The Isagoge of Athir al-Din al-Abhari (d. 1265 CE) Translated by Hamza Karamali
Copyright Hamza Karamali 2012 and 2016
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1. Author’s Introduction
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In the Name of Allah, Most Merciful and Compassionate.
/ .B/B A/ &/3<3 . @< 2 .) % ?2 . + 616 1 . - / >/ < .)<) =" < . . ; 1< .: 4/ 7/ . 9 . 8/ 7/ . % . 5 6/ . 4/ / .) ) *% . & 23 . ( / . 0 1 . -/ <) . 4 $1 $ < . J . 1 8< / > <3 . ( F . 0 / . I2 . -6 / 3 . < " . H G/ 7 . 9 . / 8/ E . 9 . F D / . - / >2 <) . =A =< . < $/ $A . C / /' 5/"< (1 K? & This is a treatise on logic in which I . I 6 / . L" L6 / . ." ;< . -6 1U S/S M1/ >? & / have have ment mentio ione ned d what what someo someone ne who who begins studying any one of the sci- /' . I< ]^E/ ^ E . \ / E . ; < Z[3< . J ./ Y .1 A/ 1' . ( / . %< 2 M6/ M6 N2N 2 . X / . 0 1 . J .< G1 & 2W . V < . A/ ences must keep in mind. <_:2 92 51 %& [I have have writ writte ten n this this trea treati tise se]] whil whilee / $1 $ . " . .1 d ./ . %.1 & 2c c . " . . b .< . I.2 2 .) - `.F & a7 . %. .6 5 ./ . 4./ < .) ) *% * . . % .6 ,.< .6 Q" Q.U . ." 5 .< . J . ./ + .1 . I.2 seeking the help of Allah Most High, for verily He is the benefactor of good I praise Allah Most High for His godgiven success, ask Him for guidance to His path, and send blessings on our master Muhammad and his family, one and all.
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ness and bounty. bounty. Isagoge:
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2. Expressions
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2.1 Kinds of Significations
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A meaningful expression’s signification of its exact meaning is called a complete signification, its signification of part of its meaning (if it has a part) is called a partial signification, and its signification of a meaning that is rationally implied by its exact meaning is called an implicative signification.
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An example is the expression, “human”, which completely signifies the concept, “rational animal”, partially signifies the concepts, “rational” and, “animal”, and implicatively signi fies the concept, “something that is ca pable of learning and writing”.
2.2 Basic Expressions
and
Composite
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2W o/F $2 (%&> 2 S $b2/ (%& f2 b9%& {|{
p^ l2 .1 V% . . ,6< 2S $2&2 . A /q ~ / PS $1 ./ b . I2 . I6/ `& 2f . b 1 . F 9% . & F! . } 2 . ` >& / / P• . %. : ?F . I. 2 nify part of its meaning, like the ex- E . I pression, “human”. < M6/ / V< 01 %& An expression is composite when it is Expressions composite.
are
either basic
or
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comprised of sub-expressions that signify part of its meaning, like the ex pression, “someone who throws stones”.
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2.3 Universal Expressions
and
Singular
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2„ . b .1 . -./ 1k . Q . ./ ( .1 . A./ /q ~ / ƒ7 . < 9 . .H o.2 .6F I. `& 2S $1 ./ b . . 2 (% . . >&/ . +6 ‡6 . . o < .) " . ;< < .B o/ $F . †% . & <… .:/ w > / 1' . I< < .) I< :2 . L . b 1 . I/ Mg < .: D / . 4/ An expression is universal when its / PE . m. l 1< . K.2 .6 I.F ` >& / predication to multiple instances, such Mg as the expression, “human”. 6U ( 9/ 8 ˆ / 3 A/ l/ 1 o / € %‰ 1 < ' I < < ) I:2 < L1 b/ I An expression is singular when its Basic expressions are either universal or singular .
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mere conception prevents its predication to many instances, such as the proper-noun expression, “Zayd”.
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3. The Five Universals
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< .B =" / . . = < . #/ E< . ; 2x . Š2 13 . A/ ~ / ƒE . 4< &/‰ . I6F `& g7 . < 9 . y H 2 . %1 >&/ .6 + ./ . - `.1 u&t 1 7/ . % `. & / ƒE . j . < $ / . 8./ .6 I. F ` >& / <‹ $ ./ b ./ . %. 1 >&/ concept, “animal” with respect to the 2) . b concepts, “human” and, “horse”. < n +1 6/ -` u& t 1 7/ %` & < B Y1 +H / < Q%6< , < € #6F < X%6/ o A universal is nonessential when it is Universals are either essential or nonessential .
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otherwise, like the concept, “something that laughs” with respect to the concept, “human”.
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3.1 Essential Universals
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Essential universals are either: (1) predicated of multiple concepts in response to the question, “What are they solely with respect to what is common between them?”, in which case they are termed genera (jins).
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essences in response to the question, “What are they?”, e.g., the concept, “animal” with respect to the concepts, “human” and, “horse”.
