Authors/Thomas Aquinas/metaphysics/liber3

Commentary on the Metaphysics Book 3. With English translation by John P. Rowan, Chicago, 1961

Lecture 1

Latin	English
lib. 3 l. 1 n. 1 Postquam philosophus in secundo libro ostendit modum considerandae veritatis, hic procedit ad veritatis considerationem. Et primo procedit modo disputativo, ostendens ea quae sunt dubitabilia circa rerum veritatem. Secundo incipit determinare veritatem. Et hoc in quarto libro, qui incipit ibi, est scientia quaedam quae speculatur. Prima autem pars dividitur in partes duas. In prima dicit de quo est intentio, in secunda exequitur propositum, ibi, est autem dubitatio prima quod et cetera. Circa primum duo facit. Primo enim dicit de quo est intentio. Secundo rationem assignat suae intentionis, ibi, inest autem investigare volentibus et cetera. Dicit ergo primo, quod ad hanc scientiam, quam quaerimus de primis principiis, et universali veritate rerum, necesse est ut primum aggrediamur ea de quibus oportet, dubitare, antequam veritas determinetur. Sunt autem huiusmodi dubitabilia propter duas rationes. Vel quia antiqui philosophi aliter susceperunt opinionem de eis quam rei veritas habeat, vel quia omnino praetermiserunt de his considerare.	338. Having indicated in Book II (331) the method of considering the truth, the Philosopher now proceeds with his study of the truth. First he proceeds disputatively, indicating those points which are open to question so far as the truth of things is concerned. Second (529), he begins to establish what is true, and he does this in Book IV, which begins: “There is a certain science.” The first part is divided into two sections. In the first, he states what he intends to do. In the second (346), he proceeds to do it (“The first problem”). In regard to the first he does two things. First, he states what he intends to do. Second (339), he gives the reasons for this (“Now for those”). He says first, then, that with a view to this science which we are seeking about first principles and what is universally true of things, we must attack, first of all, those subjects about which it is necessary to raise questions before the truth is established. Now there are disputed points of this kind for two reasons, either because the ancient philosophers entertained a different opinion about these things than is really true, or because they completely neglected to consider them.
lib. 3 l. 1 n. 2 Deinde cum dicit inest autem assignat quatuor rationes suae intentionis: et primo dicit quod volentibus investigare veritatem contingit prae opere, idest ante opus bene dubitare, idest bene attingere ad ea quae sunt dubitabilia. Et hoc ideo quia posterior investigatio veritatis, nihil aliud est quam solutio prius dubitatorum. Manifestum est autem in solutione corporalium ligaminum, quod ille qui ignorat vinculum, non potest solvere ipsum. Dubitatio autem de aliqua re hoc modo se habet ad mentem, sicut vinculum corporale ad corpus, et eumdem effectum demonstrat. Inquantum enim aliquis dubitat, intantum patitur aliquid simile his qui sunt stricte ligati. Sicut enim ille qui habet pedes ligatos, non potest in anteriora procedere secundum viam corporalem, ita ille qui dubitat, quasi habens mentem ligatam, non potest ad anteriora procedere secundum viam speculationis. Et ideo sicut ille qui vult solvere vinculum corporale, oportet quod prius inspiciat vinculum et modum ligationis, ita ille qui vult solvere dubitationem, oportet quod prius speculetur omnes difficultates et earum causas.	339. Now for those (177). Here he gives four arguments in support of this thesis: First, he says that for those who wish to investigate the truth it is “worth the while,” i.e., worth the effort, “to ponder these difficulties well,” i.e., to examine carefully those matters which are open to question. This is necessary because the subsequent study of truth is nothing else than the solution of earlier difficulties. Now in loosening a physical knot it is evident that one who is unacquainted with this knot cannot loosen it. But a difficulty about some subject is related to the mind as a physical knot is to the body, and manifests the same effect. For insofar as the mind is puzzled about some subject, it experiences something similar to those who are tightly bound. For just as one whose feet are tied cannot move forward on an earthly road, in a similar way one who is puzzled, and whose mind is bound, as it were, cannot move forward on the road of speculative knowledge. Therefore, just as one who wishes to loosen a physical knot must first of all inspect the knot and the way in which it is tied, in a similar way one who wants to solve a problem must first survey all the difficulties and the reasons for them.
lib. 3 l. 1 n. 3 Deinde cum dicit et quia quaerentes secundam rationem ponit; et dicit quod illi qui volunt inquirere veritatem non considerando prius dubitationem, assimilantur illis qui nesciunt quo vadant. Et hoc ideo, quia sicut terminus viae est illud quod intenditur ab ambulante, ita exclusio dubitationis est finis qui intenditur ab inquirente veritatem. Manifestum est autem quod ille qui nescit quo vadat, non potest directe ire, nisi forte a casu: ergo nec aliquis potest directe inquirere veritatem, nisi prius videat dubitationem.	340. [This is also necessary] (178). Here he gives the second argument. He says that those who wish to investigate the truth without first considering the problem are like those who do not know where they are going. This is true for this reason, that, just as the terminus of a journey is the goal intended by one who travels on foot, in a similar way the solution of a problem is the goal intended by one who is seeking the truth. But it is evident that one who does not know where he is going cannot go there directly, except perhaps by chance. Therefore, neither can one seek the truth directly unless he first sees the problem.
lib. 3 l. 1 n. 4 Deinde cum dicit et adhuc tertiam rationem ponit; et dicit, quod sicut ex hoc quod aliquis nescit quo vadat, sequitur quod quando pervenit ad locum quem intendebat nescit utrum sit quiescendum vel ulterius eundum, ita etiam quando aliquis non praecognoscit dubitationem, cuius solutio est finis inquisitionis, non potest scire quando invenit veritatem quaesitam, et quando non; quia nescit finem suae inquisitionis, qui est manifestus ei qui primo dubitationem cognovit.	341. Again, one would (179). Here he gives the third argument. He says that, just as one who is ignorant of where he is going does not know whether he should stop or go further when he reaches his appointed goal, in a similar way one who does not know beforehand the problem whose solution marks the terminus of his search cannot know when he finds the truth which he is seeking and when not. For he does not know what the goal of his investigations is, but this is evident to one who knew the problem beforehand.
lib. 3 l. 1 n. 5 Et quia quartam rationem ponit, quae sumitur ex parte auditoris. Auditorem enim oportet iudicare de auditis. Sicut autem in iudiciis nullus potest iudicare nisi audiat rationes utriusque partis, ita necesse est eum, qui debet audire philosophiam, melius se habere in iudicando si audierit omnes rationes quasi adversariorum dubitantium.	342. Furthermore (180). He gives the fourth argument, which is taken from the viewpoint of a judge. For a judge must pass judgment on the things which he hears. But just as one can pass judgment in a lawsuit only if he hears the arguments on both sides, in a similar way one who has to pass judgment on a philosophy is necessarily in a better position to do so if he will hear all the arguments, as it were, of the disputants.
lib. 3 l. 1 n. 6 Est autem attendendum, quod propter has rationes consuetudo Aristotelis fuit fere in omnibus libris suis, ut inquisitioni veritatis vel determinationi praemitteret dubitationes emergentes. Sed in aliis libris singillatim ad singulas determinationes praemittit dubitationes: hic vero simul praemittit omnes dubitationes, et postea secundum ordinem debitum determinat veritatem. Cuius ratio est, quia aliae scientiae considerant particulariter de veritate: unde et particulariter ad eas pertinet circa singulas veritates dubitare: sed ista scientia sicut habet universalem considerationem de veritate, ita etiam ad eam pertinet universalis dubitatio de veritate; et ideo non particulariter, sed simul universalem dubitationem prosequitur.	343. Now it must be noted that it was for these reasons that Aristotle was accustomed, in nearly all his works, to set forth the problems which emerge before investigating and establishing what is true. But while in other works Aristotle sets down the problems one at a time in order to establish the truth about each one, in this work he sets forth all the problems at once, and afterwards in the proper order establishes the things that are true. The reason for this is that other sciences consider the truth in a particular way, and therefore it belongs to them to raise problems of a particular kind about individual truths. But just as it belongs to this science to make a universal study of truth, so also does it belong to it to discuss all the problems which pertain to the truth. Therefore it does not discuss its problems one at a time but all at once.
lib. 3 l. 1 n. 7 Potest etiam et alia esse ratio; quia dubitabilia, quae tangit, sunt principaliter illa, de quibus philosophi aliter opinati sunt. Non autem eodem ordine ipse procedit ad inquisitionem veritatis, sicut et alii philosophi. Ipse enim incipit a sensibilibus et manifestis, et procedit ad separata, ut patet infra in septimo. Alii vero intelligibilia et abstracta voluerunt sensibilibus applicare. Unde, quia non erat eodem ordine determinaturus, quo ordine processerunt alii philosophi, ex quorum opinionibus dubitationes sequuntur; ideo praeelegit primo ponere dubitationes omnes seorsum, et postea suo ordine dubitationes determinare.	344. There can also be another reason [why Aristotle proceeds in this way], namely, that those problems on which he touches are chiefly those about which the philosophers have held different opinions. However, he does not proceed to investigate the truth in the same order as the other philosophers did. For he begins with things which are sensible and evident and proceeds to those which are separate from matter, as is evident below in Book VII (1566), whereas the other philosophers wanted to apply intelligible and abstract principles to sensible things. Hence, because he did not intend to establish the truth in the same order as that followed by the other philosophers, and from whose views these problems arise, he therefore decided to give first all the problems in a separate section, and afterwards to solve these problems in their proper order.
lib. 3 l. 1 n. 8 Tertiam assignat Averroes dicens hoc esse propter affinitatem huius scientiae ad logicam, quae tangitur infra in quarto. Et ideo dialecticam disputationem posuit quasi partes principales huius scientiae.	345. Averroes gives another reason [for Aristotle’s procedure]. He says that Aristotle proceeds in this way because of the relationship of this science to logic, which will be touched on below in Book IV (588); and therefore he made dialectical discussion a principal part of this science.

Lecture 2

Latin	English
lib. 3 l. 2 n. 1 Secundum ea quae praedixit philosophus, incipit praemittere dubitationes determinationi veritatis; et dividit in duas partes. In prima ponit dubitationes. In secunda causas dubitationum, inducendo rationes ad singulas dubitationes, ibi, primum ergo de quibus in primis dicimus et cetera. Dictum est autem in secundo libro, quod prius oportet quaerere modum scientiae, quam ipsam scientiam. Et ideo primo ponit dubitationes pertinentes ad modum considerationis huius scientiae. Secundo ponit dubitationes pertinentes ad prima principia, de quibus est ista scientia, ut in primo libro dictum est; et hoc ibi, et utrum principia et elementa et cetera. Ad modum autem scientiae huius duo pertinent, ut in secundo dictum est: scilicet consideratio causarum, ex quibus scientia demonstrat; et iterum res de quibus scientia considerat. Unde circa primum duo facit. Primo movet dubitationem pertinentem ad considerationem causarum. Secundo movet multas dubitationes pertinentes ad ea de quibus est scientia, ibi, et utrum substantiae principia et cetera. Dicit ergo quod prima dubitatio est quam dubitando proposuimus in fine secundi libri, qui est quasi prooemium ad totam scientiam, scilicet utrum consideratio causarum quatuor, secundum quatuor genera, pertineat ad unam scientiam, vel ad multas et diversas. Et hoc est quaerere utrum unius scientiae, et praecipue huius, sit demonstrare ex omnibus causis, vel magis diversae scientiae ex diversis demonstrent.	346. Following out his announced plan, the Philosopher begins to set down the problems which are encountered in establishing the truth; and he divides this into two parts. In the first, he gives these problems; and in the second (369), he gives the reasons for these problems, by indicating the arguments on either side of the question (“Therefore let us discuss”). Now it was stated in Book II (335) that it is necessary to seek the method of a science before seeking the science itself. Therefore he gives, first, the problems which pertain to this science’s method of investigation. Second (355), he gives the problems which pertain to the first principles with which this science deals, as has been stated in Book I (36) (“And we must inquire”). Now a science is concerned with two things, as was said in Book II (336), namely, a study of the causes by which it demonstrates and the things with which it deals. Hence in regard to the first point he does two things. First, he presents a problem concerning the investigation of causes. Second (347), he presents several problems concerning the things with which this science deals (“And there is also the problem”) He says, then, that the first problem is one which we proposed in the issues raised at the end of Book II (336), which is, so to speak, the prologue to the whole of science, i.e., whether a study of the four causes in their four classes belongs to one science or to many different sciences And this is to ask whether it belongs to one science, and especially to this science, to demonstrate by means of all the causes, or rather whether some sciences demonstrate by one cause and some by another.
lib. 3 l. 2 n. 2 Deinde cum dicit et utrum movet dubitationes de his, de quibus considerat ista scientia. Et primo inquirit de quibus considerat ista scientia sicut de substantiis. Secundo de quibus considerat ista scientia sicut de accidentibus, ibi, et utrum circa substantias et cetera. Circa primum duo facit. Primo multiplicat, quaestiones ex parte ipsius scientiae, quae est de substantia. Secundo ex parte substantiarum ipsarum, ibi, et hoc idem quoque et cetera. Circa primum ponit tres quaestiones. Supposito enim ex his quae in primo libro dicta sunt, quod ista scientia consideret principia prima, prima quaestio hic erit utrum ad hanc scientiam solum pertineat cognoscere prima principia substantiae, aut etiam ad hanc scientiam pertineat considerare de primis principiis demonstrationis, ex quibus omnes scientiae demonstrant; ut puta quod haec scientia consideret utrum contingat unum et idem simul affirmare et negare, vel non: et similiter de aliis demonstrationis principiis primis et per se notis.	347. And there is also the problem (182). Here he raises problems about the things which this science considers. First, he inquires about the things which this science considers about substances; and second (350), about substances themselves (“It is also necessary”). In regard to the first he raises three questions. For if it is supposed, from what was said in Book I (35), that this science considers first principles, the first question here will be whether it belongs to this science to know only the first principles of substances, or also to consider the first principles of demonstration, by means of which all sciences demonstrate. For example, should this science consider whether it is possible to affirm and deny one and the same thing at the same time or not? And the same thing applies to the other first and self-evident principles of demonstration.
lib. 3 l. 2 n. 3 Secunda quaestio est, si ista scientia est considerativa substantiae sicut primi entis, utrum sit una scientia considerans omnes substantias, vel sint plures scientiae de diversis substantiis. Videtur enim quod de pluribus substantiis debeant esse plures scientiae.	348. And if this science considers substance as the primary kind of being, the second question is whether there is one science which considers all substances, or whether there are many sciences which consider different substances. For it seems that there should be many sciences which consider many substances.
lib. 3 l. 2 n. 4 Tertia quaestio est, si sint plures scientiae de pluribus substantiis, utrum omnes sint cognatae, idest unius generis, sicut geometria et arithmetica sunt in genere mathematicae scientiae, vel non sint unius generis, sed quaedam earum sint in genere sapientiae, quaedam vero in aliquo alio genere, puta in genere scientiae naturalis, vel mathematicae. Videtur enim secundum primum aspectum, quod non sint unius generis, cum substantiae materiales et immateriales non eodem modo cognoscantur.	349. And if there are many sciences which consider many substances, the third question is whether all are “cognate,” i.e., whether all belong to one class, as geometry and arithmetic belong to the class of mathematical science, or whether they do not, but some to the class of wisdom and some to another class, for example, to the class of natural philosophy or to that of mathematical science. For according to the first point of view it seems that they do not belong to one class, since material and immaterial substances are not known by the same method.
lib. 3 l. 2 n. 5 Deinde cum dicit et hoc idem multiplicat quaestiones ex parte substantiae; et ponit duas quaestiones: quarum prima est, utrum dicendum sit, quod sint solum substantiae sensibiles, ut antiqui naturales posuerunt, vel etiam praeter substantias sensibiles sint aliae substantiae immateriales et intelligibiles, ut posuit Plato.	350. It is also necessary (183). Here he adds to the number of questions about substance; and he does this by raising two questions. The first question is whether sensible substances alone must be held to exist, as the philosophers of nature claimed, or whether there are in addition to sensible substances other immaterial and intelligible substances, as Plato claimed.
lib. 3 l. 2 n. 6 Secunda quaestio est, si sunt aliquae substantiae separatae a sensibilibus, utrum sint unicae, idest unius generis tantum, aut sint plura genera talium substantiarum, sicut quidam attendentes duplicem abstractionem, scilicet universalis a particulari, et formae mathematicae a materia sensibili, posuerunt utrumque genus subsistere. Et ita ponebant substantias separatas quae sunt universalia abstracta subsistentia, inter quae et substantias sensibiles particulares posuerunt mathematica subsistentia separata, scilicet numeros, magnitudines et figuras. De istis igitur quaestionibus sicut nunc moventur, perscrutandum est inferius; primo quidem disputative, secundo determinando veritatem.	351. And if there are some substances separate from sensible things, the second question is whether “they are unique,” i.e., whether they belong only to one class, or whether there are many classes of such substances. For certain men, understanding that there is a twofold abstraction, namely, of the universal from the particular, and of the mathematical form from sensible matter, held that each class is self-subsistent. Thus they held that there are separate substances which are subsisting abstract universals, and between these and particular sensible substances they placed the objects of mathematics—numbers, continuous quantities, and figures—which they regarded as separate subsisting things. Concerning the questions which have now been raised, then, it is necessary to investigate them below. He does this, first, by arguing both sides of the question, and, second, by determining its truth.
lib. 3 l. 2 n. 7 Deinde cum dicit et utrum circa inquirit utrum consideratio huius scientiae de accidentibus sit. Et ponit tres quaestiones. Quarum prima est, utrum speculatio huius scientiae sit solum circa substantias, propter hoc quod dicitur philosophia substantiae: aut etiam sit circa ea quae per se substantiis accidunt, eo quo ad eamdem scientiam pertinere videtur ut consideret subiectum et per se accidentia subiecti.	352. There is also the problem (184). Here he asks whether this science’s investigations extend to accidents; and he raises three questions. The first is whether this science, seeing that it is called the philosophy of substance, speculates about substance alone, or whether it also speculates about the proper accidents of substance; for it seems to be the office of the same science to consider a subject and the proper accidents of that subject. Q. 7: How does it differ from logic in considering these things?
lib. 3 l. 2 n. 8 Secunda quaestio est, utrum haec scientia consideret de quibusdam quae videntur esse per se accidentia entis, et consequi omnia entia: scilicet de eodem et diverso, simili et dissimili, et de contrarietate, et de priori et posteriori, et omnibus aliis huiusmodi, de quibus dialectici tractant, qui habent considerationem de omnibus. Sed tamen de huiusmodi perscrutantur, non ex necessariis, sed ex probabilibus. Ex una enim parte videtur quod cum sint communia, pertineant ad philosophum primum. Ex alia parte videtur quod ex quo dialectici ista considerant, quorum est ex probabilibus procedere, quod non pertineat ad considerationem ipsius philosophi cuius est demonstrare.	353. The second question is whether this science considers certain things which seem to be proper accidents of being and which belong to all beings, namely, sameness and difference, likeness and unlikeness, contrariety, priority, and posteriority, and all others of this kind which are treated by the dialecticians, who deal with all things. However, they do not examine such things according to necessary premises but according to probable ones. For from one point of view it seems that, since these accidents are common ones, they pertain to first-philosophy; but from another point of view it seems that, since they are considered by the dialecticians, whose office it is to argue from Probabilities, an examination of them does not belong to the consideration of the philosopher, whose office it is to demonstrate.
lib. 3 l. 2 n. 9 Tertia quaestio est, cum ad ista communia accidentia entis quaedam per se consequantur, utrum ad philosophum pertineat circa unumquodque horum solum considerare quid est, aut etiam illa quae consequuntur ad ipsa, puta utrum unum uni sit contrarium.	354. And since certain proper attributes naturally flow from these common accidents of being, the third question is whether it is the function of the philosopher to consider in regard to the common accidents only their quiddity or also their properties; for example, whether there is one opposite for each one.

