Authors/Thomas Aquinas/metaphysics/liber1/lect10

Lecture 10

Latin	English
lib. 1 l. 10 n. 1 Positis opinionibus antiquorum de causa materiali et efficiente, hic tertio ponit opinionem Platonis, qui primo manifeste induxit causam formalem. Et dividitur in partes duas. Primo enim ponit opinionem Platonis. Secundo colligit ex omnibus praedictis quid de quatuor generibus causarum ab aliis philosophis sit positum, ibi, breviter et recapitulariter et cetera. Circa primum duo facit. Primo ponit opinionem Platonis de rerum substantiis. Secundo de rerum principiis, ibi, quoniam autem species et cetera. Circa primum duo facit. Primo ponit opinionem Platonis quantum ad hoc quod posuit ideas. Secundo quantum ad hoc quod posuit substantias medias, scilicet mathematica separata, ibi, amplius autem praeter sensibilia. Dicit ergo primo, quod post omnes praedictos philosophos supervenit negocium Platonis, qui immediate Aristotelem praecessit. Nam Aristoteles eius discipulus fuisse perhibetur. Plato siquidem in multis secutus est praedictos philosophos naturales, scilicet Empedoclem, Anaxagoram et alios huiusmodi, sed alia quaedam habuit propria praeter illos praedictos philosophos, propter philosophiam Italicorum Pythagoricorum. Nam ipse ut studiosus erat ad veritatis inquisitionem, ubique terrarum philosophos quaesivit, ut eorum dogmata sciret. Unde in Italiam Tarentum venit, et ab Archita Tarentino Pythagorae discipulo de opinionibus Pythagoricis est instructus.	151. Having given the opinion of the ancient philosophers about the material and efficient cause, he gives a third opinion, that of Plato, who was the first to clearly introduce the formal cause. This is divided into two parts. First, he gives Plato’s opinion. Second (171), from all of the foregoing remarks he makes a summary of the opinions which the other philosophers expressed about the four classes of causes (“We have examined”). In regard to the first he does two things. First, he gives Plato’s opinion about the substances of things; and second (159), his opinion about the principles of things (“And since the Forms”). In regard to the first he does two things. First, he gives Plato’s opinion insofar as he posited Ideas; and second (157), insofar as he posited intermediate substances, namely, the separate mathematical entities (“Further, he says”). He says, first, that after all the foregoing philosophers came the system of Plato, who immediately preceded Aristotle; for Aristotle is considered to have been his disciple. And even if Plato followed in many respects the natural philosophers who preceded him, such as Empedocles, Anaxagoras and the like, he nevertheless had certain other doctrines of his own in addition to those of the preceding philosophers, because of the philosophy of the Italians, or Pythagoreans. For insofar as he was devoted to the study of truth he sought out the philosophers of all lands in order to learn their teachings. Hence he came to Tarenturn in Italy, and was instructed in the teachings of the Pythagoreans by Archytas of Tarenturn, a disciple of Pythagoras.
lib. 1 l. 10 n. 2 Cum enim naturales philosophos, qui in Graecia fuerunt, sequi videret, et intra eos aliqui posteriores ponerent omnia sensibilia semper esse in fluxu, et quod scientia de eis esse non potest, quod posuerunt Heraclitus et Cratylus, huiusmodi positionibus tamquam novis Plato consuetus, et cum eis conveniens in hac positione ipse posterius ita esse suscepit, unde dixit particularium scibilium scientiam esse relinquendam. Socrates etiam, qui fuit magister Platonis, et discipulus Archelai, qui fuit auditor Anaxagorae, propter hanc opinionem, quae suo tempore surrexerat, quod non potest esse de sensibilibus scientia, noluit aliquid de rerum naturis perscrutari, sed solum circa moralia negociatus est. Et ipse prius incepit in moralibus quaerere quid esset universale, et insistere ad definiendum.	152. Now Plato would seem to follow the natural philosophers who lived in Greece; and of this group some of the later members held that all sensible things are always in a state of flux, and that there can be no scientific knowledge of them (which was the position of Heraclitus and Cratylus). And since Plato became accustomed to positions of this kind from the very beginning, and agreed with these men in this position, which he acknowledged to be true in later years, he therefore said that scientific knowledge of particular sensible things must be abandoned. And Socrates (who was Plato’s master and the disciple of Archelaus, a pupil of Anaxagoras), because of this position, which arose in his time, that there can be no science of sensible things, was unwilling to make any investigation into the nature of physical things, but only busied himself with moral matters. And in this field he first began to investigate what the universal is, and to insist upon the need for definition.