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Or they are: (3) not predicated in response to the question, “What is it?” but rather in response to the question, “Which kind of thing is it, essentially?”, in which case they are termed specific differences (fasl).
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nal” with respect to the concept, “human”.
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3.2 Nonessential Universals
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the essence that it is predicated of. A nonessential universal is termed separable when it is separable from the essence that it is predicated of.
ˆB . =" ./ . . = .< . 0 ./ . ,.< F’ . J . ./ d .1 . A./ 1n &? .6F I. `& .6/ ( . . L . .2 Q ..1 I.< ˆ3 . #.< >&/ gx . o.2 > / &/ :2< .F = . %1 . ,6< <€ . #< . X% 6F . . o6/ 2 .B zF . d% 6/ . & :2 ./ @ > / ˆ /3 . #< >&/ /“ . 0 1 . 4/ . I6/ 7/ . 9 . 8 / 2h . = 6U . 42 P .B " ./ < 9 . o H 2 . L 6/ . - ?F . ,6 < 2! . G/ $2 1 . 4 > / ˆ B ="
Both inseparable and separable universals are either: (1) only predicated of a single essence, in which case they are termed exclusive universals (khassa), e.g., the concept, “something that laughs” (whether potentially or actually) with respect to the concept, “human”.
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An exclusive universal can be nonessentially defined as a universal that is only nonessentially predicated of a single essence.
2 $/ ./ 5 . %1 & :1/ . @ > / ˆ /3 . #< >&/ /‘ :/1 . ; /T . m < . = 6/ . #/ F! . 5 2 . A/ 1n &? . I6F ` >& / &/ :2< .F = . . %.1 .6< ,. <„ . b .H< . Q ../ J . ./ 2 (% . . .6/ o. g_ .6/ 5 . . %.1 & ƒ7 . < 9 . o H 2 2 .) - ?F . ,6 < 2! . G/ $2 . A > / < . -6/ &:/ . " . / 0% . & /' . I< < $1N . " < . e / > / /n . + 6/ . - `1 s . %1 Uq :/1 . w. ˆB . b ./ . 9 ..< J . ./ d .1 . I.2 /T . m.< .6/ = . . #./ /“ . 0 .1 . 4./ .6/ I. 7/ . 9 . . 8./ 2h .6/ = . . A.2 "<6U j/ $/ 8 A general universal can be nonessenOr they are: (2) predicated of many different essences, in which case they are termed general universals (‘arad ‘amm), e.g., the concept, “something that breathes” (whether potentially or actually) with respect to the concept, “human” and the concepts of other kinds of animals.
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tially defined as a universal that is nonessentially predicated of many different essences.
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4. Definitions
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Essential definitions (hadd) are com posite expressions that signify the definiendum’s essence. They are either complete (tamm) or incomplete (naqis).
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<) . 9 .< D 1 . ; > // p^ E1 . †% F . & <„ . Q .1 K< 1' . I< 2W . oF / .$ J ./ A/ ~ / 7/ . % `. & < n +1 6/ -` u& t1 Incomplete essential definitions are <„ . Q .1 K< 1' . I< 2W . oF $/ / . J . A/ ~ / 2’ . w< . Q% 6F . & g3 . 0% / . >&/ composed of the definiendum’s remote genus and proximate specific differ- // <3 . " . 5 < . Y . %/ 1 & p^ 1E . †% F . & ence, such as the concept, “rational physical object” with respect to the
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concept, “human”.
Nonessential definitions are composite expressions that distinguish the definiendum from all other concepts without signifying its essence. They are either complete or incomplete.
<„ . Q . .1 K.< 1' . I.< 2W . o.F $/ / . J . . A./ ~ / g_ .6F J%. . & 2! . G.1 $ F . %. >&/ /
Complete nonessential definitions are composed of the definiendum’s proximate genus and inseparable exclusive universals, such as the concept, “an animal that laughs” with respect to the concept, “human.”
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1' . I. < 2W . o. F $ / . J . ./ A. / ~ / 2’ . w. < .6 Q. F . .% & 2! . G. 1 $ F . %. >&/ ˆ /3 . #< &/> ˆB . =" / . . = < . 0 / . ,< .6/ L . J .2 9 ./ ( 1 . K2 g’ . J . / d 1 . 4/ ˆ . " 6F . j< $/ / . 8 7/ . 9 . . 8./ ˆ– .6/ I. 2) . - `.F &
Incomplete nonessential definitions are composed of multiple nonessential universals which, in their entirety, are inseparable from the definiendum’s essence, such as the concept, “something that walks on two feet, has broad nails, whose skin is not covered by fur, who stands upright, and who is capa ble of laughter,” with respect to the concept, “human.”
