. The use of 8l in apodosi might be justified by reference to B. 999& 27,1'. 1003 b 5. A. 1075& 10, but the interpretation as a whole is hardly satisfactory. (V

rfi (KAOYii TWV waVT{wv 1'.

217S·2

Bb

CO:;\Il\IENT AR Y

37 8

8-9. +opa yap KUK).~. For Iccal movement as the primary mo\'ement, which a thing must have if it is to ha\'e movement or change at all, cf. Phys. 260a 26-26[& 26, and for circular movement as the primary local movement 265& 13-10 16. , 9. TcWTTJI' TOUTO KlVEi. The argument is: 'But the first mover lillparls the first or minimal movement, and therefore cannot be supposed it~elf subject to it, since then we should have to look Cor something which is prior to the first mover and imparts this motion to it.' 10-11. l~ AVUyK1J~ a.p" •.• ApX~' 'Since it is not subject even to the minimal change (and lherefore, a fortiori, is not subject to generation or destruction), it is a thing that exists of necessity; and inasmuch as it exists of necessity, its existence is good, and it is in this way (se. as good or object of desire) that it is a principle', i. e. the principle of movement of the universe. 10. AvuYKn, K,,).&i~. This is to be explained bya. 10 I 5b 14 d d.pa

8.

n

cr.

lunv dTTa MBta Ka~ dKlv77Ta, oM,v (KElvot~ (UT~ platov

oM, 'If'apd. ",vUtV.

That which admits of no contingency of any kind (1072b 8) KaAw~ IXft because nothing contrary to its nature can happen to it. II. For the three senses of ' necessary' cf. a. 5. Alexander thinks that the prime mover is necessary in the sense of TO ot O{,K o.vEV TO Et;. But it has expressly been said (I. 8) to be necessary in the sense of TO p.~ (VBEX0P.EVOV lliw~ lXnv: TO ot O{,K dvfV TO E~ is simply the condition of the good, and may be a necessary evil, orov TO 1f'IEi'v TO ",Upp.e&KOV dvaYKawv iva p.~ K4P.V[l (a. [015 a 24); it is evi· dently not in this sense that the life of God is necessary. 13. AU' A1I').&i~1 'but can exist only in a single way', cf. a. 1015" II. 14~4. Having shown (a 25) that there is a prime mover which is substance and is pure activity or actuality, Aristotle assumes that .it must be such as the highest actuality or activity that we know, viz. V07JUt~1 immediate or intuitive knowledge. Further (I. 18) lhis V07JUt~. Jeing Ka()' a~~v, i. e. unconnected with any lower function such as se'nse or imagination, must be V07JUt~ of what is in itself the best, and that which is in the fullest sense V07JUt~ must be V~Ut~ of.that which is in the fullest sense best, i. e. of the 'If'pWTov ISPEKTOV (a 27), the prime mover itself. Now vov~ does know itself by sharing in the knowability of its object; for when it touches and knows it becomes knowable, so that it and its object are one. It is when it actually' touches' its object that this happens, for, while vow is that which is callable of receiving the knowable, i. e. essence, it is actual only when it actually possesses the Object, so that actuality rather than potentiality is the divine thing in vovs--actual contemplation is the pleasantest and best of all things. 14-15. 8~"y",~ fI' ••. ~"i:v, ' it is a life such as the best that we live, and live for but a short time '. Or Btaywri may be used in the more pregnant sense in which it implies both noble activity and pleasure

379 (Pol. I339 b (7). The primum lIlovens is described not as having but as being a life, because it is pure £vipyna. 15. otG ~ clpia'MJ J'LKpOlI XPOIIOII ~J'ill, i. e. when we are engaged in philosophic thought, cf. A. 982b 19-983a 10, E. N. II77 b 26. We can do this only for a short time because we are not all lvipyna and our 8uvap.Li being finite is bound to tire (cf. 0. I050b 24, E. N. I I75 a 3, De SOl1lnO 454b8). 16. 111'11 KGt ~So~ ~ '"lpYILG TOUTOU. ~&vq ~ (vipynG is clearly preferable to the vulgate ~ ~8ovq (vipyna. Aristotle uses here the language of E. N. vii. 1153& 14, which identifies pleasure and activity. In the exacter language of E. N. x (1175& 15), pleasure inevitably accompanies and completes activity. SLc). TOUTO, because they are activities. 18. SLc). TGUTG, because they are hopes and memories of these acti vities. 18-21. In order to find the connexion between these two sentences, it seems necessary to suppose that when Aristotle says that the divine V017O'Li ~ Ka(J' almlv is of TO KaU aUTO ¥LClTOV he means the conclusion to be drawn' and therefore of the divine VOVi itself', which has been exhibited as the 7f'PWTOV 0P£KTOV (a 27), in other words as the ¥LCTTOV (a 35). He then goes 011 to show how vovi knows itself; he shows that it is only in the activity of VOl1uii that VO~ becomes its object and so becomes knowable, and the distinction thus drawn between activity and potentiality leads him to the statement that the activity is better than the potentiality, that the actual exercise of (J(WPf.a. is the pleasantest and best thing in the world. 18. ~ ... ..o1JII'Li ~ KG' G~n1I1, thinking in itself as distinguished from the human thinking which depends on sense and imagination. Alexander interprets these words as meaning" KaT' lvipy(LGV VOVi in distinction from " Ka(J' ,ew and" 8VJlap.£L, but it is difficult to get this out of Ka(J' aUTqv. 19. dTOII SE IIOIL. Bz. is not justified in inferring from lo74 b 33 that 8~ should be read; the argument there is obviously different. 8~ gives a good sense here, but so does 8i. 20. KGTc). J'ITU).1J'/1L1I TOU II01JTOU. Cf. De An. 430& 8 (K({V'fI (vcii) TO v077TOV Uwa.pen. VOVi, as Alexander says (698. 7), knows primarily the intelligible form, and incidentally itself, through the fact that when it knows it becomes what it knows. Cf. De An. 430a 2 K~ a~Oi ~) '. I" "£7f'L "p.'v , ,yap . .TWV ,, "\ TO' (o' vo~ ••• V077TOi eCITW WO'7f'(P Ta, v077Ta. avru VlI.l1i a~o (CITL TO VOOVV Kal TO VOOUP.£VOV· ~ yap l7f'L~P.l1 ~ (J(WP77TLKfJ Kal TO oirrw<; (7f'LC1T77TOV TO aUTO (CITW. The identity of actualized Volii (vo~ actually engaged in VOl1ULi) with the actualized V077TOV (which has been changed from a 8wap.n v077TOV to an (V(PY(~ v077ToV by the action of vovi in VOl1ULi on it) is parallel to the identity of actualized sensation with the actualized sensible object (De An. 424& 25, 425 b 25)· The doclrine that the actual alu(Javop.£vov is identical with the actual alu~ov seems to be based on two grounds ; -

I,.

CO:\IMENT ARY (I) The metaphorical description of the apprehension of the sen· sible form as 8ix(u(Jar., and the comparison of it with the reception of the shape of a seal by wax (424" 18), lead Aristotle to think of the percipient as becoming actually qualified by the form of the object. (2) He interprets the inseparability of actual hearing from actual sound, of actual seeing from actual colour (425b 30), as implying that these are but two names for the same thing viewed from different standpoints. The first of these grounds, at any rate, is also implied in his identification of VO~ and VOf/TOV (vo~ is 8(KTu(oV TOV (,SolIS Kal 8vvrip.n TOLOVTOV dAAa. TOVTO 429" 15). VOVi must have no character of its own, that it may be able to take the character of whatever it knows (.P9& 21). And doubtless the second ground is also implied in this case, though there is no passage so explicitly implying it as that referred to above with regard to sensation (42Sb 30). 21. Glyyd"",,,. For the metaphor cf. @. IOSlb 24. 22. ,,"l rij~ o~alll~, i. e. 'of substance' in the sense of essence, cf. De All. 429" 15 8(KTIKOV TOV (,80Vi. 22-24. l"epyei Si ... "PLaTO". 'But VO~ is actual when it has its objects (instead of being merely capable of receiving them), so that (&ince actuality is better than potentiality, cr. @. 8) having them rather than being capable of having them is the most divine thing in vovi, and actual contemplation is the pleasantest and best thing,' I follow Alexander (698. 29) in the interpretation of &'1Y'y(i. 8E lxwv; for the use of lxwv cf. Bz. 111dex 305b 46. Bz.'s interpretation of l)(wv, Ijuoniam ipse in se coniine! alque ipse esl TO VOf/TOV, is hard to get out of the Greek and seems less probable, the point being the contrast of actual with potential knowledge, without special reference at this stage of the argument to the identity of knowledge and its object. Krische's interpretation of lxwv as = 'having the potentiality of thought' is rightly rejected by Bz.; the supposed parallels in Pl!J1s. :l55" 34, De An. 412& 26, 417b 5, are not convincing. Dr. Jackson (Proc. Call1b. Phil. Soc. cix-cxiv. II f.) translates ~VfP'Y(i. 8E lxwv , and it energizes continually', comparing such phrases as T{ KtnIT"'ni lxwv; and lxwv >"vaP(l.i. This idiom seems, however, to be somewhat contemptuous and therefore out of place here; cf. the instances quoted in L. and S. 1\Ir. A. J. Rahilly has an ingenious conjecture (New Ireland Revttw, October, 1909), IV((yy(L 8f lxwv lK(i.VO p.O.llov, ~(ToVrov J leT>"., 'but it is rather by possessing the former (the intelligible) that it (the intellect) becomes actualized. And so the contemplation of that which the intellect seems to have divine in it (i. e. self-consciousness) is its greatest enjoyment and good '. The transposition gives an excellent sense, but does not seem to be necessary. 23. .:\aT' lKl("ou ...~).o" TOUTO is the reading implied by Alexander (698. 35). He interprets the clause as meaning' so that the divine thing in VO~ (i.e. its self-knowledge) belongs rather to the 7r~ VOVi' (than to the actual vovs of mankind), ; (J(wpta will then mean not

p.,

3 81

• contemplation in general but • God's contemplation'. But it is difficult to supply TO lamv VOILV as the meaning of 3 80KCt b vow (Jiiov 'XI'll. We must, it seems, choose one of two interpretations: (I) • so that what reason is thought to have of the divine belongs to the prime mover (IKc{vov, cr. eKILVor I. 27) rather than to the human mind " se. since it always 'X" TO lf07/,.ov while we only sometimes do so. Then ~ (JIIJlPla. = ' God's contemplation'. (2) 'so that this (actuality) rather than that (potentiality) is what reason is thought to have of the divine '. This derives some support from 1074b 21 ITI 8( IrTI vow ~ olJuLa aiJTov CrTC VO'f1CTt" CUT&. Then ~ (JclJlpla will mean' actual contemplation' in general. So Hz. takes the passage. If IKcLvo p.allov TOVrov be read the meaning must be 'so that that which reason is thought to have of the divine belongs to the prime mover (TOWOV) rather than to the human mind '. This is slightly less natural than the two interpretations above. 114. For" '."'pea. as the actuality, opposed to e7f'IU~P."I' the potentiality of knowledge, cr. 9. 1048a 34, 1050" 12-14, Phys. 255& 34, Dt An. 412a IJ, 23, 417a 2g, G. A. 735" II, E. N. J146b.31-35. d 03v ow"'s .3 Ex,n, ':'s ~fULS 1fOTl, II 'Ilis el.e resumes what was said in 11. 14, 15. 115. .t 8~ ".auov. That God's VO"lUI" is always better than OUfS ever is has not been proved, but has been suggested in the words ~ 8( VO"lUI" ~ Kaf! a~v (I. 18), where the self-dependent v6"1UI" of God ill contra~ted with the human VO'f1CTI" dependent on sense and imagination. 116. For ~8E retrospective cf. & 26. 30-34. 3ero,8i ..• TOdT"'V. For this view cf. 1075& 36, N. 10gl" 33, log2& II. As regards the Pythagoreans, Ritter's notion that they believed in a development of the divine nature from imperfection to perfection is generally rejected by scholars. The late position of the good in the Pythagorean list of opposites perhaps fits in with the doctrine here ascribed to them. The production of the • perfect ' number ten from less perfect numbers is significant of the same tendency; and, consistently with this, the Pythagoreans assigned the higher entities and qualities to the higher numbers. Cf. Tlu%g. Ar;/h1ll. p. 55 Ast c)~OM.O" 8( p.ua. TO p.a.67Jp.a.TIKUV p.lyc8or TPIri 810.' , (') 'co , ,~, .~ 1:_' ~.I. ' , l1Tav Ell TUpaOl, 7f'01.OT7JTll Kal xpwuw (7f'IOCtfOVoP.'V7J" T7J" ."VCTIIJI" IV 7f'1.".&81, 'inlXIJIUW 8( ev It&'81, vovv 8( Kat Vyl{av Kat TO W' aiJTOv ArytiP.lvov «pWi ev lfl80p.&.8t, P.U4 TaW&' «P"IUIV IpwTa Kat «pIMav Ka, p.~w Ka' 11rtvotav l7r' c}y8048t rrvP.P~va.L TOL" O~UIV. This point, which was noted by Gruppe, affords a connexion between the Pythagoreans and Speusippus, who wrote a book on the Pythagoreans and was specially interested in the perfection of the highest number, ten (Diels i! 303.20). He no doubt considered the good to be manifested first in one of the later of the grades of substance which he recognized (Z. 1028b 21). 118. Hz.'s conjecture 81\ for 81 greatly improves the sense, and is supported by Them. 24. Ig. 311. 8,el T~ IlG1 niiv+uniiv IlT>", cf. N. log2 a 12.

COMMENTARY 35-1078& 3. Cf. @>. 1049h 17-27. 1073& a-b 17. Blass has pointed out that in this whole passage there are only two hiatuses (& 26, 34), that b 17-38 is almost free from hiatus, and 1074& 38-b 14 contains only one (b 7), while 1073b 381074& 38 is full of hiatuses. He points out further that O~O! in 1074b 3 does not refer naturally to anything that immediately precedes.

He infers that Aristotle has here incorporated, with additions, extracts from an earlier and less scientific work of his own, in which much more attention was paid to style. This view can, however, hardly be right. At least the reference to Cal\ippus' theory (r073h 32-38), and probably the whole discussion of the concentric spheres and their movers (1073& r 4-ro74b 14), belongs to the latest period of Aristotle's life. Cf. n. at beginning' of ch. 8. 5, S48ILKTa~. Bz. thinks the reference is to Phys. 267b 17, but Aristotle's mode of reference to a separate book is almost invariably fuller than this (cr. 1072& 4 n.), and, since the first ~TI clause (3-5) and the third (II, 12) clearly refer to the results of the immediately preceding argument, it is pretty certain that this one does so too. Aristotle has not, strictly speaking, shown that the primum movms is without extension, but he has proved something from which it readily follows (cf. 11. 7-11), and 818(1lCTa! expresses this fact, though rather loosely. 7. O~S~I' S' 'XIL S.sl'aluI' 4'11'I~pol' 'll'1'II'lpaO'....ivol', cr. PhJ,.f. 266& 24-b 6. 10. 3)."'1; O~K 'CI'T~I' O~S~I' 4'11'llpav ....iyI8ol;, cf. PlljIs. iii. 5, De Cotlo i. 5. 12. 'II'&.cra~ yAp at 4).).a~ KI~O'III; .1crnpaL nil; KaTG TO'll'Ol', cr. 1072b 8, 9.

The number of/hi tlernol moving principles (ch. 8). 1073& 14. Our predecessors have not been precise about this. The ideal theory does not diseuss it. It identifies Ideas with numbers, but sometimes treats them as unlimited, sometimes (but without sufficient proof) as limited by the number 10. sasa. We can use previous premises and distinctions. The first principle is an unmoved mover which causes one primary eternal motion. Since every eternal motion requires an eternal cause, and there are other eternal motions (viz. those of the planets) besides that of the first heaven, each of these requires an eternal substance as mover. It must be substance since the moved is a substance, mover is prior to moved, and only substance can be prior to substance. There must be as many such substances as there are motions. b 8. Their number must be determined by astronomy-the most akin to philosophy of the mathematical sciences-Since it alone of these sciences deals with concrete substance. It is obvious that the

motions are more numerous than the moved bodies. We proceed to gh'e a sketch of the accounts of various mathematicians. 17. Eudoxus assigned three spheres to the sun and three to the moon, (I) a sphere having the daily rotation of the fixed stars, (2) a Rphere having a yearly motion along the zodiac, (3) a sphere having a motion across the zoljiac (stretching across a greater breadth of it in the case of the moon). He assigned to the planets (I) and (2) and (3') a sphere whose poles are in the ecliptic (the poles btdlg the same for Venus and Mercury), (.') a sphere moved obliquely to (3'). Total 26. a~. CalJippus kept the same order, and the same number ofspheres for Jupiter and Saturn, but added two each for the sun and moon, and Total 33. one for each of the other planets. 38. We must suppose, for each of these bodies except the moon, counteracting spheres, one less in number than the positive spheres, to neutralize their action on the outer sphere of the next system (counting inwards). Total 55. Or if we do not add the said motions to sun and moon, we get Total 4~. 1074a 14. This is also the number of the unmoved movers (probably-we do not claim certainty). If there can be no motion which does not contribute to the motion of a star, and every substance which is impassive and in itself has attained the best is an end, this must be the total number of the unmoved substances. For if there are others, they must cause motion as ends of motion. But there cannot be other motions than those named. This is made probable by study of the moved bodies. For no motion is for its own sake or for the sake of another motion, but for the sake of the stars (otherwise there would be an infinite regress). (al. The physical universe is one. For if there were many, each would have a different individual cause, and therefore the causes would ha\'e to have malter; for, as far as form goes, it is common to many individuals. But the prime essence has not matter; for it is actualit},. Therefore the prime mover, and therefore also the universe which it moves, is one in number as well as in definition.) 38. There is an old tradition that the stars arc gods. The rest of the tradition has been added to lend sanction to the laws and on utilitarian grounds-i.e. "the anthropomorphic or zoomorphic parts of the my tho-

CO:\IMF.NT AR Y logy. But the original part, that the prime substances are gods, is inspired. It is a re1ic of that completest possible development of the arts and sciences, which must have been often achieved and often lost. Jaeger has argued forcibly (Ansi. 366-392) that while most of Bk. A is early, this chapter must have been written quite late in Aristotle's life. The theory of Callippus referred to in 1073b 32-38 as a thing of the past (~T{6(To, 1. 33) can hardly be earlier than 330-325. The chapter interrupts the discussion of the first mover in chs. 7, 9. It is written in a full and careful manner, very different from the jottings which form the rest of the book. The doctrine of the' intelligences' which move the spheres is hardly consistent with the doctrine of the single first mover in ch. 7 (cf. 1072b 13 f.), and is late-still absent in the De Molu Animalium and only tentative in Physics viii (258b 10-12, 259& 3-15). 1074831-38 seems to be a fragment belonging to the earlier and more monistic period of Aristotle's thought. 1073& 16. For ti"'O+UCreL~ = d:lrocpaVU(l<;, cf. Rhel. 1365b 27. 20. 6Te Se c:,~ "i)(pL Tij~ SeKuSo~wpu,,,ivCalV. This view is ascribed to some of the believers in ideal numbers in M. 10848 12, to Platonists generally in 1084& 31, and to Plato himself in P4Ys. 206 b 32. The doctrine was derived from the Pythagoreans, for whom cf. A. 986& 8 ; Philolau!l fro 1 I. 5; Theo Smyrn. pp. 93.19,25,99.8, 106.7 Hiller; Theologtl1l1. A rilhm. pp. 60, 6 lAst; Photius, BIoi. p. 439& 5 Bekker; Zeller i.e 504-505; Burnet, E. G. P. § 48. Speusippus connected one with the point, two with the line, three with the plane surface (the triangle), four with the solid (the tetrahedron); and 1 + 2 + 3 + 4 = 10 (neologum. Arjlhm. p. 63 f.). Cf. Z. 1028b 21 n. 24. tiKL""TOV KGl Ked' G~TO KGl KGTc\ au"lJelJ'Id~ = oilT, Ka(l .a{no?, oilT, KaT" uvp.{Jw{J7JK?'<; K~V.

29. rl)v TOU ,..a~ rl)v c11I'Mlv +opuv, the diurnal apparent motion of the whole heavens. 32. Iv Toi~ +UCnlto'L,>, Phys. viii. 8, 9, De Caelo i. 2, ii. 3-8. 33. ~,..' tiKLV.qTOU TI KLVe'La6aL Ka&' a~rl)1I Kal tiiS(ou O~O'LG~. These moving causes of the several planetary motions are, says Alexander (706. 32), not identical with the souls of the planets which Aristotle's language in De Catlo 292& 20 ff. implies. It is in virtue of their souls that the planets are able to move at all, but it is in virtue of the desire of their moving causes for God that they move eternally and uniformly. The souls of the planets, we may add, are immanent in them, but the moving causes transcend them as God transcends the cl7rAa~.. ucpa'ipa. But it must be remembered that Aristotle nowhere speaks explicitly of souls of the planets, though he ascribes to the planets action and life (De Caelo 292& 20). b I. SLc\ rl)1I etp'I"i""" atTLall ,..p6T1POIl seems to refer to a 5-1 I. 6. a1 S' a).).aL ,..epl o48e"La~ OUO'LG'>, cf. M. 2, 3. 17-1074& 14. The views of Eudoxus, Callippus, and Aristotle about the planetary system are discussed more fully by Simplicius (Comm.

in De Caelo 488. 18-24, 493, 4-506. 18}. Eudoxus' theory was first satisfactorily interpreted by Schiaparelli in Pubblicaaioni del R. Osservatorio di Brera in Mt1ano, 1875). Excellent accounts of the theory are given in Dreyer, Planetary Systems, 87-114, and in Heath, Aristarchus of Samos, 190-U4. The importance of the theory in the history of astronomy is well indicated in the following remarks by Dreyer (p. 107). ' Scientific astronomy may really be said to date from Eudoxus and Kalippus, as we here for the first time meet that mutual influence of theory and observation on each other which characterizes the development of astronomy from century to century. Eudoxus is the first to go beyond mere philosophical reasoning about the construction of the universe; he is the first to attempt systematically to account for the planetary motions. When he has done this the next question is how far this theory satisfies the observed phenomena, and Kalippus at once supplies the observational facts required to test the theory and modifies the latter until the theoretical and observed motions agree within the limit of accuracy attainable at the time. Philosophical speculation unsupported by steadily pursued observations is from henceforth abandoned; the science of astronomy has started on its career.' Simplicius derives his account largely from Sosigenes the Peripatetic (second century A. D" the teacher of Alexander Aphrodisiensis), who in turn borrowed from Eudemus' treatment of the subject in his History of Astronomy. Simplicius quotes from Sosigenes the statement that Aristotle discussed in his P~sieal Problems objections to the hypotheses of astronomers (se. Eudoxus and CaUippus) arising from the fact that even the sizes of the planets do not appear always the same. Simplicius further refers to 1073b 10-13 and 1074& 14-17 as indicating dissatisfaction with the theory of concentric spheres. But Aristotle's doubts are clearly only on points of detail. 'The theory of concentric spheres was pursued for some time after Aristotle. Schiaparelli conjectures that even Archimedes still held to it. Autolycus. the author of the treatises On the moving sphere and On risings and seth'ngs, who lived till the end of the fourth or the beginning of the third century B. c., is said to have been the first to try, presumably by some modification of the theory, to meet the difficulties which had been seen from the first and were doubtless pointed out with greater insistence as time went on. What was ultimately fatal to it was of course the impossibility of reconciling the assumption of the invariability of the distance of each planet with the observed differences in the brightness. especially of Mars and Venus, at different times, and the apparent difference in the relative sizes of the sun and moon' (Heath, 221). 17-3". On the general nature of Eudoxus' theory I cannot do better than quote Heath (p. 195). 'Eudoxus adopted the view which prevailed from the earliest times to the time of Kepler, that circular motion was sufficient to account for the movements of all the heavenly hodies. With Eudoxus this circular motion took the form of the

COl\Il\IENTARY revolution of different spheres, each of which moves about a diameter as axis. All the spheres were concentric, the common centre being the centre of the earth; hence the name of "homocentric spheres" used in later times to describe the system. The spheres were of different sizes, one inside the other. Each planet was fixed at a point in the equator of the sphere which carried it, the sphere revolving at uniform speed about the diameter joining the corresponding poles j that is, the planet revolved uniformly in a great circle of the sphere perpendiculac to the axis of rotation. But one such circular motion was not enough j in order to explain the changes in the speed of the planets' motion, their stations and retrogradations, as well as their deviations in latitude, Eudoxus had to assume a number of such circular motions working on each planet, and producing by their combination that single apparently irregular motion which can be deduced from mere observation. He accordingly held that the poles of the sphere which carries the planet are not fixed, but themselves move on a greater sphere concentric with the carrying sphere and moving about two different poles with a speed of its own. As even this was not sufficient to explain the phenomena, Eudoxus placed the -poles of the second sphere on a third, which again was concentric with and larger than the first and moved about separate poles of its own, and with a speed peculiar to itself. For the planets yet a fourth sphere was required similarly related to the three others j for the sun and muon he found that, by a suitable choice of the positions of the poles and of speeds of rotation, he could make three spheres suffice. In the accounts of Aristotle the spheres are described in the reverse order, the sphere carrying the planet being the last. The spheres which move each planet Eudoxus made quite separate from those which move the others. One sphere sufficed of course to produce the daily rotation of the heavens. Thus, with three spheres for the sun, three [or the moon, four for each of the planets and one for the daily rotation, there were twenty-seven spheres in all. It does not appear that Eudoxus speculated upon the causes of these rotational motions or the way in which they were transmitted from one sphere to another; nor did he inquire about the material of which they were made, their sizes and mutual distances. In the matter ,of distances the only indication of his views is contained in Archimedes' remark that he supposed the diameter of the sun to be nine times that of the moon, from which we may no doubt infer that he made their distances from the earth to be in the same ratio 9: I. It would appear that he did not give his spheres any substance or mechanical connexion; the whole system was a purely geometrical hypothesis, or a set of theoretical constructions calculated to represent the apparent paths of the planets and enable them to be computed.' Eudoxus of Cnidus (e. 408-355 B.C.), one of the greatest mathematicians of antiquity, was the discoverer of the theory of proportion expounded in the fifth book of Euclid's Elemmls and of the mensuration of areas and volumes by the method of exhaustion, and the first

proposer of the Julian cycle. He was a pupil of Archytas and of Plato, who is said to have suggested to him for solution the problem of planetary motion (Simp\. 488. 21). He explained his system in a book On Velocities, which like all his other works is lost. Aristotle had his knowledge of the system from Polemarchus, an acquaintance of Eudoxus. 18. rlJv ".tV 1fpWTYJV rlJv TWV cl'll').o.vwv liO'TpwV EtVo.L, i. e. the first (outermost) sphere of the sun (and similarly the first sphere of the moon) was meant to explain its diurnal motion from east (through south) to west. Aristotle means not that the first sphere of the sun or of the moon was the sphere of the fixed stars, but that it had the same motion. 19. rlJv SE SEUTlpo.v Ko.T4 Tbv SL4 ".lawv TWV t'l'S{wv (KVK.\OV), i. e. the second sphere moved in the circle which bisects the signs of the zodiac longitudinally, in other words the ecliptic, the .\oeo~ KVK.\O~ of 1071& 16 (which is different from the .\(.\oewP.(VO~ of 10n b 20). Simplicius supposes that this second sphere produced, in the case of the moon, the revolution from west to east in a lunar month, while the third sphere produced the retrograde movement of the nodes (or points of highest latitude) in about eighteen years. But it has been pointed out that if these were the relative speeds of the two spheres the moon 'would have been found for nine years north, and then for nine years south, of the ecliptic ... We must assume that the third sphere produces the monthly revolution of the moon from west to east ..• round a circle inclined to the ecliptic at an angle equal to the greatest latitude of the moon, and then that this oblique circle is carried round by the second sphere in a retrograde sense along the ecliptic in a period of 223 lunations' (Heath, 197). Simplicius' mistake goes back to Aristotle, since' Aristotle clearly implies that the second sphere corresponds to the movement in longitude for all the seven bodies including the sun and moon, whereas in fact it only does so in the case of the five planets' (ib.). With regard to the sun, Simplicius says t:lat, as in the case of the moon, the third or innermost sphere moves much more slowly than the second, but (unlike the third sphere of the moon) in the direct order of the signs (493. 15-17, 494. 6, 7, 9-1 I). 'Simplicius makes the same mistake as regards the speeds of the second and third spheres as he made in the case of the moon. If it were the third sphere which moved very slowly, the sun would for ages remain in a north or a south latitude and in the course of a year would describe, not a great circle, but (almost) a small circle parallel to the ecliptic. The slow motion must therefore belong to the second sphere, the equator of which revolves in the ecliptic, while the revolution of the third sphere must take place in about a year •.., the plane of its equator being inclined, at the small angle mentioned, to the plane of the ecliptic . • • The slightly inclined great circle of the third sphere which the sun appears to describe is thus carried round bodily in the

COMMENTARY revolution of the second sphere about the axis of the ecliptic, the nodes on the ecliptic thus moving slowly forward, in the direct order of the signs; and lastly both the second and third spheres are carried round by the revolution of the first sphere following the daily rotation' (Heath, 198). The sun's apparent motion is, as a matter of fact, along the ecliptic, so that two circles would have been enough to explain its motion. How did Eudoxus come to suppose that it moved at a small angle to the ecliptic? SimpJicius says this was inferred from the supposed observation that the sun, at the winter and summer solstices, does not always rise at the same point of the horizon (493. II-17, cf. AI. 703. 27). Schiaparelli thinks that the early astronomers inferred a movement of the sun in latitude from the observed motion of the moon and the planets in latitude. This belief was opposed by Hipparchus, but lasted long; Pliny puts the inclination at one degree, Theon at half a degree. Schiaparelli (p. 17) shows that the theory was not started to explain the precession of the equinoxes, ' which was discovered by Hipparchus, but was unknown to Eudoxus, Pliny, and Theon' (Heath, 200). , Eudoxus supposed the annual motion of the sun to be perfectly uniform; he must therefore have deliberately ignored the discovery, made by Meton and Euctemon sixty or seventy years before, that the sun does not take the same time to describe the four quadrants of its orbit between the equinoctial and solstitial points' (ib.). ~3. KUt TOUTflIV Si rill' ".iv 'II'pWT1)v "ut S~uTlpuv rill' u~v dVUL IItI(VUL" i. e. the planets shared not only the diurnal motion of the sun and the moon, but also their motion along the ecliptic. The periods of this motion, ' in the case of the superior planets, are respectively equal to the sidereal periods of revolution, and in the case of Mercury and Venus (on a geocentric system) one year. As the revolution of the second sphere was taken to be uniform, we see that Eudoxus had na idea of the zodiacal anomaly of the planets, namely that which depends on the eccentricity of their paths, and which later astronomers sought to account for by the hypothesis of eccentric circles; for Eudoxus the points on the ecliptic where successive oppositions or conjunctions took place were always at the same distances, and the arcs of retrogradation were constant for each planet and equal at all parts of the ecliptic. Nor with him were the orbits of the planets inclined at all to the ecliptic; their motion in latitude was believed by Eudoxus to depend exclusively on their elongation from the sun and not on their longitude' (Heath, 200-201). ~6. ~ TaU'lI, nearer than this to the centre of the universe, the earth. ~7. 6.'II'_WV, te. T;W uq,urpWv or TWV q,opWv. 'Of all the planets' would have been more accurate. as. rij, Si Tp(T1)' 6.'II'AIITWV TO~ 'II'o).ov, II' Tii SLA ".lC1f11V TWV t'l'S(!,,1' .tVUL, i. e. 'the third sphere had its poles at two opposite points on the

zodiac circle, the poles being carried round in the motion of the second sphere; the revolution of the third sphere about the poles was again uniform and took place in a period equal to the synodic period of the planet or the time which elapsed between two successive oppositions or conjunctions with the sun' (Heath, 201). It is not clear in which of the two possible directions this sphere rotated, but Schiaparelli shows that this does not matter for the theory. ~9. njl &~ TucipT1JI rlJv +opcb Ka.T~ TOV (.roICAOV T6V) ~.~ot",,..ll'Ov 'II'pOi TOV ~CTo., Ta.dT1JI (1C~ICAov). The fourth sphere moved in a circle inclined to the equator of the third. The inclination 'was constant for each planet but different for the different planets. And the rotation of the fourth sphere about its axis took place in the same time as the rotation of the third about its axis but in the opposite sense. On the equator of the fourth sphere the planet was fixed, the planet thus having four motions, the daily rotation, the circuit in the zodiac, and two other rotations taking place in the synodic period' (Heath, 201). The combined effect of the rotation of the third and fourth spheres is thus described by Simplicius (496.23-497. 6): 'The third sphere, which has its poles on the great circle of the second sphere passing through the middle of the signs of the zodiac, and which turns from south to north and from north to south, will carry round with it the fourth sphere which also has the planet attached to it, and will moreover be the cause of the planet's movement in latitude. But not the third sphere only; for, so far as it was on the third sphere (by itself), the planet would actually have arrived at the poles of the zodiac circle and would have come near to the poles of the .universe; bllt, as things are, the fourth sphere, which turns about the poles of the inclined circle carrying the planet and rotates in the opposite sense to the third, i. e. from east to west, but in the same period, will prevent any considerable divergence (on the part of the planet) from the zodiac circle, and will cause the planet to describe about this same zodiac circle the curve called by Eudoxus the hippopede, so that the breadth of this curve will be the (maximum) amount of the apparent deviation of the planet in latitude, a view for which Eudoxus has been attacked' (Heath, 201-202). Schiaparelli has shown how it was possible for Eudoxus, with the geometrical knowledge at his command, to arrive at the hippopede (horse-fetter) or spherical lemniscate (a sort of figure of eight) as the path of a planet so far as it is determined by the third and the fourth of its spheres. But in virtue of the second t/lopa. the lemniscate itself moves along the ecliptic. The actual motion of the planet among the fixed stars is due to the combination of these two motions. For half the synodic period the motion of the planet along the lemniscate accelerates its motion along the ecliptic, and for half of the period it retards it. When the backward motion along the lemniscate is greater than the forward motion of the lemniscate the planet retrogrades, and when the two motions are equal it ill stationary. The theory is evidently meant to explain the retro-

COl\IMENT ARY gradations and the stations of the planets; while the breadth of the lemniscate defines their motions in latitude. Except in the case of Mars, Eudoxus (according to the figures given by Simplicius 495. 26-29, 496. 6-9) assigned fairly accurately both the synodic and the zodiacal or sidereal periods, which implies the use of careful observations whether Egyptian or Babylonian. We do nol know the angles of inclination of the axis of the fourth to that of the third sphere which he assigned for the several planets, but taking the most probable angles Schiaparelli has shown that 'for Jupiter and Saturn, and to some extent for Mercury also, the system was capable of giving on the whole a satisfactory explanation of their motion in longitude, their stationary points, and their retrograde motions; for Venus it was unsatisfactory, and it failed altogether in the case of Mars. The limits of motion in latitude represented by the various hippoptdes were in tolerable agreement with observed facts, although the periods of the deviations and their places in the cycie were quite wrong' (Heath, ZI I). 30. £tVo,L S, rijll Tph'lS cr+o,(pus TOUS mSXous TWV I'Ev iiXXwv tS(oull, TOUIl SE T~S 'A+poS(TYJS Kul TOU 'EPl'ou TOUS ulhous. 'As regards Mercury

and Venus, inasmuch as their mean positions coincide with the mean position of the sun, Eudoxus must have assumed that the centre of the hippopede always coincides with the sun. This centre being on the ecliptic and at a distance df 90° from each of the poles of rotation of the third sphere, the poles of the third sphere of Mercury and the poles of the third sphere of Venus coincide' (Heath, 210). 31-35. These names for the planets are apparently late. They occur first in PI. Epino11lls 987 B f., where they are mentioned as comparatively new (the name Hermes occurs in Tim. 38 n). Plato ascribes the names to a Syrian origin, and they were in fact derived from Babylonia. In earlier Greek literature only ·EO"7I'EPO!; and 'Ewu.popo!; are mentioned by name, though the names cl>aLvwv (Saturn), cl>al8wv (Jupiter), ITvpOU!; (Mars), cl>wu.poPO!; (Venus), lTL>"/3WV are probably old (Burnet, E. G. P.3 23, n. I). 8$1. CaUippus of Cyzicus (fl. 330 B. c.) studied with Polemarchus, a friend of Eudoxus, and is said to have stayed at Athens with Aristotle, 'correcting and completing, with Aristotle's help, the discoveries of Eudoxus ' (Simpl. 493. 5-8). 33-34. TOUT' ••• Tci~LV, which is omitted by E, is doubtless a gloss like tbose (also beginning with TOilT' (UTL) which Ab has in A. 9841> 11,1'.10091\ 26. Cr. I. I053b3I. 34. TI\i I'Ev TOU ALOS Kul TIji Toil Kpovou TO alho lK£(V't! d'll'£S(Sou. As a matter of fact, Eudoxus' theory, as we have seen, works best for these planets. Callippus had eviclently 'not perceived the elliptic inequality in the motion of either planet, though it can reach the value of five or six degrees' (Dreyer, 104). Nor can he have perceived their deviations in latitude. 35. T4i S' ~XL't' KQ.l ,.yj cr£X~vn SUO ~uo £TL 'II'pocr9UEull EtVUL cr+ULPUIl,

39 1

n,

It "i).).IL cl1rOSWCJ'ILV. Simplicius tells us that' according to Eudemus, Callippus asserted that, assuming the periods between the solstices and equinoxes to differ to the extent that Euctemon and Meton held that they did, the three spheres in each case (i. e. for the sun and moon) are not sufficient to save the phenomena, in view of the irregularity which is observed in their motions' (Heath, 218). With regard to the sun, Euctemon, about 430 B. c., 'had made the length of the seasons (beginning with the vernal equinox) 93, 90, 90, and 92 days respectively ... Callippus, about 330 B. c., made the corresponding lengths 94, 92, 89, 90 days respectively' (ib. 2Is)-a much more accurate estimate. Callippus accounted for the inequality by supposing, besides the three spheres attributed by Eudoxus to the sun, a fourth with its poles on the third, and a fifth with the sun on its equator, its poles on the fourth sphere, and its axis slightly inclined to the axis of the fourth; the fifth sphere rotating at the same speed as the fourth and in the opposite direction. Thus Callippus explains the sun's unequal motion in longitude as Eudoxus explained the synodic inequalities of the planets, by a hippopedt; and' this representation of the motion of the sun is almost as accurate as that obtained later by means of the eccentric circle and the epicycle' (id. 216). Simplicius implies that Callippus assigned two new spheres to the moon for the same reason; i. e. he 'was aware of the inequality in the motion of the moon in longitude' (ib.)-a discovery which would naturally have resulted from comparing the times of lunar eclipses with the corresponding longitudes of the moon. Here again a hippopede would explain all the facts except evection. a7. TOLS S, ).OL1rOLS "WV 1r).ClVtlTlaW iKQCJ'T,!, ,,(ClV. Simplicius tells liS that 'the reason why Callippus added the one sphere which he added in the case of each of the three planets Ares,Aphrodite,and Hermes was shortly and clearly stated by Eudemlls' (497. 17-24); but he does not tell us what it was. We have already seen that Eudoxus' system fails signally with Mars. The fifth sphere was probably meant to account for the retrogradations of Mars, without assuming as Eudoxus did a synodic period other than the true one (260 instead of 780 days). Schiaparelli has been able to show how three concentric spheres instead of Eudoxus' latter two will give the planet at certain points , a much greater direct and retrograde velocity with the same motion in latitude' (Heath, 2I 5) and thus' preserve the appearances' much better. In the case of Venus and Mercury also, Callippus' fifth sphere enabled him to approach nearer to the f.lcts than Eudoxus had done. a8. Eudoxus and Callippus had offered a purely geometrical account of the planetary system; Aristotle aims at a mech,lI1ical accollnt, and cannot isolate the system of one planet frolll th.lt of the next. He therefore supposes for each' planet' excl'pt the Illoon certain spheres which' roll back' the outer sphere of the plalld just ncar ... r to the earth than the given planet, i. e. which pre\'ent the influence of Ihe forward-IllO\ ing- or Tn +ClWO"tvCl

COMMENTARY deferent spheres of one planet from affecting the next. The mode of operation of the ' backward-rolling' spheres is explained clearly by Heath. 'Suppose A, B, C, D to be the four spheres postulated for Saturn, A being the outermost and D the innermost on which the planet is fixed. If inside the sphere D we place a first reacting sphere D' which turns about the poles of D with equal speed, but in the opposite sense, to D, the rotations of D and D' will mutually cancel each other and any point of D' will move as though it wns rigidly connected with the sphere C. Again, if we place inside the sphere D' il second reagent sphere C' rotating about the same poles with C and with equal speed, but in the opposite sense, the rotations of C and C' cancel each other, and any point of C' will move as if it were rigidly connected with the sphere B. Lastly, if inside C' a third reagent sphere B' is introduced which rotates about the same poles with Band at the same speed but in the opposite sense, the rotations ofB and B' will cancel each other and any point of B' will move as if it were rigidly connected with the sphere A. But, as A is the outermost sphere for Saturn, A is the motion of the sphere of the fixed stars; hence B' will move in the same way as the sphere of the fixed stars j and consequently Jupiter's spheres can move inside B' as if the spheres of Saturn did not exist and as if B' itself were the sphere of the fixed stars' (p. 218). In this system, however, both the innermost reacting sphere of a planet and the next sphere to it, the outermost deferent sphere of the next planet, are moving with the same motion, viz. that of the fixed stars, so that the second of these two spheres is superfluous. Aristotle might thus have reduced the total number of spheres by six. 1074& 5. The subject of 'W'oLeiatcu is cI1I'aYTa, which ... O'1IVT((MuaL ,..aUaL (a1 uq,a'ipcu) l073 b 38. ~I' cfJop&I' answers to TO; cfJaLVOJUl'a 1074& I.

6. at 7. at

/,~v 6KT~, i. e. four each for Saturn and Jupiter (lo73b 23, 34). 8~ ,..ivn Ital dltocnv, i. e. five for each of the other five bodies

( lo73 b 17 and 35,23 and 37)· 7-8. TOUT..V8,/,6val lid 8ei .•. +ipna.L. •Aristotle should have realized

that, strictly speaking, the account which he gives in the Meleorologica of shooting stars, comets, and the Milky Way necessitates the introduction of four reacting spheres below the moon. For, according to Aristotle, these phenomena are the effects of exhalations rising to the top of the sublunary sphere and there coming into contact with another warm and dry substance which, being the last layer of the sublunary sphere and in contact with the revolution of the outer heavenly sphere, is carried round with it; the rising exhalations are kindled by meeting and being caught in the other substance and are carried round with it. Hence there must be a sphere below the moon which has the same revolution as that of the sphere of the fixed stars, in order that comets, .tc., may be produced and move as they are said to do. The four inner spheres producing the moon's own motion should therefore be neutralized as usual by the same number of reacting spheres' (Heath, 219).

A.

8.

10 74&

5-14

39.3

10-1~. 0 ~ •.. 'II'l"TI. The number of the spheres in the several theories is as follows:

Saturn Jupiter Mars Venus Mercury Sun Moon

Eudoxus 4

Callippus

Aristotle

4

7

3

5 5 5 5 5

26

33

7 9 9 9 9 5 55

.. . ..

..

4

3

IlI-14. .t Sa ... TlCJ'CJ'a.pciKol'Ta.. It is not evident how Aristotle 'reduces the number from 55 to 47. If CalJippus' extra spheres for the sun and the moon, and the corresponding reagent spheres of the sun, be deducted, the total is reduced only by six. Alexander makes three suggestions (706. 8-15): (I) that Aristotle subtracts the two Callippean spheres of the sun, and the two reagent spheres to correspond, and similarly subtracts four spheres from the moon, forgetting that there are here no reagent spheres to be subtracted. (2) that he subtracts all the extra spheres assigned to the sun and the moon by Callippus and himself, forgetting that two of the extra sun-spheres are needed to counteract two of the Eudoxean sun-spheres. (3) that, as Sosigenes had suggested, we should read lvvEa. for (7I'To.. Another suggestion has been made by Krische, who (followed by Schwegler and Bz.) holds that the motions to be suhtracted are the four reagent motions of Mercury which prevent its forward motions from affecting the sun, and the four reagent motions of the sun which prevent its forward motions from affecting the moon. These, he thinks, may be omitted because, the sun and the moon being far from one another and from the planets, there is no danger of their being affected by the forward movements of Mercury and the sun respectively. To this view there are three objections. (a) Aristotle says nothing of a greater isolation of the sun and the moon, and it is clear that he believed all the spheres to be in contact (De Caelo 287& 5-1 I)presumably assigning various thicknesses to the shells of the spheres. (6) The reagent spheres are spoken of as belonging to the system of the outer, not the inner, of the two planets concerned (I. I), so that the meaning required by Krische's view would have been expressed by saying' if one were not to assign 10 Mercury and 10 llu sun the motions we spoke of '. (c) Krische ignores De Caelo 291 b 35 £~o.1'1'OV~ 'YOp ~~tOS "ClI. U(~~VI'1 "'JlOMa., "tJI~EtS ~ TWJI 7r~aJlw,uJlwJI /1UTpwV lJlm. This of course refers to the forward motions only. Now the greatest number of forward motions assigned to any of the planets is five, so that Aristotle must have assigned less than five forward motions to the sun and the moon; i. e. the reduction of the total number of spheres II7S·1

cc

COMMENTARY deferent spheres of one planet from affecting the next. The mode of operation of the ' backward-rolling' spheres is explained clearly by Heath. 'Suppose A, B, C, D to be the four spheres postulated for Saturn, A being the outermost and D the innermost on which the planet is fixed. If inside the sphere D we place a first reacting sphere D' which turns about the poles of D with equal speed, but in the opposite sense, to D, the rotations of D and D' will mutually cancel each other and any point of D' will move as though it was rigidly connected with the sphere C. Again, if we place inside the sphere D' Il second reagent sphere C' rotating about the same poles with C and with equal speed, but in the opposite sense, the rotations of C and C' cancel each other, and any point of C' will move as if it were rigidly connected with the sphere B. Lastly, if inside C' a third reagent sphere B' is introduced which rotates about the same poles with Band at the same speed but in the opposite sense, the rotations ofB and B' will cancel each other and any point of B' will move as if it were rigidly connected with the sphere A. But, as A is the outermost sphere for Saturn, A is the motion of the sphere of the fixed stars; hence B' will move in the same way as the sphere of the fixed stars j and consequently Jupiter's spheres can move inside B' as if the spheres of Saturn did not exist and as if B' itself were the sphere of the fixed stars' (p. zI8). In this system, however, both the innermost reacting sphere of a planet and the next sphere to it, the outermost deferent sphere of the next planet, are moving with the same motion, viz. that of the fixed stars, so that the second of these two spheres is superfluous. Aristotle might thus have reduced the total number of spheres by six. 1074& 5. The subject of 'IfO~eicrtll~ is 4'11"4117'4, which - O'W1',O'LauL WalTa, (Ill CTf/JII&,xu) 1073b 38. ,..qv "'opO.v answers to TQ ~vOp.ua. 1074& I. 6. lit jIo~!' 4"T~, i. e. four each for Saturn and Jupiter (1073b z3, 34). 7. lit 8~ nl'Te ,,"l et"oCTW, i. e. five for each of the other five bodies (1073b 17 and 35,23 and 37). 7-8. TOII,...!' 8~ JUS!'II' o~ 8ei .•. +l"TII~. •Aristotle should have realized that, strictly speaking, the account which he gives in the Mtltorologica of shooting stars, comets, and the Milky Way necessitates the introduction of four reacting spheres below the moon. For, according to Aristotle, these phenomena are the effects of exhalations rising to the top of the sublunary sphere and there coming into contact with another warm and dry substance which, being the last layer of the sublunary sphere and in contact with the revolution of the outer heavenly sphere, is carried round with it; the rising exhalations are kindled by meeting and being caught in the other substance and are carried round with it. Hence there must be a sphere below the moon which has the same revolution as that of the sphere of the fixed stars, in order that comets, .tc., may be produced and move as they are said to do. The four inner spheres producing the moon's own motion should therefore be neutralized as usual by the same number of reacting spheres' (Heath, ZI9).

A. 8. 107480 5-14

39.}

10-12. ~ ~ .•. win•. The number of the spheres in the several theories is as follows:

Eudoxus Saturn Jupiter Mars Venus Mercury Sun Moon

.

Callippus

.

4

4

4 4 4 3 3 26

5 5 5 5 5 33

Aristotle 7 7 9 9 «} «}

5 55

12-14. .t sc ... nCl'CI'ClpciKOVTCl. It is not evident how Aristotle 'reduces the number from 55 to .. 7. If CalJippus' extra spheres for the sun and the moon, and the corresponding reagent spheres of the sun, be deducted, the total is reduced only by six. Alexander makes three suggestions (706. 8-15): (I) that Aristotle subtracts the two Callippean spheres of the sun, and the two reagent spheres to correspond, and similarly subtracts four spheres from the moon, forgetting that there are here no reagent spheres to be subtracted. (2) that he subtracts all the extra spheres assigned to the sun and the moon by CaIlippus and himself, forgetting that two of the extra sun-spheres are needed to counteract two of the Eudoxean sun-spheres. (3) that, as Sosigenes had suggested, we should read WV(a. for €7M'a.. Another suggestion has been made by Krische, who (followed by Schwegler and Bz.) holds that the motions to be suhtracted are the four reagent motions of Mercury which pre\'ent its forward motions from affecting the sun, and the four reagent motions of the sun which prevent its forward motions from affecting the moon. These, he thinks, may be omitted because, the sun and the moon being far from one another and from the planets, there is no danger of their being affected by the forward movements of Mercury and the sun respectively. To this view there are three objections. (a) Aristotle says nothing of a greater isolation of the sun and the moon, and it is clear that he beiieved all the spheres to be in contact (De Caelo 28 7& 5-11}presumably assigning various thicknesses to the shells of the spheres. (6) The reagent spheres are spoken of as belonging to the system of the outer, not the inner, of the two planets concerned (I. I), so that the meaning required by Krische's view would have been expressed by saying' if one were not to assign 10 Mercury and 10 lhe SUfI the motions we spoke of'. (c) Krische ignores De Caelo 29 1b 35 €AtiT'TOV~ 'Y¥ ~'\tO~

KG'

O'('\~V'I1

KtVOWrUt

Ktv~(t~ ~

TWV

",Aa.vwp.lvwv dO'Tpwv IvUJ,.

This of course refers to the forward motions only. Now the greatest number of forward motions assigned to any of the planets is five, so that Aristotle must have assigned less than five forward motions to the sun and the moon; i. e. the reduction of the total number of spheres

cc

394

COMMENTARY

to 47 IS not got by subtracting reagent spheres only, as Krische supposes. Dreyer (p. 114) suggests, after Martin, that Aristotle might have meant to dispense not only with the extra Callippean spheres of the sun and the moon but also with one of the Eudoxean spheres of the sun, that which was devised to explain the supposed motion of the sun in latitude, and accordingly to reduce the reagent spheres of the sun to one. This would give the number 47, but as Dreyer observes Aristotle is unlikely to. have thought of this reduction. There is at any rate nothing ill this passage to suggest it. The most probable explanation of Arist0tle's meaning is the second given by Alexander, viz. that as regards the sun and the moon Aristolle proposes to return to Eudoxus' theory. But if this be so, he holds that the sun and the moon have fewer motions than any of the planets; why then does he say in the De Cado (loc. cit.) that they have fewer motions than some of the planets? The answer is that the paradox he is examining there is that the number of motions of the heavenly bodies does not increase steadily as we proceed inward from the sphere of the fixed stars, which has one only, but first increases and then decreases. It is enough for the statement of the paradox to say that the sun and the moon have fewer motions than some of the planets, and Aristotle does not say more than the statement of the paradox requires. 14. The manuscripts and Alexander have cr+cnpwv, while Them.Cand Simpl.C have cpopwv, and read Kat Ta.~ aiu(J7JTa.~ l. 16, which is omitted by Alexander. If these last words are kept, they must refer to the spheres, and since the number of the spheres cannot be inferred from itself, ucpatpwv in I. 14 cannot stand. cpopwv is probably an early emendation which has come in for this reason. But it does not suit the context. It is not the case that Aristotle has so far enumerated motions and only now proceeds to infer corresponding spheres. Spheres have been mentioned throughout the passage I073b 171074& 14, and the enumeration in 1074& 6-14 has been expressly stated as an enumeration of spheres. ucpatpWv therefore is right. But if so, Kat Ta.~ aiu~Ta.~, as we have seen, cannot also be right. In any case the word &.PXa{ is not appropriate to the sensible things in question, the spheres, but to their movers, and it is to these that the word ol!u{a, also is in the context applied (I. 22). The argument in II. 17-24 is purely an argument from the number of the spheres (or movements) to the number of the moving causes. Goebel is therefore right in omitting Kat Ta~ aiu(J7JTa.~. 17~4. The argument is: (I) There is no motion in the heavens which does not contribute to the motion of a star. (2) Every substance which is free from outside influence (tl.1I'a8~~ I. 19 = d.K{V7JTO~ I. 15) and is enjoying the summum bonum must be an end, and must produce a motion by final causality (I. 22). In other words, All motions in the heavens are motions required to explain the behaviour of the heavenly bodies. Every perfect substance produces a motion in the heavens.

395

Therefore the number of perfect substances is the number of the motions required to explain the motion of the heavenly bodies. 20. Bz. is clearly right in proposing to read TiXo~ (which is read by two manuscripts of Alexander); this is shown by W~ TiAO~ o~a-aL cpopa .. I. 23. 21. Talha~, the 55 (or 47) unmoved movers answering to the 55 (or 47) spheres. 22-23. The movers of the planetary spheres are here said to act as final causes on the planetary spheres, as God does on the sphere of the fixed stars; i. e. a sort of desire is ascribed to the planetary spheres; cf. De Gaelo 292a 20-b 25. The relation of their movers to God is nowhere stated, but is presumably also one of desire. Though the mover is the T€Aor; cpopa.. here, the moved body is the T€Ao~ cpopa~ in I. 30; i. e. the mover is the o~ tll£Ka in the sense of the TI1I6~, and the moved is the o~ tll(Ka in the sense of the TIIIL, to use thl' language of 1072 b 2. 31-38. The unity of the universe is proved on physical grounds in De Cado i. 8, 9; Aristotle here offers the metaphysical proof which he there merely refers to, 277 b 9. Schwegler points out a difficulty into which Aristotle falls. If the immateriality of the first mover proves its uniqueness, how can there be 55 immaterial movers, as Aristotle's theory implies? The objection goes back to Plotinus, E1I11. v. I. 9 71'W~ Of Kat 71'oAAo. oVrwr; !la-wp.aTa JIITa ilAl1~"of! XWPL'ova-l1~; and is difficult to answer. Cf. Introduction, cxxxix f. On this section cf. note at beginning of ch. 33. lIaa ciple"cii 'II'oXM, tThflv EXEl. Cf. Z. 1044 a 7, De Gaelo 278" 18. 34. El~ ya.p Myo~ KaL b aho~ 'II'oXx,wv, olov civepw'll'oU, I"'KpUTfI~ S( d~. Aristotle expres~es himself rather obscurely, but the point seems to be this: One and the same definition, e. g. that of man, applies to .many individuals, but Socrates is only one, and therefore must have in him something over and above the definition of man, something to distinguish him from other men, i. e. must have ilAl1' 35-36. TO SE T( ~v Etval ... TO 'II'PWTOV, i. e. the prime mover, which has been described in 1072a 25 as pure actuality or essence. 38-b 14. For Aristotle's views on the element of truth in popular religion see De Gaelo 270b 5-9, 284" 2-13, b 3, Afe/eor. :B9 b 19-3 0 , and cf. PI. Grat. 397 c, Phil. 16 c. Towards the de/ails of popular belief Aristotle adopts a somewhat contemptuous attitude; cf. n. 1000a 9, De Gaelo 284" 18. 3. O~TOl. T~e reference is rather vague-either ~':' the beings that move the stars (a 22) or more probably to the stars themselves (,. 30). Cf. 1073" 3-b I7 n. and n. at beginning of ch. 3-8. Tel SE XOl'll'ci ••. dpfl"EVOl~. Aristotle speaks as if Cronos, Zeus, Ares, Aphrodite, and Hermes were primarily star-gods and only later had human characteristics assigned to them. This is not historically true; the application of these names to the planets is late (cf. I073 b 31-35 n.). His meaning is probably more general-that

COMMENTARY the gods of mythology have their origin in the prime forces that lie behind nature, and that early religion is right in recognizing the divine behind nature (11. 8-10). 4. For the utilitarian value of myth cf. a.. 995& 4. 5-7. The anthropomorphism of the early beliefs is referred to similarly in B. 997 b 10, Pol. 1252b 26. In Aristotle's own view the stars are really much more divine than men (E. N. 114 1 & 34). 6. Kilt TWV 4}'}'wv t4wv 6"o(oul TLI7(, Alexander refers to the Egyptian mythology, and Aristotle may have had this in mind, since he refers to barbarians, and indeed to the Egyptians, in a similar connexion (De Caelo 270b 5, Pol. 1329b25-33)' The traces of zoolatry in Greek religion are very slight and their meaning not clear. Cf. Farnell, Culls of the GreeR Slales, iii. 58-62 on the horse-headed Demeter, iv. 115-116 on Apollo AVIC(Lo~. 10. For the belief in cycles of artistic and scientific discovery cf. De Cado 270b 19, Meteor. 339 b 27, Pol. 1329b 25. Plato already has the notion; he speaks more than once of past destructions of mankind by fire or water (11·m. 22 C, 23 A-B, Crit. 109 D, Laws 676 A-677 D).

The mode if e.:l:ls!ence

of the supreme reason (ch.

