Authors/Thomas Aquinas/posteriorum/L2/Lect3

Lecture 3 Whether the quod quid signified by the definition can be demonstrated by taking convertible terms

Latin	English
	Lecture 3 (91a12-b11) WHETHER THE QUOD QUID SIGNIFIED BY THE DEFINITION CAN BE DEMONSTRATED BY TAKING CONVERTIBLE TERMS
lib. 2 l. 3 n. 1 Postquam philosophus disputative inquisivit utrum definitio significans quod quid est possit demonstrari, hic procedit ulterius ad inquirendum disputative utrum ipsum quod quid est, quod est definitionis significatum, possit demonstrative probari.	After inquiring disputatively whether the definition signifying quod quid can be demonstrated, the Philosopher continues to inquire disputatively and asks whether the quod quid itself, which is signified by a definition, can be proved demonstratively. First, he states what he intends. Secondly, he pursues his proposal (91a14).
Et primo, proponit quod intendit; secundo, exequitur propositum; ibi: syllogismus quidem enim et cetera. Movet ergo primo quaestionem: utrum possit esse syllogismus aut demonstratio eius quod quid est, ita scilicet quod concludatur hoc esse quod quid est huius; aut hoc non sit possibile, sicut supposuit ratio immediate praemissa?	First, therefore (91a12), he raises the question: Can there be a syllogism or demonstration of that which is the quod quid, namely, in such a way as to conclude that this is the quod quid of this; or can this not be done, as the immediately preceding reason supposed?
lib. 2 l. 3 n. 2 Fuit autem necessaria haec disputatio post praemissam, quia in definitione attenditur non solum ut illud quod significatur, sit quod quid est, sed etiam ut tali modo tradatur qui competat ad manifestandum quod quid est; ita scilicet quod sit ex prioribus et notioribus, et alia huiusmodi habeat quae in definitione sunt observanda. Signanter autem dicit, utrum sit syllogismus aut demonstratio: nam rationum subsequentium quaedam concludunt quod eius quod quid est non sit demonstratio, quaedam vero quod eius omnino non sit syllogismus.	Now it was necessary to undertake this disputation on the heels of the previous one, because in a definition one must be sure not only that what it signifies is the quod quid, but also that it be formulated in such a. way as to be suitable for manifesting the quod quid, i.e., in such a way as to be composed of prior and better known items and possess the other diaracteristics which mark a definition. It is significant that he says, .1 whether there be syllogism or demonstration,” for some of the reasons which follow conclude that there is not demonstration of the quod quid, and others that there is no syllogism at all of it.
lib. 2 l. 3 n. 3 Deinde cum dicit: syllogismus quidem enim aliquid de aliquo etc., procedit disputative ad ostendendum quod non sit syllogismus vel demonstratio eius quod quid est. Et primo, excludit quosdam speciales modos, quibus posset videri quod possit demonstrari quod quid est; secundo, ponit rationes communes ad hoc; ibi: amplius quomodo demonstrabit et cetera. Circa primum tria facit: primo, ostendit quod non potest demonstrari quod quid est per acceptionem convertibilium terminorum; secundo, quod non potest demonstrari per divisionem; ibi: at vero neque per divisionem etc.; tertio, quod non potest demonstrari accipiendo id quod requiritur ad quod quid est; ibi: sed utrum sit demonstrare et cetera.	Then (91a14) he proceeds disputatively to show that there is not sy1logism, or demonstration of the quod quid. First, he excludes certain special ways by which it might seem possible to demonstrate the quod quid. Secondly, he presents common reasons for this (953) [L. 6]. Concerning the first he does three things. First, he shows that quod quid cannot be demonstrated by using convertible terms. Secondly, that it cannot be demonstrated by division (91b12) [L. 4]. Thirdly, that it cannot be demonstrated by accepting that which is required for quod quid (92a6) [L. 51.