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5. Propositions
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>? 1 & < .) " .. ;.< P‘ S< .6/ z. & / PW . 4< . o6/ P3 . A r /1 . Q 6/ . % :/ 1< . = . o/ P .) " .F 9 . ( < 1 . #/ . I6F `& /E . @< > / (hamliyya), e.g., “Zayd is someone who writes,” or (2) conjunctive condi- M6/ 2 . L . F Q% . . ;6/ U .B 5 / . %< . C 6/ 2„ . ( 1 . F †% . & <“ . -/ . o6/ 1n &` . Q 6/ . % :/ 1< . = . o/ P .B 9 . D / < . J . IF 2 tional (shartiyya muttasila), e.g., “if the sun has risen, then it is daytime,” 2S /3 . 5 / . %1 & . Q 6/ . % :/ 1< . = . o/ PB . 9 ./ D < . b / . Q . I1 2 PB . " .F C< $/ 1 . \ . I6F ` >& / PS .:2 K :/ 1 . I or (3) disjunctive conditional (shartiyya munfasila), e.g., “numbers are ei&US $/ ; 1 1 >? & K1 6U >/ r / n :2 y/ A 1 n &? I`6F &
Propositions are composite expressions that can be true or false.
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ther even or odd.”
The first part of a categorical proposition is termed the subject (mawdu`) and the second part is termed the predicate (mahmul).
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The first part of a conditional proposition is termed the antecedent (muqaddam) and the second part is termed the consequent (tali).
.6U I. F3 . = ./ . I.2 7F . ( . . + ./ . A.2 ?F u& t1 2^ l2 .1 V% . . >&/ "%6/ 6U 4 E< -6F %&/ >
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.6 I. š> W P . 4.< .6 o. P3 . A r /. .6 Q%. . :/ . =o . . PB . Y ../ K./ : . I. .6 I. š 2B . " ..F X .< . / =%. . >&/ ˆW 46y< < , /„ % P"/ 3 rA/ 6Q< %:/ =o P B Y< %6G / Each of the two is either (1) singular . 6 $/ . o /‰ . (o 6 . PB . z : . Dd . . I/ . I6 š . (LQ 6 . . . I< ˆ /3 . #< &> xg . o2 > / (as in the previous examples), or (2) universally quantified , e.g., “Every q/ > ˆW . 4< . o6 ˆn . +6 š. gx . o2 . Q 6 . % :/< . = . o/ P MF / :/ . + . I2 PB . " .F H 9 . o < 2 . I6 š> human writes,” and, “No human writes,” or (3) particularly quantified , P MF / .: + / . I2 PB . " .F m l2< . K . I6 š/ > ˆW . 4< . y 6 . ,< / W . 4 . o 6 n6 . +- ‡& . 2c . 5 . ,/ . Q 6 . % :/< . = . o/ quantified , e.g., “Humans write,” and, “Humans do not write.” . Q 6 . % :/< . = . o/ € . % O . o /n : . y . A/ q n› . I6 š> W ˆ . 4< . y 6 . ,< /„ . " . %/ ˆW <46y< , / „ % 2"/ n 6+-‡&> PW 46o 2 < n 6+-‡& Propositions are either (1) affirmative, e.g., “Zayd is writing,” or (2) negative, e.g., “Zayd is not writing.”
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P„ . ( . F †% . & “ . - . o6 nš . Q%6 : . . =o. P .B " .F I< >l . % . I6 š .UB 9 . D < . J . 2 (% F . >&/ nš . Q% 6 : . . =o. PB . " .F w< . b 6 . H 4 < & . I6 š> SP .:2 K :/ . I M6 2 . LQ%. . . ;6 U .B 5 . %< . C 6 PT @6- 2 < M6(< 0%6; 6=< C6- 2 n 6+-‡& n6o
Conjunctive conditional propositions are either (1) really conjunctive, e.g., “If the sun has risen then it is daytime,” or (2) coincidentally conjunctive, e.g., “If humans are rational then donkeys bray.”
Pœ >r . I6 š S3 . 5%. & . Q%6 : . . =o. P .B "="= F . . . . #/ . I6 š .2B 9 . D / < . / bQ . . 2 (% . &> . Q% 6 :/. . = . o/ ”/ . = . ;/ PS .$ ; . I6 š> . I6 š> $/&U . V# . >› $/&U . V . \/ /n .: yA. nš . I6 š 2^ EF . †% . & &O . @ E . ; /n .: yA. n› . I6 š P3 . A r / . Q 6 . % :/< . =o . ” . = . ;/ H :2 ˆ . 9 . Š 2 2B . 5 / . -< . I6 /‘ $// A q n› 6Iš> < $0/ Y%& Disjunctive conditional propositions . Q% 6 . : . =o. ]^ &l . K ?& < &>‰ s . DbQ(% . . . . & 2n .: y . 4/ 3/ . w > / can have more than two parts, e.g., “One of any pair of numbers is either ˆ I >› P >6+2 ’ w6- >› P < 3 m&r 6Iš S35%& Disjunctive conditional propositions are either (1) strongly exclusive, e.g., “Numbers are either even or odd,” or (2) merely truth-exclusive, e.g., “This this is either a tree or a boulder,” or (3) merely falsity-exclusive, e.g., “Zayd is either in the sea or he is not drowning.”
greater than its counterpart or less than its counterpart or equal to its counterpart.”
