Authors/Thomas Aquinas/metaphysics/liber1/lect9

Lecture 9

Latin	English
lib. 1 l. 9 n. 1 Hic ponit opiniones philosophorum de toto universo, sicut de uno ente; et circa hoc duo facit. Primo ponit eorum opiniones in communi. Secundo ostendit quomodo consideratio huius opinionis ad praesentem tractatum pertineat, et quomodo non, ibi, igitur ad praesentem et cetera. Dicit ergo quod aliqui alii philosophi a praedictis fuerunt, qui enuntiaverunt, de omni, idest de universo quasi de una natura, idest quasi totum universum esset unum ens vel una natura. Quod tamen non eodem modo omnes posuerunt, sicut infra patebit. Ipso tamen modo, quo diversificati sunt, nec bene dixerunt, nec naturaliter. Nullus enim eorum naturaliter locutus est, quia motum rebus subtrahunt. Nullus etiam bene locutus est, quia positionem impossibilem posuerunt, et per rationes sophisticas: sicut patet primo physicorum.	134. Here he gives the opinions of those philosophers who spoke of the whole universe as one being; and in regard to this he does two things. First, he gives the opinion which they held in common; and second (135), he shows how a consideration of this opinion is relevant to the present treatise, and how it is not (“Therefore a consideration”). He says, then, that there were certain philosophers, other than those just mentioned, who spoke “of the whole,” i.e,, of the universe, as if it were of one nature, i.e., as if the whole universe were a single being or a single nature. However, not all maintained this position in the same way, as he will make clear below (138-49). Yet in the way in which they differ their statements are neither acceptable nor in conformity with nature. None of their statements are in conformity with nature, because they did away with motion in things. And none of them are acceptable, because they held an impossible position and used sophistical arguments, as is clear in Book I of the Physics.
lib. 1 l. 9 n. 2 Deinde cum dicit igitur ad hic ostendit quomodo consideratio huius positionis ad praesentem tractatum pertinet, et quomodo non. Et primo ostendit quod non pertinet, si consideretur eorum positio. Secundo ostendit quod pertinet, si consideretur positionis ratio, vel positionis modus, ibi, sed quidem secundum causam et cetera. Dicit ergo, quod quia isti philosophi posuerunt tantum unum ens, et unum non potest suiipsius esse causa, patet, quod ipsi non potuerunt invenire causas. Nam positio, idest pluralitas, causarum diversitatem in rebus exigit. Unde, quantum ad praesentem perscrutationem quae est de causis, non congruit ut sermo de eis habeatur. Secus autem est de antiquis naturalibus, qui tantum ens posuerunt esse unum, de quibus debet hic sermo haberi. Illi enim ex illo uno generant multa, sicut ex materia, et sic ponunt causam et causatum. Sed isti de quibus nunc agitur, alio modo dicunt. Non enim dicunt quod sint omnia unum secundum materiam, ita quod ex uno omnia generentur; sed dicunt quod simpliciter sunt unum.	135. Therefore a consideration (64). Here he shows how a consideration of this position pertains to the present investigation and how it does not. He shows, first, that it has no bearing on this investigation if we consider their position itself; and, second (137), that it does have a bearing on this investigation if the reasoning or method behind their position is considered (“Yet their opinion”). He says, then, that since these philosophers held that there is only one being, and a single thing cannot be its own cause, it is clear that they could not discover the causes. For the position that there is a plurality of things demands a diversity of causes in the world. Hence, a consideration of their statements is of no value for the purposes of the present study, which deals with causes. But the situation is different in the case of the ancient philosophers of nature, who held that there is only one being, and whose statements must be considered here. For they generated many things from that one principle as matter, and thus posited both cause and effect. But these men with whom we are now dealing speak of this in a different way. For they do not say that all things are one materially, so that all things are generated from one matter, but that all things are one in an absolute sense.