9)·

1074b 15. What must be the mode of existence of reason, if it is the most divine thing in the world? (I) If it thinks nothing, it is no better than a man asleep. (2) If it thinks, but its thinking depends on something else, it being itself only potency, not it but its thinking will be the best thing. (3) What does it think? Itself or something else? If the latter, either the same object always or different things at different times. Does it make a difference whether its object is noble or trivial? Evidently it must contemplate what is most divine, and without changing; any change would be for the worse and would infect with movement what is unmovable. 28. (Return to question (2).) If it is only a potency, (a) the continuity of its thought will be laborious; (b) its object will be nobler than it. The potency may be realized in the thinking of the worst possible object, so that the mere thinking is not what is best. 33. (Return to question (3).) Therefore, since reason is the best thing in the universe, it must think itself; its thinking is a thinking of thinking. 35. (4) But how can this be? All apprehension seems to be of another, and of itself only by the way. And (5) is it thinking or being thought that gives reason its goodness? 38. (Answer to question (4).) Where the object is immaterial it is

397 identical with the subject, and this is the case with the object of reason. 107585. (6) Is the object composite? If sq, the thought of it involves transition. No; everything immaterial is indivisible. As the human reason (or rather that of composite beings) is in a certain period of time (for it possesses its good not in this or in that but in a whole, since its good is different from itself), so is the divine self-thought throughout eternity. Aristotle now turns to the consideration of b vow, i.e. of the supreme intellect which has in ch. 7 been shown to be implied as the cause of the movement of the heavens. 1074b 16. The description of the supreme reason as the most divine M .a.L"O"'~VW" is strange, since Ta. r/lcu.vop.(va. means properly things apprehended by sense. But r/la.lv(u6a.L can also be used of what is discovered by reason (Bz. Index 80988), and seems to be used here of all the things discovered whether by sense or by reason. 16-35. There are certain difficulties, which must be met if we are to succeed in describing the supreme reason in such a way as to make it the most divine of all the things we know. (I) LI. 17, 18. We must not describe it as knowing nothing. This is to make it an unrealized potentiality, which is no fit object of worship. (2) Ll. 18-21. We must not say that it knows but something else determines it to know. This is to make it essentia11y a Bvva.p.tt;, which must be inferior to its actuality and therefore not the best thing in the world. (3) L1. 21-27. It must know (a) itself or (b) something else, and if something else, then either (i) always the same object or (ii) different objects at different times. Now the object of knowledge makes a difference to the value of the knowledge; the object of the supreme. reason must therefore be what is most divine, and therefore not different things at different times. Any change must be a change for the worse, and, apart from this, no change should be ascribed to that which has been shown in ch. 7 to be unchangeable. (ii) is thus set aside. Aristotle now (1. 28) recurs to the second difficulty, though this has already been dealt with in II. 18-21. He has in 11. 21, 22, implied that that question is not quite settled, and he returns to it because it has a bearing on the third. If the supreme reason is a mere faculty of knowing, then (a) it will find continuous knowledge toilsome (cf. ®. 1050b 24, De Somno 454 8 26), which is absurd, and (b) the object of its knowledge, which as we have seen (11. 25, 26) must be the most divine thing in the world, will be more precious than the reason or its knowing, since, if reason is a mere faculty, it is a Bwa.p.tt; TWV ~va.VTlwv and is capable of being actualized as the knowledge of the worst thing in the world, so that its mere actualization cannot be the best thing in the world.

CO:\T:\TENTARY This enables Aristotle (1. 33) to set aside not only the suggestion that the supreme reason is a mere faclllt}', but also the suggestion (3 (b) above) that it knows anything other than itself. Since it is the most divine thing in the world (\. 16), and its object is the most divine thing in the world (II. 25, 26), it must be its own object. Its knowing is a knowing of knowing. The argument is somewhat confused by the failure to keep the second and the third question distinct. For the doctrine of voIJcr.w~ v61Jcr~~ cr. 1072b 20. 18-IU. Alexander supposes Aristotle to be here setting aside the suggestion that not reason as a whole but some part of it is what strictly speaking knows (KVptoV). But this interpretation is ruled out by dAM. 8vvap.L~ 1. 20 and by .lTE vov~ ElTE v~" 1. 21, where vo~ answers to 8vvap.L~ I. 20. cLUo KVPLOV is (some external condition determining reason to activity'. 35-38. Of the two difficulties raised here, Aristotle answers the first in 38-1075a 5; he points out that the divine V~CTt~ knows itself not lv 7raplP'Yw but as its only object. The second question is left unanswered. The answer Aribtotle probably has in mind is something iike this: If A knows B and is known by C the question may fairly be asked 'is it in virtue of its knowing or of its being known that A is good? ' But when A knows itself, the question becomes 'is it because A knows A or because A is known by A that A is good?' and this is an unmeaning question. 36. u~rij~ S' lv wup
A.

9.

1074b 1 8 - 107580 10

399

perly the objects of brtUT~P.1J (Stcl.VOUl). It is therefore better to folIow Alexander's interpretation: 'As the human reason, or rather the reason of beings compounded out of matter and form'; the last words extend the remark so as to make it refer to any beings other than man who have reason and also have matter. It is awkward that cnJV(hTOV should refer in 1. 5 to the object and in I. 8 to the subject of knowledge, but this is not unlike Aristotle's manner; he is careless in such matters. For the opposition of T6 cnJV8£TOV, that which is half-divine, halfanimal, to God, cf. E. N. II77b28, 1178820. Iv TLVI XpcSV'{I. Bz. compares 1072b 15 P.IKp6V XfXlvOV ~p.iv, 25 ~~ ~p.£'i~ 7rOTl, but the comparison is misleading. EV TtYl XfXlvftl means not' for a certain time' nOr 'at certain times' but 'in a certain time '. The meaning of €V when used of time is seen from such passages • T( TWV ~ ' (S. e aT1JX!lp.aTWV • ' ) OUK ' av ~ , as E . 1\r. I 10 IlL I I £K TOIOlJTWV Y'VOITO 'll'cl,\IV (Malp.wv €V &AlYftl xpovftl, I I 74 a 2 7 O~K lCTTIV (V brftloiiv XfXlvftl AafJ'i.v Klv1JutY nA'wv Tei' (is,,, d'\'\' ,i7f'(p, (y Tei' «17f'aVTI, Meteor. 355 8 28 lv 'I( TICTI T'Tayp.lvol~ xpOVOI~ d7f'o8{8wul 'll'a.v T6 A1J
reference is therefore not to the enjoyment of the summum bonum in moments of illumination but to its progressive attainment (V fJ{ftl nA(lw (E. N 1098818). Cf. M. frf. 118584 oM' (se. lUTal ~ (Mal' \ "€V xpOVftl 'I' aT(,,", '\~"\" \' P.OVUlI aA" (V T(""ftl. It is doubtful whether XfXlvftl is to be understood with Tftl81. ••. Tftl8{ ••• OAftl TIV{ in I. 9. If it is, the meaning will be 'for it does not possess the good in this particular time or in that, but it possesses the summum bonum in a certain whole period '. If XfXlVftl is not to be supplied, the meaning is 'for it does not possess the good in this particular activity or in that, but it possesses the summum bonum in an organized life of activity'. g. 6v llUo TL is opposed to alm} a{,rii~. It is because man's summum bonum is different from himself, because he is a cnJV(J'TOV, including in him unrealized potentialities, that time is needed for their realization. God, being pure activity, pure self-thought, enjoys completely in each moment and throughout eternity the bliss which man can be said to enjoy only in a complete life. 10. Bz:s oUrw~ 8~ is not improbably right. But for Sl after a comparative clause cf. 1'. 1003b 5 n. There is a certain degree of opposition between the principal and the subordinate clause which makes 8l not unnatural; cf. B. 9998 27 n.

How the good exists in the world (ch. 10). 1075a II. Is the good a separate element in the universe, or the pervading order? It is both, as in an army-though the general is the good in a higher sense than the order, since it depends on him and

COMMENTARY not vice versa. All things are ordered together for the common weal though as in a household the higher members are less free than the lower. All must, at least in their dissolution, contribute to the whole.

Difficulties in ollur views. ~5. (I) All other thinkers make aU things out of contraries. But neither 'all things' nor • out of contraries' is right. Further, contraries cannot act on one another. Our solution is that there is a lerlium quid, the substratum. But other thinkers make one of the contraries matter (e. g. the unequal, the many). We refute this by saying that the matter which is one for all things is contrary to nothing. Further, on this view all things except the One will share in evil, since evil is one of the two elements. 36. Others do not even make the good and the bad first principles. Yet in all things the good is a principle. The former view rightly makes it a principle, but does not say whether it is final, efficient, or formal cause. b I. Empedocles has a strange view. He makes love the good, but makes it both an efficient and a material cause. Even if the same thing is both, their essence is not the same. In which capacity, then, is love a principle? It is strange also that he makes strife (which = evil) imperishable. 8. Anaxagoras makes the good the efficient cause, for reason is the source of movement; but this implies an end other than reason (unless the efficient and final cause are identified, as by us). Further, why. does he not assume a contrary to the good? II. None of those who speak of contraries use them-unless we recast their views. And no one tells us how, if all things have the same causes, some things are perishable, some not. Further, some make the things-that-are out of not-being; others to avoid this make all things one. 16. (2) No one states a proper efficient cause of generation. Those who posit two principles need a third, supreme one; and those who posit Ideas need a supreme principle. Why do particulars shar~ in Ideas? ~O. Other thinkers are bound to assume a contrary to first philosophy; we need not, since we assume no contrary to its object, for all contraries have matter and potentiality. ~4. If there is nOlhing but sensibles, there is no governing principle, no order, no generation, no celestial movements, but, as in my tho-

1\. 10. 1075& r 1-22

401

logy and in physics, we are referred from one principle always to another. 9.7. If on the other hand there are Ideas or numbers, (a) they cause nothing or at least no motion. Further, (b) how can things that are unextended produce what is extended? Number cannot be either efficient or formal cause of a continuum. Further, (c) no contrary can be the efficient cause, since all contraries are capable of not being, and their activity is at least posterior to their potentiality, so that things could not be eternal if contraries were their cause. But there are eternal things. Therefore the premises must be revised in the way we have stated. 34. (rl) No one tells us what unifies a number, or soul and body, or form and thing. The only true answer is, 'the efficient cause '. 87. {e) Those who put mathematical number first and make a series of kinds of substance, each kind with distinct principles, make the universe disjointed, with many governing principles. But such it must not have.

10758 11-15. The doctrine here stated is that goodness exists not only immanently in the world but transcendently in God, and even more fundamentally in Him, since He is the source of the good in the world, which is produced by the desire for Him as the order in an army is produced by its striving to do the will of its leader. 15. Slc\. rlJ . . TC£~LV ••• Slc\. TOUTO.... Bul. seems to mean not 'for the sake of' but' by reason of'. 16-9.3. Bz. thinks that dAX' iJJcnr£p (I. 19) answers to &U' o~X &p.o{w<;, and that Kul o~X Olh-w<; ••• CTVVTfTUKTUL is parenthetical, explaining '/I"aVTu CTVVTfTUKTU{ '/I"W<;. This leaves p.lv in \. 18 without anything answering to it, and in general seems highly unnatural. It is more natural to make two sentences as Bekker does-{ 1) '/I"aVTu B~ CTVVTfTUKTUL ••• (V(TL<; l
KTA.

19-9.9.. The freemen in the house answer to the heavenly bodies, which are bound by necessity, the slaves and animals to mankind and indeed all sublunary creatures, which are much less rjivine (E. N. 1141834) and whose actions are largely contingent. Aristotle, as Grant observes (EthiCS· i. 286), assumes freedom for man, 'not so much from a sense of the deep importance of morality, but rather from an idea of the slightness of man and of his actions in comparison with nature, and with what he would call the" diviner parts" of the universe'. 9.9.. 'For the nature of each of them is such a principle', i. e. it pro-

COMMENTARY duces obedience to duty in the higher creatures, caprice in the lower. 113. Uyw S' otov d~ y. TA SU1KPL&;jVCU c1vciYK'l 4'11'CIoO'LV 1>.8clv, C all things, even if they make no other contribution to the whole, must at least come to be dissolved " sc. so that better things may be made out of their elements. 115. Aristotle now begins a very brief discussion of some of the main metaphysical doctrines opposed to his own. 116. Xo.PL.CTT~~, cf. K. 1060& 21' n. 118. oiJ.n Si TA 'II'cil'To. OUT. TA l~ Ivo.l'T(wv dp8w~. (I) It is wrong to say that all things come from contraries. There is an eternal substance which does not come from contraries nor from anything else (1069& 30, 1071b 4). (2) Even things that are generated are not ~enerated simply from contraries; there must be a substratum as well (1069 b6 ). 30. c1'11'0.8~ yap Ta Ivo.l'T(o. ~'II" c1>'>'~>'wv. Black cannot be affected by white, but only that which is black. 311. ot TA aVLO'OV TIjI to''!' refers to Platonists, cr. N. 1087b 5, 1088 b 32, 1089 b 6, 1091b 32. Aristotle's point is that matter, the substratum of contraries, should not be made one of the contraries. 9 n~~b : ::: M Ta 'II'0>'>.d probably refers to Speusippus, cf. M. 108 5& 34. 'iJ yap Ill.'l 'iJ ".(0., 'the one matter which underlies any pair of contraries '. 35. TA yap lCaKAv o.~TA 8ciTEpOV TWV CTTOLXf(WV, i. e. the unequal is identified with the bad; cf. A. 988& 14. 37. Robin points out that in the other passages referring to this doctrine of the Pythagoreans and of Speusippus (viz. 1072b 32, 34, N. 1091a 31, 36) TO lCaA6v is mentioned several times, TO lCaIC6v never; and he would read lCaA6v. But TO 1Ca.1C6v is in place here in view of the context (cf. I. 35). b 3. 1C0.1 ws 1ll.1J' ".OpLOV yap TOU ".(y".o.TOs. That Empedocles thought of strife and love as material no less than the other elements is clear from such passages as fro 17. 18-20, especially lCa~ .pu..6rrr; Iv TOW'lV, lO'1] p.~1C6.; T( 'll'MTO'; TE. In Empedocles' time the notion of incorporeal forces did not yet exist. 5. T6 y' .tVo.L o~ Ta.~.,.o, cf. Z. 1029& 22-23 n. 6-7. For strife as the origin of evil for Empedocles cf. A. 98586. Why does Aristotle regard the indestructibility of strife as a paradox? Alexander thinks it is because in the CT.pa'i.pO<; all strife must have disappeared. This interpretation takes no account of TOWO 8' lCTTtv o.~ ; TOV 1Ca.ICOV .pVCTL<;. It must be because of its badness that Aristotle thinks strife must be perishable. He is in fact using his principle that lv TOt<: 11;:I)[OL<; oMlv lCTTL 1Ca.1C6v (@. 1051819, where see the proof). 9-10. c1Uci seems to introduce an objection-Aristotle's first objection to Anaxagoras (cf. tI.TO'II'OV I)€ Ko.( I. 10). Anaxagoras exemplifies the vagueness of early thinkers on the question whether the good is

A. 10. 107Sa 23 -

107S b 19

a final, an efficient, or a formal cause (8 38). He introduces it as an efficient cause, in the shape of reason. But since it must be for some purpose that reason produces motion, there must be another good which is a final cause. The objection is the same which is expressed in A. 988b 6-16. The argument is made clearer by placing a fulI stop after in 1. 8. Aristotle thinks that he can himself dispense with two distinct causes, an efficient and a final. The form of health, as existing in the doctor's mind, is the efficient cause of his action; and as something to be realized in the body of another, it is the final cause. Cf. Z. 1034& 24, A. 1070B ... 10-11. Aristotle complains that Anaxagoras, having recognized reason, or good, as one principle, ought to have recognized evil as another. Elsewhere Aristotle treats him as recognizing opposite principles of good and evil (A. 988& 17, cf. 989&30, b [6). His point must be that Anaxagoras does not explicitly describe the chaos as the opposite of reason or of the good, though implicitly treating it as such (989b 19). But in reality, according to Aristotle, evil cannot be a first principle (Iv "0'1 dpx'}1 oMlv 1l1TL ICQ.ICOV, e. 1051& 19). IS. 04 xp&i.".cn Toil iVa..".£OLI. The same objection is made in A. 985. 17-23 with special reference to Anaxagoras and Empedocles. iC\v ,...~ ~u8,...£crn TLI, cf. what Aristotle says of Empedocles in A. 985& 4 and of Anaxagoras in 989& 30. 13-14. Cf. the discussion in B. 1000B 5-b 21. Aristotle himself escapes the difficulty by making the things which are eternal (I) contain no matter at all, or (2) contain a matter different from that of the four elements, viz. the 7f'lp:rrrov uwp.o., which makes them capable of moving in space but not of being destroyed. 14. ot ,...iv, Hesiod and the other cosmologists, cf. 1072& 19. Aristotle regards the generation of what is from what is not as obviously wrong, and needing no argument to show that it is so. IS. ot S', the Eleatics, cr. A. 986b 10. Their view also is self-condemned, in that it abolishes difference and change. 16-1076& 4. The general trend of these remarks is, as Bz. points out, to show that Aristotle's predecessors give no satisfactory account of the cause of generation and motion. cr. II. 16, 28, 30, 37. But parts of the passage have no bearing on this question, but form a general attack on Aristotle's predecessors and especially the Platonists -II. 20-24, 28-30, 37-1076& 4. 16-17. For Aristotle's own explanation of the eternity of becoming cf. 1072& 10-18, De Gen. el Corr. ii. 10. 17. Toil Sdo 4pXc\I 'ft'OLoiicrLV refers to all Aristotle's predecessors (& 28, N. 1087& 29) or to nearly all (r. 1004 b 30). The contrary principles are, in general, form and matter, and an efficient cause is neede
let"'

Ie

'n

COMMENTARY SLa. T( ya.p l'f.Ti"Xll' ~ I'ITiXIL; se.

Tn "af)' ~"aO"'Ta TWV £18wv.

SlO-1:I4. This curious and difficult passage seems to be an allusion to Plato's recognition (Rep. 4'1'1-.J'78) of ignorance as a state of mind opposed to knowledge and related to not-being as knowledge is to being. • Other thinkers, since they recognize only two, and these contrary, principles, must recognize an ignorance related to one of them (nonbeing or matter) as knowledge is to the other (being or form). But we need not. For we make the highest knowledge refer to a first principle which stands above the contraries and itself has no contrary ; for contraries contain matter, and things containing matter exist only potentially. The ignorance which is opposed to any knowledge leads to an object opposed to the object of the knowledge; but our first principle has no opposite, and therefore for us the highest knowledge has no opposite ignorance.' SlSI. Ta. ll'o.I'T£a. here means' things possessing contrary attributes " while in _ 30 it means the contrary attributes themselves. Sl3. Ka.t SUI'C£I'IL Ta.UTa. IC1TLI'. Tav-ra seems better than Taw&.. Contraries are not potentially the same (though the same thing is potentially possessed of contrary qualities); nor, if they were, would it be in point to say so here. Tav-ra is probably subject and = Tn 1'!>"1JV 'xoVTa. Bz. (reading Tav-r&' lO"'TtV and treating Tav-ra as predicate) takes the words to mean that each contrary is potentially its contrary; quod album esl aclu, idem ntgrum est po/entia d viee versa. It is difficult to see how this can be got out of the Greek. ItI TO ll'a.lIT£OI'. One might conjecture lO"'Tlv (01 lC1Tat) lvaVTlov (or TOV waVTlov). But the text is confirmed by E. E. 122'1- 33 br£l"al ~ d:tr&'T7J oll" d~ Tn TVXOVTa Y{V£Tat, d.U,' d~ Tn £vaVT{a illTot~ lO"'Tlv IvaVT{a, though that is made easier by y{v£Tat. t:l~ means not 'is relative to " which would be 'trp6~, but something like 'leads the mind to '. The passage does not seem to have any connexion with the distinction between d'truT7J and lIyvota in @. 1051b 25, to which Bz. refers. Sl4. d TI I'~ lC1Ta.L 'l\"a.pa. Ta. a.ta&,.Ta. IlUa., 04K lC1Ta.L clpx~ Ka.t TC£eLI Ka.t yiI'EC1LI Ka.t Ta. o4pC£I'La.. If there is nothing besides sensible things, then (I) there is no first principle; for sensible things exist potentially (i. e. include an element of contingency). and if we admit nothing which exists actually we are driven back from one potentiality to another ad infinitum. (2) There will be no order; for this involves something eternal and separate from matter (K. 1060· 26). (3) There will be no generation; for this has been shown to depend on the motion of the heavenly bodies, and ultimately on the prime mover (10'126 10-18). (4) There will be no celestial movements; for they depend on a prime mover. For the consequences of denying the existence of non-sensible, eternal substance cf. B. 999 b 5. K. 1060· 26. Sl6. Ta. "pC£I'La. means the celestial movements, not the celestial bodies, for it is the former that involve a prime mover. For this use of Ta ollp4vta cf. Xen. Mem. i. I. II, PI. Crit. 107 D. Toil'IOUYOLI, the cosmologists, cr. B. 100069.

28. oun is sufficiently confirmed by Cal. 6" 2, Phys. 268b 22, De Caelo 271" IS, De Sensu 439" 32, Pol. 12S2" II. In Z. 1035" 30, Phys. 254" 26 (cf. Pol. 130Sb 15, 1320" 16) the manuscripts are divided between o~, and o~o,. l~ A"eye8wl'. Ie does not refer, as might be supposed, to material causation; Aristotle's point is that numbers cannot be either the efficient or the formal cause of extended magnitudes (I. 30). 30-34. 'But none of the contraries is essentially also a principle of production and of motion; for a contrary is capable of not being, and at any rate its period of action must come after a period of merely potential action. Hence it cannot have been making things from all eternity. Hence TQ; ($VTo, are not eternal. But there are eternal OVTo,. Hence we must give up one of our assumptions,' viz. the assumption that contraries and nothing else are the principles of things. There must be a first principle which is substance, actual, and eternal. 33. AU' InLI' must apparently mean not 'the things that are are eternal', which Aristotle is not likely to have said, but 'there are· things that are eternal', e. g. the prime mover and the heavenly bodies whose eternity has been proved in ch. 7. 34. TOUTO S' cLp1JTIU hI, sc. in 1071b 19, 20. 34-37. On this question CC. H. 6, especially 1045" 30. Form and matter, as Aristotle there points out, belong together and require only an efficient cause to unite them. 37. ot SE ~lyOI'TEI KT~. The reference is to Speusippus, who is mentioned by name in Z. 102S b 21. For the doctrine cf. N. 1090b 13. 1076" I. l1rELII'OSLWStJ. cr. the definition in Poet. 1451 b 34 AfYW 8' E7r'€I.UOO,W&q p.'v(}ov Iv ~ TQ; 17r'€l.Uo8,o, P.F.T' Q).).7JM. o~' €l/(6~ o~' clvdy"7I €lvo". The word is used again of Speusippus' theory in N. 1090b 19. 3. The word 1rO~LTe';F.cr8IU and the quotation from Homer show that clpX71 is used with reference to its meaning of • rule' as well as to its ordinary Aristotelian sense of ' originative source'. For a similar play on the meaning of clPX71 cr. An. Post. 100" 13. 4. O"K Ayu8ol' KT~. Hom. II. ii. 204. Susemihl would omit IlI'Tw, which is lacking in most of the manuscripts. But it is required by the rhythm of the sentence, and it would be particularly easy for the last word of a book to drop out in the archetype. Aristotle is not a thoroughgoing monist. He is a monist in the sense that he believes in one supreme ruling principle, God or the primum movens. But God is not for him all-inclusive. (I) The sensible world is thought of as having a matter not made by God, though the whole history of the sensible world is caused by the desire to approximate to the divine life. (2) There are subordinate spiritual beings (1073" 37, 1074" 15) which move the heavenly spheres without being moved (i. e. move them ~~ !SpEKTa), and whose relation to God is never indicated by Aristotle. Cf. Introduction, pp. cxxxvi-cxli.

COMMENTARY

BOOK

M

Much light has been thrown on the date of Bks. M and N relatively to one another and to the rest of the lJfetap1!J'sics, by Jaeger's researches in his Ans/o/e/es, pp. 181-199, 212-215. Book M, with its clear distinction between the doctrines of Plato, Speusippus, and Xenocrates, belongs to a later period than the criticism of the ideal theory in Book A. The original ideal theory is now for Aristotle somewhat out of date, and he is content to reproduce in chs. 4, 5 what he has said about it in A. 9; his efforts are now turned towards the discussion of mathematical and ideal numbers and magnitudes. The discussion is completed by 1086& 15, and he ends, as he does occasionally elsewhere (Jaeger refers to the end of A and of E. N. ix), with a literary quotation (1086& 17). The final sentence (ib. 18-21) is difficult to construe, and perhaps its last words are missing, as might easily happen at the end of a book. Syrianus tells us that some manuscripts made M end at this point. In M. 1086& 21-32 we have a preface which Jaeger (187-189) has shown to be a doublet of that at the beginning of M (1076& 8-32). The latter is much the more elaborate. It mentions, besides Ideas and numbers, the spatial magnitudes (I. 18); it distinguishes the views of Plato, Speusippus, and Xenocrates (11. 19-22). It treats the discussion of the original ideal theory as a minor matter, sufficiently discussed in the UI,mptKol A&yOl (ll. 26-29). In trying to find a date for the section M. 1086& 21-end, Jaeger concentrates on 1086b 16-19. It is not clear that he is light in supposing that when Aristotle says {3ovAop.t:(}a he must mean, as in A. 990b 9, 11,16,18,23, 99 1b 7, B. 997 b 3, 1002 b 14,' we Platonists '. RLIt. it is at any rate possible to interpret the passage as an argummlum ad hominem directed against Platonists from a Platonic standpoint. What is more convincing is that, while in 1086& 21-24 Aristotle says of the views of the materialists merely that they have been discussed in the Physics, and are inappropriate to the present discussion, in 1076& 8-10 he says that the matter of sensible things has been discussed in the P1!J'sics, and their actuality (or form) has been discussed la/er. I.e., M. ,n#.~086& 18 presupposes, while M. 1086& 21-jin. does not, the discussions of ZH@. The one version presupposes only AB; the other belongs to the time when Aristotle had worked the greater part of the Melap1!J'sics more or less into a single whole. (Jaeger, 212-215.)

Jaeger concludes that M. 1086- 2 I-end belongs to the same early period. as AB, i. e. to Aristotle's stay at Assos in 348-345 B. c. It is only natural, then, that this brief section contains more references to AB than the whole of Z-A (1086 a 34, b 2, 15). But in N. 1091& 32, oTov /3ov),j,p.'()a. Al-y(tv a.~T~ T~ clya.8~11 /(0.1 TO 8.purrov, Aristotle certainly treats himself as a Platonist. N, then, also belongs to the Assos period; and, since Xenocrates was Aristotle's companion at Assos, it is only natural that, while M criticizes him frequently and sharply (e.g. 1083b 2 x,ipurra. A.i-yfTa., A TplTOC TpOrOC), N criticizes him only in passing (1088 b 28-35, 1090b 20-32). Further, the preface in M. 9 undertakes to examine the views of those who hold that the elements (I) of Ideas or (2) of mathematical numbers are the elements of all things. The theory of Ideas is treated of in M. 1086- 32-end. N begins with a reference to the wide-spread doctrine that the elements of all things are contraries, but soon (I087 b 4) settles down to discuss the view that unity and plurality or the equal and the unequal are the elements at once of mathematical number and of all things; and to this theory (that of Speusippus, already mentioned in the preface, M. 1086- 29) and the kindred theory of the Pythagoreans, the rest of N is for the most part devoted. M. 1068& II-N. end thus forms a whole, and a whole earlier than M beginning-I086& IS.

lWo supposed Ainds t?! i",,,,aterial substance /0 be discussedmaiMmalicalobjec/s and Ideas (ch. I. 1076- 8-32). 1076& 8. We have discussed elsewhere the substance of sensible things; we have now to consider whether there is apart from these an unchangeable eternal substance. First we must sift the opinions of others on the question. 16. Some hold that mathematical objects are substances; others hold that the Ideas are. Some believe in both, some identify them, some believe only in the mathematical objects. ss. We will discuss (I) mathematical objects, asking no further questions about them but simply whether they exist, and if so, how; (II) the Ideas (briefly); (lll) and chiefly, whether the substances and principles of things are numbers and Ideas. 1076& g. ill "'~II Tn "..8&&, ••• n,.1 no doubt refers to Phys. i. lIcrr.pOII is refeded by Alexander to Plzys. ii, and by Bz.• to the latter part of the Physics. But neither of these can be described strictly as discussing • substance according to actuality', i. e. form. The position of p.Iv and 8i shows that iXTTlpOV 8i does not refer to the Physics,

COMMENTARY and the part of Aristotle's works which best answers to the description is Mel. ZH0. Bz.'s interpretation is partly actuated by the wish to show that MN do not presuppose the central part of the MtlapJ,ysir:s. Cf. Introduction, pp. xviii f. Ill. 'II'pWTOI'. Alexander's notion that 7f'pUwov means • with special care' cannot be accepted. 7f'pUwov must refer to time. A positive statement of Aristotle's doctrine of • unchangeable and eternal substance' was meant to follow. But this cannot be identified with A, which seems to be an earlier and separate work. 15. TOUT' ••• lucrx1pG(""'"EI'. The order of the words is curious, the object being to throw into prominence the opposition between "OtvOV and ~. •• And that if some doctrine is common to us and them, we may not on that account be privately dissatisfied with our· selves.' For the expression cf. A. 984& 29. \ 19. ot "iI', sr:. Plato and his most orthodox followers, cf. A. 987b 1418. 110-111. ot Ii ... iT.pOL Ii TLI'IS. Alexander ascribes to Xenocrates (745.32) and also to Speusippus (782. 32) the belief in mathematical number only; in 766.8 he ascribes to botll Speusippus and Xenocrates the identification of ideal and mathematical number, and to some of the Pythagoreans the belief in mathematicaillumber only. We may safely infer that he knew little or nothing about the matter. A comparison of Z. 1028b 21-24, where Speusippus is mentioned by name, with A. 1075b 37-1076& 3 and N. 1090b 13-20 makes it evident that it was Speusippus who rejected the Ideas and believed in mathematical number only. Asc. (379' 17) thinks it was Xenocrates who identified ideal number with mathematical, and this is strongly confirmed by the reference in 1080b 29 (where see note) to the well-known Xenocratean doctrine of indivisible lines. ot 8i, then, means Xenocrates, ZTtpot 8i TtVEI the Pythagoreans and Speusippus. Cf. Introduction, pp. lxxilxxvi. Aristotle omits the fourth possible view, ascribed to ~ Ttl in 1080b 21, the view that ideal number exists but not mathematical. all. 'II'PWTOI' "iI', chs. 2, 3. a6. E'II'ILTCI., chs. 4, 5. a7. 11'11')."', • simply, without elaboration'. Pol. 13 ... b 38 T{ Af:YOJUV T7}v ,,&.6o.putv, vVv I'~V d.7f'AcdI, 7f'a.Atv 8' Iv TOil 7f'EP' 1/"ot7/Tt~1 CPOVI'IV ua.q,irrnpov. aerol' vcS"ou XIl,,,I', • as far as the accepted manner of treatlnent requ;relo '-and it requires some discussion of all views held by thinkers of repute. Cf. ixr{o.l ZVE"o., dids "ausa, Diphilus Z""Yp#ot fro 2. 13 0~8~v ~8ICIII7f'otEi"yap Or'TO~ dAA.' ouov VOf'Ov X4ptv, and Pol. 1341 b 31 vVv 8f v0l"";;''' 8dACIII'EV, TOV~ TV7rOV,. pOvov El7f'OVTE~ 7f'Ept o.wwv. 118. T&il' l~WTEPLKW" ).6yw... The meruling of this phrase has been repeatedly discussed; the following discussions in particular may be mentioned: Dernays, Dialoge des Arislole/es, 29-93; Zeller, P1u1. der Griedlen, II. 2. (ed. 4) 112-126; Grant, Elhics of Art'sl. i, App. B; Grote, Ads/olle, ed. 3, 44-53 j Diels in Silztt11gsb. der Ber/. Alead. 1883. 477-494; Susemihl in Neue Jahrb. fiJr PhI1o/. 1884. 265-277;

cr.

8e

Susemihl and Hicks, Polilics of Ansi. 561-565. The other references to the (~WTfPtKOI. Myot in the Aristotelian Corpus are as follows: Phys. 2I7 b 30 7f'PWTOV 8( Ka>.ws txn 8ta7f'op7iuat 7f'(pt awov (i. e. xpOVOV) Kat 8to. TWV (~WTfPtKWV Mywv. E. N. 1102& 26 MYfTat 8( 7f'fpt aVr11S (i. e. ifroxT/s) Kat Iv Tois (~TfPt­ Kois Myots dpKovVTwS tVta, Kat XPYJUT£OV awois' ofov T6 p.£v d>.oyov aVr11s \ , (tvat, TO, of I\OYOV f~OV. E. N. II4o& 2 fTfPOV 8' (UTI 7f'olTJuts Kat 7f'P~tS (7f'tO'TfV0J.I.fV 8( 7f'fpt awwv Kal TOLS (EWTfptKOLS Myots). E. E. 12 I 7b 20 T6 flvat l8£av p.~ p.Ovov d.yaOov d.>..\o. Kal. d>.>.ov cWOVOVV >'£yfTat >'OytKWs Kat KfVWS' €7r£UKmTat 8£ 7f'OMOLS 7f'fpt awov TP07f'OtS Kat (V TOLS lEwTfptKOLS >'oYOts Kat (V TO'S KaTo. cpt>.oucxplav. E. E. I2 I 8 b 32 7f'aVTa ~ Td.yaOo. V(KT6S ~ (V 1f!vxfi, Kat TOWWV alpfTWTfpa TO. (V Tjj ifroXY, KaOa7f'fp 8mlfJOvp.fOa Katlv TOLS (EWTfptKOLS Mr.ots. Pol. 12 78b 30 d.>'>.a. p.~v Kat ri1s dpxl1s yf TOVS >'fyOP.£voVS Tp07f'OVS pq.8wv 8">'fLV' Kal yap (V TOLS (EWTfptKOLS Myms 8Wpt,op.fOa 7f'fpt awwv 7f'OMaKtS. Pol. 1323821 vop.luaVTas Ow lKavws 7f'oMo. >.iYfuOat Kal TWV (V TOLS UWTfptKOLS Myots 7f'fpt. ri1s dplO'TYJs ,wl1S, Kat vVV XPYJUT£OV aWoLs. With these references may be compared the following, in which similar phrases are used: De Caelo 279& 30 Iv TOLS ~KVK>'{OtS cpt>.ouocp~p.a~", E.lf. 1096& 3 (V TOL~ (YKvK>.lots, De An. 407 29 TOLS lv KOtVri YWOP.fVOtS >'OYOts. "Bernays tries to show that in all these passages except the first the reference is to Aristotle's dialogues, which were' exoteric', i. e. were published in a fuller sense than the works in which the references occur. In other words Bernays accepts the distinction, which had certainly become current by the time of Cicero, between the exoteric and the acroamatic works of Aristotle. It may be admitted that all the subjects in question were probably treated of in Aristotle's dialogues, or in other lost works of his which were pUblished in the full sense. Thus (to take the present passage and the first passage from the Eudemiatl Elhics) it is certain that Aristotle criticized the Ideas in the dialogue De P h,./osophia and in the works De Ide,s and De Bono; he may also have dealt with them, as Bernays suggests, in the dialogues De Iuslilia, Sophis/es, and Polilicus. But the meaning of >.6yOt in the Physics passage, as the preposition 8ta shows, is not 'books' but' arguments', and wo in the present passage suggests the same, in view of the frequent tendency in Greek to treat • the argument' as if it were a person, as in AlKatOS Aoyos and "A8tKOS Aoyos, ;, Myos alpin, and many other examples quoted by Diels. By a comparison of Pol. 13 2 3& 21"35 with E. N. I098b 9-18 (dealing with the same subject) Diels shows beyond a doubt that by TO. (V TOLS (~fpf.l(ois MyOtS in 1323& 22 Aristotle means the same as he does by Ta. >.rt6p.fVa in 1098b 10, i. e. that in that passage at least U. Myot means' discussions not peculiar to the Peripatetic school '. This is probably its meaning in the other passages also. The precise shade of meaning may differ in the different passages; in some the reference is to Academic doctrines, in others to discussions or distinctions which were familiar to cultivated 2~7S.2 nd

.

~.

.

.po

COMMENTARY

Athenians of no particular philosophical school. In the present passage the reference probably is to attacks on the Ideas by Antisthenes and by sophists like Polyxenus, the inventor of the 'third man' argument against the Ideas (cf. A. 990b 17 n.). Diels's conclusions do not seem to have been refuted by Jaeger's argument in Aristoteus, 257270. Jaeger thinks the present reference is to the De PhilosopMa. ~9-a~· In 8~ . . . O'Kl+L~. A further reason for brevity in the second part of the treatise, the discussion of the Ideas simpliciler. The third and main part of the treatise (TOV 7f'M{W >..Or0v) must finish by throwing light on the second problem (7f'pOi (KELV71V 8(L np, (1'K~"'fLV d7f'4VTav), so that the second discussion need not itself be elaborate. ao. 3T4V i1l'LO'KOriI'EV, chs.· 6-9.

I.

MATHEMATICAL

OBJECTS (ch. I. 1076& 32-3' 1078b 6).

1076'- a~. If they exist, they must exist either (A) in sensible things, in the way maintained by certain thinkers, or (B) separate from sensible things, or (C) in some other way.

Matlmizalical objects cannol eXIst as distinct substances (ch. 2). 1076& a8. (A) We have shown (cf. B. 998& 7-19) that mathematical objects cannot be in sensible things; (I) because two solids cannot be in the same place, (2) because it would follow that the other powers and characteristics of things must also be immanent. b 4. We now add (3) that on this theory no body can be divided. For it would have to be divided at a plane, the plane at a line, the line at a point, so that since the point is on this view indivisible, the body is so too; and if mathematical body, then also the sensible body in which it is. II. (B) Nor can mathematical objects exist aparl from sensible things. For (I) if there are separate mathematical solids, there will be (a) separate planes, lines, and points, 16. and therefore also besides (b) the planes, lines, and points of the mathematical solid there must be (c) planes, lines, and points prior to (while the former are simultaneous with) the mathematical solid. ~4. Again there will be (d) lines and points prior to the lines in these planes, and (e) points prior to those in these prior lines. 28. The accumulation is ridiculous; there is one set of solids apart from the sensibles, three sets of planes, four of lines, five of points. Which will be the objects of the mathematical sciences? a6. (2) The same argument can be applied to numbers. There

wiI be units apart from the points, units apart from the objects of sense, units apart from the objects of knowledge. 89. (3) The objects of astronomy will exist apart from sensible things, as much as geometrical objects; but how can there be moving objects such as the heavens apart from sensible things? 1077& 4. There will be objects of optics and of harmonics-voice, senses, sensibles, animals, all separate from the ordinary objects of sense. 9. (4) There will be separate objects, which are neither numbers, points, spaces, nor times, for the universal mathematics which is true of all of these alike. 14. (5) The belief violates common sense. It makes mathematical objects prior to sensible things, but really they are posterior in substance, being incomplete. ao. (6) What gives them unity? Things in lhis world are made one by soul, by a portion of soul, or the like, but what gives unity to these divisible quanta? 84. ('1) Length is generated first, then breadth, then depth, so that if that which is posterior in becoming is prior in substance, body is prior to the plane or line; and it is more complete because it is what becomes the vehicle or soul. 81. (8) Body is a substance, but lines cannot be substances, either as form, or as matter (how could a thing be composed or lines ?). 86. They may be prior in definition to body, but they are not therefore prior in substance. That is prior in substance which excels in power of separate existence; that is prior in definition whose definition is implied in the definition of something else. b 4. If attributes cannot exist apart from substances, they are prior in definition to the complex of substance + attribute, but not in substance; thus the product of abstraction is not prior nor that of addition posterior. la. Mathematical objects, then, are not more substantial than bodies, nor prior to them in being (but only in definition), nor separately existent; and since they could not be in sensible objects either (10'16& 38-b II), they exist either noL at all or in some qualified sense.

".v

107& aa. TOL' Uta8tjTOL' .tVUL dTCl. This doctrine is said (I. 39) to have been discussed ~v Toi~ 8U171'OP'7p.tUTL", i. e. in Bk. B, and the reference is clearly to 998& '1-19. The view in question is there described in a way which marks it off clearly from the ordinary

.pz

COMMENTARY

Pythagorean view (for which see A. 987h 27-29), and is attacked both there (998& 11-13) and here (b 1-3) by arguments which have force only against believers in separate Ideas of some kind. Further, in 1080· 37-b 3 the regular Pythagorean view is distinguished from another form of belief in numbers immanent in things (se. the view referred to here). We may infer that Aristotle is speaking here either of Platonizing Pythagoreans (as Robin infers) or of Pythagoreanizing Platonists. For evidence of a Platonizing school of Pythagoreans cf. Robin, 649-651. Syrian us (84. 2I) says that no Pythagoreans or Platonists held this view; but this is part of his general policy of defence of Platonism against Aristotle. 39. dP'I TGL ".lv, B. 998& I 1-15, 997 b 12-34. b I. It is rather surprising that these thinkers recognized mathematical solids as distinct from sensible solids. Planes, lines, and points might naturally be distinguished from sensible things, since all sensible things have three dimensions; but what difference could there be between mathematical and sensible solids? The answer no doubt is that by mathematical solids were meant the regular solids to which sensible objects never do more than approximate. la. TAli Q).).Gli SUVGf!.CLIl KGl +UC1CL~. Alexander (725. 21) thinks the limits of sensible bodies, i. e. planes and lines, or else the characteristics studied by applied sciences like optics and harmonics, are meant. The meaning is fixed, however, by the corresponding passage in B. 998& 11-13. The 8VVQ.""E'~ and cpvCTn~ are, quite generally, the characteristics of things, which these thinkers treated as separate Forms when consistency reqUired that they, like TO. p.G().qp.GTUCQ., should be viewed as immanent in things. 4-11. Aristotle argues as follows: 'If these mathematical solids are divisible, they are divisible along or at (KaTQ.) planes, and similarly the planes are divisible along lines, and the lines at points. But points are indivisible; so therefore are the lines, planes, and solids. But if the mathematical solids are indivisible, so must the sensible solids be. Which is absurd.' He treats the divisibility of the line at a point as implying the division of the point, and one might be disposed to question this. But the one does imply the other, according to the principles of the view he is criticizing, for (I) these thinkers cannot say, as he would, that the point is brought into actual existence by the act of division; it is a substance, always existing actually; and (2) they cannot say that the division comes between two consecutive points, since (so Alexander says, and we may suppose that he is right) they, like Aristotle, held the line to be continuous and so to have no consecutive points. II-I077b 14. Aristotle now proceeds to the second alternalive, stated in & 34, that mathematical objects ~Xist apart from sensibles (the view of Plato and of Speusippus). If there are mathematical solids apart from and logically prior to the sensible solids, there will be (I) (11. 14-16) planes, lines, and points apart from sensible planes, lines, and points.

(2) (II. 16-24) planes, lines, and points in the mathematical solids. (3) " planes, lines, and points apart from those numbered (2 ). (4) (11. 24-2'1) lines and points prior to the lines in the planes numbered (3). (5) (II. 27, 28) points prior to those in the lines numbered (4). The lines in the planes numbered (3), though introduced by 7I"a~LV (I. 24) are not meant to be a new class not mentioned before; else we should get five classes of lines instead of (as Aristotle says, 1. 32) four. They are identified with the lines numbered (3), and are mentioned anew in 1. 25 only as leading up to the further class of lines and points numbered (4). The enumeration is careless and by no means complete. Aristotle might have argued that if there are two sets of solids (sensible and mathematical), there will be two sets of planes in these solids and two sets abstracted from them; four sets of lines in these planes and four sets abstracted from them; eight sets of points in these lines and eight abstracted from them. The enumeration betrays its incompleteness by lack of symmetry. If we take the sets of mathematical objects which he mentions we get the series :-one set of solids, three of planes, four of lines, five of points; and if we add in the sensibles we get the series 2, 4, 5, 6. Neither series is symmetrical. The fact is that Aristotle begins correctly the geometrical series 2, 4, 8, 16, but tires of the U6,PCUULi and turns the series into an arithmetical one. The U6lPWULi is aT07l"Oi enough, even as stated by him. The error which lies at its base is the X"'PLupo6r; of, or assigning of separate existence to, what is only distinguishable by thought. 21. dKLvtlTOLr; = poa()."poanKoii. 38. For TO. OVTa alu6."Ta of the manuscripts it seems necessary to

read

Tel. ilVTIl, Tel. IllcrlhJTG.

TOLr; 41r0P~"'IlO"LV, B. 997 b 12-34. 1077a 2. Bz.'s EenllL is confirmed by J. 5 and B. 997 b 16.

39. lv

3. oGpll.,oV, sc. 7I"apa TOV alu()."Tov ollpav6v, cf. B. 997 h 16. 6. Tel. Klle' (KilO-Til, cf. B. 999& 26 n. 9. ypli+nllL, Alexander explains, means 8dKVVTat. cr. Top. 158b 30 oll ~l"'iyp&cp(u()aL and the use of8Laypapopoa = proposition in Cal. 14 a 39, B. 998a 25, A. 1014a 36. In all these cases it would seem that a proof aided by a figure is meant. The general mathematics here referred to, which proves attributes that are not peculiar to numbers or to spatial magnitudes or to times, is also mentioned in 1077 b 17, E. 1026& 27, An. Post. '14& 23. Eudoxus' doctrine of proportion, which is preserved in Euclid's Elements, Bk. V, is the best instance of this • general mathematics' (cf. '14 a 23). 20-24. In ... o-U".".lVELV is a digression from the main point. The question what causes the unity of mathematical magnitudes is inserted between two arguments from genesis, (I) the argument that sensible magnitudes must be prior in essence to mathematical because they

COMMENTARY ar~ later in generation (11. 18-20), and (2) the argument that solids must be prior in essence to planes and lines because they are later in generation (II. 24-28). ~O. Bz.'s TllI' Kal 'lrOT', I by virtue of what in the world' is attractive, but though Tl" 'Iron is common Tl" Kat 'lr0T€ does not seem to be recorded as occurring in this sense, and it is better to keep Bekker's reading TCV' Kal ,..eST'. ~m. fllp€, +UXijll, e. g., says Alexander, in the case of animals which have only the sense of touch and therefore only a part of the soul. For (~AOyIll~ added thus at the end of a clause ct. Bz. Index 297bU-27. Alexander illustrates ill'tl TLlIl (~AOy'tl by the case of things glued or tied together. ~4-30. Bz. points out that there is a serious ambiguIty in Aristotle's use of yaE(1'L" in this argument. yaE(1"" in the sense in which TO Y(ll((1''' OOT(polI is owlq. 'lrpo.r€POIl is natural genesis, e. g. the growth of the boy into the man. But yaE(1"" in the sense in which it can be applied to mathematical objects refers to the quite different process by which the line is generated by a moving point, the plane. by a moving line, the solid by a moving plane. The ambiguity deprives the argument of whatever value it might otherwise have possessed. ~4-~6. "'p&iTOV •.• 'ux€v evioently refers to Speusippus fro 4· 44-47 (Lang). ~7. An ambiguity is to be noticed in the meaning of 111 Jl;'O'C~ ,..p6npov in this chapter. In this line it is used of that which is later in generation, and means in effect what is T(AELOII (I. 28), and in I. 19 Tjj owlq. VUT(polI bas the corresponding meaning. So too in Phys. 260 b 18, 19 'lrpMEPOII KaT' O~(1'tall; in 0. 10503 5 T~ Eill" Kal Tjj o~u{q. 'lrpMEpa; in G. A. 742322, Rhel. 1392&21 'lrpo.r'lX)fI Tjj otJulq.; in Cal. I .. b 5, Phys. 2611> I., 265322, A. 989a 16 Tjj q,VUEL 'lrpMEPOII. But in 1077 b 2 Ta Tjj o~ulq. 'lrpMEp4 are defined as oua Xlllp"op.Ella T~ Ellla, VtrEPPru€,; i. e. of two things that is prior which can exist without the other while the other cannot exist without il. Cf. A. 1019B 2, , , ., ( ' "1 ar Iy h were Ta' KaTa' , j.,..VU'" Ka', OVfT,all 'lrpOT(p4 Ka'' .VUTEp4) are simi defined. This is said to be the primary sense of 'lrpOTEPOII Kal OOTEPOII (101911 II), and so too in 0. 1050b 6, actuality having already (a ._b 6) been shown to be prior O~(1'lq. to potentiality in the first sense described above, Aristotle proceeds to say that it is Kal KVP'IIIT(PIII" ('lrpOTEPOII ooul'1-), and explains this in the second sense. This is again one of the senses assigned to 'lrpOTEPOII in Cal. 12, where it is described as TO p.~ d.lITlUTplq,OIlKaT~ ~II TOV ElllaL d.KoAov~u", (I.a 30). Once more it is referred to in Phys. 260 b 18, where it is distinguished from TO KaT' o~ulall 'lrpMEPOII. The two senses of KaT' OWlall (or q,VU") 'lrpOTEPOII answer to two of the meanings of o~ula which are so often distinguished by Aristotle. The first sense answers to that sense of owla in which it means form, or to the'TOIl( T' considered as a fully formed or developed thing; the second to that in which it means TO VtrOKE{P.(IIOII or the roll( T' considered as somethinR capable of separate existence.

31. ~&1J yAp 'X" 'II'fIII Tli TD..,OI', cf. De Caelo 268& '1-24. "'III~, says Alexander, because fjua mere mathematical solid it lacks the qualities by which TA t!>VCT'ICA d8mro&f:iT(u ('132. 5). b 3. Sawl' ot Uyo, 'K ,wI' Uywl' is difficult. The natural translation would be •those things are prior in definition whose definitions are compounded out of the definitions of the other things', but this is the exact opposite of Aristotle's doctrine (cr. ~. IOl8 b 34, Z. I035 b 4). We might interpret &crlllll as depending on Mylllll, not on Myo" and translate 'of whose definitions the definitions of the other things are compounded', but it seems more likely that the transition from &cra to &crlllll leads Aristotle to substitute in thought an antecedent TOWIIIII for the antecedent TaWil. • Those things are prior in substance which when separated from other things surpass them in power of independent existence, and things are prior in definition to the things whose definitions are compounded out of their definitions.' Schwegler's proposal to excise IIC does not, therefore, seem necessary. For a similar confusion cf. Z. I034b 31. 4. O.,X iI",a. C)m£pX" does not mean that these characteristics are never found together, but that they are not always found together. It is not necessary to read lJ".';'PX€& (Il€t) as has been suggested. 10. 'K lI'poat4a€"" yAp Tit ~'UKiia II ),€UKlI~ a..epfll1l'ol UyeTCU. Bz. proposes TOV ~WICOV, which he takes to be Alexander's reading. He argues that • man' cannot be considered as added to • white', but rather • white' as added to • man'. On this interpretation the clause would mean something like this: • We have spoken of "white man" as if it were IIC ".pocrfUcr€IIIr; compared with" white". But really it is IIC ".pocr61cr€IIIr; only as compared with "man".' Alexander's general interpretation agrees with this, but it seems clear that he read T~ AwIC~ with the manuscripts, and interpreted this as • by virtue of white' (".pocr61cr€& TOV AwICov); v. 733. 34. This is surely an impossible interpretation. It seems better to translate' by addition to the white '. It is true as Bz. says that we cannot suppose a • white' to exist first and then to become a man. But we can think first of • white' and then add the tho'lghr of' man', and this is the Aristotelian use of ",pOcr6€cr&r;. cr. Z. 102gb 33, where we have Tii «I~~o (sc,,«I1I6p11111'oll) aw~ (sc. ~IC~) "'pocrICcicr6a.&, and Z. 5. where the definition of TO cr,p.OlI as p~r; cr&,., or of TO ¥pa as ¥pa Ccjioll is described as being IIC ".pocr61cr,,,,,. On this view the clause in question does not correct what has gone before but justifies the previous description of ~wICor; «I1I6pw'lf'or; as being IIC 'If'pocr61cr'IIIr; in comparison with ~WICOII. 15. '1'.8IXETO, as was shown in 1076- 38-b II.

.pti

COMMENTARY

Mathemalics considers as 'llhey exisled separately objects thai do not exist separatelY (ch. 3). I077b 17. (C) As the universal propositions in mathematics are about spatial magnitudes and numbers but not about them as such, so there may be proofs about sensible magnitudes but not about them qua sensible. As there are reasonings about things merely qua movable without there being an entity 'the movable' either apart from or in sensible things, so there can be reasonings about movable things qua bodies, qua planes, etc. 31. Thus we can say without qualification that mathematical objects exist, and are such as mathematicians suppose. Each science deals with objects in respect of some particular attribute and not of those incidental to it. Similarly mathematics deals neither with sensible things as such nor with separate non-sensible things, but with the attributes that belong to sensible things qua involving lines and planes. 1078& g. The simpler the object, the more exact the knowledge; arithmetic is more accurate than geometry, geometry than kinetics, the kinetics of simple movement than the kinetics of complex movement. 14. Harmonics and optics, again, study their objects not qua voice or sight but qua numbers and lines; so too mechanics. There is no mistake involved in supposing the objects separated from their concomitants, any more than in the geometer's supposition that a line is a foot long when it is not. gI. The best procedure is that of arithmetic and geometry to suppose separate what is not really so. Their objects exist potentially though not actually. 31. Since the beautiful may be found in unchangeable things though the good is confined to action, they err who hold that mathematics says nothing of the beautiful or the good. Even if it does not mention the beautiful it proves attributes that are the chief forms of beautyorder, symmetry, definiteness. b g. Since these are the causes of many results, mathematics in a sense treats the beautiful as a cause. I077b go. ~ €t"QL 8LQLpud. One might have thought that divisibility was an essential characteristic of all the objects of mathematics. But it must be remembered that points (a 12) and units (IOi8& 24) are among these objects. 33. Aristotle said in 1. 16 of mathematical objects that ollX a1l'.\w~

(ITT"'. Now he says iln laTLV c1'11')."~ 4).1J8~, d'll'fiv. They do not exist in the unqualified or strict sense, but we can say in an unqualified or general way that they exist (that d'll'A&i~ goes with fl'll'f&V is indicated by I. 3 I). d'll'A&i~,' without qualification', can mean • strictly' or , vaguely' according to the context. a6. The reading of EAb fl ry"LvOV ,.0 AEVICOV, D8' IITTLV ry"LvOV, dU' IICf{vov VIITT1v IICa.lTTov, ry"LvOV ry&"voii is unintelligible. Alexander read d ,.0 ~LfWOV AEVICOV, i tt 'ITTLV ~(LVOV, dll' IICf&vov o£ lanv lICa.CTT1J, fl h'''LvOV ryL"VOV, which with Bz.'s emendations, the reading of ~ for Vand the addition of i after the second d, gives a good sense. In a 36 the reading of the manuscripts d ry"wbi-,.o XEVKOV could be kept without the sense being much affected, but it seems best to follow Alexander as far as possible throllghout the passage. 1078& I • •t (fi> ~LfL~V r,,,,voii, 'if of the object guo healthy, then of the healthy'. III. The ordinary punctuation, with a full stop after KLvt\O'."", is misleading. It suggests that ICal p4AllTTa 4VEV ICLnFf"" introduces a higher degree of precision than 4VEV /uyIBow, as if the geometry of motionless bodies were more precise than arithmetic. Rather ICal p4A/.CITO. 4VEV ICLV.qu(",~ introduces an independent principle of distinction. ' And, while the science is most precise if it deals with unmovables, it is next best that it should study the primary kind of movement, and especially uniform movement of the primary kind.' It is not clear whether -"1V 1rtxfrrrtv is meant to distinguish locomotion from the other kinds of change (A. 1072b 8) or circular motion from other kinds of locomotion (J072b 9). Very likely it is meant to point to both distinctions. Then, just as 4VEV p.ey/Bow ICTA. places arithmetic above geometry, and p4ALlTTa 4VEV ICLnFf"'~ places geometry above all sciences of motion, lo.v 8. IC{'"ICTLV, p.a.ALlTTa ~ 1rPtirrqv places astronomy above sublunary kinetics, which studies non-circular ",opal, and still more above, say, biology, which studies alSt"'lT~ ICal "'B{ITL~. 15. ypal'JI4' refers to optics, which is subordinate to geometry, 4PL81'0£ to harmonics, which is subordinate to arithmetic (An. Posi. 75b 15). 16. The OlKfUl ••• 'II'Cl81J here mentioned are to be distinguished from the f8La 1ra.B." of I. 7. The raLa 1ra.B." were the derivative attributes which belonged to, e. g., animals gUQ male or guo female-the major terms of demonstration; the olKfia 1ra.B." are the attributes linearity and numberedness which belong directly to the objects of optics and harmonics and from which other attributes can be derived-the middle terms of demonstration. 110. Alexander's reading is sufficiently confirmed by N. 1089& 22. 118. 1'Olfrwv, humanity and indivisibility (cf. 1. 26). Alexander "'0), have read TOVrov, indivisibility (739. J4). 11\ 8uvuTCSv. Alexander takes this as subject of Innl.pXC&v and supposes that it is a geometrical attribute which Aristotle states to be capable of belonging to man even if he were not indivisible. Alexander is no doubt thinking of the sense of 8waa8cu which has led to the use of the

COMMENTARY word 'power' in its arithmetical meaning. But (I) what is said BV"au6fU in this sense is the line on which a square or a cube is erected, so that 8WGT&" in this sense is not a suitable epithet for a man, and (z) the subject of lnn¥x"" is undoubtedly &. ••• a.w!(i. Bz. takes ,.0 Swa.T6" to mean ' so far as possibility is concerned', but this with l"Slx.ETa.L is otiose, and the usage is apparently not found elsewhere. TO Svva.ro" is probably a gloss on ~AU(idr (I. 31), perhaps introduced here by a copyist who took TOm-",,, to be the antecedent of ;{ and thought that waPX-LIf needed a subject. The words are omitted by r. 30-31. 8~mll yap • • . 6}.~Kit. Aristotle means that mathematical objects exist ~MI(~, and this, since it is opposed to llfT(Alxlbf, we may interpret as -= Swap.fL. The meaning must be that mathematical objects exist neither (.) as actually and substantially present all along in sensible things (refuted 1076" 38-b II), nor (z) as substances actually existing apart from sensible things (refuted 1076b 11-1078" z I), but (3) as potentially present in sensible things and receiving actual existence by the geometer's act of X"'PLCTp.O~ Cf. ll. 21 fr. and e. 1051" 21-33' The mathematical parts into which a body can be divided are its v),:q "07JT"l, as its material elements are its vA." alrr67JT"l (Z. 1035" II, 1036& 9-11, b 32-1037" 5). 31-b 6. The thinkers here criticized are those referred to in B. 996" 32 as nil" CTOf/ILCTTtiJ" TLIf" olo" 'AplCTT&1f'7rOr;. In B" nothing is said of,.o mAOIf; these thinkers are represented simply as attacking mathematics because it never uses d.ya.6&If as a middle term. Here they are represented as saying that mathematics never uses either d.ya.80" or l(a.AOIf, and Aristotle replies that it uses the latter though not the former. This distinction of the two terms (1(a.A&If being the wider of the two, II. 31, 32) is not found elsewhere in Aristotle, though we may perhaps find a trace of it in M. A. 700b 25 ,.0 TOLcWr&If lrrn TtiJv d:yaJ)tiJ",.o 1(&1'00", d.U' olr "If TO l(a.AOIf. It is somewhat surprising to find Aristotle saying that ,.0 d.ya.6&If is d.1l1" 7rp4t", considering that it is found in every category and can be applied to God and to reason {E. N. 1096& 23}. But. though l(a.AOIf and d.yaDO" are often used synonymously, mAOIf is applicable primarily to the physically beautiful and ilya.(J&" to the morally good; or at any rate for the sake of argument Aristotle is willing to admit this restriction of the meaning of ilya.(J&If. 35. The 'pya. of beauty are the facts in the nature of the universe due to Tdl&r; and ,.0 ~p«TP.lvolf (b 2-4), i. e. to the stri"ing of nature to attain to order: and determinateness. By the AO'fO' of beauty Aristotle means Tdl&r;, avp.p.ETpla., ,.0 ~PWp1vOlf. The next sentence presents them in another light, as main species (Irs.,,) of beauty. His stricter view is that they are elements ill the definition of beaqty (cf. Poel. 1450b 36 TO l(a,AOIf I" p.r"f((J" 1(0.2 nllc& ICTT', 'involves size and order '). The p1-yr(Jor; which is mentioned in the Poeh"ts and in Pol. 1326& 33 as an element in beauty answers to ,.0 ~~p1vw here; the third element avp.p.ETpla. is mentioned in Top. 116b 21 as being thought to constitute the beauty of musical tunes.

b I. TclfLI. the spatial arrangement of the parts j C1u",lonp£o., the proportional size of the parts; TO &'PLC1,,4vov. the limitation in size of the whole. Mathematics does not speak of beauty but it proves that certain objects have these attributes, which are the very soul of beauty. 5. Iv 4>'>'OLI. Neither A. 7 (1072& 34). 8, 10, nor N. 4. nor the De Caelo really fulfils the promise here made, and it seems best to treat it as one of Aristotle's unfulfilled promises.

