Authors/Thomas Aquinas/posteriorum/L2

Lecture 1 Whether the definition which signifies the quod quid of a thing can be demonstrated

Latin	English
	BOOK II Lecture 1 (89b21-90a35) EACH OF THE FOUR QUESTIONS WHICH PERTAIN TO SCIENCE IS ONE WAY OR ANOTHER A QUESTION OF THE MIDDLE
lib. 2 l. 1 n. 1 Postquam philosophus in primo libro determinavit de syllogismo demonstrativo, in hoc libro intendit determinare de principiis eius. Est autem duplex principium demonstrativi syllogismi, scilicet medium eius et primae propositiones indemonstrabiles. Dividitur ergo liber iste in duas partes: in prima, determinat de cognitione medii in demonstrationibus; in secunda, de cognitione primarum propositionum; ibi: de principiis autem qualiter fiunt cognita et cetera. Quia enim in primo libro habitum est quod omnis doctrina et omnis disciplina fit ex praeexistenti cognitione; in demonstrationibus autem cognitio conclusionis acquiritur per aliquod medium et per primas propositiones indemonstrabiles; residuum erat investigare qualiter ista innotescant.	After determining about the demonstrative syllogism in the first book, the Philosopher intends in this [second] book to treat concerning its principles. But there are two principles of the demonstrative syllogism, namely, its middle and the first indemonstrable propositions. Therefore this book is divided into two parts. In the first he determines concerning the knowledge of the middle in demonstrations. In the second concerning the knowledge of the first propositions (99b18) [L. 20]. For since it has been established in the first book that every doctrine and every discipline takes its start from pre-existing knowledge, and since in demonstrations the knowledge of the conclusion is acquired through some middle and through the first indemonstrable propositions, we are left with the task of investigating how these come to be known.
Prima autem pars dividitur in duas partes: in prima, investigat quid sit medium in demonstrationibus; in secunda parte inquirit quomodo illud medium nobis innotescat; ibi: quomodo autem quod quid est ostenditur et cetera. Quia vero medium in demonstrationibus assumitur ad aliquid innotescendum de quo poterat esse dubitatio vel quaestio, ideo circa primum duo facit: primo enim, ponit numerum quaestionum; secundo, ex ipsis quaestionibus investigat propositum, ostendens qualiter quaestiones pertineant ad medium demonstrationum; ibi: quaerimus autem cum quaeramus et cetera. Circa primum tria facit: primo, enumerat quaestiones; secundo, manifestat compositas quaestiones; ibi: cum quidem enim utrum hoc etc.; tertio, simplices; ibi: quaedam autem alio modo et cetera.	But the first part is divided into two parts. In the first he inquires what is a middle in demonstrations. In the second part he inquires how that middle is made known to us (90a36) [L. 2]. But because the middle in demonstrations is employed in order to make known something about which there might have been doubt or question, therefore in regard to the first he does two things. First, he lays down the number of questions. Secondly, from these questions he pursues his investigation by showing how the questions pertain to the middle of demonstrations (89b38). Regarding the first he does three things. First, he enumerates the questions. Secondly, he explains complex questions (89b26). Thirdly, simple questions (89b32).
lib. 2 l. 1 n. 2 Dicit ergo primo quod aequalis est numerus quaestionum et eorum quae sciuntur. Cuius ratio est, quia scientia est cognitio per demonstrationem acquisita. Eorum autem oportet per demonstrationem cognitionem acquirere, quae ante fuerint ignota: et de his quaestiones facimus, quae ignoramus. Unde sequitur quod ea quae quaeruntur sint aequalia numero his quae sciuntur. Quatuor autem sunt quae quaeruntur, scilicet quia, propter quid, si est et quid est: ad quae quatuor reduci potest quidquid est quaeribile vel scibile.	He says therefore first (89b21) that the number of questions is equal to the number of things that are scientifically known. The reason for this is that science is knowledge acquired through demonstration. But things which we previously did not know are those of which we must seek knowledge by demonstration: for it is in regard to things which we do not know that we form questions. Hence it follows that the things we inquire about are equal in number to the things we know through science. But there are four things that we ask, namely, quia [i.e., is it a fact that], propter quid [i.e., why, or what is the cause or reason], si est [if it is, i.e., whether it is], quid est [what is it]. To these four can be reduced whatever is scientifically inquirable or knowable.
Dividit autem in I topicorum quaestiones sive problemata aliter in quatuor, quae omnia comprehenduntur sub una harum quaestionum, quae dicitur quaestio quia. Non enim ibi intendit nisi de quaestionibus ad quas dialectice disputatur.	However in Topics I he divides questions or problems into four kinds in a different way, but all of them are included under one of the questions listed here, namely, the one called quia. For in the Topics he is concerned only with questions to be disputed dialectically.
lib. 2 l. 1 n. 3 Deinde cum dicit: cum quidem enim utrum hoc etc., manifestat propositas quaestiones, et primo compositas. Ad cuius evidentiam considerandum est quod, cum scientia non sit nisi veri, verum autem significetur solum per enunciationem, oportet solam enunciationem esse scibilem, et per consequens quaeribilem. Sicut autem in II perihermeneias dicitur, enunciatio dupliciter formatur. Uno quidem modo, ex nomine et verbo absque aliquo apposito, ut cum dicitur homo est; alio modo, quando aliquid tertium adiacet, ut cum dicitur homo est albus.	Then (89b26) he clarifies the questions he laid down; and first of all the complex ones. To understand this it should be noted that science bears only on the true, and the true is not signified except by an enunciation; therefore, only the enunciation can be scientifically knowable and so inquirable. But, as it is stated in On Interpretation II, the enunciation is formed in two ways: in one way from a name and a verb without an appositive, as when it is stated that man is; in another way when some third item is set adjacent, as when it is stated that man is white.
