Authors/Thomas Aquinas/metaphysics/liber1/lect13

Lecture 13

Latin	English
lib. 1 l. 13 n. 1 Hic disputat contra opiniones Pythagorae et Platonis, qui altera principia posuerunt quam naturalia. Et circa hoc duo facit. Primo ostendit quod consideratio harum opinionum magis pertinet ad scientiam praesentem, quam praedictarum. Secundo incipit contra eas disputare, ibi, ergo qui Pythagorici sunt vocati. Dicit ergo primo, quod illi qui faciunt theoricam, idest considerationem de omnibus entibus, et ponunt, quod entium quaedam sunt sensibilia, quaedam insensibilia, perscrutantur de utroque genere entium. Unde investigare de opinionibus eorum, qui bene et qui non bene dixerunt, magis pertinet ad perscrutationem quam proponimus tradere in hac scientia. Nam haec scientia est de omnibus entibus, non de aliquo particulari genere entis. Et sic illa quae pertinent ad omnia entis genera, magis sunt hic consideranda quam illa quae pertinent ad aliquod particulare genus entis et cetera.	201. Here he argues dialectically against the opinions of Pythagoras and Plato, who posited different principles than those which pertain to the philosophy of nature. In regard to this he does two things. First, he shows that a study of these opinions rather than those mentioned above belongs to the present science. Second (202), he begins to argue dialectically against these opinions (“Therefore those who”). He says, first (98), then, that those who “make a study,” i.e., an investigation, of all existing things, and hold that some are sensible and others non-sensible, make a study of both classes of beings. Hence an investigation of the opinions of those who spoke either correctly or incorrectly, belongs rather to the study which we now propose to make in this science. For this science deals with all beings and not with some particular class of being. Hence, the things which pertain to every class of being are to be considered here rather than those which pertain to some particular class of being.
lib. 1 l. 13 n. 2 Deinde cum dicit ergo qui hic disputat contra opiniones praedictorum philosophorum. Et primo contra Pythagoram. Secundo contra Platonem, ibi, qui vero ideas. Circa primum duo facit. Primo ostendit in quo Pythagoras conveniebat cum naturalibus, et in quo ab eis differebat. Secundo disputat contra eius opinionem, ibi, ex quo tamen modo motus et cetera. Sciendum est ergo, quod Pythagorici in uno conveniebant cum naturalibus, in alio ab eis differebant. Differebant quidem in positione principiorum; usi sunt enim principiis rerum extraneo modo a naturalibus. Cuius causa est, quia principia rerum non acceperunt ex sensibilibus sicut naturales, sed ex mathematicis, quae sunt sine motu, unde non sunt naturalia. Quod autem mathematica dicuntur esse sine motu, referendum est ad illas scientias, quae sunt pure mathematicae, sicut arithmetica et geometria. Astrologia enim considerat motum, quia astrologia est media scientia inter mathematicam et naturalem. Principia enim sua astrologia et aliae mediae applicant ad res naturales, ut patet secundo physicorum.	202. Therefore those who (99). Here he argues against the opinions of the foregoing philosophers. First (99), he argues against Pythagoras; and second (208), against Plato (“But those who posited Ideas”). In regard to the first he does two things. First, he shows in what way Pythagoras agreed with the philosophers of nature, and in what way he differed from them. Second (204), he argues against Pythagoras’ position (“Yet how”). We must understand (99), then, that in one respect the Pythagoreans agreed with the philosophers of nature, and in another respect they differed from them. They differed from them in their position regarding principles, because they employed principles of things in a way foreign to the philosophers of nature. The reason is that they did not take the principles of things from sensible beings, as the natural philosophers did, but from the objects of mathematics, which are devoid of motion, and are therefore not physical. And the statement that the objects of mathematics are devoid of motion must be referred to those sciences which are purely mathematical, such as arithmetic and geometry. Astronomy considers motion’ because astronomy is a science midway between mathematics and natural philosophy. For astronomy and the other intermediate sciences apply their principles to natural things, as is clear in Book II of the Physics.
