Authors/Thomas Aquinas/metaphysics/liber1/lect14

Lecture 14

Latin	English
lib. 1 l. 14 n. 1 Hic disputat contra opinionem Platonis: et dividitur in duas partes. Primo disputat contra eius opinionem, quantum ad hoc quod ponebat de rerum substantiis. Secundo quantum ad hoc quod de rerum principiis, ibi, omnino autem sapientia. Prima dividitur in duas partes. Primo enim disputat contra hoc quod ponebat substantias species. Secundo quantum ad hoc quod ponebat de mathematicis, ibi, amplius si sunt numeri. Circa primum duo facit. Primo enim disputat contra ipsam positionem Platonis. Secundo contra rationem ipsius, ibi, amplius autem secundum quos et cetera. Dicit ergo primo, quod Platonici ponentes ideas esse quasdam substantias separatas, in hoc videntur deliquisse, quia cum ipsi quaerentes causas horum sensibilium entium, praetermissis sensibilibus, adinvenerunt quaedam alia nova entia aequalia numeris sensibilibus. Et hoc videtur inconveniens: quia qui quaerit causas aliquarum rerum, debet ipsas certificare, non alias res addere, ex quarum positione accrescat necessitas inquisitionis: hoc enim simile est ac si aliquis vellet numerare res aliquas, quas non putet se posse numerare sicut pauciores, sed vult eas numerare multiplicando eas per additionem aliquarum rerum. Constat enim quod talis stulte movetur, quia in paucioribus est via magis plana, quia melius et facilius certificantur pauca quam multa. Et numerus tanto est certior quanto est minor, sicut propinquior unitati, quae est mensura certissima. Sicut autem numeratio est quaedam rerum certificatio quantum ad numerum, ita inquisitio de causis rerum est quaedam certa mensura ad certificationem naturae rerum. Unde sicut numeratae pauciores res facilius certificantur quantum ad earum numerum, ita pauciores res facilius certificantur quantum ad earum naturam. Unde cum Plato ad notificandum res sensibiles tantum, multiplicaverit rerum genera, adiunxit difficultates, accipiens quod est difficilius ad manifestationem facilioris, quod est inconveniens.	208. Here he argues disputatively against Plato’s opinion. This is divided into two parts. First (208), he argues against Plato’s opinion with reference to his position about the substances of things; and second (259), with reference to his position about the principles of things (“And in general”). The first is divided into two parts. First, he argues against Plato’s position that the Forms are substances; and second (122:C 239), against the things that he posited about the objects of mathematics (“Further, if the Forms”). In regard to the first he does two thinks. First, he argues against this position of Plato; and second (210), against the reasoning behind it (“Furthermore, with regard to”). He says, first (103), that the Platonists, in holding that the Ideas are certain separate substances, seemed to be at fault in that, when they sought for the causes of these sensible beings, they neglected sensible beings and invented certain other new entities equal in number to sensible beings. This seems to be absurd, because one who seeks the causes of certain things ought to make these evident and not add other things, the premising of which only adds to the number of points which have to be investigated. For it would be similar if a man who wished to count certain things which he did not think he was able to count because they are few, believed that he could count them by increasing their number through the addition of certain other things. But it is evident that such a man has a foolish motive, because the path is clearer when there are fewer things; for it is better and easier to make certain of fewer things than of many. And the smaller a number is, the more certain it is to us, inasmuch as it is nearer to the unit, which is the most accurate measure. And just as the process of counting things is the measure we use to make certain of their number, in a similar fashion an investigation of the causes of things is the accurate measure for making certain of their natures. Therefore, just as the number of fewer numerable things is made certain of more easily, n a similar way the nature of fewer things is made certain of more easily. Hence, when Plato increased the classes of beings to the extent that he did with a view to explaining sensible things, he added to the number of difficulties by taking what is more difficult in order to explain what is less difficult. This is absurd.