II.

THE FORMS

(chs. 4. 5).

His/ory and crilidsm qf the theory qf Forms (ch. 4)'

1078b7. We must first examine the doctrine in its original form, apart from any theory of numbers. Ig. The founders of the dQCtrine were convinced by Heraclitus' arguments that sensible things are always in flux, and rnferred that there must be other things to serve as objects of knowledge. 17. Socrates was the first to seek general definitions-viz. of the virtues. Democritus had defined, in a way, heat and cold; the Pythagoreans had reduced the definitions of a few things to numbers. g3. It was natural that Socrates should seek definitions; for he was trying to reason. and the 'what' is the starting-point of reasoning j there was at thilt time no dialectical power such as enables people to study contraries without knowing the 'what'. Two things we may ascribe to Socrates are inductive arguments and general definition, both concerned with the starting-point of knowledge. 30. Socrates did not treat the universals as existing separately j his successors did, and called them Ideas; by the same argument they involved themselves in Ideas of all universals. 34. Objections: (i) The theory merely doubles the number of things to be explained; for there is an Idea answering to every set of things with a common Dame j there is a 'one over many' both for substances and for non-substances, both for temporal and for eternal entities. 1079& 4. (ii) Of tlie proofs of the theory, some prove nothing, others would prove the existence of Ideas of things of which the Platonists think there are none. (a.) The arguments from the existence of the sciences would prove that there are Forms of al\ things of which there

4 20

COMMENTARY

are sciences. ({3) The argument of 'one over many' would prove that there are Forms of negations. (y) The argument from the possibility of thinking when the object has perished would prove that there are forms of perishable objects. II. (8) Of the most accurate arguments some lead to Ideas of relative terms, others posit the • third man'. 14. (iii) In general the arguments about the Forms destroy what the supporters of Forms think more important than the Forms; number becomes prior to the dyad, the relative prior to number and thus to the absolute. In various ways the opinions about the Forms conflict with the first principles of the theory. 19. (iv) According to the view on which the theory is based there will be Forms of many things besides substances (for there can be a single conception, or a science, of other things); but according to the logical requirements of the theory and their actual opinions, if the Forms are shared in there are Forms only of substances. !a6. For (a) each is shared in not as an accident of something else but as something not predicated of a subject (i. e. not as anything that shares in doubleness shares in eternality because doubleness is eternal), so that the Forms must be substance. But ({3) the same names must indicate substance in the sensible world as in the ideal (else what is meant by calling the Idea • one over many'? If the Ideas and the things that share in them have the same form, there is something common, for instance, to the Idea of two and the particular two, as there is to the perishable twos and to the particular mathematical twos; if they have not the same form, they have only their name in common, as Callias and a statue may both be called' a man '.) b 3. If it be suggested that the common definition applies to a Form, and only the name of that which it is the Form of has to be added, the suggestion is unmeaning. (a) To what element in the definition is this to be added? Every element in it is an Idea, genus and differentia alike. ({3) I Formness ' will itself be a Form present in all Forms, as 'plane' is present in all its species. (Thus there is an infinite regress.) I078b 7-8. 3TL TE 3VTG 100Tl KAl "'W~ 3vTa (TO. p.affqiLaTLK&.) has been the general subject of chs. 2, 3; w&i~ ,..p6T1pG Kal "'w~ oil ,..p6TEpa the subject in particular of 10n a 17-20, 24-b 1 I. II. Who were ot "'PWTOL Tc\~ [84M ~O'aVTE~ dvaL? A comparison of 11. 12-32 with A. 987& 29-" 8 shows clearly that Aristotle means Plato. The evidence of Aristotle is against the ascription of the ideal theory to Socrates or to the Pythagoreans. It may, of course, be contended that Aristotle had no knowledge of Socrates' views except what he got from the Platonic dialogues, and that he com-

pletely misunderstood the dialogues in supposing that the doctrines ascribed to Socrates in them are ascribed to him for dramatic purposes. But that the 'mind of the school' misunderstood the dialogues so completely is unlikely and demands more proof than has yet been offered. The 'first people who said there are Ideas' are stated here, exactly as Plato was stated in Bk. A, to have been influenced by the Heraclitean doctrines (1078b 13, 987& 32), to have followed the lead of Socrates in his search for ethical definitions or universals, and to have given the name of Ideas to these universals (cf. 1078b 17-19, 30-32, with 987b 1-8). Prof. Taylor's view (Varia Socralica, 81-89) that 01 8' lxwpLuav (I. 3 I) refers to the Megarian School, the e:l8Wv cpl>"OL of the Sophisles, ignores the correspondence of the passage with that in Aristotle. The main difference between A and lid here is that lid, in using the phrase ol7rpfiYroL Tlt~ l8(a~ cpiJ!TaVT£~ ,lvaL, and in referring only to the influence of Heracliteanism in general and not of Cratylus in particular, perhaps suggests that Plato was one of a band of thinkers who by their united efforts arrived at the ideal theory. Socrates, however, was not one of this band, though he prepared the way for it j the distinction between his view and the doctrine of Ideas is stated emphatically in II. 30-32. The vague reference ol7rpwTOL Tlt~ l8(a~ cpiJuavT£~ is thoroughly characteristic of lid, which is concerned with doctrines, not with people (cr. 1076 &16-22, 1080 b 11-30). There is, of course, a distinction drawn here between the theory of Ideanumbers (which we know Plato to have held) and the first form of the ideal theory (II. 9-12). But this does not amount to a distinction, as Prof. Burnet maintains (G. P. 157) between Plato and' the first persons who said that the Forms existed'. The distinction is between the theory of Idea-numbers (a theory held in different forms by Plato and by Xenocrates) and the ideal theory as it was originally (l~ clp~) held by its first supporters (Plato and the rest of the band referred to above). Prof. Burnet tries to discount the value of Aristotle's statements about Socrates (in particular his refusal to treat Socrates as a, or the, founder of the ideal theory) by pointing out that Socrates , had been dead for thirty years when Aristotle fiM came to Athens at the age of eighteen'. He maintains that all that Aristotle knew about Socrates was derived from the Platonic dialogues, and especially from the Phaedo. But it is as near certainty as we need wish that he must have learnt much from Plato about Socrates by word of mouth. Surely the very fact that he does not take the dialogues at their face value and ascribe to Socrates everything that is ascribed to him in the dialogues shows that he had independent information in the light of which he interpreted them. Cf. Introduction, pp. xxxiii-xlv. 13. 'lrEpl rijs 4X,,ge£as, 'on the question about the truth (or real nature) of tliings '. Cf. A. 983b 2 11. TOLS 'HpallXeLTI£OLS >-6yOLS, cf. A. 987& 32 n. Cratylus is there mentioned as the Heraclitean who was Plato's fin;t master in philol>ophy.

COMMENTARY 15. +p6"1O'L'II is used here in the Platonic sense ill which it ii:l not distinguished from l7rurrqP.71 and restricted to moral questions. 17. The sentence beginning here is never properly completed; the long parenthesis, II. 19-30, causes Aristotle to forget the construction; cf. K. 1067 b 25-34' Ig-lao. The opposition Ttiiv"iv ••• tUG'L"WV ••• ot.8i nue.y6p.LOL suggests that TWV "'vlTtlewv means ' of the physicists', and that the object of Waro is • the problem of definition'; Alexander's interpretation, that Democritus 'touched on natural objects' gives a good enough sense, but the other interpretation is made certain by a comparison with P. A. 642& 24-31. ".oval' goes with ~7r~ Jl.tKpOV ;+aTo and emphasizes the slightness of Democritus' effort. Cf. PhJ's. 194a 20. lal. On the Pythagorean attempts at definition cf. A. 98Sb 29, 987& 20. lala. clvci7r7"w is not used elsewhere by AI'istotle ill this sense, and one is tempted to read &v7jyov, which Alexander uses in his interpretation and E gives as an alternative reading. But &vci7r7'(LV is used thus by other authors. ".Lp6'11 was identified with the number 7 (AI. 38. 16, 75. 23)' laa. ri &£..aLov was identified, Alexander tells us (74I. 5), with 'the numberthat divides 10 in half', i. e. 5 (cf. 721. 13). But elsewhere he says it was the first square, either 4 or 9 (38. 12), and the other evidence (E. N. I 132b 23, M. M. I 182il 14) tends more in this direction. yc£l'OI was identified with 5, the sum of the first even and the first odd number (.19. 8). laS. OG'II'fII T6T' ~v. Aristotle is quoted as having called ~no the Eleatic the inventor of dialectic (frr. 1484b 29), and Zeno was doubtless considerably senior to Socrates (PI. Par",. 127 Be), 80 that OU7r'" To.,.' ~v is meant only in a very limited sense. Aristotle means that the procedure of which we have an instance in the Parlllemaes (cr. MellO 86 E fr. and Sophistts), where the consequences of contrary hypotheses, • if one is " • if many are " are studied without any definition of one or of many having been agreed upon, was not yet a well-recognized mode of discussion in Socrates' time as it afterwards became. la6. ,-wI' lVCIVT£fIIV .t ." alh~ h-Lanll''IJ is again in Top. 105b 23 mentioned as a dialectical inquiry (7rp6-raO't~ Aoyu(1). It is rather surprising to find this particular inquiry about contr?-ries co-ordinated by Kal with the general phrase TclvaVT{a, but it is not necessary with Maier (Syll. dts Arlst. ii. 2. 168) to regard Ka2 ••• mtcrrt7P.71 as a gloss. laS. Aristotle cannot mean that Socrates was the first person who used inductive arguments or gave general definitions, but that he was the first who recognized the Importance of them and systematically used the former in order to get the latter. The inductive arguments referred to are not scientific inductions but arguments from analogy such as we often find Socrates using ill the lIft1llorabilia and in Plato's • Socratic' dialogues. For an instance cf. ~. 1025& 6-13. 34-IOSO&S agrees almost verbally with A. 990b 2-99 1b 9, with the exception of the section 1079b 3-11, which has nothing

M. 4. 107 8b 15- 1079b

I I

answering to it in Book A. The main points of divergence are noted below; for what is common to both passages cr. the notes on Book A. Alexander had the passage in his text of M but does not comment on it. Occasionally A is fuller than M (cf. 990b 26, 991& 25, b 5 with 1079& 23, b 28, 1080& 4), but for the most part M is fLlller (cf. 990b 20, 991& 4, 17, b 3,7,9 with 1079& 17, 35, b 21, 1080& 2, 6,8). Cf. A. 9 note ad inil. 36-1079& I. For 1f~El", •.. EISt) A has O'Xe8av y'O.p ZO'a-~ olJ/c IMTTw --ra eZ87] IOTt TOVroL~, a milder statement. 1079& 5. SelKVUTo.L, 990b 9 8E{KVVP.ev. Cf. 7 oZoVTaL, 990b 11 olop.e8a; 12, 20, 1080& 6 cpaO'LV, 990b 16, 23, 991b 7 cpap.ev; 14 {3ovAoVTal., 990b 18 {3ovAoVTaL AbA!., {3ovAOp.e8a EAse. 20. The M version as compared with the A version affects the use of a plural verb with a neuter plural subject; cf.l. 20 with 990b 24, 28 with 990b 31, b 12 with 99 1&9. b 3-11 is peculiar to M. It suggests an alternative course between the supposition that the Idea is uvvwvvp.ov with its particulars (& 33) and the view that it is bp.wvvp.ov (& 36, b I)-a course, however, which does not free the Platonists from difficulties. The suggestion is that the definition of an Idea is the same as that of its particulars, except that in the former we must add 'that of which it is' the Idea or pattern. E. g. the Idea of circle would be defined as 'a plane figure such that every point on the circumference is equidistant from the centre, such figure being the Idea of sensible circles'. Aristotle makes two objections. (I) To what element in the definition must the o~ IOT{, the statement of what the Idea is an Idea of, be added? To the word' centre " the word' plane " or to every word? Every element in the Idea must be ideal. (2)' Being an Idea of something' will itself be a common nature present in all Ideas, i. e. itself an Idea. 10-11. +UCrLV • • • ylvos is predicate of elvaL, and there should be a comma after f7T{7TE8ov. It is not necessary to omit TL as Christ suggests. ' " So-and-so itself" (a~o TL) will be a nature present in all the Forms as their genus, as " plane" is present in all the species of plane figure.' aVTo TL is a generalization of Platonic phrases like aVTa aya8ov, and the meaning is that Formness will itself be a Form; and this can be attacked by a TptTO'> tJ.V8PW7TO~ argument.

The Forms do 1101 explaIn Ihe challges In Ihe smsible world (ch. 5).

1079b 12. (v) The main question is, what do the Forms contribute either to eternal or to transient sensibles? (a) They cause no change in them, ({3) they contribute nothing to the knowledge of them (for, not being in them, they are not their substance),

CO~IMENT ARY

17. nor (y) to their being (if they were in them they might perhaps be their causes as white is of the whiteness of that in which it is mixed; but this view of Anaxagoras and Eudoxus is easily refuted). liS. (vi) Other things are not composed of Forms in any ordinary sense, and to call the Forms patterns and say that other things share ;11 them is empty metaphor. For (4) what is it that works with its eye on the Ideas? (fJ) It is possible to be or become anything without being copied from an original. SI. ('Y) There will be many patterns, and therefore Forms, of the same thing; to a man there will answer the Forms of animal, biped, and man. (8) The genus will be the Form of its species, so that the same thing will be pattern and copy. 35. (vii) How can the Ideas, being the substances of things, exist apart from the things? In the Phaedo they are said to be causes both of being and of becoming. 1080& 3. Yet (4) even if the Forms exist, the things that share in them do not come into being unless there is a moving cause, and (/3) many things, e.g. houses, come into existence though the Platonists say there are no Forms of them, and therefore those also of which they say there are Forms may be or come into being owing to similar causes, and not to the Forms. g. These and other more abstract and accurate arguments may be brought against the Ideas. 107gb 1II8. It is not, I think, necessary to insert op.otOV from Book A \,ilh Bonilz. 'IL is possible to be or become anything without being copied from an original.' 34. TWV '$ ylvou$ EtSWV, cf. A. 991& 31 n. 1080& 10. AOYtK6~, AoytKW~ generally in Aristotle denote a discus· sion which does not start from the OlK£L4t d.pX4{ of the subject but from verbal considerations, and is a term or reproach rather than otherwise, so that it is somewhat strange to find AOYtKfJJ'T'£fX»V coupled with d.Kpt/3((TT£fX»V, If we remember, however, that the Platonic doctrines are themselves I!aid by Aristotle to have been of this nature (1084 b 25, A. 987b 31, @. I050b 35, A. 1069& 28, N. 1087 b 21), we may infer that he means that he could produce arguments which would meet the Platonists more on their own ground and would have the precision that comes from abstraction (cr. 1078& 9, (0).

M.S. III.

1079b

28 -

1080S. 10

NUMBERS AS SEPARATE SUBSTANCES AND FIRST CAUSES

(chs. 6-9. 1086a 18).

Various wC!}'s ill whIch mmzbtrs may be cOflCeivtd as Ihe subsiatlCe oflhings (ch. 6). 1080· I~. If number is an entity whose essence is just to be number, then (I) there is an order of priority and a specific difference between the numbers, and between the units, which therefore are incomparable. ~o. or (2) all units are comparable, as in mathematical number; ~3. or (3) the units of a single number are comparable, but those of different numbers are not comparable itller se; 30. so that while in mathematical number I is added to I to make 2, in this kind of number 2 is two ones distinct from the number I ; 35. or (4) there are all three kinds of number, those described in (I). (2), and (3). 37. Further these numbers must be either separate from things or in things, i. e. composing sensible things; the latter alternative may be true of EOme or of all numbers. b 4. All those who treat the One as a first principle and a substance have adopted one or other of the above views, which are the only possible views; all the views but (I) have found support. D. (A) Some (Plato) believe in both kinds of number-that which has priority and posteriority (the Ideas) and mathematical number; they believe both to exist apart from sensibles. 14. (B) (a) Some (Speusippus) believe in mathematical number only; (b) the Pythagoreans too believe in mathematical number only, but in the sense that sensible substances are actually composed of extended units-though they cannot tell us how the first extended unit came into being. 81. (C) (a) Another thinker says only ideal number exists, and (6) some (Xenocrates) identify this with mathematical number. ~3. There is a similar variety of opinion about lines, planes, and solids. (A) Some distinguish the mathematical lines, &cc., and those which come after the Ideas; (B) some say that the mathematical objects exist, and speak mathematically about them (viz. the nonbelievers in Ideas); (C) others say that the mathematical objects exist, but do not speak mathematically, for they say that not every magnitude is divisible into magnitudes, and not every two units make a two. 30. An who treat the One as a firllt principle lIuppose numbers to IIn·1

E

e

COMl\[£NT ARY

be composed of abstract units, except the Pythagoreans, who conceive of numbers as extended. 33. These are the possible views; all untenable, but perhaps some more so than others. 1080a IS-h 4. The sentence is irregular in structure. Aristotle begins (I. 17) by stating what looks as if it were to be the first of a series of alternative hypotheses about the nature of numbers, but he proceeds to state three possible forms of this one hypothesis, differing in the view they take of the nature of unils (II. 18, 20, 23). and recurs to numbers only in 1. 35, where he states as a fresh alternative that there may be three kinds of number having the three kinds of unit respectively; finally in 1. 37 he classifies the possible views according to a different principle of division. It is noteworthy that he brings forward his classification as one arrived at a priori. not by enumeration of existing views. This awakens a certain suspicion that he may in his account of the actual views do them some injustice in order to fit them into his ready-made scheme. He says definitely, however, that each of the views he mentions had supporters, except the view that all units are incomparable (I080 h 8, cf. I081 a 35). ~ Tc1~ p.iv KTA. (I. 23), though grammatically co-ordinate with ~o, ElvCl' KTA. (I. 17), is in sense co-ordinate with ~ br~ TWV p.ova.8I1lv KTA. (I. 18) and with ~ w6V~ If/iE~~ KTA. (1. 20). The views Aristotle mentions are (I) the belief in incomparable numbers (I. 17), (a) with units all incomparable (1. 18), or (b) with units all comparable (I. 20), or (c) with the units of each number comparable with each other, but incomparable with those of other numbers (1. 23), (2) the belief in all three kinds of number, i. e. the kind (I a), the kind (I b), and the kind (I c) (1. 35). He omits (3) the belief in two kinds of number, (I a) and (I b~, (I a) and (I C • or (I b) and (I C • In ll. 21, 36 he confuses (I b), the belief in incomparable numbers whose units are all comparable, with (4), the belief in comparable numbers (whose units must necessarily be all comparable), for clearly this is what he conceives b p.affqp.aTlKO~ d.p,8~ to be. It must not be thought that this passage offers a classification of hypotheses about ideal number in particular, for the classification includes the Pythagoreans (b 16), who drew no distinction between mathematical and ideal number, and Speusippus (h 14), who believed only in the former. What we have is a classification of all the views which treated numbers as • separate substances and first causes of existing things' (a 14). Alexander, failing to notice that the Pythagoreans enter into the classification, takes it to be a classification of theories of ideal number (e.g. 743. 13), and this leads him to give an absurd interpretation of" 35-37. He takes it to mean that e.g. 3. 4.

M. 6. Io8oa. 15 - Io8o b 4 5 might be composed of units all of which are incomparable, 7, 8,9 of units all of which are comparable, 20, 30 of units such that those in 20 are comparable with each other and those in 30 with each other but those in 20 are not comparable with those in 30. It seems clear that the view referred to in " 35-37 is one which believes in the existence of three complele number series of different kinds. So far all ideal numbers are concerned, the doctrine that they are 'incomparable', i.e. incapable of being added or subtracted, multiplied or divided, is a perfectly sound one which is misunderstood by Aristotle. The ideal numbers are simply the natural numbers, I, 2, 3, &c., or in other words oneness, twoness, threeness, &c., and these of course cannot be added. You cannot add oneness to oneness because there is only one oneness; and it is equally certain that you cannot add oneness to t\Voness. And, further, Aristotle's notion of numbers as containing units, and the resulting question whether these are comparable or incomparable, is equally mistaken. The number 2 does not contain two numbers I, for there is only one number I. As against the mathematical or 'intermediate' numbers believed in by the Platonists, Aristotle's objection would have more force. There are no 'mathematical numbers' distinct on the one hand from the natural number, and on the other from the particular one-member groupg, two-member groups, &c., which are the instances of the natural numbers. The weakness of Aristotle's position is that he believes in mathematical numbers, which do not exist, and does not believe in ideal or universal numbers, which do. On the conception of d.cr6p.{3~.:"ro, d.p&8p.o[ cf. Cook Wilson in Classical Review, xviii. 247-260, especially §§ 2, 3, 5. 19. clO'Ul'~~1JTOi. The usage of crvp.{3&.Mnv. crvp.{3'A:"rOi, d.cr6p.{3~;"rot> in Aristotle shows that the word must mean' incomparable' ; and things are comparable if and only if they belong to the same kind (Phys. 248b 8, 249" 3. Top. 107 b 17, I. 1055" 6). Thus d.cr6p.{3'A:"rot> is practically equivalent to IT'£pov ~v TI{) £tllEL (1. 17), and crvp.{3~;rJT·6r;; can be coupled with d.IluJ.q,opor;; (1081" 5). Strictly, to say that two things are crvp.{3'A:rfT&. is to say that one can be expressed as a fraction of the other, or at least as greater or less than or equal to the other. But in this context crvp.{3A'f/To1 seems to mean 'capable of entering into arithmetical relations with one another-of being added and subtracted, multiplied and divided '. 35-37. otoi 6 1I'pWros .~lX&.J, cf. II. 15-20; oto, ot I'CI&.Jl'llnltol ~lyouO'" cf. 20-23; "),, ~ell'Ta. TE~EUTa.LOII, cr. 23-35. b~. T~ 1I'PWTO", 1076" 38-b I I. Aristotle is now omitting the compromise of Pythagorean and Platonic views referred to there, and taking account only of the genuine Pythagorean view. 4. Bz. argues that the view that all the numbers are immanent in sensibles has been already mentioned in I. 1, so that ~ ".&'VTas elva& is unmeaning. But Alexander evidently had these words (perhaps q".&'VTar;; p.~ elva, as well), though his interpretation of them cannot be

COMMENTARY right; and so have all the good manuscripts. The solution of the difficulty is to treat ol1X Wno~ . • • o.llT8-qni as parenthetical. 'The numbers must be either transcendent, or immanent •.• either some immanent and not others, or all immanent.' 6. CFXI8&1' is explained by 1I'A;V ICTA., I. 8. 7. a~~ou TLvOt, i. e. the 1J.1I'ILpOV in the case of the Pythagoreans, the , great and small' or indefinite dyad in the case of the Platonists. IO-II. oa yil.p ••• dp"I'ivous. We shall see how Aristotle can say this if we remember that (a.) he confuses (.) above with (I b), and (P). since the view (I a) is not held by any one (II. 8, 9). (3 a) and (3 b) disappear with it and (3c) takes the place of (2). There thus remain (A) the belief in (I b) (II. 1.-21). (0) the belief in (I c) (II. 21, 22), (C) the belief in both (II. lI-q). and (D) the confusion of the two (II. 22, 23). II. ot ~I', who believed in both, means Plato and his orthodox followers; cf. A. 987b 1.-18. Aristotle thinks of the Platonic TO. p.er~ as of the type (I b), thougb they were more probably of the type (.). 14. ot 8i means Speusippus; cf. 1076& 20-2 I n. 15. ftl' (not TO) 'lrPWTOI' TWI' Svrwl' is somewhat strange; ill the light of 1083& 23 (also on Speusippus) TO. 8~ p.a.9-qp.a.TUCo. elvo.& K0.2 roU~ &.p&ep.oi'f 1I'ptfrrOVf TWV OVTIIIV one may conjecture that TOV should be omitted. 16. The Pythagoreans, like Speusippus, believed in mathematical number only; but they differed from him, as from all Platonists. in holding numbers to be actually present in things (cf. & 37-b .). Mr. Cornford holds. with much probability, that the Pythagorean doctrine here referred to is not the mystical system of Pythagoras but a scientific system of number-atomism which was developed in the fifth century and was the forerunner of Atomism proper. He summarizes the main features of this system as follows: '( I) there is only one kind of number-namely, mathematical number. (2) This number does not exist separately, but sensible substances are composed of it .•. (3) These numbers do 110t consist of abstract units, but the units are conceived as having spatial magnitude. (.) They are described as "indivisible magnitudes" (I083 b 13)' (5) Things or bodies are identified with numbers composed of the indivisible magnitudes or monads (1083 b 12 sqq.). (6) The Pythagoreans regarded numbers as generated-the process of generation being, of course, identical with the physical generation of the sensible world (1091& 17 sqq.)' (C/. Quart. xvii. 8). Cf. N. 1092b 8-15 n. 19. 'Ir~~1' oil f'OI'CIo8LItWI'. The Platonists, like Aristotle, thought of numbers as composed of ullextended units; the Pythagoreans thought of them as extended and having extended units. In other words they had not reached the notion of arithmetic as distinguished from geometry. Aristotle uses d.p&ep.O~ d.pr.8P.""'&KO~ in the same sense as dp&ep1Jr p.ova.8,,(O~ (1083 b 16). Zeller thinks (i.' .83-488) that in stating the Pythagorean units to be extended Aristotle is drawing a mistaken inference from the Pythagorean view that bodies are composed of numbers; he admits, however, that the Pythagorean

M. 6. Io8ob 6-25 cosmology implies the treatment of numhers as spatial. But at the time of the Pythagoreans the notion of non-corporeal reality did not exist, so that they necessarily thought of the units as extended. There is some ground for holding that they called them ityKOL (Burnet, E. G.P. § 146). ~O-ln. 31fwS &~ •.. iO£Ko.CI'W. Cf. N. 1091a 15, where we learn that the Pythagoreans 'say that when the One had been put together whether out of planes or out of surface or out of seed or out of they know not what, immediately the nearest part of the infinite began to be drawn and limited by the limit '. The general sense of the present passage is: 'The Pythagoreans construct the universe out of numbers having spatial units; but how the first unit was constructed as an extended thing they cannot tell '. 'They had not', as Mr. Cornfo~d observes (C/. Quart. xvii. 9), 'reached the position of fully developed atomism, which postulates an indefinite plurality of atoms or monads as an ultimate and eternal fact.' ~I. It is not easy to identify c1)')'~ ••• T~S, who believed in ideal number only. Alexander's suggestion that it was a Pythagorean can hardly be right, since Aristotle never ascribes the belief in Ideas to Pythagoreans. It must be a Platonist, but further than this we cannot go. Elsewhere in enumerating the views held Aristotle omits this one (1076a 19-22, 1086a2-13, cf. 10SOb 24-30). Jaeger would remove the difficulty by treating ~VLOL as a variant for £lvClL and removing £lvaL in I. 23 as a later addition due to the intrusion of ~VLOL. But Alexander and Syrianus had our text; and it is not particularly surprising that Aristotle should mention here a view he does not mention elsewhere-a view which is almost certain to have been held by some Platonist. ~~. By the lV~OL who identified ideal and mathematical number Aristotle probably means Xenocrates. Cf. 1076a 20-21 n.; Z.102S b 24 n. ~4. ot "Iv answers to 01 ,uv in I. I I and refers to Plato. ~5. Tel "ETel TelS l&lo.s. Cf. A. 992b 13 OlJ8(VCl 8' ~X£L Myov oll8, Ta p.ETa TO~ d.pL8p.ov,> P.~KTJ KClt (ll'lll'£8a KClt CI'T£P'&' ••• TClWCl yap mJTE £r~ olOv Tf ,lvClL (oll y&.p dow d.pL8p.ol) O~Tf TO. P.fTCle.J (p.Cl8TJp.aTLKo. yap fK£'ivCl) o~, Ta rp8C1pT&., d.lla ll'MW T(TClpTOV l1.AAo rpCllvETCl' TOWO TL y(VO'>. Just as Plato distinguished the Idea of' two' from the many 2'S of which arithmetic speaks, he distinguished 'the straight line itself', 'the triangle itself', 'the cube itself', from the many straight lines, triangles, and cubes of which geometry speaks. In the earlier form of his theory he spoke of these as Ideas, but when he came to call the Ideas numbers he no longer called these Ideas, since they were not numbers. Accordingly he called them (or Aristotle calls them for him) TO. p.ETa TO.,> lUCl'> or Ta p.ETa TOV,> d.pL8p.ov,>. Just as mathematical number is prior to mathematical lines, planes, and solids, being U (AClTTOVWV, the Ideas of numbers were prior to these quasi-Ideas of lines, planes, and solids. Ta p.(Ta Ta,> 18(Cl'> (TOU'> d.pl8p.ov,>) : l8fClL (,i8TJTLKOt d.p,8p.ol) : : p.Cl8TJp.C1TLKa p.~KTJ KTA. : p.a8TJP.ClTLKOt rlpL8p.ol.

COMMENTARY ~6. CIt ,"I' answers to ot 8l in I. 14 and means Speusippus and the Pythagoreans. ~8. ot 84 answers to 1,,&0& 8l in I. 22 and means Xenocrates. {N 0 one is mentioned answering to 4ll0i T&i in I. 21, and this view is difficult to distinguish from that of Xenocrates.} 0(, Tlp."fU8o.& p.lyf8Oi 7rcl" fli p.ryl8T/ (I. 29) is a clear allusion to the doctrine of indivisible lines, of which the main supporter was Xenocrates, though it is also ascribed by Aristotle to Plato {A. 992" 20}. ~g. oG8' 61roLo.croiil' ,,0l'c£80.s 8uc£80. .tVo.L is not strictly relevant here, where spatial magnitudes are being spoken of, but is rather illustrative. Xenocrates speaks of mathematical magnitudes in a non-mathematical way, supposing that the units in one mathematical number (as Plato had supposed that the units in one ideal number) are specifically different from those in another, so that a unit of 2 + a unit of 3 would not make lI. 30-33. Aristotle here recurs from T?L P.fT?L T?LS i8lo.i to numbers, and repeats what he has said in 11. 17-20. 36. "ii}.}.ol' So to-fill 8c£Tlpo. TWI' h4plJJI'. Aristotle means the view ot Xenocrates, which Xf{pUTTo. 1I.fyfTQ.I. (1083 b 2), combining as it does 860 diJ4PT{o.i, misdescribing mathematical number and also being open to all the Objections against ideal number (1083 b 3).

Examinatiotl

of Plato's view (ch.

7-8. 1083& 20).

1080b 37. (A) We must first examine whether the units are comparable, and if not, in which of the two senses they are not. 108Ia 5. (I) If all are comparable and not different in kind, we get only mathematical number, and the Ideas cannot be the numbers thus produced (for there is but one Idea of each thing, e. g. of man, while there is an indefinite number of similar numbers, e. g. threes; ISil. but if the Ideas are not numbers, they cannot exist (for the first principles are said to be first principles of number, and the Ideas cannot be classed as either prior or posterior to numbers). 17. {lI} If all units are incomparable, (a) the number so produced is not mathematical number (which is composed of undifferentiated units). SIll. Nor is it ideal number, for 2 will not be the first product of I and the indefinite dyad, and be followed by 3, 4, &c. (the unit.'! in II not being prior or posterior to one another), since if one unit is to be prior to the other, it will be prior to the II which they compose. SIIg. (h) The units will be prior to the numbers after which they are named, e. g. the third unit (the second in the number 2) will be prior to the number 3.

M. 6.

I o8o b

26-36

35. Though no one has supposed the units incomparable in this way, the view agrees sufficiently with the principles of these thinkers. If there is a first unit, there will be priority and posteriority among the units, and similarly among the twos; but though they recognize a first unit and a first two, they do not recognize a second or a third. b 10. (c) If all the units are thus incomparable, there cannot be a 'two itself', a 'three itself', &c. For whether the units are different or not, the numbers must be generated by successive additions of I; but if so, they are not generated as these thinke."S say they are, from the One and the indefinite dyad. 18. For the number two is a part of the number three, and this 01 the number four, whereas they generate four from the number two and the indefinite dyad and make it consist of two twos other than the number two; gg. otherwise 4 will consist of the number 2 and another 2, and the number 2 will consist of the One itself and another I, and if so, the element in 2 other than the One itself cannot be the indefinite dyad, since it produces one unit, not a definite 2. g7. (d) How can there be other twos besides the number 2? How can they be composed of prior and posterior units? These suppOSitions are quite fictitious. But if the conclusions are absurd, the first principles must be wrong. 35. (3) If the units in different numbers are different but those in the same number not different, equal difficulties follow. 108ga I. (a) Since the ideal ten is no ordinary number and the fives in it no ordinary fives, the units in the one five must be different from those in the other; i. e. the theory inconsistently wilh itself implies that five of the units in 10 are different from the other five. 7. If the units in 10 differ, there must be other fives in 10 than those we have named, but if so, what sort of tens do they make? These thinkers recognize no other 10 in the number 10. II. They must, as we have assumed (I. 3) that lhey do, suppose the number 4 to be composed of no chance twos, for they say the indefinite dyad received the definite dyad and made two dyads. 15. (6) How can the number 2 be something apart from the two units? Either by participation of one in the other, as 'white man', which shares in 'white' and in 'man', is apart from them, or by one part being a differentia of the other, as 'man' is apart from 'animal' and 'two-footed' go. (c) The units in 2 or in 3 cannot be one by contact, mixture, or position; there is nothing apart from the units any more than a pair of men is anything apart from the two men. The indivisibility

COMMENT ARY of the units makes no difference; points are indivisible, but a pair of points is nothing apart from the single points. ~6. (d) The theory implies that there will be prior and posterior twos, threes, &c. The twos in 4 are prior to those in 8, and generated the fours in 8 as 2 generated them, so that, since the 2 is an Idea, they also are Ideas. a~. So too the units in 2 generate the units in 4, so that all the units are Ideas and an Idea is composed of Ideas, and therefore that of which the Idea is an Idea is similarly composite, e. g. animals are composed of animals. b I. (t) To make the units different in any way is absurd and artificial; unit differs from unit neither in quantity nor in quality, and a number which is neither greater nor less than another must be equal to it and identical with it; if it is not, neither will the twos in 10 be without difference, as the theory supposes them to be. II. (f) If one unit and another unit always make two, a unit in 2 and a unit in 3 will make a 2. Now (a) this will consist of units differing in kind; (13) will it be prior or posterior to the number 3? Presumably prior, since one of the ullits is simultaneous with 3 and the other with 2. 16. Wt say that one and one (e. g. good and evil) always make two; but tltey say that not even one unit and another unit always make a two. 19. (g) The number 3 must surely be greater than the number 2, but if so, it will contain a number equal to and without difference from the number 2; which it cannot, if there is priority and posteriority between any two numbers. ~a. (It) On this view the Ideas cannot be numbers. Those who say all units are different are right in supposing this to be implied in there being Ideas; for the Form is unique, but if units are without difference, the twos and the threes will be without difference too. ~8. These thinkers are bound to say that in counting' one, two' we do not add one to the original one; for then (a) generation would not he from the indefinite dyad, and (P) an Idea would not be produced, since if it were it would contain another Idea, and all the Ideas would ultimately be parts of one Idea. a~. Thus what they say agrees with their hypothesis; but it destroys many of the truths of mathematics. They will say that there is a difficulty in the question whether we count by successive additions of I or by constructing each number separately. But we do both j it is absurd to suppose a separate kind of number to which the latter process applies.

43.1 108Sa I. (I) What is the differentia of a number, and of a unit, if a unit has any? Units must differ in respect either of quantity or of quality, but neither is possible. (4) If units differed in quantity, numbers equal in number of units would differ from each other. Are the first units greater or less than the later? All this is absurd. 8. ({3) They cannot differ in quality. They have no qualities, for in numbers quality depends on quantity. They cannot get quality either from the One, which has none, or from the indefinite dyad, which gives quantify. 14. If units differ in some other way, these thinkers ought to have said why this difference must exist, or at least what difference they mean. Thus if the Ideas are numbers, the units cannot be all comparable, nor incomparable in either of the two ways.

Examinali(m oj'lhe views oj' olhtr Plalmllsls and oj Ihe Pylhagoreans (ch. 8. 1083& 20_b 23). I083a 20. (B a) The views of other thinkers are no better, viz. of those (Speusippus) who do not believe in Ideas but in mathematical objects, and make numbers the primary realities, and the One their first principle. 24. For it is paradoxical that there should be a first I, but not a first 2. 3, &c. If only mathematical number exists, the One is not a first principle (for if it were, it would be different from other ones, and there must then be a two different from other twos); if the One is a first principle, the numbers must be such as Plato supposed them, i. e. incomparable. 35. If both Plato's doctrine and that of Speusippus lead to impossible results, nllmber cannot exist apart. b I. (C b) The worst view is that ideal number and mathematical are the same (Xenocrates). This view falsifies the nature of mathematical number, and involves further the difficulties incidental to the belief in ideal number. 8. (B b) The Pythagorean view escapes some difficulties by not making number exist apart, but has peculiar difficulties arising from the supposition that bodies are composed of mathematical numbers. 13. For there are no indivisible magnitudes, or at any rate units have no magnitude, and therefore bodies cannot be composed of them, as the Pythagorean view implies. 19. Thus none of the ways of treating number as self-subsistent is satisfactory; therefore it is not self-subsistent.

COMMENTARY Aristotle first (1080b 37) discusses the theory of incomparable numbers (which, we are told in 1083.32, was the view of Plato). Then (1083.20) he proceeds to the theory of Speusippus, then (1083 b I) to that of Xenocrates, and last ( I 08 3b 8-19) to that of the Pythagoreans. 1081·1. ltvnp 8"'~o,",,, 1080·18-Z0, 23-35. 4. 11'~ €ts-r,Tuccii AI. 748. I. Cf. 108011 22, and .".pct,rq 8vQ<; 1080" 26 and MN passim, .".pt;YrOlf I'~"O!I, .".MTO!I, p&JJo<; De An. • o.b 20, 17rt~If€to.t 7rPWTUt K. 1060b 13. 7. Bz.'s proposal to omit TOil, is supported by 1. 12, but is not absolutely necessary. As he himself say!!, we may render the manuscript reading' and the Ideas cannot be 'the numbers thus produced '. II-IS. 1Mn0 oH~..... 61I'cno.oG... E. g. any of the threes in nine will be the Idea of man as much as any other, and the uniqueness of the Idea will be destroyed. 14. This is the first use in the Melap~sics of the phrase clOptaTO!I &,4<;. Doubt has been felt as to whether the phrase refers to the doctrine of Plato, or to that of his followers. The description of the material principle as the' great and small' is certainly ascribed to Plato (cf. A. 987b 20, 26, 988& 13, 26). In N. 1088b 28 Aristotle says €lulU TtJf€<; ot 8vd& I'~If dOptaTOlf 7rOtOVO't Tc\ I'€TA ToV life\<; UTOtX€Uw, Tc\ B' 8.lftO'Olf Svo'X€po.lvovO'tlf ~.\OyCII<; Btl}, TA UVI'Po.{lfOlfTo. &8Vlfo.To.. I. e., the adoption of the indefinite dyad as material principle seems to be described as an amendment of the description, which we can safely ascribe to Plato, of the material principle as the unequal. On the other hand the unequal and the indefinite dyad are coupled as belonging to the same theory in N. 1088· 15. So, too, in J083 b 23-32, N. 1090b 3210gl" 5 the great and small and the indefinite dyad seem to be both referred to Plato. Cf. Theophr. Mel. 33, Hermodorus apt Simpl. Ph),s. 247. ~o-2.8. 18, and AI., Simpl., Syr., Asc. passim. The J'eference of the indefinite dyad to Plato was doubted or denied by Susemihl {Gmel. Entwield. ii. 532 fT.}, Zeller in Pial. Siud. (222), Trendelenburg (De Ii. el Num. 48-51), Heinze (Xmocr. 10-15). On the strength of two passages (which are inadequate for the purpose) Heinze maintains that the phrase originated with Xenocrates (Theophr. Mel. II, Plut. De An. Procr. ii. I, 2. IOU D x). Zener later gave up his doubts, and there is no reason to distrust the evidence of Hermodorus, Alexander, .tc. In N. 1089" 35, though the expressions' great and small' and 'indefinite dyad' are distinguished, there is nothing to show that they were not used by the same thinkers to designate the same thing. And 1088 b 28 does not tell us that' the indefinite dyad' was a later phrase than 'the unequal', but merely that some thinkers (Xenocrates is probably included) retained the former, while discarding the latter because it made one o( the first principles something merely relative. Zeller thinks that Plato described only the material principle of ideal and malllt1nal;cal numbers as the indefinite dyad. But the silence of MN as to the derivation of sensible things from it proves nothing, since these books are not concerned with the derivation of sensible

=

M.

7.

[081& [-24

things. The Philebus certainly describes the d7rft.p[o. as the material cause in aU OI1CT[o., without special reference to numbers (7rc:£YTo. TO. vVv &YTo. Iv T!fl7ro.YT[ 23 c.). On the whole subject of the indefinite dyad cr. Robin 6,P-654. 15. at 4pXa.l Ka.l TA CTTOLxcia. = TO ~v Ka.L 't7 8vOS 't7 d6pLCTTOi. The argument seems to be: 'the only principles put forward by these thinkers are put forward as principles of number. If, then, they are also the principles of the Ideas, which they are clearly meant to be-, the Ideas must be (I) identical with numbers, which we have shown they are not, or (2) prior or posterior to, causes or effects or, numbers, which they evidently cannot be, since they are composed of a different kind of units. Therefore the Ideas are left without any dpXo.l at all'. The order of the words is against Apelt's proposal to interpret I. 15 , and the principles (se. or the Ideas) are said to be also the elements of number'. 17. Aristotle passes now to the view according to which even the units in one number are incomparable with one another. Considering that this view had found no supporter (1080b 8, 1081 a 35), the space Aristotle devotes to it (1081 a 17-b 33) is disproportionate. !U-!Z9 is a difficult piece or argument. Alexander supposes 11. 21-23 to mean that if the units are incomparable each with each, the numerical series will be destroyed because the numbers will be all formed simultaneously (H9. 19), and this view is adopted by Robin (note 285, iii). But this is contrary to Aristotle's usage, according to which 'incomparability' implies the very opposite of simultaneity; TO /Ltv 7rp&r6v TL a.fJTov TO 8' IX6/LfVOV 1080a 17 is synonymous with d.cnJ/LPA"f]TOi ib. 19. Alexander, continuing to misunderstand the passage, thinks that Aristotle should have said (1. 23) ~ 'Y4p 3./La. 0.1 ••• p.ovc:£&~ 'YfWWYTo.L ~ ol1X 3./La.. This means that Alexander is quite at sea. Bz. perceives the general nature of the argument as it stands in the received text, viz. that Aristotle offers two proofs to show that the supposition of units incomparable each with each is contrary to the Platonic view of ideal number as forming the series I, 2, 3, 4, &cc. (11.21-23), one proof being given in 11. 23-25, another in 11.25-29; and that really what Aristotle professes to show (that OI1K (CTTa.L 't7 8vO.~ 7rptf¥rq) is proved only by the second proof. The argument can be made right by the alteration of one word-by reading brc[ for (7rf!To. in 1. 25 (l7rUTa. has probably come in through the influence of (7r(!To. in I. 22). Then the argument runs thus: 'For the two will on this hypothesis not proceed first from the one and the indefinite dyad, and then the other numbers, as the Platonists say" 2, 3, 4 "-for they generate the units in the first (i. e. the ideal) two simultaneously-since if the one unit in the two were prior to the other (as it must be, on the hypothesis ofincomparability, cr. 1080& 17,19), it would be prior also to the two which is composed of them. Thus the order would be not, as they say, I, 2, 3, 4., but I, first unit in 2, 2, second unit in 2, fir&t unit in 3,' &cc. For the combination Wft fl cr. 1087& 21. !14. 1\ wpWTol chrwv, se. T~V TWV flawv dp,8/L~v flvo.! (cr. I. 21). A com-

parison with 1086a II, N. 1090b 32, where Aristotle is referring to a doctrine which marks Plato off from Speusippus and Xenocrates (cf. 1076& 19-21 nn.). shows that here also Plato is meant• • ~ 4v£CI'WV (ECJ'e&a8lvrwv yAp .ylllOlITO). The unequals are the great and the small (1083b 23. N. 1091a 24). Plato. according to Aristotle. represented the One as producing the units in 2 by equalizing the great and the small. But Aristotle speaks with some hesitation as to how this was done (I083 b 23-25). It is noteworthy that the material principle is never spoken of as TO. ctVLCJ'1I but always as ,.0 ctVLCJ'OV. and it seems probable that Plato did not think of two things. the great and the small. but of one thing. the great-and-small. i. e. indeterminate quantity. and that he represented this as simply being determined into the successive numbers by the operation of the One or formal principle. Cf. Introduction. lxi f. 30-31. ,.wI' au",v ........LIIO. 1(. the first unit in 2. 31-P. Tp£TOV ••• 1(. the second unit in 2. 3!a. The principal clause begins irregularly with c:lOTf. as often in Aristotle. Cf. Ind. Ar. 873a 31-44. 33. The reading of Ab AI.• r>.iKoVTIIL, would require a strange perversion of order. the antecedent of c:lv being then III p.ov&.8«. The reading of EJI. ~lYOVTIIL. gives an excellent sense and must be adopted. , The units will be prior to the numbers after which they are called; the third unit (i. e. the second unit in 2) will be prior to the number 3. and so on.' b 1-3. Ttl, TE ya.p ••• 'II'pWrov. 'It is natural that there should be prior and posterior units, if there is also a first nnit or first one'-se. the ideal one. 6-8 is a parenthetical recurrence to the point made in a 21-29. 8-10. It is doubtful whether Aristotle's attack is quite fair. The Platonists spoke of the Ideal One as the first One not in the sense that it was the first member of a series of units. but in the sense that it was the principle of the whole class of units. The word • first' is iIlchosen. since it seems to make the universal a member of the class which it constitutes; but there is not necessarily any serious confusion in the thought. 1!a-I4. 'Whether the units are without specific difference or not. number must be counted by addition', i. e. each number must be arrived at by adding I to the previous number. This is a successful enough appeal to common sense. but is something of a fJtlilio principIi'. The Platonists simply denied the premise that the numbers were reached by addition, and gave quite a different account of their generation. 17-19. 'The numbers cannot be generated as they try to generate them, out of the indefinite dyad and the One; for three is generated not from the indefinite dyad and the One but from the number two and a unit.' !al. AU' does not. as AI. 753. 9 and Bz. suppose, introduce a possible objection to the previous argument. It points out the contradiction between the actual facts (11.18-20) and the Platonic account

'V.

437 (II. aI, 22). Jaeger's addition of d is ingenious, but not strictly necessary. ~!Z-~6. 'If the two a's in .. are not distinct from the a itself, .. will be composed of the a itself and another a, and similarly a of the One itself and another one; so that the element other than the One itself will not be (as they said) the indefinite dyad, since the second element generates one unit (the second unit in the a), not (as the indefinite dyad does) a definite dyad: According to the Platonic account (as represented by Aristotle) the indefinite dyad 'received the definite dyad and made two dyads' (I08a R 13)· ~7-aa. Aristotle

passes here from particular arguments to a general protest against the absurdity of the position created by supposing all units, even those in the same number, to be incomparable. 30. ciT01I'ci. Alexander (754. 12) and Syrianus (131. I) may have read d.8vvaTa, or this may be their interpretation of dT01I'a. For dT01I'a Kat rAaup.aTW&q and for the meaning of rAaup.aTWIi." cr. 108a b a-i. al. 4vdYK1J S' KT).. I. e., if each number is derived not (as common sense says) from the previous number by the addition of I, but (as the Platonists say) from the One and the indefinite dyad, each number is as it were a special creation, differing in kind from all others, and thus we get an ideal two, an ideal three, &c. 108~a I. 0101' ycip, ' for, for example'. !Z-4. What does Aristotle mean by saying that the ' 10 itself' is not any chance number nor composed of any chance 5's or units? The meaning seems to be that, the 10 itself being an ideal number, the numbers contained in it must be numbers of a special kind, viz. ideal numbers, just as the units in it are supposed by these thinkers to be of the special type described in I081 b 35-37. Now two Ideas cannot be specifically the same; therefore the two 5's in 10 differ specifically; and therefore the units in them differ specifically; thus five of the units in 10 differ specifically from the other five, which is contrary to the hypothesis we are examining. There seems to be no allusion to the presence of numbers other than 5 in 10 (AI. 755. 12), nor to the specific difference between 10 and the 5's in it (Bz.). 7-11. In II. 8, 9 (after p.~), 10 it is not clear (as Bz. thinks) that Alexander read EO'OVTIU; it seems better to keep the reading of aU the good manuscripts, Jv£O'oVTaL, which Alexander may be merely misinterpreting. Jv rii 8EKciBL in 1. I I rather confirms iV£O'OVTaL, and quite a good interpretation may be given to the word. If the units in the 10 differ specifically, will there be no other 5's in the 10 than the two already mentioned? (I ) We can hardly suppose that there are not. Aristotle does not say why, but the reason obviously is that if you take, say, three units from the first 5 and two units from the second, you will get a new 5 different from the original two. (2) If there are these other 5's in the 10, what sort of 10 will they constitute? Apparently another loin the 10 itself, but the Platonists do not suppose that there is any such thing.

COMMENTARY 11-15. Aristotle now proceeds to confirm what he has already used as a premise (1. 3), viz. that the 10 itself is not composed of any chance 5's. He infers the mode of composition of the 10 from the mode of composition of the 4. This, according to the Platonists, is not produced by successive additions of specifically like units, but by the action of the indefinite dyad, which received the definite dyad or 'z itself' and made two dyads. For a similar use of cLUc\ JL~v ••• 'Yf confirming a view of the opponent's position which has already been stated (' they not only say so but they must say so ') cf. r. 1007 b Zo-Z9 laTo.L 'Yap TO o.brO IelU TPL~P~ 1C0.1 TOLXO~ 1C0.1 lI.V()pw1T~1 d 1C00Ta 1To.VTOS TL ~ 1C00To.f/J~CTo.L ~ cl1To4>~o.L Iv8ixfTo.L • • • cLUc\ JL~ AflCTiov 'Y' o.~OLS 1C00Ta 1I'o,VTOS 1To,VTOS) ~v lCo,T4CPaCTLV ~ ~v d..".of/Jo,CTLV. 13. ).o.~OiiCTo., 'having received', not' having taken '. The material principle receives the formative principle as the female receives the seed, which is the formal principle of generation. For the analogy cr. A. 987b 33-988& 7, and for the literal sense of Ao.JL{34VfLV cf. H. A. 559b 8, 577& 31, 3z, 578& 14, 63Z& z8. I7-lao. The union might be of the nature (a) of the accidental union of a subject with an attribute, or (b) of the intimate and essential union of genus with differentia. For the difference cr. Z. 1030. 11-14, 1037 b 13-ZI . 17. The manuscript reading JL(()I~fL ()o,TlPOV ()4TfpoV (' one will participate in the other ') does not offer a grammatical parallel to the other alternative ~ cn-o.v 11 ICTA. Christ is therefore right in proposing f'o(8i~(L 8o.Tipou 80.Tipou (' by participation of one in the other '). 18. f'oniX" yAp TOUT"'''. We should expect JL£TI}{fL 'Yap b lI.v()fXIl1T~ Toil AWlCoil, answering to JLf()i~fL ()o.TlpoV ()o.TEpoV. But Aristotle is not careful about consistency of expression where his general meaning is clear. laO-lal. As instances of things which are ~v d,f/Jv, pitfL, ()ICTfL Alexander mentions a bundle of sticks, mead, and the stones in a house. ~LS means complete fusion; the distinction between d.4>~ and ()ICTLS is not so clear, but probably d.f/J~ means mere contact which may be accidental, while ()ICTLS does not necessarily imply contact but does imply intentional arrangement. Cf. H. I04Zb 15-zo. 30-31. • As the definite or ideal Z produced (by co-operation with the indefinite dyad) the z's in 4, so these z's (again by co-operation with the indefinite dyad) produced the two 4'S (more strictly, the four 2'S) in 8.' 31 _b I. The argument in n. 26-3 I was directed to showing that some z's are prior to others. But in the course of the argument Aristotle IIhowed that the 2'S in 4 discharge a function analogous to that of the ideal z. He now draws another inference from this, viz. that therefore they also must be Ideas. And so, too, will be the units in the ideal z which similarly (by co-operation with the indefinite dyad) produce the units in 4. Thus the units in any numbt. are Ideas. Ideas will be composed of Ideas. The Idea of one animal will contain the

<

439

Ideas of other animals, and therefore one animal itself will contain other animals. Jaeger points out that EIJAb read !BEo.t after 8v"~ in 1. 32 (he infers from AI. 758. 2I that Alexander also read !BEQ.L; but 758. 25 has !BEo.). He concludes that ~ 7rpWrr, T(Tp"~ has dropped out before Ko.& ~ 7rpWrr, 8v"~. But the argument in 11. 28-32 is that the dyads in 4, since they generate the tetrads in 8 as the first dyad generates them, must be Ideas as much as the first dyad; a reference to the first tetrad would be out of place. i8io.t has come in because the eye of the writer of the archetype travelled on to !BEo.t later in the line. For the idiomatic Ko.{ before ~ 7rP~ 8v"~ cf. N. I08g& 16. b I. ct TOdTWV lSi," daev. Christ's suspicion of these words seems quite unfounded, and it seems clear that Alexander read them (759· 4). They may be taken in either of two ways. (I) We may render' if there are Ideas of animals', or (2) we may take olov • • • '~v as parenthetical and render 'if the Ideas are Ideas of the sensible things'. 6. l'0vuStKOv, cf. I080b 19 n. Aristotle means that while as regards two concrete groups we might find some difficulty in admitting the disjunction' they are either equal or unequal', we can find no difficulty about two abstract numbers. 11-16. From the premise that if we add one unit to another we always get a 2, two objections to the view here attacked follow: (I) the 2 thus formed will be composed of units specifically different, which contradicts the view in question; and (2) it will be hard for the thinkers in question to say whether it is prior or posterior to the 3. It would seem more likely to be prior, since one of its elements is prior to and the other simultaneous with the 3. Why then should the PIatonists not say that it is prior? Aristotle does not say why, but no doubt he means that it will be awkward for them thus to put a number between :3 and 3. !ZI-!Z!Z. &;j).ov ••• lVEcrTt Tti SueiS~. 'Clearly there is in 3 a number equal to 2.' !Z!Z-!Z3. 'But the :3 in 3 cannot be equal to the 2 itself, if there is a first and a second number " i. e. if 2 and 3 are numbers qualitatively different from one another. Cf. I080a 17, 19, where TO p.£v 7rpWTov Tt o.Vrov (i. e. TOV dpdJp.ov) TO 8' 'X0P.EVOV is synonymous with d.uUp.f3>':r/To~. !Z3-!Z4. 'Nor will the Ideas be numbers,' sc. as common sense understands numbers. !Z6. WPOTEPOV, I08Ia 5-17. !Z8-30. 'For which reason they must say that when we count thUS, •. I, :3", we do not do this by adding I to the previous I.' 3!Z. weinCl. Tel. dSlJ 'vO~ l'iplJ, i. e. all the Forms would be parts of the Form which is the largest number. 34-37. Alexander's commentary (762. 17-763' 3) may be summarized thus: 'The Platonists raise this difficulty, whether when we count" I, :3" we count by addition or by successive divisions of 10. They say we cannot do so in either way; not in the former becaut;e

CO:\Il\IENTARY then we should be treating the units as comparable, and not in the latter because then we should make the Idea of 10 contain the Ideas of the smaller numbers. We must confine both addition and division to mathematical number, and recognize ideal number as otherwise produced. But we actually count, says Aristotle, in both ways. If the number is definite, like 8, we divide it into its proper parts; if it is indefinite we add unit to unit till we reach the number we wish to determine. But what does he mean by indefinite number? Perhaps he means that the numbers included in 20 are indefinite and of the nature of matter relatively to 20. And so, he says, it is absurd on the strength of this superficial d:",oplo. to say that each of the numbers is a separate Idea and substance'. Bz. seems right in supposing that Alexander had before him words which do not exist in our text (cf. especially 762. 32 d.llO. 1I'Wr dJp&ITTOII ,l1l" 'Tall dpL()p.611 j); and there are traces of something similar in Syr. As regards Ko.'T4 p.cpl8o.t; Alexander's interpretation is probably guesswork. A better interpretation has been suggested by Apelt. He quotes, for the meaning of p.cplt;, Pluto Quaesl. Conv. ii. 2. 644 c 'Ta. 8'1p.Outo. 8c""",0. 1I'pOt; p.'pl8a. yl'Y",rio.t, which means • to be served separately by portions, so that each guest has his separate dish '. Aristotle's point seems to be this: The Platonists deny many of the accepted truths of mathematics (for 7I'OU4 dVo.LP0VuW cf. 1086& 9). E. g. they think they will put us in a difficulty by asking us whether we count by addition or by separate portions, i. e. constructing each number independently. If we say' • by addition', they will answer • then you are not grasping the nature of abstract number'; if we say • by separate portions', they will answer • then you are already admitting a number other than mathematical number '. But in fact we can regard the process in either way; it is absurd to rest the doctrine of two entirely different kinds of number on so superficial an d1l'Oplo.. 1083- I-51. Aristotle's own view is that numbers have a differentia, but units have not. 4. The grammar requires 611'cipX"v (which Alexander seems to have probably read, 763. 9) instead of the manuscript reading lJ7ro."xov• A},},' Ap,8"", !lo.TA TO 'IrOcnS'" • but number qua number differs in respect of fjuatllity'. 9-10. oll.i .. yap ... deal. Cf. De Caelo 299" 17, where Aristotle remarks that indivisibles cannol have 1I'o.~ because all 1I'o.~ are divisible. II. By the quality of number Aristotle means such attributes as compositeness O( primeness) and being • plane' or • solid' (having two or three factors); cr. A. lo:zob 3. These attributes, according to Aristotle, attach to a number in virtue of its quantity. 151. riil Sud,", the indefinite dyad. Ia. Bz.'s reading 'Il'ocrcnrcn&" is evidently right, though it is read only by Syr. and the second hand of E. The word seems to be a hapax

n

leg()lIle1loll, but OV07l'O!O~ (b 36, IOS2& 15) supplies an analogy, and the

play on words supplies a motive, for the coinage. 17-lg. IITL ••• +ovcpov summarizes 10SI& 5-17; Ig-~o. OilTC ••• TP01l'WV summarizes 10SI& 17-b 35, b 35-IOS3& 17. ~O_b I. Aristotle here passes from Plato's views (cf. 1. 32) to discuss those of Speusippus. Cf. 1076& 20-21 11. !Z4~7. Aristotle shows that Speusippus was inconsistent in that while retaining as the formal cause of number the One, conceived as a separate substance and distinguished from mathematical units (cf. Z. 102Sb 21 n.), he did not similarly believe in a Two or Three distinguished from the many twos and threes of arithmetic. 3~. Wawcp nMTWV aCylv is important as showing that the whole discussion in loSob37-IOS3& 17 was a discussion of Plato's views rather than of those of his followers. Speusippus is discussed much more briefly in IOS3& 20_b J, and Xenocrates in b I-S. The imperfect tense indicates that Aristotle is thinking of Plato's lectures rather than of published works. This is the only reference to Plato by name in MN. 35. ctP'lTClL, 10Sob 37-IOS3& 17. b~. 6 TPLTOS TP01l'OS, that of Xenocrates, 10Sob 22, 23. Aristotle omits here the view of llio~ T!S (I oSob 21) that ideal number is the only number that exists. 6. ,..,,,KllvELv, cf. N. 1090b 29 EUT! 8' oil XOAE7I'OV &rO!oO'ovv ~7I'08EO'E!~ AaP.f3o.VOVTO~ JIoo/(p07I'o!Eiv /(Ilt
f

COMMENTARY

ARGUMENTS AGAINST ALL THEORIES OF SELF-SUBSISTENT NUMBER

(ch. 8. 1083 b 23-9. 1085b 34).