Lecture 3

Latin	English
lib. 3 l. 3 n. 1 Postquam philosophus movit quaestiones pertinentes ad modum considerandi huius scientiae, hic movet quaestiones pertinentes ad res de quibus ista scientia considerat. Et quia ista scientia considerat de principiis primis, ut in primo dictum est, ideo movet hic quaestiones de principiis rerum. Prima autem rerum principia ponebantur et species et mathematica. Unde primo movet quaestiones pertinentes ad species. Secundo quaestiones pertinentes ad mathematica, ibi, adhuc autem utrum numeri, aut longitudines et cetera. Circa primum duo facit. Primo quaerit quae sunt principia. Secundo qualia sunt, ibi, amplius autem utrum principia numero aut specie determinata et cetera. Quia vero principia ponebantur universalia separata, primo quaeritur utrum universalia sint principia. Secundo utrum res separatae sint principia, ibi, maxime vero quaerendum est et cetera. Circa primum ponit duas quaestiones; quarum prima est, utrum genera sint principia et elementa rerum, aut ea in quae sicut in ultima dividitur quodcumque singulare existens. Et ratio huius dubitationis est, quia elementum est ex quo primo componitur res, et in quod ultimo dividitur. Invenimus autem duplicem modum compositionis et divisionis: unum scilicet secundum rationem, prout species resolvuntur in genera. Et secundum hoc videntur genera esse principia et elementa, ut Plato posuit. Alio modo secundum naturam sicut corpora naturalia componuntur ex igne et aere et aqua et terra, et in haec resolvuntur. Et propter hoc naturales posuerunt esse prima principia elementa.	355. Having raised questions pertaining to the method of investigation which this science uses, the Philosopher now raises questions pertaining to the things which this science considers. And since this science considers first principles, as has been stated in Book I (35), he therefore raises here questions pertaining to the principles of things. Now both the Forms and the objects of mathematics were held to be the first principles of things. Therefore, first, he raises questions concerning the Forms; and second (366), concerning the objects of mathematics (“And in addition to these”). In regard to the first he does two things. First, he asks what things are principles; and second (361), what sort of beings they are (“Further, we must inquire”). And since separate universals were held to be the principles of things, he asks, first, whether universals are the principles of things; and second (357), whether separate entities are the principles of things (“But most of all”). Concerning the first he asks two questions. The first is whether genera constitute the principles and elements of things, or the ultimate parts into which each individual thing is dissolved. This question arises because an element is that of which a thing is first composed and into which it is ultimately dissolved. Now we find a twofold mode of composition and dissolution. One has to do with the intelligible constitution, in which species are resolved into genera, and according to this mode genera seem to be the principles and elements of things, as Plato claimed. The other mode of composition and dissolution has to do with the real order; for example, natural bodies are composed of fire, air, water and earth, and are dissolved into these. It was for this reason that the natural philosophers claimed that the elements constitute the first principles of things.
lib. 3 l. 3 n. 2 Secunda quaestio est, supposito quod genera sint principia rerum, utrum principia sint universalia dicta de individuis, scilicet species specialissimae, quas genera appellat secundum Platonicorum consuetudinem, quia continent sub se plura individua, sicut genera plures species; aut magis sint principia prima generalissima, ut puta quid sit magis principium, utrum animal vel homo, qui est principium quoddam secundum Platonicos, et magis vere existens quam singulare. Oritur autem haec dubitatio propter duas divisiones rationis. Quarum una est secundum quam genera dividimus in species. Alia vero est secundum quam species resolvimus in genera. Semper enim videtur illud quod est ultimus terminus divisionis esse primum principium et elementum in componendo.	356. And assuming that genera are the principles of things, the second question is whether the principles of things are to be identified with the universals which are predicated of individual things, i.e., the lowest species, which he calls genera after the usage of the Platonists, because the lowest species contain under themselves many individuals just as genera contain many species; or whether it is rather the first and most common genera that constitute principles, for example, which of the two is more of a principle, animal or man; for man is a principle according to the Platonists, and is more real than any singular man. Now this problem arises because of two divisions which reason makes. One of these is that whereby we divide genera into species, and the other is that whereby we resolve species into genera. For it seems that whatever is the last term in a process of division is always the first principle and element in a process of composition.
lib. 3 l. 3 n. 3 Deinde cum dicit maxime vero quaerit de principiis ex parte separationis: et movet quatuor quaestiones, quarum prima est, cum primi naturales posuerint solum causam materialem, utrum aliquid aliud praeter materiam sit causa secundum se, aut non.	357. But most of all (186). Here he inquires whether separate entities are the principles of things; and he raises four questions. For since the first philosophers of nature posited only a material cause, the first question is whether besides matter there is anything else that is a cause in the proper sense or not.
lib. 3 l. 3 n. 4 Secunda quaestio est, supposito quod aliquid praeter materiam sit causa, utrum illud sit separabile a materia, sicut posuit Plato, aut sicut posuit Pythagoras.	358. And granted that there is some other cause besides matter, the second question is whether it is separable from matter, as Plato held, or as Pythagoras held.
lib. 3 l. 3 n. 5 Tertia quaestio est, si est aliquid separabile a materia, utrum sit unum tantum, sicut posuit Anaxagoras, aut plura numero sicut posuit Plato et ipse Aristoteles.	359. And if there is something separable from matter, the third question is whether it is a single thing, as Anaxagoras claimed, or many, as Plato and Aristotle himself claimed.
lib. 3 l. 3 n. 6 Quarta quaestio est, utrum aliquid sit praeter synolon, id est simul totum, aut nihil; aut in quibusdam sit aliquid, et in quibusdam non: et qualia sint in quibus sunt et qualia in quibus non. Exponit autem quid sit synolon vel simul totum, scilicet quando praedicatur aliquid de materia. Ad cuius intellectum considerandum est quod Plato posuit hominem et equum et ea quae sic praedicantur, esse quasdam formas separatas. Per hoc autem homo praedicatur de Socrate vel Platone, quod materia sensibilis participat formam separatam. Socrates ergo vel Plato dicitur synolon vel simul totum, quia constituitur per hoc quod materia participat formam separatam. Et est quasi quoddam praedicatum de materia. Quaerit ergo philosophus hic utrum quod quid est individui, sit aliquid aliud praeter ipsum individuum, vel non: aut etiam in quibusdam est aliud et in quibusdam non aliud. Quam quidem quaestionem philosophus determinabit in septimo.	360. The fourth question is whether there is anything “besides the synolon,” i.e., the concrete whole, or nothing; or whether there is something in certain cases and not in others; and what kind of things they are in those cases in which there is something else, and what kind of things they are in those in which there is not. And he explains what a synolon or concrete whole is; i.e., it is matter when something is predicated of it. Now in order to understand this we must note that Plato claimed that man and horse, and universals which are predicated in this way, are certain separate Forms; and that man is predicated of Socrates or Plato by reason of the fact that sensible matter participates in a separate Form. Hence Socrates or Plato is called a synolon or concrete whole, because each is constituted as a result of matter participating in a separate form. And each is, as it were, a kind of predicate of matter. Hence the Philosopher asks here whether the whatness of the individual thing is something else in addition to the individual thing itself, or not; or also whether it is something rise in the case of some things and not in that of others. The Philosopher will answer this question in Book VII (7356).
lib. 3 l. 3 n. 7 Deinde cum dicit amplius autem movet quaestiones circa modum existendi principiorum. Et quia ens dividitur per unum et multa, per actum et potentiam, primo quaerit quomodo sint principia secundum unitatem et multitudinem. Secundo quomodo sint secundum actum et potentiam, ibi, et potestate aut actu. Circa primum movet quatuor quaestiones: quarum prima est, utrum principia sint determinata secundum numerum, aut secundum speciem. Puta quia dicimus tria esse principia naturae. Potest autem intelligi, vel quia sunt determinata secundum numerum, ita scilicet quod sola una numero forma sit principium naturae, et sola una numero materia et privatio. Et potest intelligi quod sit determinata secundum speciem, ita, scilicet, quod sint multa principia materialia quae conveniant in specie materialis principii, et sic de aliis. Et quia quidam philosophorum assignabant causas formales, sicut Platonici, quidam autem solas materiales, sicut antiqui naturales, addit quod ista quaestio habet locum in rationibus, idest in causis formalibus, et in subiecto, idest in causis materialibus.	361. Further, we must inquire (187). Here he raises questions about the way in which principles exist. And since being is divided by the one and many, and by act and potency, he asks, first, whether these principles are one or many; and second (365), whether they are actual or potential (“Again, we must inquire”). In regard to the first he asks four questions: Q. 12 The first is whether the principles of things are limited in number or in kind; as we say, for example, that there are three principles of nature. Now the statement that they are limited in number can mean that the principle of nature is numerically a single form and a single matter and privation. And the statement that they are limited in kind can mean that there are many material principles which have in common the specific nature of material principle, and so on for the rest. And since some of the philosophers, such as the Platonists, attributed formal causes to things, while others, such as the ancient natural philosophers, attributed only material causes to things, he adds that this question is applicable both “in the intelligible structures,” i.e., in formal causes, “and in the underlying subject,” i.e., in material causes.
lib. 3 l. 3 n. 8 Secunda quaestio est, utrum corruptibilium et incorruptibilium sint eadem principia aut diversa. Et si sint diversa, utrum omnia sint incorruptibilia, vel corruptibilium principia sint corruptibilia et incorruptibilium incorruptibilia.	362. (2) The second question is whether the principles of corruptible and of incorruptible things are the same or different. And if they are different, whether all are incorruptible, or whether the principles of corruptible things are corruptible and those of incorruptible things are incorruptible.
lib. 3 l. 3 n. 9 Tertia quaestio est, utrum unum et ens significent ipsam substantiam rerum et non aliquid aliud additum supra substantiam rerum, sicut dicebant Pythagorici et Platonici, vel non significent ipsam substantiam rerum, sed sit aliquid aliud subiectum unitati et entitati, scilicet ignis aut aer, aut aliquid aliud huiusmodi, ut antiqui naturales posuerunt. Hanc autem quaestionem dicit esse difficillimam et maxime dubitabilem, quia ex ista quaestione dependet tota opinio Platonis et Pythagorae, qui ponebant numeros esse substantiam rerum.	363. (3) The third question is whether unity and being signify the very substance of things and not something added to the substance of things, as the Pythagoreans and Platonists claimed; or whether they do not signify the substance of things, but something else is the subject of unity and being, for example, fire or air or something else of this kind, as the ancient philosophers of nature held. Now he says that this question is the most difficult and most puzzling one, because on this question depends the entire thought of Plato and Pythagoras, who held that numbers are the substance of things.
lib. 3 l. 3 n. 10 Quarta quaestio est, utrum principia rerum sint sicut quaedam universalia, vel sicut aliqua singularia, idest utrum ea quae ponuntur esse principia habeant rationem principii secundum rationem universalem, vel secundum quod unumquodque eorum est aliquid et singulare.	364. The fourth question is whether the principles of things are “somehow universals or are in some sense singular things,” i.e., whether those things which are held to be principles have the character of a principle in the sense of a universal intelligible nature, or according as each is a particular and singular thing.
lib. 3 l. 3 n. 11 Deinde cum dicit et potestate quaerit utrum principia sint secundum potentiam vel secundum actum. Et haec quaestio maxime videtur pertinere ad principia materialia. Potest enim esse dubitatio, utrum primum materiale principium sit aliquod corpus in actu, ut ignis aut aer, ut antiqui naturales posuerunt, aut aliquid existens in potentia tantum, ut Plato posuit. Et quia motus est actus existentis in potentia, et est quodammodo medium inter potentiam et actum, ideo adiungit aliam quaestionem, utrum principia sint causae rerum solum secundum motum, sicut naturales posuerunt sola principia motus, vel materialia, vel efficientia: vel etiam sint principia aliter quam per motum, sicut Plato posuit per quamdam participationem huius sensibilia ab immaterialibus causari. Has autem quaestiones ideo se movisse dicit, quia magnam dubitationem habent, ut patet ex discordia philosophorum circa eas.	365. Again, we must inquire (188). Here he asks whether these principles exist potentially or actually. This question seems to refer especially to material principles; for it can be a matter of dispute whether the first material principle is some actual body, such as fire or air, as the ancient philosophers of nature held, or something which is only potential, as Plato held. And since motion is the actualization of something in potency, and is, in a sense, midway between potentiality and actuality, he therefore adds another question: whether the principles of things are causes only in reference to motion, as the philosophers of nature posited only principles of motion, either material or efficient, or also whether they are principles which act in some other way than by motion, as Plato claimed that sensible things are caused by immaterial entities by a certain participation in these. Futhermore, he says that these questions have been raised because they present the greatest difficulty, as is clear from the manner in which the philosophers have disagreed about them.
lib. 3 l. 3 n. 12 Deinde cum dicit adhuc autem movet quaestiones pertinentes ad mathematica, quae quidem principia rerum ponuntur: et movet duas quaestiones. Quarum prima est, utrum numeri et longitudines et figurae et puncta sint quaedam substantiae, ut Pythagorici vel Platonici posuerunt; vel non, sicut posuerunt naturales.	366. And in addition to these (189). Here he raises questions concerning the objects of mathematics, which are posited as the principles of things. He raises two questions. The first is whether numbers, lengths, figures and points are somehow substances, as the Pythagoreans or Platonists held, or whether they are not, as the philosophers of nature held.
lib. 3 l. 3 n. 13 Secunda quaestio est, si sunt substantiae, utrum sint separatae a sensibilibus, ut posuerunt Platonici, aut in sensibilibus, ut Pythagorici.	367. And if they are substances, the second question is whether they are separate from sensible things, as the Platonists held, or exist in sensible things, as the Pythagoreans held.
lib. 3 l. 3 n. 14 Moventur autem quaestiones istae tamquam disputandae infra et determinandae: quia in his non solum difficile est veritatem inquirere, sed etiam non est facile bene dubitare de eis, inveniendo scilicet probabiles rationes dubitationis.	368. Now these questions are raised as problems which must be debated and settled below, because in these matters it is not only difficult to discover the truth, but it is not even easy to debate the matter adequately by finding probable arguments for either side of the question.

Lecture 4

Latin	English
lib. 3 l. 4 n. 1 Postquam philosophus movit quaestiones, quae faciunt dubitationem in ista scientia, hic incipit de eis disputare; et dividitur in tres partes. In prima disputat de quaestionibus pertinentibus ad considerationem huius scientiae. In secunda de quaestionibus pertinentibus ad substantias, ibi, amplius autem utrum sensibiles substantiae et cetera. In tertia parte de quaestionibus pertinentibus ad principia substantiarum, ibi, et de principiis utrum oporteat genera et elementa et cetera. Circa primum tria facit. Primo enim disputat de consideratione huius scientiae quantum ad causas per quas demonstratur. Secundo quantum ad prima demonstrationis principia, ibi, at vero de principiis demonstrationis et cetera. Tertio quantum ad ipsas substantias, ibi, totaliter quae substantiarum utrum una est et cetera. Circa primum duo facit. Primo enim resumit quaestionem de qua disputare intendit, concludens ex ipso enumerationis ordine, quod primo disputandum est de istis, de quibus primum dictum est in enumeratione quaestionum, utrum scilicet ad unam scientiam vel ad plures pertineat speculari omnia genera causarum; ut sic ordo disputationis ordini quaestionum motarum respondeat.	369. Having raised the questions which cause difficulty in this science, Aristotle begins here to treat them dialectically. This is divided into three parts. In the first part, he treats the questions which pertain to the method of investigation of this science. In the second (403), he treats the questions which pertain to substances (“Furthermore, there is”). In the third (423), he treats the questions which pertain to the principles of substances (“Concerning the principles”). In regard to the first he does three things. First, he argues dialectically about this science’s method of investigation, with reference to the causes by means of which it demonstrates; second (387), with reference to the first principles of demonstration (“But insofar”); and third (393), with reference to substances themselves (“And there is the problem”). In regard to the first he does two things. First, he takes up again the question about which he plans to argue dialectically, concluding from the order in which the questions have been listed that it is necessary first to debate those issues which were stated first in the list of questions, namely, whether it is the function of one science or of many to investigate all the classes of causes; so that in this way the order of argument corresponds to the order in which the questions have been raised.
lib. 3 l. 4 n. 2 Secundo ibi unius enim ponit rationes ad quaestionem; et circa hoc tria facit. Primo enim ponit rationem ad ostendendum, quod considerare omnia genera causarum non pertineat ad unam scientiam. Secundo movet alteram quaestionem: supposito quod ad diversas scientias pertineat diversa genera causarum considerare, cuius causae consideratio pertinet ad philosophum primum. Et disputat ad diversas quaestionis partes; et hoc, ibi, at vero si scientiae causarum sunt plures et cetera. Tertio ex hac disputatione secunda concludit conclusionem primarum rationum, ibi, quapropter videtur alterius esse scientiae et cetera. Circa primum ponit duas rationes; dicens, quod cum unius scientiae sit considerare contraria, quomodo erit unius scientiae considerare principia, cum non sint contraria? Quae quidem ratio si secundum superficiem consideretur, nullius videtur esse momenti. Videtur enim procedere ex destructione antecedentis, ac si sic argumentaretur: si principia sunt contraria, sunt unius scientiae: ergo, si non sunt contraria, non sunt unius scientiae.	370. For how will it be (191). Second, he gives the arguments relating to this question; and in regard to this he does three things. First (191), he gives an argument for the purpose of showing that it is not the office of a single science to consider all the classes of causes. Second (193:C 376), assuming that it belongs to different sciences to consider the different classes of causes, he asks which class of cause it is that is investigated by first philosophy. He argues on both sides of this question (“But on the other hand”). Third (197:C 386), he draws from this second dispute the conclusion of the first arguments (“But-with regard to”). In regard to the first (191) he gives two arguments. He says that since it belongs to one science to consider contraries, how will it belong to one science to consider principles since they are not contrary? This view, if it is considered superficially, seems to be of no importance; for it appears to follow from the destruction of the antecedent, as if one were to argue thus: if principles are contraries, they belong to one science; therefore, if they are not contraries, they do not belong to one science.
lib. 3 l. 4 n. 3 Posset ergo dici, quod philosophus in his disputationibus non solum probabilibus rationibus utitur, sed etiam interdum sophisticis, ponens rationes quae ab aliis inducebantur. Sed non videtur esse rationabile, quod in tanta re tantus philosophus tam frivolam et parum apparentem rationem induxisset. Unde aliter dicendum est, quod si quis recte consideret naturam diversorum, quae ad eamdem scientiam pertinent, quaedam pertinent ad unam scientiam secundum sui diversitatem, quaedam vero secundum quod reducuntur ad aliquod unum. Multa quidem igitur alia diversa inveniuntur pertinere ad unam scientiam, secundum quod reducuntur ad aliquod unum; puta, ut ad unum totum, vel ad unam causam, vel ad unum subiectum. Sed contraria et quaelibet opposita pertinent ad unam scientiam secundum se ipsa, eo quod unum est ratio cognoscendi alterum. Et ex hoc efficitur ista propositio probabilis, quod omnia diversa, quae sunt contraria, pertineant ad unam scientiam. Unde sequeretur, si principia sunt diversa et non sunt contraria, quod non pertineant ad unam scientiam.	371. Therefore it can be said that in these disputes the Philosopher not only uses probable arguments but sometimes also uses sophistical ones when he gives arguments introduced by others. But it does not seem reasonable that in such an important matter so great a Philosopher would have introduced an argument which is both trifling and insignificant. Hence a different explanation must be given, namely, that if one rightly considers the nature of the various things which belong to the same science, some belong to a single science-insofar as they are different, but others insofar as they are reduced to some one thing. Hence many other different things are found to belong to one science insofar as they are reduced to one thing, for example, to one whole, one cause, or one subject. But contraries and all opposites belong essentially to one science by reason of the fact that one is the means of knowing the other. And from this comes this probable proposition that all different things which are contraries belong to one science. Therefore, if principles were different and were not contraries, it would follow that they would not belong to one science.
lib. 3 l. 4 n. 4 Deinde cum dicit amplius autem secundam rationem ponit, quae talis est. Diversorum pertinentium ad unam scientiam, quaecumque scientia considerat unum considerat et aliud, ut patet in contrariis, quorum diversitas secundum se pertinet ad unam scientiam non per reductionem ad aliquid aliud unum: sed non quaecumque scientia considerat unam causam considerat omnes causas: ergo consideratio omnium causarum non pertinet ad unam scientiam.	372. Furthermore, in the case of (192). Here he gives the second argument, which runs thus. In the case of different things which belong to one science, whatever science considers one also considers another. This is evident in the case of contraries, which are different and belong essentially to one science without being reduced to some other unity. But not every science which considers one cause considers all causes. Therefore the study of all the causes does not belong to a single science.
lib. 3 l. 4 n. 5 Minorem probat per hoc, quod diversae scientiae sunt de diversis entibus; et multa entia sunt, quibus non possunt attribui omnes causae. Quod primo manifestat in causa, quae dicitur, unde principium motus: non enim videtur, quod possit esse principium motus in rebus immobilibus. Ponuntur autem quaedam entia immobilia, et praecipue secundum Platonicos ponentes numeros et substantias paratas. Unde, si qua scientia de his considerat, non potest considerare de causa quae est unde principium motus.	373. He proves the minor premise thus: Different sciences deal with different beings, and there are many beings to which all the causes cannot be assigned. He makes this dear, first, with regard to that cause which is called the source of motion; for it does not seem that there can be a principle of motion in immobile things. Now certain immobile things are posited, especially by the Platonists, who claim that numbers and substances are separate entities. Hence, if any science considers these, it cannot consider the cause which is the source of motion.
