The Ways to Wisdom
Aquinas Day By Day

74

Aquinas’s topic:  logic of arguments:  another kind of demonstration of the fact

Scripture:

Aquinas’s text:  Expositio libri Posteriorum , Bk. 1, lec. 24

Here Br. Thomas explains demonstration of the fact where the middle term is a remote cause rather than an effect.

After clarifying with examples how there can be demonstration of the fact through an effect, the Philosopher here shows how there can be demonstration of the fact through middle terms that are not immediate. About this he does two things.  First, he clarifies his thesis.  Second, he shows how middles are related to conclusions in this type of demonstration (78b27). Concerning the first he does three things:  first, he states his intention; second, he clarifies it with an example (78b14); third, he puts it in syllogistic form (78b24).

Therefodre, he says first (78b13) that there is demonstration of the fact and not of the reason why, not only in thing proven through an effect but also “where the middle is set outside.” Now a middle is said to be set outside when it is different from the major term, as happens in negative syllogisms; or a middle is said to be set outside when it is outside the genus, as being something more common and not convertible with the major term. That there cannot be a demonstration of ther reason why through a middle of this kind he proves on the ground that demonstration of the reason why is through a cause. But this kind of middle is not a cause, properly speaking.

Then (78b14) he clarifies what he said with an example, saying that if someone wants to prove that “a wall does not breathe because it is not an animal,” he does not have a demonstration of the reason why and does not have the cause. Because if not being an animal were the cause of not breathing, it would be necessary that being an animal would be the cause of breathing, which is false. For there are many animals that do not breathe. For it is necessary, if a negation is the cause of a negation, that the affirmation be the cause of the affirmation, for example, not being warm and cold in due measure is the cause why someone does not get well, and being warm and cold in due measure is the cause why someone does get well. The converse is also true, if an affirmation is the cause of an affirmation, the negation is the cause of the negation. But this does not happen in the case at hand, because the affirmation is not the cause of an affirmation, since “not every animal breathes.”

Then (78b24) he puts this example in syllogistic form and says that the syllogism must be arranged in the second figure. And this is so because in the first figure it cannot happen that when the conclusion is negative that the major is affirmative, as the example requires. For “to breathe,” which is the major term, must be joined with “animal,” which is the middle term, in an affirmation. But “wall,” which is the minor term, must be joined with “animal,” which is the middle, in a negation. Consequently, the major must be affirmative and the minor negative. But such a thing never occurs in the first figure, but only in the second.

Therefore, let “animal,” be A, that is, the middle term; let “breathe” be B, that is, the major extreme: and let “wall” be C, that is, the minor extreme. It therefore follows that “A is in every B,” because everything that breathes is an animal; but “A is in no C,” because no wall is an animal. So it follows that “B is in no C,” that is, that no wall breathes. Now if the proximate middle were used, it would be demonstration of the reason why.  For example, if it were shown that a wall does not breathe because it does not have lungs. For whatever has lungs breathes, and also the reverse.

Postquam manifestavit philosophus per exempla, qualiter demonstratur quia per effectum; hic ostendit qualiter demonstratur quia per non immediata. Et circa hoc duo facit: primo, manifestat propositum; secundo, ostendit qualiter in huiusmodi demonstrationibus media se habeant ad conclusiones; ibi: comparantur autem huiusmodi et cetera. Circa primum tria facit: primo, proponit intentum; secundo, manifestat per exemplum; ibi: ut quare non respirat etc.; tertio, ordinat in forma syllogistica; ibi: syllogismus autem et cetera. Dicit ergo primo quod non solum in his quae probantur per effectum demonstratur quia et non propter quid, sed etiam in quibus medium extra ponitur.

Dicitur autem medium extra poni quando est diversum a maiori termino, ut accidit in syllogismis negativis. Vel medium extra poni dicitur, quando est extra genus, quasi communius, et non convertitur cum maiori termino. Quod autem per tale medium non possit demonstrari propter quid probat ex hoc, quod demonstratio propter quid est per causam. Tale autem medium non est causa proprie loquendo.

Deinde cum dicit: ut quare non respirat etc., manifestat quod dixerat per exemplum, dicens: ut si quis velit probare, quod non respirat paries, quia non est animal, non demonstrat propter quid, nec accipit causam. Quia si non esse animal esset causa non respirandi, oporteret quod esse animal esset causa respirandi: quod falsum est. Multa enim sunt animalia quae non respirant. Oportet enim, si negatio est causa negationis, quod affirmatio sit causa affirmationis; sicut non esse calidum et frigidum in mensura est causa quod aliquis non sanetur, et esse calidum et frigidum in mensura est causa quod aliquis sanetur. Similiter autem est e converso, quod si affirmatio est causa affirmationis, et negatio est causa negationis. In praemissis autem hoc non contingit, quia affirmatio non est causa affirmationis; quia non omne quod est animal respirat.

Deinde cum dicit: syllogismus autem etc., ordinat praedictum exemplum in forma syllogistica, dicens quod syllogismum praedictum oportet fieri in media figura. Et hoc ideo est, quia in prima figura non potest esse, quando conclusio est negativa, quod maior sit affirmativa; quod oportet in praedicto exemplo esse. Nam respirare, quod est maior terminus, oportet quod coniungatur cum animali, quod est medius terminus, secundum affirmationem. Sed paries, quod est minor terminus, oportet quod coniungatur cum animali, quod est medium, secundum negationem. Et sic oportet quod maior sit affirmativa et minor negativa. Quod quidem nunquam fit in prima figura; sed solum in secunda. Accipiatur ergo animal a, idest medius terminus; b respirare, idest maior extremitas; et paries c, idest minor extremitas. Sic igitur a est in omni b, quia omne respirans est animal; in nullo autem c est a, quia nullus paries est animal: quare sequitur quod etiam b in nullo c sit, scilicet quod nullus paries respiret. Si autem acciperetur medium propinquum, esset demonstratio propter quid. Ut si ostenderetur quod paries non respiret, quia non habet pulmonem. Omne enim habens pulmonem respirat, et e converso.

[Introductions and translations © R.E. Houser]

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