The Ways to Wisdom

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Aquinas’s topic:  logic of arguments: a second definition of demonstration


Aquinas’s text: Expositio libri Posteriorum , Bk. 1, lec. 4

Here Br. Thomas explains Aristotle’s second definition of demonstration, one which opens up six criteria for a demonstrative argument.

Then (71b17) he defines the demonstrative syllogism by comparing it to its end, which is to know scientifically. In regard to this he does three things. First, he asserts that to know scientifically is the end of a demonstrative syllogism or is its effect, since to know scientifically seems to be nothing other than to understand the truth of some conclusion through demonstration. Second (71b18), he defines demonstration through this kind of end, saying that a demonstration is a scientific syllogism , that is, one producing scientific knowledge. Third (71b18), he explains what he means by “scientific,” saying that a syllogism is called “scientific” through which we know scientifically, in so far as we possess it, lest someone think a scientific syllogism is one by means of which some scientific knowledge is put to further use.

Then (71b19) he concludes from the foregoing a definition of the demonstrative syllogism taken from its matter. And about this he does two things. First, he draws his conclusion, second he clarifies it (71b24).  And about the first point he does three things.

First (71b20), he sets forth the consequence in which he concludes to the material definition of demonstration from the premises laid down above. And he says that if “to know scientifically” signifies what we have said, namely, “to know the cause of a thing, etc.”, then it is necessary that “demonstrative science,” that is, science acquired through demonstration, proceed from propositions which are “true, first, and immediate,” that is, not demonstrated by some middle term, but clear through themselves—they are called “immediate” as lacking a middle demonstrating them and “first” in relation to other propositions proven through them—and furthermore they are “better known than, prior to, and causes of” the conclusion.

Second (71b22), he gives a reason for not adding another element that it might seem should be added, namely, that demonstration proceeds from proper principles. But he says that this point is understood by means of what he has said.  For since the propositions in a demonstration are the causes of the conclusion, it is necessary that they be its proper principles. For it is necessary that causes be proportioned to effects.

Third (71b23), he manifests the necessity of the foregoing consequence, saying that although a syllogism does not require these conditions in the premises from which it proceeds, a demonstration does require them, for otherwise it would not produce science.

Deinde, cum dicit: dicimus autem etc., definit syllogismum demonstrativum per comparationem ad finem suum, qui est scire. Circa quod tria facit. Primo, ponit quod scire est finis syllogismi demonstrativi sive effectus eius, cum scire nihil aliud esse videatur, quam intelligere veritatem alicuius conclusionis per demonstrationem. Secundo, ibi: demonstrationem autem etc., definit syllogismum demonstrativum per huiusmodi finem: dicens quod demonstratio est syllogismus scientialis, idest faciens scire. Tertio, exponit hoc quod dixerat scientialem; ibi: sed scientialem etc., dicens quod scientialis syllogismus dicitur, secundum quem scimus, in quantum ipsum habemus, ne forte aliquis syllogismum scientialem intelligeret, quo aliqua scientia uteretur.

Deinde, cum dicit: si igitur est scire etc., concludit ex praedictis definitionem syllogismi demonstrativi ex materia sumptam. Et circa hoc duo facit: primo, concludit; secundo, manifestat eam; ibi: verum quidem igitur oportet esse et cetera. Circa primum tria facit.

Primo, ponit consequentiam, qua demonstrationis materialis definitio concluditur ex praemissis, dicens quod si scire hoc significat quod diximus, scilicet, causam rei cognoscere etc., necesse est quod demonstrativa scientia, idest quae per demonstrationem acquiritur, procedat ex propositionibus veris, primis et immediatis, idest quae non per aliquod medium demonstrantur, sed per seipsas sunt manifestae (quae quidem immediatae dicuntur, in quantum carent medio demonstrante; primae autem in ordine ad alias propositiones, quae per eas probantur); et iterum ex notioribus, et prioribus, et causis conclusionis.

Secundo, ibi: sic enim erunt etc., excusat se ab additione alterius particulae, quae videbatur apponenda: quod scilicet demonstratio ex propriis principiis procederet. Sed ipse dicit quod hoc intelligitur per ea, quae dicta sunt. Nam si propositiones demonstrationis sunt causae conclusionis, necesse est quod sint propria principia eius: oportet enim causas esse proportionatas effectibus.

Tertio, ibi: syllogismus quidem etc., manifestat praemissae consequentiae necessitatem, dicens quod licet syllogismus non requirat praemissas conditiones in propositionibus, ex quibus procedit, requirit tamen eas demonstratio: aliter enim non faceret scientiam.

[Introductions and translations © R.E. Houser]

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