lib. 1 l. 10 n. 3 Unde et Plato tamquam eius auditor, recipiens Socratem, idest sequens suscepit hoc ad inquirendum in rebus naturalibus, quasi in eis hoc posset evenire, ut universale in eis acciperetur de quo definitio traderetur, ita quod definitio non daretur de aliquo sensibilium, quia cum sensibilia sint semper transmutantium, idest transmutata, non potest alicuius eorum communis ratio assignari. Nam omnis ratio oportet quod et omni et semper conveniat, et ita aliquam immutabilitatem requirit. Et ideo huiusmodi entia universalia, quae sunt a rebus sensibilibus separata, de quibus definitiones assignantur, nominavit ideas et species existentium sensibilium: ideas quidem, idest formas, inquantum ad earum similitudinem sensibilia constituebantur: species vero inquantum per earum participationem esse substantiale habebant. Vel ideas inquantum erant principium essendi, species vero inquantum erant principium cognoscendi. Unde et sensibilia omnia habent esse propter praedictas et secundum eas. Propter eas quidem inquantum ideae sunt sensibilibus causae essendi. Secundum eas vero inquantum sunt eorum exemplaria.	153. Hence, Plato, being Socrates’ pupil, “accepted Socrates,” i.e., followed him, and adopted this method for the purpose of investigating natural beings. He did so believing that in their case the universal in them could successfully be grasped and a definition be assigned to it, with no definition being given for any sensible thing; because, since sensible things are always “changing,” i.e., being changed, no common intelligible structure can be assigned to any of them. For every definition must conform to each thing defined and must always do so, and thus requires some kind of immutability. Hence universal entities of this kind, which are separate from sensible things and that to which definitions are assigned, he called the Ideas or Forms of sensible things. He called them Ideas, or exemplars, inasmuch as sensible things are made in likeness to them; and he called them Forms inasmuch as [sensible things] have substantial being by participating in them. Or he called them Ideas inasmuch as they are principles of being, and Forms inasmuch as they are principles of knowledge. Hence all sensible things have being because of them and in conformity with them. They have being because of the Ideas insofar as the Ideas are the causes of the being of sensible things, and “in conformity with them” insofar as they are the exemplars of sensible things.
lib. 1 l. 10 n. 4 Et quod hoc sit verum, patet ex eo, quod singulis speciebus attribuuntur multa individua univocorum, idest multa individua univocae speciei praedicationem suscipientia et hoc secundum participationem; nam species, vel idea est ipsa natura speciei, qua est existens homo per essentiam. Individuum autem est homo per participationem, inquantum natura speciei in hac materia designata participatur. Quod enim totaliter est aliquid, non participat illud, sed est per essentiam idem illi. Quod vero non totaliter est aliquid habens aliquid aliud adiunctum, proprie participare dicitur. Sicut si calor esset calor per se existens, non diceretur participare calorem, quia nihil esset in eo nisi calor. Ignis vero quia est aliquid aliud quam calor, dicitur participare calorem.	154. The truth of this is clear from the fact that “many individuals of the same name” are attributed to one Form alone, i.e., there are many individuals which have the same Form predicated of them, and predicated by participation. For the Form or Idea [of man] is the specific nature itself by which there exists man essentially. But an individual is man by participation inasmuch as the specific nature [man] is participated in by this designated matter. For that which is something in its entirety does not participate in it but is essentially identical with it, whereas that which is not something in its entirety but has this other thing joined to it, is said properly to participate in that thing. Thus, if heat were a self-subsistent heat, it would not be said to participate in heat, because it would contain nothing but heat. But since fire is something other than heat, it is said to participate in heat.
lib. 1 l. 10 n. 5 Similiter autem cum idea hominis separata nihil aliud habeat nisi ipsam naturam speciei, est essentialiter homo. Et propterea ab eo vocabatur per se homo. Socrates vero vel Plato, quia habet praeter naturam speciei principium individuans quod est materia signata, ideo dicitur secundum Platonem participare speciem.	155. In a similar way , since the separate Idea of man contains nothing but the specific nature itself, it is man essentially; and for this reason it was called by him man-in-itself. But since Socrates and Plato have in addition to their specific nature an individuating principle, which is designated matter, they are therefore said to participate in a Form, according to Plato.
