Authors/Thomas Aquinas/physics/L1/lect9

LECTURE 9 THE OPINION OF ANAXAGORAS THAT THE PRINCIPLES ARE INFINITE IS REFUTED

Latin	English
	LECTURE 9 (187 a 27-188 a 18) THE OPINION OF ANAXAGORAS THAT THE PRINCIPLES ARE INFINITE IS REFUTED
lib. 1 l. 9 n. 1 Positis diversis opinionibus naturalium philosophorum de principiis, hic prosequitur unam earum, scilicet opinionem Anaxagorae, quia haec opinio videbatur assignare causam communem omnium specierum motus. Et dividitur in duas partes: in prima ponit rationem ipsius; in secunda obiicit contra eam, ibi: si igitur infinitum et cetera. Circa primum tria facit: primo praemittit ea quae Anaxagoras supponebat, et ex quibus argumentabatur; secundo ponit suae rationis processum, ibi: si enim omne quod fit etc.; tertio ponit eius responsionem ad quandam tacitam obiectionem, ibi: apparere autem et cetera.	58. Having set forth the opinions of the natural philosophers concerning the principles, he here pursues one of these opinions, namely, that of Anaxagoras. For this opinion seemed to assign a common cause for all the species of motion. The discussion is divided into two parts. In the first part he sets forth Anaxagoras’ argument; in the second part he raises objections against it, where he says, ‘Now the infinite ...’ (187 b 7 #64). Concerning the first part he makes three points. First he sets forth those things which Anaxagoras supposed and from which he argues. Secondly, where he says, ‘The one, they reasoned ...’ (187 a 33 #62)2 he sets forth the order of his argument. Thirdly, where he says, ‘But things, as they say ...’ (187 b 2 #63), he sets forth Anaxagoras’ response to a certain tacit objection.
lib. 1 l. 9 n. 2 Duo autem supponebat Anaxagoras, ex quibus procedebat. Quorum primum est quod etiam ab omnibus naturalibus philosophis supponebatur, quod scilicet ex nihilo nihil fiat. Et hoc est quod dicit, quod Anaxagoras ex hoc videbatur opinari esse principia infinita, quia accipiebat communem opinionem omnium philosophorum naturalium esse veram; hanc scilicet, quod id quod simpliciter non est, nullo modo fiat. Quia enim hoc supponebant tanquam principium, ad diversas opiniones processerunt.	59. Anaxagoras assumed two things from which he argued. The first of these is a point which is assumed by all of the natural philosophers, namely, that nothing comes to be from nothing. And Aristotle says that, because of this, Anaxagoras seemed to have held the opinion that the principles are infinite. For he accepted as true the common opinion of all philosophers of nature, namely, that what simply is not in no way comes to be. For they assumed this as a principle and then developed their different opinions.
lib. 1 l. 9 n. 3 Ut enim non cogerentur ponere aliquid de novo fieri quod prius omnino non esset, posuerunt aliqui omnia prius simul extitisse, vel in aliquo uno confuso, sicut Anaxagoras et Empedocles; vel in aliquo principio materiali, scilicet aqua, igne et aere; vel in aliquo medio illorum. Et secundum hoc duos modos factionis ponebant. Qui enim posuerunt omnia simul praeexistere sicut in uno principio materiali, dixerunt quod fieri nihil aliud est quam alterari: ex illo enim uno principio materiali omnia fieri dicebant per condensationem et rarefactionem eiusdem. Alii vero, qui ponebant omnia praeexistere simul sicut in aliquo uno confuso et commixto ex multis, dixerunt quod fieri rerum non est aliud quam congregatio et segregatio. Et omnes hi decepti fuerunt quia nesciverunt distinguere inter potentiam et actum. Ens enim in potentia est quasi medium inter purum non ens et ens in actu. Quae igitur naturaliter fiunt, non fiunt ex simpliciter non ente, sed ex ente in potentia; non autem ex ente in actu, ut ipsi opinabantur. Unde quae fiunt non oportet praeexistere actu, ut ipsi dicebant, sed potentia tantum.	60. Lest they would be forced to hold that something new comes to be which previously was in no way at all, some held that all things from the beginning existed together, either in some one confused state, as Anaxagoras and Empedocles held, or in some natural principle, such as water, fire, and air, or some intermediate between these. And in accordance with this they posited two modes of production. Those who held that all things pre-existed together as in one material principle said that to come to be is nothing other than to be altered. For they said that all things come to be from that one material principle through its condensation and rarefaction. Others, however, who held that all things pre-existed together in some one confused state and mixture of many, said that the coming to be of things is only a joining together and a separation. All of these philosophers were deceived because they did not know how to distinguish between potency and act. For being in potency is, as it were, a mean between pure non-being and being in act. Therefore, those things which come to be naturally do not come to be from nonbeing simply, but from being in potency, and not, indeed, from being in act, as they thought. Hence things which come to be did not necessarily pre-exist in act, as they said, but only in potency.
