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VIVARIUM AN INTERNATIONALJOURNAL FOR THE PHILOSOPHY AND INTELLECTUAL LIFE OF THE MIDDLE AGES AND RENAISSANCE inparticular totheprofane sideofmediaeval vivarium is devoted philosophy andtheintellectual lifeoftheMiddle AgesandRenaissance. - C.H. Kneepkens, - H.A.G.Braakhuis, L.M. de Rijk,(Leiden) EDITORS (Nijmegen) - D. Perler, E.P. Bos, (Leiden) (Madison) (Groningen) W.J.Courtenay, - M.G.M.vanderPoel,(Nijmegen). (Basel) Board: Prof. C.H.Kneepkens. oftheEditorial Secretary be addressed Allcommunications, thoseofa business should nature, except Faculteit derLetteren, toC.H.Kneepkens, Groningen, Vakgroep Rijksuniversiteit TheNetherlands. P.O.Box716,9700AS Groningen, Mediaevistiek, - -J.E. - Albert ADVISORY TullioGregory, Zimmermann, Murdoch, (Cologne) (Rome) COMMITTEE (Cambridge, MA). PUBLISHERS Brill, TheNetherlands. Leiden, PUBLISHED Twiceyearly. andEUR XLII(2004)(320pp.):EUR 138(USD172)forinstitutions, SUBSCRIPTION Volume and Price includes inclusive 67(USD83)forprivate subscribers, ofpostage packing. online subscription. volumes orders orders areaccepted forcomplete only, taking Subscription onanautoOrders effect with thefirst issueofanyyear. mayalsobeentered ifthey arereceived willonly beaccepted matic basis.Cancellations continuing thecancellation theyearinwhich before October 1stoftheyearpreceding ifmade issues willbemet, free ofcharge, istotakeeffect. Claims formissing for forEuropean customers andfivemonths within three months ofdispatch customers outside Europe. should be sentto: orders Subscription BrillAcademic Publishers Stratton Business Park, Drive, Pegasus Biggleswade SGI8 8QB,United Bedfordshire Kingdom 601604 Fax:+44(0)1767 Tel.:+44(0)1767 604954; E-Mail:
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Introduction
WILLIAMJ. GOURTENAY
One mightthinkthatafterdecades of intensiveresearchon Jean Buridan therewould not be room foranothervolume of essays.The factremains, however,as Jack Zupko recentlyobserved,"Buridan left an enormous number of writings,most of which have never been edited, let alone properlystudied.Althoughinterestin Buridan has increasedat least tenfold since the 1970s, many of the finerpoints of his thought,his exact positionson a varietyof particulartopics and locad debates,are stillnot in this special issue of Vivarium seek to well known."1The contributions on those local debates of Buridan the understanding specifically improve cenat the Universityof Paris in the second quarter of the fourteenth contextin whichBuridanwas teachturyby lookingboth at the university ing, debating,and writingas well as specificdebates on issues of crucial importancein the facultyof arts at that time. contextat Paris and bringsinto The firstessay exploresthe university and the discussiona numberof recentdiscoveriesabout the institutional social structureof the facultyof arts that modifythe understandingof Buridan's role as teacher and disputant.Among these are the masterpupil relationship,especiallyas it concerns the teachingcareers in the is providedon those facultyof arts.Along the way some new information with whom Buridan debated in the 1330s and 1340s. Hans Thijssen expands on one of those themes,namelythe extentto which therewas a Buridan school, by exploringthe relationof Buridan and Albert of of quantityand projectilemotion. Saxonyon two issues:the understanding From several different standpoints,institutional, geographical,and intellectual,Thijssen rejectsthe notionof a Buridan school in the fourteenth century. The next two essaystreatspecificissues in Buridan's thought,placing and earlierapproaches.Jack Zupko themin the contextof contemporary of the human addressesBuridan'sviews on the nature and immortality 1J. Zupko, Buridan , NotreDame,IN 2003,xiv. John Vwarium 42,1
BrillNV,Leiden, © Koninklijke 2004 - www.brill.nl Alsoavailable online
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intellect,disputingOlaf Pluta's recent assertionthat Buridan favored of the intellecton Alexander of Aphrodisias'denial of the immortality the grounds of its material nature.2Similarly,Stefano Caroti looks at Buridan's treatmentof the problem of intensionand remissionof forms in his finalcommentaryon the Physics{de ultimalectura ), comparingit to the approaches of Walter Burley,Nicole Oresme, Albertof Saxony, and JohannesMarcilius of Inghen. The last two essaysexamine debates that engaged Buridan at an earlier point in his career.Jean Celeyrettelooks at Buridan'streatiseon the point, which he developed in debate with Michael de Montecalerio. Celeyrettefollowsthe developmentof Buridan's thinkingon this topic fromthatearliertreatisethroughthe two last versionsof Buridan'scomFinally,Dirk-JanDekkerconcludesthe volmentaryon Aristotle'sPhysics. ume with an introductionand edition of Buridan's treatiseon relation etconvenientiis. The treatisealso provides diversitatibus entitledDe dependentiis, withwhom a view of the argumentsof two of Buridan'scontemporaries from a master and one the he debated, Picard English-Germannation. the debate on Buridan'srelationto Ockham or the Beyond furthering existenceof a Buridan school, these essaysprovideimportantnew information that may help uncovermore on the identitiesand viewpointsof Buridan's immediatecontemporariesat Paris. And that,in turn,should of Buridan in the academic world in lead towarda betterunderstanding which he lived. Universityof Wisconsin Department ofHistoiy
2 O. Pluta,Persecution TheParisian Statute andtheArtofWriting. 1, 1272,andIts ofApril Etudes médiévale. Bakker delapensée , in:P.J.J.M. offertes (ed.),Chemins Consequences Philosophical à Z^non Kaluza , Turnhout 2002,563-85.
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The University of Pans at theTimeofJean Buridanand Nicole Oresme WILLIAMJ. COURTENAY
The purposeof the followingremarksis to exploremore deeplythe institutionalcontextin which Buridan and Oresme pursued theiracademic careers, namely the thirty-five year period between the beginningof Buridan's teachingcareer at Paris (c. 1325) and the date of his death (c. 1360), whichprecededby only a fewyears Oresme's move fromParis to Rouen to assume his dutiesas dean of the cathedral(1364). Much has been writtenabout both men as well as the Universityof Paris at this time,but a more precise (and updated) understandingof the structure, operation, and resources of the universityat that time has not been broughtto bear on the relationshipof theircareers and of othersassociated with them. and itsMeaning and Discipleship Institutional Structure for Communication The medievalUniversityof Paris was a corporationcomposed of largely autonomousgroups.This applies not only to its divisioninto fourseparate facultiesof arts,theology,canon law, and medicine,but was true of the fournationsof the facultyof arts.Colleges of secularstudentsas well as the conventsthatservedas houses of studyforvariousreligiousorders Colleges came under thejurisoperatedforthe mostpart independently. dictionof the university, faculties,or nationsonly insofaras the masters and studentswho held bursesin them also belonged to nationsand faculties.Conventswere even more autonomousand came under thejurisdictionof the university only insofaras theirstudentmemberssoughta university degree or theirregentmasterparticipatedin the meetingsand academic exercisesof the facultyof theology. At the same time the boundariesthat separatedthese different groups were porous and allowed a certaindegreeof contactand communication. This was notsimplybecausetheschoolsof thenationsin therue du Fouarre and theconventsand collegesthroughout the Latin Quartertopographically existedside by side. Studentsin the facultyof artshad the rightto attend BrillNV,Leiden, © Koninklijke 2004 online- www.brill.nl Alsoavailable
Vivarium 42,1
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lecturesof mastersoutsidetheirnation,1especiallywhenduringa particular term or year no master in their own nation offeredlectureson some beforeproceeding curricular authoritative textneeded to fulfill requirements their and determination.2 to examination by verynaturebrought Disputations membersof these various groups togetherboth as participantsand as audience.Accessprivilegesto libraries,even the librariesof religiousorders, could be extendedto favoredindividuals,althoughborrowingprivileges to theirown members.Thus, althoughmuch ofa were usuallyrestricted student'sacademic lifewould be spentwithinthe confinesof the groupto whichhe owed his allegiance,it would have been almostimpossibleforhim not to be exposed to the ideas and viewpointsof those in othergroups. and the interactionof the groupsthat comBoth the self-containment are the university importantin order to understandissues of conprised intellectual and discipleshipor schoolsof thought.Inasmuch influence, tact, as Buridanbelongedto the facultyof arts,as did Oresme beforebecoming a masterof theologyby 1342, albeit in two different nations,we need to theiracademic of thatfacultyaffected structure look at how theinstitutional their careers and potentialrelationship. In lieu of a matriculationlist, which neitherthe universitynor the nationsat Paris maintainedin the fourteenth century,incomingstudents in artsenrolledby mutualagreementwitha masterwho wouldsubsequently be responsibleforoverseeingtheirstudies.The masterso chosen had to on thebasis belongto the nationwithwhichthe studentwould be affiliated the of geographicalorigin.3For purposes of enrollmentand affiliation, 1 See thestatute Parisiensis citedas Universitatis of 1290in Chartularium (henceforth 4 vols.,Paris1889-1897, ed. H. Denifleand É. Châtelain, II, 46-7,#570. CUP), 2 in theartsfaculty surcoursesattended no listoflecture bya student Although ofViennain the vivesfromthisperiodforParis,an examplefromtheUniversity Parisiensis Chartularii Universitatis citedby Deniflein Auctarium latefourteenth century, vol.I, Paris1894,xxixcitedas AUP), ed. H. Denifleand E. Châtelain, (henceforth in thefacmasters different whotookcoursesunderthirteen showsa student XXX, theRhenish, butat leastfivefrom theAustrian nation, ultyofarts,mostofthemfrom and practices of Viennawerebased and Saxonnations.The structure Hungarian, on theParisianmodel. 3 In mostcasestheboundaries of withtheboundaries of thenationscoincided all thediocesesin theecclesiastigroupsof dioceses.The Frenchnationcomprised and Lyon,as wellas thedioceses of Sens,Tours,Bourges, cal provinces Besançon, in thearts ofReims,Soissons, Metz,Verdun, Toul,andstudents Châlons-sur-Marne, Partsof thediocesesof Liège,Trier,and fromItaly,Spain,and Portugal. faculty Rouen(theFrenchVexin)werealso includedin theFrenchnation.The Norman of ofRouen,withtheexception to thediocesesoftheprovince nationcorresponded thosefromthediocesesofBeauvais, theFrenchVexin.The Picardnationincluded and all diocesesnorthand east edgeofPicardy, Noyon,and Laon on thesouthern
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specifictown or village,and in some cases even the bank of the riveron whichit was located,would determinethe nationto whichone belonged.4 In all probabilitythe masterselectedhad to be a regentmaster,that is one activelylecturingat the time,just as the masterunder whom one eventuallydetermined,was licensed,or inceptedhad to be regentunless, in specialcircumstances, one obtaineda dispensationto be promotedunder a non-regent master.5Once havingenrolledwitha master,one was legally a studentin the nation,faculty,and university. The supervising masterchosen by the studentnot onlybelongedto his nation;in most cases he was chosen initiallyfromthose who came from The choice mightbe based on the same countryor regionas the student.6 a recommendationfromsomeone in the home region or throughthose at Paris a studentmightknow fromhome or througha network.Or the choice mightsimplyresultfromavailable residentialspace in the house or rentedrooms of a master.7Given these limitationson choice for an incomingstudent,it is unlikelythat the choice would have been based on the scholarlyreputationof the master,and even less on his intellectual outlook.At the same time,shared accommodationswitha masteracross meantthattheywouldcome to knoweach other a periodofyearsinevitably would masters who also servedas house-masters and that well, supervising have close oversightof the academic and personal developmentof their students.
Cambrai, Tournai, (thus Liège)up to theleftbankoftheMeuse/Maas (Thérouanne, ofthedioceseofUtrecht). a portion ofHollandand a smallportion including 4 A bitter and Picardnationsover in 1358between theEnglish erupted struggle whocamefromtheboundary of a student theproperaffiliation regionof thetwo a preciseboundary was drawnup, marking considerable nations. After negotiation, border(AUPI, 233-6;CUPIII, and townsthatlayalongtheagreed-upon therivers 56-9,#1240). 5 In 1370 to be allowedto overseethedetermiHenryofLangenstein petitioned nationof twostudents, regent duringthat despitethefactthathe was notactively del'enDe l'organisation seeAUPI, xxxii;Ch. Thurot, year(AUPI, 375).On regency, de Paňsau Moyen-Age dansl'université 1850,91; Madelaine , Paris-Besançon seignement à lafinduXVe del'Université dePansdesorigines Toulouse,La Nation Anglaise-Allemande deParis del'Université siècle , Paris1939,108-9;MineoTanaka,La nation anglo-allemande Paris1990,150-3. à la finduMoyen Age, 6 Most whichmarked thetranmasters at thetimeofdetermination, supervising or regionof thecandidate, werefromthecountry sitionfromauditorto bachelor, oftheEnglish as can be seenin therecords nation;see Tanaka1990(op.cit.,above, n. 5), 169-70. 7 in theEarlyFourteenth Parisian Scholars 1999, , Cambridge Century W.J.Courtenay, 81-91.
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A studentmight need to change his supervisingmaster during his course of studiesbecause the latterwas for a time not in residenceor activelyteaching,or for other reasons.8Such changes were withinthe group of regentmastersin the nation to which the studentbelonged,a patternthat can be seen in the Proctor'sRegisterof the Englishnation forthe fourteenth centuryand in thoseforthe Frenchand Picard nations in the fifteenth at the degreestage, Changes occurredfrequently century.9 in a result of the of regencyof often as pattern interruptions probably masters.In the course of these shifts,studentssoughtout long-termmasters whose control of the space resourcesof the nation, whose power and whose influencein theirhome region would withinthe university, their careers. help Usually two or threemasterswere responsibleforhalf to two-thirds of thosedetermining, beinglicensed,or incepting.And when senior mastersaccepted new applicantsfor tutelageor sponsorship,evidence suggeststhat financialconsiderationsplayed an importantpart.10 Cases of supervising mastersfromoutsidethe nationof the studentwere and rare fromthenation.11 Almost extremely requireda specialdispensation all theseexceptionswere occasionedby the quota limitations forlicensing, which obliged nations that had reached their annual limit to seek an available opening in the quota of another nation.12Such arrangements and temporary,not instructional. were administrative The outside master sponsoringthe candidatewould have to be sufficiently informedabout the latter'sacademic and moral qualifications, but no directsupervision was required. 8 Tanakahas tracedin detailthe masters at ofchangesin supervising frequency seeTanaka1990(op.cit.,above,n. 5), 141-85.A caseofa change timesofpromotion; in thesupervising in theFrenchnationin 1329-1330 master ofa student thatmay in Gourtenay reasonsis described 1999(op.cit., havebeenbasedon morepersonal whocamefromthedioceseof Meauxand thus above,n. 7), 49-56.The student, of theFrenchnation,was,in 1329,underthe belongedto theParisianprovince ofa regent master fromthedioceseofTroyes, whichfellwithin theSens supervision of thenation.In 1330thestudent masterfrom province changedto a supervising hisowndiocese. 9 See AUPI forthe nationin thefourteenth oftheEnglish AUP register century; vol. IV, ed. C. Samaranand E.A. Van Moé, forthePicardnationfromthelate fifteenth and AUP, vol. V, ed. C. Samaranand E.A. Van Moé, forthe century; Frenchnationin themiddleofthefifteenth century. 10Tanaka1990 cit.,above,n. 5), 171.Whether students (op. wealthy sought superor seniormasters to accepta highpervisionfromseniorregent masters, preferred was thesame. ofwealthy theresult students, centage 11See the of the case ofJohannesNicolaiand masterMichaelde discussion below. Montecalerio 12Tanaka1990(op.cit.,above,n. 5), 153-4,268.
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master In normalcircumstances, how much directiondid the supervising over In a master who took the case of what kind? and of sponsorgive, ship at the time of licensingor inception,the relationshipwas probably and financial.If the same mastersupervisedthe stusolelyadministrative dent fromhis time as auditorthroughto inception,the relationshipwas or obviouslylonger and more personal,but not necessarilyinstructional ideological. How oftena student'ssupervisingmasterwas also his teacheror tutor is not known.Even if the studentchose or feltobliged to attendthe lectures of his master,one need not, and probably could not, fulfillthe requirementsof the arts curriculumby attendingonly lecturesgiven by one's master.The nationdid expect and certainlypreferredthatstudents would take theirinstructionaltrainingfromamong the lecture courses providedby the mastersin the nation. In 1290, however,the facultyof artsprohibitednationsfrommaintaininga closed shop, and studentswere free to attend lecturesofferedby mastersoutside their nation.13Thus, of any maswhilestudentscould hear lecturesand, obviously,disputations ter in the facultyof arts,instructionalsupervisionand promotion,with very few exceptions,had to be fromamong the regentmastersof the nation. Close extended contact between a studentand a master only occurredwithinthe nationand probablytook the formof advisingrather than intellectualformation.The latter,where it occurred,was probably a private,developmentalexperiencebased on attendanceat various lecturesand disputations,and on extensivereadingof texts,commentaries, and treatises. determinations, What does thisanalysismean forthe relationof Buridanand Oresme, or of Albert of Saxony or Marsilius of Inghen with either?And what does it have forthe existenceand meaningof a Buridanschool implications at Paris? Firstof all, the proceduresoutlinedabove mean that although Nicole Oresme mighthave attended lecturesby Jean Buridan, would probablyhave heard him dispute,and certainlyhad access to his written work,Buridanwould not have been the supervisingmasterunderwhom thatrole. he studied.One or more mastersin the Norman nationfulfilled of for Albert holds true The same principle Ricmestorp Saxony, whose licensing,and inception supervisingmasterat the time of determination, was Albertof Prague, a prominentmasterin the Englishnation but not Marsilius of Inghen one fromthe same home region as Ricmestorp.14 13CUPII, 46. 14AUPI, 149,150,152.
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inceptedunderWilhelmBuser,both of whom were in the Englishnation and came fromthe same regionof Holland.15Similarly,HenryHeimbuch of Langensteindetermined,was licensed,and inceptedunder Hermann Consul of Saxony, again both in the English nation and both from None of these was a pupil or discipleof the famouspredeGermany.16 cessorwithwhom theirnames are oftenlinkedin the literature.Oresme was not a discipleof Buridan or studiedunder him in any officialway, nor did Albertof Saxony studyunder the directionof eitherof them. theremay Each belonged to a different nation,and whateversimilarities be in theirthoughtof specificissues,thatwould have been derivedfrom readingor occasionalattendanceat disputationsor lectures,not fromlong This is not to deny personalcontactin the same academic environment. It is to of their ideas. some only say that the lattertwo parallelsamong in the normal sense of that Buridan or students of were not disciples phrase. If a Buridanschool existed,and I thinkit is a label thatobscures of intellectual more than it enlightens,it was based on a compatibility context. outlookon certainissues,not on any institutional One case of a studentin the facultyof arts who was allowed to have thatextended a supervising masterfromoutsidehis nationin a relationship across six weeksor more is of particularinterest,both because it was unusual and because it relates to Buridan's career. In November 1345 a obtaineda dispensation fromtheEnglish Danish student, JohannesNicolai,17 nation to allow him to respondand determineduringLent 1346 under Michael's a masterfromthe French nation,Michael de Montecalerio.18
15AUPI, 272.On Buser,seeG.H. Kneepkens, Willem Buser ofHeusden's ObligationesScholastische 'Obrogatum' in: K. Jacobi(ed.),Argumentationstheorie. Treatise zu Forschungen York-Köln korrekten Leiden-New undsemantischen denlogischen 1993,343Folgerns, Regeln 62, at 343-4. 16AUP I, 279,284,285. 17UnlessthedateM.CCC.XXIXin themanuscript sourceis a scribalerrorfor fromanother Nicolaide Dacia shouldbe distinguished M.GGC.XLIX,thisJohannes of thesamenamewhostudiedat Parisin 1329and whomadean Danishstudent De puntate artislogicae thatcomplemented ofWalterBurley's extract ofthosesections Nicolaiwas later The earlier withOckham'sSumma or contrasted Johannes logicae. in Linköping; Wiss.Bibl.,CA 8° 67, lectorat theconvent theFranciscan Erfurt, lector frater IoannesNicholai, de logicaBurleordinavit f. 123v:"Hancextractionem Parisiusanno Domini de custodiaLincopensi, Daciae, quandostuduit provinciae M.CCC.XXIX. . ." 18Montecalerio, Leben Buridan. Studien discussed zusáném , Johannes byBerndMichael, desspäten Mittelalters Theorien imEuropa seiner undzurRezeption seinen Werken , doc. diss. in thisissueof Berlin1985,vol.II, 451-2,and byJeanCeleyrette FreieUniversität willbe thesubjectofa separate Vivarium, study.
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familyname or place name correspondsto Moncalieri on the southern edge of Turin in Italy,and he would thus have belonged to the Bourges of the provinceof the Frenchnation. In 1342, in responseto the rotulus of Paris submitted at the time of the coronation of Clement University VI, Michael receiveda provisionas canon with expectationof prebend in the cathedralchapterat Turin.19Presumablythatexpectationhad not been realized by 1346, since he was stillregentmasterat Paris.20How long before 1342 Montecaleriohad been a masterof arts is not known. He wrote a determinato de puncto , which attacked the opinions of Jean Buridan on the same subject,to which Buridan respondedin his own determinatio de puncto . Both treatisesappear in the same manuscript.21 If these two textsdate to the same period as Buridan's questiodepossibilitate existendi secundum eademet nonexistendi simulin eademinstanti , which appears later in the same manuscriptand is dated 1335, then Montecalerio's career as a masterin the facultyof arts spanned at least a decade.22 master,and why Why didJohannesNicolai seek an outsidesupervising did he choose Montecalerio?No Danish master appears to have been regentin the Englishnation at the time he asked fora dispensation,but otherregentmastersin the Englishnationwere available.Johannes'petimusthave been argued on different tion,therefore, grounds.It would be to conjecturean early stage of the Wegestreit, that the student interesting wanted a supervisingmasterwho was a realistand could not findsuch among the available mastersin the English nation. This is unlikelyin lightof the campaignwithinthe Englishnation in 1341 againstthe secta Occamica , and because Conrad of Megenberg,a leading opponentof the Ockamists,apparentlyreturnedto Paris in the winterof 1346 to oversee the Lenten determinationof anotherstudentin the English nation, Albertof Prague.23Althoughchangesin the inceptionoaths between1355 and 1365 removed the language forbiddingthe scientiaOccamica?* it is improbablethatJohannesNicolai could not have founda realistmaster 19Rotuli Parisienses. tothePopefrom theUniversity Supplications ofPans, vol. I: 13161349, ed. W.J.Courtenay, Leiden2002,118. 20AUP I, 94, wherethenameis written as MonteCalvario. 21One ofthetwo Buridan's treatise is Paris,Bibl.Nat.lat. manuscripts containing 16 621,if.196r-202r. The onlyknowncopyofMontecalerio's treatise is in thesame ff.214r-223v. is in theprocessofediting Montecalerio's manuscript, JeanCeleyrette work. 22Ibid.,ff.233r-237r. 23AUPI, 93. 24W.J. TheRegisters the Courtenay, oftheUniversity ofPansandtheStatutes against Scientia Occamica 29 (1991),13-49,at 40-4. , in: Vivarium,
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had ontologybeen a major consideration.A forhis 1346 determination later he under LaurentiusPetriof Denmark,who had been year incepted trainedby Nicholas Drukken,who in turnowned worksof Ockham and whose writingson physicswere anti-realist.25 Johannes Nicolai's decision to seek a supervisingmaster outside his nationwas probablyoccasionedby the limitedavailabilityof lecturespace under the controlof his nation,and his inabilityor reluctanceto pay the rentalcostsof a privatearrangementoutsidethe nation. 1346 was a highdemandyearon lectureroomsfordetermination by studentsin the English in exceeded three times the remainder of the century.26 nation, only Parallel to the arrangementby which a candidate in one nation seeking to be licensedcould avoid the quota limitsin any one year by arranging to be licensedunder a masterin a nationthathad not filledits quota, so faced withthe inabilityto finda perhaps a candidate fordetermination, masterin his own nationwho controlledspace forlecturesby thosedetermining,mightreceive permissionto make arrangementswith a master in anothernation that did have space. As a masterwho had probably been regentformanyyearsin the Frenchnation,yetwho, as an Italian, underhis supervision, Michaelde Montecaleiio mayhave had fewerstudents for a determiningstudent have been able to lecture may provide space at a mutuallyacceptable financialarrangement. The case ofJohannesNicolai and masterMichael de Montecaleriois an exceptionto the rule that studentswere supervisedby a masterfrom theirown nation,usuallyby one fromtheirown countryor region.This particularinstancewas probablya resultof temporaryexpediencybrought on by an unusuallyhigh demand forlecturespace forthose determining in the English nation. The selectionof a supervisingmasterin normal circumstanceswas based on geographyand, if a change was needed, on the power and self-advantagea senior masterin the nation could offer - and to a student.But magisterialsupervisiondid not necessarily probably - include rarely any intellectualformation.The shaping of philosophical was more likelya resultof classroomexperience, outlookor commitment libraryaccess, privatereading and study,and personal contactsoutside of the nation and the curriculum. the formalstructures
25See introduction de Dacia, Opera toNicolausDrukken , ed. N.G. Green-Pedersen and K.H. Tachau, and S. Ebbesen,Hauniae1997,xvii-xxi, xxiv;WJ. Courtenay of at Paris,1339-1341 andtheEnglish-German Ockham Nation , in: History , Ockhamists, 2 (1982),53-96. Universities,
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in medievalParisis difficult intellectual formative relationships Identifying of the facultyof arts, because it could occur outsidethe normalstructures because it was rarelyacknowledgeddirectly,and because in most cases it was probably a resultof listeningand reading ratherthan personal contact.The highera reputationof a particularmaster,the largerwas And the moreprolific the audienceforhis ideas and supporting arguments. To thatextentwe can assumethat he became,thelargerwas his readership. Buridanhad an impactamong studentsand mastersin the facultyof arts far outfar outsidethose in the Picard nation and, throughhis writings, side Paris. For example, Buridan's commentarieson Aristotle'sPhysics were disseminatedby manyscholarsoutsidehis nation,especiallythrough German scholars in the English nation who carried copies to Prague, Erfurt,and elsewherein centraland easternEurope, and throughItalians in in the French nation who carried those worksto Italian universities, some cases well beforethe Great Schism.Anotherexample would be the influenceof Ockham's writingsand thoughtat Paris, since it would be a fair assumptionthat those associated with the sectaoccamicaas well as otherswho, like Gregoryof Rimini,adopted much of Ockham's natural philosophynever met Ockham personally. In a fewcases the intellectualdebt of a studentor junior colleague to a regentmasteris acknowledged.One mustbe careful,however,not to confuseacademic courtesy(forexample,such expressionsas "my reverend master"or "my reverendfather")with academic filiationin the sense of a master/pupilrelationship.Yet there seems to be more than mere at stake when the secular masterof arts and later theologian, Höflichkeit Marsiliusof Inghen,referredto the Cistercianmasterat Paris,James of Eltville,as "magistermeus bone memorie,magisterJacobus de Erbaco," whose opinionshe oftenechoed.27This same master,a theologianlecturing in a religiousconventat Paris, also had a profoundinfluenceon Henry of Langenstein,who upon leaving Paris in 1382 spent severalmonthsat s monasteryof Eberbach, where the latterwas abbot, and where Eltville' com"reread" to the monksEltville'scommentaryon the Sentences Henry at Paris.28 and read initially posed
26Tanaka1990(op.cit.,above,n. 5), 282. 27Marsilius libros sententiarum of Inghen,Questiones 1501; , Strasbourg super quattuor Frankfurt /Main1966,f. 475v. repr. 28D. 6 (1956),146, in:Augustiniana, Theolog)) ofthe14thCentury Trapp,Augustinián 274,at 252.
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It would be unwise and unnecessary,however,to expand these cases of intellectualinfluenceinto "schools".Those concernedprobablydid not thinkof themselvesor their intellectualformationin that way. More it highlightssimilaritiesof thoughton a few issues at the importantly, in otherareas. We are betterservedby of expense neglectingdifferences scholasticsissue by issue rather medieval of the relationship analyzing than in termsof "schools of thought". Scholars for University Support of artsshaped of thefaculty structure Otherfactorsoutsidetheorganizational the academic environmentat Paris in the time of Buridan and Oresme. Among the more importantof thesewere financialresourcesof students and masters,the impact of colleges,and access to books and libraries. In the second decade of the fourteenth centurythe leadershipof the to a Paris launched of strengthenand expand the campaign University financialsupportavailable to studentsand masters.They called upon cardinals,bishops,and abbots,eitherdirectlyor by means of papal pressure, to increasethe amountof supportforscholarsfromtheirdiocesesthrough the reservationand assigningof beneficesand prebends.A number of prelatesrespondedfavorablyto this plea, which in 1316 coincidedwith a shiftin papal policy thatpermittedthe Universityof Paris to submita list of petitionsfrommastersto which pope John XXII mightrespond by assigningexpectationsof beneficesin the giftof variouspatrons.Several prelatesalong witha few secularpatronsestablishedcollegesat Paris for the ostensiblesupportof poor students.Withina twenty-year period(13141334) the numberof collegesat Paris almostdoubled.29Althoughfinancial addressed in the eyes of university need was never sufficiently scholars, had been achievedin the firsthalfof the fourconsiderableimprovement teenthcentury. Behind the language of "supportforpoor scholars"statedin university lettersand petitionsas well as in the statutesof college foundations,the specificgroup that was targetedor that benefitedby the new sourcesof fundingwere not thepooreststudents,and in mostcases were not students submittedto at all. The rotuli , or scrollsof petitions,that the university 29H. Rashdall,TheUniversities in theMiddle , ed. F.M. Powickeand Ages ofEurope inthe A.B. Emden,3 vols.,Oxford1936,I, 537-539;A.L. Gabriel,TheCollege System Fourteenth Movement the Forward The F.L. in: Universities Fourteenth , of (ed.), Udey Century , Columbus1961,79-124. Century
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the papacy were limitedto thosewho were alreadymastersin one of the fourfaculties. Viewed fromthatperspective, theuniversity intendedbenefice supportto be directedto teachers,not students,and achievinga place on the listwas based on seniorityand the abilityto pay the requiredfee, not on thebasis of financialneed, althoughoccasionallysuch considerations were used to structurethe lists.30Similarly,appointmentto bursesat the newlyfoundedcollegeswere grantedto mastersof arts or advanced stuwho were alreadyat Paris.The system dents,oftenthosewithconnections, did not facilitate,nor was it probablyintendedto facilitate,the abilityof poor scholars to come to Paris. One had to be there already, and to have been therefora numberof years.Moreover,specificlimitationson the amount of ecclesiasticalor personal income that could be received whileholdinga bursewere usuallystatedin the college statutes,although such provisionswere not always strictly observed.Thus the targetgroup forcollegefellowships or burseswere youngmastersin the facultyof arts who were studyingfora higherdegree,or advanced studentsin the facultyof artswho had alreadyshownthe talentthatwould resultin a similaracademiccareer.Most students, especiallythosewhosemainqualification was poverty,were passed over. In the case of the rotuli , the limitations on wealth or income that were legislatedin college statutesplayed no role in the process. Masters of noble background,who could and often did petitionthe pope directlyor throughfamilymembers,also petitioned rotulus throughthe university alongsidetheirless fortunatecolleagues. Both Buridanand Oresme profitedby the availabilityof collegeburses. Early in his career,probablyas a youngmasterof arts,Buridanobtained a burse at the Collège du Cardinal Lemoine, foundedin the firstdecade of the fourteenth century.If the statutesof the college were enforced,31 he resignedhis fellowshipwhen he was elected rectorof the university in December 1327. Between then and his acquiringa benefice,namely the parish church of Hies northof Lens in Picardy,his principalif not sole means of incomewas fromthe feesof his students.When he obtained thatfirstbeneficein 1330, it was not a resultof the expectationhe had received in the rotulus of 1329 but was provided by the abbot of the monasteryof St-Vaast at Arras.32In the case of Oresme, he receiveda 30For in therotulus of 1349,all fournations listedfirst thosemasters who example, had notyetobtained a benefice, followed bythosewhohad one or morebenefices butat a levelof incomethepetitioner considered see Rotuli Parisienses insufficient; , vol.I, 305-443. 31M. Félibien, Histoire dela villedeParis , vol.5, Paris1725,608,611. 32For Buridan's in 1329and 1330,see Rotuli Parisienses , vol. I, 52-4. provisions
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burse in theologyin 1348 at the Collège de Navarre,six or seven years afterbecomingregentmasterin the facultyof arts.33Navarre,unlikethe Collège du Cardinal Lemoine, allowed fellowsof the college to receive income froman ecclesiasticalbeneficeup to a certainlevel,withoutlosing theirburse in the college. College affiliationplayed an importantrole in scholarlyproduction. Althoughthe majorityof those who receivedburses in various colleges have leftno worksthathave survived,mostmasterswhose workswe have were associated with colleges at some time in their academic career. Buridan is not known to have held a college burse afterleaving the Collège du Cardinal Lemoine,but his earlierassociationwould have given him continuedaccess to its library,should he have needed it. Oresme was connectedwith the Collège de Navarre, as were severalproductive 34 masters,and he became its Grand Masterin 1356. The Sorbonne,albeit a college for theologians,had one of the largestlibrariesin medieval Paris,and manyof itsmemberswere activein publication,again illustrating For and scholarlyproductivity.35 the close connectionof college affiliation is known to of not like Marsilius scholar who, Inghen, everyproductive have been associatedwitha college,thereare manymore who were.And whetheror not Conrad of Megenberghad any connectionwiththe college forGermanmastersand students,his earlyconnectionwiththe Cistercian house of studiesgave him access to that library,one of the largercolrichin textsfromOxfordand Cambridge.36 lectionsin Parisand particularly The supportthat came by way of papal provisions,althoughunequal did in distribution and influencedby social class and personalconnections, between masters.There is not,however,a directcorrelation benefituniversity the numberof ecclesiasticalpositionsand income acquired and the productivityof Parisian scholars.The point has been made by comparing the careers of Buridan and Oresme.37A comparisonof two contemporariesin the Picard nation,Buridanand Egidiusde Feno, is equallytelling. Reward: discussion ofthisissue,see W.J.Courtenay, Fora moreextended Philosophy's médiéetphilosophie de théologie Income theEcclesiastical , in:Recherches ofJeanBuridan 68 (2001),163-9. vales, 33On Oresme'sacademiccareer,see NathalieGorochov, deNavarre de Le Collège duXVesiècle(1418),Paris1997,680-1;W.J.Courtenay, safondation (1305)au début Oresme TheEarlyCareer , in: Isis,91 (2000),542-8. ofNicole 34Gorochov1997 cit.,above,n. 5), 680-1. (op. 35R. Rouse,TheEarlyLibrary in: Scriptorium, 21 (1967),42-71, oftheSorbonne, 227-51. 36On seeW.J.Courtenay, withtheCollègede St-Bernard, connection Megenberg's 35 (1937),102-24. in: Vivarium, ThePansTears, Conrad of Megenberg. 37 2001 (op.cit.,above,n. 5). Courtenay
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Both Buridanand Feno were regentmastersof artsin the 1330s. Feno, a realist,was one of the opponentsagainstwhom Buridan argued in sevin his De depenbetween 1332 and 1335, specifically eral determinations et convenientiis de diversidiver sitatibus determinationis dentiis, (1332), Defensiones 38Buridan ad speciem his Tractatus de relationibus tategeneris and (1333), (1334). mastersin the Picard nation who and Feno were among the sixty-four petitionedBenedictXII foran expectationof beneficeat the time of the new pope's coronationin 1335.39Buridanreceivednothing.Feno was among the eightwho did receive an expectation.Many of those in the faculty of artswho were awarded something, includingthosein the Picard nation, were simultaneously studentsin a higherfaculty,usuallytheology.In the case of Feno, his provisionwas not a simplebeneficebut an expectation of a canonicalprebendin a much sought-after collegiatechurch,St-Pierre at Lille. Feno had probablyjust begun his studiesin the facultyof theology by 1335, since by 1343 he was a fellowof the Sorbonne,had completed his twoyearsas biblicalcursor,and was preparingto read the Sentences .40By thattimehe had obtainedtheprebendat Lille and receivedfromClement VI an expectationof a canonical prebend in the cathedral chapter at Tournai. Withinthe next fewyears he obtained a canonical prebend at Courtrai,became dean of its chapter,and in 1350, by then doctor of theology,he was granteda canonical prebend and the lectorshipin theologyat Arras.41Buridan,by contrast,had receivedverylittlein the way of beneficesupportduringhis career,and the expectationof a canonical prebend at Arras that he had been grantedby ClementVI never materialized. The differencebetween their different rates of success in this area can probablybe ascribedto Feno's havingstudiedtheology,obtaining a burse at the Sorbonne,knowingits provisorPierre Roger (the future ClementVI) personally,and completinghis doctorate.AlthoughBuridan sometimesreferredto a fellowarts masteras "doctor,"substantialecclesiasticalincomewentlargelyto thosescholarswho were doctorsin thenormal senseof thattitle,namelymastersof theology,canon law, or medicine.
38Michael1985 cit.,above,n. 427-43. {op. 5), 39CharlesVulliez, Autour d'unrotulus adressé deParisà Benoît XII (1335): parl'Université lerôledesmaîtres èsartsdela nation de Rome. , in: Mélangesde l'Ecolefrançaise picarde 114 (2002),359-369.On Feno'sprovision, see Rotuli Parisienses I, 75. Moyen Age, 40Rotuli Parisienses 191-2. I, 41Analecta deClément VI(1342-1352), ed.U. Berlière, , vol.I: Suppliques Vaticano-Bélgica Rome-Bruxelles-Paris 1906,#1955.
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in Arts Buridanand theLength Careers of Teaching It has long been supposed that Buridan was unique in teachingin the and seekinga degreein yearswithoutstudying facultyof artsforoverthirty a higherfaculty.He was certainlythe most famousmasterto followthat career path, but it now appears that he was not the only one to do so. Before examiningthe other cases, some cautionaryremarksneed to be made. First,it would be incorrectto state categoricallythat Buridan never studiedin a higherfaculty,such as theology.We simplyhave no evidence that he did, and there are several examples of arts mastersat Paris whose supplicationsto the papacy or lettersof provisiondescribe themsimplyas mastersof arts,althoughone supplicationdated in between the othersmentionsthat the individualwas also studyingin theology. Thus the failureto mentionstudyin a higherfacultywhen supplicating the pope is no guaranteethat the individualmasternever did so. We have very few documentsconnectedwith Buridan that are of the type that would mentiontheologicalstudyeven had he undertakenit. Thus, while he never attaineda degree in theologyor in any otherhigherfaculty,we cannotsay withcompleteassurancethathe neverstudiedtheology. As to the length of his teaching career withoutevidence of higher study,thereare severalotherexamplesfromthe same period.42Petrusde Vallepartiswas masterof arts by 1331, supplicatedin the rotuliof 1342 that and 1349, and again in 1362. If his regencywas not interrupted, The same would mean a teachingcareer in artsof over thirty-one years. holds true for Robertus Fabri, Honoratus de Porta, Henricus Bobei, JohannesChacardi,JohannesDurandi,JohannesSieranviller,and Petrus Melmete- ¿illwith teachingcareers in arts of thirtyyears or more. In the case of Guillelmusde Moreto,regentin artsforover thirty-four years, years,and Andreas de JohannesBaril, regentin arts forover thirty-four Sancto Clodoaldo, regentin arts for over thirty-seven years, we know thattheyalso studiedin a higherfaculty,canon law in the case of Moreto and theologyin the case of Baril and Sancto Clodoaldo. Long careers withoutevidence of studyin a higherfacultyare certainlyrare, but the uniquenessof Buridan in this regardcan no longerbe maintained. This should caution us against seeing in Buridan the beginningof a devotedsolelyto philosophyand intentionally careerself-consciously passthat a theologicaldegree offered.Those career the opportunities ing up 42Thefollowing Rotuli vol.I, andRotuli Parisienses aretakenfrom Parisienses, , examples and E.D. Goddard, Leiden2003. vol.2: 1352-1378 , ed. W.J.Courtenay
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who completedstudyin a higherfacultygained ecclesiasticalpositions that broughtconsiderableincome. It is possible, of course, that these otherexamples of long teachingcareers in arts were also attemptingto make the teachingof philosophya career in itself.I suspect,however, records thatmotivationswere more mixed,and the absence of university that would prove continuousregencyor the certainabsence of studyin a higherfacultymakes conclusionsin this area hypothetical. The availabilityof new sources and evidence forthe Universityof Paris in the fourteenth centuryputs the careers of Buridan and Oresme in a richercontext.It helps us understandmore preciselythe academic strucin whichtheylived and wrote.It clarifiesthe means tureand environment of influenceamong mastersand students,separatingthose contextsthat were unlikelyto have produced any shapingof intellectualoutlookfrom those that are more viable. It has also broughtto lightnew information Michael de Montecalerio on some of the opponentsof Buridan,specifically In the de Feno. so and Egidius originalityand importance of doing Buridan and Oresme has not been diminishedbut ratherenhanced by seeing them more clearlyin the contextin which theylived. Madison, Wisconsin of Wisconsin University
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Introduction and sixteenthcenturiesJohn Buridan enjoyed Throughoutthe fifteenth a reputationas a prominentmasterof artsat Paris. The manuscriptsand early printededitionsof his workswere widelydisseminatedin all corsuch ners of Europe and became requiredreadingat many universities, as Vienna, Prague, Krakow, Rostock,and Saint Andrews.1But how was his impact among thosewho knew him personally,among those residing in Paris in the firsthalfof the fourteenth century?Did Buridanhave any close followersor students?As far as I am aware, thereis no contemporary Parisian evidence to the effectthat there existed a school of "Buridanists"in the same way as there were schools of Thomists or Scotists.Even so, one mightask whetherthereis some evidenceto idenParis.2 tify,in retrospect,a school of Buridan in fourteenth-century * Thisarticle in every meus senseof is dedicated to HenkBraakhuis, magister possible ofhissixty-fifth Partsofthisarticle formed thebasis theword,on theoccasion birthday. de la Renaissance I gavein March2000at theCentre d'Etudes oflectures Supérieures in NewYork.I thank in Toursandin April2002at theMedieval JoelBiard Academy DirkI thank PaulBakker, William kindinvitations. andGyulaKlimafortheir Courtenay, fortheir andMichiel Streijger helpful suggestions. JanDekker, Sarnowsky Jürgen 1 B. Michael, Werken undzurRezeption seiner . Studien Leben Buridan zuseinem , seinen Johannes FreieUniversität Mittelalters Theorien imEuropa desspäten Berlin, , 2 vols,Ph.D.dissertation 1985,vol.1,239-398. 2 AtthispointI should thatin 1551a "Maison de Buridan" is attested mention already andindicated on oldmaps.See note15.Could ofthePicardnation, amongtheschools leftto theuniversity at hisdeath?See Michael thishavebeenthehousethatBuridan ofthesources, which 1985[op.cit., above,n. 1),vol.1,237,esp.n. 533foran indication from Therealsois someevidence thefifteenthareall laterthanthefourteenth century. a viewwhichis heldby Dominicus ofFlandria thinker (d. 1479),whomentions century XII libros of Flandria, See Dominicus "Buridanists." IV, Quaestiones super Metaphysicorum, Frankfurt am Main,1967,fol.16ra:"Aliivero 1523,reprinted q. 2, a. 5; ed. Venetiis analoestunusunitate unumconceptum suntquiponunt quitamen conceptus praecisum, sicutsuntburidanistae entis, , quiponunt univocationis, quodconceptus giae,etnonunitate est ex partereiconceptibilis si veroaccipiatur secundum si accipiatur se, estunivocus; tamen." analogus, praecisus © Koninklijke BrillNV,Leiden,2004 - www.brill.nl Alsoavailable online
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If we take PierreDuhem (1861-1916) as a startingpoint,thisquestion seemsto have been examinedfornearlya century.EspeciallyafterDuhem's studies,the Buridan School at the Universityof Paris won everybody's admirationand was established as a historicalfact. In brief,Duhem claimed that the accomplishmentsof seventeenth-century science, as in in Galilei and had essence been achieved Descartes, exemplified already in the fourteenth centuryat the facultyof arts in Paris, and particularly, the school of by John Buridan.3With respect to this school, Duhem offeredthe followingobservationsin his Système du monde : Les enseignements furent trèsfidèlement reçuset développés [de Buridan] pardes maîtres de Helmstoedt, surnommé Albert de Saxe,parTémon éminents, parAlbert le filsduJuif, La faculté desArts parNicoleOresme, parJeanMarsile d'Inghen. unedemi-siècle, l'Ecolede Buridan.4 de Parisfutainsi,pendant And again: à et Albert de Saxe,la Scolastique ne trouve plusriende nouveau AprèsBuridan il advient la lecture diresurla nature du mouvement; comme des presque toujours, nousannonce le déclinde l'Écolede Paris.5 oeuvres de Marsile d'Inghen Nowadays,historiansof scienceagree thatDuhem's visionof the Buridan school as an anticipationof seventeenth-century natural philosophyis in this has not diminished the any way high esteemforthe wrong.Yet, Buridan school. Even severe criticsof Duhem, such as AnnelieseMaier and Marshall Clagett,have emphasized that the school of Buridan was one of the two most prominentschools of medieval naturalphilosophy (the otherbeing the school of Thomas Bradwardine(d. 1349) at Merton College in Oxford,also knownas the Oxford Calculators).Accordingto Maier, the precise teacher-studentrelations between the members of the Buridan school were unknown,althoughthe school was clearlycharacterizedby "its unitaryteachingtraditionand its intellectualphysiognomy."6Even thoughMaier was more cautiousthan Duhem, the picture that thus emergedwas that of the Buridan school as a coherentinner circle of studentsand followers,withJohn Buridan himselfat its center. The existenceof a Buridan school in fourteenth-century Paris has been
3 Pierre Lesystème dumonde. Histoire desdoctrines dePlaton à Copernic Duhem, , cosmologiques vol.6, 697 andalsovol.8, 200,215-6,and225.I am notsuggesting Paris,1914-1958, thatthenotion ofa Buridan schooloriginated withthestudies byDuhem. 4 Duhem1914-1958 (op.cit.,above,n. 3),vol.6, 698. 5 Duhem1914-1958 (op.cit.,above,n. 3),vol.4, 361. 6 Anneliese im14.Jahrhundert Galileis Maier,Die Vorläufer , Roma1949,3.
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repeated in many subsequentpublications,if sometimesonly as a label of convenience.7 Since the timeof Duhem, muchfurther knowledgeof Buridan'sthought, of that of his alleged followers,and of the intellectualand institutional Paris has accumulated.8In lifein fourteenth-century aspectsof university in criticaleditions,or have become available some crucial texts addition, are in the course of completion.All this material,broughttogetherby many scholars,providesan invitationto draw togethersome threadsand of the so-called Buridan school. to offera new interpretation A portrait of theBuridanschool In orderto set the stage forthisstudy,I would like to recallbrieflysome striking biographicaldetailsof the membersof the Buridanschool. It has been portrayedto consistof the followingfive thinkers: John Buridan (d. ca. 1360), Albertof Saxony (d. 1390), Nicole Oresme (ca. 1320-1382), ThemonJudeus{flor.1349-1360),and Marsiliusof Inghen{ca. 1330-1396).9 JohnBuridanoriginatedfromthe diocese of Arras,and hence,belonged We do to the Picard nation. He twice servedas rectorof the university. not know under which masterBuridan took his degree,but it certainly was not Ockham, as the seventeenth-century historianDu Boulay claimed in his Histoirede l'université de Paris.John Buridan was the most prolific Aristotlecommentator of the group,ifnot of the entirefourteenth century. He made major contributions to logic, physics,metaphysics, and ethics. 7 Somescholars caution. Michael1985{op.cit., haveexpressed See,forinstance, above, n. 1),vol.1, 281-2,andmostrecently Michael Albert J. Fitzgerald, ofSaxony's Twenty-Five A Critical Edition onLogic. circaLogicam, Leiden-BostonQuestions ofHisQuaestiones Disputed ofSaxonywasa pupilof Köln2002,1-14,whotakesissuewiththeviewthatAlbert Buridan. 8 Fora survey oftheliterature seeJ.M.M.H.Thijssen, LateMedieval Natural Philosophy. inScholarship Some Recent Trends de Philosophie etThéologie 67 Médiévales, , in:Recherches ofa oftheproblematic and 188fora first sketch (2000),158-90, esp. 177-85, concept coherent "Buridan school." 9 Forthebiographical I haverelied Michael1985 onthefollowing studies: information, Theorie Diearistotelisch-scholastische above,n. 1),esp.vol.1,79-238; Sarnowsky, {op.cit., Jürgen Alberts vonSachsen desAristoteles derBewegung. Studien zurPhysik zumKommentar , Münster 1989, Oresmes Kommentar desAristoteles Mcolaus zurPhysik Kirschner, , Stuttgart esp. 11-54;Stefan deThémon maître L'oeuvre 1997,esp.15-37;HenriHugonnard-Roche, astronomique Juif, parisien vonInghen, libros duXIVesuele,Genève-Paris 1973;Marsilius Quaestiones quattuor super vonManuelSantos Bd.I. Super Sententiarum. 1-7;bearbeitet Qmestiones Noya,Leidenprimům, Köln-Boston 2000,esp.pp.xvii-xxvi.