Circa primum tria facit: primo, praemittit quaedam quae sunt necessaria ad propositum ostendendum; secundo, inducit rationem; ibi: si enim ipsius ca proprium est etc.; tertio, manifestat inconveniens quod sequitur; ibi: oportet autem in duabus propositionibus et cetera.	In regard to the first he does three things. First, he prefaces certain notions required for showing the proposal. Secondly, he induces a reason (91a17). Thirdly, he discloses the inconvenience which follows (91a32).
lib. 2 l. 3 n. 4 Circa primum praesupponit duo. Quorum primum pertinet ad syllogismum, scilicet quod omnis syllogismus probat aliquid de aliquo per aliquod medium, ut ex superioribus patet. Aliud autem pertinet ad ipsum quod quid est, quod est per syllogismum probandum; ad quod requiruntur duae conditiones. Quarum una est quod quod quid est sit proprium: quaelibet enim res habet propriam essentiam sive quidditatem. Et quia non omne quod est proprium alicui pertinet ad essentiam eius, sicut risibile homini; ideo requiritur secunda conditio, quod praedicetur in quid. Et has duas conditiones necesse est sequi tertiam, scilicet ut quod quid est sit convertibile cum eo cuius est.	With respect to the first (9104) he presupposes two things: the first of these pertains to the syllogism, namely, that every syllogism proves something about something by means of some middle, as is clear from the above. The other pertains to what is to be proved by the syllogism, namely, the quod quid, for which two conditions are required. The first of these is that the quod quid be proper, for each thing has its own proper essence or quiddity. But because not everything which is proper to something pertains to its essence, a second condition is required, namely, that it be predicated in quid. Furthermore, a third condition must follow on these two, namely, that the quod quid be convertible with that of which it is.
lib. 2 l. 3 n. 5 Deinde cum dicit: si enim a ipsi c est proprium etc., ponit rationem ad propositum ostendendum. Et circa hoc tria facit: primo, dicit qualem oporteat esse syllogismum qui concludit quod quid est, si hoc sit possibile; secundo, concludit inconveniens, quod ex hoc sequitur; ibi: si ergo quod quid est etc.; tertio, exemplificat in terminis; ibi: et omnino si est monstrare et cetera. Circa primum tria facit: primo enim ostendit quid requiratur ad syllogismum concludentem quod quid est, ex eo quod est proprium; secundo, quid requiratur ex eo quod praedicatur in quid; ibi: at vero et si a etc.; tertio, ostendit quod sine his talis syllogismus esse non possit; ibi: si vero aliquis et cetera.	Then (91a17) he lays down a reason in support of his proposal. Regarding this he does three things. First, he states what sort of syllogism would be required for concluding a quod quid, if this were possible. Secondly, he concludes to the inconvenience that follows from this (9145). Thirdly, he uses terms to exemplify this (91a28). Concerning the first he does three things. First, he shows what is required for a syllogism concluding the quod quid so far as it is something proper. Secondly, what is required so far as it is predicated in quid (9108). Thirdly, he shows that without these characteristics such a syllogism would not be possible (91a21).
Dicit ergo primo quod si a, quod est probandum de c tanquam quod quid est eius, est proprium ipsi c (quod requiritur ad quod quid est, ut dictum est), oportebit quod primum, scilicet a, sit proprium medio, quod est b: nam si a excedit b, quod universaliter praedicatur de c, sequitur quod a multo magis excedat c. Et similiter manifestum est quod oportebit b esse proprium ipsius c: nam si b excedat c, sequitur quod a, quod praedicatur universaliter de b, excedat c; et sic non erit proprium eius, ut supponebatur. Relinquitur ergo quod si aliquis syllogismus sit, qui concludit quod quid est, oportet esse talem habitudinem terminorum eius, ut omnes ad invicem convertantur.	He says therefore first (9108) that if A which is to be proved of C as its quod quid is proper to C (which is required of the quod quid, as has been said), it will be necessary that the first, namely, A, be proper to the middle which is B; for if A exceeded [i.e., were more universal than] B, which is predicated universally of C, it would follow that A exceeds C even more. In like manner, it is clear that B will have to be proper to C: for if B were to exceed C, it would follow that A, which is predicated universally of B, exceeds C; consequently, it would not be proper to it, as was supposed. What remains, therefore, is that if there is to be a syllogism concluding quod quid, the terms will have to be so related that all are mutually convertible.