lib. 1 l. 9 n. 4 Deinde cum dicit: amplius ex eo etc., ponit secundum quod supponebat. Dicebat enim quod contraria fiunt ex alterutris: videmus enim ex calido fieri frigidum et e converso. Et ex hoc concludebat quod, cum ex nihilo nihil fiat, quod unum contrariorum praeexistit in altero. Quod quidem est verum secundum potentiam, nam frigidum est potentia in calido: non autem actu, ut Anaxagoras aestimabat, propter hoc quod nesciebat accipere esse in potentia, quod est esse medium inter purum non esse et esse actu.	61. Next where he says, ‘Moreover the fact that ...’ (187 a 32), he mentions the second thing which Anaxagoras assumed. Anaxagoras said that contraries come to be from each other. For we see the cold come to be from the hot, and vice versa. And from this he concluded that, since nothing comes to be from nothing, one of the contraries pre-exists in the other. And this is true, of course, in respect to potency. For the cold is in the hot in potency, but not in act, as Anaxagoras thought. For he was not aware of being in potency, which is a mean between pure non-being and being in act.
lib. 1 l. 9 n. 5 Deinde cum dicit: si enim omne quod fit etc., ponit deductionem rationis ipsius. Et procedebat sic. Si aliquid fit, necesse est quod fiat aut ex ente aut ex non ente. Sed horum alterum excludebat, scilicet quod aliquid fieret ex non ente, propter communem opinionem philosophorum supra positam. Unde concludebat reliquum membrum, scilicet quod aliquid fiat ex ente: puta si aer fit ex aqua, quod aer prius existit. Non autem diceretur quod aer fiat ex aqua, nisi in aqua praeexisteret aer: unde volebat accipere quod omne quod fit ex aliquo, praeexisteret in eo ex quo fiebat. Sed quia hoc videbatur contra id quod apparet sensui (non enim apparet ad sensum quod illud quod generatur ex aliquo, praeexistat in eo), ideo hanc obiectionem excludebat per hoc quod ponebat, quod id quod fit ex aliquo, praeexisteret in eo secundum quasdam partes minimas, quae sunt nobis insensibiles propter suam parvitatem. Puta si aer fit ex aqua, partes aliquae minimae aeris sunt in aqua, non autem in illa quantitate in qua generatur: et ideo per congregationem illarum partium aeris ad invicem et segregationem ex partibus aquae, dicebat fieri aerem. Habito igitur hoc, quod omne quod fit ex aliquo, praeexistat in eo, assumebat ulterius omne ex omni fieri: unde concludebat quod quodlibet esset in quolibet permixtum secundum partes minimas et insensibiles. Et quia infinities unum ex alio fieri potest, infinitas partes minimas in unoquoque esse dicebat.	62. Next where he says, ‘The one, they reasoned ...’ (187 a 33), he sets forth the deductive order of the argument. Anaxagoras proceeded as follows. If something comes to be, it is necessary that it should come to be either from being or from nonbeing. But he excluded one of these alternatives-namely, that something should come to be from non-being. He does this because of the common opinion of the philosophers mentioned above [#59]. Whence he concluded that the remaining member was correct, namely, that a thing comes to be from being. For example, if air comes to be from water, then air pre-existed. For it cannot be said that air comes to be from water unless air pre-existed in water. Hence he wished to say that everything which comes to be from something pre-existed in that from which it comes to be. But because this seemed to be contrary to what appears to the senses (for it is not apparent to the senses that that which is generated from something pre-exists in it), he forestalled this objection by holding that that which comes to be from something pre-exists in it as certain most minute parts which are not sensible to us because of their smallness. For example, if air comes to be from water, certain minute parts of air are in the water, but not in that quantity in which it is generated. And so he said that by the gathering together of these parts of air by themselves, and by their separation from the parts of water, air comes to be. Having accepted, therefore, that everything which comes to be from something pre-exists in it, he further assumed that everything comes to be from everything. Whence he concluded that everything would be mixed in everything else as minute, non-sensible parts. And because an infinite variety of things can come to be from another, he said that infinite minute parts were in each thing.
