Authors/Thomas Aquinas/posteriorum/L1/Lect29

Lecture 29 Syllogism of ignorance in regard to mediate propositions

Latin	English
	Lecture 29 (80b17-81a37) SYLLOGISM IGNORANCE IN REGARD TO MEDIATE PROPOSITIONS
lib. 1 l. 29 n. 1 Postquam philosophus ostendit quomodo syllogismus ignorantiae fit in propositionibus immediatis, hic ostendit quomodo fit in propositionibus mediatis. Et primo, quomodo concludatur propositio negativa falsa, quae opponitur affirmativae verae; secundo, quomodo concludatur affirmativa falsa, quae opponitur negativae verae; ibi: si vero sit affirmativus et cetera. Circa primum duo facit: primo, ostendit quomodo hoc fiat in prima figura; secundo, in secunda: ibi: sed per mediam figuram et cetera. Circa primum tria facit: primo, ostendit quomodo fit syllogismus ignorantiae in propositionibus mediatis, per medium proprium; secundo, quomodo fit per medium quidem non proprium, sed tamen similem habitudinem habens ad terminos, sicut medium proprium; ibi: similiter autem est, et si ex alia ordinatione etc.; tertio, ostendit quomodo fit praedictus syllogismus per medium extraneum; ibi: si vero non per proprium medium et cetera.	After showing how a syllogism of ignorance in regard to immediate propositions is made, the Philosopher here shows how it is made in regard to mediate propositions. First, how a false negative proposition is concluded which is opposed to a true affirmative. Secondly, how a false affirmative is concluded which is opposed to a true negative (81a16). Concerning the first he does two things. First, he shows this in the first figure. Secondly, in the second (81a4). In regard to the first he does three things. First, he shows how a syllogism of ignorance is constructed in mediate propositions through a proper middle. Secondly, how one is constructed through a middle which although not proper has a relationship to the terms, a relationship akin to that of a proper middle (80b27). Thirdly, he shows how such a syllogism is constructed through an extraneous middle (80b32).
lib. 1 l. 29 n. 2 Dicit ergo primo quod, quando syllogismus concludens falsum, fit in propositionibus, quae non sunt individuae, idest immediatae, si accipiatur proprium medium, unde fit syllogismus, non potest esse utrasque propositiones esse falsas, sed solum maiorem. Et exponit quid nominet proprium medium. Ex quo enim propositio, cuius contraria syllogizatur, est mediata, oportet quod praedicatum syllogizetur de subiecto per aliquod medium. Potest ergo illud idem medium accipi ad concludendum oppositum. Puta, haec est propositio mediata: omnis triangulus habet tres angulos aequales duobus rectis; medium autem per quod syllogizatur praedicatum de subiecto, est figura habens angulum extrinsecum aequalem duobus intrinsecis sibi oppositis. Si ergo velimus probare quod nullus triangulus habet tres angulos aequales duobus rectis per hoc idem medium, erit syllogismus falsitatis per proprium medium. Et ideo dicit quod medium proprium est, per quod fit syllogismus contradictionis, idest ad oppositum. Puta in praedicto exemplo: sit a triangulus, b habere tres, medium c figura talis. In prima autem figura necesse est minorem esse affirmativam, et ideo oportet quod illa, quae erat minor in syllogismo vero, maneat non conversa nec transmutata in suam oppositam in syllogismo falsitatis. Unde oportet quod semper sit vera. Sed maior propositio veri syllogismi convertitur in negativam contrariam; et ideo oportet quod maior sit falsa. Puta si dicamus: nulla figura habens etc. habet tres etc.; omnis triangulus est figura talis; ergo et cetera.	He says therefore first (80b17) that when a syllogism is constructed which concludes something false in propositions which are not individual, i.e., not immediate, if the “proper middle” through which the syllogism is formed be taken, then both propositions cannot be false, but only the major. He explains what he means by “proper middle.” For since the proposition whose contrary is to be syllogized is mediate, it is required that the predicate be syllogized of the subject through some middle. Therefore, the same middle can be employed to conclude the opposite. Say that the mediate proposition is “Every triangle has three angles equal to two right angles.” The middle through which the predicate is syllogized of the subject is, “A figure having an exterior angle equal to the two opposite interior angles.” Now if we would prove through the same middle that no triangle has three angles equal to two right angles, it will be a syllogism of falsity through a proper middle. Hence he says that a proper middle is one through which the syllogism of contradiction is made, i.e., leading to the opposite conclusion. In the above example, A would be “triangle,” B, “having three...” and C, the middle, “such a figure.” Now in the first figure the minor must be affirmative; therefore, that which was the minor in the true syllogism must remain unconverted and not changed into its opposite in the syllogism of falsity. Hence it must always be true. But the major proposition of the true syllogism is changed into its contrary negative; hence the major must be false. For example, we might say: “No figure having an exterior angle equal to the two opposite interior angles has three angles equal to two right angles; but the triangle is such a figure: therefore, no triangle has three angles equal to two right angles.”