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6. Propositional Reasoning
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6.1 Contradiction
<Œ . VA 6/ . ` u6< t 1 . , <' . " . J ./ " .F X < . = / . %1 & 2ž s/ . J .< Š1 & :2/ . @ 2c . w2 . Q 6/ . F J% . & /n : . y .2 . 4./ 1n &? <) . 4.< &/O . %.< E< . X . . J . ./ = .1 . A./ 2Ÿ . " . .1 0 ./ . ,.< &/ P3 . A r /1 . Q 6/ . % :/ 1< . = . o/ UB . , UB . w / dict each other, they must be identical in eight aspects: (1) their subject, (2) &/ &/ h: . ( .2 . 0 . 1 . / (. . .% >&/ <… : . j . 2 : 1 . (./ . .% & their predicate, (3) their time, (4) their place, (5) their relation, (6) their po- < Hx . y .2 . %. 1 >&/ p^ l .1 V.2 . .% >&/ &/ :< / . = .2 . %. 1 >&/ B . ;./ .6 j . / ` u&/t 1 > tentiality and actuality, (7) their wholeness and part-ness, and (8) their ˆW 46/< y< , /„ "/ % P1 3 A/ r1 aPW 46/< o P 3 A/ r Ž1 1 0/ - < $F †%&/ 1 > Contradictory opposition (tanaqud) is for two propositions to differ in affirmation and negation such that the difference intrinsically implies the truth of one and the falsity of the other, e.g., “Zayd is writing,” and “Zayd is not writing.”
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conditions.
An example is “Zayd is writing,” and “Zayd is not writing.”
2B . Y ../ %.< .6F +% . . & /E . @.< .6/ ( . . - `./ & . /./ aPn &:/ . " . . #./ ˆn .6/ + . . - `.1 & gx . o.2 .6/ Q .. % :/ 1.< . = . . o./ 2B . " . .F m l2 1.< . V% . . & ˆn &:/ "/ 0< , /„ "/ % <1 n +1 6/ -` u& t1
The contradiction of an affirmative universally quantified proposition is its corresponding negative particularly quantified proposition. For example, the contradiction of, “Every human is an animal,” is, “Some human is not an animal.”
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2B . Y ../ K./ :2 . (% . . & /E . @.< .6/ ( . . - `.F & .B< " ..F < 9 ..H y .2 . %.1 & /./ 2c . 5 1 . , > // aˆn &:/ . " . 0 / . ,<
The contradiction of a negative universally quantified proposition is its corresponding affirmative particularly quantified proposition. For example, the contradiction of, “No human is an animal,” is, “Some human is an animal.”
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Fq `& . ( 6/ . L 2 . Q . " / . ,1 / 2c . w2 . Q 6/ . F J% . & 2T . = F . 0 / . J . A/ / /q n< . 46/ M:2 . D . 0 1 . / (% . >&/ 13 . w/ <' . "J 1 . . " .F < 9 . y H 2 . %1 & Fn ut? < ./ aPW . 4< . o6/ ˆn . + 6/ . - `1 & gx . o2 . Q 6/ . % :/ 1< . = . o/ &/ PW . 4.< .6/ y . . ,.< // aPW . 4< . o6/
Contradictory opposition between quantified propositions requires that the propositions differ in quantity because it is possible for two universally quantified propositions to both be false at the same time (e.g., “Every human writes,” and “No human writes.”) and it is possible for two particularly quantified propositions to both be true at the same time (e.g., “Some human writes,” and “Some human does not write.”).
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6.2 Conversion
Uq : . ( . 2 . 0 .1 . I./ /… : . j .2 : 1 . (./ . % & $ ./ " . . D .< . A./ 1n &? :/ . @.2 2„ . y .1 . 5 ./ . %.1 & &/ <) %6/0 , << W A < T A<3 DF1 J%&/ > < ) %6/< 0< , <Œ VA` 6/ u&/t 1 >
Conversion (‘aks) is the transposition of the subject and predicate in a way that preserves the proposition’s negation or affirmation as well as its truth or falsity. [h: Commentators explain that mentioning falsity is a mistake in the original text.]
2‘ 23 . D 1 . A/ 1‰ `& UB . " .F < 9 . o H 2 2„ . y < . 5 / . Q . 41 / /q B .2 " .F < 9 . y H 2 . %1 & .2B Y ./ K/ :2 . (% . >&/ Pn &:/ . " . #/ gx . o2 2‘32 . D 1 . A/ /q >/ Pn :1&/ . " . #/ ˆn . + 6/ . - `1 & gx . o2 . Q 6/ . % :/ 12 . w gx . o2 . Q 6/ . 9 . w1 2 & &/‰ `& . Q 6/ . - ?F ut < UB . " .F m l2 1< . K 2„ . y < . 5 / . Q .1 4 / x/ . , Pn . + 6/ . - š1 aPn . + 6/ . - `1 & &/
The affirmative universally quantified proposition does not convert to a universally quantified proposition because it is possible for a proposition like, “All humans are animals,” to be true without its converse, “All animals are humans,” being true.