lib. 1 l. 9 n. 6 Deinde cum dicit: apparere autem etc., excludit quandam tacitam obiectionem. Posset enim aliquis obiicere: si infinitae partes cuiuslibet rei sunt in quolibet, sequetur quod res nec ab invicem differant, nec ab invicem differre videantur. Ad hoc ergo quasi respondens dicit, quod res videntur differre ab invicem, et nominantur etiam diversa, ex eo quod maxime superabundat in eis; cum tamen infinita sit multitudo partium minimarum quae continentur in aliquo mixto. Et sic nihil est pure et totaliter album aut nigrum aut os, sed id quod plus est in unoquoque, hoc videtur esse natura rei.	63. Next where he says, ‘But things, as they say ...’ (187 b 2), he excludes a certain tacit objection. It is possible for someone to object as follows. If infinite parts of everything are in everything, it would follow that things neither differ from each other nor appear to differ from each other. Therefore, as if he were answering this objection, Anaxagoras says that things appear to differ from each other and ‘are diversely named because of that which is dominant in them, even though there s an infinite number of minute parts contained in any mixture. And so nothing is purely and totally white or black or bone. Rather, that which abounds in each thing seems to be the nature of that thing.
lib. 1 l. 9 n. 7 Deinde cum dicit: si igitur infinitum etc., improbat positionem praedictam. Et circa hoc duo facit: primo improbat eam absolute; secundo comparat eam ad opinionem Empedoclis, ibi: melius autem et cetera. Circa primum duo facit: primo ponit rationes ad improbandum opinionem Anaxagorae; secundo improbat modum positionis, ibi: nequaquam et cetera. Circa primum ponit quinque rationes. Quarum prima talis est. Omne infinitum est ignotum, secundum quod est infinitum. Et exponit quare dicit secundum quod infinitum; quia si est infinitum secundum multitudinem vel magnitudinem, erit ignotum secundum quantitatem; si autem est infinitum secundum speciem, puta quod constituatur ex infinitis secundum speciem diversis, tunc erit ignotum secundum qualitatem. Et huius ratio est, quia id quod est notum apud intellectum, comprehenditur ab ipso quantum ad omnia quae ipsius sunt; quod non potest contingere in aliquo infinito. Si igitur alicuius rei principia sunt infinita, oportet ea esse ignota, vel secundum quantitatem vel secundum speciem. Sed si principia sunt ignota, oportet esse ignota ea quae sunt ex principiis. Quod probat ex hoc, quia tunc arbitramur nos cognoscere unumquodque compositum, cum scimus ex quibus et quantis sit, idest quando cognoscimus et species et quantitates principiorum. Sequitur igitur de primo ad ultimum, quod si principia rerum naturalium sunt infinita, quod naturales res erunt ignotae, vel secundum quantitatem vel secundum speciem.	64. Next where he says, ‘Now the infinite ...’ (187 b 7), Aristotle refutes the above mentioned position. Concerning this he makes two points. First he disproves the position absolutely. Secondly, where he says, ‘... and it is better...’ (188 a 17), he compares it to the opinion of Empedocles. Concerning the first part he makes two points. First he sets forth arguments to disprove the opinion of Anaxagoras. Secondly, where he says, ‘The statement that...’ (188 a 5 #72), he disagrees with Anaxagoras’ way of understanding his own position. Concerning the first part he gives five arguments. The first of these is as follows. Every infinite thing, in that respect in which it is infinite, is unknown. He explains why he says ‘in that respect in which it is infinite’. If it is infinite in respect to multitude or magnitude, it will be unknown in respect to quantity. If, however, it is infinite in respect to species (for example, if it is composed of an infinite variety of species), then it will be unknown according to quality. And the reason for this is that what is known by the intellect is grasped by the intellect with respect to all that belongs to that thing. But this cannot happen with regard to something infinite. If, therefore, the principles of a thing are infinite, they must be unknown either in respect to quantity or in respect to species. But if the principles are unknown, those things which are from the principles must be unknown. He proves this as follows. We think that we know any composite when we know from what and from how many [principles] it is composed, i.e., when we know both the species and the quantity of the principles. It follows, therefore, from first to last that, if the principles of natural things are infinite, then natural things are unknown either in respect to quantity or in respect to species.