lib. 1 l. 29 n. 3 Deinde cum dicit: similiter autem est etc., ostendit quomodo fit praedictus syllogismus per medium extraneum, sed simile proprio. Et dicit quod similiter syllogizabitur, si medium accipiatur ex alia ordinatione. Puta si a demonstretur de b per c, et accipiamus in syllogismo falsitatis medium non c, sed d, ita tamen quod d etiam contineatur universaliter sub a et praedicetur universaliter de b, puta si accipiamus pro medio figuram contentam tribus lineis rectis; quia hic etiam necesse est minorem propositionem, scilicet db, manere sicut erat in syllogismo concludente verum, quamvis per proprium medium; maiorem autem propositionem necesse est transmutari in contrariam: et ideo semper minor erit vera, et maior semper erit falsa. Et quantum ad modum arguendi ista deceptio est similis ei, quae fit per proprium medium.	Then (80b27) he shows how the aforesaid syllogism is constructed through a middle which is extraneous but like the proper. And he says that it will be syllogized in like fashion if the middle is taken from another ordering. For example, if A had been demonstrated of B through C, and we were to take in the syllogism of falsity not C but D as the middle, in such a way, however, that D is also contained universally under A and predicated universally of B: say if we took for the middle, “a closed figure of three lines,” because here too the minor proposition DB must remain as it was in the syllogism which concluded the true, although through a proper middle. But the major proposition will have to be changed into its contrary. And so the minor will always be true and the major always false. But as to the mode of the argument, this deception is similar to that which is formed through the proper middle.
lib. 1 l. 29 n. 4 Deinde cum dicit: si vero non per proprium etc., ostendit quomodo fit syllogismus falsitatis per medium extraneum, et dissimile proprio. Potest autem hoc medium hoc modo accipi, ut contineatur universaliter sub a, et de nullo b praedicetur. Et in hoc casu oportebit utrasque propositiones esse falsas, quia oportebit, ad hoc quod fiat syllogismus in prima figura, accipere propositiones e contrario, ut scilicet accipiamus maiorem negativam et dicamus, nullum d est a, et minorem affirmativam, et dicamus: omne b est d: et sic patet utrasque esse falsas. Et haec quidem terminorum habitudo inveniri non potest in convertibilibus, sicut in subiecto et passione, quae per aliquod medium de subiecto concluditur. Manifestum est enim quod non potest accipi aliquid, de quo passio universaliter praedicetur, quod a subiecto universaliter removeatur. Sed haec habitudo potest inveniri, quando propositio est mediata, ex hoc quod superius genus vel passio superioris generis praedicatur de ultima specie; puta si dicamus: omnis homo est vivus. Vivum enim potest concludi de homine per medium, quod est animal. Si ergo accipiamus aliquid, de quo vivum universaliter praedicetur, sicut est oliva, quae vere removetur ab homine universaliter, erit habitudo terminorum, quam quaerimus. Haec enim erit falsa: nulla oliva est viva; et minor erit similiter falsa: omnis homo est oliva; et similiter conclusio erit falsa: nullus homo est vivus, quod est contrarium propositioni verae mediatae.	