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Albertof Saxonyis probablybestknownas thefounderof theUniversity howof Vienna in 1364. Beforehis involvementwiththisnew university, career in Paris. He took his degreesin ever, he enjoyed a distinguished the artsfacultyin Paris in 1351, under masterAlbertof Bohemia. Before he arrivedin Paris, he probablystudiedin Erfurt.Originatingfromthe regionof Helmstedt,he belonged to the English-Germannation. Several officesat this nation. In 1353 he startedstudyingthetimes,he fulfilled but ology, probablynevertook his degree. From 1366/67 untilhis death on July 8, 1390, he was Bishop of Halberstadt.Alberttoo wrote many commentaries.Especially his commentarieson De cáeloand the Physics were influentialand survivein many copies. Nicole Oresme was born in thevicinityof Caen. His name firstappears in university recordsin 1346, as a studentof theologyat the Collège de Navarre. From a papal letterthat was recentlyrediscovered,we now know that in 1342, he alreadywas a masterof arts.10In 1356, Oresme became rectorof the Collège de Navarre, which means that he must have had his doctoratein theologyby then. In 1377, he was nominated Bishop of Lisieux. He died on July 11, 1382. Oresme is well knownfor of some of Aristotle'streatises.He also wroteLatin his Frenchtranslations et corruptione commentarieson De anima , Metheora , , De cáelo,De generatione Besides the factthat he belonged to the Norman nation, and the Physics. not much is knownof Oresme's career at the arts faculty. ThemonJudeusoriginatedfromMünsterin Westphalia,and, as a consequence, belonged to the English-Germannation. Like Albert,he too career as an officerof thisnation.Between 1349 and had a distinguished 1353 he was absentfromParis,probablybecause of the Plague, as Henri Hugonnard-Roche conjectured.During this period Themon taught in Erfurtat the school of the Scotch BenedictineAbbey of St. Jacob, one Note that Albertof Saxony also of the so-called German Schottenklöster. stayedin Erfurtduringthat period. It is unknownwhetherthey knew each otherfromErfurt,but theycertainlymust have knowneach other fromthe English-Germannation. In 1361 Albertsucceeded Themon as receptor of that nation. Themon wrote a commentaryon Aristotle's His otherworksare treatiseson astronomy.11 Metheora. 10See William TheEarly Career Oresme , in:Isis,91 (2000),542-8. ofNicole J. Courtenay, 11It hasnowbeenestablished thatThemondiedin 1361.See William J. Courtenay tothePopeFrom theUniversity Rotuli Parisienses: andEricD. Goddard, , ofParis Supplications vol.II: 1352-1378 2004,5. , Leiden-Köln-Boston
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Marsiliusof Inghen was born near the city of Nijmegen. He is first mentionedin the recordsin 1362, when he took his degree in arts at WilliamBuser of Heusden. Like Albert Paris underhis Dutch countryman and Themon, he belonged to the English-Germannation,in which he offices.He was rectortwice (1367; 1371), and held many administrative at the papal court. In 1366 he startedto studytheuniversity delegate ology in Paris, but only took his degree in 1395/96 in Heidelberg.His to Germanywas connectedwith his involvementwith the transference foundationof the new universityof Heidelberg (1386). Most influential among the many Aristotlecommentarieshe wrote,was the one on De et corruptione. generatione If one reviewsthe biographiesof thesefivemasters,severaldetailsare striking.With the exceptionof Themon, they all commentedon many worksby Aristotle,some of them even several timeson the same work. All of them were secular mastersat the arts facultyin Paris. However, nations.All of them held importantadministheybelonged to different trativeofficesfortheirrespectivenation.Two of them,Albertof Saxony, and Marsiliusof Inghen,became even involvedin the foundationof new universities, namelyVienna and Heidelberg.With the exceptionofJohn Buridan, they all at some point in theircareer, moved on to theology. Two of them,Albertof Saxony and Nicole Oresme, eventuallybecame bishops. In brief,theyall were prominentpersonalities,both in intellectual affairsas in mattersof governmentand administration. In my attemptto seek new perspectiveson the Buridan school,I have been followingtwo, ratherobvious, lines of inquiry.The firstapproach is institutional. The second line of inquiryis doctrinal.Both hark back hison medieval notionsof "school" that are stillused in contemporary toriography.12 The BuridanSchool:theInstitutional Perspective The basic medievalmeaningof "school" was thatof the classroomwhere the teaching took place. The city of Paris hosted many such schools, located in specificareas. They were the venues of medieval intellectual life.What role did specificlocationshave in the makingof late-medieval (natural)philosophy?Or, in otherwords,how probable is it that Albert 12William inFourteenth-Centwy Schools andScholars , Princeton, NJ England J. Courtenay, au XIIIesiècle desuniversités , Roma1987,43-5. 1987,171-5andOlgaWeijers, Terminologie
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of Saxony,Nicole Oresme,ThemonJudeus and Marsiliusof Inghenwere studentsin Buridan'sschool, as has been assumed in much of the scholarlyliterature?Do occasional referencesto "my master"in the worksof some of these authors,if they apply to Buridan at all, have a deeper significance,or are they standardformsof courtesyto address (senior) colleagues?13 The facultyof artsin Paris was the combinationof foursmallerunits, the French,Picard, Norman and English-Germannations.Geographical origin determinedto which nation a master or studentwould belong. Together,the nations acted as the facultyof arts,presided over by the rector.In addition to theircommon duties,such as the confermentof degrees and the establishmentof the curriculum,the nations exercised activitiesas separate corporate components.Each nation had its own revenues,treasury,seal, patron saints,and authorityto regulate officers, its own members.The head of the nationwas the proctor.Among other things,he summonedthe assembliesof the membersof his nation and presidedover theirmeetings. Since teachingwas organisedby nation,the questionwhich I needed to investigatewas, whetherthe "Norman" Oresme, and the "AngloGermans" Albertof Saxony, Themon Judeus, and Marsilius of Inghen could possiblyhave been studentsof the "Picard" John Buridan.14This lead questionraisedotherquestionssuch as how the schoolsof the nations were organised,and which studentstheyrecruited.Probablydue to the littlehas been writtenon theseaspects povertyof the sources,surprisingly In what of university follows,I shall presentboth well-knownand history. less widelyknownaspects of the schools of the nationsin Paris.15 13Courtenay of attention tothisdimension 1987(op.cit.,above,n. 12),191hasdrawn In theQuaestiones etcorruptione master." libros Degeneratione theepithet , super "my(reverend) of ed.Venice1501(photomechanical Frankfurt a.M.,1970),fol.106va,Marsilius reprint in thisway:"Etquiahecopiniomihiprobabilis nescio refers toBuridan apparet, Inghen Bridan ideoearn sipassionatus ex opinione meimagistři Johanni magistři quiearnposuit, in suispartibus to et earnimmediate declarare intendo." propono According persuadere Laphysique deBruges deBuridan etletraité ducield'Albert deSaxe Benoît Patar, , 2 vols,Longueuil inAlbert ofSaxony's three suchreferences Quaestiones super (Québec)2001,vol.1,507*-8* libros De cáelo should alsobe readas references toJohnBuridan. Patarconsiders thecourofSaxony as proof thatAlbert wasa pupilofBuridan. tesytitles 14Notethat,forreasons ofchronology, of itmayhavebeenimpossible thatMarsilius everpersonally metJohnBuridan, sincethelatter havebeendead Inghen mayalready whenMarsilius cameto Paris. 15Whatfollows is heavily indebted to thefollowing Auctarium Chartularii publications: Universitatis Parisiensis andEmileChatelain, Paris1894,vol.1,pp.xxvi, ed.HenriDenifle duvieux Paris xxxiii; , 5 vols,Paris1866-1897, Adolphe Berty, Topographie historique esp.vol.5
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From the minutesof the meetingsheld by the English-Germannation it appears that many as recordedin its proctors'book {liberprocuratorum), of the nation'sexpenseswent to the purchase,upkeep,and repairof the schools. On the basis of these records,it is even possible to reconstruct more or less accuratelythe location of the nations'severalschoolsin the Rue de Fouarre.The schoolsof the Frenchnationwere adjacent to those of the Normans,which in theirturnwere next to those of the Picards and the English-Germannation. On the oppositeside of the streetwere additionalschools of the Picards and of the English-Germannation. At As fromthe second half times,the nationswould even share a building.16 of the fourteenth century(1358), the Rue de Fouarre was closed offat barriers. wooden They servedto preventthe depositof litterin nightby the streets,about which the mastershad bitterlycomplained.Although according to regulationsfromthe early fourteenthcentury,it was forbidden to set up schoolsoutsideof the Rue de Fouarre,in the latterhalf of that century,the nations had to seek other locations for schools,in order to accommodatethe increasingnumberof studentsand masters. In any case, it is clear that each of the nations rented,owned and maintainedbuildingswhich theydistributedamong theirmastersforthe purposeof teaching.From the Frenchand Picard nationswe have records about how the schools were assigned to theirmasters.Only the regent masters,thatis, those masterswho were activelyteaching(notjust residing) duringthe Grand Ordinary,a definedperiod of timewhichran from October 1 untilEaster,were entitledto have a school assignedto them. By 1371, underthe rectorshipof Marsiliusof Inghen,the old customwas abolished under which masterswere to retainthe schools theyhad used in the previousyear. Instead, the schools were now distributedamong the regentmasterseach year betweenthe feastof Bartholomew(August, 24) and Saint Remigius(October, 1), the beginningof the academic year. One of the major dutiesof any master,of course,was to supervisethe studyof his students.But where did these studentscome from?Thanks to a prosopographicalstudyby Mineo Tanaka it is possible to give an impressionof the geographicaloriginsof the studentpopulation of the
ofthedifferent thelocations a map,showing which includes centrale del'université), (Région theMiddle intheUniversity Nation schools; ofParisduring GrayC. Boyce,TheEnglish-German Universities intheMediaeval PearlKibre,TheNations , Cambridge, 1927,113-49; Ages, Bruges Mass.1948,82-97. 16In 1393Picards ofschools ownedbytheEnglish-Germans. theupperstory occupied ofthebuilding. aroseoverthemaintainance Controversy
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English-Germannation.17Tanaka was interestedin studyingthe relations whichstubetweenstudentsand masters.To thispurpose,he investigated dentstook a degree underwhich master.He focusedon the threemajor the license (determinatici), stagesin the academic career: the determination in the interested Tanaka was licentia and the mainly ), (i inception(inceptio).18 instance in academic for the of the that occurred study, supervision patterns in the number of studentswho took all three degrees under the same master,or who switchedto another supervisorafterthe determination, or afterthe license. His prosopographicstudymakes one point abundantlyclear.Studentstooktheirdegreeswithmastersof theirown nation.19 More in particular,they seemed to seek out mastersfrom their own Occasionally,it did happen thata candidateobtainedhis license region.20 under a master from another nation. However, this practice was due to the fixednumberof bachelorsthat each nationwas allowed to examine for the license each month.21The proctor's book of the EnglishGerman nation singlesout the candidateswho took theirlicense under a masterof anothernationwithan epithet.They are called normanizatus , , but they remained members of the Englishdizatus,or gallicatus jbicar German nation.22 The nations did not take lighdytheirprerogativeover the academic degrees. Two bitterdisputesabout the boundaries of the nations were over the inceptionof candidates.In 1266, precipitatedby controversies Jean de Ulliaco, residentof a diocese of Beauvais, and hence belonging
17MineoTanaka,La nation deParisà lafinduMoyen del'Université Age, angio-altemande Paris,1990. 18Notethatonlyregent Thisis thedetermination. masters wereallowedto supervise twoexams. nottruefortheother 19Tanaka1990(op.cit.,above,n. 17),156-85. 20The results of ofa geographical coincide withtheresults ofTanaka'sstudy analysis onthebasisofdifferent carried outbyWilliam theParisacademic Courtenay, community forinstance, thelodgHe tooconcluded andtoa different source material that, purpose. ties.See William to regional or linguistic wasaccording community ingoftheacademic A Social Portrait Fourteenth Parisian Scholars inthe 1999, , Cambridge Century. Early J.Courtenay, 81-91. 21"On March16, 1338,thefaculty whowouldbe ruledthatofthesixteen scholars the in artsat Ste.Geneviève eachmonth, sixwereto be from examined forthelicense andtwofrom theEnglishandPicardnations, theNorman French foureachfrom nation, at eachaudition." See Kibre1948 German ofwhichhalfwouldbe examined nation, and ed. HenriDenifle Universitatis Parisiensis, (op.cit.,above,n. 15),101,and Chartularium 4 vols,Paris1889-97, vol.2, 474. ÉmileChatelain, 22Tanaka1990(op.cit.,above,n. 17),153-4.
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to the Picard nation,wishedto inceptin the Frenchnation.The Picards, however,not only claimed him, but seized him bodily.23 More interesting for our purpose is another conflict,which arose in 1356, and which involvedsome of the main charactersof the Buridan school. In that year, a certainJohn Mast passed throughthe Rue du Fouarrewiththe beadles of the Picard nationto seek the permissionfrom the mastersof artsto incept,as was the custom.24 Master ThemonJudeus from the English-Germannation, however, refusedhis approval. He pointedout thatJohnMast had alreadydeterminedin the English-German nation.25The earlierdisputebetweenthe two nationsover Mast's degrees stillhad not been resolved.For thisreason,he had to refrainfromattaching himselfto eithernation. The ensuing discussionsbetween the two nations,which dragged on untilthe end of 1358, are well documented. The conclusion of the debate was that the English-Germansand the Picards settledon the riverMeuse in the Low countriesas the boundary betweentheirtwo nations.The geographicaland linguisticramifactionsof the debate need not concernus here. What is interesting is, that Buridan the case of the Picards beforethe committeeof John presented deputieswhich had to decide the dispute;26that Themon Judeus substitutedthe absent proctorof the English-Germannation,and that among thosemasterswho signedthe finalagreementwere not onlyJohnBuridan, but also Albertof Saxony. As usual, the meetingwas rounded offin a tavern.Afterthe treatywas signed,the masterscelebratedin a pub called "At the grange" (Ad grangiam). Part of the bill was paid by a master William Buser of Heusden, who not only happened to be a local from the contestedregion,but who also was the masterunderwhom Marsilius
23Chartularium Universitatis vol.1,nr.409. Parisiensis, 24See GrayC. Boyce,TheControversy over the Between the andPicard Boundary English-German in:H. Vander Linden e.a. (eds),Études d'Histoire intheUniversity Nations ofParis(1356-1358), dédiées à la mémoire deHenri Pirenne oftheincident , Bruxelles 1937,55-66foran analysis anda discussion ofthesources. 25Auctarium Parisiensis Chartularii Universitatis mensis , vol.1, 206:"Item19adieejusdem factaeratcongregado nomine bacalario, Julianum apudSanctum pauperum super quodam volebat ettransiisset cumbedellis nacionis Mast,Leodiensis Johannis dyoc., quidumincipere ad petendum licenciam a magistris facultatis ut artium, Pycardie pervicumStraminis morum suaindictafacúltate eisplaceret, Themo est,siincepcio respondit magister Judeus insuanacione, nacionis fuit etsuperhoc Anglicane, quodnon,eo quodaliasdeterminans ortafuisset lisinter nacionis etnacionis exeoquod Pycardie Anglicane predictarum, maģistros ad suamnacionem, fuisset nacioeumdicebat et superhocdiscussum pertinere quelibet infacúltate setenere debetad unamnacionem predicta, quodnecmagis quamad aliam..." 26Auctarium Chartularii Universitatis Parisiensis , vol.1, 212-8.
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of Inghenwould inceptfouryearslater.27At the basis of the disputeover the nations'boundarieswere financialconcerns.The studentshad to pay a fee to the nation for theirexams, and it was this financialdimension which caused the commotion. I believe,that it is highlyquestionableto view The episode illustrates, Albertof Saxony,Nicole Oresme and ThemonJudeus as studentsat the schoolsof the PicardJohn Buridan.As mentionedabove, in the cases of Albertof Saxony and Marsiliusof Inghen, it is even attestedthat they took their degrees with masterAlbert of Bohemia and William Buser, who came fromthe same regionsas theirgraduates.On the respectively, basis of the above evidencefromuniversity sources,the most immediate the doctrinalaffiliations taskin Buridanresearchlies,I think,in untangling that are reflectedin the writingsby Buridan himselfand in those by his alleged followers. TheBuridanschool:thedoctrinal perspective With respectto examiningBuridan's doctrinalfollowingin fourteenth, centuryParis,I willlimitmy attentionto his commentarieson the Physics and relate them to the commentaryby Albert of Saxony. This choice on the Physics seemsnaturalforseveralreasons.First,Buridan's Quaestiones stood at the heart of the entireconcept of a Buridan school. Moreover, thereare a fewindicationsin the scholarlyliterature,about which more And finally,we can now benefit below,thatAlbertused Buridan'sPhysics. on the Physics fromthe editionof Albertof Saxony's Quaestiones by Benoît Patar and the nearlycompletededitionof one of Buridan's texts.28 If we want to understandthe impact of Buridan'sPhysics upon Albert of Saxony, we must rememberbrieflysome factsabout its transmission. are being attribon the Physics At presenttwo long versionsof Quaestiones uted to John Buridan. One has been handed down in fourmanuscripts The otherversionhas and is sometimesreferredto as the tertialectura.29 27Auctarium Parisiensis Chartularii Universitatis , vol.1, 233-6. 28Albert etQuaestiones in hasbeeneditedin BenoîtPatar,Expositio ofSaxony's Physics 1999. Edition deSaxonia attrïbutae. Aristotelis adAlbertům , 3 vols,Louvain-Paris critique Physicam ultimam secundum octolibros A critical ofJohnBuridan's edition Quaestiones Physicorum, super OlafPluta, lecturam is beingprepared Dekker, Dirk-Jan including bya teamofeditors, and Renaissance at theCenterforMedieval and thepresent MichielStreijger author, at Nijmegen Natural University. Philosophy 29Thisimplies ofBuridan's earlier versions be twoother, thatthereshould Quaestiones Iftheyexistat all,theyhavenotbeenidentified on thePhysics. yet.
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been preservedin 31 manuscriptsand one printededitionfrom 1509.30 it is commonlylabeled as the ultimalectura. In the survivingtestimonies, The latteris longer, seems to precede the ultimalectura. The tertialectura in thatthereare more quaestiones , but also more elaborateargumentsand a more polishedstyle.There seem to be few,ifany,doctrinaldivergences In the shortpreface to the Quaestiones between the two versions.31 super ultimam lecturam octolibrosPhysicorum Aristotelis , secundum , as the fulltitleusually runs,this textis introducedas Buridan's authorizedversion.32 Aristotelis have Albertof Saxony's Quaestiones superoctolibrosPhysicorum been handed down in 18 manuscriptsand at least fiveprintededitions.33 in the manuscripts, I thinkthat thereis On the basis of the attributions of thiswork:it is a genno reason whatsoeverto doubt the authenticity uine text by Albertof Saxony. This observationmay seem redundant, were it not that Benoît Patar, the editorof the Quaestiones superoctolibros Aristotelis , has rejectedAlbert'sauthorship.He believesthatthis Physicorum textis aprimalectura byJohnBuridan,and consequendyrefersto Buridan's as the secundalectura .34In addition,it seems that the firstfive tertialectura 30See Dirk De tijdßlosofie vanJohannes Buridanus % Ph.D.thesis, (f ca. 1360 Jan Dekker, ofNijmegen, 2003,99-103. University 31The tidesofthequaestiones oftheultima lectura aregiveninJ.M.M.H.Thijssen, The onthePhysics andtheir Relation totheQuestions onthePhysics Short Redaction Questions ofBuridan's toMarsilius doctrinale etlittéraire du moyen-âge, attributed d'histoire , in:Archives ofInghen in M. Markowski, lectura areprovided 52 (1986),237-66,esp.240-5.Thoseofthetertia I-VIIIlibros Aristotelis deNicolas Oresme in:Mediaevalia LesQuaestiones retrouvées?, super Physicorum 26 (1982),19-41,esp.37-41.See nowalsoBenoîtPatar2001 Polonorum, Philosophica fora comparison ofthetitles. A. Maier,^wei ., above,n. 13),vol.2, 350-419, {op.cit Das Problem derintensiven derscholastischen , dieImpetustheorie, Naturphilosophie. Größe Grundprobleme withrespect totheimpetus Roma1968,370-8compared bothversions theory. J.M.M.H. over hetoneindige. Eenonderzoek naarzýntheorie over hetoneindige in Buridanus Thijssen, Johannes hetkader vanzýnwetenschapsennatuurfilosofie , 2 vols,Nijmegen 1988,vol.1, 7-71compared oftheinfinite. withrespect to Buridan's bothversions theory 32Approximately uthabetur halfofthemanuscripts offer thefollowing "Bonum, preface: tantoestmelius etdivinius. Ethicorum communius, , quantoestmultis Propter quod primo meisprecibus inclinatus multorum de discipulis seuscholaribus egoaliquascribere praeethancillisscripturam commude difficultatibus libriprimi Aristotelis, Physicorum sumpsi - utdicunt - multa inscholis audita adiutorio sinealicuius nicare, scripturae quianonpossent de omissis etminus benediccommendare. memoriae Superquibusegopetoetsupplico autemsi quaefuerint convenientia multas haberegrates tisobtinere de inventis veniam, See Dekker orationes." etbonorum scholarium 2003{op.cit.,above,n. 30),11 and 102. 33Sarnowsky 1989{op.cit.,above,n. 9), 439-40,and 450,and Patar1999{op.cit., above,n. 28),38*-59*. 34I cannotgo intothearguments whichseems here,butletthefollowing quotation, BenoîtPatar2001{op.cit.,above, to capture Patar'spointofdeparture, speakforitself. du n. 13),vol.2, 399*:"Il fautdoncaffirmer dèsmaintenant avecforceque la Physique 477n'estpaset nepeutpas êtred'Albert de Saxe,quandbienmêmetousles manuscrit
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books of a laterversionof Albert'sQuaestiones have been preservedin one has It not been studied here. manuscript.35 For the presentcomparisonof Albert'sand Buridan's Physics , I have singledout two case-studies.The firstconcernsthe problem of quantity or spatial extension,whereas the second one concernsBuridan's theory of impetus.I was led to thischoice by a suggestionfirstmade in Jürgen Its implicaSarnowsky'sfundamentalstudyof Albertof Saxony's Physics. tionsforthe whole idea of a Buridanschool,however,were,to myknowledge, neverfurtherexplored.Sarnowsky'sthesis,forwhich I will provide on the some additional evidence, is that Albert of Saxony's Quaestiones lectura and his ultimalecneed to be placed betweenBuridan'stertia Physics tura.Albertknew Buridan's tertialectura of the Physicsand respondedto it. Buridan in his ultimalectura , in turn,respondedto Albertof Saxony's 36 on the Quaestiones Physics. Substance and Quantity In general,medievalthinkersbelieved that spatial extensionbelonged in the categoryof quantity,and that some substances,such as bodies, have extensionas theirmost importantfeature.However, not only the substance of body, but also many of its qualities were considered to be forinstance,werebelieved extended.The dimensionsof Socrates'whiteness, to coincide with Socrates himself,that is, with substance.But is it really or accurate to equate quantitywith substanceand quality,respectively,
dela planète le luiattribueraient. etde touslesincunables de touslesmanuscrits colophons connue a conIl fautau contraire soutenir oeuvre queBuridan qu'ils'agitde la première 477preserves an anonymous ." Themanuscript sacréà la Physique copyofthetext Bruges Noneoftheknown manuis attributed to Albert ofSaxony. thatin othermanuscripts attributes thistexttoJohnBuridan. scripts 35Thelaterredaction inthemanuscript Welcome Medical hasbeenpreserved London, L 15,fols.lra-99vb. Books6-8inthismanuscript coincide with Albert's Historical Library, in Sarnowsky and arestudied 1989(op.cit.,above,n. 9),451-60, usualtext.Bothversions inJürgen PlaceandSpaceinAlbert Commentaries on further Sarnowski, ofSaxony's compared andPhilosophy, 9 (1999),25-45.Mostrecendy, thePhysics , in:ArabicSciences Sarnowsky onthePhysics attributed toAlbert ofSaxony, hasestablished thatyetanother commentary ofErfurt. See EinAlbert vonSachsen wasac tually zugeschriebener byTheodoric composed ausderMitte des14.Jahrhunderts 27 (2002),449-74. , in:Medioevo, Physikkommentar 36Sarnowsky oftherel1989(op.cit.,above,n. 9),50-1,and58-9.Notethateditions invol.2 ofPatar2001(op.cit., evanttexts areavailable above,n. 13),vol.2. Pataredited as partofhis,as I believe, failed toprovethatBuridan theseandother attempt fragments ofthetextgenerally attributed to Albert ofSaxony. Forthesake is theauthor actually I willrefer ofconvenience, to Patar'sedition ofthepassages thatarequotedhere.
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should quantitybe considereda separateentity?Originally,thisontological question arose in the theologicalcontextof Christ'squantityin the Eucharist,but it came to be developedinto a genuinephilosophicaldocIn additionto theoreticalarguments(eitherof a theologicalor a trine.37 philosophicalnature),also argumentsfromexperienceplayed a role in the debate. The most importantof these is the argumentfromcondensation and rarefaction.Brieflystated,the phenomenonof condensation seemed to teach thatthe extensionor quantityof a given and rarefaction substancecan vary,whereas the "amount" of substanceand its quality remainconstant:no new partsof substanceare added, nor any destroyed (in contrastto the phenomena of growthand diminution).This experience was taken as a proof that extensionand quantitywere reallydistinctfromsubstanceand its qualities. It was the extensioninheringin substancethat was corruptedand generatedin the process of condensation and rarefaction,not the substanceitself.William Ockham, on the other hand, argued that the condensationand rarefactionof substances is caused by the local motionof the parts of substance.In condensation and rarefaction, the parts come spatiallycloser togetheror more distant fromeach other,respectively, than theywere before.38 Anneliese Maier had noticedthatJohn Buridanand Albertof Already held Saxony divergentopinionson the issue of the ontologicalstatusof Buridan quantity. argues that quantity,or more accurately,magnitude Albertof Saxony, on the , and substanceare reallydistinct.39 [magnitudo) otherhand,deniesthatsubstanceand quantityare reallydistinct. According to Maier, Albertof Saxony in his commentaryon the Physics seemed to respond to two argumentsof Buridan.40She did, however,not include in the comparison,and did not furtherdevelop the Buridan's tertia lectura of her implications insightsforthe chronologyof these worksor forthe 37The mostrecent to thetheological of the ramifications large-scale studydevoted debateaboutquantity is P.J.J.M. La raison etle miracle. Lesdoctrines Bakker, eucharistiques 1999,esp.vol.1, 120-55. (c. 1250-c. 1400),2 vols.,Nijmegen 38Ockham's views arediscussed inAnneliese der Maier, Hintergründe Metaphysische spätscholastischen McCordAdams,William Ockham: , Roma 1955,192-3and Marilyn Naturphilosophie orNaturalist?, Voluntarist 2 vols.,NotreDame 1987,vol.1, 178-84. 39Buridan inhisdiscussion ofthisontological refers tomagnitude, problem consistenly is actually moreprecise, rather thanquantity. Histerminology sincethedebatewasabout thosequantities thatarecontinuous, as a quantitas continua i.e.,magnitudes (defined permaSee alsoMaier1955{op.cit.,above,n. 38), nens ), andnotaboutthosethatarediscrete. 210forthispoint. 40Maier1955{op.cit.,above,n. 38),219-21.Buridan's viewsare discussed on pp. 210-8.
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relationshipbetween Buridan and Albert of Saxony. Nevertheless,her doctrinalobservations,and those by JürgenSarnowskyand Joël Biard, who also studiedthis debate, provide an excellentcontextto reveal the on the Physics .41 betweenBuridan'sand Albert'scommentaries relationship and The intricaciesof the different con need not conargumentspro cern us here. What I would like to focus on, are the two argumentsin Buridan'stextto whichAlbertseems to respond.They both hingeon an of the phenomenonof condensationand rarefaction.Even interpretation medieval authors frequentlyreferredto condensationand rarthough efactionwhen seekingsupportfortheirown view of substanceand quantity,these two particularargumentsdid not appear in the debate prior to Buridan and Albertof Saxony.42 In the tertialectura of his Quaestiones on the Physics , rightat the begin), Buridandevelopsan argumentfrom ningof his own solution(determinatio condensationand rarefactionthatinvolvesan elaborate experiment.The argumentis expresslydirectedagainst those who claim that substance to and quantitycoincide,and who attributecondensationand rarefaction local motion,which causes the parts of substanceto be more distantor closer togetherfromone another,withoutthe additionor corruptionof quantity. viamantiquam est secundum Adistam quodnullasubstantia quaestionem respondeo nonestmagnitudo. Et ad hocadducoprimounam sivequodmateria magnitudo resextensa sitmagnitudo concedunt enimquodomnis rationem naturalem: ponentes localemsecundum fieripermotum rarefactionem et condensationem quempartes ad invicem ad obtinendum ab invicem vel approximantur substantiae elongantur locumabsquehocquodquantitas minorem corrumpatur.43 derivedfromexpeAgainstthisview,Buridanpresentsa counter-example, fill them with air [and to rience.If one opened a pair of bellows (vesica ) thenpluggedthe opening],"you would be unable to noticeablycondense the air in the bellowsby compression,such thatit would noticeablyobtain 41Sarnowsky dela 1989{op.cit.,above,n. 9),92,andJoëlBiard,Conception sémiologique dela quantité danslenominalisme duXIVesiècle science etstatut , in:G. Federici ontologique parisien Vescovini andFr.Barocelli e astrologia nelTrecento scienza , Padova1992, (eds),Filosofia, europeo andJoelBiard, De la logique à laphysique: etmouvement selon Albert 135-54, quantité esp.150-3, deSaxe 3 (1996),361-74,esp.366-7.Patar2001{op.cit., , in:Les Etudesphilosophiques, andBuridan's believes thatAlbert's textsareabout above,n. 13),vol. 1, 355*wrongly different doctrinal andthattheir viewsarecompatible. issues, 42I am basingmyself in Maier1955{op.cit.,above,n. 38),141-223. on thematerial refer andrarefaction, areRichard theauthors tocondensation who,inthiscontext, Among ofMediavilla, William andFrancis de Marchia. Ockham, 43JohnBuridan, tertia in:Patar2001{op.cit.,above,n. 13),vol.2, 21,1.75-82. lectura,
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a smaller space." Buridan wonders why this is so. Accordingto him, neitherthe air's matter,nor its substantialform,nor its qualityare the obstacle.44Consequendy,anotherdispositionof the air resiststhe efforts to condense its parts closer togetherin the bellows,and thisis the air's "magnitude":"et illa non erit aliud quam magnitudo."In otherwords, on the basis of this experiment,Buridan concludes that magnitude,i.e., quantity,is distinctfromthe air's matter,formor quality. Tuncponoquodvesicaimpleatur aere:manifestum estquodtupercompressionem nonpoteris iliumaeremnotabiliter condensare itaquodnotabiliter obtineat minorem tubenehabespotestatem movendi Petoergoquid locum;et tarnen ipsumlocaliter. etquidresistit inminorem locum. Constat prohibet quodtunonpotesipsum ponere nonresistit, loco;nec quodmateria quia multoplusde materia possetin minore forma aerisresistit, forma salvata aerem, sua,posse quiaperalterationem experimur condensali et rarefieri ad duplum. fiolam vitQuod sicpotest experiri. Capiamus reamet calefaciamus earnsupercarbones, os fiolaein aqua;videposteaponamus bimus condensabitur quod,quandoaerinfiólainclusus refrigerabitur, quodintantum in fiolaet replere medietatem fiolaene remaneat quodoportebit aquamascendere aerisnonrepugnabat vacuum; ergoex forma quintupossesiliumaeremcompriSednecetiamrepugnabat expartecaliditatis mendo condensare. velfrigiditatis, quia multo veletiamde frigiditate loco.Ergopraeter plusde caliditate possetin minore hoceritibialiadispositio hocprohibens et illanonerataliudquammagnitudo, de cuiusnaturaestfacere distare: tuncenimnonpoteras illamcorrumpere persuam sednatura actionem etrarefacere condensare compressionem, perhuiusmodi poterat et nontupercompressionem.45 Buridan proves the same point by anotherargumentfromcondensation and rarefaction,which followsrightafterthe experimentwith the bellows. Suppose that God would condense or rarefya lump [globus)of air The condensationor rarefactionwould entail which includeseverything. a change or motion fromone dispositioninto another one. Hence, in additionto the substanceof air, one has to assume the existenceof other whichexplainthischange. Or, in otherwords,if air rarefies, dispositions, it is in a different state[modus se habendi)than before.Since, however,the air itselfremainsthe same, the different mode of being can only have been caused by an additionaldisposition;and this preciselyis the air's magnitude. Item.Ponamus casumquodsitunusglobusaeris,omnibus aliiscircumscriptis, et autcondenset; constat etomnis mutatio Deusiliumrarefaciat quodibieritmutatio; in aliam;igitur velmotus estde unadispositione substantiam aeris oportet praeter 44Thattheformoftheair is nottheobstacle in a separate is proven experiment, theheating ofairin a cup{fiola). involving 45JohnBuridan, tertia lectura , in:Patar2001(op.cit.,above,n. 13),vol.2, 21,1.83-22, 1.5 witha slighdy modified punctuation.
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secundum Et nonpotestdici ponerealias dispositiones quas eritilia mutatio. suntloca,quia secundum dietam nonessetibi quodillaedispositiones positionem et noscircumscribebamus omnia extrinsecum; aliquislocus,cumlocussitcontinens extrínseca. Item.Illeaer,si rarefieret, aliomodose haberet nonesset quamante;et tarnen aliusaer;igitur illemodusse habendi differt ab aere,et nonpotest differre nisisit Etistaratiopotest fortificari addita;etiliaestmagnitudo dispositio quamquaerimus. . . ,46 persyllogismum expositorum. In quaestio6 of book 1 of his Quaestiones on the Physics[utrum omnisres extensasit quantitas Albert of takes on both ), Saxony arguments.They , that is, in the argumentsagainst his appear in the argumentsquodnon, own thesisthatsubstanceand quantitycoincide.Argumentsix and seven which Albertlists,and which he attributesto quidam , clearlyecho the above line of reasoning,culled fromBuridan's tertia lectura . Argumentsix is a paraphrase of Buridan's experimentof the condensationand rarefactionin a pair of bellows. It repeatsthat neitherthe air's matter,nor its form,nor its qualitypreventsthe bellows frombeing compressed. utrum omnis resextensa sitquantitas. Consequenter quaeritur Arguitur quodnon.. . . Sexto.Arguunt sic'situnavesicaplenaaere;tunccomprimenti illamaliquid quidam invesicaresistit; existens sedhocnecestmateria aerisnecforma aerisnecqualitas aeris.Tuncsic:quantitas aerisin vesica aeris;videtur ergoquodhocsitquantitas resistit et nonmateria ñequequalitas comprimenti ñequeforma ipsiusaeris;igitur aerisestdistincta ab his,etperconsequens istanonsuntquantitas; etcum quantitas nonomnem remextensam istasintextensa, essequantitatem. sequitur Quodautem materia aerisnonrésistât, aerisnonrepugnarei staresubquanpatet, quiamateriae titate ex eo quodilianondeterminat sibialiquam Nec certam extensionem. minore, etiamforma aerisresistit, formae aerisnonrepugnarei staresubextenquiasimiliter sioneminore; undesubmultominore extensione salvaretur forma aeris.Necetiam diciquodqualitas aerissicutestcaliditas, humiditas, résistât, potest quiaillissimiliter nonrepugnaret essesubextensione minore.47 , rephrases Argumentseven, also explicitlyattributedto the same quidam Buridan'sargumentthatthe rarefactionof a body witha size of one foot intoa body of twofeet,everything else beingdestroyed[by divineomnipotence], can only be explained if one assumes that somethingnew has been added to the body. But only its size (
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J.M.M.H. THIJSSEN sednonperhabitudinem et comparationem eiusad aliquodextrinpriusse habuit; sibiextrinsecum ex quo quodlibet videtur annihilatum; secum, ponitur igitur quod intrinsece se habeataliterquampriusse habuit. Sed nonpossetintrinsece aliterse haberequampriusse habuit, nisialiquaresde novoessetsibisuperaddita; sednon et extensior; videtur essealiaquamnovaquantitas videtur sit igitur quodquantitas unaressuperaddita reiextensae.48
Albertresolvesthe experimentfromthe bellows by pointingout that it - not is the formof "the mass of air" [formaexistens in tantamassamateriaè) the air's formabsolutelytaken- which resiststhe compression.The rarefactionof a body fromone to two feet,on which the other argument hinges, is attributedto the local motion of the parts [solumper motum In the hypothetical case thateverything externalto the body has localerri). been destroyed,and, consequently,the body is not in a different dispositionrelativeto anythingexternally, it is stilltruethatits partsare more distantfromone another. Ad sextam de vesicadicoquodnecmateria aerisresistit, necforma sed abstracta, forma intantamassamateriae. existens Undebeneverum estquodforma aerispossetbeneessesubminore cumtarnen quantitate quandononessetintantamateriae; estintantamassamateriae, cumnonpossit stareinmateria densa, quantumcumque ipsaestilludquodresistit comprimenti. Ad aliamdicoquodsi aliquodcorpus rarefiat annihilato, pedale,omniextrinseco dicoquod,quamvis ad nihilextrinsecum se habeataliterquam quodfiatbipedale, adhucquaelibet prius,tarnen parseiusad aliamhabetse aliterquamprius, quia ab ea quampriusdistabat et nonperacquisitionem alicuius reinovae, magisdistat Ex hocpatetad argumentum.49 sedsolumpermotum localem. Buridan,in Book 1, q. 8 of his ultimalectura , seems to provide a direct in to As Albert's text. the tertia lectura , Buridanhere too defends response the thesisthat substanceand magnitudedo not coincide: nullasubstantia est magnitudo. The structureof the argumentwhich Buridan presentsin supportof his thesisis rathercomplex. FirstBuridan presentsa number of traditionalargumentsagainst the thesis that substanceand quantity coincide. Even thoughthese argumentssupportBuridan's own view, he findsthe majorityof themunconvincing.In orderto disclosetheirflaws, Buridan sets out to refutethemone by one, as if he himselfwere a proponent of the view that substanceand quantityare identical.50 Istaquaestio estvaldedifficilis. Multienimponunt, etspecialiter moderni quodomnis resextensa estmagnitudo auctoritates etrationes, etdifficile est priusfactas propter demonstrare Underationes deductae utinpluribus sunt, oppositum. quaeinoppositum 48Patar1999{op.cit.,above,n. 28),vol.2, 82,1.59-83,1.68. 49Patar1999{op.cit.,above,n. 28),vol.2, 90,1.3-91,1. 15. 50See alsoMaier1955[op.cit.,above,n. 38),211.
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evadi.Ne aliquisaliquibus illarum rationum sunt.Ideopossunt faciliter sophisticae et utilli,qui voldemonstrationibus, acquiescat tamquam quodessetinconveniens, sciantevadereillasrationes sibi untistamopinionem tenere, quae in contrarium factae volorespondere ad illasrationes.51 sunt,egoac si essemde illaopinione, Afterthus having willinglyassisted his opponents by refutingthirteen argumentsin supportof his own view, Buridan stillmaintainsthat no substancecoincideswith quantity. Nonobstante tamenquodsicpossunt solvivelevadirationes praedictae, egopono conclusionem estmagnitudo.52 quodnullasubstantia , Buridan providesthe argumentswhich Only at this stage of the quaestio he findsreallyconvincing.The most importantproof for his own view withthe bellows.The ultima lectura basicallyrepeats again is the experiment the experimentfromthe tertialectura , thoughin a more carefullydeveloped versionand with a more drawn-outconclusion. idemsecundum substantiam Hoc declaratur potest supponendo quodaer manens et frigefactionem. rarefieri et condensali multum Quod experipercalefactionem multum calefiat aerinterior mentaliter quia,si fiolavitrea supercarbones, apparet, in aqua frigida culoversosuperius, cum intantum rarefit quod,si os fiolaeponatur illein tantum horámtemporis aerinterior condensabitur refrigerabitur, perparvam in fiolam ne eiusrepletionem, aquamascendere usquead mediam quodoportebit obtinet minorem locuminsubduplo condensatus sitvacuum, quam quiaaerinterior velcomPosteaperexperientiam ante,cumessetrarior. egosuppono quodtrahendo tu nonpotesaeremin tantum, aeremsinecalefactione velfrigefactione, primendo tupotesper velrarefacere, sicutdictum scilicet ad duplum condensare est,quantum Namsi laterafollis sintpervelfrigefactionem; calefactionem quodpatetinfollibus. beneomniaforamutintra sitaerisplenitudo etobstruantur fecte ab invicem elevata, latera follis ad subduplum, immonecad aliquam inafollis, tunonpoteris comprimere condentu nonpotesnotabiliter notabilem quantitatem; igitur percompressionem silaterasintnonperfecte sedmediomodoab invicem sareaerem. elevata, Similiter, tunonpoteris notabiliter elevare laterafoletomniaforamina obstruantur, amplius Hoc tamentu posses,si possespertractionem notabiliter lis,ne sitdarevacuum. Tuncigitur rarefacere aeremsicuttupossespercalefactionem. quaero,quidprohicondensare notabiliter aeremexistentem inter laterafollis betquodegononpossem Constat laterum veletiamnotabiliter rarefacere percompressionem perelevationem? a dimensionem distinctam benequodcausahuiusreddinonpotestnisiponamus a caliditate ethuiusmodi materia etforma, etfrigiditate qualitatibus; quaepraedicta 51The passages ofBuridan's libros secundum ultimam Ieduram Quaestiones super Physicorum, arequotedfrom theforthcoming critical edition. BooksI andII havebeenprepared by OlafPluta. Thefollowing twomanuscripts havebeenusedtoestablish thetext: Copenhagen, Det kongelige cod. 1801fol.(C),fol.13rbandKraków, Biblioték, Nykongelig Sämling, Bibliotéka cod. 1771(G),fol.lOra.A slightly different edition ofBookI, Jagielloñska, in Patar2001[op.cit.,above,n. 13),vol.2, ultima lectura canbe found q. 8 ofBuridan's 120-4. 52JohnBuridan, ultima lectura , C, fol.14raandG, fol.lOvb.
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J.M.M.H. THIJSSEN omniasintextensa sicut unomodomotu, solum cumomnibus localem, quemvocamus sibiinhaerentibus movetur. Sedhuiusmodi dimensionem nospossumus totum salvare. Dicimus enim ponendo sicmagnitudo, dat quodsicutalbedodatessealbumformaliter, quaeestextensio, esseextensum etmagnum. Etsicutineodemsubiecto datessealbius plusde albedine etplusde caliditate itaplusde magnitudine maiusetextensius. Ideoetiam calidius, sicutidempriusalbumnonpotest fieri albiusnisipergenerationem in eo albedinis cumalbedine necfieri minus albumnisipercorruptionem albepraecedente, partis itaidemexistens nonpotest fieri maiussinealiquageneratione dinis, magnum magnitudinis cummagnitudine nec fieriminusexistens sine praeexistente, magnum Modoultradicimus ad hoc habilibus corruptione magnitudinis. quodin subiectis sicutad calefactionem naturaliter levitatis etad frigefactionem consequitur generatio levitatis etgeneratio sicetiam ad huiusmodi calefactionem corruptio gravitatis, sequitur naturaliter et ad frigefactionem levitatis et generatio partialis magnitudinis corruptio Et credoquodhocsitrarefactio et condensatio. Raritas enim generatio gravitatis. nihilaliudestin materialibus multamagnitudo, etdensitas quamin paucamateria estin multamateria Et dicimus ultraquodde huiusmodi paucamagnitudo. magnitudine nonpotest velcorrumpi vel aliquiditanotabile generali percompressionem tractionem sicutpercalefactionem et frigefactionem, sicutnecetiamde gravitate et levitate. Et sicapparet causaet ratiopraedictorum essedispositasicmagnitudine a substantia tincta etqualitate.53
Next, in the section that immediatelyfollows,Buridan takes issue with otherscholars(alii),who attributethe condensationand rarefaction "solely to the local motionof the parts [of air]." Sed videtur mihiquodaliide praedictis nonpossunt convenienter reddere causam, cumenimdicunt velrarefactio velcorquodnonfiatcondensatio pergenerationem sedsolumpermotum localem ruptionem magnitudinis, partium perquemapproximantur ad invicem velelongantur. Et egopossum movere localiter undique corpora veltrahendo. simul pellendo Quidenimprohibet quodegononpossum comprimere aeriscondensando ad obtinendum minorem locum? Materia enimnonobstat, partes inmulto minori loco.Necforma substantialis aerisobstat, quiaplusdemateria posset sitin minori locoaerecondensato sicutdicquiailiatotaforma perfrigefactionem, tumest.Neccaliditas obstat secundum seipsam, licetforte obstet inquantum sequitur ad earngeneratio nammulto invaldeminori magnitudinis, plusde caliditate posset ferro estmulto Si tudicasquodobstat loco,quiainparvoignito plusde caliditate. ex parteraritatis, distincta est,egoconcedo, quaea praedictis quiatuneillararitas estmagnitudo veldimensio quamegoquaero.Illienimsicutnonpossunt magnia praedictis tudinem distinctam itanecraritatem.54 ponere, Althoughthisview was also defendedby William Ockham, it is directed, I think,againstAlbertof Saxony. In the tertialectura , Buridan also mentionedthe view thatcondensationand rarefaction were sometimesattributed to local motion, but only now, in the ultimalectura , this view is restructured as a counter-argument his with thebellows. against experiment 53JohnBuridan, ultima lectura andG, fol.lOvb-llra. , C, fols.14ra-14rb, 54JohnBuridan, ultima lectura andG, fol.lira. , C, fols.14rb-14va,
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Buridan concludes his argumentfromthe bellows with an additional argument,which we already encounteredin Albert of Saxony's text, namely the argumentof the rarefactionof a one-footbody into two mode of being feet.The rarefactioncauses the body to be in a different than before. However, since everythingoutside of this body has been mode of being is not annihilatedby divine omnipotence,this different with respectto somethingexternalto the rarfiedbody, but intrinsically. modes of being are preciselywhat Buridan labels And these different "magnitudes." Si enimcorpus aliisrationibus. sicpersuaden Conclusio nostra aliquibus pedale principalis potest divinam et rarefiat sibiextrínseca sintannihilata, et omniacorpora perpotentiam etnon constat doneesitbipedale, quodalioetaliomodose habetpriusetposterius, Etistosmodosexpartereialiosab invicem intrinsece. ad aliquodextrinsecum, igitur aliamatecumnosponamus vocemus quodnonsitpriusetposterius 'magnitudines,' Et sicde aliis.55 autfrigiditas. velaliacaliditas riavelaliaforma substantialis There is some further evidence,not previouslynoticed,thatstronglysug, and was geststhatAlbertof Saxony respondedto Buridan's tertialectura In the tertia lectura , Buridanlabels his own priorto Buridan'sultimalectura. are different as the via antiqua and substance that , the quantity position traditionalview, which harksback on Aristotleand Averroes. est secundum viamantiquam Ad istamquaestionem quodnullasubstantia respondeo nonestmagnitudo.56 sivequodmateria magnitudo Albertof Saxony,however,when he comes to speak of the positionthat reportsthatit was held by some of quantityand substanceare different, his contemporariesand most thinkersfromthe past. Albertsinglesout the two argumentsthe "sixth" and the "seventh,"which were deemed particularlyimportantby proponentsof thisview. ad secundo recitabo unamopinionem; In istaquaestione ponamconclusiones primo scienad primum illiusopinionis. Quantum quibuspatetimprobatio quaestionem, sit modernorum etplurium dumestquodestopinio antiquorum quodquantitas aliquorum a re et quanta,rectesicutalbedoestresditincta a re extensa una resdistincta multum Et istirationem sextám etseptimám albedinem. habente reputant proistaopinione.01 The "sixthand seventharguments"to which Albertrefers,are the sixth and seventhargumentsquodnondiscussedabove: the argumentfromthe bellows,and the argumentof the rarefaction by divineomnipotence,both 55JohnBuridan, ultima lectura , C, fol.14va,andG, fol.lira. 56JohnBuridan, deBruges lectura in Patar,La physique tertia , 21,1.75-76. 57Patar1999{op.cit.,above,n. 28),vol.2, 85,1. 14-86, 1.21 (Book1,q. 6).