lib. 1 l. 9 n. 8 Secundam rationem ponit ibi: amplius autem si necesse est etc.: quae talis est. Si alicuius totius partes non habent aliquam determinatam quantitatem, sive magnitudinem vel parvitatem, sed contingit eas quantascumque esse vel secundum magnitudinem vel secundum parvitatem; necesse est quod totum non habeat determinatam magnitudinem vel parvitatem, sed contingat totum esse cuiuscumque magnitudinis vel parvitatis: et hoc ideo, quia quantitas totius consurgit ex partibus. (Sed hoc intelligendum est de partibus existentibus actu in toto, sicut caro, nervus et os existunt in animali: et hoc est quod dicit, dico autem talium aliquam partium, in quam cum insit, scilicet actu, dividitur aliquod totum: et per hoc excluduntur partes totius continui, quae sunt potentia in ipso). Sed impossibile est quod animal vel planta vel aliquod huiusmodi habeat se indeterminate ad quantamcumque magnitudinem vel parvitatem: est enim aliqua quantitas ita magna, ultra quam nullum animal extenditur, et aliqua ita parva, infra quam nullum animal invenitur; et similiter dicendum est de planta. Ergo sequitur ad destructionem consequentis, quod neque aliqua partium sit indeterminatae quantitatis, quia simile est de toto et de partibus. Sed caro et os et huiusmodi sunt partes animalis, et fructus sunt partes plantarum: impossibile est igitur quod caro et os et huiusmodi habeant indeterminatam quantitatem vel secundum maius vel secundum minus. Non ergo est possibile quod sint aliquae partes carnis aut ossis quae sint insensibiles propter parvitatem.	65. At the point where he says, ‘Further if the parts ...’ (187 b 14), he gives the second argument, which is as follows. If the parts of a whole do not have a determinate quantity, either great or small, but can be any size, either great or small, it is not necessary that the whole have a determinate greatness or smallness. Rather the whole could have any size. This is so because the quantity of the whole comes from the parts. (But this must be understood of the parts existing in act in the whole, as flesh and nerve and bone exist in an animal. Hence he says, ‘... by parts I mean components into which a whole can be divided and which are actually present in it’ (187 b 15). And by this he excludes the parts of a continuous whole which are in the whole in potency.) But it is impossible that an animal or a plant or some such thing be related indeterminately to any size, whether great or small. For there is some quantity so large that no animal exceeds it in size. So also there is some quantity so small that no animal is found to be smaller. And the same must be said of plants. Therefore by denying the consequent it follows that the parts are not of indeterminate quantity. For what is true of the whole is true of the parts. But flesh and bone and things of this sort are parts of an animal, and fruits are parts of plants. Therefore it is impossible that flesh and bone and such things should have an indeterminate quantity, either greater or smaller. Therefore it is not possible that there should be certain parts of flesh or bone which are non-sensible because of smallness.
