Authors/Thomas Aquinas/posteriorum/L2/Lect2

Lecture 2 Whether the definition which signifies the quod quid of a thing can be demonstrated

Latin	English
	Lecture 2 (90a36-91a3) WHETHER THE DEFINITION WHICH SIGNIFIES THE QUOD QUID OF A THING CAN BE DEMONSTRATED
lib. 2 l. 2 n. 1 Postquam philosophus ostendit quod omnis quaestio est quodammodo quaestio medii, quod quidem est quod quid est et propter quid, hic incipit manifestare qualiter medium nobis innotescat; et dividitur in partes duas: in prima parte ostendit quomodo quod quid est et propter quid se habent ad demonstrationem; in secunda parte ostendit quomodo oporteat investigare quod quid est et propter quid; ibi: quomodo autem oportet venari et cetera. Prima autem pars dividitur in partes duas: in prima, manifestat quomodo se habeat ad demonstrationem ly quid est; in secunda, manifestat quomodo se habeat ad demonstrationem ly propter quid, quod significat causam; ibi: quoniam autem scire opinamur cum sciamus causam et cetera.	After showing that every question is in some sense a question of the middle, which is the quod quid and the propter quid, the Philosopher now begins to make manifest how the middle becomes known to us. And it is divided into two parts. In the first part he shows how the quod quid and propter quid are related to demonstration. In the second part he shows how the quod quid and propter quid should be investigated (96a22) [L. 13]. The first part is divided into two parts. In the first he manifests how the quid est is related to demonstration. In the second he manifests how the propter quid which signifies a cause is related to demonstration (94a20) [L. 9]. In regard to the first he does two things. First, he states his proposal. Secondly, he pursues his proposal (90b1).
lib. 2 l. 2 n. 2 Circa primum duo facit: primo, dicit de quo est intentio; secundo, prosequitur propositum; ibi: principium autem sit futurorum et cetera. Dicit ergo primo quod quia omnis quaestio, ad cuius determinationem demonstratio inducitur, est quaestio medii, quod est quid et propter quid, oportet primo dicere per quem modum hoc ipsum quod quid est nobis ostendatur, utrum scilicet per demonstrationem, vel per divisionem, vel quovis alio modo. Et iterum oportet dicere quis sit modus reducendi ea quae apparent de re, ad quod quid est. Et quia definitio est oratio significans quod quid est, oportet etiam scire quid sit definitio et quae sint definibilia. In his autem hoc ordine procedemus: primo quidem opponendo; secundo autem veritatem determinando.	He says therefore first (90a36) that since every question for whose solution a demonstration is adduced is a question of the middle which is quid and propter quid, our first task is to declare how the quod quid is made known to us, namely, is it through demonstration or division or some other way. Furthermore, we must point out how to reduce to the quod quid those items of a thing that are apparent. And because a definition is a statement which signifies the quod quid, it is necessary also to know what a definition is and why certain things are definable. Consequently we shall proceed in these matters in the following way. First, by raising difficulties. Secondly, by establishing the truth (93a1) [L. 7]. Then (90b1) he pursues his proposal in the order stated. First, he proceeds dialectically by raising difficulties. Secondly, by determining the truth (93a1) [L. 7].
lib. 2 l. 2 n. 3 Deinde cum dicit: principium autem sit futurorum etc., exequitur propositum ordine praedicto. Unde primo, procedit circa praemissa disputative opponendo; secundo, veritatem determinando; ibi: iterum autem speculandum est quid horum et cetera. Circa primum duo facit: primo, procedit disputando de ipsa definitione, quae significat quod quid est; secundo, de ipso quod quid est per definitionem significato; ibi: ipsius autem quid est utrum syllogismus et cetera. Circa primum tria facit: primo, inquirit disputative utrum omnium quorum est demonstratio, sit definitio; secundo, utrum e converso omnium quorum est definitio, sit demonstratio; ibi: quid autem cuius est definitio etc.; tertio, utrum alicuius eiusdem sit definitio et demonstratio; ibi: sed utrum si non omnis et cetera.	In regard to the first he does two things. First, he proceeds by disputing about the definition which signifies quod quid. Secondly, about the quod quid which is signified by the definition (91a12) [L. 31. Concerning the first he does three things. First, he inquires disputatively whether there is definition of all things of which there is demonstration. Secondly, whether conversely there is demonstration of all things of which there is definition (91b19). Thirdly, whether there can be definition and demonstration of the same thing (90b27).
