|Aquinas Day By Day|
Aquinas’s topic: logic of arguments: an example of syllogizing
Scripture: Aquinas’s text: Expositio libri Posteriorum , Bk. 1, lec. 1
Br. Thomas here uses a helpful example to clarify what we know ahead of time when we learning deductively by using syllogisms. This example, where Aristotle described a syllogism concluding that “this figure inscribed in a semicircle has three angels equal to two right angles,” shows that from the beginning of the Posterior Analytics Aristotle had been concerned to insure that demonstrative science extends all the way down to particulars.
Then [Aristotle] clarifies this with an example. Since to infer a conclusion two propositions are required, namely, a major premiss and a minor premises, when the major proposition is known, the conclusion is not yet known. Therefore, the major proposition is known before the conclusion not only in nature but also in time. Moreover, if in the minor proposition something is brought forward or used that is contained under the universal proposition which is the major, but it is not evident that it is contained under this universal, then the conclusion is not yet known, because the truth of the minor proposition will not yet be certain. But if the minor proposition includes a term about which it is clear that it is contained under the universal in the major proposition, then the truth of the minor proposition will be clear, because what is included under the universal shares in the same knowledge, and so one has knowledge of the conclusion at once. For example, suppose someone were to demonstrate in the following way: Assume “every triangle has three angles equal to two right angles.” When this is known, he will not yet know the conclusion. But when he later adds: “this figure inscribed in a semicircle is a triangle,” then he knows at once that it has three angles equal to two right angles. But if it were not clear that this figure inscribed in the semicircle is a triangle, the conclusion would not be known as soon as the minor was stated; but it would be necessary to search further for a middle term by which to demonstrate that “this figure is a triangle.”
By giving this example of things which are known prior in time to the conclusion, the Philosopher says that someone obtaining knowledge of a conclusion through demonstration knew beforehand in time this proposition, namely, that “every triangle has three angles equal to two right angles.” But when he brings forward this premiss, namely, that “this figure in the semicircle is a triangle,” at the same moment of time he knew the conclusion, because the premiss brought forward shares in the evidence of the universal under which it is contained, so that there is no need to search further for a middle term.
Et hoc ulterius manifestat per exemplum. Cum enim ad conclusionem inferendam duae propositiones requirantur, scilicet maior et minor, scita propositione maiori, nondum habetur conclusionis cognitio. Maior ergo propositio praecognoscitur conclusioni non solum natura, sed tempore. Rursus autem si in minori propositione inducatur sive assumatur aliquid contentum sub universali propositione, quae est maior, de quo manifestum non sit quod sub hoc universali contineatur, nondum habetur conclusionis cognitio, quia nondum erit certa veritas minoris propositionis. Si autem in minori propositione assumatur terminus, de quo manifestum sit quod continetur sub universali in maiori propositione, patet veritas minoris propositionis: quia id quod accipitur sub universali habet eius cognitionem, et sic statim habetur conclusionis cognitio. Ut si sic demonstraret aliquis, omnis triangulus habet tres angulos aequales duobus rectis, ista cognita, nondum habetur conclusionis cognitio: sed cum postea assumitur, haec figura descripta in semicirculo, est triangulus, statim scitur quod habet tres angulos aequales duobus rectis. Si autem non esset manifestum quod haec figura in semicirculo descripta est triangulus, nondum statim inducta assumptione sciretur conclusio; sed oporteret ulterius aliud medium quaerere, per quod demonstraretur hanc figuram esse triangulum.
Exemplificans ergo philosophus de his quae cognoscuntur ante conclusionem prius tempore, dicit quod aliquis per demonstrationem conclusionis cognitionem accipiens, hanc propositionem praescivit etiam secundum tempus, scilicet, quod omnis triangulus habet tres angulos duobus rectis aequales. Sed inducens hanc assumptionem, scilicet, quod hoc quod est in semicirculo sit triangulus, simul, scilicet tempore, cognovit conclusionem, quia hoc inductum habet notitiam universalis, sub quo continetur, ut non oporteat ulterius medium quaerere.
[Introductions and translations © R.E. Houser]