lib. 1 l. 9 n. 9 Videtur autem quod hic dicitur, contrarium esse divisioni continui in infinitum. Si enim continuum in infinitum divisibile est, caro autem continuum quoddam est; videtur quod sit in infinitum divisibilis. Omnem igitur parvitatem determinatam transcendet pars carnis secundum divisionem infinitam. Sed dicendum quod licet corpus, mathematice acceptum, sit divisibile in infinitum, corpus tamen naturale non est divisibile in infinitum. In corpore enim mathematico non consideratur nisi quantitas, in qua nihil invenitur divisioni in infinitum repugnans; sed in corpore naturali consideratur forma naturalis, quae requirit determinatam quantitatem sicut et alia accidentia. Unde non potest inveniri quantitas in specie carnis nisi infra aliquos terminos determinata.	66. It seems, however, that what is said here is contrary to the statement that a continuum is divisible to infinity. For if the continuous is divisible to infinity, and flesh is, indeed, a kind of continuum, it seems that flesh is divisible to infinity. Therefore, some part of flesh, according to a division to infinity, goes beyond every determinate smallness. But it must be pointed out that although a body, considered mathematically, is divisible to infinity, the natural body is not divisible to infinity. For in a mathematical body nothing but quantity is considered. And in this there is nothing repugnant to division to infinity. But in a natural body the form also is considered, which form requires a determinate quantity and also other accidents. Whence it is not possible for quantity to be found in the species of flesh except as determined within some termini.
lib. 1 l. 9 n. 10 Tertiam rationem ponit ibi: amplius si omnia et cetera. Et circa hoc duo facit: primo praemittit quaedam ex quibus argumentatur; secundo ponit deductionem rationis, ibi: remota enim et cetera. Circa primum tria proponit. Primum est quod omnia simul sunt secundum positionem Anaxagorae, ut dictum est; ex quo vult deducere ad inconveniens. Dicebat enim Anaxagoras, ut dictum est, quod omnia huiusmodi, scilicet quae sunt similium partium, ut caro et os et similia, insunt invicem, et non fiunt de novo, sed segregantur ex aliquo in quo praeextiterunt; sed unumquodque denominatur a plurimo, idest a pluribus partibus in re existentibus. Secundum est quod quodlibet fit ex quolibet, sicut ex carne fit aqua per segregationem, et similiter caro ex aqua. Tertium est quod omne corpus finitum resecatur a corpore finito: hoc est, si ab aliquo corpore finito quantumcumque magno auferatur multoties corpus finitum quantumcumque parvum, toties poterit auferri minus a maiori, quod totum maius consumetur a minori per divisionem. Ex his autem tribus concludit quod principaliter intendit, scilicet quod non sit unumquodque in unoquoque, quod est contrarium primo istorum trium positorum. Sic enim contingit in rationibus ducentibus ad impossibile, quod concludatur finaliter destructio alicuius praemissorum.	67. He gives the third argument where he says, ‘Again according to the theory ...’ (187 b 23). Concerning this he makes two points. First he sets forth certain things which are the basis of the argument. Secondly, where he says, ‘For let flesh ...’ (187 b 28 #68), he sets forth the deductive order of the argument. Concerning the first part he proposes three things. The first is that according to the position of Anaxagoras, as was said above [#62], all things are together. And from this Aristotle wishes to reduce Anaxigoras’ argument to absurdity. For Anaxagoras said, as was pointed out [#62ff], that all things which are of a certain kind, i.e., all things which are of like parts, such as flesh and bone and the like, are in each other, and do not come to be from nothing, but are separated from that in which they pre-exist. And each thing is named from that which abounds in it, i.e., from the largest number of parts existing in the thing. The second point is that everything comes to be from everything, as water comes to be by separation from flesh, and in the same way flesh comes to be from water. And the third point is that every finite body is reduced by a finite body. That is, if from some finite body, however large, a finite body, however small, is taken away, the smaller can be taken away from the larger until eventually the greater whole is consumed by the smaller through division. And from these three points Aristotle concludes what he primarily intended, namely, that each thing is not in each thing. And this is contrary to the first of these three points. For in arguments which lead to absurdity the denial of one of the premises is the final conclusion.
