Authors/Thomas Aquinas/posteriorum/L1/Lect16

Lecture 16 Demonstration is not of perishable but of eternal matters

Latin	English
	Lecture 16 (75b21-36) DEMONSTRATION IS NOT OF PERISHABLE BUT OF ETERNAL MATTERS
lib. 1 l. 16 n. 1 Postquam ex superioribus philosophus concluserat quod demonstratio non concludit ex extraneis principiis, nunc iterum ex superioribus intendit concludere quod demonstratio non est de corruptibilibus. Et circa hoc duo facit: primo, ostendit quod sempiternorum et non corruptibilium est demonstratio; secundo, ostendit qualiter sit eorum quae sunt ut frequenter; ibi: eorum autem et cetera. Circa primum duo facit: primo, ostendit quod demonstratio non sit corruptibilium, sed sempiternorum; secundo, ostendit idem de definitione; ibi: similiter se habet et cetera. Circa primum duo facit: primo, proponit conclusionem intentam; secundo, ponit rationem probantem ipsam; ibi: quod autem universaliter et cetera.	After concluding from the above that demonstration does not conclude from extraneous principles, the Philosopher intends to conclude something else from the above, namely, that demonstration is not of destructible things. Concerning this he does two things. First, he shows that demonstration is of eternal and not of destructible things. Secondly, he shows how it is of things that occur now and then (75b32). Concerning the first he does two things. First, he shows that demonstration is not of perishable but of eternal things. Secondly, he shows that the same is true of definition (75b30). In regard to the first he does two things. First, he proposes the intended conclusion. Secondly, he sets down the reason proving it (75b24).
lib. 1 l. 16 n. 2 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.	Therefore first (75b21), he sets down two conclusions, one of which follows from the other. The first is that the conclusion of this demonstration which we are now discussing and which we can call demonstration in the full sense must be eternal: which, of course, follows from what has been stated so far, namely, that the propositions of a syllogism should be universal: which he signified by “said of all.” The second conclusion is that neither demonstration nor science is of destructible things, i.e., absolutely speaking, but only accidentally.
lib. 1 l. 16 n. 3 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.	Then (75b24) he presents an argument to prove the proposed conclusions. It is this: It is not the character of a destructible non-eternal conclusion to contain what is universally so, but what is so for a time and in certain instances. For it has been established above that “said of all” contains two things, namely, that it is not such as to be so in one case and not in another, or so at one time and not at another. But in destructible things we find that at one time something is so and at another not so. Hence it is clear that “said of all” or “said universally” are not found in destructible things. But where a conclusion is not universal, at least one of the premises is not universal. Therefore, a destructible conclusion must have followed from premises, one of which is not universal. Accordingly, when we add to this the fact that demonstration absolutely must be from what is universal, it follows that a demonstration cannot have a destructible conclusion, but must have an eternal one.
lib. 1 l. 16 n. 4 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.	Then (75b30) he shows that definition, too, is not of destructible but of eternal things. The reason for this is that demonstration, both as to its principles and conclusions, is of eternal and not of destructible things. But a definition is either a principle of a demonstration, a conclusion of a demonstration, or a demonstration with a different ordering of its terms. Therefore, a definition is not of destructible, but of eternal things.
lib. 1 l. 16 n. 5 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.	For a better understanding of this passage it should be noted that it is possible to give different definitions of the same thing, depending on the different causes mentioned. But causes are arranged in a definite order to one another: for the reason of one is derived from another. Thus the reason of matter is derived from the form, for the matter must be such as the form requires. Again, the agent is the reason for the form: for since an agent produces something like unto itself, the mode of the form which results from the action must be according to the mode of the agent. Finally, it is from the end that the reason of the agent is derived, for every agent acts because of an end. Consequently, a definition which is formulated from the end is the reason and cause proving the other definitions which are formulated from the other causes.
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.	Therefore, let us lay down two definitions, one of which is formulated from the material cause, for example, that a house is a shelter composed of stones, cement and wood; the other being formulated from the final cause, namely, that a house is a shelter protecting us from the rain and heat and cold. Now the first definition can be demonstrated from the second in the following way: Every shelter protecting us from rain, heat and cold should be composed of wood, cement and stones; but a house is such a thing: therefore...