lib. 1 l. 9 n. 3 Et ratio huius diversitatis est, quod antiqui naturales apponebant motum illis, qui ponebant unum principium et unum ens, dicentes ipsum esse mobile. Et ideo per aliquem modum motus, sicut per rarefactionem et condensationem poterant ex illo uno diversa generari. Et per hunc modum dicebant generari totum universum secundum diversitatem, quae in partibus eius invenitur. Et tamen quia non ponebant variationem secundum substantiam, nisi secundum accidentia, ut supra dictum est, ideo relinquebatur quod totum universum esset unum secundum substantiam, diversificatum tamen secundum accidentia. Sed isti dicebant illud quod ponebant esse unum penitus immobile. Et ideo ex illo uno non poterat aliqua diversitas rerum causari. Et propter hoc nec secundum substantiam nec secundum accidentia pluralitatem in rebus ponere poterant.	136. The reason for this difference is that the ancient philosophers of nature added motion to the view of those who posited one being and one principle, and said that this one being is mobile; and therefore different things could be generated from that one principle by a certain kind of motion, i.e., by rarefaction and condensation. And they said that the whole universe with respect to the diversity found in its parts is generated in this way. Yet since they held that the only change affecting substance is accidental, as was stated above (75), the conclusion then followed that the whole universe is one thing substantially but many things accidentally. But these thinkers [i.e., the Eleatics], said that the one being which they posited is immobile in an absolute sense; and therefore a diversity of things could not be produced from that one being. For since this being is immobile they could not posit any plurality in the world, either substantial or accidental.
lib. 1 l. 9 n. 4 Deinde cum dicit sed quidem hic ostendit quomodo eorum opinio pertineat ad praesentem perscrutationem. Et primo generaliter de omnibus. Secundo specialiter de Parmenide, ibi, igitur hi. Dicit ergo primo, quod licet diversitatem rebus auferrent, et per consequens causalitatem, tamen eorum opinio est propria praesenti inquisitioni, secundum tantum quantum dicetur: quantum scilicet ad modum ponendi, et quantum ad rationem positionis.	137. Yet their opinion (65). Here he shows how their opinion is relevant to the present inquiry. First, he deals with all of these thinkers in general; and second (142), with Parmenides in particular. He says, first, that although they did away with diversity in the world, and consequently with causality, nevertheless their opinion is relevant to the present study to this extent, let us say: as regards the method by which they establish their position and the reason for their position.
lib. 1 l. 9 n. 5 Parmenides enim qui fuit unus ex eis, videtur tangere unitatem secundum rationem, idest ex parte formae. Argumentatur enim sic. Quicquid est praeter ens, est non ens: et quicquid est non ens, est nihil: ergo quicquid est praeter ens est nihil. Sed ens est unum. Ergo quicquid est praeter unum, est nihil. In quo patet quod considerabat ipsam rationem essendi quae videtur esse una, quia non potest intelligi quod ad rationem entis aliquid superveniat per quod diversificetur: quia illud quod supervenit enti, oportet esse extraneum ab ente. Quod autem est huiusmodi, est nihil. Unde non videtur quod possit diversificare ens. Sicut etiam videmus quod differentiae advenientes generi diversificant ipsum, quae tamen sunt praeter substantiam eius. Non enim participant differentiae genus, ut dicitur quarto topicorum. Aliter genus esset de substantia differentiae, et in definitionibus esset nugatio, si posito genere, adderetur differentia, si de eius substantia esset genus, sicut esset nugatio si species adderetur. In nullo etiam differentia a specie differret. Ea vero quae sunt praeter substantiam entis, oportet esse non ens, et ita non possunt diversificare ens.	138. Parmenides, who was a member of this group, seems to touch on unity according to intelligible structure) i.e., according to form; for he argued as follows: besides being there is only non-being, and non-being is nothing. Therefore besides being there is nothing. But being is one. Therefore, besides the one there is nothing. In this argument he clearly considered the intelligible structure itself of being, which seems to be one, because nothing can be understood to be added to the concept of being by which it might be diversified. For whatever is added to being must be other than being. But anything such as this is nothing. Hence it does not seem that this can diversify being; just as we also see that differences added to a genus diversify it, even though these differences are outside the substance of that genus. For differences do not participate in a genus, as is stated in the Topics, Book IV, otherwise a genus would have the substance of a difference. And definitions would be nonsense if when a genus is given the difference were added, granted that the genus were the substance of the difference, just as it would be nonsense if the species were added. Moreover a difference would not differ in any way from a species. But those things which are outside the substance of being must be non-being, and thus cannot diversify being.
lib. 1 l. 9 n. 6 Sed in hoc decipiebantur, quia utebantur ente quasi una ratione et una natura sicut est natura alicuius generis; hoc enim est impossibile. Ens enim non est genus, sed multipliciter dicitur de diversis. Et ideo in primo physicorum dicitur quod haec est falsa, ens est unum: non enim habet unam naturam sicut unum genus vel una species.	139. But they were mistaken in this matter, because they used being as if it were one in intelligible structure and in nature, like the nature of any genus. But this is impossible. For being is not a genus but is predicated of different things in many ways. Therefore in Book I of the Physics it is said that the statement “Being is one” is false. For being does not have one nature like one genus or one species.