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“Some animals are humans,” will also be true because the original proposition entails the existence of something that is both a human and an animal.
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The affirmative particularly quantified proposition also converts to a particularly quantified proposition by the same reasoning.
/€ . %< ‰/ > aUB . " F . < 9 . o H 2 U .B Y ./ %< . G 6/ 2„ . y < . 5 / . Q . 41 / 2 .B " F . < 9 . y H 2 . %1 & .2B Y ./ %< . +% 6F . >&/
The negative universally quantified proposition converts to a negative universally quantified proposition. This is self-evidently true because whenever, “No human is a boulder,” is true, “No boulder is a human,” must also be true.
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2) . - `.F .6 ;./ a6U . I. >2 l2 . %. .6/ L . . %./ /„ . y .1 . 8./ /q .B2 " ..F m l2 1.< . V% . . & .2B Y ../ %.< .6F + . . %.ˆ >&/ /q >/ aˆn .6 + . / . -. `1 .6 ,. < /„ . " . . 1 %./
The negative particularly quantified proposition does not have a converse because it is possible for “Some animal is not human,” to be true without its converse being true.
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7. Deductive Arguments
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1“ . ( / . < 9 . G H 2 7/ . J . I/ ˆh :1&/ . w ?& 1' . I< P• . % :2 ?F . I Ph :/ .1 w :2 / . @ 2‹ . " 6 . = < . %1 & $/ 2 Š£ Ph :/1 w L<6/ 4&/ O %< L16/ Q/ 8 / _ l/ %<
A deductive argument (qiyas) is a composition of propositions which, when accepted as true, intrinsically entails the truth of another proposition.
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gx . o2 > / P• . % :2 ?F . I ˆ! . + 1 . K< gx . o2 . Q 6/ . % :/ 1< . = . o/ PE . -< $<&/ . J . w1 & . I6F `& :2 ./ @ > / P¤ S< # ˆ 6/ ! +<1 K g x y/2 ; P ¤ S< # ˆ 6/ • %? :2F I
Deductive arguments are either: (1) categorical syllogisms (qiyas iqtirani), such as, “Every corporeal body (jism) is composed and everything that is composed is created, therefore every corporeal body is created,”
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U .B 5 / . %< . C6/ 2„ . ( 1 . F †% . & <“ . -/ . o6/ 1n &` . Q 6/ . % :/ 1< . = . o/ PE . m< . Q 6/ . . J 1 . G < 1 & . I6F ` >& / ˆS :2 . K. :/ 1 . ( . . ,.< /„ . " . .1 %./ M6/ 2 . L . . F Q%. . & <' . y% .< . P3 . K.2 :/ 1 . I. M6/ 2 . L . . F Q%. . .6/ ;. ˆB 5
or: (2) conditional syllogisms (qiyas isthithna’i), such as, “If the sun has risen then it is daytime, but it is not daytime, therefore the sun has not risen.”
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7.1 Categorical Syllogisms
The term that is repeated in both premises of a categorical syllogism is called the middle term (hadd awsat). The subject of the conclusion is called the minor term (hadd asghar). The predicate of the conclusion is called the major term (hadd akbar).
&¥3 . #/ 7F . ( . + / . A2 <‹ . " 6/ . < =% . & &/ $/ / . . z1 ?& &¥ 3 . #U 7F . ( . + / . A2 <Œ .:2 9 . R 1 . / (% . & 2… .:2 j :/ 1 . I > / /” . G/ >? 1 & $/ / Y1 o? & &¥3 #/ 7F (/ +/ A 2 ) 2% (1:2 0/ I/ >
The premise that contains the minor term is called the minor premise and the premise that contains the major term is called the major premise.
[/ $1 . . z2 7F . ( . + / . 42 $/ 2 . . z1 ? u&t 1 . L" 6/ . . ;< E< . J . %F & 2B . I/ < H3 . = / . 2 (% . >&/ [/ $1 Y2 o7F (/ +2 4 2 $/ Y1 o? u&t 1 L"< 6/ ; E< JF %&/ >
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VW*C# OR7* U2<# /%* I2>MX T5!5!
7.1.1 The Figures of the Categorical Syllogism
2h .6 y . . \.1 ? u&/t1 > Us . y .1 . \./ 7F . ( . . + ./ . 4.2 <• . " . . % ¦F.< . J%. . & 2B . ¡ . .? " . .1 @./ > / PB /5 M?/,1 &
The compositional form of the premises is called the figure of the categorical syllogism. The categorical syllogism has four figures.