lib. 1 l. 10 n. 6 Hoc autem nomen participationis Plato accepit a Pythagora. Sed tamen transmutavit ipsum. Pythagorici enim dicebant numeros esse causas rerum sicut Platonici ideas, et dicebant quod huiusmodi existentia sensibilia erant quasi quaedam imitationes numerorum. Inquantum enim numeri qui de se positionem non habent, accipiebant positionem, corpora causabant. Sed quia Plato ideas posuit immutabiles ad hoc quod de eis possent esse scientiae et definitiones, non conveniebat et in ideis uti nomine imitationis. Sed loco eius usus est nomine participationis. Sed tamen est sciendum, quod Pythagorici, licet ponerent participationem, aut imitationem, non tamen perscrutati sunt qualiter species communis participetur ab individuis sensibilibus, sive ab eis imitetur, quod Platonici tradiderunt.	156. Now Plato took this term participation from Pythagoras, although [in doing so] he made a change in the term. For the Pythagoreans said that numbers are the causes of things, just as the Platonists said that the Ideas are, and claimed that sensible things of this kind exist as certain imitations of numbers. For inasmuch as numbers, which have no position of themselves, received positions, they caused bodies. But because Plato held that the Ideas are unchangeable in order that there might be scientific knowledge of them, he did not agree that the term imitation could be used of the Ideas, but in place of it he used the term participation. However, it must be noted that, even though the Pythagoreans posited participation or imitation, they still did not investigate the way in which a common Form is participated in by individual sensible things or imitated by them. But the Platonists have treated this.
lib. 1 l. 10 n. 7 Deinde cum dicit amplius autem hic ponit opinionem Platonis de mathematicis substantiis: et dicit quod Plato posuit alias substantias praeter species et praeter sensibilia, idest mathematica; et dixit quod huiusmodi entia erant media trium substantiarum, ita quod erant supra sensibilia et infra species, et ab utrisque differebant. A sensibilibus quidem, quia sensibilia sunt corruptibilia et mobilia, mathematica vero sempiterna et immobilia. Et hoc accipiebant ex ipsa ratione scientiae mathematicae, nam mathematica scientia a motu abstrahit. Differunt vero mathematica a speciebus, quia in mathematicis inveniuntur differentia secundum numerum, similia secundum speciem: alias non salvarentur demonstrationes mathematicae scientiae. Nisi enim essent duo trianguli eiusdem speciei, frustra demonstraret geometra aliquos triangulos esse similes; et similiter in aliis figuris. Hoc autem in speciebus non accidit. Nam cum in specie separata nihil aliud sit nisi natura speciei, non potest esse singularis species nisi una. Licet enim alia sit species hominis, alia asini, tamen species hominis non est nisi una, nec species asini, et similiter de aliis.	157. Further, he says (70). Here he gives Plato’s opinion about the mathematical substances. He says that Plato posited other substances—the objects of mathematics—in addition to the Forms and sensible things. Moreover, he said that beings of this kind were an intermediate class among the three kinds of substances; or that they were above sensible substances and below the Forms, and differed from both. The mathematical substances differed from sensible substances, because sensible substances are corruptible and changeable, whereas the mathematical substances are eternal and immobile. The PIatonists got this idea from the way in which mathematical science conceives its objects; for mathematical science abstracts from motion. The mathematical substances also differed from the Forms, because the objects of mathematics are found to be numerically different and specifically the same, otherwise the demonstrations of mathematics would prove nothing. For unless two triangles belonged to the same class, geometry would attempt in vain to demonstrate that some triangles are alike; and the same thing is true of other figures. But this does not happen in the case of the Forms. For, since a Form is just the specific nature itself of a thing, each Form can only be unique. For even though the Form of man is one thing, and the Form of ass another thing, nevertheless the Form of man is unique, and so is the Form of ass; and the same thing is true of other things.