(I) How are llu numbers producedfrom Ihe malerial principle I

I08ab faa. Is (0) each unit derived from the great and ,the small, equalized, or (b) one from the small, another from the great? If (b), then (0.) the elements are not all present in everything j (ft) the units are not without difference in nature; (y) what of the odd unit in 3? Perhaps this is why they make the One itself occupy the middle place in odd numbers. 30. If{a), then (0.) How will 2 be a single entity? How will it differ from a unit? (ft) The unit is prior to the two and therefore must be an Idea of an Idea. And it must have been generated before the two. From what, then? Not from the indefinite dyad, for this makes not units but twos. (2) How many ideal numbers are lherel

36. Number must be either infinite or finite, if it is self-subsistent. But (a) it cannot be infinite. For (a.) infinite number is neither odd nor even, but the generation of numbers whether by addition or by multiplication is always either of odd or of even numbers. 1084& 7. (fJ) If every Idea is an Idea of something, and the numbers are Ideas, infinite number wiII be an Idea of something, which is neither possible on their theory nor reasonable in itself. 10. (b) If number is finite, how far does the series go? They should tell us both how far it goes, and why it goes just so far. If it stops at 10, then (a.) the Forms will soon run short. E.g. the kinds of animal will exceed the numbers up to 10. 18. (ft) If the number 3 is the Idea of man, then all the other threes will be Ideas of man, or at any rate men; thus there wiII be an infinite number of men. faI. (y) If the smaller number is a part of the greater when composed of the addible units contained in a single number, then if the horse is 4 and man is 2, man will be a part of the horse. faS. (8) It is absurd that there should be an Ideaof loand notohl. fa7. (r) There are, and come to be, things of which there are not Forms. The Forms. then, are not the causal agencies. fag. (C) It is absurd if the number·series up to 10 is more of an entity than 10, though never generated as a unity. Yet they treaf the series up to 10 as a complete number. At least they generate the

..3 succeeding entities, the void, proportion, the odd, &c., within the series up to 10, assigning some to the first principles, others to the numbers. Further, they identify spatial magnitudes (lines, &c.) with numbers short of 10. (3) What IS the nature

of the

One r

b 2. If number is self-subsistent, is I, or 2, 3, &c., prior? Inasmuch as the number is composite, the one is prior; inasmuch as the universal or (orm is prior, the number is prior, being to the units as form to matter. 7. The right angle is in a sense prior to the acute, viz. in definition and because it is determinate; the acute angle is in a sense prior, because it is a part of the right angle. The acute angle is prior as matter; the right angle which is the union of form and matter is prior because nearer to the form. 13. How, then, is the One a first principle? 'Because it is indivisible.' But both the universal and the particular or element are indivisible. They are first principles in different senses, however; the former is first in definition, the latter in time. 18. They make the One a first principle in both ways. But this is impossible; it cannot have the primariness both of form and of matter. Both the number and the unit are in a sense one, but if the number is actually one (not a mere aggregate), the units exist only potentially. 23. The cause of the mistake is that they were inquiring from two points of view, that of mathematics and that of general definitions; from the former they treated the One (i.e. the first principle) as a point, merely divested of position, a minimal material part analogous to the atoms, while from the latter they treated the unity which is predicated of each number as a formal element in the number. These characters, however, cannot belong to the same thing. 32. But if the One must only be without position, differing from the unit merely by being a first principle, and the number 2 is divisible while the unit is not, the unit is liker the One than the number 2 is, and therefore each unit in 2 is prior to 2. But they generate the number 2 first. 1085& I. Further, if the number 2 Iii one thing and the number 3 is one thing, they make, together, a 2. What, then, is the origin of this 2 ? a. Does the number 2, or one of the units in it, come next after I ?

COMMENTARY

(4) Diffimllits about thejirst principles oj' geometrical objects. 7. Similar difficulties arise about the genera posterior to number-the line, the plane, the solid. (a) Some derive them from the kinds of great and small, lines from the long and short, planes from the broad and narrow, solids from the deep and shallow. There is a difference of opinion about the formal principle answering to the One. 14. These views involve many impossible results. (i) Lines, planes, and solids are cut off from one another, unless their first principles go together so that the broad and narrow is also long and short (in which case the plane would be a line and the solid a plane). laO. (ii) The same difficulty arises as with regard to number; long, l:ihort, .tc., are allrilmtes of spatial magnitude, not the mailer of it, any more than straight and curved are. (la3. We may put the same difficulty that arises with regard to species when we posit the existence of universals, viz. whether it is , animal' itself or some other ' animal' that is present in a particular kind of animal. Similarly if the One and the numbers are selfsubsistent, is the unit which we recognize in a number the One itself ?) 31. (b) Others derive magnitudes from the point (which is akin to the One) and an element akin to plurality. The same difficulties follow. 35. For (i) if the matter is one, line, plane, and solid will be the same; (ii) if it is different, the matters either go together or not, so that the plane either will not contain a line or will be a line.

(5) The difficulty oj'gmerating 1lumbers and spalialmagnitudes as Ihe Pla/omsts generate them. b 4. The difficulties which attend the great and small as material principles of number, attend plurality also if this be taken as the material principle (Speusippus). One thinker generates number from the plurality which is universally predicated, the other generates it from a particular plurality, viz. the first (the dyad). (a) In both cases we may ask whether the elements are united by mixture, position, fusion, generation, .tc. IlZ. (b) Each unit must be composed of the One and either plurality or a part of plurality. Now the unit, being indivisible, cannot be a plurality, while if its material element be a part of plurality, (el) each of the p~uts must be indivisible, and it is not, as they say, plurality, but

a part of it, that is the material principle; (P) number is being derived from a pluralily of indivisibles, i. e. from another number. 23. (c) We may inquire with regard to these thinkers too, whether that number is infinite or finite. There was a finite plurality from which the finite units were derived, and there is another' plurality itself' which is infinite plurality. Which kind of plurality is the first principle? 27. (d) Similarly (cf. a 32-34) a point cannot be derived from the 'point itself' and an interval, nor from the' point itself' and an indivisible part of an interval j for spatial magnitudes are not, like number, composed of indivisible~. SUMMING UP OF CRITICISM OF IDEAL NUMBERS

(ch.9. 108li b 34-1086818).

108Sb 34. These objections show that number and spatial magnitudes are not self-subsistent, as is shown also hy the diversity of views about nllmbe~. (I) Those who believed only in the objects of mathematics (Speusippus) did so because they saw the difficulties about the Ideas. 1086a S. (2) Those who thought of the Ideas as numbers, and did not see how, if the first principles are what they suppose them to be. mathematical number could exist apart from ideal number (Xenocrates), made them the same in name, but really did away wilh mathematical number. II. (3) The first thinker who held that Forms existed and were numbers, and that mathematical objects existed (Plato), naturally separated them. 13. All are partly right and (as their mutual contradictions show) partly wrong. Their error springs from the wrongness of their assumptions. 1083b 23-108Sb 34. So far Aristotle has distinguished the various modes of conceiving numbers as substantial entities, and has criticized them separately. Now he attacks the general view which was common to the Pythagoreans and the Platonists, no longer drawing the distinctions drawn in 1080· 15-1083b 19. His criticisms from now onwards may best be classified not according to the thinkers attacked but according to the subjects on which he attacks the whole of the two schools. These fall. as Bz. has pointed out, into five groups. (I) 1083b23-36. How are the numbers produced from the material principle? (2) 10831• 36-1084102. How many ideal numbers are there?

COMMENTARY (3) 1084b la--108Sa 7. What is the nature of the One? (.) 1085& 7-b 4. On the principles of geometrical objects. (5) 108Sb 4-34. On the difficulty of generating numbers from unity and multitude, and spatial magnitudes from similar principles. la3. Aristotle begins with a difficulty arising out of Plato's (cf. 1081 a 2.) description of the units in the ideal two as produced through the equalization of the great and small by the One. Aristotle appears, as Bz. points out, to have misconceived the nature of the Platonic material principle. It was no doubt conceived as a principle which was both great and small; i.e., it was indeterminate quantity. But Aristotle habitually speaks of the great and the small as if they were two distinct principles, and his argument here turns entirely on this point. We may note a significant looseness in Aristotle's way of referring to the principle. Sometimes (and, we must suppose. more correctly) it is TO p.rya. Kat P.LKpOV, e.g. B. 998b 10, M. 1083 b 32, 1085& 12, N. 1087 b 8. At other times it is TO p.eya. Kat TO plK(JOV, e.g. A. 987b 20, 988& 26, M. I083 b 27, 1085a 9, N. 1087 b II, 14, 16, and this is what the argument here requires. la8-30. 'Further, what account can the Platonists give of the units in the ideal Three? One of them is an odd unit and cannot be assigned to the great or to the small (Since these produce only one unit each); which is perhaps why they make the ideal One the middle unit in odd numbers.' For the fact that they did so cf. Diels, Vorsokr." 270. 18. And why should they not? we might ask. Aristotle's answer would doubtless be that if they make the One a purely formative principle in the case of even numbers, they have no right to make it one of the material elements of odd numbers. We can hardly suppose, however, that they did this; it is more likely that they represented the One as a sort of arbiter (cr. AI. 767. 17 ~v ri7~ p.ova.8o~ p.nTLT({av) between the tendencies to excess and to defect. 30-3la. 'If each of the units in the ideal Two comes from both the great and the small, these being equalized, how will the ideal Two be a single entity composed of the great and the small? Or how will it differ from one of its units? " sc. if each of the units turns out to be what they describe the ideal Two as being, viz. what is produced by the co-operation of the One and the-great-and-the-small (which 8v01row~ ~v 1. 36). 36. c1cSPLaTO~ 8ucl~. Robin quotes this as one of the few passages definitely relating to Plato in which this term is used. The other passages he cites are N. 1088& 15, 1091a 5, besides various places in later writers (Robin, 643-5). 37. X"'PLaTOII yap 1I'OLOUCI'L. Aristotle holds that if you regard number as a separately existing substance, you have to say that it actually is finite or that it actually is infinite, and both alternatives are impossible; he believes himself to escape the difficulty by holding that number does not exist as something given for all time, but only in the process of counting, and that it is potentially infinite in the sense that, however high a number has been counted, a higher can be counted. A({7I'UaL

447 8Wa.p,fL flvat TO 1l.7I'fLPOV Phys. 206& IS, b 13; M~ laTl TO 1l.7I'ftpoV, T.f clfl cLUo Kal cLUo Aap,{J&'vfu8at 206& 27: it is not a T08, ." like a man

or a house but like a day or a contest, whose being is not that of a ~ubstance but is always in course of destruction or generation. 1084& 4-7. The peculiar words 71'[7I'TfLV, lp,7I'[7I'TfW (not elsewhere found in Aristotle, nor, perhaps, in other authors, in this conne~don) are probably Academic terms to express the mode of generation of numbers. There are three cases: (I) By addition (~l p,lv) of I to an even number an odd number is produced. (2) By multiplication (~8l 81) (0) of I by 2 a power of 2 is produced, (6) of an even number by an odd number, an even number not a power of 2 is produced. d~ TO & is apparently to be supplied with lp,7I't7I'ToVa-q~, being understood from Aclt/J' lvo~ 8t7l'.\acrt~Op,fV~. while with ~8l 8, Tbiv 71"ptTTbiv we must supply in thought the d~ TOV /J.pTtOV of II. 4, 5. The main opposition is that between generation of numbers by addition and by multiplication, the latter being subdivided. Accordingly Aristotle says ~l 8, nj~ p,f.V 8v&.8o~, meaning to continue with Tbiv 8f. 71'fptTTbiv. But by an oversight he cominues with ~l 8, Tbiv 71'fptTTbiv. Alexander offers a more elaborate classification, which doubtless preserves some real information about the Pythagorean and Platonic arithmetic (cf. Heath, Gk. lIfalh. i. 71-74). According to him every genesis of number is (I) clPTuJ.Kt~ llPTta (powers of 2, = (2 a) above), or (2) d.pno7l'lptCTt1'O~ (products of an odd number and 2), or (3) 71'fpKTtT&.PTt~ (products of an odd number and 4 or a higher power of 2), or (4) 71'pWrr, Kal d.aVV6fTo~ (prime numbers), or (5) 8fVTlpa Kal crVV(JfT~ (composite odd numbers), or (6) Ka(l ~avn,v p,'v iifVTlpa KI1' aW(JfTO~ 71'~ cLUov 8f. 71'pw-rr, Ka, clO'WfJfTO~ (pairs of composite numbers which are prime to one another). Alexander supposes that (I), (2 a), and (26) of Aristotle's classification are identical with (4), (I), and (2) of his own, and that Aristotle omits the rest 8,a {Jpaxv'A.oy{av (769. 21). But it is evident that a t'omplele classification is necessary to Aristotle's purpose. Aristotle's (I) includes Alexander's (4) and (5); his (26) includes Alexander's (2) and (3); and Alexander's (6) has no proper place in the classification, since it depends on a relation between two I'lumbers, not on a quality of one. g. oi;',. kaTA rill' .l."I' ll'8lX£TCI', i. e. it is incompatible with the notion of the Idea as a principle of limit; oun ICCITA ).6YOl', i. e. it is unreasonable in itself, since it implies the existence of an actual infinite. 10. TciTTOUO't y' OUT.. TA, [&Ca,. The manuscript reading (,.a.TTovcr& ~ oJ.r", ft~ 181a~) can hardly mean, as Alexander supposes, 'but they

COMMENTARY limit the series of ideal numbers to 10 '. Since thi~ is not mentioned till I. 12, it cannot be what 01n-W means here. The word would have to refer to I. 'I, and mean' but they conceive of the Ideas as Ideas of something. and of the numbers as being Ideas '. Schwegler's emendation is undoubtedly right; T&'TT01XT[ y' KTA. = ' i. e. for those who arrange the Ideas as they do', i. e. identifying each Idea with a finite number. IlZ••t "...fYOVTf'> l8la.. 7rfpt ••• TWV tlpL8p.wv OT~ p.€V W'> 7rfpt tl7rftr,:V Alyovuw ~T' 8, W'> P.lXPL '"i'> 8fK&.8~ wpLCTp.lvwv. In PhJ's. 206 32 the doctrine is ascribed to Plato by name: p.(XPL yap 8fK&'&,> 'll"OL" TOV tlpL8p.6v. Speusippus is probably also referred to (cf. z. 1028b 21 n.). The origin of the view is of course to be found in the fact that the Greeks used a decimal system and in the reverence paid by the Pythagoreans to the number 10; cf. A. 986& 8 and Philolaus fro I I Diels. 10 was the sum of the first four numbers, the TfTpa~, which had a special significance because they were the principles of the point, the straight line, the triangle, and the tetrahedron respectively. 15. Bz. (Ind. Ar. I25& 5) takes a~T6 as predicate; 'each number up to 10 is a thing-itself (an Idea)'; cf. Top. 16z& 28. It seems better to take alrro ~KaCTT~ tlpL(}p.6,> together = ~ fl87]T'LKO'> tlp,8p.6'>, as Alexander does ('1'10. 23), and p.lxp' 8'K&'&" as predicate. alrro ~KaCTTo,> d.pt8p.6,> = 'the series of numbers which are the several things·themselves (the Ideas of the several things) '. For alrrO ;KaCTTO'> cr. Top. 162& 2'1. E. N. 1096& 35·

16. ,-wI' l" T06-rO'~ Ap,8",w" is usually interpreted as 'the numbers within these limits', i. e. between I and 10. But on this view what is the point of tlAA' iJp.w'> (I. 1'1)? That suggests that in spite of there being a large variety of numbers to choose the Ideas of different kinds of animals from, there would not be enough. Now the notion of numbers contained in other numbers is clearly in Aristotle's mind (cf. II. 18, 19 and notes) and is expressed similarly by lv. May it not be that Aristotle uses Iv TOVrOL'> in a double sense? 'The Idea of horse must be one of the numbers contained in these, i.e. either one of the numbers between I and 10, or one of the numbers contained in those between I and 10.' IS-IU. There is little to be said for Christ's transposition of this section to I. 25. 01n-w'> refers quite as naturally to I. 14 as it would to \. Z2 (~ IK TWV crvP.{lA7]T'WV p.ova8wv). IS. at aUaL TpLd8.~. Alexander explains this ('1'10. 30) as at Tpt&.8,,> '"i'> alrro,E&.8o'> Kat TedV AOL7rWV, and similarly Bz. thinks the 3'S included in the other ideal numbers (cf. 1082& 2, 28, b 13) are meant. Against this Robin argues (p. 351, n. 'I) that on the view here criticized the ideal numbers are limited to ten, and the' other 3'S ' in these will be only 14 in number (I in 4, I in 5, 2 in 6, 2 in '1, 2 in 8, 3 in 9. 3 in 10), so that the conclusion /1.7r£LPOL (UOVTaL /1.V(}pw7rOL (:. 20) will not follow. He therefore supposes Aristotle to be now taking account of mathematical numbers, which are not limited to IC, and saying that

M. 8. I084IL 12-30

449

each 3 contained in them, since it is like the ideal 3, will be some sort of a man, even if not an ideal man. We may either suppose this, or suppose Aristotle to be taking account of a further complication within the series of the ideal numbers. Besides the 14 3'S of which Robin takes account, there will be the 3 which is in the 4 which is in the 5. the 3 in the 4 which is in the 6, the 3 in the 5 which is in the 6, the 3 in the 4 in the 5 in the 6, .tc. A list which may fairly be called 1J:,mpov is thus produced. Ig. 61H1o.L yOoP o.t l" TOLl o.~TOLI °4PL8".0". Bz. supposes l8ial to be the noun implied by aI, and takes the phrase to mean I the Ideas consisting in identical numbers '. But Tpm8(i is the only word that can be supplied; and further Bz.'s interpretation assumes that the cLUa.I TpuI.86 are Ideas, which Aristotle expressly leaves uncertain (II. 20, 21). It seems better to suppose, with Robin (p. 352), that Aristotle means that the 3 which is in the 4 itself is like the 3 which is in the 4 which is in the 6, and the 3 which is in the 6 itself is like the 3 which is in the 6 which is in the '1 itself, and so on. Yet even this interpretation is not quite satisfactory, since to justify al cLUa., (all the other) TpuI.8(i Aristotle ought also to mean that the 3 in the 4 itself is like the 3 in the 6 itself. But probably Aristotle overlooked this point. SO-SI. I If each 3 is an Idea, each of the numbers will be Man Hin.self: The assignment of numbers to the different Ideas by Aristotle is arbitrary; it is quite unnecessary to read Tp&&'i for 8v&.i with Christ to bring the sentence into conformity with 11. 14, 18. lZ'I-sg. Bz. thinks this is an interpolation, belonging to the criLicism not of ideal numbers but of Ideas in general (cr. 1080- 2-8). The passage is, however, interpreted by Alexander and Syrianus without any suspicion of its spuriousness, and it seems quite possible to connect it with what precedes, if we interpret (ra,., as meaning ideal numbers, which in view of the repeated identification of Ideas with numbers we are entitled to do. Aristotle has just referred (II. 25-2'1) to the arbitrary assertion of the existence of Ideas of numbers up to 10, and the arbitrary denial of their existence beyond that point. Here he poinLs to a similarly arbitrary distinction. I Forms are introduced to explain being and becoming. Yet some things (negations 10'19- 9, relations 10'19- 12, manufactured objects 1080& 5) are and become without being supposed to have Forms answering to them. Why have they not Forms? The fact that the Platonists can dispense with Forms in these cases shows that Forms are not the causes of being and becoming: 30. ".a}.).6" TL 3". It seems pretty clear that Alexander and Syrianus had the same reading as our manuscripts. Alexander interprets it as meaning /Ca2 Tawa TO ~ /CaT' aln-oW ,u;.>.>..Ov TL IS., ICTA.; SO also Syrian us (Alexander may have read in the next clause /Cal for /CalTO'). Bz.'s proposal to read d h d.p&fJplJi p.fxp& n;i 8(/C&.80i, p.G.U.Ov TI ~v TO tv /Ca~ clBoi ICT.\. has not the authority of the Greek commentators; and the accusative absolute is not probable. The interpretations of Alexander and Syrianus do 110t commend themselves. According to Alexander the

ss.

COMMENTARY argument is: 'If the One is both the Form ofthe 10 and ungenerated, while the 10 has come into being. there will be an I I who~ Form is the One and whose matter is the decad '. According to Syrianus the One in question is the One which is the formal principle of number. and what it is in relation to all the numbers. the ideal 10 is in relation to the other tens, the hundreds. and the thousands. for which reason it was The meaning seems to be: 'Further. it called 8n1f'fpoBoVP.o.a. is paradoxical if the number series up to 10 is more of an entity ana a Form than the 10 itself; to this we may object that there is no generation of the series as a unity. while there is of the 10. Yet they try to speak as if the number series up to 10 were complete'. Certain Platonists may have said something (we do not know what) to justify Aristotle in describing them as holding the series up to 10 to be more of an entity than the 10 itself j once grant this and Aristotle's objection becomes plain. He objects that. as the Platonic theory only describes the origin of the numbers severally and not of the series ~ the series cannot form a true entity or Form. ag. Ta. "'cS,,_"CII. 'the derivative entities'. aa. rlo u"cS" itT).. Alexander explains that the space between the even numbers 2, ..... 6. 8. or again between the odd numbers 3. 5. 7. 9 was the Idea or pattern of the void (this may be an inference from Pkys. 2I3b 27 TO yap 1(0'01' 8l.Opl'ftv T7Jv cfJVuw a.thidv. se. Tidv d.pr.f)p.&iv. but it is of the Pythagoreans that Aristotle says this); that' 2 ...... (6). 8' was the pattern of arithmetical and '2. 3. 6. 9' the pattern of geometrical proportion j that the number I was the Idea of oddness j while movement and good were derived from the One. rest and evil from the indefinite dyad. Thus he takes TO; cLUa (I. 35) to refer to TO 1(0'01', T7Jv dvaAay[a.v, TO frfptTT&V. T~ cIllo. T~ TOta.Vra.. On the other hand Theophrastus (Mel. 312. 18-313. 3 Br. = fr. xii. I I fin .• I I Wimm.) says that the Platonists derived place. Ihe void. the infinite from the indefinite dyad, and certain other thmgs, e.g. soul. from the numbers and the One. Robin accordingly (p. 317) takes TO 1(0'01'. clvaAoy[a.. T~ 7rfptTTOV. as well as 1([I'1/".t... t1'T'flqt... dya.f)6v. 1(0.1(01' to have been derived from the ¥Xa.[ (the One and the indefinite dyad). and thinks that TO; cIllo. (1. 35) is left here without illustration but means what Theophrastus describes as .;vx.; I(a.~ IJ.A'A.' dTTU. With Theophrastus' statement that the void was derived from the indefinite dyad cf. PIzys. 209b I I nA&Tlllv T7Jv 1$>':'11' 1(0.2 T7Jv xwpav TathO cfJ"JCTw ftl'l1t. odd is actually described ill I. 36 as identified by the Platonists with one of the ¥Xa.[. the One. In this the Platonists followed the Pythagoreans. who described the formal principle indifferently as the limit and the odd. The best explanation of the reference to proportion is furnished by Syrianus. who points out that instances of all the three fundamental dvaAoyla.t can be found without going beyond the number 10: arithmetical dvaAoy[a.. e. g. I. 2. l j geometrical. e.g. I. 2 ..... ; harmonic. e.g. 2.3. 6. For the derivation of mtJfJemml from the indefinite dyad cf. K. 1066& II. where we are told that some thinkers describe movement as frfpOrryra. 1(0.2 clvttJ'Onp-a. 1(0.1 TO

p.ova...

wo...

n,

4iil /L~ C;v (which = TO /Liya Kal. TO /LIKpOV Phys. 192& 7), and A. 99 21> 7· Eudemus also says that Plato identified movement with the great and small (ap. Simpl. Phys. 431. 6, 13, p.•p. 18, 42. 8 Spengel). For the reference of good and evIl to the One and the indefinite dyad respectively cf. A. 988& 14. 36-37. 'And so they identify the odd with the One (a principle, not a number); for if oddness had depended on the first odd 1lumber, how would 5 (which according to tbe theory has not the ideal 3 in it) be odd?' To say that the number 3 is the principle of oddness would imply deriving 5 from the union of 2 and 3, whereas according to the Platonic view it is otherwise derived. The force of 810 seems to be this: The Platonists derived all derivative entities either from the first principles or from the numbers up to 10. Now oddness could not be derived from a number such as 3. because this would not explain the oddness of any other number (the numbers being supposed independent of each other); Ilurifore it had to be derived from one of the principles, and of the two the One rather than the indefinite dyad was indicated for the purpose. For the force of ll' rfi Tpw.81 cf. Eucken, Sprachgebrauch d. Ar.

P·23·

37-b 2. ITL ••• SEKASOS. 'Further, magnitudes and the like extend, they say, only up to a certain point, e. g. there is the first or indivisible line, then the two, &c.; these entities also extend only up to 10.' Aristotle is giving a further ground for his statement that the Platonists treat 10 as the perfect or complete number (1. 3 I). They recognize first the primary or indivisible line (their substitute for the 'point' of geometrical theory, A. 992& 22). ~ 7rP6,T'7/ ypa/L/L~ /1Top.or; is difficult, and it seems best to read ~ 7rP~ ypa/L/L~, ~ C1.Top.or;. (Alternatively we might omit 1) after olav as Schwegler proposes, and translate I first comes the indivisible line'; but ~ is more likely to have been omitted after 7rP~ than to have been inserted after olav.) I know of no exact parallel to 7rP~ ypa/L/L~ in this sense, but in A. 992& 2 I the indivisible line is called tlpx.71 ypa/L/LT,r;, and ~ T£ tlpX~ 7rp/Mov Kal. TO

7rpw-rov tloo,

Top.

I 2I b

9.

Certain Platonists (A. 992& 21, De Alt. 404b 16-24 suggest that Plato himself was among them, while a comparison with N. I090b 2032 suggests that Xenocrates also is referred to) connected the point or indivisible line with the number I, the line with 2, the plane with 3. the solid with 4 (N. I090b 22, Z. I036b 14, H. 1043& 33); and

1+ 2 + 3 + 4 = b 4-13.

10.

The discussion whether the One or number is prior may be compared with the discussion in Z. 10, I I, where the same illustration (the right and acute angles) is used (I034b 28, I035b 6, 1036& 14). The present passage seems to be written without any reference to the previous one. 7. aTL r:lpLaTGL K"l T'ii }.Oy,. Two reasons for the priority of the right angle are given, (I) that it is definite, while the acute angle may be of any size between 0° and 90° t and (2) that it is involved in the

COMMENTARY definition of the acute angle while the acute angle is not involved in ils definition. IlZ. N 411+'" i. e. what is elsewhere called TO U tlp..poiv (A. 1071- 9), or TO rrvvap..p1Jl (H. 10.3& 22). lJ tlpdJp.o<;, which is here treated as a compound of form and matter, was in 1. 6 described as form. 14-15. The list of three things that are indivisible-the universal, the particular (for the meaning of TO VrL p.lpov<; cf. Meleor. 359b 30, N. E. 1107- 30), and the element-is somewhat embarrassing, since in the passage as a whole only two things are opposed to each other (e. g. TO p.lv 15, TO 8116, 7rOTlpw<; 16). Alexander seems not to have read KaL TO C1TotX€iov, but it is TO €7rL p.lpov<; that could be best dispensed with, since it is the opposition of universal or form to element, not to particular, that is insisted on through the greater part of the passage (cf.II.•, 5; 19,20). At one point, indeed (11.9-12), the opposition of number to one is seen to be more truly that of whole to element; and the whole (TO o.\ov TO €K T7J<; V.\"I<; KaL TOV €l80v<;) = the particular (TO f7rL p.lpovr;); but for the most part number is treated as a universal. In fact the relations of whole and part, and of universal and particular, are not kept sufficiently distinct. The difficulty may be escaped in various ways. (I) We might read Ta. 81 in 1. 16 and take it to refer to both the particular and the element, TO p.lv referring to the universal. (2) We might suppose TO €7rL p.lpov<; to be added for the sake of completeness though it does not enter into the argument and is forthwith ignored. (3) We might suppose that KaL TO C1TotX€iov is explicative of TO VrL p.lpov<;. The mention of TO Ka6oXov, we may suppose, led Aristotle to its natural opposite TO (7rL p.lpovr;, which elsewhere means the particular, but, the relations of whole and part and of universal and particular being here confused, Aristotle uses TO (7rL p.lpov<; in the sense of 'part' and explains his usage by adding Kat TO C1TotXe:iov. This use of 17rL p.lpov<; would be to some extent in line with the uses of KaTa. p.lpor;, tlva. p.lpor;, 7rapa. p.lpor;, Iv p.lpn quoted in lnd. Ar. • S5 b 3-23.-0f these possibilities the last is. in view of the dichotomy which pervades the passage, the most probable. 15-16. dUel. Tp61r01' 4>">"01' KT>". An opposition of' indivisible in Myor;' and 'indivisible in time' would be quite unparalleled in Aristotle, and no reasonable meaning can be attached to it. Alexander explains that the universal is indivisible in Myor; because' footed two-footed animal' is not divisible into other .\OyOt and €l8"1 as 'animal' is into 'man' and' horse '-which is evidently nonsense; and that the particular is mdivisible in time because my form is not prior in time to mewhich, besides interpreting TO (7r1. p.lpovr; in a sense which we have seen reason to doubt, is a very unnatural interpretation of 'indivisible in I,'me'. Nor does any better interpretation of this last phrase seem possible. Weare driven, then, to suppose that TpOrOV cLUov KTA. does not qualify' indivisible'. Ifwith Bekker we read a full stop before tl.\M, we may take TpWOV cUAov as qualifying tlpxr1' 'The Olle is

.53

said to be dpx~ because it is indivisible. But the universal as well as the element is indivisible. Yes, but their consequent primariness is of different kinds.' We thus get the ordinary opposition of 'If'pOTfPOV My't' and XfJOv't', for which cf. ll. 12, 13, Z. 1028& 32, 1038b 27, @. 1049b II, Phys. 265& 22. Accordingly in I. 16 Aristotle asks not , in which sense is the One indivisible?' but 'in which sense is the One dpm?' 18. KUt (KUT
454

COMMENTARY

or element in the definition predicable of each number, as well a~ a material part of it. For this line of thought about TO lv, which led the Platonists to treat it as the very essence of real things. cf. B. 996& 4. 998b 1'1, 1001& 4. 20, I. 1053b 9. 20, K. 1059 b 2'1, 1060b 3. 82. Tmum S" ••• 6",C£PXILI', 'but one thing cannot be at the same time a material and a formal element in one other thing '. Cf. I. 19. 82-34. It Si ... c1pX~' 'But if the One itself must only be without position (for it differs in no respect except in that it is a first principle): What the One differs from only by being a first principle is the unit; but its being without position distinguishes it from the point (I. 26). Thus the two clauses have not any such connexion as yap indicates, and can hardly be right as they stand. Alexander feels no difficulty, but gives an impossible interpretation; and Bz'.s interpretation, which takes 1J.6ITovas if it could mean ¥xucav, does nothing to meet the difficulty. The proposed emendations of 1J.6ITov (cl8talplTov Schwegler, d.uUv6lTov Bywater) would give a satisfactory sense if it were not for /Lavov, but in the presence of /Lavov are unsatisfactory. Two suggestions may be made. (I) It is just possible that 1J.6(TOV may be used in a new sense. Each unit has, on the Platonic view, a setting or 6lut.. in some particular number; all that distinguishes the One which is the formal principle of number is that it has no such particular setting, that it is 1J.61Tov. It would not be unlike Aristotle to use 1J.61To.. thus in a different sense from that which it bore in I. 2'1, but the suggested use of 1J.61To" is apparently without parallel. (2) We might suppose p.ova8tICav to have been corrupted into /Lavov 1J.8t1COV, and this to have been altered through a reminiscence of \. 2'1 into p.Ovov 1J.6(TOV. 33-34. The use of o~e.l'~ ... ~ for oMwt IJ.U't' ... ~ or oM(v~ •.• clAA' ~ is irregular, but cf. Kiihner, ii. 2. § 540, Anm. 4. 1085& 1-2. The argument is not, as Bz. says, the same as that in 1081& 25-35. It is simply this: If one thing added to another always makes a two, the two itself and the three itself make a two, and a two of whose generation the Platonists can give no account. They cannot derive it from the One and the indefinite dyad, since what these originate is the two itself, the three itself, and so on. 3. 4+~ ,ul' OIlK lerrLI', cf. 1082& 20, P1!Ys. 227& 20. Only those things touch one another ~v Til dKpa. iJ.p.a 226 b 23, so that things which have not extent, such as units or numbers, cannot touch, though they can be successive. Iv TO'" ¥t6p.o'i.. is ambiguous; Aristotle means that there is not contact but only succession, both as between units in a number (I. 4) and as between numbers (\. 6). 4-5. aallll' ... TPLC£SL might be taken either with what precedes or with what follows. The meaning may be (I) TO S' l~(~ .. lUTtY lv Tar.. p.Gv&.utY ouwv /L~ lUTt IJ(Tatv, or (2) 7I'OT(pov al /Lov&.8( .., OuCdV /L~ IUTL /LIT~, l~(~... In either case ~ rii TpW,& is embarrassing, since it is only the units in 2 that Aristotle goes on to speak of; but it is specially embarrassing if ouwv leTA. be taken as in (2). Therefore (I) seems preferable. Then al Iv rii 8v&.8t is to be understood as the subject of l~(~ (,lut) in I. 5.

4.35 6. Bz. reads T~ If/>(~c; and claims the authority of Alexander. But it is not clear what Alexander read, so that it seems better to retain the manuscript reading TWV If/>(e1jc;, which gives a good sense. Aristotle does not here state the objections which follow if (I) the units, or one of the units, in two, or (2) two itself, are to succeed the number one directly. The objection to (I) is that then there is a two (composed of the number one + one of the units in two) before there is the number two itself (cf. 1081 110 32). The objection to (2) is that the first unit in two, being prior to the second unit, should be prior to the two composed of them (1081& 25-27). 7. ,-wI' u(JTepol' yel'liil' TOU 4PL61'ou, 'the kinds posterior to number '. These are also caIled Til /LeTa. TOVC; ap!8/Lovc; A. 992b 13, TO. /L(Ta. Ta<; iUa<; M. 1080b 25. For the priority of numbers to geometrical objects cf. A. 982110 26, Z. 1028 b 21 n. 9. ot I'~I' ya.p. lnpo! 8i does not come tiIl 1. 32. The Platonic opinions mentioned regarding the material principle of spatial magnitudes are (I) That it is the various kinds of the great and the small (1085110 9, A. 992& II, N. I090b 37). Some, if we may believe Alistotle, did not distinguish the great and the small which is the material principle of number from that which is the material principle of spatial magnitudes (B. IOOlb 19). AI. 228. 10, Asc. 207.37, Syr. 48. 20 think Plato himself is here referred to, and this may well be so. Others divided the great and smaIl into the many and few, which is the apx~ of number, and the long and short, the broad and narrow, the deep and shallow, which are the apxa{ of spatial magnitudes (N. 1089 b II). (2) That it is something analogous to 7r'A1j8oc;, i. e. something which is to spatial magnitudes what multitude is to numbers ( 1085& 33). 7r'A1j8oc; is mentioned in various places as the material principle of number according to some Platonists (b 5, N. I087 b 6,27, I091b 31, 1092& 28, 35). A comparison of I091b 30-35 with 1091& 29-b 3, and with A. I072b 30 (where he is mentioned by name), makes it pretty certain that Speusippus is the thinker referred to. Cf. AI. 823. 12. Plut. De An. Procr. ii. I, 2. IOI2 DE, ascribes the view to Xenocrates, but his testimony is of less worth. 13-14. 'As regards the principle in such objects which answers to the One (i. e. which is for geometrical objects what the One is for numbers), different thinkers hold different views.' AI. 777. 17 distinguishes two views. (I) Some thought that the ideal numbers were the forms of geometrical objects-two the form of the line, three of the plane, four of the solid. (2) Others thought that the One was their form. Both views are suggested in B. 100lb 24. (I) This view is mentioned in N. 1090b 22, Z. 1036b [3. It may be that the holder of this view was Xenocrates, for in Z. 1028b 24. after saying that Speusippus severed the various classes of being from each other, Aristotle continues with the words lVWL 8t TO. /Ltv (,871 lea, TOVC; Jp!8/LoVC; TJ,V atJT1,v EXElV f/>aut f/>VCTu' (this shows that Xenocrates is

CO:\IMENT ARY ' O( .. ' UJ\Aa '" \ (xop.(va, • , " Kat (1I't1l'(oa, • , ~ ques t'lon, Cl.r M • 107 6& 20 n.) ,TO. rpap.",a'> pAXfJL 11'~ Tf]v TOU o~paVOU o~u{av Ka~ Ta alu071T4. I. e. these thinkers linked up the various classes of entity, and made rpap.p.a.. Kilo' (1I'l1l'(Ba dependent on the numbers. Cf. Theophr. Mel. 313. 4 Br. = fro xii. 12 Wimm. The view of Zeller (ii. I.~ 949, n. 2) that Plato was the holder of this view seems less probable. AI. 777. 16, Syr. 154· 9 refer the view to Plato, but we have seen reason to believe that they knew little about early Platonism. Cf. Robin, pp. 295-298. We have no further information about view (2), but (3) a third view is expressed in I. 32, the view that the formal principle was the point, considered as analogous to the One. Cf. b 27. The persons who held this view are identified by Aristotle with those who took the material principle to be olov 71'>"~Oo,>, and we saw (I. 9 n.) that Speusippus is meant. It could not be either Plato or Xenocrates that is referred to, for they did not believe in points (for Plato cf. A.

. In

992& 20). 16. cl'll'oXEAu"lv" 1'1 is caught up by Tawo 1'( I. 20. The argument in II. 16-20 may be put thus: If long and short, broad and narrow, deep and shallow are the characteristics of the lines, the planes, the solids respectively, either (I) what is broad or narrow is not long or short, so that lines and planes are quite cut off from each other, or (2) it is, in which case the plane is a line. 19-20. The point of En 8t ••• cl'll'o809~aET''L; seems to be: 'How will they describe the principles of excess and defect which are to angles and figures what the long and short is to the line, the broad and narrow to the plane, &c. ? ' 20. To.~,.o TE au"fI,,(vlL TOLS 'll'Ept Tc\V clpL9,,6v, sc. uvp.{3alvovuLV.

Long and short, &c., are, as much as straight and curved, attributes (to be exact, they are properties, which are Kafi aW4 in the latter of the senses stated in An. Post. i. 4. 73& 34-b 3) of the line, 110t its matter, just as great and smalI are attributes, not matter, of number, A. 992b 2, N. 1088& 17. 23-31. Adstotle now introduces, in the middle of his discussion of the principles from which the Platonists derived geometrical object~, an argument against the general theory of ideal numbers existing apart from sensible things. The section breaks the continuity of the thought, and is evidently out of place. 23. 'll'C£VTIIIV ••• TOUTIIIV appears to be neuter-' all these cases '. 24. TWV ct8wv TWV ~s ylvouI, cf. A. 991& 31 n. 25. Alexander and Bonitz take this in the sense of ' ascribes separate existence to', but it seems doubtful jf the word can mean this; nor is either of the suggested emendations very plausible. I believe that 0ii has its ordinary meaning and that the argument runs thus: 'A question which can be applied to all these Platonic beliefs is that which must be faced in the case of species of a genus, when one posits the existence of universals, viz. whether it is 'animal' itself that is present in the particular species of animal, or an ' animal' distinct from' animal' itself. If we do not assign separate existence to the

9n.

457 universal there is no difficulty; if we do assign separate existence to the One and the numbers, the question is difficult, not to say impossible.' 86. fj Iftpo.. CII~G 140u. Jaeger reads 'CPO" for and renders 'or an animal distinct from the sensible animal'. But this would be a mere synonym for TO '«?o" a~, whereas nTEpo" ••• ~ suggests alternatives. The meaning is made clear by ll. z9-31. 87-88. X"'p~aTOG SI ... TOG • ..011 KCllt ni.. clp~8"w.., ' the One and the numbers being separate from sensible things'. 31. It seems quite possible, pace Bz., to retain CII".,o !fOci T~, in the sense of' is one thinking a thing-itself (or Idea)?' Cf. 1079b 9. 38. TO~CII.sT1J1l A1JIl, the various forms of great and small, 1. 9. Iftpo~ SI, apparently Speusippus, cf. I. 13 n. 33. ItCilt au1J1l A1JIl, cf. I. 9 n. For the construction dll7Ji ilA"1~ OLCIII TO '/I"A~9~ cr. De An. 4Z4b z, G. A. 766b 13. 8S-b 4. Aristotle here reduces those who made the material principle of ILryl9-q 'something analogous to '/I"A~9~' (I. 33) to the same dilemma to which he reduced those who made the principle • the kinds of great and small' (& 9-zo). b S. lit TOG bOil ItCilt 'Ir~~80UIl, the view of Speusippus, cf. a 9 n., Z. loz8 b Zl n. 6. O'lrlllll S' oa .. ~lyoucrL, 'but however they speak '. AlyoVUL is participle, cr. Top. 12Sb 33, De Sensu 444" IS, Pol. 13 1 9b 37. 7. TOil lit TOG • ..011 ••• 4op£aTOu. Plato is probably referred to, as well as Xenocrates. For the evidence cf. Robin, pp. 641-654. g. c\ S'=o{ l/( ToiiE"~ ICTA., I. 7. II. CIIt CII"TCII£, which is read by the ve/us versio and apparently by Alexander, gives a better sense than the manuscript reading a~aL. Christ's conjecture aVral is nearer to the manuscripts, but the crasis does not appear to be used by Aristotle. The passage suggests 10SZ& ZO, but the point is not the same. There the question was. How are the units combined into numbers? here it is, How are the formal and the material principle combined? On IL'itL~ and 9luL~ cf. 10SZ& ZO. /(paULS is a kind of ILUL~ (Top. 12Zb z6)-the kind that belongs to fluids; though sometimes the words are used interchangeably (Pol. u6z b IS). Cf. AI. De llJisi. xiii. 22S. 7. 25 Br. 18-88. From the supposition that each unit is derived from the One and a part of plurality, three difficulties might seem to be deduced: (I) each of the parts of plurality must be indivisible, so that a divisible is composed of indivisibles (which is absurd},-unless we are to make the part of plurality itself a plurality and the unit divisible (which is equally absurd); (z) the elements will be not the One and plurality but the Olle and a part of plurality; (3) this plurr.:ity of indivisible parts which is supposed to be an element of number will be itself a number. But there is a difficulty ill this interpretation. In 1. 33 number is said to be composed of indivisible parts. That each of the parts of plurality should be indivisible (I. IS) is, then, in itself no difficulty. cl8Ialp(To" (I. IS) •.. 8lalpETlj" (I. 19) is not a complete 1&71·1 G g

,c;ov

CO:\DIENT ARY objection; the following words leal ..• (Vo~ must go with it. The first objection then is that each of the parts of plurality will be indivisible, and thus the material principle will not be 7rA7j6o~ at all; and there are only two objections, not three. 1'(, then, in I. 18 is caught up not by 1e01 in I. 19 but by ;1'1 in I. 21. In all this, Bz. remarks, Aristotle ignores the facts (I) that Plato probably did not think of number as containing units at all, (2) that he meant by the material principle of number something which was a mere potentiality and could not be charged with being an actual number. But as regards the first point, we must remember that Aristotle is here attacking not Plato but Speusippus (cf. I. 5 n.), who did not believe in ideal but only in ordinary mathematical number (cf. 1076& 20-2 I n.), and is therefore more open to Aristotle's attack. 22. Ta yap 'lfMi90~ 48Lcnp'T"'v lOTlv 4pL91'~' cr. Z. I039a 1:1 n. 23. KlIol 'If.pl1'O~ 03,0", Uyol'1'lIo' KT>'. A similar question has already (1083 b 36) been asked regarding the theory which derived number from the One and the indefinite dyad; Aristotle is now considering the theory which derives number from the One and 7r>"7j6~. But it is not quite the same question that is asked. In 1083 b 36 the question was, ls number finite or infinite? Here the question is. Is the number which we have shown the original 7r>"7j6o~ to be (I. 22) finite or infinite? That this is what Aristotle is asking is shown by I. 26 7rOIoV otv 7r>"7j6~ OTOLXelov. 'lfepl TO~ OUT'" >'.!'yoI'1'IIoS. The manuscripts read 7rap&. I(1'A., and Bz. Ind. Ar. 562& 7 interprets 7rap&. as 'according to', but this use seems unparalleled in Aristotle. Alexander seems not to have had the preposition, and to have taken TOV~ oi'frw >..E-yoV1'a~ as object of 'rrr"f/Tlov ; but this is not an Aristotelian construction. 24. KIIoC, at first sight difficult, may be explained by the following paraphrase: 'Since the units produced from the 7r>"7j8~ and the One were finite, the 7rA7j6o~ also must have been finite '. 26. IOTL TC • • • U'lfELPOV. Alexander explains 'and plurality is different from infinite plurality'. (Though he does not use the word it would not be safe to infer with Christ that he did not read it.) So too Bz. The only objection to this interpretation is that if we adopt it, II. 24-26 give no reason at all why the original plurality should not have been finite. But Aristotle evidently thinks that he is putting Speusippus into a difficulty. Perhaps, then, we should interpret the whole passage thus: 'There was, according to Speusippus. a finite plurality from which and the One the units were derived. And there is another plurality which is "plurality itself" and infinite plurality. Which sort of plurality, then, is the material principle in number? ' 27-34. Aristotle now passes from the views of Speusippus about the derivation of numbers to his views about the derivation of spatial magnitudes (stated in a 32-34). The objections stated here to the

awo,

459 derivation of points are clearly akin to those raised against the derivationofunits in 11.12-21. Line 29 answers to 14j 30,31 to 15-17; 3 1-34 (less closely) to 17-21. ~9. o~ yAp ••• UUT'I, 'for this is not the one point which alone exists'. 36. Tp61rou~. Alexander knew both this reading and 7r~01J't, and preferred the latter, interpreting it as TOU" M30foTlpov .. (782. 25). But this is awkward, considering that Aristotle uses A 7rpilrro.. immediately after (loS6& II) in the chronological sense. It is equally awkward to suppose that Plato, Speusippus, and Xenocrates could be grouped as 01 7rpilrrOt in the chronological sense, since in loS6& I I Plato is distinguished from the other two as A 1rpilrro... It seems better, then. to read with EJ Tp01rOV .., which is used quite similarly in 1080b ., 10, 35. IOS3 b 2, loS6& 31. There is perhaps, as Goebel remarks, a special appropriateness in the use of the musical term TpOrO" with 8w.cpwv(iv. lo86&~. ot "iv, sc. Speusippus. Cf. 1076& 20-21 n., 10Sob I •• 4. TOil ctS"TtKoil 4pL9/'Oil. This phrase, which occurs again in N. 10SSb 3., 1090b 35. seems to stand for the ideal, i. e. universal or natural, numbers, as opposed to the so·called mathematical numbers. It has no necessary connexion with the presumably later theory which said that all Ideas were numbers. N or has it any connexion with the' figurate numbers', i. e. the numbers which can be represented by a regular geometrical pattern. such as .'. or :: . This way of thinking of numbers was an early Pythagorean device, and is referred to in N. 1092b 12, but the expression d81l'nKo" dpdJp.o .. comes not from the old Pythagorean usage of (180 .. = ux~p.u but from the developed Platonic sense of (180... It is a synonym for A &.pt(Jp.o.. A TWV d8wv (IOSI" 21, N. 1090b 33) or 01 lv Toi.. (~8(u, dp,6p.o{ (N. 1093 b 21). 5. ot Si, sc. Xenocrates. cr. 1076" 20-2 In., 10Sob 22, 1083 b 2. 5-6. TA ELS" ••• 1I'0LELV, 'wishing to make the Ideas at the same time also numbers '. 7· Alexander (7S3. 3) seems to have omitted Tcl~, and Jaeger follows him, taking TUVrU" as = TO; (t81l' But there would be no special point here in the description of the (t~ as dpxut. A comparison with 1081& I2-J 7. N. 1090b 36 shows the point to be that if the One and the great-and-small are taken as the first principles, it is hard to deduce both the Ideas and mathematical numbers from them. If TUUm.. be kept, the reference is to the discussion of the One and the great-and-small in IOS3 b 23-1085b 3.. But Ta.. aWl£" would be rather more pointed, and may be the true reading. II-I~. 6 S~ lI'pW~ ••• ,tvaL. SC. Plato (AI. 783. 22). For the phrase cr. 107Sb I I. for the doctrine 1076& 19 n .• 1080b I I. According to the manuscript reading Plato is described as laying it down (J) that the Ideas existed, (2) that they were numbers, (3) that mathematical objects existed; IXWpwIV is left rather awkwardly

COMMENTARY without an object. There is therefore something to be said for Christ's proposal to omit the second elva'. This gives the sense 'He who first posited that the Ideas were also numbers naturally separated the Ideas and the mathematical objects '. Cook Wilson's proposal to put .lva, after dpdJpov'> gives a still better sentence. 17. ICa.T"E1fLXa.pl'0'" Diels, Vors. fro I •• Ahrens (De Dzal. Dor•• 57) writes the verse of Epicharmus thus: d.pT{w'> T( yap X'X(lCTa' Keli8Vf o() KaAW'> 'xov I 4>a{V(Ta,.

CRITICIS&I OF THE DOCTRINE OF IDEAS

(M. 9. 1086& IS-N.

2.

1090& 2).

(A) II assigns separale exislen.-e 10 universals (M. 9. 1086& 18-10. 108 7& 25)· 18. So_much for the numbers; with regard to the first principles, what those say who are speaking of sensible substance only is a question for physics; we must discuss the statements of those who believe in non-sensible substances, Ideas and numbers, whose principles are the principles of all things. ~9. Those who believe in mathematical numbers only may be deferred; we must discuss the believers in Ideas. They treat the Ideas as universals and at the same time as existing apart and as being particulars. 34. The reason of this impossible combination is that they thought that since sensible particulars were in constant fiux, universals must be something apart from these. b~. Socrates by reason of his definitions gave the impulse to this view, but did not separate the universals from the particulars. He was right, for knowledge implies a universal; it is the separation that causes the objections to the Ideas. 7. His successors, seeing that if there are substances apart from sensibles they must exist separately, could find no others than these universals to assign separate existence to, and therefore assigned it to them. The result is that their universals and their particulars are practically the same kind of thing. 14. We may state a difficulty already discussed which affects non-believers as well as believers in Ideas: if we do not suppose substances to exist apart. we annihilate substance; if we do suppose them to do so, what are we to say of their elements? ~O. (I) If we make these particulars, then (a) things will be no

more in number than their elements, and (b) the elements will be unknowable. For suppose syllables to be substances, and their elements (the letters) the elements of substances. 84. Then (a) each syllable will be a unique individual, and therefore also each letter; and therefore there will be nothing but the letters. aa. (b) The elements will be unknowable. For knowledge is of the universal, as is clear from the nature of demonstration and definition. 37. (2) If the first principles are universal, either the substances composed of them will be universal, or what is not substance will be prior to substance. For the universal is not-substance, the first principle is universal, and the first principle is prior to what is composed of it. 1087- 4. These difficulties arise when people derive the Ideas from elements, and at the same time treat the Ideas as existing apart from the substances that have the same form. But (a) if there- are many a's and b's and no ' a itself' or 'b itself' apart from the many, there can be an infinite number of similar syllables; and so with substances and their elements. 10. (b) The view that knowledge is universal, so that the first principles of things must be universal and not separate substances, is true only in a sense. 15. The potentiality of knowledge, being universal and indefinite, is of the universal and indefinite, but the actuality is definite and of the definite, individual and of the individual; what the grammarian studies is ' this a', and' a ' only indirectly because this a is an a. al. If the principles had to be universal, their compounds would have to be universal, and then there would be no self-subsistent substance. But it is only in one sense that knowledge is universal. 108& ao. Bz.'s proposal to read ""E'ff'"0'p.',,0,, or ""11r£tO'P.i.voV'i for the second 'II'1'II'I'O'l'iVOl does nothing to remove the difficulty. The manuscript reading is as old as Alexander. The sentence though careless is not unnatural. Aristotle writes oM/a piiUov as if something like 4" l",.t80l7J could be supplied from the previous clause; but he happens to have written in the previous cla.use A" ",."u6rl7J, which with ",.p?J'i T?J ""£LfT~"a, would make nonsense.-Cf. note at beginning of Book M. al. Syrianus tells us (160.6) that some manuscripts made Book N begin 11t this point. Certainly there seems to be a greater change of subject than at 1087& 29. So far, Aristotle has been discussing the question whether Ideas and numbers exist independently of particular

COMMENTARY things; now he proposes to discuss' the first principles and the first causes and elements '. In essence 1086:1 21-1087& 25 is a preface to N, and with N forms a parallel and probably earlier treatment of the subject dealt with in M. init.-I086& 18. Cf. note at beginning of Book M. In the discussion now entered upon two distinct questions arise: (I) whether Ideas and numbers could serve as the elementary principles of things; (2) whether the account given by the Platonists of the principles of Ideas and numbers is satisfactory. The two questions are, as Bz. observes, not kept very clearly apart by Aristotle. ~3. Iv TOit 'lfEpl +.lUEW5. Alexander refers to Phys. ii. 3, where the doctrine of the four causes is stated, and De Gen. tI Corr. ii. 5, where the four elements are deduced. But the reference is more probably to Phys. i. 4-6, De Caelo iii. 3, 4, De Gm. tI Corr. i. I, where the views of the materialists are discussed. ~9. ot "lv, the Pythagoreans and Speusippus, cf. 1076& 20-2 In., 1080b 14. 30. iJlJ'TCPOV, N. 1090& 7-15, 20_b 20, 1091& 13-22. 3~. KmecS}.OU TE [Ills 0"ULm5] 'IfOlOUUl Ta.5 tSlm5. 'They make the Ideas universal as substances' does not give the right sense; the substantiality of the Ideas should not be emphasized in this half oC the sentence, but only their universality. Jaeger is probably right in treating W5 oW-ta5 as a variant of W5 xwpurra5 which has found its way from the margin into the wrong part of the text. 33. Kml TWV Kmr IKmlJ'Tov, 'and belonging to the class oC particulars'. Koi. is unmeaning if we take TooV Ka6' lKalJTOV as depending on XWpurro.5. 34. Sl1JnP1JNl suggests a reference to Book B (cC. similar references in r. 1004& 32, I. 1053b 10, A. 1076a 39, b 39, M. 1086 b 15); and B. 1003& 'I is quite relevant. The same point has been discussed in Z. 13. There is nothing in M. 4, 5 (which Bz. suggests) that quite suits the reference. 35-37. mtTlov ••• 1'lfO£ouv. The traditional text would mean: 'The reason why these characteristics (universality and separate existence) were combined together by those who described the Ideas as universal was that they did not regard the Ideas as substances identical with sensible things'. This is evidently in more than one respect a weak sentence. It is completely cured by jaeger's conjecture that 18(a5 is a gloss which supplanted oiJuta5, and that oiJu{a5 later found its way from the margin into its traditional position. His reading gives the excellent sense: 'the reason why these characteristics were combined by those who described their substances as universal was that they did not identify substances
M. 9. 1086&. 2.1 -

10. 1086b 22

s.a TOU~ &plCr"ous, 'by reason of his definitions '. A less direct connexion is implied than would have been conveyed by the genitive. 5. &rJ~oi. For ~Aoi impersonal and intransitive cf. Ind. Ar.IH" 15-1'1. 10. l~leI!CI'a.v, cf. A. 992b 10 n, 15. TOi5 ,,~ UyOUCI'LV refers both to Speusippus, who did not accept the doctrine of Ideas (& 29 n.), and to non-Platonists. lv Tois SLa.1I'Opt\"a.cr,v, B. 999 b 24-1000" 4, 1003& 5-17. 18-19. clva.'p~CI'I!' .•• ~lyl!'v. 'One will be destroying substance in

that sense in which we understand "substance".'