Potest igitur quaestio formata referri, vel ad primum modum enunciationis, et sic erit quasi quaestio simplex; vel ad secundum modum, et sic erit quaestio quasi composita, vel in numerum ponens, quia videlicet quaeritur de compositione duorum.	Therefore the questions we form can be reduced either to the first type of enunciation so that we get, as it were, a simple question; or to the second type, and then the question will be, as it were, complex or put in number, because, namely, the question concerns the putting together of two items.
Circa hunc ergo modum enunciationis duplex quaestio formari potest. Una quidem, an hoc sit verum quod dicitur. Et hanc quaestionem primo exponit, dicens quod cum de aliqua re quaerimus utrum illa res sit hoc aut illud, et sic quodammodo ponimus in numerum (accipiendo scilicet duo, quorum unum est praedicatum et aliud subiectum; puta cum quaerimus utrum sol sit deficiens per eclipsim vel non, et utrum homo sit animal vel non), tunc dicimur quaerere quia: non ita quod hoc quod dico quia sit nota vel signum interrogationis, sed quia ad hoc quaerimus ut sciamus quia ita est. Cuius signum est, quia cum invenerimus per demonstrationem, quiescimus a quaerendo; et si in principio hoc scivissemus, non quaereremus utrum ita sit. Inquisitio autem non cessat, nisi habito eo quod quaerebatur. Et ideo cum quaestio qua quaerimus utrum hoc sit hoc, cesset habito quod ita est, manifestum est quid huiusmodi quaestio quaerit.	According to this latter type a twofold question can be formed: one of them is whether this is true which is stated. This question he expounds first, saying that when we ask concerning some thing whether that thing is this or that, so that in effect we are somehow putting it in number, namely, by taking two things one of which is predicate and the other subject, as when we ask if the sun is failing because of an eclipse or not, and is man an animal or not, then we are said to ask quia: not in the sense that the word “quia” functions as a question mark, but because we are asking in order to find out quia [i.e., that] it is so. An indication of this is that when we have discovered it through demonstration, we cease our questioning; and if we had known it at the very beginning, we would not have asked whether it is so. But inquiry does not cease until that is obtained which was asked. And so, since the question in which we ask whether this is this ceases once we have certified that it is so, it is clear what a question of this kind asks.
lib. 2 l. 1 n. 4 Deinde cum dicit: cum autem scimus etc., manifestat consequentem quaestionem, quae etiam in numerum ponit; et dicit quod cum scimus quia ita est, quaerimus propter quid ita sit. Puta, cum scimus quia sol est deficiens per eclipsim, et quod terra est mota in terraemotu, quaerimus propter quid sol deficiat, aut propter quid terra moveatur. Hoc igitur sic quaerimus, ponentes scilicet in numerum.	Then (89b28) he clarifies the next question which also puts in number, ‘I saying that when we know that it is so, we ask propter quid [i.e., why] it is so. For example, when we know that the sun is failing through an eclipse and that the earth is moved during an earthquake, we ask why the sun is failing or why the earth is being moved. Therefore we ask it in this way, namely, by putting in number.
lib. 2 l. 1 n. 5 Deinde cum dicit: quaedam autem alio modo etc., manifestat alias duas quaestiones, quae non ponunt in numerum, sed sunt simplices. Et dicit quod quaedam quaerimus alio modo a praedictis quaestionibus, scilicet non ponentes in numerum; utpote si quaeramus an sit Centaurus vel non: hic enim simpliciter quaeritur de Centauro an sit, non autem quaeritur an Centaurus sit hoc, puta album vel non. Et sicut scientes quia hoc est illud, quaerebamus propter quid, ita etiam scientes de aliquo quia est simpliciter, quaerimus quid sit illud, puta quid est Deus, aut quid est homo. Haec igitur et tot sunt illa quae quaerimus: quae cum invenerimus, dicimur scire.	Then (89b32) he clarifies the other two questions which do not put in number but are simple. And he says that we ask certain things in a manner different from the aforesaid questions, namely, by not putting in number; as when we ask whether or not there be centaurs, for in this case the question we ask concerning the centaur is simply whether it exists and not whether the centaur be this, say white, or not. And just as when we knew that this is this, we then asked why, so once we know of something simply that it is, we ask what it is, for example, what is God or what is man. These then and so many are the things we ask; and when we have found the answer, we are said to know scientifically.
lib. 2 l. 1 n. 6 Deinde cum dicit: quaerimus autem cum quaeramus etc., ostendit qualiter praedictae quaestiones se habeant ad medium. Et circa hoc tria facit: primo, proponit quod intendit; secundo, manifestat quod dixerat; ibi: dico autem quia etc.; tertio, probat propositum; ibi: contingit itaque in omnibus quaestionibus et cetera.	Then (89b38) he shows how the aforesaid questions are related to the middle. Concerning this he does three things. First, he states what he intends. Secondly, he explains what he had said (90a2). Thirdly, he proves his proposition (90a5).