Then (80b32) he shows how a syllogism of falsity is made through a middle which is extraneous and unlike the proper. For a middle can be taken such that it is contained universally under A but is predicated of no B. In this case both propositions will have to be false, because in order that the syllogism be formed in the first figure, it will be necessary to take propositions to the contrary, namely, a major which is negative, for example, “No D is A,” and the minor affirmative, for example, “Every B is D.” Clearly then both are false. Now this relationship of terms cannot be found in things convertible, say in a subject and its proper attribute which is concluded of the subject through some middle. For it is obvious that no middle can be taken such that the proper attribute would be universally predicated of it, and that middle be removed universally from the subject. But this relationship can be found when the proposition is mediate, for example, when a higher genus or the proper attribute of a higher genus is predicated of an ultimate species, as when we say, “Every man is living.” For “living” can be concluded of man through the middle, “animal.” Therefore, if we should take something of which “living” would be universally predicated, say “olive,” but would be universally removed from man, the relationship of terms that we are seeking will result. For this will be false, “No olive is living”; and the minor, too, will be false, “Every man is an olive.” Similarly, the conclusion will be false, “No man is living,” which is contrary to the true mediate proposition.
Contingit etiam maiorem esse veram et minorem esse falsam; puta si accipiamus pro medio aliquid, quod non contineatur sub a, puta lapidem. Tunc enim maior, quae est a.d, erit vera, scilicet, nullus lapis est vivens; quia lapis non continetur sub vivo: sed minor erit falsa, scilicet, omnis homo est lapis. Si enim esset haec vera, prima existente vera, sequeretur quod conclusio esset vera, cum tamen dictum sit quod sit falsa. Non autem potest esse e converso quod minor sit vera si sit medium extraneum, quia medium extraneum non poterit universaliter praedicari de b. Oportet autem semper minorem affirmativam accipere in prima figura.	It also happens that the major may be true and the minor false. For example, if we take as middle something which is not contained under A, say “stone”; then the major, AB, will be true, namely, “No stone is living,” because “stone” is not contained under “living,” but the minor will be false, namely, “Every man is a stone.” For if the minor remained true, while the first Was true, then the conclusion would be true, whereas it has been said that it is to be false. However, the converse does not occur, i.e., that the minor be true when the middle is extraneous, because such a middle cannot be predicated universally of B. But in the first figure the minor taken must always be an affirmative statement.
lib. 1 l. 29 n. 5 Deinde cum dicit: sed per mediam figuram etc., ostendit quomodo fit syllogismus ignorantiae negativus in secunda figura. Et dicit quod non potest contingere in secunda figura, quod utraque propositio sit falsa totaliter. Si enim debeat concludi haec falsa, nullum b est a, contraria verae; oportet quod a universaliter praedicetur de b. Unde non poterit aliquid inveniri, quod universaliter praedicetur de uno, et universaliter negetur de altero; sicut supra dictum est, cum agebatur de syllogismo ignorantiae in immediatis.	Then (81a5) he shows how a negative syllogism of ignorance is made in the second figure. And he says that in the second figure it cannot occur that both propositions be totally false. For if we are to conclude the false proposition, “No B is A,” contrary to the true, it would have been required that A be predicated universally of B. Hence nothing will be able to be found which would be universally predicated of one and universally denied of the other, as has been established above when we treated concerning the syllogism of ignorance in immediates.