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advanced by Buridan and reportedby Albert.This contextties the opinio modernorum to the positionofJohn Buridan. aliquorum The change of perspectivebetweenAlbert'sQuaestiones on the Physics , and Buridan's tertialectura is interesting. Buridan perceiveshimselfas a followerof the "ancientway," the via antiqua.But throughthe eyes of his Parisiancontemporary So the same docAlbert,he is one of the moderni. trinalposition,namelythatsubstanceand quantityare distinct,can both be labelled "antiquus" and "modernus." In the ultimalectura , Buridan introducesyet another change of perhe can claim thatin particular"moderns"hold theviewspective.There, opposite to his own that substance and quantityare identical. The observationis absentin the tertia lectura , but,then,he had not yetencountered Albertof Saxony, a modernus a who defendedpre, contemporary, this and who had, moreover,challengedsome of Buridan's cisely position own arguments. Istaquaestio utrum omnis resextensive etsitualiter habens extra [seil, partem partem estmagnitudo] estvaldedifficilis. Multienimponunt, etspecialiter moderni quodomnis resextensa estmagnitudo auctoritates et rationes, etdifficile est propter priusfactas demonstrare oppositum.58 The impetus Theory The second case studyconcernsthe theoryof impetuswhichJohnBuridan and others developed to explain the continuationof projectilemotion afterthe contactbetweenmover and moved object had been dissolved. Buridanintroducedthe notionof "impetus"to denotean impressedforce, which he conceivedas a qualitywhose natureit is to move the body in which it is impressed.In what way does this theoryteach us anything about the relationbetweenBuridan and Albert? In her groundbreaking studyabout the impetustheory,AnnelieseMaier compared Albert of Saxony's discussion of the impetus theoryin his on the Physicsto Buridan's ultimalectura Quaestiones , and concluded that the formerheavilydepended on the latter.However,she noted one peculiar fact:Albertseemed to avoid the terminology of impetus , and preferred the termsvirtus motiva or qualitasmotiva.™ Let us recurto the relevanttexts, which had alreadybeen edited by AnnelieseMaier.60 58JohnBuridan, ultima lectura , C, fol.13rb,andG, fol.lOra. 59Maier1968(op.cit.,above,n. 31),264. 60Maier1968(op.cit., thetextofBuridan's ultima above,n. 31),207-14provides lectura,
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a proiicientê) In book 8, q. 13 (undemoveatur post separationem proiectum views as Albertdiscussesprojectilemotion.61He presentsfour different to why a projectilecontinuesits motion afterit has lost contactwith a mover. The firstthree views which he discusses,have their origin in The fourthview, which he qualifiesas the truestview Aristotle'sPhysics. veriorem nunc ), is Buridan's theory.It attributesthe projecreputo (quampro tile's motion to a certainmotiveforce,a virtusmotiva.Six times in this motiva sibi impressa motiva , or just talis , virtus , Albertrefersto virtus quaestio is identifiedas a quality,which is innate to move. motiva virtus. This virtus veriorem. Et estquodproiiciens Aliaopinioestquampronuncreputo imprimit motivam quae estquaedamqualitasquae innataest proiecto quandamvirtutem movere . . .62 Even thoughAlberthere adheres to Buridan's view, his terminologyis In book 8, q. 12 in sharp contrastto the one used in the ultimalectura. which is devoted to the causes of projectilemotion (utrum proiectum post moveatur ab aerevela quo moveatur exitům a manuproiicientis ), Buridanuses the no less than 41 times.Only once does he use the termvirtermimpetus for the and then only when he introducesthe term impetus tusimpressa , firsttime in his quaestio. sibiquendam mobile movendo mihidicendum Ideovidetur impeimprimit quodmotor motivam illiusmobilis.63 virtutem tum velquandam Why would Albert of Saxony preferthe term virtusmotivaover impetus when he expresseshis adherenceto Buridan's theory?Unless, of course, he was not familiarwith this term,because he did not know the ultima lectura , as I have been arguingabove. A comparisonbetweenAlbert'stext seems to settlethe matter. and Buridan's tertialectura In the tertia lectura , Buridan discussesprojectilemotionin book 7, q. 5 extrínseco moveatur a motore eiusa manuproiicientis postexitům (iutrum proiectum Seventeentimes,Buridan refersto virsibi inhaerente). intrinseco vela motore vis impressa tusmotiva , or just ilia vis, when explainingthe con, vismotiva, tinuationof a projectile'smotion. There, he also gives his well-known characterizationof this vis motivaas a qualitywhich is naturallyapt to
the onpp. 372-5sheprovides text.In theaddenda, ofSaxony's andonpp.260-3Albert tertia lectura. textofBuridan's 61Patar1999(op.cit.,above,n. 28),vol.3, 1070-5. 62Patar1999(op.cit.,above,n. 28),vol.3, p. 1074,1.94-96. 63Patar2001(op.cit.,above,n. 13),vol.2, p. 211,1.34-36.
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move the subject upon which it has been impressed.For as Buridan quotes with approval: estquaedam natuDicuntaliqui:probatur qualitas permanentis quodiliavismotiva subiectum suum. . .64 raequaeestinnatamovere It is the same definitionwhich Albertof Saxony gave (see above). The ' occurs term ' impetus , always in cononly threetimesin the tertialectura if as Buridan were nectionwiththe term'visimpressa ,' explainingan unfamiliarsynonym.All threeoccurrencesstand togetherin one passage. Ex hocetiamredditur continue ratioquaremotusnaturalis ipsiusgravis magiset Nama principio solagravitas movetipsumgrave,et movendo magisvelocitatur. seuquondam vim motivam inipsogravi, ettunc impetum imprimit ipsicummotuquendam movetur istudgravenonsoluma gravitate sedcumhoccumiliavi;ideovelocius iliavissive ilkimpetus movetur. Etperconsequens ideoiterum velocius moveaugeatur; turet siccontinue motus velocitatur. Sed nuncestvaldemagnadubitatio: quaeres estiliavissiveilleimpetus ?65 The way in which Albertof Saxony discussesBuridan's impetustheory seems to providefurther evidenceforthe thesisthathis Quaestiones on the between Buridan's tertia lectura his are located and Physics chronologically m ultimalectura.When writinghis Quaestiones , Alberthad no access to the ultimalectura , avoided the neologism , and, in line with the tertialectura the of virtus motiva He traditional which "impetus". preferred terminology was also used in the tertialectura ,67 Conclusion on the The relativeorderof Buridan'sand Albertof Saxony's Quaestiones , whichwas was based on textualand doctrinalcomparisons,seems Physics to be confirmed,or in any case, not contradicted,by the littlethat is is knownabout the dates of originof these works.Buridan's tertialectura dated around 1350, whereas the ultimalecturawas composed sometime 64JohnBuridan, tertia lectura , in Patar2001{op.cit.,above,n. 13),63,1.71-73. 65JohnBuridan, lectura tertia , in Patar2001(op.cit.,above,n. 13),61,1.51-52,1.57. 66As indicated this 1989(op.cit.,above,n. 9),50 already above,Sarnowsky suggested ofAlbert ofSaxony's hedid on thechronology butsincehewasfocusing order, writings, fortheconnection between ofthisrevised notdrawoutthefullimplications chronology andAlbert. Buridan 67Thisis notto suggest whocoinedthetermimpetus. The term thatit wasBuridan ofMarchia. See Maier1968(op.cit., virtus motiva above, ultimately maygo backtoFrancis between on1.202-203 and1.204.Thephilosophical n. 31),166-80, forinstance relationship on pp. 200-1. de Marchia andBuridan is briefly discussed Francis
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between 1352 and 1357.68Albert of Saxony's Quaestiones superoctolibros This is date after 1351. are to be dated suggestedby shortly Physicorum remarkstie the textto Albert'sopenone of itscopies,whose introductory ,69Since Albert of Saxony ) on Aristotle'sPhysics ing lecture (principium the Quaestiones on the Physics 1 1 it seems that in of 35 the summer , incepted at Paris after the was the firstworkthathe read completionof his studies there. that Furtherstudyof passages fromBuridan's and Albert'sQuaestiones doctrinaldisagreementsmay corroboratethe proposed reveal significant At the same time,theymay help solve new questionsabout chronology.70 the productionof scholasticworks,and about the impact that Albertof (ratherthan the reverse). Saxony may have had on Buridan'sultimalectura the have been must Buridan Physicssince the late teaching Although in 1330s, he wrote his commentariesmuch later life.Albertof Saxony, on the other hand, wrote his commentaryrightafterhaving completed his degree. Why did Buridan feel it necessaryto revise his tertialectura , remarkthat the work and writea new commentary?Is the introductory is writtenat the request of his studentsmerelya commonplace;and if not, what about the previousgenerationsof his studentswho had to do Did the appearance of Albert'scomwithouthis writtencommentary?71 :? Was it, for in role a shaping the ultimalectura mentaryplay pivotal 68The evidence known to Edmond wasalready thedatesofcomposition concerning Maier.See Michael1985[op.cit FaraiandAnneliese ., above,n. 1),vol.2, 606-8. 69It is themanuscript was F. 345,which Wissenschafdiche Erfurt, Allgemeinbibliothek, 'a comdickPhilosophus readsas follows: in 1360inCologne. Itsincipit written "Quoniam informationem ideopropter etprioribus munibus inbuicionemque priusestinchoandum', dismeo voloistamquestionem librotanquam in istoprimo scolarium iuvenum proprincipio 1989(op.cit.,above,n. 9), 18-9,and49. . . ." See Sarnowsky Utrum scientia putare: 70Onesuchfurther ofplace{locus) is thediscussion explored topicthatcanbe fruitfully 1989[op.cit.,above,n. 9), 51, n. 199,andfurther in book4, suggested bySarnowsky Phänomene unddie . . Extrakosmische mundum in his eSiextra aliquod corpus fieret developed ' des andAndreas Schule 14.Jahrhunderts der'Pariser , in:JanA. Aertsen Speer Raumvorstellungen York1997,131-44.Different imMittelalter , Berlin-New (eds),RaumundRaumvorstellungen fromGod'sabsolute to reasoning withrespect Buridan andAlbert between approaches andthe God's Absolute inJürgen Power, Experiments, Thought Sarnowsky, powerareindicated Carotiand Pierre Paris in the'NewPhysics' , in: Stefano ofXlVth-Centuiy ofNature Concept duXIVesiècle Souffrin 1997,179-201. , Florence (eds),La nouvelle physique 71Although arelinked toteachandQuaestiones thatExpositio itisgenerally acknowledged relation between theprecise unclear muchisstill attheartsfaculty, concerning ingpractices therelationA first startofstudying andactualteaching. ofsuchworks theproduction From Oral texthasbeenmadebyChristoph orallecture andwritten Fliieler, shipbetween onAristotle's Buridan's Commentaries Commentaries: Lecture to Written , in: Sten Metaphysics John inLanguage andCognition Medieval L. Friedman & Russell Ebbesen , Copenhagen (eds), Analyses 1999,497-521.
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thatBuridanexpanded instance,underthe influenceof Albert'sQuaestiones in comparisonto his previoustertialectura the ultimalectura , and that he moved the discussionof projectilemotionfrombook 7 to book 8?72Recent work on the logic ofJohn Buridan and Albertof Saxony shows a pattern similar to the one broughtto attentionhere: it is Buridan who respondsto Albertof Saxony, ratherthan the reverse.73 Althoughall I have covered here are a few passages fromBuridan's on the Physics and Albert'sQuaestiones , the main driftof thisarticleis that the common notion of a Buridan school needs to be qualified.I hope that the reader has come to share my thoughtthat futurestudiesin this area would benefitfroma greaterreadinessto perceiveJohn Buridan, Albert of Saxony, Nicole Oresme, Themon Judeus, and Marsilius of mastersof Inghen as a small intellectualnetworkof nearlycontemporary other's work and at times who were familiar with each arts, responded to one another.This conceptseems more adequate than thatof a unified Buridan school in explainingthe dynamicsof conflictand alliance that we encounterin the texts.74 Nijmegen Instituut Philosophisch
72Aristotle's to disbook8, esp.266b 27-267a 5 is themostlogicalcontext Physics inconnection withPhysics theproblem canalsobe raised motion. cussprojectile , However, ofthings thatdo nothave discusses themotion book7, esp.241 b 24,whereAristotle thatis inmotion must inthemselves, andtheaxiomthateverything ofmotion thesource . . .). be movedbysomething [omne quodmovetur 73Christoph derTermini. EineUntersuchung zurPerutilis Kann,DieEigenschaften logicaAlberts to the York-Köln vonSachsen, Leiden-New 1994,14-8hasconvincingly contrary argued, isprior toBuridan's Summa Perutilis ofSaxony's received view,thatAlbert (that logicae logica See also Summulae deDialéctica Buridan's thatcontains is,a treatise plushiscommentary). from Buridan's derived 2002[op.cit.,above,n. 7),esp.5-30forother examples Fitzgerald works on logic. 74It alsobetter in unraveled Carotiandpublished fitsthelatestevidence, byStefano on thePhysics Oresme's ofSaxonytookintoaccount thatAlbert thisfascicle, Quaestiones andRemission Discussion onIntention Some Remarks onBuridan's as well.See Stefano , in Caroti, whichalsopoints theforthcoming article See further thisfascicle. Sarnowsky, byJürgen Oresme andAlbert Oresme: onNicholas ofAlbert ofSaxony Nicole ata dependency ofSaxony's in:Stefano Caroti intheVoid TheProblems Vacuum andMotion onthePhysics: , of Commentar)) " . . .", Florence dissensio doctores estmagna andJeanCeleyrette 2004,161-74. (eds), Quiainter onAristode's viewisThemon ofthisalternative Yetanother illustration commentary Judeus' seemsto have NicoleOresmein histurn, Albert ofSaxony. In it,he attacks Metheora. 1989(op.cit.,above, See Sarnowsky Themon's from commentary. copiedlongpassages citedthere. n. 9),esp.p. 41 n. 150,andp. 52,andtheliterature
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and Natural On Buridan' s AllegedAlexandrianism: Heterodoxy Paris in Philosophy Fourteenth-Century JACKZUPKO
'De Anima'John In the thirdand finalversionof his Questions onAristotle's Buridan devotes four questions near the beginningof Book III to the nature of the human intellect:whetherit is the substantialformof the human body (Q.3); whetherit is a forminheringin the human body (Q.4); whetherthereis one intellectby which all men understand(Q.5); and finally,whetherthe human intellectis everlasting[ perpetuus] (Q.6). What is unusual about these questionsis that they discuss not a problem or puzzle fromthe actual text of De Anima , which was the subject that arose among authoritiestryof Buridan'slectures,but a controversy ing to fillout Aristotle'sambiguous remarksabout whetherthe human soul can survivethe death of the body. As is well known,Aristotlesays that only the part of the soul that actuallydoes the thinkingis "immortal and eternal"when separatedfromthe body {De An. III.5.430a23-25). to say.1But what he could have What Aristotlemeant by thisis difficult in late antiquityas well as meant was a matterof enormouscontroversy of the human in the Middle Ages, when the questionof the immortality soul was treatedby Christian,Islamic, and Jewishthinkersalike. Indeed, modernphilosophicalpsychologyowes much to the intensediscussionof this question throughoutthe medieval period.2 It is no accident that Descartesarrivesat the conclusionthathe is a thinkingthing;the notion has been withwestthatthinkingis somehowbound up withimmortality ern philosophyalmost since the beginning. Althoughthe vast majorityof questionsin Buridan'scommentariescorrespond to lemmas fromthe text he is lecturingon, only Q.6, the last of the fourquestionson the nature of the human intellect,is based on 1 See,e.g.,D. W. Hamlyn, II andIII, Oxford Aristotle's De Anima, Books 1968,139-40. 2 I havesketched in mySubstance someoftheconnections andSoul:TheLateMedieval F. Brown Minds: TheRelations Modern , in:Stephen ofEarly (ed.),Meeting ofthe Origins Psychology Between Medieval andClassical Modern , Turnhout 1998,121-39.See also European Philosophy 13ofmyJohn Buridan: Portrait Arts Master , NotreDame2003. ofa FourteenthCentury chapter © Koninklijke BrillNV,Leiden,2004 - www.brill.nl Alsoavailable online
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somethingAristotleactuallysays in thiscase the aforementioned ambiguous remark.So we need to ask why he feltbound to raise the issue, devotingseveral questionsto topics hardlyeven mentionedin Aristotle, given that he was supposed to be lecturingon De Anima.The answeris that he was doing what any good teacherwould do: divergingfromthe He assignedtextin order to help his studentsappreciateits significance. is absolutelycandid about his intentionshere. In the firstquestionof the group, aftersettingout the initialargumentsfor and against the thesis thatthe intellectis the substantialformof the human body,he says,"this question has been raised to distinguishopinions about the intellect,so thatwe will see how theyagree and disagree;later,we will inquireabout theirdifferences".3 famosae Accordingto Buridan,"therehave been threerenowned[magis ] opinions about this intellect":that of Alexander of Aphrodisias,that of Averroes,and finally,what he calls "the truthof our faith[ventas fideinos" tra^ (QDA3 III. 3: 22-23). He proceeds to summarizethem for his students.There is the materialistview of Alexander,accordingto whichthe human intellectis the materialformof the body, and hence unable to surviveits death; the monopsychismof Averroes,who argues that the human intellectis a unique, immaterialformable to survivebodilycorruptionbecause it is not actuallyin the body; and the truthof the faith, accordingto whichthe human intellectis actuallyin the body as itsform, but also able to survivebodilydeath and corruption.These appear to be the only "renownedopinions". No othersare mentioned.And only the opinion of the Catholic faithis designatedas "the truth[veritas]". There is a remarkin Q.6, the last question of the group,that nicely bookends the entirediscussion."The truthof this question is apparent fromthe preceding",Buridan says,meaningthe opinion of the Catholic faiththat the human intellectis everlasting,"but it has been raised so thateverything mightbe reviewedtogether".4 By way of summarizingthe discussionof the previousquestions,he then statesthe conclusionssome3 "Istaquaestio in de ipsointellectu utvideatur motaestad distinguendum opiniones All et quodposteainquiratur de differentiis earum." etin quo differunt, quo conveniunt from Buridan's inlibros Aristotelis DeAnima secundum tertiam siveultimam Quaestiones quotations Buridan's Mind: AnEdition andTranslation Ieduram of of myJohn Philosophy [QDA^' arefrom ' with andCritical onAristotle's De Anima III ofhis Questions Book (Third Redaction), Commentary 1989(UMI #9001313). andInterpretative CornellUniversity , Ph.D. dissertation, Essays arebybook,question, andpagenumber. References 4 "Veritas ex praecedentibus, sedmotaestutomniarecollihuiusquaestionis apparet simul" (QDA3III.6:48). gantur
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rationibus one mightreach ifhe were "to use naturalargumentsalone [solum his and intelnaturalibus means of evident to senses uteretur^' by principles lect, "withouta special and supernaturalrevelation[sinespecialiet supernaturali .5 There followsa listof seven conclusionswe can reach revelatione]" about the metaphysicalattributesof the human intellectualsoul on the basis of naturalreason alone. Buridan describesthem almost as if he is settingout the logical space withinwhich reason can operate: CI If the human intellecthas always existed,it will always exist in the future.6 This is the standardmetaphysicalclaim that the human intellect'severmeaningthatit cannot cease to existat some lastingnessis bi-directional, futuretime if it has always existedin the past. It is worthpointingout that on Buridan'sview, naturalreason does not assentto anything having been made throughcreation.It is properlyconcernedwith thingsthat come into existencethroughgenerationonly (QDA3 III.6: 49). it would be (i) generated C2 If the human intellectis not everlasting, and also (ii) corruptible,(iii) derivedfroma materialpotentiality, (iv) materiallyextended,and (v) numericallymany, in keeping with the numberof individualhuman beings.7 Accordingto the second conclusion,an intellectthat is not everlasting fromits body, as we could subwill be metaphysically indistinguishable stitute'body' for 'intellect'above and attributes(i)-(v) would still hold. Indeed, with the addition of the thesisthat the human soul inheresin the human body, which seems naturalto associate with (i)-(v),we arrive at what Buridan calls as "the opinion of Alexander" (QDA3 III. 6: 51). C3 If the human intellectis not generated(or corruptible,or derived froma materialpotentiality, etc.), it would be everlasting.8
5 "Et enumero si sinefidecatholica solum primoconclusiones quas aliquisponeret rationibus ex speciebus habentibus evidentiam sensus uteretur, perprincipia pernaturam etintellectus, sinespeciali et supernaturali revelatione" (QDA3III.6: 48-9). 6 "Prima[conclusio] estquodsi intellectus essetperpetuus a parteante,ipseessetpera partepost"(QDA3 III.6:49). petuus 7 "Secunda[conclusio] estquodsi intellectus nonessetperpetuus a parteanteet a et corruptibilis et eductus de potentia materiae et extensus partepost,ipseessetgenitus extensione et multiplicatus materiae individuorum" (QDA3III.6:49). multiplicatione 8 "Tertia conclusio infertur exsecunda exopposito ad opposipraecedendo consequentis tumantecedentis: scilicet nonesteductus de potentia materiae, quodsi intellectus ipseest
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Buridan notes that C3 followsfromC2 above by the logical rule permittingus to move "fromthe opposite of the consequentto the opposite of the antecedent"in a good consequence. C4 If the human intellectis not derivedfroma materialpotentiality, it does not inherein matter.9 C4 followsfromC3, we are told, because if an everlastinghuman intellect inheredin the matterof the body, it would continueto inherein it when thatbody becomes a corpse or continuouswiththe earth- which, " Buridan insists,"no one would say [nullusdiceret] (presumablybecause it is contradictory forthe human intellectto informanythingotherthan a living,human body) (QDA3III. 6: 50). Althoughhe does not explicitlysay so, the positiondescribedin C3-4 correspondsto what Buridan earlier refersto as "the opinion of Averroes"(QDA3 III. 3: 22). We then move on to a series of 'meta-conclusions',or conclusions based on the conclusionsalready statedin C 1-4: C5 In the followingtwo groups,six attributesare "consequences of each other":10 The Alexandrian Position The human intellectis: (i) not everlasting (ii) generatedand corruptible (m) derivedfroma material potentiality (iv) inherentin matter (v) materiallyextended (vi) numericallymany
The Averroist Position The human intellectis: (i) everlasting (ii) not generatedor corruptible (iii) not derivedfroma material potentiality (iv) not inherentin matter (v) not materiallyextended (vi) not numericallymany
Buridansaysthatthesetwoattribute lists(whichI have labeled'Alexandrian' and 'Averroist')can be inferredfromCI -4. In other words, the metasi nonestextensus, et si nonestmultiplicatus, et similiter, perpetuus; ipseestperpetuus; III.6:49). ipseestperpetuus" {QDA3 9 "Quartaconclusio: de potentia materiae, ipsenoninhaeret quodsi nonesteductus materia" (QDA IIL6: 50). 10"Quinta esseperpetuum, intellectum conclusio: consequuntur: quodhaecsexsemutuo nonesseeductum depotentia noninhaerere nonessegenitum neccorruptibilem, materiae, Et similiter extensione et nonessemultiplicatum. nonesseextensum materiae, materiae, nonesseperpetuum, essegenitum sexopposita illorum se mutuo: scilicet, consequuntur inhaerere esseextende potentia vel corruptibilem, esseeductum materiae, materiae, Haec enimtotaconclusio infertur ex praecedentibus" sumet essemultiplicatum. (QDA III.6: 50).
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physicalattributesassociated with Alexandrianmaterialismforma logiassociatedwithAverroistmonopsycallyconsistentset,as do the attributes the members of one set are chism; simplythe negationsof the members of the other.What Buridan appears to be doing here is presentingthe of human opinionsof Alexanderand Averroesto his studentsas antinomies reason, i.e., as equally plausible positionsbetween which we have no rationalgroundsto decide. This is the 'logical space' on the questionof the soul's immortality alluded to above. C6 The human intellectinheresin the human body.11 Buridan says that this sixthconclusionis "categorical",meaning that it can be assertedall by itselfratherthan as followingfromsome other assumptionabout the human intellect,such as its being everlastingor materiallyextended.He adds thatthis"was previouslypositedand proved [haecfuitpriuspositaetprobata :]", a referenceto his presentationin Q.4 of four"naturalarguments"againstthe Averroistpositionthat the intellect is not actuallyin the body. These argumentsare not explicitlyidentified with the Alexandrianposition,although Buridan does think"a pagan philosopherwould maintainthe positionof Alexander [putoquodphilosoAlexandři phuspaganusteneret opinionem ]" 'QDA3 III. 4: 32]. They are: Al A separateintellectwould not be part of the essence or substance of a human being because it would be extrinsicto it.12 A2 A separate intellectwould be eitherone or many; not one since contradictory psychologicalstateswould be in the same subjectat the same time,e.g., ifyou believe P and I believe not-P (the argumentfor thisalternativeis givenin the next question,at QDA3III. 5: 42-43); not many, because in that case our separate intellectswould not move when our bodies do, leading to the absurditythat my intellectis no closer to me than it is to you.13 11"Sextaconclusio estcategorica: humānus inhaeret humano" quodintellectus corpori addition fromseveral (QDA3III.6: 50). I heredropthepossibly spurious manuscripts, in thehuman "inheres thematter in thehuman 'inheres bodywithout (or perhaps, bodyor '- the 'sine ' or'sive matter inquestion haveeither matena anditis hard materiae' manuscripts to tellwhich, in scribal a giventhatthewordsarevirtually indistinguishable shorthand), which in oneofthebestmanuscripts, is attested Wien,ÖNB 5454. reading 12"Prima estquiaaliterillanonessetde essentia velhomononessetessenhominis, tialiter unumaliquid"(QDA.3 III.4: 32). 13"Secunda ratioestquiavelponeretur intellectus omnium hominum, quodessetunicus velquodessent secundum hominum. Sed utrumque inconveplures pluralitatem apparet niens. Primum inconveniens estquodponatur sicutpostvidebitur. Etetiamdeclaro unicus,
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jack zupko A3 Many separate intellectswould not explain how Socrates understandssomethingbut not Plato, since thereis no relationbetweenthe intellectand theirbodies; therefore, parsimonycompelsus to positonly one separate intellect(Buridanconcedes that this argumentis "close" to the precedingone).14 A4 A separateintellectwould have to be everlastingand unique, since naturalreason does not recognizeany way for thingsto come to be - in which case it would also be corin timeotherthan by generation ruptible,like the body.15
With the shortcomings of the Averroistpositionnow evident,we can turnto the Alexandrian: C7 The humanintellectis generableand corruptible, extended,derived, inherent,and multiplied.16 Buridanexplicitly identifies C7 as "the opinionof Alexander",notingthat it is "inferred",althoughhe does not say what it is inferredfrom(presumablyfromC6, the categoricalassertionof whichwould yieldthe other
quodnondebetponialiusmihiet aliustibi,si nonessetinhaerens, quia:Ponamus quod ilHsintA (tuus)et B (meus). Tuncoportet et quodnonsint rationis, quodsinteiusdem ad motum mobiles tuumvelmeum, cumnoninhaereant nobis.Ideointellectus A non essettibiproximior velmagisapproximatus B estmihi, nece converso, quamintellectus scilicet nostrum Ideorationaturalis nondictaret antequam uterque intelligeret. quodA essetmagistuusquammeus"(QDA III.4: 32). 14"Tertiaratioestpropinqua scilicet Sortis velmovetur praecedenti: quodintellectus de locoad locumcumSorte, velnon.Si dicasquodsic,hocnonvidetur naturaliter dicsibi(nonenimpossetdarimodusperquemhocfieret, utrum tum,cumnoninhaereat tactuvelpulsu;nonenimpossetdiciqualisessetalligatio intellectus ad corpusSortis, moveretur cumcorpore hocnonpotest anteSortis, dici,specialiter propter quodcontinue Si verodicasquodnonmoveretur de locoad locumcum quamSortes aliquidintelligeret). tuncdistaret ab intellectu suo.Ideononposset nisitudiceres Sorte, intelligere peripsum, essetubiqueperindistantiam, sicutdiceremus de deo.Et tuncnon quodilleintellectus essetponendus nisiunus,quia ita essetmihiproximus sicuttibi,specialiter antequam nostrum Ideo possemperistumita intelligere sicuttu,et ita esset uterque intelligeret. fictitium aliumtibietaliummihi.Undeob hoccredidit Commentator ponere quodesset unicus, (QDA III.4: 33). quodposteaimprobabitur" 15"Quartaratioestquiahumana autetiam nondictaret fide, ratio, fides, circumscripta tuusessetantequam tu esses,nisiponeretur et unicus, sicut quodintellectus perpetuus Si autemessetfactus voluit Commentator. de novo,hocautessetpermodum creationis, authocessetpermodum fide,nondictaret, quodrationaturalis, circumscripta generationsnaturalis, et tuncesseteductus de potentia materiae et inhaerens" (QDA3III.4: 33-4). 16"Septima conclusio infertur etcor(quaeeratopinioAlexandři): quodestgenerabilis inhaerens et multiplicatus" extensus, eductus, (QDA3III.6: 51). ruptibilis,
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fiveAlexandrianattributessaid to be consequencesof each otherin C5). C7, or of claiming Notice, however,that Buridan stops shortof asserting that the opinion of Alexanderis true,since he has alreadyreservedthat judgmentforthe opinionof the faith.In fact,he says thatwe mustfirmly maintainthat"not all of theseconclusionsare true,since theyare against the Catholicfaith",even though"the opposingconclusionsare not demonstrablewithouta special and supernaturalrevelation".17 Our tour of Q.6 is almostcomplete.The doctrineof the faithis next enumeratedin six conclusionsor theses parallel to those found in the Alexandrianand Averroistpositions.Accordingto thisview:18 The Doctrine of the Faith The human intellectis: (i) everlasting (ii) not generatedor corruptible (iii) not derivedfroma materialpotentiality (iv) inherentin matter (v) materiallyextended (vi) numericallymany In other words, the position of the faithon the nature of the human intellectcombinesthe firstthreeattributes(i-iii)of the Averroistposition and the last threeattributes (iv-vi)of the Alexandrianposition.Good logician that he is, Buridan realizes that these attributescannot be conseopposed quencesof each other.Therefore,he tellsus, "all of the authorities to these conclusions must always be denied, even though we cannot demonstratetheiropposites".19 17"Sed tarnen suntverae,quia tenendum estquodnonomnesconclusiones firmiter conclusiones nonsuntdemonfidem catholicam. Sed credoquodoppositae suntcontra revelatione" et supernaturali strabiles sinespeciali (QDA III.6: 51). 18"Nuncnarrandae conclusiones velpropositiones suntsineprobationibus quaein hac sunttenendae. fidem catholicam materia secundum Quarumprimaestquodintellectus a partepost.Secundacona parteante,sedestperpetuus humānus nonestperpetuus sedcreatus; nec nonestproprie clusioestquodintellectus naturali, genitus generatione et tarnen nonannihilisedestannihilabilis, estproprie naturali, corruptibilis corruptione nec de potentia estquodisteintellectus nonesteductus batur. Tertiaconclusio materiae, hominum. estquodestmultiplicatus secundum extensus. multiplicationem Quartaconclusio vivithomo,et est humano seumateriae quamdiu Quintaestquodestinhaerens corpori revertetur" a corpore et iterum (QDA III.6: 51). separabilis 19"Etomnesauctoritates suntsemper opponuntur negandae, quaehiisconclusionibus earumdemonstrare" licetnonpossumus (QDA3III.6: 51). oppositas
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Buridan signalssomethingimportantto his studentsby not asserting the opinion of Alexander. For if none of the propositionsdefinitiveof the Alexandrianpositionis categoricallyasserted,no consequenceswill follow from them, in which case we can conclude nothingabout the nature of the human intellectfromhis assumptions.For demonstrative which Buridan definesas a proofit is necessaryto constructa syllogism, Otherwise, "consequencethatassertsthe antecedentand the consequent".20 whetherthe human intellectis everlastingremainsa dialecticalquestion, where doubt cannot be eliminated.In Buridan's mind, the difference between the dialecticianand the demonstratoris in how theyask their questions."The dialecticianasks his questionsin the formof a disjunction of both sides of a contradiction,givingthe choice to the respontheproposition dent",he says,"but the demonstrator propoundsassertively to be proved,and then it is a question,forit is a dubitableproposition, but the same [proposition]afterthe demonstrationis the conclusion".21 Since demonstrationis aimed at removingdoubt concerninga proposition fromthe minds of those consideringit, therecan be no optionsfor the respondent,no alternativewaysforthe dialecticto unfold.The movementis alwaysfroma questionor "dubitableproposition,whichis turned into a certainand known conclusion".22 by a demonstration Now it mightbe objectedhere thatthe Alexandrianpositionis demonstrablefor Buridan because he assertsC6 categorically.C6 appears to satisfythe fourthmemberof that position,and we know fromC5 that if we can demonstratejust one of the attributesthe otherswill follow because theyare all consequencesof each other,as follows: PI If anythinginheresin matter,it is not everlasting. P2 The human intellectinheresin matter[fromC61 C Therefore,the human intellectis not everlasting 20Johannes Buridan: Summulae: De syllogismis , 5.1.3,in:GyulaKlima(tr.), Buridanus, John et deDialéctica 'Summulae 2001,309: "consequentia ' NewHaven-London consequentis antecedentis assertive." 21Johannes Summulae: Dedemonstrationibus Buridanus, , 8.3.2,ed.L. M. deRijk,Groningenenimquaerit subdisiunctione de utraque Haren2001,64, 17-20:"Dialecticus parteconautemproponit assertive . . . Demonstrator danselectionem tradictions, respondenti et etillatuncestquaestio, demonstrandam, quiaestdubitabilis propositio, propositionem in Klima2001(op.cit.,above,n. 20), estconclusio"; transi, eadempostdemonstrationem 666-7. 22Summulae 8.3.3,ed. De Rijk,69, 2-3:"dubitabilis propositio, quae perdemonstrain Klima2001(op.cit.,above,n. 20), certaet scita";transi, tionem efficitur conclusio 670-1.
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And so on for the other attributesin the Alexandrianposition.Buridan thus appears committedto Alexandrian materialismabout the human he has said about the truthof the opinintellect,contraryto everything ion of the faith. conundrum.But its Obviously,the textof C6 presentsan interpretive in of Olaf the is much Pluta, who in a recent eyes greater significance article argues that Buridan was an Alexandrian materialistabout the human intellectwho, because of the threat of persecutionby Church "did not dare to give all his argumentsagainstimmortality".23 authorities, Instead, he expresses his materialism obliquely, arguing in favor of Alexander's position on the basis of natural reason "leaving aside the Catholic faith [fidecatholica circumscripta :]", and leaving it for "the reader to draw the finalconclusion[fromC5 and C6] concerningthe question of immortality, namelythatthe human intellectconsequentlyis not everlastingand hence immortal".24 is not new. CommentatorsfromGeorg Schwartz This interpretation have read in the fifteenth centuryto KonstantyMichalskiin the twentieth as evidence that he Buridan's apparent ambivalencetowardsAlexander But as AnnelieseMaier observedin replyto Michalski's was an Alexandrist.25 "one cannot reallysay that he [i.e., Buridan] decides in interpretation, favorof the teachingof Alexanderof Aphrodisias;throughouthis argumentsand conclusions,Buridan goes his own way, and then statesonly As we have seen,Buridan thathis resultsagree withthoseof Alexander".26 when he tries to Alexander with imaginewhata pagan philosoonly agrees alone. But Buridan is not on natural reason based would conclude pher a pagan philosopher.Indeed, any claim thatBuridanwas an Alexandrian is goingto run headlonginto the followingfacts:(1) he neverassertsthat Alexander'sopinionon the intellectis true(thoughhe does say thisabout 23OlafPluta,Persecution Statute ArtofWriting. TheParisian andthe 1, 1272,andIts ofApril dela pensée médiévale. Etudes , in:PaulJ.J. M. Bakker (ed.),Chemins Philosophical Consequences Turnhout à ¿(énon 2002,575. Kaluza, offertes 24Pluta2002(op.cit.,above,n. 23),583. 25ForSchwartz, seeL'Influence seePluta2002(op.cit., above,n. 23),584-5.ForMichalski, Internationale dansla psychologie duXIVesiècle dAverroès etdAlexandre , Bulletin dAphrodisias Classed'Histoire et et Lettres, Classede Philologie, de l'Academie Polonaise desSciences de Philosophie (1928),14-6. 26Anneliese Maier:"mankannauchnicht eigentlich sagen,dasser sichfürdieLehre undSchliessen Buridan Alexanders vonAphrodisias entscheidet: gehtimArgumentieren mitdenen dannnur,dassseineErgebnisse durchaus seinen eigenen Wegundkonstatiert derspätscholastischen Alexanders übereinstimmen" , Naturphilosophie (Metaphysische Hintergründe derSpätscholastik Studien zurNaturphilosophie , vol.4, Roma1955,27).
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the contraryopinion of the faith);27 (2) he does assertthat "not all [of conclusions are true";28(3) he says thingselsewherethatare Alexander's] with what he would have known of Alexander'sposition,29 incompatible forexample,thatAlexanderdoes not positan immaterialintelremarking, lect, "as we do [sicutnosponimus ]";30 and (4) there is never any suggestionin the Quaestiones in libros Aristotelis De Animaor elsewherein his writings that he hopes to redeem Alexander for Christianphilosophy,which is surelythe sortof projecthe would take up ifhe reallythoughtAlexander was right. But Pluta is undeterred.He argues that Buridan had good reason to his truepositionon the intellectbecause of the ArtsFacultyStatute disguise of April 1, 1272, which he describesas a "landmarkstatutein the history of persecutionof philosophicalthought"that became "a forceful instrumentto curtail and control any heterodoxphilosophicalthought during the later Middle Ages".31Originallydirected against the Latin the statutedecreed that mastersand bachelorsin the faculty Averroists, of arts at Paris could no longer dispute properlytheologicalquestions, e.g., concerningthe Trinityand the Incarnation,and thatwhen a question concernedboth faithand philosophy,it mustbe determinedon the side of the faith,and any argumentsgoing against the faithmust be resolvedor declared to be simplyand absolutelyfalse.32Violatorsof the 27"TertiaopinioestVeritas fideinostrae . . (QDA3III.3: 22). 28"Sed tarnen firmiter tenendum estquodnonomnesconclusiones suntverae..." butpresumably he meansthefirst threecon(■ QDA3III.6: 51).He doesnotsaywhich, clusions (i-iii)oftheAlexandrian position. 29I say"wouldhaveknown" becauseit is relevant to thisdebatethatBuridan seems withAlexander whodiscusses andcritiques Averroes, acquainted onlyindirectly, through hismaterialist viewin theCommentarium inDe Anima knewwell. , whichBuridan Magnum ThereAlexander's viewis described as an opinion, butit is opposed to theopinions of Themistius andTheophrastus, whoseemcloserto theposition Averroes adoptshimself. If Buridan didknowsomeofAlexander's ofDe Inteliectu workdirectly (a translation by GerardofCremona hadbeenaroundsincethetwelfth he givesno indication century), ofthis. 30Speaking howintelligible inthesoul oftheproblem ofexplaining canremain species after theactofthinking is complete andlaterbe recalled atwill,Buridan almost concedes, wouldnottouchAlexander, "itis apparent to methatthisdifficulty whodoes wistfully, mihiquodiliadifficultas notpositan immaterial soulas we do [apparet nontangeret nonponentem intellectum immaterialem sicutnosponimus]" Alexandrům, (QDA3III.15: seeRolfSchönberger, Relation ab Vergleich: DieRelationstheorie 172).Foradditional passages, desJohannes Buridan imKontext seines Denkens undderScholastik , Leiden1994,425,n. 31. 31Pluta2002{op.cit ., above,n. 23),569. 32The LatintextoftheStatute is citedin Pluta2002(op.cit.,above,n. 23),570, n. 21.
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statutefaced the stiffpenaltyof being permanentlyexcluded fromthe facultyand branded as hereticsunlesstheypubliclyrecantedwithinthree days. "Sufficeit to say", Pluta remarks,"that this statuteforced the philosophersto modifytheirwritingsubstantially; theyhad to startwrit'between the lines'".33 ing Was Buridan cowed by the threatof exclusionto hide his heterodox beliefs'betweenthe lines'? He does seem to thinkAlexanderhas the best positionif one cleaves only to natural reason, but why do that if you knowthe truthas revealedin scriptureand churchteaching?That would be like sayingthat if I put my telescope away and relied on naked-eye - an interobservations,I would conclude that the universeis geocentric estingintellectualexercise,perhaps,but not to be confusedwithwhat is actuallythe case. In addition,the assumptionthat Buridan was theologelse we know about him icallysubmissiveclashes withalmost everything as a teacherof philosophy.He was a staunchdefenderof the autonomy of his facultywho, thoughsensitiveto curricularboundaries,frequently crossedthem anywayin treatingimportantquestionsin naturalphilosophy.34Thus, we findin his writingsdiscussionsof God as omnipotent,as , as impartinginexhaustible capable of freelycreatingotherbeingsex nihilo motionto celestialorbs at the momentof theircreation,as possessedof a perfectintelligencewhose activitymakes human understandingpossible, and as the source of the beatitudethat is the perfectionof human happiness.What these examples share, of course, is a creaturelyorientation.God is in each case studiedin relationto creatures,whose matter and motionnaturallydraw our mindsupwardsto theirprinciples,as well as providingus with evidentappearances throughwhich the divine author of these principlesmay be known. This much is proper to the arts faculty.In theology,however, God and creaturesare considered throughthe divinelightof revelation:"theologyhas foritsprinciplesarticles [of faith],which are believedquite apart fromtheirevidentness' the artículos créditos '35 There is an ologiaverohabetproprincipiis absqueevidential 33Pluta2002{op.cit.,above,n. 23),571. 34See Zupko2003{op.cit.,above,n. 2), 139-45, andEdithSylla,'Ideoquasimendicare intellectum humanum': TheRoleofTheology inJohn Buridan's Natural oportet , in:J.M.M.H. Philosophy andJackZupko(eds.),TheMetaphysics andNatural Buridan Thijssen , LeidenPhilosophy ofJohn Boston-Köln 2001,221-45. 35JohnBuridan, In Metaphysicen Aristotelis Paris1518,BookI, Questiones argutissimae, a. M. 1964.The zurAristotelischen , Frankfurt Q. 2, f.4ra-rb. Rpr.as Kommentar Metaphysik dateis erroneously ofthereprint original publication givenas 1588on thefrontispiece edition.
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betweenthe two approaches,whichcan be importantpracticaldifference seen in the way Buridan argues forthe existenceof intellectualmemory in humans withoutspeculatingabout the role such a facultymightplay in a disembodiedintellect,or examines the relationbetween God and creatureswithoutgoing on to considerthe relationbetweendistinctpersons of the Trinity.Since the latterquestionsinvolveexaminingthe consequencesofparticulardoctrinesor articlesof faithratherthanconstructing fromevidentprinciples,theyare off-limits demonstrations to the philosoif even the is the matter same. pher, subject But perhapsBuridanwas not being submissivein endorsingthe orthodox position.Perhaps he was only being crafty,sayingwhat needed to be said in public to remainabove suspicion,leavinghintsof his real views in his commentariesfor his followersand other cognoscentito read 'between the lines'. Here Pluta invokesthe godfatherof the hermeneutics of suspicion,Leo Strauss.Citing Strauss's 1941 essay,Persecution and theArtof Writings he contendsthatthe constantthreatof persecutionmade medievalphilosophers"particularly inventivein developingtechniquesof which enabled them to shroud theirtrue beliefs".36One techwriting, Strauss identifies is contradiction of the orthodoxview: nique surreptitious ... ifan ablewriter whohasa clearmindanda perfect oftheorthodox knowledge viewand all itsramifications, contradicts and as it werein passing surreptitiously oneofitsnecessary or consequences whichhe explicidy presuppositions recognizes andmaintains thathe wasopposed to else,we can reasonably everywhere suspect theorthodox as suchand wemuststudy hiswholebookalloveragain,with system muchgreater careandmuchlessnaïveté thaneverbefore.37 "As a result",Pluta argues,"it makes no sense to enumeratepassages in which a givenauthoraffirms that,forexample,the human soul is incorand hence immortal,if the very same indivisible, poreal, incorruptible, author providesstrongphilosophicalargumentsfor the mortalityof the soul somewhereelse- withoutmakingany attemptto refutethese argumentson naturalgrounds".38 The slightest hintof unorthodoxy is sufficient to undermineour assumptionthat an author means what he says. This turnsBuridan'sclaims that are inconsistent reading,of course,effectively withAlexander,includinghis explicitrejectionof materialismas regards the humanintellect, intoevidenceforthe thesisthathe was an Alexandrian.
36Pluta2002{op.cit ., above,n. 23),564. 37Strauss 1941,32; quotedin Pluta2002(op.cit.,above,n. 23),568,n. 19. 38Pluta2002[op.cit.,above,n. 23),569.