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E . ;. .< Uq: . (. .2 . . 0 . I. .1 /n .6 o. ./ 1n &` /” . G . ./ >? 1 u& t1 F3 . 0 . ./ . .% & Fn u?t < 2x . y 1 . F †% . & :2/ . L . ;/ [/ . Y $ . 1 y 2 . %1 & E< . ; . 8 6U :2 . j :/ 1 . I [/ $1 . . g D% . & /n . o 6/ 1n >&` / 2k . ,< $ &F . % & :2/ . L . ;/ <„ . y 1 . 5 / . %1 . ,6< /n . o 6/ 1n >&` / 2h >?F u& t1 Uq .:2 ( . 0 1 . I/ /n . o6/ 1n >`& / 2Ÿ . %< . % 6F . & :2 ./ L . ;/ . ( 6/ . < L" . . ;< . 86U :2 . j :/ 1 . I E< -6F %& :2 / L/ ; (<6/ L"< ; The second figure returns to the first <„ . y < . 5 / . ,/ ?F u&t 1 7/ . % ` & g3 . 4 $/ 1/ . A . L 6/ . Q .1 I < E< . - . % 6F . & 2x . y 1 . F †% . >&/ figure through conversion of the major premise. The third figure returns to the [/ $1 . . g D% . & <„ . y 1 . 5 / . ,< < .) " .1 % `/ & g3 . 4 1/ . A$/ 2Ÿ . %< . %6F . >&/ [/ $1 . Y . y 2 . %1 & first figure through conversion of the minor premise. The fourth figure re- <„ . y 1 . 5 / . ,< >? 1 & &/ turns to the first figure by reversing the order or through conversion of both 5"< 6U (/ K < ' "/ J/1 IH <3 =2/ (%& The first figure is when the middle term is the predicate of the minor premise and the subject of the major premise. The fourth figure is the opposite. The third figure is when the middle term is the subject in both premises. The second figure is when it is the predicate in both premises.
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premises.
2x . y 1 . F †% . >&/ 2h >?F u&t 1 :2/ . @ <œ . J 6/ . - `1 u&t 1 2' . < " .H Y ./ %1 & 2x . I < . y 6 . %1 >&/ 2) . % / ~ &¥3 . K< / P! . " . = < . J ./ + 1 . I2 Pk . Y .1 C/ ?F u&t 1 7/ %` & E< -6F %& The second figure only concludes <) . " . .1 J . ./ I./ < H3 . = ./ . I.2 <ž /s . J . .< Š.1 & /3 . Q ..1 8.< E< . -. .6F %. . & 2§ . J ..< Q ..1 A.2 .6/ ( . . - `.F >& / when its premises differ in affirmation and negation. < Œ VA` 6/ u6
The figure that concludes most com pletely and most clearly is the first figure. The fourth figure is extremely unnatural to reason with. Someone with a sound nature and intellect will not need to return the second figure to the first.
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<_ .:2 9 . 5 2 . 9 . %1 < M6/&U . " . 5 / . I< 2x . 5 / . V 1 . A2 ~?F u&t 1 2x . y 1 . F †% . >&/ 2) . Q . . 1 I.< /§ . J . ./ Q . .1 J . ./ + .1 . 2 ". . /% > &UM: . J . . 2 G.1 2S /x . 5 . / . V .1 . " . .2 %.< 2N 2S M:< . Q . ./ ;./ [/ $1 . . g D% . & 2Œ . VA 6/ . ` & .<) K< . J 6/ . - `1 & 2 $/ . \ 1 > / . L 6/ . 9 . og 2 2W . %< . R 6/ . / (% . & [/ $1 Y2 y1 %& 2B "H 92F o/< >
The first figure is the criterion of the knowledge of conclusions so we will describe it in order for it to be an example from which the details of other figures can be concluded. The condition of its having a conclusion is that the minor premise be affirmative and the major premise be universally quantified.
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PB 5// ,1 M? & 2B V22 $2 j/ >
It has four concluding modes:
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(1) “Every corporeal body is com posed and everything that is composed is created, therefore every corporeal body is created,”
ˆ• . % :2 ? F . I Px . o 2 > / P• . % :2 ? F . I u&t? 1 2Œ $F .1 X% . & P¤ 3/ 021 I ˆ ! +<1 K g x y/2 ; P ¤ 3/ 021 I :
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(2) “Every corporeal body is com posed and nothing that is composed is beginningless, therefore no corporeal body is beginningless,”
<• . % :2 ?F . (% . & /' . I< ^1E . \/ /q >/ P• . % :2 ?F . I ˆ! . + 1 . K< gx . o2 E< . - . %6F . & ˆ! A3/ =< ,
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(3) “Some corporeal body is composed and everything that is composed is created, therefore some corporeal body is created,” and
ˆ• . % ¨2 H.< . I. gx . o.2 > / P• . % :2 ?.F . I.
(4) “Some corporeal body is composed and nothing that is composed is beginningless, therefore some corporeal body is not beginningless.”