For this use of

{3ovA(cr8at Afy(W cf. N. 1089& 20, 1091" 32, PI. Laws 892 C 2. When W~ {3ovA6p.({)a Alyf,tv is interpreted thus, Alexander's &rrEP oll {3ovA6p.({)a ('18'1. 25) is seen to be not a variant reading but a paraphrase. Bz. supposes Aristotle to be admitting that the refusal to posit substances

separate from sensibles leads to the negation of substance, and accordingly takes w5 {3ovA6p.IE{)a AfyUV to mean ' as we are willing to admit for the sake of argument', But this is not (I think) idiomatic Greek, and no reason can be suggested why for the sake of argument Aristotle should admit something so entirely contrary to his own view. He is in fact saying something quite different: 'If one does not suppose substances to exist separately, and in the way in which individual things are said to exist, one will destroy the kind of substance that we wish to maintain '. The question of the chapter is a general one, involving those who do not believe in Ideas as well as those who do (I. 15). Aristotle agreed with the Platonists in supposing substances to exist separately (the substances they meant being Ideas, i. e. entities which were supposed to combine universality with independent existence, while the substances he means are individuals). He therefore dismisses at once the supposition that substances do not exist separately, and passes (I. 19) to the supposition that they do, which occupies the rest of the chapter. Are their elements unique individuals or universals? (I) If individuals (Aristotle is no doubt thinking here of expressions like' the One', "he indefinite dyad '), then (a) the substances will be unique individuals also, and (6) the elements will be unknowable. (2) If universal, the substances will be universal and no true substances. Aristotle's own view is that the elements, and the substances, are neither unique individuals nor universals. All that is substantial is individual, but individuals are not necessarily unique; there may be many of a kind. And what is true of substances is true also of their elements (I 08 '1& '1-10). So Aristotle meets objection (I a); (I b) he meets by the assertion that in a Eense knowledge is ofindividuals (1087& 10-25); (2) he leaves alone, since his view is that the elements are individuals, though not unique individuals. cr. note at beginning or Book M. asa-aa. 'crrwcra.v ••. ,,61'01' TA crrOLxcia.. The main point of these lines may be put thus: If each letter of the alphabet were a unique individual, then you could never by any process of composition get any more at one time than just A, B, C, &c., each occurring once.

COMMENT AR Y You could not have. for instance, a syllable BA and a syllable BC. Similarly, if the elements of substances were unique individuals. substances would be miserably limited in their number. Aristotle professes to be assuming that the elements are unique individuals (II. 20, 21). But he complicates the argument by deducing this (II. 2'1, 28) from the unique individuality of the composite substances, which he first states as following from their being separate substances (II. 22-2'1), and then establishes by reference to what the Platonists actually say (lTL ••• TLBiac",v 1. 2 '1). s7. 6"wllUf'O" is used here in the sense more properly expressed by CT1JJI~JlVp.ov (cf. Ind. Ar. 514& 25-31, b 13-18), as often when there is no point in emphasizing the difference between the two words. ITL 8' ... TL84a.Clw, a parenthetical remark to the effect that the numerical singleness of the Idea is not a mere supposition of Aristotle's, but is actually believed in by the Platonists. 'They posit that "the just what a thing is" is in each case one.' For aw~ 8 ZUTt cf. Cral. 389 D 6 a~ IKIWo & lO'T&JI {,vop.a.,Phaedo '18 D 3 aw~ ZKaO'TOV &lO'TL, Symp. 2 I I C 8 Pii a~ TIAfVTWV &lO'TL KaMV, P arm. 133 D 8 Ol1K awov 810"11'OTOV"8,prov, &lO'TL &O"II'~, IKIlvov 8oliAO" lO'TLJ·. & lO'TL appears as a more or less technical name for an Idea in Phaedo '15 B I, D 2, Rep. 50 '1 B '1. 59'1 c 9. &:c. Cf. similar phrases in Theael. (46 E 9, Phzl. 62 A 2. sg-30. Ita.Tc\~" a..no" ).&Y0l' ... Ita.l i1~>'", 'according to the same argument by which in the case of the syllables there will not be more than one instance of the same syllable '. For OJl1rlP = Ka.8' OJl1rfP cf. A. Q91h8 n. 35. Prof. Shorey in Class. Phzl. viii. 90-92 holds that d ,,1\ here and in I. 36 means not' unless' but' but only that '. He argues that in 1. 33 kno~ledge is said to be 'of' universals, i. e. to have universal conclusions as well as universal premises (cf. Plzys. 189& 5-'1. Z. 1039b 2'1), and that singular propositions never occur as conclusions in Aristotle s logical writings. This use of fl ,.,.~ is found, e. g., in Ar. EfJ. 186. Av. 168 (, Lys. 943, Thes",. 898, and Alexander so interprets the words here ('190. I).-There are, however, occasional references in Aristotle to the occurrence of singular propositions as the minor premise or conclusion of syllogisms (e.g. An. Pro 43& 3'1-40), and in the absence of any evidence of this idiomatic use of Ii ,.,.~ in Aristotle, it seems preferable to suppose that Aristotle has in miftd a syllogism of the form: All triangles have their angles = two right angles. This figure is a triangle . • . • This figure has its angles = two right angles. Cf. An. Posl. '11& 19-29 (where the same example occurs). 36. 6p8a.C is as much in accordance with Aristotelian usage as dp8a.i", and it is better to keep the better attested reading. 37-108,- 4. cl).U "~,, . . . leJTll'. According to the manuscript reading the argument is: 'But if the principles are universal, or for that matter if the substances composed of them are universal, nonsubstance will be prior to substance; for the universal is not sub-

stance, and the element or principle is universal, and an element or principle is prior to the things of which it is principle and element'. There is manifestly no argument here j the second clause makes nonsense of the passage. All that is needed is to insert ~ before laTo.£ in 1087. I. 'But if the principles are universal, either the substances composed of them are also universal or non-substance will be prior to substance.' Cf. 1087· ZI l7rE~ d dva'Y'"I T4~ dPX4~ 1C0.86)"ov .11'0.£, dva'Y'"I 1C0.~ T4 llC TWrIllV lCa86)"ov. When the first ~ once came to be misunderstood as 'or " the second was bound to drop out. Syrianus (164. 36) treats the clause beginning ~ lCal as apodosis, and therefore probably read the second ~. Aristotle has already (II. 20-37) shown the difficulties that arise if the elements of substances be taken to be numerically single. He has now (1086 b 37-1087. 4) shown that if the elements are universal, either non-substance will be prior to substance (which is absurd) or the substances will be universals; but this contradicts the very notion of substances, which is that they are ICEXIIlPLCTP.lva.&, 1C0.' T~V Tp07rOV TOVroV ~~ Al'YETaL T4 1C0.8' ilCaaTa TWV tJVTIIlV (I 086 b 17). Jaeger treats 37 ~ ..• 1087. I 1C0.80>..0v as a gloss intended originally to have come after OfJCT{o.~ in 1087. I. But the clause goes back to Alexander (790' 9), and the insertion of ~ cures the passage more f,imply. 108'.4-10, in spite of 7raVTo., refer especially to the difficulty expressed in TOCTo.VT' laTo.L T4 &VT4 Orra.7rEP T4 aTOLXEio. (1086 b 21, cf. 1087.9, 10); II. 10-25 deal with the other difficulty, O~IC l7rLaTytT4 T4 aTOLXEio. (1086 b 22). 5-6. Ko.l ••• KlxwpLCI'l'ivol' has given much trouble. Alexander has two interpretations. (J)' And when they claim that there is a single separate o.fJTOEi8o~ distinct from the substances which are sensible and have in them the Ideas' (791. 2). The Greek evidently will not bear this meaning. (2)' And when they claim that there is a single o.woEi8~ separate from the substances, i. e. from the Ideas, which have in them the dPXLIC~V Iv or o.woEi8~· (791.5). Besides misreading T~ o.w~ Et80~ as T~ o.fJTOEi8o~. this introduces a notion which the context does not warrant, the notion of a hierarchy among the Ideas. The passage is concerned solely with the relation between separately existing substances and their element!!. In view of the failure of Alexander's interpretations Bomtz proposed the omission of 1C0.' l8'0.~. His proposal entirely removes the difficulty; the two clauses bv ••• l8'0.~ and 7ra.pO. • • • ICEXlIlpLCTP.'VOV then answer exactly to the original statement of the question. 41' 8' TL~ 8j T4~ O~CT{o.~ (here = the Ideas) XlIlpLCTTd~, 7rW~ 8~CTEL TO. aTOL}(ELa. 1C0.' T4~ dpxo.~ o.wwv; (r086bI9)· 7-10. Aristotle here states his own mode of escape from the difficulty raised in 1086 h 22-32, just as in ll. 1:3-25 he states his mode of escape from the difficulty raised in 1086b 32-37. 7. Aristotle says ~cnr.p as if he were arterwards going on to state the true view about the elements of substances. of which the true

COMMENTARY view about the elements of syllables is an illustration; but the i:Kr7rep clause gives his meaning sufficiently and the principal clause never appears. Cf. B. 1000& 1 n. 13. 'xci ,..ci).IUT' cl'll'OPL~V TWV ).cX8illT"'v. Aristotle means that this presents the greatest difficulty not to the Platonists but to every one, whatever his views about Ideas may be (1086 b 15), and therefore proceeds to modify what he has said (Tll '\'''Ya/Levov) in 1086 b 33. that knowledge is of universals. The modification is contrary to his usual view, which is that actual knowledge is of universals. The doctrine of the Posterior Analytics cannot be understood in any other sense, and other works as well occasionally state the doctrine quite explicitly. De An. 417"22 has TWV K~(/ (KaaTOV ~ KaT' f.VEfYYCLav at(1'/)"1(1't<;, ~ l)' f.'TT'~/L"1 T(;'IV Ka/)o'\'ov, where the l'TT't(1'r1/L"1 meant must be ~ KaT' f.VEpyetaV as the at(1'/)"1(1'I<; is. cr. Z. 10391. 27 TWV OOO-IWV TWV ai(1'~wv TWV Kafl (KaaTa olin OPI(1'/Lll<; oilT' d'TT'al)(ltt<; laTlV. Yet the doctrine of the present passage is implied in De An. 417& 28 0 8' ~l)"1 /)(WPWV, f.Vn'\'(X({f/- t,v Kal KVPIW<; f.7T'IaTa/L(vo<; TeSSC TO A, and, according to one reading, in @. 1048&34 (Myo/L(v) f.7T'IaT~/Lova Kal roy /L~ /)(111POVVTO, Av ~vvaTo<; V /)(wp~(1'al roSIE f.V(Py£lf/-. In neither of these passages is the doctrine introduced to escape from difficulties such as that put forward here; it is a genuine part of Aristotle's theory, though perhaps inconsistent with another part. Usually knowledge is opposed to sensation as being of the universal while sensation is of the particular, but occasionally Aristotle admits that knowledge is of the universal in the particular, as he admits (An. Post. 87 b 28, De An. 424ft 2r-24) that sensation is of that in the particular which is universal. Cf. pp. cviii-cx. I,. Bz.'s excision of TOU is, in spite of Alexander's attempt at an interpretation, absolutely necessary. aa. Wa'II'EP 111'1 TWV d.'II'oSIELtlEwv, because a'TT'op(lt,<; must be in the first figure (A". Post. i. 14), and in that figure universal premises always give a universal conclusion.

,..,v

BOOK N (B) The itka/theory treats cOlltraries as first prindples (ch. 1. 1087& 29-b 33). 1087&a9. All philosophers make the first principles contraries, the first principles of unchangeable substances as well as those of the objects of physics. Now, since there cannot be anything prior to the first principle of all things, the first principle cannot be an attribute of something else, for then that other would be prior to it. But

all generation from contraries implies a subRtratum, so that all contraries are attributes of a subject and none is self-subsistent; therefore no contrary is strictly a first principle. b 4. Now the Platonists make one of the contraries-viz. the unequal (the dyad of the great and small) or plurality-the material principle, and its contrary, I the One " the formal principle. IIa. Further, they state the first principles badly, whether they describe the material principle (a) as the great and small, or (b) as the many and few, or (c) as the exceeding and the exceeded. These diversities make no difference to any but the verbal objections. IaI. If you treat the exceeding and the exceeded in general as th~ principle rather than the great and small, you should say that number in general is derived from the elements previously to the number two; but they do not say this. !a6. Others oppose (d) 'the other', or (e) plurality, to the One. If the One has any contrary, it is plurality; but even this antithesis iR wrong, because it would follow that the One is few.

Ob/ections (ch.

I.

lo87 b 33-2. lo88 b 35).

(I) Oijedion relative 10 Ihe formal principle. 33. 'The one' evidently means a measure. It always has a substratum, in harmony the semi tone, in length the finger, &c., and generally in qualities a quality indivisible in kind, in quantities a quantity indivisible to the senses; there is no substantial 'One itself'. 1088& 4. This is natural, for 'one J means a measure of some plurality, and number a measured plurality or a plurality of measures (so that one is not a number). 8. A measure must be something common to the things measured i I horse' is the measure of horses, I living being' is the measure of a man, a horse, and a god, I class' is perhaps the measure of I man', I white', and I walking'. (2) Ob/edions relalive 10 Ihe malmol principle. 15. Those who make the dyad an indefinite something composed of great and small say what is neither plausible nor possible. For (a) these are, like odd and e\'en, &c., attributes rather than the RUbstratum of numbers and magnitudes. IaI. (6) Great and small are relative terms, and therefore belong to the least substantial of all the categories. Relation is an accident of quantity, and always implies a substratum.

COMMENTARY

!ag. Its unsubstantiality is shown by this, that of it alone there i'l no generation, destruction, nor change, as there is increase and diminution in respect of quantity, alteration in respect of quality, motion in respect of place, generation and destruction in respect of substance; a thing becomes greater or smaller without itself changing, if its correlative becomes smaller or greater. b I. (c) The matter of a thing is what is potentially that thing; but relation is neither potentially nor actually substance. Non-substance cannot be an element in substance. 4. (d) Elements are not predicated of their compounds, but many and few are predicable of number, long and short of line, &c. S. If there is a plurality (e. g. two) which is simply t few', there must be one which is simply' many' (e. g. 10 or 10,000). But if the many and few are elements in number, either both or neither should be predicable of it.

(3) Objed/on to regardh'g eimw/ mlilies as composed of demenls. 14. Can eternal things be composed of elements? If they were, they wOldd have matter. That which is composite is generated from its elements, but that from which a thing is generated is that which is potentially it. Now that which is potential need not become actual. Therefore that which has matter, however long it lasts, is capable of not being and is therefore not eternal. !as. Those who make an indefinite dyad the material principle, but avoid calling it the unequal, avoid only the objections incidental to making the unequal (a relative term) an element. Tlu mistake on which the theory resls (ch.

2. 108Sb 35-1090& 2).

35. The chief reason why the Platonists turned to such causes was their archaic statement of the problem. They thought all things would be one, viz. 'being itself', if they did not oppose Parmenides' dogma and prove that not-being is; they thought that if things are many, they must be composed of being and something else. 108g& 7. But (I) if' being' has many senses (substance, quality, &c.), what sort of unity will all things be if not-being does not exist? Will all substances be one, all qualities, &c., or all things in whatever category they are? It is impossible that one thing (not-being) should cause the diversity between the different categories. 15. (2) What sort of not-being combines with being to make things? Not-being has different senses answering to the categories. 110. Plato means by t not-being' the false; whence it was said that

we must presuppose something false, as geometers assume the line which is not a foot long to be a foot long; but in fact geometers assume nothing false, and this sort of not-being will not account (or the generation or destruction of anything. !a6. It is from not-being in another sense, viz. the potential, that generation takes place. 31. The inquiry seems to be how being in the sense of substance ill many; for what these thinkers generate is numbers, lines, and bodies. But it is absurd to ask how there are many substances and not how there are many qualities or quantities. The indefinite dyad cannot be the cause of there being many colours, for instance; for then colours would have been numbers and units. b!a. If they had considered this, they would have seen the cause of the plurality of substances also; for it must be at least analogous. This error is also the cause of their treating as the material principle a relative term (viz. the unequal) which is not really opposed to beillg or to the One but is one kind of being. 8. They ought to have asked how relations are many; but while they ask how there are many units besides the One, they do not ask how there are many unequals besides the Unequal. Yet they use many unequals-great and small, many and few, long and short, etc. IS. It is necessary to presuppose for each thing that which was potentially it; the author of this theory indicated what in his view is potentially substance, viz. the relative-he might as well have said quality-which is neither potentially the One or being nor the contradiction of them, but a kind of being. !a0. Much more, if he was asking how things are many, was it necessary 110t to confine himself to substances or to qualities. !a4- In the categories other than substance there is another problem as to how things are mallY; no doubt, since they do not exilst apart, they are many through the substratum taking on many qualities, etc.; but there must be a matter for each category, only it cannot be one existing apart from substances. sS. But in the case of substance we can see how the individual is many things, if we avoid the mistake of treating the same thing both as an individual and as a nature; the real difficulty here is how there are many actually existing substance$. p. A • this' and a quantity are not the same, but the Platonists do not tell us how existing things in general are many, but how there are many quantities; for every number indicates a quantity and 80 does the unit. On the other hand, if a • this' and a quantity are treated as Lbe sallle, mauy cOlllrauictiollli follow.

COMMENT ARY 1087" lag. ~s ~O'Co.s To.dn)S, i. e. the clK{vrrrOS olxT{a. which has been the subject of Hook M (cf. 1076& I I). Aristotle has already at 1086& 21 passed from the discussion of the Idea-numbers, which were the clK{vrrrOS olJu{a. that the Platonists believed in, to the discussion of the first principles of the Idea-numbers, so that the transition now made is really not from the d.K{vrrros olJu{a. to its principles but from one question about the principles to another. This difficulty is correctly stated by Bz., but his proposal for its solution, the reading of clTr0pf.a.s for olJu{a.s, does not commend itself; AIt:xander read olxTf.a... and interpreted it as we have done. We have already seen (1086& 21 n.) that there was an early divergence in the manuscripts as to where N should begin. It might be suggested that the original beginning was at 1086& 21 (or 18), and that the present clause or the whole sentence was added by an early copyist who divided the books at this point and felt the lack of a formal introduction. But it seems more probable that 1086- 18 and 1087- 29 were two alternative transitions, both written by Aristotle, to the question of the principles of Idea-numbers, or in other words that 1086- 18-1087- 25 is a fragment which does not really belong to the main structure of MN but was introduced by an early editor as dealing with the same subject. In any case the distinction between M and N as dealing, the one with clK{vrrrOS olJu{a., the other with its first principles, is not well maintained; we hear a good deal in M of the One and the indefinite dyad. b I. TOii8', i. e. Vn-OK({P.(JIOV TC. 3. For the UYGt cf. Cal. 3b 24-27. 4. n.).' lTlpa., i. e• .Ill' .q clp~ lTlpa.. ot 81 itT).. Aristotle proceeds to show (II. 4-12) that the Platonists fall into the error (exposed in & 36-b 4) of making contraries the first principles. 5. ot "Iv = (I. 9) b TO dvLtTOV Ka.l tv A'"tWV. Plato is no doubt meant, since in M. 1081& 24 we have (lTf WtT7rfP b TrpWTOS dTrwV U clvwwv. Cf. AI. 796. 23. Tiji to''!', which is read by all the manuscripts and by Alexander (796. 26), is difficult, since w.. Tovro ~v TOV TrA~80vs 0&0.1' "'.lULY explaiqs why these thinkers opposed TO dvLtTov instead of TrA1j80s to TO lv, and this clause would be unnecessary if TO lv had already been identified with TO luov. Jaeger is probably right in treating Tc:i lu,!, as a gloss. 6. ot 8i = (I. 8) Tc? a'. The expression TrA1j8os seems to belong to Speusippus, cf. Z. 1028 b 21 n., M. 1085& 9 n. In the lIght of the evidence there cited, we may ignore Alexander's statement that it is the Pythagoreans (796. 32) or Pythagoras himself (ib. 34) that Aristotle is referring to. Xenocrates may possibly also have used the expression in this context (Plut. De An. Procr. ii. 1,2, lOla D E, cr. Aet. i. 3. 23). lla. Alexander reads d.pI.8p.~ AOy,!, a' ov, and apparently takes the words to mean that the unequal, though in point of fact the same thing as the great and the small, has a different definition. But it seems more probable that the manuscript reading is right, and that

the meaning is: Plato treats the unequal (or the great and the small) as one and does not draw the distinction that though definable by a single de6nition it contains within itself a plurality, se. the great and the smalL This has more point in the context. Obviously contraries go in pairs, and Aristotle is confirming his statement that the Platonists make their first principles contraries by showing that for Plato the One and the-great-and-the-small are but two things. Aristotle himself in accordance with his usual misinterpretation of the great and small (cf. M. I083 b 23 n.) insists on treating them as three (I. 14). This interpretation is rendered certain by comparison with 1088& 15. 111--18. clllc\ ,,~v ... cl1rOS,S6C1.ULV: i. e., apart from the general error of making contraries the first principles, the Platonists describe the first principles or elements badly. 16. ot Si TA w~~ Kul c\~'yov. These thinkers are distinguished from those who posited the great and small, and, Plato being the chief of the latter thinkers (the doctrine is ascribed to him by name in A. 98'lb 20, 26, 988& 13, 26, Phys. 187& 17,203& 15, 209b 35), the former must be disciples who modified the expression for the reason here assigned, viz. that the great and small was more litted to serve as the principle of spatial magnitudes than of numbers. The other passages where the 'many and few' are referred to are 1088R 18, 1089b 12, A. 99z& 16. 17-18. 01 S~ ••• TA 4wcpixov KCl.l TlJ 4wcpcX6"cvov. Sext. Emp. p. 531 Bekker treats these as essential terms of the Pythagorean division of concepts, and Robin (p. 659) !.uggests that it may be 'acousmatic' Pythagoreans of the school of Hippasus that Aristotle has in mind; but the evidence is too vague to warrant any certain conclusion. 110, litI. ~OY'Kcl'l appears to take two somewhat different shades of meaning according as it is used with BvuxcpcUr.'l or with d.7r08c{~,~. In the former case it means, as ill r. 1005b 22 AoyLICe\~ 8vuxcpc{u~. E. E. 1221 b '1 Tc\~ CTVICcx/lUJlT'{u~ Tc\~ AoyLICa~, very much what we mean by 'quibbling' {almost = (TO-PLUTLICal ivoXA~(TE&~ De Int. 17& 36). We may connect this with the definition of a AoyL/Co~ A6y~ as IIC y,cv8w", i"8oEw,, 8, (Top. 162 b 27). With d.'II"08E{tcL~ the meaning seems rather to be • abstract'. cf. G. A. 747 b 28 Mylll AoyL/c.q" (d.'II"o&~",) 8Lc\ TOVTO, OTL oUlf' ICa.8oAov p4).A0'" 'll"OPplllTiplil TW" OUeE""" iUT~" d.pxw". lI4. Apelt's proposal oi ICo1 for lK rests on the supposition that rii~ 8va8~ means the indefinite dyad, not, as it evidently does (cf. AI. 798. 14), the ideal Two. Cf. A. 990b 20. lit6. ot S~ .•. clVTLTLeiCl.aLV. Alexander (798. 23) refers this view to , other Pythagoreans '{d. I. 6 n.),and with this we may compare Damasc. De P,;"e. c. 306 Arist. fro 1514& 24 'Ap&UTaT'A~ 8~ i" To,~'ApXllTEloL~ mopE' ICa~ IIvOayopa" " ruo ,. "'" JA7J" ICIlAE'''. The latter statt:ment is most improbable, since Aristotle in his preserved works never refers to the views of Pythagoras. But he may well have ascribed the view to ct:rtain Pythagoreans, and there may easily have been late Pythagoreans, influenced by Platonism, who adopted such a view. Cf. Robin, pp. 650, 660. lit7. ot S~ w~~8ot, cf. I. 6 n.

=

472

CO:\E\IENT ARY

a."~. Alexander read aw~ (798. 34), and evidently takes to be opposed to T,a.lm>, • the same', and ruo to a.wo, • the thing itself'. But in I. 105 ... b 15 TO ruo is opposed to TO Ta.WO, and there is 110 trace in Aristotle of such a distinction between fnpov and llio; the two words are synonymous. Presumably one of the thinkers he is criticizing used the words TO lT~POV and TO Ta.WO, another the words TO llio and Ta~To. 31. 8cSks, i. e. 7r18avOn,Tos, says Alexander. TIVOS Ue-r,s is • something that can really be called an opinion '. Cf. the use of lvSoeos. 33. T~ 8' Iv ClTL l'iTPOV '"Il'a(v'L. This is the strictest sense of 'one', I. 1052b 18, 1053 b .... 34. TL IT,pov ~1rOKC(I'CVOV, something, different in each genus, which is the subject to. which • one' belongs as an attribute. 35. 8£CerLS. Cf.~. 10J.6 b 22 n. 36. flcierLS means the dipody-cf. schol. in Heph. p. 124 ed. Westphal {3aulS 8i (UTL TO (K SVO 7rOSWV UVV(<1T1lKOS, TOV /A-~V O.pcm TOV S~ 8(U(1 7ra.po.M./A-{3avop.fvov; ib. p. 151 SiX(TaI SE (the iambic metre) (V /A-~v ri1

30.

(T~poV

7rpWT[1 {3aun ra/A-{3ov Kal U7ro.,s,iov. 10SSa g-3. TO I'~V •.• a.~erLV.

Alexander explains (799. 21) that the finger is indivisible in (T&s because it is not divided into fingers but into half-fingers, which are different in ,TSos from the finger; while the Sl,uls is indivisible KaTo. ~v aru8y/ulV because it is the smallest soundhe means of course the smallest interval. This account of' indivisible in ,lBos' is not a natural one, and does not agree with Aristotelian usage. In Aristotle the phrase seems to apply (I) to infimae species (B. 999& 3); (2) both to genera and to species, in virtue of the core of identity in each (~. 1016& 19; Aristotle says there ~v dBtalp(TOV TO ~lBos Kam ~v aru8y/o"IV, so that KaTu TO ,ISos and KaTu ~v a'lu~ulV is a distinction not always maintained); this seems to be the meaning also in I. 1052& 31; (3) to that which cannot be divided into parts different in kind from the whole (~. 1014& 27-this contrasts strongly with the meaning Alexander assigns)-i. e. to elements. In I. I the indivisible in quantity is opposed first to the indivisible in quality (1052b 35) and then to the indivisible in ,tSos (1053& 20, cf. De An. 430b I",), and the indivisible in ,lBos is evidently meant to be the same as the indivisible in quality. Further, Kam ~v alu~ulv, 7rpOs ~v alrr~ulV is used in describing the indivisible in quantity (1053& 5, 23). Evidently, then, TO /A-EV KaTU TO (130s refers to (V /A-~V Tois 7rolois 7rOIOV TI, and TO BE 'JTpOs ~" aru8Y/O"IV to (V BE Tois 7rouois 7rOUOV TI (I. I). The latter refers to quantitative units such as have been mentioned in 1087 b 34-37; the former to IIpecies and genera, which have conceptual unity (~v ~ VOy/UIS p.{a I. 1052& 30); of these, instances are given in II. 9-1 ... .-

5. Ka.l 6 c1p,81'0'; ClTI 1rMj8o,; 1"l'fTp1Jl'ivov Ka.l 1rMj80,; l'iTP"'V, ~.

cr.

1020· 13 n., Z. 1039& U n. 6-S. 8LO ••• Iv. Sir T. Heath thinks (Gk. Math. i. 69) that this doctrine may be of Pythagorean origin. It appears in Nicom.lnlrod. Arilh1ll. ii. 6. 3, 7.3, and is implied by Euclid (El. "ii, Defs. " 2).

473

Some of the Pylhagoreans called the unit &'pt()/LOV KaL p.optlJJV /L(()optOV (Iamb!. I1Z N,com. Ar. Itztrod.) p. I I. 10). Perhaps the first to treat I as a number were the followers of Chrysippus, who called it 7r>"~9o'i tv, magnitude one (ib. 1 I. 8). g. (t L'InI'OL ••. &v8plJJ'lrO'i. Lines 10, II indicate that the d clause should relate not to the measure but to the things measured, so that Bz.'s conjecture (which is confirmed to some extent by Alexander) seems necessary. Bywater's proposal to excise TO /L€TpoV in I. 8 (J. of P. xxxii. Ill) does not meet the whole difficulty. 15-16. ot Sf .•. f.I.LKpoii. This is one of the passages which indicate that Plato used the phrase' indefinite dyad', for TO avtuov and TO /Liya Ka/. /LtKpOv are phrases characteristic of his doctrine. For similar passages cr. 10901> 32-1091& 5, M. 10831> 23-36, and see Robin, pp. 643-653. 15. T~V SUGSa Si. S€ has its usual adversative force. The first clause !>tates the uni ty of the avtuov, the second its twofold nature (cf. 1087 b 912). Thus Trendelenburg's proposal to omit Sl is unnecessary. ~3· T&'W KAT'IyOpLWV is clearly a gloss on 71'avTlJJv. The description of relation as the least substantial of the categories is unique in Aristotle, but cf. E. N. 1096" 2 I. ~5. With eL n lTEPOV there is no difficulty in supplying VA1J (uytv. ~9-35. There is no distinct kind of change which can be called change in respect of relation, as there is change in respect of substance, quality, quantity, and place. Change in respect of a relation is always due to change, in one of these olher respects, of one of the relata. A thing may change in respect of a relation when "t does not change at all, but its correlative changes. This indicates, Aristotle observes, that relation is a superficial category. The statement that relation is the only category which has not a specific kind of change answering to it implies a list of categories including only substance, quality, quantity, place, relation. This precise list is not found elsewhere. But Aristotle probably has in mind a list of eight categories without K(!u()at and 'Xftv (which occur only in Cal. Ib 27, Top. 103 b 23), and omits 71'O£(W and 7rauXftv as being practically equivalent. to KtV1JUt'i itself(cf. Phys. 22Sb 13 = K. 1068& 14), and 7rOT€ because, while time is involved in change, there is obviously no change which is merely in respect of time. There is an excellent conspectus of the forms in which the list of categories appears in Aristotle, in Apelt, Ed/r. B. Gesch. d. Gr. PhI'l. pp. 140, 141• The subsidiary character of relation is nowhere stated in the Categories; this distinction between it and the other categories belongs more properly to metaphysics than to logic. b 6. Kal X"'pl, KaL lI.I'a, e. g. two is merely few, the largest number is merely many, but three is many relatively to two, few relatively to the other numbers. 8-IL .t Sf ~ .•. I'~pLa. The sentence is very difficult. Various solutions of the difficulty may be proposed: (1) The manuscript readInN

H

h

414

COMMENTARY

ing may be translated 'if plurality is a class of which one member is always few'. This, however, is very unnatural. (2) Alexander 802. 31 says Aeyf& .t Si S~ It~l laT~ T~ 'II').~8ot, AlYlJ)v T~ 'II')'~801 ,..qv 8v&&, 1Ca.(J' ~ TO lnpov pASpt.ov T7i~ lvG.VTtWul~ lCaT7f'lopliTar., olov TO 6>..1:yov. This suggests the reading ot TO p.& Ml, TO d>..l:yov; we may understand lCaT7f'loplLTa.& from 1. 6 (cr. I. 12). (3) All the difficulties would be removed by a change of two letters if we read 71'Aij(Jot a AeyOp.EV cll~ dAlyov. But it is hard to see how this could have been corrupted into the manuscript reading. 10. Bz.'s omission of It~£ is necessary. 14-sa8. The argument is : Things that have elements are complexes. Complexes have matter. What has matter is capable of ceasing to be. What is capable of ceasing to be is not eternaL Therefore things that have elements are not eternal. The argument is put forward in opposition to the Platonic doctrine that the numbers have elements and are eternal. 16. d 1t~1 del iaT~. Alexander understands as the subject of this TO ~~ ot. But a remark of this sort about the elements would be irrelevant to the argument. Bz. is therefore right in taking the subject to be TO U a~ov OV (cr. l. 20). What the passage requires is the insertion of commas after lerTI and IC/J.V in line 11. What Aristotle is saying is that even if a thing is eternal, yet, if it !tad been generated, it would have been generated out of the elements of which it is composed. This corresponds to what he says in n. 20-21, ' however true it be that number or anything else that contains matter exists for ever, it must be capable of not being'. 18. We must either take TOUTO &YLYVlTCn as predicate of ylyvuac or read TOVTOV a ylyvuac. lI4. lv 4).).o~, ).6yo~,. The reference may be either, as Alexander says, to the De Caeto (I. 12, not I. 1 as Bz. says) or to E>. 1050b 1 If. It is not safe to assume with Bz. that MN never refer to I'EZHE>. lI8-35. Christ thinks that this section belongs to the latter part of ch. I. But it is quite appropriate that after mentioning the general difficulties (cf. d7l''>''w~ I. 14) that attend the derivation of number from elements (II. 14-28), Aristotle should now point out that by giving up the term /J.VLCTOV certain particular difficulties, though not the general difficulties, are escaped. lI8-30. The passage suggests at first sight that the description of the material principle as' the indefinite dyad' was a modification of an earlier description of it as 'the unequal' . Yet Aristotle couples the two phrases as occurring in the same theory (1088a 15), and implies that the phrase' indefinite dyad' goes back to Plato (1090b 32 -1091a 5, M. 1083 b 23-32). His meaning here is that owing to certain difficulties some thinkers abandoned the phrase 'the unequal'

N. I. 1088 b 10-2. 1089& 20

but retained' the indefinite dyad '. Cf. Robin, pp. 643-653. Xenocrates is probably meant, as there is evidence connecting the phrase , indefinite -dyad' particularly with him (M. 1081 a 14 n.). I08g& lI-6. Aristotle plainly has the Soplzillel in mind; cr. such passages as 237 A, 256 E. 4. o~ yAp •.. iol'Tu = fro 7 in Diels, Vorl. In PI. Soplz. 237 A the best manuscripts are divided between TOW' oMap:jj (BT) and TOW' 0(, BafL~ (W) i here EJ have TOVrO BafLV, Abr TOW' o(,8a.fL71, Alexander has TOWO fL7JBafL~' and only inferior manuscripts have TOVro Ba~. Simpl. PIzys. 135. 21, 143. 31, 244. I has TOVrO BafLV (best manuscripts), which is clearly the right reading. 5. clVclYK1J is the right case after I~I 1.2 i Bz.'s proposal of clva-yK7JV is a mistake. Aristotle is thinking of such passages as Soplz. 241 D. iK TOV ()I'TOS KaL ruov TLJlOS is explanatory of o;;"'w, and should therefore be preceded and followed by commas. 7. lin seems to be an emblem a from I. 8. Cf. H. 1043& 34 n. g-IO. 1I'0LOV 03v ••• IlTTeu; • What sort of unity will all things that are constitute, if that which is not be not admitted to be? ' Aristotle means that Plato hastened to maintain the existence of TO fLV ()v without considering what sort of unity of all things Parmenides' denial of TO fLTt ov implied-whether a unity of substance, or of substance with all the other categories. Aristotle asks • what sort of unity do all things make?', and interprets this (I. 10) as meaning' what things make the unity?'. The question he addresses to the Platonists realIy is ' do you mean that alI substances make a one of substance, or that all the categories make a one which embraces them all?' Cf. Phyl. 185& 20-30. Bz.'s 71'01a is impossible, and the text needs no emendation. n. ~ 1I'cll'Ta.. KaL IOTOJ. ••• UTJp.aiVIL is evidently meant to convey the same meaning as the last of the possibilities stated before it. Now the meaning of KaL IOTaL KTA. is 'and will substance, quality, &c., form all together a single unity'. This seems to justify Bz. in reading ~ before 71'IlIITa. (It is read by Jr, and omitted by EAb AI.) Thus there are three alternatives. The unity may be (I) a unity of substance, (2) a unity of quality, &c., separately from substance, (3) a unity of all the categories together. Ill. Bz.'s ov does not seem necessary. Iv TL = one genus or category. IlI-15. tl>J..' ih01l'0v ••• 11'011. Aristotle now points out that TO fLTt 131' will not save Plato fro~ a unity of the third kind, if that was what he feared. It might divide the world into two parts, but it could not divide it into ten. p.la.v +.l0'LV nvcl = TO fLTt 131'. yevop.lV1Jv,' having been called into play by the doctrine '. 17. Jaeger is probably right in supposing (IvaL to have dropped out by haplography; thi'l is more likely than that av()pw7Tos should hav~ been corrupted into I1v()pw7l'0v. Alexander's b fLTt I1v()pw7ToS (806. Ifj) is probably only his interpretation of TO fLTt I1v()pW7rov. lIO. Either the manuscript >'lylLv or Alexander's A('Y" give:6 a

COMMENTARY possible sense. (I)' He means by "not-being" the false and everything of that sort '. (2)' He means the false and calls that kind of eJ'ltity not-being '. The manuscript reading is the more idiomatic (cf. M. 1086 b 18-19 n.), and the other has probably arisen from a failure to understand it. The reference is to Plato (Sop". 237 A, 240), but Plato only says that there cannot be "'Ev8o<> unless there is not-being; he does not identify the two. lZI-lIaa. &LO ••• I'~ 1fO&LII£III'. Apparently some Platonist (not, as far as we know, Plato) argued that, just as geometry has to assume what is false in order to prove what is true, so philosophy must assume the false or non-existent in order to explain the true or existent. The charge against geometry that it makes false assumptions goes back to Protagoras (B. 998& 3). cr. An. Pro 49 b 35, An. Post. 76b 41. lZ4. O.} ya.p il' T;; av).).0YLerl" ." 1fpo.,_L,. Alexander expl.1ins (806. 34) O~ rap ;, 1f'puTE£1I0P.ivq Ka~ ypaf/lop.lll7J ypap.p.v (II T4l uv>.Aoywp.l(l Ka~ Tjj «i1f'OOEltn 1f'apaAap.{3all(Tat, &,u.';' 1I00VP.ivq. This, however, is an unexampled sense of 1f'pO-raer!s. Proclus ,,, Eucl. (p. 203. 5) uses the term 1f'pOTaerLs for the enunciation of a proposition, TtllOS 8E80p.£lIov Tt ..~ CVTOVP.EII011 (ITTlII; e.g. in Eucl. i. I 8l80Ta! (MEW. 1f'E1f'Epa.IT,uIl'l (ib. 208. 4). So too in the case mentioned here the geometer says 8l8OTa! ypap.P.V 1f'o8!G.ta and seeks to prove something about it or to construct some figure on it. But supposing the given line is not a foot long, what then? It does not matter, says Aristotle; the 1f'pOTalT!s is not part of the proof. Strictly the ",(v80s occurs not in the 1f'pOTaIT!S or general enunciation but in what Proclus calls the lK8EIT!S or settmg out of the particular data. But in Aristotle's time 1f'pOTalT!S may have been used to cover botlt. In M. 1078& 20 Ta£s 1f'puTaITEITL is used (in a similar context) in its more ordinary sense of' premises '. lZ6. TO ••• KGTc\ Ta., merEL' I'~ 01', 'the P.V 011 taken according to its different cases', such as those named in n. 16-19. 1f'TWIT!S is as general in its meaning as 'case' (cf. its use in geometry). The only exact parallel to the present use in the Aristotelian corpus is E. E. b' , . n' I 2 I 7 29 TO ayavoll Ell EKaCTT?l TWII 1f'TClHTEWII = TWII KarrrYOpl.W1I (ITT! Ie'

...

" (

A

A

)

,

TOVTWII. 34. TO T£ ICJ'TL is in apposition to T~ Oil, 'being, in the sense of

substance '.

a5. 1f~ &~ ~ 1fOLa. ~ 1fwei, se, 1f'ollA (ITT!II. b a. TO ya.p G~O KGt TO "-I'.u.OYOl' GLTLOl', ,it

is the same thing or something analogous that is the cause'. Aristotle means v).:'1, which is the same in all the categories, or analogically the same; i. e. in all things matter and form are in the same relation to one another, cr. Z. ~029~ 23, A. 1070b 17, 25. IlZ. For 1f0).~ 6)'£yol' cf. 1087 b 16, 1088b 5-13. A. 992& 16, IS-lZO is a digression. Plato defined that which is potentially sub.'Itance as T~ 4I1L1TOII, which is a 1f'~ T!. This is as bad as if he had &,ud that what is potentially being is quality-which, so far from

477 being the potentiality or negation of being, is merely one kind of being. ~O. C,cnriP i).ix81), & 34. ~S. ill'(aTCWLV. Bz. prefers the interpretation of this as = d7l"OKptO'tV, which occurs once in one manuscript of Alexander (811. 27). But Alexander's commentary there shows that this is a mere copyist's error. Alexander really interpreted the word as meaning d7l"oplall (816. 8, 12, 21, 811. 27), and this meaning alone agrees with the Aristotelian usage oU7I"lCTTO.cTt'; (cf. Phys. 196& 36, E.E. 1236b 33) and of it/)tOTallat (cf. 1090" 2 and Ind. Ar. 305& 2-17). l7l"lcT'T'O.cTt<; is an arresting of the attention, and this is caused by a problem or d7l"opla. Bzo's preference for the meaning 'answer' is no doubt due to the fact that the words immediately following, Bta yap • • • 7I"OUa, answer a question instead of propounding one. But these words are concessive and preparatory to the problem, which is stated in KalTOt • •• TWII ollutWII. The special difficulty attaching to the minor categories is that of assigning to each a matter which shall render plurality possible without being separable from substance.-Alexander is quite at sea about 11. 25-28. ~7. It seems impossible to interpret the ItvaL after ,,"oAAa. We should either read Ii." all with Apelt (or IUft or IOTat) or treat Illlat as an emblema and understand lun. ~9. 'XIL TLVc\ ).6yol'. Alexander explains as 'contains a difficulty', but the only meaning the phrase seems to have in Aristotle is 'is intelligible' (Ind. Ar. 436& 48-54), and this suits the context perfectly. Aristotle has assumed in I. 26 that a v".OKIlp.1II011 becomes and is many, i.e. comes to have and has many attributes. Now he continues • it is intelligible how the individual thing can be many, if we do 110t confusedly suppose that a thing can be both an individual and a certain characteristic ',-the confusion with which Aristotle habitually charges the Platonists. If an individual were a characteristic, it could not be many in the sense of being many characteristics, but there is no reason why a genuine individual should not be many in the sense of having several characteristics.-Alexander's interpretation of 11. 29, 30, adopted with reserve by Bz., seems impossible. 30-31. a"T1J Si ..• o~alaL. ' The problem that really arises out of the facts about substance is this, how there can be many actually existing substances ',-not how one thing can be many in the sense of having many attributes. 3~. ~c\ "'~I' KGllt, 'but also if', not' but even if '. 35. It".~ ••• clSLGlpITOI'. The manuscript reading seems to mean that if the unit is not some finite measure it is the limiting case of quantity-infinitesimal quantity; it is always quantity of some kind. But On is superfluous, and the opposition of p.(TPOII to TO KaTa TO 7I"OUOII dBLalpuolI is not Aristotelian. Alexander (812. 23) says (cPtOTalllt KaAbir; 'A.fyWII, 11 p.:q iJ.pa .q p.o.,o.<; oll 7I"OUOII, BtOTt P.(TPOII dpt8p.ov Ka~ BtOTt KaTa 71"0(1'011 d.BtalpuOt;. Cf. Syr. 176. 6. This suggests the reading d p.:q P.(TpolI Kat TO KaTa KT'A.. 'The unit indicates a quantity unless it

COMMENTARY means a measure or what is indivisible in quantity.' ' Measure' and 'indivisible in quantity' are not, indeed, absolute synonyms, for the measure may be an 'indivisible in quality' (I. I053 b 4-7), but TO fv is a measure of quantity primarilY (lo52b 20, 1053 b 5). For a similar confusion between 6T! and Kat in the manuscripts, where Alexander preserves Ka4 cf. H. 1043& 28. The error probably arose from the misreading of a contraction. Even if 'unit' means not a quantity but what is indivisible in quantity, it reflrs to quantity and thus confirms Aristotle's point. log()& I-~ 'lrO~).c\'l ••• iVUI'TLI.HJ€L'l. Alexander (812. 19) mentions two. (I) If substance is quantity, then since quantity is an accident, substance will be an accident. (2) Substance as substance will be a substratum; as quantity it will be in a substratum.

CRITICISM OF THE THEORY OF NUMBERS

(ch.

2. 1090& 2-6. I093 b 29).

(A) The theorJ! that mathematic-al numbers exist separalely (ch. 2. 1090& 2-3. 10911\ 12). 10gO&~. (I) How are we to be convinced that the numbers exist? For the believers in Ideas they act as causes of existing things, since each number is an Idea. 7. But why should we believe one who sees the difficulties about the Ideas but posits mathematical number; what causal value has this? It is not asserted to be the cause of anything, but a self-subsistent entity, nor does it turn out to be the cause of anything; the theorems of arithmetic are true of sensible things, and do not imply selfsubsistent mathematical number. 16. (a) Those who hold that there are Ideas and that these are numbers (Plato) fail to show why there must be Ideas, and therefore why self-subsistent number must exist. ~o. (b) The Pythagoreans, because they saw many attributes of numbers belonging to sensible bodies, thought things must be numbers -not separately existing numbers but numbers of which things were made. ~5. (c) Those who believe in mathematical number only (Speusippus) cannot say this; they only said that the objects of the sciences could not be sensible things. We maintain that they are. If mathematical objects existed apart, their attributes would not be found in bodies. 30. The Pythagoreans are free from objection on this score, but in constructing bodies out of numbers seem to be speaking of other bodies than those we perceive

479 35. while those who treat number as self-subsistent are open to the objection made above (I. 29). b 5. (d) Some treat the limits, point, line, and plane, as separate entities. But (i) at this rate the limit of a walk should be a substance, and (ii) at all events the limits do not exist apart from the things of which they are limits. 13. (2) One might point out that the prior genera contribute nothing to the later; (a) if number did not exist, spatial magnitudes could still exist for those who believe in mathematical objects only (Speusippus); and if these did not exist, the soul and sensible things could still exist. But nature is not episodic like a bad tragedy. lIlO. (b) The believers in Ideas (Xenocrates) escape this objection, for they construct magnitudes out of matter and number, lines out of the number two, planes out of three, solids out of (our. But (i) are these magnitudes Ideas, or what are they? They contribute nothing to sensible things, any more than the mathematical objects referred to above (I. 15). 1Il7. (ii) No mathematical proposition is true of them, unless one starts a new set of assumptions. 311l. (c) The first thinkers who believed in both ideal and mathematical number (Plato) cannot tell us how the latter exists. They make it intermediate between ideal and sensible number. If it is derived from the great and small, it is the same as ideal number; if not, the elements are getting rather numerous. If the formal principle in both kinds of number is a One, how does the One take these two forms, if at the same time number cannot on Platonic principles be derived from anything but the One and the indefinite dyad? logla 5. The theory is evidently like Simonides' 'long story', which slaves spin when they have nothing sound to say. The great and smaIl seem to complain of their ill-treatment; for they cannot generate any number but two and its powers.

logo" lIl--logla IlIl is a discussion of the doctrine of separately existing numbers, coveriqg much the same ground as that covered in M. 2, 3, and it seems impossible to detect the distinction Bz. draws between the two passages: 'Illic ipsa rei natura disputandi legem et ordinem praescribit, hic vero eorum philosophorum, qui res mathematicas per se esse statuerunt, sententias singulas respicit et refutat: M and N cannot have been meant to form parts of a single treatise; they were originally independent essays. 4. etalv. Alexander 812. 30 interprets this as ElO'~ X"'ptOTO{, and this is confirmed by 11. I 1-13.

COMl\fENT ARY

TIj ,..." ya.p 181u, TLe.,..I,,'l" This applies to Plalo (cr. M. 10768 KT).. (I. 7) applies to Speusippus (cf. M. 1076820-21 n.). Aristotle returns to these two views respectively in n. 16-20 and in 11. 25-30, and to both alike in 35-b 5. Thirdly, he discusses the views of the Pythagoreans in n. 20- 25, 30-35. II. depends on afTwv, which can be supplied from afT&~ I. 13. 15. Kueebr.p 1)'lx81), M. 3, especially 1077 b 17-22. I6-lIO refer to Plato, lIo-lIS to the Pythagoreans, as-30 to Speusippus, 30-35 to the Pythagoreans, 3S-b 5 to Plato and Speusippus alike. The views of Plato, who believed in both mathematical and ideal number, apart from sensible things, of Speusippus, who believed in mathematical number apart from sensible things, and of the Pythagoreans, who believed in mathematical number existing in sensible things, are to some extent played off against one another. E.g. in b 2 in attacking the view of Plato and Speusippus Aristotle says the Pythagoreans (A IvaVTw~p.EV~ AOyO~) can make out as good a case for the opposite view. 16-19. The best interpretation of this very difficult sentence seems to be got by reading, as Bessarion perhaps did, T~ before "a,u in J. 17, omitting TO in I. 18, and reading laTtV in I. 19. 'As for those who assert that the Ideas exist, and that they are numbers, by their assumption -in virtue of the method of setting out each term apart from its instances-of the unity of each general term they try at least to give some account of why they believe number to exist.' I take the subject of laTtV to be number, which Is the subject of the whole discussion (cf. II. 3 f., 10, 13, 20). It is imposSible to say what Alexander read, except that he does not seem to have had TO. Other attempts to deal with the sentence are (I) that of Winckelmann, who keeps the manuscript reading and translates 'those who posit the Ideas .•• try at least to say how and why it is pOSSible, according to the doctrine which separates each kind of thing from its many particulars, to assume each to be a unity'. The objections to this are that (a) TO is unexplained, and (6) the order in which the words are taken is intolerably unnatural. (2) Bz. suggests "aTlt. TlI 1,,8.CTLv. • • AaP.~&.VELv. This leaves the difficult TO, and it neglects a passage which in some respects illustrates the present passage, Z. 1031 b 21 "aTlt. .,..q., 1,,8.CTtV dv&'Y"ll Q, T& .lva& l1.p.t/JIIl. (3) Maier proposes TlI "aTlt. .,..q., 1,,8.CTtV ••• AaP.~&.VEtV lv T& '"aUTOv. But if, as he says, the subject of laT&V (SIi:) is lv T& '''aaTov, then TlI ••• Aap.~dvftV is left without a construction, while if TlI . • . Aap.~dvELV lv T& '"aUTO" is the subject, the order is highly unnatural. (.) Bullinger proposes Aap.~&.vOVTf~ Q, for Aap.fJdVftV TlI lv, which gives much the same sense as the reading we have adopted but is somewhat less probable as an emendation. (5) Prof. Joachim proposes Tii "aTlt. .,..q., 1,,8fCTtV IKGaTO" 1f'apO. Tlt.1f'oAAlt. Aap.p&'VELV, lv T& l"aaTOV 1f'ELpidvTa& ICTA. The reading adopted in I. 18 as being the better attested, 1f'IIl~ for m teal, does not affect the main difficulties of the passage. 17. For the meaning of ',,8fCT&~ cr. A. 992b 10 n., Z. 103,b 21, 19 n.). T~ 81

oae.""

N. 2. 1090" II -

3.

1090b 2 I

M. 1086b 10. Ps.-Alexander here describes the process very much as Alexander describes it in A. gglb 10. The procedure according to him is as follows: You adduce particular o.llT6vrJ., e. g. Plato, Socrates, Alcibiades, Dion. You then argue 'Man is either the same as Socrates or different. If it were the same, it would not be also present in Plato. Therefore it is different from Socrates, and similarly from Plato and from all the other individuals. There is, therefore, one thing apart from the many men, and this is man himself. Similarly with horses, oxen, Bec.' This account of the Platonic 1,,(JelT'll is probably correct. sS-!l6. TOi, S~ •..•,8".0", i.e. Speusippus, cf. M. 1076& Io-U n. These thinkers cannot justify their belief in the substantial existence of numbers by saying that sensible things are composed of them i their own language precludes this (cf. I. I I). They therefore only said that the objects of the sciences could not be sensible things (o.ln-&w I. 27 refers to T~ 0.lcr97rr~ ITwp.a.TQ. 1. 22, d.ppDJ'lo., cWpa.vd!l, and ,,-ollc\ cLUa. II. 14, IS), and must therefore be immaterial but substantial numbers. sB. ei1l'01'I'" M. 3. as-37. an ... +UX~" must be taken to give the reason for ~p.­ P&'VOVIT'. not for XIIJPLa'T'OV 7I'OwMell; otherwise ,lva.L ••• XlIJpLm elva, is otiose. 37. 1T0.'"" +Vx~", 'fawn on, flatter, the soul'. Cf. t/lo.rllp~ yoliv 4..' d".,A.TIIIV t 1T00lvI' P.I Soph. O. C. 319. X"p,cml. The subject of IlvQ.L should be Ten. ¥,(Jp.6v (cf. I. 3S 01 8~ x"'pmv 7I'o,oVvTell). But Aristotle has, not unnaturally, passed in thought to a vague subject such as To.m; it is not necessary to adopt Bz.'s conjecture XlIJpLlTTov. b s. KGt.. • KG', 'both . • • and '. ~ lvaNTuWp.EVOll AOyOll means ,I,.,. Pythagorean argument (& 10-15). &pn "'1I'Op~IhJ, & 19· S. ,11T1 Si n,,',. The persons meant are probably Pythagoreans. They seem to be distinguished from Plato (Z. 1018 b IS, Ig), and from the Platonists (B. 1001&8, II). II. oG "~,, clUd answers irregularly to M' l. 8. IS. ,lv!, St'. T~ IlT}(00To. cWITUu. 15-16. ,.a "1J8~" • • • iJlTTlpo". Speusippus' doctrine is similarly characterized in Z. 1018b U (where he is mentioned by name) and in A. 107Sb 37. TOLll T~ p.a.lJqp.a.T'''~ p.Ovov elva, t/lo.p.ivOLll (I. 17) also shows that Speusippus is meant; cr. M. 1076& 10-1 I n. 19. nELcroSLW&1J" used in the same connexion in A. 1076& I. so-po A comparison with De An. 404b 16-17 has led some interpreters to suppose that Plato is referred to, but the phrase 'CLVILV ,.c\ p.a.9TJp.a.T'''~ "0.171'0,,LV 18lo.ll T"'~ll86la.ll (I. 28) at once suggests Xenocrates (cf. M. 1080b 28, I086 a 10), and this is confirmed by Alexander's interpretation of 7I'pOITyA,xOP.EVOL (IOgob 31). From the thinkers here referred to Aristotle distinguishes in 1. 31 01 7I'P;;WCIL, i. e. Plato (01 7I'p{jmJL is replaced by 1"'Lvov in 10gl& S). Sl. TOUTO ,"If IK+,dYIL, • this objection escapes', i. e. fails to hit them.

n."

COMMENTARY There seems to be no quite similar use of lKq,IVy€tV in Aristotle, but cf. EOLKIV oiJTIAlu{ yE UKo7l'ovp.lvOL~ 8La.q,EVy€tV 1093b 9. 26-27. o~8~v ydp ... aUI'lId~~ETcu, i. e. Xenocrates' assumption of P.a.8"1p.a.TLKa which were Ideas does as little to explain the sensible world as Speusippus' assumption of P.a.fir,p.a.TLKa which were not Ideas. It appears from this passage that as Xenocrates identified ideal with mathematical numbers, he identified ideal with mathematical figures. By i8&o.L 8&ta.L is meant the belief in indivisible magnitudes. 30. I'aKp07l'OULI', cf. p."IKVV€tv M. lo83 b 6 and p.D.KpO'i Myo'i 109 1B 7. aUI'ECp"I',cf. I093b 27, De Div. 464b4, G. A. 716&4. It is short for TO~ Myov'i UVVI{pILV, for which cf. E. N. I 147& 2 I. 31. 'lrpoayXLXcSI'EI'OL TGL'i llllaL~ TA I'a&rJI'aTLKd. 7rpouyAtX0p.D.L occurs with a different construction in A. 986& 6 .i T{ 71'OV 8">""7I'E, 71'POUE')'MXOVTO TOU uvv€tpop.lV"lv 71'iiua.v awoi'i ElvaL T7jv 71'pa.yp.D.TElav. Alexander interprets (8 I 6. 37) uVV ~8ovii 71'POUTL8la.UL Ta. p.D.fir,P.a.TLKa. Ta.i'i l8laL'i Ka.t l8la.'i am-a. 71'OLOVULV. y'AlX0p.D.L occurs with the accusative (PI. Hipparch. 226 E, and in some manuscripts of Hipp. Epp. ix. 364 Littre), and it seems quite possible for the two elements in 71'pou-yAtxop.aL to govern Ta.i'i l8laL'i and TfJ. p.a6"1p.D.TLKa respectively. Cf. Hdt. iii. 2I yijv lli"lv 71'pouKTiiu6a.L Tjj lllJ1JTwv. 37. The manuscript reading, l~ a~~ou III TLVOS I'LKPOU Kat I'EY~OU· TA yAp I'Eyl81) 'lrOLI'L, may be dealt with in various ways. (I) We may omit the colon and the yap (the reading implied in Bessarion, and possibly in AI. 817. 7 ; but cf. 817. 14). (2) We may read T{VO'i for TLVO'i, and translate' from what other small and great can he construct mathematical numbers? He already constructs spatial magnitudes out of O1Ze other '. But the supplying of 'out of one other' is difficult. (3) Christ's p.E')'&'>"ov o~ is open to the same objection. 109I& 2-3. Kat d ... lv. Aristotle here passes to the formal cause and says' if some One is the formal principle of each of the two kinds of number, unity will be something common to these two Ones '. 3-5 The point here is: how can there be this plurality of Ones, if at the same time, as Plato says, number or plurality is generated only by the union of One with an indefinite dyad? Plurality, which is said to involve a material principle, breaks out even in the formal principle. 3. TGUTG 'lro).).L For the absence of the article cf. Xen. An. iv. 7. 5 oAtyOV'i TOVTOV'i d.v8pW7I'ov'i, Lys. 7. 10 Tl6V"1KE Ta.Wa. Tpla. ET"I, and Kuhner, Griech. Gramm. § 465 Anm. 6 a. 5. Trendelenburg remarks that here it is only' One and an indefinite dyad " not Ihe indefinite dyad, that is ascribed to Plato. But this is probably unimportant. Cf. M. lo81 a 14 n. lKE'LI'OI'. Aristotle has previously said o~ 71'PWTOL (1090b 32), but clearly has had Plato in his mind. 7. 6 ILI''''I'Cllou I'aKp~s AcSyos. The scholiast on Eur. Phoen. 215 quotes a verse from Simonides of Amorgos : T{ Tawa. 8La. P.a.KpWV Mywv d.vl8pa.p.ov;

But Aristotle seems to point to some more striking phrase or passage than this; further, he never refers by name to Simonides of Amorgos, and often to Simonides of Ceos, so that we need not doubt that the latter is meant. Alexander says that in the "AT4KTo, Simonides represented the sort of story that a ..lave will tell to cover his failure in some duty (fr. IS9 Bergk.). Cf. Rhe/. 141Sb 23. Perhaps the reference is to a mime like those of Sophron and Epicharmus; cf. Schneidewin in Rh. J1.-lus. vii. 460-463. We may compare Eur. Iph. in Au/. 313 P.4KpOW. ~~ ~oiiAOi t,y AEy'''~ A6yov~. Antisthenes contemptuously called definition a p.aKpO~ MyOi (H. 1043b 25). 10. The great and the small cannot (Aristotle maintains) produce any number save 2 and its powers, since it is ~v07l"O'~ (M. IOS2& 14, IOS3 b 35). In order to derive other numbers the Platonists had to use (contrary to their own principles) addition as well as multiplication (M. IOS4& 4).

