The Ways to Wisdom
Aquinas Day By Day


Aquinas’s topic:  logic of arguments:  demonstration of the eternal


Aquinas’s text: Expositio libri Posteriorum , Bk. 1, lec. 16

At Posterior Analytics 1.7, Aristotle had directly faced the challenge of extending demonstrative science beyond the strictures Plato had put on it.  He stretched “science” from the realm of eternal and unchanging being to the individual, changing things that make up the physical world.  To do so, Aristotle argued in two steps.  Here is Br. Thomas’s commentary on the first step of Aristotle’s argument, where he agrees with Plato that science discovers unchanging and “eternal” truths.

After concluding from what came earlier that demonstration does not draw conclusions based on extraneous principles, the Philosopher now intends to conclude something else from what he said earlier, namely, that there is no demonstration about destructible things [corruptibilibus]. … Therefore, first (75b21) he sets down two conclusions, one of which follows from the other. The first is that the conclusion of the kind of demonstration with which we are now dealing, and which we can call demonstration in the full sense, must be eternal [perpetuum].  This follows from what was said above, namely, that the propositions from which a syllogism comes should be universal.  This he signified by “said of all.” The second conclusion is that there is no demonstration or science of destructible things, that is, speaking absolutely, but only incidentally.

Then (75b24) he presents an argument to prove these conclusions, which is this: A conclusion about the destructible and non-eternal does not contain in itself what is universally so but only what is so some time and in some respect.  For it was said above that “said of all” contains two points, namely, that it is not in one case but not in another, or at one time but not at another. But in all destructible things one finds it is at one time so and at another not so. Consequently, it is clear that in destructible things are not found “said of all” or said “universally.” But where a conclusion is not universal, at least one of the premises must not be universal. Therefore, a desctructible conclusion must have followed from premises, one of which is not universal. Therefore, when we add to this the fact that an absolute demonstration must be from universals, it follows that a demonstration cannot have a destructible conclusion, but must have an eternal one.

Then (75b30) he also shows that definition, too, is not about destructible things but about eternal things, using this kind of reasoning:  Demonstration, in both its principles and conclusions, is about eternal and not destructible things. But a definition is either a principle of a demonstration or a conclusion of a demonstration or a demonstration with a different order in its terms. Therefore, a definition is not about destructible, but eternal things.

To understand this passage, one ought to know that it is possible to give different definitions of the same thing, based on different causes. Now the causes are related to each other in a definite order. For the reason for one is taken from another. For the reason for the matter is taken from the form, since the matter must be such as the form requires. And the efficient cause is the reason for the form, for since an agent makes something like itself, the mode of the form which results from the action must be based on the mode of the agent. And from the end is taken the reason for the agent, for every agent acts for the sake of an end. Therefore, a definition which is taken from the end is the reason and cause proving the other definitions which are taken from the other causes.

Therefore, let us lay down two definitions of a house, one of them is taken from the material cause and is this:  a house is a shelter composed of stones, cement, and wood.  A second definition is taken from the final cause and is this:  a house is a shelter protecting us from the rain and cold and heat. Now the first definition can be demonstrated from the second, as follows:  Every shelter protecting us from rain, heat and cold should be composed of stones, cement, and wood; but a house is this sort of thing; therefore, etc.

Therefore, it is clear that the definition taken from the end is the principle of the demonstration, while the definition taken from the matter is the conclusion of the demonstration. Now both can be combined in one definition, as follows:  A house is a shelter composed as was said, protecting us from rain, cold, and heat. Such a definition contains all that was in the demonstration, namely, a middle and a conclusion. Therefore, such a definition differs from a demonstration in its arrangement, because it differs from a demonstration only because it is not arranged in a syllogistic mood and figure.

Postquam ex superioribus philosophus concluserat quod demonstratio non concludit ex extraneis principiis, nunc iterum ex superioribus intendit concludere quod demonstratio non est de corruptibilibus. … Primo ergo ponit duas conclusiones, quarum una sequitur ex altera. Prima est quod necesse est conclusionem demonstrationis huius de qua nunc agitur, et quam possumus dicere simpliciter demonstrationem, esse perpetuam; quod quidem sequitur ex hoc, quod supra habitum est, scilicet quod propositiones, ex quibus fit syllogismus, debent esse universales: quod significavit per dici de omni. Secunda conclusio est quod neque demonstratio, neque scientia est corruptibilium, loquendo simpliciter, sed solum secundum accidens.

Deinde cum dicit: quod autem universaliter etc., inducit rationem ad probandum propositas conclusiones: quae talis est. Conclusionis corruptibilis, et non sempiternae, non est in se continere quod est universaliter, sed aliquando et sic. Dictum est enim supra quod dici de omni duo continet, scilicet quod non in quodam sic et in quodam non, et iterum, quod non aliquando sic et aliquando non. In omnibus autem corruptibilibus invenitur aliquando sic et aliquando non. Unde patet quod in corruptibilibus non invenitur dici de omni, sive quod est universaliter. Sed ubi conclusio est non universalis, oportet aliquam praemissarum esse non universalem. Conclusio ergo corruptibilis oportet quod sequatur ex praemissis, quarum altera non sit universalis. Cum ergo huic coniunxerimus quod demonstratio simpliciter semper debet esse ex universalibus, sequitur quod demonstratio non possit habere conclusionem corruptibilem, sed sempiternam.

Deinde cum dicit: similiter se habet etc., ostendit quod etiam definitio est non corruptibilium, sed sempiternorum, tali ratione. Demonstratio quantum ad principia et conclusiones est sempiternorum et non corruptibilium; sed definitio vel est principium, vel conclusio demonstrationis, vel demonstratio positione differens; ergo definitio non est corruptibilium, sed sempiternorum.

Ad intellectum autem huius literae sciendum est quod contingit definitiones diversas dari eiusdem rei, sumptas ex diversis causis. Causae autem ad invicem ordinem habent: nam ex una sumitur ratio alterius. Ex forma enim sumitur ratio materiae: talem enim oportet esse materiam, qualem forma requirit. Efficiens autem est ratio formae: quia enim agens agit sibi simile, oportet quod secundum modum agentis sit etiam modus formae, quae ex actione consequitur. Ex fine autem sumitur ratio efficientis: nam omne agens agit propter finem. Oportet ergo quod definitio, quae sumitur a fine, sit ratio et causa probativa aliarum definitionum, quae sumuntur ex aliis causis. Ponamus ergo duas definitiones domus, quarum una sumatur a causa materiali, quae sit talis: domus est cooperimentum constitutum ex lapidibus, cemento et lignis. Alia sumatur ex causa finali, quae sit talis: domus est cooperimentum prohibens nos a pluviis, frigore et calore. Potest ergo prima definitio demonstrari ex secunda, hoc modo: omne cooperimentum prohibens nos a pluviis, frigore et calore oportet quod sit constitutum ex lapidibus, cemento et lignis; domus est huiusmodi; ergo et cetera. Patet ergo quod definitio, quae sumitur a fine, est principium demonstrationis; illa autem, quae sumitur a materia, est demonstrationis conclusio. Potest tamen utraque coniungi, ut sit una definitio, hoc modo: domus est cooperimentum constitutum ex dictis, defendens a pluvia, frigore et calore. Talis autem definitio continet totum quod est in demonstratione, scilicet medium et conclusionem. Et ideo talis definitio est demonstratio positione differens; quia in hoc solo differt a demonstratione, quia non est ordinata in modo et figura.

[Introductions and translations © R.E. Houser]

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