lib. 1 l. 10 n. 8 Patet autem diligenter intuenti rationes Platonis, quod ex hoc in sua positione erravit, quia credidit, quod modus rei intellectae in suo esse sit sicut modus intelligendi rem ipsam. Et ideo quia invenit intellectum nostrum dupliciter abstracta intelligere, uno modo sicut universalia intelligimus abstracta a singularibus, alio modo sicut mathematica abstracta a sensibilibus, utrique abstractioni intellectus posuit respondere abstractionem in essentiis rerum: unde posuit et mathematica esse separata et species. Hoc autem non est necessarium. Nam intellectus etsi intelligat res per hoc, quod similis est eis quantum ad speciem intelligibilem, per quam fit in actu; non tamen oportet quod modo illo sit species illa in intellectu quo in re intellecta: nam omne quod est in aliquo, est per modum eius in quo est. Et ideo ex natura intellectus, quae est alia a natura rei intellectae, necessarium est quod alius sit modus intelligendi quo intellectus intelligit, et alius sit modus essendi quo res existit. Licet enim id in re esse oporteat quod intellectus intelligit, non tamen eodem modo. Unde quamvis intellectus intelligat mathematica non cointelligendo sensibilia, et universalia praeter particularia, non tamen oportet quod mathematica sint praeter sensibilia, et universalia praeter particularia. Nam videmus quod etiam visus percipit colorem sine sapore, cum tamen in sensibilibus sapor et color simul inveniantur.	158. Now to one who carefully examines Plato’s arguments it is evident that Plato’s opinion was false, because he believed that the mode of being which the thing known has in reality is the same as the one which it has in the act of being known. Therefore, since he found that our intellect understands abstractions in two ways: in one way as we understand universals abstracted from singulars, and in another way as we understand the objects of mathematics abstracted from sensible things, he claimed that for each abstraction of the intellect there is a corresponding abstraction in the essences of things. Hence he held that both the objects of mathematics and the Forms are separate. But this is not necessary. For even though the intellect understands things insofar as it becomes assimilated to them through the intelligible form by which it is put into act, it still is not necessary that a form should have the same mode of being in the intellect that it has in the thing known; for everything that exists in something else exists there according to the mode of the recipient. Therefore, considering the nature of the intellect, which is other than the nature of the thing known, the mode of understanding, by which the intellect understands, must be one kind of mode, and the mode of being, by which things exist, must be another. For although the object which the intellect understands must exist in reality, it does not exist there according to the same mode [which it has in the intellect]. Hence, even though the intellect understands mathematical entities without simultaneously understanding sensible substances, and understands universals without understanding particulars, it is not therefore necessary that the objects of mathematics should exist apart from sensible things, or that universals should exist apart from particulars. For we also see that sight perceives color apart from flavor, even though flavor and color are found together in sensible substances.
lib. 1 l. 10 n. 9 Deinde cum dicit quoniam autem hic ponit opinionem Platonis de rerum principiis: et circa hoc duo facit. Primo ponit quae principia rebus Plato assignavit. Secundo ad quod genus causae reducuntur, ibi, palam autem ex dictis et cetera. Circa primum duo facit. Primo ponit cuiusmodi principia Plato assignaverit. Secundo ostendit quomodo Plato cum Pythagoricis communicet, et in quo differat ab eis, ibi, unum tamen substantiam. Dicit ergo primo, quod quia secundum Platonem species separatae sunt causae omnibus aliis entibus, ideo elementa specierum putaverunt esse elementa omnium entium. Et ideo assignabant rebus pro materia magnum et parvum, et quasi substantiam rerum, idest formam dicebant esse unum. Et hoc ideo, quia ista ponebant esse principia specierum. Dicebant enim quod sicut species sunt sensibilibus formae, ita unum est forma specierum. Et ideo sicut sensibilia constituuntur ex principiis universalibus per participationem specierum, ita species, quas dicebat esse numeros, constituuntur secundum eum, ex illis, scilicet magno et parvo. Unitas enim diversas numerorum species constituit per additionem et subtractionem, in quibus consistit ratio magni et parvi. Unde cum unum opinaretur esse substantiam entis, quia non distinguebat inter unum quod est principium numeri, et unum quod convertitur cum ente, videbatur sibi quod hoc modo multiplicarentur diversae species separatae ex una quae est communis substantia, sicut ex unitate diversae species numerorum multiplicantur.	159. And since the Forms (159). Here he gives Plato’s opinion concerning the principles of things; and in regard to this he does two things. First, he states the principles which Plato assigned to things; and second (169), the class of cause to which they are reduced (“From the foregoing”). In regard to the first he does two things. First, he tells us what kind of principles Plato had assigned to things. Second (160), he shows in what respect Plato agreed with the Pythagoreans, and in what respect he differed from them (“Yet Plato”). He says, first, that, since the Forms are the causes of all other beings according to Plato, the Platonists therefore thought that the elements of the Forms are the elements of all beings. Hence, they assigned as the material principle of things the great and small, and said that “the substance of things,” i.e., their form, is the one. They did this because they held these to be the principles of the Forms. For they said that just as the Forms are the formal principles of sensible things, in a similar way the one is the formal principle of the Forms. Therefore, just as sensible things are constituted of universal principles by participation in the Forms, in a similar way the Forms, which he said are numbers, are constituted “of these,” i.e., of the great and small. For the unit constitutes different species of numbers by addition and subtraction, in which the notion of the great and small consists. Hence, since the one was thought to be the substance of being (because he did not distinguish between the one which is the principle of number, and the one which is convertible with being), it seemed to him that a plurality of different Forms might be produced from the one, which is their common substance, in the same way that a plurality of different species of numbers is produced from the unit.