(Il) Absurdi!>, of ascribing genera/ion 10 Ihe numbers if Ihese are Ihough/ofaselernal(ch. 3.1091&12-4.1091&29). I!I. It is absurd to ascribe generation to eternal things, as the Pythagoreans certainly do. They say that when the One had been put together the nearest part of the unlimited began to be dra WII and limited by the limit. 18. But the discussion of these thinkers is more appropriate to physics; we are seeking the principles of unmovable things. logla !IS. They say the odd is not generated, implying that the even is, viz. from the equalization of the great and the small. These, then, must previously have been unequal, so that the account is meant to be historical, and not merely logical. logla 1lZ-!lg. Bz. points out the connexion between this passage and 10SSb 14-35. Aristotle there showed that eternal things cannot be constructed out of elements. Here he shows that the Pythagoreans and Platonists actually proposed to explain the generation of eternal things. 15-18. This is one of the comparatively few passages which throw light on the general Pythagorean cosmology. Aristotle's suggestions as to the mode of composition of T~ ~y (i. e. the spatially extended first unit, M. 10SOb 20-21 n.) are not necessarily based on anything the Pythagoreans had said; they might be merely derisive conjectures of his own, like his suggestions about the constitution of the Platonic numbers in 1092& 21 ff. (where f1'7rfpp.a occurs again, ib. 32). But in one respect he uses the Pythagorean terminology, for xpo,a.~ is doubtless used in the Pythagorean sense of 'surface' (De Sensu

COMMENTARY 4S98 so). Aristotle is here referring to the Pythagorean generation of solids by fluxion from planes, of planes from lines, and of lines from points. Again, his reference to seed probably implies that some Pythagoreans thpught of the generation of numbers as akin to that of living things. For the conception of the ' nearest parts of the infinite ' being' drawn and limited by the limit' (here apparently - the One) cf. Anatol. p. So Heib. (Diels, Vors. 112. I) np, ~,~ t/lvaw 'EOTla~ .,.plnrov Iv pia" l8piia6cu, Philol. fro '1 Diels n\ 'lrpG.TOV dpp.orr(JIv, Tc\ lv, Iv Tid, p.iafl)' Ta~ crt/w.tpa.~ lOTla "CIA,,,"", fr. 17 A ,,6a~ fr~ IOTtv, ;*'1'0 8~ yt'Y"'a6a., 4'1rc\ TaU piaov. The' infinite' is the air (Phys. 204831). 'lrVfUp.a. (USb 23). or ~ (Stob. Eel. i. 18. I b - Diels 276. 43),-things not distinguished in the early period of Pythagoreanism (cf. Anaximenes). The One is thought of as being in the centre of a shapeless mass of air or vapour and gradually introducing shape and limit into it, working from within outwards. The' drawing in' is further described as' breathing', and the wind or void drawn in is said to keep the units apart (Phys. U3b 24). 'This is ',as Prof. Burnet remarks (E. G. P. § 53), 'a very primitive way of describing the nature of discrete quantity'. It will be observed that the Pythagoreans are trying to describe at one moment the formation of the number system and that of the physical universe, which is just what on their principles they were bound to do. The number One is identified with the central fire, as two was with the earth and seven with the sun. 15-17. " ••• OT&' For similar tautology cf. Ind. Ar. 53 8b 33-39. Ig. '1" ....p1 +dalfl)!I. There is much to be said for Bywater's proposallt..,.OJ;.w I" 'T'(J 'lrfpl t/lva'fI)~. Aristotle discusses the Pythagorean cosmology in such passages as Phys. iii. 4, De Caelo ii. 2, 9. 13. 83-8g. Though so far Aristotle has mentioned only the Pytha. goreans (I. 13), he now proceeds to argue that the Platonic account of the origination of things from the principles is chronological, not merely logical. For their failure to give any account of the production of odd number cf. A. 987b 34 n. It is hard to believe that they seriously denied the derivativeness of odd numbers. Zener supposes that it was only the first odd number (3) that they treated as ungenerated, as it is their original ('lrPW1'1w) generation of even number that is referred to in 1. 24; if they assumed the number 3 without generating it, they might be said to deny the derivativeness of odd number, though they gave a derivation for odd numbers other than 3. Syrian us' explanation is probably the correct one--viz. that the Platonists were speaking , symbolically'; C likening odd number to the gods, they naturally say it is ungenerated, while, taking even number as analogous to things that have matter in them, they call it generated and liken it to a dyad; but none the less the! derive the series of even and odd numbers from the same princillies ; i. e. they described the odd numbers as ungenerated because they likened them to the One, the principle of pure form, and the even numbers as generated because they likened them to the indefinite dyad, the principle of matter and change.

.e.Telt.,,,

!Z8. O~ TOU eEwp;jaGllvEKlV. Alexander tells us (819. 37) that Aristotle is here attacking Xenocrates' interpretation of Plato; for this cr. De Caelo 279 b 32-280& 2, which the Greek commentators interpret as referring to Xenocrates. A similar interpretation of the Platonic !froXoyovla. as logical, not temporal, was offered by Xenocrates and Crantor (Plut. An. Procr. 3. 1013)' From Prod. in Euclid. ed. Friedlein, p. 77. 15-78.8, we may infer that Speusippus is also referred to.

(C) Relalion belwem lhejirsl principles and the good (ch. 4. 109Ia29-5. 1092a21 ). !Zg. It is a difficult question whether the good and the beautiful are among the first principles or are later. 33. The cosmologists seem to agree with some moderns who treat them as later owing to the objection which confronts those who make the One a first principle; but the objection is not to the ascribing of goodness as an attribute to the principle, but to making the One actually the constituent element in things. b 4. Similarly the cosmologists say that not the first beings-Night, Ouranos, Chaos, Ocean-but Zeus rules the world; 8. but those whose treatment is not purely mythical, such as Pherecydes and the Magi, identify the first generator and the best, as do Empedocles and Anaxagoras. Of the believers in unchangeable substances some identify the One with the good, but make oneness its essence. 16. It is strange if it is not as being good that self-sufficiency and eternality belong to the primary being; but truly they belong to it just because it is good. The first principle, then, is good. !ZO. But that this good principle should be the One, or an element of numbers, is impossible. Difficulties arise (to avoid which some make the One the principle of mathematical number only): !Z5. (I) Each unit becomes essentially a good, and we get too many goods. !Z6. (2) Every Form becomes essentially a good. But if there are Forms only of goods, the Forms are not substances; while if there are Forms also of substances, all animals, plants, &c., will be goods. 31. (3) The contrary element will be the bad itself. One thinker avoided describing the One as good, just because it would follow that plurality was bad. Others accept the identification of the unequal with the bad.

COMMENTARY 35. It follows that (a) all things partake of the bad except the One;

(f3) the numbers share it in a purer form than the spatial magnitudes; (y) the bad is the place of the good and shares and desires in that which destroys it; (8) the bad is the potentiaJIy good. IOg!l& 5. These conclusions follow from treating (I) every principle as an element, (2) the contraries as principles, (3) the One as first principle, (4) the numbers as the primary substances, self-subsistent, and Forms. g. If, as we have seen, it is impossible either to put or not to put the good among the first principles, evidently the account of the first principles must be wrong. It is wrong, too, to argue that because living things come from something indefinite and undeveloped, the first principles of all things must be undeveloped; the undeveloped seed comes from a fuJIy developed parent. 17. Again, it is absurd to make place simultaneous in origin with the mathematical solids (for they are not anywhere), and to say that they must be somewhere without saying what their place is.

10gI& !lg-log!lQ 17. The relation of the good to the &.PXa{; and the views of Speusippus and the Pythagoreans about it, have already been briefly discussed in A. I072b 30 If. 30. E~1fOp~UaVT~ l1f~T(I'YJU~V, ' a reproach to anyone who makes light of it'. 31. d1fop(av I'tv. The 8£ clause does not come till b 16. 32. o!ov lIouMI'Eea )'lyE~v a~TO TO dyaeol'. Cf. note at beginning of Book M. 33. 1fapcl. I'EV yOop. The 8£ clause does not come till b 13. 34. T';IV eEoMywv. Though Aristotle uses 8(OAOyLK~ as a synonym for first philosophy, 8(OAo)'OL never means, in his works, anything but the cosmologists, such as Homer and Hesiod, as opposed to the q,VULKO(; cr. B. 1000& 9, A. I07Ib 27, I075b 26. So 8(OAoy{a Jl;Ieleor. 353& 35, 8£oAOY£LV A. 983b 29. TWV I'UV null' refers, as A. 1072 b 3 I shows, to the Pythagoreans and Speusippus. 37. Aristotle does not specify what the 8vux£pna was which Speusippus tried to avoid. He must mean that Speusippus, observing that Plato (who is meant by (VLOL in b I), through treating the One as first principle and regarding it as good (cf. A. 9881\ I4), fell into difficulties (such as those which Aristotle points out passz'm), tries to avoid them, not, as he should have done, by ceasing to regard the abstract One as first principle, but by ceasing to regard the first principle as good. b 2. Two mistakes are here ascribed to Plato: (I) he regarded the One as a first principle, (2) he regarded it as that sort of principle which is an actual constituent element in its product, viz. in number. A fuller

list of the mistakes involved is given in 1092& 6: (I) he m,lkes every first principle an element, (2) he treats contraries as first principles, (3) he makes the One a first principle, (4) he treats the numbers as the first substances, separately existent, and Forms. For the differt:nce between element and first principle ct. a. I, 3, Z. 1041b 31, A. 1070b 25. 4. ot ••• 'II'OL1JTu1 ot clPXULOL = 01 (J£oAlryoL a 34. 5. VdKTU Kul o4puvcSv. Zeller (i.G 122 ff.) enumerates four Orphic cosmogonies, of which the first is referred to by Plato (Grat. 402 B, Tz'm. 40 D-41 A) and Aristotle (cf. A. 107 I b 26) and described by Eudem us (ap. Damasc. c. 124). Aristotle supposed it to have been put into writing by Onomacritus (fr. 1475& H). According to this system, Night came first and gave birth to Earth and Heaven. The children of Earth and Heaven were Ocean and Tethys (Orpheus, fro 12 Diels). Musaeus is said to have derived all things from Night and Tartarus (fr. I4); Epimenides, from Air and Night (fr. 5); Acusilaus, from Chaos, Night, and Erebus (fr. I). Aristophanes (Av. 694) makes the birds sing of Erebus and Night as the first parents. The chief other Orphic system is the' rhapsodic' cosmogony dating from the third century B. C. and described by Damascius (c. 12 3), which places Chronos in the first place, followed by Aether and Chaos, &c. Zeller argues convincingly for the priority of the first-named system, but Lobeck and others took the opposite view. Tannery shows in A. G. P. xi. 13-17 that the rhapsodic cosmogony differed from the original Orphic cosmogony not by transforming it so much as by adding to it. For the place of Night in the cosmogonies cf. A. I07Ib 27, 1072& 8, 19. 6. Xc£o~, Aristotle is here referring to the Hesiodic system; he elsewhere quotes Hesiod's (Theog. I 16) , " , , ' . ,., 'll'aVTWV /LEV 'll'pWT/.crra X~ ,},(vn, aVTap ('II'(LTa yat (/JpVCTT(PVO'> (A. 984b 27, Ph)ls. 208 b 30). Acusilaus is said also to have made Chaos the first parent (frr. I, 2). 'KEUVcSv. The reference is presumably to Homer (cr. A. 983b 30 and II. xiv. 201). The same view is ascribed to Orpheus by Plato (Grat. 402 B) and by Eudemus (Diels, Vors. 476. 16). TodTOL~ "iv is answered irregularly by E'II'(' KTA. I. 8. g . •EpEKdS1J~' Pherecydes of Syros (a younger contemporary of Anaximander, C. 600-525), placed Zeus (Heaven), Chronos (Time), and Chthonia (Earth) at the beginning of things (Diels, Von. s 201. 18,23, 202. 4),--or Zeus, Chthonia, and Eros (201. 32). It is his placing of Zeus at the beginning that warrants Aristotle's statement about him here. In other respects too his system marks an advance on earlier cosmogonies (Zeller, i.' II7). 10. ot MdYOL, i. e. the hereditary caste of priests who took the place of the' fire-kindlers ' of the Zoroastrian religion. They are one of the six Median tribes mentioned by Herodotus (i. IOI). Diog. Laert. (Prooem. 8) tells us that ill the dialogue on Philosophy

COMMENTARY Aristotle identified their two principles, Ormuzd and Ahriman, with Zeus and Hades. Eudoxus is said to have visited the East with a view to acquiring its astronomical knowledge, and seems to have aroused in the Academy a deep interest in Zoroastrianism (cr. Jaeger, Ads/. 133-138). I~. 17T0LXl!iol': Love was for Empedoc1es one of six material elements. dpx~l': Reason was for Anaxagoras a motive principle set over against everything else-not a
=

1'''

•

, .uyu6~) IIII' •

f1l7r0p'U

=

25. 311'1, 4yuHI'TL, species of the genus good, cr. r. I003b 33 n. ~8. 'If there are Ideas only of the qualities which are the species of the quality good, the Ideas (will not be Ideas of substances and therefore) will not be substances.' For the missing step of the argument cf. A. 990b 29-991& 2 II.

32. c\ ".11' = Speusippus; cr. M. 1085a 9 n., b 5 n. His theory differs in two ways from that of Plato: (I) (I. 23) he treats the One as principle only of mathematical number (the only kind of number he believed in); (a) (1,33) he did not connect the One and the good, but described the good as coming in only at a later stage of the evolution of the world (a 35). But how is this to be reconciled with the statement (E. N. 1096b 6) that he placed the One lv rO Tc7,., d.ra();;'" UVUTotxlq.l Aristotle must mean that Speusippus put the One in the series to which all good things belonged, though he did not think of it as itself a good. 35. ot 81 = Plato and Xenocrates. 37-10951& I. ~ov &KpclTOU ••• "...,1",,1(. because the numbers are more directly derived than the spatial magnitudes from the original material principle. Spatial magnitudes are 'the genera posterior to number' (M. 1085&7). 109. I. X. . . .tl'lllo, a reminiscence of nin. 52 A B. cr. Pltys. a09b II. 2. 6piycafCl& TOU +&UpnKoU, cf. Phys. 19a& 18-a5.

3· For parallels to the superfluous 3n cr. Ind. At'. 87 ab 39-48. 12. nl, i. e. Speusippus; cr. A. 107ab 30-34 n.

13-15. Speusippus' argument is represented as follows:

(I) The One is the beginning of all things. (2) All beginnings are imperfect.

Therefore the One is imperfect. From this Aristotle draws a consequence of his own probably not drawn by Speusippus: (3) What is imperfect cannot be said really to be. The One is imperfect. Therefore the One is not. Aristotle denies the premiSe numbered {a} above. 17-21. The char~e of 'producing place simultaneously with the mathematical solids and of 'assigning place to them without saying what their place is' has little connexion either with what precedes or with what follows. Alexander takes it to refer to Plato i but Plato's ~~pa (which Aristotle often refers to as ,.o".~, e. g. Pltys. a08 b 7, 209& 8, 15, De Catlo 309b a4-a6) was eternal. It seems more probable that (as Ravaisson, Brandis, and Zeller suppose) Speusippus is referred to. In that case the section continues the attack 011 him made in II. 11-17. S} rianus throws some light on the later Platonic theory of place or space by saying that four kinds were recognized-the place of physical bodies, that of IvvAa (l8r, (viz. matter), that of mathematical bodies (viz. f/xI,VT4CTla), that of ttVAot Mrot (~ ttVIII or 8tavOllTtK~ 1/roX'7). In. c\ TcSWOi, 'Iheir place', which is evidently not the same kind of place that sensible solids have.

I

i

CO:\Il\IENT ARY

49 0

(D) Rela{~o.n bthvttn !lumber alld ils firsl principles (ch. 5. 1092& 21-b S~ SI. These thinkers ought to have distinguished the meanings of , froni ' and then told us in which sense number is derived 'from' its principles. Not by mixture, for (I) not everything can be mixed; (2) what is produced by mixture is different from its elements, so that the One would then not exist apart, as they want it to do. s6. Not by composition, for (I) that implies position; (2) number would then be two distinct things, the unit + plurality. Number cannot be derived from elements which inhere in it (for this applies only to things that are generated), nor as from seed (for nothing analogous to seed can come off from the indivisible One). Is it derived from its contrary? This implies a substratum which persists. These thinkers seem to derive number from contraries; a substratum tuerefore is implied. b Again, why are all other things that are derived from contraries or have contraries perishable, while number is not? The contrary of a thing ahtJays tends to destroy it.

aa.

a.

logs· SI-:b 8. This section seems to refer primarily to Speusippus. Cf. Introduction, p. Ixxii. ss-sa. 8LE}.o".lvou~ ••• laT'". Aristotle's suggestions here as to the sense of £K have little connexion with his classification in a. 24. S4. ".'eE~, cf. A. ~S9b I n. Two reasons are given why the One cannot be supposed to be 'mixed' with the great and small. (I) Not any and every sort of thing can be mixed. This follows from the definition of the P'KTOV as & &v EiJOP'aTOV av 'If'a.6-rrr'KOV V Ka.2 'If'O'7JT'KOV (Dt Gen. eI Corr. 32Sb 20); again plyvvra., ~V Til IlTxa.Ta. lv (Dt Sensu 447· 3 0). Further, li'lf'4pXEW BEi XWP'aTOV £KaTEpov TWV P'XfJlvrwv' TWV Be 'If'a.fJwv oM£v xwpmv (Dt Gen. tI Corr. 327b 21), and great and small are 'If'afJ''1 (IOSS& 17). pi~'r is an affair of material things, and to speak of it as existing between the One and the indefinite dyad is a mere metaphor. (2) The product of mixture is something different from its elements, so that after the mixture had been achieved the One would no longer exist as a separate and distinct entity; cr. Dt Gen. tl Corr. 327b 22-26 for the doctrine that the constituents exist only potentially when once the mixture has been made. The second TE in 1. 25 serves to introduce not, as Bz. supposes, a third argument, but (as Alexander takes it to do) the second part of the same argument. s6. clUa. auv8laE'. ",wfJ£IT'r differs from pi~'r as mechanical from chemical combination (Dt Gen. eI Corr. 32S& 3-I7} 30. 'aT, ".~v • . • oU. Alexander says Aristotle is here subdividing ITVv8EIT'~. It seems more likely that pU,r and aVvfJEIT'r are treated as

49 1

subdivisions of generation U (lI1J'7rapxolITlIlv, from material constituents present potentially (in the case of P.i~L'» or actually (in the case of aVVO(CTL'» in the resultant. From this is to be distinguished the generation of a thing from an efficient cause which is nol present in the thing (.1. 1023& 26,29; cf. 1013& 4,7, A. I070b 22 for the meaning of (vv1rapxnv). 3 g · 4).)"':'s cl1fO CT!riPI'a.TOS ; Cf. 1091 &16. Alexander (825. 30) takes this as an instance of ~ (K P.~ Ivv1rapxoVTlIlv, as dAAa suggests, and takes '1lv(CTL'> to refer to artistic production. Bz. supposes that dUa indicates not as in 11. 26, 33 the transition to a fresh alternative, but as in 11. 24, 27, 32 (dAA' oliX orov KTA.) an objection to the alternative under discussion. , Only those things which '1lyvfTaL can be said to be l~ lIIV'7rapxoVTlIlv. But can we suppose that number ylYVfTaL W'> d1ro CT!r(pp.aTO'>?' Bz. is evidently right as against Alexander in saying that '1lv(CTL'> cannot = artistic production as against natural generation. It either means natural generation as opposed to artistic production or includes both (Z. 1032& 26). On the other hand, Bz. seems not to be right in taking W'> d1ro CT!r(pp.aTo'> to be a case of W'> (~lIIV'7rapXOVTlllV. cnr(pp.a, no doubt, means sometimes the seed of plants, in which the male and female elements are united, and which may be said to be 'present in' the plant that grows from it; but it seems more likely to mean, as it constantly does, the male element in animal reproduction, which is no part of the offspring but only its efficient and formal cause (G. A. 729 b 1-21, 3S, 730b 10-19,716&4-7. 76Sb II). The supposition that number comes from its principles ws U lvv1raPXOVTlIlv is sufficiently refuted by the answer that it is only things that are generated (whether naturally or artificially) that are lK I'~ 1ll1J'7rapxoVTlIlv. 4).).' o~X otcSv T( TOU cl8La.LpiTOU TL cl1f()'8I!LV. Bz. interprets thus: 'To explain growth from seed, something must be supposed to come off from the seed; but nothing can come off from the indivisible One '. But it is no part of Aristotle's theory to suppose that in generation something comes off' from the seed; rather the seed comes off from the male parent (for this use of d1r(AO(iv cf. Meleor. 466b 9, P. A. 641b34, G.A. 72IbI2 etpassim). 33. cl).).' ':'s lK TOU lVa.VT(OU I'~ e)1fOl'iVOVTOS; Aristotle now passes to another case of production (K p.~ (lI1J'7raPXOvToS. Production from a contrary which does not persist (cf. a. 994& 24, 30) is dAAO{IIlCTL,>, not '1lv(CTL'> &1rA1j; for'l(v(CTL'> &1rA1j is '1(V(UL'> KaTa ~v ollCT{av, and an oliCTla. has no contrary (1087 b 3 n.); '1lv(CTLS &1rA1j is p.(TaPOA~ KaT' d,,,,,trpaCTLV, from the absence of a substance to its presence, not from one contrary to another (P hys. 22 S& 12- I7), and it involves no persisting sensible substratum (De Gen. el Corr. 319b 14,33), while the kind of production here in question does involve such a substratum (1092& 34). 34-b 3. The argument against the suggestion that number comes from a contrary which does not persist runs thus: 'What comes from its contrary presupposes also something that persists. Now number

COMMENTARY is represented as coming from contraries. Therefore there must be something else, from which, as well as from one contrary, number is produced '. The reasoning is evidently fallacious. The major premise states that when A is produced from ils contrary B, a substratum C is presupposed. The minor states that number is according to the Platonists produced from Iwo conlraries. Production of a thing from its contrary, and production of a thing from two contraries, are quite different, and there is a fallacy of four terms. Aristotle perhaps means to say that instead of deriving number from the One and plurality the Platonists should have derived it (since it is itself plurality) from the contrary of plurality, viz. the One, and from something which can be the substratum at one time of oneness, at another of plurality, as the change from white to black implies a substratum which can be either; but if this be his meaning, he does not express it clearly. 35. a !,ll'. In the light of 1091 b 32 and A. I072b 3 I it is clear that this means Speusippus; d. M. I085 a 9 n., b 5 n. Plutarch (De An. Procr. ii. I. 2, IOU D :a) tells us that Xenocrales spoke of the material principle as plurality, but of this we cannot be so sure. a 81 (b I) means Plato. b 4. ClaA lVAl'Tlwl' contains the ambiguity commented on in the note on a 34-b 3; it might mean things of which each is produced from its contrary, or things each of which is produced from two contraries. K&V IK 71'aVT~~ V, 'even if all the contrary is used up' (which refers to this case alone, not to or~ leTTIV lvallTla) shows that the former is meant. The contrary which has been used up in making a thing is conceived of as stiIl potentially present in it (lvtnrtipxov 1. 6) and capable of destroying it, no less than a contrary which is outside the thing CH~ lvtnrtipxov). 7. otOI',.o Vl!iK~ TO !,iY!,A, in Empedocles' system.

Ie

(E) Numbers as causes of olher things (ch. 5.

1092b 8-6. 1093 b 29)'

8. We are not told how numbers are the causes of substances, whether (I) as boundaries (as points are of spatial magnitudes, or as Eurytus determined the number of each thing by counting the pebbles he used in tracing its outline), or ( 2 ) because harmony, man, and everything else is a ratio of numbers. 15. But (I) how can attributes, like white, be numbers? (2) The ratio is the substance of a thing; the number is merely matter. The number is always a number of something, of portions of fire or earth or of units; the substance is 'so much to so much " i. e. a ratio of mixture of numbers. lI3. Thus number is neither efficient, material, formal, nor final cause of things.

493

26. What is the good that comes from the fact that a mixture is expressible in numbers? (I) It is more important that honey-water should not be too strong than that its elements be in any particular ratio. 30. (2) The ratios of mixture involve not numbers merely but the addition of numbers, not 'thrice two' but 'three of one to two of onotlur', while in mUltiplication the genus must be the same. 10938 1. (3) If all things share in number, (a) it does not follow that a thing's number is its cause, (b) many things have the same number and will therefore, on the theory in question, be the same. 13. There are seven Pleiads and there were seven against Thebes, but the nature of the number seven is not the cause of their being seven. 20. They say there are only the three double letters, S'ltZ, because there are just three concords; but the number is in either case arbitrary. We are reminded of the methods of the old Homeric scholars. Other numerical comparisons which the Platonists make are equally frivolous. b 7. The lauded characteristics of numbers are not causes in any of the senses of ' cause' ; but these thinkers do show in a sense that goodness belongs to the odd, the straight, &c. There is a sort of correspondence between the straight in length, the even in breadth, the odd in number, the white in colour. ~I. (4) It is not the ideal numbers that are the causes of harmonic relations and so forth (for equal ideal numbers are different in kind), so that this affords no reason for believing in Ideas. ~4 These difficulties show that mathematical objects are not separate from sensible objects, and that the first principles are not those which these thinkers put forward. 109~b 8-1093b ~9. Aristotle now passes from the alleged genesis of numbers to the alleged genesis of things out of numbers. The following considerations show that he has in milld the Pythagoreans and perhaps also the Platonists who most resembled them: (1) The mention of Eurytus. (2) The reference to the connexions established between numbers and movements of sun and moon, and the periods of animal life (1093& 4-6, cf. A. 986& 3-8). (3) The reference to the significance of the number '1 (1093& 13). (4) The reference to the two UVC1TOLXLaL (1093b 11-14). It is only at 1093 b 21 that Aristotle turns to the Platonic theory of Idea-numbers. 8-15. Mr. Comford suggests with much probability (Class. Quart.

COMMENTARY

.J94

xvii. 10 f.} that the second of the alternatives here mentioned, the view that 'things embody or represenl numbers, not are numbers', is the original Pythagorean doctrine; and that the first alternative, 'the crude materialistic view .•. that things are numbers, and numbers consist of monads, which are the terms or boundary-stones (OpOl) marking out the void "field" (xwpa) in the geometrical patterns of numbers " figured" by pebbles', is a later, fifth-century doctrine. Aristotle's doubt as to the meaning of the Pythagoreans may well be due to his not having distinguished successive phases of their doctrine. Cf. M. 1080b 16 n. 10. We rna)' infer from Theophr. Mel. II Wimm. = 312. 15 Br. that the source of Aristotle's information about Eur)'tus was Archytas. Eur)'tus belongs to the beginning of the fourth century; he was a disciple of Philolaus. Alexander tells us that his method was to sketch the outline of, e. g., a man with coloured pebbles, and then to say that the number of pebbles he had used, say 250, was the number of man. This is a travesty of the method of limits according to which the early Pythagorealls represented the line by the number 2 (the number of points required to determine it), the surface by 3, the solid by 4 (cf. Z. 1036b 8 n.). The same process was as it were worked backwards when the numbers were' reduced to the forms of triangle and square' (I. 12). 3 (".), 6 (":'.) and all numbers of the form

!!..I + n were triangular (cf. Pluto Pial. Quaesl, 2. 1003 F). Nicomachus 2

of Gerasa (Inlrod. Arilh1ll. ii. 8-1 I) and Theo of Smyrna (pp. 31-33 Hiller) represent numbers by a'S arranged in various geometrical patterns: a

2

3

4

5

6

9

aa

a

aa aa

a aa aa

aaa aaa

aaa aaa aaa

aa

• Square' and' cube' survive as names for kinds of numbers; 'linear', , plane " 'solid " ' triangular', 'oblong', 'pentagonal " and other names which belong to the same geometrizing order of thought have passed out of current lise, but, as Prof. Burnet observes, we still represent numbers ill this Pythagorean way on dice and dominoes, and we still call numbers fi~ures. On' figured numbers' cr. Heath, Euclid, vol. ii. 288 f., Gk. Malh. i. 76-84, Burnet, E. G. P. § 47, G. P. 53, Iamblichus, Inlrod. p. 56. 26 If. Pistelli. According to Lucian (B{wv 1rpo.Ul" 4) the 'triangular numbers' were recognized by Pythagoras himself. 13. +UTWV is surprising when the instances given have been man and horse. Chdst conjectures '~wv Ka~ cpvrwv from Alexander (827. 26), but it is by no means clear that Alexander read this (cf. 826. 35), and it seems more likely that Aristotle uses cpvrov in its older and wider sense of' living being', which is found in Plato (Soph. 233 II: 8, Rep.

495 40r A 4, Ti1ll. 90 A 6). Aristotle may be quoting from Archytas' account of Eurytus. 15-16. Tel. Si S~ 1rclGtJ ••• gep,...6v. This is an objection to the first suggested mode of treating numbers as causes of things (II. 9-13); you can make an outline of a man, but how are you to sketch the outline of a 'lrolJot;; ? 16-17. OTl Si •.• S~~ov is an objection to the second suggested mode (II. 13-15); if harmony is a AOYOt;; tlpdJp.(;w, the numbers are merely the matter, the ratio is the essence. 18. 6 S' clPl9,...ot;; '»"1) is in verbal contradiction with O1iTf ~A1J I. 24, and Schwegler would read ~A1Jt;; (cf. AI. 827. 40 b 8£ d.pdJp.&t;; ••• TO 'lroO'OV EO'Tl '"it;; iKaO'TOV ~A1)t;;). Aristotle's view, however, is that d.pdJp.ot;; O'WJLC1TlKot;; (I. 22) (i. e. amounts of certain simpler forms of matter, numerically determined) is the ~A1) of a compound, though d.pdJp.ot;; p.ovo.8!Ko.. (I. 20) is not the ~A1) of any material thing but only the measure of its constituents; so that both statements are true, though of number in different senses. 19. Tpla. 1rUpOt;; y;jt;; S€ Suo. This suggestion is clearly framed on the analogy of Empedocles' analysis of boneTat;; 8vo TWV &KT~ P.fP(WV MXf N~~t;; o.tyA1)t;;, T(O'O'o.pa 8' 'Hcpo.{O'To!o' TO. 8' &O'T(o. AfVKo. y(VOVTO (De An. 4 10& 5). clPl9".ot;; . • • 1rUPlVOt;; \l y~ivot;;. Cf. the d.pdJp.o~ p.1)ALTo.!, cp!o.XiTo.L, numbers of apples (or of sheep), of bowls, &c" which Geminus (cf. Procl. in Eucl. i, p. 40. 2-5) and the scholiast on the Charmidts (165 E) describe as studied by AOY!O'TLK~ in distinction from d.pLBp.1JTL~ (Heath, Hisl. of GR. Malh. i. 14, ii. 442). 25. If number is in no sense the cause of things, how is it related to them? Aristotle nowhere gives a positive theory of number (the nearest approach is in M. 3), but his answer might be that number is an OlK€LOV 'lraBO!: of their matter. 27. lv eG~oYlcrr't' means not, as Alexander says, Iv d.p·dIP, i. e. in a ratio like I : 2 or I : 4, but' in an easily reckoned ratio' (illustrated in De Sensu 439 b 25-440& 6 by 3 : 2 and 3 : 4). It excludes (I) ratios of which either term is an irrational, and perhaps also (2) ratios which cannot be expressed in terms of numbers within the series 1-10. 28. lv 1replTTIj, in a ratio like that of I : 3 (Alexander) or possibly like that of 2: 3 (n: n + I). For the virtues of the odd number according to the Pythagoreans cr. A. 986& 18 n. TptS Tpla.. The meaning of this difficult phrase is clear from 1. 32. A.ristotle supposes the Pythagoreans, when they say Tpl.t;; 8vo, to mean , Ihree to two '. When they gave Tpl.t;; Tp{o., then, as the recipe for P.f>..{KpaTOV, they meant that if you lake three parts of honey you must take three parts of the other ingredient (milk in Homeric times, later water). Alexander's mention of a third ingredient, saffron, seems due to a misinterpretation of Tp~t;; Tp{a,; it is contrary to his statements about p.€AlKpo.Tov elsewhere and to those of other writers. cr. Columella xii. 12. 29. lv OG9JVl My't'. Aristotle does not mean that the constituents

COMMENTARY could be in no ratio; he means that the particular ratio does not matter provided there is enough water. 80. il"pelTOII, not of course absolutely /lxpa.TOII (for then there would be no ratio), but d.Kpa.TiuffPO'" 80-1093& I. Aristotle's statement that' 3 to 2', not' 3 times 2 " is the right way of stating the formula of a mixture is evidently right. A mixture is got not by taking the same thing over and over again but by taking two or more things in a given ratio. Multiplication means the addition of things of the same kind (TO a~o 8" yivos ,Tva, I" TarS 1I"olla1l"Aa.ut~'ULV 1. 32). If a given kind of body could be properly represented as ABr, 1. e. as 1 X 2 X 3, it must be 'measured by A', i. e. it must consist of a unitary amount of some substance, taken six times. If another kind of body could be properly represented as aEZ, i. e. as 4 X 5 X 7, it must similarly consist of four portions of some substance, tllken 35 times. /Jxrr, Tcfi a~cfi 1I"4vTa (se. JUTP6u8~) (I. 35) seems to mean , so that all the things in whose formula a certain number occurs must consist of a larger or smaller number of portions of a single elementary substance'. It follows that the number of fire cannot be BErZ (2 X 5 X 3 X 7) and at the same time the number of water 2 X 3. 2 X 5 X 3 X 7 = 6 X 35, and a unitary amount of fire would simply consist of 35 unitary amounts of water (which Aristotle treats as absurd). 109S&I-IS. There seem to be two arguments used here. (I) 11. 3-9. If all things share in number (this is not a mere concession to the adversary, but is Aristotle's own view), there is nothing surprising in the fact that some things (e. g. the periods of movement of sun and moon, the periods of the life of animals) should be designated by square and cube numbers, or by numbers related as equal or as double and half to one another. This is no warrant for treating the numbers as the eallSe of the phenomena. (2) II. 9-13. It was assumed that different things could fall under the same number. Then, on the view which is being considered, they will be the same thing, which is absurd. This interpretation involves treating bcBixerO ff 1. 9 as not depending on cl (Bekker, Bz.) but starting a fresh sentence. ff often introduces a new objection (e. g. A. 991& 27~ 4- For the number of the motions required to account for the motions of the sun and the moon cf. A. 1073b 17, 35. 8. 4I1dY"'I.1I TOm" CM'p4+• •" 'all things must move within these limits' (i.e. be designable by square or cube, equal or double, numbers);

8.,

cf.

,ro~ CTTpi~,u8~. lSI. The sun and the

moon on Aristotle's view have, each of them, five proper motions (A. I073b 17, 35), and this makes them a good enough illustration of his meaning. The Pythagoreans themselves assigned dIfferent numbers to them (2, 7). IS_b 4. Syrianus says that no important Pythagorean quoted trivialities such as those which Aristotle here ridicules, as instances of the power of numbers. He refers to the Pythagorean Prorus as having written about the number 7 (the treatise really belonged in all proba-

497

bility to Alexandrian times, Diels, Vors. 267. 22), but says he confined himself to showing how many things 'nature does in seven years, months, or days'; while others wrote about the number 10. He retorts on Aristotle by pointing out that Aristotle himself does reverence to the number 3 in the .De Caelo (268& 13), and forcibly reduces the flavours and the colours to seven each (.De Sensu 442& 19). On the number 7 in Greek cultus, mythology, philosophy, and medicine cf. Roscher in AM. der phil.-hisl. Kl. der K. Sliehs. Gesellschqft d. Wissenschqften, vols. xxi, xxiv, esp. xxiv. 24-43 on the Pythagoreans. The numerical fact about 7 which interested the Pythagoreans was that within the decade it alone has neither product nor factor (Philo\. fro 20 Diels). 14- X0p&l ~ dpp.o"lat (J Abr AI.) is not very natural, since seven chords are very different from seven modes or harmonies. E's reading XopS,,\ " 4pl'0"',, is strongly confirmed by Prob!. 918& 13 (= 922 b 3) ~"a T( ol clPX
.t"

COMMENTARY be an unnatural combination, and further

~

co

ooB, not 8u (A. 993& 5).

brUpf.pcraL must be taken as implying nothing with regard to the order

of the two sounds combined. ~6. 1I'X,(oul Y' at au".+wv(a~, i. e. new combinations (such as the eleveuth) can be made out of the primary concords. But you cannot combine two double consonants to produce a new consonant. 137-138. TOLl 4pxa(0~1 ••• 1I'apopwaLl'. The reference is probably to allegorizing interpreters of Homer such as Pherecydes of Syros (c. 600-525), Theagenes of Rhegium (fl. 525), Metrodorus of Lampsacus (d. 464), Anaxagoras (c. 5°0-427), and Democritus (fl. 420). Cf. Diels, Vors. s i. 376. 15-17, 414. 9-24, ii. 67. 21,22,203.27-204. 7, 205· 26-206. 10, Sandys, Hisl. of Classical Scholarship, i. 29, 30. ~9. at n ".iaa~ ~ ".~v lvvia ~ &~ 6KTw. The piooaL are the fourth and the fifth, the chief notes intermediate between the keynote and the octave. The fourth and the fifth answer to the ratios 8 : 6, 9 : 6. 30. TO '11'01 &(I(a'1I'Td. The epic verse has seventeen syllables, if we assume a spondee only in the last place. Alexander takes (V ".'f.v Tii BEtU{l to mean • in the first half of the verse', and this is confirmed by the fact that' right' and' left' were technical terms for the first and second parts of a lyric system. The alternative is to suppose that , right' is the part after the caesura KaTa. Tp[TOV TPOX"Lov, the commonest caesura in Homer; this too has nine syllables. Wilamowitz in Ber!. Classiker/exle, v. 2. 14 I, and S. E. Bassett in Class. Phil. xi. 458460 defend Alexander's interpretation oi "6 8EtWV. For the identification of the right with the dpxr1 of movement cf. H. A. 498b 6, I. A. 705b 18, De Caelo 285b 16 (cf. 284b 6, where the Pythagoreans are referred to). Bassett quotes many instances to show that TO BEtU)V was used by the metricists of the section of the verse which came first, e. g. Mar. Vict. 108. 16 Keil 'arma virumque cano . .. Huius incisioni quae syllaba c1auditur, si alteras duas adicias, ut tertium pedem trisyllabon compleas, erit hoc trimetrum 8EtLOV', i. e. the three dactyls at the beginning of the line form the colon dexlrurn or clPKTLKOV (cf. Mar. Vict. 74. 8 K., Plotius 514. 28 K.). Further, Aristotle would naturally mention the first half of the line first. And, finally, {3"{VEoo()"L refers not to caesura but to scansion in feet. The earliest Greek definition of caesura ~s in Aristides Quintilianus (p. 52 Meibom), in the second or third century A. D. b 13-4. The meaning is that there are 24 noles on the flute, from the {3o".{3v~ (an onomatopoeic word for the deepest note) to the highest. "0".1.>""" is an Ionic word meaning the whole nature of a thing (p.l>"~ = limb); cf. Hipp. De Arlie. iv. 108 L., De Ana/om. viii. 540, De Gland. viii. 556,

499

De Nulr. ix. 106. Here, however, there is probably a reference to tune). Nicom. ap. the music of the spheres, cf. A. 986& 2 f. (",,>..~ Photo Bibl. I44 b 25 says it was used as a name for the number 1, and in TIleol. Arilhm. p. 36 Ast we are told that the Pythagoreans, following Orpheus, applied it to the number 6; but the present passage shows that it was with the number 24 that it was identified. 9. WTWCJ" y. G'II01rOUI'ivoL!,' if we look at them in the critical way in which we have been looking at them, they seem to vanish away' For the dative cf. 1090b 20 TO~ cS~ Ta! lcSiM TL(J(",ivOL<; TOVrO ",~V

=

(1I~(Vy€L. 10. _

S".'pLG'I'lvw., 'lrep' Tcl.! Apxd!, .:\. I, 2.

Bekker and Bonitz read alTLov (UTW. (KCLVO JLiVTOL 71'OLOVCrL ~o.V(pOv KT>". Christ reads o.tTWV (UTW. ~<; ",MOL 7I"OLIIVUL, ~av(pOV liT>". ~<; is better attested than (K(i:VO, but Christ's punctuation gives a false antithesis between ~<; ",~v >..iyovu{ TWf<; lIat atTto. 7I"OLOVuL rij<; ~VU(IJ)<; and ~<; ",iVTOL 7I"OLllVuL. Diels's punctuation removes this difficulty. Aristotle makes a concession to the Pythagoreans. Their view that numbers are the causes of good and evil evaporates on examination.; but they make it clear that in some sense the good' belongs' to certain numbers. The seasons of the year and of life go 'together' with certain numbers. There is an analogical relation between things in different 'categories' (loosely used here for genera), whereby oddness in number may correspond to straightness in a line, evenness in a surface, and perhaps even to good in things which can be either good or evil. But all this is mere correspondence and not causation 18. G'UG'TOLX'o.!, cf. A. 986& 23 n. 13. TO 'lrepLTTO." cf. A. 986& 18 n., 23. Ta I~ed, cf. A. 986& 25 n. TO lcrc(IIL! ferO., is probably the right reading, since it preserves a rare but genuine Pythagorean phrase (cf. M. Jlf. 1182& 14 oli yap (G'Tw.q BLKo.LOO"UV'I1 &'PL(J",O<; WaIlL<; iuo<;, Sf. 'as Pythagoras said it was', and PI. Theael. 148 AI),. and accounts best for the variants luov Ab, lcrdpdJp4v E. WaKL<; rUOV = TCTpO.YIJ)VOV, which occurs in the O"VO"TOLXto. of the good, A. 986& 26. 14. at Su.,d",,! l.,C.,., APL'''''''. It is doubtful whether this means the 'powers', in the mathematical sense (cf. .:\, IOI9 b 34, @. 1046& 8, De Lin. I"sec. 910& 2), of certain numbers (T(TpO.YfJ)VOV occurs in the O"VO"TOLx{a of the good in A. 986& 26, and cf. TCTpaywvov<;,II'6Pov<; 1093& 1), or whether it means the powers of certain numbers, in the non-technical sense of' power '. b{wv is in favour of the latter view; according to A. 986& 26 one would suppose the square of any number to be in the O"VO"TOLXto. of goods. Alexander gives the second interpretation, and illustrates lv{wv by TCTpa.yWVfJ)V, TPLYWVuJV (numbers like I, 3 (= I + 2), 6 (= 1 + 2 + 3»), leo.ywvfJ)V (numbers like I, 6 (-= 1+5), 15 (= 1+5+9». "'0. ycl.p ';po.L 110.1 APL'~! TOLOCJ'S', 'for the seasons and a certain kind of number (the square number 4) go together '. There may also be a reference to the comparison, ascribed by Aristides Quintilianus (Musica, iii, p. 145 Meib.) to Pythagoras, of the seasons to the conII.

500

COMMENT ARY

cords; spring is to autumn the fourth, spring to winter the fifth, spring to summer the octave, so that the four seasons are to one another as 6, 8, 9, 12. Plut. On the Birth of the Soul in the Timaeus 1028 f. ascribes the same view to the Chaldaeans. 17. CTull"I"'~jlCWLV,' chance coincidences '. otULA cl>">"~>"OL~ 'II'cillTa., i. e. the normal in each class corresponds to the normal in every other class. go. tCTw~, i. e. for the sake of argument Aristotle is willing to allow the superiority of the odd number, on which the Pythagoreans laid such stress. 21. It is not Idea-numbers but ordinary mathematical numbers that are at the base of musical harmony and the like, for equal Idea-numbers, like Idea-units, differ in kind (M. 6-8), whereas the theory of harmony implies that equal numbers are identical. 2101-23. SLa;4IlpoUCTL yap • • • ICAL yap At jlo.,cl&e~. From the fact that Plato treated the different numbers as different in kind Aristotle infers that the units were also different in kind, and from this that equal numbers composed of different units were different in kind. 1017. For O'U."LPAL used absolutely cf. I090b 30 n.

INDEX VERBORVM a privativum 22 b32 dl3apls 4 b I~ d')'a90" = 011 i"f"a 982 b 10, 983" 32, 996&24, b U , 13 b2 5, 59'36 syn. "aAo" 13"22,91"30 dist. "GAo" 78"31 dist. alVl5,.."0,, d. 13b27 U'1JA4t"'1 TO .010" 20 b 23, cf. ib. 13 .Gn dpxft 75' 38, cf. ib. n, b8, II .ws IXOllul .pas TO d. 1'.1 UTOIXffa 91" 30, cf. 92 &9 oli6iv AI')'EIII TaS JAIl9'1JAIlTIK4S i.lu,",,,as .EP! d, 78" 31 "A'''riI'' d. ,,02 UII"oO.l'T'1V .1. 21 b 19 TO If.''EII'O'' 8 b 27 tis TO 1f.".III0" .1"OTEA.IITijual 983" 18 Pyth. 986" 26 Plat. 31'31-bU, 84&35 d,),a"iiu9al 980" 23 d')'d"'1ulS 980' 22 d')'O"'1TO" 76" 15 d')'."'1TO" 999 b 7 If.')'"ola opp. TO tlbl"al 982 b 20, cf. 75 b 23 dist. ",.uBos, d"4T'1 52" 2 1f.')'''OJUTOS 995&2,36"9 .1')'1'01"01'1'01 986b 27 d')'6""auTol 985 &14 d-yWvlo" 20" 35 dll""p.Tos I. r, 84 b 14, 85 b 16-22 "aTa TO .0uO" ("01'.1 n)" alu9'1uIII), "am TO .Taos 999&2, 16'19,21, b23, 89 b 35, cr. 88&2 1'" .13.1 14"27 Els d3q 999 &4 KGTa XpO"o" 16" 6 cl. awo TO i" I b 7 d. UTI')'''~ 2 b 4 syn. d"AoUs 14 b 5 d ••pOs 16' 33 4BI40POS 16&18, 38&16, 54 b4 d. ,.o"ciBu 81 b 13, 36, 82 b 27 1131"ta Pytb. 990& 24 If.&"as 61" 22, 25 I1BIOpiuTOJS 986" 34 dBp6s 17b8 II.3PWUIS 65 b 20 Mwapla ftOuaxws 19b20 deC. 46"29 d. &0p'u9.iua ~ UIIVflA'I",.I,,'1 1'9' 1Ie1tT1"9'55 b8, 58b 27 dllwaT.w 36b7, ~8"13 111161'01'0" ullpI3al"fI 2b 32, 47bIl, 19 dist. ",.Vllas d. ftouaxws 12b21 47 b 14 11••1"CIC ib. 5 dllllV". TOn-.pO" 998 &19 dfplllos 49" 26

dqp (Anaximenes) 66 b 21 If.9.TO"!) ,.o"as 16b25, 30, 84b27, 33 d9p'''' 998b I Af,),,,,a 15 &25 At')'ll"TOS 981 b 23 .1tll'1Aos Emp. ob8 dtll&os. Bla,.I".III dtll&a 98.. &16 a. "al dict.'f1Ta 987b16, 15til4 1'.1 Milia 990b 8, cf. 991'10 oM,,, 11111'&,." d. 5';) b 7 t" Tois d. oM~" "0,,6,, ~I& 20 ouula alu9'1T~ 11. 69" 31, 25 lira'"f"'1 .1""1 d. ouula" A. 6 dpa Tel d. I" UTOIX.lOJV 88 b 14 If.TO"O" ')'."'UI" 1rolli" diBlOJ" 91 "12 alpfTo" Ill' abTo 72' 35 alulq,.a lOb 32, 63 b4 atu9'1u!S 980' 22, 27, 29, b 25, 981 b 10, 986b 32, 999 b3, IOb 2, 3,36 &6,88&3 al "ol"al alu9quIIs 981 b 14 !) ar. dAAofOJuls 9 b 13 alUlqT~p'O"

6i "2

alu9'1Tos 987 8, 14, 997b12, IOb 32 , 78 b 16 niW 01. d.1 ~O"TOJ" 987" 33, cr. 999 b4, 10'3, 36b28,69b3 f"lU"",""?S •• pl Tfin, 01. ou" OUU'1s 987 & 34, Z. 15 opp. JAIllqJA41'1"~ 989b 31, 990 &15 coni. ,,1"'1uIS 989 b31, 36 b 28 opp. "Of1TOS 990' 31, 999 b 2, 25 b 34, 36 &3.9, 43 b 29, 45" 34 opp. .13qT'''OS 90 b 36 .0T.pO" TaS al. obulas p.6vas .1"CIC OT{O" 997' 34. 2 b 12, 59" 39 01. ouulal 1/1.'1" 'xolI<71 42' 25 al. '"aI'TIQ,u,u 61 " 32 ouula al. 69 & 30 alT'lu9," TO 1".1pxii 6"17, cr. 20 alTla syn.dpx>7 982b9, 983b4, 986b3;S, 989 ti 23. 13 "17 ftpOn-q 01. 983' 25, cf. 3" 31 011'"'1' IXII 984 b 19 TOU KaTa uII,..IJ.I3'1KOs 01. 65 &7 01. TfUUGpU 70b 26 ftOT.po" ",iis ~ ftoAAw" fftlU'"1pGw 9'OJpijuCIC TaS 01. 995 b6 alTliiu9C11985" 21, 13 b 13 011'101'0" 65" I I alTlo". uOta" ft.pl 1'.1 ft~a of. lnroAap.il:4Jtollul ft,u,TfS 981 28, cC. 982 & 13 1'.1 'E dpxijs of. 983" 24 5yn. dpx;, ib. 29, 990&2, 3ti2t 13"16, 6g b ~,3 'YD. OToex'''''' 25 5, +~" 5.

INDEX VERBORV;\f

502 69&26,

71&25,

86&22

Af",(oTal

T.Tpaxws 983" 36, 996 ° 5, .... " 33, oble {1"'lEIpa Ta ai. a. 3 1I0TfPO" /j d.olo""", frtIUTTJ/.wJII

A... ,..as

600Jpijuai lIo"Ta Ta "'(f"f/ TW" al. 9,6" 20 1I0uaxws 13 "16, 4. 2 lIa"Ta ai. ",(O"f/Ta leal Ta a'l. MBla 26" 17 6apTa &".11 Toil ",(I",("ou9al Mal /JOlPOuIJa. E. 3 TW" MaTa UIlp.POpf/leaS Tel af. leaTa UIlp./JOPf/leOS 27" 8, cf. 65 &6 Ta '"'('YVTaTa at. ..4 I Ta Ie."OWTa ai., Ta Ills c! A0'Y0s 7°"21 alrlw 72°39, 75'10 dlel"'lula 988b 3,44 ° 19 dlCE"flTor. Ta", d. 984' 31 'UTI" d. TIS VUIS 10"34, cf. 69"33, A. 6,73" 24, 33 1I0uaxws 68 ° 20 dleoAoll60'" 981"27,989'33,3"23,18" 36, 43 ° 3, 47 b 3 dlCooio." 980 ° 23 iUcpa TOS A0'Y0s 9" 4 4Kp
°

iUcpa 3["35

4Kporri,Plo" 24" 25 tiAft60,a 983°3,988"20,993"3°, b17, 20, Sb 3, 9bl, 78bl3 d\f/IJ~s tllI.;" 989°7, 6b29, 7°:\2. 12" 28,17°34,21°1, 25"14. 77 b 3 1 , 33 TI d. oli 'nUT.po" TO 1'0.1..1..0" d. 9"1 TOUT", d. I I " 3 TI Ta d. ib. 25, 12 "9, e. 10 TO Ills d. ill' E.4. 17" 31, e. 10,65"H d~f/60vf'" lIfPI TI 10" 9, lI'PI TI"OS b 24 dAf/IJooiouIJa. KaTci TI"OS 10"8, II" 16, 62"34 tiAf/9."WTEPO" 9" 3 'AAKJpo".'" Hom. 9 .~o 6.A0'Y0s 999°23,2"29,83'8 d. BII"dI'm 46°2,48'4,5°°33 aAuls 65 20 al'a 68 b 26 li.J
°

°

dp.opfts 73&6

dp.fTcifJAflToS 14°28, 19&3? dp.OT4"0IUTOS 15" 32 d"''Yfts 989 b 15, 17 li.p.IKTOS 989 I dp.olPaios Emp. 0° 15 dp."oxop.."ol 23" II dp.vBpiils 985 "13, 988" 23,993 "13 dp.IUPf/TftUlp.oS 996° 27,10"17 6.1'01. TO It dp.o'" 29'6, 71"9 TO 6.1'0184" 12 dpi/Js 'YE lIOJS H" 2 d"d'Y'I" fls Ta" 1..6",(0", Tq" dpXt7'" TOUS dp<9p.oois, '"IP"(flll", etc. 983" 28, 4" I, 36b12 , 51"3°, 994 b1 7, 4° 28 , 34, 55"29, 61"12,82"37 ols 'Y"OJPIp.lJJT.pO" 4°"20 'Ypap.p.q" 5 1 "25 d"a'Yleaio" IOb 2 8 1I0ua')(ws 4. 5, 72" I I ~ d"o<lS TWr d. 31 cllloB.I",,';OIlU'" d"a",(KaloTfpo" 25 13 d"4"'("'f/ def. 6°32 1I0ua')(ws 26°28, 64°33 -it d. 62"21, 71010 opp. Ills 1111 Tc) 110M, UIIp.fJ.Pf/IeOS 25" 15, 18, 20, 26"28, 27 b8 , 64"3365"3 o"a'YOJ"ftl 5"1, 27blt,61"1I, 16 d"alp'''' 990°18, 12 15, 62 b l1, 79"14, 82° 33 Ta ElIluTauIJal 994" 20 obula" 7"20. 86"18 dEl d"alp'''' tCTTill 40" 7 pass. 989" 27,99 2 ° 9 , b 29, 6 8, 65" 14 "'"a'pollp.f"",,, "'"alpoiTal 17 ° 18, 7' "35 d"aKdp."Tflll 994· 3 dv41..AoIOJTos 73" , I dv~o'Yia. leaT' d. ~'" etc. 16 3 2 , 34, 17'2,18"13,7°"32, b 26, 84'33 dva1..0'Y0" 43'S, 48b7, 93b19 Ta d. UIIVOpO" 48" 37 Trfi d. TabT" 70 b 17,7'":1: 26,93°18 Ta aUTa leal Te}&..89 4 d"41..ilo,,, TOUS 1..o.,.ol/S 63 18 d"aAIITIKci 5 4 'A"ata'Yopas 984"11-16, ° 18,985",821, 988"17, 28, 989"3o-°H, 991" 16,9"27,12"26,63°25-30,69L2I32, 72'5, 75°8, 79°20, 910II citatur 7 ° 25,9°25-28,56°28 'A"atip.a"Bpos 69 2 2

°

32"

°

°

°

°

°

°

'A"at'p.lvf/s 984" 5

d"4"T'I" oIs TOUr dplIJp.oils 78° 22

°

o"aTp0"ft 13 14 d"alptu6al lIpOS TI 4" 25, 26, 45 ° 28 d"llpci "oBa 75 " 21 dvBpla"T01l0If/TI~

°

13 6 d"Bplll"TOll0l0S [3 36- 1 4 " 15 d"Bpai'pal 74" 2, 9, d"(P'YauTor 48 4 0"'11. TW" OUUIW" 6.. 71"1

°

°

II

INDEX VERBORVl\1 d.9ponrOflIJEts 9EO[ 997 b 10, 74 bS 468ponros. TO av9p&'rr,*, El,,1U 6" 337"1 cl."'fIlIJ~s~S"2-Ie cI."v. 9pt»tro" "(EII"'I 32"~S. 33 32, 70"8, 27,b 34,92"16 d.llrlo. Pyth. 990"~4 v.l. 41110o" ~2b33 TO Ii. Acad. l5"33. 87 ti S, 9, 88"IS, b29• 32,89 6-IS, 91b3s, cf. 81"25 civlaoTl]s I ti 23 cl"op.ol0l",n,r 24 "16 d"Op.olOIl 18"19,24"21 clvopollaE Emp. Ob IS d"Ta"a'rw9IU 40" 22 aJITEltrEIV 996 ti I I clvTIlJlltOS 995 b 3 avn9'aEls TETpaXWS 54" 23 dIT'ltE'fI'"OJf 17"3, 18"II, 18, ti8, 43"1, s4 tiI 5 dllTlltEla9al. avTlltElfiElllU daEls II b 14, 62 "6, 10, 22, 33, bIZ flfTafloAlI fls Ta clvT",dflElla II 34, 69 b4, cf. 57" 31 dVTI"E[flE"(II IJlaopal 16" 25 d"TI"ElfI,"a troaaxws A. 10, 55 &38, 57" 33 dist. l"allTlo" 69 b 5 dIlTI}"I,,(f"" 24 b 34 •A"T,a/Uvflol 4~ b 24 'AlITla9''''1s 24632 dllTlaTplE'" 16 b 28, 61"17 dvTIaals r. 3-6, 12 b 2, K. 5, 6, 67 b 14, 21, 22 flETatu dllTIdaEQIs ou6." r. 7, s5bI, 63 19, 69"3 triiaa /JUllafll' If.fla Tils d. 50 b9, 31 dist. aTlp'lOIS, l"aVnQT'IS,Ta trpOs 1'1 55" 38 TO NaTa 1'11" d. 63" 21, 24 clvTIX6Q1" 986" 12 d,,"rro9'Tos 5 b 14 4IIQl 992 "17, 7 b9, 16" 29 clvQITIpt» 99°"6,5"34,16"3° d"QlTaTQl99 8b 18 dv&'""p.os 33"14, 56"25 dtlQl/Aa '"' dtr03f1.n-,M1/ dp~ 997" 7, II, 5"20, b33 , 90"36 = sententia Ib7, 77"3 1 dOllJol 983" 4 dOpaTolI ~ 2 b 34 d6ptaTos 989 b 18, 10" 3, 63" 28, 92" 13 d. TO 3wafiE' 6", ~ /lA'I, TO allflfl.{3'1' "eSS 7b29, 37"27,65"25 cf. 311as drra"(op,riEIV 91 b 23 d...a9"a 46" 13 dtra9!ls 991 b 26, 19" 31 syn. aflET'" flA'ITOS, dllaAAolQITOS 19"27,13"11 dtral3,"ala sb 3, 6"6 dtrallJEIITOI 43 b 24 dwallTiiv 36 "14, 63 b 13 d..wTl]ols 9"20 If.waf 2o b 7 d.aTii" 51 b 25 dmT'I dist. ""("ola 52" 2

50 3

IitrallaTOS ,,1"'1als 72 " 2 I dtrElp&a opp. ifitrElp[a 981 ":, opp. trlpas 988 "28 IitrElpo", 1'6 a.~, K. 10 "trElpol al dpXal Anaxag. 984" 13 4.. TO ill Mel. 986 b 21 TO Ii. ouala" ,1"(11 P~th. 987 "16, 99°"9, cf. 986" 23, 4 33 I" flE.,MolI t
a

INDEX VERBORVM
CilrOl
d...ola.lllEu9e1l 984" 3, 993 b J 7 4 2 "7 a7l'01l'fd...0411a.1 TI ...pIn TI 12&13 '11o.0'1S. .rB-q Tiiw d...O4O'EQlII Plat. 990 b 13,79"10 dist. O'Tlp'1O'ls 4" I 2 T~ IIIa.IITioll d..oIlO'ia. ~ d. ib. 15 1...Ifp.1 12"9, cf.46b13 d. T~ Jlq .Tllell 12 " 16 eel d... ~ TOj) Ii d. 22b 32 d. O'TfP'lTII<;' 56"17, 29 - d,..{,a.vulS 73" 16 d...oopC syo. d,,640'1S 46b 14 droifn1l,.O'iJal 10"31 Ii...Tfu9a.1998"2, a"34, I4bU, 2S,68 b 27, 69"13 metaehorice 984"28, 985b24' 988 "a9, 69 24 dnp'1"011 a3&1 dp.TF! T.AflQlO'ls Tif 21 b 20 d. dpl9JloS dpI9Jl'1T1 1<6s 5" 31,9°" 14 dllveIl""'II TWV d. ';0'111986"9,73"20, 84 "12, 3a T~V d. IIoJli'OllTfS dp~v .Tva.1 986"16,76"31 ap.9Jl0j) O'TOIXf'a., 'YlllfO'IS, "'09'1 986"17, 87 b 15, 84"3. 91"29, 99°"19. 4 blO, 90"21, cf. 986" 20, 84 b 28, 89 b 12 TOil d. Tqll ovO'iall d...c:iVTQIJI 987"19. I b 26, 76&CI. 80"13, 83"23, 92b16, cf. 987 a4, 1 ~ a5.] qo" ~3 frP;;'TOI ,1'. 987b3., sa"ts, 81"5 d. II0'1TOl, a./0'9'1TOi 990" 30. 90 b36 coni • •CB-q 991 b9, 80 b a2. 86"6, 91 b 26 coni. b 13fell 76"20, 80 l2, 81"7, 90b37 A~rl dpcll'iiw, etc. 99 1bl 3, 17, 19, 92 14, 31, cr. 985b33 31c1 Tl '" o d. 992"1,44"3, 45"8 dpc9Jl~, I
60 b 29, 87bU T~ b! Ellla.1 dpxii TlllilO'Tev dpc9JlOv Elllell 16 b 18, 21" 13, 52 b a4, cr. 88"6 def. 20& 13,39" 12, 53&30, 57&3, 85b22, 88"5 01 d. ...010£ TIVES ao b 3 dll0'Yflll fir TOUr d. 36 bU coni. dpluJ.Ws 43 b 34. 45" 8 ~ Ivlnfla. ~ Iopa 83" 1 ov O'IIJl/3AflToUS .rVeIl TOUr d. Plat. ib. 34 d. dpl9JlfITlI<6s 83 b 16 6....ECpof, 1Tf ...Epa.uJlllloS ib. 36 d a' III~s & ..MO'Ia.,6JlfVOS 84" 6 dq obI< lUTlv III ToiS d •• T~ 3' Itj>.{ijs 85" 4 d. d3'1TII<6s 86" 5, 88 b 34, 90 b35 opp. A6'Y0s 87 b I a d • ...6pIVOS, .,I,'"0S 9a b 20 III dpl9~ fTlleIl ib. 27 d. TETpC'YQlIIOl, 1<6/301 93" 7 'r4 JlET4 TOUS d. 99a b 13, cf. 85"7 dPCO'TEPOII 986" 24 'AplO'TI ....OS 996" 3a II.PCO'TOV .p b 2I dpl
12

x

dPJlOIII.,.q 997 b aI, 78" 14 dpJloIIIl<077" • 5',93 bU , l ..i TIIIOS 81" a.PJ.'OTTflll TIVI 22" a 20 dPPfV 988"5, I. 9 Pyth. 986"24 dpp.,9JlIO'TOS 14 b a 7 apulS 19 b 16 v.I. dPT40'9a.1 3 b 17 apTloII Pyth. 986"18,24,99°"9. 66 b 21 Plat. 84" 3-7, 9 1 " 24 dpT16T'1S 4 b I I dpXail
INDEX VERBORVM rI.tfIpo, d. Anaxag. 984 &I 3 Tal d. IIlfa TCb &aTd tlVtlTOIxill" Af"IO,uflflS Pyth. 986& u TIlvarrla Gpxa1 986 b3, 4 II 3 I, 87 &30 dA.,eil1TlJT'GI 993 II 23 '111"" do "'1 994 &I ." 1'011 A610.., ." ,.fj brO""I""" 996&, dll'OlIlIlf'f',"1 do 996ba6, ce. 99311a8 /3fiJa,O'f'llT'GI 5 b9, II, 18, u, 6"5 'Y"0IP&JWr6.,." 5 b I 3 d"lIrOIf,.O. ib. '4 'II,tlT01'lpII. 6a" 3 '116T.po" ,.el "(1"1 ~xat 998& u .fa", dp&9pfi I" 999 a5, ab3I, 601129, A. 4, 5 ,.;",
1&'10.

