Aquinas Day By Day


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


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


            Aristotle laid out the requirements for demonstrations in Posterior Analytics 1.6-12, but then in c. 13 he introduced a distinction between two kinds of demonstrations.  There the reader finds out that he has been presenting the stronger sort of demonstration, which is called “demonstration of the reason why (demonstratio propter quid),” so named because the demonstration gives the reason why a fact is true.  The lesser kind is called “demonstration of the fact (demonstratio quia),” because it proves the conclusion is a fact but does not explain why the conclusion is true.  Aristotle took his terminiology from two of the four questions he listed at Posterior Analytics 2.1.  About propositions, as opposed to terms, all questions reduce to two kinds:  a question of fact [Is it true that the planets are near?] or a question of why [Why are the planets near?].  Aquinas’s explanation of these two kinds of demonstrations is central to his own thought, as in his arguments for the existence of God.  Cf. Summa theologiae 1.2.2.


After determining about demonstration of the reason why (propter quid), the Philosopher here [c. 13] shows the difference between demonstration of the fact (quia) and demonstration of the reason why.  And he does two things about this:  first, he shows how they differ in the same science; second, in different sciences (78b33) [lec. 25]. Concerning the first point he does two things: first, he states a twofold difference between the two kinds of demonstration in the same science; secondl he makes them clear through examples (78a30).


Therefore, he says first (78a22), as was said above, that demonstration is a syllogism producing scientific knowledge and that it proceeds from the causes of a thing, both “first” and “immediate” causes.  Now one should understand this as referring to demonstration of the reason why.  But there is a difference between knowing “the fact that a thing is so” and “why it is so.” Since demonstration is a syllogism producing scientific knowledge, as was said, it is necessary that a demonstration which produces knowledge of the fact differ from a demonstration which produces knowledge of the reason why. This difference should be considered first in the same science and then in sciences that are different.


In one science, both the demonstrations mentioned above differ based on the two things required for demonstration in the strict sense, which produces knowledge of the reason why, namely, that it come “from causes” and “from immediate” causes. Therefore, in one way scientific knowledge of the fact differs from knowledge of the reason why because there can be knowledge of thefact even if the syllogism is not through what is “not mediate,” that is, through an “immediate” principle, but is through mediate principles.  For in this case a first cause is not used, while science of the reason why is based on a first cause.  And so it will not be scientific knowledge of the reason why.


They differ in a second way, because science of the fact comes about when the syllogism is not “through middles,” that is, mediate, but through immediate premisses, but is not through a cause but through “convertence,” that is, through effects that are convertible and immediate. However, such a demonstration comes about through what is better known, namely, to us; otherwise it would not produce scientific knowledge. For we do not reach knowledge of the unknown except through something better known. For nothing prohibits it jfrom happening that for two things “equally predicable,” that is, convertible, one of which is the cause and the other the effect, sometimes the better known is not the cause but the effect. For sometimes the effect is better known than the cause for us and based on sensation, even though the cause is always better known absolutely and by nature. In this way, through an effect better known than the cause there can be demonstration which does not produce knowledge of the reason why but only knowledge of the fact.

Postquam philosophus determinavit de demonstratione propter quid, hic ostendit differentiam inter demonstrationem quia, et demonstrationem propter quid. Et circa hoc duo facit: primo, ostendit differentiam utriusque in eadem scientia; secundo, in diversis; ibi: alio autem modo et cetera. Circa primum duo facit: primo, ponit duplicem differentiam utriusque demonstrationis in eadem scientia; secundo, manifestat per exempla; ibi: ut quod prope sint planetae et cetera.

Dicit ergo primo: superius dictum est quod demonstratio est syllogismus faciens scire, et quod demonstratio ex causis rei procedit et primis et immediatis. Quod intelligendum est de demonstratione propter quid. Sed tamen differt scire quia ita est, et propter quid ita est. Et cum demonstratio sit syllogismus faciens scire, ut dictum est, oportet etiam quod demonstratio quae facit scire quia, differat a demonstratione quae facit scire propter quid. Et horum quidem differentia primo consideranda est in eadem scientia; postea consideranda est in diversis.

In una autem scientia dupliciter differt utrumque praedictorum, secundum duo quae requirebantur ad demonstrationem simpliciter, quae facit scire propter quid; scilicet quod sit ex causis, et quod sit ex immediatis. Uno igitur modo differt scire quia ab hoc quod est scire propter quid; quia scire quia est si non fiat syllogismus demonstrativus per non medium, idest per immediatum, sed fiat per mediata. Sic enim non accipietur prima causa, cum tamen scientia, quae est propter quid, sit secundum primam causam. Et ita non erit scientia propter quid.

Alio modo differunt, quia scire quia est quando fit syllogismus non quidem per media, idest per mediata, sed per immediata, sed non fit per causam: sed fit per convertentiam, idest per effectus convertibiles et immediatos. Et tamen talis demonstratio fit per notius, scilicet nobis: alias non faceret scire. Non enim pervenimus ad cognitionem ignoti, nisi per aliquid magis notum. Nihil enim prohibet duorum aeque praedicantium, idest convertibilium, quorum unum sit causa, et aliud effectus, notius esse aliquando non causam, sed magis effectum. Nam effectus aliquando est notior causa quoad nos et secundum sensum, licet causa sit semper notior simpliciter, et secundum naturam. Et ita per effectum notiorem causa potest fieri demonstratio non faciens scire propter quid, sed tantum quia.

[Introductions and translations © R.E. Houser]