lib. 1 l. 10 n. 10 Deinde cum dicit unum tamen hic comparat opinionem Platonis Pythagorae. Et primo ostendit in quo conveniebant. Secundo in quo differebant, ibi, pro infinito. Conveniebant autem in duabus positionibus. Quarum prima est quod unum sit substantia rerum. Dicebant enim Platonici, sicut etiam Pythagorici, quod hoc quod dico unum non probatur de aliquo alio ente, sicut accidens de subiecto, sed hoc signat substantiam rei. Et hoc ideo, quia, ut dictum est, non distinguebant inter unum quod convertitur cum ente, et unum quod est principium numeri.	160. Yet Plato (72). Here he compares the position of Plato with that of Pythagoras. First, he shows in what respect they agreed; and second (160), in what respect they differed (“But to posit”). Now they agreed in two positions; (1) and the first is that the one is the substance of things. For the Platonists, like the Pythagoreans, said that what I call the one is not predicated’ of some other being as an accident is of a subject, but signifies a thing’s substance. They said this, as we have pointed out (159), because they did not distinguish between the one which is convertible with being and the one which is the principle of number.
lib. 1 l. 10 n. 11 Secunda positio sequitur ex prima. Dicebant enim Platonici (similiter ut Pythagorici) numeros esse causas substantiae omnibus entibus. Et hoc ideo quia numerus nihil aliud est quam unitates collectae. Unde si unitas est substantia, oportet quod etiam numerus.	161. (2) The second position follows from the first; for the Platonists, like the Pythagoreans, said that numbers are the causes of the substance of all beings; and they held this because [in their opinion] number is just a collection of units. Hence if the one is substance, number must also be such.
lib. 1 l. 10 n. 12 Deinde cum dicit pro infinito hic ostendit in quo differebant. Et circa hoc duo facit. Primo enim ponit differentiam inter eos. Secundo differentiae causam, ibi, unum igitur et numeros et cetera. Est autem ista differentia in duobus. Primo quantum ad hoc Pythagorici ponebant (ut dictum est) duo principia, ex quibus constituebantur, scilicet finitum et infinitum: quorum unum, scilicet infinitum, se habet ex parte materiae. Plato vero loco huius unius quod Pythagoras posuit, scilicet infiniti, fecit dualitatem, ponens ex parte materiae magnum et parvum. Et sic infinitum quod Pythagoras posuit unum principium, Plato posuit consistere ex magno et parvo. Et hoc est proprium opinionis suae in comparatione ad Pythagoram.	162. But to posit (73). Here he shows in what respect they differed; and in regard to this he does two things. First, he states how they differed. Second (164), he gives the reason for this difference (“Therefore, his making”). Now this difference involves two things. First, the Pythagoreans, as has already been stated, posited two principles of which things are constituted, namely, the limited and the unlimited, of which one, i.e., the unlimited, has the character of matter. But in place of this one principle—the unlimited— which the Pythagoreans posited, Plato created a dyad, holding that the great and small have the character of matter. Hence the unlimited, which Pythagoras claimed to be one principle, Plato claimed to consist of the great and small. This is his own opinion in contrast with that of Pythagoras.
lib. 1 l. 10 n. 13 Secunda differentia est, quia Plato posuit numeros praeter sensibilia, et hoc dupliciter. Ipsas enim species, numeros esse dicebat, sicut supra habitum est. Et iterum inter species et sensibilia posuit mathematica (ut supra dictum est) quae secundum suam substantiam numeros esse dicebat. Sed Pythagorici dicunt ipsas res sensibiles esse numeros, et non ponunt mathematica media inter species et sensibilia, nec iterum ponunt species separatas.	163. The second difference is that Plato held that numbers are separate from sensible things, and this in two ways. For he said that the Forms themselves are numbers, as was pointed out above (159); and he also held, as was stated above (157), that the objects of mathematics are an intermediate class between the Forms and sensible things, and that they are numbers by their very essence. But the Pythagoreans said that sensible things themselves are numbers, and did not make the objects of mathematics an intermediate class between the Forms and sensible things; nor again did they hold that the Forms are separate from things.