Circa primum sciendum est quod praedictarum quatuor quaestionum, quarum duae ponunt in numerum et duae non ponunt, primam utrarumque in unam coordinat, scilicet quaestionem quia et quaestionem an est. Et dicit quod cum quaerimus quia hoc est hoc, aut cum quaerimus de aliquo simpliciter si est, nihil aliud quaerimus quam utrum aliquod medium ipsius quod quaerimus sit invenire vel non. Quod non dicitur secundum ipsam formam quaestionis. Non enim cum quaero an sol eclipsetur, vel an homo sit, ex ipsa forma quaestionis quaero an sit aliquod medium, quo possit demonstrari vel solem eclipsari, vel hominem esse: sed si sol eclipsatur, vel homo est, consequens est quod sit aliquod medium invenire ad demonstrandum ista quae quaeruntur. Non enim fit quaestio de immediatis, quae etsi vera sunt, non tamen habent medium; quia huiusmodi, cum sint manifesta, sub quaestione non cadunt. Sic ergo qui quaerit an hoc sit hoc, vel an hoc sit simpliciter, ex consequenti quaerit an sit huiusmodi medium. Quaeritur enim in quaestione si est, vel quia est, an sit id quod est medium; quia id quod est medium est ratio eius, de quo quaeritur an hoc sit hoc, vel an simpliciter, ut infra dicetur. Non tamen quaeritur sub ratione medii.	In regard to the first it should be noted that two of the aforesaid questions put in number and two do not. From the first member of each of these groups, he forms another grouping composed of the question that it is and the question if it is. And he says that when we ask that this is this, or when we simply ask concerning something, if it is, we are not asking anything else than whether or not a middle is to be found of that which we ask; and this is something not conveyed by the form of the question. For when I ask whether the sun is eclipsed or whether man exists, it is not obvious from the form of the question that I am asking whether there is some middle by which it might be demonstrated that the sun is eclipsed or that man exists; but if the sun is eclipsed or man does exist, the consequence is that some middle can be found to demonstrate the things which are inquired. For no one forms a question concerning immediate things which, although they are true, do not have a middle, since things of this sort, being evident, do not fall under a question. Thus, therefore, one who asks whether this is this or whether this absolutely is, as a consequence is asking whether there is a middle of this sort. For in the question if it is or that it is, one is asking whether that which is a middle exists, because that which is the middle is the reason of that concerning which one asks whether this is this or simply whether it is, as will be explained below. Nevertheless the question is not being asked under the aspect of middle.
Contingit autem, invento quod quaeritur per has duas quaestiones, cognoscere aut quia est aut si est: quorum alterum est cognoscere esse simpliciter, alterum esse in parte, sicut cum cognoscimus quod homo est albus; quia esse album non significat totaliter esse hominis, sed significat ipsum esse aliquid; et ideo cum homo fit albus, non dicitur generari simpliciter, sed generari secundum quid. Sed cum dicitur, homo est, significatur ipsum esse simpliciter; et cum homo fit ens, dicitur generari simpliciter.	Now it happens that having found the answer to what is asked by these two questions, one knows either that it is or if it is: one of which consists in knowing the existence absolutely; but the other in part, as when we know that man is white, because to be white does not signify the existence of man in his entirety but signifies him to be something. This is why when a man is becoming white, we do not say that he is coming to be absolutely, but in a qualified sense. But when it is asserted that man is, his existence is signified absolutely, so that when a man comes to be, he is said to become absolutely.
Cum ergo cognito quia est, quaerimus propter quid est, aut cognito si est, quaerimus quid est, tunc quaerimus quid sit medium. Et hoc similiter est accipiendum non secundum formam quaestionis, sed secundum concomitantiam. Non enim qui quaerit causam propter quam sol eclipsatur, quaerit ipsam ut medium demonstrans, sed quaerit id quod est medium: quia consequens est ut, hoc habito, possit demonstrare. Et eadem ratio est de quaestione quid est.	Therefore, when we know that it is and ask why it is, or when we know if it is and ask what it is, we are asking what is the middle. And as in the other cases, so here, this is gathered not from the form of the question but by way of concomitance. For one who seeks the cause why the sun is eclipsed is not seeking it as a middle which demonstrates, but he is seeking that which is a middle, because it is by way of consequence that once he has it, he can demonstrate. And the same applies to the question what is it.
lib. 2 l. 1 n. 7 Deinde cum dicit: dico autem quia aut si est etc., manifestat quod dixerat, quod quia est et si est differunt sicut in parte et simpliciter. Cum enim quaerimus utrum deficit luna aut utrum augetur, est quaestio in parte: in huiusmodi enim quaestione quaerimus si luna est aliquid; puta si deficiens, vel aucta, aut non. Sed cum quaerimus an luna sit, sive an nox sit, est quaestio de esse simpliciter.	Then (904) he manifests what he had said, namely, that that it is and if it is differ as in part and absolutely differ. For when we inquire whether the moon is waning or waxing, it is a question in part, since in a question of this type we are asking if the moon is something, namely, is it waning or has it waxed or not. But when we ask whether the moon exists or whether it is night, the question bears on existence absolutely.
lib. 2 l. 1 n. 8 Deinde cum dicit: contingit itaque in omnibus etc., probat propositum, scilicet quod praedictae quaestiones pertineant ad medium. Et primo, probat per rationem; secundo, probat per signum; ibi: quod autem sit medii et cetera.	Then (90a5) he proves his point, namely, that the aforesaid questions pertain to the middle. First, he proves it with a reason. Secondly, with a sign (90a24).
Concludit ergo primo ex praemissa manifestatione quod in omnibus praedictis quaestionibus, vel quaeritur an sit medium, scilicet in quaestione quia et in quaestione si est; vel quaeritur quid est medium, scilicet in quaestione propter quid et in quaestione quid est.	He concludes therefore first (90a5) from the explanation given above that in all the aforesaid questions one is either asking whether there is a middle, namely, in the question that it is and in the question if it is, or what the middle is, namely, in the question why and in the question what is it.
Et probat quod quaestio propter quid quaerat quid sit medium. Manifestum est enim quod causa est medium in demonstratione, quae facit scire; quia scire est causam rei cognoscere. Causa autem est quod quaeritur in omnibus praedictis quaestionibus. Quod primo manifestat in quaestione quia. Cum enim quaeritur utrum luna deficiat, quaeritur secundum modum supra expositum, utrum aliquid sit causa defectus lunae vel non. Et consequenter hoc manifestat in quaestione propter quid. Cum enim scimus quia est aliquid causa defectus lunae, quaeritur quid sit causa; et hoc est quaerere propter quid.	And he proves that the question why inquires what the middle is. For it is obvious that a cause is the middle in a demonstration which enables one to know scientifically, because to know scientifically is to know the cause of a thing. But it is precisely the cause that is being sought in all the above questions. That this is so he manifests first in regard to the question that. For when it is asked whether the moon is waning, then according to the manner explained above, what is being asked is whether or not something is the cause of this waning. Then he shows this for the question why. For once we know that something is the cause of the moon’s waning, we ask what the cause is; and this is to inquire why.