Potest tamen altera tantum esse totaliter falsa, quaecunque sit illa. Et hoc manifestat primo in secundo modo secundae figurae, in quo maior est affirmativa et minor negativa. Sit ergo medium sic se habens ad extrema, ut universaliter de utroque praedicetur sicut vivum praedicatur universaliter et de homine et de animali. Si ergo accipiatur maior affirmativa, ut dicamus, omne animal est vivum; et accipiatur minor negativa, ut dicatur, nullus homo est vivus; maior erit vera et minor falsa, et conclusio falsa. Similiter etiam si accipiamus in primo modo secundae figurae maiorem negativam, ut dicamus, nullum animal est vivum; et minorem affirmativam, ut dicamus, omnis homo est vivus; erit maior falsa et minor vera, et conclusio falsa. Ex his dictis epilogando concludit dictum esse quando et per quae possit fieri deceptio, si syllogismus deceptivus sit privativus.	But one or the other of them can be totally false. And he manifests this first in the second mood of the second figure where the major is affirmative and the minor negative. Thus, let the middle be related to the extremes so that it is predicated universally of both, as “living” is predicated universally of man and of animal. Then if we take the major affirmative, say “Every animal is living,” and the minor negative, . say “No man is living,” the major will be true, the minor false, and the conclusion false. In like manner also, if in the first mood of the second figure we take the major negative, say “No animal is living,” and the minor affirmative, say “Every man is living,” the major will be false, the minor true, and the conclusion false. Having said these things he sums up and concludes that he has stated when and through which kinds of premises deception can occur, if the deceptive syllogism is privative [negative].
lib. 1 l. 29 n. 6 Deinde cum dicit: si vero sit affirmativus etc., ostendit quomodo fiat affirmativus syllogismus deceptionis in propositionibus mediatis. Et primo, quando fit per proprium medium; secundo quando fit per medium simile proprio; ibi: similiter autem et si ex alia etc.; tertio, quando fit per medium extraneum; ibi: cum vero fit per non proprium et cetera.	Then (81a16) he shows how an affirmative syllogism of deception is formulated in mediate propositions. First, when it is formulated through a proper middle. Secondly, when it is formulated through a middle similar to a proper middle (8140). Thirdly, when it is formulated through an extraneous middle (81a25).
Dicit ergo primo quod si fiat syllogismus deceptionis affirmativus in propositionibus mediatis, si accipiatur proprium medium, ut supra expositum est, impossibile est quod utraque sit falsa. Quia cum talis syllogismus non possit fieri nisi in prima figura, utraque existente affirmativa, necesse est quod minor propositio maneat hoc modo, sicut erat in vero syllogismo. Unde oportebit maiorem propositionem esse mutatam, scilicet de negativa in affirmativam; unde oportebit quod sit falsa. Puta si velimus concludere quod omnis homo sit quantitas, quod est contrarium huic, nullus homo est quantitas, cuius proprium medium est substantia; accipiemus istam falsam, omnis substantia est quantitas, et hanc veram, omnis homo est substantia.	He says therefore first (8106), that if an affirmative syllogism of deception is to be formulated in mediate propositions, if a proper middle such as explained above be taken, it is impossible that both propositions be false. For since a syllogism of this kind can be formed only in the first figure, both propositions being affirmative, it is required that the minor proposition remain as it was in the true syllogism. Hence the major will have to be changed, namely, from negative to affirmative, so that it will have to be false. For example, if we desire to conclude that “Every man is a quantity,” which is the contrary of the statement, “No man is a quantity,” whose proper middle is “substance,” we will take the false proposition, “Every substance is a quantity,” and the true proposition, “Every man is a substance.”
lib. 1 l. 29 n. 7 Deinde cum dicit: similiter autem et si etc., ostendit quomodo fit syllogismus ignorantiae, quando accipitur medium non proprium, quod sit eiusdem ordinis, sed ex alia coordinatione. Puta si dicerem: omne agens est quantitas; omnis homo est agens; ergo omnis homo est quantitas. Oportet enim hic minorem manere, maiorem vero mutari de negativa in affirmativam. Unde et haec deceptio similis est priori deceptioni, sicut dicebatur in syllogismo privativo.	Then (81a20) he shows how a syllogism of ignorance is formed when a non-proper middle is taken which is not of the same order but from some other ordering. For example, if I say, “Every agent is a quantity; every man is an agent: therefore, every man is a quantity.” For it is necessary in this case for the minor to remain, but the major will have to be changed from negative to affirmative. Hence this deception is similar to the previous deception, as was stated in the privative syllogism.