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/' . I.< /^ 1E . \./ /q >/ P• . %. : ? F . I.2
VW*C# OR7* U2<# /%* 2Y2KR T5!50
7.1.2 Premises of the Categorical Syllogism
A categorical syllogism is either: (1) composed of two categorical propositions as in the examples shown above;
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1' . I. < /W . o. .F $ / . J . ./ A. / 1n &? .6 I. F `& gE . -. < $&/ . J . .< w. p1 q & ‹ 2 .6 " . ./ = . .< . %. .1 >&/ $/ F I (/6/ o < ' "JF1 "< 91 (/ #
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2„ . ( 1 . F †% . & <“ . -/ . o 6/ 1n &` . Q 6/ . % :/ 1< . = . o/ <' . " .1 J ./ 9 ./ D < . J .F I2 1' . I< . I6F ` >& / 2 . L . / . F Q. . % & /n .6 o./ .6 ( M6 ./ . 9 . .F o.2 > / PS : . K.2 : 1 . I./ M6 2 . L ./ . F Q. . % .6 ;./ UB . 5 ./ . %.< .6 C./ <“ . -./ .6 o./ 1n &` 2§ . J . .< Q . .1 A. 2 PB . ¡.? . . ." X . < . I. 2 2 1M u6 t? 1 . ;. &US : . K.2 : 1 . I./ PB ¡"& / conditional syllogisms, e.g., “Every number is either even or odd and every >? 1 & <œ >F1 l . %. & <œ >/1 r .6F I. `& :2/ . L . . ;./ ˆœ >/1 r gx . o.2 > / PS $/ .1 ;. >? 1 & Pœ >/1 r even number is either the double of an even number or the double of an odd 2œ >F1 l . % & 2œ >/1 r >?1 & PS $/ . ;1 . I6F `& ˆS /3 . 8/ gx . o2 /§ . J . Q < . A1 2 /1 r number therefore every number is either an odd number or the double of an /1 r 1 >?& or: (2) composed of two conjunctive conditional propositions, e.g., “If the sun has risen, then it is daytime and whenever it is daytime, the earth is illuminated therefore if the sun has risen, the earth is illuminated,”
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even number or the double of an odd number.”
VZ2S[OP7* U2<# /%* T50
7.2 Conditional Syllogisms
“ . - . o 6 nš B2 . "C . $F . †% . . ;6 E . m . QJG 6 . . . q& ‹6 . "=%. . & . I6 ›> /' . " . . 8./ 2§ . JQA .2 . . _F3 . = ./ . 2 (% . . & <' . " . . 8./ 2^ .6 Q . . . < JG . . .6 ;. U .B 9 .. D .< . J . .F I.2 : . L;. . -6 . +6 š. 2^ EF . †% . & &O . @ 1“ . -/ . o6 nš . Q 6 . % :/< . = . o/ E . % . J%6F . & 2^ .6/ Q . . . .1 J . .< G.1 >&/ Pn :/&/ . " . . #./ :2 . L . . ;./ Pn .6 +. . š 2) . Q . .F < y% . . Pn &:/ . " . . #./ 1n `& . Q 6/ . % :/ 1< . = . o/ <_ F3 . = / . 2 (% . & /c . "= . . -/ 2§ . J .1 Q . A1 2 E< . % . J% 6F . &
If the conditional premise of a conditional syllogism is conjunctive, then affirming the antecedent entails the consequent, e.g., “If this thing is a human then it is an animal but it is, in fact, a human, therefore it is an animal,” and denying the consequent entails a denial of the antecedent, e.g., “If this thing is a human then it is an animal, but it is not an animal, therefore it is not a human.”
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<' . " .1 8/ 2^ . Q 6/ . .1 J .< G1 . ;6/ UB . " . F < =" . . = < . #/ UB . 9 ./ D < . b / . Q .1 I2 1“ . -/ . o 6/ 1n >`&/ . Q 6/ . % :/ 1< . = . o/ E< . - . %6F . & p^ l2 . V% 1 . & /c . " . = < . -/ 2§ . J . Q < . A1 2 <' . A /1 ^ l2 . V% 1 . & <3 . #/ ?& /„ . " . %1 / 2 .) - ?F & 2§ . J . Q < . A1 2 Pœ >/1 r .2) Q . < y% F . PS $/ . ;1 >? 1 & Pœ >/1 r . I6F `& 2S/3 . 5 / . %1 & .6 K. U >/ 1 r /„ . " . .1 %. / 2) . -. ?F & 2§ . J . .< Q . .1 A. 2 PS $ .1 ;./ 2) . Q . .F < y. . .% >? 1 & ˆS $ .1 b . / . ,. < E<- %& 6F /' "/ 8 2 1 § J1 Q2< A (<6/ @< 3 #?/ &
If the conditional premise of a conditional syllogism is disjunctive and strongly exclusive then (1) affirming one of the two terms entails the denial of the other, e.g., “Numbers are either even or odd and this number is even therefore it is not odd,” and (2) denying one of the two terms entails the affirmation of the other.
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8. The Matter of Deductive Arguments
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P_ +1 6/ w? & 2 "<6F Q"< =/ "1 %&/ >
There are [h: six] kinds of propositions that noninferentially afford certain knowledge.