lib. 1 l. 14 n. 2 Et quod ideae sint aequales numero, aut non pauciores sensibilibus, de quibus Platonici inquirunt causas (quibus Aristoteles se connumerat, quia Platonis discipulus fuit) et determinaverunt procedentes de his sensibilibus ad praedictas species, manifestum est si consideretur, qua ratione Platonici ideas induxerunt: hac, scilicet, quia videbant in omnibus univocis unum esse in multis. Unde id unum ponebant esse speciem separatam. Videmus tamen, quod circa omnes substantias rerum aliarum ab ideis invenitur unum in multis per modum univocae praedicationis, inquantum inveniuntur multa unius speciei et hoc non solum in sensibilibus corruptibilibus, sed etiam in mathematicis, quae sunt sempiterna: quia et in eis multa sunt unius speciei, ut supra dictum est. Unde relinquitur quod omnibus speciebus rerum sensibilium respondeat aliqua idea. Quaelibet igitur earum est quoddam aequivocum cum istis sensibilibus, quia communicat in nomine cum eis. Sicut enim Socrates dicitur homo, ita et illa. Tamen differunt ratione. Ratio enim Socratis est cum materia. Ratio vero hominis idealis est sine materia. Vel secundum aliam literam, unaquaeque species dicitur esse aliquid univocum, inquantum scilicet est unum in multis, et convenit cum illis de quibus praedicatur, quantum ad rationem speciei. Ideo autem dicit aequales, aut non pauciores, quia ideae vel ponuntur solum specierum, et sic erunt aequales numero istis sensibilibus, si numerentur hic sensibilia secundum diversas species, et non secundum diversa individua quae sunt infinita. Vel ponuntur ideae non solum specierum, sed etiam generum; et sic sunt plures ideae quam species sensibilium, quia ideae tunc erunt species omnes, et praeter haec omnia et singula genera. Et propter hoc dicit aut non pauciores quidem, sed plures. Vel aliter, ut dicantur esse aequales, inquantum ponebat eas esse sensibilium; non pauciores autem sed plures, inquantum ponebat eas non solum species sensibilium, sed etiam mathematicorum.	209. That the Ideas are equal in number to, or not fewer than, sensible things, whose causes the Platonists seek (and Aristotle includes himself among their number because he was Plato’s disciple), and which they established by going from sensible things to the aforesaid Forms, becomes evident if one considers by what reasoning the Platonists introduced the Ideas. Now they reasoned thus: they saw that there is a one-in-many for all things having the same name. Hence they claimed that this one-in-many is a Form. Yet with respect to all substances of things other than the Ideas we see that there is found to be a one-in-many which is predicated of them univocally inasmuch as there are found to be many things which are specifically one. This occurs not only in the case of sensible things but also in that of the objects of mathematics, which are eternal; because among these there are also many things which are specifically one, as was stated above (157). Hence it follows that some Idea corresponds to each species of sensible things; and therefore each Idea is something having the same name as these sensible things, because the Ideas agree with them in name. For just as Socrates is called man, so also is the Idea of man. Yet they differ conceptually; for the intelligible structure of Socrates contains matter, whereas that of the ideal man is devoid of matter. or, according to another reading, each Form is said to be something having the same name [as these sensible things] inasmuch as it is a one-in-many and agrees with the things of which it is predicated so far as the intelligible structure of the species is concerned. Hence he says that they are equal to, or not fewer than, these things. For either there are held to be Ideas only of species, and then they would. be equal in number to these sensible things (granted that things are counted here insofar as they differ specifically and not individually, for the latter difference is infinite); or there are held to be ideas not only of species but also of genera, and then there would be more ideas than there are species of sensible things, because all species would be Ideas and in addition to these each and every genus [would be an Idea]. This is why he says that they are either not fewer than or more. Or, in another way, they are said to be equal inasmuch as he claimed that they are the Forms of sensible things. And he says not fewer than but more inasmuch as he held that they are the Forms not only of sensible things but also of the objects of mathematics.
lib. 1 l. 14 n. 3 Deinde cum dicit amplius autem hic disputat contra Platonem quantum ad rationem suae positionis. Et circa hoc duo facit. Primo tangit modos in generali, quibus rationes Platonis deficiebant. Secundo exponit illos in speciali, ibi, quia secundum rationes scientiarum. Dicit ergo primo, quod secundum nullum illorum modorum videntur species esse, secundum quos nos Platonici ostendimus species esse. Et hoc ideo quia ex quibusdam illorum modorum non necessarium est fieri syllogismum, idest quasdam rationes Platonis, quia scilicet non de necessitate possunt syllogizare species esse: ex quibusdam vero modis fit syllogismus, sed non ad propositum Platonis: quia per quasdam suas rationes ostenditur, quod species separatae sunt quarumdam rerum, quarum esse species Platonici non putaverunt similiter, sicut et illarum quarum putaverunt, esse species.	210. Furthermore, with regard to (104). Here he argues dialectically against the reasoning behind Plato’s position; and in regard to this he does two things. First, he gives a general account of the ways in which Plato’s arguments fail. Second (211), he explains them in detail (“For according to those”). He says, first, that with regard to the ways in which we Platonists prove the existence of the Forms, according to none of these are the Forms seen to exist. The reason is that “no syllogism follows” necessarily from some of these ways, i.e., from certain arguments of Plato, because they cannot demonstrate with necessity the existence of the Ideas. However, from other arguments a syllogism does follow, although it does not support Plato’s thesis; for by certain of his arguments there are proved to be Forms of certain things of which the Platonists did not think there are Forms, just as there are proved to be Forms of those things of which they think there are Forms.
