Authors/Thomas Aquinas/posteriorum/L2/Lect4

Lecture 4 Whether quod quid can be demonstrated by the method of division

Latin	English
	Lecture 4 (91b12-92a6) WHETHER QUOD QUID CAN BE DEMONSTRATED BY THE METHOD OF DIVISION
lib. 2 l. 4 n. 1 Postquam philosophus ostendit quod non potest demonstrari quod quid est per terminos convertibiles, hic ostendit quod non potest demonstrari per viam divisionis. Et circa hoc duo facit: primo, ostendit propositum; secundo, excludit quamdam solutionem; ibi: contingit autem solvere et cetera. Circa primum duo facit: primo, ostendit propositum per rationem communem omnibus quae syllogizari possunt; secundo, ostendit propositum quantum ad ea quae sunt propria ei quod quid est: ibi: quid enim prohibet et cetera.	After showing that quod quid cannot be demonstrated with convertible terms, the Philosopher now shows that it cannot be demonstrated by the method of division. And in regard to this he does two things. First, he shows what he proposes. Secondly, he excludes a certain solution (91b28). Concerning the first he does two things. First, he shows what he proposes by using a reason common to all things which are syllogized. Secondly, he shows it with reasons proper to that which is quod quid (91a45).
lib. 2 l. 4 n. 2 Dicit ergo primo quod, sicut non potest demonstrari quod quid est per terminos convertibiles, ita etiam non potest demonstrari per viam divisionis: per quam etiam nihil syllogistice probatur, sicut dictum est in resolutione circa figuras, idest in I priorum analyticorum. Sicut enim in posterioribus analyticis docetur resolutio usque ad principia prima, ita etiam in prioribus analyticis fit resolutio ad prima quaedam simplicia pertinentia ad dispositionem syllogismi in modo et figura.	He says therefore first (91b12) that just as the quod quid cannot be demonstrated by convertible terms, so neither by the method of division through which, as a matter of fact, nothing is proved syllogistically, as was established in Resolutions Touching Figures, i.e., in Prior Analytics I. For just as in the Posterior Analytics resolution to first principles is taught, so in the Prior Analytics resolution is made to certain first simple items which pertain to the arrangement of the syllogism in mood and figure.
lib. 2 l. 4 n. 3 Quod autem per viam divisionis non possit aliquid syllogizari probat per hoc, quod in via divisionis non ex necessitate sequitur conclusio, existentibus praemissis (quod requiritur ad rationem syllogismi): sed ita se habet in via divisionis, sicut et in via inductionis. Ille enim qui inducit per singularia ad universale, non demonstrat neque syllogizat ex necessitate. Cum enim aliquid syllogistice probatur, non est necessarium ulterius quod vel syllogizans interroget de conclusione, nec quod respondens det ei conclusionem: sed necesse est quod conclusio sit vera, praemissis existentibus veris. Hoc autem non accidit in via divisionis, sicut manifestat per exempla. Proceditur enim via divisionis cum, accepto aliquo communi quod per multa dividitur, remoto uno, concluditur alterum. Puta si entium aliud est animal et aliud inanimatum, habito quod homo non sit inanimatum, concluditur quod sit animal: sed ista conclusio non sequitur, nisi respondens det quod homo vel sit animal vel inanimatum.	That something cannot be syllogized by the method of division he proves from the fact that in this method, given the premises, the conclusion does not follow of necessity, which it should, considering the nature of a syllogism. Rather, the same thing happens in the method of division as happens in the method of induction. For one who induces through singulars to the universal does not demonstrate or syllogize from necessity. For when something is proved syllogistically, it is not necessary to make further inquiry concerning the conclusion or to ask that the conclusion be conceded; what is necessary is that the conclusion be true, if the premises laid down are true. But, as he shows with certain examples, this does not happen in the method of division. For the method of division consists in assuming something common which is divided into at least two members, so that, one being removed, the other is concluded. For example, if beings are so divided that on the one hand is animal and on the other lifeless things, then having established that man is not a lifeless thing, it is concluded that he is animal. But this conclusion does not follow, unless the hearer grants that man is either an animal or a lifeless thing.