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It is to know what to say to such an interpretation.39 It is difficult not evidence where a to close contrary conspiracytheory, uncomfortably only does not count against the theory,but also confirmsthe existence of a conspiracy.Be that as it may, I do not believe Pluta's interpretation can be sustainedon textualgrounds.To see why not, we need to conundrummentionedabove. Recall returnto its source,the interpretive that Buridan does not actuallyrefuteAlexander'sheterodoxpositionon the intellectby naturalarguments,as seems to be requiredby the 1272 of resolvingit: "sednobisestdifficilis Statute,but onlypointsto the difficulty " solutio (QDA3 III.6: 52). Furthermore,his categoricalassertionthat the humanintellectinheresin the humanbody seemsto entailtheAlexandrian position,althoughhe does not actuallydraw this conclusion.Why does he leave it at that? To begin with the conundrum,Buridan does not conclude that the fromC6 to theAlexandrian is materialbecausetheinference humanintellect This is not is fallacious. immediatelyevidentfromthe text of position if two we look but just questionsearlierwe will see BuridandefendQ.6, ing, in replyto Averroes,the view that the human intellectinheresin the human body in a definitiveor non-commensurable way (i.e., whole in whole and whole in part),ratherthan circumscriptively (i.e., whole in whole and partin part),as materialformsdo (QDA3III. 4: 30-36).40Thus,41 we canspeakofit is movedbycontrary whenit is saidthattheintellect motions, carin theconsecrated hostwhenonepriest justas wespeakofthebodyofChrist to theleft.ForthebodyofChrist andanother to theright riesthebodyofChrist init,justas thesizeofthehost norbya motion movedinitself is neither inhering in it doesnotinhere This is exactlywhat we would expect Buridan to argue if he holds that the human intellectis not a materialform.But then the sense of the 39I saythisin partbecauseStrauss ofphilosophy is nottakenseriously byhistorians thecanstillbe found hisdisciples intheEnglish-speaking world, among'political though owesomeforthissurely science(thereasons in departments ofpolitical ory'specialists of The bestknown owndisdainforprofessional to Strauss' critique philosophy). thing texts is MylesBurnyeat's ofphilosophical Strauss as an interpreter entitled, provocatively inPlatonic Political Studies a Secret without , inthe , a review Philosophy essayofStrauss's Sphinx NewYorkReview ofBooks,39.9(May30, 1985),30-6. 40Thistextis discussed A Study toBodies? in myHowAreSouls Related at length ofJohn 11in as chapter 46.3(1993),575-601, ofMetaphysics, Buridan , in:TheReview reprinted Zupko2003{op.cit.,above,n. 2), 175-82. 41". . . quandodicitur dicisicutde corpore motibus contrariis, potest quodmoveretur ad dextram etalterad fert Christi inhostia consacrata cumunuspresbiter Christi corpus sicutnec necmotusibiinhaerente, NonenimcorpusChristi sinistram. perse movetur, hostiae sibiinhaeret" (QDA3III.4: 35). magnitudo
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betweentheproposition Buridan predicate'. . . inheresin matter'is different in asserts C6 and the fourth of the Alexandrian categorically proposition position.Therefore,the inferencefailsby the fallacyof equivocation.42 Movingto thefirst point,a muchmoreplausibleexplanationof Buridan's concessionthat it is not easy to refuteAlexander'spositionby natural argumentsis that he was simplybeing honestwith his audience. There are no decisive argumentsagainst the thesisthat the human intellectis a materialformif we limitourselvesto what appears to be true based on sense, memory,and experience.In fact, none of the three famous opinions not that of Alexander,not that of Averroes,and not that of the faith turnsout to be demonstrableby naturalreason.But thismeans that the question of whetherthe human intellectis everlastinghas for Buridan the statusof a dubium , or a questionwhere doubt can alwaysbe be and legitimately entertained, demandsthathis approachto it be dialectical ratherthan demonstrative. Needless to say,Buridanhimselfis hardly agnosticon the question,thoughhe realizes that neitherhe nor anyone else is in a positionto demonstratethe truthabout the human intellect by means of principlesin naturalphilosophy.Whetherit can be demonis anotherquestion,whichthe theologiansmustresolve stratedtheologically forthemselves.That is why he pointsout that "the determination of this doubt pertainsmore to metaphysicsor to the facultyof sacred theology",43in connectionwithwhich "severaltheologianshave raised the following quodlibetalquestion:whetherChristwas a human being during the triduum , i.e., the threedays when his body was in the sepulcherwithout a soul and his soul was among the dead withouta body".44 As for what Buridan actuallybelieved,it seems to me that we must invoke here anotherhermeneuticalprinciple,the principleof charityin to theAlexandrian whichrequiresthatwe takehis non-assent interpretation, 42Plutamisses all thisin hisdiscussion, onlythat"Weneednotenumerate remarking forth thearguments Buridan Averroes" (Pluta2002{op.cit.,above,n. 23), brings against 581). 43Plutacorrectly oftheimmortality oftheinteloutthatthere is no discussion points he treats thisas further on Aristotle's lectin Buridan's , though commentary Metaphysics evidence ofBuridan's tacitAlexandrianism above,n. 23),584,n. 53). (Pluta2002{op.cit., is notraisedin his theimmortality Butthereis againa better question explanation: and forthesimplereasonthatAristode didnotraiseit there, commentary Metaphysics on Aristotle. Buridan first andforemost tobe commenting tookhimself 44"Etfinaliter ad metaphysicam huiusdubitationis dicamus pertinet quoddeterminatio illudquodlibetum: moverunt vel ad facultatem sacrae.Undeplurestheologi theologiae in triduo sineanimaeratin sepulchro erathomo,scilicet utrum Christus quandocorpus in inferno" III.6: 53-4). et eiusanimasinecorpore {QDA3
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positionat face value, to mean that he was not an Alexandrian.This thesisis neitheresotericnor controversial.Its only virtueis that it fits what Buridan actuallysays. Atlanta,Georgia, USA EmoryUniversity Department ofPhilosophy
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* SomeRemarkson Buridan1 s Discussionon Intension and Remission
STEFANO CAROTI
In his recentpaper on John Buridan'sdiscussionon intensionand remission of qualitiesJoel Biard1fillsa gap in AnnelieseMaier's analysis,whose firstpart of Zwei Grundprobleme derscholastischen Naturphilosophie (namely Das Problemderintensiven Grösse )2 is still the most complete introduction to the medieval Parisian discussionon this topic; Edith Sylla's contributions,3importantas they are, are focused on English authors. In this paper I will: a) lay stresson the importanceof the commentarieson Aristotle'swritingson natural philosophyfor this topic as well as for setsofproblems,suchas thosediscussedin RichardSwineshead's establishing Libercalculationum , just to mentionone of the workswhose influencecontinued in the XVth Century;4b) try to set in a larger contextJohn Buridan's discussionon intensionand remissionin his Physicscommen.5 taryde ultimalectura first The point actuallydoes not need much stress,because in recent years researchon the medieval traditionof commentarieshas substan-
* I am verygrateful William toJeanCeleyrette, and Edmond Mazetfor Courtenay their remarks. 1J. Biard,L'être etla rémission de etla mesure dansl'intension desformes Blaise Buridan, (Jean in:Medioevo, 27 (2002),415-47(415-33onJohnBuridan). Parme), 2 A. Maier,^weiGrundprobleme Das Problem derintensiven derscholastischen Naturphilosophie. Roma1968,3-109,see74,n. 2 concerning Grösse. DieImpetustheorie Aufl., , 3. erweit. John Buridan. 3 E.D. Sylla,Medieval theOxford Calculators , in: Archives ofthelatitude offorms: concepts du MoyenAge,48 (1973),223-83;ead.,Medieval d'Histoire Doctrinale et Littéraire fortheHistory The"Merton Schoolin:Archive ofExactSciences, ofQualities: Quantifications andtheMathematics 8 (1971),9-39;ead.,TheOxford Calculators 1320-1350 , New ofMotion York-London 1991. 4 C. Lewis,TheMerton inLateSixteenth Seventeenth andKinematics andEarly Tradition Century , Padova1980. Italy 5 Acutissimi octo Buridani Subtilissime reverendi super Johannis questiones Magistři philosophi Dullaert de et revisea Magistro libros Aristotelis , diligenter Johanne recognite Physicorum a./M.1964), in edibusDionisii Nachdr.: Frankfurt Roche,Paris1509(unver. Gandavo, hereafter Q¿Phy. BrillNV,Leiden, © Koninklijke 2004 - www.brill.nl Alsoavailable online
Vivarium 42,1
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new evidence as far as intentiallyincreased.6I shall present,therefore, sion and remissionis concerned. 1. Intension and Remission and RelatedTopicsin XIVthCentury Parisian Commentaries The questionsof Buridan'sPhysics , hereafter commentary(ultimalectura u.l.) devotedto intensionand remissionare the questions3-5 of the third book: 1) III, 3: "utrumqualitatescontrarie ut albedo et nigredo,caliditaset frigiditaspossintse compatisimulin eodem subiectosecundumaliquos gradus ipsarum". 2) III, 4: "utrumqualitas secundum quam est alteratioper se proprie dictacontinuaet temporalisacquiriturtota simulvel pars postpartem". 3) III, 5: "utrumin alterationepars qualitatisque priusacquiriturmanet cum parte que posteriusacquiritur".7 8 the In Buridan's Physicscommentaryknown as de tertialectura sequence of the questionsis different: the firstdiscussed(the thirdquestionof the Illrd book) correspondsto the fourthof the ultimalectura , the second one to the fifth,and the thirdand last one to the thirdof the ultimalectura , whichis the openingquestionof thisredaction.9The Physics commentary 6 A. Maierù,University inMedieval Leiden, tr.anded. byD.N. Pryds, Training Europe NewYork-Köln desdisciplines à la Faculté 1994;L. Holtzet O. Weijers (eds),L'enseignement desArts(ParisetOxford XIIIeXVesiècles). Actes ducolloque international , Turnhout 1997;G. C. Leonardi, S. Perfetti nelV occidente latino Fioravanti, (eds),Il commento (sec.XIII-XV). filosofico Attidelcolloquio dallaSISMELe dallaSISPM 19-22ottobre Firenze-Pisa 2000,organizzato , Turnhout hasgivenmanybasiccontributions in thisfieldeither 2002.OlgaWeijers as 3danslesFacultés an author oras an editor; I shallquotehereonlyherLa edisputatio desarts au moyen Turnhout 2002. , âge 7 Buridan, if.42vb-48ra. Q.Phy., 8 B. Michael, Buridan: Studien seinen Werken undzurRezeption seiner zuseinem Leben, Johannes Theorien imEuropa desspäten Mittelalters FreieUniversität , Berlin, 1985,Bd. 2, 578-94for theredaction deultima lectura detertia lectura. OnJohnBuridan , and574-7fortheredaction seenowJ.M.M.H. andJ.Zupko(eds),TheMetaphysics andNatural Thijssen Philosophy ofJohn Leiden-Boston-Köln Buridan. Portrait 2001; J.Zupko, Arts Buňdan, John ofa Fourteenth-Century Master , NotreDame,Ind.2003. 9 I quotefrom themsCittàdelVaticano, III, 3: "utrum ChigiE VI 199,ff.37va-38rb: dictaacquiratur simulvelcontinue qualitas que estalteratio proprie parspostpartem, verbi utrum incalefactione totacaliditas, gratia queperalterationem acquiritur, acquiratur totasimulvel una parseiuspostaliam";ff.38rb-40ra: III, 4: "utrum parsqualitatis maneat cumpartequeposteaacquiritur"; ff.40ra-42rb: acquisita peralterationem III, 5: "utrum contrarie se invicem simul ineodemsubiecto secundum qualitates possunt compati
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editedunderthename ofJohannesMarciliusInguenhas thesame sequence of questions as Buridan's commentaryde tertialectura , while the other Parisian commentatorsfollow the order of Buridan's ultimalectura.If Oresme's Physicscommentarycan be dated no later than 1347/8,10he could be creditedwith the responsibility of changingthe order of disin his commentaryde ultima a also Buridan cussion, change accepted by lectura , which is probablylater than Oresme's.11 is not,however,the onlyplace whereBuridan The Physics commentary discussesthe intensionand remissionof forms.In the firstbook of hisDe he deals with the related topics of et corruptione generatone commentary12 : the permanenceof the elementaryqualitiesin the mixedbody and reactio 1) I, 19: "utrumomne agens agendo repatiaturet omne passumpariendo reagat". 2) I, 20: "utrumpossibilesit esse actionema proportioneequalitatisvel etiam a proportioneminorisequalitatis". 3) I, 21: "utrum forme substantialeselementorumsuscipiantmagis et minus". 4) I, 22: "utrumformesubstantialesmaneant in mixto". 5) I, 23: "utrummixtiosit possibilis".13 Problems concerningthe permanence of the elementaryqualities in a can be foundin mixed body, as well as intension,remission,and reactio et corruptione ,14Aegidius Albert the Great's paraphrases of De generatione on the firstbook of De generatione Romanus also discussesin his quaestiones
ineodemsubiecto utrum secundum eandem rationem verbigratia ipsarum, aliquosgradus I amvery cumaliquograducaliditatis". frigiditatis ipsiuspossetsimulessealiquisgradus detertia lectura comforthetranscriptions from Buridan's toJeanCeleyrette Physics grateful mentary. 10S. Kirschner, mitEdition Kommentar desAristoteles. Kommentar Oresmes Nicolaus zurPhysik vonVier sowie derQuaestionen zu Buch5, zu Buch3 und4 deraristotelischen Quaestionen Physik 1997,28-37. Stuttgart 11Michael1985(op. cit.,above,n. 8),Bd. 2, 606-8. 12We havetworedactions either oftheExpositio or oftheQuaestiones , Michael1985 I haveusedthetextofthemsBerlin, Staatsbibliothek, above,n. 8),Bd.2, 628-48. {op.cit., lat.fol.387,if.129ra-156vb. 13Ms Berlin, lat.fol.387,ff.141va-146rb. Staatsbibliothek, 14Albertus elementorum, loci,De causis omnia, V, 2: De natura proprietatum Opera Magnus, i. W. 1980,I, 1,p. 24 "EtestdigresMünster Degeneratione etcorruptione , ed. P. Hossfeld, ethabetcontrarium", substantia siodeclarans p. 131and magiset minus recipit qualiter : I, 6, pp. 169-76. thelastTractatus ofthefirst bookon mixtio
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"utrumsubstantiasuscipiatmagis et minus,utrumin acciet corruptione dentibuspossitinvenirimagis et minus proprie".15 In commentingon Aristotle'sPhysicsmedieval authorsblend together different materials,not onlyfromAristotle'sotherphysicalworks,but also fromoriginaltreatises,especiallythosewrittenforuniversity students,like habenunitate et augmentatione de activitate, Walter Burley'sTractatus formarum to mentionone of the mostimportiumcontraria magisetminus,16 suscipientium to the medievaldiscussionon intensionand remission. tantcontributions William Ockham resortsto a quotaIn his Quaestiones in librosPhysicorum in discussing"whetheraccordetcorruptione tionfromAristode'sDe generatane and ing to the Philosophercontraryformscan be in the same subject",17 in the last questionshe deeply analysesBurley'spositionsconcerningthe activityof elementaryqualities in alterationand problems of temporal limitsconnectedto thiskind of motion.18 Ockham's use of Burley'sTractatus providesstrongevidenceof the circulation of ideas in the higher level of education. This circulationis confirmedby Burley'sfinal redactionof his Physicscommentary,where he repliedto Ockham's objections.19 Taking into account that problems were raised de activitate discussedin Burley'sTractatus primus) (or Tractatus one can easily realize how intricateis the also in a theologicaldispute,20 15Aegidius libro De generatione subtilissime , Venetiis, Romanus, Quaestiones primo super De generatione See NicoleOresme, Giunta1518,ff.60ra-61ra. Lucantonio Quaestiones super ofSaxony's Albert for München S. Caroti, etcorruptione 1996,139-58 , hrsg. JohnBuridan's, on thesetopics. etcorruptione commentaries De generatione ofInghen's andMarsilius 16I useherethetitleoftheexplicit in ms.Vat.lat.817, contained oftheTractatus an with So-called. "Tractatus seeL.M. de Rijk,Burley's f.203ra.On theTractatus primus", 34 in:Vivarium, sitmaxima "Utrum contradictio Additional Edition ofthe Questio oppositio", (1996),161-91. 17Guillelmus naturalis et Summula libri Brevis summa de Ockham, philosophiae Physicorum, N.Y. 1984 St.Bonaventure, Aristotelis inlibros , q. 86,ed. St.Brown, Quaestiones Physicorum contrariae sintin eodem sitquodformae intentio Philosophi (OPh,VI), 630: "Utrum I De "Contra: to theproblem: a positive answer theargument subiecto against primo"; se". noncompatiuntur etperconsequens uniusestcorruptio e: generatio alterius, generation 18Fromquestio sitcausasufficiens sufficienter 139("utrum quodcalorignis possit probari remississitotalis
ponensfrigiditatem ignis")to theend,questio151("utrum formae fieri remissionem rationabiliter mametcaliditatem peradmixtionem"), ponere possit inlibros , ed. Brown Ockham, Quaestiones (above,n. 17),773-813. Physicorum ' 19E.D. Sylla,Walter onAristotle's Practice as a Commentator , in:Medioevo, Physics' Burley's ' andtheMathematics commentaries 27 (2002),301-72;Ead.,Walter ofAlteration, Burley's Physics' 6 (2001),149-84. in:EarlyScienceandMedicine, 20De Rijk1996{op.cit.,above,n. 16),162-4,(and164,n. 16forGeraldOdonis'use Giraldus OdonisOFM, Opera sitmaximaoppositio"; "utrum contradictio of Burley's York-Köln Vol.1 Logica 1997,8, n. 25) , ed. byL.M. De Rijk,Leiden-New Philosophica. andSylla2002{op.cit.,above,n. 19),302-3.
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the medievalphilophilosophicaltraditionin the Middle Ages. In studying from the universities one should, in any sophical productionstemming case, avoid runningthe riskof consideringthe presenceof the same topics in the same places (eventuallyalso in different ones) merelyas the outcomeof teachingroutine.The evidentanalogiesin the topicsdiscussed do not always conceal a slavish attitudetoward either a master or a school; sometimesfroma set of questionson the same topic it is possible to ascertainthe different positionsheld in the classrooms. and intension This is the case also for the discussionon contrariety ParisianPhysics commentariesby and remissionin the fourteenth-century John Buridan,Nicole Oresme, Albertof Saxony and JohannesMarcilius of Inghen. There is a certainagreementamong them about the need to discuss togetherthe problem of the presence of contraryqualities in a but not concerningtheplace where substanceand intensionand remission, one should discussthese topics:John Buridan and JohannesMarciliusof Inghen21discussthemin the thirdbook,whileNicole Oresme22and Albert of Saxony23do so when commentingon the fifth.There is no complete agreementalso concerningthe orderof discussion,as we have seen, with lectura and JohannesMarciliusof Inghen's Buridan'scommentaryde tertia as the last with topic, contraryto all othercommencontrariety dealing ultima lectura included. Buridan's de taries, In both commentariesthat we can consider models of fourteenthcenturyParisian commentaries I mean John Buridan's and Nicole Oresme's we find a heavy presence of Walter Burley's Tractatus primus 21Johannes Marion octo libros Marcilius , Lugduni, perJohannem Super Physicorum Inguen, in alteratione a./M. 1964),III, 3-5:"utrum 1518(unver. Nachdr.Frankfurt qualitas maneatcumpartesecundo in intensione utrum subito; parsprimoacquisita acquiratur essesimul", ff.37rb-40va. forme contrarie utrum possint acquisita; 22 NicoleOresme, ineodem; contraria sintsimul , V, 6-9:"utrum Questiones super Physicam ad partem; utrum ad gradum sivepartis forma intendatur utrum gradus peradditionem alteronon utrum contrarium intendatur ex extremis; mediaintercontraria componantur cf.Kirschner 1997{op.cit.,above,n. 10),395-417. remisso", 23Albertus coninAristotelis de Saxonia, , V, 9-11:"utrum Quaestiones Physicam qualitates ineodemsubiecto; utrum se simul earum trariae secundum compati possint aliquosgradus totasimulvel secundum in intensione post partem acquiratur qualitasquae acquiritur maneat cumqualitate in intensione alicuius utrum que primoacquiritur qualitas partem; ad inAristotelis et Quaestiones cf.B. Patar,Expositio 'Physicam' acquiritur"; quae posterius - Louvain-Paris On Albert Louvain-la-Neuve Albertům deSaxonia 1999,III, 825-64. attributae, derBewegung. Studien Theorie Die aristotelisch-scholastische seeJ. Sarnowsky, of Saxony, zum 1989;seealsoJ. Sarnowsky, desAristoteles Alberts vonSachsen Kommentar zurPhysik , Münster des14.Jahrhunderts ausderMitte EinAlbert vonSachsen , in: zugeschriebener Physikkommentar on thefifth book. 27 (2002),449-73and472forthequestions Medioevo,
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without and secundus. John Buridan uses Burley'sso-called Tractatus primus a Nicole Oresme introduces solution mentioninghim;24 explicitlyattributed to Gualterus , a positionwhichpresentssome analogieswiththatwhich Oresme consideredthe best one25and has recourseto Burley'sarguments withoutmentioninghis source. The use of thiswork by the two masters,and above all by Buridan, has a certainimportance,because in the Tractatus Walter Burleysystemdesinit aticallyresortsto some of the new languages of analysislike incipit/ and maximum/ with intension and remission and minimum, which,together in reactio can be considered a relevant innovation the Parisian , philosophicaluniversity productionsof the second halfof the XlVth century.26 Buridan's implicitquotation of Burleyis in the ¿^-argumentsof the opening question III, 3 of his Physicscommentary(u.L), afterthe first6 The implicit argumentsdedicatedto stressingthe notion of contrariety.27 referenceto the Tractatus primusis introducedas an argumentagainstthe interactionof contrarydegreesin alteration;28 actuallythisargument(the seventhof the openingťorc-arguments) is apparentlythe firstof a second series of argumentsagainst the presence of contrariesin the same sub24Biard2002(op.cit.,above,n. 1),416-7. 25S. Kirschner, Oresme onIntension andRemission inHisCommentary onAristotle's ofQualities ' 38 (2000),255-74, , in:Vivarium, Physics' esp.272-4. 26E.D. Sylla,Transmission totheconofthenew ofthe fourteenth physics century from England tinent duXIVesiècle , in:S. CarotietP. Souffrin , Firenze 1997,65(eds),La nouvelle physique 110. Theinfluence ofBurley's workis notlimited tothepassageI amstudying here;the between thearguments usedinthethree couldreveala greater use, comparison questions eventhough we haveto be verycautious, sincethesearguments in werewidely diffused university teaching. 27In thethird Buridan refers forthefirst timein thesequestions togradus , argument f.42vb:"Item,oppositio contrarietatis attenditur secundum rationem non Q¿Phy, speciei, secundum rationem hocegosuppono . . . Secundoquiain eodemdecimo individuorum, videtur Aristoteles intendere sitdifferentia et (seil.Metaphysice) quodcontrarietas specifica secundum differentiam Ex hocautemsupet formalem. quoddebeatattendi specificam ab omnifrigiditate differt postovidetur sequiquodomniscaliditas specieet perconseab omnigradufrigiditatis differt quensetiamomnisgraduscaliditatis specie,et per cumnonpossint staresimulineodem, caliditatis consequens, sequitur quodnullus gradus staresimulcumaliquogradufrigiditatis"; itis probable thatalsohereBuridan has possit in mindBurley's conviction thatcontraries It is thefourth belongto thesamespecies. conclusion thatis deemed seemsCittàdelVaticano, dubious, BAV,Vat.lat. presented videlicet caloretfrigus, albedoet 817,f.203ra:"Quartaconclusio: contraríe, quodforme sunteiusdem nigredo, speciei specialissime". 28Buridan, starecum ., f. 42vb:"Itemomnessie concedentes Q.Phy graduscaliditatis in calefactione dicunt de caliditate gradibus frigiditatis quodomnino quantum acquiritur, tantum de frigiditate et e converso. Et ideosi potest ostendi corrumpitur quodcaliditas remitti sinegeneratione alicuius iliapositio etopinio debetextotoauferri". possit frigiditatis,
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stance,and againstthe explicationof the intensionof a qualitythrough the remissionof the contraryquality.I thinkthatwe have enoughevidence that this sectionof the firstpart was directedagainstBurley'sposition. In additionto precisetextualelements,whichwill be presentedbelow, thereare some otherindicationsabout Buridan'sborrowingsfromBurley. The first,and probablythe weakest,is the presencein thisseriesof cowargumentsof at least three arguments,which are to be found also in ;29the scholasticoriginof both works,however, primus Burley's Tractatus makes this evidence ratherscanty. the afterthe determination In the repliesto the opening cow-arguments, firstargumentof thisseriesis called ratiolonga,30 probablybecause Buridan consideredthispart of the questionas a whole, which can be confirmed by the factthat his repliesdo not followthe openingargumentsas precisely as the previousones. By far the greaterevidence for the use of by Buridanis providedby the verytextof the firstarguBurley'sTractatus ment of this second seriesof cow-arguments: and without canbe reduced Sometrytoprovethathotness anycoldness; generating toprovethistheyargueas follows. arepermanent hotness andcoldness First, things. butno last ofa permanent instant oftheexistence is a first there Second, thing, Aristode forthisreasonin theVlllthbookofthePhysics instant; saysthatthelast from whichresults to thething as belonging mustbe considered instant change. in time;itis clearfrom theVlthbookofthe arenotimmediate instants Third, there is time.31 twoinstants thatbetween every Physics 29Theconfirmatio ofsudouttheimpossibility ofthisseries ofthefirst points argument thesame Tractatus in Burley's a topicwhichis central denchangein alteration, primus' ofthisseries couldbe saidoftheseventh .,f.43ra:"Itemsequitur (Buridan, Q.Phy argument in nigrum . . ."),seemsVat.lat.817, priusdeveniretur quodin motude alboin rubeum The colors. andif.210rb-211va f.210vb, hot,coldandlukewarm concerning concerning f.43ra:"Itemex quo tudicisquodper ofthisseries(Buridan, fourth Q.Pty., argument unusgradus removetur caliditatis unumgradům sequitur quod frigiditatis, qui acquiritur . . .") is thesameas thatused et repugnantiam illihabent ad invicem incompossibilitatem see ofa form; instant oftheexistence in thefirst theneedofan agens against byBurley msVat.lat.817,f.208rb. 30Buridan, ., f.44rb:"Adaliamrationem longam". Q.Phy 31Buridan, "Tuncergoaliquinituntur ., if.42vb-43ra: quodcaliditas probare Q.Phy et ad hocponunt remitti sinealiquageneratione suppositiones. frigiditatis potest suntresnature et frigiditas permanentis. Quarum primaestestquodcaliditas inesseetquodnonestdare reipermanentis instans Secunda estquodestdareprimum debetattribui dicitur in esseipsius; undeoctavoPhysicorum instans ultimum quodinstans posteriori passioni. intemsiveimmediata nonsuntsibiinvicem Tertiasuppositio: próxima quodinstantia inter ostendetur ubi enim huius debet ex sexto hoc et , quecumque quod apparere pore, medium". esttempus duoinstantia
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Of these threesuppositiones , the second and thirdrelyupon the twofondamenta introducedby Burleyin discussingthe fourthconclusion32 of his Tractatus : primus I takeforgranted inAristotle' twobasicnotions natural Thefirst is that philosophy. of theexistence thereis a first instant of a permanent thingwhichis produced a qualitative Thereis no problem evenif thisnotion, through change. concerning Aristotle wouldneverhavesaid:thelastinstant oftimein whichchangeoccursis thefirst instant of thething thatchange, otherwise produced through something wouldmovetoward a form thatitalready has. The secondbasicnotion is thatofsomething or destroyed permanent produced alteration there is nolastinstant ofitsexistence. Thisnotion is recorded through by and it wouldbe trueevenhad he notwritten Aristode, it,becauseoncehaving thelastinstant ofitsexistence, itwouldpassawaynotin time,andtheregranted forenotthrough alteration.33 of Burley'sTractatus Actuallythe twofondamenta correspondto the second in Buridan's and the thirdsuppositio is a suppositio Physicscommentary, directconsequenceof Burley'stwofondamenta . The notionexposed in the firstsuppositio of Buridan's commentaryis a very importantelementin 34 the discussionconcerningthe second conclusionof Burley'sTractatus. 32Vat.lat.817,f.209vb:"Nuncrestât viderede quartaconclusione et de rationibus suis.Quartaconclusio eratquodforme videlicet caloretfrigus, albedoetnigredo, contrarie, sunteiusdem Istamconclusionem etauctoritates. speciei specialissime. probavi perrationes Perrationes secundo tertio moralem, primo logice, phisice, perrationem quarto perrationem medicinalem. Primaratiotalisest:quandocumque distant distantia aliquaduo equaliter formali a perfectissimo inaliquaspecie, siunumillorum duorum sitinillaspecie, reliquum eritin illaspecie". 33Vat.lat.817,f.21Ora:"Etsuppono duofundamenta in scideclarata ab Aristotele entianaturali. Primum estquodreipermanentis de novoproducte inesseperalterationem estdareprimum in quo habetesse.Et hecestplanaetsiAristoteles instans nondixisset eam:quodin ultimo instanti mensurantis alterationem habetterminus alteratiotemporis nisprimo ad formam esse,quiaaliteraliquidmoveretur quamhabet. Secundum fundamentum estquodreipermanentis velcorrupte producte peralterationem nonestdareultimum in quo habetesse.Et hancscribit instans Aristoteles, et veraessetquamvis Aristoteles eamnonscripsisset, instans quiasi essetdareultimum in quo talisreshaberet nonin tempore, et ita nonper esse,ilia rescorrumperetur alterationem". 34It is thesecondratio thatconcerning in usedbyBuridan , after , a notion repugnantia thisseries of¿wz-arguments (seenote29),Vat.lat.817,f.208rb:"Secundo potest probari interformam successivam et formam perdifferentiam permanentem que esttalis:forma sedsemper et in potentia, successiva, quianonesttotasimul, aliquaparseiusestfutura ideoforma successiva dumest,requirit causamefficientem. Sed forma semper, permacausamagentem, eo nens,eo quodesttotasimul, ideo,quandoforma est,nonrequirit iamhabitaest.Cumergoinprimo inquoiaminducta instanti estforma quodtotaforma substantialis totaforma estfactainmateria, nonrequiritur subiecto, protuncaliquodagens velefficiens formam". Alsothecasus Buridan's theabsence , inwhich following suppositiones of a contrary an alteration in whicha quality is diminished quality during (remissio ) is
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I thinkthat these elementstogetherare enough to permitthe hypothA comparisonbetween fromBurley'sTractatus. esis of Buridan'sborrowings the two last redactionsof Buridan's Physicscommentary,that is de tertia and de ultimalectura , providesfurtherevidence. Buridan's commentaryde with the has the same break in the opening row-arguments, tertialectura of a seriesof argumentsagainstthosewho tryto prove that introduction intensionand remissioncan be explained throughthe varyingpresence commenof degreesof contraryqualities.The textof the de tertialectura the at even in more is this confused, though problem stakeis tary place there is some remissqualityin a that that to demonstrate is, identical, substancewithoutthe presence of a contraryquality.35What in the de ultimalectura commentaryis introducedthroughan orderedseriesof supof Burley'sdiscussion a (in way verynear to the twofondamenta positiones is of the fourthconclusion of his Tractatus primus) here presentedas a series of quotationsfromAristotle'sPhysics , and notablyfrompassages limits. and and minima maxima temporal concerning Furtherevidence for the use of Burleyin discussingthe topic of the role of contraryqualitiesin intensionand remissionis providedalso by Albertof Saxony's Physics commentary.Albertdiscussesthe topic of the in a substancein book five,as did Nicole of contrary qualities presence Oresme. But even thoughwhen choosingthe place of discussionhe follectura lows Oresme,Albertreliesupon the textof Buridan'sde tertia , from whichhe takesa long passage in his fourth¿wz-argument.36 Albert,moreover, dedicates the last arguments(here numeratedseparately,afterthe
in Burley's Tractatus thesecond to thatfollowing is verysimilar , even stated, fundamentum thatcontrary is different atstake heretheproblem belong qualities (todemonstrate though to thesamespecies). 35I usethetextofthemsCittàdelVaticano, somecorBAV,ChigiE VI 199,(with Wissenschafltliche from themsErfurt, rections Allgemeinbibliothek, Ampl.F. 298),which hasbeentranscribed (seenote9),ChigiE VI 199,f.40rb:"Itemaliqui byJeanCeleyrette dicunt caliditatis demonstrare credentes frigiditatis, quod compati gradui gradům ponendo de caliditate remissa estaliquisgradus in caliditate corrumpitur quiaquantum frigiditatis, ostendi Et sicideo,sipotest de frigiditate. tantum inremissione caliditatis, quod generatur concludi debebit sinealiquafrigiditate, remissam sitdarecaliditatem (thatis propositum ostendo arenotin thesamesubstance). thatcontrary quodsitdarecalidiIgitur qualities sine remississimam estdarefrigitatem sinefrigiditate remissam tatem pertaleenthimema: Antecedens sinefrigiditate. remissa estcaliditas Primo, quiain caliditate, probatur. igitur illud ut habetur naturalibus estdareminimum, Secundo, primoet octavoPhysicorum. dareprisicoportet ad frigidum, de calidissimo antecedens confirmatur, quiasi sitmotus ex octavoPhysicorum in quo eritfrigiditas, můminstans quodestdare quiasoletallegari estnature etfrigiditas in essereipermanentis, instans permanentis". primum 36See Thijssen's Ed. Patar1999{op.cit., above,n. 23),III, q. V, paperinthisvolume.
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first)in discussingBurley'sposition.37That Albertis discussingBurley's positioncan be easilydetectedby the presenceof some of Burley'sarguments38 as well as by the introductionof a second opinion in the second the of question,just beforethe repliesto the openingrow-arguments: part is contrary to every ofhotness totheother degree every degree According position, Thisposiwithanyofcoldness. ofhotness is compatible andno degree ofcoldness, themixture ofcontrary andremission obtainthrough tionexcludes thatintension thepresence of doesnotfollow from ofhotness Forinstance, theremission forms. from tothisposition, Intension offorms, ofcoldness. somedegree depends according remissam cumqua nonstataliquis Estdarealiquamcaliditatem 9, 826,27-39:"Quarto. formas contenet exeo quodponentes tatis falsa.Consequentia ; ergoquestio gradus frigidi remissionem hoc propter secundum trarias se compati ponunt aliquosgradusipsarum contrariarum undevolunt ad invicem; quantum qualitatum quodin remissione ipsarum caliditate remissa de alia;ergocumqualibet de una,tantum introducitur abiicitur ponunt remissam staresinefrigidiSi ergoprobabitur aliquamcaliditatem aliquamfrigiditatem. estdarefrigiditatem illorum nonvalet.Antecedens remississimam, tate,positio probatur: Antecedens seucumquanonstatfrigiditas. remissam sinefrigiditate, ergoestdarecaliditatem inprimo utvidetur velieAristoteles estdareminimum, exeo quodinnaturalibus probatur text. et octavohuius "; seenote35 forBuridan's 37Ed. Patar1999(op.cit.,above,n. 23),828,88-92:"Nono.Ponentes talemcomposearum secundum contrariarum sibilitatem posuerunt quodremisaliquosgradus qualitatum suicontrarii". nonfieret nisiperadmixtionem sioqualitatis 38Ed. Patar1999(op.cit.,above,n. 23),828-9,96-100:"Tertio. sic Nam,si remissio essent simul suicontrarii, tuncin coloremedio,sicutin pallido, fieret peradmixtionem Sed ex eo quodibiestalbedoremissa. hocfalsum. albedoetnigredo; tenet, Consequentia sedcolorem necnigredinem, ex eo quodsensus nonpercipit ibialbedinem falsitas patet, Ed. Patar1999(op.cit., msVat.lat.817,f.219va-b. cf.Burley, above, Tractatus, medium"; cumergoaersit Elementi debetessequalitas n. 23),829,5-9:"Quinto. simplex; simplicis simestqualitas elementům quameiushumiditas sequitur quodtameiuscaliditas simplex, remissa sinepermixeiusestqualitas remissa; ergoestaliquaqualitas plex;sedcaliditas msVat.lat.817,f.210vb.Ed. Patar cf.Burley, tionequalitatis sibicontrariae"; Tractatus, fieri tran1999(op.cit.,above,n. 23),829-30,21-6:"Septimo. quodnonposset Sequitur hocinconfieri transitům de alboin nigrum; nisipriusoporteret situsde alboin rubeum remittitur videtur tenere ex eo quodintalitransitu veniens. albedo;et,cum Consequentia videtur suicontrarii, scilicet nonpossit essesinepermixtione talisremissio sequi nigredinis, Thislastargument Tractatus , msVat.lat.817,f.211rb-va. est";cf.Burley, quoddictum in Buridan's canbe found alsoin whatI havecalledthesecondseriesof^«-arguments f.43ra).Another deultima lectura Q.Phy., JohnBuridan, commentary, (arg.5 ofthisseries, thesecondseries ofSaxony's canbe found three ofAlbert commentary among arguments deultima lectura ofJohnBuridan's 1) ed. Patar1999(op.cit.,above,n. 23), commentary: . . ."; cf.JohnBuridan, essetduplexmotus 829, 1-4:"Quartosequitur quodcalefactio . . ."); 2) ed. essetduplexmotus f. 43ra(arg.6: "Item,sequitur Q.Phy., quodcalefactio Patar1999(op.cit., above,n. 23),829,10-20"Sexto.Sequitur quodessetdarecaliditatem f.43rb(arg.9); 3) ed. Patar1999(op.cit.,above, infinitam . . ."; cf.JohnBuridan, QPhy., ettarnen nonhabetconn. 23),828,90-2:"Sedproboquodnon,quialumenremittitur, fitperadmixtionem suicontrarii"; cf.JohnBuridan, trarium; ergononomnisremissio ofthisseries aremanyreferences tolightalsoin f.43rb,thelastargument (there Q¿Phy., Tractatus). Burley's
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STEFANO CAROTI fromthehighest fromtheirdistance fromdegree0, and remission theirdistance between that,as whatis in themiddle up and Theythink degreeoftheseforms. a quality which is between in contrary downis notactually places,thuslukewarm, andcoldofhotness ofdegrees is notconstituted hotness andcoldness, bya mixture andfareither increase itshotness cancontinuously ness.Lukewarm bybeingfarther likewhat ofhotness, tothehighest andnearer 0 ornearer therfrom degree degree thecentre andhigher is higher is continuously bygoingawayfrom moving upward to thesphere oftheMoon.In sucha nearer andnearer oftheworldandgetting tothisposition. obtain andremission Theyaddalsoanother according wayintension remitted without andsometimes is intended hotness sometimes simile: anymixture withtherectiwithout as a lineis moreor lesscurved withcoldness, anymixture one.39 whilethefirst is thecommon is true, I think thatthissecondposition linear.
This long quotationcloses withAlbertof Saxony's evaluationconcerning solutionsabout the presence of contraryqualitiesin a the two different substance as well as the way in which intensionand remissionoccur. Somethinghas evidentlychanged in the academic milieu: if Buridan's commentariespermitus to grasp a certaingrowinginterestin the topic of the presence of contraryqualities and the related problem of intenin sion and remissionfromthe de tertiato the ultimalectura redaction,40 39Ed. Patar1999[op.cit.,above,n. 23),838,20-41:"Aliaopinioponitquemlibet calidinecaliquem essecontrarium caliditatis cuilibet gradum frigiditatis gradui gradum et remisEt istaopinioponitintensionem tatispossestarecumaliquogradufrigiditatis. nonponitremissionem formae. Verbigratia, alterius nonfieri sionem peradmixtionem formarum sedponitintensiones alicuius fieri caliditatis frigiditatis, gradus peradmixtionem earuma gradibus et remissionem illarum formarum a nongradibus fieri penesrecessum Undeistaopinioimaginatur earundem. summis quod,sicutilludquodestin locomedio necitatepiditas, nonoportet et deorsum intersursum quae quodsitin lociscontrariis, etaliquosfrigicaliditatis habetaliquosgradus etfrigiditatem, caliditatem inter estqualitas a mediomundi et continue fitaltiusperrecessum sursum et sicutquodmovetur ditatis; eiusa nongradu orbislunae,ita aliquatepiditas ad concavum accessum perrecessum incalefaciendo. Sic continue fitintensior summum eiusad gradum etaccessum caliditatis etadducit aliud de remissione; etproportionaliter deintensione ergoistaopinioimaginatur alicuius minor sinepermixtione estmaior, simile: nam,sicutcurvitas aliquando aliquando alicuius remissior sinepermixtione estintensior, itacaliditas rectitudinis, aliquando aliquando The verocommuniorem". Istamsecundam veriorem, primam reputo opinionem frigiditatis. in quesofSaxony is introduced thesetwosolutions between sameopposition byAlbert cumqualimaneat alicuius inintensione tionV, 11 ("utrum acquiritur qualitas queprimo ed. Patar1999{op.cit.,above,n. 23),848-9,18-23;855, tatequaeposterius acquiritur"), unatenet suntduaeopiniones. 67-71:"De istaquaestione qualiQuarum quodquaelibet licetbenesitdivisibilis in partes divisione et indivisibilis tasestforma graduales, simplex non Et istaopinioponitquodqualitas subiecti. secundum praecedens quantitativas partes istam inintensione, ethocoportet manet cumsequente ponit postquam opinionem ponere, . . . Aliaopinioponitquodinintensione indivisibilem talemqualitatem qualitas praecedens et quodintenestdivisibilis et quodquaelibet manetcumsequente, gradualiter, qualitas a gradu, recte etremissio ad prius, siofitperadditionem gradus perablationem posterioris ad gradum". sicutintensio gradus peradditionem 40In bothcommentaries ofarguments to setaparta series chooses theauthor (whatI
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Albertof Saxony's Physics commentaryan explicitdescriptionof the solution is introducedaccordingto which the presence of contraryqualities in a substanceis untenable,and, what is more relevant,this solutionis consideredsuperiorto the common view (the only one to be found in Buridan's commentary,if we except the argumentsin the second series of arguments). There is another reason for a so long a quotation fromAlbert of Saxony's Physicscommentary:the two examples he gives to betterillus- the trate this position about the absence of contrariesin a substance local motion and a curved line- are those used by Nicole Oresme in introducingwhat he presentsas the fourthopinion,the one he holds as the best one:41 andtheeasis themostreasonable itis tobe notedthatthefourth Second, position howa degree iestone;itdoesnotinvolve problems concerning passesawayorcomes the or howtheycanbe together. to thisposition to be before another, According otherthanto be nearer andnearer to thehighest intension ofa quality is nothing while ifthereis sucha degree, or to becomemoreand morequalified, degree, from thequality's is either to be lessandlessqualified or to be removed remission perfection.42
in thedeultima lectura havecalledthesecondseries oftheopening , morecow-arguments); in a moresystematic hints to Burley's is presented over,thediscussion way,withclearer as we haveseenabove. Tractatus, 41Thefourth in thefirst dedicated tocontrariety cursorily presented question opinion, in thelastofthisseries contrariandremission, is discussed andintension (V, 9: "utrum and nonremisso", ed.Kirschner 1997(op.cit., umintendatur altero above,n. 10),410-7), "In questione videndum est as representing thegenuine aristotelian solution: considered contraria suntsimul, esseAristotelis, secundum que videtur qualiter quartam opinionem, et secundo de quesito", 1997(op.cit.,above,n. 10), Oresme, V, 9, ed. Kirschner ÇKPhy., 411,35-6. 42Ed. Kirschner sciendum 1997(op.cit., "Secundo, above,n. 10),p. 414,157-62: quod necoportet facere difficultates unusgradus estrationabilior etfacilior quarta opinio qualiter autgeneratur aut qualiter suntsimul, sed iuxtaearnaliquidintendi priuscorrumpitur nonestnisiaccedere et approximari ad summum, si est secundum aliquamqualitatem estfieri minus taleetrecedere ab daresummum, velquodilludfiatmagistale,etremitti Ulamqualitatem". solution themeasure of esseperfecto secundum Oresme's concerning in Richard Liber calcuintension andremission is thefirst recorded Swineshead's position lationum ofSaxony's is thesecond, seeRichard Liber calculationum , , whileAlbert Swineshead, cuius1498,f.Ira:"Prima Girardengum positio ponitquodintensio Papié,perFranciscum illius etremislibetqualitatis attenditur summo latitudinis, penesappropinquationem gradui a gradusummo. Secundapositio habetattendi siopenesdistantiam ponitquodintensio In his a nongradu, etremissio a graduperfectissimo". penesdistantiam penesdistantiam mentions theGreat's intenWalter Albert Burley Physics commentary position concerning sionandremission, whenalteration is notbetween seeWalter contraries, Burley, Expositio inocto libros de Luere1501(unver. Hildesheim, Venetiis, Nachdr., Physicorum perSimonem NewYork1972),f. 159va:"Notandum secundum dominum hicquodnonfit Albertům
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fromOresme's,sincehe measuresintenAlbertof Saxony'ssolutiondiffers sion on the basis of a quality'sdistancefroma zero degree("penes recessum a non gradibusillarumformarum")and remissionon the basis of the distancefromthe highestdegree,while Oresme favorsa solutionconsideringonlythegreateror lesserdistancefromthe highestdegree.Oresme, however,as far as I know43is the firstParisian commentatorto give to Burley's Burley'ssolutionso relevantan importance.He presentsexplicitly on third as the contrariety: opinion position the nordoesonefollow aretheytogether neither to thethird position According instant. Thisis at every newform is a completely there alteration butduring other, Walter Burley's position.44 fromthe thirdone, as can be The fourthsolutionis not very different easily grasped fromthe final remarkin the general presentation,where thissolutionfromthe thirdone (that Oresme feelsobliged to distinguish is Burley's),layingstresson the different ontologicalconvictionsconcerning in accidents("et in quolibet instanti, quo est alterado, est novum accidens, sed non sicut imaginaturtertiaopinio"). The differencebetween Oresme and Burleyconcerningthe ontologicalstatusof accidentsrelies and innovative actuallyupon what can be consideredthe mostinteresting
a contrario. aut separationem contrarii et remissio intensio peradmixtionem semper ut de non habet intenditur illud enim bono, contrarium, quodnon patet quod Aliquando alicui.Et quando nonadmiscetur et privatio sedprivative habetcontrarium oppositum; Hoc ab optimo. et remissio ex recessu fitex accessuad optimum sicest,tuncintensio Albertus". 43Thisis true,ofcourse, on of Oresme's thepriority commentary Physics accepting ofSaxony's. Albert 44Oresme, 1997{op.cit ., above,n. 10),396,46-8:"Tertia V, 6, ed. Kirschner Q¿Phy., etposteaalia,seddumest suntsimulnecestunaperunumtempus estquodnumquam secundum estnovaforma in quolibet instanti alteratio sui,et illa estopinio quodlibet comcontraria mediainter inquestion is discussed Thissolution Gualterii". V, 8 ("utrum soluTheother 1997{op.cit., ed.Kirschner exextremis", above,n. 10),406-10). ponantur estquodtaiesforme 1997{op.cit.,above,n. 10),396,44-8:"Prima ed. Kirschner tions, suntsimul Secundaestquodnumquam et intenso. essesimulsubesseremisso videntur sunt unapostaliam. . . Quartaest,utcredo,quodnullomodocontraria nisisuccessive et in et deorsum, sicutintersursum nisisolumin respectu, necestibi medium simul, tertia sednonsicutimaginatur estnovum in quo estalteratio, accidens, instanti, quolibet in questions are discussed andthesecondsolutions The first V, 6 respectively opinio". 1997{op.cit.,above,n. 10),395-400) ed. Kirschner sintsimulin eodem", ("u.contraria ad partem", sivepartis ad gradům intendatur andV, 7 ("u.forma gradus peradditionem inhis is Ockham's 1997{op.cit.,above,n. 10),400-6).Thesecondsolution ed.Kirschner IV-VIII, ed. in libros de Ockham, Aristotelis, Physicorum , see Guillelmus Expositio Expositio St.Bonaventure, G. Etzkorn, G. Leibold, F. Kelley, G. Gài,J.Giermek, R. Wood,R. Green, N.Y. 1985(OPh,V), 500,36-37.
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by Oresme in his Physics philosophicalsolution adopted systematically modi rerum.AÒ Since Oresme' s the Physicscommentarywas commentary, , it is highlyprobprobablywrittenbeforeBuridan's one de ultimalectura able that Buridan'sdecisionto change the order of discussionas well as the way of introducinga series of argumentsthat is closer to Burley's textis a directconsequence of Oresme's sympathiestowardBurley. The order of discussionis not somethingof minorimportance.In the scheme of Buridan's de ultimalectura commentary,as well as in Oresme's and Albertof Saxony's,the solutionconcerningthe presenceof contrary qualities in a substance is considered a preliminarystep in discussing intensionand remission.In the scheme of Buridan's de tertialectura and in JohannesMarciliusof Inghen's commentary,the problemof continuity in the alterationhas priorityover that of the presence of contrary qualitiesin a substance. If the positiondefendedby Oresme is probablyat the originofJohn to the de ultimalectura Buridan's changes fromthe de tertialectura Physics is it Buridan's and not Oresme's model that imposes itself commentary, on theParisiancommentators likeAlbertof SaxonyandJohannesMarcilius of Inghen,46 who probablyalso knewthe textscomingfromOxfordwhere intensionand remissionplay a centralrole. ' 45S. Caroti, Laposition deNicole Oresme surla nature dumouvement (eQuestiones super Physicam etsémantiques d'Histoire Doctrinale III, 1-8):problèmes , in:Archives gnoséologiques, ontologiques etLittéraire du MoyenÂge,61 (1994),303-87, etE. Mazet,La J. Celeyrette esp.335-42; hiérarchie desdegrés d'être andPhilosophy, 8 (1998),45-65; chezOresme , in:ArabieSciences Kirschner 2000{op.cit.,n. 25),255-74. 46In question inintensione forme maneat cumparte III, 4 ("utrum parsprimo acquisita secundo ofInghen Marcilius introduces fourwaystosolvethisprobJohannes acquisita") Marcilius de Inghen, f.38va-b: "Notandum lem;seeJohannes QPhy., quodde istaquestionesuntquattuor vierespondendi. Primavia estquodintensio fitsolumper qualitatis a contrario. Verbigratia si ignisagatinaquamcaliditas inaquanonintendepurationem diturperadditionem caliditatis ad caliditatem, sedpercorruptionem frigiditatis apparet caliditas intensior ... Et sic dicentes est ponunt quodquilibet gradusalicuius qualitatis sedtarnen remissus mixtionem contrarii . . . Secunda viaestquod summus, apparet propter intensio in adventu fitpermaiorem additionem tarnen illiusmaioris qualitatis gradus, . . . Tertiaviaestquodintensio fitperadditionem gradus precedens corrumpitur qualitatis ad gradum simul . . . Quartavia,quenondiffert a precegradus utroque graduremanente dentinisimodoloquendi, intenditur necremittitur, sedsubiecponitquodnullaqualitas tumdicitur intendi et remitti secundum As forthepresence of contrary qualitatem". in a substance Marcilius records three Marcilius de solutions; Johannes qualities Johannes forme contrarie essesimul. Et de hocsunt Ill, 5, f.39va:"utrum Q.Pky., Inghen, possunt tresviedicendi. Primaestquodin alteratione de summo calidoad summum frigidum estaliquem uniusstarecumaliquogradualterius, in continue impossibile gradum ymmo alteratione estqualitas totaliter nova,itaquodnonestadditioalicuius gradusad alium de eademqualitate, nec etiamad suumcontrarium . . . Secundavia estquod gradum
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s de ultimalectura and Remission inJohnBuridan' 2. Contrariety , Intension PhysicsCommentary In orderto have more elementsfora deeper acquaintancewithBuridan's discussionon contrariety, intension,and remission,it is usefulto bear in mind the different positionsdiscussedin the ruedu Fouarrein the middle of the fourteenthcentury.We have already quoted Albert of Saxony's solutionsconcerningthe presenceof contraryqualrecordof two different in as ities a substance;47 forthe waysintentionand remissionoccur,Albert and the sucalso mentionstwo different solutions,the addition-theory Nicole Oresme, who defendsa succession-oftheories.48 cession-of-forms formstheory,is more generousand listsfoursolutions,withthreedifferent ones insidethe succession-of-forms theory(probablyincludingOckham's).49 JohannesMarciliusof Inghen,who sideswiththe additiontheory,ascribes the Thomisticpositionto the additiontheory.50 In John Buridan'sPhysics commentary(u.l.)we do not findsuch explicit hintsto consentto mentionof different solutions,but thereare sufficient intensionand remissionin the general put his discussionon contrariety, et in hoc poteststarecumaliquogradualterius, numquam gradusuniuscontrariorum de in modoponendi, Seddifferì convenit cumprecedenti. quiaponitquodin alteratione inducatur successive totafrigiditas ad calidum aliquis priusquam primoexpellitur frigido ad calidcontinue habilitatur subiectum itaquodremovendo caliditatis, frigiditatem gradus . . . Tertiaviaestquodaliqui caliditas introducitur et tuncexpulsa totafrigiditate itatem, caliditas nunsedsumma starecumaliquibus caliditatis, gradibus frigiditatis possunt gradus caliditatis citrasummum tamen starecumsumma gradus frigiditate. Quilibet quampotest de summo ete converso. Et ideoin alteratione starecumaliquofrigiditatis frigido potest alius inducitur unusgradus calidum ad summum statím, frigiditatis quandocorrumpitur caliditatis". 47See p. 68. 48Albert ofSaxony, V, 10,ed. Patar1999(op.cit.,above,n. 23),844,56-66: Q¿Phy., velsecundum totasimul in intensione "utrum partem acquiratur quaeacquiritur, qualitas afterthedistinction thetwosolutions Albert introduces in thisquestion postpartem"; thelatandqualitative ofthequantitative thedivisibility between partsofthesubstance, admitcommuniter omnes "Primam divisionem terbeingdenied theory: bythesuccession intensibilem unaponitqualitatem suntopiniones, divisione sedde secunda tunt, quarum etipsaesseintensiorem habere etremissibilem graduum plurium peraccumulationem gradus Aliaautemopinioponithuiusaccumulationem et remissiorem graduum. pauciorum per subiecti. divisionem nisisolumsecundum nonessedivisibiles modiformas quantitativam et indicontinue estaliaet aliaqualitas Et istaopinioponitquodin intensione simplex In thefollowsubiecti". divisione visibilis quantitativas partes quaeestsecundum excepta maneatcum in intensione alicuius quae primoacquiritur qualitas ("utrum ingquestion see Patar1999 is introduced, thesamedistinction acquiritur") qualitate quae posterius (op.cit.,above,n. 23),849,18-25;855,67-71. 49It is thesecondsolution, seen. 44. 50See note46,thefourth via.