lib. 1 l. 14 n. 4 Deinde cum dicit quia secundum hic prosequitur istos modos in speciali. Et primo prosequitur secundum, ostendendo quod sequitur per rationem Platonis species esse aliquorum, quorum species non ponebat. Secundo prosequitur primum, ostendens quod rationes Platonis non sunt sufficientes ad ostendendum esse ideas, ibi, omnium autem dubitabit aliquis et cetera. Circa primum ponit septem rationes: quarum prima talis est. Una rationum inducentium Platonem ad ponendum ideas sumebatur ex parte scientiae: quia videlicet scientia cum sit de necessariis, non potest esse de his sensibilibus, quae sunt corruptibilia, sed oportet quod sit de entibus separatis incorruptibilibus. Secundum igitur hanc rationem ex scientiis sumptam, sequitur quod species sint omnium quorumcumque sunt scientiae. Scientiae autem non solum sunt de hoc quod est esse unum in multis, quod est per affirmationem, sed etiam de negationibus: quia sicut sunt aliquae demonstrationes concludentes affirmativam propositionem, ita sunt etiam demonstrationes concludentes negativam propositionem: ergo oportet etiam negationum ponere ideas.	211. For according to (105). Here he examines in detail the arguments by which the Platonists establish Ideas. First, he examines the second argument; and he does this by showing that from Plato’s argument it follows that there are Forms of some things for which the Platonists did not posit Forms. Second (225), he examines the first argument; and he does this by showing that Plato’s arguments are not sufficient to prove that Ideas exist (“But the most”). In regard to the first member of this division he gives seven arguments. The first is this: one of the arguments that induced Plato to posit Ideas is taken from scientific knowledge; for since science is concerned with necessary things, it cannot be concerned with sensible things, which are corruptible, but must be concerned with separate entities which are incorruptible. According to the argument taken from the sciences, then, it follows that there are Forms of every sort of thing of which there are sciences. Now there are sciences not only of that which is one-in-many, which is affirmative, but also of negations; for just as there are some demonstrations which conclude with an affirmative proposition, in a similar way there are demonstrations which conclude with a negative proposition. Hence it is also necessary to posit Ideas of negations.
lib. 1 l. 14 n. 5 Deinde cum dicit et secundum hic ponit secundam rationem. In scientiis enim non solum intelligitur quod quaedam semper se eodem modo habent, sed etiam quod quaedam corrumpuntur; aliter tolleretur scientia naturalis, quae circa motum versatur. Si igitur oportet esse ideas omnium illorum quae in scientiis intelliguntur, oportet esse ideas corruptibilium inquantum corruptibilia, hoc est inquantum sunt haec sensibilia singularia; sic enim sunt corruptibilia. Non autem potest dici secundum rationem Platonis, quod scientiae illae, quibus intelligimus corruptiones rerum, intelligantur corruptiones horum sensibilium; quia horum sensibilium non est intellectus, sed imaginatio vel phantasia, quae est motus factus a sensu secundum actum, secundum quod dicitur in secundo de anima.	212. Again, according to the argument (106). Here he gives the second argument. For in the sciences it is not only understood that some things always exist in the same way, but also that some things are destroyed; otherwise the philosophy of nature, which deals with motion, would be destroyed. Therefore, if there must be ideas of all the things which are comprehended in the sciences, there must be Ideas of corruptible things as such, i.e., insofar as these are singular sensible things; for thus are things corruptible. But according to Plato’s theory it cannot be said that those sciences by which we understand the processes of corruption in the world attain any understanding of the processes of corruption in sensible things; for there is no comprehension of these sensible things, but only imagination or phantasy, which is a motion produced by the senses in their act of sensing, as is pointed out in The Soul, Book II.