lib. 2 l. 3 n. 6 Deinde cum dicit: at vero et si a in eo quod quid est etc., ostendit quid debeat habere syllogismus praedictus, ex eo quod concludit id quod praedicatur in eo quod quid est. Et dicit quod oportet hoc modo syllogismum procedere, ut maior extremitas, quae est a, praedicetur in eo quod quid de medio, quod est b; et b similiter praedicetur in eo quod quid de minori extremitate, quae est c; et sic concluditur quod a praedicetur de c in eo quod quid est.	Then (91a18) he shows what the syllogism in question must have, if the condition is to be fulfilled that what it concludes be predicated in quod quid. And he says that such a syllogism must be so formulated that the major extreme, which is A, be predicated in quod quid of the middle, which is B; in like manner, B will have to be predicated in quod quid of the minor extreme, which is C. In this way it can be concluded that A is predicated of C in quod quid.
lib. 2 l. 3 n. 7 Deinde cum dicit: si vero aliquis non accepit sic duplicans etc., ostendit quod praedictus modus syllogizandi requiratur. Et dicit quod si aliquis non ita accipiat terminos duplicans, idest observans duas conditiones praedictas, vel potius accipiens quod quid est ex duabus partibus, non sequitur ex necessitate quod a praedicetur de c in eo quod quid est. Sed et si ex una tantum parte praedictae conditiones observentur, non sufficit ad propositum. Etsi enim detur quod a praedicetur de b in eo quod quid est, non propter hoc sequitur quod praedicetur in eo quod quid de quibuscunque praedicatur b qualitercunque. Et sic sequitur quod ex utraque parte oporteat accipere quod quid est: ita scilicet quod non solum a sit quod quid est ipsius b, sed etiam ipsum b sit quod quid est ipsius c, tanquam convertibiliter et in eo quod quid praedicatum.	Then (91a21) he shows that the aforesaid way of syllogizing is required. And he asserts that if one does not so take the terms by “thus duplicating,” i.e., observing the two conditions laid down above, i.e., taking the quod quid on the side of both, it does not follow of necessity that A would be predicated of C in quod quid. Indeed, if the aforesaid conditions are observed on the part of one only, it is not sufficient for the purpose intended. For even if A were predicated of B in quod quid, it would not on that account follow that it must be predicated in quod quid of everything of which B might happen to be predicated in some random way. Consequently, it follows that the quod quid must be taken on the side of both in such a way, namely, that not only must A be the quod quid of B, but also that B must be the quod quid of C, as being predicated convertibly and in quod quid.
lib. 2 l. 3 n. 8 Deinde cum dicit: si igitur quod quid est et quod quid erat esse etc., ducit ad inconveniens: quia si, sicut ostensum est, ex utraque parte invenitur non solum praedicari aliquid in eo quod quid, sicut genus praedicatur de specie, sed etiam quod ex utraque parte sit quod quid erat esse, quod significat definitio, sequitur quod quid erat esse prius fuisse in medio termino; idest quod medius terminus sit quod quid erat esse minoris extremitatis: et ita supponitur quod oportebat probare, scilicet quidditatem ipsius c.	Then (91a25) he leads to the inconvenience: for if, as has been indicated, not only is there found on the side of both something which is predicated in quod quid-as a genus predicated of a species-but it is further found on the side of both that this something is the quod quid erat esse-which a definition signifies-it follows that the quod quid erat esse was already in the middle term, i.e., that the middle term is the quod quid erat esse of the minor extreme. Consequently, we would have been supposing the very thing we had set out to prove, namely, the quiddity of C. [quod quid erat esse refers to the essential nature of a being.]