lib. 1 l. 9 n. 11 Deinde cum dicit: remota enim ex aqua etc., deducit argumentationem: et assumit quod in praecedenti argumentatione conclusum est. Dicit enim quod si ex aqua removeatur caro (dum scilicet ex aqua generatur caro), et si iterum ex residua aqua fiat alia segregatio carnis; quamvis semper remaneat minor quantitas carnis in aqua, tamen magnitudo carnis non excedit aliquam parvitatem, idest contingit dare aliquam parvam mensuram carnis, qua non erit minor aliqua caro, ut ex superiori ratione apparet. Hoc ergo habito, quod aliqua sit parva caro qua nulla sit minor, sic procedit. Si ex aqua segregatur caro et iterum alia caro, aut stabit ista segregatio aut non. Si stabit, ergo in residua aqua non erit caro; et sic non erit quodlibet in quolibet: si autem non stabit, ergo in aqua semper remanebit aliqua pars carnis; ita tamen quod in secunda segregatione sit minor quam in prima, et in tertia minor quam in secunda. Et cum non sit descendere in parvitatem partium in infinitum, ut dictum est, illae minimae partes carnis erunt aequales et infinitae numero in aliqua aqua finita: alioquin non procederet in infinitum segregatio. Sequitur igitur, si segregatio non stat, sed semper in infinitum removetur caro ex aqua, quod in aliqua magnitudine finita, scilicet aqua, sint quaedam finita secundum quantitatem et aequalia ad invicem et infinita secundum numerum, scilicet infinitae minimae partes carnis: et hoc est impossibile et contrarium ei quod supra positum est, scilicet quod omne corpus finitum resecatur ab aliquo corpore finito. Ergo et primum fuit impossibile, scilicet quod quodlibet esset in quolibet, ut Anaxagoras posuit.	68. Next where he says, ‘For let flesh...’(187 b 28), he develops his argument and assumes what was concluded in the preceding argument. He says that if flesh is removed from water (since flesh is generated from water), and if again another separation of flesh is made from the remaining water, then although there will always remain a smaller quantity of flesh in the water, still the size of that flesh is not less than a certain smallness, i.e., there happens to be a certain small measure of flesh than which there will not be any smaller flesh, as is clear from the argument given above. Therefore, having established that there is some small particle of flesh than which there is no smaller, he proceeds as follows. If from water flesh is separated, and again other flesh, the process of separation will either stop or it will not. If it stops, then there is no flesh in the remaining water, and everything will not be in everything. If it does not stop, then some part of flesh will always remain in the water. Thus in the second separation the remaining flesh is smaller than in the first, and in the third it is smaller than in the second. And since we cannot proceed to infinity in smallness of parts, as was said, then the smallest parts of flesh are equal and infinite in number in some finite body of water. Otherwise separation could not proceed to infinity. It follows, therefore, that if the separation does not stop, but flesh is always removed from water to infinity, then in some finite magnitude, e.g., water, there are certain things which are finite in respect to quantity, and equal to each other, and infinite in respect to number, namely, the infinite smallest parts of flesh. But this is impossible and contrary to what was said above, namely, that every finite body is reduced by some finite body. Therefore the first point, namely, that everything is in everything, as Anaxagoras held, is also impossible.
lib. 1 l. 9 n. 12 Considerandum est autem quod non sine causa philosophus apposuit aequalia in hoc ultimo inconvenienti ad quod ducit. Non enim est inconveniens quod in aliquo finito sint infinita inaequalia, si attendatur ratio quantitatis: quia si dividatur continuum secundum eandem proportionem, erit procedere in infinitum, ut puta si accipiatur tertium totius et tertium tertii et sic deinceps; sed tamen partes acceptae non erunt aequales secundum quantitatem. Sed si fiat divisio per partes aequales, non erit procedere in infinitum, etiam si sola ratio quantitatis in corpore mathematico consideretur.	69. We must note that it is not without reason that the Philosopher used the term ‘equal’ in stating the last absurdity to which this position leads. For if the nature of quantity is considered, it is not absurd that an infinity of unequal parts be in a finite body. For if a continuum is divided according to the same proportion, it will be possible to proceed to infinity, for example, if we take a third of a whole, and then a third of the third, and so on. In this case, however, the parts were not taken as equal in quantity. But if the division is made according to equal parts, we will not be able to proceed to infinity even if we consider only the nature [ratio] of quantity which is found in a mathematical body.