lib. 1 l. 14 n. 6 Deinde cum dicit amplius autem hic ponit tertiam rationem, quae continet duas conclusiones, quas certissimis rationibus dicit concludi. Una est, quia si ideae sunt omnium, quorum sunt scientiae, scientiae autem non solum sunt de absolutis, sed etiam sunt de his quae dicuntur ad aliquid, sequitur hac ratione faciente quod ideae sunt etiam eorum quae sunt ad aliquid: quod est contra opinionem Platonis; quia cum ideae separatae sint secundum se existentes, quod est contra rationem eius quod est ad aliquid, non ponebat Plato eorum quae sunt ad aliquid, aliquod esse genus idearum, quia secundum se dicuntur.	213. Again, according to the most (107). Here he gives the third argument, which contains two conclusions that he says are drawn from the most certain arguments of Plato. One conclusion is this: if there are Ideas of all things of which there are sciences, and there are sciences not only of absolutes but also of things predicated relatively, then in giving this argument it follows that there are also Ideas of relations. This is opposed to Plato’s view. For, since the separate Ideas are things which exist of themselves, which is opposed to the intelligibility of a relation, Plato did not hold that there is a class of Ideas of relations, because the Ideas are said to exist of themselves.
lib. 1 l. 14 n. 7 Alia conclusio est quae ex aliis rationibus certissimis sequitur, quod scilicet sit tertius homo. Quod quidem tripliciter potest intelligi. Uno modo quod intelligatur, quod homo idealis sit tertius a duobus hominibus sensibilibus, qui communis hominis praedicationem suscipiunt. Sed haec non videtur eius esse intentio, licet non tangatur secundo elenchorum: haec enim est positio contra quam disputat: unde ad hoc non duceret quasi ad inconveniens.	214. The second conclusion is one which follows from other most certain arguments, namely, that there is “a third man.” This phrase can be understood in three ways. First, it can mean that the ideal man is a third man distinct from two men perceived by the senses, who have the common name man predicated of both of them. But this does not seem to be what he has in mind, even though it is not mentioned in the Sophistical Refutations, Book II; for this is the position against which he argues. Hence according to this it would not lead to an absurdity.
lib. 1 l. 14 n. 8 Alio modo potest intelligi, ut dicatur tertius homo, scilicet qui sit communis et homini ideali et homini sensibili. Cum enim homo sensibilis et homo idealis conveniant in ratione, sicut duo homines sensibiles, et sicut homo idealis ponitur tertius praeter duos homines sensibiles, ita alius homo debet poni tertius praeter hominem idealem et hominem sensibilem. Et hoc etiam non videtur hic esse eius intentio, quia ad hoc inconveniens statim alia ratione ducet: unde esset superfluum hic ad idem inconveniens ducere.	215. The second way in which this expression can be understood is this: the third man means one that is common to the ideal man and to one perceived by the senses. For since both a man perceived by the senses and the ideal man have a common intelligible structure, like two men perceived by the senses, then just as the ideal man is held to be a third man in addition to two men perceived by the senses, in a similar way there should be held to be another third man in addition to the ideal man and one perceived by the senses. But neither does this seem to be what he has in mind here, because he leads us immediately to this absurdity by means of another argument. Hence it would be pointless to lead us to the same absurdity here.
lib. 1 l. 14 n. 9 Tertio modo potest intelligi, quia Plato ponebat in quibusdam generibus tria, quaedam scilicet sensibilia, mathematica et species, sicut in numeris et lineis et omnibus huiusmodi. Non est autem maior ratio quare in quibusdam rebus ponantur media quam in aliis; ergo oportebat etiam in specie hominis ponere hominem medium, qui erit tertius inter hominem sensibilem et idealem: et hanc etiam rationem in posterioribus libris Aristoteles ponit.	216. The third way in which this expression can be understood is this: Plato posited three kinds of entities in certain classes of things, namely, sensible substances, the objects of mathematics and the Forms. He does this, for example, in the case of numbers, lines and the like. But there is no reason why intermediate things should be held to exist in certain classes rather than in others. Hence in the class of man it was also necessary to posit an intermediate man, who will be a third man midway between the man perceived by the senses and the ideal man. Aristotle also gives this argument in the later books of this work (2160).