lib. 2 l. 3 n. 9 Deinde cum dicit: et omnino si est monstrare quid etc., manifestat quod dixerat in terminis. Puta si volumus monstrare quid est homo, sit c, idest minor extremitas, homo; a vero, idest maior extremitas, sit quod quid est hominis, puta animal bipes, vel aliquid aliud huiusmodi. Si ergo hoc oporteat per syllogismum probari, necesse est quod definiatur aliquod medium, scilicet b, de quo omni a praedicetur; et ad hoc medium pertinebit quaedam alia media definitio, quae scilicet erat definitio minoris extremitatis. Unde sequetur quod hoc etiam medium sit quod quid est hominis. Et ita qui sic syllogizat, accipit supponendo id quod oportebat ostendere, scilicet quod b sit quod quid erat esse hominis.	Then (91a28) he clarifies what he has just said, using terms. Thus, if we wish to show what man is, let C, i.e., the minor extreme, be “man,” and A, the major extreme, be the “quod quid of man,” say “two-footed animal,” or something similar to this. Therefore, if this is what we intend to prove by the syllogism, it is necessary to find the definition of some middle, namely, B, such that A will be predicated of every B. Furthermore, to this middle will pertain some other middle definition which, namely, was the definition of the minor extreme. Hence it will follow that this middle will also be the quod quid of man. Consequently, one who syllogizes in this way would be supposing what he was required to prove, namely, that B is the quod quid erat esse of man.
lib. 2 l. 3 n. 10 Deinde cum dicit: oportet autem in duabus etc., manifestat quomodo hoc inconveniens sequatur ex praemissis. Et circa hoc tria facit. Primo, ostendit modum quo convenienter hoc manifestetur. Et dicit quod id quod dictum est, oportet considerare in duabus propositionibus, quae sint primae et habeant terminos immediate sibi inhaerentes. Possibile enim esset per plures propositiones hoc ostendere, ex quibus plures syllogismi constarent; vel etiam esset possibile duas solas propositiones accipiendo, accipere eas mediatas. Sed quia oportet semper reducere ad duas primas immediatas, ideo, ut brevior et expeditior sit consideratio, assumamus a principio tales propositiones, et sic maxime poterit manifestari propositum.	Then (91a32) he shows how this inconvenience follows from the premises. To this end he does three things. First, he indicates the method by which this may be fittingly done. And he says that what has been said should be considered in two propositions which are first and which have terms that belong to each other immediately. For it would be possible to prove our point either with several propositions (which would lead to several syllogisms), or with only two propositions, but taking them as mediate. But because in the final analysis we must always arrive at two immediate propositions, then for the sake of brevity and dispatch let us assume such propositions from the very start. Thus we shall be able to manifest our point quite easily.
lib. 2 l. 3 n. 11 Secundo, ibi: qui quidem itaque per conversionem etc., proponit quod intendit; et dicit, concludens ex praemissis, quod illi qui volunt demonstrare per terminos convertibiles quod quid est alicuius rei, puta quid est anima, vel quid est homo, vel quodcunque aliud huiusmodi, necesse est quod incidant in hoc quod petant principium. Et inducit exemplum de definitione animae secundum Platonem. Quia enim anima vivit, et est corpori causa vivendi, sequitur quod differat a corpore per hoc quod corpus vivit per aliam causam, anima vero vivit per seipsam.	Secondly (91a35), he states what he intends and says, concluding from the foregoing, that those who would demonstrate through convertible terms the quod quid of some thing (say, what is a soul, or what is man, or anything else of this sort), necessarily commit the fault of begging the question. And he cites as an example Plato’s definition of soul. For since the soul is alive and is the body’s cause of being alive, it follows that it differs from the body in the fact that the body lives in virtue of some cause other than itself, but the soul lives in virtue of itself. But Plato posited that number is the substance of all things: for he failed to distinguish between one, which is converted with being and refers to the substance of that of which it is predicated, and one which is the principle of number. As a consequence, it followed that the soul as to its substance is a number, just as any other thing containing many things in itself.