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contextof university debates. We have already seen that the changes in the discussing problemof the presence of contraryqualitiesfromthe de tertialectura to the de ultimalectura commentarycould suggesta growing intereston this topic. In questionIII, 5 of Buridan's de ultimalectura in Physicscommentary, a replyto an argumentagainst the addition theory,we find the same attitudewe have alreadyseen inJohannesMarciliusof Inghen(who probably depends on Buridan)to prove that the positionaccordingto which it is the subjectto be changedin intensionand remission(a positionheld can't be used against by the 'thomistic'party,to use a genericdefinition) the additiontheory:51 I reply, totheother, andsaythatproperly noquality isincreased probability, speaking normademoreintense; it is rather thesubstance thatis mademoreintense. We thatquality is intensified grant onlyin thisprecise way.52
51Thefourth if.45vb-46ra: JohnBuridan, cow-argument, Q¿Phy., "Quarto, arguitur quod modum nonpossitfieri caliditas intensior perpredictum quamante,quiavelpriorpars essetintensior veltotum ex eisaggregatum. Sed quodlibet ilioquamantevelposterior rumestimpossibile. Probatio: nonpotest diciquodparspriorsitintensior primo, quam sicutde magnitudine; modosi lineepedalialialineapedālis ante,quiaoportet imaginari addatur nonpropter hocillaprimalineapedāliseritmaiorquamante,immosolumesset licetcongregatum essetbipedale. Itaergoprima additionem pedālis, parscaliditatis propter secunde nonessetintensior essetintensius. Etiamnonpotest quamante,licetcongregatum dicide hoccongregato, cumfitintensius quiaquodintenditur, quamessetante,necesse estquodpriussitminus intensum etposterius sedcongregatum nonerat magisintensum; et pariratione necparsposterior intensum, intenditur, priusminus quianoneratprius, I amverygrateful forme". toJeanCeleyrette quianoneratante,ergosicnonfitintensio forhaving thissolution; on thistopicseeJ. Celeyrette, suggested J.-L.Solére,Godefioid deFontaines etla théorie dela succession dansl'intensification desformes E. Faye, , in:P. Bakker, C. Grellard delapensée médiévale. Etudes à J^énon Kaluza , Turnhout 2002, (eds),Chemins offertes ofInghen seen. 46. 79-112.ForMarsilius 52JohnBuridan, ., f. 48rb:"Ad aliamrespondetur Q.Phy probabiliter quodloquendo nonintenditur necfitintensior, sedsubiectum id estfitintenintenditur, proprie qualitas siustale.Et ad talemsensum et nonad aliumconceditur intenditur". The quodqualitas Thomistic solution is regarded as compatible withtheaddition theevidently byBuridan thatexplains intension offorms oryandalsowitha formofthesametheory through addition is thelatinwordfortheresult oftheformer andlatter ("congregatum" quality an intensification), diciquodquali., f.48rb:"Velpotest undergoing JohnBuridan, Q.Phy eademessetpriusminus tasnonsicintenditur, intensa etpostmagis intensa; quiatotaliter sedad istum sensum dicitur estintensior intendi, quiacontinue qualitas que estposterius et plurium tantorum graduum quamessetqualitas que essetprius.Et aliietiamdicunt necparsposterior sedcongregatum; ad istum intenditur, sensum, quodnecparsprior quia esseintensior, nonquodipsaeratante,sed intensior qualitascongregata incipit quam estquodhecsolutio et precedens revertuntur in qualitas que eratante.Et manifestum estex parterei,et suntvere". idem,quantum
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In this part of the fifthquestion of the thirdbook we can find some tracesof othersolutions.I shall returnto thisquestionlater.I shouldlike beforehandto point out the presencein questionV, 3 of an explicitreference to an adversarius , whose solutionis obviouslyagainstthe presence of contraryqualitiesin a substance(the thirdquestionof the thirdbook deals with this topic, as already mentioned): of the de ultimalectura to thecoldis changing from thehottest thatifsomething degree Again:I assume butcontinuously, hotness cannot est,themostintense part passawayinstantaneously, couldsay,therefore, later.The opponent after part;andthiswillbe demonstrated until hotness is totally comestobe inthatsubstance thatnocoldness passedaway.53 withWilliamOckham,whose could be identified Here Buridan'sadversarius convictionsabout intensionand remissionare echoed in this passage. Some indirectsuggestionsto an alternativesolution,however,can be detectedin the second questionon the thirdbook, where the natureof alterationis the topic at stake (III, 4). Before analysingthis passage it should be noted that Buridan'spositionabout alterationis ratheranomalous if compared with his position concerningthe nature of motion, motions.54 anothertypeof the threeAristotelian Actuallyas foralteration Buridan is convincedthat thereis no need to explain such a qualitative fromthe changingqualityitself,while change throughsomethingdifferent for the local motion he admittedexplicitlya special qualityin addition 53JohnBuridan, ad frigidissimum, de calidissimo si fiatmotus ., f.48vb:"Iterum, ÇKPhy intensissima totacaliditas et probabitur post,quodnonsimulcorrumpitur egosuppono, Diceret sedcorrumpitur motus, ergoadversarius parspostpartem. que eratanteinitium estcorrupta". It in subiecto de frigiditate ilio,doneetotacaliditas quodnichilgeneratur intoaccount thatBuridan, in replying oftheadversarius to thisposition is precisely taking arecorrectly on whatcontrary hisposition considered, lukewarm, John qualities develops scilicet f.49ra:"tuncergoponoquartam conclusionem, Buridan, quodimpossibile ÇKPhy., essesimulin eodemsubiecto, contrariarum formarum estaliquosgradus quia,quamvis tamennullasunt caliditatis et aliquigradus sintsimulin tepidoaliquigradus frigiditatis, simul velpartes, immohecestimpossibilis: illigradus sintgradus contraria gradus quorum nonsuntgradus velpartes Dlienimgradus velpartes contrariorum. suntgradus existentes velintensissime intensissime caliditatis quiaillenonsunt,et eiusquodnichil frigiditatis, scilicet sextaconclusio, ... Ex dictis estparsvelgradus estnichil quodcontrarisequitur sed ex quantitate rationibus ex simplicibus nonattenditur etasformarum formarum, sed earumincompossibilitas, sicutapparet attendi contrarietas Sic enimdeberet graduum. Sedfrigiditatis cumpossint essesimul. nonestincompossibilitas, ad caliditatem frigiditatis ad intenutintensissime estincompossibilitas, ad caliditatem tantorum tantorum graduum velmedio Sed intense ad remissam intensam. ad multum intense velmultum sissimam, ofintensity Thehighest nullaestincompossibilitas". ad invicem modoremissarum degree are both10 degrees andtherefore twocontrary is fixedto 10 degrees, having qualities See Biard2002(op.cit ., above,n. 1),430-1. incompatible. 54Biard2002(op.cit.,above,n. 1),416.
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to the mobile.55The same economyprincipleis followedby Buridan in identifying qualityand its degrees. solutionsof the problemdiscussedin questionIII, The two conflicting 4 are the "tota simul" vs. the "gradualis" acquisitionof the quality in Buridan agrees with the firstsolutionas far as the essential alteration.56 of stability form,and reliesupon a linguisticanalysisin order to explain the intensionof qualitiesthroughdifferent degrees: isintensified, thatform. Whenhotness Theform is thesame,likethenamesignifying aresignified as whensomething whichgradual thenamesthrough changes change, as suchdo notchange: hotness Namessignifying theessence is hotter andhotter. motion canbe continuthesame. . . Duringtheheating is always process actually whenhot hotter andhotter, andthisoccurs becomes ousonlyifthesamesubstance in the essential or through either is acquired changes successively through changes therefore thatessence cannotchange, Butit hasbeenalready established degrees. as folofhotness. Thisconclusion canbe confirmed thischangeconcerns degrees in thesamewayin lows:it mustbe granted thatsomechangeoccursin theform namessignifying forms as suchcanwhichnamessignifying forms actually change; in theform like canchange, likehotness, butnamessignifying notchange, degrees hotter andlesshot.57 between This solutionis acceptedby Buridanas valid onlyifno distinction main and is introduced.58 Buridan's preoccupationin dealgradus qualitas ing with alterationis to grant continuitywithoutintroducinga change between intothe qualitativeform'sessence,as well to refuseany distinction
55J. Biard,Le statut dumouvement dansla philosophie naturelle buridanienne , in: Carotiet Souffrin (eds)1997(op.cit.,above,n. 26),141-59. 56JohnBuridan, utrum estsicdivisif.45ra:"Multiergodubitaverunt Q.Phy., qualitas duasconbilisetutrum sicparseiuspostpartem Et quidamde hocposuerunt acquiritur. totasimulessentialiter; secundafuitquod clusiones: primafuitquodqualitas acquiritur nonacquiritur totasimul, gradualiter". qualitas 57JohnBuridan, f. 45ra-b:"Sicutmanetidemnomensignificans sic formam, QPhy., manet forma eadem.Sed,cumcaliditas continue nomen intendatur, significans gradualiter Sednomen benemutatur, utquodpriusestminus calidum, signifiposteamagiscalidum. canssimpliciter essentiam nonmutatur: estenim anteetpost. . . (ed.calidum) Sedin calefactione nullaessettalissuccessio fit quandoidemsubiectum quodfitcalidum nisiacquireretur caliditas velsecundum distinctionem essentialem calidius, parspostpartem velsecundum Seddictum estquodnonsecundum essentialem, gradualem. ergodicendum nomen estquodsecundum Et confirmatur istaconclusio: sicutenimmutatur gradualem. ita proportionabiliter debetconcediquodmutetur licetnon formam, forma, significans mutetur nomen formam secundum essentiam ut. . . caliditas, forme, significans simpliciter tamen mutatur nomen formam utminus calidum etmagis calidum". significans gradualiter 58JohnBuridan, f. 45rb:"Istaopiniononapparet michivera (ed.nisi) QPhy., ad sensum videtur enimymaginari distincti ab exponatur improprium; quodsintgradus essentia caliditatis et quodcontinue sitaliuset aliusgradus et nonsitalia et alia essentia.Et hocnoncredoesseverum".
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degreesand qualities.His convictionsabout the natureof motionas somethingintrinsicto the mobile are anticipatedhere, and theywill be more deeply discussed in the questions devoted to local motion. Buridan is in order to grantto alterationthe forcedto have recourseto a dispostilo essentialpropertyof motion: Thefirst conclusion is thatduring theheating somehotness is acquired sucprocess in thesamesubstance andin thesamepartofthesubstance, becauseif cessively thisprocess is continuous, thesubstance mustbe successively hotter and necessarily hotter. Thischangein thedegreeofhotness canbe explained onlybyintroducing a newdisposition, which in thesubstance; in fact,be wasnotpreviously itcannot, therelationship between thatsubstance andsomething other outexplained through sidesubstance, becauseifeverything is excluded thesubstance which is hotexcept terand hotter, thischangestillexists. It cannotbe explained, moreover, through either different connections or different localdispositions between thepartsofthe substance.59 In alterationthisdispositio is not somethingdifferent fromthe qualityitself, to what for local motion. Buridan's solutionconcerncontrarily happens in because he introduces alteration is therefore some ing way anomalous, two different of ways conceivingmotion. EvidentlyBuridan is here confrontedwith a solutionthat maintains the distinctionbetweengradusand qualitas , a solutionhe findsso untenable as to run the risk of abandoning the commonlyadmittedunitary view of the different Aristoteliantypesof motion (namelylocal motion 59JohnBuridan, estquodcontinue in calefactione ., f. 45rb:"Primaconclusio Q.Phy caliditatis ineodemsubiecto caliditatis etaliquid aliquid acquiritur prius acquiritur posterius et secundum eandem estquodsi a calefit eius,quianecesse continue, partem quodcontinuesitminus calidum etmagiscalidum. Sedipsam(seil,caliditatem) sicaliter se habere nonposset salvalinisiperaliquam existentem, posterius dispositionem quenoneratprius vele converso, cumnonpossitsalvari ipsiusad aliquemextrinsecum, perhabitudinem retento solumquodcontinue calefiat, circumscripta, quiaomniextrínseco perintellectum adhucsicaliter etaliter se haberet etcumhocetiamsalvari nonpossit habiperdiversam velsitum The reference is notto thediscussion on tudinem partium ipsiusad invicem". ofthesecond Buridan aboutartificial localmotion, buttothequestions book,where speaks a figurato f.45ra:"Naminquestione de distinctione seeJohnBuridan, Q^Phy^ figure things, visum fuitquodnonpotest nisialtero modorum salvari priusdictorum quodaliquisaliter etaliter Sedconcesso se habeatad posterius. est,si a sitcalidius quodnecesse quamante, nonsolum sedinipsoa, omnes extrinsece, aliquidessequodantenoneratvele converso, velaliquidcaliditatis, scilicet aut concederent parsautgradus quodilludaliudsitcaliditas "utrum estresdistineta huiusmodi". SeeJohnBuridan, ff.30va-31rb: II, 3, QPky., figura 3e 'res 3inalcuni a figurato"; commenti alla'Physica3 seeS. Caroti,'Modirerum artificiales parigini Studi inmemodelsecolo XIV, in:S. Carotie R. Pinzani meorum sociorum3. (eds),e0brogatum ña diLorenzo Pozzi , Milano2000,189-213; J. Celeyrette, 'Figura/ figuratum3 parJeanBuridan etNicole doctores estmagna dissensio33. Oresme , in:S. CarotiandJ. Celeyrette (eds),"Quiinter Lesdébats dephilosophie naturelle à ParisauXIVesiècle , Firenze 2004,97-118.
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between and alteration).Accordingto Buridan,arguingforthe distinction to a and is tantamount alteration fluxusadded considering degrees qualities to the quality,a solutionrejectedby him, at least as far as alterationis considered.60 to identify Buridan'stargethere. As alreadyremarked,it It is difficult is unlikelythat he is refuting Burley,as is the case in the previousquestion concerningthe presenceof contraryqualitiesin the same substance. The positionwhich forBuridan is the worstone, so much so that he is solutionsconcerninglocal motion and ready to propose two different - the distinction alteration betweendegreesand qualities- is not Burley's. Even if one doesn't take into account Buridan's strangedecision of adoptinga twofoldview of motion,his solutionof grantingthe intension of a qualitythroughthe acquisitionpart by part of such a quality,and at the same timeof excludingdegreeswhen consideredsomethingdifferent fromquality,is ratherastonishing.Actuallythe same objectionthatcould be directedagainst the additiontheorythroughthe addition of degrees is valid for the part by part additionas well. One could venturea hypothesis:in his Tractatus primusWalter Burley .61In the middle of the uses the term 'modus'as synonymouswithgradus in fourteenth Nicole Oresme his was sponsoring, century Physics commentary
60JohnBuridan, f.45rb-va: "Secunda conclusio estquodgradus caliditatis non QŤhy., scilicet si ponamus illudquodpriusacquiriestaliaresa caliditate, quodin calefactione Tuncergoconclusio turetquodposterius vocentur caliditatis. acquiritur gradus probatur, et quodcontinue quiaponamus quoda sitcalidum perunamtotamdiemfiatcalidius. Tuncergocontinue caliditas acquiritur gradusaliuspostalium,sednonacquiritur que iamerat;ergo,cumomnisillaalteratio sitcalefactio, nonest sequitur quodcalefactio motusad caliditatem ad terminům ad quem,quodestinconveniens . . . Item tamquam illigradusadditiponerentur omnino frustra, illos,salquia quicquidsalvatur ponendo varetur sineillis,scilicet ut aliasdicebatur, et continuitas, successio, quia ita possumus dicerequodcontinue sicutgradus ... acquiritur parscaliditatis postpartem, postgradum Iterum rationes alicuius videntur sitpartibilis quecumque apparentis arguere quodqualitas inpartes unapriusetaliaposterius ineodemsubiecto, illesimiliter queacquiruntur arguèrentde illisgradibus, illeessetuna forma acciquoniam quicumque gradussignaretur, in parteque priusacquiritur dental sicutcaliditas et essetdivisibilis et in partem que Ettuncquereretur utrum illepartes essent eiusdem rationis ad invicem posterius acquiritur. veldiversarum, sicutquerebatur de caliditate, et sic nichilprodest poneretalesgradus additos. Et iterum hoc essetponerein alteratione fluxum additum secundum qualitati quamestalteratio, quodpriusfuitimprobatum". 61Vat.lat.817,f.215vb:"Dicoquodcontraria distant formaliter ratione seu graduum in eis";on theidentification modorum andmodus between seeJ.L.Solére,Plusou gradus moins: levocabulaire dela latitude desformes, in:J. Hamesseet C. Steel,L'élaboration duvocabulaire auMoyen Actes duColloque International deLouvainetLeuven, 12la-Neuve philosophique Age. 14 septembre ThomasofSutton. 1998,Turnhout 2000,437-88,esp.477 concerning
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as a very effectivetheoryfor in a very systematicway, the modirerum in natural philosophy.It is possiblethatBuridan's solvingmanyproblems as somethingdifferent fromquality viewed steadyrefusalof the degrees fromthe are different is directedto Oresme's convictionthat modirerum is not like two res. reswhose modithey are, even thoughthis difference Oresme explicitlyremarksthatthisparticularontologyis more efficacious than Burley's,not only in introducingthe fourthsolution,but also in questionI, 6, always dealing with intensionand remission.62 This problemdeservesmore research.Here I limitmyselfin noticing thatwe can findin Buridan'sdiscussionconcerningintensionand remission an implicitreferenceto Oresme's positionin the thirdand last questo theopening^-arguments, tiondedicatedto thistopic(III, 5). In replying solutions: and preciselyto the last one,63Buridan presentstwo different andwill.Godcooperates Somesaythatthisorderis produced byGod'sknowledge He is theprincipal or better, thathappens, witheverything agent.Andthereand will. to God'swisdom others foresomedegrees according passawaybefore to be and to coming Otherssaythatthereis an inverse according arrangement arethefirst to laterthanothers whicharegenerated away:thatis degrees passing passaway.64 The second solutionis probably Oresme's, who in his Physicscommentary argues for such a solutionin replyingto an objection in which a recurs:65 secundus passage fromBurley'sTractatus 62Oresme, "Tertia f.4ra-rb: Biblioteca 7-7-30, Sevilla, Capitular y Colombina, QPhy., de albedine sicutymaginatur sitdivisibile si aliquodaccidens difficultas: intensa, intensive, Ad quoddicobreviter ex gradibus. quodnon;ymoalbedoestforma quodsitcomposita ideoquando vel'essealbum'simpliciter intensive> aliudest'essealbumremisse', estaliud'essealbumintense' Undetotaliter solvit essent contra ex alio.Modomulterationes eas,et hoc,sedGualterus componitur dicoquodtaliscompositio istamviam.Secundo, facilius secundum adhucsolverei graduin disputatione. Et possunt etgratia admicti alispotest assigexempli perymaginationem nonquoditasitin re,sedpropter naritalesgradus proportiones quasdam pernuméros, de talibus". velconsequentia mathematicas que habentur 63JohnBuridan, calif. 46ra:"Deindeetiamarguitur quodnonestpossibile QPky., aliisremanentibus, ditatem sicremitti quiaomnes graduum aliquorum percorruptionem coretiamsuntuniformiter etomnes ad invicem, rationis sunteiusdem approximati gradus invicem. Ideonullaessetratioquarealiqui. . . prius extra cumnonsintsitualiter rumpenti, velomnes". simulcorrumperentur quamalii,et ideomulti corrumperentur 64JohnBuridan, ex Dei f.48rb:"Adaliamdicunt aliquiquodordoprovenit QPhy., Illi immo fit ad omne scientia etvolúntate, ergo gradus agit principaliter. quod coagit, qui Aliidicunt quodilligradus quosDeusseitetvultpriusesseauferendos. priusauferuntur illipriuscorrumpuntur". et quiposterius generantur, generantur, postetposterius 65Ed. Kirschner 1997(op. cit.,above,n. 10),405,175-ö0:JNono, sequitur quodtota
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andremission of as follows: thereis a simile between theintension One canreply remisanddownward: intension islikemotion whiteness andmotion upward, upward Alltwo-foot areas suchidentical, buttheyare downward. sionlikemotion segments becauseoneis naturally aboveanother different as faras their is concerned, position itis at another whenitmoves anda moving is at oneofthembefore upward, thing in thiskindofmotion is thefirst to be leftwhenthe andthelastto be reached movesdownward. thing thissegment, which doesn't refer toplace Wemustconceive thesameconcerning I mean:these aresonaturally areequivalent, butthey buttoessence; degrees arranged a difference: is thefirst to be lost.Thereis,however, thatthelastto be obtained intension andnotthrough localmotion. We can reply forms cometo be through areequally on thefactthatdegrees on thisbasisto theargument, distant; relying butnotaccording their formal thisis trueaccording tolocaldistance, arrangement. On thecontrary, thedegree whichfirst comesto be is notyetnearto theagent, havebeencorrupted, likea thing which canactuponitonlyafter thoseinbetween thelowerpartsbefore theupperones.66 downward cannot moving passthrough One could wonder if Buridan's actual targetwas Nicole Oresme, since the solutionhe explicitlyregardsas the best is the succession-of-forms as modirerum .67Oresme'sdiscussionof intentheory,withformsinterpreted sion and remissionin his Physicscommentaryis, however,rathercomplex, because even if he does not conceal his sympathyfor the fourth solution,he also presentssome argumentsforthe additiontheoryin questionV, 7. ProbablyAnnelieseMaier had in her mind thisquestionwhen she placed him among the advocates of the additiontheory.68 caliditas simul etsubito Patetconsequentia, sinteiuscorrumperetur. quia,cumistigradus demrationis et equaleset equaliter aproximad pari aliumetequecito,etitaarguitur de partiratione eademratione unum, qua corrumperet buseorum, et videtur citiusdebeatcorrumpi, resistit et etiam quiaminus quodremissus Et si estibiordo,et quiaillequiintroducebatur primo, corrumpatur. onein Burley's De intensione etremissione echoesthethird (ed. 1496, quare";theargument ff.2vb-3rb), 1997{op.cit.,above,n. 10). quotedbyKirschner 66Ed. Kirschner 1997{op.cit.,above,n. 10),405,181-95"Respondetur quodymaginandum estsicutde albedine et motusursum et deorsum: intensio estsimilimotui suntequales sursum etremissio motui distantie deorsum; modo,sicutomnes partes pedālis et eiusdem unaestsupra speciei quoadhoc,tamenquoadhocdifferunt quodnaturaliter mobile essesubunadeindesubalia,quandoadscenaliam,etprimo oportet perordinem turquandodescendit. Itaquodammodo dit, iliaqueultimo acquiritur, primo deperdi estin proposito de istadistantia nonlocalisedformali, ymaginandum quodistigradus, licetsintequales, tamen suntsicordinati etideoquiultimo naturaliter, acquiritur, primo tur.In hoctamen estdissimille: talisforma etnon deperdi quodperintensionem acquiritur localem. Tuncad probationem, cumdicitur permotum quodsuntequaliter aproximad; verum estproximitate eorumformalem; ordinem locali,sed nonsecundum ymoprimo introductus nonestaproximatus doneccorrumpet sicquodagenspossit agereinilium, aliossuperiores, sicutetiammobile nonpotest inferiorem nisi deorsum transiré distantiam pertransiret superiorem". 67Kirschner 2000(op.cit.,above,n. 25),265-74. 68Maier1968(op.cit.,above,n. 2), 358-9.
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That the actual target of Buridan's criticismwas probably Nicole Oresme69is suggestedalso by the persuasio followingthe argumentfor a the same quality,whereBuridan different of order degrees among precise revivesa topic on which he was completelyat variance with Oresme, viz. the relationshipbetweenmatterand privation: wantsforms thatit at present has is presented: matter Forthisa certain argument The morematter bookofthePhysics. as Aristotle saysin thefirst onlypotentially, informs andtherefore thisquality matter themoreitwants, lackshotness, strongly. andtherefore the moreat thebeginning oftheheating lackshotness Matter process, inform itmorestrongly.70 ofhotness degrees and appetitus materie In discussingprivatio John Buridanis resolutein rejecting any distinctionbetweeneitherof them and matter: as privated is thesamething It seemsthatthisquestion (I, 23 "Whether privation ofthese thatwhatlackssomeforms, canbe easily setded privation matter") bysaying this arethesame. . . Andmoreover whichhasthempotentially andmatter forms andthesentence 'matter thatthename'privation' couldbe solvedsaying problem Andin is abletohave'havethesamedenotation. which itnaturally lackstheform in the thissameform, ofa form is thesameas matter thiscaseprivation lacking man.Andifwe consent is therunning samewayin which'thata manis running' 'thatthisform can as thesentence hasthesamemeaning thatthename'privation' in thiscaseprivation wouldbe that is notthere', be in thatmatter, butit actually in matter . . .71 form which is potentially
69We don'tfindin Oresme's in recorded someoftheelements Physics commentary on whichmorewillbe saidbelow, likethepersuasio thissolution, Buridan's concerning to it,seeJohnBuridan, andtheobjection ., f.48rb:"Sedaliquiobiciunt ponendo Q.Phy etultrapermitcalididatem intensam faciat simulinstanter casumquodDeusin subiecto illigradus a frigido tunccorrumperentur modonaturali. tatprocedere naturam Quomodo velaliquipriusetaliiposterius. utrum simul omneš Respondetur quod,licet superveniente, ad forineisponere ordinem tamen omneš Deusgeneraret simul, quantum posset gradus etiterum essent ac sisuccessive etmodonaturali illisubiecto, tiorem adherentiam generati, et conservare etiamtaliter corrumperentur". quodnumquam posseteosgenerare 70JohnBuridan, videlicet ., f.48rb:"Etad hocponitur quod quedampersuasio, Q¿Phy utapparet ratione futuras sivegenerandas formas materia huius, privationis, primo appétit caliditantomagisappétit id estratione qua careteis.Quantoergomagiscaretcaliditate, careat sibi.Ergo,cummagis caliditas sibiadveniens ideoetiamtanto tatem, magisadheret adherent". fortius in principio caliditate calefactionis, priusadvenientes gradus 71JohnBuridan, "Videtur ., ff.26vb-27ra: (I, 23: "utrum priquodistaquestio Q.Phy etprivafaciliter vatioestmateria quodidemestprivatum possetsolvidicendo privata") dicendo modopossetsolviistaquestio . . . Adhuctertio tioetmateria quodidem privata carere 'materiam et perhancorationem intelligere perhoc nomen'privatio' possumus 'hominem sicut carens ista Et sic est materia est habere'. innata forma, forma, privatio quam idemquod vellemus Etsiperhocnomen currere' esthomoquicurrit. intelligere 'privatio' et nonessetalemin ea', tunc 'talemformam posseessein materia perhancorationem in potentia". essetforma privatio
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is notsomething is thatthematter's desiretoward theform Thesixth conclusion different from matter.72 if only Oresme, on the contrary,is a firmchampion of theirdistinction, In that between res and modus rei. a weak like distinction, questhrough tion I, 15 of his PhysicscommentaryOresme presentsthree different solutionsconcerningprivatio , of which the firstis identical with Buridan's.73This solutionis the firstto be criticisedonce the thirdsolution is introduced: andwith withAristotle, withexperience Thethird is themostconsonant way,which anditis thefirst conclusion oftheoldphilosophers, is thefollowing, theconvictions is notmatter, butrather substance. Thisis theproof: thefirst way.Privation against ifmatter werethesame,'thatwhich lackssomething' and'privation', andprivation wouldbe synonymous. 'blind'and'blindness' it,buttheconsequent Theyconcede as whoin Categories is against Aristotle, saysthatif'blind'had thesamemeaning ofthesamesubstance; but'blind'canbe said 'blindness', theycouldbe predicated manis notblindofa man,whileblindness cannot be saidofa man.Andtherefore In a secondway:ifmatter andprivation were is notprivation. ness, justas matter the wouldbe no difference between Aristotle andPlatoconcerning thesame,there ofnatural . . . Thethird is according toAverroes: basicnotions argument philosophy arenotthesame. . . andmatter matter doesn't privation passaway,andtherefore alltypes ofprivation, suchas ugliness, mala general argument concerning Fourthly, hasthesamemeaning as 'a man etc.;andI assumethat'blindness' ice,blindness is thefollowing: whoisblind'and'malice' as "a manwhois bad". . . Theargument
72JohnBuridan, f.28ra:"Sextaconclusio estquodappetitus appétit QPhy., quomateria formam nonestresdistincta a materia". 73Oresme, f.lira:"Primus msSevilla, Biblioteca 7-7-30, QPhy., Capitular y Colombina, estaliquid,quia estmateria ita quodhecnomina modusest privatio privata, et'privatio' sedtarnen 'subiectum' 'materia', supponunt proeodem, 'privatio' scilicet carere forma subiectum, que nataestessein .Et ideouniversaliter aliquid, sinonima et 'privatio', 'cecum'et 'cecitas', et sicde aliis. istanomina 'privatum' velfuit, itaetiamprivatio Et sicutresprivata erit,que noneritprivata erit,que nonerit velfuit.Istapotest intentio Aristotelis, privatio probari, quiahecvidetur quiadicitquod suntunumin numero, et differunt ratione. Et exponitur: id estdiffimateria et privatio idemsignificent, tamen nonunum nitione quia,licethecnomina exprimente quidnominis, connotant. frustra fitmultitudo ubisufficit etperhocprobatur Secundo, paucitas; primo nonsuntpluratribus, Modoomniapossunt salvari huius quodprincipia quia sufficiunt. tantum duoprincipia, sicutpatetex solutione ponendo argumentorum, queomniasolvunnominum". The secondsolution is thatbased turpertalesexpositiones et connotationes a position Oresmeattributes thatin othercontexts analysis, exclusively upona linguistic toOckham, seeOresme, f.lira: "Secundus modus estquodprivatio nonestmateQ.Pky., hocestprotantoquod nonestprivatio, esseprincipium, ria,ymoproprie sed,si dicatur hocnomine esseveram; etestista: intelligitur quedam propositio copulativa, quamoportet 'subiectum estetquedamforma nonestinsubiecto esthabere'. Etideonon quamnatum estaliuddicereprivationem esseprincipium, nisiquodad transmutationem naturalem sitvera,ac si hocnomencausabrevitatis loco requiritur quodheccopulativa poneretur istarum propositionum".
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The same criticismagainsta reductionistattitudecan be foundin quesnature : tion I, 20 concerningthe appetitus 74Oresme, f. lira: "Tertius Biblioteca 7-7-30, Sevilla, QPhy., Capitular y Colombina, concordat dictis Aristotelis etetiam sensui naturali etetiam dictis modus, antiquoquimagis contra modum. Et estista:quodmateria non rum,estiste:etsitprimaconclusio primum Probosic,quiasequeretur estprivatio, sedsubiectum. quodistaessent synonima: 'privaestcontra 'cecitas'. sedconsequens 'cecum', tum','privatio', Consequentiam ipsiprobant, in Postpredicamentis, ubidicitquod,si cecucecitas de Aristotelem utrumque verohomonullo tuncverominime; sedcecusdicitur eodempredicaretur, homo,cecitas itanecmateria est.Secundo, mododicitur. Et ideosicuthomononestcecitas, privatio etpositionem inter Aristotelis sic:siitaesset, positionem sequitur quodnonessetdifferentia ratione de principiis rerum naturalium . . . Tertio, Piatonis Commentatoris, arguitur quia nonestmateria . . . Quarto, materia manet etnoncorrumpitur; arguogeneergoprivatio de quacumque sicutde turpitudine, de malitia, cecitate raliter etc.,et supono privatione, essececum';aut'malitia' nonestalliudquam'hominem quam'hominem quod'cecitas' et re Tuncarguitur sic:illadistinguntur essemalum', nisiin casuubiestunushabitus. et dilectum, et aliudper unumestbonum, nonsuntidem,quorum antiquum, cognitum Modosicestquodnatura hominis oditum. estmalum etnovum, ignotum oppositum et tamenhomicidium velessehomicidam homicide et dilecta, estbona,antiqua, cognita esseetdebetesse, etmalum, velcecumvelaliquidtaleincasupotest ignotum sic:Sor taliposset fieri unussillogismus ettalia.Etideode quolibet expositorius arguendo Sortem essehomicidam esta diligendus, patrismeivelSor esse quiaproximus; Conclusio estfalsa, etc.esta me. cecumestSor;ergoSoressehomicidam usuloquendi, estfalsa. sitfalsapatetexcommuni etmaior vera,ergominor Quodconclusio Wefindin 'Sortem essemiserum' etc.esta me". diceretur quianumquam inordertojusdivisions inside schematic thisquestio I, 15oneofthenumerous ontology rerum f. 1Iva: "Proistoestunadistinctio modi , see Oresme, Q.Phy., quodensdicitur tify et ideoimpossibile estinvestigare veriet equivoce, sicutpatetprimohuius, multipliciter essedivisio talis:quod 'ens'diciunomodo.Ad propositum tatem potest quiymaginatur et individuum 'ens'proalicoperse existente, unomodoaccipitur demonstratum, estens,sicutSor;ethocquiahabetoperationem sictotumde genere substantie proprie. vel Secundomodo,accipitur 'ens','esse'proessentia aliqua,sicutpropartesubstantie < accidentali; manusetalbedo forma etsicdicuntur essemateria, forma , subdividi. secundum communem viam.Etistemodus Tertio, prosignificabili posset capitur currere'. sicutest'Sortem sicutin conditione affirmativa, Quarto, procondicomplexe, > affirmative < significabili verbigrada'Sorpossemoveri etnegative; tionequasiypotetica sub continetur estquedamconditio et nonmoveri' 'quies';et omnisprivatio que dicitur < sicut'Sor> ad condi tionem merenegativam extendi istomodo.Ulterius possetlargius non"' noncurrere' vel'intelligentiam
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itmustbe notedthatsucha natural desire is nothing different from either Secondly, an inclination or an appetite or a natural motion. ForthisreasonAverroes saysin comment 81 thatmatter's desireis itsinclination in thesameway to be informed, inwhich wesaythatwhena stick is bentitwillbendbacktotheopposite side.For thisreasonit couldbe defined a natural ofthethird potency typein thecategory in orderto distinguish ofquality, itcarefully a specialname;thatis to say through thata termbelonging to thiscategory denotes a natural itsdesire thing, connoting fora form ithasonlypotentially.75 In both cases, namelyprivatio and appetitus nature , Oresme has a position from Buridan's, who probably is the implicittargetof quite different Oresme's criticisms. Dealing withintensionand remissionBuridandoesn't raise the problemofprivatio and appetitus nature , butjust mentionsit while discussinga solutionthat can also be found in Oresme's Physicscommentary.I wonderif Buridan'sreferenceto thesequestionsfromthe first book rightat thisplace, that is when a solutionidenticalwith Oresme's is introduced,can be regardedas casual or ratheras deliberate.I leave open the question,providingonlythe textsreferredto by Buridanas well as those fromOresme's Physics commentary. 3. Conclusions I thinkthatJohn Buridan's discussionon intensionand remissionin his Physics is veryimportantfora numberof commentaryde ultimalectura different reasons. Firstand foremost,it is importantbecause we findin it some precious hintsof the growinginteresttoward a topic which is one of the most relevantaspects of the new physicaland logical problems debated in Paris in the centralyears of fourteenth century.Walter Tractatus De and intensione et remissione Burley's primus conveythe essential , minima, philosophicalproblems raised by intension,remission,maxima and reactio . Even thoughhe is less enthusiastic forthesetopics , desinit incipit thansome of his contemporaries, likeNicole Oresme,Buridanwas certainly aware of the foundationalelementsthroughreadingBurley'swritings.
75Oresme, Biblioteca f.15rb:"Secundo, ., Sevilla, 7-7-30, Q.Phy Capitular y Colombina, notandum naturalis nonestaliudnisiinclinatio velquidamappetitus quodtalisappetitus seumotus nature. UndeCommentator eodemcommento 81: appetitus materie estquod materia habetde motuad recipiendum id estde inclinatione, sicutdiceremus formam, inclinatur ad replicandum ad unampartem velad aliam.Ideopotest dicinatuquodvirga ralispotentia de secunda itaquod alicaresdistincta speciequalitatis, signata per nomen illiusspeciei; velsaltem talisspeciei remnaturalem, connoaliquodnomen signât tandotalemappetì tum".
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In the threequestionsdevotedto the discussionof intensionand remishimsion thereis, moreover,some evidence that Buridan is confronting selfnot onlywithpositionsof past masters,likeWalterBurley,the advocate of the succession-of-forms theory;thistheory,in fact,was defended,even in a modifiedform,by Nicole Oresme in the same yearswhen Buridan I thinkthat the argumentsagainstthe dislecturedon Aristotle'sPhysics. tinctionbetweendegreesand qualitiesin dealing with the way intension and remissionoccur could be directedagainstNicole Oresme, and precisely against his way of defendingthe addition theory,the theoryto which in itselfBuridan also adheres. To put the philosophical debates transmittedby fourteenth-century commentarieson Aristotleinto theirhistoricalcontextis essentialas well as difficult. Behind the term 'aliqui' some of the more widespreadand - but not discussed alwayseasilyidentified importantdoctrinesare often concealed. Buridanis more reticentthan Oresme,who mentionsOckham and Burleyin his Physics commentary.But even Oresme doesn't mention the name of Ockham when introducingthe second solutionconcerning intensionand remission. Albertof Saxony sides withthe succession-of-forms theory,contraryto Buridan, even though,at least as far as these questionsare concerned, his model is certainlyBuridan.Albertis, togetherwithOresme, the most authoritativeadvocate of this theory.Johannes Marcilius of Inghen, a solutions,withchampion of the addition theory,recordsfour different fromOresme,who omittedtheThomistic out includingOckham's,different view, which can be foundin JohannesMarciliusof Inghen's. records Moreover,Buridan in his Physicscommentaryde ultimalectura some solutionsconcerningeithercontraryqualitiesor intensionand remission, but he is not as explicitin presentingthem as are the otherscommentatorsconsideredhere. He certainlyadheres to the additiontheory solution,and thereforethe seriesof argumentsagainstthe succession-ofevokes no surprise.In discussing formstheoryechoing Burley's Tractatus how intensionand remissionoccur, however, Buridan is very critical againsta distinctionbetweendegreesand qualities,which is defendedin of the additiontheory;Oresme is probablyreferred Oresme'spresentation to again as far as the order of parts or degrees that undergointension and remissionis concerned.If we considerthese elements,togetherwith naturediscussedin some and appetitus the referenceto topics like privatio refrain from cannot the first we of book, suspectingthat one questions of the principaltargetsof Buridan'sdiscussionis actuallyNicole Oresme or some othermasterof arts under Oresme's influence.
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What remainsinexplicableforme is Buridan's decision to change his point of view concerningmotion: alteration,in fact,is not a property added to the changingquality,as is the case for local motion.Buridan between is quite criticaleven againstthosewho tryto introducedistinctions has to be A coincidence noted. curious as and degrees qualities, already emphasized: in the questions of the firstbook cursorilyreferredto in are analysedfroma philosophicalperand appetitus nature q. Ill, 5, privatio is to be foundin dealing with alteration.76 similar to that which spective Universitàdi Parma di Filosofia Dipartimento
76See alsoS. Caroti, inJohn Buridan's natural Generatio/ ontological problems philosogenerare: 27 (2002),373-413. , in:Medioevo, phy
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du pointchezJean Buridan La problématique JEANCELEYRETTE
La richessede la physiquede Buridan n'est plus à démontrer:la rigueur de la méthodedu maîtrepicard et la cohérencede ses positionsfontde ultimam un des ouvrages ses Questionssur la Physique , ditessecundum lecturam' de philosophienaturelleles plus achevés du Moyen Age tardif.Une autre , dite de tertialectura , version, inédite, de ces Questions sur la Physique à des considérée comme enseignements généralement correspondant antérieursdu maître,a probablementété rédigéepar lui2. Cette version faitapparaîtrequelques variationsremarquablesavec celle de Yultimalectura 3. En revanche les versions abrégées utiliséespour l'enseignement notammentdans les universitésd'Europe centrale4n'ont probablement pas été rédigéespar Buridan,mais par des maîtresde ces universités. Dans la physiqueburidanienneun problèmeremarquableest celui du point car la question de son existencephysique et de son statutsont non seulementdans les deux versionsdes Questions traités,et différemment, mais sur la Physique , également dans une question séparée, éditée en 1961 par V. Zubov5. Cette questiona été écritedans le cadre d'une po1Johannes octo libros Aristotelis acutissime , Paris1509. Buridanus, Questiones super Physicorum à cetteédition en UL. Les citations seront abrégée 2 Les références au manuscrit Erfurt manuscrits seront 298,notéTL, maisles autres n° 6, Cracovie 635.Surlesdifférents ontétéconsultés: ChigiVI 199,Arch.dép.Toulouse des diverses versions de sa Physique et l'étatactuelde leur manuscrits buridaniens seinen Werken und Buridan: Studien authentification voirB. Michael, zu seinem Leben, Johannes desspäten Mittelalters dedoctorat, Université seiner Theorien imEuropa zurRezeption , Thèseinédite de Berlin, 1985,560-616. 3J. Celeyrette, dans:S. Caroti atum et NicoleOresme», «Figura /figur parJeanBuridan Florence doctores estmagna etJ. Celeyrette dissensio, 2004,97-118. (eds),Quiainter 4J.M.M.H. onthePhysics «TheShort Redaction ofJohnBuridan's Questions Thijssen, Attributed to Marsilius ofInghen», dans:Archives to theQuestions and TheirRelation duMoyen etLittéraire d'Histoire Doctrinale Age,52 (1985),237-66. 5 Les références et les concepts du pointau à l'éd.V. Zubov,«JeanBuridan seront en QP, faite Studies andRenaissance XIVesiècle», dans:Medieval , 5 (1961),63-95,abrégée et 203v,et BN Lat.2831,123r-129v. BN Lat.16621,196r-202v à partir des manuscrits trèsgénérale surla question d'unemiseen perspective sonédition Zubovfaitprécéder Guillaume sontcitésoutreBuridan, danslaquelle ducontinu etdesindivisibles d'Ockham, de Saxe,NicoleOresme etc. Gauthier Albert Burley, BrillNV,Leiden, © Koninklijke 2004 - www.brill.nl Alsoavailable online
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lémique avec un autre maîtreparisiendit de Montescalerioaujourd'hui mieux connu6,les textes des deux adversairesfigurantdans le cahier scientifiqued'Etienne Gaudet (BN Lat. 1662 1)7. Le problème est repris dans qu. IV-3 de la tertialectura (TL), et enfindans qu. VI-4 de Yultima lectura (UL)8. Dans cettedernièrequestionil énonce successivement que le point,qui n'est pas rien, est une partie divisibledu continu.Cette position,a priori paradoxale, est différente de celle qu'il défenddans QP, ce que n'a vu Zubov9. De plus le savant russe n'a pas regardéla pas parfaitement Il fautajouter que le problèmeposé par le concept de point tertia lectura. renvoieà celui du rapportentreobjet physiqueet objet mathématique, et la notion ici géométrique,dont on connaîtl'importancepour Buridan10; TL de est très dans mais l'est présente peu, tant mathématique point dans QP que dans UL. Tout ceci justifieun examen complémentaireet quelque peu détaillé. Nous examineronssuccessivementcommentBuridan traitedu statut sont différents du point dans les troistextes.Ces traitements et, de plus, à buridanienne doit être celle de Guillaume d'Ockham, l'approche comparée et dans l'article 1 notammentdans ses questions58 à 63 sur la Physique de sa questionDe quantitatexx . Cette comparaisonsera faiteà la suite de la présentationde la questionsur le point.
6 A proposde l'identité de ce maître, Michael1985{op.cit.,supra , n. 2),451-2envitravaux de W.J.Courtenay la question est sageplusieurs hypothèses. Aprèsles récents désormais Voirla contribution à ce volume tranchée. de W.J.Courtenay de Vivarium et uneétudesurMichelde Montecalerio à paraître. 7 Surlescahiers d'Etienne GaudetvoirZ. Kaluza,Thomas deCracovie, Wroclaw 1978. 8 On notequ. IV-3 la question 3 surle livreIV de la Physique. Dansla tertia lectura les surla structure du continu sontabordées dansle livreIV et nondansle livre questions VI comme dansYultima lectura descommentaires surla Physique). (etla plupart 9 Aprèsavoirnotéquelquesdifférences de détailentreles deuxtextes Zubov1961 toutes cesmodifications on trouve despas, n. 5),46 écrit:«Malgré {op.cit.,supra parfois /.. ./ En peude motsonpourrait direquele texte desQuestions sagespresque identiques surla Physique et le textede la Questio depuncto , sontcomplémentaires». 10J.M.M.H.Thijssen, «Buridanon Mathematics», dans: Vivarium , XXIII (1985), 55-78. 11Guillelmus de Ockham, Brevis summa libriPhysicorum, Summula naturalis et philosophiae inlibros Aristotelis OPhVI, StBonaventure, NY 1984, Quaestiones , ed. St.Brown, Physicorum de Ockham,Tractatus de quantitate ettractatus de corpore Christi 555-73;Guillelmus , ed. C. Grassi, OTh X, St Bonaventure, NY 1986,3-85.
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La question surle point( QP) Comme nous l'avons dit la question de Buridan se situe dans le cadre d'une polémique avec le maîtrede Montescalerio.En faitle traitéadverse (TM)12, commence par réfuterplusieursargumentsde Buridan,mais la question de celui-ci contientaussi des contre argumentsrépondantaux réfutationsde Montescalerio,réfutationsqui d'ailleurs ne semblentpas toujoursêtre prises très au sérieux;si bien que la question de Buridan donne une idée assez claire des points en débat. Elle est divisée en trois parties décrites de la façon suivante dans Yexplicit: Io argumentsde Buridan et rejet de la solutionadverse 2° exposé des argumentsadverses,rejet de ces dernièreset solution 3° présentationpuis rejet de certainsdoutes contrela solution13. La partie polémique proprementdite correspondaux deux premières parties que nous allons résumerà grands traits;lorsque des arguments de Montescalerioserontévoqués nous les resitueronsen note par rapport au plan général de son traité. Dans la premièrepartie14Buridan établitclassiquementque les points, qu'ils soient continuantsou terminants,ne peuvent existerni en puissinonils seraientl'un à côté de l'autre, sance ni en acte dans le continu15; ce que ni lui ni son adversairene concèdent.La positionde Montescalerio est qu'il y a deux typesde partiesdu continu,certainesdivisibles,d'autres et que le toutn'estpas ses parties;son objectionest que toute indivisibles, présentéepour les pointsvaudraitégalementpour les parl'argumentation ties proportionnellesdu continu,ce qui est réfutépar Buridan. Enfin
12Notonsque dansla tablede fol.195rdu manuscrit BN Lat.16621,il estindiqué 11 foliosalorsqu'enfaitil s'étendde fol.214rà fol.223v.On voit commecouvrant Par ailleurs fol.22lr unelacuneest ontété arrachées. d'ailleurs feuilles que certaines conservé estdoncincomplet. Le texteactuellement indiquée parvacat. 13QP 95: «Explicit Io Bridam continens de puncto determinata permagistrům questio rationum adversarii cum solutionis rationes eiuscumexclusione 2° recitationem adversarii, conetremotionem dubitationum earumetsolutione, 3° motionem exclusione aliqualium 3danslesFacultés desarts aumoyen La 'disputatio VoiraussiO. Weijers, tradicta». âge,Turnhout 2002,46-7. 14QP, 63-73. 15L'argumentation Brevis Summa estchezOckham, , n. 11),qu. 61,562. {op.cit.,supra
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contre Montescaleriopour qui le point est un accident réel, Buridan prouve qu'un point ne peut être ni une substanceni un accident16. trois Buridanprésenteet réfutesuccessivement Dans la seconde partie17 comme une succesLe se Montescalerio. de présente premier arguments sion de 8 propositions,tendantà établirque la divisiondu continuest une corruption;cela signifiequ'une chose est corrompue,et ce ne peut les 8 êtreque le point continuant.Buridan réfuted'abord soigneusement il ont été faites en ces réfutations Puis supposant ajoute que propositions. comme son adversairequ'une divisionest un changementinstantané;or, dit-ilil n'existepas en physique de divisionqui ne soit une séparation de parties,si bien qu'une divisionn'est autre qu'un mouvementlocal ou plusieurs mouvementslocaux. Le second argument,qualifié d'ancien, affirmeque si le point continuantn'était pas une chose distinctede la ligne on pourraitécarterles unes des autrescertainespartiesdu continu, puis les rapprocher,et que rien ne seraitdétruitni créé; ainsi les parties qui étaient en continuitédeviendraientcontiguëset tout continu serait un contigu.La réfutation s'appuie notammentsur une analysedu procescas physiques,la divisiondes pierres,le feu,l'eau etc. sus dans différents Le troisièmeargumentaffirmeque puisqu'on voit la couleur d'un corps il faut bien que la surface opaque et que cette couleur est superficielle, soit quelque chose. La réfutationtrès rapide nie que la couleur soit avec l'exemple d'une feuilled'or. Buridan ne prend visiblesuperficielle mentpas l'argumenttrès au sérieux18. C'est dans la troisièmepartie19que Buridan va donner sa propre solution. Cette partie commencepar une liste d'objections- nommées logice dubitationes qui tendentà établirque les pointssont des choses distinctes des corps dans lesquels ils sont. Ces mêmes objections,ou presque, se de la Physique et de Yultimalectura dans les questionsde la tertia retrouvent Nous constituent les rationes allons elles nous examiner; principales. y que 16La présentation à la première desarguments de Buridan correspond parpolémique etlesparLe parallélisme entre lespoints, tiede TM. Cf.TM 214r-v. indivisibles, parties la seconde tiesproportionnelles, estétablien unesuitede propositions qui constituent nonseulement l'existence du point se termine de TM. Celle-ci parla proposition: partie il existe. Cf.TM 214v-217v. n'estpas absolument maisau contraire impossible, 17QP, 73-78, QP, 83-84pour QP, 78-83pourle deuxième; pourle premier argument; le troisième. 18Les troisarguments la troisième constituent et unepartiede leursréfutations partie en 218r-221v, en 221v-222v, et en 222vsuccessivement de TM. Ellessontprésentées 223v. 19QP, 84-95.