lib. 1 l. 14 n. 10 Deinde cum dicit et omnino hic ponit quartam rationem quae talis est. Quicumque per suam rationem removet aliqua, quae sunt apud eum magis nota quam ipsa positio, inconvenienter ponit. Sed istae rationes, quas Plato posuit, de speciebus separatis, auferunt quaedam principia, quae Platonici dicentes esse species magis volunt esse vera quam hoc ipsum quod est, ideas esse: ergo Plato inconvenienter posuit. Minorem autem sic manifestat. Ideae secundum Platonem sunt priores rebus sensibilibus et mathematicis: sed ipsae ideae sunt numeri secundum eum, et magis numeri impares quam pares, quia numerum imparem attribuebat formae, parem autem materiae. Unde et dualitatem dixit esse materiam. Sequitur ergo quod alii numeri sunt priores dualitate, quam ponebat sicut materiam sensibilium, ponens magnum et parvum. Cuius contrarium Platonici maxime asserebant, scilicet dualitatem esse primam in genere numeri.	217. And in general (108). Here he gives the fourth argument, which runs as follows. Whoever by his own reason he does away with certain [principles] which are better known to him than the ones which he posits, adopts an absurd position. But these theories about the Forms which Plato held do away with certain principles whose reality the Platonists (when they said that there are Ideas) were more convinced of than the existence of the Ideas. Therefore Plato’s position is absurd. The minor premise is proved in this way. According to Plato the Ideas are prior both to sensible things and to the objects of mathematics. But according to him the Ideas themselves are numbers; and they are odd numbers rather than even ones, because he attributed odd number to form and even number to matter. Hence he also said that the dyad [or duality] is matter. Therefore it follows that other numbers are prior to the dyad, which he held to be the matter of sensible things, and identified with the great and small. Yet the Platonists asserted the very opposite of this, that is to say, that the dyad is first in the class of number.
lib. 1 l. 14 n. 11 Item si, sicut per superiorem rationem probatum est, oportet esse aliquas ideas relationum, quae sint secundum se ad aliquid, et ipsa idea est prior eo quod participat ideam, sequitur quod hoc ipsum quod est ad aliquid est prius absoluto quod secundum se dicitur. Nam huiusmodi substantiae sensibiles, quae participant ideas, absolute dicuntur. Et similiter de omnibus est quaecumque illi qui sequuntur opinionem de ideis dicunt opposita principiis per se notis, quae etiam ipsi maxime concedebant.	218. Again, if, as has been proved by the above argument (213), there must be Ideas of relations, which are self-subsistent relations, and if the Idea itself is prior to whatever participates in the Idea, it follows that the relative is prior to the absolute, which is said to exist of itself. For sensible substances of this kind, which participate in Ideas, are said to be in an unqualified sense. And in like manner whatever those who follow the opinion about the Ideas say of all things is opposed to self-evident principles which even they themselves are most ready to acknowledge.
lib. 1 l. 14 n. 12 Deinde cum dicit amplius autem hic ponit quintam rationem, quae talis est. Ideae ponebantur a Platone, ut eis competerent rationes sive definitiones positae in scientiis, ut etiam de eis scientiae esse possent. Sed intelligentia una, idest simplex et indivisibilis, qua scitur de unoquoque quid est, non solum est circa substantias sed etiam de aliis, scilicet accidentibus. Et similiter scientiae non solum sunt substantiae, et de substantia, sed etiam inveniuntur scientiae aliorum, scilicet accidentium: ergo patet quod ad aestimationem, secundum quam vos Platonici esse dicitis ideas, sequitur quod species non solum essent substantiarum, sed etiam multorum aliorum, scilicet accidentium. Et hoc idem sequitur non solum propter definitiones et scientias, sed etiam accidunt multa alia talia, scilicet plurima, ex quibus oportet ponere ideas accidentium secundum rationes Platonis. Sicut quia ponebat ideas principia essendi et fieri rerum, et multorum huiusmodi, quae conveniunt accidentibus.	219. Again, according to the opinion (109). Here he gives the fifth argument, which is as follows: Ideas were posited by Plato in order that the intelligible structures and definitions of things given in the sciences might correspond to them, and in order that there could be sciences of them. But there is “one concept,” i.e., a simple and indivisible concept, by which the quiddity of each thing is known, i.e., not only the quiddity of substances “but also of other things,” namely, of accidents. And in a similar way there are sciences not only of substance and about substance, but there are also found to be sciences “of other things,” i.e., of accidents. Hence according to the opinion by which you Platonists acknowledge the existence of Ideas, it evidently follows that there will be Forms not only of substances but also of other things, i.e., of accidents. This same conclusion follows not only because of definitions and the sciences, but there also happen to be many “other such” [reasons], i.e., very many .reasons why it is necessary to posit Ideas of accidents according to Plato’s arguments. For example, he held that the Ideas are the principles of being and of becoming in the world, and of many such aspects which apply to accidents.