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<' . " 1 . Q . }/ p1 q & • 2 . D 1 . -< 23 . #< : &/ . % & . Q 6/ . % :/ 1< . = . o/ P . " 6F . % >? F< & . @6/ 23 . #/ ?& p^ l2 V%& 1 /' I 2< ! ©1/ 8? & gx 2y %&/1 > (2) Observational judgments (musha- M6F 2 . Q% . >&/ PB . w $1 < / . † . I2 2„ . ( 1 . F †% . & .6/ Q . % :/ 1< . = . o/ P &/3 . @/ .6/ † . I2 > / hadat), such as, “the sun is shining,” and “the fire is burning.” PB w< $1/ 0 I2 (3) Tested judgments (mujarrabat), p^ $1 &/ bF D9< % P B 9H L/ (1) Basic judgments (awwaliyyat), such as, “one is half of two,” and “the whole is greater than the part.”
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such as, “Sagmunya relieves yellowsickness.”
< . - 1' . I< PS . b M:2 6/ . J . + / 1 . I2 $/ < . ( . / =% . & M:22 . - . Q 6/ . % :/ 1< . = . o/ P . " 6F . G< 13 . #/ > / <„ (F1 †%& (5) Mass-transmitted observations ) . "98 . . . ) . *%. . & 7 . 9z . . P3 . ( .F . 0 ./ . I.2 .6/ Q .. % :/ 1.< . = . . o./ P $<&/ . 4. :/&/ . J .. I.2 > / (mutawatirat), such as, “Muhammad (Allah bless him and give him peace) a/ :2 .F Y . g Q% . & 7 . 8 FS & ! . 9G. > (4) Intuited judgments (hadsiyyat), such as, “the light of the moon comes from the light of the sun.”
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claimed prophecy miracles.”
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manifested
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Pœ >/1 r 2B . 5 / . , M? 1/ u&t 1 . Q 6/ . % :/ 1< . = . o/ . L 6/ . 5 / . I/ . L 6/ . 42 . G 6/ . " 6/ . w< . A6/ . X 6/ . w > // 2_ . + 6/ . = < . - p1 q & :2 ./ @ > / <' . @1 H / 6/ A< +/ J2 (< ,
(6) Subconsciously inferred judgments (qadaya qiyasatuha ma‘aha), such as, “four is an even number,” which is deduced via an intermediary premise present in the mind, namely, that four can be divided into two equal parts.
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9. The Five Arts
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ˆ .B " . < Q" . . = < . A/ ˆ . I6/ < H3 . = / . I2 1' . I< P• . % ?F .: I2 P‹ . " 6/ . w< :2 / . @ 2n . @6/ $2 1 . Y . %1 & < "<6F Q"< =/ "1 %& <œ J16/ -` ut < Dialectics (jadal) is a syllogism com- ˆ .6 I./ < H3 . = ./ . I.2 1' . I.< P• . %. : ?F . I.2 P‹ .6 " . ./ w.< : / . @.2 > / 2h /3 . V./ . .% >&/ posed of premises that are well-known or accepted among the generality of /3 . Q . .1 8. < >? 1 & <‹ .6 Q. F . .% & /3 . Q . .1 8. < ˆB . ( ./ . 9 . .F + . / . I. 2 >› M: ˆ / . L .2 . † . 1 . I. / people or between the two disputing parties, e.g., “Justice is good,” and P™ Y/"< w 2 ! 9g ©%&/ 2 > P ' +// # 2 h 13 51/ %& Q<6/ %1 :/ =/ o < ' "/ (11 D/ d%& Proof (burhan) is a syllogism that is composed of certain premises and thus affords certain conclusions.
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“Oppression is bad.”
ˆ .6/ I. < H3 . = ./ . I.2 1' . I.< P• . % :2 ?.F . I. P‹ .6/ " . . w.< /E . @.< > / 2B . ,./ .6/ R . . / d% . . >&/ ˆB -:2/ Q1 ©/ I 1 >? & <) ; ˆ "< 3 =// J1 52 I ˆ ’ d/1 \ 1 ' I ˆ< B %:2/ Y1 =/ I
Rhetoric (khataba) is a syllogism that is composed of premises that are accepted because they are presented by someone who one admires or a syllogism that is composed of probabilistic premises.
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ˆ .6 I./ < H3 . = ./ . I. 2 1' . I.< P• . %. : ?F . I.2 P‹ .6 " . ./ w. < : / . @.2 > / $ .2 5 .1 . < H †. . .% >&/ 2c Y/ =1< Q/ 4 1 >? & 2„ bF1 Q%& L16/ Q< I 2 ” +Y1 < Q/ 4 ˆ B 9F "// d/ J2 I Fallacious reasoning (mughalata) is a ˆ .6/ I. < H3 . = ./ . I./ 1' . I.< P• . % :2 ?.F . I. P‹ .6/ " .. w.< /E . @.< /> 2B . R ./ . %./ .6/ . . 2 (% . . >&/ syllogism composed of false premises that resemble true or well-known 1' . I.< >? 1 & M:< . L . 2 . † .1 . ( ./ . %.1 .6 ,.< >? 1 & ˆ IH6/ <3 =2/ I The only reliable argument is proof. $1 2 "/ e / q 2n @16/ $2 Y1 %& :2 / @ 2 3/ (21 51 %&/ > The end. 7L/ J1 -& Poetics (shi‘r) is a syllogism that is composed of imagined premises that one is attracted to or repulsed from.
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