Authors/Thomas Aquinas/metaphysics/liber3/lect12

Lecture 12

Latin	English
lib. 3 l. 12 n. 1 Postquam philosophus inquisivit utrum principia sint eadem vel diversa, hic inquirit quomodo se habeat ipsum unum ad hoc quod sit principium: et circa hoc tria facit. Primo inquirit, an ipsum unum sit principium. Secundo inquirit an numeri, qui ex uno oriuntur vel consequuntur, sint principia rerum, ibi, horum autem habita dubitatio et cetera. Tertio inquirit utrum species, quae sunt quaedam unitates separatae, sint principia, ibi, omnino vero dubitabit aliquis et cetera. Et circa primum tria facit. Primo movet dubitationem. Secundo ponit opiniones ad utramque partem, ibi, hi namque illo modo. Tertio ponit rationes ad utramque partem, ibi, accidit autem si quidem et cetera. Dicit ergo primo, quod inter omnes alias quaestiones motas una est difficilior ad considerandum, propter efficaciam rationum ad utramque partem, in qua etiam veritatem cognoscere est maxime necessarium, quia ex hoc dependet iudicium de substantiis rerum. Est ergo quaestio ista, utrum unum et ens sint substantiae rerum, ita scilicet quod neutrum eorum oporteat attribuere alicui alteri naturae quae quasi informetur unitate et entitate, sed potius ipsa unitas et esse rei sit eius substantia: vel e contrario oportet inquirere quid sit illud, cui convenit esse unum vel ens, quasi quaedam alia natura subiecta entitati et unitati.	488. Having asked whether the principles of things are the same or different, the Philosopher now asks how unity itself could have the nature of a principle; and in regard to this he does three things. First, he asks whether unity itself is a principle; second (502), he asks whether numbers, which arise or follow from unity, are the principles of things; and third (515), whether the Forms, which are certain separate unities, are the principles of things. In regard to the first he does three things. First, he raises the question. Second (489), he gives the opinions on both sides (“For some think”). Third (490), he advances arguments on both sides (“But if anyone”). He says, first (266), that of all the different questions which have been raised, one is more difficult to consider because of the weight of the arguments on both sides, and that this question is also one about which it is necessary to know the truth, because our decision about the substances of things depends on it. Now this question is whether unity and being are the substances of things, not so that either of them must be attributed to some other nature which would be informed, as it were, by unity and being, but rather so that the unity and being of a thing are its substance; or, in an opposite way, whether it is necessary to ask what that thing is to which unity and being properly belong, as though there were some other nature which is their subject.
lib. 3 l. 12 n. 2 Deinde cum dicit hi namque ponit opiniones ad utramque partem: et dicit, quod philosophorum quidam opinati sunt naturam rerum se habere uno modo, quidam alio. Plato enim et Pythagorici non posuerunt quod unum et ens advenirent alicui naturae, sed unum et ens essent natura rerum, quasi hoc ipsum quod est esse et unitas sit substantia rerum. Alii vero philosophi de naturalibus loquentes, attribuerunt unum et ens aliquibus aliis naturis, sicut Empedocles reducit unum ad aliquid notius, quod dicebant esse unum et ens. Et hoc videtur esse amor, qui est causa unitatis in omnibus. Alii vero philosophi naturales attribuerunt quibusdam causis elementaribus, sive ponerent unum primum, ut ignem vel aerem, sive etiam ponerent plura principia. Cum enim ponerent principia rerum materialia esse substantias rerum, oportebat quod in unoquoque eorum constituerent unitatem et entitatem rerum, ita quod quicquid aliquis poneret esse principium, ex consequenti opinaretur, quod per illud attribuitur omnibus esse et unum, sive poneret unum principium sive plura.	489. For some think (267) Here he gives the opinions on each side of the question. He says that some philosophers thought that reality was of one kind, and some of another. For Plato and the Pythagoreans did not hold that unity and being are the attributes of some nature, but that they constitute the nature of things, as though being itself and unity itself were the substance of things. But some philosophers, in speaking about the natural world, attributed unity and being to certain other natures, as Empedocles reduced the one to something better known, which he- said is unity and being; and this seems to be love, which is the cause of unity in the world. But other philosophers of nature attributed these to certain elementary causes, whether they posited one first principle, as fire or air, or more than one. For since they would hold that the material principles of things are the substances of things, it was necessary that each of these should constitute the unity and being of things; so that whichever one of these anyone might hold to be a principle, he would logically think that through it being and unity would be attributed to A things, whether he posited one principle or more than one.