lib. 2 l. 4 n. 4 Et est attendendum quod satis convenienter comparavit divisionem inductioni. Utrobique enim oportet supponere quod accepta sint omnia quae continentur sub aliquo communi: alioquin nec inducens poterit ex singularibus acceptis concludere universale, nec dividens ex remotione quarumdam partium poterit concludere aliam. Patet igitur quod inducens, facta inductione quod Socrates currat et Plato et Cicero, non potest ex necessitate concludere quod omnis homo currat, nisi detur sibi a respondente quod nihil aliud contineatur sub homine quam ista quae inducta sunt. Similiter etiam nec dividens, si probaverit quod hoc coloratum non sit album nec pallidum, non potest ex necessitate concludere quod sit nigrum, nisi detur sibi a respondente quod nihil aliud contineatur sub colorato nisi ea quae assumpta sunt in divisione. Et quia investigantibus quid est homo, oportet accipere non solum genus, quod est animal, sed etiam differentiam; ulterius in suo exemplo procedit quod, si omne animal aut gressibile est aut aquaticum, et accipiat quod homo, quia non est aquaticum animal, sit totum hoc quod est animal gressibile, non ex necessitate sequitur ex dictis; sed oportet quod hoc etiam supponat datum sibi a respondente, scilicet quod animal sufficienter dividatur per gressibile et aquaticum. Et quia quandoque per plures divisiones proceditur ad accipiendum quod quid est alicuius rei, ideo, praemissis duabus divisionibus in suo exemplo, subdit quod nihil differt quod sic procedatur in multis aut in paucis. Eadem enim est ratio in omnibus. Et sic ulterius concludit quod procedentes per viam divisionis, etiam circa ea quae contingit syllogizari, non utuntur probatione syllogistica.	It might be remarked here that he quite fittingly compared division to induction. For in both cases one is required to suppose that he has listed all the things contained under some general heading; otherwise, the person inducing could not conclude a universal from the singulars he assumed, nor could the person dividing conclude to one member just because the others have been eliminated. Thus it is obvious that one cannot in virtue of the fact that Socrates and Plato and Cicero run, induce of necessity the conclusion that every man runs, unless his audience concedes that nothing more is contained under man than the ones listed. In like manner, one who divides cannot, in virtue of having proved that this colored object is neither white nor grey, conclude of necessity that it is black, unless his audience grants him that nothing else is contained under colored object than the things mentioned in the division. And because a person investigating what man is must assume not only the genus which is animal but also the difference, he goes on to say in his example that if every animal is either of the land or of the water and it is established that because man is not a water animal, he is this whole which is land animal, that statement does not follow of necessity from the premises: rather it is further required that he suppose his audience to have granted him something, namely, that animal is sufficiently divided into those of the land and those of the water. And because in some cases several divisions are used in obtaining the quod quid of a thing, the fore, after laying down two divisions in his example, he adds that it makes no difference whether few or many are used. For the formality is the same in all. And thus he concludes once more that those who proceed by the method of division, even in matters that could be syllogized, do not use a syllogized proof.
lib. 2 l. 4 n. 5 Deinde cum dicit: quid enim prohibet hoc verum etc., inducit duas rationes proprias ei quod quid est. Quarum prima est, quia non omne quod vere praedicatur de aliquo, praedicatur in eo quod quid est, nec significat essentiam eius. Si ergo detur quod per viam divisionis sufficienter probetur quod totum hoc, scilicet animal gressibile, vere praedicetur de homine; non tamen propter hoc erit probatum quod praedicetur de eo in eo quod quid est, vel ostendat quod quid erat esse, idest quod demonstrat essentiam rei.	Then (91b25) he induces two reasons proper to the quod quid. The first of these is that not everything which is truly predicated of something is predicated in quod quid or signifies its essence. Therefore, even if it be conceded that one has sufficiently proved by the method of division that this whole, namely, land animal, is truly predicated of man, it does not on that account follow that it is predicated of it in quod quid or that it shows the quod quid erat esse, i.e, that it demonstrates the essence of the thing.
lib. 2 l. 4 n. 6 Secundam rationem ponit ibi: amplius quid prohibet aut apponere et cetera. Essentia enim cuiuslibet rei declaratur per aliqua certa, quibus nec addere oportet nec subtrahi. Nihil autem prohibet quin ille qui procedit per viam divisionis, aut apponat aliquid supra ea quae sufficiunt ad ostendendum quod quid est, aut auferat aliquid eorum quae ad hoc sunt necessaria, aut etiam quod supergrediatur vel excellat essentiam rei, utpote si sit communius quam ipsa res; quod fit dum subtrahuntur differentiae ultimae, quibus ea quae sunt communia contrahuntur. Unde per divisionem non probatur sufficienter quod quid est. Et hoc est quod concludit, quod in via divisionis praetermittuntur praedictae conditiones; ut scilicet id quod concluditur, praedicetur in eo quod quid est, et quod nec excedat nec excedatur.	Then (91b26) he gives the second reason. For the essence of a thing is declared through certain definite items which may neither be added to or subtracted from. But there is nothing to hinder one who proceeds by the method of division from adding something over and above the items which suffice for showing the quod quid, or from subtracting some of the things which are necessary for this, or from going beyond and exceeding the essence of the thing, as when it is more common than the thing itself—which happens when the ultimate differences which contract common things are removed. Hence the quod quid is not sufficiently proved by division. And this is what he concludes, namely, that in the method of division the above-mentioned conditions are not satisfied, i.e., the conditions that what is concluded be predicated in quod quid and that it neither exceed nor be exceeded.