lib. 1 l. 9 n. 7 Sed Melissus considerabat ens ex parte materiae. Argumentabatur enim unitatem entis, ex eo quod ens non generatur ex aliquo priori, quod proprie pertinet ad materiam quae est ingenita. Arguebat enim sic: quod est generatum, habet principium; ens non est generatum, ergo non habet principium. Quod autem caret principio, et fine caret; ergo est infinitum. Et si est infinitum, est immobile: quia infinitum non habet extra se quo moveatur. Quod autem ens non generetur, probat sic. Quia si generatur, aut generatur ex ente, aut ex non ente; atqui nec ex non ente, quia non ens est nihil, et ex nihilo nihil fit. Nec ex ente; quia sic aliquid esset antequam fieret; ergo nullo modo generatur. In qua quidem ratione patet quod tetigit ens ex parte materiae; quia non generari ex aliquo prius existente materiae est. Et quia finitum pertinet ad formam, infinitum vero ad materiam, Melissus qui considerabat ens ex parte materiae, dixit esse unum ens infinitum. Parmenides vero, qui considerabat ens ex parte formae, dixit ens esse finitum. Sic igitur inquantum consideratur ens ratione materiae et formae, tractare de his pertinet ad praesentem considerationem, quia materia et forma in numero causarum ponuntur.	140. But Melissus considered being in terms of matter. For he argued that being is one by reason of the fact that being is not generated from something prior, and this characteristic pertains properly to matter, which is ungenerated. For he argued in this way: whatever is generated has a starting-point. But being is not generated and therefore does not have a starting-point. But whatever lacks a starting-point lacks an end and therefore is unlimited. And if it is unlimited, it is immobile, because what is unlimited has nothing outside itself by which it is moved. That being is not generated he proves thus. If being were generated, it would be generated either from being or from non-being. But it is not generated from non-being, because non-being is nothing and from nothing nothing comes. Nor is it generated from being, because then a thing would be before it came to be. Therefore it is not generated in any way. In this argument he obviously treats being as matter, because it is of the very nature of matter not to be generated from something prior. And since limitation pertains to form, and unlimitedness to matter, Melissus, who considered being under the aspect of matter, said that there is one unlimited being. But Parmenides, who considered being under the aspect of form, said that being is limited. Hence, insofar as being is considered under the aspect of form and matter, a study of these men is relevant to the present investigation; because matter and form are included among the causes.
lib. 1 l. 9 n. 8 Xenophanes vero qui fuit primus inter dicentes omnia esse unum, unde etiam Parmenides fuit eius discipulus, non explanavit qua ratione diceret omnia esse unum, nec sumendo rationem aliquam ex parte materiae, nec ex parte formae. Et sic de neutra natura scilicet neque de materia neque de forma visus est tangere hos id est pertingere et adaequare eos irrationalitate dicendi; sed respiciens ad totum caelum dixit esse ipsum unum Deum. Antiqui enim dicebant ipsum mundum esse Deum. Unde videns omnes partes mundi in hoc esse similes, quia corporeae sunt, iudicavit de eis quasi omnia essent unum. Et sicut praedicti posuerunt unitatem entium per considerationem eorum quae pertinent ad formam vel ad materiam, ita iste respiciens ad ipsum compositum.	141. But Xenophanes, who was the first of those to say that everything is one (and therefore Parmenides was his disciple), did not explain by what reasoning he maintained that all things are one, either by arguing from the viewpoint of matter, or from that of form. Hence, with respect to neither nature, i.e., neither matter nor form, does he seem “to come up to these men,” that is, to reach and equal them in their irrational manner of arguing. But concerning the whole heaven he says that the one is God. For the ancients said that the world itself is God. Hence, seeing that all parts of the universe are alike insofar as they are bodies, he came to think of them as if they were all one. And just as the foregoing philosophers held that beings are one by considering those things which pertain either to matter or to form, in a similar way these philosophers maintained this position regarding the composite itself.