lib. 3 l. 12 n. 3 Deinde cum dicit accidit autem ponit rationes ad utramque partem. Et primo ponit rationes pro opinione Platonis et Pythagorae. Secundo ponit rationes in contrarium pro opinione naturalium, ibi, at vero si erit et cetera. Circa primum, utitur tali divisione. Necesse est ponere quod vel ipsum unum et ens separatum sit quaedam substantia, vel non: si dicatur quod non est aliqua substantia quae sit unum et ens, sequuntur duo inconvenientia. Quorum primum est, quod dicitur unum et ens quod sint maxime universalia inter omnia. Si igitur unum et ens non sunt separata quasi ipsum unum aut ens sit substantia quaedam, sic sequitur quod nullum universale sit separatum: et ita sequetur quod nihil erit in rebus nisi singularia: quod videtur esse inconveniens, ut in superioribus quaestionibus habitum est.	490. But if anyone (268). Here he gives arguments on both sides of the question. First, he gives arguments in support of the view of Plato and Pythagoras. Second (269:C 493), he gives arguments on the other side of the question, in support of the view of the philosophers of nature (“But, on the other hand”). In regard to the first (268), he makes use of elimination as follows. It is necessary to hold either that unity and being, separate and existing apart, are a substance, or not. Now if it is said that unity and being are not a substance, two untenable consequences will follow. The first of these is this: unity and being are said to be the most universal of all, and therefore, if unity and being are not separate in such a way that unity itself or being itself is a certain substance, it will then follow that no universal is separate. Thus it will follow that there is nothing in the world except singular things, which seems to be inappropriate, as has been stated in earlier questions (C 443).
lib. 3 l. 12 n. 4 Aliud inconveniens est, quia numerus non est aliud quam unitates: ex unitatibus enim componitur numerus. Unitas enim nihil aliud est quam ipsum unum. Si igitur ipsum unum, non sit separatum quasi substantia per se existens, sequetur quod numerus non erat quaedam natura separata ab his quae sunt in materia. Quod potest probari esse inconveniens, secundum ea quae dicta sunt in superioribus. Sic ergo non potest dici quod unum et ens non sit aliqua substantia per se existens.	491. The other untenable consequence is this. Number is nothing else than units, because number is composed of units; for a unit is nothing else than unity itself. Therefore, if unity itself is not separate as a substance existing of itself, it will follow that number will not be a reality separate from those things which are found in matter. This can be shown to be inappropriate in view of what has already been stated above. Hence it cannot be said that unity and being are not a substance which exists by itself.
lib. 3 l. 12 n. 5 Si ergo detur alia pars divisionis, scilicet quod aliquid sit ipsum unum et ens separatum existens, necesse est quod ipsum sit substantia omnium eorum, de quibus dicitur unum et ens. Omne enim separatum existens, quod de pluribus praedicatur, est substantia eorum de quibus praedicatur. Sed nihil aliud praedicatur ita universaliter de omnibus sicut unum et ens; ergo unum et ens erit substantia omnium.	492. Therefore, if the other part of the division is conceded, that there is something which is unity itself and being itself, and that this exists separately, it must be the substance of all those things of which unity and being are predicated. For everything that is separate and is predicated of many things is the substance of those things of which it is predicated. But nothing else is predicated of all things in as universal a way as unity and being. Therefore unity and being will be the substance of all things.
lib. 3 l. 12 n. 6 Deinde cum dicit at vero obiicit ad partem contrariam; et ponit duas rationes, quarum secunda incipit ibi, amplius si indivisibile et cetera. Circa primum duo facit. Primo ponit rationem. Secundo ostendit quomodo ex ratione inducta quaestio redditur difficilis, ibi, utrobique vero difficile et cetera. Est ergo prima ratio talis. Si est aliquid, quod est ipsum ens et ipsum unum, quasi separatum existens, oportebit dicere quod idipsum sit unum quod ens. Sed quicquid est diversum ab ente non est; ergo sequetur secundum rationem Parmenidis, quod quicquid est praeter unum sit non ens. Et ita necesse erit omnia esse unum; quia non poterit poni quod id quod est diversum ab uno, quod est per se separatum, sit aliquod ens.	493. But, on the other hand (269). Then he argues the other side of the question; and he gives two arguments. The second (271:C 496) of use these begins where he says, “Further, if unity itself.” In regard to the first he does two things. First, he gives the argument. Second (270:C 494), he shows how the question is made difficult as a result of the argument given (“But there is a difficulty in either case”). The first (269) argument, then, is as follows: if there is something which is itself being and unity as something ,existing separately, it will be necessary to say that unity is the very same thing as being. But that which differs from being is non-being. Therefore it follows, according to the argument of Parmenides, that besides the one there is only non-being. Thus all things will have to be one, because it could not be held that that which differs from the one, which is essentially separate, is a being.