lib. 3 l. 4 n. 6 Secundo manifestat idem de causa finali, quae habet rationem boni. Boni enim natura non videtur posse inveniri in rebus immobilibus, si hoc concedatur, quod omne quod est bonum secundum se et propter suam naturam, est finis. Et hoc modo causa est, inquantum propter ipsam et causa eius omnia fiunt et sunt. Dicit autem, quod est bonum secundum se et propter suam naturam, ad excludendum bonum utile, quod non dicitur de fine, sed magis de eo quod est ad finem. Unde quae sic solum dicuntur bona inquantum sunt utilia ad aliud, non sunt bona secundum se et propter suam naturam. Sicut potio amara non est secundum se bona, sed solum secundum quod ordinatur ad finem sanitatis, quae est secundum se bona: finis autem, et cuius causa fit aliquid, videtur esse terminus alicuius actus: omnes autem actiones videntur esse cum motu. Ergo videtur sequi, quod in rebus immobilibus non possit esse hoc principium, scilicet causa finalis, quae habet rationem boni. Et quia quae sunt per se existentia absque materia, necesse est quod sint immobilia, ideo non videtur esse possibile, quod sit aliquid autoagathon, idest per se bonum, ut Plato ponebat. Omnia enim immaterialia et non participata vocabat per se existentia, sicut ideam hominis vocabat hominem per se, quasi non participatum in materia. Unde et per se bonum dicebat id quod est sua bonitas non participata, scilicet primum principium omnium.	374. Second, he shows that the same thing is true of the final cause, which has the character of good. For it does not seem that the character of goodness can be found in immobile things, if it is conceded that everything which is good in itself and by reason of its own nature is an end. And it is a cause in the sense that all things come to be and exist because of it and for its sake. However, he says “everything which is good in itself and by reason of its own nature” in order to exclude the useful good, which is not predicated of the end but of the means to the end. Hence those things which are said to be good only in the sense that they are useful for something else arc not good in themselves and by reason of their own nature. For example, a bitter potion is not good in itself but only insofar as it is directed to the end, health, which is a good in itself. But an end, or that for the sake of which something comes to be, seems to be the terminus of an action. But all actions seem to involve motion. Therefore it seems to follow that this principle, i.e., the final cause, which has the character of goodness, cannot exist in immobile things. Further, since those things which exist of themselves apart from matter must be immobile, it therefore does not seem possible that “an autoagathon,” i.e., a good-in-itself, exists, as Plato held. For he called all immaterial and unparticipated things entities which exist of themselves, just as he called the Idea of man, man-in-himself, as though not something participated in matter. Hence he also called the good-in-itself that which is its own goodness unparticipated, namely, the first principle of all things.
lib. 3 l. 4 n. 7 Et ad hanc rationem confirmandam inducit quoddam signum. Ex hoc enim quod finis non potest esse in rebus immobilibus, videtur procedere quod in scientiis mathematicis, quae abstrahunt a materia et motu, nihil probatur per hanc causam, sicut probatur in scientia naturali, quae est de rebus mobilibus, aliquid per rationem boni. Sicut cum assignamus causam quare homo habet manus, quia per eas melius potest exequi conceptiones rationis. In mathematicis autem nulla demonstratio fit hoc modo, quod hoc modo sit quia melius est sic esse, aut deterius si ita non esset. Puta si diceretur quod angulus in semicirculo est rectus, quia melius est quod sic sit quam quod sit acutus vel obtusus. Et quia posset forte aliquis esse alius modus demonstrandi per causam finalem, puta si diceretur, si finis erit, necesse est id quod est ad finem praecedere: ideo subiungit, quod nullus omnino in mathematicis facit mentionem alicuius talium pertinentium ad bonum vel ad causam finalem. Propter quod quidam sophistae, ut Aristippus, qui fuit de secta Epicureorum, omnino neglexit demonstrationes quae sunt per causas finales, reputans eas viles ex hoc quod in artibus illiberalibus sive mechanicis, ut in arte tectonica, idest aedificatoria, et coriaria, omnium rationes assignantur ex hoc quod est aliquid melius vel deterius. In mathematicis vero, quae sunt nobilissimae et certissimae scientiae, nulla fit mentio de bonis et malis.	375. Moreover, with a view to strengthening this argument he introduces an example. For, from the fact that there cannot be an end in the case of immobile things, it seems to follow that in the mathematical sciences, which abstract from matter and motion, nothing is proved by means of this cause, as in the science of nature, which deals with mobile things, something is proved by means of the notion of good. For example, we may give as the reason why man has hands that by them he is more capable of executing the things which reason conceives. But in the mathematical sciences no demonstration is made in this way, that something is so because it is better for it to be so, or worse if it were not so; as if one were to say, for example, that the angle in a semi-circle is a right angle because it is better that it should be so than be acute or obtuse. And because there can be, perhaps, another way of demonstrating by means of the final cause (for example, if one were to say that, if an, end is to be, then what exists for the sake of an end must first be), he therefore adds that in the mathematical sciences no one makes any mention at all of any of those things which pertain to the good or to the final cause. And for this reason certain sophists, as Aristippus, who belonged to the Epicurean school, completely disregarded any demonstrations which employ final causes, considering them to be worthless in view of the fact that in the servile or mechanical arts, for example, in the “art of building,” i.e., in carpentry, and in that of “cobbling,” all things are explained on the grounds that something is better or worse; whereas in the mathematical sciences, which are the noblest and most certain of the sciences, no mention is made of things good and evil.
lib. 3 l. 4 n. 8 Deinde cum dicit at vero interponit aliam quaestionem: et primo proponit eam. Et habet duas partes. Prima enim pars quaestionis est. Si diversae causae considerentur a pluribus scientiis, ita quod altera scientia sit alterius causae considerativa, quae illarum debet dici scientia quae quaeritur? Idest philosophia prima? Utrum scilicet illa quae considerat causam formalem, aut quae considerat causam finalem, vel quae considerat aliquam aliarum? Secunda pars quaestionis est, si aliquae res sint quae habeant plures causas, quis maxime cognoscit rem illam eorum qui considerant illas causas?	376. But on the other hand (193). Here he interjects another question. First, he states this question, which has two parts. The first part of the question is this. If different causes are considered by many sciences, so that a different science considers a different cause, then which of these sciences should be called the one “that is being sought,” i.e., first philosophy? Is it the one which considers the formal cause, or the one which considers the final cause, or the one which considers one of the other causes? The second part of the question is this: If there are some things which have many causes, which one of those who consider those causes knows that subject best?
lib. 3 l. 4 n. 9 Secundo cum dicit contingit enim manifestat partem secundam quaestionis per hoc, quod una et eadem res invenitur, quae habet omnes modos causarum: sicut domus causa unde principium motus, est ars et aedificator. Id vero cuius causa vel finis causa domus est opus, idest usus eius, qui est habitatio. Causa vero sicut materia est terra, ex qua fiunt lateres et lapides. Causa vero sicut species vel forma, est ipsa ratio domus, quam artifex praeconceptam mente in materia ponit.	377. For it is possible (194). He clarifies the second part of the question by the fact that one and the same thing is found to have every type of cause. For example, in the case of a house the source of motion is the art and the builder; the reason, for which, or the final cause of the house, “is its function,” i.e., its use, which is habitation; its material cause is the earth, from which the walls and floor are made; and its specifying or formal cause is the plan of the house, which the architect, after first conceiving it in his mind, gives to matter.
lib. 3 l. 4 n. 10 Tertio ibi igitur ex reassumit quaestionem, scilicet quam dictarum scientiarum possumus vocare sapientiam, secundum ea quae de sapientia prius determinavimus in principio libri: utrum scilicet illam, quae considerat causam formalem, vel quae considerat causam finalem, vel aliquam aliarum causarum. Et ponit consequenter rationes ad singulas trium causarum: dicens, quod ratio quaedam videtur de qualibet scientia, idest quae est per quamcumque causam, quod appelletur nomine sapientiae. Et primo quantum ad scientiam quae est per causam finalem. Dictum est enim in principio libri, quod ista scientia, quae sapientia dicitur, est maxime principalis et ordinativa aliarum, quasi subditarum. Sic igitur inquantum sapientia est senior, idest prior ordine dignitatis, et principalior quadam auctoritate ordinandi alias, quia non est iustum quod aliae scientiae contradicant ei, sed ab ea accipiant sua principia, sicut ei servientes; videtur quod illa scientia, quae est finis et boni, idest quae procedit per causam finalem, sit digna nomine sapientiae. Et hoc ideo, quia omnia alia sunt propter finem, unde finis est quodammodo causa omnium aliarum causarum. Et sic scientia, quae procedit per causam finalem, est principalior. Cuius signum est, quod artes illae, ad quas pertinent fines, principantur et praecipiunt aliis artibus, sicut gubernatoria navifactivae. Unde, si sapientia est principalis et praeceptiva respectu aliarum, maxime videtur quod procedat per causam finalem.	378. Therefore from the things (195) Here he takes up again the question as to which of the aforesaid sciences we can call wisdom on the basis of the points previously established about wisdom at the beginning of this work (14:C 36), namely, whether it is the science which considers the formal cause, or the one which considers the final cause, or the one which considers one of the other causes. And he gives in order arguments relating to each of the three causes, saying that there seems to be some reason why “every oxie of the sciences,” i.e., any one which proceeds by means of any cause at all, should be called by the name of wisdom. First, he speaks of that science which proceeds by means of the final cause. For it was stated at the beginning of this work that this science, which is called wisdom, is the most authoritative one, and the one which directs others as subordinates. Therefore, inasmuch as wisdom “takes precedence,” i.e., is prior in the order of dignity and more influential in its authoritative direction of the other sciences (because it is not right that the others should contradict it but they should take their principles from it as its servants), it seems that that science “which deals with the end and the good,” i.e., the one which proceeds by means of the final cause, is worthy of the name of wisdom. And this is true because everything else exists for the sake of the end, so that in a sense the end is the cause of all the other causes. Thus the science which proceeds by means of the final cause is the most important one. This is indicated by the fact that those arts which are concerned with ends are more important than and prior to the other arts; for example, the art of navigation is more important than and prior to the art of ship-building. Hence, if wisdom is pre-eminent and regulative of the other sciences, it seems that it proceeds especially by means of the final cause.
lib. 3 l. 4 n. 11 Deinde cum dicit inquantum vero inducit rationem de causa formali. Dictum est enim in prooemio libri, quod sapientia est primarum causarum, et eius quod est maxime scibile, et quod est maxime certum. Et secundum hoc videtur quod sit substantiae, idest per causam formalem: quia inter diversos modos sciendi, magis dicimus scire illum qui scit aliquid esse, quam qui scit aliquid non esse. Unde et in posterioribus philosophus probat, quod demonstratio affirmativa est potior quam negativa. Inter eos autem, qui sciunt aliquid affirmare, unum alio magis dicimus scire. Sed inter omnes maxime dicimus scire illum, qui cognoscit quid est res, non autem qui scit quanta est, vel qualis, et quid possit facere vel pati. Sic igitur in cognoscendo ipsam rem absolute perfectissimum est scire quid est res, quod est scire substantiam rei. Sed etiam in aliis cognoscendis, puta proprietatibus rei, magis dicimus scire singula, de quibus sunt demonstrationes, quando etiam de ipsis accidentibus vel proprietatibus scimus quod quid est; quia quod quid est non solum invenitur in substantiis, sed etiam in accidentibus.	379. But insofar as wisdom (196). Here he introduces the arguments relating to the formal cause. For it was said in the prologue of this work (26:C 51) that wisdom is concerned with first causes and with whatever is most knowable and most certain. And according to this it seems to be concerned with “substance,” i.e., it proceeds by means of the formal cause. For among the different ways of knowing things, we say that he who knows that something exists, knows more perfectly than he who knows that it does not exist. Hence in the Posterior Analytics the Philosopher proves that an affirmative demonstration is preferable to a negative demonstration. And among those who know something affirmatively, we say that one knows more perfectly than another. But we say that he knows more perfectly than any of the others who knows what a thing is, and not he who knows how great it is, or what it is like, or what it can do or undergo. Therefore, to know a thing itself in the most perfect way absolutely is to know what it is, and this is to know its substance. But even in knowing other things, for example, a thing’s properties, we say that we know best every single thing about which there are demonstrations when we also know the whatness of their accidents and properties; because whatness is found not only in substance but also in accidents.
lib. 3 l. 4 n. 12 Et ponit exemplum de tetragonismo, idest quadratura superficiei aeque distantium laterum non quadratae, quam quadrare dicimur, cum invenimus quadratum ei aequale. Cum autem omnis superficies aeque distantium laterum et rectorum angulorum ex duabus lineis contineatur, quae rectum continent angulum, ita, quod totalis superficies nihil est aliud quam ductus unius earum in alia, tunc invenimus quadratum aequale superficiei praedictae, quando invenimus lineam quae sit media in proportione inter duas lineas praedictas. Puta, si linea a, ad lineam b se habet sicut linea b ad lineam c, quadratum lineae b est aequale superficiei, quae continetur in c et a, ut probatur in sexto Euclidis.	380. He gives the example of squaring, i.e., squaring a surface of equally distant sides which is not square but which we say we square when we find a square equal to it. But since every rectangular surface of equally distant sides is contained by the two lines which contain the right angle, so that the total surface is simply the product of the multiplication of one of these lines by the other, then we find a square equal to this surface when we find a line which is the proportional mean between these two lines. For example, if line A is to line B as line B is to line C, the square of line B is equal to the surface contained by C and A, as is proved in Book VI of Euclid’s Elements.
lib. 3 l. 4 n. 13 Et apparet manifeste in numeris. Sex enim est medium in proportione inter novem et quatuor. Novem enim se habet ad sex in proportione sesquialtera, et similiter sex ad quatuor. Quadratum autem senarii est trigintasex. Quod etiam perficitur ex ductu quaternarii in novenarium. Quater enim novem sunt trigintasex. Et simile est in omnibus aliis.	381. This becomes quite evident in the case of numbers. For 6 is the proportional mean between 9 and 4; for 9 is related to 6 in the ratio of 11/2 to 1, and so also is 6 to 4. Now the square of 6 is 36, which is also produced by multiplying 4 by 9; for 4 x 9 = 36. And it is similar in all other cases.
lib. 3 l. 4 n. 14 Deinde ponit rationem de causa movente circa generationes videmus enim quod circa generationes et actiones, et circa omnem transmutationem maxime dicimur aliquid scire quando cognoscimus principium motus, et quod motus nihil est aliud quam actus mobilis a movente, ut dicitur in tertio physicorum. Praetermittit autem de causa materiali, quia illa imperfectissime se habet ad hoc quod sit principium cognoscendi: non enim fit cognitio per id quod est in potentia, sed per id quod est in actu, ut infra in nono dicetur.	382. But with regard to processes (197) Here he gives an argument pertaining to the cause of motion. For in processes of generation and actions and in every change we see that we may say that we know a thing when we know its principle of motion, and that motion is nothing else than the actuality of something mobile produced by a mover, as is stated in the Physics, Book III. He omits the material cause, however, because that cause is a principle of knowing in the most imperfect way; for the act of knowing is not caused by what is potential but by what is actual, as is stated below in Book IX (805:C 1894)
lib. 3 l. 4 n. 15 His igitur positis ad secundam quaestionem pertinentibus, inducit rationem ex eisdem rationibus supra positis ad primam quaestionem, scilicet quod alterius scientiae sit considerare omnes istas causas, eo quod in diversis rebus diversae causae videntur habere principalitatem, sicut in mobilibus principium motus, in scibilibus quod quid est, finis autem in his quae ordinantur ad finem.	383. Then after having given those arguments which pertain to the second question, he introduces an argument which is based on the same reasons as were given above (191:C 370 ff.) in reference to the first question, namely, that it is the office of a different science to consider all these causes by reason of the fact that in different subject-matters different causes seem to have the principal role, for example, the source of motion in mobile things, the quiddity in demonstrable things, and the end in things which are directed to an end.
lib. 3 l. 4 n. 16 Hanc autem quaestionem Aristoteles in sequentibus expresse solvere non invenitur: potest tamen eius solutio ex his quae ipse inferius in diversis locis determinat, colligi. Determinat enim in quarto, quod ista scientia considerat ens inquantum est ens; unde et eius est considerare primas substantias, non autem scientiae naturalis, quia supra substantiam mobilem sunt aliae substantiae. Omnis autem substantia vel est ens per seipsam, si sit forma tantum; vel si sit composita ex materia et forma, est ens per suam formam; unde inquantum haec scientia est considerativa entis, considerat maxime causam formalem. Primae autem substantiae non cognoscuntur a nobis ut sciamus de eis quod quid est, ut potest aliqualiter haberi ex his quae in nono determinantur: et sic in earum cognitione non habet locum causa formalis. Sed quamvis ipsae sint immobiles secundum seipsas, sunt tamen causa motus aliorum per modum finis; et ideo ad hanc scientiam, inquantum est considerativa primarum substantiarum, praecipue pertinet considerare causam finalem, et etiam aliqualiter causam moventem. Causam autem materialem secundum seipsam nullo modo, quia materia non convenienter causa est entis, sed alicuius determinati generis, scilicet substantiae mobilis. Tales autem causae pertinent ad considerationem particularium scientiarum, nisi forte considerentur ab hac scientia inquantum continentur sub ente. Sic enim ad omnia suam considerationem extendit.	384. However, we do not find that Aristotle explicitly solves this question later on, though his solution can be ascertained from the things which he establishes below in different places. For in Book IV (533) he establishes that this science considers being as being, and therefore that it also belongs to it, and not to the philosophy of nature, to consider first substances; for there are other substances besides mobile ones. But every substance is either a being of itself, granted that it is only a form; or it is a being by its form, granted that it is composed of matter and form. Hence inasmuch as this science considers being, it considers the formal cause before all the rest. But the first substances are not known by us in such a way that we know what they are, as can be understood in some way from the things established in Book IX (1904); and thus in our knowledge of them the formal cause has no place. But even though they are immobile in themselves, they are nevertheless the cause of motion in other things after the manner of an end. Hence inasmuch as this science considers first substances, it belongs to it especially to consider the final cause and also in a way the efficient cause. But to consider the material cause in itself does not belong to it in any way, because matter is not properly a cause of being but of some definite kind of being, namely, mobile substance. However, such causes belong to the consideration of the particular sciences, unless perhaps they are considered by this science inasmuch as they are contained under being; for it extends its analysis to all things in this way.
lib. 3 l. 4 n. 17 His autem visis, rationes inductas facile est solvere. Primo enim nihil prohibet diversas causas ad hanc scientiam pertinere unam existentem, licet non sint contraria, quia reducuntur ad unum, scilicet ad ens commune, sicut dictum est. Similiter nihil prohibet, etsi non quaelibet scientia consideret omnes causas, quin aliqua scientia possit considerare omnes vel plures earum inquantum reducuntur ad aliquid unum. Sed specialiter descendendo, dicendum est, quod nihil prohibet in immobilibus considerari et principium motus, et finem sive bonum; in immobilibus inquam quae sunt tamen moventia sicut sunt primae substantiae: in his autem quae neque moventur nec movent, non est consideratio principii motus, nec finis sub ratione finis motus, quamvis possit considerari finis sub ratione finis alicuius operationis sine motu. Sicut si ponantur esse substantiae intelligentes non moventes, ut Platonici posuerunt, nihilominus tamen inquantum habent intellectum et voluntatem oportet ponere in eis finem et bonum, quod est obiectum voluntatis. Mathematica autem non moventur, nec movent, nec habent voluntatem. Unde in eis non consideratur bonum sub nomine boni et finis. Consideratur tamen in eis id quod est bonum, scilicet esse et quod quid est. Unde falsum est, quod in mathematicis non sit bonum, sicut ipse infra in nono probat.	385. Now when these things are seen it is easy to answer the arguments which have been raised. For, first, nothing prevents the different causes in this science from belonging to a single existing thing, even though they are not contraries, because they are reducible to one thing—being in general—as has been stated (384). And in a similar way, even though not every science considers all of the causes, still nothing prevents one science from being able to consider all of the causes or several of them insofar as they are reducible to some one thing. But to be more specific, it must be said that in the case of immobile things nothing prevents the source of motion and the end or good from being investigated. By immobile things I mean here those which are still causes of motion, as the first substances. However, in the case of those things which are neither moved cause motion there is no investigation of the source of motion, or of the end in the sense of the end of motion, although an end can be considered as the goal of some operation which does not involve motion. For if there are held to be intellectual substances which do not cause motion, as the Platonists claimed, still insofar as they have an intellect and will it is necessary to hold that they have an end and a good which is the object of their will. However, the objects of mathematics neither are moved nor cause motion nor have a will. Hence in their case the good is not considered under the name of good and end, although in them we do consider what is good, namely, their being and what they are. Hence the statement that the good is not found in the objects of mathematics is false, as he proves below in Book IX (1888) .
lib. 3 l. 4 n. 18 Ad quaestionem vero secundam iam patet responsio; quia ad hanc scientiam pertinet consideratio trium causarum, de quibus rationes inducit.	386. The reply to the second question is already clear; for a study of the three causes, about which he argued dialectically, belongs to this science.