Et eadem ratio est in aliis duabus quaestionibus, ut per sequentia manifestat. Dicit enim quod, sive accipiamus aliquam rem esse non hoc aut hoc (puta cum dico homo est albus, aut grammaticus), sed accipiamus ipsam substantiam esse simpliciter; sive etiam non accipiamus rem aliquam esse simpliciter, sed rem aliquam esse aliquid, ponendo in numerum, (sive illud aliquid sit de numero eorum quae praedicantur per se, sive de numero eorum quae praedicantur per accidens), sive hoc modo sive illo accipiamus rem esse, causa eius est medium ad demonstrandum ipsam.	The same applies to the other two questions, as he shows in the following way. For he says that whether we assert not that something is this or that (for example, when I say that man is white or is a grammarian), but that the substance itself exists absolutely; or do not assert that some thing exists absolutely, but that some thing is something by putting in number (whether that something be a thing predicated per se or a thing predicated per accidens); no matter in which of these ways we take the thing to be, its cause is the middle for demonstrating it.
Exponit autem consequenter quod dixit, simpliciter substantiam esse, cum quaerimus de luna, aut de terra, aut de triangulo, aut de quolibet subiecto an sit, et ad hoc demonstrandum accipitur aliquod medium. Dico autem rem esse aliquid, cum quaerimus eclipsim de luna, aut aequalitatem, aut inaequalitatem de triangulo, aut de terra utrum sit in medio mundi vel non. Et ostendit quod non differt quantum ad propositum utrolibet modo accipiatur rem esse; quia in omnibus praedictis idem est quid est et propter quid.	Then he explains what he means by a substance to exist absolutely when we inquire concerning the moon or the earth or a triangle or any other subject whether it is and then take some middle to demonstrate this. I say that a thing is something when we inquire concerning eclipse in regard to the moon, or equality or inequality in regard to triangle, or whether it is in the middle of the universe or not in regard to the earth. And he asserts that as far as the present point is concerned it makes no difference which way a thing is taken to be, because in all these cases what it is is the same as why.
Et hoc manifestat primo in defectu lunae. Si enim quaeratur quid est defectus lunae: respondetur quod est privatio luminis a luna propter terram, quae obiicitur inter ipsam et solem. Et hoc idem respondemus si quaeratur propter quid luna deficit. Dicimus enim quod luna deficit propter defectum luminis ex oppositione terrae.	He manifests this first of all in regard to the waning, of the moon. For if one asks what is the eclipse of the moon, the answer is that it is the absence of light in the moon because of the earth’s being set between it and the sun. And this same answer is given when it is inquired why the moon is eclipsed. For we say that the moon is eclipsed because there is a lack of light due to the earth’s opposition.
Et idem manifestat in alio exemplo. Si enim quaeratur quid est consonantia: respondetur quod est ratio, idest proportio numerorum secundum acutum et grave. Et rursum si quaeratur propter quid acutum consonat gravi: respondetur propter id quod habent numeralem proportionem acutum et grave. Sic ergo quaestio quid est et quaestio propter quid redeunt in idem subiecto, quamvis differant ratione. Unde quia cum quaeritur propter quid, quaeritur quid sit medium, ut ostensum est, relinquitur quod cum quaeritur quid est, similiter quaeratur medium.	Then he manifests the same idea with another example. For if one asks what is a chord, the answer is given that it is a numerical ratio according to high and low notes. Again, if one asks why a high note and a low note are concordant, the answer is given that it is because the high note and the low note have a numerical ratio. And so the question what is it and the question why reduce to the same thing subjectively, although they differ in formality. Hence because the question why leads us to inquire what the middle is, as has been shown, what is left is that when one asks what is it, the middle is likewise inquired.
Et idem ostendit in quaestione quia. Ut enim dictum est, consonantia est ratio in numeris acuti et gravis: cum ergo quaeritur utrum acutum et grave consonent, quaeritur utrum sit aliqua ratio numeralis acuti et gravis; et hoc est medium ad demonstrandum quod acutum et grave consonant. Relinquitur ergo quod in quaestione quia quaeritur an sit medium. Cum autem acceperimus quia est aliqua ratio numeralis acuti et gravis, quaeremus quae sit illa ratio. Et hoc est quaerere quid vel propter quid.	Then he shows the same thing in regard to the question that. For, as has been said, concordance is a numerical ratio between high and low notes. Men, therefore, one asks whether a high and low note concord, he is inquiring whether there is some numerical ratio of the high and low note; and this is the middle for demonstrating that a high and a low note concord. Consequently in the question that, one inquires whether there is a middle. But once we have found that there is a numerical ratio of the high and low note, we then ask what that ratio is: and this is to ask what or why.
lib. 2 l. 1 n. 9 Videtur hic Aristoteles dicere quod definitio passionis sit medium in demonstratione. Sed considerandum est quod definitio passionis perfici non potest sine definitione subiecti. Manifestum est enim quod principia, quae continet definitio subiecti, sunt principia passionis. Non ergo demonstratio resolvet in primam causam, nisi accipiatur ut medium demonstrationis definitio subiecti. Sic igitur oportet concludere passionem de subiecto per definitionem passionis, et ulterius definitionem passionis concludere de subiecto per definitionem subiecti. Unde et in principio dictum est quod oportet praecognoscere quid est, non solum de passione, sed etiam de subiecto; quod non oporteret nisi definitio passionis concluderetur de subiecto per definitionem subiecti.	Here Aristotle seems to say that the definition of a proper attribute is the middle in demonstration. However it must be remarked that the definition of the proper attribute cannot be completed without the definition of the subject. For it is obvious that the principles which the definition of the subject contains are the principles of the proper attribute. Hence a demonstration will not reach the first cause unless one takes as the middle of demonstration the definition of the subject. And so the proper attribute must be concluded of the subject by means of the definition of the proper attribute; furthermore, the definition of the proper attribute must be concluded of the subject through the definition of the subject. This is why it was laid down at the very beginning that one must know beforehand the what is it not only of the proper attribute but of the subject also; which would not be required unless the definition of the proper attribute were concluded of the subject through the definition of the subject.