lib. 1 l. 9 n. 9 Deinde cum dicit igitur ii his specialiter intendit dicere quomodo opinio Parmenidis ad perscrutationem praesentem pertineat; concludens ex praedictis, quod quia diversitatem ab entibus auferebant, et per consequens causalitatem, quantum ad praesentem quaestionem pertinet, omnes praetermittendi sunt. Sed duo eorum, scilicet Xenophanes et Melissus, sunt penitus praetermittendi, quia aliquantulum fuerunt, agrestiores, idest minus subtiliter procedentes. Sed Parmenides visus est dicere suam opinionem, magis videns, idest quasi plus intelligens. Utitur enim tali ratione. Quicquid est praeter ens, est non ens: quicquid est non ens, dignatur esse nihil idest dignum reputat esse nihil. Unde ex necessitate putat sequi quod ens sit unum, et quicquid est aliud ab ente, sit nihil. De qua quidem ratione manifestius dictum est primo physicorum.	142. As we have stated (66). His aim here is to explain in a special way how the opinion of Parmenides pertains to the present investigation. He concludes from the foregoing that, since these men did away with (~) diversity in the world and therefore with (~) causality, all of them must be disregarded so far as the present study is concerned. Two of them—Xenophanes and Melissus—must be disregarded altogether, because they are a little too “rustic,” i.e., they proceeded with less accuracy. But Parmenides seems to have expressed his views “with more insight,” i.e., with greater understanding. For he employs the following argument: besides being there is only non-being, and whatever is non-being “is thought to be nothing”; i.e., he considers it worthy to be nothing. Hence he thought that it necessarily followed that being is one, and that whatever is other than being is nothing. This argument has been treated more clearly in the Physics, Book I.
lib. 1 l. 9 n. 10 Licet autem Parmenides ista ratione cogatur ad ponendum omnia esse unum; tamen quia sensui apparebat multitudinem esse in rebus, coactus sequi ea quae apparent, voluit in sua positione utrique satisfacere, et apparentiae sensus et rationi. Unde dixit quod omnia sunt unum secundum rationem, sed sunt plura secundum sensum. Et inquantum ponebat pluralitatem secundum sensum, potuit in rebus ponere causam et causatum. Unde posuit duas causas, scilicet calidum et frigidum: quorum unum attribuebat igni, aliud terrae. Et unum videbatur pertinere ad causam efficientem, scilicet calidum et ignis; aliud ad causam materialem, scilicet frigidum et terra. Et ne eius positio suae rationi videretur esse opposita, qua concludebat quod quicquid est praeter unum, est nihil: dicebat quod unum praedictorum, scilicet calidum, erat ens: alterum vero quod est praeter illud unum ens, scilicet frigidum, dicebat esse non ens secundum rationem et rei veritatem, sed esse ens solum secundum apparentiam sensus.	143. But even though Parmenides was compelled by this argument to hold that all things are one, yet, because there appeared to the senses to be many things in reality, and because he was compelled to accept what appeared to the senses, it was his aim to make his position conform to both of these, i.e., to what is apprehended both by the senses and by reason. Hence he said that all things are one according to reason but many according to the senses. And inasmuch as he held that there is a plurality of things according to the senses, he was able to hold that there is in the world both cause and effect. Hence he posited two causes, namely, the hot and the cold, one of which he ascribed to fire, and the other to earth. And one of these—the hot or fire—seemed to pertain to the efficient cause, and the other—cold or earth—to the material cause. And lest his position should seem to contradict the conclusion of his own argument that whatever is besides being is nothing, he said that one of these causes—the hot—is being, and that the other cause—the one besides being, or the cold—is non-being, according to. both reason and the truth of the thing itself, and is a being only according to sensory perception.
lib. 1 l. 9 n. 11 In hoc autem aliquo modo ad veritatem appropinquat. Nam principium materiale non est ens in actu cui attribuebat terram; similiter etiam alterum contrariorum est ut privatio, ut dicitur primo physicorum. Privatio autem ad rationem non entis pertinet. Unde et frigidum quodammodo est privatio calidi, et sic est non ens.	144. Now in this matter he comes very close to the truth; for the material principle, which he held to be earth, is not an actual being. And in a similar way, too, one of two contraries is a privation, as is said in Book I of the Physics. But privation does not belong to the intelligible constitution of being. Hence in a sense cold is the privation of heat, and thus is non-being.