Lecture 5

Latin	English
lib. 3 l. 5 n. 1 Postquam disputavit de prima quaestione quae erat de consideratione causarum, hic intendit disputare de consideratione principiorum demonstrationis, ad quam scientiam pertineat; et circa hoc tria facit. Primo movet quaestionem. Secundo disputat ad unam partem, ibi, unius igitur esse et cetera. Tertio disputat ad aliam partem, ibi, at vero si alia et cetera. Dicit ergo primo, quod dubitatio est de principiis demonstrationis, utrum considerare de his pertineat ad unam scientiam vel ad plures. Et exponit quae sunt demonstrationis principia. Et dicit, quod sunt communes conceptiones omnium ex quibus procedunt omnes demonstrationes, inquantum scilicet singula principia propriarum conclusionum demonstratarum habent firmitatem virtute principiorum communium. Et exemplificat de primis principiis maxime sicut quod necesse est de unoquoque aut affirmare aut negare. Et aliud principium est quod impossibile est idem simul esse et non esse. Est ergo haec quaestio, utrum haec principia et similia pertineant ad unam scientiam vel ad plures. Et si ad unam, utrum pertineant ad scientiam quae est considerans substantiam, vel ad aliam. Et si ad aliam, quam earum oportet nominare sapientiam vel philosophiam primam quam nunc quaerimus.	387. Having debated the first question which had to do with the study of causes, Aristotle’s intention here is to argue dialectically about the science which is concerned with the study of the first principles of demonstration; and in regard to this he does three things. First, he raises the question. Second (388), he argues one side of the question. Third (391), he argues on the other side of the question. Accordingly, he states, first, the problem relating to the first principles of demonstration, namely, whether the study of these principles belongs to one science or to many. Further, he explains what the principles of demonstration are, saying that they are the common conceptions of all men on which all demonstrations are based, i.e., inasmuch as the particular principles of the proper demonstrated conclusions derive their stability from these common principles. And he gives an example of first principles, especially this one, that everything must either be affirmed or denied [of some subject]. Another principle which he mentions is that it is impossible for the same thing both to be and not to be at the same time. Hence the question arises whether these principles and similar ones pertain to one science or to many. And if they pertain to one science, whether they pertain to the science which investigates substance or to another science. And if to another science, then which of these must be called wisdom, or first philosophy, which we now seek.
lib. 3 l. 5 n. 2 Deinde cum dicit unius igitur obiicit ad unam partem quaestionis, scilicet ad ostendendum quod non est unius scientiae considerare principia omnia, supple demonstrationis, et substantiam. Et ponit duas rationes: quarum prima talis est. Cum omnes scientiae utantur praedictis principiis demonstrationis; nulla ratio esse videtur quare magis pertineat ad unam quam ad aliam: nec etiam videtur rationabile, quod eorum consideratio pertineat ad omnes scientias, quia sic sequeretur quod idem tractaretur in diversis scientiis, quod esset superfluum. Videtur igitur relinqui, quod nulla scientia consideret de principiis istis: ergo per quam rationem non pertinet ad aliquam aliarum scientiarum tradere cognitionem de huiusmodi demonstrationis principiis, per eamdem rationem non pertinet ad scientiam cuius est considerare de substantia.	388. Now it would be (199). Here he argues one side of the question with a view to showing that it is not the office of one science to consider all first principles, i.e. the first principles of demonstration and substance. He gives two arguments, of which the first runs thus: since all sciences employ these principles of demonstration, there seems to be no reason why the study of them should pertain to one science rather than to another; nor again does it seem reasonable that they should be studied by all sciences, because then it would follow that the same thing would be treated in different sciences; but that would be superfluous. Hence it seems to follow that no science considers these principles. Therefore, for the very same reason that it does not belong to any of the other sciences to give us a knowledge of such principles, for this reason too it follows that it does not belong to the science whose function it is to consider substance.
lib. 3 l. 5 n. 3 Secunda ratio ponitur ibi simul autem, quae talis est. Modus de quo est cognitio in scientiis est duplex. Unus modus secundum quod de unoquoque cognoscitur quid est. Alius modus secundum quod cognitio per demonstrationem acquiritur. Primo autem modo non pertinet ad aliquam scientiam tradere cognitionem de principiis demonstrationis, quia talis cognitio principiorum praesupponitur ante omnes scientias. Quod enim unumquodque horum sit ens ex nunc novimus, idest statim a principio cognoscimus quid significent haec principia, per quorum cognitionem statim ipsa principia cognoscuntur. Et, quia talis cognitio principiorum inest nobis statim a natura, concludit, quod omnes artes et scientiae, quae sunt de quibusdam aliis cognitionibus, utuntur praedictis principiis tamquam naturaliter notis.	389. But at the same time (200). Here he gives the second argument, which runs thus. In the sciences there are two methods by which knowledge is acquired. One is that by which the whatness of each thing is known, and the other is that by which knowledge is acquired through demonstration. But it does not belong to any science to give us a knowledge of the principles of demonstration by means of the first method, because such knowledge of principles is assumed to be prior to all the sciences. For "we already know" what each one of them is, i.e., we know from the very beginning what these principles signify, and by knowing this the principles themselves are immediately known. And since such knowledge of principles belongs to us immediately, he concludes that all the arts and sciences which are concerned with other kinds of cognitions make use of these pinciples as things naturally known by us.
lib. 3 l. 5 n. 4 Similiter autem probatur, quod praedictorum principiorum cognitio non traditur in aliqua scientia per demonstrationem; quia si esset aliqua demonstratio de eis, oporteret tria tunc principia considerari; scilicet genus subiectum, passiones, et dignitates. Et ad huius manifestationem, subdit, quod impossibile est de omnibus esse demonstrationem: non enim demonstrantur subiecta, sed de subiectis passiones. De subiectis vero oportet praecognoscere an est et quid est, ut dicitur in primo posteriorum. Et hoc ideo, quia necesse est demonstrationem esse ex aliquibus, sicut ex principiis, quae sunt dignitates, et circa aliquod, quod est subiectum, et aliquorum, quae sunt passiones. Ex hoc autem statim manifestum est ex uno horum trium, quod dignitates non demonstrantur; quia oporteret quod haberent aliquas dignitates priores, quod est impossibile. Unde praetermisso hoc modo procedendi tamquam manifesto, procedit ex parte subiecti. Cum enim una scientia sit unius generis subiecti, oporteret quod illa scientia, quae demonstraret dignitates, haberet unum subiectum. Et sic oporteret, quod omnium scientiarum demonstrativarum esset unum genus subiectum, quia omnes scientiae demonstrativae utuntur huiusmodi dignitatibus.	390. But it is proved in the same way that a knowledge of these principles is not presented to us in any science by means of demonstration, because if there were demonstration of them, then three principles would have to be considered, namely, some subjectgenus, its properties and the axioms. In order to clarify this he adds that there cannot be demonstration of all things; for subjects are not demonstrated but properties are demonstrated of subjects. Concerning subjects, however, it is necessary to know beforehand whether they exist and what they are, as is stated in Book I of the Posterior Analytics. The reason is that demonstration must proceed from certain things as principles, which are the axioms, and be about something, which is the subject, and [be demonstration] of certain things, which are properties. Now according to this it is immediately evident of one of these three, i.e., the axioms, that they are not demonstrated, otherwise there would have to be certain axioms prior to the axioms; but this is impossible. Therefore, having dismissed this method of procedure as obvious, he proceeds to consider the subject-genus. For since one science has one subject-genus, then that science which would demonstrate axioms would have one subject-genus. Thus there would have to be one subjectgenus for all demonstrative sciences, because all demonstrative sciences use axioms of this kind.
lib. 3 l. 5 n. 5 Deinde cum dicit at vero obiicit ad aliam partem. Si enim dicatur, quod alia scientia sit, quae est de huiusmodi principiis, et alia, quae est de substantia, remanebit dubitatio quae ipsarum sit principalior et prior. Ex una enim parte dignitates sunt maxime universales, et principia omnium, quae traduntur in quibuscumque scientiis. Et secundum hoc videtur quod scientia, quae est de huiusmodi principiis, sit principalissima. Ex alia vero parte, cum substantia sit primum et principale ens; manifestum est, quod prima philosophia est scientia substantiae. Et si non est eadem scientia substantiae et dignitatum non erit de facili dicere cuius alterius sit considerare veritatem et falsitatem circa dignitates, si non est primi philosophi qui considerat substantiam.	391. But on the other hand (201). Here he argues the other side of the question. For if it is said that there is one science which deals with sucn principles, and another which deals with substance, the problem will remain as to which of these sciences is the more important and prior one. For, on the one hand, since the axioms are most universal and are the principles of everything that is treated in any of the sciences, it seems that the science which deals with such principles is the most important one. Yet, on the other hand, since substance is the first and principal kind of being, it is evident that first-philosophy is the science of substance. And if it is not the same science which deals with substance and with the axioms, it will not be easy to state to which of the other sciences it belongs to consider the truth and falsity of these axioms, i.e., if it does not belong to first philosophy, which considers substance.
lib. 3 l. 5 n. 6 Hanc autem quaestionem determinat philosophus in quarto huius; et dicit, quod ad philosophum potius pertinet consideratio dignitatum, inquantum ad ipsum pertinet consideratio entis in communi, ad quod per se pertinent huiusmodi principia prima, ut maxime apparet in eo quod est maxime primum principium, scilicet quod impossibile est idem esse et non esse. Unde omnes scientiae particulares utuntur huiusmodi principiis sicut utuntur ipso ente, quod tamen principaliter considerat philosophus primus. Et per hoc solvitur ratio prima. Secunda autem ratio solvitur per hoc, quod philosophus non considerat huiusmodi principia tamquam faciens ea scire definiendo vel absolute demonstrando; sed solum elenchice, idest contradicendo disputative negantibus ea, ut in quarto dicetur.	392. The Philosopher answers this question in Book IV (590) of this work. He says that the study of the axioms belongs chiefly to the [first] philosopher inasmuch as it pertains to him to consider being in general, to which first principles of this kind essentially belong, as is most evident in the case of the very first principle: it is impossible for the same thing both to be and not to be [at the same time]. Hence all the particular sciences use principles of this kind just as they use being itself, although it is the first philosopher who is chiefly concerned with this. And the first argument is solved in this way. But the second argument is solved thus: the [first] philosopher does not consider principles of this kind in such a way as to make them known by defining them or by demonstrating them in an absolute sense, but by refutation, i.e., by arguing disputatively against those who deny them, as is stated in Book IV (608).