lib. 1 l. 9 n. 13 Quartam rationem ponit ibi: ad haec autem si omne etc.: quae talis est. Omne corpus remoto aliquo fit minus, cum omne totum sit maius sua parte; cum autem quantitas carnis sit determinata secundum magnitudinem et parvitatem, ut ex dictis patet, necesse est esse aliquam minimam carnem; ergo ab ea non potest aliquid segregari, quia sic esset aliquid minus minimo. Non igitur ex quolibet potest fieri quodlibet per segregationem.	70. He gives his fourth argument where he says, ‘Another proof may be added ...’ (187 b 35). The argument is as follows. Every body becomes a smaller one when something is taken from it, because every whole is greater than its parts. Since then the quantity of flesh is determinately great or small, as is clear from what was said above, there must be some smallest bit of flesh. Therefore from this nothing can be separated, because the remaining flesh would be smaller than this smallest piece of flesh. Therefore it is impossible that everything comes to be from everything by separation.
lib. 1 l. 9 n. 14 Quintam rationem ponit ibi: amplius autem in infinitis corporibus etc.: quae talis est. Si infinitae partes uniuscuiusque sunt in unoquoque, et quodlibet est in quolibet, sequetur quod in infinitis corporibus sint infinitae partes carnis et infinitae partes sanguinis vel cerebri: et quantumcumque inde separentur, adhuc remanent ibi. Sequeretur ergo quod infinita sunt in infinitis infinities; quod est irrationabile.	71. At the point where he says, ‘Lastly in each ...’ (188 a 3), he gives his fifth argument, which is as follows. If infinite parts of each thing are in each thing, and everything is in everything, it follows that infinite parts of flesh and infinite parts of blood and brain are in an infinite number of bodies. And regardless of how much is separated, the same amount would always remain. Therefore it would follow that the infinite is in the infinite infinitely. But this is unthinkable.
lib. 1 l. 9 n. 15 Deinde cum dicit: nunquam autem segregandum esse etc., improbat praedictam positionem Anaxagorae quantum ad modum ponendi. Et hoc dupliciter: primo quia non intelligebat propriam positionem; secundo quia non habebat sufficiens motivum ad ponendum eam, ibi: non recte autem et cetera. Dicit ergo primo quod in hoc quod dixit, quod segregatio nunquam finietur, nescivit quid diceret, quamvis aliquo modo verum dixerit; quia accidentia nunquam possunt separari a substantiis, et tamen ponebat permixtionem non solum corporum sed etiam accidentium. Cum enim aliquid fit album, dicebat quod hoc fiebat per abstractionem albedinis prius commixtae. Si igitur colores et alia huiusmodi accidentia ponantur esse commixta, ut ipse dicebat; si aliquis, hoc supposito, dicat quod omnia commixta possunt segregari, sequeretur quod sit album et sanativum, et non sit aliquod subiectum de quo dicantur et in quo sint; quod est impossibile. Relinquitur igitur hoc verum esse, quod non omnia commixta possunt segregari, si accidentia etiam commisceantur. Sed ex hoc sequitur inconveniens. Ponebat enim Anaxagoras quod omnia a principio erant commixta, sed intellectus incoepit segregare: quicumque autem intellectus quaerit facere quod impossibile est fieri, est indecens intellectus. Quare inconveniens erit intellectus ille impossibilia intendens, si vere velit, idest totaliter velit segregare: quod est impossibile et secundum quantitatem, quia non est minima magnitudo, ut Anaxagoras ponebat, sed ex quolibet minimo potest aliquid auferri; et secundum qualitatem, quia accidentia non sunt separabilia a subiectis.	72. Next where he says, ‘The statement that ...’ (188 a 5), he disproves the position of Anaxagoras according to Anaxagoras’ own understanding of it. He does this in two ways. First he shows that Anaxagoras did not understand his own position. Secondly, where he says, ‘Nor is Anaxagoras...’(188 a 13),1 he shows that Anaxagoras did not have sufficient evidence for holding this position. He says, therefore, first that although Anaxagoras has in a certain respect spoken the truth, he himself did not understand what he said when he held that the process of separation would never end. For accidents can never be separated from substance; yet he held that there was a mixture not only of bodies but also of accidents. When something becomes white, he said that this happened by an abstraction of white from the previously existing mixture. If then colours and other accidents of this sort are mixed together, as he said, and if someone on this supposition says all things that are mixed can be separated, it would follow that there would be white and healthy, and yet there would be no subject of which these are predicated and in which they are. But this is impossible. Therefore the truth is that if accidents are in the mixture it is impossible that all mixed things can be separated. Another absurdity results from the following. Anaxagoras held that all things were mixed from the very beginning, but intellect began to separate them. Now any intellect which attempts to do what cannot be done is not worthy of the name intellect. Hence that intellect will be inconsistent, intending the impossible, if it truly wishes this, i.e., wishes to separate things completely. For this is impossible both from the point of view of quantity, because there is no smallest magnitude, as Anaxagoras said, for from any small quantity something can be subtracted, and from the point of view of quality, because accidents are not separable from their subjects.