lib. 1 l. 14 n. 13 Sed ex alia parte secundum quod Plato opinabatur de ideis, et secundum necessitatem, qua sunt necessariae sensibilibus inquantum scilicet sunt participabiles a sensibilibus, est necessarium ponere quod ideae sint solum substantiarum. Quod sic patet. Ea quae sunt secundum accidens non participantur: sed ideam oportet participari in unoquoque inquantum non dicitur de subiecto. Quod sic patet. Quia si aliquod sensibile participat per se duplo, idest duplo separato (sic enim appellabat Plato omnia separata, scilicet per se entia): oportet quod participet sempiterno; non quidem per se, quia tunc sequeretur quod dupla sensibilia essent sempiterna, sed per accidens: inquantum scilicet ipsum per se duplum quod participatur est sempiternum. Ex quo patet quod participatio non est eorum quae accidentia sunt, sed solummodo substantiarum. Unde secundum opinionem Platonis non erat aliquod accidens species separata, sed solum substantia: et tamen secundum rationem sumptam ex scientiis oportebat quod esset species etiam accidentium, ut dictum est.	220. But, on the other hand, according to Plato’s opinion about the Ideas and according to logical necessity, insofar as the Ideas are indispensable to sensible things, i.e., “insofar” s as they are capable of being participated in by sensible things, it is necessary to posit Ideas only of substances. This is proved thus: things which are accidental are not participated in. But an Idea must be participated in by each thing insofar as it is not predicated of a subject. This becomes clear as follows: if any sensible thing participates in “doubleness itself,” i.e., in a separate doubleness (for Plato spoke of all separated things in this way, namely, as self-subsisting things), it must participate in the eternal. But it does not do this essentially (because then it would follow that any double perceived by the senses would be eternal), but accidentally, i.e., insofar as doubleness itself, which is participated in, is eternal. And from this it is evident that there is no participation in things which are accidental, but only in substances. Hence according to Plato’s position a separate Form was not an accident but only a substance. Yet according to the argument taken from the sciences there must also be Forms of accidents, as was stated above (219).
lib. 1 l. 14 n. 14 Deinde cum dicit haec vero hic ponit sextam rationem, quae talis est. Istae res sensibiles substantiam significant in rebus quae videntur et similiter illic, ut in rebus intelligibilibus, quae substantiam significant, quia tam intelligibilia quam sensibilia substantiam ponebant: ergo necesse est ponere praeter utrasque substantias, scilicet intelligibiles et sensibiles, aliquid commune eis quod sit unum in multis: ex hac enim ratione Platonici ideas ponebant, quia inveniebant unum in multis, quod credebant esse praeter illa multa.	221. But these things (111). Then he gives the sixth argument, which runs thus: these sensible things signify substance both in the case of things perceived by the senses and in that of those in the ideal world, i.e., in the case of intelligible things, which signify substance; because they held that both intelligible things and sensible ones are substance. Therefore it is necessary to posit in addition to both of these substances—intelligible and sensible ones—some common entity which is a one-in-many. For the Platonists maintained that the Ideas exist on the grounds that they found a one-in-many which they believed to be separate from the many.