lib. 1 l. 10 n. 14 Deinde cum dicit unum igitur hic ostendit causam differentiae. Et primo secundae. Secundo causas differentiae primae, ibi, dualitatem autem fere et cetera. Dicit ergo quod ponere unum et numeros praeter res sensibiles, et non in ipsis sensibilibus, sicut Pythagorici fecerunt, et iterum introducere species separatas, evenit Platonicis propter scrutationem, quae est in rationibus, idest propter hoc quod perscrutati sunt de definitionibus rerum, quas credebant non posse attribui rebus sensibilibus, ut dictum est. Et hac necessitate fuerunt coacti ponere quasdam res quibus definitiones attribuuntur. Sed Pythagorici qui fuerunt priores Platone, non participaverunt dialecticam, ad quam pertinet considerare definitiones et universalia huiusmodi, quarum consideratio induxit ad introductionem idearum.	164. Therefore, his making (74). Here he gives the reason for the difference. First, he gives the reason for the second difference; and then (165), the reason for the first difference. He says, then, that the Platonists adopted the position that both the one and numbers exist apart from sensible things and not in sensible things, as the Pythagoreans claimed; and they also introduced separate Forms because of the investigation “which was made into the intelligible structures of things,” i.e., because of their investigation of the definitions of things, which they thought could not be attributed to sensible substances, as has been stated (150). This is the reason they were compelled to hold that there are certain things to which definitions are assigned. But the Pythagoreans, who came before Plato, were ignorant of dialectic, whose office it is to investigate definitions and universals of this kind, the study of which led to the introduction of the Ideas.
lib. 1 l. 10 n. 15 Deinde cum dicit dualitatem autem hic ostendit causam alterius differentiae, quae scilicet ex parte materiae est. Et primo ponit causam huiusmodi differentiae. Secundo ostendit Platonem non rationabiliter motum esse, ibi, attamen e contrario. Dicit ergo quod ideo Platonici fecerunt dualitatem esse numerum, qui est alia natura a speciebus, quia omnes numeri naturaliter generantur ex dualitate praeter numeros primos. Dicuntur autem numeri primi, quos nullus numerat, sicut ternarius, quinarius, septenarius, undenarius, et sic de aliis. Hi enim a sola unitate constituuntur immediate. Numeri vero, quos aliquis alius numerus numerat, non dicuntur primi, sed compositi, sicut quaternarius, quem numerat dualitas; et universaliter omnis numerus par a dualitate numeratur. Unde numeri pares materiae attribuuntur, cum eis attribuatur infinitum, quod est materia, ut supra dictum est. Hac ratione posuit dualitatem, ex qua sicut aliquo echimagio, idest ex aliquo exemplari omnes alii numeri pares generantur.	165. But his making (75). Here he gives the reason for the other difference, that is, the one concerning matter. First, he gives the reason for such a difference. Second (166), he shows that Plato was not reasonably motivated. He accordingly says that the Platonists made the dyad [or duality] to be a number of a different nature than the Forms, because all numbers with the exception of prime numbers are produced from it. They called prime numbers those which are not measured by any other number, such as three, five, seven, eleven, and so on; for these are produced immediately from unity alone. But numbers which are measured by some other number are not called prime numbers but composite ones, for example, the number four, which is measured by the number two; and in general every even number is measured by the number two. Hence even numbers are attributed to matter, since unlimitedness, which belongs to matter, is attributed to them, as has been stated above (125). This is why he posited the dyad, from which as “a matrix,” or exemplar, all other even numbers are produced.