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en présenterons plus loin quelques-unes,avec leursréponsesdans les trois textes. La solutionest ensuiteénoncée sans justificationparticulière:«point» est un nom privatifcomme «cécité». Car, dit Buridan, de même que «cécité» signifieabsence de vue dans l'œil, «point» signifieabsence de divisibilitéou d'extensiondans la grandeur,et «instant»absence de succession dans le temps20.Les significations des deux typesde point qui interviennent classiquementdans le continu,«point terminant»{punctum et «point continuant»( punctum sont alors données: un terminons) continuons) entre continuant est une absence d'extension deux parties de la point ligne qui se touchentcontinûment,et un point terminantune absence d'extensionde la ligne au-delà de sa grandeur.Tout ceci est appuyé par une série de citationsd'Aristoteet d'Averroès. L'objection immédiateà cette solutionest alors qu'un certainnombre de propositions affirmatives qui ontle mot«point»pour sujetsonthabituellement considéréescomme vraies. Buridan d'ailleursne le contestepas et par exempleil concède que: «un point est dans une ligne» ou «un point est indivisible»sont des propositionsvraies. Mais alors, comme il admet «A est B» soit vraie il faut aussi que pour qu'une propositionaffirmative «A» «B» un même et ens, que supposentpour «point», qui est sujet, devraitsupposerpour une chose réelle. La réponse de Buridan est alors la suivante:un termeprivatif,en soi, implique le syncatégorèmenon , et un tel termene suppose pas pour un ens,c'est-à-direpas au sens propre; si bien que quand le mot «est» est adjacent à un nonensil n'est pas posé vraimentet affirmativement de celui-ci21.C'est le cas pour les propositionsprécédenteset la signification des phrasesprécédemmentcitéess'obtientcomme pour la proposition«la cécité est dans l'œil» (cecitasest in oculo ), équivalenteà «l'oeil est, et il n'y a pas de vue en lui» (oculusestet nonestin eo visus).Ainsi «dans une ligne il y a un point terminant»{punctumterminons estin linea ) est équivalenteà «une ligne est et il n'y a pas eius en elle d'extensionau-delà de sa grandeur»{lineaestetultraquantitatem nonestin ea extensio ), et la proposition«un point est indivisible»{punctum 20QP, 86: «Adevidentiam omnium sciendum solutionis istarum questionum quodhoc Namsicutcecitassignificai carennomenpunctum estnomenprivativum, sicutcecitas. in magcarentiam divisibilitatis seuextensionis tiamvisusin oculo,itapunctum significai in tempore». successionis et similiter instans carentiam nitudine, 21QP, 87: «hocverbum de nonente. 'est'adjacensnonponitur vereet affirmative in se dictionem sciDicendum eritquodterminus sincategorematicam, privativus implicai nonsupponit 'non'.Ideoquia dictiosincategorematica licethancdictionem significative nonsupponit». privativus proprie sumpta, sequitur quodterminus
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à «entre les parties de la ligne il n'y a rien de divisible» est indivisibile) etc. linee nihilestdivisible) {inter partes Dans la conceptionadoptée dans QP, un point n'est donc pas une chose réellementexistante.Le faitqu'il puisseêtreune imaginationmathématique n'est pas mentionnébien que Buridan le dise à propos de la ligne et l'explique de façon trèsclassique: cetteimaginationqui est fausse car ceux-ci ne considèrentla quantité qu'en suffitaux mathématiciens, tant qu'elle est mesuréeou mesurable,or le résultatde cette mesure ne change pas quand on suppose qu'existentdes lignesayant des longueurs sans largeur,et quand on ne le suppose pas. Ce point de vue sera largement développé dans qu. IV-3 (TL). EnfinBuridanévoque, pour la rejeter,une autre opinionqui pose que les mots «point», «ligne», «surface»,supposentpour une même chose le corps dans lequel sont le point,la ligne,la surface-tout en connotant différemment. Pour les tenantsde cette opinion,dit-il,cettepropriétéest commune à tous les noms privatifs;pour eux les propositionssuivantes sont vraies: «un point est un corps», «une ligne est une surface»etc, de même que «la privationest la matièreprivée» et «la cécité est l'œil». Nous retrouverons cetteopinionlorsque nous feronsla comparaisonavec Ockham. Il faut s'arrêtersur l'argumentationdonnée pour rejetercette dernière opinion. Le point de départ est une citationdes Catégories:«privation» n'est pas «être privé» ( privari ), car la cécité est une privation;or «être esse n'est cecum) aveugle»( pas «cécité»,sinonl'un et l'autretermedevraient êtreprédiquésde la même chose; et, dit Aristote,ce n'est pas du toutle cas, car un hommeest dit aveugle,en aucune manièreil n'est dit cécité22. Buridan refuseici l'identification de la privationet de la chose privée, identification dans ses deux versionsde la Physique23;mais qu'il accepte 22QP, 89: «Aliiautemaliquidicunt linea,superficies quodpunctum, proeademre licetaliudetaliudvelaliter etaliter connotant. hasproposupponunt Propter quoddicunt sitiones esseveras:"punctum estcorpus", "lineaestsuperficies" ethuiusmodi. Etitadicunt in aliisnominibus Ideoconcedunt estprivatio, privativis. quodmateria quodoculusest cecitas. Sedilludnonvidetur mihiverum necessede intentione Aristotelis. Quodapparet in Postpredicamentis ubidicitur sie:"Privari veroet haberehabitům nonesthabitus etprivatio.Privatio namestcecitas, cecumautemessenonestcecitas. Cecumveroesseprivariestetnonprivatio". "Namsi dicitur dicens: idemcecitas etcecumesse, Quodprobat de eodempredicaretur. Nuncverominime; sedcecusdicitur vero homo,cecitas utrumque homonullomododicitur". mihimelius Ideovidetur diceresicutdictum fuit». Cf.Catég., 10,12b. 23Celey rette , n. 3). (op.cit.,supra
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surtoutpour justifiercette positionil soutientque ne peuventpas être assimilés«privation»et «être privé»,«cécité» et «être aveugle»,alors que où cette assimilationest acceptée de façon constantedans la tertialectura elle est le pointde départde plusieursargumentations. Voyonspar exemple qu. 1-21 (TL), la privationest-ellela matièreprivéeou en est-elledistincte24.Dans cette question après avoir affirmél'identitéin re de la te sembledire privationet de la matièreprivéeil soulève un doute: Aristo 7 que le faitd'être mû est la même chose que le moudans Métaphysique vement; le fait d'être figuréque la figure,le fait d'être blanc que la blancheur.De la même façon le faitd'être aveugle et la cécité seraient la même chose, de même que le faitd'êtreprivéet la privation;or l'aveugle et le faitd'être aveugle ne sont pas la même chose non plus que la chose privéeet le faitd'êtreprivé.Il semblealors qu'on puisseen déduire que la chose privéeet la privationne sontpas la même chose. La réponse est la suivante:tout comme la blancheurest le faitd'être blanc, la privation est le fait d'être privé (et donc «cécité» est synonymede «être aveugle»).Mais le faitd'êtreprivéet la chose privéesontla même chose, à «être blanc» qui car "être privé" n'ajoute rien au sujet,contrairement suppose pour une dispositionréelle (la blancheur)ajoutée au sujet25.On sont directement voit que conclusionet argumentation opposées à ce qui est dit dans QP. avecOckham Comparaison Les conceptionsdu point évoquées dans QP doivent être rapprochées, comme il a été dit plus haut, de celles d'Ockham. Regardonsplus précisémentcommentce derniertraitede l'ontologiedu point. Les deux textesockhamistesmentionnésétantvoisins,nous nous appuieronssur la sermonis que «un point question 63: est-ce qu'on doit concéder de virtute estens")26et sermonis de virtute hecsit concedenda est un ens?»(utrum Upunctus donneronségalementles référencesau traitésur la quantité. Ockham commence le traitementde la question en annonçantdeux façonsde répondre,c'est-à-diredeux conceptionsselon lui acceptables. La premièreest présentéeainsi: le nom «point» a une signification déterminéeet peut supposerpour quelque chose,c'est néanmoins,comme 24TL, 10ra-va: a materia». velquodsitdistincta sitmatenaprivata «Utrum privatio 25Argumentation citéedansCeleyrette , n. 3). (op.cit.,supra 26Ockham, 63. Le in libros , n. 11),question ., ed. Brown(op.cit.,supra Quaest. physic ed. Grassi(op.cit., dequantitate, dansle Tractatus mêmedéveloppement , n. 11). supra figure
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le nom «privation»,un nom connotatifet dans sa définitionquidnominis on doit poser une négation:«point» suppose pour une ligne et connote l'absence de continuitéou de longueurau-delà de la dimensionde cette ligne. Dans cette conception,«privation»est mis pour «sujet ou matière privée»,«pointterminant»pour «lignede tellelongueuret pas plus» (linea sermonis on peut bien tantelongitudinis et nonultra)etc., si bien que de virtute dire que les propositions:«un point est une ligne» (punctusest linea ) ou estres)sont vraies. «Point» dénote alors «un point est une chose» (punctus une chose réelle,et ceci est expriméen disantqu'il s'agit d'un nom positif27.C'est la dernièrepositionprésentéedans QP et qui est rejetéepar Buridan. La seconde conception pose que le nom «point» est équivalent en à un complexequi, grammaticalement, ne peut supposerpour signification chose. Le de ce complexe par le nom «point» quelque remplacement n'estjustifié,dit Ockham, que par des raisonsd'élégance ou de brièveté, si bien que lorsqu'un énoncé contientle mot «point», il n'est pas intermais doit être considérécomme une expression sermonis prétablede virtute figurée;ceci peut permettrede concéderque des propositionscomme «un pointest une chose indivisible»ou «un point n'a pas de parties»sont des propositionsvraies. Mais quel est ce complexe?Ockham l'exprimepour «point terminant»:«la ligne est étenduejusque là mais pas plus loin» lineaetnonultra )28,le complexeéquivalantau mot «point» (tantum protenditur étantici une proposition.Plus loin se demandantsi «point» est positifou
27Question «In istaquestione n. 11),567.9-568.3: sunt 63, ed. Brown(op.cit.,supra, duo modidicendi. Primus estquodhoc nomen'punctus' estnomencategorematicum certam etprecise habens etfinitam habetvimnominis significationem, potentis supponere et nonabsolutum ita quodin eius proaliquo/.. ./ Esttamennomenconnotativum definitione debetponinegatio, sicutde omnibus nominibus exprimente quidnominis 'primodum tamenistum dicoquodde virvatio','cecus','limen'etc.Intelligendo ponendi, tutesermonis hecestvera"punctus estens","punctus estaliquid", estres"».Cf. "punctus Tractatus dequantitate, ed. Grassi{op.cit.,supra , n. 11),21.367-23.396. 28Question «Secundus modus dicendi 63,ed.Brown , n. 11),568.42-569.62: (op.cit., supra insignificando estquodhocnomen /.. ./ aequivalet alicuicomposito exnomine 'punctus' rectoetverbovelexnomine reddere verbo, obliquoetverboquodnonpotest suppositum etideode virtute sermonis nonpotest grammatice loquendo; proaliquosupponere. Logice insignificando isticomplexo "tantum lineaetnon loquendo 'punctus' equivalet protenditur ultra" /.. ./Ettaliaponuntur ingrammatica, causametri causaornaaliquando aliquando tusutin rhetorica, causabrevitatis utin philosophia. /.. ./ Intelligendo istum aliquando modum dicoquodistanonestconcedenda de virtute sermonis estens", dicendi, "punctus sedestdistinguenda eo quod'punctus' velimproprie. Primomodo potest accipiproprie estfalsaquiadenotatur estunaparvaresindivisibilis quodpunctus quae sitens,et hoc Si secundo estfalsum. modoaccipiatur sicestverasecundum intentionem et auctorum,
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non il raisonneainsi: de même que les propositions«le faitde voir un homme est quelque chose de positif»et «le faitde voir un homme n'est les propositions pas quelque chose de positif»ne sontpas contradictoires, «ne pas être étendu au-delà est quelque chose de positif»et «ne pas être étendu au-delà n'est pas quelque chose de positif»ne sont pas contradictoires;ainsi «un point est quelque chose de positif»et «un point n'est Si bien pas quelque chose de positif» ne sont pas contradictoires29. totalement disle n'est une écrire: pas privation point qu'Ockham peut ni de sermonis ce n'est chose tinctede la ligne,car de virtute , quelque positifni quelque chose de privatif30. de celle Cette seconde conceptiond'Ockham paraît a prioridifférente de Buridan en ce que pour ce dernier,le concept de point est purement privatif.En faitla positionburidaniennes'accorde avec celle d'Ockham sur le faitque le point est un complexeprivatifqui peut s'exprimerpar comme «le faitpour la ligned'êtreétenduejusque une expressioninfinitive là mais pas plus loin». Pour Ockham, en effet,touteexpressioninfinitive est mise pour la propositioncorrespondante,ici «la ligne est étendue jusque là mais pas plus loin» ce qui explique que les complexeséquivalents au mot «point» soientdans le texteockhamistetantôtdes proposiBuridan au contrairedistingue tions, tantôtdes expressionsinfinitives. dans tous ses textesla propositionde son signifié,tout en se refusantà considérerque ce signifiépuisse êtreune entitéréelleseulementsignifiable de façon complexe(
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de cette proposition,distinctde la proposition,est une pure privation, «point» ne suppose pour rien. Il n'empêche que les deux points de vue ne provient sontau fondidentiques:un pointest un non ens;la distinction non ens du fait les deux du de différentes. façons que que philosophesparlent 3 surPhysique IV (tertia est-ceque lespointssontdes choses Question lectura): indivisibles de la ligne ?32 Donnons d'abord brièvementle plan de la question. Après les raisonsprincipales,celles qui ont déjà été signaléesqui tendent à prouver qu'un point indivisibleexiste,Buridan montre,comme dans QP mais de façon beaucoup moins détaillée,qu'il ne peut exister dans une ligne de choses indivisibles,appelées «points»,et qui seraient distinctesde celle-ci,car on pourraiten déduire,d'une part que la ligne serait composée de ces points,d'autre part que ceux-ci seraientl'un à côté de l'autre. Or dans les deux questionsprécédentes33 il a montréque chacune de ces deux situationsétaitimpossible.Certainsdes autresarguments figurantégalementdans la premièrepartie de QP sont ajoutés, par exemple que les points ne peuvent être ni en acte ni en puissance, que Dieu pourraitles enlever de la ligne, qui ensuite serait finie sans avoir de termesetc. Si bien qu'il est répondu brièvementà la question, et de façon évidemmentnégative. En fait cette réponse n'est présentéeque comme un préalable. Car c'est la résolutiondes raisonsprincipalesqui constituele corps de la question. Cette résolutionest faitedans le cadre de deux conceptionsdont il dit qu'elles sont toutesdeux acceptables34. Uimagination mathématique La premièreconceptionest la suivante:lorsqu'on considèreun continu physiqueon imaginequ'existentdans une ligne des choses indivisiblesqui en sont les extrémités, ou qui fontque les partiesse touchentou sont en continuitéou sur lesquels se faitla divisionde la ligne en ses parties.Le etlescomplexe à Parisau XIVesiècle», dans:CarotietCeleyrette, 2004(op.cit., signiftcabilia , n. 3). supra 32TL, 23vb-24vb: «utrum in linea». punctasintresindivisibiles 33Qu. IV-1 (TL), 23ra-rb: «utrum in linea»;qu. punctasintsibiinvicem próxima «utrum IV-2(TL),23rb-vb: lineacomponatur ex punctis». 34TL, 24ra:«Propter solutiones rationum notandum estquodduplexinvenitur usus huiusnominis et uterque ususestconveniens». "punctum"
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mot «point» a alors la même signification que l'énoncé: «chose indivisible ayantune positiondans la ligne»,et lorsqu'onl'utiliseon faitcomme si ces choses indivisiblesexistaient;mais dit-ilcettesignification est fictive, car le mot «point» est mis pour une fiction,exactementcomme l'est le mot «vide». Ainsi les propositions«un point est indivisible»,«un point est dans une ligne» sont faussesde virtute sermonis car «point» ne suppose pour rien. Il y a là une vraie difficulté, et on a vu que dans QP Buridan admetet d'autresdu même genresontvraies.Ici l'échaptaitque ces propositions qu'elles sontvraies, patoireestla suivante:on peut concéderimproprement en prenantle mot «point» et l'expression«chose indivisible»matériellement.Car du faitqu'il a la même signification que l'énoncé «chose indivisibleayant une positiondans une ligne», on peut dire que «point» est «chose indivisibleayant une positionsur la ligne» et donc concéder les deux propositionsprécédentes,exactementcomme on peut concéderque la propositionsuivanteest vraie «le vide est un lieu non remplide corps». Buridan souligneque comme cette premièreconceptiondu point est elle est légitimecar ceux-cin'affirment celle des mathématiciens, pas l'existence réelle des pointsmais l'imaginent,et c'est de cette existenceseulementimaginéequ'ils tirentdes conclusions.Plus précisémentla géométrie alors. . ., ne faitque des raisonnements (si les pointsexistaient hypothétiques si dans le ciel existaientles épicyclesou les excentriques,etc), même si pour des raisons de brièveté ses énoncés semblentimpliquer que les hypothèsessont vraies. Ce type de raisonnement,dit-il,suffitau mathématicien car il ne s'intéresseaux grandeurs qu'en tant qu'elles sont mesurables;or pour mesurerune grandeurde troispieds par exemple (à d'un pied) il peut être plus commode d'imaginer l'aide d'un instrument la longueur,et comme cela n'influepas sur le des sur qu'existent points les imagineen sachantqu'il s'agit d'une fausse le mathématicien résultat, c'est ce est dit dans QP à propos de la ligne. Mais en qui imagination; car philosophienaturelle,un raisonnementhypothétiqueest insuffisant, on doit déterminers'il en est ainsi des choses ou non. Là où la géométrie la philosophienaturelle,elle, doit déterminer raisonnehypothétiquement, s'il en est ainsi réellement. On voit que l'imaginationmathématiquea dans TL une importance beaucoup plus considérableque dans QP, surtoutelle y est théorisée. Alors qu'elle a fait l'objet d'une simple remarque incidenteelle est ici l'une des deux conceptions acceptables du point, qui va permettreà Buridande répondreà toutesles objections.Dans QP il en va différemment et lorsque pour répondreil est faitappel aux mathématiques,ce qui est
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rare c'est simplementpour dire que l'objectionvientdes mathématiques et que la réponse doit se fairedans le même cadre. nomprivatif «point» La seconde conceptiondu mot «point» est décritede la façon suivante: le nom «point» est un nom privatif.On retrouvealors la formulation par laquelle Buridan a introduitsa solutiondans QP, et on s'attendà ce que la même conceptionsoit exposée, ce qui semble confirmépar l'explicaà propos de la grandeuret du tion qui suit: «point», «instant»signifient la ou, ce qui revientau même, signifient tempsl'absence de divisibilité, divisibiliténégativement35. Mais à cet endroit au lieu de reprendrele développementde QP, Buridanintroduitune distinctionsur le mot négation,disantà propos de la grandeurou du temps,qu'on peut comprendreune négation de la divisibilitéde deux façons, une premièrequ'il nomme «absolue», une autre «secundum quid». Des pointsou des instantsqui correspondraient à une divisibiliténiée de façonabsolue,n'existeraient pas, car aucune grandeurou aucun temps n'existesans divisibilité.Le point de vue évoqué ici est celui de QP. Et il ne le retientpas. Buridan envisage ensuitele cas où la négationest comprisesecundum , mais non de façonabsolue. Il commencepar une explicationgénérale quid, et peu claire: la négationporte sur «tout» utilisédistributivement et distribuantles partiesquantitatives. Le mot «point»est expliquépar l'énoncé: «une grandeurmaisjamais toutela grandeur»,le mot «instant»par: «un temps et jamais tout le temps»36.Tout en conservantla même termide celle de QP: le mot nologie la solution donnée est très différente il est encore dit mais ici «point» privatif, suppose pour quelque chose. Le point,terme(ou commencement)d'une ligne,est une partie divisible de la ligne; c'est une grandeur, mais on dit que ce n'est pas toute la grandeurpour la raison suivante: on prend «tout» distributivement 35TL, 24rb:«istanomina'punctum' 'instans' circamagnitudinem et temsignificant vel significant circamagnitudinem et tempus divisibilitatem divisibilitatis, puscarentiam negative». 36TL, 24rb:«Aliomodopotest circamagnitudinem autemet tempus divisibilinegari tasitaquodnonsimpliciter sedtarnen distributione factaperhocnomen'totum' quod distribuit Ettunchocnomen partes quantitativas. 'punctum' exponitur perhancorationem: et nullatotamagnitudo, 'totum' /.. ./ et sicetiamhoc distributive magnitudo capiendo nomen'instans' idemsignificai etnullum totum quodhecoratio: tempus tempus».
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on le faitportersur les par(c'est-à-direau sens divisé)et implicitement tiesquantitativesde cettegrandeur;comme certainesd'entreelles ne sont pas à l'extrémité(ou au début) il n'est pas vrai que toutesles partiesde la grandeursont terme(ou commencement).Une objectionpourraitêtre qu'avec cette définitionune ligne a plusieurspoints commencementset plusieurspoints extrémitéscar commentun point (c'est-à-direune parde tie) commencementest-ildéterminé?Les exemplesdonnés permettent définis et extrémité ne sont terme ils font car pas que apparaître répondre à une divisiondéterminéede la ligne: «si absolumentmais relativement on imagine un morceau de bois de 10 pieds, son commencementn'est pas une chose indivisiblemais en est une partie,à savoirla première;et il en est ainsi, car si on imaginece bois diviséen deux parties,une sera dite la premièrepartie et l'autre la dernière,et si on l'imaginediviséen trois,ou en cent, il y aura encore une premièrepartie et ainsi de suite. de premièrespartiesde Par conséquentil est clair qu'il y a infiniment ce morceau de bois, à savoir une moitié, un tiers,un quart et ainsi Mais entretoutesces premièrespartiesil n'y en a aucune indéfiniment. qui soitpremièretotalement/. . ./; car si on en diviseune en deux, seule une des deux moitiéssera dite première,et l'autre non.37». Dans cette conception«point» suppose pour une partie et pas pour rien, et cela n'empêche pas Buridan de dire qu'il s'agit d'un nom privatif.En fait «point», «ligne», «surface» et «corps» supposentpour la même grandeurdivisiblesuivantles troisdimensionsmais ils la signifient Une grandeur,en tantqu'elle en l'envisageantselon des raisonsdifférentes. est divisiblesuivantles troisdimensions,est appelée «corps»,suivantdeux dimensions,est appelée «surface», suivant une dimension,est appelée on l'ap«ligne»,et lorsqu'on l'envisagecomme dégagée de sa divisibilité, pelle «point»38. 37TL, 24rb:«Undegratiaexempli huius X pedum, principium lignum ymaginemur scilicet sedestaliquaparsipiusligni, pars;unde prima ligninonestaliquaresindivisibilis, unaeritprima in duasmedietates, dividi sicestdareprimam quiasi ymaginetur partem et unaeritprima, in trestertias, adhucillarum dividi et si ymaginetur etaliaeritultima, Ideopatet in centesimas adhucessetunaillarum si divideretur primaet sicin infinitum. unatertia, unaquartaet sic unamedietas, suntprimepartes ligni,scilicet quodinfinite nullaestquesitprimatota;undesi tusignes illasprimas Tarnen ininfinitum. inter partes iam in duemedietates si dividatur centesimam ipsanonesttotaprimaquoniam primam ideononeratverum unaestprimaetalianonprima; medietatum illarum quodillatota le mot«infinite» «infinite suntprimepartes», Dansl'expression essetprima». centesima de a un senssyncatégorématique en première par«infiniment que nousrendons position infinite continuo in quolibet «utrum Cf.qu. III-18 (UL),61rb-62vb: parties». premières 6Ibisrb-vb. suntpartes»; particulièrement: 38TL, 24va:«Aliquando secundum quodipsaestdivisibilis magnitudinem intelligimus
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de celle de QP et des C'est cette dernièreconceptiontrès différente deux conceptionsdéveloppées par Ockham, qui est seule retenue dans Yultimalectura (qu. VI-4) et y est longuementdéveloppée et argumentée. 4 surPhysiqueVI (ultimalectura): est-ceque lespointssontdes choses Question indivisibles de la ligne?39 Disons toutde suiteque dans cettequestionle point comme imagination mathématiquen'estpas évoqué. Buridany développeuniquementsa conception d'un point divisible.Mais alors que dans TL il l'a donnée sans il l'énonce ici au termed'un processusargumentatif marqué justification, immédiatement rationes huit conclusions. Celles-ci suivent les principales par et Voppositum. La premièreconclusionest que les corps sontlimités,et que pour qu'ils le soient il faut que les limitesexistentréellement.Quoi qu'elles soient on les appelle «surfaces»pour un corps,«lignes»pour une surface,«points» pour les lignes40.Les pointsexistentdonc réellement,et ils ne sont ni de pures privations(comme dans QP), ni de simplesfictionsmathématiques (comme dans la premièrepositionde TL). La deuxièmeconclusionest que dans une ligne,ou plus généralement une grandeur,des points qui seraientdes choses indivisiblesn'existent pas41.Il l'a montrédans les questionsVI- 1 et VI-2 en montrantque de l'existencede pointsindivisibleson peut déduire deux propositionscontradictoires: dans la premièreil a établi que de l'existencede pointsindivisibleson peut déduire qu'ils sont à côté l'un de l'autre et qu'ils ne peuvent pas l'être, et dans la seconde que sous les mêmes hypothèses touteligne finieseraitcomposée de points,et qu'aucune ne le serait.La conclusionest confirméepar des argumentscomplémentaires déjà utilisés dans QP. etmensurabilis etsecundum istam rationem vocamus earn'corpenesillastresdyametros, autem estdivisibilis etmensurabilis secundum duasdyametpus';aliquando intelligitur prout rosnoncurando de tertia, et sicillamagnitudo vocatur tertio modopotest 'superficies'; et mensurabilis secundum unamdyametrum noncurando de intelligi proutestdivisibilis aliisduabus, etsecundum illamrationem vocatur intel'linea';seddicatur 'punctum' prout absolvi ab omnitotadivisibilitate». ligitur 39UL, 96rb-98va: «utrum in linea». punctasuntresindivisibiles 40UL, 96va:«Prima/.. ./ quodnecesseestin corporibus essesuperficies, lineaset suntterminata et noninfinita, et nonsuntterminata sineterminis, punctaquiacorpora ideonecesse estesseterminos corporum». 41UL 96vb:«Secundaconclusio estquodnonsuntin lineavelmagnitudine puncta que sintresindivisibiles».
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La troisièmeconclusion déduite logiquement des deux précédentes énonce que pointset instantssont des choses réelles,qui n'étantpas indivisiblessont divisibles:tout point est une ligne, toute ligne est une surface, toute surfaceest un corps, si bien qu'on peut dire que tout point est un corps42. La quatrièmeconclusionprécisece que sont ces choses: toutpoint est une partie de la ligne,et il ne s'agit pas de la ligne totale car une ligne totale est ce qui n'est pas une partie d'une autre ligne43.Autrementdit un point est une partie propre de la ligne donnée, c'est-à-direque non seulementce n'est pas la ligne donnée, mais que ce n'est même pas une ligne en acte sinon ce seraitune ligne totale.Par ailleurstoutpointpeut d'une ligne;mais,ajoute Buridan, toujoursêtreconsidérécommeextrémité cette extrémitén'est pas quelque chose d'extrinsèqueet de séparé de la ligne,car le corps (la ligne on le rappelle est un corps) est limitéet il le resteraitmême s'il n'existaitrien d'autre en dehors de lui. La positionayantété clairementdonnée,les troisconclusionssuivantes s'en déduisent. La cinquièmeénonce que la ligneest composée de pointset est divisée en points,à savoir en ce qui avant divisionétaient des points (c'est-àdire des partiespropres)quoique après divisionce ne soit plus des points (puisque ce sont des lignesen acte, c'est-à-diredes lignestotales)44. La sixièmeconclusionest que de n'importequelle ligneil y a un terme qui en est la premièrepartie et un termequi en est la dernièrepartie45. Il ne s'agit là que de la répétitionde ce qui est dit plus haut. La septièmeconclusionreprendla définitionqui a été donnée dans TL, une grandeurmaisjamais toutela grandeur,en disantqu'aucun continu n'a pour termetoute une partie en prenant«tout» syncatégorématiquement46.
42UL, 97ra:«Tertia et suntresdivisibles etinstantia conclusio quiasunt, quodpuncta /.. ./ ideoetiamsequitur nonsuntindivisibles, quodomnepunctum ergosuntdivisibiles esttempus». et omneinstans estcorpus 43UL, 97ra:«Quartaconclusio estparslinee,itaquodnon estquodomnepunctum linee». lineámque nonestparsalterius estaliquatotalis linea,etvocototalem 44UL, 97rb:«Quintaconclusio expunctis et manifeste quodlineacomponitur sequitur erantpunctalicetnonsintpunctapost in puncta, scilicet dividitur que antedivisionem linee». divisionem quiasunttotales 45UL, 97rb:«Sextaconclusio estprima lineeterminus estquodcuiuslibet parseiusvel suntprimaet ultima ultima parseius». pars,immoeiustermini 46UL, 97rb:«Septima continui conclusio estquodnullius aliquatotaparsestterminus eius,etcapiohocnomen"tota"sincategorematice».
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Cette conclusionest évidentecar si on imagine une divisionen deux de la partieconsidérée,seule une des deux moitiéssera termedu continu. A prioriune des grandesdifficultés de la positionexposée ici est la relation avec le concept mathématique.Un point est définidans les Eléments comme ce qui n'a pas de partie,et donc est indivisible.Commentpeuton dire que les pointsburidanienssont indivisibles?C'est l'énoncé d'un doute posé immédiatement après la septièmeconclusion.La réponse est en quatre parties. Elle commencepar rappelerque l'indivisibilité seraitune propriétédes pointsmathématiquessi ceux-ci existaient;mais que ceux-ci ne sont que des fictionsqui suffisentaux mathématiciens.Le lien avec les points physiquesn'apparaîtqu'ensuite,notammenten soulignantqu'une extrémité d'une ligne (et tout point peut toujoursêtre considérécomme tel) n'est sermonis mais seulementau sens où il n'est pas pas dit indivisiblede virtute divisible en parties dont chacune serait extrémitéde cette ligne. Un point buridanienpeut donc être dit indivisiblemais ce n'est qu'en un sens dérivé. On peut toutefois énoncerla propriétésuivante:un continuétantdonné, il a une extrémitéinfiniment petiteet c'est la huitièmeconclusion.Cette conclusionest expliquée ainsi: le point extrémitéd'une ligne peut être aussi petitqu'on veut. On peut en effetenvisagerune divisionde la ligne en deux, ou en quatre,en huitet ainsi indéfiniment. Mais un pointdéterminé n'estjamais infiniment petitpuisqu'il s'agit d'une partie47.Bien au contraireil peut être deux fois plus grand qu'un autre, ou quatre fois etc. L'apparentecontradiction tientau faitque dans le premiercas «point» est pris de façon confuse(pour une infinitéde parties),dans le second, de façon déterminée(pour une partie fixée). Il n'en restepas moinsque la propriétéqui vientd'être donnéejustifie d'une lignecomme un point, que les mathématiciens imaginentl'extrémité indivisible et que ce pointmathématiquepuisseêtreconsidérécomme fictif, une abstractiondu point physique. La conceptiondu point développée dans UL de façon très élaborée est bien semblableà la seconde des conceptionsjugées acceptablesdans TL mais avec un caractèreachevé qu'elle ne possédaitpas dans la version précédente. 47UL,97va:«Octavaconclusio scilicet ininfinitum continui finiti quodcuiuslibet parvum estterminus /.. ./ Sedtarnen nonsequitur scilicet sitininfinitum econverso, quodpunctum immopunctum parvum, potestdiciduodecima parsalicuiuscontinui que nonestin infinitum parva».
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Les réponses aux dubitationeslogice La modificationsuccessivede points de vue de QP à TL puis à UL a du été me semble-t-ildémontrée- en tout cas au niveau des définitions Il à voir comment ces modifications de reste conceptuelles concept point. sont mises en oeuvre dans les solutionsdes objections.Nous pouvons en avoir une idée assez clairecar, comme nous l'avons dit,ce sontles mêmes que Buridan a résoluesdans les troistraités.C'est là quelque chose de suivantla positionqui est adoptée ces remarquablecar, naturellement, objectionssont plus ou moins pertinentes.Ceci nous conduit à revenir sur leur place dans les troistraités.Dans QP c'est à partird'elles et de leurs solutionsqu'est construitela 3e partie,celle où Buridan expose sa position; dans TL elles constituentcomme il a été dit le corps de qu. IV-3; dans UL si leur importancerelativeest moindre,elles occupent néanmoinsl'équivalentde deux foliossur les quatre consacrésà qu. VI-4. On ne peut donc pas les considérercomme de simplesarguments il est même possible de dire que c'est tout autant à partir préliminaires; de ces objections que des conceptions théoriques du point que veut défendreBuridan que sont construitsles textes,au moins la 3e partie de QP et qu. IV-3 (TL). Si bien qu'il nous fautles examinerau moins partiellement. Dans QP ellessontnumérotéesde 1 à 14, dans TL puis dans UL plusieurs sont regroupéesmais pour plus de clarténous garderonsla numérotation de QP. Par souci de brièveténous n'en présenteronsque quelques-unes avec leurs réponsessuccessivementdans QP, dans TL avec le point de vue de l'imaginationmathématique,noté TLb dans TL avec le second point de vue, noté TL2, enfindans UL. Objection n° 1. Dans la définitionde la sphèreou du cercle,qui sont de vrais entia,on pose un point (le centre).Si donc celui-ciest une privation la définitionn'est pas acceptable car elle définitle plus connu (le cercle ou la sphère)à partirdu moins connu (une privation)48. Réponse de QP: L'objection est réfutéecar il n'est pas nécessaireque tous les noms intervenantdans la définitionsupposentpour des choses réelles,et que certainssoient des noms privatifsne présentepas d'inconvénient.Par exemple«cercle» est un nom connotatif qui contientdans sa définitiondes termes comme «ligne» ou «surface» qui sont aussi 48QP, 85:«Hocpunctum autspere, etnon indifinitione verientis, putacircuii ponitur ibitamquam perignotiora». privatio, quiaessetdifinitio ponitur
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Buridan ajoute qu'on pourraitrépondreautrementen disant privatifs49. les définitions du cercle et de la sphèresont mathématiques;en effet que un corps sphérique ou circulairenaturel a un centre qui n'est pas un point mais un corps. Réponse de TLji Conformémentà ce qu'il pose en préalable aux mathémaréponsesdonnéesavec la conceptiondu pointcommeimagination tique, il réécritl'objectionsous formeconditionnelle:«si les points existaientla définition du cercleseraitetc». Et une telledéfinition ne présenterait aucun inconvénient.Il répètequ'on peut imaginerque les pointsexistent car pour tout ce qui concerne les mesures et les propriétésmathématiques qui font intervenirle cercle, le résultatne dépend pas de leur existence50. Réponse de TL2: Elle affirmequ'un concept positifpeut être défini d'un nom privatifmais évidemmentpas du nom expripar l'intermédiaire mant la privationdudit concept (une ligne ne peut être définieà partir d'une absence de ligne). En effet,s'il est vrai que la signification d'un termeprivatifest toujoursmoins connue que celle du termepositifdont il est l'opposé, il n'est pas vrai qu'elle soit moins connue que celle de tout termepositif51. Réponse de UL: Quand dans la définitiondu cercle on pose le mot «point» ce mot suppose pour quelque chose qui est la premièreou la dernièrepartie d'un corps52.Et il explique plus loin cette réponseen disant qu'un cercle (ou une sphère) a une partie centralequi est appelée centreet une partie périphériqueappelée circonférence. La partie centrale est termedes rayonsdu cercle (ou de la sphère),et si elle n'est pas indivisibleabsolument,elle est indivisibleau sens qu'il a donné plus haut 49QP, 90:«Adprimam diciquodhocnomen 'circulus' estnomen connotativum potest etnonsolumrerum insuasignificatione sedclaudit dictiones connotativas extra, quasdam "linea"et"superficies"; claudit enimin se significationem terminate etsicclausuperficiel ditin sua ratione rationem Dico:nonoportet nomenacceptum in privationis. quodlibet eiusdiffinitione /.. ./ supponere si describitur proaliquaverare,necestinconveniens peraliquodprivativum». 50TL, 24rb:«Undediffinitiones circuii etspereessent bonesi essent taliapuncta, etiam essequiasivesintsivenonsintprovenit idemquantum ad mensuras etpropoymaginantur sitiones mathematicas». 51TL, 24rb:«Dicendum estigitur describitur quodnomenpositivům aliquando per nomenprivativum nontarnen sibioppositum, pernomenprivativum quia omneprivativum estminus notum cuiopponitur, sednonoportet omneprivaquamilludpositivům tivum omnipositivo esseignotius». 52UL, 97v:«Dicitur circuii velspereponitur dicetur quodindifinitione punctum, post hocdebeatintelligi; conceditur etiamquodhocnomen'punctum' quomodo proaliquo supponit, quiaprocorpore quodestprimavelultima parsalicuius corporis».
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dans le doute qui suit la 7e conclusion.Cette solutionest confirméepar le fait que la terrequi est un corps est dite centrenaturelde toute la sphère du monde53. Objection n° 2: Il y a quelque chose par quoi les partiesdu continu sont unies54. Réponse de QP: Les partiesdu continuqui se touchentcontinûment ne sont unies par aucune chose distincted'elles; elles sont unies l'une à l'autre55. Réponse de TL^ La formeconditionnellede l'objectionest: les parties du continu seraient unies par un point si le point existaitet les extrémitésdes deux parties seraientle même point indivisible.Elle ne présentealors aucun inconvénient56. Réponse de TL2: Il y a quelque chose par quoi les moitiésd'un continu sont unies, et c'est une certainepartie qui a une partie commune avec chaque moitié;on l'appelle «point» du faitqu'il n'est pas vrai que touteune partiea cettepropriété(celle d'avoir une partiecommuneavec chaque moitié)en prenant«tout» syncatégorématiquement57. Réponse de UL: C'est la même que la précédentemais plus détaillée: si une ligne A et une ligne B sont en continuitéet si on les imagine toutesdeux diviséesen 10, alors à partirde la dernièrepartiede A (vers B) et la dernièrede B (versA), est forméeune ligne continuedont une partie est termede A et l'autre est termede B. C'est en ce sens qu'on peut dire que deux continussont unis par un termecommun58.
53UL, 98r:«Sedsecundum in circulo velsperaestparsmediaque vocatur veritatem etomnium circuii centrum etparsextrema circumferentia, semidyametrorum quevocatur indivisiet illaparsmedianonestsimpliciter velspereillaparsmediadicitur terminus; sitterinplures indivisibilis bilisseddicitur partes quarum quelibet quianonestdivisibilis illiuscircuii velspereet quiaetiamin infinitum minus omnium parva semidyametrorum lineevellinearum esttalisparsmedia,et dicitur semidyamepunctum quiaestterminus naturale totalis essecentrum Undedicimus terram tralium. speremundi». 54QP, 85: «Aliquid continui estad quodpartes copulantur». 55QP, 90:«Partes ab eiscopuad nullam remdiversam se continue continui tangentes ad aliam». sedutraque lantur, copulatur 56TL, 24rb:«Ad punctum si essetcopularentur parteslineeet ultimacontinuorum indivisibile». idempunctum essent 57TL, 24 va: «Concedo lineecopulantur et etiamquodaliquidestad quodmedietates sedquianullatotaestutramque medietatem illudestparsquedam communicans, utramque ideoillamvocamus medietatem communicans 'punctum'». 58UL 97v:«Si lineaA et lineaB suntadinvicem et utrumque continue imaginetur B etultima decimaipsius A versus decimaipsius tuncex ultima in decern decimas dividi lineeA etaliaparsesttercuiusunaparsestterminus B versus A estunalineacontinua communem». ad terminům continua sensum lineeB; sicergoad istum minus copulantur
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Objection n° 5: La sphère touche le plan selon quelque chose59.La suite du syllogismequi manque dans QP et se trouvedans TL (et UL) s'exprimeainsi: et ce n'est que selon un point,donc un point est quelque chose60. Réponse de QP: Quand un corps en touche un autre il le touche en mais pas divisive tant que tout, en prenant«tout» unitive parce que cela signifierait que n'importequelle partiedu premiertouchen'importequelle C'est ici la mineure,implicite,du syllogismequi est de l'autre61. partie réfutée. Réponse de TL^ La propositionconditionnelleest: si le point existait la sphèretoucheraitle plan selon un point62. Réponse de TL2: C'est la même que dans QP mais les expressions ». et «distributive» utiliséessont «categorematice» pour «unitive» pour « divisive selon la Buridan ajoute: étant donné une partie du plan sphère quoi touche le plan, on peut toujoursen enleverune partieselon quoi elle ne le touche pas; et c'est la raison pour laquelle on dit qu'elle touche le plan selon un point63.Non seulementla mineureest réfutée,comme dans QP, mais Buridan explique égalementici pourquoi on dit que le contact se fait en un point, et il le fait en reprenantce qu'il a dit pour expliquer en quel sens un point est divisible. Réponse de UL: C'est la même réponse que dans TL2, un peu plus . », «syncategorematice»64 détaillée,avec la terminologie« categorematice Objection n° 7: si le point n'existaitpas, tirerune ligne d'un point à un autre,comme l'admet le mathématicien,seraittirerde rien à rien. Réponse de QP: dire qu'une ligne est tiréed'un point à un autre c'est simplementdire que la ligne a une extensiondéterminéeet n'est pas étendueau-delà.Que cetteréponsecorrespondebien à la solutionthéorique exposée dans QP, où le point est une pure privation,est confirmépar après: de même «la cécité est dans l'analogie développéeimmédiatement l'œil» ne signifiepas que quelque chose qui serait la cécité soit dans l'œil65. 59QP, 85: «Speratangit secundum planum (Zubov:supra) aliquid». 60TL, 23vb:«etnonnisisecundum estaliquid». punctum, igitur punctum 61QP, 91: «Oportet alterum se scirequodcorpustangens corpus, ipsumsecundum 'totum' unitive /.. ./ sednonsecundum totum divisive». totum alterum, tangit capiendo 62TL, 24 rb. 63TL, 24 va: «Undesignata quacumque partesivemagnasiveparvasecundum quam adhucpotest de illaparteauferri ideodicaliquaparssecundum quamnontangit, tangit, iturtangere secundum punctum». 64UL, 97vb. 65QP,92:«Dicendum ad punctum depuncto ducisignificat illam: secundum quodlineam
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Réponse de TL^ La propositionconditionnelleest: si les points existaienton pourraittirerune ligne d'un point à un autre66. Réponse de TL2: La proposition«d'un point à un autre on peut tirer une droite» est concédée, mais avec le sens suivant:d'une grandeurà une grandeuron peut tirerune grandeurrectiligne,mais pas de toute une grandeurà toutel'autre(«tout»étantpris syncatégorématiquement)67. de la Réponse de UL: L'explicationest semblablemais la signification la distance entre deux ainsi: est corps quelconques proposition exprimée est une dimensioncorporellerectiligne68. Bien entendunous l'avons dit, selon le point de vue défenduces objecà résoudre. ou plus ou moinsdifficiles tionssontplus ou moinspertinentes, Il est clair que celles qui viennentde propositionsmathématiquescomme les objections1, 5, 7 ont des solutionsimmédiatesdans TLb mais beaucoup plus délicates avec les autres points de vue. On peut même dire que les solutionsdans TL2 et UL de l'objection 7 ne sont pas trèsconvaincantes.Il n'en est que plus remarquableque Buridan ait tenu à y répondresans se bornerà dire que la propriétéproblématiquevientdes ce qui reviendraità peu près mathématiquesoù elle ne faitpas difficulté, à la réponsede TLj. Les réponsesde TL2 et UL sont en généralproches mais la rédactionde UL, beaucoup plus élaborée,est plus claire,en particulierdu faitde l'introductiond'exemples. Surtouttoutesces réponses sont en cohérence avec la positionthéoriqueexposée dans la question. Il n'en est pas de même avec QP où plusieurssolutionsalternatives peuvent être données dont certainesne correspondentpas à la conception du point comme pure privation.Enfinmême si le second point de vue de celui de QP le mot de TL (qui est celui de UL) est très différent faitde cette terminoloet du nom est encore privatif; appelé «point» y celle comme de certaines commune qui est faiteà l'obréponses QP, gie de à leurs n° 5, sont analogues homologues TL2. jection esse Et sicutcecitatem nonultraextendi. hincindeextensam certam quantitatem aliquam idemquod illudesse in oculo,ita de punctoad punctum in oculonon significat ut earnducide nihiload nihilsedhabetaliamreductionem, lineámducinonsignificat dictum est». 66TL, 24 rb. 67TL, 24va:«Dicoetiamquodde punctoad punctum linearecta,id estde ducitur de nullatotaad aliamtotam sedtarnen rectamagnitudo ad magnitudinem magnitudine rectamagnitudo». ducitur 68UL, 98ra:«Dico quod sic de omnipunctoad omnepunctum rectam contingit cordistantia estdimensio ab invicem duocorpora lineámducerequiainter quecumque recta». porea
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Conclusion En décrivantles conceptionsdifférentes présentéeset mises en oeuvre dans les troistextes,nous avons soulignéque la conceptionprivativedu point défenduedans QP est beaucoup plus conformeaux conceptions ockhamistesque cellesqui sontexposées,et adoptées,dans les deux autres textes.Faut-ilpour autant dire que QP est un texte davantage marqué par l'influenceockhamisteque les deux autres?Certainementpas partout car par exemple la positionqui est expriméedans QP sur la privation est la plus éloignéede celle d'Ockham. L'analyse des différentes positions de Buridan ne peut sûrementpas se faireen renvoyantmécaniquement à une influenceplus ou moins grande du Venerabilis inceptor. Un autre point importantest la réintégration de l'imaginationmathématique.Que le pointsoitune pure imaginationmathématiqueestprésenté dans TL comme une des deux réponsespossibles,ces deux réponsesapparaissantcomme les deux termesd'une alternativepuisque aucun lien n'est fait entre elles. Dans UL la descriptionplus riche que dans TL de la mathéconceptionphysiquedu point,justifiela possibilitéd'une abstraction du aboutit au matique qui partant point physique point mathématique. L'exposé de UL crée ainsi une cohérence entre les deux conceptions exposées dans TL. Aucun élémentmatérielne permetde dire, entreQP et TL, quel est le textele plus ancien. Ni les indicationsdonnées dans BN Lat. 16621, ni les quelques renseignements fournispar W. Courtenay sur Michel de Montecalerio,s'il est bien le maîtrede Montescalerioavec qui a débattu de trancher.Toutefoisl'examen internedes textes Buridan,ne permettent bien aller dans le sens d'une prioritéde QP et malgré tous les paraît a à dangersqu'il y proposerune telleconclusionon est trèstentéde parler d'une modificationde point de vue de QP à TL puis à UL, incontestablementpostérieuraux deux autres textes. En effetalors que les sur des sujets importants(réalitédes conclusions,sinon l'argumentation, statut de la TL de sont analogues à celles de UL, sur points, privation) les mêmes sujets les conclusionsde QP et celles de UL sont opposées. Bien entenduil serait naïf de croire que le traitéle plus «ockhamiste» est nécessairementle plus ancien. Les exemplesdans l'œuvre de Buridan de tellesmodifications de point de vue sont très rares et même si nous ne pouvons expliquervraiment celle-ci,nous pouvons dire qu'elle est le signe de l'existenced'un débat universitaire: selon touteprobabilitéla structure du continua été un sujet de discussionsvivesà l'Universitéde Parisjusqu'à la findes années 1350.
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De façon plus générale pour un maître à la carrièresi longue, distinguerentreles positionsconstammentsoutenueset celles sur lesquelles il a varié ne contribuepas seulementà une meilleureconnaissancede Buridan,mais au-delà fournitdes renseignements précieux sur le climat intellectuelde la Faculté des arts au milieu du XIVe siècle. de Lille III CNRS-Université UMR Savoirset Textes
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s Treatise JohnBuridan' et convenientiis: De dependentiis,diversitatibus An Edition
DIRK-JANDEKKER
Introduction The treatiseDe dependentiis et convenientiis counts among the , diversitatibus earliestworks ofJohn Buridan. It was writtenas a contributionto a philosophicaldebate at the universityof Paris that began in 1331 and continueduntil 1334. The debate probablystartedwithBuridan'smeta, several conclusions of physical treatiseDe diversitate generisad speciem In reply,Buridan wrote which were attackedby other Parisian magistři. two new treatises.One of these,our De dependentiis etconveni, diversitatibus entiisof 1332, deals with the ontological statusof relations.The other, determinations de diversitate ad speciem of 1333, is a more Defensiones generis direct defense of Buridan's original conclusions in De diversitate generis ad speciem and discusses the way genus and species are related to each other.Althoughwe do not know whetherthese repliesprovokedany reaction of the opponents,it is certainthat in 1334 Buridan honored the request to writeone final treatiseabout the disputed topics; this is De 1 relationibus.