lib. 3 l. 12 n. 7 Deinde cum dicit utrobique vero ostendit quomodo ista ratio difficultatem facit in opinione Platonis ponentis numerum esse substantiam rerum: et dicit quod ex utraque parte sequitur difficultas contra eum, sive dicatur quod ipsum unum separatum sit substantia quaedam, sive quod non sit. Quodcumque enim horum ponatur, videtur impossibile esse, quod numerus sit substantia rerum. Quia si ponatur quod unum non sit substantia, dictum est prius, quare numerus non potest poni substantia.	494. But there is a difficulty (270). Here he shows how this argument creates a difficulty in the case of the position of Plato, who held that number is the substance of things. He says that Plato faces a difficulty in either case, whether it is said that this separate one is a substance or not. For whichever view is held, it seems impossible that number should be the substance of things. For if it is held that unity is not a substance, it has already been stated (269:C 493) why number cannot be held to be a substance.
lib. 3 l. 12 n. 8 Si autem ipsum unum fuerit substantia, oportet quod eadem dubitatio ponatur circa unum et ens. Aut enim praeter ipsum unum, quod est separatum per se existens, est aliud aliquod unum, aut non. Et si quidem non sit aliquod aliud unum, non erit iam multitudo, sicut Parmenides dicebat. Si autem sit aliquod aliud unum oportebit, quod illud aliud unum, cum non sit hoc ipsum quod est unum, quod sit materialiter ex aliquo quod est praeter ipsum unum, et per consequens praeter ens. Et sic necesse est ut illud aliquid, ex quo fit illud secundum unum, non sit ens. Et sic ex ipso uno quod est praeter ipsum unum, non potest constitui multitudo in entibus: quia omnia entia aut sunt unum, aut multa, quorum unumquodque est unum. Hoc autem unum est materialiter ex eo quod non est unum nec ens.	495. But if unity itself is a substance, the same problem will arise with respect to both unity and being. For either there is some other unity besides this unity which exists separately of itself, or there is not. And if there is no other, a multitude of things will not exist now, as Parmenides said. But if there is another unity, then that other unity, since it is not unity itself, must have as a material element something that is other than unity itself, and, consequently, other than being. And that material element from which this second unity comes to be, will have not to be a being. Thus a multitude of beings cannot be constituted from this unity which exists apart from unity itself, because all beings are either one or many, each of which is a one. But this one has as its material element something that is neither unity nor being.
lib. 3 l. 12 n. 9 Deinde cum dicit amplius si ponit secundam rationem; et circa hoc tria facit. Primo ponit rationem. Secundo solvit eam, ibi, sed quoniam et cetera. Tertio ostendit adhuc difficultatem remanere, ibi, sed quomodo ex uno et cetera. Dicit ergo primo, quod si ipsum unum separatum sit indivisibile, sequitur secundum hoc, aliud, quod supponebat Zeno, quod nihil sit. Supponebat enim Zeno, quod illud, quod additum non facit maius, et ablatum non facit minus, non est aliquid existentium. Hoc autem supponit ac si idem sit ens quod magnitudo. Manifestum est enim quod non est magnitudo, illud scilicet quod additum non facit maius et subtractum non facit minus. Sic ergo si omne ens esset magnitudo, sequeretur quod illud, quod non facit maius et minus additum et subtractum, non sit ens.	496. Further, if unity (271). Here he gives the second argument; and in regard to this he does three things. First (271:C 496), he gives the argument. Second (272:C 498), he criticizes it (“But this”). Third (273:C 499), he shows that the difficulty remains (“Yet how will continuous quantity”). He says first (271), then, that if this separate unity is indivisible, there follows from this the other position, which Zeno assumed, that nothing exists. For Zeno supposed that that which when added does not make a thing greater and when taken away does not make it smaller, is nothing in the real order. But he makes this assumption on the grounds that continuous quantity is the same as being. For it is evident that this is not a continuous quantity—I mean that which when added does not make a thing greater and when subtracted does not make it smaller. Therefore, if every being were a continuous quantity, it would follow that that which when added does not make a thing greater and when subtracted does not make it smaller, is non-being.