lib. 1 l. 10 n. 16 Deinde cum dicit attamen e contrario hic ostendit Platonem irrationabiliter posuisse. Et circa hoc duo facit. Primo enim ex ratione naturali ostendit hoc. Secundo etiam ponit rationem naturalem, quae Platonem movebat ad suam opinionem, ibi, videtur autem ex una materia. Dicit ergo quod quamvis Plato poneret dualitatem ex parte materiae, tamen e converso contingit, sicut attestantur opiniones omnium aliorum philosophorum naturalium, qui posuerunt contrarietatem ex parte formae, et unitatem ex parte materiae, sicut patet primo physicorum. Ponebant enim rerum materiam aerem, vel aquam, aliquid huiusmodi, ex quo diversitatem rerum constituebant per rarum et densum, quae ponebant quasi principia formalia. Non enim est rationabile ponere sicut Plato posuit. Et hoc ideo quia ex materia viderunt philosophi multa fieri per successionem formarum in ipsa. Illa enim materia, quae modo substat uni formae, post modum substare poterit pluribus, uno corrupto et alio generato. Sed una species sive una forma solum semel generat, idest constituit aliquid generatum. Cum enim aliquid generatur accipit formam quidem, quae forma eadem numero non potest alteri generato advenire, sed esse desinit generato corrupto. In quo manifeste apparet quod una materia ad multas formas se habet, et non e converso una forma ad multas materias se habet. Et sic videtur rationabilius ponere ex parte materiae unitatem, sed dualitatem sive contrarietatem ex parte formae, sicut posuerunt naturales, quam e converso, sicut posuit Plato.	166. Yet what happens (76). Here he proves that Plato made unreasonable assumptions; and in regard to this he does two things. For, first, he proves this by an argument from nature. Second (167), he gives the argument based on the nature of things, which led Plato to adopt this position (“And from one matter”). He says that, although Plato posited a dyad on the part of matter, still what happens is the contrary of this, as the opinions of all the other natural philosophers testify; for they claimed that contrariety pertains to form and unity to matter, as is clear in Book I of the Physics. For they held that the material principle of things is air or water or something of this kind, from which the diversity of things is produced by rarefaction and condensation, which they regarded as formal principles; for Plato’s position is not a reasonable one. Now the natural philosophers adopted this position because they saw that many things are generated from matter as a result of a succession of forms in matter. For that matter which now supports one form may afterwards support rnany forms as a result of one form being corrupted and another being generated. But one specifying principle or form “generates only once,” i.e., constitutes the thing which is generated. For when something is generated it receives a form, and the same form numerically cannot become the form of another thing that is generated, but ceases to be when that which was generated undergoes corruption. In this argument it is clearly apparent that one matter is related to many forms, and not the reverse, i.e., one form to many matters. Thus it seems more reasonable to hold that unity pertains to matter but duality or contrariety to form, as the philosophers of nature claimed. This is the opposite of what Plato held.
lib. 1 l. 10 n. 17 Deinde cum dicit videtur autem hic ponit rationem e converso ex his sensibilibus acceptam secundum opinionem Platonis. Videbat enim Plato quod unumquodque recipitur in aliquo secundum mensuram recipientis. Unde diversae receptiones videntur provenire ex diversis mensuris recipientium. Una autem materia est una mensura recipiendi. Vidit etiam quod agens, qui inducit speciem, facit multas res speciem habentes, cum sit unus, et hoc propter diversitatem quae est in materiis. Et huius exemplum apparet in masculo et femina. Nam masculus se habet ad feminam sicut agens et imprimens speciem ad materiam. Femina autem impraegnatur ab una actione viri. Sed masculus unus potest impraegnare multas feminas. Et inde est quod posuit unitatem ex parte speciei, et dualitatem ex parte materiae.	167. And from one matter (77). Here he gives an opposite argument taken from sensible things according to the opinion of Plato. For Plato saw that each thing is received in something else according to the measure of the recipient. Hence receptions seem to differ according as the capacities of recipients differ. But one matter is one capacity for reception. And Plato also saw that the agent who induces the form, although he is one, causes many things to have this form; and this comes about because of diversity on the part of matter. An example of this is evident in the case of male and female; for a male is related to a female as an agent and one who impresses a form on matter. But a female is impregnated by one act of a male, whereas one male can impregnate many females. This is why he held that unity pertains to form and duality to matter.