lib. 1 l. 13 n. 3 Conveniebat autem Pythagoras cum naturalibus quantum ad ea quorum principia quaerebat. Disputabat enim et tractabat de omnibus naturalibus. Tractabat enim de generatione caeli, et observabat omnia quae accidunt circa partes caeli, quae dicuntur diversae sphaerae, vel etiam diversae stellae: et quae accidunt circa passiones vel circa eclipses luminarium, et quae accidunt circa operationes et circa motus corporum caelestium, et circa eorum effectus in rebus inferioribus; et singulis huiusmodi dispensabat causas, adaptando scilicet unicuique propriam causam. Et videbatur etiam in hoc consentire aliis naturalibus, quod solum sit illud ens, quod est sensibile, quod comprehenditur a caelo quod videmus. Non enim ponebat aliquod corpus sensibile infinitum, sicut alii naturales posuerunt. Nec iterum ponebat plures mundos, sicut posuit Democritus. Ideo autem videbatur aestimare quod nulla entia essent nisi sensibilia, quia non assignabat principia et causas nisi talibus substantiis. Nihilominus tamen causae et principia, quae assignabat, non erant propria et determinata sensibilibus, sed erant sufficientia ascendere ad superiora entia, idest ad entia intellectualia. Et erant adhuc magis convenientia quam rationes naturalium, quae non poterant extendi ultra sensibilia, quia ponebant principia corporea. Pythagoras vero, quia ponebat principia incorporea, scilicet numeros, quamvis non poneret principia nisi corporum sensibilium, ponebat tamen entium intelligibilium, quae non sunt corpora, principia pene, sicut et Plato posterius fecit.	203. Now Pythagoras agreed with the philosophers of nature concerning the things whose principles he sought; for he discussed and treated all natural beings. He dealt with the generation of the heavens, and observed everything that happens to the parts of the heavens, by which are meant the different spheres, or also the different stars. He also considered what happens to its affections, or to the eclipses of the luminous bodies; and what happens to the operations and motions of the heavenly bodies, and their effects on lower bodies. And he used up causes on particular things of this kind by applying to each one its proper cause. He also seemed to agree with’ the other philosophers of nature in thinking that that alone has being which is sensible and is contained by the heavens which we see. For he did not posit an infinite sensible body as the other philosophers of nature did. Nor again did he hold that there are many worlds, as Democritus did. He therefore seemed to think that there are no beings except sensible ones, because he assigned principles and causes only for such substances. However, the causes and principles which he laid down are not proper or limited to sensible things, but are sufficient for ascending to higher beings, i.e., intellectual ones. And they were better fitted to these than the theories of the natural philosophers which could not be extended beyond sensible things, because these philosophers claimed that principles are corporeal. But since Pythagoras posited incorporeal principles, i.e., numbers, although he only posited principles of sensible bodies, he came very close to positing principles of intelligible beings, which are not bodies, as Plato did later on.
lib. 1 l. 13 n. 4 Deinde cum dicit ex quo tamen hic ponit tres rationes contra opinionem Pythagorae: quarum prima talis est. Pythagoras non poterat assignare, quomodo motus adveniat rebus, quia non ponebat principia nisi finitum et infinitum, par et impar, quae ponebat principia sicut substantia, sive materialia principia. Sed oportebat eum concedere motum rebus inesse. Quomodo enim esset possibile sine motu et transmutatione esse generationem et corruptionem in corporibus, et operationes eorum, quae geruntur circa caelum, quae per motus quosdam fiunt? Patet quod nullo modo. Unde cum Pythagoras consideravit de generatione et corruptione, et eis quae geruntur circa caelum, patet quod insufficienter posuit non assignans aliqua principia motus.	204. Yet how (100). Here he gives three arguments against the opinion of Pythagoras. The first is this: Pythagoras could not explain how motion originates in the world, because he posited as principles only the limited and unlimited and the even and odd, which he held to be principles as substance, or material principles. But he had to admit that there is motion in the world. For how could there be generation and corruption in bodies, and how could there be any activities of the heavenly bodies, which occur as a result of certain kinds of motion, unless motion and change existed? Evidently they could not exist in any way. Hence, since Pythagoras considered generation and corruption and the operations of the heavenly bodies without assigning any principle of motion, his position is clearly unsatisfactory.