lib. 1 l. 29 n. 8 Deinde cum dicit: cum vero sit non etc., ostendit quomodo fiat syllogismus deceptionis affirmativus per medium extraneum; et dicit quod si accipiatur tale medium extraneum, quod contineatur sub maiori extremitate, tunc maior propositio erit vera, et minor falsa. Potest enim a, quae est maior extremitas, de pluribus universaliter praedicari, quae non sunt sub invicem; puta habitus de grammatica et virtute. Haec enim est mediata, nulla grammatica est virtus. Possumus ergo concludere contrarium huius, scilicet: omnis grammatica est virtus, per aliquod medium, quod contineatur sub virtute; et tunc maior erit vera, et minor falsa. Puta si dicamus: omnis temperantia est virtus; omnis grammatica est temperantia; ergo omnis grammatica est virtus.	Then (81a25) he shows how an affirmative syllogism of deception is formulated through an extraneous middle. And he says that if an extraneous middle be taken such that it is contained under the major extreme, then the major will be true and the minor false. For A, the major extreme, can be predicated universally of many things that are not under one another, say “habit” of grammar and virtue. For this is mediate, “No grammar is a virtue.” There we can conclude the contrary of this, namely, “All grammar is virtue,” through a middle which is contained under virtue. Then the major will be true and the minor false. For example, we might say: “All temperance is a virtue; grammar is temperance: therefore, all grammar is a virtue.”
Si vero accipiatur aliquod medium, quod non sit sub a, maior semper erit falsa, quia accipitur affirmativa. Sed minorem contingit esse cum hac quandoque quidem falsam, et tunc ambae erunt falsae, puta si dicamus: omnis albedo est virtus; omnis grammatica est albedo; ergo etc.; quandoque autem potest esse vera: nihil enim prohibet, sic se habentibus terminis, quod a removeatur ab omni d, et d sit in omni b, sicut est in his terminis, animal, scientia, musica. Animal enim, quod est maior extremitas, removetur universaliter ab omni scientia; unde haec, quae sumitur ut maior in syllogismo ignorantiae, omnis scientia est animal, est falsa. Minor vero, scilicet, omnis musica est scientia, est vera; sed conclusio falsa contraria negativae verae mediatae. Contingit etiam quod et a sit in nullo d, et d in nullo b, ut dictum est.	But if a middle is taken which is not under the major extreme, the major will always be false, because it will be affirmative. But the minor may sometimes be false with such a major; then both will be false. For example, if we should say: “Every whiteness is a virtue; all grammar is whiteness: therefore....” But sometimes it can be true. For when the terms are so related, there is nothing to hinder A from being removed from every D, and D from being in every B, as happens in these terms, namely, “animal,” “science,” “music.” For the major extreme, “animal,” is removed universally from all science; hence this proposition which is taken as the major in the syllogism of ignorance is false, namely, “Every science is an animal.” But the minor, namely, “All music is science,” is true. And the conclusion will be false, being contrary to the true mediate negative. It can also happen that A is in no D, and D in no B, as has been said.
Sic igitur patet quod quando medium non continetur sub maiori extremitate, possunt esse utraeque falsae et altera earum, quaecunque contingit, quia et maior et minor potest esse falsa: maior autem non potest esse vera, sic se habentibus terminis, ut supra dictum est. Ultimo autem epilogando concludit manifestum esse ex praedictis, quot modis et per quas propositiones veras vel falsas possunt fieri deceptiones per syllogismum, tam in propositionibus immediatis, quam in propositionibus mediatis, quae demonstratione probantur.	Thus it is evident that when the middle is not contained under the major extreme, they may both be false or just one of them, because the major and the minor may be false. However, with the three terms so related, as we have said above, the major cannot be true. Finally (81a35), he summarizes and concludes that it is plain from the foregoing how many ways and through which alignment of true and false propositions it is possible to construct deceptions through syllogisms, both in immediate propositions and in mediate propositions, which are proved by demonstration.