Et hoc patet per exemplum. Si velimus de triangulo demonstrare quod habet tres angulos aequales duobus rectis, accipiamus primo pro medio quod est figura habens angulum extrinsecum aequalem duobus intrinsecis sibi oppositis, quod est quasi definitio passionis. Quod iterum demonstrare oportet per definitionem subiecti, ut dicamus: omnis figura tribus rectis lineis contenta habet angulum exteriorem aequalem duobus interioribus sibi oppositis; sed triangulus est huiusmodi; ergo et cetera. Et idem patet si velimus demonstrare quod vox acuta et gravis consonent: accipiemus definitionem passionis, ut hic dicitur, scilicet quod habent proportionem numeralem; sed rursus ad hoc demonstrandum oportet accipere definitionem gravis et acuti. Nam gravis vox est quae in multo tempore nata est movere sensum, acuta autem quae in modico tempore; modici autem ad multum est proportio numeralis; ergo vocis acutae et gravis est proportio numeralis. Nec refert si aliter definiatur acutum et grave. Oportet enim in eorum definitione ponere aliquid ad quantitatem pertinens; et sic necesse erit concludere in eis proportionem numeralem.	This is clear from the following example: If we wish to demonstrate of triangle that it has three angles equal to two right angles, we first take as middle the fact that it is a figure having an exterior angle equal to its two opposite interior angles-which is, as it were, the definition of a proper attribute. But this in turn must be demonstrated by the definition of the subject, so that we would say: “Every closed figure of three straight lines has an exterior angle equal to its two opposite interior angles; but the triangle is such a figure. Therefore...” And the same is true if we were to demonstrate that a high note concords with a low note: for we would state the definition of the attribute which in this case consists in their having a numerical ratio; but then to demonstrate this attribute we would have to take the definition of high note and of low note. For a low note is one which is apt to act on the sense for a long time, whereas a high note is one which does so for a short time: but between the long and the short there is a numerical ratio. Therefore, there is a numerical ratio between a high note and a low note. And if the high note and the low note were defined some other way, it would make no difference. For in any case something pertaining to quantity would have to appear in their definition, so that it would be necessary to conclude that there is a numerical ratio between them.
lib. 2 l. 1 n. 10 Deinde cum dicit: quod autem medii sit quaestio etc., ostendit propositum per signum sensibile. Et dicit quod ea in quibus medium est sensibile, manifeste ostendunt quod omnis quaestio sit quaestio medii: quia scilicet quando medium per sensum innotescit, nullus relinquitur quaestioni locus. Tunc enim quaerimus in rebus sensibilibus secundum aliquam praedictarum quaestionum, quando medium non sentimus: sicut quaerimus an sit defectus lunae vel non, quia non sentimus medium quod est causa faciens deficere lunam. Sed si essemus in loco qui est super lunam, videremus quomodo luna subintrando umbram terrae deficeret; et ideo circa hoc nihil quaereremus, nec si est nec propter quid est; sed simul utrumque nobis fieret manifestum.	Then (90a44) he manifests his point by means of a sensible sign. And he says that those cases in which the middle is perceptible by sense clearly show that every question is a question concerning a middle, because, namely, when the middle is known through the senses, no room is left for a question. For we ask one of the aforesaid questions in matters pertaining to sense, when the middle does not appear: thus, we ask whether or not there is an eclipse of the moon because we do not sensibly perceive the middle which is the cause making the moon to be eclipsed. But if we were to situate ourselves in a place above the moon, we would see how the moon became eclipsed by entering the earth’s shadow. Then we would no longer ask if it is or why it is, but both would at once be obvious to us.
lib. 2 l. 1 n. 11 Et quia posset aliquis obviando dicere quod sensus est singularium, ea vero quae quaeruntur sunt universalia, sicut et ea quae sciuntur; et ita per sensum non videtur quod possit nobis innotescere id de quo est quaestio: ideo quasi obviationi respondens subiungit quod ex hoc ipso quod sentiremus particulare, scilicet quod, hoc corpus lunae tunc subintrat hanc umbram terrae, statim accideret nobis quod sciremus universale. Sensus enim noster esset de hoc quod nunc lumen solis obstruitur per oppositionem terrae; et per hoc manifestum esset nobis quod luna nunc deficit. Et quia nos coniiceremus quod semper hoc modo accideret lunae defectus, statim in nostra scientia sensus rei singularis fieret universale.	But because someone could object that sense-perception bears on singulars—whereas it is universals that are being asked about, just as it is universals that are scientifically known—and consequently, it does not seem that the matter under question can be made known through sense; therefore, as though in answer to this objection he adds that it is precisely because we do sense the particular (namely, that this body of the moon enters this shadow of the earth), that we happen at once to know the universal. For our sense would observe the fact that the light of the sun is now blocked by the earth’s opposition; and through this it would be clear to us that the moon is now eclipsed. And because we would conjecture that the eclipse of the moon always occurs in this way, the sense knowledge of the singular would immediately become a universal in our science.