lib. 1 l. 13 n. 5 Deinde cum dicit amplius autem hic ponit secundam rationem. Pythagoras enim ponebat ex numeris componi magnitudines. Sed sive hoc probet, sive concedatur, non poterat ex numeris assignare causam, quare quaedam sunt gravia, quaedam levia. Quod ex hoc patet, quia rationes numerorum non magis adaptantur corporibus sensibilibus quam mathematicis quae sunt non gravia et levia. Unde patet, quod ipsi nihil dixerunt plus de corporibus sensibilibus, quam de mathematicis. Et sic patet, quod cum corpora sensibilia, ut ignis et terra et huiusmodi, inquantum talia, addant aliquid supra mathematica, nihil proprium de istis sensibilibus dixerunt secundum veram aestimationem. Et sic iterum patet, quod insufficienter posuerunt, praetermittentes assignare causas eorum, quae sunt propria sensibilibus.	205. And further (101). Here he gives the second argument. For Pythagoras claimed that continuous quantities are composed of numbers. But whether he proves this or takes it for granted, he could not give any reason on the part of numbers as to why some things are heavy and others light. This is clear from the fact that his theories about numbers are no more adapted to sensible bodies than they are to the objects of mathematics, which are neither heavy nor light. Hence they obviously said nothing more about sensible bodies than they did about the objects of mathematics. Therefore, since sensible bodies, such as earth and fire and the like, considered in themselves, add something over and above the objects of mathematics, it is evident that they said nothing proper in any true sense about these sensible bodies. Thus it is also evident that the principles which they laid down are not sufficient, since they neglected to give the causes of those [attributes] which are proper to sensible bodies.
lib. 1 l. 13 n. 6 Deinde cum dicit amplius autem hic ostendit tertiam rationem, quae procedit ex hoc, quod Pythagoras videbatur ponere duo contraria. Ponebat enim ex una parte, quod numerus et numeri passiones sunt causa eorum quae sunt in caelo, et omnium generabilium et corruptibilium a principio mundi: ex alia vero ponebat, quod non erat aliquis alius numerus praeter istum numerum ex quo constituitur mundi substantia, numerum enim substantiam rerum posuit. Hoc autem quomodo est accipere, cum idem non sit causa suiipsius? Nam Pythagoras ex hoc dicit demonstrari, quod unumquodque horum sensibilium est numerus secundum substantiam suam, quia in hac parte universi sunt entia contingentia, de quibus est opinio, et quae subsunt tempori inquantum aliquando sunt et aliquando non sunt. Si autem generabilia et corruptibilia essent partim supra aut subtus, in ordine universi esset inordinatio, vel per modum iniustitiae, dum, scilicet, aliqua res sortiretur nobiliorem locum vel minus nobilem quam sibi debeatur: aut per modum discretionis, inquantum corpus si poneretur extra locum suum, divideretur a corporibus similis naturae: vel per modum mixtionis et confusionis, dum corpus extra suum locum positum oportet permisceri alteri corpori, sicut si aliqua pars aquae esset in aliquo loco aeris, vel in loco terrae. Et videtur in hoc tangere duplicem convenientiam corporis naturalis ad suum locum. Unam ex ordine situs, secundum quod nobiliora corpora sortiuntur altiorem locum, in quo videtur quaedam iustitia. Aliam autem ex similitudine vel dissimilitudine corporum locatorum adinvicem, cui contrariatur discretio et permixtio. Quia igitur res secundum quod determinatum situm habent, in universo convenienter se habent, quia situs in modico mutaretur sequeretur inconveniens, ut dictum et manifestum est, quod omnes partes universi sunt ordinatae secundum determinatam proportionem; omnis enim determinata proportio est secundum numeros. Unde ostendebat Pythagoras, quod omnia entia essent numerus. Sed ex alia parte videmus quod magnitudines constitutae in diversis locis sunt plures et diversae, quia singula loca universi consequuntur propriae passiones, quibus corpora diversificantur. Nam aliae sunt passiones corporis existentis sursum et deorsum. Cum igitur Pythagoras ratione praedicta dicat omnia sensibilia numerum, et videamus accidere diversitatem in sensibilibus secundum diversa loca, utrum sit idem et unus numerus tantum, qui est, in caelo, idest in toto corpore sensibili quod in caelo includatur, de quo oportet accipere quod est substantia uniuscuiusque sensibilis? Aut praeter hunc numerum qui est substantia rerum sensibilium, est alius numerus qui est eorum causa? Plato autem dixit alium numerum, qui est substantia sensibilium, et qui est causa. Et quia ipse Plato existimavit sicut Pythagoras, numeros esse ipsa corpora sensibilia et causas eorum, sed numeros intellectuales aestimavit causas insensibilium, numeros vero sensibiles causas esse et formas sensibilium. Quid quia Pythagoras non fecit, insufficienter posuit.	