Lecture 6

Latin	English
lib. 3 l. 6 n. 1 Postquam disputavit duas quaestiones pertinentes ad considerationem huius scientiae, hic disputat tertiam, quae est de consideratione substantiarum et accidentium. Et dividitur in partes duas, secundum quod circa hoc duas quaestiones disputat. Secunda incipit ibi, amplius autem utrum sensibiles substantiae et cetera. Circa primum tria facit. Primo movet quaestionem, quae est, utrum omnium substantiarum sit una scientia, aut plures scientiae considerent diversas substantias.	393. Having debated the questions the third question, which pertains to which pertain to the scope of investigation of this science, he now treats the study of substances and accidents. This is divided into two parts inasmuch as he discusses two questions on this point. The second (403) begins where he says, “Furthermore, there is.” In regard to the first he does three things. First, he raises the question whether there is one science that considers all substances, or whether there are many sciences that consider different substances.
lib. 3 l. 6 n. 2 Secundo ibi siquidem ergo obiicit ad primam partem; scilicet ad ostendendum quod una scientia sit de omnibus substantiis: quia si non esset una de omnibus substantiis, non posset assignari, ut videtur, cuius substantiae sit considerativa haec scientia, eo quod substantia, in quantum substantia, est principaliter ens. Unde non videtur quod magis pertineat ad considerationem principalis scientiae una substantia quam alia.	394. If there is not (203). Second, he argues the first side of the question with a view to showing that there is one science of all substances. For if there were not one science of all substances, then apparently it would be impossible to designate the substance which this science considers, because substance as substance is the primary kind of being. Hence it does not seem that one substance rather than another belongs to the consideration of the basic science.
lib. 3 l. 6 n. 3 Tertio ibi unam vero obiicit in contrarium, dicens quod non est rationabile ponere unam esse scientiam omnium substantiarum. Sequeretur enim quod esset una scientia demonstrativa de omnibus per se accidentibus. Et hoc ideo, quia omnis scientia demonstrativa aliquorum accidentium, speculatur per se accidentia circa aliquod subiectum: et hoc ex aliquibus conceptionibus communibus. Quia igitur scientia demonstrativa non speculatur accidentia nisi circa subiectum aliquod, sequitur quod ad eamdem scientiam pertineat considerare aliquod genus subiectum, ad quam pertineat considerare per se accidentia illius generis, et e converso, dummodo demonstratio fiat ex eisdem principiis.	395. but it is unreasonable (204). Third, he argues the other side of the question, saying that it is unreasonable to hold that there is one science of all substances. For it would follow that there would be one demonstrative science of all essential accidents. And this is true because every science which demonstrates certain accidents speculates about the essential accidents of some particular subject, and it does this from certain common conceptions. Therefore, since a demonstrative science considers the accidents only of some particular subject, it follows that the study of some subject-genus belongs to the same science that is concerned with the study of the essential accidents of that genus and vice versa, so long as demonstrations proceed from the same principles.
lib. 3 l. 6 n. 4 Sed quandoque contingit quod demonstrare quia ita est, per aliqua principia, pertinet ad aliquam scientiam, et demonstrare principia ex quibus demonstrabatur quia ita est, pertinet ad unam scientiam, quandoque quidem ad eamdem, quandoque vero ad aliam. Ad eamdem quidem, sicut geometria demonstrat, quod triangulus habet tres angulos aequales duobus rectis, per hoc quod angulus exterior trianguli est aequalis duobus interioribus sibi oppositis, quod tantum demonstrare pertinet ad geometriam. Ad aliam vero scientiam, sicut musicus probat quod tonus non dividitur in duo semitonia aequalia, per hoc quod proportio sesquioctava cum sit superparticularis, non potest dividi in duo aequalia. Sed hoc probare non pertinet ad musicum sed ad arithmeticum. Sic ergo patet, quod quandoque accidit diversitas in scientiis propter diversitatem principiorum, dum una scientia demonstrat principia alterius scientiae per quaedam altiora principia.	396. But sometimes it happens to be the function of some science to demonstrate from certain principles that a thing is so, and sometimes it happens to be the function of some science to demonstrate the principles from which it was demonstrated that a thing is so, sometimes to the same science and sometimes to a different one. An example of its being the function of the same science is seen in the case of geometry, which demonstrates that a triangle has three angles equal to two right angles in virtue of the principle that the exterior angle of a triangle is equal to the two interior angles opposite to it; for to demonstrate this belongs to geometry alone. And an example of its being the function of a different science is seen in the case of music, which proves that a tone is not divided into two equal semitones by reason of the fact that a ratio of 9 to 8, which is superparticular, cannot be divided into two equal parts. But to prove this does not pertain to the musician but to the arithmetician. It is evident, then, that sometimes sciences differ because their principles differ, so long as one science demonstrates the principles of another science by means of certain higher principles.
lib. 3 l. 6 n. 5 Sed supposita identitate principiorum non potest esse diversitas in scientiis, dummodo sint eadem accidentia et idem genus subiectum, quasi una scientia consideret subiectum, et eadem accidentia. Unde sequitur, quod scientia quae considerat substantiam consideret etiam accidentia; ita quod si sint plures scientiae considerantes substantias, erunt considerantes accidentia. Si vero una earum sola sit quae consideret substantias, una sola erit quae considerabit accidentia. Hoc autem est impossibile; quia sic sequeretur non esse nisi unam scientiam, cum nulla scientia sit quae non demonstret accidentia de aliquo subiecto: non ergo ad unam scientiam pertinet considerare omnes substantias.	397. But if it is assumed that the principles are identical, sciences could not differ so long as the accidents are the same and the subject-genus is the same, as if one science considered the subject and another its accidents. Hence it follows that that science which considers a substance will also consider its accidents, so that if there are many sciences which consider substances, there will be many sciences which consider accidents. But if there is only one science which considers substances, there will be only one science which considers accidents. But this is impossible, because it would then follow that there would be only one science, since there is no science which does not demonstrate the accidents of some subject. Therefore it is not the function of one science to consider all substances.
lib. 3 l. 6 n. 6 Haec autem quaestio determinatur in quarto huius, ubi ostenditur quod ad primam scientiam, ad quam pertinet considerare de ente inquantum est ens, pertinet considerare de substantia inquantum est substantia: et sic considerat omnes substantias secundum communem rationem substantiae; et per consequens ad eam pertinet considerare communia accidentia substantiae. Particularia vero accidentia quarumdam substantiarum pertinet considerare ad particulares scientias, quae sunt de particularibus substantiis; sicut ad scientiam naturalem pertinet considerare accidentia substantiae mobilis. Verumtamen in substantiis est etiam ordo: nam primae substantiae sunt substantiae immateriales. Unde et earum consideratio pertinet proprie ad philosophum primum. Sicut si non essent aliae substantiae priores substantiis mobilibus corporalibus, scientia naturalis esset philosophia prima, ut dicitur infra in sexto.	398. This is treated in Book IV (546) of this work, where it is shown that the examination of substance as substance belongs to the first science, whose province it is to consider being as being; and thus it considers all substances according to the common aspect of substance. Therefore it belongs to this science to consider the common accidents of substance. But it belongs to the particular sciences, which deal with particular substances, to consider the particular accidents of substances, just as it belongs to the science of nature to consider the accidents of mobile substance. However, among substances there is also a hierarchy, for the first substances are immaterial ones. Hence the study of them belongs properly to first-philosophy, just as the philosophy of nature would be first philosophy if there were no other substances prior to mobile corporeal substances, as is stated below in Book VI (1170).
lib. 3 l. 6 n. 7 Deinde cum dicit amplius autem ponit aliam quaestionem de consideratione substantiae et accidentis. Et circa hoc etiam tria facit. Primo movet quaestionem, quae est, utrum consideratio huius scientiae sit solum circa substantiam, aut etiam circa ea quae accidunt substantiis. Puta si dicamus quod lineae, superficies et solida sint quaedam substantiae, ut quidam posuerunt, quaeritur utrum eiusdem scientiae sit considerare ista, et per se accidentia horum, quae demonstrantur in scientiis mathematicis; aut alterius.	399. Further, there is the problem (205). Here he raises another question regarding the study of substance and accidents. Concerning this he does three things. First, he raises the question whether the investigation of this science is concerned with substance alone or also with the attributes that are accidents of substances. For example, if we say that lines, surfaces and solids are substances of some sort, as some held, the question arises whether it belongs to the same science to consider such things and also their proper accidents, which are demonstrated in the mathematical sciences, or whether it belongs to another science.
lib. 3 l. 6 n. 8 Secundo ibi nam si obiicit ad unam partem. Si enim eiusdem scientiae est considerare accidentia et substantias; cum scientia quae considerat accidentia sit demonstrativa accidentium, sequitur quod scientia quae considerat substantiam, sit demonstrativa substantiarum: quod est impossibile: cum definitio declarans substantiam, quae significat quod quid est, non demonstretur. Sic ergo non erit eiusdem scientiae substantias considerare et accidentia.	400. For if it is the concern (206). Second, he argues one side of the question. For if it belongs to the same science to consider accidents and substances, then, since a science which considers accidents demonstrates accidents, it follows that a science which considers substance demonstrates substances. But this is impossible; for the definition of a substance, which expresses the quiddity’ is indemonstrable. Hence it will belong to the same science to consider substances and accidents.
lib. 3 l. 6 n. 9 Tertio ibi si vero obiicit in contrarium: quia si diversae scientiae considerant substantiam et accidens, non erit assignare quae scientia speculetur accidentia circa substantiam, quia talis scientia considerabit utrumque, cum tamen hoc videatur ad omnes scientias pertinere: quia omnis scientia considerat per se accidentia circa subiectum, ut dictum est.	401. But if it is the concern (207). Third, he argues the other side of the question: if different sciences consider substance and accident, it will not be possible to state which science it is that speculates about the accidents of substance; because the science which would do this would consider both, although this would seem to pertain to all sciences; for every science considers the essential accidents of its subject, as has been explained.
lib. 3 l. 6 n. 10 Hanc autem quaestionem determinat philosophus in quarto huius; dicens, quod ad eam scientiam, ad quam pertinet considerare de substantia et ente, pertinet etiam considerare de per se accidentibus substantiae et entis. Non tamen sequetur quod eodem modo consideret utrumque, scilicet demonstrando substantiam, sicut demonstrat accidens; sed definiendo substantiam et demonstrando accidens inesse vel non inesse, ut plenius habetur in fine noni huius.	402. The Philosopher answers this question in Book IV (570) of this work, saying that it is also the office of that science which is concerned with the study of substance and being to consider the proper accidents of substance and being. Yet it does not follow that it would consider each in the same way, i.e., by demonstrating substance as it demonstrates accidents, but by defining substance and by demonstrating that accidents either belong to or do not belong to it, as is explained more fully at the end of Book IX (1895) of this work.

Lecture 7

Latin	English
lib. 3 l. 7 n. 1 Postquam disputavit philosophus quaestiones pertinentes ad considerationem huius scientiae, hic disputat quaestiones pertinentes ad ipsas substantias, de quibus principaliter considerat ista scientia. Et circa hoc tria facit. Primo movet quaestiones. Secundo ostendit unde accipi possint rationes ad unam partem, ibi, quomodo ergo dicimus et cetera. Tertio obiicit ad partem contrariam, ibi, multis autem modis habentibus difficultatem et cetera. Circa primum movet duas quaestiones: quarum prima est, utrum in universitate rerum solae substantiae sensibiles inveniantur, sicut aliqui antiqui naturales dixerunt, aut etiam inveniantur quaedam aliae substantiae, praeter sensibiles, sicut posuerunt Platonici.	403. Having debated the questions which pertain to the scope of this science, the Philosopher now treats dialectically the questions which pertain to the substances themselves with which this science is chiefly concerned. In regard to this he does three things. First, he raises the questions. Second (406), he indicates the source from which arguments can be drawn in support of one side of the question (“Now the way”). Third (407), he argues on the other side of the question (“But while they involve”). In regard to the first part of this division he raises two questions. The first question is whether sensible substances alone are found in the universe, as certain of the ancient philosophers of nature claimed, or whether besides sensible substances there are certain others, as the Platonists claimed.
lib. 3 l. 7 n. 2 Secunda quaestio est, supposito quod sint aliquae substantiae, praeter sensibiles, utrum illae substantiae sint unius generis, aut magis sint plura genera harum substantiarum. Utramque enim opinionem recipit. Quidam enim posuerunt praeter substantias sensibiles esse solas species separatas, idest per se hominem immaterialem, et per se equum: et sic de aliis speciebus. Alii vero posuerunt quasdam alias intermedias substantias inter species et sensibilia, scilicet mathematica, de quibus dicebant esse mathematicas scientias.	404. And assuming that besides sensible substances there are certain others, the second question is whether these substances belong to one genus, or whether there are many genera of substances. For he considers both opinions. For some thinkers held, that in addition to sensible substances there are only separate Forms, i.e., an immaterial man-in-himself and horse-in itself and so on for the other classes of things, whereas others held that there are certain other substances midway between the Forms and sensible things, namely, the objects of mathematics, with which they said the mathematical sciences deal.
lib. 3 l. 7 n. 3 Et huius ratio est, quia ponebant duplicem abstractionem rerum: puta abstractionem intellectus, qui dicitur abstrahere uno modo universale a particulari, iuxta quam abstractionem ponebant species separatas per se subsistentes. Alio modo formas quasdam a materia sensibili, in quarum scilicet definitione non ponitur materia sensibilis, sicut circulus abstrahitur ab aere. Iuxta quam ponebant mathematica abstracta, quae dicebant media inter species et sensibilia, quia conveniunt cum utrisque. Cum speciebus quidem, inquantum sunt separata a materia sensibili; cum sensibilibus autem, inquantum inveniuntur plura ex eis in una specie, sicut plures circuli et plures lineae.	405. The reason for this view is that they posited on the part of the intellect a twofold process of abstracting things: one whereby the intellect is said to abstract the universal from the particular, and according to this mode of abstraction they posited separate Forms, which subsist of themselves; and another [whereby the intellect is said to abstract] from sensible matter certain forms in whose definition sensible matter is not given, for example, the abstraction of circle from brass. And according to this mode of abstraction they posited separate objects of mathematics, which they said are midway between the Forms and sensible substances, because they have something in common with both: with the Forms inasmuch as they are separate from sensible matter, and with sensible substances inasmuch as many of them are found in one class, as many circles and many lines.
lib. 3 l. 7 n. 4 Deinde cum dicit quomodo ergo ostendit quomodo ad unam partem argumentari possit; et dicit quod hoc dictum est in primis sermonibus, idest in primo libro, quomodo species ponantur causae rerum sensibilium, et substantiae quaedam per se subsistentes. Unde ex his quae ibi dicta sunt in recitatione opinionis Platonis, accipi possunt rationes ad partem affirmativam.	406. Now the way in which (209). Then he shows how it is possible to argue one side of the question, saying that it has been stated “in our first discussions,” i.e., in Book I (69:C 151), how the Forms are held to be both the causes of sensible things and substances which subsist of themselves. Hence, from the things which have been said there in presenting the views of Plato, arguments can be drawn in support of the affirmative side of the question.
lib. 3 l. 7 n. 5 Deinde cum dicit multis autem obiicit ad partem negativam. Et primo ad ostendendum quod non sunt species separatae a sensibilibus. Secundo ad ostendendum quod non sunt mathematica separata, ibi, amplius autem siquis praeter species et cetera. Supra autem in primo libro multas rationes posuit contra ponentes species: et ideo illis rationibus praetermissis ponit quamdam rationem, quae videtur efficacissima; et dicit, quod cum positio ponentium species separatas, multas habeat difficultates, illud quod nunc dicetur non continet minorem absurditatem aliquo aliorum, scilicet quod aliquis dicat quasdam esse naturas praeter naturas sensibiles, quae sub caelo continentur. Nam caelum est terminus corporum sensibilium, ut in primo de caelo et mundo probatur. Ponentes autem species, non ponebant eas esse infra caelum, nec extra, ut dicitur in tertio physicorum. Et ideo convenienter dicit, quod ponebant quasdam naturas praeter eas quae sunt in caelo. Dicebant autem contrarias naturas esse easdem secundum speciem et rationem, et in istis sensibilibus: quinimmo dicebant illas naturas esse species horum sensibilium; puta quod homo separatus est humanitas hominis huius sensibilis, et quod homo sensibilis est homo participatione illius hominis. Hanc tamen differentiam ponebant inter ea, quia illae naturae immateriales sunt sempiternae, istae vero sensibiles sunt corruptibiles.	407. But while they involve (210). Here he advances reasons for the negative side. He does this, first (210), for the purpose of showing that the Forms are not separate from sensible things; and, second (211:C 410), for the purpose of showing that the objects of mathematics are not separate (“Furthermore, if anyone”). Now above in Book I (103:C 208) he gave many arguments against those who posited separate Forms; and, therefore, passing over those arguments, he gives the line of reasoning which seems most effective. He says (210) that while the position of those who posit separate Forms contains many difficulties, the position of those which is now given is no less absurd than any of the others, i.e., that someone should say that there are certain natures in addition to the sensible ones which are contained beneath the heavens. For the heavens constitute the limit of sensible bodies, as is proved in Book I of The Heavens and the World. But those who posited the Forms did not place them below the heavens or outside of it, as is stated in Book III of the Physics. Hence, in accordance with this he says that they posited certain other natures in addition to those which exist in the heavens. And they said that these opposite natures are the same as these sensible things both in kind and in their intelligible constitution, and that they exist in these sensible things; or rather they said that those natures are the Forms of these sensible things. For example, they said that a separate man constitutes the humanity of this particular man who is perceived by the senses, and that a man who is perceived by the senses is a man by participating in that separate man. Yet they held that these differ in this respect, that those immaterial natures are eternal, whereas these sensible natures are corruptible.
lib. 3 l. 7 n. 6 Et quod ponerent illas naturas easdem istis patet per hoc, quod sicut in istis sensibilibus invenitur homo, equus, et sanitas, ita in illis naturis ponebant hominem per se, idest sine materia sensibili, et similiter equum et sanitatem; et nihil aliud ponebant in substantiis separatis, nisi quod erant materialiter in sensibilibus. Quae quidem positio videtur esse similis positioni ponentium deos esse humanae speciei, quae fuit positio Epicureorum, ut Tullius dicit in libro de natura deorum. Sicut enim qui ponebant deos humanae speciei, nihil aliud fecerunt quam ponere homines sempiternos secundum suam naturam, ita et illi qui ponebant species nihil aliud faciunt quam ponunt res sensibiles sempiternas, ut equum, bovem, et similia.	408. That they hold those natures to be the same as these sensible things is clear from the fact that, just as man, horse, and health are found among sensible things, in a similar way they posited among these natures “a man-inhimself,” i.e., one lacking sensible matter; and they did the same with regard to horse and health. Moreover, they claimed that nothing else existed in the class of separate substances except [the counterpart of] what existed materially in the sensible world. This position seems to be similar to that of those who held that the gods are of human form, which was the position of the Epicureans, as Tully states in The Nature of the Gods. For just as those who held that the gods are of human form did nothing else than make men eternal in nature, in a similar way those who claimed that there are Forms do nothing else than hold that there are eternal sensible things, such as horse, ox, and the like.
lib. 3 l. 7 n. 7 Est autem valde absurdum, quod id quod secundum suam naturam est corruptibile, sit eiusdem speciei cum eo, quod per suam naturam est incorruptibile: quin potius corruptibile et incorruptibile differunt specie, ut infra dicetur in decimo huius. Potest tamen contingere quod id quod secundum suam naturam est corruptibile, virtute divina perpetuo conservetur in esse.	409. But it is altogether absurd that what is naturally corruptible should be specifically the same as what is naturally incorruptible; for it is rather the opposite that is true, namely, that corruptible and incorruptible things differ in kind to the greatest degree, as is said below in Book X (895:C 2137) Of this work. Yet it can happen that what is naturally corruptible is kept in being perpetually by Divine power.
lib. 3 l. 7 n. 8 Deinde cum dicit amplius autem obiicit contra ponentes mathematica media inter species et sensibilia. Et primo contra illos, qui ponebant mathematica media, et a sensibilibus separata. Secundo contra illos, qui ponebant mathematica, sed in sensibilibus esse, ibi, sunt autem et aliqui qui dicunt et cetera. Circa primum duo facit. Primo ponit rationes contra primam opinionem, secundo obiicit pro ea, ibi, at vero nec sensibilium et cetera. Contra primum obiicit tribus viis: quarum prima est, quod sicut scientia quaedam mathematica est circa lineam, ita etiam sunt quaedam mathematicae scientiae circa alia subiecta. Si igitur sunt quaedam lineae praeter lineas sensibiles, de quibus geometra tractat, pari ratione in omnibus aliis generibus, de quibus aliae scientiae mathematicae tractant, erunt quaedam praeter sensibilia. Sed hoc ponere ostendit esse inconveniens in duabus scientiis mathematicis.	410. Furthermore, if anyone (211). Then he argues against those who claimed that the objects of mathematics are midway between the Forms and sensible things. First (211:C 410), he argues against those who held that the objects of mathematics are intermediate entities and are separate from sensible things; and, second (215:C 417), against those who held that the objects of mathematics exist but exist in sensible things (“However, there are”). In regard to the first he does two things. First, he introduces arguments against the first position. Second (214:C 416), he argues in support of this position (“Nor again”). He brings up three arguments against the first position. The first argument is this: just as there is a mathematical science about the line, in a similar way there are certain mathematical sciences about other subjects. If, then, there are certain lines in addition to the sensible ones with which geometry deals, by the same token there will be, in all other classes of things with which the other mathematical sciences deal, certain things in addition to those perceived by the senses. But he shows that it is impossible to hold this with regard to two of the mathematical sciences.
lib. 3 l. 7 n. 9 Primo quidem in astrologia, quae est una scientiarum mathematicarum, cuius subiectum est caelum et caelestia corpora. Sequetur ergo secundum praedicta, quod sit aliud caelum praeter caelum sensibile, et similiter alius sol et alia luna, et similiter de aliis corporibus caelestibus. Sed hoc est incredibile: quia illud aliud caelum, aut est mobile, aut immobile. Si est immobile, hoc videtur esse irrationabile, cum videamus naturale esse caelo quod semper moveatur. Unde et astrologus aliquid considerat circa motum caeli. Dicere vero quod caelum sit separatum, et sit mobile, est impossibile, eo quod nihil separatum a materia potest esse mobile.	411. He does this, first, in the case of astronomy, which is one of the mathematical sciences and which has as its subject the heavens and the celestial bodies. Hence, according to what has been said, it follows that there is another heaven besides the one perceived by the senses, and similarly another sun and another moon, and so on for the other celestial bodies. But this is incredible, because that other heaven would be either mobile or immobile. If it were immobile, this would seem to be unreasonable, since we see that it is natural for the heavens to be always in motion. Hence the astronomer also makes some study of the motions of the heavens. But to say that a heaven should be both separate and mobile is impossible, because nothing separate from matter can be mobile.
lib. 3 l. 7 n. 10 Deinde ostendit idem esse inconveniens in aliis scientiis mathematicis, scilicet in perspectiva, quae considerat lineam visualem, et in harmonica idest musica, quae considerat proportiones sonorum audibilium. Impossibile est autem haec esse intermedia inter species et sensibilia; quia si ista sensibilia sint intermedia, scilicet soni et visibilia, sequetur etiam quod sensus sunt intermedii. Et cum sensus non sint nisi in animali, sequetur quod etiam animalia sint intermedia inter species et corruptibilia; quod est omnino absurdum.	412. Then he shows that the same view is unacceptable in the case of other mathematical sciences, for example, in that of perspective, which considers visible lines, and “in the case of harmonics,” i.e., in that of music, which studies the ratios of audible sounds. Now it is impossible that there should be intermediate entities between the Forms and sensible things; because, if these sensible things—sounds and visible lines—were intermediate entities, it would also follow that there are intermediate senses. And since senses exist only in an animal, it would follow that there are also intermediate animals between the Form animal, and corruptible animals; but this is altogether absurd.
lib. 3 l. 7 n. 11 Deinde cum dicit dubitabit autem secunda via talis est. Si in illis generibus, de quibus sunt scientiae mathematicae, invenitur triplex gradus rerum; scilicet sensibilia, species, et intermedia; cum de omnibus speciebus et omnibus sensibilibus videatur esse similis ratio, videtur sequi quod inter quaelibet sensibilia et suas species sunt aliqua media: unde remanet dubitatio ad quae rerum genera se extendant scientiae mathematicae. Si enim scientia mathematica, puta geometria, differt a geodaesia, quae est scientia de mensuris sensibilibus, in hoc solum quod geodaesia est de mensuris sensibilibus, geometria vero de intermediis non sensibilibus, pari ratione praeter omnes scientias, quae sunt de sensibilibus, erunt secundum praedicta quaedam scientiae mathematicae de intermediis: puta si scientia medicinalis est de quibusdam sensibilibus, erit quaedam alia scientia praeter scientiam medicinalem, et praeter unamquamque similem scientiam, quae erit media inter medicinalem quae est de sensibilibus, et medicinalem quae est de speciebus. Sed hoc est impossibile; quia cum medicina sit circa salubria, idest circa sanativa, si medicina est media, sequitur quod etiam sanativa sint media praeter sensibilia sanativa et praeter autosanum, idest per se sanum, quod est species sani separati: quod est manifeste falsum. Relinquitur ergo, quod istae scientiae mathematicae non sunt circa aliqua quae sunt media inter sensibilia et species separatas.	413. Again, one might (212). The second argument [which he uses against the possibility of the objects of mathematics being an intermediate class of entities separate from sensible things] is as follows. If in those classes of things with which the mathematical sciences deal there are three classes of things—sensible substances, Forms and intermediate entities, then since the intelligible structure of all sensible things and of all Forms seems to be the same, it appears to follow that there are intermediate entities between any sensible things at all and their Forms. Hence there remains the problem as to what classes of things are included in the scope of the mathematical sciences. For if a mathematical science such as geometry differs from geodesy, which is the science of sensible measurements, only in this respect that geodesy deals with sensible measurements, whereas geometry deals with intermediate things which are not sensible, there will be in addition to all the sciences which consider sensible things certain [other] mathematical sciences which deal with these intermediate entities. For example, if the science of medicine deals with certain sensible bodies, there will be in addition to the science of medicine, and any like science, some other science which will be intermediate between the science of medicine which deals with sensible bodies and the science of medicine which deals with the Forms. But this is impossible; for since medicine is about “healthy things,” i.e., things which are conducive to health, then it will also follow, if there is an intermediate science of medicine, that there will be intermediate health-giving things in addition to the health-giving things perceived by the senses and absolute health, i.e., health-in-itself, which is the Form of health separate from matter. But this is clearly false. Hence it follows that these mathematical sciences do not deal with certain things which are intermediate between sensible things and the separate Forms.
lib. 3 l. 7 n. 12 Deinde cum dicit similiter autem tertiam viam ponit, per quam destruitur quoddam, quod praedicta positio ponebat; quod scilicet esset aliqua scientia circa sensibiles magnitudines: et sic si inveniretur alia scientia circa magnitudines, ex hoc haberetur quod essent magnitudines mediae. Unde dicit, quod hoc non est verum quod geodaesia sit scientia sensibilium magnitudinum, quia sensibiles magnitudines sunt corruptibiles. Sequeretur ergo quod geodaesia esset de magnitudinibus corruptibilibus. Sed scientia videtur corrumpi corruptis rebus de quibus est. Socrate enim non sedente, iam non erit vera opinio qua opinabamur eum sedere. Sequeretur ergo quod geodaesia vel geosophia, ut alii libri habent, corrumpatur corruptis magnitudinibus sensibilibus; quod est contra rationem scientiae, quae est necessaria et incorruptibilis.	414. Similarly, neither (213). Then he gives the third argument [against the possibility of the objects of mathematics being an intermediate class]; and in this argument one of the points in the foregoing position is destroyed, namely, that there would be a science of continuous quantities which are perceptible; and thus, if there were another science of continuous quantities, it would follow from this that there would be intermediate continuous quantities. Hence he says that it is not true that geodesy is a science of perceptible continuous quantities, because such continuous quantities are corruptible. It would follow, then, that geodesy is concerned with corruptible continuous quantities. But it seems that a science is destroyed when the things with which it deals are destroyed; for when Socrates is not sitting, our present knowledge that he is sitting will not be true. Therefore it would follow that geodesy, or geosophics as other readings say, is destroyed when sensible continuous quantities are destroyed; but this is contrary to the character of science, which is necessary and incorruptible.
lib. 3 l. 7 n. 13 Posset tamen haec ratio ad oppositum induci: ut dicatur quod per hanc rationem intendit probare, quod nullae scientiae sunt de sensibilibus. Et ita oportet quod omnes scientiae vel sint de rebus mediis, vel sint de speciebus.	415. Yet this argument can be brought in on the opposite side of the question inasmuch as one may say that he intends to prove by this argument that there are no sciences of sensible things, so that all sciences must be concerned with either the intermediate entities or the Forms.
lib. 3 l. 7 n. 14 Deinde cum dicit at vero obiicit pro praedicta positione in hunc modum. De ratione scientiae est, quod sit verorum. Hoc autem non esset, nisi esset de rebus prout sunt. Oportet igitur res, de quibus sunt scientiae, tales esse, quales traduntur in scientiis. Sed sensibiles lineae non sunt tales, quales dicit geometra. Et hoc probat per hoc, quod geometria probat, quod circulus tangit regulam, idest rectam lineam solum in puncto, ut patet in tertio Euclidis. Hoc autem non invenitur verum in circulo et linea sensibilibus. Et hac ratione usus fuit Protagoras, destruens certitudines scientiarum contra geometras. Similiter etiam motus et revolutiones caelestes non sunt tales, quales astrologus tradit. Videtur enim naturae repugnare, quod ponantur motus corporum caelestium per excentricos, et epicyclos, et alios diversos motus, quos in caelo describunt astrologi. Similiter etiam nec quantitates corporum caelestium sunt tales, sicut describunt eas astrologi. Utuntur enim astris ut punctis, cum tamen sint corpora magnitudinem habentia. Unde videtur quod nec geometria sit de sensibilibus magnitudinibus, nec astrologia de caelo sensibili. Relinquitur igitur, quod sint de aliquibus aliis mediis.	416. Nor again will (214) Here he argues in support of this position, as follows: it belongs to the very notion of science that it should be concerned with what is true. But this would not be the case unless it were about things as they are. Therefore the things about which there are sciences must be the same in themselves as they are shown to be in the sciences. But perceptible lines are not such as geometry says they are. He proves this on the grounds that geometry demonstrates that a circle touches “the rule,” i.e., a straight line, only at a point, as is shown in Book III of Euclid’s Elements. But this is found to be true of a circle and a line in the case of sensible things. Protagoras used this argument when he destroyed the certainties of the sciences against the geometricians. Similarly, the movements and revolutions of the heavens are not such as the astronomers describe them; for it seems to be contrary to nature to explain the movements of the celestial bodies by means of eccentrics and epicycles and other different movements which the astronomers describe in the heavens. Similarly, neither are the quantities of the celestial bodies such as the astronomers describe them to be, for they use stars as points even though they are still bodies having extension. It seems, then, that geometry does not deal with perceptible continuous quantities, and that astronomy does not deal with the heaven which we perceive. Hence it remains that these sciences are concerned with certain other things, which arc intermediate.
lib. 3 l. 7 n. 15 Deinde cum dicit sunt autem obiicit contra aliam positionem. Et primo ponit intentum. Secundo inducit rationes ad propositum, ibi, non enim in talibus et cetera. Dicit ergo primo, quod quidam ponunt esse quasdam naturas medias inter species et sensibilia, et tamen non dicunt ea esse separata a sensibilibus, sed quod sunt in ipsis sensibilibus. Sicut patet de opinione illorum, qui posuerunt dimensiones quasdam per se existentes, quae penetrant omnia corpora sensibilia, quas quidam dicunt esse locum corporum sensibilium, ut dicitur in quarto physicae, et ibidem improbatur. Unde hic dicit, quod prosequi omnia impossibilia, quae sequuntur ad hanc positionem, maioris est negocii. Sed nunc aliqua breviter tangere sufficit.	417. However, there are (215) Here he argues against another position. First, he states the point at issue. Second (216:C 418), he brings in arguments germane to his purpose (“It is unreasonable”). Accordingly, he says, first (215), that some thinkers posit natures midway between the Forms and sensible things, yet they do not say that these natures are separate from sensible things but exist in sensible things themselves. This is clear regarding the opinion of those who held that there are certain self-subsistent dimensions which penetrate all sensible bodies, which some thinkers identify with the place of sensible bodies, as is stated in Book IV of the Physics and is disproved there. Hence he says here that to pursue all the absurd consequences of this position is a major undertaking, but that it is now sufficient to touch on some points briefly.
lib. 3 l. 7 n. 16 Deinde cum dicit non enim inducit quatuor rationes contra praedictam positionem: quarum prima talis est. Eiusdem rationis videtur esse quod praeter sensibilia ponantur species et mathematica media, quia utrumque ponitur propter abstractionem intellectus: si igitur ponuntur mathematica esse in sensibilibus, congruum est quod non solum ita se habeant in eis, sed etiam quod species ipsae sint in sensibilibus, quod est contra opinionem ponentium species. Ponunt enim eas esse separatas: et non esse alicubi.	418. It is unreasonable (216). Then he brings four arguments against this position. The first runs as follows. It seems to be for the same reason that in addition to sensible things the Forms and objects of mathematics are posited, because both are held by reason of abstraction on the part of the intellect. If, then, the objects of mathematics are held to exist in sensible things, it is fitting that not only they but also the Forms themselves should exist there. But this is contrary to the opinion of those who posit [the existence of] the Forms. For they hold that these are separate, and not that they exist anywhere in particular.
lib. 3 l. 7 n. 17 Secundam rationem ponit ibi, amplius autem quae talis est. Si mathematica sunt alia a sensibilibus, et tamen sunt in eis, cum corpus sit quoddam mathematicum, sequitur quod corpus mathematicum simul est in eodem cum corpore sensibili: ergo duo solida, idest duo corpora erunt in eodem loco; quod est impossibile, non solum de duobus corporibus sensibilibus, sed etiam de corpore sensibili et mathematico: quia utrumque habet dimensiones, ratione quarum duo corpora prohibentur esse in eodem loco.	419. Furthermore, it would be (217) Here he gives the second argument, which runs thus: if the objects of mathematics differ from sensible things yet exist in them, since a body is an object of mathematics, it follows that a mathematical body exists simultaneously with a sensible body in the same subject. Therefore “two solids,” i.e., two bodies, will exist in the same place. This is impossible not only for two sensible bodies but also for a sensible body and a mathematical one, because each has dimensions, by reason of which two bodies are prevented from being in the same place.
lib. 3 l. 7 n. 18 Tertiam rationem ponit ibi, et non esse moto enim aliquo movetur id quod in eo est: sed sensibilia moventur: si igitur mathematica sunt in sensibilibus, sequetur quod mathematica moveantur: quod est contra rationem mathematicorum, quae non solum abstrahunt a materia, sed etiam a motu.	420. Furthermore, if anyone (211). Then he argues against those who claimed that the objects of mathematics are midway between the Forms and sensible things. First (211:C 410), he argues against those who held that the objects of mathematics are intermediate entities and are separate from sensible things; and, second (215:C 417), against those who held that the objects of mathematics exist but exist in sensible things (“However, there are”). In regard to the first he does two things. First, he introduces arguments against the first position. Second (214:C 416), he argues in support of this position (“Nor again”). He brings up three arguments against the first position. The first argument is this: just as there is a mathematical science about the line, in a similar way there are certain mathematical sciences about other subjects. If, then, there are certain lines in addition to the sensible ones with which geometry deals, by the same token there will be, in all other classes of things with which the other mathematical sciences deal, certain things in addition to those perceived by the senses. But he shows that it is impossible to hold this with regard to two of the mathematical sciences.
lib. 3 l. 7 n. 19 Quartam rationem ponit ibi totaliter autem quae talis est. Nihil rationabiliter ponitur nisi propter aliquam causarum; et praecipue si ex tali positione maius inconveniens sequatur. Sed ista positio ponitur sine causa. Eadem enim inconvenientia sequentur ponentibus mathematica esse media et in sensibilibus, quae sequuntur ponentibus ea non esse in sensibilibus, et adhuc quaedam alia propria et maiora, ut ex praedictis patet. Haec igitur positio est irrationabilis. Ultimo autem concludit quod praedictae quaestiones habent multam dubitationem, quomodo se habeat veritas in istis.	421. He does this, first, in the case of astronomy, which is one of the mathematical sciences and which has as its subject the heavens and the celestial bodies. Hence, according to what has been said, it follows that there is another heaven besides the one perceived by the senses, and similarly another sun and another moon, and so on for the other celestial bodies. But this is incredible, because that other heaven would be either mobile or immobile. If it were immobile, this would seem to be unreasonable, since we see that it is natural for the heavens to be always in motion. Hence the astronomer also makes some study of the motions of the heavens. But to say that a
lib. 3 l. 7 n. 20 Has autem quaestiones pertractat philosophus infra, duodecimo, tertiodecimo et quartodecimo huius, ostendens non esse mathematicas substantias separatas, nec etiam species. Et ratio quae movebat ponentes mathematica et species sumpta ab abstractione intellectus, solvitur in principio decimitertii. Nihil enim prohibet aliquid quod est tale, salva veritate considerari ab intellectu non inquantum tale; sicut homo albus potest considerari non inquantum albus: et hoc modo intellectus potest considerare res sensibiles, non inquantum mobiles et materiales, sed inquantum sunt quaedam substantiae vel magnitudines; et hoc est intellectum abstrahere a materia et motu. Non autem sic abstrahit secundum intellectum, quod intelligat magnitudines et species esse sine materia et motu. Sic enim sequeretur quod vel esset falsitas intellectus abstrahentis, vel quod ea quae intellectus abstrahit, sint separata secundum rem.	422. Now the Philosopher treats these questions below in Books XII, XIII and XIV of this work, where he shows that there are neither separate mathematical substances nor Forms. The reasoning which moved those who posited the objects of mathematics and the Forms, which are derived from an abstraction of the intellect, is given at the beginning of Book XIII. For nothing prevents a thing which has some particular attribute from being considered by the intellect without its being viewed under this aspect and yet be considered truly, just as a white man can be considered without white being considered. Thus the intellect can consider sensible things not inasmuch as they are mobile and material but inasmuch as they are substances or continuous quantities; and this is to abstract the thing known from matter and motion. However, so far as the thing known is concerned, the intellect does not abstract in such a way that it understands continuous quantities and forms to exist without matter and motion. For then it would follow either that the intellect of the one abstracting is false, or that the things which the intellect abstracts are separate in reality.