lib. 3 l. 12 n. 10 Et adhuc perfectius si aliquid velit hoc verificare, oportebit quod omne ens sit magnitudo corporalis. Corpus enim secundum quamcumque dimensionem additum et subtractum facit maius et minus. Aliae vero magnitudines, ut superficies et lineae, secundum aliquam dimensionem additam facerent maius, secundum autem aliquam non. Linea enim addita lineae secundum longitudinem facit maius, non autem secundum latitudinem. Superficies autem addita superficiei facit quidem maius secundum latitudinem et longitudinem, sed non secundum profunditatem. Punctus autem et unitas nullo modo faciunt maius vel minus. Sic ergo secundum principium Zenonis sequeretur quod punctus et unitas sint omnino non entia, corpus autem omnimodo ens, superficies et linea quodammodo entia et quodammodo non entia.	497. And better still, if any particular thing were to bear this out, every being would have to be a corporeal continuous quantity. For anything added to or subtracted from a body in any one of its dimensions, makes the body greater or less. But other continuous quantities, such as lines and surfaces, become greater insofar as one dimension is added, whereas others do not. For line added to line in length causes increase in length but not in width; and surface added to surface causes increase in width and in length but not in depth. But a point and a unit do not become greater or less in any way. Hence according to Zeno’s axiom it would follow that a point and a unit are non-beings in an absolute sense, whereas a body is a being in every respect, and surfaces and lines are beings in one respect and non-beings in another respect.
lib. 3 l. 12 n. 11 Deinde cum dicit sed quoniam solvit propositam rationem: et dicit, quod quia Zeno proponendo tale principium speculatur onerose, idest ruditer et grosse, ita quod secundum ipsum non contingit aliquid esse indivisibile, oportet quod aliqua responsio praedictae rationi detur, et si non sit ad rem, sit tamen ad hominem. Dicemus autem quod unum etsi additum alteri non faciat maius, facit tamen plus. Et hoc sufficit ad rationem entis, quod faciat maius in continuis, et plus in discretis.	498. But this (272). Here he criticizes the argument which has been given. He says that Zeno, by proposing such an axiom, speculated “clumsily,” i.e., in an unskilled and rude manner, so that according to him there cannot be anything indivisible. And for this reason some answer must be given to the foregoing argument; and if not to the point at issue, at least to the man. Now we say that even though a unity when added to something else does not make it larger, it does cause it to be more. And it is sufficient for the notion of being that in the case of what is continuous it should make a thing larger, and that in the case of what is discrete it should make it more.
lib. 3 l. 12 n. 12 Deinde cum dicit sed quomodo ostendit difficultatem, quae adhuc remanet Platonicis post praedictam solutionem. Et inducit duas difficultates. Quarum prima est, quia Platonici ponebant, quod illud unum indivisibile, non solum est causa numeri, qui est pluralitas quaedam, sed etiam est causa magnitudinis. Si igitur detur, quod unum additum faciat plus, quod videtur sufficere ad hoc quod unum sit causa numeri, quomodo poterit esse quod ex tali uno indivisibili, aut ex pluribus talibus, fiat magnitudo, ut Platonici posuerunt? Simile enim hoc videtur, si aliquis ponat lineam ex punctis. Nam unitas est indivisibilis sicut et punctus.	499. Yet how will (273). Then he states the difficulty which still faces the Platonists after the above solution. And he advances two difficulties. The Ifirst of these is that the Platonists held that the one which is indivisible is the cause not only of number, which is a plurality, but also of continuous quantity. Therefore, if it is granted that when a one is added it makes a thing more, as would seem to suffice for the one which is the cause of number, how will it be possible for continuous quantity to come from an indivisible one of this kind, or from many such ones, as the Platonists held? For this would seem to be the same thing as to hold that a line is composed of points. For unity is indivisible just as a point is.