1 Abouttheseworks: BerndMichael, Buridan: Studien seinen zu seinem Leben, Johannes Werken undzurRezeption Theorien seiner imEuropa desspäten Mittelalters , Berlin1985,II, 425Burìdan ontheOntological A First Status Relations. Presentation 54;J.M.M.H.Thijssen, ofCausal dedependentiis, diversitatibus etconvenientiis in:Albert Zimmermann "Questio ofthePolemic andAndreas undNatur imMittelalter , Berlin1991,234-55,esp.236Speer(eds.),Mensch 7. De diversitate ad speciem is notknownto havesurvived in anymanuscript. Of generis theotherworks no complete havebeenpublished editions ofDe yet.A partialedition inThijssen1991,238-51.The edition etconvenientiis of , diversitatibus dependentiis appeared De relationibus wasannounced Relation alsVergleich. DieRelationstheorie byRolfSchönberger, desJohannes Burìdan imKontext seines Denkens undderScholastik , Leiden1994,372,n. 6. Buridan's deuniversali as De differentia universalis adindividuum Quaestiones , alsoknown , which isanother ofhisearly'polemical' wasedited Iohannes (Duae works, Buridanus, byS. Szyller, deuniversali ' in:Przeglad , 3 (1987),135-78. quaestiones Tomistyczny © Koninklijke BrillNY Leiden,2004 - www.brill.nl Alsoavailable online
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It has been suggestedthat Buridan's so-called 'polemical' worksoriginated in the context of formal academic disputations.2Our treatise shows some characteristicsin structure,styleand terminologythat support this suggestion.Especially the structureof the author's determinatio at the end, and the formula-likedeclarationof sinwith its recapitulatio cere intentionsmay be mentionedhere.3Buridan's opponentsin De deare two anonymousmastersof artsat etconvenientiis , diversitatibus pendentiis the universityof Paris. One of them belongs to the Picard nation and is referredto as Picardus , the otherbelongs to the English nation and is called Anglicusý Althougha formaldisputationwas an affairof the magistřiratherthan of students,Buridan does referto his studentsand his teachingpracticeseveraltimes.5The treatisealso containsan interesting remarkabout Buridan'sapproach to authorities.6 The theme of the disputationis the ontological status of relation.7 The questionsat stake are whethercausal relationsadd anythingto the essence of the effectof a cause, whetherthe agreementor difference between two thingsis anythingadded to theiressence,and whetherrelations of relationsare possible. The structureof the disputationis as that follows.Buridan begins by repeating three statementsconclusiones he had already put forwardat an earlieroccasion, probablyin the lost ' dansles 2 Michael1985(op.cit., La 'disputatio above,n. 1),I, 245-6;Olga Weijers, Turnhout 25-49. aumoyen desarts Facultés 2002, , âge 3 "Etprotestor illudquod etsustinere sedsolumaddiscere quodnihilmaliintendo, Et supplico verum etaliaquae ad haecsequuntur. mihividetur quodsitfasunicuique in nihiltarnen inspeculativis, metaminconvenientiae alteriomnem nostrum imponere autinfide." moribus (p. 123,11-15). 4 Michaelconjectured de Feno(thelatinized wasAegidius thatthePicardmaster see doubtsaboutthissuggestion: nameofGillesvanderHoye),butThijssen expressed 1991{op.cit., Michael1985(op.cit., above,n. 1),237. above,n. 1), II, 443;Thijssen 5 Forexample: meisinlegendo" coramscholaribus "declaravi (p. 142,5-6);"etbeani sciunt" (p. 131,33). 6 Seeintherecapitulation Lindicit[sc.Picardus] quodforte (p. 144,19-24):"Tertio sibiacquiesco, Ethuicresponsioni sibicredere. necoportet illiusopinionis, fuit colniensis siveLincolniensis, fundare superaliquamauctoritatem, quia nolomein hac opinione etetiamipsifuerunt faciliter siveAristotelis, siveAverrois, exponuntur, quiaauctoritates eosexponere Tamenplusvellem homines. quamnegare." probabiliter 7 OtherplaceswhereBuridandiscusses thesametopicare:IohannesBuridanus, München ed.Johannes inPraedicamenta, 1983,69-106(qq. 10-14); Schneider, Quaestiones In Praedicamenta Summulae: Iohannes 1994,46-61(§ , ed. E.P. Bos,Nijmegen Buridanus, BadiusAsParisiis: Iod. Aristotelis In Iohannes , Buridanus, Metaphysicen quaestiones 3.4); etdiversitates convenientiae 1518,y qq. 5-9(ff.29rb-32vb), censius, esp.y 6: "Utrum veldiversis" additaerebusconvenientibus sintressivedispositiones ad invicem rerum sintdispositiones rerumad invicem siveeffectuationes causalitates and V,8: "Utrum causisetcausatis". additaeillisrebus,
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ad speciem treatiseDe diversitate , and that apparentlyset offthe opgeneris He also criticism. providesa briefargumentationfortheseconponents5 clusions.Then the opponentstake the stage.Firstcomes the anonymous Picard master who puts forwardfivestatementswith arguments,then the anonymous English master carries in two more objections. After a shortformula-likedeclarationof sincereintentionsBuridan proceeds He summarizesthe opponents' arguments withhis solution(determinatici). The explanation of these five and respondswith fivemore conclusiones. statementsis the core of the treatise.Finally,Buridan summarizesthe entirediscussion. Buridan's views regardingthe ontologicalstatusof relationare summarized in the threeconclusionsthat are given at the beginningof the treatise.First,the dependence of an effectupon its cause does not add anythingto the essence of the effect.Second, iftwo beingsagree in their essence, then this agreement does not add anythingto their essence. Third, iftwo beings are in a relationof dependence, agreementor differenceto each other,thenthisrelationdoes not existextramentally. Both opponents involvedin the disputationdefend realistpositions. Their purpose is to attackthefirstand second conclusionput forwardby Buridan. The Picard mastertriesto show thatthe essence of an absolute to explain its dependence upon somethingelse. being is not sufficient He argues thatifthiswere the case, i.e., ifthingscould be in a relation to other thingsjust by being themselves,then we could not distinguish cause and effect.Therefore,somethingmust be added to the essence of the effectin order forit to be the effectof a cause. Only if we are to explain dealing withrelativebeings theirrelativeessence is sufficient theirdependence and no furtheraddition is required.In neithercase is anythingadded to the cause, because the cause never depends on the effect,but alwaysthe otherway round. In a similarvein the Picard mastertriesto show that if two absolute beings agree or differin nature,then theiragreementor differenceis somethingreal that is added to each essence. In the case of two agreerelativebeings, theirrelativenature already sufficesto ing or differing explain theiragreementor difference. The English master also attacks Buridan's conclusions. He tries to show thata dependencycan be destroyedwhile the dependentbeing itselfremainsin existence.Therefore,dependencyand a dependentbeing are reallydistinctfromeach other.Also, the English masterdenies that a relationcan relate to anotherrelation,because thiswould lead to an infiniteregress.
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In his response Buridan argues that relationscan be foundedon relations.We could thinkof the posteriority of Socrates' fatherhoodwith an reason whyrelationcould to Socrates as There is no example. respect or terminus not serve as one of the terms,eitherfiindamentum , of another relation.For example, let us say that a relationa (e.g., Socrates' fatherhood) is posteriorwith respectto its foundationb (e.g., Socrates). This which itselfis a relation,is foundedupon relation
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Manuscripts survivesin two codices: Klosterneuburg,StiftsBuridan'sDe dependentiis bibliothekcod. 291, ff.163ra-172ra (siglumK); and Praha, Státní knihovna cod. VIII Ell (Truhlář 1536), ff.239r-249v (siglum P).9 The Klosterneuburgmanuscriptwas writtenin the 14thcentury,the Prague 10 manuscriptin or around 1419. ManuscriptP was not copied directly fromĶ because K has an omission due to homoeoteleutonthat is not presentin P.11In additionto our treatise,both codices also contain Burdeterminations de diversitate ad speciem but no other idan's Defensiones generis textsthatare relatedto the debate. I have checked in particularforthe presence of any treatisesthat the opponents may have writtenin reply, but did not findany.12 Finallya fewwordsabout the criticaledition.I have recordedall variant readingsin the criticalapparatus withexceptionof variantswithout differencein meaning, such as ille/iste etc. The reader will , ergo/igitur notice that,when both witnessesare at variance, the older manuscript does not always have the betterreading.Therefore,I have decided to 9 Bothcodicesaredescribed inMichael1985(< ., above,n. 1),427-8.See briefly op.cit codicum Latinorum alsoJoseph Publica Truhlár, Catalogus manuscriptorum quiinC.R.Bibliotheca I willrefer universitatis asservantur tothe , Praha1914,I, 567.In thisarticle atque Pragensis foliation rather thanbythe15thcentury folionumbers Praguemanuscript byitsmodern In Thijssen1991(op.cit., whicharepartly call above,n. 1),235 an incorrect preserved. number forthePraguecodex. (VII E 11)isgiven 10Michael1985(op.cit. cod.VIII E 11,f. above,n. 1),II, 427;Praha,Státní knihovna, inthesamehandas ourtreatise ofBuridan's deuniversali 238v(explicit Quaestiones , written andimmediately Iohannis Buridani de it):"Expliciunt magistři preceding quaestiones universali finitae annoDominim°cccc°xix° antefestum nesciocuiusetcetera." 11Thishomoeoteleuton, foundon f. 17lrbK (p. 146,8 oftheedition), alsoproves inThijssen1991(op.cit., thatthesuggestion be theautoabove,n. 1),237thatK might cannolonger be upheld. graph, 12Buridan's inbothK (onlyqu. 1)andP, deuniversali Quaestiones , preserved polemical arenotdirecdy related toDe dependentiis etconvenientiis , diversitatibus , although theycontainreferences tothelatter treatise deuniversali Quaestiones , ed. Szyller, 16223, (Buridanus, and 17528"29). The untitled andanonymous treatise known as De natura numeri 16918"19, etunitatum, attributed to Buridanandpreserved in K (if.205vb-215vb), is notrelated P contains either. sevenanonymous thatdo Finally, manuscript quaestiones metaphysical notseemtoberelated tothedebate, treat similar Theirtidesare: although they subjects. universalia sintmaxime difficilia sintpriora (1) Utrum (f.283v);(2) Utrumuniversalia secundum intellectum (f.283v);(3)Utrum speciessitmagisprincipium quamgenusvel e contra eius(f.285r);(5) (Utrum) (f.284v);(4)Utrum genussitparsspecieietsittotum a singulari inspeciebus universale sitseparabile sitpriuset (f.285v);(6)Utrum semper sicutvidetur dicerePhilosophus posterius (f.286r);(7)Utrum speciessitnobilior genere (f.286v).
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adopt variantreadingsfromboth K and P in the text.Conjectureshave been reduced to a minimum.I have adjusted the orthographyof the text to the spellingof classical Latin (but with u/v distinction)and applied punctuationaccordingto modern standards.Sources thatare cited in the texthave been identifiedas much as possible. Referencesto Aristotleand Averroesin the sources apparatus are to Aristoteles Latinusand the editioIuntina referencesto Grosseteste'scommentaryon , respectively; are to the Rossi edition.13Because thisis the oldest the Posterior Analytics textwrittenby Buridan that is known to have survived,the quotations fromBuridan'searlierworkscould not be identified. Nijmegen RadboudUniversity Nijmegen ofPhilosophy Department
13Robertus libros Commentarius inPosteriorum , ed.Pietro Rossi, Grosseteste, Analyticorum Firenze1981.
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Edition IOHANNISBURIDANI ET GONVENIENTIIS DE DEPENDENTIIS,DIVERSITATIBUS Ad defensionemveritatisquam quidam impugnarenitunturde dependentiiseffectuumex suis causis et de convenientiiset diversitatibusre5 rum ad invicem,volo nunc reiterareconclusionesquas de hoc alias satis vel nimis succinctedeclaravi. Quarum prima est quod dependentia effectusex sua causa nihiladdit in effectudependenteultraeius essentiam. Secunda est quod convenientiaevel diversitatesessentialesseu quidditativae,cuiusmodisuntconvenientiaevel diversitatesaliquorum secundum 10 speciem aut secundum genus, nihil addunt in rebus sie convenientibus vel diversispraeter suas essentias.Tertia conclusio est quod huiusmodi dependentiaevel convenientiaevel diversitatesprout sunt relationesdinon suntpraeteranimam. stinetaea fundamentis, conclusionum ) (Probatio 15 (1) Primam conclusionemprobavi alias inducendo in diversisgeneribus causarum. In causa efficientesic. Effectusdependet ab agente in hoc quod produciturab eo. Et si dependet se ipso non per dependentiam realem sibi additam,habeo propositum.Si autem hoc sitper dependentiam realem superadditam,tunc ilia dependentia iterumdependet ab 20 aliquo agente a quo producitur,cum ipsa habeat esse post non-esse.Et si dependet se ipsa et non per dependentiamaliam realem superadditam, pari rationepoteramusstarein primo,quia nulla ratiovideturcogere de uno quae non cogat de alio. Si vero ipsa dependet per aliam dependentiam additam et realem,quaeram iterumde illa ut prius,et procedam in in essentialiterordinatis,quod reputoinconveniens. 25 infinitum Et eodem modo processi de causa finaliet suo effectu,quod non repeto. Sed repeto de causa materiali,ut per hoc appareat quod saepe dubitatumfuit,scilicetutruminhaerentiaaccidentissitde essentiaaccidentis. 30 Dixi ergo quod forma dependet a materia per hoc quod ipsa inhaeret materiae,aut per hoc quod materia subiciturei, quod idem est. Si 163rbK autem hoc sit per dependentiamrealem sibi additam, tune illa depen8 est]om.K 30-31 inhaeret] K 32 autem]om.K inhaereat
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dentia eritaccidens reale et in subiectoreali,et sie dependebititerumab ilio subiecto,cum ei inhaereatvel cum illud subiectumsibi subiciatur.Si autem sic dependeat non per aliam dependentiamsibi realiteradditam, tuncpari rationestandumerat in primo. Si vero per aliam, procedam in 5 infinitum. Similiterrepetode causa formali,nam materiadependet a formaper hoc quod informaturea, sive sit forma substantialissive accidentalis. Si autem hoc est per dependentiamrealem additam, ilia dependentia eritaccidens informansmateriam,et sic materia iterumdependebitab illa, et procedaturultraut prius. Iterum hanc conclusionemconfirmavi10 auctoritateLincolniensissecundo Posteriorum , ubi dicit quod dependentia uniuscuiusqueentisex primo principionihilmultiplicatin re dependente. Quod si verum sit, non apparebit ratio cogens quin hoc possit dici de aliis causis et suis effectibus. (2) Secundam conclusionemprobavi primo quia res causatae habent 15 suas essentialesconvenientiasvel diversitatessecundumquod dependent ex causis eisdem vel diversis.Causae enim eaedem vel convenientessunt natae causare effectusconvenientes,et diversae diversos.Cum ergo illae dependentiaenihilmultiplicantin re,videturrationabilequod etiam nec illae convenientiaevel diversitatesaliquid multiplicant, quia si in de- 20 dicere aliter de convenulla ratio hoc concessum fuerit, coget pendentiis nientiisvel diversitatibus. Secundo probavihanc conclusionemsic. Si a et b suntformaesimpli- illa dices diversaeessentialiterper diversitatemrealitersuperadditam vel 25 versitasvoceturc- , tunc oportetquod c et a sintdiversaessentialiter per aliam diversitatemrealiteradditam, et tunc procedam in infinitum; vel non per aliam diversitatemsed se ipsis,et tunc pari rationestandum 239vP erat in primo. Similiterest de convenientiis:nam Socrates convenitPla163vaK toni specie, et si hoc est per convenientiamsibi realiteradditam, tunc cum illa convenientiacapiam aliam convenientiameiusdem speciei. Et 30 tunc illae convenientiaeconveniuntspecie vel per aliam convenientiam vel non per sibi iterumrealiteradditam,et tunc procedam in infinitum; aliam sed se ipsis,et tunc eodem modo standumerat prius. sunt maiores et minoresconIterum,dicebam quod in intelligentiis venientiaeet diversitatesearum ad invicem.Cum tarnennihil sit in eis 35 Posteriora InAnalitica I I Robertus 2, 1,29i83"84 Grosseteste, forma add.K 11-12 depen1 etinsubiecto reali]om.K 2 illud]eiusK 7 sive2] P 1 K 6 rationis add. dependet dependent] dentia]
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ultra suas essentias,sicut supponebam ex duodecimo Metaphysicae , nec hoc intendonunc declarare,quia nimisessetextrapropositum. (3) Tertiam conclusionem breviterprobavi, quia convenientiae,deproutsuntrelationeset distinctaea fundamenpendentiaeet diversitates 5 tis,vel suntrealiterpraeteranimam in illisfundamentis,et tunc addunt ultraeorum essentias,quod est remotum;vel non suntpraeteranimam, et sic habeturhaec tertiaconclusio. , sc.Picardi) ('Conclusiones opponentis Duas primas istarumtriůmconclusionumduo venerabilesmagistřini10 tunturdestruere,tam arguendo contra eas quam solvendo earum rationes. Quidam enim multumsubtiliteret ordinatead destruendumdictas conclusionesponitquinqué conclusiones. (1) Prima est quod dependentia causati formaliterabsolūti ex sua causa multiplicaiveram formamrealem superadditamentitatiilliuscau15 sati formaliterrespectiviex sua causa. (2) Secunda conclusio est quod dependentia causati formaliterrespectiviex sua causa nihilreale multiplicatsuper essentiamilliuscausati. (3) Tertia conclusio est quod dependentia causati ex sua causa nihil multiplicatin causa, sive causa fueritformaliterabsoluta sive respectiva, 20 et sive etiam effectusfueritformaliterabsolutusvel respectivus. (4) Quarta conclusio est quod identitāteset diversitatesessentiales pluriumrerumformaliterabsolutarummultiplicantveras formasreales in utroque extremorum. (5) Quinta conclusio est quod identitāteset diversitatesessentiales 25 pluriumrerumformaliterrespectivarumnihil multiplicantin rebus eisdem aut diversis. adprimam conclusionem (Rationes Picardi) Ad primam conclusionemarguitprimo sic. Si dependentia causati formaliterabsolūtiex sua causa nihilreale multiplicaretin causato, tunc in 30 causato ut sic nihil esset nisi formaliterabsolutum,cum illud causatum 163vbK ponatur esse formaliterabsolutum. Sed si in causato nihil sit nisi for1 Cf.Aristoteles, 12,6, 107lb20-21 Metaphysica 10 earum]eorum J 15 formaliter ... causa]om.K 16 formaliter] om.K 26 aut] velK 31 si]om.K
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maliterabsolutum,tunc causatum non habet habitudinemad causam. Ista consequentiapatet,quia habitudo non est ens formaliter absolutum, immo formaliter respectivum.Et si causatum non habet habitudinemad causam, tunccausatumnon dependebita causa. Ista consequentiapatet, quia dependentia est quaedam habitudo,et si dependentiafueritrealis, 5 tunc habitudo eritrealis,et si fueritper intellectum,tunc erithabitudo per intellectum.Sed si causatum non dependet ex causa, tunc causatum non est causatum. Ista consequentia patet, quia pro alio causatum non dicituresse causatum nisiquia dependet ex causa. Sed hoc ultimum 10 consequens implicaicontradictionem;ergo et cetera. Secundo arguitursic. Si dependentia causati formaliterabsolūti niad hil reale multiplicaretin causato, tunc causatum non plus referretur causam quam causa ad causatum; consequens est falsum,ergo et antecedens. Falsitas consequentispatet quinto Metaphysicae capitulo de ad interilla quae suntde primo 15 aliquid, ubi Philosophusdans differentiam vel secundo modo relativorumet illa quae suntde tertiodicitsic: "secundum numerumquidem igituret potentiamdicta ad aliquid omnia sunt ad aliquid, eo quod ipsum quod quid est alteriusdicituripsum quod est, sed non eo quod aliud ad aliud; mensurabilevero et scibileet intelligibile 240rP eo quod aliud ad ipsum dicitur,ad aliquid dicuntur.Nam intelligibile20 significai,quia ipsius est intellectus."Et super hoc dicit Commentator quod relatioest duobus modis,scilicetrelatioin substantiautriusquerelativi,aut relatio in substantiaalteriustertiiet in altera propterillud. ad inviPatet ergo quod relativatertiimodi non aequaliter referuntur in eius 25 substantia existentem relationem mensurabile cem. Immo, per ad mensurabileper rerefertur ad mensuram,sed mensuranon refertur lationemexistentemin substantiaeius; modo certumest quod relationes causae ad causatum et e contra sunt de isto tertiomodo, quia effectus in suo esse mensuratura causa. Sed consequentia est plana, quia nulli dubium est quin causa referaturad suum causatum relationehabente 30 esse formaleab anima et esse fundamentalein re extra. Ad hoc iste confirmâtdietam rationemostendendo quod causatum 164raK referturreali relationead causam et causa non referturreali relatione ad invicem ad causatum, quia si causa et causatum mutuo referrentur InMetaphysica 14 Aristoteles, 5, 15,fol. 5, 15,1021a26-31 21 Averroes, Metaphysica 129vG ... aliquid]om.K 17 add.K 3 si] sicKP 16-18 secundum 2 est]formaliter om.KP 23 dicitP 20 eo ... intelligibile] numerum quidem]om.KP 18 dicitur] K om. K altero 33 non] altera]
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relationereali, tunc sicut causatum constituiturper causam, ita causa constitueretur per causatum; quod est falsum,quia tunc idem respectu eiusdem et eodem modo esset causa et causatum; quod implicai contradictionem.Sed consequentia tenetpro tanto quia causa et causatum 5 suntin tertiomodo relativorum.In quo modo illud quod refertur ad alterumrelationereali fundatain ipso, constituitur alterum. Et istam per rationem innuit Commentator quinto Metaphysicae capitulo de ad aliquid, ubi exponens tertiummodum relativorumdicitsie: "Et intellectus non referturad intelligentem, sed ad intellectum,quoniam si ita esset, 10 tunc intellectusconstitueretur per intelligentem;sed videturesse e converso. Ex quo consequereturquod illud quod constituiturper aliquid constituâtillud,scilicetquia contingitut causa constitueretur per causatum. Et sic idem esset in respectueiusdem causa et causatum insimul." Et hanc rationemsecundumexpositionemCommentatorisinnuitPhilo15 sophus in hac littera:"Non est autem intellectusad illud cuius est intellectus;bis enim idem dictumutique erit." Patet ergo quod causatum refertur reali relationead causam, quia constituitur per illam. Sed causa non refertur reali relationead causatum,quia tunc e contraconstituereturper ipsum. Tertio arguit sic. Quandocumque de aliquibus circumscriptoomni 20 realiter. opere intellectusverificaripossunt contradictoria,illa differunt īsta patet per primůmprincipium.Sed sic est de causato formaliterabsoluto et de eius dependentia ex causa, quia dato quod numquam intelligeremus,adhuc causatum formaliterabsolutumnon esset habitudo 25 ad aliud, quia impossibileest quod eadem natura, et hoc in causatis et finitissitformaliterabsoluta et formaliterad aliud. Sed dato etiam quod nihilintelligeremus, tarnende potentiaessethabitudo ad aliud, quia ipsa est illud quo causatum dependet ex causa et habet formaliterhabitudinem ad causam, dato quod non intelligamusquia nisi praeterintellec30 tum causatum dependeretex causa et per talem dependentiamhaberet habitudinemad causam, tunc praeter intellectumcausatum non esset 164rb/T causatum,sicutpriusarguebatur.
7 Averroes, In Metaphysica 5, 15,fol.129vH 14-15 Aristoteles, 5, 15, Metaphysica 1021a31-33 10 esse]om.KP 18 reali]iter. K 25 eadem]eodemP 26-27 Sed ... aliud]om.P
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conclusionem ad secundam Picardi) (Rationes Primo Deinde iste arguit ad suam conclusionem secundam tripliciter. sic. Natura non facit de duobus quod potest facere uno, quia ageret otiose; sed causatum formaliterrespectivumpotest actu dependere ex sua causa sine aliquo superaddito,cum ipsum sitformaliteret essentiali-5 terad aliud se habens siveprincipiumformalead aliud se habendi. Secundo sic. Illud in quo non potest fundarirelatio realis, non dependet ex causa per dependentiamrealiteradditam; sed in causato formaliterrespectivonon potestfundarirelatiorealis,quoniam omne illud quod fundatdependentiamest necessario independens,quia aliternon 10 Ergo quod fundatrelationemad termiplus fundaretquam fundaretur. 240vP num dependentemoportetipsum esse independenstali dependentia,et per consequens oportetipsum esse absolutumper privationemrespectus ad terminům.Sed causatum formaliterrespectivumnon est sic absolu15 tum; ergo non potestfundarealiquam relationemrealem. Tertio arguitper rationemmeam, scilicetquia procedereturin infinitum in essentialiterordinatis. conclusionem Picardi ad tertiam } (.Rationes Deinde arguitad suam tertiamconclusionemsic. In ilio nihil multiplicai dependentia causati ex causa, quod ut sic non est ad aliquid, quia 20 Sed causa ut sed solum quia alterumad ipsum refertur. ipsum referatur, sed solum quia alterumad causa non est ad aliquid quia ipsa referatur, ut patet ex supra allegatiscapitulo de ad aliquid quinto ipsam refertur, Metaphysicae. Item. Secundo quia sequereturquod in prima intelligentiaesset ac- 25 cidens superadditumsuae naturae,cum ipsa sitprima et maxime causa aliorum.Consequens tarnenest absurdumsecundumomňes. conclusionem ad quartam Picardi) (.Rationes Deinde arguitsic ad quartam conclusionemquaestionis sicut arguebat ad primam,quia si identitāteset diversitatesnon essentrelationesreales 30 a suis fundamentisformaliterabsolutis,tunc in rebus eisdem différentes 24 Aristoteles, 5, 15,1020a26-31 Metaphysica P 7 Secundo]SecundaK 22 quia2]om.P 26 cumipsa]iter.
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non esset ut sic nisi formaliterabsolutum;et tune non haberenthabitudinem ad invicem,cum habitudo ad aliud non sit quid formaliterabsolutum,et tune non essenteaedem, quia contradictionemimplicai quod unum sitidem alteriet non habeat aliquam habitudinemad ipsum.Ergo 5 res eaedem non erunteaedem; quod est falsum. 164vaK Secundo arguitquia praeterintellectumpossuntverificancontradictoria de re formaliterabsoluta et de sua identitāte,quia res formaliter absoluta non est habitudo ad aliud, sed identitasipsius ad aliam rem est formaliterhabitudo ad aliud, quia contradictionemimplicai quod res sit 10 eadem alteriet non habeat habitudinemad ipsam. Et hoc non est nisi per identitatem.Ergo identitasdifferìpraeterintellectuma re absoluta quae dicitureadem. Tertio arguitsic. Ponamus quod Socrates vixeritper decernannos et Plato generaturhodie, manifestumest tunc quod intellectunon intelli15 gente Socrates habet nunc identitatemspecificamcum Platone, et heri non habebat. Et ita in Socrate est de novo generatahuiusmodiidentitas. Et tarnennihilde esse Socratisest de novo generatum,quia duravitper decernannos, ut positumest. Ergo talisidentitasest aliquid reale praeter essentiamSocratis. ad quinterni 20 (Rationes conclusionem Picardi) Deinde arguitsic ad quintamconclusionemsicutfecitad secundam,nec plus, nec minus;ideo non repeto.Sic ergo patet quo modo iste subtiliter arguitcontraconclusionesmeas. alterius se.Anglici ('Conclusiones } opponentis, 25 Sed adhuc quidam alter sic arguitcontra meam primam conclusionem. Primo accipit quod potentia materiae pro respectuest alia ab essentia materiae secundum Commentatoremprimo Physicorum , tunc quia corin adventu formae et non tunc materia, rumpitur quia est de genere relationiset non materia. 30 Secundo accipit quod potentiamateriae praedicta est praeteroperationem intellectus,quia sive intellectusintelligatsive non, ipsa tamen corrumpiturin adventuformae,quod non esset si essetab anima. InPhysica 27 Averroes, 1,7,fol.41rE-F 3 eaedem]eodemP 14 quod]inadd.KP 18 estaliquidreale]om.K 21 sic]om.K
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Tunc eodem modo arguitde Socrate dependentein sua generationea spermateet a virtutehominisexistentein spermateet ab influentiacaeli influxain eo. Nam ista dependentia corrumpiturSocrate permanente, ergo non est sibi eadem. Consequentia patet de se. Probaturantecedens, quia corruptospermatevel virtuteexistentein eo corrumpiturilla de- 5 pendentia,quoniam a re quae non est nihildependet. Sed constatquod ad corruptionemhuius spermatisnon corrumpiturSocrates. Etiam. Socrates est de praedicamentosubstantiae,et dependentiaest 164vbK de praedicamentorelationis,quia dependens diciturad aliud dependens 241rP et non diciturdependens nisi per dependentiam.Nec potest dici quod 10 ilia dependentia sit solum per animam, quia praeter omnem operationem animae effectusdependet a suis causis, et hoc est per dependentiam. Etiam si ilia dependentia non esset realiterdistinctaab effectu dependente,tunc ratio Commentatorisde potentiamateriae nihilvaleret,quia dicereturquod materianon estpotens ad recipiendumformam 15 per potentiamformaliterquae sit ad aliquid, nisi per intellectum;quod est inconveniensdicere, quia hoc dicere est ponere omnem relationem esse ab anima, quod est- ut iste dicit- contra Commentatoremprimo et contraPhilosophumquintoMetaphysicae , qui distinguitinter Physicorum relationemrealem et relationemrationis,et ponit muitosmodos relatio- 20 num realium;ergo et cetera. Secundo istearguitcontraprimamconclusionemmeam et secundam per dicta mea in quibusdam aliis conclusionibus.Nam una conclusio mea est quod convenientiaessentialiseffectuumest secundum dependentiam eorum ex eisdem causis in univocis,vel secundum dependen- 25 tiam unius ab altero ut in analogis. Et hoc in sequenti determinatione magis declarabitur. Tunc contra primam conclusionem meam arguit sic. Homo et asinus non ut dependentessunt diversivel saltemnon conveniunt,ergo ut dependentesadhuc ab eadem causa sunt diversivel saltem non conve- 30 niunt.Quod est contrame. Et patet consequentia,quia dependentiailla nihiladdit in re, ergo reduplicatavel non reduplicatanon mutatveritatem. Similiterdiceturquod homo et asinus accepti non ut conveniunt, sunt diversi,ergo accepti ut conveniuntsunt diversi,cum convenientia 35 nihiladdat in re. Sed hoc consequens est falsum,ergo et cetera.
InPhysica 18 Averroes, 5, 15 1,7,fol.41rE-F 19 Aristoteles, Metaphysica K 34 sunt2] om.P | cum]om.P 13 si]quasiP: quiasiK 28 arguit sic]sicarguitur
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intentione Buridani) {De sincera Ista igitursunt quae alii dubitaveruntcontra conclusiones quas posui prius. Quibus repetitisprocedam iterumsic. Primo repetam responsiones quibus istivolueruntevadere radones quibus conclusionesmeas pro5 baveram. Et huiusmodievasiones tollam,ut radones meae in vigoresuo non solum remaneant apud provectos,sed etiam apud iunioreslucide appareant remanere.Postea removeboradones illorumquas iam reperii. 165raK Et ad differentiam ponendam interillos duos doctoresqui in praesenti mihi contrariantur, ego vocabo unum Picardum et alterum proposito 10 Anglicum,quia Parisiusnomine communi unus est de natione Picardorum et alter de natione Anglicorum.Et protestorquod nihil mali intendo,sed solum addiscere et sustinereillud quod mihivideturverumet alia quae ad haec sequuntur.Et supplico quod sitfas unicuique nostrum imponerealteriomnem metam inconvenientiaein speculativis,nihilta15 men in moribusaut in fide. rationum ( Recapitulatio opponentium) Anglicus ergo ad primam rationem meam de dependentiisrespondet quod effectusabsolutusdependet ab agente per dependentiamsibi realiteradditam. Sed illa dependentiase ipsa dependet ab agente,et non per 20 aliam dependentiam realitersibi additam. Et eodem modo respondet Picardus. Sed quando dicitur:"Non est aliqua ratio cogens quod unum illorum in dependendo ab agente magis requiratdependentiamsibi realiteradditam quam alterum",ad hoc dicit Anglicus quod immo, quia regula 25 est, ut dicit, quod quando aliquid inest aliquibus accidentaliteret denominative,oportetquod insit alicui formaliteret quidditative.Modo omnia absoluta dependent accidentaliteret denominativeper dependentiam,ideo oportetquod dependentiase ipsa dependeat formaliteret quidditative. 30 Item ad idem. Iste alibi assignat aliam rationem,quia scilicet absolutumbene potest fundarerelationemrealem, sed relatio non potest fundarerelationemproptertria:primo quia essetprocessusin infinitum, secundo quia relatio esset relativa,tertioquia tunc essent plures modi
14-15 tamen] etnonP 17 meam]mecum I
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relationumdistinguendipenes fundamentaquam tria,cuius oppositum istedicitesse notumex quintoMetaphysicae. Picardus autem aliam rationem assignat in hoc, scilicetquod absolutum dependet per additum,et relativumnon. Hoc enim est, ut dicit, quia natura in formaliterabsoluto debuit et potuit facere talem addi- 5 tum, sed hoc natura non potuit neque debuit in formaliterrespectivo. Natura quidem in absoluto debuit,quia non potuitaliquod ens formaliterabsolutumfacerehabere habitudinemad alterumper se ipsum. Et ipsa potuit,quia ens formaliterabsolutumest tantae virtutisquod in eo potest fundarirelatio realis superaddita. Sed in respectivonatura non 10 debuit, quia potuit causatum formaliterrespectivumfacere dependere per se ipsum. Nec etiam potuit,quia ens formaliterrespectivumnon est tantae virtutisquod in eo possitfundarirelatiorealissuperaddita. Et sicutdictumest de dependentiaeffectusex causa agente,ita ipsi respondentde dependentiaex finevel ex materiavel ex forma,nisi quod 15 Picardus de dependentiamateriaea formadicitquod materiadependet a formaper dependentiamadditam. Et cum dicitur:"Illa dependentia informatmateriamet ita materia dependet ab ea", ipse concedit quod aliquo modo dependet ab ea, sed dicit quod hoc est sine aliquo addito. Et cum dicitur:"pari ratione standumerat in primo", dicit quod non, 20 quia in primo natura debuit et potuit, sed non in secundo. In primo quidem natura debuit,quia oportetut materia dependeat ex sua causa per se dante sibi esse substantiale;et hoc non potest esse per se ipsam. Etiam naturapotuit,quia tam materia quam formasuntentia absoluta, ita quod unum potuitfundaretalem relationemet aliud terminare.Sed 25 in secundo natura non debuit, quia illa dependentia non dat materiae aliquod esse substantiale,sed esse accidentale solum. Et ideo natura non debuitesse sollicitade dependentiamateriaeex tali causa. Etiam natura non potuit,quia illa dependentiaest ens formaliterrespectivum,et ideo non potestterminaretalem relationem.Nam omne illud quod terminât 30 dependentiam alteriusoportet ipsum esse independens independentia opposita dependentiae illius cuius dependentiam terminât:nam aliter Et ad istam intentionemdicit non plus terminareiquam terminaretur. Commentatorquarto Physicorum quod nisi locus quiesceret,frustraloca35 tum moveturad ipsum. InPhysica 2 Aristoteles, 4,4,f.140rA 5, 15,1020b26-3234 Averroes, Metaphysica dicitP 19 sed... addito]om.K 20 dicitur] sicA' 17 dicitur] 1 tria]om.P 14 sicut] K 23 hoc]om.K 33 Et]om.K natura dicitP 22 materia]
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Quia rationemmeam de qua nunc locutum est credo esse demon- 165vaK strativamsi modo debito sustineatur,et non est a demonstrationerecedendum occasione responsionumcavillosarum,quia sic fortescientia posset in ignorantiamvertivel in deceptionem,ideo declarandum est 5 quo modo deficiuntrationesnunc statimrecitatae. Et est advertendumprimo quod ambo priusdietimaģistriin hoc concordantmecum, quod in relationibusrealibussubordinatisnon contingit in infinitum procedere. Secundo concordantmecum quod dependentia habens causam dependet ex illa causa, et edam quod convenientiaalilo qua convenitsecundum speciem alteri convenientiaecum qua est eiusdem speciei,et est diversaspecificeab aliqua alia relationecum qua non est eiusdem speciei; et similiterde diversitate.Tertio concordant mecum in hoc quod super dependentiameffectusex sua causa non potest fundarirelatio realis. Et eodem modo concordant quantum ad hoc de 15 convenientiaet diversitate, sicutapparebitpost. Sed mihi discordant,quia dicunt effectumabsolutum non posse a causa dependere nisi per dependentiam realitersibi additam, nec altericonvenirevel esse diversumnisi per convenientiamvel diversitatem realiteradditam. Secundo discordantmihi, quia dicuntrelationemnon 20 posse fundarealiam relationem.Et per ista duo voluntrationemmeam annullare. ('Conclusiones Buridani) responsoriae Volo ergo contra ista declarare quinqué conclusiones.Prima est quod 242rP relatio potest fundarisuper relationemita quod alia et alia formaliter 25 sive essentialitereritrelatiofundanset relatiofundata. Secunda est specialiterdescendendo ad propositumquod essendo dicto modo relationemfundantemaliam a relatione fundata,tamen dependentia potest fundarisuper dependentiam et super convenientiam et super diversitatem,et similiterconvenientiapotestfundarisuper de30 pendentiamet convenientiamet diversitatem,et similiterdiversitassuper dependentiamet convenientiamet diversitatem.Et loquor hic accipiendo dependentiam,convenientiamet diversitatemprout sunt essentialiterrespectussive relationes.
5 rationes] K 9-10 aliqua]aliaK 27 fundantem] P 31 fundante responsiones K | Etloquor]om.K convenientiam] consequentiam
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Tertia conclusio erit quod si dependentiae vel convenientiaevel di165vbK versitatesquae sunt relationesfundataesuper res absolutas,sunt reales, tunc etiam convenientiaevel diversitatesvel dependentiae, quae sunt relationesfundataesuper praedictas dependentias,convenientiasvel di5 versitates,eruntreales. hamodo res erit causatum absolutum conclusio quo quod Quarta bens causam potestesse absoluta, dependet se ipso essentialitera causa circumscriptoomni eius accidente,sive absoluto sive respectivo. Quinta conclusio erit quod dependentiae,convenientiaevel diversitates,quae sunt relationesfundatae super res absolutas,non sunt in re 10 praeteranimam. (Probatio primaeconclusionis) Primam conclusionem probo sic. Quaecumque relatio fundata super aliquod absolutum est posteriornaturaliterilio fundamentoabsoluto, īsta, credo, concediturab omnibus. Sed illa posterioritas,qua illa re- 15 latió, puta paternitas,est posteriorsuo fondamento,est quaedam relatio. Ista est necessaria specialiterapud illos qui dicunt dependentiam effectusa causa esse relationem,quia non minus illa posterioritasdicit habitudinemad fundamentumquam illa dependentia ad causam, vel etiam quam diversitasSocratis ad illud cui est diversus.Sed ista 20 posterioritasnecessario fundatursuper illam relationem,puta paternitatem,in habitudinead fundamentumipsius paternitatis.Hoc apparet ex terminis,quia aliternon diceremusquod paternitasest posteriorfundamento suo. Etiam ficticiumesset quod illa posterioritasesset relatio sine fundamento.Et absurdum esset quod fundareturtamquam super 25 immediatumfundamentumsuper fundamentumpaternitatis,cum illud fundamentumnon dicaturesse posterius,sed prius.Nec fundatursuper animam, capiendo fundamentumprout hic loquimurde eo, scilicetpro ad aliud. Hoc patet,quia eo quod relationefundatasuperipsumrefertur dicendo "Paternitasest posteriorsuo fundamento"non referimusani- 30 sed solum ipsam paternimam ad illud fundamentumtali posterioritate, tatem;ergo paternitas,quae est relatio,fundatposterioritatem, quae est alia relatio.Et sic relatiouna potestalteramrelationemfundare. licetsit Sed mihivideturquod Picardus diceretquod illa posterioritas, est Ideo a alia relatio non est tarnen alia, 35 relatio, probo quod paternitate. K inv. K 28 loquimur] 21 illamrelationem] loquuntur
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quia relationesquae sunt ad diversos terminossunt diversae necessario. Nam omnes concesseruntusque nunc quod relationesdistinguuntur166raK ad distinctionemterminorum,quod est quia esse relationisest ad suum terminům.Sed constatquod paternitaset illa posterioritasad diversos 5 terminosdicuntur,quia paternitasad filiumdiciturseu ad ilium qui est filius,sed illa posterioritastamquam ad propriumterminůmdiciturad patrem seu ad ilium qui est pater.Quod patet ex vi verborum,quia dicimus quod paternitasest posteriorsuo fundamento,scilicetilio qui est pater. Isti duo magistřifortefugiendodicerent,sicut iam videtur Anglicus dixisse,ut post videbitur,quod intentioeorum est quod relatiorealisnon fundatursuper relationemaliam, sed relatiorationisbene. Ideo dicereturquod illa posterioritasest relatiorationis.Sed licetsic dicendo concedatur haec prima conclusio mea, tarnenadhuc volo ostenderequod ilia 15 posterioritasnecessario concedenda est ab eis relatio realis et distincta a paternitate.Hoc enim probo per radones eorum, quibus arguebant 242vP quod dependentia causati absolūti ex causa est relatio realis distinctaa causato. Primo per primam rationemPicardi sic. Si posterioritaspaternitatis 20 ad eius fundamentumnon adderei aliquid reale in paternitate,sequereturquod in paternitatenullus esset respectusnisi ad filium.Ista paab albedine sicut respectivumab tet,quia paternitasprout distinguitur absoluto, nullam habitudinemdicit nisi ad filium.Ipsa enim non dicit formaliter habitudinemad suum subiectumtamquam ad terminůmplus 25 quam accidens absolutum,cum impossibilesit relationemeandem dici formaliter ad diversosterminos,ut dictumfuitet magis diceturpost. Sed si in paternitatenihil sit formaliterrespectivumnisi ad filium,tunc paternitasnon habebithabitudinemad suum subiectumvel fundamentum. Et per consequens non eritnaturaliterposterioreo, quia posterioritasest 30 quaedam habitudo. Sed istud consequens non minus est falsumquam quod causatum non dependeat a causa, et hoc dato quod anima non intelligeret. Item. Per secundam rationemipsius arguitursic. Quandocumque de aliquibus circumscriptoomni opere intellectusverificaripossuntcontra35 dictoria,ilia sunt diversa realiter.Sed sic est de paternitateet de eius posterioritatead suum subiectum,quia dato quod non intelligeremus,166rbif 10
1 suntdiversae] iter. K 16 enim]estK | quibus]quiK 17 excausa]om.P 21 resP 34 intellectus] P | possunt] esset]eritK 32 intelligeret] intelligit intelligimus P prout
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tarnenpaternitasesset formaliterhabitudo ad filium;sed posterioritas qua ipsa est posteriorfundamentonon est habitudo formaliterad fi- nisi dicas lium, sed ad fundamentumpaternitatis quod eadem relatio est formaliterad diversosterminos,quod non est concedendumnec iste concedit,quia in tertiarationesuae quartae conclusionisipse contradi- 5 cit quod si Socrates vixeritper decern annos et hodie generaturPlato, necesse est quod in Socrate sitde novo generataidentitasquae est idem specie Platoni. Probatio,quia est idem ei et priusnon erat. Modo ex hoc non posset concludi talisgenerationovae identitatisin Socrate,si eadem dici ad diversosterminos,quia diceremquod ad 10 relatiopossetformaliter esse Socratem eundem Platoni sufficitidentitasquam praehabebat ad Iohannem, vel alia relatioquaecumque in eo praeexistens. Item. Per rationemAnglici arguitursic. Paternitasest posteriornaturalitersuo fundamentodato quod non intelligeremus;et non est posteriornisi per posterioritatem;ergo posterioritasest praeter animam 15 relatiofundatasuperpaternitatem,sicutipse arguebatquod effectusdependei ab agente dato quod anima non intelligeretet non dependet nisiper dependentiam.Ergo dependentiaest relatiorealisfundatasuper causatum. Et sciendum quod, sicut argutumest de paternitateet de posterio- 20 ritateeius ad suum fundamentum,ita posset argui de omni relatione Et sicut de poquam istiponerentesse realem, et de sua posterioritate. inhaerentia ita de eius sterioritate est, argui potest paternitatisargutum ad suum subiectumaut de eius dependentiaex aliis causis,et universaliterde omni habitudinehabente originemex natura rei secundumquam 25 nos possemuspaternitatemcomparare ad quodcumque aliud. Dico ergo colligendo ea quae iam in hac prima conclusioneprobata sunt, quod primo probatum est quod super relationempotest fundari relatio. Secundo quod relatio fundansest alia a relatio fundata.Tertio 166vaK quod per rationesillorumnon solum concluditurquod relatiofundans 30 est realis, sed etiam quod relatio fundataest realis. Et quia ipsi dicunt hoc esse falsum,ideo sequiturquod suae rationesnon erantdemonstrativae,sed sophisticae. contra conclusionem) (Solutiorationum primam 1 esset]estK 2 ipsa]ipseK 3 nisi]nonP 4 quod]quia P 8 Modo]ideo K P 23 arguipotest] inv. K 10 dici]om.P 20 de2]om.P 22 ponerent] poneret 27 hac]hancK
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Tunc volo solvereradones eorum quibus nisi suntprobare quod relatio non fundatrelationem.Prima rado Anglici erat quod esset processusin infinitum.Sed ponendo has relationesab anima ego sibi concedo, quia anima non potest in infinitumreflecterese super se et suam operatio5 nem. Alia ratio sua erat quia sequereturquod relatioessetrelativa.Sed hoc 243rP non reputo inconveniensin entibus animae, nam scientia est scita et intellecta. intelligentia Alia ratio sua erat quia tunc essentplures modi relationumquam illi 10 tres quos posuit Aristotelesquinto Metaphysicae. Dico quod non, quia dependentiaex causa debet ad tertiummodum reduci semper,sed convenientiadebet reduci ad illas relationesquas Aristotelesdicebat sumi secundumunum, cuiusmodisuntidem, aequale et simile.Et e converso diversitasdebet reduci ad relationessumptas secundum multa. Et hoc 15 est valde darum. Ratio vero Picardi prima fuittalis. Capiendo earn generaliter,natura non facitpluribusquod potest facere uno; sed ens formaliterrespectivum potestreferriad aliud sine aliquo superaddito,cum ipsum sit formaliteret essentialiterad aliud se habens; ergo natura ad referendum 20 ipsum nihilfacitin eo superadditum.Dicendum est concedendo maiorem. Sed ad minorem dicendum est quod ens formaliterrespectivum refertur se ipso sine addito ad suum propriumterminům,sed dico quod ad quodcumque aliud ab ilio proprioterminoipsum non magis se ipso refertur quam accidens quodcumque absolutum.Et voco propriumter25 minum entis formaliterrespectivigeneraliterillum a quo respectivum ab absoluto. Et voco propriumterminůmalicuius entisfordistinguitur maliterrespectiviin speciali illum a quo unaquaeque relatio ab omni alia relationedistinguitur. Verbi gratia,in generalidico quod relationon ab accidente absoluto distinguitur per habere subiectumvel causam ef30 ficientemvel finalem,quia haec omnia habet accidens absolutum; sed ab absoluto per habere se ad terminůmad quem de essendistinguitur tiali significatoet conceptu dicit habitudinem.Verbi gratia, similitudo de suo significatoet conceptu essentialinon dicit habitudinemad suam 166vbK causam efficientem, nec ad suum finem,nec ad suum subiectum;sed 10 Aristoteles, 5, 15, 1020b26-32 12 Aristoteles, 7, 6b20-27; Metaphysica Categoriae , 15,1021a9-10 Metaphysical 1 quibus]quiK 4 non]om.P 6 quiasequeretur] om.K 8 intelligentia] intellectio K 9 quia]quodK | quam]quodK 26 proprium inv.K 28 alia] terminům] alteraK
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dicit solum habitudinemsubiectisui sive sui fundamentiad illud quod est ei simile.Similiterexemplificoin speciali. Si sex suntduplum ad tria et triplůmad duo, dico quod istarumrelationumterminipropriinon Sed sunt suum subiectum,scilicetsex, quia per hoc non distinguuntur. sui terminipropriisunt dimidium et subtriplumsive duo et tria, nam 5 per ista duplum et triplůmfundata in senario vel super senarium diDico ergo quod si dependentia,quae est relatiocausati ad stinguuntur. causam, sic ad propriumterminůmreferaturad suum subiectumvel fundamentum,sicutcum dicimusipsam esse posterioremnaturalitersuo fundamento,illa non magis referturad illud subiectumse ipsa quam 10 accidens absolutum ad suum subiectum,quia ipsa, ut est relatio,non magis est essentialiteret formaliterad suum subiectumquam accidens absolutum,sed solum,ut est relatio,ipsa est essentialiteret formaliterad propriumterminům,scilicetad causam. Et sic potestdici de paternitate 15 et omnibusaliis relationibusquas istidicuntesse reales. Secunda ratio istiusfuitquia fundansrelationemdependentemdebet esse independens,aliternon plus fundaretquam fundaretur;sed relatio non est independens;ergo non potestfundarerelationem.Dicendum est ad maiorem quod fundansrelationemdebet esse independensad illum terminůmad quem dependet relatio fundata tamquam ad terminům 20 propriumet formalem.Sed possibile est quod dependeat ad alium terminům. Verbi grada, paternitas,ut visum fuit,fundatposterioritatem; illa autem posterioritasdependet ad prius ut ad terminůmproprium; ideo paternitasnon dependet ad priusut ad terminůmproprium,sed ad 25 filium. Tertia ratio istiusfuitquia procedereturin infinitum.Sed ad hoc iam responsumfuit. Adhuc est alia ratio istius,scilicetquia super relationemnatura non debuit fundare,nec potuit,aliam relationem.Primo dicit quod non de94.Q, jp Potu^ facererelationemreferriper se ipsam. Sed ad hoc iam 30 167raK ^11^' dictumest quod verum est ad terminůmsuum proprium,sed non plus potuitrespectivumquam absolutumfacerereferrise ipso ad aliud quam ad suum terminůmproprium. Item. Dicit quod natura non potuit relationemfundaresuper relationem,quia ens formaliterrespectivumnon est tantae virtutisquod in 35 eo possit fundarirelatio realis. Sed ad hoc dicendum est quod ad fundandum relationemnon requiriturquod fundamentumhabeat aliquam P 23 utad terminům] P 8 sic]sicutKP 21 possibile] 6 fundata] fundato probabile K iter.