Lecture 8

Latin	English
lib. 3 l. 8 n. 1 Postquam philosophus disputavit de quaestionibus motis de substantiis, hic disputat de quaestionibus motis de principiis. Et dividitur in partes duas. In prima disputat de quaestionibus, quibus quaerebatur quae sunt principia. Secundo de quaestionibus quibus quaerebatur qualia sint principia, et hoc ibi, adhuc autem utrum substantia. Circa primum disputat de duabus quaestionibus. Primo utrum universalia sint principia. Secundo utrum sint aliqua principia a materia separata, ibi, est autem habita de his disputatio et cetera. Circa primum disputat duas quaestiones: quarum prima est, utrum genera sint principia; secunda, quae genera, utrum scilicet prima genera, vel alia, ibi, ad hoc autem si maxime principia sunt genera et cetera. Circa primum duo facit. Primo movet quaestionem. Secundo disputat. Secunda ibi, ut vocis elementa et cetera. Est ergo quaestio prima de principiis, utrum oportet recipere vel opinari quod ipsa genera, quae de pluribus praedicantur, sint elementa et principia rerum, vel magis sint dicenda principia et elementa ea, ex quibus unumquodque est, sicut ex partibus. Sed addit duas conditiones: quarum una est cum insint, quod ponitur ad differentiam contrarii et privationis. Dicitur enim album fieri ex nigro, vel non albo, quae tamen non insunt albo. Unde non sunt eius elementa. Alia conditio est qua dicit primis, quod ponitur ad differentiam secundorum componentium. Sunt enim corpora animalium ex carnibus et nervis quae insunt animali non tamen dicuntur animalis elementa, quia non sunt haec prima ex quibus animal componitur, sed magis ignis, aer, aqua et terra, ex quibus etiam existunt carnes et nervi.	423. Having debated the questions which were raised about substances, the Philosopher now treats dialectically the questions which were raised about principles. This is divided into two parts. In the first he discusses the questions which asked what the principles of things are; and in the second (456), the questions which asked what kind of things the principles are (“Again, there is the problem”). In the first part of this division he discusses two questions: first, whether universals are the principles of things; and second (443), whether any principles are separate from matter (“But there is a problem”). In regard to the first he discusses two questions, of which the first is whether genera are the principles of things. The second (431) asks which genera these are, whether the first genera or the others (“Again, if genera”). In regard to the first he does two things: first, he raises the question; and second (424), he treats it dialectically (“Just as the elements”). The first question has to do with the principles of things: whether it is necessary to accept or believe that those genera which are predicated of many things are the elements and principles of things, or rather that those parts of which every single thing is composed must be called the elements and principles of things. But he adds two conditions, one of which is “inasmuch as they are intrinsic,” which is given in order to distinguish these parts from a contrary and a privation. For white is said to come from black, or the non-white, although these are not intrinsic to white. Hence they are not its elements. The other condition is what he calls “the first things,” which is given in order to distinguish them from secondary components. For the bodies of animals are composed of flesh and nerves, which exist within the animal; yet these are not called the elements of animals, because they are not the first things of which an animal is composed, but rather fire, air, water and earth, from which flesh and nerves derive their being.
lib. 3 l. 8 n. 2 Deinde cum dicit ut vocis disputat ad hanc quaestionem: et circa hoc tria facit. Primo ostendit, quod ea, ex quibus primis aliquid componitur, sint principia et elementa. Secundo obiicit ad partem contrariam, ibi, inquantum autem cognoscimus unumquodque et cetera. Tertio excludit quamdam responsionem qua posset dici, quod utraque sunt principia et elementa, ibi, at vero nec utrobique et cetera. Circa primum primo ponit tres rationes: quarum prima procedit ex naturalibus, in quibus manifestat propositum secundum duo exempla: quorum primum est de voce dearticulata, cuius principium et elementum non dicitur esse commune, quod est vox, sed magis illa, ex quibus primis componuntur omnes voces, quae dicuntur literae. Secundum exemplum ponit in diagrammatibus idest in demonstrativis descriptionibus figurarum geometricarum. Dicuntur enim horum diagrammatum esse elementa non hoc commune quod est diagramma, sed magis illa theoremata, quorum demonstrationes insunt demonstrationibus aliorum theorematum geometralium, aut omnium, aut plurimorum; quia scilicet aliae demonstrationes procedunt ex suppositione primarum demonstrationum. Unde et liber Euclidis dicitur liber elementorum, quia scilicet in eo demonstrantur prima geometriae theoremata, ex quibus aliae demonstrationes procedunt.	424. Just as the elements (221). Here he treats this question dialectically; and in regard to this he does three things. First, he shows that the first things of which anything is composed are its principles and elements. Second (224:C 427), he argues the opposite side of the question (“But if we know”). Third (227:C 430), he rejects one answer by which it could be said that both of these [i.e., genera and constituent parts] are the principles and elements of things (“But it is not”). In regard to the first he gives three arguments. The first of these proceeds from natural phenomena, in which he makes his thesis evident by two examples. The first example which he gives if that of a word, whose principle and element is not said to be the common term word but rather the first constituents of which all words are composed, which are called letters. He gives as a second example, diagrams, i.e., the demonstrative descriptions of geometrical figures. For the elements of these diagrams are not said to be the common term diagram but rather those theorems whose demonstrations are found in the demonstrations of other geometrical theorems, either of all or of most of them, because the other demonstrations proceed from the supposition of the first demonstrations. Hence the book of Euclid is called The Book of Elements, because the first theorems of geometry, from which the other demonstrations proceed, are demonstrated therein.
lib. 3 l. 8 n. 3 Secundam rationem ponit ibi amplius autem quae procedit in rebus naturalibus. Et dicit quod illi, qui ponunt elementa corporum vel plura vel unum, illa dicunt esse principia et elementa corporum, ex quibus componuntur et constant tamquam in eis existentibus. Sicut Empedocles dicit, elementa corporum naturalium esse ignem et aquam, et alia huiusmodi, quae simul cum his elementa rerum dicit, ex quibus primis cum insint corpora naturalia constituuntur. Ponebant autem praeter haec duo, alia quatuor principia, scilicet aerem et terram, litem et amicitiam, ut in primo dictum est. Non autem dicebat, nec Empedocles nec alii naturales philosophi, quod genera rerum essent earum principia et elementa.	425. Furthermore, those who (222). Here he gives the second argument which also employs certain examples drawn from nature. He says that those who hold that the elements of bodies are either one or many, say that the principles and elements of bodies are those things of which bodies are composed and made up as intrinsic constituents. Thus Empedocles says~ that the elements of natural bodies are fire and water and other things of this kind, which along with these he calls the elements of things; and natural bodies are constituted of these first things inasmuch as they are intrinsic. Moreover, they [i.e., the philosophers of nature] held that in addition to these two principles there are four others—air, earth, strife and friendship—as was stated in Book I (50:C 104). But neither Empedocles nor the other philosophers of nature said that the genera of things are the principles and elements of these natural bodies.
lib. 3 l. 8 n. 4 Tertiam rationem ponit ibi adhuc autem quae procedit in artificialibus: et dicit quod siquis velit speculari naturam, idest definitionem indicantem essentiam aliorum corporum a corporibus naturalibus, scilicet artificialium, puta si vult cognoscere lectum, oportet considerare ex quibus partibus componitur et modum compositionis earum, et sic cognoscet naturam lecti. Et post hoc concludit quod genera non sunt principia entium.	426. And again if anyone (223). Here he gives the third argument, which involves things made by art. He says that if someone wished to “speculate about their nature,” i.e., about the definition which indicates the essence of other bodies than natural ones, namely, of bodies made by human art, for example, if one wished to know a bed, it would be necessary to consider of what parts it is made and how they are put together; and in this way he would know the nature of a bed. And after this he concludes that genera are not the principles of existing things.
lib. 3 l. 8 n. 5 Deinde cum dicit quod si cognoscimus obiicit ad partem contrariam: et ponit tres rationes, quarum prima talis est. Unumquodque cognoscitur per suam definitionem. Si igitur idem est principium essendi et cognoscendi, videtur, quod id quod est principium definitionis sit principium rei definitae. Sed genera sunt principia definitionum, quia ex eis primo definitiones constituuntur: ergo genera sunt principia rerum quae definiuntur.	427. But if we know (224). Here he argues the other side of the question. He gives three arguments, the first of which is as follows. Each thing is known through its definition. Therefore, if a principle of being is the same as a principle of knowing, it seems that anything which is a principle of definition is also a principle of the thing defined. But genera are principles of definitions, because definitions are first composed of them. Hence genera are the principles of the things defined.
lib. 3 l. 8 n. 6 Secundam rationem ponit ibi et si est quae talis est. Per hoc accipitur scientia de unaquaque re, quod scitur species eius secundum quam res est: non enim potest cognosci Socrates nisi per hoc quod scitur quod est homo. Sed genera sunt principia specierum, quia species constituuntur ex genere et differentia: ergo genera sunt principia eorum quae sunt.	428. And if in order to (225) Here he gives the second argument, which runs thus. Scientific knowledge of each thing is acquired by knowing the species from which it gets its being, for Socrates can be known only by understanding that he is man. But genera are principles of species, because the species of things are composed of genera and differences. Therefore genera are the principles of existing things.
lib. 3 l. 8 n. 7 Tertiam rationem ponit ibi videntur autem et sumitur ex auctoritate Platonicorum, qui posuerunt unum et ens esse principia, et magnum et parvum, quibus utuntur ut generibus: ergo genera sunt principia.	429. Moreover, some of those (226). Here he gives a third argument, which is based on the authority of the Platonists, who held that the one and being are the principles of things, and also the great and small, which are used as genera. Therefore genera are the principles of things.
lib. 3 l. 8 n. 8 Deinde cum dicit sed non possibile excludit quamdam responsionem, qua posset dici quod utraque sunt principia; dicens quod non est possibile dicere utrobique esse principia, ut elementa, id est partes ex quibus componitur aliquid, et genera. Et hoc probat tali ratione. Unius rei una est ratio definitiva manifestans eius substantiam, sicut et una est substantia uniuscuiusque: sed non est eadem ratio definitiva quae datur per genera et quae datur per partes ex quibus aliquid componitur: ergo non potest esse utraque definitio indicans substantiam rei. Ex principiis autem rei potest sumi ratio definitiva significans substantiam eius. Impossibile est ergo quod principia rerum sint simul genera, et ea ex quibus res componuntur.	430. But it is not possible (227) Here he excludes one answer which would say that both of these are principles. He says that it is impossible to say that both of these are “principles,” i.e., both the elements, or the parts of which something is composed, and genera. He proves this by the following argument. Of each thing there is one definite concept which exposes its substance, just as there is also one substance of each thing. But the definitive concept which involves genera is not the same as the one which involves the parts of which a thing is composed. Hence it cannot be true that each definition indicates a thing’s substance. But the definitive concept which indicates a thing’s substance cannot be taken from its principles. Therefore it is impossible that both genera and the parts of which things are composed should be simultaneously and being cannot be genera of all the principles of things.
lib. 3 l. 8 n. 9 Deinde cum dicit adhuc autem disputat secundam quaestionem. Et primo movet eam. Secundo ad eam rationes inducit ibi, nam siquidem universalia et cetera. Dicit ergo quod si ponamus quod genera sint maxime principia, quae oportet existimare magis esse principia? Utrum prima de numero generum, scilicet communissima, aut etiam infima, quae proxima praedicantur de individuis, scilicet species specialissimas. Hoc enim habet dubitationem, sicut ex sequentibus patet.	431. Again, if genera (228). Then he treats the second question dialectically. First, he raises the question; and second (432), he brings up arguments relative to this question (“For if universals”). Accordingly, he says that if we hold that genera are the principles of things in the fullest sense which of these genera should be considered to be the principles of things to a greater degree? Must we consider those “genera” which are first in number, namely, the most common, or also the lowest genera, which are proximately predicated of the individual, i.e., the lowest species. For this is open to question, as is clear from what follows.
lib. 3 l. 8 n. 10 Deinde cum dicit nam siquidem obiicit ad propositam quaestionem: et circa hoc tria facit. Primo enim inducit rationes ad ostendendum quod prima genera non possunt esse principia. Secundo inducit rationes ad ostendendum, quod species ultimae magis debent dici principia, ibi, at vero et si magis. Tertio obiicit ad propositum, ibi, iterum autem et cetera. Circa primum ponit tres rationes: quarum prima talis est. Si genera sunt magis principia quanto sunt universalia oportet quod illa quae sunt maxime universalia, quae scilicet dicuntur de omnibus, sint prima inter genera et maxime principia. Tot ergo erunt rerum principia, quod sunt huiusmodi genera communissima. Sed communissima omnium sunt unum et ens, quae de omnibus praedicantur: ergo unum et ens erunt principia et substantiae omnium rerum. Sed hoc est impossibile; quia non possunt omnium rerum esse genus, unum et ens: quia, cum ens et unum universalissima sint, si unum et ens essent principia generum, sequeretur quod principia non essent genera. Sic ergo positio, qua ponitur communissima generum esse principia, est impossibilis, quia sequitur ex ea oppositum positi, scilicet quod principia non sunt genera.	432. For if universals (229). Here he argues about the question which was proposed; and in regard to this he does three things. First, he introduces arguments to show that the first genera cannot be principles. Second (231:C 436), he introduces arguments to show that the last species should rather be called the principles of things (“But, on the other hand”). Third (234:C 441), he debates the proposed question (“But again it is”). In regard to the first (229) he gives three arguments, of which the first runs thus: if genera are principles to the extent that they are more universal, then those which are most universal, i.e., those which are predicated of all things, must be the first genera and the principles of things in the highest degree. Hence there will be as many principles of things as there are most common genera of this kind. But the most common of all genera are unity and being, which are predicated of all things. Therefore unity and being will be the principles and substances of all things. But this is impossible, because unity and being cannot be genera of all things. For, since unity and being are most universal, if they were principles of genera, it would follow that genera would not be the principles of things. Hence the position which maintains that the most common genera are principles is an impossible one, because from it there follows the opposite of what was held, namely, that genera are not principles.
lib. 3 l. 8 n. 11 Quod autem ens et unum non possint esse genera, probat tali ratione. Quia cum differentia addita generi constituat speciem, de differentia praedicari non poterit nec species sine genere, nec genus sine speciebus. Quod autem species de differentia praedicari non possit, patet ex duobus. Primo quidem, quia differentia in plus est quam species, ut Porphyrius tradit. Secundo, quia cum differentia ponatur in definitione speciei, non posset species praedicari per se de differentia, nisi intelligeretur quod differentia esset subiectum speciei, sicut numerus est subiectum paris, in cuius definitione ponitur. Hoc autem non sic se habet; sed magis differentia est quaedam forma speciei. Non ergo posset species praedicari de differentia, nisi forte per accidens. Similiter etiam nec genus per se sumptum, potest praedicari de differentia praedicatione per se. Non enim genus ponitur in definitione differentiae, quia differentia non participat genus, ut dicitur in quarto topicorum. Nec etiam differentia ponitur in definitione generis: ergo nullo modo per se genus praedicatur de differentia. Praedicatur tamen de eo quod habet differentiam, idest de specie, quae habet differentiam in actu. Et ideo dicit, quod de propriis differentiis generis non praedicatur species, nec genus sine speciebus, quia scilicet genus praedicatur de differentiis secundum quod sunt in speciebus. Nulla autem differentia potest accipi de qua non praedicetur ens et unum, quia quaelibet differentia cuiuslibet generis est ens et est una, alioquin non posset constituere unam aliquam speciem entis. Ergo impossibile est quod unum et ens sint genera.	433. That being and unity cannot be genera he proves by this argument: since a difference added to a genus constitutes a species, a species cannot be predicated of a difference without a genus, or a genus without a species. That it is impossible to predicate a species of a difference is clear for two reasons. First, because a difference applies to more things than a species, as Porphyry says; ‘ and second, because, since a difference is given in the definition of a species, a species can be predicated essentially of a difference only if a difference is understood to be the subject of a species, as number is the subject of evenness in whose definition it is given. This, however, is not the case; but a difference is rather a formal principle of a species. Therefore a species cannot be predicated of a difference except, perhaps, in an incidental way. Similarly too neither can a genus, taken in itself, be predicated of a difference by essential predication. For a genus is not given in the definition of a difference, because a difference does not share in a genus, as is stated in Book IV of The Topics; nor again is a difference given in the definition of a genus. Therefore a genus is not predicated essentially of a difference in any way. Yet it is predicated of that which “has a difference,” i.e., of a species, which actually contains a difference. Hence he says that a species is not predicated of the proper differences of a genus, nor is a genus independently of its species, because a genus is predicated of its differences inasmuch as they inhere in a species. But no difference can be conceived of which unity and being are not predicated, because any difference of any genus is a one and a being, otherwise it could not constitute any one species of being. It is impossible, then, that unity and being should be genera.
lib. 3 l. 8 n. 12 Deinde cum dicit amplius autem secundam rationem ponit, quae talis est. Si genera dicuntur principia quia sunt communia et praedicantur de pluribus, oportebit quod omnia quae pari ratione erunt principia, quia sunt communia, et praedicata de pluribus, sint genera. Sed omnia quae sunt media inter prima genera et individua, quae scilicet sunt coaccepta cum differentiis aliquibus, sunt communia praedicata de pluribus: ergo sunt principia et sunt genera: quod patet esse falsum. Quaedam enim eorum sunt genera, sicut species subalternae; quaedam vero non sunt genera, sicut species specialissimae. Non ergo verum est, quod prima genera sive communia sint principia prima.	434. Further, those things (230) Then he gives the second argument, which runs thus: if genera are called principles because they are common and predicated of many things, then for a like reason all those things which are principles because they are common and predicated of many will have to be genera. But all things which are intermediate between the first genera and individuals, namely, those which are considered together with some differences, are common predicates of many things. Hence they are both principles and genera. But this is evidently false. For some of them are genera, as subaltern species, whereas others are not, as the lowest species. It is not true, then, that the first or common genera are the principles of things.
lib. 3 l. 8 n. 13 Praeterea. Si prima genera sunt principia, quia sunt principia cognitionis specierum, multo magis differentiae sunt principia, quia differentiae sunt principia formalia specierum. Forma autem et actus est maxime principium cognoscendi. Sed differentias esse principia rerum est inconveniens, quia secundum hoc erunt quasi infinita principia. Sunt enim, ut ita dicatur, infinitae rerum differentiae; non quidem infinitae secundum rerum naturam, sed quoad nos. Et quod sint infinitae, patet dupliciter. Uno modo siquis consideret multitudinem ipsam differentiarum secundum se. Alio modo siquis accipiat primum genus quasi primum principium. Manifestum enim est quod sub eo continentur innumerabiles differentiae. Non ergo prima genera sunt principia.	435. Further, if the first genera are principles, because they are the principles by which we know species, then differences will be principles to a greater degree, because differences are the formal principles of species; and form or actuality is chiefly the principle of knowing. But it is unfitting that differences should be the principles of things, because in that case there would be an infinite number of principles, so to speak; for the differences of things are infinite, so to speak; not infinite in reality but to us. That they are infinite in number is revealed in two ways: in one way if we consider the multitude of differences in themselves; in another way if we consider the first genus as a first principle, for evidently innumerable differences are contained under it. The first genera, then, are not the principles of things.
lib. 3 l. 8 n. 14 Deinde cum dicit at vero ostendit, quod species specialissimae sunt magis principia quam genera; et ponit tres rationes, quarum prima talis est. Unum secundum Platonicos maxime videtur habere speciem, idest rationem principii. Unum vero habet rationem indivisibilitatis, quia unum nihil est aliud quam ens indivisum. Dupliciter est autem aliquid indivisibile: scilicet secundum quantitatem, et secundum speciem. Secundum quantitatem, quidem, sicut punctus et unitas: et hoc indivisibile opponitur divisioni quantitatis. Secundum speciem autem, sicut quod non dividitur in multas species. Sed inter haec duo indivisibilia prius et principalius est quod est indivisibile secundum speciem, sicut et species rei est prior quam quantitas eius; ergo illud quod est indivisibile secundum speciem, est magis principium eo quod est indivisibile secundum quantitatem. Et quidem secundum quantitatis numeralis divisionem videtur esse magis indivisibile genus, quia multarum specierum est unum genus: sed secundum divisionem speciei magis est indivisibilis una species. Et sic ultimum praedicatum de pluribus quod non est genus plurium specierum, scilicet species specialissima, est magis unum secundum speciem quam genus. Sicut homo et quaelibet alia species specialissima, non est genus aliquorum hominum. Est ergo magis principium species quam genus.	436. But on the other hand (231). Then he shows that the lowest species are principles to a greater degree than genera. He gives three arguments, of which the first runs thus: according to the Platonists it is the one which seems to have “the nature,” 3 or character, of a principle to the greatest degree. Indeed, unity has the character of indivisibility, because a one is merely an undivided being. But a thing is indivisible in two ways, namely, in quantity and in species: in quantity, as the point and unit, and this is a sort of indivisibility opposed to the division of quantity; and in species, as what is not divided into many species. But of these two types of indivisibility the first and more important one is indivisibility in species, just as the species of a thing is prior to its quantity. Therefore that which is indivisible in species is more of a principle because it is indivisible in quantity. And in the division of quantity the genus seems to be more indivisible, because there is one genus of many species; but in the division of species one species is more indivisible. Hence the last term which is predicated of many, which is not a genus of many species, namely, the lowest species, is one to a greater degree in species than a genus; for example, man or any other lowest species is not the genus of particular men. Therefore a species is a principle to a greater degree than a genus.
lib. 3 l. 8 n. 15 Deinde cum dicit amplius in quibus secundam rationem ponit, quae procedit ex quadam positione Platonis; qui quando aliquid unum de pluribus praedicatur, non secundum prius et posterius, posuit illud unum separatum, sicut hominem praeter omnes homines. Quando vero aliquid praedicatur de pluribus secundum prius et posterius, non ponebat illud separatum. Et hoc est quod dicit quod in quibus prius et posterius est, scilicet quando unum eorum de quibus aliquod commune praedicatur est altero prius, non est possibile in his aliquid esse separatum, praeter haec multa de quibus praedicatur. Sicut si numeri se habent secundum ordinem, ita quod dualitas est prima species numerorum, non invenitur idea numeri praeter omnes species numerorum. Eadem ratione non invenitur figura separata, praeter omnes species figurarum.	437. Further, in the case of (232). Then he gives the second argument, which is based on a certain position of Plato; for at one time Plato held that there is some one thing which is predicated of many things without priority and posteriority, and that this is a separate unity, as man is separate from all men; and at another time he held that there is some one thing which is predicated of many things according to priority and posteriority, and that this is not a separate unity. This is what Aristotle means when he says “in the case of those things to which prior and subsequent apply,” i.e., that when one of the things of which a common term is predicated is prior to another, it is impossible in such cases that there should be anything separate from the many things of which this common term is predicated. For example, if numbers stand in such a sequence that two is the first species of number, no separate Idea of number will be found to exist apart from all species of numbers. And on the same grounds no separate figure will be found to exist apart from all species of figures.
lib. 3 l. 8 n. 16 Et huius ratio esse potest, quia ideo aliquod commune ponitur separatum, ut sit quoddam primum quod omnia alia participent. Si igitur unum de multis sit primum, quod omnia alia participent, non oportet ponere aliquod separatum, quod omnia participant. Sed talia videntur omnia genera; quia omnes species generum inveniuntur differre secundum perfectius et minus perfectum. Et, per consequens, secundum prius et posterius secundum naturam. Si igitur eorum quorum unum est prius altero, non est accipere aliquod commune separatum, si genus praeter species inveniatur, erunt schola aliorum, idest erit eorum alia doctrina et regula, et non salvabitur in eis praedicta regula. Sed manifestum est quod inter individua unius speciei, non est unum primum et aliud posterius secundum naturam, sed solum tempore. Et ita species secundum scholam Platonis est aliquid separatum. Cum igitur communia sint principia inquantum sunt separata, sequitur quod sit magis principium species quam genus.	438. The reason for this can be that a common attribute is held to be separate so as to be some first entity in which all other things participate. If, then, this first entity is a one applicable to many in which all other things participate, it is not necessary to hold that there is some separate entity in which all things participate. But all genera seem to be things of this kind, because all types of genera are found to differ insofar as they are more or less perfect, and thus insofar as they are prior and subsequent in nature. Hence, if in those cases in which one thing is prior to another it is impossible to regard anything common as a separate entity, on the supposition that there is a genus apart from species, then “in the case of other things the teaching” will [differ], i.e., there will be another doctrine and rule concerning them, and the foregoing rule will not apply to them. But considering the individuals of one species, it is evident that one of these is not prior and another subsequent in nature but only in time. And thus according to Plato’s teaching a species is separate. Since, then, these common things are principles inasmuch as they are separate, it follows that a species is a principle to a greater degree than a genus.
lib. 3 l. 8 n. 17 Deinde cum dicit amplius autem tertiam rationem ponit quae sumitur ex meliori et peiori: quia in quibuscumque invenitur unum alio melius, semper illud quod est melius, est prius secundum naturam. Sed horum quae sic se habent non potest poni unum genus commune separatum: ergo eorum quorum unum est melius et aliud peius non potest poni unum genus separatum. Et sic redit in idem quod prius. Haec enim ratio inducitur quasi confirmatio praecedentis, ad ostendendum, quod in speciebus cuiuslibet generis invenitur prius et posterius.	439. Further, where one thing (233) Here he gives the third argument, which makes use of the notions “better or worse.” For in all those cases where one thing is better than another, that which is better is always prior in nature. But there cannot be held to be one common genus of those things which exist in this way. Hence there cannot be held to be one separate genus in the case of those things in which one is better and another worse; and thus the conclusion is the same as the above. For this argument is introduced to strengthen the preceding one, so to speak, i.e., with a view to showing that there is priority and posteriority among the species of any genus.
lib. 3 l. 8 n. 18 Et ex tribus his rationibus concludit propositum; scilicet quod species specialissimae quae immediate de individuis praedicantur, magis videntur esse principia quam genera. Ponitur enim genitivus generum loco ablativi more Graecorum. Unde litera Boetii planior est, quae expresse concludit huiusmodi praedicata magis esse principia quam genera.	440. And from these three arguments he draws the conclusion in which he is chiefly interested, namely, that the lowest species, which are predicated immediately of individuals, seem to be the principles of things to a greater degree than genera.
lib. 3 l. 8 n. 19 Deinde cum dicit iterum autem obiicit in contrarium tali ratione. Principium et causa est praeter res quarum est principium et causa, et possibile est ab eis esse separatum. Et hoc ideo quia nihil est causa sui ipsius. Et loquitur hic de principiis et causis extrinsecis, quae sunt causae totius rei. Sed aliquid esse praeter singularia non ponitur, nisi quia est commune et universaliter de omnibus praedicatum: ergo quanto aliquid est magis universale, tanto magis est separatum, et magis debet poni principium. Sed genera prima sunt maxime universalia: ergo genera prima sunt maxime principia.	441. But again it is not (234). Here he argues the opposite side of the question, as follows: a principle and a cause are distinct from the things of which they are the principle and cause, and are capable of existing apart from them. And this is true, because nothing is its own cause. He is speaking here of extrinsic principles and causes, which are causes of a thing in its entirety. But the only thing that is held to exist apart from singular things is what is commonly and universally predicated of all things. Therefore the more universal a thing is, the more separate it is, and the more it should be held to be a principle. But the first genera are most universal. Therefore the first genera are the principles of things in the highest degree.
lib. 3 l. 8 n. 20 Harum autem quaestionum solutio innuitur ex hac ultima ratione. Secundum hoc enim genera vel species universalia principia ponebantur, inquantum ponebantur separata. Quod autem non sint separata et per se subsistentia ostendetur in septimo huius. Unde et Commentator in octavo ostendet quod principia rerum sunt materia et forma, ad quorum similitudinem se habent genus et species. Nam genus sumitur a materia, differentia vero a forma, ut in eodem libro manifestabitur. Unde, cum forma sit magis principium quam materia, secundum hoc etiam erunt species magis principia quam genera. Quod vero contra obiicitur ex hoc quod genera sunt principia cognoscendi speciem et definitiones ipsius, eodem modo solvitur sicut et de separatione. Quia enim separatim accipitur a ratione genus sine speciebus, est principium in cognoscendo. Et eodem modo esset principium in essendo, si haberet esse separatum.	442. Now the solution to these questions is implied in this last argument. For according to this argument genera or species are held to be universal principles inasmuch as they are held to be separate. But the fact that they are not separate and self-subsistent is shown in Book VII (1592) of this work. Hence the Commentator also shows, in Book VIII, that the principles of things are matter and form, to which genus and species bear some likeness. For a genus is derived from matter and difference from form, as will be shown in the same book (720). Hence, since form is more of a principle than matter, species will consequently be principles more than genera. But the objection which is raised against this, on the grounds that genera are the principles of knowing a species and its definitions, is answered in the same way the objection raised about their separateness. For, since a genus is understood separately by the mind without understanding its species, it is a principle of knowing. And in the same way it would be a principle of being, supposing that it had a separate being.