lib. 1 l. 14 n. 15 Et quod hoc ponere sit necessarium, scilicet aliquod unum praeter substantias sensibiles et praeter species, sic ostendit. Aut enim ideae et sensibilia quae participant ideas sunt unius speciei aut non. Si sunt unius speciei, omnium autem multorum in specie convenientium oportet ponere secundum positionem Platonis unam speciem separatam communem, oportebit igitur aliquid ponere commune sensibilibus et ipsis ideis, quod sit separatum ab utroque. Non potest autem responderi ad hanc rationem quod ideae quae sunt incorporales et immateriales non indigent aliis speciebus superioribus; quia similiter mathematica quae ponuntur a Platone media inter sensibilia et species, sunt incorporea et immaterialia: et tamen, quia plura eorum inveniuntur unius speciei, Plato posuit eorum speciem communem separatam, qua etiam participant non solum mathematica, sed etiam sensibilia. Si igitur est una et eadem dualitas, quae est species vel idea dualitatis, quae quidem est etiam in dualitatibus sensibilibus quae sunt corruptibiles, sicut exemplar est in exemplato et in dualitatibus etiam mathematicis quae sunt multae unius speciei, sed tamen sunt sempiternae, eadem ratione in eadem dualitate, scilicet quae est idea et in alia quae est mathematica, vel sensibilis, erit alia dualitas separata. Non enim potest reddi propter quid illud sit, et hoc non sit.	222. The need for positing a one apart from both sensible substances and the Forms he proves thus: the Ideas and the sensible things which participate in them either belong to one class or not. If they belong to one class, and it is necessary to posit, according to Plato’s position, one common separate Form for all things having a common nature, then it will be necessary to Posit some entity common to both sensible things and the Ideas themselves) which exists apart from both. Now one cannot answer this argument by saying that the Ideas, which are incorporeal and immaterial, do not stand in need of any higher Forms; because the objects of mathematics, which Plato places midway between sensible substances and the Forms, are similarly incorporeal and immaterial. Yet since many of them are found to belong to one species, Plato held that there is a common Form for these things, in which not only the objects of mathematics participate but also sensible substances. Therefore, if the twoness [or duality] which is the Form or Idea of twoness is identical with that found in sensible twos, which are corruptible (just as a pattern is found in the things fashioned after it), and with that found in mathematical twos, which are many in one class (but are nevertheless eternal) ‘ then for the same reason in the case of the same twoness, i.e., the Idea two , and in that of the other twoness, which is either mathematical or sensible, there will be another separate twoness. For no reason can be given why the former should exist and the latter should not.
lib. 1 l. 14 n. 16 Si autem detur alia pars, scilicet sensibilia quae participant ideas non sunt eiusdem speciei cum ideis: sequitur quod nomen quod dicitur de ideis et de substantia sensibili dicatur omnino aequivoce. Illa enim dicuntur aequivoce, quorum solum nomen commune est, ratione speciei existente diversa. Nec solum sequitur quod sint quocumque modo aequivoca, sed simpliciter aequivoca, sicut illa quibus imponitur unum nomen sine respectu ad aliquam communicationem, quae dicuntur aequivoca a casu. Sicut si aliquem hominem aliquis vocaret Calliam et aliquod lignum.	223. But if the other alternative is admitted—that sensible things, which participate in the Ideas, do not have the same form as the Ideas—it follows that the name which is predicated of both the Ideas and sensible substances is predicated in a purely equivocal way. For those things are said to be equivocal which have only a common name and differ in their intelligible structure. And it follows that they are not only equivocal in every way but equivocal in an absolute sense, like those things on which one name is imposed without regard for any common attribute, which are said to be equivocal by chance; for example, if one were to call both Callias and a piece of wood man.
lib. 1 l. 14 n. 17 Hoc autem ideo addidit Aristoteles quia posset aliquis dicere quod non omnino aequivoce aliquod nomen praedicatur de idea et de substantia sensibili, cum de idea praedicetur essentialiter, de substantia vero sensibili per participationem. Nam idea hominis secundum Platonem dicitur per se homo, hic autem homo sensibilis dicitur per participationem. Sed tamen talis aequivocatio non est pura; sed nomen quod per participationem praedicatur, dicitur per respectum ad illud quod praedicatur per se, quod non est pura aequivocatio, sed multiplicitas analogiae. Si autem essent omnino aequivoca a casu idea et substantia sensibilis, sequeretur quod per unum non posset cognosci aliud, sicut aequivoca non se invicem notificant.	224. Now Aristotle added this because someone might say that a name is not predicated of an Idea and of a sensible substance in a purely equivocal way, since a name is predicated of an Idea essentially and of a sensible substance by participation. For, according to Plato, the Idea of man is called “man in himself,” whereas this man whom we apprehend by the senses is said to be a man by participation. However, such an equivocation is not pure equivocation. But a name which is predicated by participation is predicated with reference to something that is predicated essentially; and this is not pure equivocation but the multiplicity of analogy. However, if an Idea and a sensible substance were altogether equivocal by chance, it would follow that one could not be known through the other, as one equivocal thing cannot be known through another.