lib. 2 l. 4 n. 7 Deinde cum dicit: contingit autem solvere in accipiendo etc., excludit quamdam solutionem. Et primo, proponit eam; secundo, excludit ipsam; ibi: sed syllogismus tamen et cetera. Dicit ergo primo quod contingit solvere ea quae obiecta sunt, ex eo quod aliquis dicat quod dividendo accipiat omnia quae praedicantur in eo quod quid est; et ita per consequentiam ad divisionem faciat id quod primo intenditur, ut scilicet constituat definitionem significantem quod quid est, et nihil relinquat eorum quae requiruntur ad definiendum. Et si haec duo faciat, scilicet quod omnia, quae accipit per divisionem, praedicentur in eo quod quid, et omnia huiusmodi cadant in divisione, ita quod nihil desit, necessarium est quod id quod est inventum sit quod quid est. Et huiusmodi necessitatis ratio est quia, acceptis omnibus quae praedicantur in eo quod quid, nullo derelicto, iam id quod inventum est, oportet esse quoddam individuum, idest individuam rationem talis rei; ita scilicet quod non indigeat ulteriori divisione ad hoc quod approprietur huic rei.	Then (91b28) he excludes a certain solution. First, he proposes it. Secondly, he excludes it (91b33). He says therefore first (91b28) that one might solve our objections by saying that when a division is made, one could be taking all the things that are predicated in quod quid, so that as a consequence of the division he accomplishes what was primarily intended, namely, that he obtains a definition signifying the quod quid and leaves out nothing which is required for defining. And if he does these two things, namely, if all the items he assumes in the division are predicated in quod quid and all such things are included in the division so that nothing is left out, then it is necessary that what is obtained be the quod quid. And the reason for this necessity is that in taking everything which is predicated in quod quid and leaving nothing out, that which is found must be something individual, i.e., the individual notion of such a thing, so that no further division is required for it to be appropriate to this thing.
lib. 2 l. 4 n. 8 Deinde cum dicit: sed syllogismus tamen non inest etc., excludit praedictam solutionem: et dicit quod quamvis necesse sit, praedictis existentibus, aliquid individuum fieri, sicut expositum est, tamen praedicta via non est syllogistica; quamvis cognoscere faciat quod quid est per alium modum. Et hoc non est inconveniens, scilicet quod aliquid alio modo manifestetur quam per syllogismum. Ille enim qui utitur inductione, non probat syllogistice, sed tamen aliquid manifestat.	Then (91b33) he excludes this solution, saying that even though under the aforesaid conditions something individual is necessarily obtained, as explained above, the method is nevertheless not syllogistic; although it might make one know the quod quid in some other way. And this is not unbecoming, namely, that something be manifested in a way other than by a syllogism: for one who uses induction does not prove anything syllogistically, but yet he does manifest something.
Quod autem ille qui per divisionem ad definitionem pervenit, non faciat syllogismum, ostendit per quoddam simile. Si enim inducatur conclusio ex maiori propositione, subtracta media, et concludens dicat quod hoc necesse est sequi ex praemissis, poterit interrogare respondens, propter quid sit necessarium: quod non accidit in syllogistica probatione. Unde talis modus argumentandi non est syllogisticus. Ita etiam in terminis divisivis non fit syllogismus, quia semper restat interrogatio propter quid. Puta si aliquis volens notificare quid est homo, accipiat per viam divisionis quod homo est animal mortale bipes, vel habens pedes, sine pennis; ad quamlibet appositionem praedictorum poterit convenienter quaeri propter quid sit necesse. Ille enim qui ad manifestandum quod quid est conatur, non solum dicet, sed etiam probabit per divisionem, secundum quod ipse opinatur, quod omne quod est sit mortale aut immortale. Et quamvis detur quod per hanc divisionem possit demonstrare propositum, tamen non est necesse quod ratio sic conclusa sit definitio; quia forte ea ex quibus constat ratio talis, non praedicantur in eo quod quid est, vel excedunt substantiam definiti. Sed etsi contingat quod talis ratio sit definitio, non tamen per syllogismum probatur quod definitio sit, ut ex supra dictis patet.	That one who reaches a definition by way of division does not achieve a syllogism he shows by something similar. For if a conclusion is induced from a major proposition, the second proposition being omitted, and the person concluding declares that this must follow from the premises, the hearer could ask why it is necessary—which is something that does not happen in a syllogistic proof. Hence such a method of arguing is not syllogistic. Similarly, in terms of division no syllogism is achieved, because t lie question why always remains. Thus, if someone wishing to disclose what man is were to assert by the method of division that man is a two-footed mortal animal, or one that has two feet but no wings, then as h adds one item to another in his division, he could be asked in regard to each one, why is it necessary. For one who sets out to manifest a quod quid by division will not only assert but also prove—in keeping with what he thinks—that everything which exists is mortal or immortal. And although it be granted that through this division he might be demonstrating his proposition, nevertheless it is not necessary that the notion’ so concluded be a definition; for perhaps the items out of which such a notion is formed are not predicated in quod quid or exceed the substance of the thing defined. But even though such a notion might happen to be a definition, it is nevertheless not proved by the syllogism to be a definition, as is clear from what has been established above.