Lecture 9

Latin	English
lib. 3 l. 9 n. 1 Postquam philosophus disputavit quaestionem de universalibus, utrum sint principia, hic consequenter movet quaestionem de separatis, utrum scilicet aliquid sit separatum a sensibilibus, quod sit eorum principium. Et circa hoc pertractat duas quaestiones: quarum prima est, an universalia sint separata a singularibus. Secunda est, an sit aliquid formale separatum ab his quae sunt composita ex materia et forma, ibi, amplius autem si quam maxime et cetera. Circa primum tria facit. Primo describit dubitationem. Secundo obiicit ad unam partem, ibi, nam si non est et cetera. Tertio obiicit ad partem aliam, ibi, at vero et cetera. Est ergo haec dubitatio de eo quod tactum est in ultima ratione praecedentis quaestionis, utrum scilicet universale sit separatum a singularibus, sicut praemissa ratio supponebat. Et hoc est quod dicit, de qua ratio nunc existit, idest de qua immediate praecedens ratio praecessit. De hac autem dubitatione ita dicit: primo quod est habita, idest consequenter se habens ad praemissa: quia sicut iam dictum est, ex hoc dependet consideratio praecedentis quaestionis. Nam si universalia non sunt separata, non sunt principia: si autem sunt separata, sunt principia. Secundo dicit de ea, quod est difficillima omnium dubitationum huius scientiae. Quod ostenditur ex hoc quod eminentissimi philosophi de ea diversimode senserunt. Nam Platonici posuerunt universalia esse separata, aliis philosophis contra ponentibus. Tertio dicit de ea quod est maxime necessaria ad considerandum, quia scilicet ex ea dependet tota cognitio substantiarum tam sensibilium quam immaterialium.	443. Having debated the question whether universals are the principles of things, the Philosopher now raises a question about their separability, namely, whether there is anything separate from sensible things as their principle. In regard to this he considers two questions. The first (443) Of these is whether universals are separate from singular things. The second (447) is whether there is any formal [principle] separate from things which are composed of matter and form (“Further, if there is something”). In regard to the first he does three things. First, he describes the problem. Second (444), he argues one side of the question (“For if there is nothing”). Third (445), he argues the other side of the question (“But if this is”). Accordingly, this problem arises with regard to a point mentioned in the last argument of the preceding question, namely, whether a universal is separate from singular things, as the aforesaid argument supposed. He describes this problem as “the one with which our analysis is now concerned (235),” i.e., the one which immediately preceded the foregoing argument. And he speaks of it in this way: first, that “it is connected with,” i.e., is a consequence of, the foregoing one, because, as has already been stated, the consideration of the preceding question depends on this. For if universals are not separate, they are not principles; but if they are separate, they are principles. Second, he speaks of this problem as the most difficult of all the problems in this science. This is shown by the fact that the most eminent philosophers have held different opinions about it. For the Platonists held that universals are separate, whereas the other philosophers held the contrary. Third, he says that this problem is one which it is most necessary to consider, because the entire knowledge of substances, both sensible and immaterial, depends on it.
lib. 3 l. 9 n. 2 Deinde cum dicit nam si non obiicit ad ostendendum, quod universalia sint separata a singularibus. Singularia enim sunt infinita: infinita autem cognosci non possunt. Unde singularia omnia cognosci non possunt nisi inquantum reducuntur ad aliquid unum, quod est universale. Sic igitur scientia de rebus singularibus non habetur, nisi inquantum sciuntur universalia. Sed scientia non est nisi verorum et existentium: ergo universalia sunt aliqua per se existentia praeter singularia.	444. For if there is nothing (236). Here he advances an argument to show that universals are separate from singular things. For singular things are infinite in number, and what is infinite cannot be known. Hence all singular things can be known only insofar as they are reduced to some kind of unity which is universal. Therefore there is science of singular things only inasmuch as universals are known. But science is only about things which are true and which exist. Therefore universals are things which exist of themselves apart from singular things.
lib. 3 l. 9 n. 3 Deinde cum dicit at vero si obiicit in contrarium hoc modo. Si necesse est universalia esse aliquid praeter singularia, oportet quod genera sint praeter singularia, vel prima generum, vel etiam ultima, quae sunt immediate ante singularia. Sed hoc est impossibile, ut ex praecedenti dubitatione patet; ergo universalia non sunt a singularibus separata. Hanc autem dubitationem solvit philosophus in septimo huius, ubi ostendit multipliciter universalia non esse substantias per se subsistentes. Nec oportet, sicut multoties dictum est, quod aliquid eumdem modum essendi habeat in rebus, per quem modum ab intellectu scientis comprehenditur. Nam intellectus immaterialiter cognoscit materialia: et similiter naturas rerum, quae singulariter in rebus existunt, intellectus cognoscit universaliter, idest absque consideratione principiorum et accidentium individualium.	445. But if this is (237) Then he argues the other side of the question in this way: if it is necessary that universals be something apart from singular things, it is necessary that genera exist apart from singular things, either the first genera or also the last, which are immediately prior to singular things. But this is impossible, as is clear from the preceding discussion. Therefore universals are not separate from singular things. 446. The Philosopher solves this problem in Book VII (659:C 1592) Of this work, where he shows in many ways that universals are not substances which subsist of themselves. Nor is it necessary, as has often been said, that a thing should have the same mode of being in reality that it has when understood by the intellect of a knower. For the intellect knows material things immaterially, and in a similar way it knows universally the natures of things which exist as singulars in reality, i.e., without considering the principles and accidents of individuals.
lib. 3 l. 9 n. 4 Deinde cum dicit amplius autem prosequitur de alia quaestione: utrum scilicet aliquid sit separatum a compositis ex materia et forma: et circa hoc duo facit. Primo movet quaestionem. Secundo prosequitur eam, ibi, si igitur et cetera. Circa primum considerandum est, quod primo movet quaestionem, utrum universale sit separatum a singularibus. Contingit autem aliquod singulare esse compositum ex materia et forma: non tamen omne singulare ex materia et forma est compositum, nec secundum rei veritatem: quia substantiae separatae sunt quaedam particulares substantiae, quia per se stantes et per se operantes; nec etiam secundum opinionem Platonicorum, qui ponebant etiam in mathematicis separatis esse quaedam particularia, ponendo plura ex eis in una specie. Et quamvis dubitari possit, utrum etiam in his quae non sunt composita ex materia et forma, sit aliquid separatum sicut universale a singulari, tamen hoc maxime habet dubitationem in rebus compositis ex materia et forma. Et ideo dicit, quod maxime est dubitabile, utrum sit aliquid, praeter simul totum etc. idest praeter rem compositam ex materia et forma. Et quare dicatur simul totum compositum, exponit subdens, ut quando praedicatur aliquid de materia. Ponebat enim Plato quod sensibilis materia participabat universalia separata. Et ex hoc erat quod universalia praedicantur de singularibus. Et ipsae participationes universalium formarum in materialibus sensibilibus constituunt simul totum, quasi universalis forma per modum participationis cuiusdam sit de materia praedicata. In his autem quaestionem trimembrem proponit: utrum scilicet praeter omnia huiusmodi sit aliquid separatum, aut praeter quaedam eorum et non praeter alia, aut praeter nihil eorum.	447. Further, if there is something (238). Here he raises another question, namely, whether anything is separate from things composed of matter and form; and in regard to this he does two things. First, he raises the question. Second (239:C 448), he proceeds to deal with it (“If, then, there is”). In regard to the first it should be observed that he first raises the question whether a universal is separate from singular things. Now it happens to be the case that some singular things are composed of matter and form. But not all singular things are so composed, either according to the real state of affairs, since separate substances are particular because existing and operating of themselves, or even according to the opinion of the Platonists, who held that even among separate mathematical entities there are particulars inasmuch as they held that there are many of them in a single species. And while it is open to dispute whether there is anything separate in the case of those things which are not composed of matter and form, as the universal is separate from the particular, the problem is chiefly whether there is anything separate in the case of things which are composed of matter and form. Hence he says that the point which causes most difficulty is whether there is something “apart from the concrete whole,” i.e., apart from the thing composed of matter and form. The reason why a composite thing is called a concrete whole he explains by adding “when something is predicated of matter.” For Plato held that sensible matter participates in separate universals, and that for this reason universals are predicated of singular things. These participations in universal forms by material sensible things constitute a concrete whole inasmuch as a universal form is predicated of matter through some kind of participation. Now in regard to these things he raises a question which has three parts, namely, whether there is anything that exists apart from all things of this kind, or apart from some and not from others, or apart from none.
lib. 3 l. 9 n. 5 Deinde cum dicit si igitur prosequitur praedictam dubitationem: et circa hoc duo facit. Primo obiicit contra hoc, quod poni posset nihil separatum esse ab his quae sunt composita ex materia et forma. Secundo obiicit ad oppositum, ibi, sed si hoc et cetera. Circa primum, obiicit duplici via. Primo quidem ex hoc, quod ea quae sunt composita ex materia et forma sunt sensibilia: unde proponit quod ea quae sunt composita ex materia et forma sunt singularia. Singularia autem non sunt intelligibilia, sed sensibilia. Si igitur nihil est praeter singularia composita ex materia et forma nihil erit intelligibile, sed omnia entia erunt sensibilia. Scientia autem non est nisi intelligibilium: ergo sequitur quod nullius rei sit scientia: nisi aliquis dicat quod sensus et scientia sunt idem, ut antiqui naturales posuerunt: sicut dicitur in primo de anima. Utrumque autem horum est inconveniens: scilicet vel quod non sit scientia, vel quod scientia sit sensus: ergo et primum est inconveniens, scilicet quod nihil sit praeter singularia composita ex materia et forma.	448. If, then, there is (239) Here he proceeds to deal with this problem; and concerning it he does two things. First, he argues against the position that nothing can be held to be separate from things composed of matter and form. Second (244:C 454), he argues the other side of the question (“But again if anyone holds this”). In regard to the first (239) he advances two arguments. First, he argues from the principle that those things which are composed of matter and form are sensible things; and therefore he proposes that those things which are composed of matter and form are singulars. However, singular things are not intelligible but sensible. Therefore, if there is nothing apart from singular things which are composed of matter and form, nothing will be intelligible but all beings will be sensible. But there is science only of things which are intelligible. Therefore it follows that there will be no science of anything, unless one were to say that sensory perception and science are the same, as the ancient philosophers of nature held, as is stated in Book I of The Soul. But both of these conclusions are untenable, namely, that there is no science and that science is sensory perception. Therefore the first position is also untenable, namely, that nothing exists except singular things which are composed of matter and form.
lib. 3 l. 9 n. 6 Deinde cum dicit amplius autem secundo obiicit ex hoc quod composita ex materia et forma sunt mobilia. Inducit talem rationem. Omnia sensibilia composita ex materia et forma corrumpuntur et in motu sunt: si igitur nihil sit praeter huiusmodi entia, sequetur quod nihil sit sempiternum nec immobile.	449. Further, neither will anything (240). Second, he argues on the grounds that things composed of matter and form are mobile. He gives the following argument. All sensible things composed of matter and form perish and are subject to motion. Therefore, if there is nothing apart from beings of this kind, it will follow that nothing is eternal or immobile.
lib. 3 l. 9 n. 7 Deinde cum dicit at vero ostendit esse inconveniens, scilicet quod nihil sit sempiternum et immobile: et primo ex parte materiae. Secundo ex parte formae, ibi, amplius autem cum sit et cetera. Dicit ergo primo, quod si nihil est sempiternum, non est possibile esse generationem alicuius rei. Et hoc probat sic. Quia in omni generatione necesse est aliquid quod fit, et aliquid ex quo fit. Si ergo id ex quo fit aliquid, iterum generatur, oportet quod ex aliquo generetur. Aut ergo necesse est quod in infinitum procedatur in materiis, aut quod stet processus in aliquo primo, quod sit aliquod primum materiale principium non generatum: nisi forte dicatur quod generetur ex non ente, quod est impossibile. Si autem in infinitum procederetur, numquam posset compleri generatio, quia infinita non est transire: ergo vel oportet ponere aliquid ingenitum materiale principium, aut impossibile est esse aliquam generationem.	450. But if there is (241). Here he shows that this conclusion is untenable, namely, that nothing is eternal and immobile. He does this, first, with respect to matter; and second (242:C 451), with respect to form (“Further, since generation”). Accordingly, he says first (241) that if nothing is eternal, it is impossible for anything to be generated. He proves this as follows. In every process of generation there must be something which comes to be and something from which it comes to be. Therefore, if that from which a thing comes to be is itself generated, it must be generated from something. Hence there must either be an infinite regress in material principles, or the process must stop with some first thing which is a first material principle that is ungenerated, unless it might be said, perhaps, that it is generated from non-being; but this is impossible. Now if the process were to go on to infinity, generation could never be completed, because what is infinite cannot be traversed. Therefore it is necessary to hold either that there is some material principle which is ungenerated, or that it is impossible for any generation to take place.
lib. 3 l. 9 n. 8 Deinde cum dicit amplius autem ostendit idem ex parte causae formalis: et ponit duas rationes: quarum prima talis est. Omnis generatio et motus necesse est quod habeat aliquem finem. Et hoc probat, quia nullus motus est infinitus, sed cuiuslibet motus est aliquis finis. Hoc autem planum est in illis motibus, qui finiuntur in suis terminis. Sed videtur habere instantiam in motu circulari, qui potest esse perpetuus et infinitus, ut probatur in octavo physicorum. Et quamvis supposita sempiternitate motus, tota continuitas circularis motus sit infinita, secundum quod circulatio succedit circulationi, tamen quaelibet circulatio secundum speciem suam, completa et finita est. Quod autem ei succedat alia circulatio, hoc accidit quantum ad circulationis speciem.	451. Further, since generation (242). Here he proves the same thing with respect to the formal cause; and he gives two arguments, the first of which is as follows. Every process of generation and motion must have some terminus. He proves this on the grounds that no motion is infinite, but that each motion has some terminus. This is clear in the case of other motions which are completed in their termini. But it seems that a contrary instance is had in the case of circular motion, which can be perpetual and infinite, as is proved in Book VIII of the Physics. And even though motion is assumed to be eternal, so that the entire continuity of circular motion is infinite insofar as one circular motion follows another, still each circular motion is both complete in its species and finite. That one circular motion should follow another is accidental so far as the specific nature of circular motion is concerned.
lib. 3 l. 9 n. 9 Et quod dixerat de motu universaliter, specialiter ostendit de generatione: non enim potest esse aliqua generatio una infinita, quia non potest aliquid generari quod impossibile est pervenire ad finem generationis, cuius finis est factum esse. Et quod factum esse sit terminus generationis, ex hoc patet: quia quod generatum est, necesse est esse quando primo factum est, id est quando primo terminatur generatio eius. Oportet igitur quod cum forma secundum quam aliquid est, sit terminus generationis, quod non sit procedere in infinitum in formis, sed quod sit aliqua forma ultima, cuius non sit aliqua generatio. Omnis enim generationis finis est forma, ut dictum est. Et sic videtur quod sicut materiam, ex qua aliquid generatur, oportet esse ingenitam, ex eo quod non proceditur in infinitum, ita etiam quod formam aliquam oportet esse ingenitam, ex hoc quod in infinitum non procedatur in formis.	452. The things which he said about motion in general he proves specially in regard to generation; for no process of generation can be infinite, because that thing cannot be generated whose process of generation cannot come to an end, since the end of generation is to have been made. That its being made is the terminus of generation is clear from the fact that what has been generated must exist “as soon as it has come to be,” i.e., as soon as its generation is first terminated. Therefore, since the form whereby something is, is the terminus of generation, it must be impossible to have an infinite regress in the case of forms, and there must be some last form of which there is no generation. For the end of every generation is a form, as we have said. Thus it seems that just as the matter from which a thing is generated must itself be ungenerated because it is impossible to have an infinite regress, in a similar way there must be some form which is ungenerated because it is impossible to have an infinite regress in the case of forms.
lib. 3 l. 9 n. 10 Deinde cum dicit amplius autem secundam rationem ponit quae talis est. Si materia aliqua est prima quia est ingenita, multo rationabilius est quod sit substantia, idest forma ingenita, cum per formam res habeat esse; materia vero magis sit subiectum generationis et transmutationis. Si vero neutrum eorum sit ingenitum, nihil omnino erit ingenitum; cum omne quod est, pertineat ad rationem materiae vel formae, vel sit compositum ex utroque. Hoc autem est impossibile, ut nihil sit ingenitum, sicut probatum est. Ergo relinquitur quod necesse est aliquid esse praeter synolon, idest simul totum, idest praeter singulare compositum ex materia et forma. Et hoc dico aliquid quod sit forma et species. Materia enim per se non potest esse separata a singularibus, quia non habet esse nisi per aliud. De forma vero hoc magis videtur, per quam est esse rerum.	453. Further, if matter exists (143). He gives the second argument, which runs thus. If there is some first matter which is ungenerated, it is much more reasonable that there should be some substance, i.e., some form, which is ungenerated, since a thing has being through its form, whereas matter is rather the subject of generation and transmutation. But if neither of these is ungenerated, then absolutely nothing will be ungenerated, since everything which exists has the character of matter or form or is composed of both. But it is impossible that nothing should be ungenerated, as has been proved (242:C 452). Therefore it follows that there must be something else “besides the synolon,” or concrete whole, i.e., besides the singular thing which is composed of matter and form. And by something else I mean the form or specifying principle. For matter in itself cannot be separated from singular things, because it has being only by reason of something else. But this seems to be true rather of form, by which things have being.
lib. 3 l. 9 n. 11 Deinde cum dicit sed si hoc obiicit in contrarium. Si enim aliquis ponat aliquam formam esse separatam praeter singularia composita ex materia et forma, erit dubitatio in quibus hoc sit ponendum et in quibus non. Manifestum enim est quod hoc non est ponendum in omnibus, praecipue in artificialibus. Non enim est possibile quod sit aliqua domus praeter hanc domum sensibilem compositam ex materia et forma.	454. But again if anyone (244). Here he argues the other side of the question. For if one holds that there is some form separate from singular things which are composed of matter and form, the problem arises in which cases this must be admitted and in which not. For obviously this must not be held to be true in the case of all things, especially in that of those made by art. For it is impossible that there should be a house apart from this sensible house, which is composed of matter and form.
lib. 3 l. 9 n. 12 Hanc autem dubitationem solvit Aristoteles partim quidem in duodecimo huius: ubi ostendit esse quasdam substantias a sensibilibus separatas, quae sunt secundum seipsas intelligibiles: partim vero in septimo huius, ubi ostendit formas et species rerum sensibilium non esse a materia separatas. Non tamen sequitur, quod de rebus sensibilibus non possit haberi scientia, vel quod scientia sit sensus. Non enim oportet, quod eumdem modum essendi habeant res in seipsis, quem habent in consideratione scientis. Quae enim seipsis materialia sunt, ab intellectu immaterialiter cognoscuntur, ut etiam supra dictum est. Nec etiam oportet, si forma non est separata a materia, quod generetur: quia formarum non est generatio, sed compositorum, ut in septimo huius ostendetur. Patet ergo in quibus oportet ponere separatas formas, et quibus non. Nam omnium eorum quae sunt secundum suam naturam sensibilia, formae non sunt separatae. Sed illa quae sunt secundum naturam suam intelligibilia, sunt a materia separata. Non enim substantiae separatae sunt naturae horum sensibilium, sed sunt altioris naturae, alium habentes ordinem in rebus.	455. Now Aristotle solves this problem partly in Book XII (2488) of this work, where he shows that there are certain substances separate from sensible things and intelligible in themselves; and partly in Book VII (1503), where he shows that the forms or specifying principles of sensible things are not separate from matter. However, it does not follow that no science of sensible things can be had or that science is sensory perception. For it is not necessary that things have in themselves the same mode of being which they have in the intellect of one who knows them. For those things which are material in themselves are known in an immaterial way by the intellect, as has also been stated above (446). And even though a form is not separate from matter, it is not therefore necessary that it should be generated; for it is not forms that are generated but composites, as will be shown in Book VII (1417) of this work. It is clear, then, in what cases it is necessary to posit separate forms and in what not. For the forms of all things which are sensible by nature are not separate from matter, whereas the forms of things which are intelligible by nature are separate from matter. For the separate substances do not have the nature of sensible things, but are of a higher nature and belong to another order of existing things.

Lecture 10

Latin	English
lib. 3 l. 10 n. 1 Postquam philosophus inquisivit quae sunt principia, et utrum sint aliqua a materia separata, hic inquirit qualia sint principia. Et primo inquirit de unitate et multitudine ipsorum. Secundo inquirit, utrum sint in potentia vel in actu, ibi, his autem affine est quaerere et cetera. Tertio utrum principia sint universalia vel singularia, ibi, et utrum universalia sint et cetera. Circa primum duo facit. Primo inquirit qualiter principia se habeant ad unitatem. Secundo qualiter ipsum unum se habeat ad rationem principii, ibi, omnium autem et cetera. Circa primum tria facit. Primo inquirit specialiter de principio formali, utrum sit unum omnium existentium in una specie. Secundo inquirit idem de omnibus generaliter principiis, ibi, amplius autem et cetera. Tertio inquirit, utrum eadem sint principia aut diversa corruptibilium et incorruptibilium, ibi, non minor autem et cetera. Circa primum duo facit. Primo movet dubitationem. Secundo obiicit ad quaestionem, ibi, sed impossibile est. Est ergo dubitatio, utrum sit una substantia, idest forma omnium existentium in una specie, puta hominum.	456. Having asked what the principles are, and whether some are separate from matter, the Philosopher now asks what the principles are like. First (245:C 456), he asks whether the principles are one or many; second (287:C 519), whether they exist potentially or actually (“And connected with these problems”); and third (290:C 523), whether they are universals or singular things (“And there is also the problem”). In regard to the first he does two things. First (245:C 456), he inquires how the principles stand with respect to unity; and second (266:C 488), what relationship unity has to the notion of principle (“But the most difficult”). In regard to the first he does three things. First, he inquires specially about the formal principle: whether all things that are specifically the same have a single form. Second (248:C 46o), he asks the same question of all principles in general (“And again one might”). Third (250:C 466), he asks whether corruptible and incorruptible things have the same principles or different ones (“Again there is the problem”). In regard to the first he does two things. First, he introduces the problem. Second (246:C 457), he debates it (“But this is absurd”). The problem (245), then, is whether all things that belong to the same species, for example, all men, have a single substance or form.
lib. 3 l. 10 n. 2 Deinde cum dicit sed impossibile obiicit ad unam partem quaestionis: scilicet ad ostendendum quod non sit una forma omnium existentium in una specie: et hoc duabus rationibus, quarum prima talis est. Ea quae sunt in una specie, sunt multa et differentia: si igitur omnium in una specie existentium sit una substantia, sequetur quod ea quorum substantia est una, sint multa et differentia: quod est irrationabile.	457. But this is absurd (246). Then he advances arguments on one side of the question, to show that all things belonging to one species do not have a single form. He does this by means of two arguments, the first of which runs thus. Things that belong to one species are many and different. Therefore, if all things that belong to one species have a single substance, it follows that those which have a single substance are many and different. But this is unreasonable.
lib. 3 l. 10 n. 3 Deinde cum dicit simul autem hic ponit secundam rationem, quae talis est. Illud, quod est in se unum et indivisum, non componitur cum aliquo diviso ad constitutionem multorum. Sed manifestum est quod materia dividitur in diversis singularibus. Si igitur substantia formalis esset una et eadem, non esset assignare quomodo singulum horum singularium sit materia habens talem substantiam, quae est una et indivisa, ita quod singulariter sit simul totum habens haec duo, scilicet materia et formam substantialem, quae est una et indivisa.	458. And at the same time (247) Then he gives the second argument , which runs thus. That which is one and undivided in itself is not combined with something divided in order to constitute many things. But it is evident that matter is divided into different singular things. Hence, if substance in the sense of form is one and the same for all things, it will be impossible to explain how each of these singular things is a matter having a substance of the kind that is one and undivided, so that as a singular thing it is a concrete whole having two parts: a matter and a substantial form which is one and undivided.
lib. 3 l. 10 n. 4 In contrarium autem non obiicit, quia rationes, quae ad sequentem quaestionem proponuntur ad oppositum praedictarum rationum, sunt etiam illae quae sunt propositae supra de separatione universalium. Nam si sit universale separatum, necesse est ponere unam numero substantiam eorum quae conveniunt in specie, quia universale est substantia singularium. Huius autem quaestionis veritas determinatur in septimo huius, ubi ostendetur, quod quid est, idest essentiam cuiuslibet rei non esse aliud quam rem ipsam, nisi per accidens, ut ibi dicetur.	459. Now he does not argue the other side of the question, because the very same arguments which were advanced above regarding the separateness of universals are applicable in the inquiry which follows it against the arguments just given. For if a separate universal exists, it must be held that things having the same species have a single substance numerically, because a universal is the substance of singular things. Now the truth of this question will be established in Book VII (588:C 1356) of this work, where it is shown that the whatness or essence of a thing is not other than the thing itself, except in an accidental way, as will be explained in that place.
lib. 3 l. 10 n. 5 Deinde cum dicit amplius autem movet dubitationem de unitate principiorum in communi. Utrum scilicet principia rerum sint eadem numero, vel eadem specie et numero diversa: et circa hoc duo facit. Primo ponit rationes ad ostendendum, quod sint eadem numero. Secundo ad oppositum, ibi, at vero et cetera. Circa primum, ponit tres rationes et praemittit dubitationem, dicens, quod idem potest quaeri universaliter de principiis rerum, quod quaesitum est de substantia, utrum scilicet principia rerum sint eadem numero.	460. And again one might (248). Here he raises a difficulty concerning the unity of principles in general: whether the principles of things are numerically the same, or only specifically the same and numerically distinct. And in regard to this he does two things. First, he advances arguments to show that they are numerically the same. Second (249:C 464), he argues on the other side of the question (“But, on the other hand”). In regard to the first (248) he gives three arguments; and he introduces the problem, saying that the same question which was raised about substance can be raised about principles in general, i.e., whether the principles of things are numerically the same.
lib. 3 l. 10 n. 6 Et inducit primam rationem, ad ostendendum, quod sint eadem numero. Non enim invenitur in principiatis nisi quod ex principiis habent: si igitur in principiis non inveniatur unum numero, sed solum unum specie, nihil erit in principiatis unum numero, sed solum unum specie.	461. He introduces the first argument to show that they are numerically the same. For things composed of principles merely contain what they receive from these principles. Therefore, if principles are not found to be one numerically but only specifically, the things composed of these principles will not be one numerically but only specifically.
lib. 3 l. 10 n. 7 Secunda ratio talis est: quia illud quod est ipsum unum vel ipsum ens, oportet quod sit unum numero. Dicit autem ipsum unum vel ipsum ens, unitatem aut ens abstractum. Si igitur principium rerum non sit unum numero, sed solum unum specie, sequetur, quod nihil sit ipsum unum et etiam ipsum ens, idest quod ens et unum non per se subsistant.	462. The second argument runs thus: unity itself or being itself must be numerically one. And by unity itself or being itself he means unity or being in the abstract. Hence, if the principles of things are not one numerically but only specifically, it will follow that neither unity itself or being itself will subsist of themselves.
lib. 3 l. 10 n. 8 Tertia ratio est, quia scientia habetur de rebus per hoc, quod unum invenitur in multis, sicut homo communis invenitur in omnibus hominibus; non enim est scientia de singularibus, sed de uno quod invenitur in eis. Omnis autem scientia vel cognitio principiatorum dependet ex cognitione principiorum. Si igitur principia non sunt unum numero, sed solum unum specie, sequitur, quod scientia non sit de rebus.	463. The third argument is this: science is had of things because there is found to be a one-in-many, as man in common is found in all men; for there is no science of singular things but of the unity [i.e., common attribute] found in them. Moreover, all science or cognition of things which are composed of principles depends on a knowledge of these principles. If, then, principles are not one numerically but only specifically, it will follow that there is no science of beings.
lib. 3 l. 10 n. 9 Deinde cum dicit at vero si obiicit in contrarium tali ratione. Si principia sunt unum numero, ita quod quodlibet principiorum in se consideratum sit unum, non erit dicere de principiis existentium, quod hoc modo se habent sicut principia sensibilium. Videmus enim in sensibilibus, quod diversorum sunt diversa principia secundum numerum, sed eadem secundum speciem; sicut et eorum quorum sunt principia, sunt diversa secundum numerum, sed eadem secundum speciem. Sicut videmus quod diversarum syllabarum secundum numerum, quae conveniunt in specie, sunt principia eaedem literae secundum speciem, sed non secundum numerum. Si quis autem dicat quod non est ita in principiis entium, sed omnium entium principia sunt unum numero; sequetur quod nihil sit in rebus praeter elementa; quia quod est unum numero, est singulare. Sic enim appellamus singulare quod est unum numero, sicut universale quod est in multis. Quod autem est singulare, non multiplicatur nec invenitur nisi singulariter. Si igitur ponatur quod omnium syllabarum essent principia eaedem literae numero, sequeretur quod illae literae nunquam possent multiplicari, ut scilicet essent duo aut plura: et sic non posset seorsum inveniri in syllaba ista ba, vel da. Et eadem ratio est de aliis literis. Pari igitur ratione si omnium entium sint principia eadem numero, sequetur quod nihil sit praeter principia: quod videtur inconveniens: quia cum principium alicuius sit, non erit principium nisi sit aliquid praeter ipsum.	464. But, on the other hand (249). Here he argues the opposite side of the question in the following fashion. If principles are numerically one so that each of the principles considered in itself is one, it will be impossible to say that the principles of beings exist in the same way as the principles of sensible things. For we see that the principles of different sensible things are numerically different but specifically the same, just as the things of which they are the principles are numerically different but specifically the same. We see, for example, that syllables which are numerically distinct but agree in species have as their principles letters which are the same specifically though not numerically. And if anyone were to say that this is not true of the principles of beings, but that the principles of all beings are the same numerically, it would follow that nothing exists in the world except the elements, because what is numerically one is a singular thing. For what is numerically one we call singular, just as we call universal what is in many. But what is singular is incapable of being multiplied, and is encountered only as a singular. Therefore, if it is held that numerically the same letters are the principles of all syllables, it will fd1low that those letters could never be multiplied so that there could be two of them or more than two. Thus a could not be found in these two different syllables ba or da. And the argument is the same in the case of other letters. Therefore, by the same reasoning, if the principles of all beings are numerically the same, it will follow that there is nothing besides these principles. But this seems to be untenable; because when a principle of anything exists it will not be a principle unless there is something else besides itself.
lib. 3 l. 10 n. 10 Haec autem quaestio solvetur in duodecimo. Ibi enim ostendetur quod principia quae sunt intrinseca rebus, scilicet materia et forma, vel privatio, non sunt eadem numero omnium, sed analogia sive proportione. Principia autem separata, scilicet substantiae intellectuales, quarum suprema est Deus, sunt unum numero unaquaeque secundum seipsam. Id autem quod est ipsum unum et ens, Deus est; et ab ipso derivatur unitas secundum numerum in rebus omnibus. Scientia autem est de his, non quia sint unum numero in omnibus, sed quia est unum in multis secundum rationem. Ratio autem quae est ad oppositum verificatur in principiis essentialibus, non autem in principiis separatis, cuiusmodi sunt agens et finis. Multa enim possunt produci ab uno agente vel movente et ordinari in unum finem.	465. Now this question will be solved in Book XII (2464); for it will be shown there that the principles which things have, namely, matter and form or privation, are not numerically the same for all things but analogically or proportionally the same. But those principles which are separate, i.e., the intellectual substances, of which the highest is God, are each numerically one in themselves. Now that which is one in itself and being is God; and from Him is derived the numerical unity found in all things. And there is science of these, not because they are numerically one in all, but because in our conception there is a one in many. Moreover, the argument which is proposed in support of the opposite side of the question is true in the case of essential principles but not in that of separate ones, which is the class to which the agent and final cause belong. For many things can be produced by one agent or efficient cause, and can be directed to one end.