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virtutem,nisi aliquis velitomnem entitatemvocare virtutem.Sed in intellectuestvirtusqua potestsive absolutumsive respectivumconferread aliud, et sic formarevel efficererelationemsuper illud tamquam super fundamentum.Immo potestdici quod quia relatioest minimaevel nul5 lius virtutis, ideo non potestintellectuiresisterequin intellectuscomparet earn alteriquam suo terminoproprio,et per consequens quin possitsuper eam fundarerelationem. Item. Si fundamentumdebeat habere aliquam virtutemad hoc quod possit fundarerelationem,quod non credo, tunc dicendum esset quod 10 relatio virtutemtalem habet, cum probatum sit quod de facto relatio fundatursuperrelationem.Et ut sic ad unum dicere,non suntnisiverba in dicendo quod hoc habet virtutemet hoc non, nisi ad hoc adducatur ratio efficaxquare sic est in hoc et non sic in ilio. Iterum. Ut expediar de hoc quod iste dixit quod relatio non potest 15 terminarerelationem,quia omne quod terminâtdependentiamalterius oportetquod sitindependensindependentiaopposita dependentiaeillius - nam aliter non cuius dependentiam terminât plus terminareiquam terminaretur ad hoc brevitersufficeret dicere sicut de fundaredictum fuit.Sed tarnencausa solacii et propter addiscere debet dari talis di20 stinctiode terminorelationis.Relatio duplicem habet terminům,scilicet formalemet materialemsive fundamentalem.Terminusformalisest relatio alia correspondensilli et sibi opposita relative,terminusfundamentalisvel materialisest fundamentumrelationisquae est terminus formalis.Verbi gratia,paternitatisterminusformalisest filiatio,et eius 167rbK 25 terminusmaterialisest fundamentumfiliationis.Et sic duae relationes quae ad invicem opponunturrelativeterminantse invicem formaliter, et ad invicemdicunturformaliter.Ideo dictum est in libro Praedicamentorum quod omnia relativa,si convenienterassignenturad illud ad quod dicuntur,oportet quod dicantur ad convertentiam.Sed materialister30 minus paternitatisest illud super quod fundaturfiliatio.Et tunc relatio et illud ad quod diciturnon dicunturad convertentiam,propternon bonam, id est non formalemassignationemtermini.Et hoc totumdéclarai pulchre Aristotelesin Praedicamentis et beani sciunt,ideo transeo. Et sicutdixi de dici ad convertentiam, ita debet dici de esse simulnatu35 raliter. 27-28 Aristoteles, 7,6b28 Categoriae 6-7 superearn]iter. K 13 sic]sicutK K 34 de esse]ad esseK determinai
22 relatioalia] ino.K
32-33 declarat]
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Dico ergo quod terminusformaliscuiuslibetrelationisest essentialiter relatio,et sic est dependens formaliterad aliud. Sed hoc non est ad illud ad quod dependet relatioquam terminât.Et sic terminus,licet sit formaliterdependens,tarnennon dependet illa dependentia quam teret requiritur5 minât,sed est talisdependentiaindependens.Et hoc sufficit ad esse terminůmformalemalicuius relationis.Verbi gratia,paternitas dependet ad filiationemet filiatioad paternitatem,etiam paternitasterideo non dependet dependentiafiliatiominât dependentiamfiliationis, nis. Et sie etiam filiatioterminâtpaternitatem,ideo dependentia quae est paternitasnon dependet. Et si dicaturibi: "ergo est circulus",et ego 10 244rP concedo si velis extremaoppositionisvocare circulum,aliternon. Et si dicas: "Numquam terminabiturdependentia si terminaturad dependens", dico quod numquam terminabitursic quod ipsa non sit amplius Nam paternitassic terdependentia,sed terminabiturquantum sufficit. minaturad filiationemquod non diciturad aliquid ultra formaliter, et 15 sic etiam filiatioterminaturad paternitatemquod non diciturformaliter ad aliquid ultra,sicutunus punctussic terminâtlineam quod ipsa ex illa parte non proceditultra,et alterpunctussic quod non proceditultraex 167vaK altera parte. Sed de terminomaterialidico quod ipse est independens tam dependentia relationisquam fundat,quam dependentia relationis 20 oppositae. Ideo optimepotestet fundarerelationemet terminarematerialiter,licetsitvere dependens ad aliud aliqua vera dependentia. secundae (Probatio conclusionis) Deinde probo secundam conclusionem,quae erat descendendo ad propositum. Et probo primo quod super diversitatemfundaturdependen- 25 tia, quoniam si Socrates est diversusa Brunello diversitatespecificasibi realiteraddita, sicut isti dicunt, oportet quod illa diversitassit in Socrate tamquam in subiecto. Ergo dependet a Socrate, et hoc non est nisi per dependentiam,sicutipsi arguunt.Tunc ergo vel ista dependentia fundatursuper Socratem tamquam super fundamentumproprium 30 et immediatum,aut super diversitatemSocratis ad Brunellum.Si super habeo propositum.Si super Socratem,hoc est impossibile, diversitatem, quia tunc Socrates dependerei illa dependentia, quod non est verum: immo diversitasest qua illa dependentia dependet a Socrate. Nec poK 10 ibi]illiK 1 relationis] K 2 aliud]illudK 6 relationis] locutionis rationis K 29 dependentiam] 15 aliquid]aliudÄ* 17 aliquid]aliudK 22 vera]naturali P dependentia
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testdici quod ilia diversitaset illa dependentia sinteadem relatio,cum sintad diversosterminoset diversorum.Nam diversitasest Socratis ad ad Socratem. Et eodem modo Brunellum,et dependentiaest diversitatis probaturquod de potentiafundatursuper convenientiamspecificamSo5 cratisad Platonem,quia ilia convenientiadependet a Socrate. Similiterprobo quod dependentia fundatur super dependentiam, quia forma dependet a materia ita quod super formamfundaturdependentia a materia. Sed illam dependentiam necesse est dependere a forma.Relatio enim dependet necessario a suo proprio fundamento. 10 Modo illa dependentiaquae est a formanon habet pro immediatofundamento formam,quia forma non dependet a forma,nec materiam, quia materia non dependet a forma sicut a fundamento.Ergo restât quod non fundaturnisi super dependentiamformae a materia. Et hoc etiam patet ex vi verborum,quia tali dependentia, scilicetrelationisa 15 fundamento,dicimus dependentiam formae a materia dependere a forma. Nec potest aliquis dicere quod eadem relatio sit dependentia qua formadependeta materiaet dependentiaqua illa dependentiadependet 167vbK a forma.Sunt enim alteriuset alterius,et etiam ad alterum.Una enim 20 est formaead materiam,et alia est dependere ad formam. Ita etiam probo quod convenientiafundatursuper dependentiam, quia dependentia Socratis a suo generanteconvenitspecie cum dependentia Platonis a suo generante.Ergo convenientiafundatursuper dependentiamrespectualterius.Nec potest dici quod convenientiailla et 25 illa dependentia sint eadem relatio, quia sunt aliorum et ad alia. Est enim dependentia Socratis ad suum generans et convenientiaest illius dependentiaead aliam dependentiam.Et sic etiam potestprobari quod 244vP vel superconvenientiam.Simiconvenientiafundatursuperdiversitatem litereodem modo potestprobariquod diversitassuperquodlibet illorum 30 triumpotestfundari.Et sic patet illa secunda conclusio.
P 8 est]om.K 10 Modo] 1 sint]suntP 2 est]om.K 3 diversitatis] diversitas P 14 verborum] materia IdeoK 11 formam, qua P | materiam] quia]formae K 15 dependentiam] P 19 ad] alterum et K 24 alterius] illorum dependentia P | aliam]illamK 28 super] add.P 27 dependentiae] dependentia dependentiae P om.K 29 diversitas] diversis
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tertiae (.Probatio conclusionis) Deinde probo tertiamconclusionem.Et accipio pro exemplo convenientiam fundatamsuper dependentiam:verbi gratia, Socrates dependei a suo generanteet Plato dependet a suo generante.Et sic una dependentia fundatursuper Socratem et alia super Platonem.Iterumdependentia 5 Socratis convenitspecie cum dependentia Platonis.Et sic super dependentiam Socratis fundaturconvenientia,sicut in alia conclusione videbatur.Probo ergo quod si dependentia fundata super Socratem est relatio realis,quod etiam convenientiafundatasuper illam dependentiam est relatiorealis,quia quandocumque aliqua duo habent easdem causas 10 si unum est reale, alterumest reale. Hoc est realitatisvel non-realitatis, notum per se. Sed illa convenientiaet illa dependentia habent easdem causas realitatisvel non-realitatis. Ergo et cetera. Probatio minoris,quia omnes rationes quibus isti magistřivolunt demonstraredependentiam Socratisesse realem,non minuscontradicuntde illa convenientiaquam 15 de illa dependentia. Nam posito quod dependentia Socratis et dependentia Platonissuntreales secundumistos,ego arguam sic per rationem Picardi primam. Si convenientiadependentiae Socratis ad dependentiam Platonisnihiladderet realiterin illa dependentia,sequereturquod 168raK in illa dependentia nihil esset ut sic quod esset formaliteret essentia- 20 literrespectusad dependentiamPlatonis. Ista consequentia patet, quia licet dependentia Socratis a suo generantesit essentialiteret formaliter respectusad aliud, scilicetad generans,tamen ipsa non est essentialiter et formaliterrespectusad dependentiamPlatonis,tum quia eadem relatio non est essentialiteret formaliterad duos terminos,tum quia etiam 25 corruptoPlatone et eius dependentianon corrumpiturdependentiaSocratis.Et tamen impossibileest relationemmanere sine ilio ad quod ipsa dicituressentialiteret formaliter. Sic ergo clara est illa consequentia.Sed si in dependentia Socratis nihil sit essentialiteret formaliterrespectivum ad dependentiamPlatonis,tunc dependentia Socratisnon habebit 30 habitudinemad dependentiamPlatonis;ergo dependentia Socratisnon conveniretspecie cum dependentiaPlatonis,quia convenientiaunius ad alterum est habitudo ipsius ad illud, ut iste concedit. Sed illud consequens est impossibile,cum illae dependentiaesinteiusdem speciei. Ergo 35 et cetera.
om.P 10 easdem] eademP 25-27 tum 8 est]aliaadd.K 9-10 quodetiam... realis] P om.P 27 manere] remanere ... Socratis]
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Item. Secundum prius dicta, si Socrates convenientiareali convenit Platoni, illa convenientiadependet a Socrate, et sic super earn fundaturdependentia.Tunc arguo quod ilia dependentiaest relatiorealisper secundam radonem Picardi sic. Si dependentiailliusconvenientiaea So5 crate non diceretaliquid reale additumilli convenientiae,sequiturquod illa convenientiaquae est effectusSocratis,non plus referretur ad Socratem qui est causa eius quam e contra,et sic causatum non plus referreturad causam quam causa ad causatum,quod istereputaipro inconvenienti.Et patet consequentia,quia non est dubium quin per relationem 10 habentem esse suum formaleab anima potest Socrates referriad illam convenientiamsicutcausa ad causatum; et tunc sicutipse procedebat tu procedas ultra,scilicetquod non plus illa convenientiaconstitueretur per Socratem quam e contra. Item. Revertorad convenientiamfundatamsuper dependentiam si15 cut in prima rationeaccepl. Et tunc arguo per tertiamrationemPicardi sic. Quandocumque de aliquibus circumscriptoomni opere intellectus168rbiT realiter.Sed sic est de depossuntverificancontradictoria,illa differunt pendentia Socratis a sua causa et de convenientiaillius dependentiae ad dependentiam Platonis,quia dependentia Socratis est formaliteret 20 essentialiterad generansut ad terminům,et non ad dependentiamPlatonis; sed convenientiaest essentialiteret formaliterad dependentiam 245rP Platonis,ut ad terminům,et non ad generans;ergo et cetera. Item per rationemAnglici arguo sic. Corrupto Platone corrumpitur convenientiaSocratis ad Platonem, quia Socrates, qui est homo, non 25 convenitcum ilio quod non est. Sed non corrumpiturdependentia Socratisa sua causa. Ergo illa convenientiaest aliud ab illa dependentia. Nec potest dici quod illa convenientiasit ab anima, si illae dependentiae fueruntpraeteranimam, quia praeteromnem operationemanimae illae dependentiae sunteiusdem speciei. Et sic conveniuntspecie et non 30 nisi per convenientiam.Etiam, si tu diceres quod illa dependentia non convenitformaliterper convenientiamquae sit ad aliquid, scilicet ad aliam dependentiam,nisi per animam, tunc ego similiterpossem dicere quod materia non est potens ad recipiendumformamper potentiam formaliter quae sitad aliquid, nisiper intellectum.Et procede ultrasicut 35 ipse procedebat. Patet ergo quod omnes causae quas isti assignaverunt ad probandum quod convenientiae,diversitateset dependentiae fundatae super absoluta sunt relationesreales, concluduntaequaliter de fun5 diceret] P 8 causaad] causatP differret
11 causaad] causatP
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datis super respectiva.Et sic probata est minor rationisprincipalisad hanc conclusionemtertiam,scilicetquod eaedem sunt causae realitatis vel non-realitatisin convenientiis,diversitatibus et dependentiisfundatis super absoluta et fundatissuper respectiva. Et adhuc confirmatur ilia minor,quia nulla videturratioefficaxquod 5 relatio sit nisi realis, aliqua quod suum naturaleet propriumfundamentům est reale et similitersuus terminus.Si ergo illa sit causa sufficiens, statim sequitur,ex quo dependentia Socratis et dependentia Platonis sunt reales,quod convenientiaspecificaunius ad alteramsit relatiorea168vaK lis. Nec valet dicere quod absolutumpotestfundarerelationemrealemet 10 respectivumnon, quia hoc esset sine rationeponere illud quod quaerimus et de quo disputamus.Nec valentmotiva quibus hoc dictumposset habere apparentiam,sicutiam declaravi prius in prima conclusione.Et ut sic ad unum dicere,pura fictioest dicere sic de uno duorumet non sic de alio, ubi nullae rationesplus probant de uno quam de alio, et quod 15 si rationesfacientesdubitare solvunturde uno, ipsae solvuntureodem modo de alio. Modo sic est hic, ut apparuitper te et plenius apparebit. (.Probatio quartaeconclusioni) Tunc probo quartam conclusionem,scilicetquod causatum absolutum modo quo res habens causam potestdici absoluta, dependet se ipso es- 20 sentialitera causa circumscriptoomni eius accidente,sive absoluto sive respectivo.Et arguo sic. Socrates praeter animam dependet ab agente aut non nisi per resuo. Aut ergo dependet ab ilio se ipso essentialiter, lationem sibi additam. Istam divisionemomnes concedunt. Sed huius divisionissecundum membrumest impossibile;ergo primumest neces- 25 secundimembri,quia si Socratespraeter sarium.Probo impossibilitatem animam dependet ab agente et non nisi per dependentiamsibi realiter additam, tune illa dependentia,cum habeat esse post non-esse,dependet iterumpraeter animam ab agente a quo produciturin esse. Aut ergo se ipsa essentialiterdependet ab ilio agente, aut per aliam depen- 30 dentiam iterumsibi realiteradditam. Secundum non est possibile,quia Nec primumest possibile,quia sequiturquod 245vP procedereturin infinitum. dependentia Socratis,quae est relatiofundatain eo, dependeretab ilio agente prius naturaliteret immediatiusquam Socrates. Consequens est falsum,ergo et antecedens.Probo falsitatemconsequentis,quia oportet 35 in K 6 quod]quiaK 7 similiter] om.K 32 possibile] inv. 2 conclusionem tertiam] K possibilitate
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concedere quod ilia dependentia est accidens existensin Socrate tamquam in subiecto,et per consequens ipsa est posteriornaturaliterSocrate. Modo si ipsa est posteriornaturaliterSocrate, oportetquod ipsa posteriusnaturaliterproducaturin esse ab agente quam Socrates. Cum 5 ergo nec Socrates,nec illa dependentiadependeant ab ilio agente nisi in hoc quod producunturin esse ab eo, sequiturquod illa dependentianon 168vbK dependet prius naturaliterab ilio agente quam Socrates, immo, posterius naturaliteret mediante Socrate, sicut effectusper accidens alicuius agentisdependet ab ilio agente medianteeffectuper se. 10 Tunc probo consequentiam,quia illud quod se ipso essentialiterest aliquid, est illud aliquid prius naturaliteret immediatiusquam illud sed solum per alterum. quod non est illud aliquid se ipso essentialiter, Si ergo dependentiailia est se ipsa dependens essentialiterab agente,et Socrates non nisi per illam dependentiam,patet quod illa consequentia 15 erat necessaria. Et confirmoarguendo in modo loquendi quorundam sic. Certum est quod Socrates est prior naturaliterquacumque dependentia quae est accidens ipsius. Tunc ergo in ilio signo pro quo Socrates est prior naturaliterilla accidentalidependentia,vel ipse dependet ab agente a quo 20 producitur,vel non. Si sic, ergo se ipso essentialiteret non per dependentiamadditam. Si non, ergo pro ilio signo non dependet ab ilio a quo producitur;quod implicat contradictionem,quia pro alio Socrates ab agente suo dependere non diciturnisi quia ab eo in esse producitur. contra conclusione (Solutiorationum quartam m) 25 Tunc respondeo ad rationes aliorum contra istam conclusionem. Ad cuius evidentiamest sciendum quod sicut causa aliqua potest esse per se vel per accidens alicuius effectus, ut domificatorest causa per se domus et musicusest causa domus per accidens, ita aliquid potestdependere ab alterodupliciter:uno modo per se et essentialiter, alio modo per 30 accidens. Iterumper se dupliciter,quia uno modo aliquid dependet ad alterumessentialitertamquam ad terminůmcum quo est simulnatura, et diciturad convertentiam:verbi gratia, paternitasad filiationem.Et tale est essentialiterrelatiovel de genere vel de praedicamentorespectivo.Alio modo aliquid dependet essentialiterad alterumtamquam ad 3 Modo]IdeoK 11 aliquid1] aliudP | aliquid2] aliudP 12 aliquid]aliudP 19 ab agente] om.K 25 istam] istaK 28 domusperaccidens] domus peraccidens K 33 velde2]seuK
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illud per quod est,tamquam per illud quod est causa eius et prius naturalitereo. Et sic quodeumque ens praeterDeum dependet essentialiter ad aliud vel ab alio, quia prima substantiacausata a Deo non solum 169raK est a Deo vel propterDeum secundum sua accidentia, si habeat aliqua accidentia,sed etiam secundum suam essentiam.Et tale dependens 5 non oportetquod sit essentialiterrelatio sive de praedicamentorespectivo,quia iam dictum est quod a tali dependentia nihil absolvitur,sive secundum suam substantiam,sive secundum sua accidentia,nisi Deus. Sed dico quod aliquid dependet accidentaliterad alterumper hoc quod aliquid sibi additumvel attributumdependet. Et hoc est dupliciter:aut 10 quia immediatefundatillud quod essentialiterest ad alterum,aut quia Verbi gratiade primo: haec albedo ad illam 246rP illifondamentoconiungitur. aliam albedinem dependet, quia similitudofondata super eam dependet. Sed verbi gratia de secundo: nix dependet ad cygnumdependentia similitudinis, quia coniungituralbedini super quam fondatursimilitudo 15 essentialiter dependet. Et iste modus est magis per accidens quam quae Et adhuc prior. possentdari alii modi magis per accidens,sed non curo. Sed scias quod in his essentialiterse ipsisdependentibusnihilest aliud in re praeter animam dependens quam dependentia qua dependet essicut non est aliud in re praeter animam ens et entitasquae 20 sentialiter, est ens, nec esse rei et essentiaqua res est,sicutnunc suppono et alias, si possum, declarabo. Nec mirerisquia loquendo specialiterde dependentia qua res essentialiterdependet ex causa, sive res illa sit absoluta sive respectiva,vel loquendo de causalitatequa res essentialiterest causa, licet sit absoluta, ego puto quod dependens et dependentia,et causa et 25 causalitas sunt nomina transcendentia,quae rebus cuiuslibetpraedicamenti possunt applicari, et quae praeter animam nihil multiplicantin rebus quibus applicantur.Dimitto tarnennunc loqui amplius de huiusnisi quod adhuc dico quod sicutnon modi nominibustranscendentibus, differt entitaset res quae diciturens, vel unitas et res quae dicituruna, 30 nisi per nostrummodum intelligendi,ita non differtin praedictisde169rbK pendentiaet res quae diciturdependens,nisi per nostrummodum intelligendi. Quo modo autem per modum intelligendidistinguanturpraeEt alias, si potuero per Dei gradicta, debet videri quarto Metaphysicae. 35 tiam,declarabo. 34 Aristoteles, 4, 2 Metaphysica K | etiam]etP 9 ad] perK 11 fundat] a materia 2 ens]om.K 5 accidentia] K 32 modum] om.K 33 distinguantur] K 24 essentialiter fundet distinguatur est]inv. P
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Tunc dico ad primam radonem Picardi, quae videtur esse contra istam quartam conclusionem,et contra quintam, quam nunc suppono et postea probabo. Quando dicitur:"Si dependentia causati formaliter absolūtiex sua causa nihilreale multiplicareiin causato, tunc in causato 5 nihil esset nisi formaliterabsolutum", dico quod verum est prout abcontra dependens ad terminůmcum quo est simul solutumdistinguitur natura et diciturad convenientiam.Sed bene est ibi dependens a causa, quia dixi illud causatum esse dependens essentialitera causa. Et quando dicitur:"ergo causatum non habet habitudinemad causam", concedo 10 loquendo de habitudinequae est de praedicamentorelationis.Sed si tu velisvocare habitudinemillam dependentiamqua tale causatum dependet essentialitera causa, quae non est aliud quam sua essentiapraeter nostrummodum intelligendi,tunc dico quod causatum illud habet habitudinemad causam. Et isto modo breviterpatet quod causatum est 15 causatum et se habet ad causam sicut dependens ab ea se ipso, et non per habitudinemvel dependentiamquae sit de praedicamento relationis, sed quae est ipsamet substantiacausati. Tamen anima secundum exigentiamnaturarumintellectarumpotest causam et causatum ad invicem conferre,et sic formaresuper eas relationesmutuas, quae vere 20 dicunturad convertentiamet sunt simul natura, quia intellectusconferendonon potest intelligerehoc esse causatum ab ilio quin intelligat illud esse causam huius et e contra. Ad secundam rationem eius, quando dicitur: "tunc causatum non ad causam quam causa ad causatum", dico quod causaplus referretur ad causam relationedistinctaab ipso quam causa 25 tum non plus refertur ad causatum. Sed dico quod causatum magis dependet a causa quam 246vP e contra, loquendo de omni dependentia, quia licet ipsum dicatur ad causam per relationemfundatamsuper ipsum et e converso,tamen cum hoc causatum dependetse ipso essentialitera causa, cum habeat esse ab 30 ea, et non e converso.Et de isto esse aliquid seu de isto dependentivel 169vaK relativo,aut quo modo vis nominare,quo quidem esse effectusest essentialisa causa et quod quidem esse non est aliud quam essentiacausati, debet intelligiquod unum constituitur per alterum,et non e converso. de necessitate rei est effectusest quod sua substanSimiliter,quia quae 35 tia sit ab alio, ideo non potestperfecteintelliginisi per illud a quo est ex parte sua posset intelligiperfectesine alio. Licet ergo anima formet 1 Tunc]om.P 11 illam]illaK 17 sed]Si P | substantia] om.P 19 formare] om.K 21 esse]estK 23 quandodicitur] om.K 24 plus]om.P 24-25 causatum] om.K 34-35 substantia] causaK
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super causam et causatum relationesad invicem,tarnenrelatiofondata super causatum dicituresse in substantiaeius non subiective,sed fundamentaler, et in anima subiective.Et relatio fondata super causam non dicituresse in substantiaeius, propterhoc quod effectusper necessitatemsuae substantiaeest fondativustalis relationis,et non causa, vel 5 propterhoc quod intellectusnon potestperfecteintelligeresubstantiam effectussine collatione eius ad causam. Non sic autem est de causa. Et hoc in idem redit.Et secundum hanc veram sententiamdebent intelligi verba Aristoteliset Commentatoris. Ad tertiamrationem istius dicendum est quod de causato absoluto 10 et de dependentia quae est relatio fondata per animam super ipsum, verificantur contradictoria,sed non praeter animam, cum talis dependentia sit ab anima. Sed dico quod de ilio causato et de essentialidecontradictoriapraeteranimam. pendentia eius a causa non verificantur Et quando dicitur:"Illud causatum non est formaliterhabitudo cum sit 15 absolutum",dico quod ipsum non est habitudo vel dependentiaad terminům cum quo sit simul natura et dicatur ad convertentiam.Et ita dico quod ilia essentialisdependentia non est talis habitudo, sed dico quod illud causatum absolutumesse essentialiterdependentiaa causa a Et si tu velis vocare illam 20 qua ipsum est illud quod est substantialiter. essentialemdependentiam habitudinemessentialem,tunc dicam quod causatum absolutumest essentialitertalis habitudo,sicutvisumfuit. Ad primamrationemAnglicidicendumest quod in ea suntsex defectus. Primo deficitquia dicit quod omnem relationemesse ab anima est contraAristotelemet Commentatorem.Dico enim quod numquam Ari- 25 stoteleset Commentatorhoc negaverunt.Et dico ut dem aliis materiam ut mihi alias visum fuit,ad probandum studendi,quod ratio difficilior, 169vbK quod aliqua est relatio realis,est quia similitudoet dissimilitudoapparent sensui exteriori,ergo proveniuntintellectui.Sed forteposset dici quod sensus est virtusanimae cognoscitivaequae ita potestconferreet 30 per consequens relationesformareinterea quae per se sentit,sicut intellectusinterea quae intelligit.Sed de hoc non me determinoquoad nunc. Secundo deficitdicendo quod dicere potentiammateriae et dependentiasa causis et diversitateset convenientiasesse ab anima, est dicere 35 omnem relationemesse ab anima. Hoc autem est falsum,sicut dicere quod homo et equus habent pedes non est dicere quod omne animal habet pedes. 28 realis]quaeadd. P 29 forte] quodadd.KP 32 de]ad P
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Tertiodeficitquando vultprobare quod dependentiacausad ab agente est diversa a causato. Primo enim arguit sic: quia dependentia Socratisa suo generantecorrumpiturcorruptogenerante,et tarnenSocrates non corrumpitur.Dicendum est quod si capitur dependentia prout 5 est a causa, non sicut ad terminůmcum quo sit simul natura, tunc vel Socrates secundum suam substantiamdependet ab ilio agente, et sic dico quod illa dependentianon corrumpitursubstantiaSocratismanente, nam quod inest alicui secundum se semper inest sibi ipso manente; vel Socrates dependet ab agente non secundum suam substan10 tiam, sed solum secundum suum fieri,et tunc dicam quod ilia dependentia non est eadem Socrati secundum suam substantiam,sed secundum suum fieri. Item. Quando ipse addit quod Socrates est de praedicamento sub- 247rP stantiaeet dependentiaest de praedicamentorelationis,hoc solutumfuit 15 per distinctionemde dependentia. Quarto deficitquia concesso secundum ipsum quod potentia materiae ad formamgenerandam sit praeter animam, ipse non potestprobare illud quod intendit,scilicetquod dependentia Socratis a suo generantecorrumpaturcorruptoilio generante,dum tarnenSocrates ma20 neat, quia potentia materiae est ad terminůmqui non est sed erit in futuro.Ergo ad relationemesse realem non requiriturexistentiatermini, sed sufficit quod eritde futuro.Modo ita potero dicere quod dependentia Socratis ab agente est realis quia suus terminusfuit.Hoc enim sufficit.Nec oportetquod existât,quia non est ratio quare futurummagis 25 sufficiatquam praeteritum.Nam ita bene posuit Aristotelesquinto Merelationessecundum tempuspraeteritumsicutsecundum fututaphysicae rum. Quinto deficitquia non percipitdistinctionemquae communissime 170ra/T soletfieride potentiamateriae,scilicetquod illa potentiapotestsumipro 30 subiectopotente,et sic est idem quod materia,et sic materia est se ipsa potens non aliquo alio; vel potestsumi pro respectuad formamfundato supermateriam,et sic non est de essentiamateriae.Sic ergo dicam quod dependentiapotestsumi pro subiecto dependente,et sic est idem quod essentiailliusrei dependentis,licetilla res sitde praedicamentoabsoluto. 35 Et sic illa res absoluta se ipsa dependet et non aliquo alio; vel potest 25 Aristoteles ,Metaphysical, 15,1021a21-23 3-4 tamen... corrumpitur] P 4 est]om.K causamSocratis noncorrumpere K 25 ita]om.K 32 essentia] esseP 35 et2]om.P capitur] capiatur
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sumi pro respectuet cetera,et sic non est de essentiailliusrei,sed est ab anima, ut probabiturpost. Sexto deficitdicendo quod potentia materiae pro respectusit praeter animam, nam contrariumhuius alias declaravi coram scholaribus meis in legendo. Sed nunc transeode hoc, quia est alia specialisdifficul-5 tas, nisi quod ad satisfaciendummodicum istimagistroostendo sibi quo modo illa potentiacorrumpiturin adventuformae,licet sitab anima. Et dico primo quod potentia materiae pro respectuad formamformaliterper animam super materiamper collationemad formamfuturam ut futuraest- et dico "ut futuraest" saltem contingenter. Et dico 10 quod conceptusanimae vel ea quae formatasuntab anima mediantibus conceptibuseius, tunc dicunturvera, quando in re est debita correspondentia; sed quando non est, tunc dicunturfalsa. Tunc ergo, quia ens uno modo diciturde vero et non-ensde falso,ut patet sextoMetaphysicae^ ideo talia quando vertunturde vero in falsum,dicunturcorrumpi,cum 15 corruptiosit de ente in non-ens.Et ideo solemus dicere quod sententia vel opinio est corruptaquando est falsa. Modo constatquod sic vertunturentia animae de vero in falsumquando in re debita correspondentia vertiturin indebitamsecundum praedicta. Ergo sic corrumpidicuntur. 170rbií Sed constatquod si forma futurain materia fiatei praesens, tunc po- 20 tenda quae est respectusfundatussuper materiamper collationemad formamfuturamut futura,non habebit iam debitam correspondentiam in re quam priushabebat. Ideo sic corrumpidiciturin adventuformae. Ad aliam rationemistiuspatet ex dictissi quis bene considerei.Nam 247vP vel ipse loquitur de dependentiis,convenientiiset diversitatibusessen- 25 tialibus hominis et asini, et sic nihil sunt aliud quam homo et asinus, et ideo dicere homo et asinus ut non dependentesnon est aliud dicere quam homo et asinus ut non-homoet non-asinus,quod nihilest dicere. Dico ergo quod tales convenientiae,diversitatesvel dependentiae non possunt a talibus circumscribi.Vel ipse loquitur de dependentiis,con- 30 venientiiset diversitatibus prout sunt relationesanimae fundataesuper hominem et asinum, et distinetaeab eis, et sic concedo quod homo et asinus ut non dependent ab eisdem causis, id est, ut non intelliguntur dependere ab eisdem causis, vel saltem ut non venimusin conceptum eorum per easdem causas a quibus dependent aut per accidentia pro- 35 venientiain eis ex illiseisdem causis, sic nullo modo conveniunt,id est, 14 Aristoteles, 6, 2, 1026a34-35 Metaphysica K 17 Modo]IdeoK 18 quando... debita]iter.
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non intelliguntur convenire.Sed tunc non sequitur"ergo ut dependent non conveniunt",quia talis dependentia bene addit aliquid non in horniněet asino, sed in intellectu.Sic etiam dico quod dicendo homo et asinus ut non conveniunt,si loquamur de convenientiaessentiali,nihil 5 est aliud dicere quam homo et asinus ut non-homoet non-asinus.Si tarnencapiatur convenientiaet diversitaspro relationibusanimae, sic est aliud et aliud ipsos esse convenienteset diversos,quia intelligimuseos esse convenienteset esse diversossecundum quod in eorum notitiasper alia et alia devenimus,ut declaravialias. 10 (Probatio ) quintaeconclusionis Deinde probo quintam conclusionem,quam usque nunc aliqualitersupposui, scilicet quod dependentiae, convenientiaevel diversitates,quae sunt relationesfundataesuper res absolutas,non suntin re praeterani- 170vaK mam. Arguo sic. Si dependentiae,convenientiaevel diversitatesfunda15 tae super absoluta essentpraeteranimam, sequiturquod convenientiae, diversitateset dependentiae fundatae super huiusmodi praedictas dependentias,convenientiasvel diversitatesessent praeter animam. Consequens est falsum;ergo et antecedens.Falsitasconsequentispatet,quia aliterprocedereturin infinitum, quod est inconveniens.Et illi hoc con20 cedunt,quia per tertiamconclusionem,quam nunc ante probavi. Item. Natura non facitpluribusquod potestfacereuno: istamconcedunt isti magistřiet alii philosophi. Sed natura potest facere quod ens absolutum se ipso dependet essentialitera causa, ut probatum est in quarta conclusioneimmediatepraecedente.Ergo naturapropterdepen25 dere illud absolutuma causa non facitin ilio absoluto aliam dependentiam sibi realiteradditam, sed dico quod intellectusnecessario format illam dependentiamrelativamsi perfectedebeat causatum intelligere, ut priusdictumfuit. (.Recapitulatio ) 30 Sic ergo patentevidenterpraedictae quinqué conclusiones.Et patet quo modo illa ratio quam alias feci de processu in infinitum in dependentiis erat necessaria et omnino impossibilisad solvendum,quoniam omnia dicta nunc fundatafueruntsuper illam rationem.Et apparet quo modo 21 uno]uniK
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evasiones aliorumfueruntsolutae- vel quandoque narrativesolum sine probatione,cum tarneneis probatio incumbat quia non est ponenda in natura pluralitassine ratione cogente,ut dixi alias; et in hoc omnes philosophiconcordant. Deinde. Quia conclusionemquam per rationempraedictam proba- 5 veram confirmaviauctoritateLincolniensissecundo Posteriorum dicentis 248rP quod dependentia a prima causa nihilmultiplicaiin re dependente,rePrimo quod nihiladdit absolutum,sed bene spondetPicardus tripliciter. addit aliquid relativum.Sed hoc non valet,quia illam auctoritatemdicit ad ostendendumquod quaestio "si est" non ponit in numerummodo 10 170vbK quo reputaturponere in numerumubi relatioattribuitur absoluto; esset enim quaestio "quia est". Secundo dicitquod illa auctoritassic intelligitur quod dependentianihil in re dependentemultiplicat,sed bene multiplicaiin re absoluta. Sed hoc nihil est, quia per illam propositionemvolebat ostendereuniversa- 15 litervel saltem specialiterin substantiis,quod esse dictum de eis nihil multiplicat. Tertio dicit quod forteLincolniensisfuitillius opinionis,nec oportet sibi credere.Et huic responsionisibi acquiesco, quia nolo me in hac opinione fundaresuper aliquam auctoritatem,sive Lincolniensis,sive Aver- 20 rois,sive Aristotelis,quia auctoritatesfaciliterexponuntur,et etiam ipsi fuerunthomines. Tarnen plus vellem probabilitereos exponere quam negare. Item. Dicit Anglicusad hanc rationemvel auctoritatemquod ilia propositi non debet reputaride mente Lincolniensis,quia cum illam pro- 25 positionem dedisset ad solvendum quandam dubitationem,statimsubiunxit aliam solutionem,innuens per hoc quod prima non erat de mente sua. Et ego bene scio quod subiunxitaliam solutionem;tamen aeque assertiveposuit primam sicut secundam, et magis explicavitprimam quam secundam. Et cum hoc illae duae solutionesnon discordant: 30 ideo tantumlicet negare unam sicutaliam. Ergo dicat istequod Lincolniensisfuitilliusopinioniset regratiaborsibi. Ex dictisitaque syllogizareoportetbrevissimede convenientiiset diversitatibussicut syllogizatumfuitde dependentiis.Nam quinqué conclusionesquas immediateprobavi non plus possuntapplicari dependen- 35 Posteriora 6 Robertus 2, 1,29183'84 Grosseteste, InAnalytica 2 cumtamen]inv.P etnonP 28 tamen]
P 20 aliquam]aliamK: illamP 13 intelligitur] intelligunt
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tiis quam convenientiiset diversitatibus.Et hoc est clarissimuminspicientipraedictain prima conclusione,in secunda et in tertiaet in quinta. De quarta vero non est magnum dubium, quia Socrates et Plato prius naturaliterconveniuntspecie quam duae relationes.Etiam Socrates et 5 Brunellusprius naturalitersuntdiversispecie quam illae diversitateseorum quae sunt relationesfundatae super eos. Immo forteillae diversitates non differunt specie, ergo impossibileest dicere quod illae con- 17IraK venientiaese ipsis conveniantvel illae diversitatesse ipsis sint diversae quin multofortiushic dicaturde substantiisse ipsis.SimiliterSocrates et 10 Plato suntprioresuniversaliter convenientiisipsorumad invicem.Si illae convenientiaesintrelationesadditae, ergo in ilio priori,cum Socrates et Plato sinteiusdem speciei,oportetquod se ipsis,non convenientiaaddita conveniant.Et formesistasradones sicutformataefuerintde dependentiis,et omnia alia factasicuttibivisumfueritexpedire. 15 Item. Nullus potest dicere quod Deus sit diversusab aliquo nisi se ipso. Tamen omnes rationesquae adducunturad probandum quod Socratesnon est diversusa Platone vel Brunellose ipso, possuntretorqueri. Consimilitersuper diversitatemDei ad alia. Ergo nihil concluduntomnes. Sed dicit Picardus ad hoc quod non oportetprimam causam esse 20 diversamab aliis per aliquid sibi additum,propterinfinitatem et illimitationemsuae perfectionis;hoc est tamen necessariumin aliis. Sed hoc dictum est sine probatione et contra ipsum, quia omnes rationessuae tenduntad metam contradictionis.Deus vero proptersuam infinitatem vel illimitationemnon compatiturcontradictoriasimul, nec ea facere 25 potest. Buridani ) (Responsiones Nunc volo ostenderequo modo isti debiliterresponderuntad rationes 248vP meas quas alias feceramad probandum istas convenientiasvel diversitates nihil addere in rebus convenientibusvel diversissuper earum essen30 tias. Prima ratio summatimerat quod dependentia nihil multiplicatin re dependente;sed res conveniuntsecundumquod dependentex eisdem causis, et sunt diversae secundum quod dependent ex diversiscausis; ergo convenientiaeet diversitatesnihilmultiplicant. Primo istinegant dependentiasnihil multiplicare;sed probatumfuit, 35 ideo male negant. Secundo Picardus dicit quod si dependentiae nihil 2 et1]om.K 9 multo] multaP 17 seipso]om.K
11 sint]suntP
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17lrbK multiplicant,tune non sequiturquod convenientiaeet diversitatesnihil multiplicant.Sed dico quod licet non sequaturvirtuteformaesyllogisticae nunc datae, tarnensequiturquia concedentiquod dependentianon multiplicai,nulla apparebit ratio cogens quod convenientiaevel diversinisicoacti. 5 tatesmultiplicent.Sed non debemusponere multiplicationem et cetera. Ergo Ad aliam rationemmeam, quando diciturquod si a et b suntdiversa, vel se ipsis sunt diversa,vel per diversitatemadditam, dicunt quod per diversitatemadditam. Et quando dicitur:"Illa voceturc, tunc c et a sunt diversa", dicunt quod verum est se ipsis, sicut dicebant de dependen- 10 tiis,quia sicutdicebat Anglicus,regula est quando aliquid inestaliquibus accidentaliteret denominative,quod insitalicui formaliteret quidditative. Sed ista regula nulla est. Nam albedo inest homini accidentaliter et denominative,et tamen nulli inestformaliteret quidditative,nisi dicatur quod ipsa sibi ipsi inest quidditativepropterhoc quod albedo est 15 essentialiteralbedo, et hoc improprieest loqui valde. Et iterumad removendumillam responsionemet evasiones, ego arguebam replicando convenientiamsuper diversitatemet e contrasic. Capio duas convenientias eiusdem speciei, et capio aliam rem quae non est eiusdem speciei et illa res voceturè, tunc 20 cum alia convenientianec cum alia diversitate, dico quod illae convenientiaesunt diversae ab ipso b plus quam inter se. Et non sunt diversae se ipsis,quia convenientianon est essentialiter diversitas.Ergo suntdiversaeper diversitatemadditam. Tunc capio cum ista diversitatealiam diversitatemeiusdem speciei. Istae tunc magis conveniuntinterse quam cum è, sed non se ipsis, cum diversitasnon sit 25 formaliterconvenientia;ergo per convenientiamiterumadditam. Et sic procedam in infinitum. Sed contra istam replicationemmeam dicit Picardus quod ego mihi contradico,quoniam si duae paternitatesconveniuntspecie et differunt numero,quaeriturutrumidem in quo conveniuntsit illud idem in quo 30 vel aliud. Si idem, ergo cum convenientiaet diversitasnon differunt, différanta rebus eisdem vel diversis,sequitur quod illud idem realiter 17lva K quod est convenientiasit illud idem quod est diversitas.Quod tamen ego negaviproutistemihi imponit.Si sitaliud, ergo convenientiavel diversitasillorumpaternitatumdifferìab eis, quod ego negavi,ut istedicit. 35 Deinde ipse respondetad illam replicationemdicens quod duae conveK om.K | per1]propter P 8 velseipsissuntdiversa] convenienties 1 convenientiae] P 33 illud] K 17 evasiones] consimiles K 16 improprie est]inv. I per2]propter K differunt om.K 35 differì]
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ab aliquo tertioquam interse, et duae diversitanientiaeplus differunt tes plus conveniuntinterse quam cum tertio.Et hoc non est per aliquid superadditum,quia huiusmodiconvenientiaevel diversitatessunt entia formaliter respectiva.Et cum diciturquod hoc est impossibile,quia con5 venientianon est essentialiterdiversitas,nec diversitasconvenientia,dicit quod verumest secundum eundem gradum convenientiaevel diversità-249rP tis, sed secundum alium et alium gradum nullum est inconveniens.Et ita est in proposito.Unde illud idem realiterquod est convenientiaspecificaest diversitasnumeralis.Similiterquod est convenientiageneralis 10 est diversitasspecifica. Sed ego nescio quo modo talia possintdici, nam ponendo sicut ipse ponit,quod convenientiaspecificaSocratis ad Platonem est relatiorealis, et similiterdiversitasnumeralisipsius ad Platonem est relatiorealis, licet concedereturquod haec convenientiaet haec diversitassinteadem 15 relatio,tarnende isto nihil arguebam. Sed dicebam quod haec convenientia est diversa specie ab ipso ¿, et dicebam quod illa convenientia non est essentialiterilla diversitasqua diciturdiversa ab ipso b. Ponamus quod b sit albedo vel paternitas,nam ut prius dictumfuit,eadem relatio non est formaliterad diversosterminosnec diversorumfunda20 mentorům.Modo illa convenientiaest Socratis ad Platonem,illa autem diversitasnon est Socratis ad Platonem, sed est illius convenientiaead albedinem vel paternitatem.Et illi convenientiaeSocratis ad Platonem correspondeirelatioquae est convenientiaPiatonisad Socratem. Sed diversitatiilliusconvenientiaead albedinem correspondeirelatioquae est 25 diversitasalbedinis ad illam convenientiam.Modo relationesnon sunt eaedem quando correlationessibi oppositae sunt diversae.Etiam remanente Socrate et Platone remanetconvenientiaSocratis ad Platonem,si 17IvbK sit relatiorealis. Et tamen diversitasqua illa convenientiaest diversa ab albedine corrumpiturcorrupta albedine, quia amplius non est diversa 30 ab ea loquendo proprie.Et sicut dico de diversitatequa illa convenientia est diversaab ipso b, ita dicendum est de convenientiaqua diversitas convenitalteridiversitati.Et hoc est facilevidereconsiderantipraedicta, ideo transeo. Item. Non bene credo quod relatiodiversitatisnumeralisSocratis ad 35 Platonem sit eadem cum relationeconvenientiaespecificaeSocratis ad Platonem,quia Socrates et Plato possunt cognosci esse diversinumero,
1 ab aliquo]absoluto P 15 dicebam] dicoÄ* 25 illam]illaK P 28 Et]om.K convenientia
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quando tarnennon sciunturconvenirespecie: ut si ita de longe videantur quod ignoremusutrumsinthominesvel equi vel arbores.Etiam convenientia sive identitasspecificasumitursecundum unum, ut dicitAristotelesquinto Metaphysicae capitulo de ad aliquid. Et ex opposito diversitas sumitursecundummulta.Modo non est idem esse multanumeroet esse 5 unum specie. Socrates enim est unus specie et non est multa numero. numero et non conveniuntspecie; Item, Socrates et Brunellusdifferunt est idem convenientia non ergo specificaet diversitasnumeralis.SimiliterSocrateset Plato conveniuntin genere,et tamen non differunt specie; 10 ergo non est idem convenientiageneraliset diversitasspecifica. Sic ergo multipliciter deficiuntdicta istius.Tunc respondeo ad rationem suam in qua dicitme mihicontradicere.Quando arguitur:"Si duae numero,quaeriturutrumsit paternitatesconveniuntspecie et differunt dico quod illae paternitaidem in quo conveniuntet in quo differunt?" essentialisive 15 tes eodem et secundum idem sui conveniuntet differunt 249vP fundamentaliconvenientiavel diversitate.Sic enim non est aliud convenientia quam diversitas,quia idem est et secundum idem sui quod potest fundarerespectumconvenientiaeet respectumdiversitatis.Tamen 172raK convenientiaspecifica,prout est relatiofundatasuper illas paternitates, non est idem quod diversitasnumeralis,quae est relatiofundatasuper 20 easdem paternitates.Nam intellectusalio et alio modo intelligendoillas paternitatesfundatsuper eas aliam et aliam relationem,scilicetconvenientiam et diversitatem.Et ista non contradicunt,sed prius probata suntesse necessaria.De illisautem modis intelligendidiversisnon pertinet ad quaestionem istam,sed ad quaestionem de diversitatespeciei ad 25 individuum. Anglicus autem aliter respondei ad illam rationem meam, dicens quod si relatiofundatursuper relationem,ilia est relatiorationis,et non realis,et ideo duae diversitatesconveniuntnon per convenientiamquae in sua speci- 30 est relatiorealis,sed conveniuntrealiteret fundamentaliter vero et extrinseceper relationemrationis.Sed fica quidditate,formaliter nunc ego regratioristi reverendomagistro,qui mihi concedit quod ad exaliqua differrespecie realitervel convenirespecie realitersufficiunt convenientia vel diversitate cum tra animam suae specificaequidditates 3-4 Aristoteles, 5, 15,1021a 11-12 Metaphysica K 3 secundum] 1 quando]quodKP 2 ignoremus] quodK 7 conignoramus in add.P 12 dicit]dicesK iterK | differunt] in add.P 9 conveniunt] veniunt] K 31 vero] P 28 fundatur] fundetur verum 15 eodem]eedemKP 18 respectum] K 33 aliqua]om.P om.K I relationem] relationis
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quae suntrelationesrationis.Ergo cum in re non sitponenda pluralitas sine necessitate,ego non ponam in Socrate et Brunello aliquas relationes reales. Ipsi enim sunt diversispecie et convenientesgenere realiter et fundamentaliter per suas specificaset generales quidditates,sed for5 maliteret extrinseceper relationesrationis.Non enim est alia ratio in absolutiset in respectivisquantum ad hoc, ut superiusvidebatur. Et haec ad praesenssufficiant de ista quaestione.
1 cum]om.P 2 aliquas]aliasKP 5 relationes] K 6 in]om.K 7 de relationis istaquaestione] ad istamquaestionem K | Et ... quaestione] add.Explicit quaestio de dependentiis etconvenientiis etdiversitatibus determinata Iohannem permagistrům ° Buridan annoDomini1332 K
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