lib. 1 l. 9 n. 12 Deinde cum dicit igitur ex hic recolligit ea, quae dicta sunt de opinionibus antiquorum; et circa hoc duo facit. Primo recolligit ea quae dicta sunt de opinionibus antiquorum naturalium. Secundo quae dicta sunt de opinionibus Pythagoricorum qui mathematicam introduxerunt, ibi, Pythagorici et cetera. Concludit ergo primo ex dictis, quod ex his praedictis, qui idem considerabant, scilicet esse causam materialem rerum substantiam, et qui iam incipiebant per rationem sapere causas rerum inquirendo ipsas, accepimus eas quae dictae sunt. A primis namque philosophis acceptum est quod principium omnium rerum est corporeum. Quod patet per hoc, quod aqua et huiusmodi quae principia rerum ponebant, quaedam corpora sunt. In hoc autem differebant, quod quidam ponebant illud principium corporeum esse unum tantum, sicut Thales, Diogenes, et similes. Quidam vero ponebant esse plura, sicut Anaxagoras, Democritus et Empedocles. Utrique tamen, tam isti qui ponebant unum, quam illi qui ponebant plura esse, huiusmodi corporea principia ponebat in specie causae materialis. Quidam vero eorum non solum causam materialem posuerunt, sed cum ea addiderunt causam unde principium motus: quidam eam unam ponentes, sicut Anaxagoras intellectum, et Parmenides amorem: quidam vero duas, sicut Empedocles amorem et odium.	145. From what has been said (67). Here he summarizes the remarks which have been made about the doctrines of the ancient philosophers; and in regard to this he does two things. First, he summarizes the remarks made about the doctrines of the ancient philosophers of nature; and second (147), those made about the doctrines of the Pythagoreans, who introduced mathematics. Therefore from the above remarks he concludes, first, that from the foregoing philosophers, who adopted the same opinion, namely, that the material cause is the substance of things, and who were already beginning by the use of reason to know the causes of things by investigating them, we learn the causes which have been mentioned. For from the first philosophers it was learned that the principle of all things is corporeal. This is evident from the fact that water and the like, which are given as the principles of things, are bodies. However, they differed in this respect, that some, such as Thales, Diogenes and similar thinkers, claimed that there is only one corporeal principle, whereas others, such as Anaxagoras, Democritus and Leucippus, held that there are several corporeal principles. Yet both groups, i.e., both those who posited one principle and those who posited many, placed such corporeal principles in the class of material cause. And some of them not only posited a material cause but added to this the cause from which motion begins: some holding it to be one, as Anaxagoras did in positing intellect, and Parmenides, love, and others to be two, as Empedocles did in positing love and hate.
lib. 1 l. 9 n. 13 Unde patet quod praedicti philosophi qui fuerunt usque ad Italicos, scilicet Pythagoram, et absque illis idest separatam opinionem habentes de rebus non communicando opinionibus Pythagoricorum, obscurius dixerunt de principiis, quia non assignabant ad quod genus causae huiusmodi principia reducerentur: et tamen utebantur duabus causis, scilicet principio motus et materia; et alteram istarum, scilicet ipsam unde principium motus, quidam fecerunt unam, ut dictum est, quidam duas.	146. Hence, it is clear that these philosophers who lived down to the time of the Italians, or Pythagoreans, “and [were] independent of them,” i.e., who had their own opinions about reality and were unaware of those of the Pythagoreans, spoke obscurely about the principles of things; for they did not designate to what class of cause such principles might be reduced. Yet they made use of two causes, i.e., the source from which motion begins and matter: some saying that the former—the source from which motion begins—is one, and others two; as has been pointed out (145).
lib. 1 l. 9 n. 14 Deinde cum dicit Pythagorici vero hic recolligit quae dicta sunt a Pythagoricis, et quantum ad id quod erat commune cum praedictis, et quantum ad id quod erat eis proprium. Commune tamen fuit aliquibus praedictorum et Pythagoricorum, quod ponerent duo principia aliqualiter eodem modo cum praedictis. Sicut enim Empedocles ponebat duo principia contraria, quorum unum erat principium bonorum, et aliud principium malorum, ita et Pythagorici: ut patet ex coordinatione principiorum contrariorum supposita a Pythagoricis.	147. Now the Pythagoreans (68). Here he summarizes the opinions expressed by the Pythagoreans, both what they held in common with the foregoing philosophers, and what was peculiar to themselves. Now the opinion common to some of the foregoing philosophers and to the Pythagoreans was this that they posited, in a sense, two principles in the same way as the foregoing philosophers did. For Empedocles held that there are two contrary principles, one being the principle of good things, and the other the principle of evil things, and the Pythagoreans did the same thing, as is clear from the co-ordination of contrary principles which they posited.