Et ex hoc exemplo concludit quod idem est scire quod quid est et propter quid. Nam ex hoc quod videmus terram interpositam inter solem et lunam, sciremus et quid est defectus lunae et propter quid luna deficit: quorum unum, scilicet scire quid est, refertur ad scientiam qua scimus de aliquo quod simpliciter sit, non autem quod aliquid insit alicui; sed propter quid refertur ad cognitionem eorum quae insunt, sicut cum dicimus quod tres anguli sunt aequales duobus rectis, aut maiores aut minores. Ultimo autem epilogando concludit principale propositum, scilicet manifestum esse ex praedictis, in omnibus quae quaeruntur esse medii quaestionem.	And so from this example he concludes that knowing the quod quid [quod quid refers to any or all of the items that constitute the essential nature of a thing.] and the why are the same. For from the fact that we observe the earth situated between the sun and moon, we would know scientifically both what an eclipse of the moon is and why the moon is eclipsed. And one of these, namely, the knowledge what it is, is reduced to the science by which we know that something simply is, and not that something is in some thing. But the why is reduced to our knowledge of things that are in some thing, as when we say that three angles are equal to or greater than or less than two right angles. Finally, he summarizes and concludes the main point, namely, that it is clear from the foregoing that in all questions there is question of the middle.

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.

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.

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.

Lecture 5 Whether a quod quid can be demonstrated by taking that which is required for a quod quid

Latin	English
	Lecture 5 (92a6-b3) WHETHER A QUOD QUID CAN BE DEMONSTRATED BY TAKING THAT WHICH IS REQUIRED FOR A QUOD QUID
lib. 2 l. 5 n. 1 Postquam philosophus ostendit quod non potest demonstrari quod quid est, nec per convertibiles terminos, nec per viam divisionis, hic ostendit ulterius quod non potest quod quid est demonstrari, accipiendo id quod requiritur ad quod quid est. Et circa hoc duo facit: primo, ostendit propositum; secundo, concludit ex omnibus praemissis quod nullo modo quod quid est demonstrari possit; ibi: qualiter igitur definiens et cetera. Circa primum duo facit: primo, inducit rationes proprias ad propositum; secundo, inducit quamdam rationem communem ad id quod nunc dicitur, et ad id quod supra dictum est; ibi: ad utrosque autem et cetera. Circa primum duo facit: primo, ostendit quod non potest demonstrari quod quid est per hoc quod accipiatur id quod pertinet ad rationem eius quod quid est; secundo, ostendit quod non potest demonstrari quod quid est huius rei, ex hoc quod accipitur quod quid est alterius rei; ibi: ex suppositione autem et cetera. Circa primum duo facit: primo, movet quaestionem; secundo, argumentatur ad propositum; ibi: aut iterum accipit et cetera.	After showing that the quod quid cannot be demonstrated either by convertible terms or by the method of division, the Philosopher here shows that it cannot be demonstrated by taking that which is required for a quod quid. In regard to this he does two things. First, he shows what he proposes. Secondly, he concludes from all of the foregoing that there is no way in which quod quid maybe demonstrated (92a34). Concerning the first he does two things. First, he employs reasons proper to what he proposes. Secondly, he employs a reason common to what is now being said and to what was said above (92a28). Concerning the first he does two things. First, he shows that the quod quid cannot be demonstrated by taking that which pertains to the notion of its quod quid. Secondly, he shows that the quod quid of this thing cannot be demonstrated by taking the quod quid of some other thing (9240). In regard to the first he does two things. First, he raises the question. Secondly, he argues for his proposal (92a9).
lib. 2 l. 5 n. 2 Quaerit ergo primo, utrum contingat demonstrare quid sit aliquid secundum suam substantiam, ex tali suppositione, per quam accipiatur quod quid erat esse alicuius rei, ex illis conditionibus quae sunt propriae ei quod quid est. Puta si aliquis probet quod animal gressibile bipes sit quod quid est hominis, accipiens pro medio quod haec ratio convertitur cum homine, et constat ex genere et differentia. Haec autem sola requiruntur ad hoc quod quid est, et totum hoc quod dictum est, est proprium ei quod quid est, quia est esse illi, scilicet ei quod est quod quid est: quasi dicat quod hoc quod est esse rationem convertibilem, ex genere et differentiis constantem, est omnino idem ei quod quid est.	He asks therefore first (92a6) whether one might demonstrate what something is according to its substance by supposing that the quod quid of a thing can be obtained if one satisfies the conditions which are proper to the quod quid: for example, if one were to prove that two-footed land animal is the quod quid of man, having taken as middle the fact that this notion is converted with man and is composed of genus and difference; which are the only conditions required for a quod quid. Furthermore, this whole, which has been stated, is proper to the quod quid because it is the being or reality of it, i.e., of that which is quod quid. It is as though he were saying that being a convertible notion composed of a genus and difference is exactly the same as being the quod quid.
lib. 2 l. 5 n. 3 Deinde cum dicit: an iterum accepit etc., obiicit ad praedictam quaestionem duabus rationibus, ostendens quod non potest quod quid est praedicto modo demonstrari. Quarum prima est, quia sicut praemissi modi demonstrandi deficiunt in hoc quod accipiunt id quod quaeritur, ita est in proposito. Accipitur enim et in hoc modo probationis quod quid erat esse; puta dum accipitur quod omnis ratio convertibilis, constans ex genere et differentiis, significat quod quid est: et ita inconveniens est probatio. Necesse est enim id ad quod demonstratio inducitur, non supponere quasi medium; sed potius per aliud medium demonstrare.	Then (92a9) he lodges two objections against the above question, showing that the quod quid cannot be demonstrated in the way it suggests. The first of these is that just as the previously mentioned ways of demonstrating failed because they assumed the very thing in question, so too in the present instance. For it, too, assumes the quod quid erat esse, as for example when it is assumed that every convertible notion composed of genus and difference signifies the quod quid est; consequently, the proof is not acceptable. For one must never take as middle the very thing the demonstration is intended to prove; rather it is necessary to demonstrate it through some other middle.