lib. 3 l. 12 n. 13 Secundam difficultatem ponit ibi at vero et dicit: si quis existimet ita, quod numerus sit effectus ex uno indivisibili, et ex aliquo alio quod non sit unum, sed participet unum sicut quaedam materialis natura, ut quidam dicunt; nihilominus remanet quaerendum propter quid, et per quem modum illud, quod fit ex illo uno formali et alia natura materiali, quae dicitur non unum, quandoque est numerus, quandoque autem est magnitudo. Et praecipue si illud non unum materiale sit inaequalitas, quae significatur per magnum, et sit eadem natura. Non enim est manifestum quomodo ex hac inaequalitate quasi materia et uno formali fiant numeri; neque etiam quomodo ex aliquo numero formali et hac inaequalitate quasi materiali fiant magnitudines. Ponebant enim Platonici quod ex primo uno et ex prima dualitate fiebat numerus, ex quo numero et a qua inaequalitate materiali fiebat magnitudo.	500. But even if someone (274) Here he gives the second difficulty. He says that if anyone were to think that the situation is such that number is the result of the indivisible one and of something else which is not one, but participates in the one as a kind of inaterial nature, as some say, the question would still remain why and how that which comrs from the one as form and from another material nature, which is called the not-one, is sometimes a number and sometimes a continuous quantity. The difficulty would be most acute if that material not-one were inequality, as is implied in the continuously extended, and were to be the same reality. For it is not clear how numbers come from this inequality as matter and from the one as form; nor again is it clear how continuous quantities come from some number as form and from this inequality as matter. For the Platonists held that number comes from a primary one and a primary two, and that from this number and material inequality continuous quantity is produced.
lib. 3 l. 12 n. 14 Huius autem dubitationis solutio ab Aristotele in sequentibus traditur. Quod enim sit aliquod separatum, quod sit ipsum unum et ens, infra in duodecimo probabit, ostendens unitatem primi principii omnino separati, quod tamen non est substantia omnium eorum quae sunt unum, sicut Platonici putabant, sed est omnibus unitatis causa et principium. Unum autem, secundum quod dicitur de aliis rebus, dicitur dupliciter. Uno modo secundum quod convertitur cum ente: et sic unaquaeque res est una per suam essentiam, ut infra in quarto probabitur, nec aliquid addit unum supra ens nisi solam rationem indivisionis. Alio modo dicitur unum secundum quod significat rationem primae mensurae, vel simpliciter, vel in aliquo genere. Et hoc quidem si sit simpliciter minimum et indivisibile, est unum quod est principium et mensura numeri. Si autem non sit simpliciter minimum et indivisibile, nec simpliciter, sed secundum positionem erit unum et mensura, ut as in ponderibus, et diesis in melodiis, et mensura pedalis in lineis: et ex tali uno nihil prohibet componi magnitudinem: et hoc determinabit in decimo huius. Sed quia Platonici aestimaverunt idem esse unum quod est principium numeri, et quod convertitur cum ente; ideo posuerunt unum quod est principium numeri, esse substantiam cuiuslibet rei, et per consequens numerum, inquantum ex pluribus substantialibus principiis, rerum compositarum substantia consistit vel constat. Hanc autem quaestionem diffusius pertractabit in tertiodecimo et quartodecimo.	501. The solution of this problem is treated by Aristotle in the following books. For the fact that there is something separate, which is itself one and being, he will prove below in Book XII (2553), when he establishes the oneness of the first principle which is separate in an absolute sense, although it is not the substance of all things which are one, as the Platonists thought, but is the cause and principle of the unity of all things. And insofar as unity is predicated of other things it is used in two ways. In one way it is interchangeable with being, and in this way each thing is one by its very essence, as is proved below in Book IV (548); and unity in this sense adds nothing to being except merely the notion of undividedness. Unity is used in another way insofar as it has the character of a first measure, either in an absolute sense or with respect to some genus. And this unity if it is both a minimum in the absolute sense and indivisible, is the one which is the principle and measure of number. But if it is not both a minimum in an absolute sense and indivisible, it will not be a unit and measure in an absolute sense, as a pound in the case of weights and a half-tone in the case of melodies, and a foot in the case of lengths. And nothing prevents continuous quantities from being composed of this kind of unity. He will establish this in Book X (1940) of this work. But because the Platonists thought that the one which is the principle of number and the one which is interchangeable with being are the same, they therefore held that the one which is the principle of number is the substance of each thing, and consequently that number, inasmuch as it is composed of many substantial principles, makes up or comprises the substance of composite things. But he will treat this question at greater length in Books XIII and XIV of this work.