lib. 1 l. 9 n. 16 Deinde cum dicit: non recte autem etc., improbat praedictam positionem quantum ad hoc, quod non habebat sufficiens motivum. Quia enim videbat Anaxagoras quod aliquid fit magnum ex congregatione multarum partium similium parvarum, sicut torrens ex multis guttis, credidit ita esse in omnibus. Et ideo dicit Aristoteles quod non recte accepit generationem similium specierum, idest quod semper oporteret aliquid generari ex similibus secundum speciem. Quaedam enim ex similibus generantur et in similia resolvuntur, sicut lutum dividitur in luta; in quibusdam autem non est sic, sed quaedam generantur ex dissimilibus. Et in his etiam non est unus modus, quia quaedam fiunt ex dissimilibus per alterationem, sicut lateres non ex lateribus sed ex luto; quaedam vero per compositionem, sicut domus non ex domibus sed ex lateribus. Et per hunc modum aer et aqua fiunt ex alterutris, idest sicut ex dissimilibus. Alia littera habet sicut lateres ex domo: et sic ponit duplicem modum quo aliquid fit ex dissimilibus, scilicet per compositionem, sicut domus fit ex lateribus, et per resolutionem, sicut lateres fiunt ex domo.	73. Next where he says, ‘Nor is Anaxagoras ...’ (188 a 13), he disproves this position by reason of the fact that Anaxagoras did not have sufficient evidence. Since Anaxagoras saw that a thing is made large by the coming together of many small parts which are similar, as a stream is made from many brooks, he believed this to be the case for all things. And thus Aristotle says that Anaxagoras did not correctly understand the generation of things of the same species, i.e., he did not understand that a thing is not always generated by things which are similar in respect to species. For some things are both generated from and are resolved into things like unto themselves, as clay is divided into bricks; in other instances, however, this is not so. For some things are generated from that which is dissimilar. And in these instances there is not merely one mode of production. For some things are made by alteration from that which is unlike, as the sides of a house are made from clay and not from sides; whereas other things are made by composition, as the house is not made of houses, but of sides. It is in this way that air and water come to be from each other, i.e., as from the unlike. Another reading here is ‘as the sides are from the house’. And thus he sets forth a twofold way in which things come to be from the unlike, i.e., through composition, as the house is made of sides, and by resolution, as the sides come to be from the house.
lib. 1 l. 9 n. 17 Deinde cum dicit: melius autem etc., improbat positionem Anaxagorae per comparationem ad opinionem Empedoclis: et dicit quod melius est quod fiant principia pauciora et finita, quod fecit Empedocles, quam plura et infinita, quod fecit Anaxagoras.	74. Next where he says, ‘... and it is better ...’ (188 a 17), he disproves the position of Anaxagoras by comparing it with the opinion of Empedocles. He says that it is better to make the principles smaller in number and finite, as Empedocles does, than to make them many and infinite, as does Anaxagoras.