lib. 2 l. 5 n. 4 Secundam rationem ponit ibi: amplius sicut neque in syllogismo etc.; quae sumitur ex similitudine syllogismi. Cum enim aliquis syllogizat, non oportet quod accipiat definitionem syllogismi ad syllogizandum; quia ea ex quibus procedit syllogismus, hoc modo se habent, quod semper quodlibet eorum est aut tota propositio, idest universalis seu maior, aut est pars, idest particularis seu minor, quae sumitur sub maiori. Et ita definitio syllogismi non est aliquid eorum ex quibus procedit syllogismus. Et similiter si aliquis velit syllogizare quod quid erat esse alicuius rei, non oportet quod accipiat quid sit quod quid erat esse: sed oportet hoc seorsum haberi in mente, praeter ea quae ponuntur in definitione vel syllogismo. Huiusmodi enim rationes syllogismi et definitionis se habent in definiendo et syllogizando, sicut regulae artis, ad quas debet aspicere artifex in operando. Artifex autem qui facit cultellum, non facit operando regulam, secundum quam operatur: sed secundum regulam, quam habet in mente, examinat an cultellus bene sit factus. Ita etiam ille qui syllogizat non accipit rationem syllogismi in syllogizando: sed per rationem syllogismi examinat syllogismum factum an sit bonus.	Then (92a11) he gives the second reason, which is based on a likeness to a syllogism. For when a person syllogizes, he is not required to use the definition of syllogism in order to syllogize; because the items from which a syllogism proceeds are such that each item is either a whole proposition, i.e., a universal or major proposition, or a part, i.e., a particular or minor proposition subsumed under the major one. Consequently, the definition of a syllogism is not one of the things from which a syllogism proceeds. In like manner if someone wishes to syllogize the quod quid erat esse of something, he is not required to mention what a quod quid erat esse is; but he must have this in reserve in his mind over and above the items which are put in the definition or in the syllogism. For these notions of a syllogism and of a definition function in defining and syllogizing as rules of art which an artisan must respect in his works. Now an artisan who makes a knife does not do so by establishing the rules according to which he works, but in the light of the rules he has in his mind he examines whether the knife was made well. So, too, a person who syllogizes does not mention the notion of a syllogism as he syllogizes, but in view of the notion of a syllogism he examines the syllogism he made, in order to see whether it is good.
Unde si aliquis dubitet, syllogismo facto, an sit syllogizatum vel non, poterit syllogizans obviare, ostendendo quod sit syllogizatum, ostendendo quod syllogismus sit tale aliquid. Similiter etiam ei qui intendit syllogizare quod quid erat esse, convenit ut habeat seorsum in mente rationem eius quod quid erat esse: ut si aliquis dicat quod non est syllogizatum quod quid erat esse, ipse dicat quod immo, quia tale aliquid ponitur quod quid erat esse. Sic ergo patet quod syllogizans quod quid erat esse, neque debet sumere quid est syllogismus, neque quid est quod quid erat esse.	Hence if a person should wonder, once a syllogism has been formed, whether it syllogized or not, the one who formed the syllogism can settle this doubt by showing that it does syllogize, on the ground that a syllogism is such and such a thing. So, too, a person who intends to syllogize the quod quid erat esse should have reserved in his mind the notion of what a quod quid erat esse is, so that if someone should say that a quod quid erat esse has not been syllogized, he can answer that it has, because such and such is put down as the quod quid erat esse. Thus, therefore, it is clear that a person who syllogizes a quod quid erat esse should not state what a syllogism is or what a quod quid erat esse is.
lib. 2 l. 5 n. 5 Deinde cum dicit: et si ex suppositione etc., ostendit quod non potest demonstrari quod quid est unius rei ex quod quid est alterius rei. Et circa hoc duo facit: primo, proponit quod intendit; secundo, probat propositum; ibi: etenim hic accipiens et cetera. Dicit ergo primo quod etiam non probatur quod quid est, si aliquis velit hoc probare ex suppositione quod quid est alterius rei. Puta si aliquis sic procedat accipiens quod idem sit esse divisibili et malo, idest quod divisio sit quod quid est mali, et ulterius argumentetur sic: in omnibus quae habent contrarium, contrarii est contrarium quod quid est; sed bono est contrarium malum, et indivisibile est contrarium divisibili; sequitur ergo quod indivisibile sit quod quid est ipsius boni. Et sumuntur ista exempla secundum opinionem Platonis, qui posuit quod eadem est ratio unius et boni. Videmus enim quod unumquodque appetit unitatem sicut proprium bonum. Unum autem est idem quod indivisibile; et sic per oppositum sequitur quod malum sit idem quod divisibile. Unumquodque enim refugit divisionem sui, quia per hoc tendit ad diminutum et imperfectum.	The (92a20) he shows that the quod quid of one thing cannot be demonstrated from the quod quid of another thing. Concerning this he does two things. First, he proposes what he intends. Secondly, he proves what he proposes (92a23). He says therefore first (92a20) that the quod quid is not proved, if someone wished to prove it by supposing the quod quid of some other thin ; for example, if someone were to proceed in such a way as to assume that the being or reality of divisible and of evil is the same, i.e., that division is the quod quid of evil, and then argued in the following manner: “In all things which have a contrary the quod quid of one contrary is a contrary; but the contrary of good is evil, and of divisible the contrary is indivisible: therefore, it follows that indivisible is the quod quid of the good.” And these examples are taken according to Plato’s opinion that the notion of the one and of the good are the same. For we notice that everything seeks unity as its own good. But one is the same as indivisible; and so in virtue of the opposition it follows that evil is the same as divisible. For everything shuns division of the self, because through division it tends to what is shattered and imperfect.