Circa primum duo facit: primo, dicit de quo est intentio; secundo, exequitur propositum; ibi: dubitabit enim utique aliquis et cetera. Dicit ergo primo quod inter ea quae in futurum dicenda sunt, principium oportet sumere ab eo quod est convenientissimum habitarum, idest consequentium rationum. Quod quidem est de hoc quod posset aliquis dubitare utrum contingat idem et secundum idem scire per definitionem et demonstrationem.	In regard to the first he does two things. First, he states his intention. Secondly, he pursues his proposal (90b1). He says therefore first (90b1) that when a number of items are planned for discussion, one should take his start from the item which is most fruitful in settling the “had,” i.e., the subsequent, problems. This would mean that in our case we should begin with the fact that someone might wonder whether the same thing and according to the same aspect could be known through definition and demonstration.
lib. 2 l. 2 n. 4 Deinde cum dicit: definitio quidem enim quod quid est etc., probat quod non omnium quorum est demonstratio, sit definitio. Et hoc quadrupliciter. Primo quidem, quia definitio est indicativa eius quod quid est; omne autem quod pertinet ad quod quid est, praedicatur et affirmative et universaliter; ergo definitio est solum eorum contentiva sive significativa, quae praedicantur affirmative et universaliter. Sed non omnes syllogismi sunt demonstrativi conclusionum affirmativarum universalium; sed quidam sunt negativi, puta omnes qui sunt in secunda figura; quidam vero particulares, puta omnes qui sunt in tertia figura. Non ergo omnium est definitio, quorum est demonstratio.	Then (90b4) he proves that there is not definition of all things of which there is demonstration. This he does in four ways, the first of which is the following: a definition is indicative of the quod quid; but anything which pertains to the quod quid is predicated both affirmatively and universally: therefore, a definition contains or signifies only those things which are predicated affirmatively and universally. But not all syllogisms demonstrate affirmative universal conclusions: in fact some are negative, as for example, all those in the second figure; and some are particular, as for example, all those in the third figure. Therefore, there is not definition of all things of which there is demonstration.
lib. 2 l. 2 n. 5 Secundo, ibi: postea neque eorum quae sunt etc., ostendit idem dicens quod neque definitio etiam potest esse omnium eorum quae concluduntur per syllogismos affirmativos, quod contingit esse solum in prima figura, sicut demonstrative syllogizatur quod omnis triangulus habet tres angulos aequales duobus rectis. Huius autem quod dictum est, scilicet quod non omnium quae sic syllogizantur, possit esse definitio, ratio est, quia scire aliquid demonstrative nihil aliud est quam demonstrationem habere. Ex quo patet quod si omnium horum scientia solum per demonstrationem habetur, non est eorum definitio. Ea enim quorum est definitio, cognoscuntur per definitionem. Sequeretur igitur quod aliquis non habens horum demonstrationem sciret ea; eo quod nihil prohibet aliquem habentem definitionem non simul habere demonstrationem; quamvis definitio sit demonstrationis principium. Non enim quicunque cognoscit principia, scit conclusionem deducere demonstrando.	Secondly (90b7), he shows the same thing when he says that there cannot even be definition of all things which are concluded through affirmative syllogisms-which occurs only in the first figure, as when it is demonstratively syllogized that every triangle has three angles equal to two right angles. Now the reason for this statement, namely, that there cannot be definition of all things thus syllogized, is that to know something demonstratively is nothing else than to have a demonstration. From this it follows that if the science of all these things is had only through demonstration, there is not definition of them. For things which have a definition are made known through their definition. Otherwise it would follow that a person who does not have a demonstration of these things would have scientific knowledge of them, for the simple reason that nothing hinders a person who knows the definition from not having at the same time the demonstration-although the definition is a principle of the demonstration. For not everyone who knows the principles knows how to deduce the conclusion by demonstrating.
lib. 2 l. 2 n. 6 Tertio, ibi: sufficiens autem fides est etc., ostendit idem per inductionem, ex qua potest fieri praemissae conclusionis sufficiens fides: quia demonstratio est eorum quae per se insunt, ut patet ex his quae in primo habita sunt. Nullus autem unquam cognovit per definitionem neque aliquid eorum quae per se insunt, neque etiam aliquid eorum quae per accidens insunt; non quod accidentium, quae per se vel per accidens insunt, non possunt esse aliquae definitiones, ut habetur in VII Metaph.; sed quia eius quod est inesse per se vel per accidens, quod syllogismus concludit, nullus unquam dedit definitionem.	Thirdly (9014), he shows the same thing through an induction from which a conviction can arise sufficient for admitting the above-mentioned conclusion. He says, therefore, that demonstration is concerned with things which are per se in something, as is clear from what has been established in the first book. But a definition never gives anyone a knowledge of those items which are per se in a thing, much less of those which are in it per accidens-not that there cannot be definitions of accidents which are in a thing per se or per accidens; but because no one has ever given the definition of that which is to be in a thing per se or per accidens, which the syllogism concludes.