206. Further, how are we (102). Here he gives the third argument, which is based on the fact that Pythagoras seemed to hold two contrary [positions]. For, on the one hand, he held that number and the attributes of number arc the cause both of those events which occur in the heavens and of all generable and corruptible things from the beginning of the world. Yet, on the other hand, he held that there is no other number besides that of which the substance of things is composed; for he held that number is the substance of things. But how is this to be understood, since one and the same thing is not the cause of itself? For Pythagoras says that the former position may be demonstrated from the fact that each one of these sensible things is numerical in substance; because in this part of the universe there are contingent beings, about which there is opinion, and which are subject to time inasmuch as they sometimes are and sometimes are not. But if generable and corruptible things were partly above or partly below, there would be disorder in the order of the universe: either after the manner of injustice, i.e., insofar as some being would receive a nobler or less noble place than it ought to have; or after the manner of separation, i.e., in the sense that, if a body were located outside its own place, it would be separated from bodies of a like nature; or after the manner of mixture and mingling, provided that a body located outside its proper place must be mixed with some other body, for example, if some part of water occupied a place belonging to air or to earth. In this discussion he seems to touch on two ways in which a natural body conforms to its proper place: one pertains to the order of position, according to which nobler bodies receive a higher place, in which there seems to be a kind of justice; and the other pertains to the similarity or dissimilarity between bodies in place, to which separation and mingling may be opposed. Therefore, insofar as things have a definite position, they are fittingly situated in the universe. For if their position were fitting would result, inasmuch as it has been stated and shown that all parts of the universe are arranged in a definite proportion; for every definite proportion is numerical. And it was from this that Pythagoras showed that all things would be numbers. But, on the other hand, we see that the continuous quantities established in different places are many and different, because the particular places in the universe correspond to the proper attributes by which bodies are differentiated. For the attributes of bodies which are above differ from those which are below. Hence, since Pythagoras by means of the above argument affirms that all sensible things are numbers, and we see that the difference in sensible bodies is attributable to difference in place, the question arises whether the number which exists “in the heavens” i.e., in the whole visible body which comprises the heavens, is merely the same as that which must be understood to be the substance of each sensible thing, or whether besides this number which constitutes the substance of sensible things there is another number which is their cause. Now Plato said that there is one kind of number which is the substance of sensible things, and another which is their cause. And while both Plato himself and Pythagoras thought that numbers are both sensible bodies themselves and their causes, Plato alone considered intellectual numbers to be the causes of things that are not sensible, and sensible numbers to be the causes and forms of sensible things. And since Pythagoras did not do this, his position is unsatisfactory.
lib. 1 l. 13 n. 7 Concludit autem in fine quod ista sufficient de Pythagoricis opinionibus, nam eas tetigisse sufficit.	207. In concluding Aristotle says that these remarks about the Pythagoreans’ opinions will suffice; for it is enough to have touched upon them to this extent.