/3ll1I1,f'" EI. rI.lflpol' Ob 28, 6"9, 12 &12, b U , Ub9, 33btt 4 1bn I"XP' ,."'c\. /3. dpXijl 27 I a ''11' dprlv ,,41 T'Aor 50& 7 /3a31,_ 'tlTl"l3all"" 17" a9 Tel /3alll,."" ,.el /3alll,o" 28& 20, 24 /343&(1'1. 994 &9 /J490. 20&12, 14 /3a.9~ lflii Ta."f",6" 99a&I3, 15,20&:11, 85&lI,89 bI 3 I3RlII.u(Ja, .""Ia. ulIMalJal. 93 &30 /34"alluOi "'XIIG, 996 &34 /3apu 20" U /3apUT'1I 20 II 10 /34UI. geom, 51 &28 metr. 87 b 36 /31/3a.lo. ~. ~p&"o" etc. 8&16, 17, 9&2, II '3 /31a opp. 'rr&9~ 9 &18, II &15 "0

Kk

506

INDEX VERBORVM

/lialo" .ai ~ /J., coni. clm'Y_o" 15 & 26.30 /luz'ftJ9al ftpaS lm08fI11" 82 b 3 /lilJlo" 15&26, 28, 36 syn. _ptl "w111" b l5 /lAEftoll1 pGAAo" 986b 28 /lo;;'" cIIf ~Mopfm 91 &10 /lo6por 25 & 16 /lop.JJvf 93 b 3 fJovAfl16al opp. 1I.hflll l1aiin, &ap6poiiv ~ b 19, 2 0 28 /lovAfl16al AE'Yfl" 86 1~.89&20,91&32 /lovA'ITor 72 &28 fJPO"T;;'" 41 & 2 5 fJfilAor 67 &II • 'YaA~"" 43 &24

'Y4po. Pyth. 78b 23 'Y1"'111S. al 'Y. ft.pl Ta "as' l"alTTo" 981 & 17, cr. 42&3°, 70&15 'Yf"II1f1 III1Tfpo", ."VI1f1 ftp6TfPO" 989& 15, 50& ... 77 &26 pOTa£1J Toli .l"al .al p~ .l"al 994&27, cr. 55bll, 9 1b 34 'Y. VI11.ai opp. ftOI~I1f1' 32 &16, 26 m 'Y. I) p~" "O'lI11S ~ II~ "ol'll1ls b 15 'YEI1I111' I" TIIIO, Tlll1Tal 33 b II '''Ia d"ov 'Y' II1TI "al ob. 'I1TI" 44 b 21 def.67b22, 6gb 10, 88&33 'Y' dftAil 67b23, 24, 68&35, 69blO, 88&.~3 dist. ,,,i"'1I11S 67 b 31, 68 &2 ob" IITTI 'Yf"il1fOJS 'Y."0111S 68 &15 'Yf"'1TO' 27&29, 44 b 3, 69 b 25, 26 'Y"''';;''' Ta" oUpa"o" 989 II 34 Ta" clp46p6" 60 b8 'Yfll"'1TO', 1111.'1 'Y' 42 b6 'Y1"oSfI3GIII 99 I &31 ora., w. 'Y1"ovr 5 7 b 7, 58 &22, 79 b34, cr. 998b24' 30&12, 38 &5, 85 &24 dist. 060Aov 992 b 12, 15 b 28, 28 b 35 'Y. ToA.VTGfa, ftpfilTa, 'l1xaTa, civCIIT4TGI, l~aTa 995 b 2~ 998b I~, 18,999& I, a3 &27,34 &I, 37 30, 59 27 ftOTOPO" Ttl 'Y. I1TCKXf'" 998& 21, 14 b II, cr. 42 &14'':;9 b 21-27, 69&27 clpx:a1 Ttl 'Y. TGI" /,pll1pfi111 998 b 5 obX ofo" Tf ollTf Ta ollTO TO 011 fl"lJI 'Y' ib. 22. 45 b6 'Y' coni. 61"11 PO', ofllar 098 b I 3-999 &23, 16 b 32,23 b 18, 24, '25, Z. la, 39&26, 57 b 7', 59 b 36-:-60& 5 coni.1l1a'I>Dpa 998b 31, 14~1I, 16&24, 37 bl 9, 21,39& a6, 42b32, ~9b33 ftol1axiin 4. 28 'Y' wr ilA'I 24 8,38&5,58&23 Ta 'Y. oll. obl1ia 42&21, 53bn, cf. Z. 13 Ta 1I1a1po" 1I1alpfi 4 'YI"" 4 ffllll def.54 b 54b28, cr. 24 b9, 58&7 30, 57 b 38 pfTafJ
a"

.1.

'YfGl/laal1ia 997 b 26, 32 'YfGlpIT",,' 9gB &I, 4, 5&11, 31, 78 &25, 89&22 'YfGlpfTpia 996b 34, 997 b 27, 19 b33, 46 &8 'YOGlPfTpI"o, 983 &20, 992 &21, 61 b3 'Yil 989&9 49&20, 22 npo"l11S 65 b 20 'Y1'Y".t16al. IJcXiin 'Yi'Y"fTai Toll. i" TOiiIJ. 994 &22 Tal 'YI'Y"OJAf"O" pfTa£1I Toli Il"TO. "al p~ Il"TOS ib. 28 ,.a 'Y. IXfI ilA'I" 32& 20 'Yi'Y"OTIJI l" Til. I1Tfpl,l1fGl' Mal Toli bfto."p'''ov 33 &8, cC. 55 b 12, 62 b 26, 69 b 18, ao, 88 b 17 'Y. Ti, I. Tlllor, b.. TIIIO, 999 b6, 10& 2°,32&13, b3I , 33&24, b 12, 44 b2 4, 'Y' ."VI1f1, TEX"f/, old TDwo, 49 b 28 paTOV Z. 7, 9 cllllivaTo" 'Y. d P'llJi" "poDmipxoi 32b31, cr. 33b12, 49 b 35 'Y' Ta tTIi"oAo" Z. 8, 42 &30, cf. 34 b8, 43bI8, 44 b2 3, 69 b 35 'Y' it 6p01""POll, I1I1"QIIIVPOII 34&22, 49b28, 7°&5 'Y. d,,11."", p~ d..AfiI. 42 b 7 &tl To Toil 'YI'Y"opo"OV 'Yf'YfvijI16al TI 49 b '35 'YI'Y"OJI1I0' 42 b 18 'Yo,,~ dist. I1ft.ppaTa 7I b 3 I 'YpappaTa 0& 3 'YpappaTI.os 64 b 24, 26 'YpappaT.q 3 b 20 exemplum Tail tTIIp/lf/l'lI
n'''o,

o

/laapo"Ia I 7b u IJciItTIIAo" l.i"fl po"o" erato 10& 13 6rro/lGAAovl1. 63 &8 IwlzAAa£Is To»" II. 11&33 /lapp Parm, 89 & 4

INDEX VERBORVM lIEi""o" 4a b ao

airm 1'ch apxm

A~",olJtI'II1

.111C1l Pyth.

986&22

aOMalm 93 &30 1I0MUs. .,.IA•• I) II. Pyth. 986 &8 Plat. 73-ao, 8a-I-1I,84-12, 29- b2 11'1('1"1(&" 18&23, a2, 3a, 23" la, 56&a6, [68 b 25 a.f.o" 986& a4, 93 b I lIEtlpO' 42b 17 lI.iipo, .,.a 991b30, 2b15, 59b8, II,

o"

60-9, 6a-Il,

22

a"Aoiiotrans. 86 b5 ~AGlalf disl. drullll£Ir 25 b 16 A"""ef'l.,.or 985b4-ao, 9-27, b I l , 15, 39-9,42b II, 69baa, 78bzo II",","'I~ lntoA,,"'Ir 989 &I I a.a 13&28, b 33 a.a '1'1 opp. IlTi 981 b la, 41 &10 aiel '1'1 wpiil'l'o" 983 &a9 a.U."'fK'I'JM199 S- 25,14-36,5 1&a2 1I1,..,.pcil/>0l" 54 - 30 1I1,."Y""ri 981bI8,~8aba3, 7abl4 aUIBoalf 19 b 5, 21 10 "OIJ',.Xiilr A. 19 1l&tJ91'Y'l Democr. 985b 15, 4 Zb 14 IJ&,.Ipt'" at b 33, 51 b 3, 69& g4 mathem. a " log.8-19,al!sz7,6J 3 a."lpliaBcli 4& a8, a8& 10, 29 I a.mlptlJ'I' 16b4, 5 mathem.994 b2 3, a&19, bIOI. 48b16, 6ob14, 19 l0lt. 27bl?,37 28, 67ba6, 72ba TGI" i",..,.,..Q/I1 54 & 30 1I10lPfTOII 20 - 7, 77 b 20 /ll,.e.iaB,.I 8 b30 , u b II, 63 b I 3&CllCOal''III'Ir 986-6 3&CllCplll'III 984-11, 98e &24, a8, 75 &l3 11'"1"11'11984&15,988 33 1I1uf'lTle~", XpOlJM1 57b8, 10, 19 ll1aAl..,.IJ'9tu 989 b 33, :\,b 20, 7 - 20, 78 & 29 "'por ,.bTUII 6 8 iE of'llJ'I'0ii lab7 IIItJAdr..II ?86 &7 1I1,.A.eTleOi 995 b 23, 4 b 17 1I1"A.RTlln~ 98t3a, 4b25 II. IIJ'Xu, oihrGl~" 78 a5 lIuiMo(1f 1l)· 2 3&tJAiilJ'cu d"opt,." 63 b8, 13 3&"I'ciXlaBoi 99a &20 1I1"I'iTPOIJ dlJ'alJ,...rpitJ 983-16, cr. 20, U & 33, 17&35, 19ba4, 24b19, 47 b6 , 5IbU ,53- 1 7 1I11Ji-"I>'lJ'tJ"T.'" 6a b 34 a.allo.iaBai 74 b a5 /ll,."o"T.eor 25 b6 "1I1a"0".,.0,, 31 &30, 3 I disl. 110,,'1'611 12 &2 WIIOIC1 l2&a, 13-ao. 31-31,32. 25b6. 17. a7ba7 28, 3a&28 -IIO('J. 984 - 5. g86 ~ 10, 9- 16 opp. Ai.,..", 985&4 l.A..,", b"oAatJoill 9- 4, 36 b3, 73 b I a awcino. ~ lIIalpo, I) II.

_iii"

a7 b33 1J'1JI'."A.oeij Tii' a. 6!i&u arc) a. .,.1.,.".IJ'9tu & 5, d. 32 - a8, 70b 31 a.,."op.'" 991 &9, 995 &28. 35, b 5. 996& 17,999&31,9&23. 59&19, b15, 79 b u, 21.85&25,86-19.34 1I1a.op'll''' 53 b lo. 76bl. 86"15 1I1,.pBpoii" 986b6, ~89&3a. 2ba7, 41b2 a.,.aa'l>'1"t,,," 986 22 1l1cill"l"ll'a log. 55&9 mathem.85 bao a.Gl/>iC"" I. 4 .,.~"o. 18 - a6, cr. 54 28 3&a.,.t ")'1W1) clrIIpc). Due .rllEi 3&a'l>iP" I. 9 1I1,.I/>.p611TGIf 8 bII 1I1",/>.V..,IIII a &27. 93 b 10 3&GI/>Bopci 5 I &2I &af/lOpci ~b23. 998ba5.ao, 4-14. 20& 33-ba b 15• 4 zb1 5, 57 b 4- 19, 58& 30, 59 t 33 1rOAAlh &vAoi II. 980 &a7 II. .,.pti. Democr. 985 b 13. 42 b U dist. .""""'10.,.,,., b'por'l' 4 &21, 54 b 23-55 &33, 58& 11 dllTlelll'.",.I II. 16&25, cf. 48b4, 57 b5 TiiI" II. 42 b3a cl lIui .,.iiII1 II. Au'Y0' opp. Au.,.o. illo"occl. 45 b 17 43 - 19 deC. 58 &7 .,.fllOlJi II. ib. 8 ou "oloi II. I) /lA" b6 "piilTai II. 61 b 14 TU df'lBI'0ii 3&,.l/>Opci, eeU I'0"cillor, d 141'1'111 83- I 1I1a.,,0rr woaaxOls 18& 12 I'0llallE. II. 81 33, 35 IIIG1/>Q111'' ' 85 b 36 III1JXGlpt'.aB,.I 23&a3 3&,..".vlloa9tu 5bU. 9&11, 14.61b34 /lIIla(I' 41 b 10 1I.3tJarm.'.Ieclr 982 &28 &3acrRaAI,",,TlpO. TiilII alTtGlII ib. 13 IJ&Maeflll 981b7 1I1110"al - IJ'IJ'YXGlpt'" 6&24 IlUpxoa9ml '1'1 988 b :n .,.pi '1'1110' 48 &30 1I.0pGl'l'a.. 0 &20 IItolTlS 16 b al, 53&12. 87 b 35 al II. IIv053&15 1I1IX"" 63& 31 1I1tlJ'TalJ'9tu 985 &25, 59 &I .. IIlRlUo'78b23 def. 61 &24 eumplum .,.oi; IJ'lJl-'llftJ"ecITol 15 b 20-26.

49

e,.ft

.,.i""

1

7- 8

ll.eololJ'v"'I Pyth. 985b29 AIO'YI"'Ir 98t &5 AiOllVlJ'lC1 23 10 1I.0piC,," 55 b 8 IJ&Glf'llJ'l'i",.. opp. .,.IIXOiiIJ'IU 986- 32, cr. 58b 27 11••aT,.. IrmllOls, 1I1Dp1lJ"1'io", etc. 27 b 18, 29&1, 4B b37, 996b8, 14 3&op&al'o, 5b23. 48&a, ao 3&°""981&29 =IlTI6a&6 1I1"Aaal,.,0:..,,01 aI/>' 1"0.84 &6 1I1"AciIJ'IOJI ao b 34 1Il"01J,, 38- 23

508

INDEX VERBORVM

&TTc)" Tc) 8" 69 b 15 36yf14 63 b 25, 76& 14 lfOJ~fTPallTal1lCl 62 b 33 11TT,/A'I ~9 b 33, 34 ".(iTCIOS 3. 74 b 13 fXOlITal TillOS 36('Is 87 3 I 7Blal 36(a. 90b 29 &£a'flll 9&1 I, 13 opp. 1".[I1Tal1l1al 8 b 28, 30 1Io6A' 982 b 29 lluas dist. a,,,.AaI11011 987 &26 coni. /A1"(a Mal J.IIMp611 Plat. 987 b 26 (d. 33), 988&13, 87 b 7, 10,88&15 ¢apral tuallu 991 &4 ".~'1 TWv dpill/Aw" 999&8, cf. 8S b 10, 88b9 = aUTO· YpCI/A/AT, Plat. 36 b 14, ce. 43 &34 B. d6p61115 2Sb23. 27&6, 32& 28, 33b8, 64&13, 49 6 9 - coni. i:A'I 43&28, bl0, 49&23, 5°&15, b27, 60& 20 69b14, 70b12, 71&10, 75b22, Tc) Illllla/All Mal Tc) 881.1, 92 &3 "'fP'Y';~ (II ".Ws II1TIII 45 b 21 B. clAO"(Ol, /AOTa Ao.,OIl 8. 2, Sob 33, cf. 47 b 31 ..ws TO cI".fIPOII Mal TO MO"c)II AflfTtU 1l1111ci/Af1 48 b 9- I 7 ".OTf Illlll«/AOI fMatTTOII 8. 7 ".p6TOPOII '"IP'Y~la Blllla/AfOJs 8. 8 oVII~II Blllla/An dt3lo11 50 b8 cI/AIJ rils dllTlciCT'OJS ib. 31, cf. 7 I b 19 ".p6T.PO" B. IlloP'YfiCls 71 b 24, cf. 3 &1 - pim '/A. flflplm IIu"ClJ.llII d".OTfAf'" 981 &I Tp6".or T;;I ll. 4 b 34 BvvaJ.IIs - l1I'II1TT,/A'I/ 18&30, S~&31,cf. 27&5 = signifi· catio 52 7 ClI II. Mew dp<9,.iw 93 b1 4 116"Cl119C1I Tc) ClUTO 11 &7 ~III14Tc)II ".OI1C1XWs 19" 33, b 28, 8. 4, 48&37 coni. '"IlfX'T(u 47&36,

SOb 11 II. oTlla. 47 b 8 "'"o,TOJS TClUTO" II. Tdll4llTlCl 51 &6 II. 49 b 13 fir Tc) 3. 74'11 Tc) B. adv. 78& 28 v.I. IIvo Ta ".OAAa TWII d,vllPOJ"l"OJV 986 &3 I 1I110".010S 82&15. 83b36 BIII1MOAICl - d".oplCl 997 b 5, 74 b 17 BVI1MOAOII I b I

BIII1TIIXO'S 983 &I

BlIl1xopalllnll TI ~Cll/Tois 984&29 TIIIOS 76&15 n 88 b 30

BlIl1XfPflCl 995&33. 8S b 17, 86&4, b U , 90&8, 91&37, b l , U AOYIMcai 5b22,87b20 b BIII1XfP;; 81b37, 8S 6, 86b7, 88b31 I1waln" II. 63 b 32 InV'rfpoII ClfTIOII 14& 5 <"(M1CIAos 13 &6, 35 b 26 lyp'I"Y0pOs 48b I l"(pT,yopl1lS 72 b 17

e

.,xoIPfw oti 32. b 2 fir cilllalpoTCI •• '9fAol f1"ClI 13 27 53&23 v.I. illllor 981 b 25 190s, Ill' opp. 611 .. 981 b 5, cf. 47 b 32 MaTa TQ f. 994 b 32 flBllItu 980&21. 981 &24, 28. 983& 25. 993b23, 99~b2l, 39, 996b15, 19, 28& 36 syn. 1".[I1T4I1/141 983 &30, b2l,994 b20 flB'l/TIMOS 86 &5, 88 b 34, 90 b 35 dllos 0Pr>. /lA'I 988 &3, 5°&15, 69 b 34, 70& 2, b II, 84 b 10, cf. 35 &8 T;;r /lA'IS /AiiMoII 6". ClfTIO" 29&6, 41 b8 yl"os .Ill..", 991& 31 .iB'I/ Ws 11"°111 57bZ' 58 &22, 79 b 34, 85&34, cf. coni. lfllOS 999 &4, 998 24, 30 &U 23 bl8 , 24, 2 38 &7, 57 b 7, 59ti37-3~ = yillos 58 26, 3', 7 1 &27, cf. 58 28, 59&10, 71&~5 TiiI" IIF1TC»" AClfjfj" 1"'I1T~~"'" Tb T';V d. AAfjoill 998 b 7 lall,Alp.0Tov MClTa TO d. 99f 3, cf. 2b 24, 16 b 32, 18&1~, b8, 49 18, 29,58 &18 szn. fUJfXIYi1 999 b16 • 15&5, 17 b26 , :\3 5, 44 b 22, 52 &123,60" 22, b 20, cf. 22. to coni. Tl ~II fTVal, oUl1iCl 13&26, 3°&12, 32 b I. 33 b 5,35 b 16,32, 41 b8,44" 36, SOb 2, 84 b 10 coni. A&-t0S, dp
e,

INDEX VERBORVM Z. 10, I I T3 E130s II< TOO 'Yl"ollt IOpOJ" 39 &26, 57 b 7 syn. ft's 44b 33 0pp" u."lprJulS, ib., 70b II I" (lA'Is f,3E' 983 b 7, 984 "J7 -.,8'1 Plat. A. 6, 9, 999"3, B. 6, 28 b 20, 31 b 14, IS, 36b IS-20, Z. 14, 01 59&1(,13, M. 4,5,84&'3-29 ."a d . ."dU".,.." Al'Y0"TEI 9118b I, 9~ob 19, 997 b2 , 79"I~, cr. 4 2&11, 75 19 ."a."GJv E1. U."O'Xfla 987b 19 ff. ."OJ., dW~UEIII" 990b 13, 79&9 Ef3Ti 'u.".,,&,,6ua uu., 1,0& 18, cr. 14, 99Ib7 d p.f9.RTa ."t\ •• 990 b 28 coni. d".9p.ol 9~lb9' Bob 22, 8t"u, 8a b 3, 86" 4, 90 il3, 9 I b 26 ."ci fi. alu9'1."a MIl,a 997b12 ."GJv·d. alria 33b26 wp(js ."cis 'Yf"'UflS I .,,3 d. h.po" Ral TOJ., I<"T'I'Y0p,OJ., il
»

e

.T"",

°

b •.,.,81"al 86 b I ~1C.,.((J.u9al 3 • '0 v.1. 'RTO"W."EPOS 989 b 30 IRTpo...q 89" I 11Clp.,,, Spo" 40b 2 'ICEU'Y"" .",,,1 90 b 21 il<';'/I 25 "9, 12 'A''YK.",Ial".u9a, 28" 28,9' &36 ~"'1fIlXOs 46"3t, 48&4 ." "'''''. "ouaXlIIs 23" 24 ;'" T6 I. 1-3 Ka."d ."a" A6'Yo", ."i)" iiA"I'" ni" aialhjaw g86 b 19, 20, 32 dp,9p.f>, Ka.,,' .llIo., ""."a 'Y/"os, Ka.,,' d"aAO"fI"" 999b25, 33, 2b 24, 16b31, 33b31, 39"28,54"34, 60 b 29 Ka."a Ta UII"EXls, "ou6", "0,6" 14 b 25 UII,,.X.lq., .rll." A6W 16b9 d4>ii, ,..1(", 91uE' 82" 20 A6"f9', dp,9p.f> 87bl2 a"."a mW 988bn ,,, h·l "ouGJ" 9go b 7, 13,991"2, 40b 29 ~Ul< 'u.", 'Y1"os, :uuia 9!t8b22, 1&5; 25,5"9, cf. 40 18, 45 6, I. 2.59 el,70b7 Kal."a IS" 998b22, 1&54,3b23,4b5, 5"9. I2,4 0bI6, 45 b6, 1.2, 59b28, 31, 60 b5, 70b7 d3,alpE"'0" 999" 2, 41 " 19 "pels ;", I
,,,.,,a

'If

21,

5 10

INDEX VERBORVM

lVRVTlo" 13b12, 18"2~-3S, 54"25, b.~2, 1.4, 5, 7,5Sba6,75 21-24,31,92"3, 33-b8 Td"aJlTla elpXa! TWII illlT"'" 986b 3, 4 b 30, 75" 28-32, b 12, 87" 30 civa'Y'Tal Tdv. fls T»" apx»v TavT7/V 4"1, cr. b 27 ll«CTIS 12"9 TWII I. TO aUTO .13os 3ab2 ou trOvTa TelllallTla "(1"(V'CT9cu elM"A."", 44 b as, cr. 69 b 7 auu,,9fTa ciAA..qAa", 57 b 22 eltra97j IIw' elU"AGlII 75"30 coni. trp6s TI 56b 36, 57" 37 II< TWII i. Ta /-,.Ta(U I. 7 Ta I. TijS auTijs I trlCT~ WIS 61"19, cr. 996"20, 78b26 /-,~9~v oUCTIq. I. 68" II I. Ilpo"Ta 57 b ll .IIallTlOT7JS 995 b 22, 55 "16- b IS, 58" II, 63 b 17 dist. BI,,Opla, h.p6T7Js, dVTI«CTIS, CTTlf171CTIS, trpOs TI 4" ao, 55 b I ISUI TI ~ /-"" tro..' TqJ .CB.I iT.pa 'vallTIQ/C1IS ~ B' oil I. 9 'IIallTloVCT9al TIIII 990b 22, 79" 18 Iva"TIGls BlaEpoIITa 57 b I I ,,,allTIWCTfIS 986bl, 63b28, 69b6, 13 .11 TV OUCTIq. •• lX'III 18 b 3 = I"allTIOT7JS 1.3, 4, ~8"8 trpWTal •• TaU OIlTOS 61 "12, 13, cr. b 5 aICT97JTa! •• "32 troA.A.as IItro/-,III.I" I. 9°"2 ivapl9/-,os 99 I b 2 2 'vau'.Tal Emp. 9 b 19 .IIB.I' /lCTOII blSEXfTal 982" 9, 26 b 25 TaS .,,3'X0/-,Evas eltrop[as 988b 21 TO .,,3'x0/-,.II0ll = '' OCTOII 1ll3E~Tal 9 b 34 coni. IIwaTo" 47"26,50 II Ill&aTplfj .. II tr.p[ TIIIOS 989b27 'II.I
i, i,

47" 30, 50" 22 d ist. IlBo,,» ~ l. 72bl6 lv.p'Y';" 72"11, 13 Ta ''''nOiillTa I"CTIS H" 9 coni. 'IIlnfla 47"3°,5°"22, 65h22 ."T'II,IS 9" 17 '"Tpatpij"tu 985 b 25 llII1wapX"" 986b 7, 13" 4, 7, 24, 14" 26, b,S, 18, 70b22, 92"30 "UIS 44 b 32,7°"12 ~ TOU .Cllolls t 55 b I2 .. dtra9.[as 46 "13 .,ICTTau9cu 9 b 29 I,GI A.afj.", TI 2I b 13, 55" '2 •• ~II I
INDEX VERBORVl\I ',uaOa,. Tei lWuJAf,'a 84" 33 lwoJA'I'OIS 23"24, 3°"22 lIr'Xfll' 5" 26 fW' TWOS 993 b 17, 996h 21, 999" 7, b 27. 2 b 2I 'I' .". "oMii'1I' 9')Ob 7.13.991" 2, 40b 29 i,,2 TWII Ka8' ~l(aO'Ta o· I, 3~ b 28 TOU waaxfU' 19" 26. t 7~ 35 irr2 ~uvi :6,b 3~ frr2 1rA'o~,

.,,1

UTi TO aliI/EXES

1I'oAv,

HI'

tV

v.

'JI'OA-V,

6apa 33" 21 TI 79 b 3 .W'''(',(vfI10a, 987"29, 35"12, 36"31, h6 f"'('1T.i'v 988 "16 l"dJlJJA'i'v 48"21 '",8lJJA'IT"I' 72" 27 h'''f'Wf'I' 84" 13 ....'JAf".i'crOa' 8 b 28 • "'JAf1...< 26 b 4 .w'JA~.,a 71 b 30 Efr'P.Uptov

2 J• 2

zl'

<"'''f1l0l' 16 b 28. 76b ;;-~~, i9 h 10 I1xii!tll I. 2{ J, 45' Mi, 79 ':; f7T"roAa;OJ~

987. 2 2

f.".nro"au~"'fpo"

993 b 13 lfrlrrovos 50b 26 ....'I1It.t{laI19a' 4 b 16, 5 b 7 •• II1It.t{I's 983b2. 989b27 '",I1ItO".;V lta80AolJ, ltaTa JAlpos 3" 23, 5" 29 TWOS 37 b 28 ;"II1TaI18", syn. flllll'a, 982" 30. b 21, 994b20. 8b27, 30 • "'I1Tal1lS 89 b 2.'i .W'I1T~JA'I 981" 2, 3. b 26 apX'ItOJT'pa, v"''1pfTovl1a, etc. 982"14-'7, b 4 • 27, 31,983"5, 99 6blO TOW .( apxii< aiTlw. £W'OT~I''1 <)83"25, cf. 2Sb6 a.' .""I1T~JA'IS 985"16 - ."'I1T~JA'I< w.pl T"" aI119'1T"'I' OUIt OVI1'1S 98 7" 34 01 1..6"(0' 01 awo T"'I' .""I1T'II''''1' 990 b 12 iJ"fP Tais lW'I1T~l'alS ainol' 992" 29 T"'. OI'TOIV Aap.i'v ."'I1T~!t'll' TO T"'. fl1I",I' Aap.;. 998b7, cf. 31b6 opp. aiI19'1I1's 999 b 3 lta9uAolJ 3" 15, 59b26, cf. 60 b 20, 86b37. 87"11-25 1I,al'O'JT'It;' 25 b6 WP"ItT'~, "'0''1T'It~, 8'OIP'lTlIt~ 25 b 18-26,64 "16-19, cf.982b9 WO''1T,ltcU ••'I1TijJAa'46b 3, 75" , OV TOU I1lJ!tpffl'lItUTOS 26 b 4, 27"20, 64b31, 65"4, 77 b 34 0pp. ll,,(a 39 b 32 coni. A",,(os 46b 7, 59 b 26, 77 b 28 I"TpOV T"'I' .pa"(,u,.TOII' 53" 31, 57"9 I) i. wfpl Iv "(1I'osl) I'la 55" 32, cf. 3 b 13 coni • .,III1T'1/TOl' 56 b 36, 57" 8-12 Tal'anla TijS aVTijs .. 61"19, 78 b 26, cf. 996"20, 4"9 opp. a"(vo,a 75b21-24 •• ",TTol' 87"15 ""I1T'I/'OI',ltus 39 b 3 2 ''''I1-r.q!tOll' 4 8 " 34 ' •• I1T'ITOl' 982b2,996bI3, 3"14,21"29, 5 6b 36, ~7"8-12

.'p'

51

I

f"'Tl8fva, TfAos 42 & .. • "lTIl'al' 56" 31

."'TI!t'lI1" 91"30 .,,,o.v,,a 2" 4, 19"1, 20" 14, 22" 30, 29 b 17-21, 60 b 15 l. "pWTa. 60 b 13

ffrlCPfPftV TO EVIl'VTiolf 12 & 9 'E"IXapJAo< 10"6, 86"17 ~",x .. p(i'cr8a, pass. 8~b6 ;"OS hexam. 93" 30 "'To. Pyth. 93' 13 'p;;'v. fpWl'fl'OV 7l b 3 in0l' opp. 0navov 13 b 3 dist . • v'p"(fla ~o" 23 wpo 'nOlJ 31"16 .p'I1T1ltol "",,(0' I 2 " 19 'EPJAijs 73 b 32 fV TqJ Ai9", 2 " 23, lib 7,48" 33, cf. 50" 20 'EpJA6T1!to< 9S4 b 19 EPOS Hes. 984 b 29 opO. 4 &21 h'p68aA/-Ios 23" 5 hipOls 48" 30 '0, T6 988"14, ~2b26, 93bJ2 .u1Ia,p.61''1ltfl' 48 26 EII1Io(os 9~1"17, 73hI7, 79b21 ,v'I9n 62 34 .u~801s 24 b 32 Ev'II'OS I:;" 29 fMu 986-' 25, 93 b 13, 19 fMu,,(P"JAl'o< 54" 3 ,u9us 4"5, 3 Ib 3', 45"36 EMlJOIpla 994" 2 Eutl1lTOS 9"19 fl,ItII''1TOS M'(os 991 "16, 79 b 20 .UAf)'(,I1TOS ae,9JAus 92 b 27 .vAO"(0s 991 26, 999 b 13, 0" 23, 60"18, 74b28, 77"2~ 85"15, 91"7, b 20 OUIt Ell. 996b 33, 997 "18, b 19, 998" II dist. dva"(lta;ol' 7'\," 16. 81 b 4, cf. Ob 31 , 74"24, 81"37, 2 fVAg. "(OIS 989" 26, 78b 23, 86" 12, 88"6, b 30

EV.

(f1J1'.'rrlfl'TfC,

A6ETat,

(1V","

fllp'Ilt. 26 b 13, 75"31, 80 b lo fVJA.TaltlVf}Tos 19" 28 EVVOV)(OS 19 b 19 EiJOP'I1TOS 56 b 13 EV"Op'i'v 995" 27, 91" 30 T'I'OS 996& 16 fuwopia 995 " 29 .UpUI1TEPI'OS Hes. 984 b 28 EllplJTOS 92 b 10

INDEX VERBORVM .brlAfla "is ma"Dias 98"," '" .ixpllis 3 b 3 '~II;;'S 987 b 3'" .lJX'Pf" 25" 2,90 14 't/>4Pp.OTT .. " 986"6 1<1>'£;;' "'"9. 68 b 33-69"1"" 69" 20 dist.1I'pOS;", f115"1I, 27b24 arithm. 80"20, 85"'" 'tfHCTTQ"1ll n)" 314"0Ia,,, CTI01IIla 93" 20 Z.IIS 73 b 34, 91 b6 Cfj" Till; GVTacr[IllS opp. TiX"TI 980b 26 TO 9.ppo" Tfi Irypfi 983 b 24 def. 45 hu Z";,,_ Ib7 'MCTII 983" 2 2 '~Blo" 73b20, 2~ TO;; geo;; 72 26-30 'fio" z. I"" b6 'fia '''Ia 311llpoup.lla \P 40 13

'an}

t'"

11

obicientis 29 b 29, 70b 10, 75" 6 respondentis 3°"3, 31"24, 33b2l, 58" 36, 74 b 38 corrigentis 43"9 b 23 ty'I'0"I"OJTaT'1 l1l'ICT"";P'1 9¢ b 10 1139 22bl9 ~30n} ~ l"'P'Y'la 72 b 16 tt911t1l 981 b 25, 987 b I ~. ,lp.Ta[ 78b 18 ~lul<{a opp. Ina 984 "12 I1luos 71"15, pbl7, 22,35,74"12 ~",&""Alo" 35 9, 10 ~ l" ~. 51" 27 ~,..oAlo" 12"12, 21"1 ~JA1o"os 33 b 33, 34" 2, b 3 ~plCTfia ill TU /lATI 48" 33, cf. 17 b 7 'Hpa"A.i3a1 58" 24 'HpasAdT'IOI M[Ill, "0,.01 987" 33, 78 b

'6s

I", ~pal
'HpcisAfiTOS 984" 7,5 b 25,10"13,12" 24, ~4, 62"3 2, 63 b2 4 ttl'ipa 5yn. poArr 19" 31 .;. "(,,&'plpa 29 b 9 ~P'p,,,, 10"36, 12b23 ~p.po;;" 986"

,

~5

"IP'P."I'"' I~ a 30

'HCTl030s 984 b 23,989"10.0"9 citntur 98", b 27 ~TTaCT9al wo "i. ''1rqCT.OJS 98"," 30

eo";;s

983 b ao, 98"," 2 eomll.la 23 b II 6a;;JIll 983 "14 9allpci,.. " 982 b 12 9allpoCTT"" 63"36, 82 b 21 9.GCT91ll 86" 31

9.w" 26"20,64"37, 72b2l

., fll.ffpllXfI TO 9. n)v oll.'1" VCTIII 7",b 3 Ta 9"a a6"18 9f1OTQT'1 hrrCTTI,p.'1 983"5 TfiN IU"op.i"OJII 9.. oTaTo" 74 b 16 90iQJS flpqCT9al 74 b9 9.p./Alo. 13" 5 9.oAo"{.'" 983 b 29 900Ao"(I";' 26"19, 64 b 3 9.oll.6"(01 0"9, tlb27, 7Sb26, 91"34 9,6. 983 "6, 7 a 25, 29. 30 dpx.; TIS 983"8 TO ,,, d 9. Xen. 986ba4 ;, 9. Emp. 0"29 9.ol 997bIO, 74 b2 -9 9lpp.a"CTIS 67 b 12 9.pp.allTII<6s aob 29 9'pp.a"TOS ao b 29 9.pp.os. TO 9. Parm. 987"1 TO 9. 70bl2 9'PPOT'1S 3 2b8 , ;14"26, a7 9lCTlsmath. 28Sb15, 16 b 26, 22"'3, b" ",2bI9, 7Zb3o,82"21, 85bU log. 3 2 " 7, 63 3 2, 8"'"9 90T6s 16 b 30 90OJp"" 1I'.pt TIIIOS 983" 3;1, 3 b 35. 4 b I, etc. Tf9,wP'1Tal l10PTI"Ws I b 14 5yn. l1l'lCT"o1I'"v 3"21, cf. 23 TO 3" UI)" 3"21, S"3, cf. 3 b 15 1I'.pt TI 27b28 II< ;",os 38 b 34 opp. l1l'ICTT";I'01" 48" 34, cr. SO"12, 14 TaS dllX4S 61b19. cr. 996b 25. 59" a", TO;; 9. ;"o&a ?1"28 9.",P'1J.IG 83b18. 90"13, b 28. 93 bl 5 9'OJp'1TI";' 9~3 b 20, E. I, 75" 2 T"'Of 982" 29. 9, S "16 1I'.pt TI 9.OJp'1TII<6s 5"35. 2sba6, 6 1b l l 9'OJpia 989~ 25: 993" 30, 5" 29. 61" 29 TO fj3ICTTO" I4"al, "0"" 51b24.72b21 9AoCTTU" 46" 25 9plIlI. ••" 12 b 14, 76" 28 9vpa 993 b S

<1'11&. <1>90"'''' TO 9. !i83"1

TOCTIS 9"21 IOTp.llupfJ'OS 19" 18 IOTpl,,6. 3bl-4, 60b;l3-61"S, 7°"3°, b 33 131a PInt. 987b8, A. 9, 31"31-b 16.

INDEX VERBORVM 39b12, 70·28, M. 1,4, 5, 83 b 3484·26,86·z6-b7,9Ib28,29 01 Tar I. alTIQf TlfUp.II0'J A'')'ollTfJ, etc. 990·

Itcup6r Pyth. 985 b 30, 990·23, 78b22 Ix" Tllld Ittup/w 43 b 25 ItClitOffa9.w 93 b 26 ltaltor. T3 It. O''1palllfl T3 ffOI':II ao b l3, cf. ib. 13 Ta Italto, T3 Italto" 51" 15-21, 7s b 7 "AdIU Ta It. Ten, a0ya9c,II 985. 2 Pyth. 986. 26 T3 It. 90T'POII Ten, IITOlX.[Q/II Acad. 75·

34,90·16,b20.~ObI4,39·25,73·19,

86.31, b14, 78 12 I. 'rWII ffp6r TI 990 b 16,79· U ob3.plall ItIT'" "plO'aO'llcu 4o • 8 XIU/Hcrr1ib.9, 86·33 ffaO'a pffJ'IITi, 40· 27 tta8oAolI 42. 15,86·33 coni. ap,9poi 76"20, 80 b I2 t 81 • 7, 90b 37 Td ptTa Tarl3EQf 80 25 -Tc\ O'xfipa Tfjr 1.29·4 f&or 990.18, lob a, 16, 64b22 r. "a91] 4bIl, 15,16 rIIr f. mrapx'''' 38b23 '"r0910'fIr, 30{cu 86" 10, 90b 29 IBI'1 42. 7 lalM 61 b 18 'IA,ar T9i O'IIII'X.iill 30b 9,cf. ·9, 45.13 I,.aTIOII 29b27-30·2, 45.26 -1""aO'Of 984. 7 "I""lUll 98+. 3 100a,fO'9a1 pass. 81· 25 1001iItlr fO'oll 93 b 13 IO'apl9por 93· 30 100axa.r 13.16, 54.14 IO'O')'Q/Illor 54 b a I1I0rA.llpoII 16· 3 I fllor def. 21· Il, 56· .'2, 82 b 7. trWr dvTlltflTal T9i ""oy6.A~, ltal T9i JUItP9i 1.5 TQ r. Plat. 75' .~3, 87 b s v. I. rUM caDte asseverantis 9h;'· 26, 995· 17,5.6,10, Isb33, a6·15 10001linAIr 16.31 1000Tf]r 4 b II, S4 b 3 ItIT"II 70b 25 i'tlTaO'9at 999b8, o~ 28,

7°·4

100Xval",," 48b 19, 27 100X"aula 13bl, 48b19, a9 100XVr &aA.ltTlq 78b a5

'ITaAlltol 987. 10, 31, 988. 26 '1IUIIEr 24·33 lta9".0'9at

41· [5, 16

lIa9tva.", 10 8

1ta90AoII disl. ')'Illor 992bU, 15ba8, a8 b

coni. lIaTa ..allTIU", 1t01llOll, o,,"'~ 999&20, 3.8, a3ba9 opp. 1t'l9' '_TOil, 'O'xaToII, ItGTa p'por, lrl pEpollr, O'TOIXfloll 0"1, 18b33, 71.28. 59ba6, 6ob3a, 84bl4 r6T'poll al dpxal 1ta96AoII 3· 7. 60 b 1923, 69.27. M. 10, cr.71·ao Ta It.ollit obO'icu 3.8, Z. 13, 53b16, 60 b 21, 87"a, cf. 69·a6, 27, 71·ao 1tG9' allTa blflipxfl I 7 b 35 def. a 3 b a9, 38b I I T9i It. al 13'IU O'II"arTOIIO'''' 42. I 5, 86· 32 h'O'TiIP'1 Tc", It. 59 b a6, 60 b aOt 87 ·17, cf. 999" 28, 3 ·13. 36" 28, 86 5 1tGI explicative 13&7, 20 b 3, 38&7,49& 9, 7 2b22 , 89 b 3. etc. 1t4111orp.11'O'TlpIUf 989 b 6 L U"·2 34

35, cr. ib. 37,84·35, 91b34 KaAAlar 981 "8, etc. KOAAI ....or nb 32 ltaAoIIsYII. a')'doll 13·H, 91.30 dist. aoya9uII 78. 31-b 5 ",a,IIop.lloII It., It. 72.28 Pyth.93bJ3 To} 1t00AIO'To.. p~ III apxii .1..41 72 b 32 Itllprr-q 40bl3 lt0p"T.III. 1I.ltapp''''1 ')'fJ4pp4 16· I2 ltapl1vAOII 986. 25 ltap'ItVAOTf]' 37 b 2 ItOpl/1U 16· 10

a..

ItO.II&w 998.3 Itapala 13·5, 35ba6, 44 bl 7

ltaTO T' A,,),.0'9a, 987 b9, 998 b8, 4· 19, 18.36 19· I2 -1<0.9' fItO.O'TOII. al ')'.II'1O'.1S ff.pl Tc\ 1tO.9' I. flO'III 981. 17 .fT. p~ 10''' T' "apel Ta It. r. 999.26, ct 60·3 TI 999 b 33 ff6T.po" al ap~l wr Ta 1ta9' 'ltaO'Ta 3 • 7, 71 • ao, 86 21 &YII ••II'p')'oma 14.21, cr. 13b36 lIaTa ~II af0'91]0'''' ffp6T.p4 18 b 33 p.QJ.AOII obO'ial 69.29 -ltd' 'T'POII, dAAo 13 b 7, 39 b 10,49.25 -1ta9' allTo 990b 21, aO·14-26, aa·24-36, a9b14, 16, 29t 30b 22, 31 • a8 II. abo 1tO.111p{j"a 31 13 -lta9' /I A. 18, 3a·2a T3 Itaf}' oil 7·34, 49.28 ltaTaAfAflppllla 74 b 2 ltaTaAA!JAM 41 • 33 v.!. ItO.Tap.Tp'w 23bls ltaTapfIII,a 44 • 35 ItaTavaAlO'It"" TI .fr T' 990· 3 SBY'GJfOE'"

53 b J

ItO.TaO'It.ua('III ,),'"'0'111, oilO'lar, etc. 984 b 25,60·18, 991ba8, 80 b l8 ItaTalb1U 7 b aI, I I b ao ltaTa.,.aO'IS dist. 40'1S 5 I b a4 ltannOpfW lr[ T",or 998 b I6, 24,999· 15 ItaTO TI"or 9~·20, 23 ti 3[, 60 b5 Ta lIaT'1')'OpoVpflltl 70b '. cf. 28·13 1tO.Tf]')'op11p.a a8· 33.53 b 19 ltaTf]')'opia 4.29, 18.38, 29·a2, b a3 , 32.15, 34b10, 47·34,65b8 68·8, 88·a3, 89·a7, b l4 O'xfjpa,O'X!J' paTa Tfjr It. 16 b 3:\: 17· 23. 24 b 13, 26.36, 5 1.35, 54 29 O'IIO'TO'Xia ,""II. 54"35, 5 R• 14 ltaTTIT'por 43 b a8, 54 b J2 itclTIU 992• 18, 994·[9

1

INDEX VERBORVM KCl;;O'or 981"u

lull""" C},,6I'1lTIl 4°"1 I

Itr ,w., tr'l-

I'("OJ" 47blO tr."oAo"(fi" 9~ I "31, 79 b 26 Dem. 985b5, 9"38 trl"6,,, '1'6 48 10 Acad. 84" 33 /led Itfnjt 1..1"(",, 99 3"38 Itfpd.WVafJo.< 42 b 29 1t,."aAtuO" 42 A 4 1t'
Ig

cr.

cr.

Z:

ItpaO'I' 42b16, 851>13 Parm.9b23 KpaT';Ao, 987"32,10"12 "piO'If Pyth. 99°"24 "",Tf,,,,o,, 63" 3 trPI""". Ite'n)" AllpSa...,II' 989"7 Kpo"o, 73 35 ItpvO'ToAAor 43"9 ",;SOI d",I/I'01 93" 7 It';ItAor 16 b 16, 36"1-18 ~ ltultAIfI 0pD. 72b9, cf. 71bU, 72"22 ,,"ItAoopiO'. 53" 28 ICtiAIO'IS 6j) b 19 v.l. ItVP"OS <)81 b II, 10 b 13, 20"4, b 14,48" 10, 55°32, 74b19 '1'0'. It• .,.;;' ovO'ill, 24" 24, cf. 35 b 25 ""plOl' 3 b 16, 15 b 12, 45 b 36, 48" 12 trIIplDlT/poJI50 b6 "wAv,,,, '1'",6, 49"9 AOpSo""" 13b7, 53b3, 53"37 /led Tijl I ..O'."fOJ'Yiir 25" 10 ",pi '1'1"01 53 b II .,.a O'TOIX,ill 69" 33 AdljlO'."O'. 74bU AI£ar 3b38 1..''''''0'1'0'1'0'' 982" I A,111t1 ....o198 S 4, 71b 33, 72"7 A,"tr6" 991" 15,63 b 36-30 exemJllum TO;; 0'1I,.S,S",,6'I'or 17"1~, 18, b 28, 39 b '7-3 0 "9, Z. 6, 37 15,44b2l\, 77 b 5-11,36 Aftt/!'" 18"34, 55"37 Ail/",or 33"7 Almp6" 44"33, 46"34 1..0"(("0'1/01 47 b 7 1..0"(,,,6, 5bU, 80"'0, 87b30,2' AOOYItrGn 39b13, 3°"35,41"38,69"38 AO"(10'1'6r 980 b 38 1..6"(or opp. lIIO"OIIl 9" 30, I I " 4 Ao.,ov XO"''' 9"31, II b 3,cf. 13"6 .,.p tfJOJVU A~or 9"U -A. IX'II' ~,,, 981 "15,9g6 9.6"13, 10"17 'I'oir A. O'ItNIf 987 b 3 I 01 II' '1'01; A6-yoll 50b3~, cf. 84b35 opp.
6."

4","

INDEX VERBORVM aiaiJ'1als 986b 19,32, 39bZO, 58b 10, 18, 6.'23, 704'~04 coni. .130r, fIOfHIWI 996b8, 36 5, .3'20, .2'28, 69 b34> 8.. b II opp. {/IIOJIG 6 b I, 30'7 A. Toil TI ~., fl.,OI, :"ijs oaial..Sl3'z7, 16'33, 2. b Z9, Z9b20, 31 • 11, III' 10, z8' 35 ~ /tGiTA T~II' A. oaiaiGl2!\b z8,;I;.b I3, 15,37'17. S.b II dist. 6p.a,,&s 30' I •• ;17 b 1 • ..I I., Tn;s A. ApXIll1 996' Z T4.1oS AoI-yo. ..i,. .. 70' 22 6 A. Tij. oaiaias fr. 9,28 b 11, 2. b 29 ~ alll'fxEiIf ~ Elilol ~ AuW 16b9 T4 b T';; A. b 23 23, 33'1, cr. 15b25 "lp'1 Ao')'ov Z. 10, II, cr. 16' 35 ol~a.\VfI" TO~S A. 63 b 18 Tf/ A. XOlplaTU., ',Z? coni. bla"';',,'1 ..6 b 7, 59 b 26 TEpa Aow, opp. oaiallf .9 b II, 77 J, cr. ISb32, 28'3Z, 38b27, 5.'28, 78'10 AoW, dpliJpf/ ,., 87ti12, cr. 8. b15 arithm. 985 b3Z, 991 b I 3, 17,19,993'17, Ib30, 53'16,61 b l, 92bI., 31 ...T4 T.)... A. 18b27 cr. d.,QAo')'o., Ao.30pl.. 13'10, 23' 30 Ao£els tWltAor 71 ' 16 Ao£0ilaiJ..1 73 b 20, 29

51 5

" ... iJ&.,,,., 980b 23, 2. JIG.,6., 985 ti II, 992 b5 pGpTvpo. l..-4,)"a/J11I 995' 8 """"'PEW 69' 25 6 Ao,),or JIG,,"pE; 87 b 3 ,.4)('1'. A0130pl..s 13 '9, 23' 30 ,.4')'11 ...1 JIolltp6., 20'23 Plat. 987b20, 988'z6. 998blOt 83b2., 32, 87 b8 16, 88'16, 90 37. 21'10 TU lI...flpo" I. " ....1". 987 26 Plltpa" 1t..1 ,,1')'11 99z' u ,ra., TOil IA. Ital Toil p. 85'9, 13, cr. 992'13 - ..oils ol.,TlItElTI1I Tel raw Tf/ ". n2 Tf/ 1'. 1. 5 "E')'BAo"lpEl" 989' 6 Mo.,,,,...ol 46 b29 Pf')'f'or990'26, 20'9, 11,53"18,25, 83 bl 3 "f,.ItTOS 990b28, 4°'27,79'25 p"otll Plat. 987bg-I., 21, 45b8, 8l' 17 ,ll1l11 ...T4 ". 31bl8, 45'18 ,,19030r 983'Z3, b., 984'z8, 76'9, 86' 24, 91' 20 "oA...,E.. 20 b 10 ,.,A'Ta., 50' ,.,AEltp..TO., 4Z 17, 92 b 29 MIAlaaor 986 b 19 p/AITT.. 980b 23 pfAo..-o.ta 993 b 15 AII~QlI'.5bIO 1'1" omiuum 981 b 9 ,.4., concessive Ava" 995' 29 ,,~., 0;., in apodosi 983'23 46b 18 AOl/3iialJal 63' 2 AMrIO., '"' I,.4Tloll 6 b26 T4 pfpl3as 82 b 36 "E,..apar d#TI!/>l&afOlf 27 b 20, n MO')'CH 91blO ,,'PltITO., 2.' 13 ,,'por ..oaGl~oiIr A., 25, 3.b32 opp. pDl/fJIGTI1 98Sb2., 992'32, 996"Z9, &Ao., 993 6 Tel at.,.IO" Toil "CH'W • '9,77 b18 ~ • ., ToCS ". olppo.,ltt; ..poiITo., ,.. 3. ' 26 p. TOO AcI-yov, 997bU 1.1a.".26'9 JI49r1p.. TI.6. 997b2, 61'28,77'9,80' Toil ffpG.,JlGTOS Z. 10J I I ." "'Pfl 989b 12, 3" 22 K ..T.. ,upos 5"29 36 IiA'I lA4tJ.,JA ..TI/tOlTfpa 99z b 2 .,.6 ...1 plpovs 84b I . olpl,,,ar 1'. M. 6, 86' 5, cr. 76' 20 plao., TI 294 '11-19 Mol plaw 61' ~ p. 26'7-26, 61b32, 6.'32, d. 21, 63til9 pi".,. flipEall 996b" 981b23, 78'33 ~,.. IXfl ..I pla..1 93' z9 4' 7 "'OI'lTlttlill dist. 1'. 'lIIaTijJAI1I 64' I, cr. 78' 33 .,.a 1'. JAETa£V JllT4 T..iIT.. IITI69b3S, 70'. pOT ../34UfI., TCHf ...U.al 983 b10 ....,.a Plat. 987 b 15, 99z b 16,995 b I 7,2 b I., Tel ...oaO." ...010., 10' 23 Pf"'GI£~ 28 b zo, 59b6, 69'35 opp. T4 T..UT ..
,u..

.z"'r.-

Ii

",,u. •..

"'pq

o

INDEX VERBORVM

5 16

I'fT09f(lfPEIJI l .. b 3, ao'2S, 21b17. a6 p.ETaOpal "ol.".lttal 991'22, 79ba6 p.fTa,/>opf 15' II, a 4 • 8 ltaT4 p.ETa~p&. 19 b 33, aJb a9 P.ETawlU Emp. 9 b ao p.ETIX"" 990b30-991'3, 37bI8, 7S b 19, ao, 8a'18 T4p.ETlxoIITa991· 14, bS, 79 bl8 ",ETlllllU IllTEli9EII 41 • 10 "fpl TI .... b.. "'ETOX~. ltaT4 ",ETOrill 30' 13 "'ETPEW 983'17,53'33 ",.TprJTor 98~·ao. aJ 'a9, s6 b aa v.l. ",ETp'OrrEPO" 987' 10 v.l. ",ITpo" Tc) I" 52b18. 7a·33. 87 b 33 up'fJir 5a b 36 trvy'fE"ls 53' a5 d&alpETOII 88' a '''I(I~''''1 ",. TWv "pa"rIolBT"'" 53'31, 57'9 "OllT"'" ",. 1/.119p"'11or Prot. 53' 36, 62 b I .., cf. 19,63' .. ",IXp' "pOI a8 b 26 ",;;ItOS ao'la p.'1MEIII 83 b6 "''1Ti,E(l9al Parm. 98.. b a7 ",;;Tlr Emp. 9 b 19 "''1XIUIfi XPi;(l9al 985' I 8 "''1)(fJJ'Itr/] 78' 16 111-"''''11. Anax. la'a8 Emp. 69baa, 75 b ",9 ab 7 ",i"r"lIt19lU 989 b a. ..a b a9 01 p.EIIl"rp.fllOI 91 b8 IIlItpoAo-rit1. 995' 10 IIlltpop.Epl(lTaTo" 989' I

I..

IIlItP"'" v. p.l"ra IIlltpOTflS Anax. 56 b 30 p.l"''1f1t1. 9 88 ' 7 p.lp.'1(1/s P)'th. 987 b II, 13

",,£IS 989b .. , .. 3'13. 82'21, 85bll,

9 2'2"

",",1''1 980 ' a9, b 25. a6, a8, a9 p."'1p.O"EV,," 980 b a 2

p.olla/liltol dpl9p.ol 80 b 19, 30, 82 b6, 83bl7,9abao ",OliOS def. 16ba5, 30. 84ba6, 89 b 35 (lTI"rp.ij IJ.9ETor 8.. b 26, cf. 69' u flo dflOfllIE&s 991 b 24 ",. a.o~pOI, d(lVp.fJA'ITOI 9~2' 3. M. 6-8 Tlr p.OllQllOS IIlaOpa 83' a fIOJlaX"s ,,0'29, 76b'a9 p.ollaxii 16 b 26 p.ollax;;'s 99S h'15. 997'3~, 1a'29

",r,,,..,, 7.. • ..