lib. 2 l. 2 n. 7 Quarto, ibi: amplius si definitio substantiae etc., ostendit idem per rationem, quia definitio est notificatio substantiae: tum quia substantia principaliter definitur, accidens vero per posterius, definitione quae est per additamentum, ut habetur in VII Metaph.; tum etiam quia accidens non definitur, nisi quatenus significatur per modum substantiae per aliquod nomen. Haec autem de quibus sunt demonstrationes, non sunt substantiae, nec per modum substantiae significantur, sed per modum accidentium, scilicet secundum inesse aliquid alicui. Unde concludit non esse possibile quod definitio sit omnis eius cuius est demonstratio.	Fourthly (90b16), he shows the same thing with a reason, namely, that the definition makes the substance known: first of all, because substance is defined in a primary way, whereas accident is defined secondarily by means of a definition which adds something alien, as is stated in Metaphysics VII; and secondly, because an accident is not defined save insofar as it is signified after the manner of a substance by employing a noun. But the things upon which demonstrations bear are not substances nor things signified after the manner of substances, but things signified after the manner of accidents, namely, after the manner of something inhering in some thing. Hence he concludes that it is not possible that there be a definition of everything of which there is demonstration.
lib. 2 l. 2 n. 8 Deinde cum dicit: quid autem cuius est definitio etc., inquirit an e converso demonstratio sit omnis eius cuius est definitio. Et ostendit quod non, duplici ratione; quarum prima iam supra tacta est. Unius enim, in quantum est unum, videtur esse una scientia, idest unus modus cognoscendi. Unde si id quod est demonstrabile, vere scitur per hoc quod habetur demonstratio de eo, sequitur quoddam impossibile si per definitionem sciri possit; quia habens definitionem sciret aliquid demonstrabile absque hoc quod haberet demonstrationem: quod videtur inconveniens. Et haec ratio fuit secundo posita inter praemissas.	Then (90b19) he inquires whether conversely there is demonstration of everything of which there is a definition. And he shows that there is not for two reasons, the first of which has already been touched upon above. For it seems that of one thing, precisely as it is one, there is one science, i.e., one way of knowing it. Hence if that which is demonstrable is truly known scientifically in virtue of the fact that a demonstration is had of it, then something impossible follows, if it can also be scientifically known through a definition: for the one having the definition would be knowing something demonstrable without having the demonstration-which seems absurd. And this reason was the second of the four previously presented.
lib. 2 l. 2 n. 9 Secundam rationem ponit ibi: amplius principia demonstrationum et cetera. Definitiones enim sunt principia demonstrationum, ut in primo habitum est; sed principia non sunt demonstrabilia, quia sic sequeretur quod principiorum essent principia, et quod demonstrationes in infinitum procederent; quod est impossibile, ut in primo ostensum est. Unde sequitur quod definitiones sint indemonstrabiles, tanquam quaedam prima principia in demonstrationibus. Et sic non omnium quorum est definitio, est demonstratio.	Then (90b23) he gives the second reason. For definitions are principles of demonstrations, as was established in Book I; but the principles are not demonstrable—otherwise it would follow that there are principles of principles and that demonstrations would proceed to infinity, which is impossible, as we have shown in the first book. Hence it follows that definitions are not demonstrable, being as they are first principles in demonstrations. Consequently, there is not demonstration of all things of which there is definition.