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.	Thus it is clear that the definition formulated from the end is the principle of the demonstration, whereas the one formulated from the matter is the conclusion of the demonstration. However, the two can be combined in the following way to form one definition: A house is a shelter composed of the aforesaid, protecting us from rain, cold and heat. But such a definition contains all the elements of a demonstration, namely, a middle and a conclusion. Accordingly, such a definition is a demonstration differing merely in the arrangement of its terms, because the only way it differs from the demonstration is that it is not arranged in a syllogistic mode and figure.
lib. 1 l. 16 n. 6 Sciendum est autem quod quia demonstratio non est corruptibilium, sed sempiternorum, neque definitio, Plato coactus fuit ponere ideas. Cum enim ista sensibilia sint corruptibilia, videbatur quod eorum non posset esse neque demonstratio, neque definitio. Et ideo videbatur quod oporteret ponere quasdam substantias incorruptibiles, de quibus et demonstrationes et definitiones darentur. Et has substantias sempiternas vocabat species vel ideas.	Here we might remark that because demonstration, as well as definition, is not of destructible but of eternal things, Plato was led to posit “Ideas.” For since sensible things are destructible, it appeared that there could be neither demonstration nor definition of them. As a consequence it seemed necessary to postulate certain indestructible substances concerning which demonstrations and definitions could be given. These eternal substances are what he calls “Forms” or “Ideas.”
lib. 1 l. 16 n. 7 Sed huic opinioni occurrit Aristoteles superius dicens quod demonstratio non est corruptibilium nisi per accidens. Etsi enim ista sensibilia corruptibilia sint in particulari, in universali tamen quamdam sempiternitatem habent. Cum ergo demonstratio detur de istis sensibilibus in universali, non autem in particulari, sequitur quod demonstratio non sit corruptibilium, nisi per accidens; sempiternorum autem est per se.	However, Aristotle opposed this opinion above, when he said that demonstration is not of destructible things except per accidens. For although those sensible things are destructible as individuals, nevertheless in the universal they have a certain everlasting status. Therefore, since demonstration beais on those sensible things universally and not individually, it follows that demonstration is not of destructible things except per accidens, but of eternal things per se.
lib. 1 l. 16 n. 8 Deinde cum dicit: eorum autem quae etc., ostendit quomodo eorum, quae sunt ut frequenter, possit esse demonstratio, dicens: quod eorum quae saepe fiunt, sunt etiam demonstrationes et scientiae: sicut de defectu lunae, qui tamen non semper est. Non enim luna semper deficit, sed aliquando. Haec autem quae sunt frequenter, secundum quod huiusmodi sunt, idest secundum quod de eis demonstrationes dantur, sunt semper: sed secundum quod non sunt semper, sunt particularia. De particularibus autem non potest esse demonstratio, ut ostensum est, sed solum de universalibus. Unde patet quod huiusmodi, secundum quod de eis est demonstratio, sunt semper. Et sicut est de defectu lunae, ita est de omnibus aliis similibus.	Then (75b32) he shows how there can be demonstration of things that occur now and then, saying “that there are science and demonstrations of things that occur frequently, as the eclipse of the moon,” which is not always. For the moon is not always being eclipsed, but only now and then. Now things that occur frequently, so far as they are such, i.e., so far as demonstrations are given concerning them, are always; but they are particular, so far as they are not always. But demonstration cannot be of particulars, as we have shown, but only of universals. Hence it is clear that these things, insofar as there is demonstration of them, are always. And as in the case of the eclipse of the moon, so in all kindred matters.
Consideranda tamen est differentia inter ea. Quaedam enim non sunt semper secundum tempus, sunt autem semper per comparationem ad causam: quia nunquam deficit, quin posita tali causa, sequatur effectus; sicut est de defectu lunae. Nunquam enim deficit, quin semper sit lunae eclypsis, quandocunque terra diametraliter interponitur inter solem et lunam. In quibusdam vero contingit quod non semper sunt, etiam per comparationem ad causam: quia videlicet causae impediri possunt. Non enim semper ex semine hominis generatur homo habens duas manus; sed quandoque fit defectus vel propter impedimentum causae agentis vel materiae. In utrisque autem sic ordinandae sunt demonstrationes, ut ex universalibus propositionibus inferatur universalis conclusio, removendo illa, in quibus potest esse defectus vel ex parte temporis tantum vel etiam ex parte causae.	However, there are certain differences to be noted among them. For some are not always with respect to time, but they are always in respect to their cause, because it never fails that under given conditions the effect follows, as in the eclipse of the moon. For the moon never fails to be eclipsed when the earth is diametrically interposed between sun and moon. But others happen not to be always even in respect to their causes, i.e., in those cases where the causes can be impeded. For it is not always that from a human seed a man with two hands is generated, but now and then a failure occurs, owing to a defect in the efficient cause or material cause. However, in both cases the demonstration must be so set up that a universal conclusion may be inferred from universal propositions by ruling out whatever can be an exception either on the part of time alone, or also of some cause.