lib. 1 l. 9 n. 15 In hoc tamen non eodem modo, quia Empedocles illa principia contraria ponebat in specie causae materialis, ut supra dictum est. Pythagorici autem addiderunt quod erat eis proprium supra opinionem aliorum; primo quidem quia dicebant quod hoc quod dico unum finitum et infinitum non erant accidentia aliquibus aliis naturis, sicut igni aut terrae, aut alicui huiusmodi. Sed hoc quod dico unum finitum et infinitum, erant substantiae eorumdem, de quibus praedicabantur. Et ex hoc concludebant quod numerus, qui ex unitatibus constituitur, sit substantia rerum omnium. Alii vero naturales, licet ponerent unum et finitum, seu infinitum, tamen attribuebant ista alicui alteri naturae, sicut accidentia attribuuntur subiecto, ut igni, vel aquae, vel alicui huiusmodi.	148. However, they did not do this in the same way; because Empedocles placed these contrary principles in the class of material cause, as was stated above (111), whereas the Pythagoreans added their own opinion to that of the other thinkers. The first thing that they added is this: they said that what I call the one, the limited and the unlimited are not (~) accidents of any other natures, such as fire or earth or the like, but claimed that what I call the one, the limited and the unlimited constitute the (+) substance of the same things of which they are predicated. From this they concluded that number, which is constituted of units, is the substance of all things. But while the other philosophers of nature posited the one, the limited and the unlimited, they nevertheless attributed these to another nature, as accidents are attributed to a subject, for example, to fire or water or something of this kind.
lib. 1 l. 9 n. 16 Secundo addiderunt super alios philosophos, quia inceperunt dicere et definire de ipso quid est, scilicet substantia et rerum quidditate. Sed tamen valde simpliciter de hoc tractaverunt, superficialiter definientes. Non enim attendebant in assignandis definitionibus nisi unum tantum. Dicebant enim quod si aliquis terminus dictus inesset alicui primo, quod erat substantia illius rei; sicut si aliquis aestimet quod proportio dupla sit substantia dualitatis: quia talis proportio primo in numero binario invenitur. Et quia ens primo inveniebatur in uno quam in multis, nam multa ex uno constituuntur, ideo dicebant quod ens est ipsa substantia unius. Sed haec eorum determinatio non erat conveniens: quia licet dualitas sit dupla, non tamen idem est esse dualitatis et dupli, ita quod sint idem secundum rationem, sicut definitio et definitum. Si autem etiam esset verum quod illi dicebant, sequeretur quod multa essent unum. Contingit enim aliqua multa primo inesse alicui uni, sicut dualitati primo inest paritas et proportio dupla. Et sic sequitur quod par et duplum sint idem: similiter quod cuicumque inest duplum sit idem dualitati, ex quo duplum est dualitatis substantia. Quod quidem etiam et Pythagoricis contingebat. Nam multa et diversa assignabant quasi unum essent, sicut proprietates numerales dicebant idem esse cum proprietatibus naturalium rerum.	149. The second addition which they made to the views of the other philosophers is this: they began to discuss and to define “the whatness itself,” i.e., the substance and quiddity of things, although they treated this far too simply by defining things superficially. For in giving definitions they paid attention only to one thing; because they said that, if any given definition were to apply primarily to some thing, this would be the substance of that thing; just as if one were to suppose that the ratio “double” is the substance of the number two, because such a ratio is found first in the number two. And since being was found first in the one rather than in the many (for the many is composed of ones), they therefore said that being is the substance itself of the one. But this conclusion of theirs is not acceptable; for although the number two is double, the essence of twoness is not the same as that of the double in such a way that they are the same conceptually, as the definition and the thing defined. But even if their statements were true, it would follow that the many would be one. For some plurality can belong primarily to something one; for example, evenness and the ratio double belong first to the number two. Hence [according to them] it would follow that the even and the double are the same. And it would likewise follow that that to which the double belongs is the same as the number two, so long as the double is the substance of the number two. This, indeed, is also the conclusion which the Pythagoreans drew; for they attributed plurality and diversity to things as if they were one, just as they said that the properties of numbers are the same as the properties of natural beings.
lib. 1 l. 9 n. 17 Sic igitur concludit quod tot est accipere a prioribus philosophis, qui posuerunt tantum unum principium materiale, et ab aliis posterioribus qui posuerunt plura principia.	150. Hence, Aristotle concludes that it is possible to learn this much from the early philosophers, who posited only one material principle, and from the later philosophers, who posited many principles. LESSON 10 The Platonic Theory of Ideas ARISTOTLE’S TEXT Chapter 6: 987a 29-988a 17