Ponebat autem Plato quod numerus est substantia omnium rerum: eo quod non distinguebat inter unum quod convertitur cum ente, quod significat substantiam eius de quo dicitur, et unum quod est principium numeri; et ita sequebatur quod anima substantialiter sit numerus, sicut et quaelibet alia res multa in se continens. Item ponebat Plato quod vivere sit quoddam moveri. Duobus enim distinguitur vivum a non vivente, scilicet sensu et motu, ut dicitur in I de anima; et ipsum sentire sive cognoscere dicebat esse quoddam moveri. Sic ergo dicebat animam esse numerum seipsum moventem: dicebat etiam animam esse id quod est sibi causa vivendi. Si quis ergo velit probare quid est anima, quia scilicet est id quod est sibi causa vivendi, et assumat pro medio quod anima est numerus seipsum movens, necesse est hoc petere, scilicet quod anima sit numerus seipsum movens: ita scilicet quod hoc sit idem ipsi animae, tanquam quod quid est eius. Alioquin non sequeretur quod si aliquid est quod quid est numeri moventis seipsum, quod sit quod quid est ipsius animae.	Likewise Plato posited that to live is one of the ways of being moved. For the living are distinguished from the non-living on two scores, namely, sense and movement, as it is stated in On the Soul I. Furthermore, he asserted that sensing or knowing is one way of being moved. Thus, therefore, he said that the soul is a self-moving number in addition to saying that the soul is its own cause of being alive. Consequently, if anyone desired to prove what a soul is, namely, that it is something which is its own cause of being alive, and assumed as middle that the soul is a number which moves itself, it would be necessary to beg this, namely, that the soul is a self-moving number, such that this is identical with the soul as being its quod quid. Otherwise, it would not follow, if something is the quod quia of self-moving number, that it is the quod quid of the soul itself.
lib. 2 l. 3 n. 12 Tertio, ibi: non enim si consequitur etc., probat propositum, scilicet quod talis probatio contineat petitionem principii; et dicit quod non sequitur quod maior extremitas, quae est a, sit quod quid est minoris extremitatis, quae est c, ex hoc quod a sequitur ad b et b sequitur ad c; sed sequitur simpliciter quod a insit c. Et si ulterius detur quod ipsum a sit quod quid est alicuius, et praedicetur universaliter de b, non adhuc sequitur quod a sit quod quid est ipsius c: manifestum est enim hoc quod est animali esse, idest quod quid est animalis, praedicari de hoc quod est homini esse, idest de eo quod est quod quid est hominis. Sicut enim verum est quod animal universaliter praedicatur de homine, ita verum est quod definitio animalis universaliter praedicetur de definitione hominis, non tamen ut sint omnino unum et idem.	Thirdly (91b1), he proves his proposal, namely, that such a proof involves begging the question. And he says that it does not follow from the fact that A follows on B and B on C, that the major extreme, A, is the quod quid of the minor extreme, C; what follows is simply that A is in C. And if it is further granted that A is the quod quid of something and is predicated universally of B, it does not yet follow that A is the quod q uid of C: for it is plain that this, i.e., the quod quid of animal is universally predicated of this which is man’s quod quid. For just as it is true that animal is universally predicated of man, so it is true that the definition of animal is universally predicated of the definition of man; but that does not mean that they are entirely one and the same.
Sic igitur patet quod si aliquis non sic accipiat terminos, ut primum sit omnino unum et idem medio, et medium ultimo, non poterit syllogizari quod a, quod est primum, sit quod quid est ipsi c, quod est ultimum, et essentia eius. Si vero accipiantur termini modo praedicto, sequitur quod priusquam concludatur, accipiatur in praemissis quod quid est ipsius c, scilicet ipsum b. Ex quo sequitur quod non sit demonstratio, sed petitio vel acceptio principii.	And so it is clear that unless one takes the terms in such a way that the first is entirely one and the same with the middle, and the middle with the last, it will not be possible to syllogize that A, which is the first, is the quod quid of C—which is the last—and its essence. But if the terms are taken in that way, it follows that prior to its being concluded, the quod quid of C, namely, B, was assumed in the premises. From this it follows that there is not a demonstration but a begging or assuming of the question.