lib. 2 l. 2 n. 10 Deinde cum dicit: sed utrum si non omnis etc., inquirit utrum sit possibile quod alicuius eiusdem sit definitio et demonstratio, etsi non omnis eiusdem. Et ostendit quod non, tribus rationibus. Quarum prima est, quia definitio est manifestativa eius quod quid est et substantiae, idest essentiae cuiuslibet rei. Demonstrationes autem hoc non manifestant, sed supponunt; sicut in mathematicis demonstrationibus arithmeticae supponitur quid est unitas et quid est impar; et simile est etiam in aliis demonstrationibus. Ergo non est eiusdem demonstratio et definitio.	Then (90b28) he inquires whether it is possible for there to be definition and demonstration of the same thing in some cases even though not of all. And with three reasons he shows that there is not. The first of these reasons is that a definition is manifestive of the quod quid and of the substance, i.e., of the essence, of a thing. Demonstrations, on the other hand, do not manifest this but suppose it: thus in mathematical demonstrations it is supposed from arithmetic what unity is and what odd is; and the same applies in other demonstrations. Therefore, there is not demonstration and definition of the same thing.
lib. 2 l. 2 n. 11 Secundam rationem ponit ibi: amplius omnis demonstratio etc.; quae talis est. In eo quod per demonstrationem concluditur, praedicatur aliquid de aliquo vel affirmative vel negative: sed in definitione non praedicatur aliquid de aliquo; sicut in hac definitione, homo est animal bipes, neque animal praedicatur de bipede, neque bipes de animali. Et similiter in hac definitione, circulus aut triangulus est figura plana, nec planum praedicatur de figura, neque e converso. Si enim partes definitionis adiungerentur sibi invicem, oporteret quod praedicatio intelligeretur per modum convenientem definitioni, scilicet in eo quod quid est. Hoc autem non videmus. Nec enim genus praedicatur in eo quod quid est de differentia, neque e converso. Non ergo eiusdem est definitio et demonstratio.	Then (90b33) he presents the second reason and it is this: In the conclusion of a demonstration something is predicated of something either affirmatively or negatively; but in a definition nothing is predicated of anything: thus in the definition that man is a two-footed animal, neither animal is predicated of two-footed nor two-footed of animal. Likewise in the definition that a circle or a triangle is a plane figure, neither plane is predicated of figure nor figure of plane. For if the parts of a definition were to be joined to one another, the resulting predication would have to be understood in a manner which suits a definition, namely, in quod quid. But this we do not observe. For the genus is not predicated quod quid of the difference, nor the difference of the genus. Therefore, there is not definition and demonstration of a same thing.
lib. 2 l. 2 n. 12 Tertiam rationem ponit ibi: amplius alterum est quod quid est etc.; et dicit quod alterum est manifestare quod quid est et quia est, ut patet in differentia quaestionum supra posita: sed definitio ostendit de aliquo quid est; demonstratio autem ostendit affirmative vel negative aliquid esse de aliquo vel non esse. Videmus autem quod alterius rei alia est demonstratio, nisi illa duo se habeant ad invicem sicut totum et pars; quia tunc una et eadem esset demonstratio de utroque. Sicut demonstrato quod triangulus habet tres angulos aequales duobus rectis, similiter etiam ostensum est de isoscele, qui se habet ad triangulum sicut pars ad totum. Sed non ita est in his duobus, quia est et quid est: neutrum enim est pars alterius.	Then (90b38) he gives the third reason and says that it is one thing to manifest the quod quid and another the quia, as is clear from the difference between the questions listed above; but the definition shows the quid of something, whereas a demonstration shows either affirmatively or negatively that something is or is not so of something. But we see that for different things different demonstrations are required, unless those two different things are related as whole and part: for in that case there would be one and the same demonstration concerning both. Thus, the demonstration that a triangle has three angles equal to two right angles applies also to isosceles, which is related to triangle as part to whole. But that is not the case in these two things, namely, in the quia and in the quid; for neither is a part of the other.
lib. 2 l. 2 n. 13 Ostensum est igitur quod nec omnis cuius est definitio, sit demonstratio, neque e converso. Et ex hoc ulterius concludi potest quod nullius eiusdem sint; et quod definitio et demonstratio neque sint idem, neque unum sit in alio sicut pars subiectiva in suo toto; quia oporteret quod etiam ea quorum sunt, se haberent per modum totius et partis, ita scilicet quod omne definibile esset demonstrabile, aut e converso. Quod supra improbatum est. Ultimo epilogando concludit usque ad hoc processum esse opponendo.	Therefore, it has been established that there is not demonstration of everything of which there is definition, nor conversely. Furthermore, it has been possible from this to conclude that these are not of the same thing, and that definition and demonstration are neither the same nor is one in the other as a subjective part in its whole—otherwise it would be necessary that even those things of which they are be related after the manner of whole and part in such a way, namely, that everything definable would be demonstrable, or vice versa—which was disproved above. Finally, he summarizes and concludes that so far we have proceeded by opposing.