Aquinas Day By Day

295

Aquinas’s topic:  logic of arguments:  demonstrations of the fact and the reason why

Scripture:

Aquinas’s text:  Expositio libri Posteriorum , Bk. 1, lec. 23

Br. Thomas here explains Aristotle memorable examples of the difference between demonstration of the fact and demonstration of the reason why.          

Then (78a30) [Aristotle] clarifies the difference by examples. And this section is divided into two parts. In the first, he gives an example of demonstration of the fact that is through an effect; in the second, of demonstration of the fact that is through a mediate cause (78b13) [lec. 24]. The first is sub-divided into two parts. In the first, he gives an example of a syllogism through a convertible effect; in the second, of a syllogism through a non-convertible effect (78b10). The first is divided into two parts, based on the two examples he gives, the second of which begins at (78b3). Concerning the first he does two things. First, he gives an example of demonstration of the fact through an effect; second, he teaches how it can be converted into a demonstration of the reason why (78a39).

Therefore, he says first (78a30) that there is demonstration of the fact through an effect when one concludes that the planets are near because they do not twinkle. For not twinkling is not the cause why the planets are near, but the reverse is true: for the planets do not twinkle because they are near. For the fixed stars twinkle because in gazing at them sight is obscured because of their distance. Therefore, let the syllogism be formed thus:  “Everything that does not twinkle is near; but the planets do not twinkle; therefore, they are near.” Here let C be the planets, that is, let “planets” be the minor extreme.  Let B be “not twinkling,” that is, let “not twinkling” be the middle term.  And let A be “to be near,” that is, “to be near” is taken as the major extreme. Then the proposition, “Every C is B,” is true, because the planets do not twinkle. Also it is true that “Every B is A,” because every star that does not twinkle is near. Now the truth of a proposition like this must be obtained through induction or through sensation, because the effect here is better known to sense than the cause. And so, the conclusion, “Every C is A,” follows. This is the way it is demonstrated that the planets or the wandering stars are near. Therefore, this syllogism is not of the reason why but of the fact.  For it is not because they do not twinkle that planets are near but rather, because they are near, they do not twinkle.

Then (78b3) he presents another example of this kind of demonstration, saying that “in this way,” that is, by means of a demonstration of the fact, “one demonstrates that the moon is round through its phases,” according to which it waxes and wanes every month. They argue thus: Everything which waxes by describing a circule is circular; but the moon waxes in this way; therefore, it is circular. Put in this way, it is a syllogism demonstrating the fact.  But “if the middle is interchanged,” that is, if “circular” is made the middle term and “waxes” the major term, “it becomes a demonstration of the reason why.” For the moon is not circular because it waxes in this way, but because it is circular it undergoes such phases. Therefore, let C be “the moon,” that is, the minor extreme; let “waxing” be A, that is, the major extreme, and let “circular” be B, the middle term. In this way it must be understood as a syllotism of the fact.  By conversion it becomes a syllogism of the reason why.

Deinde cum dicit: ut quod prope etc., manifestat praedictam differentiam per exempla. Et dividitur in duas partes: in prima, ponit exempla de demonstratione quia, quae est per effectum; in secunda, de demonstratione quia, quae est per causam mediatam; ibi: amplius in quibus medium et cetera. Prima in duas: in prima, ponit exempla de syllogismo qui fit per effectum convertibilem; in secunda, de syllogismo qui fit per effectum non convertibilem; ibi: in quibus autem media et cetera. Prima dividitur in duas partes secundum duo exempla quae ponit; secunda pars incipit ibi: item sic lunam et cetera. Circa primum duo facit: primo, ponit exemplum de demonstratione quia, quae est per effectum; secundo, docet quomodo posset converti in demonstrationem propter quid; ibi: contingit autem et cetera.

Dicit ergo primo quod demonstratio quia per effectum est, si quis concludat quod planetae sunt prope propter hoc quod non scintillant. Non enim non scintillare est causa quod planetae sint prope, sed e converso. Propter hoc enim non scintillant planetae, quia sunt prope. Stellae enim fixae scintillant, quia visus in comprehensione earum caligat propter earum distantiam. Formetur ergo syllogismus sic: omne non scintillans est prope; planetae sunt non scintillantes; ergo sunt prope. Sit in quo c planetae, idest accipiatur planetae quasi minor extremitas. In quo autem b sit non scintillare, idest non scintillare accipiatur medius terminus. In quo autem a sit prope esse, idest prope esse accipiatur ut maior extremitas. Vera igitur est haec propositio: omne c est b, quia planetae non scintillant. Et iterum verum est quod omne b est a, quia omnis stella non scintillans prope est. Huiusmodi autem propositionis veritas oportet quod accipiatur per inductionem, aut per sensum, quia effectus hic est notior causa quantum ad sensum. Et sic sequitur conclusio quod omne c sit a. Et sic demonstratum est quod planetae sive stellae erraticae sunt prope. Hic igitur syllogismus non est propter quid, sed est quia. Non enim propter hoc quod non scintillant, planetae sunt prope, sed propter id quod prope sunt, non scintillant. …

Deinde cum dicit: item sic lunam demonstrant etc., ponit aliud exemplum ad idem, dicens quod sic (idest demonstratione faciente scire quia), demonstrant quod luna sit circularis per incrementa, quibus scilicet omni mense augetur et minuitur, sic argumentantes: omne quod sic augetur quasi circulariter, circulare est; augetur autem sic luna; ergo est circularis. Sic igitur factus est syllogismus demonstrans quia. Sed e converso, posito medio ipsius, fit syllogismus propter quid, scilicet si ponatur circulare ut medius terminus, et augmentum ut maior extremitas. Non enim ideo circularis est luna, quia sic augetur, sed quia circularis est, ideo talia augmenta recipit. Sit ergo luna in quo c, idest minor extremitas; augmentum in quo b, idest medius terminus; circularis autem in quo a, idest maior extremitas. Et hoc intelligendum est in syllogismo quia. E converso autem in syllogismo propter quid.

[Introductions and translations © R.E. Houser]