P.0PVXWTfPOII 91;7'10 p.op~ coni. .100s 999 b 16. Ii' 5, 17 b

as, a9'3, 33 b6 .... ba3 , 52 aa, 60' u, b 26 coni. Ao"'(os .. a' a9 coni. Ill'P"rfia ..3'26, 28, 31 ~ flo TfAor I(lTt 23' 3.. ~ l(lxoTflIlA'I ttal ~ ",. b TauTo ..5 18 I'0V(lIIt(,S. exemplum TOV (lVI'fJEfJ'IItOTOI ISbI7-3I, 17'8·-17, ba8-I8' 3. a6bl7-ao, 31'a7, ba3, 6 .. b a3-a6 p.v"" ..8 b a I'v911t;;'s 0'18. 7.. b.. p.li90s 98a b 19. 7.. b I I'v9wlI'Is ~9S'" ",vp'a 88 II I'Vp'OItIl 7'16

Jlai 3.. '17. ,...bI6, 19 JlaVTaI 23',6 IIEOTfl 93 b 3 v. I. IIEiltos Emp. 99.. '7. 0·a7. 7a'6, 7S b 7 IIfltTap o· 12, 17 Nfl'Ea 18 b l8 IIf01987'3 2 II'111fp.ia ..3· U II~TfI 18 b 28, 57'a3 ~tf>"'" 98.. b1 7 IIoEi" 990bl ... 99.. ba3, 2", a6,6 b ro, 3 ab6 ,8 110'11'11. 990baS, 79'21 ParDI.9b25 110'1(111 16 b l opp. 110£'1(111 32bl5 dist. afa9f1(11S 36'6 coni. Ao-ros 5a' 30, b I. 75' 3, cf. 991 b 27 dist. II0VS A. 9, cr. 51' 30 II0~(lE"" IIO'l(l1S 7.. 3..

t'

V0'lTIItOll 5 a • 3 1I000TOS opp. 11.1(19.".01 990' 31, 999 b 2,

36'3.

10,

.. 3b30,

..5'3... 70b7

IIOf1TOII dist. lIcallOflTOII 12' 2 dist. OpEltTOII 7a'26 Tc) "pOrrOll II. ib. a7

",ETaA'II/I" TOV ". b a0 IIoflOl 995· ... Hb 5 "oflOv XOp'II 76' a7 h II0(lOS a7 10,68'22, 26 JIOvp.'1" la a7' as II0VS 70' a6, A. 7, 9 II., ttal ."VI1IS 99a • 30 Tijr ~p.ETlpas !/Nx;;s
INDEX VERBORVM E,

IIl1l'rpo1~la 93 & ~o Ea~96s 5.. b!3

EE'IIIto,TEptJ coni. d.,lIOWToT'pa 995 &3 S•• o."Ii~'1s 986b 31, 10&6 EWli~al TI ftw 611T01J1 5 b 15

"1'B.·IIlIpla 6 b I Q

U~IIIlOS 9901i6, 991&6, 34&U, f,sba5. ~9&14,86b27 6/lAWvl'GIs A'YEII90. 3&34> 30 &3 2 ,46&6, 60 b 33 ii~o,..a, coni. A6'Y0' 6 b a, 30&9 0pp • ."pii'Yl'G

;;.,"'OS 85&13, 89bl" /Ill. 990b8, 997b30, I .. &U T61l. syn. oVilla 38b 34, 69 b 11,89&11, b32 TollE 1'1 I b 32, 17 ti25, 29&28,3°.4, 39830, 32, b 4, 42827, 2<), 49 8 3.5, 70& 10, 13, etc. To8. l~ Tw8. 30 b IS, 36 b 23 d8t 9BI 'sa, QQOb I

1l1l0,,0I.j Tel ""'&"II'G 984 &18 dllels fls OVilla. 3 b 7 ./. ilAA'IAa 55 &7 "pcl61l0u 44 &a.. o/",.ior Ao,.os ~4 b33 0/"'."' mi9'1 TOU 'Yi.alls 58 &37, b U o/",ElOlS Ai'Y.1I911l 14&7 oltda 26 b6, 7°&14, 75&'9 .. clvEII ilA'Is 70&16 0/",01l6I'fJOls 50&37-33, 65 b 19,66&3,6 o/Noll0l""'" a6 b 10, 50&~6, 70b2 9, 33 0/",01l0"",,,611 49 b 14 o/",oll0l'0s 14&~3, 25, 26b37 olo~ explicative 18b1S,17, 33&34, 5S b a8, 70ba3, 71&4, 78b3 O"'TeiS 8~&30 l>Ai.,oll 1.6 OA''''';T'IS 984 &I 0, ~6 b 30 oAo~ 993b6, 13 n, 2.. &12, S~aa2. 69&19 "OI1axws A. 26 dist. fla" a.. &3 = "'Oll/,OS 75& II syn. lIu"oAoII 84 b II oAGls 990 b I 7, I 3 & ~9, 31,14&2, II, u, 18 a ll 5yn. N:a90AolI 98ab6, ~3b~9, 29b6, 33 b a6,71&~3

6AoT'I' ~ 3 b 36 6I'GAos 78 &13, 93 b 30 dl'aAoT'IS 3~ b 7, 43 & 26 dl'aAu~E'~ 33 b 19 '01''1",'''01 93 & 27 ·OI''1POS 9 b 28 citatur 76&4 01'''"' 980 &24 ul'0'YE"f,s 981 b26, 5t b29 ullO.IIl;'s 991b24, ~ 16. ~l, 13b31, 14& 30, 24 b8, 33&2 .. ,67&9, 71&17 UI'OI0l'fP;'S 984 &14 Ol'o,o~ .8&15, 21&11, 54 b 3 .. ~iiluiS TOU 6. Tq. 6. ob6 1l1'0IOTpO"GIS 3 b4, 8&10 lillOlwl'GTa 985b~7 oIlOAo.,.j~ 4~&6,

69&31 .bplll"'EIP Til 01'0Ao.,ovl'00" 985&23, cr. 991bZ7 uIlOAo-,olll'i"GlS 989&3, o&as 61'0llE (lall/'E." 89& 3 UI'OTpUflGlS a3 &a4 61'01) "a~Ta !mllx. 7 b ~6, 69 b ~I, 23, 29, 71 b 38, 7a&20

6 b aa

~~O,.aCEIJ9aI

',,1

TIIII Emp. 15 &2 6EllrliT'I 93 b 3 b Olf.p I&~6, 3 33, u&~8, 30&3.9IbZ5, etc. a"IIlIlGl Emp. 0& 30 UlfOIlOIlOW 52 b 29 6"OTEOU~ 49 &I 1l,,/nEPOil ITIIX.II al&7, cr. ai&Ii', b1 3 • 65&13 .!frTI"'" 997b20, 78&14 Ttl a. 77&5 6pa.980&a5 /llrGlfla Emp. ob7 Ilpalllf 50& 24 OpaTIN:O. 49 b 15 iiplallo~ opp. 'nOlI 13 b 3 api-yE1I911l 980 &21, 7a &39 aPENT6" 72 & 26 6PfEIs 48&11,71&3 ap9l, ('YGI"la) 36&18-21 dplCEW 3 &6 d",9,.q. dipllIl'i"o. l b 18, Tel ';'PIIIl'fI'OII 78 b I cr. 6 b I, 4 dpl'ElI9oc coni. TI itITl", oilllia, ",a86AOIl 987&al, a6&4, 64&U, 78b18, a8 :Iliall ovllf,.ta" IIlTI.6",1I11118a. 4°& 8 - di",lIl'i~Qls ~o b 33 tJ",II,.oS 3°&7, 31&1, Z. 10-13 'E tJ. IlUJAEN:Tio" 12 b 7, cr. &3, ". 2Z sy". Til TI ~~ El"... 3°&7, 31&13, ",,&1 dist. A6'Yos 30&16, 37 b J2 TW~ ",a8' '",aIlTa, TiiI~ aI1l8'1TW~ 36 &5, 39 b '18 TOU ",..90Aoll 36&38, cf. 987b3 /Jea TI Els Z. u, H. 6 &I N:aTQ Tas Il&IIlPfllECS 37 ba8 6. '''IIIT'II'O~I ",oS ;l9b32 6 6. d",8,.os TIS 43 b 34, cr. 45&7 Soc. 86b3 U",IITI",elS Ao,.o. 43 b31 d",IIT6s 998 b6 IIp'''Of 983b31 Emp.Ob 16 tJPl'iJ a3al8, a3 6. IMI "'poalpEII.s 15&27, cr. ba coni. ."UIIIS 23&9 opos 92b9 5yn. 6",II,.os 30&S, 38& ~I, 39&~0, 43&u, b~6, a9, 46&15, 49&5, 5Zb 9. 55 &33 ",owels 6. 987 b6 Tw" ."pels 6pD1f 4°&6 opp. ba.,orri, Tel d~.iA.o.,o~ IIwOpii~ 48 &

ov

36

ullaX&i. 17&~3 ullaxwlI"Ep 18&5 aIlTOU~ Emp. 993&17 UTI opp. 1l&6TI 98 I &29, b 13 N:al Tel El~ 41 &J 5 obUs 42 b 19 ouAol'iA.la 93 b4 oli" in apodosi 983 &33, 2 b 25. OVpIi"lll, Tel 75 b ~6

T.) aTI

~7 b a8

INDEX VERBORVM ''&'0' ..oeraxlil, A. 21 Opp. ouer... 983b10, 98SbIl, 989b3, 2&2, 38b 28, 71 &2 d(M8pGJII ... 98Sb29, cf.

ri.., ..u (l'"

~&27

IS b34,20&19

986&17,

coni. erlJp/J./J""6,, "t""er~2.!gb3, 30&14, 71&2 "a" b alrrcl:"":t 4 6, Ig&l, 30b19, 31, cr. 997&7, JI,90&30 oll<.i'a, i'ala 58&37, 32, 78&7, 16 0pp. ""0".1"."0" 4g&'9 1',""'/JoA~ Tel ... 6g b u ..tIlaapc4J3", 995 &5

t

un

wGAcu 01 6g& 2g rral';J;.tIlOI 983 b 28, 74 b I ..a" dist. 610.011, trei".,.,. 24&1-10 Tel rill 69&19, 73&,29, 76&1 trG"lI trGIITGIr 10 & 9 treillTOII 10&9, 3S b'4, 36bao, 48&18 rrapcl TaiiTa Ai'Perllll g87 8 rrapcl TV ..A.vp6.11 5 I &26 npa(JoA.{,36bz4 rrap6."I'1I111l 33 & 17 np6.5""I"a 13&27 Plat. 9gl&21 27, 2g, 31.1gb2S, 31• 33, 35 rrapa8f1"1paTIItfIIr 99s &7 _p6.Bolor 12&18

fftlpal
rrapav'Tf/ 18 b z8 rrapa..A,erIOII lIIerrr.p 78 b34 rrapa..A"erIOl' 985 b 20 rrapallTOT", 18 b'7 rrapa~poII.", 9b6, 31 treipE"I"lIJ' 40 b II ..ap.''''''.111 9' & 12 npll<(Jaerlf 89 b4 rrap.AtlAaTaI Emp. 0 b 16 v.I. IftlpIAI
T",6,

INDEX VERBORVl\f "OllT«[as 76b 33 "E'R..aapaTw3fJs 81 b30,82 b3.85 &IS ""OTOS syn. h"~II•• a 20·12, I .. "A.aTTOW. "."A.da9aI986b8 "A.aTv Kol aTE"6,, Plat. 992.12, 88 b8 "A.aTvs oP"os Emp. Ob '5 DA..\T."" A. 6, 988.26, 990&30. A. 9, 996.6. 1·9, IO b 12. 19· ... 26 b '4, 28bl9, 53bI;\, 64b29, 7 Ib 32-7 2·3, 83.32 Pkaedo 991b3, 80·2

Hippias Minor 25"6

I"

""flaau 93· ""oo,,a(..11 T9/ A.o,,),'I' 994 b 18 "A.oo"axws I5 bI 3. 14 ,,>..rryds "aA.as Tuno", 985 ·'5 "A.fj90STi 20&8,10. H&22, 57&3 opp. uA.,,,),OT'IS. rll 98.. &10, 986&24, 4&10, 17,85·33, b5- 32 , 87b6, 8, 27-32. 91b3I,34,92&28.35 "'''pWTov85 b9 "A..)II 6.>..1.' #/981 &18 v.1. d~pu Dem. 985 b5. 9& 28 "A.'1polia9a.1 b"o l.xolas 988 &6 "A'Ialoll lOb 16 "A.w9i"'l0/"ia 33&19 ""i")'os 26 b 3.. "o/Jlaia 52b33, 78&20, 89&23

"oMT'Is 38 & '5 ,,09ill "0' 69 b 26 "o"i" dist. "pO.TTOW 25 b 2 2 ,,),lll'CTI" ,,010iCT9al ~ "(i"'(ll.a9al 988 b 31 "o''1a,,,...."0'' pass. 21 & 23 "0"'" ~ "aax.", 68&9. cr. 14. b 16 'fIoi'la .. dist. ,,),,",an 32&27 dist. ""'1CTIS b 10, 15 "OIf}TTis 982b32, 983b32 (v. I.). 995&8. 23&I9.9 Ib .. "OI'lTI".) '''laTTi,..'1 982.1, bll. 25b21. 25, 26b5 ...6b 3, 6,,&1, 75&1 TO "01'lTI"6,, 21 & 15 ... 8 & 6 "OI'lTO" 25b22 "016" l .. b 26, 28&12, 15, 83&11. 89b26 "oaaxws 1:1. 14, 68 b 18 01 dp19,..01 "0101 TI"" 20b 3 TO 'fl. T~S cL",a,..I,,'1s ~va.OIs 63 & 27 ,...Tapo".) KaTa TO ". 69bIO.cf.IO&23 lIaT.po" TO 'fl. Toli "oaoi/83 &I I "oulT"s 22 b I 5 ,,0A.IT.v.CT9al 76 & 3 'fIOA."OKIS T~S ~""pas 47& 10 "oA.A.a"AdalO" 20b 21: 2I &3 "oA.>"a,,"aalwa .. s 92 33 "oA."axws 9~2bI9. 3&33, 28&5. 10, 6o b32,6I 12,7 1&3 1,37. 89&7 'fIO"A.oaT",..tploII 20 b 28 'fI6"01 73 b 28, 31 "OA.VKa,.."TOS Parm. 9 b 23 DoA.6"AElTOS 13b35-I4&I5 'fIoA.lI"olpa"I'I Hom. 76&4 IfOA.';S. 'fIoMo TO ,,, laTtll 987 &27 Ta ". I'lat. b 10 "oA.v Kal l>A,")'oll Acad. 992&16, 87bl6, 88&18. 89b12 'fIoA.>..o opp. TO lv 1.3,6.75" 33 dist. 'fIoA.v 56bl5 cLs hI TO 'floAtS 25& 15, 18, 20, 26b30, 27&21-25, 64 b 35 ",,1011 Parm. 9 b 25 ''fI1 'fIA.lo" or"al 46. I "OP~WTfPO" 1,4"'" 'fToO'aKIS frOUO' 20 b 5 'fIoaaxws, TO 'fI.pl TOU 28&11. 52&16 'fIoaoll 'fIoaaxws 1:1. 13 opp. .Taos 999&3, 10&24, 16b23 ,,, KaTR TO 'fIoau" 14 b 25 'fI01I" TOU 'fl. 20& 19 "(,"("waIC.Tol ~ i,,1 ~ dp,9,..9/ 52 b 21 TO 'fl. T~S 6.op'aTolI cf>VCTOOlS 63&28 ,..
"OCTO"OIU" 83 &'3 • 'fIoTI 993 b 29, !i2 &5 "UTOPO", III 6."T.91ao, 55 b 32, cr. 56& 18 110T'p"'S 75& I I "ov. ,..oTaPoA..) ItOTa TU 69 b 10 11pa")'pa ",.liaos 24 b I 7-2" "po"),,..ania 987"30. 59bI8 "pa'Y,..aTovoa901 987 b 2, 989 b 33, 995 b 32. 25 bI 7,64&3

INDEX VERBORVl\I

5 20

"paKTI,,6s 981 b5 .,. ,.,.,nftp'l 993 b ai, asbal, as, 26bS "'(KI."r611 as b a 3, a4, 59 &36 .,pO£lf .,f,x T,) "ai' hlllTTOII 981&17 dist. "III'IITIS 48 b aI .,paTTflll a3 &18 dist. .,Olf'" as baa .,PflTfJ,$TIITOII 983 b33 ."po.1-Yflll 98s b a4 .,polllpflTlS 4b2S, Is&a7, aobas ~.,. clpx;', "';".011 13&21, 18baS, 48&11 dist. Opf(IS 48&11 .,POIlIPfTI,,6f a &3 ",polllpfT611 as 24 flpOllrrOp!", 99~ b 2 "POllIT"flll 993 14 "PO"(f-Yfll,,1T9111 70 &21 "P01I,,(""'IT"flll 99a b31 "p030(.1,.", JI b 6 "po.13illlll 992 b 27 "pof"fnf,,, 47 b33 "pofrr11TTG1T9111 5 bS .,polpX'1T9111 990b6 , 995&33, 91&35 "poi'IIIal .Is 11.,.lpOll 60& 36 .,po"01,...,,os 989 b a8 "po1..a.,..fJ.1ll.III 50 b S "po"'1>"II"I,.", 996 &33 .,p6s TI 6. 15, 56b3~ 35, 57&S, 16,68& 1I,70b3,88&al- 2, 89ti6, 14 TW" .,pos TI 13/111 ?90bI6, 79&12 0PP, TO "119' IIUTO 990 b 20 T,) fI pOS TI fl"IITTII "'DITIS Tlf 88 &23, 30, cr. 990 b 20 flpOS ill 3 &33, 30b 3 flpas 11>..>"'1>"11 11&1 .,poaa"(flll /o1lJ91..wr 74 b4 flPOITII-Y0Pf,$.", 996 b I ° flpolTa.,0"plllfIT9111 7 &19 fI POITllflOIIlllfIT9111 89 b 16 "pOlTanflll Tl TI~I 83 b IS, 91 b33 flpolryl"(11.,,9111 49 & 10 "polT-y>..lX.1J9111 986 &7, 90 b31 flPOu3fllT9tu 55 & 15 "pou3lopl'.1T9111 5b 21, a 7, 48 &17 "'POlTfi'llal 29 b 19 "POlTffllTl9illlll Q87 &IS "POIT'I/t611TOJf 58 & aa "pOlT9flTlf logice 3 b31 I" "poIT9ilT.0JS 98a&a7, a9b30, Z. fI, 77blO math. 994b30, 66 b I, 8I b l ... , 9 2b 31 "poIT/tIlT'!'Y0p''''9a1 54 &I 6 flpGlT/tfllT9tu a9 b .H ",pOlT>"II,..fJall.III 82 b 35 flPOITT,9illlll I b8, 12, 16, 30"33 flpoIT",iPflT9a, 63" a9

e

flPOITOpa 0&14

"polT."vfIT9111 14 b ~I "pOTIIITIS 996b31, Sb a8, 78&ao, 89&25 "pOTfPO~ /tai ~11T,poII ..oallXws 6. II -Yfll41T.. , ",VlTfl 989&16, cr. 5°&5, 77& a7 /tIlTa rc)" >..&-yo", n}II a11T",ITIII 18 b33 /tllrei ",,$ITIII ttcU OVIT£II"

19 &a r~ .TIIIII l1"fl/ cLUft>..0111 34 b 3a >..6,,(9', xpO"9'. -y."ilTf' 38b2 7 A6-y9', oval", XpO"9' 49 bII 1.6"(9' S4"a9, 78 "9, cr. 3S bS oVITI" 77" a7 A6-y9', OUIT;" 77 b I III oTs r,) ... /tal ~. 999&6 tl".9,..o" Ixo"Ta r,) fI, /till ~. 80 b Ia ."poripOJS 1.1-Y'1T9a, 13 b 31 - .,piilro", rl 3 b 16, 3°&1°, 3t b 3 .... IIlrlll 983& as, cr. 98a b a, ~ 16 I( o~ -yi-Y"fTaI ...,.&1rOl/983 '9,989&1,998&23, as, 13"4, b 7, 14"a6, sa l4 "'. 111.'1 IS&7, 44&18, 49&25, cr. 16"ao syn. ,.lJplOJs 15&13, bll, aO&5, b I4 , cr. 46"16 fI, floAAIIXWs as"3a syn. 1r,lTa"ru 982 b II, 983 b6 fl. dpI9poI987b34,S2&8 ...p&rrOJSl6 b 8, 18b4, 22&3, 17, 28&3°, 3°&22, 2~, b5, 31"13, 49bl3 "'POV...aPXflll 9" 26 "'PoVP'Y01/ 983 b 4 "'pOXfIPOS 98abI3, 54b12 fiPOJTII"(6(K1.s 998&3, 7b22, r. 5, 47&6, 53&35, K. 6 "pOrrllTrOS Parm. 984 b 26 'WTWITU 89&27

fil/9a-y6paf 986 &\0 v. 1. fi1J9a-y6Cf101 985 a.~-986b8, 987&1327, II, 23, 31, 989b29-9go&32, 996&6, 1&10, 36b 18, 53 b 12, 72 b31, 78bal, 80 b 16, 31, 83b8-19, 90&203S, 91&13 fIU,.",)II nl pa"Oll 985 b II ,,1/,,"ow9al 4a b28 ..lip 984&7, 989&a, 1"15,67&5,7°"19 .,vplllOS 6 d;'p 49 & a6 frIIppOS 54 b 13 fiW>"Of 981&4 h9v,..OJs 114>
a

fmrIt sa ba9 ""'pl(fl" 7S b u "1/9,..os 87b36 "IIITPOS Atom. 985 b 15, 16, 42 b 14 lTaillfl" n}II 'II/X;'II go &37 1T.1p( 993 &19, ao, 7°"19 IT.>";',,'I nbl7, 22, 36, 74&la ITfPIIOS 74 b 18

INDEX VERBORVl\l tIT/,.uUrflr 1ta.8' ~r6s, fr 6 b 14 tlT/J1fio~ 980.21,981 b7, 998.6 lIi'(J1a 93· 24 II1J1ci~dist.ltoi)'01' 25b31-26·I,Z.5, 10 IIIJ1~ dist. 1t00"6itJS Z. 5, 37· 31 ~IJlQI"i3'1r 982 b30, 91.7 IIlti"os 16·u, 12 IIltblallJla 43· 32 IIltffItJlITlltOS 4i&16 IIltblTftTtJat 28 15, 29b25, 76·u 1I1t.IJO.I1T4 13 b 18 IIltl",1I TevUS 986 b 13, 989 b 29 flfpi TII'OS 992b9, ~·32, bl, etc. nTfpO" 76·10 lBia 73.18 I} i" Tois "0'Y0lr II. 987 b 32 IIltla'Ypllcpill 24 b 23 lI1
fIf,.

IIltU!OS 986. 26, 53 b31

IIltll ..llt' 996.34 IIJ111 993·5 v.I. 1I0.ill A. I, 2, 996b9. Sb l • 59.18-3.... 60·10, 61b33, 75b20 1I0000ilJl 995 12 1I0."i'fafJa.I J11191ltiils 0·18 1I0III,.q. 996.32, 4 b 17, 26 b 15 1I0000IIITlltl, 4 b 18, 23, 26 Plat. rrEpl Te) J1~ 8" 26 b 14 II. IAf'(Xo, 32 ·6, 49 b 33 ~OOIr"ijS 15· 30 110<1alS, i"a"TluT'IS, Td "pUs '1'1 ~5·33-bz9, cf. 4aU IIT'P'l""I<~ d,,6<111" 56· 17, 24 IIT'P'lTIlt;;'. ib. 29 IITI'YJI;' 992 ·19, 2 &32. b4, 16 b 26... a 8, Gob 18, Gg·I2, 76b6-3S, 84b26, 27,85.32, b27 - 31 IITOIX.io" = Iittera 993.10,23.36. 34 b 26, 27, 35.11, 14, 41b13, 86 b z3-

e

5 21

32,87.8 = elementum 985&25, 986b7, 9, 989.4, 6, 31, 99~bI8. 993·9,1·18,S9b23,84bI5,86b2C-87·5, 88 b 3, 15-32 coni. df'x;', afTlo" Q83 b 10. 989beo, 99Sbz8, 998 • u, zs"s, 42.5, 59 z3, 69. 26, 70· 34-bI6, 71·ZS, 86.22,87. 2,9 1.31 dist.dl'Xlj41 b31.70bU-26,87b 13- 1S. TW", 3.a"eap.p.d~w" 998 & 26 "OTf~" awal''' .IIT. Ta II. 2 b 33 flOllaxws .:I. 3 u. TfTTapa Emp. 985& 32, cf. 998&31 TW" .law" UTO'X.ia Plat. Q87 b 19 IITOIX.IQl4illTaTO" 9 88b 35 1IT0i)cos 92 b 34 IIToXa'.II(Ja.I 27· 3 IITp4T'IIJ1a 75· 13 IITpa T'I-yOS 75 a 14 IITplE1I9al flfpi '1'1 4 b lZ I" '1'""" 93 • 9 IITPO'Y'YuAo", TO 70a 3 IITPO'Y'YIIA~s 35 • 14 ~T"t 983b32 1I11'Y'Y'"ljS995 b 12, 47b31, S3·Z4, 76 "18 IIl1ylt.ia91Jl opp. 3JlJIIfjllb Zb 2, 27 b 21, 51 b 2-19, 34, 35 lit TI"O~ 57 b33, 70b6 I} 1I.,.,1t'"I'I,,'1 06111a 54 b5 lI.,.,ltdpfrG opp. M".9fTII 76 b 18 III1'YIaA.IJlOW 52" I 7 1I.,.,.,."fl" 984".0,985"24, 26. 989".6 lIuyltP'1I1S 984.15, 988b3z, 35 IIII'Yltp'TUle)" XpiilPII 57 b9, 10. 19 IIl1ltO."a,,'l'7jS 21 b 18, zo III1A"a/J1, 23"36, 34b26. 27, 35"10, 15,16, 41bU, 86ti23-30, 87.10 III1A"ap/Ja.,"" 998b28, 35"28,34, 37 b 3I Te) IIWfIA'IPJlf"O" 25 b32, 35· 23,25,36.27, nbs, 58bZ 1111"'1A'IPpi,,'1 T~ BflrTllt~ 55 b 8 1I11""o,(iCfll(Ja.1 med. 42" 3 pass. 22· 21

1I11""0'YIIIJ!6. 990b 10, 79&6 II. "pWTOI 14 b 2 ilt ToV TE 111'1'1" 01 II. 34· 3z, 78b2 4 I1IIJI/Jai.fl" = con venire 83 b 4 = evenire 98zb22, 988.. = concludi posse 987·z7. 989.22, bl, 16, 990 b 19, 991hZ4' 998"9, 17, Ob 3• 2ti31. 4Z "12, 56 b 5 -1I11p./JE/J'II
INDEX VERBORVM 31 b 23 ovll.,J,. itlTi "',pi a!'IT.) 9(OIp[a a6 b 3, ee. 64b31, 65&4 TClVTel l
59&a

tlllp/ltiAA.tl9at TIl'l 991 &9, 76& 2, 79 b 13 tlllp/lA"Tul p.ovallE. M. 6 tlllp/l6AtJUJ. 995 &I I tllIP.,.l.fllf 77 & 24 tlllp.p.fTptu 4 b II, 711 b I tlUP.P.'TPOS 13&33. 19b2." 24 b ao alJp.."lpatlJIG 13 b 20 alJP..,,[7rT'1 (vA~. 26 b 13 tllI,.."A'''ftl9a1 7ba, 14&13, 19, 6ab5,

63 ba 3

tlllp.."A", a7b29, 65&n aolP.7rTOI,.,. 93 b 17 tllIJlll>Gllal 993&23, u&I9 tllI/J4ItS.I •• tllI"""'I>"I
a8 tlUJI'I>IIt1lf 14bU, 4ObI5, 69&13, 70&Il tlUJl'l>IITO. 993 &I b OIl/4I(>",,,,a def. 43&10, 92 b 14,cf. 991 tlllptIIlII'lal 93 - 20

."

m

tlwG1'11If 991&18, Ob U , 42&3, 79bn awu9pol,.a9a1 99:1 b 3 aw,.I.,lov 15&21, b 3 all"""f19,u.a91Jl 63 & 21 a_p.""'T'poV 62 b 4 IIwap.'I>01, T6 43 & U aw,.IIa1'"'.I. 084 & 19 alJlllJllalpEW 59" 30, 38, 60& I aw,,"'6'f>aal. 56 & 35 IrIlVaftT.1If 27b32 Tllfl 42&16 "'pU' TI 46bU, 78bIO (Ir Tu!'IT6 86&35 awapp.6TTfllf 986 b 1 3 aWOJ/Ils 6g & 9 auvIJlapo. 45 b I 1 fr. alJlfllfal"ll &13 awlll,.p9p0liv 989b5 allvIJVIJ'clplVO. 31 &6,43&4 awll.llvaa· pl.a 30bl6

aWf1'1'I/f a b 3 a all•• llpEWIV Tfj A6oy.,. ~87 &2 awdpfllf 995& 10,90 30, 93 ba 7 aliI" upa,.l." ."ptz1'PUTlla. 986&7 tIII.'X.la 16b9, IS, 50b26 tIW'XflV 23&U tIW'XfS I4b25, 16&1," 5, 69&1\-11 'l>ua.l, /JE" drA&is, etc. 16&4, 23b32, 40b1S, 5a&I9 i",' Iv, i."j Iluo 20& II, 61 &33, b 24 Tel a. Tils v~a.OIS 74b29 au""" 995 &3 a{;.9,alc fonuae et materiae '3bU, 45 b II elementorum 14 D ~7, 4a b 16, 43&I3,9a&a6 subiechet pre· dieali a7b19,67b26 aW9ETov

ilf Tt;r 1111.", Ifai Til. 1'0".,..'

a3& 31t d. 75&8 a. ovala 43& 30, cr. 57 27 '1I'r1 Iful lfaTel Nt GAAIls nTnoptUf auv9fTCl 29ba3 opp.

aTolx.iov 70b8, 88 b IS

tIIIV"T';

23 b2 ,S7 b2 7 allV•••,.1 'allToli 6a & 35 0Ilv[aTatl9lJl, a"",aT,,"'V,.I. al,.,.9",.,.TI t

VIi

awollos 33 17 v.l. aol"oAos 35 &6, bIll, 29 a. owla 33 b 17,37&26,30,32 Te) a. 99S b i\5, 99t32, 29&5, 3~&n, b H , 36 &2, 39 20, 601i24, 77b8 aWfJpav 984b2 Tel cI.ciA070. 48&37 alJlfollala. 45 b 9, 13 aWT"TT.I" 75&16,19 ,t1WTEivflv ."prSs TI SO &a 3, 74& 18 tlWTI9f",., 12&4, 24b19, 51bl0 aUvTOPOS 41 &ao aWT0l'OI. g88&18 aw&J.llp.of 987b10, 993b25, 6 18 il< tlIJIfOJlfUP.OIl 1'1"¥"fTal owlu 70&5 avaTolxl,. 986&23, 4bZ7, s.b 35 , 58&13 .O"T~ I} 'T'pa a. 72&31, 35 a. Toli "aAafi 93bJ2 a.",.ipa 33&30, b1 4 , 34bU, 35&32 aaiPlll T&iv "tlTpOII' A. 8 axijJIG -= /Jllap.Os Atom. 985 b 14, 42 b 14, 19 math. 999&9, 2&21, 70&a3 ,."[.,,,Ilov, .j,96oypap.p.o., Tpl1'OJIfo. 24 b I, 54 & 3, g2 b 12 .,ailTaI' a. "9i uals988ba3 tlNpflltll' 76 b 29 tlOIprSS 401.9, 41bU, 44& .. , 45&9, s,.b 22 aOlTf1pta 9 J b 18 TritlS 984bI7, 985 b14, Ubi, 42bI5, 78 blOt." ltIT•• iv .,p ota[, 38& 33

ordomundi 75&13-IS,b2S Taparlli6 & 2

•

TaIlT6.,,,. 18& 7 T"XO. /Je"T6. !j,2 ba7 TI " • 31994 18

TIAflO,.lVOIO XprS.OIO Emp. 0 b15 T'A.IO" deC. 23 &34, 55 &II ."oa,.X&is

INDEX VERBORVl\I .6. 16 T. » 3••as Pyth. 986.8 l'lnt. 84.32 .,fKJ,.,.yt T. 16"17 TO T. I" ToCS ,. Tiiill dpX;;'" Pyth. Speu&. 72" 34, cr. 9 2·13 T.AdIllS 21"27 T.Alllls62"z7 T.A.l_ls 2I b 20 T.A.IITGUw. tis ~ """p'TCU T. 983 b9 , 11.0.",,'"0" T. ."pOs TO ct. 70· 31 .130s 16·20 T.•130s 18bS, 61·24 T''''"~ diat. TIAos 2 I b z8 TIAos 31" 23-29 coni. oli r".... 994 b 9,13.33,59.38, cr. 994"16, 74·30 coni. ,.o".,w, 23· 34 coni. 51.16 T.'."IS.i"..14 z·4 T.TfKJ"YIII"IC.... 996" 21 T.TpO."YIII"0ll 54" 2 Pvth. 986. 26 60,.9,.01 T. 93·7, d 9Z'U T'TpatOS 76 b32 T'TpO..""XII 63· 31 T.TpM 90" 23 TiX", 2'1°"28-981"27 6o.o~I"'1 &a '"Is 1,..".lpl..s 981.3 opp.I,.'lfflpl.. ib. 25, "8 disi. 981 "26, cr. 46"3 - '''Ion-q,.., 99t·S dist. II0Us, 3V"",.IS, &cI"",.. 25 22, 32.28, 33"8 .,1",,'IIBcu ",VII.I, TIX"f/, d.o T.. wo,.aToII Z. 7-9, Cr.2S"22 dlst. "'Vlllr 33"8,70.7, 17 !J T. TO .Taor 34.24, 70·15 -yf.,.,.,.cu ,...s;,I1.1 47" 33, d. 46" 37 Ta ...Ta TI)(II"" 70·17 T. d.pXIT••TO"I...I 13.13 trx"l"ls dist. '".rlpos 981 • 3 I '"INTOS li·lo, 16·22, 23·,8 TIS'.,..I a 14, 6a·:I3, "II, 85·'5 TI"OS 984·" fls ,.1.." t/JUIIIII 69· 35 n,...t Emp. 0"14 TII"OI' 983"33, 64"4, 74"31, 26, 30 TI/AI.".aT'II"I~"", TIJAlWraTo" .,IIIos 983.5,75"'°, 26·21 TlpM.os 993"15,16 Tis. TO TI 26·a6, 45 b33, 69"9, 89 b TO TIlIITI 25"31,27baa, '28·11, 8 17,30·17, etc. Tel TI illTI" Z5"31, I,,'T;; '1'1 Z7" z8 ;, TlltlTl ~4 ·15 flrTI" InrJ.P]('UI 23·27, cr. ZO·18, 24 • r." Til TIIIITI 1I'''.o"ax,,"s 30. 17, cf. 25 31 I. TOU TlltlTUI 01 ","AAo..,I.,.p.ol a4· 31, 711 b 24 Til Tt ~" Ellla. a8"34, Z 4-6, 8, 45"3, ;4·35 coni. o~"ja 983·z7. 9118 .34, 99a·. 18. '7·31, 2a·9, ~1·18. 3z"z, 14. 35"16, 37· z3. 38"14, 7r.·2 COlli. .pl.,.,.4s, ,,4..,os 994" 17. 16&a3. Ii b ZI. 30&6. 45 blJ, 2~" 28 coni. ono~ 13. 1 7; 30&~2. 33"7. 35· 16.4,,&36 TII.,.I fI" z9 27 v.1. ",4.,.1~" .l"al 3 1 "9, '9 .,.,./tpll.,.a tr6.AolI 34" 25, 35· 34 "'''".,.I.S 20":19

'".n....

,,,It,,,.1,,..,

,..T4

T,..,TOS 20"30 TOIOUTOS ad en quae sequuntur pertinens 987"4.998 • 10,26"22 TO,.o) math. 994"25. 60" 14 log. 38.28 TOIII"', ~A., 42"6 TU"'OS 67.8-31. 68"26, 92.17-31 ,.'T../3oAyt ...TA TullO" 4a· 34, 69" 13 TOII"""'''Xiiis 13" 4, 17· 24 T,4"'C" 988 • 4 TpI",.a9..1 Emp. Obl 4 Tpl.,_O" 9a"U T• .,.O /lvo 6pHs 'XOI' 25· 32, cr. 51 • 24, 86" 35 T"'"I"';PIO" 20" a7 .,.plTOS '..sPIIIIl'OS 990" 17, a9· 2, 59"8, 79. 1 3 Tp'Tom"lS 18"z8

.,.,..,..,.os 76"30

TP'xD /lICUpfTO" 16"'7 TPori, Democr. 985 b 16, 17, 42" 14 »A!01l TponI 983. 15 TPOII'IS 13·~ Tp6I1'OI alT11IIII 996b5. 13"17. z9 11"'1IUt/JllA..IOV,.."OI T. 5 z .11 T"1:X4"'I". TO 6"oT.P· TIIX' a7" 17, 13. cr. 21.7.64"36.65.9,12 TU1f9I If",T.. 1 29·7 ,"""Aos a3 • 4. 47· 8 TUX., 981·S,65·Z7-·a coni • .,... wopIlTO" 984" 14, 32.'9 dist• .,..wopIl"'W 70·6 .,1.,,,.IIBcu .,.IX"11, tU"'.I, TVXII, T;; ..wO/AaT" 70·6, cr. 3z·Z9. 49·4 b-raciCr1ll981 ·18, :16"37 ",.lcJ"'I" 17.28, 3:1"18 ",.1.la ~4·IO. a8, 29. 68·u, :16, 70·17, Z3, a8 ~""'I"OS .3·a5, 60"37, 77"36 bllaT09p1,.".", Emp. 0· 31 ~1IIIp 983"21,3 1 ~A., 983"7---984.18, H. 3. 4 sln. 11.0••1"."0" 983·z9, u·18, Zt 9, 42.32, 61"U, 70·II. cr. 985 10, 988·II,992"', 4'"9 dial. ho.d"."o" 29.2, 4z·27, .... "9 - IE oli oyi.,.,.TIU 3Z·17, cr. 4Z·32, 69"? I" GA'Is da'i 98a"7, 984.17 lipxl} dIr ~. 986.17, cr. 983"7, 46&23 opp. Ao.,os,!J olI.,.1a. r) uTel TOr Ao-,o.., '''TfAIXOIlI. bln.la 986"20, 74&34, 84"9, 38"6. 43&6, 45·35. 71"21, 76.9 0fP. olaor, lU'Pri 988.3, 29.4,6,41 8,5°.15,7°.' CODi. 9iiAv 988·2-\> a4&35, cr. ....·35 6o")'m,ros 999 IJ ."tMm/ 15·7. 17·5,44&18, 49· z5, cr. 23·'7 • .,.ow dlovr ~. 23" Z -,I"or dis G• 24"8, 38.6,68.23, d. '3"2 111tTfrrri. "0f1~ 25"34, 36 .91 37·34,

INDEX VERBORVl\l 45 &34, cf. 36 b 35 iI. T;;''' iUJ8'1,.aTI""''' 59 b 16, cf. 993 b 3 coni. ltiv'Ials 36 &3 G.l1aUTa Tel ,),1,),"0' ,.ova EX" ilA'I" 33 &30, 42 &26, 44 b 37 alTta Toil au,./Jo/J'IItOTOS 37& 13 110TOPO" o(,ata Z. 3, 43 &27 tlef. 29 & 20 iJ.,),YOJaTOS Ital' aiml" 36 & 8 dO(JIaTO" 37&37, 49bl coni. ~,;­ "a,.,s ~3"27, b9 , 49&33,50"':;, b37, 60&30, 69b14, 70b13, 71&10,751022, 88 b l, 92&3, cr. 39"39 TO".,..q, ,),0""'1'rii 42b6, 69b26, cr. 42&32-b" 44 10 7, 50bH !) ''''P'Yfia Ii.AA'I Ii.AA'Is iI. /tal uAo')'os 43 &12, cr. 691034 iJ laXdT'I iI. /tal !) ,.0Pf/ Ta(,TU 4~ b 18 oll 110.0' ~11lf/>~paI"fa9al 70&9 Til '"a"Tia Il. EXOI 75 b 32 v. oiJala vA.ltus. TO vAlltu" 35&8 44&15,49&36,77&36 bAI""'s 78& 31 v"aM'IAa 18 b I "miPXf'" 37 b ,6, 40&15 V110PXO'" lta9' abTu 3&22, 25&31, "12, 30b23 Tel b"opxo"Ta opp. Tt laTI 36& 3 3 vwaT'I57&H iJ"O'val 69b6 ;"'.va"TtO" 85 &15 l/frffnpOpcov

:J 1 a ;3

b,,'p !)piis 0& I 5, cf. 77& 30 "'tfp/JoA.q 2I b 15 ""OpiXfI" 84 & 17 b110PfXO", bl1fPOXO,.0"0" 30 b 28, 31&4,6,57&13, 87bl8 bl1lp9upo" 421019 ;nlfpox~ coni. EMol"'.S 993106, 41012, 4 3 "25, 3~, 5 2b 30 iJl1fp11'lOO" fCS T. 27 b 6 ~l1~pfT?iI~a .1,naT"If'l983 & I t ' '1'(1. u au = l1fJIUTO" ItIVO,,", 70& I, cf. 33& 24 b110 n)" aUT~" lii"aplJl, ,.ta" 1,,,aT,,,.'1'" etc. 18 &29, 55 &31 , 61"15,63 10 37,93"10 TOW.) TfJ" up",," 60" 30 Vrro/JaMo", TO" Ml9> 4 bl8 vl1ulloa,s. It b. 5 &I 3, 55 b34 ~" civa')'ltaw" EXfl" TO" tTIOW tuvl'''Ta o(,X V. 510 16 = "pUTaalS 13&16, 10 30 l1pOS TfJ" b. 82 b 32 r3.al Ital 0(, ,.a"'paTlltal V. 86& 10, cf. 83106 coni. dpXat 86& 15 ltaTd TaS b. 90 &27 b110ltaTOJ 74 & 4 V110ltfiala. = sumptum esse tamquam fundamentl1m 983b16, 33"1,990&9, 67,"15-24, 68&4, 5"i3~2~ ~110Itfl,.O"O" - liA'I, ,.0P'l"/, To .It TOUTOJ" 38b36-29&3, d. 38105, 4 2"J6, 49&

38 = ilA'I983&30, 984&33, n&19, 24 b 9, 43&13, to&II, 88&18, cf. 985b 10, 993 b I, 43 9 l1pQ,TO", TtAouTa""', laxaTo" 16& 19,32& 190 34 b 10, 16&33,17b34 ')'/"osiJ·997 a6 ,16& 36, cr. 997 &30, 34 b 3 ~ TO lit TOVTOJ" (res concreta) 996&3, 19&5, 31b16, 44 b9, cf. I &8 opp. 11010s, au,./Jt/J'IItOS Ib 3 1, IOb 34, 7&35, cr. 37bl6 Ital' v"oltfl,.l"ou 9901031, I b3 1, 7&35, 17b13, 16,39&8, 66bl4, 79&38, 87& 35, 10 I TO b, ~ Til WO TO ')'Ivos uVTa 983&33,104, 53 b3, 63b31 iJ11oAa,./Jo".", 998 &H, 5 b 36 ;"foAo'".''' 48b 16 iJ"uAWls 981&7, 983&6, 73&17 v. dpxaia Ital llq,.OTI,..q 989 &I 3 b"o,.."o." intrans. 3&3, 69b8, 70&35 10..6')'0", '"ovTIQ,afls6&26, go&3 iJ"U110,,", 38& 10-33 b"O"TO';O", 984 b 33 vl1oTlIU"al 988 &3;; med. 986bl4, 47 b 10, 89& 23 ltaAlils 54 b 33 Aap/Ja.·oual TU Tt laT." bl1OTIII,.flllJl 64&8 vl1oTurroVa9a. 28 b 31 baTfp"'Y."fj 91 & 33 ilaTfpo", v, l1pOTfpO" v'1PloAlo" 21 &I at".a9a1 II &I 7-33 opp. Ao')'os 988&3, 87b3 !) liA'I TO~O TI T~ tf>aI"fa9a. 70& 10 """"U,.fllO" opp. 1/11 4b19, 131027, 73&38 syl1, /loItO;;" 9 &8, cf. 989 b 30 TO . T'"t 'aT. . 11&18 TO . 986"31, Td . d"o~o;;IIal 73 10 9 b I, 74 b16 36,74& I alull I I b30 tiltoAos 16&1, 42bl7 OAaltpos 24&28 tival, d"oti"lJl 8&4- b J 91,),0'" Ital . 51b2~ OIIOpOS. Ta O"'pti 993 &35 Tel OII.pa T;;''' 90iOJ" 36 &18 O"Taaia 98010 26, IOb 3 1,.1101 fill a"Taatav 34" 34, 35 &6 !) d"o T"'OS . 34 b 36 = Uta 62 b34 ti"Taa,.a 990b q, 79& II tipa')'t 810 16 tialS syn. /taToOals8&9, 62&34 dist. ltaTaOalS 51" 25 d"TIItO.,.Oval . 11 10 14, 62&6- 3t, b17,63b16 auAOJS ,),"OJaTa 29 '10 'p.", Tch d"oli"tm 5 &26 . &IIo,.a l11i TI 63 &16 TO op6,..IIa ltaTIl TOY ovpavull 990. II "OPfItUllqS 91109 9aPTl,Itf/ dp"" I ~" ~ I ",9apT(ls. cp. oua.a 69 & 31 oVa'a

INDEX VERBORVl\'I ~ 1/>. dpX17 13· 20 ."Ullfl Opp. III' '90r. T/X"7/, Tqi Ob,.op~. ., dicl 1110-

"olar 98Ib .... 32.12, 65. 27, 7°.6.17 l/>ulllf dist. IIM,..r 33 b 8, ...9 b 8 dist. T/X"'1 l3b8, 70·7 opp. /llo 52· 23, 71 35, cf. 15b15, 33 b33 ,.cl I/>Ullfl 11""0 ' ... b19, 27. 32, cf. 3... • 2;1. 7°.5,17 = flA'1 , ... b33, 9Sib 13. 2 ... ·... = flllo., EvTfA/XfIO,

cr.

IEIf 15.5,32.2"" ....... 9,7°.11 ,.e) _,.cl n}Jf l/>uIII" 986bu Tel Tii -,."llIfl fltTTfPO" Tji 1/>. flplrrfpOl' 98t 15 ~Ua" opp. "pds ';,..&s 29 4 l/>uIII"'Xf'" 15.5,32&23 '" obtTlo 993b2, 997b6, 1·11, 3.27, l ... b 36. 15.12,19.2, 31·30',53b9, 21, 6... b II, 88·23 1)1/>1I111f PD"'1"Ow I" TOC; !f>9op,.oir owlo ...3 b 23 1/>. Vy~ 983b26 1/>. K"'''''I~ 98 ... b7 ~ TOO d-,aflOO, ,.OU dOpitTTOII, ,.ou _KOU .". 99... bI 3, 996·23. 10· ..., 75 b7 Tel flOlel" rijr .p'II1'I"'lr .". 63· 28 xpf;,.,.. .r ,.., 1/>., etc. 985 bI, 988' 22, 998.6, 3b2~ 69·35, 89'7 IIA'I, Walla, ~ TOw 0",..,,,, ,.OU /lAOII"', 987 b 2, t·32. 10·7, 98... b9, 75.11, ce. 993 2 ,.cl flfpll/>. 983. 33, 985. 12, 988·u. 989.2"" 86·2", 01 flfP! 1/>. A6-,oc 990·7 01 fI.P! .". = 01 I/>IItTloA6oyo1 1·12, 6·3, 50b2 .... 62 b26 ~ 1/>. r" ,.1 -,1,,01 Wr"" 5·3... Emp.IS·l 72b33, 92'13 I/>u,.qi 1I,..olor 6·15 tfJGIr 986.25,53'31

,.iii"

"""6,,

xaAK6r

1... ·12,

3... '1J xaMf; lI!f>tupo 33.-30, 3... b II xoor 72.8, 91b6 Hes·98... b28 XGpIIII,.O,.OI 6o· 25 XtJp&ftT7'/pGIr 75· 26 XfIPOT/X"'Ir 981 • 3', b... xoAthll'll 981 • U xopBal IfI,.4 93· ' ... Xpflo 980· 22 Xpf;1I1f opp. dlli",.. 982'21 opp. (1'1"''' 50·2", XpolJ 91. 16, 93 b2I )(p6"Of IIl1p/lf/l'lKe). flOII';" 20· 29 dlh/llG,.o" ](116"0" I) I) 'l'flapfillGl 71 b7 coni. N:l"'llllf ib. 9 flpIiJTO", flp6,..po" xp6"9' 28.32, 38b27, xaAKoii,.

",.a

19 b1l

-,.,,1119,..

Xpwpo IIIGKp',.IK'''', lIu-,Kp'''11t6" 57 b9 XU,..olI6·22 X.,Aal"'I" 25 • II Xthpa Plat. 92. I XGlpiC"" 989 b3, 16 b2, ...ob6, 28, 78b 3 1 ,86" ... x.,plr 998. 18, 68 b26 fll1Gl, bwdpXfl"

INDEX VERBORVM

5 26

X' 99[bl, 3, 79 b 36, 40b 37

I'otiP 37b3~ 34

X·

XOIPCITp6s g89 4

XOIpuTTdp 5"[0, 17b35, 35b38, 36"9, 14,38"34, 040"9, 59b13. 60"8, 78b 30,86"33 A6")'9', d",AQ/' 43"39, 30 ""nd" -p4Hrfi 48 b [5

"'",,~(a93"30

cf. ~5b 14.43"35. 7i" 3 r,

';3.1011 lOb II

",.il30s A. 39 def. I l b 35 T~ W, ",. FI iiI' E. 4, 8. [0 dist. cl&l. l'a.TOl' 47 b 14 = 011. Ii.. Plat. 89" 30 "'cS.f;os 41" 35

'n"'G/fO' 983 b30, 9 1 b6

"'VXTJ

afTIOP Toil .1..al Ttl '"' 17 b 16,

"01'/

43 b 3 Til, I/J. T3 A6-yop .lxop .6 b I dist. 1I0ils 70" 36 ""(lal' (,"'0,.111 .. /1 dllu/fGTOP ib. Pyth. 985 b 30 Plat. 73"2 rlvxf'lJI' (lTIP'/1T1f 70b I 3

",.AA('o(l1o& 985" 5, 993 "15

",.v3TJ' 6.P'pOIrtOs 35" 3

U

rI. , ..la, '.OIpqITIlI Toil
w311'~"

••• w31 31

31" 10

ws fI...o'" 980"25, 98Sb3I. 998b32, 10" 30, 36b9. 28b7, 8S b II, 87 b 19

w(lall.£ 36610 /fJ(lTO in apodosi 3 b 33. 81" 33

INDEX TO THE INTRODUCTION AND COMMENTARYl Anaxagoras 98-410 15, J8bS, 71 b 37 , 7~"19

A naxilllander 988" 30, ~3" 10. 66 b 35 Anaximenes 984.27.988"30,996"89053 bI 5- 16 Antisthene. 5b3-5. 6"5-8.11"7-13 Aristippus 78"31-b6 Aristotle: metaphysical doctrine lxxvi-cxxx method of metaphysics Ixxvi f., 3" 31, 25b7-18 subject of metaphysics Ixxvii-lxxix further determination of subject lxxix-lxxxii the categories lxxxii-xc substance the main subject of meta· ph)'Sics xci-xciii substratum xciii f. essence xciv-cvii the universal cvii-cxi essence is Sll bstance cxi-cxi v principle of indivi,luation cxv-exix analysis of becoming cxix-cxxiv natural genemtion cxx artistic production exx f. spontaneous production cxxi potentialit:y :\IId actuality cxxiv-cxxx rational and irrational powers cxx v vindication of the conception of capacity cxxvi f. actuality and movement cxxvii f. priority of actuality cxxviii-cxxx A ristotle'. theology cxxx-cliv the' active reason' cxliii-cxlix A ristotle, references to other works: Post~rior Ana!yl;cs 35" 3-4. 37 b 8 Physics 983" 33. 985" 13. 986 b 30, 988"31.993"11. -42b8, -49b.~6. 59".H, 63b31. 73"3 2 • 76 "9,86" 33 D~ Caelo 986"12(1). 981)"/-4. 73" 32, 86"23. 88b3-4~) lJe Gen. el Cor".42 8,63,10 31 .86" 23 • Ni,'omacheall Elides 9RI "3:; De BOliO 4"1 (I;. 10:14 \ 1).54" 3'J (I) De COII'rariis -4"3 (I). b 3-4 (I). 5-1" 30 (1)

lJe ldtis 21"19 De Pythagoreis 986" 13 (I), 31" 19; 36b8 Asyndeton 75" 7 Atomists If! b 5, 8-4 b J7 Binary structure 983b 16, ~b 14-36,3" 33-b li. 17"10-13. 2-4"8-9, 66".~134, 68 b ll, 75"7 Democritus 39 b ZI-33 Diogenes 996"8-9 Eleatics 98-4 "39. 986b 12.38 h~, 75 b I;; Emblemata in text 98t"12, 983"1-4. b 33, 985"10, 986"33-36,39 r., 987" 16, b lO, 2l, 990bl9, 993"16, 995" 19, I b 15, -4"5, 16, 33, 5"8,6"38. 10 6, 33, 9" 34, b 7, 16" 3.. , 17 b 3. 19b36, 33, 30"1, 37&5, b 2, 38& .. , 39 b 37, 30.3, 31 b 30,33 &18,3 .. &31. 30, 37"10, 31, .p b 13. 30, 43& I i, 3.. , H&18, -45bl.IO,-46&17.-47b3I, -48:30, 33, .. ~b8, 51 hi. 53bl-4, 31, 56 IS,33. S7"3-4, 59&30,63 b6, 37, 38, 6-4b33, 37, 66&3li. 67b6, 68 b 3, 69&33,73&2-4, b 5 , 73 b 33. 7-4"16. 78 &38, 79 bl .. , 81&35, 85b33. 86" 33,37, b 30, 87&6, 17, b S• 88&23, b lO, 8~&7' 38, b 37, 90"18, 91"1, b8,9 3 1-4,93 b 3 Empedocles 98-4 b 5, 994 &6-7, -4 b 33. 38 b S, SOb 3J, S3bIS-16, 9 3b 7 Fitzgerald's canon xxxix-xli Heraclitus 984&37, 996 "S-9, 1"15 Hesiod <)83 b 37 Hiatus 73"3 b 17 Hippasns 99 6 "8-9, 1 "15 Homer 983 b 30, 31 Infinitive, with ...I irregularly omitted l .. b6, 3°"1-3, 3 1bll , 33&33 Itacism 35" Ia Mathematics, origin of 981 b 33 Megaric schoolS b 3S

1 This index is simply supplementary to the In,lex V~r6,,.,,,,,, E. g. under 'Plato' will be found only references to paslagel in which Aristotle does not explicitly mention him.

528 INDEX TO INTRODUCTION AND COMMENTARY ,Welajlnys;cs, stiucture of xhi-xxxiii the connected treatises xv-xxiv tbe outlying books xxiv-xxix inserted fragments xxx-xxxi earliest editions of Mel. xxxi-xxxiii text of c1v-c1xvi

Parmenides 4 b 31 Partitive genitive, subject implied in 31"U, 70b7-8, 33 Plato 995bI6,' 998b9, Ib33, 3"11, b 13-3 3,8".\1, '7 b 19, 30"36. 3'"39. 33 b1 9, 36bI3-'7, 39"36. b 19, !il" 17-31, 57b8, 58b)8, 60 b 6-9, 69· 34-36, 70"21-36. 71 b 16. 73"30. 75b30-34. 76&'9, "1I-i7 b '4. 81" 34, 84"13. 85 b 7, 9. 86"11-13. ;13, 87b,6,89"30,90"4,b30-33,91"35, b 18 Plato's views, origin of xlv-xlviii 'earlier and later theory of Ideas' xlviii-Ii ideal numbers and ideal spatial magnitudes Ii f. T" "'fT4(6 liit-ivii derivation of ideal numbers from their first principles lvii-lxiv derivation of ideal spatial magnitudes

and their place in the theory lxivlxvii identification of Ideas with numbers lxvii-lxxi l'latonists 990b9, 997 b 3. 998"7, 3 b 13, 4 b ;l3, 38b34. 36b'3-'7, 40b 3-;1, H b 34, 50b35. 56&10,66"1', 69"36,75"33, M, Npssim Plural verb with neuter plural subject 985"37,79"30 hotngoras 999 b 3 Proverbs 983" 3. 18, 993 b 5. 9 b 38 Pythagoreans 998b9, 3"11, 4b31-3l, '7bI9, 28bS, 16, 36"8, 60 b6, 66" lib 7:>"37, i6A30-2', 87 bl i, z6, 9 0 2,9 1 "34 Sight 980" 23 Socrates xxxiii-xlv Soph ists 76 b 9 Speusippus 69"34~(j, 7f,"3i, b3i, 80 b '4, 36, 83"10- b l, 84"13, 85"~2. b 5, 37-~3. 86"3, 39, 87b6,37,9~".f. 35-36. 15-16, 9'"34, 37, b H-2~, 3 3, 9 3 "u. 13-'5. 17-31 ,35 Thnles 98,,"37.9'.16"8-9 Xenoclales 38 b 14, 36-27, 69"3-1-36, 76"30-3', 80 b 33, 38, 83b3. 86"5. 90b 30-30.9' b 35

,..." setting aside irrelevant suggestion 99.. "33

B. i" apodos; 999 A37.

I, 5. 59 b 33, il" 34,75"10 BI auti Tf confused in MSS. 3 b 30-32

Il'Tf1l.fXfl .. 47" 30 tTl

BTl

superfluous 91" 15-17,93"3

oM. after tl 49"10, 53 b 18 IM'olXfio" 985"35

.130. 987 b E

1I'lIfx0,..fl'ol')( lI"I'''To" '9 b 33

fwd and

oro" introducing a comparison 33 b ,6

confused in MSS. 16 b II

'%"'ItPAT,,', form of cases 981 "'9 Tf, use of 991" 23 ill MSS:3bU

T. and III confused

Tb Tl ~" .1,,"1 983" 27 Toll. TI I b 33

at beginning of elliptical sentence 3' b 8-9

ICIIIU7rfP

1111." 983b7 /Jllr.".p at heginning of e1\ipticnl stn· lence 0"', 49" 3-5.87"7