lib. 2 l. 5 n. 6 Deinde cum dicit: etenim hic accipiens etc., probat propositum, scilicet quod non possit demonstrari quod quid est; et hoc duabus rationibus. Quarum prima est, quia etiam in hoc modo probationis demonstrat aliquis accipiendo quod quid erat esse, et ita accipit quod oportet probare.	Then (92a23) he proves what he has proposed, namely, that the quod quid cannot be demonstrated: and this by giving two reasons. The first of these is that even according to this method one demonstrates by assuming the quod quid erat esse, and thus he assumes what he should have proved.
lib. 2 l. 5 n. 7 Secundam rationem ponit ibi: accipit autem ad demonstrandum etc.; et dicit quod non solum est inconveniens quod accipiatur quod quid erat esse ad demonstrandum, sed et alterum inconveniens fit quod accipitur quod quid erat esse ad demonstrandum quod quid erat esse: quia etiam in demonstrationibus in quibus probatur hoc de hoc, puta passio de subiecto, accipitur pro medio quod quid erat esse, non tamen quod quid erat esse quod accipitur, est ipsummet quod debet concludi, vel aliquid quod habeat eamdem rationem et convertatur. Eamdem autem rationem habet quod bonum sit indivisibile, et malum divisibile; et haec duo convertuntur, quia posito uno ponitur alterum, et e converso.	Then (92a24) he gives the second reason, saying that not only is it improper to take the quod quid erat esse when demonstrating, but this impropriety is compounded when one takes a quod quid erat esse to demonstrate a quod quid erat esse: because even in demonstrations in which this is proved of this, say a proper attribute of a subject, a quod quid erat esse is taken as middle; nevertheless the one so taken is not the very thing which was to be concluded or something which has the same notion and is converted. But good and indivisible, and evil and divisible, have the same notion; and each pair is converted, because one being posited, the other is posited, and vice versa.
lib. 2 l. 5 n. 8 Deinde cum dicit: ad utrosque autem et secundum divisionem etc., inducit rationem communem contra eum qui demonstrat ex suppositione et divisione; et dicit quod eadem oppositio habet locum contra utrosque, scilicet contra eum qui vult demonstrare quod quid est per divisionem, et contra eum qui utitur suppositione quod quid est in syllogismo. Manifestum est enim quod definitio significat unum aliquid: unde ea quae ponuntur in definitione, ad significandum unitatem, debent poni absque copula; puta ut dicatur quod homo est animal gressibile bipes, non autem debet dici quod homo sit animal et bipes. Unde si aliquis vult probare quod quid est, oportet quod probet ex his, quae assumuntur, fieri unum. Sed non est necessarium, secundum praedictas vias divisionis et suppositionis, quod ex his quae accipiuntur ad definiendum, fiat unum praedicatum: sed poterit esse quod sint multa, puta si dicatur quod homo est grammaticus et musicus. Videtur igitur quod secundum vias praedictas, non probetur quod quid est.	Then (92a28) he presents a common reason against anyone who demonstrates from supposition and division. And he says that the same opposition is directed against both, namely, against one who tries to demonstrate the quod quid by division and against one who proceeds by laying down the quod quid in the syllogism. For clearly a definition signifies something which is one: hence to signify this oneness the items laid down in the definition should be arranged without a conjunction; thus one should say that man is a two-footed land animal, but not that man is an animal and two-footed. Hence if anyone desires to prove the quod quid, he must prove that one thing is formed from the things assumed. But it is not required, according to the above-cited methods of division and supposition, that one predicate be formed from these items which are taken for defining: since there might be several, for example, if one should state that man is grammatical and musical. It seems therefore that according to the ways mentioned above, the quod quid is not proved.
lib. 2 l. 5 n. 9 Deinde cum dicit: qualiter igitur definiens etc., concludit ex praemissis quod nullo modo potest probari quod quid est; et dicit: si igitur neque per terminos convertibiles, neque per divisionem, neque per suppositionem demonstratur quod quid est, quomodo igitur definiens poterit demonstrare substantiam rei vel quod quid est? Iam enim ex praemissis patet quod non probat, sicut manifestum faciens ex his quae sunt per se nota, quod necesse sit alterum aliquid sequi per ea quae dicta sunt, quod requiritur ad demonstrationem.	Then (92a34) he concludes from the foregoing that there is no way to prove the quod quid, saying: if then the quod quid cannot be proved either by convertible terms or division or opposition, how will the definer be able to demonstrate the substance of a thing or the quod quid? For it is now clear from the foregoing that he does not prove it according to the method whereby, in virtue of items that are per se known, one manifests that something else must follow through things which are said-which is required for a demonstration.
Relinquitur autem praeter tres modos quartus modus, qui est per inductionem. Sed nec contingit probare quod quid est per singularia manifesta, ita scilicet quod aliquid praedicetur de omnibus, et non sit aliquid eorum quod aliter se habeat: quia sic inducendo non demonstrabit quod quid est, sed demonstrabit aliquid esse vel non esse, puta quod omnis homo est animal, vel nullus homo est lapis.	However, besides these three modes there is a fourth, namely, through induction. But it turns out that the quod quid cannot be proved by manifest singulars, namely, in such a way that something is predicated of all and is not anything that might be otherwise: because one who thus proceeds by induction will not demonstrate the quod quid but will demonstrate that something is or is not; for example, that every man is an animal, or that no animal is a stone.
Nullus autem alius modus relinquitur ad demonstrandum quod quid est: nisi forte modus demonstrationis qui est ad sensum, sicut cum aliquid demonstratur digito. Manifestum est autem quod hic modus non potest competere in proposito: quia quod quid est non est obiectum sensus, sed intellectus, ut dicitur in III de anima. Relinquitur ergo quod nullo modo possit demonstrari quod quid est.	But no other method is available for demonstrating the quod quid, save perhaps the method of demonstrating something to the senses, as when something is pointed out with the finger. But it is obvious that this method cannot be invoked in the present instance, because the quod quid is not an object of sense but of intellect, as it is stated in On the Soul III. It remains, therefore, that there is no way in which the quod quid can be demonstrated.