lib. 1 l. 10 n. 18 Est autem attendendum quod haec diversitas inter Platonem et naturales accidit propter diversam de rebus considerationem. Naturales enim considerant tantum quae sunt sensibilia, prout sunt subiecta transmutationi, in qua unum subiectum successive accipit contraria. Et ideo posuerunt unitatem ex parte materiae, et contrarietatem ex parte formae. Sed Plato ex consideratione universalium deveniebat ad ponendum principia sensibilium rerum. Unde, cum diversitatis multorum singularium sub uno universali causa sit divisio materiae, posuit diversitatem ex parte materiae, et unitatem ex parte formae. Et tales sunt mutationes illorum principiorum, quae posuit Plato, idest participationes, vel ut ita dicam influentias in causata: sic enim nomen immutationis Pythagoras accipit. Vel immutationes dicit inquantum Plato mutavit opinionem de principiis, quam primi naturales habuerunt, ut ex praedictis patet. Et sic patet ex praedictis, quod Plato de causis quaesitis a nobis ita definivit.	168. Now we must note that this difference between Plato and the philosophers of nature is a result of the fact that they considered things from different points of view. For the philosophers of nature considered sensible things only insofar as they are subject to change, in which one subject successively acquires contrary qualities. Hence they attributed unity to matter and contrariety to form. But Plato, because of his investigation of universals, went on to give the principles of sensible things. Therefore, since the cause of the diversity of the many singular things which come under one universal is the division of matter, he held that diversity pertains to matter and unity to form. “And such are the changes of those principles” which Plato posited, i.e., participations, or, as I may say, influences in the things generated. For Pythagoras understands the word change in this way. Or Aristotle says “changes” inasmuch as Plato changed the opinion which the first philosophers of nature had about principles, as is evident from the foregoing. Hence it is evident from the foregoing that Plato dealt thus with the causes which we are investigating.
lib. 1 l. 10 n. 19 Deinde cum dicit palam autem hic ostendit ad quod genus causae principia a Platone posita reducantur. Dicit ergo, ex dictis palam esse quod Plato usus est solum duobus generibus causarum. Causa enim ipsa, idest causa, quae est causa ei, quod quid est, idest quidditatis rei, scilicet causa formalis, per quam rei quidditas constituitur: et etiam usus est ipsa materia. Quod ex hoc patet, quia species quas posuit sunt aliis, idest sensibilibus causae eius quod quid est, idest causae formales: ipsis vero speciebus causa formalis est hoc quod dico unum, et illa videtur substantia de qua sunt species: sicut ens unum ponit causam formalem specierum: ita magnum et parvum ponit earum causam quasi materialem, ut supra dictum est. Et hae quidem causae, scilicet formalis et materialis, non solum sunt respectu specierum, sed etiam respectu sensibilium, quia unum dicitur in speciebus: idest id quod hoc modo se habet ad sensibilia, sicut unum ad speciem, est ipsa species, quia ea dualitas quae respondet sensibilibus pro materia est magnum et parvum.	169. From the foregoing (78). Here he shows to what class of cause the principles given by Plato are referred. He says that it is evident from the foregoing that Plato used only two kinds of causes. For he used as “one” cause of a thing the cause of its “whatness,” i.e., its quiddity, or its formal cause, which determines its quiddity; and he also used matter itself. This is also evident from the fact that the Forms which he posited “are the causes of other things,” i.e., the causes of the whatness of sensible things, namely, their formal causes, whereas the formal cause of the Forms themselves is what I call the one, which seems to be the substance of which the Forms are composed. And just as he holds that the one is the formal cause of the Forms, in a similar fashion he holds that the great and small are their material cause, as was stated above (159). And these causes—the formal and the material cause—are referred not only to the Forms but also to sensible substances, because [there is some subject of which] the one is predicated in the case of the Forms. That is to say, that which is related to sensible substances in the same way as the one is to the Forms is itself a Form, because that duality which relates to sensible things as their matter is the great and small.
lib. 1 l. 10 n. 20 Ulterius Plato assignavit causam eius quod est bonum et malum in rebus, et singulis elementis ab eo positis. Nam causam boni ascribebat speciei, causam vero mali materiae. Sed tamen causam boni et mali conati sunt investigare quidam primorum philosophorum, scilicet Anaxagoras et Empedocles, qui ad hoc specialiter aliquas causas in rebus constituerunt, ut ab eis possent assignare principia boni et mali. In hoc autem quod boni causas et mali tetigerunt, aliquo modo accedebant ad ponendum causam finalem, licet non per se, sed per accidens eam ponerent, ut infra dicetur.	170. Furthermore, Plato indicated the cause of good and evil in the world, and he did this with reference to each of the elements which he posited. For he made Form the cause of good and matter the cause of evil. However, some of the first philosophers attempted to investigate the cause of good and evil, namely, Anaxagoras and Empedocles, who established certain causes in the world with this special end in view that by means of these causes they might be able to give the principles of good and evil. And in touching upon these causes of good and evil they came very close to positing the final cause, although they did not posit this cause directly but only indirectly, as is stated below (177).