Lecture 11

Latin	English
lib. 3 l. 11 n. 1 Postquam philosophus inquisivit universaliter, utrum principia sint eadem numero omnia quae sunt unius speciei, vel eadem specie, hic inquirit utrum eadem numero sint principia corruptibilium et incorruptibilium: et circa hoc tria facit. Primo proponit quaestionem. Secundo inducit rationem ad ostendendum quod non sunt eadem principia corruptibilium et incorruptibilium, ibi, nam si eadem et cetera. Tertio inducit rationes ad ostendendum quod non sunt diversa, ibi, si vero diversa et cetera. Dicit ergo primo, quod quaedam dubitatio est, quae non minus relinquitur modernis philosophis Platonem sequentibus, quam fuit apud antiquos philosophos, qui etiam dubitaverunt, utrum corruptibilium et incorruptibilium sint eadem principia vel diversa.	466. Having investigated in a general way whether all principles belonging to one species are numerically the same, the Philosopher inquires here whether the principles of corruptible and incorruptible things are numerically the same. In regard to this he does three things. First (250:C 466), he raises the question. Second (251:C 467), he introduces an argument to show that the principles of corruptible and those of incorruptible things arc not the same (“For if they are the same”). Third (264:C 483), he introduces arguments to show that they are not different (“But if the principles”). He says first (250), then, that there is a problem which has been neglected no less by the modern philosophers, who followed Plato, than by the ancient philosophers of nature, who also were puzzled whether the principles of corruptible and incorruptible things are the same or different.
lib. 3 l. 11 n. 2 Deinde cum dicit nam si eadem obiicit ad ostendendum quod non sunt eadem principia corruptibilium et incorruptibilium: et circa hoc tria facit. Primo ponit rationem. Secundo improbat solutionem positae rationis, quam poetae theologi adhibebant, ibi, qui quidem et cetera. Tertio excludit solutionem quam adhibebant quidam philosophi naturales, ibi, a dicentibus et cetera. Dicit ergo, quod si ponantur corruptibilium et incorruptibilium esse eadem principia, cum ex eisdem principiis idem sequatur effectus, videtur quod omnia vel sint corruptibilia, vel omnia sint incorruptibilia. Relinquitur ergo quaestio quomodo quaedam sunt corruptibilia et quaedam incorruptibilia, et propter quam causam.	467. For, if they are the same (251). Here he advances an argument to show that the principles of corruptible and of incorruptible things are not the same. In regard to this he does three things. First (251:C 467), he gives the argument. Second (252:C 468), he criticizes the solution of the proposed argument which the theological poets gave (“The followers of Hesiod”). Third (255:C 472), he criticizes the solution which some philosophers of nature gave (“However, from those who”). He says first (251), then, that if the principles of corruptible and of incorruptible things are held to be the same, since from the same principles there follow the same effects, it seems that either all things are corruptible or all are incorruptible. Therefore the question arises how some things are corruptible and others incorruptible, and what the reason is.
lib. 3 l. 11 n. 3 Deinde cum dicit qui quidem excludit solutionem poetarum theologorum. Et primo ponit eorum solutionem. Secundo obiicit contra praedictam positionem, ibi, palam quod haec omnia sibi nota dicentes et cetera. Tertio se excusat a diligentiori improbatione huius positionis, ibi, sed de fabulose et cetera. Circa primum considerandum est, quod apud Graecos, aut naturales philosophos, fuerunt quidam sapientiae studentes, qui deis se intromiserunt occultantes veritatem divinorum sub quodam tegmine fabularum, sicut Orpheus, Hesiodus et quidam alii: sicut etiam Plato occultavit veritatem philosophiae sub mathematicis, ut dicit Simplicius in commento praedicamentorum. Dicit ergo, quod sectatores Hesiodi, et omnes, qui dicebantur theologi, curaverunt persuadere solis sibi, et nos alios spreverunt; quia scilicet veritatem, quam intellexerunt, taliter tradiderunt, quod eis solum possit esse nota. Si enim per fabulas veritas obumbretur, non potest sciri quid verum sub fabula lateat, nisi ab eo qui fabulam confixerit. Ii igitur Hesiodistae prima rerum principia deos nominaverunt; et dixerunt, quod illi de numero deorum, qui non gustaverunt de quodam dulci cibo, qui vocatur nectar vel manna, facti sunt mortales; illi vero qui gustaverunt, facti sunt immortales.	468. The followers of Hesiod (252) He criticizes the solution given by the theological poets. First (252:C 468), he gives their solution. Second (253:C 470), he argues against it (“And it is clear that”). Third (254:C 471), he gives the reason why he does not criticize this position with more care (“But with regard to those”). Concerning the first (252) it Must be noted that there were among the Greeks, or philosophers of nature, certain students of wisdom, such as Orpheus, Hesiod and certain others, who were concerned with the gods and hid the truth about the gods under a cloak of fables, just as Plato hid philosophical truth under mathematics, as Simplicius says in his Commentary on the Categories.’ Therefore he says that the followers of Hesiod, and all those who were called theologians, paid attention to what was convincing to themselves and have neglected us, because the truth which they understood was treated by them in such a way that it could be known only to themselves. For if the truth is obscured by fables, then the truth which underlies these fables can be known only to the one who devised them. Therefore the followers of Hesiod called the first principles of things gods, and said that those among the gods who have not tasted a certain delectable food called nectar or manna became mortal, whereas those who had tasted it became immortal.
lib. 3 l. 11 n. 4 Potuit autem sub hac fabula aliquid veritatis occulte latere, ut scilicet per nectar et manna intelligatur ipsa suprema bonitas primi principii. Nam omnis dulcedo dilectionis et amoris ad bonitatem refertur. Omne autem bonum a primo bono derivatur. Potuit ergo esse intellectus eorum quod ex participatione propinqua summae bonitatis aliqua incorruptibilia reddantur, sicut quae perfecte participant divinum esse. Quaedam vero propter longe distare a primo principio, quod est non gustare manna et nectar, non possunt perpetuitatem conservare secundum idem numero, sed secundum idem specie: sicut dicit philosophus in secundo de generatione. Sed utrum hoc intenderint occulte tradere, vel aliud, ex hoc dicto plenius percipi non potest.	469. But some part of the truth could lie hidden under this fable, provided that by nectar or manna is understood the supreme goodness itself of the first principle. For all the sweetness of love and affection is referred to goodness. But every good is derived from a first good. Therefore the meaning of these words could be that some things are incorruptible by reason of an intimate participation in the highest good, as those which participate perfectly in the divine being. But certain things because of their remoteness from the first principle, which is the meaning of not to taste manna and nectar, cannot remain perpetually the same in number but only in species, as the Philosopher says in Book II of Generation. But whether they intended to treat this obscurely or something else, cannot be perceived any more fully from this statement.
lib. 3 l. 11 n. 5 Deinde cum dicit palam quod obiicit contra praedictam positionem: et dicit, quod praedicti Hesiodistae quid significare voluerint per ista nomina nectar et manna, fuit eis notum, sed non nobis. Et ideo quomodo afferantur istae causae ad istam quaestionem solvendam, et ad incorruptionem praestandam rebus, dixerunt supra nostrum intellectum. Si enim intelligantur ista verba secundum quod sonant, nullius efficaciae esse videntur. Dii enim, qui gustaverunt nectar et manna, aut gustaverunt propter delectationem, aut propter necessitatem essendi. His enim de causis aliqui sumunt cibum. Siquidem sumpserunt ista propter delectationem, non possunt nectar et manna esse eis causa existendi, ita quod per hoc incorruptibiles reddantur: quia delectatio est quoddam consequens ad esse. Si autem propter necessitatem essendi praedicta sumpserunt, non erunt semper iterum cibo indigentes. Videtur ergo quod corruptibiles existentes prius tamquam cibo indigentes, per cibum facti sunt incorruptibiles. Quod iterum videtur inconveniens; quia cibus non nutrit in sua specie, nisi corruptus transeat in speciem nutriti. Quod autem est corruptibile, non potest alii incorruptionem praestare.	470. And it is clear (253). He argues against the aforesaid position. He says that the meaning which these followers of Hesiod wished to convey by the terms nectar or manna was known to them but not to us. Therefore their explanation of the way in which these causes are meant to solve this question and preserve things from corruption is beyond our understanding. For if these terms are understood in their literal sense, they appear to be inadequate, because the gods who tasted nectar or manna did so either for the sake of pleasure or because these things were necessary for their existence, since these are the reasons why men partake of food. Now if they partook of them for the sake of pleasure, nectar and manna could not be the cause of their existence so as to make them incorruptible, because pleasure is something that follows on being. But if they partook of the aforesaid nourishment because they needed it to exist, they would not be eternal, having repeated need of food. Therefore it seems that gods who are first corruptible, as it were, standing as they do in need of food, are’made incorruptible by means of food. This also seems to be unreasonable, because food does not nourish a thing according to its species unless it is corrupted and passes over into the species of the one nourished. But nothing that is corruptible can be responsible for the incorruptibility of something else.
lib. 3 l. 11 n. 6 Deinde cum dicit sed de fabulose excusat se a diligentiori huius opinionis investigatione: et dicit quod de illis, qui philosophari voluerunt fabulose, veritatem scilicet sapientiae sub fabulis occultantes non est dignum cum studio intendere. Quia si quis contra dicta eorum disputaret secundum quod exterius sonant, ridiculosa sunt. Si vero aliquis velit de his inquirere secundum veritatem fabulis occultatam, immanifesta est. Ex quo accipitur quod Aristoteles disputans contra Platonem et alios huiusmodi, qui tradiderunt suam doctrinam occultantes sub quibusdam aliis rebus, non disputat secundum veritatem occultam, sed secundum ea quae exterius proponuntur.	471. But with regard to those (254). Here he gives his reason for not investigating this opinion with more care, He says that it is not worth our while to pay any attention to those who have philosophized “by using fables,” i.e., by hiding philosophical truth under fables. For if anyone argues against their statements insofar as they are taken in a literal sense, these statements are ridiculous. But if one wishes to inquire into the truth hidden by these fables, it is not evident. Hence it is understood that Aristotle, in arguing against Plato and other thinkers of this kind who have treated their own doctrines by hiding them under something else, does not argue about the truth which is hidden but about those things which are outwardly expressed.
lib. 3 l. 11 n. 7 Deinde cum dicit a dicentibus disputat contra responsionem quorumdam philosophorum naturalium. Et circa hoc tria facit. Primo recitat rationem. Secundo ponit responsionem, ibi, etenim quam existimabit et cetera. Tertio improbat ipsam, ibi, videbitur autem et cetera. Dicit ergo primo, quod praetermissis illis, qui sub fabulis veritatem tradiderunt, oportet a tradentibus veritatem per modum demonstrationis inquirere de quaestione praedicta: scilicet, si ex eisdem principiis sunt omnia existentia, quare quaedam existentium naturaliter sunt sempiterna, quaedam vero corrumpantur. Et quia nec ipsi causam dicunt quare hoc sit, nec rationabile est sic se habere, ut ex eisdem principiis existentium quaedam sint corruptibilia, quaedam sempiterna: videtur manifeste sequi quod non sunt eadem principia nec causae corruptibilium et sempiternorum.	472. However, from those who make assertions (255). Then he argues against the answer given by some of the philosophers of nature; and in regard to this he does three things. First (255:C 472), he gives the argument. Second (256:C 473), he gives the answer (“For the explanation”). Third (257:C 474), he criticizes it (“Yet even hate”). Accordingly, he says, first (255), that, having dismissed those who treated the truth by using fables, it is necessary to seek information about the aforesaid question from those who have treated the truth in a demonstrative way, by asking them why it is that, if all beings are derived from the same principles, some beings are eternal by nature and others are corrupted. And since these men give no reason why this is so, and since it is unreasonable that things should be as they say (that in the case of beings having the same principles some should be corruptible and others eternal), it seems clearly to follow that corruptible and eternal things do not have the same principles or the same causes.
lib. 3 l. 11 n. 8 Deinde cum dicit etenim quam ponit quamdam solutionem: et dicit, quod ratio assignata circa praedictam dubitationem, quae maxime videtur esse conveniens ad quaestionem, est quam assignavit Empedocles: qui tamen idem passus est cum aliis: quia ratio quam assignavit, non est conveniens, sicut nec aliorum, ut ostendetur. Posuit enim quaedam principia communia corruptibilium et incorruptibilium; sed posuit quoddam principium esse causam specialem corruptionis, scilicet odium elementorum: ita scilicet quod adiunctio huius causae ad alia principia facit corruptionem in rebus.	473. For the explanation (256). Then he gives one solution. He says that the explanation given to the aforesaid question which seems to fit it best is the one which Empedocles gave, although he was subject to the same error as the others, because the explanation which he gave is no more adequate than theirs, as is about to be shown. For he maintained that corruptible and incorruptible things have certain common principles, but that a special principle, hate, causes the corruption of the elements in such a way that the coming together of this cause and another principle produces corruption in the world.
lib. 3 l. 11 n. 9 Deinde cum dicit videbitur autem improbat praedictam rationem Empedoclis: et hoc tripliciter. Primo quidem ostendendo, quod ratio ab eo assignata non convenit suae positioni. Secundo ostendendo, quod non est sufficiens, ibi, similiter quoque ipsius transmutationis et cetera. Tertio ostendendo quod non est ad propositum, ibi, attamen tantum solum dicit et cetera. Circa primum tria facit. Primo ostendit suam rationem non convenire aliis eius positionibus ex parte odii. Secundo ex parte ipsius Dei, ibi, propter quod et cetera. Tertio ex parte amoris, ibi, similiter autem nec amor et cetera. Dicit ergo primo, quod inconvenienter Empedocles ponit odium esse causam corruptionis: quia non minus secundum eius positionem videtur esse causa generationis in omnibus rebus, nisi in una re tantum. Ponebat enim omnia alia essentialiter composita ex odio simul cum aliis principiis, nisi solus Deus, quem ponebat compositum esse ex aliis principiis praeter odium. Deum autem appellabat caelum, sicut supradictum est in primo, quod Xenophanes ad totum caelum respiciens, ipsum unum dicit esse Deum. Ponebat autem Empedocles caelum esse compositum ex quatuor elementis, et ex amicitia: non autem ex lite sive ex odio, considerans indissolubilitatem caeli. Sed quantum ad alias res dicebat, quod omnia sunt ex odio quaecumque sunt, erunt vel fuerunt: sicut arbores pullulantes, et viri, et feminae, et bestiae quae sunt animalia terrestria: et vultures, quae sunt volantia diu viventia: et pisces nutriti in aqua, et dii longaevi. Videtur autem hos deos vocare vel stellas, quas ponebat quandoque corrumpi, licet post longum tempus: vel Daemones quos ponebant Platonici esse animalia aerea. Vel etiam dii quos ponebant Epicurei in forma humana, sicut supra dictum est. Ex hoc ergo quod omnia animalia praeter unum sunt generata ex odio, potest haberi quod odium sit causa generationis.	474. Yet even hate (257). Here he criticizes Empedocles’ argument, and he does this in three ways. First (257:C 474), he does this by showing that the argument which Empedocles gave is not in keeping with his position; second (261:C 478), by showing that it is not adequate (“Moreover, he does not”); third (263:C 481), by showing that it is not to the point (“Yet he alone speaks”). In regard to the first he does three things. First, he shows that Empedocles’ argument does not agree with his other views about hate; second (258:C 476), that it does not agree with his view about God himself (“For this reason”); and third (260:C 477), that it does not agree with his view about love (“Nor, similarly”). Accordingly, he says, first (257), that Empedocles’ position that hate is the cause of corruption is untenable, because according to his position hate also seems to be the cause of the generation of all things except one. For he held that everything else is composed essentially of hate along with the other principles, with the exception of God alone, whom he claimed to be composed of the other principles without hate. Moreover, he called the heavens God, as was stated above in Book I (49:C 101), because Xenophanes, after reflecting upon the whole heaven, said that the one itself is God. And Empedocles, considering the indestructibleness of the heavens, held that the heavens are composed of the four elements and love, but not of strife or hatred. But in the case of other things he said that all those which are or were or will be, come, from hate, such as sprouting trees, and men and women, and beasts (which are terrestial animals), and vultures (which are flying and long-lived animals), and fish (which are nourished in the water), and the long-lived gods. And by the gods he seems to mean either the stars, which he held are sometimes corrupted, although after a long period of time, or the demons, which the Platonists held to be ethereal animals. Or by the gods he also means those beings whom the Epicureans held to be of human form, as was stated above (210:C 408). Therefore, from the fact that all living things except one are generated from hate, it can be said that hate is the cause of generation.
lib. 3 l. 11 n. 10 Et praeter hoc etiam ex alia ratione. Manifestum est enim secundum positionem Empedoclis quod, si non esset odium in rebus, omnia essent unum. Odium enim est causa distinctionis secundum Empedoclem. Unde inducit verba Empedoclis dicentis, quod quando omnes res in unum conveniunt, ut puta quando fit chaos, tunc ultimum stabit odium separans et dissolvens. Unde litera Boetii habet: ea enim convenit, tunc ultimam scit discordiam. Et sic patet quod, cum esse mundi consistat in distinctione rerum, odium est causa generationis mundi.	475. And in addition to this there is another reason [why hate can be said to be the cause of generation]; for according to Empedocles’ position it is evident that, if hate did not exist in the world, all things would be one, since hate is the reason why things are distinct, according to Empedocles. Hence he quotes Empedocles’ words to the effect that, when all things come together into a unity, for example, when chaos comes into being, hate will stand last of all, separating and dissolving things. Hence the text of Boethius says: “When it comes together, then chaos knows the ultimate discord.” Thus it is clear that, since the being of the world consists in the distinction of things, hate is the cause of the world’s generation.
lib. 3 l. 11 n. 11 Deinde cum dicit propter quod ponit secundam rationem sumptam ex parte Dei: et dicit, quod cum Empedocles poneret odium non esse de compositione Dei, accidit secundum rationes eius, quod Deus, qui est felicissimus secundum omnium dicta, et per consequens maxime cognoscens, sit minus prudens omnibus aliis cognoscentibus. Sequetur enim, secundum positionem Empedoclis, quod non cognoscat omnia elementa, quia non habet odium; unde non cognoscit ipsum. Cognoscit autem simile simili secundum opinionem Empedoclis qui dixit, quod per terram cognoscimus terram, per aquam cognoscimus aquam et affectum, idest amorem vel concordiam cognoscimus per affectum, idest amorem vel concordiam: et similiter odium per odium, quod est triste sive grave vel malum secundum literam Boetii, qui dicit discordiam autem discordia malum. Sic igitur patet, quod Aristoteles reputat inconveniens, et contra id quod ponitur Deus felicissimus, quod ipse ignoret aliquid eorum, quae nos scimus. Sed quia ista ratio videbatur esse praeter propositum, ideo ad principale propositum rediens, dicit, quod redeundo ad illud unde prius erat ratio, manifestum est quod accidit Empedocli quod odium non sit magis causa corruptionis quam existendi.	476. For this reason (258). Here he gives a second argument, which pertains to the deity. He says that, since Empedocles would hold that hate is not a constituent of the divine composition, it follows, according to his arguments, that God, who is said by all men to be most happy, and consequently most knowing, is less prudent than all other beings who have knowledge. For according to Empedodes’ position it follows that God does not know the elements because He does not contain hate. Hence He does not know himself. And like knows like according to the opinion of Empedodes, who said that by earth we know earth, by water water, “and by affection,” i.e., love or concord, we know affection, or love or concord. And in a similar way we know “hate by hate,” which is sadness, whether unpleasant or evil, according to the text of Boethius, who says that “by evil discord we know discord.” It is evident, then, that Aristotle thought this untenable and contrary to the position that God is most happy because He himself would not know some of the things that we know. And since this argument seemed to be beside the point, therefore, returning to his principal theme, he says (259) that, in returning to the point from which the first argument began, it is evident, so far as Empedocles is concerned, that hate is no more a cause of corruption than of being.
lib. 3 l. 11 n. 12 Deinde cum dicit similiter autem ponit tertiam rationem ex parte amoris: et dicit, quod similiter etiam amor non est causa generationis vel existendi, ut ipse ponebat, si alia eius positio attendatur. Dicebat enim quod cum omnia elementa in unum congregabuntur, tunc erit corruptio mundi. Et sic amor corrumpit omnia: ergo quantum ad totum mundum amor erat causa corruptionis, odium autem generationis. Quantum autem ad singulares odium erat causa corruptionis et amor generationis.	477. Nor, similarly, is love (260). Here he gives the third argument, which pertains to love. He says that in like manner love is noe the cause of generation or being, as Empedocles claimed, if another position of his is considered. For he said that, when all the elements are combined into a unity, the corruption of the world will then take place; and thus love corrupts all things. Therefore, with respect to the world in general, love is the cause of corruption, whereas hate is the cause of generation. But with respect to singular things, hate is the cause of corruption and love of generation.
lib. 3 l. 11 n. 13 Deinde cum dicit similiter quoque ostendit quod ratio eius non fuit sufficiens. Dicebat enim quamdam transmutationem esse in rebus odii et amicitiae, ita scilicet quod amor quandoque omnia uniebat, et postmodum omnia odium separabat. Sed causam, quare sic transmutabatur, ut quodam tempore dominaretur odium, et alio tempore amor, nullam aliam dicebat, nisi quia sic aptum natum est esse.	478. Moreover, he does (261). Here he shows that Empedocles’ argument is not adequate. For Empedodes said that there exists in the world a certain alternation of hate and friendship, in such a way that at one time love unites all things and afterwards hate separates them. But as to the reason why this alternation takes place, so that at one time hate predominates and at another time love, he said nothing more than that it was naturally disposed to be so.
lib. 3 l. 11 n. 14 Et ponit consequenter verba Empedoclis, quae, quia in Graeco metrice scripta sunt, habent aliquam difficultatem et diversitatem a communi modo loquendi. Sunt autem haec verba eius, sed itaque magnum odium in membris nutritum est, et ad honorem intendebat perfecto tempore, qui mutabilis dissolvit sacramentum. Litera vero Boetii sic habet sed cum magna discordia in membris alita sit in honores: quia processit completo anno, qui illis mutatis amplo rediit sacramento. Ad cuius intellectum notandum est, quod loquitur poetice de toto mundo, ad similitudinem unius animalis, in cuius membris et partibus primo quidem est magna convenientia, quam amorem nominabat sive concordiam: sed postea paulatim incipit aliqua dissonantia esse, quam dicit discordiam. Et similiter in partibus universi a principio erat magna concordia, sed postea paulatim nutritur odium quousque odium praecedat ad honorem, idest ad hoc quod dominetur super elementa. Quod quidem fit perfecto tempore quodam determinato, vel completo quodam anno, quem ponebat Empedocles: qui, scilicet odium et discordia, vel annus mutabilis existens dissolvit sacramentum, idest unionem praeexistentem elementorum, vel annus sive odium rediit amplo sacramento, quia quadam potentia et secreta virtute rediit ad dominandum in rebus.	479. And next he gives Empedocles’ words, which, because they are written in Greek verse, are difficult and differ from the common way of speaking. These words are (262): “But thus mighty hate was nourished among the members and rose to a position of honor when the time was fulfilled, which being changeable dissolved the bond.” But the text of Boethius runs thus: “But when mighty discord in the members was promoted to a place of honor, because it marched forward in a completed year, which, when these things have been changed, returns to a full bond.” Now in order to understand this it must be noted that he speaks poetically of the whole world as though it were a single living thing in whose members and parts there is found at first the greatest harmony, which he calls love or concord, and afterwards there begins to exist little by little a certain dissonance, which he calls discord. And, similarly, in the parts of the universe at first there was maximum concord, and afterwards hate was nourished little by little until it acquired “the place of honor,” i.e., it acquired dominion over the elements. This comes about when a completed time is reached or a year is completed, as Empedocles held, “which” (hate or discord, or the year), being changeable, dissolves “the bond,” i.e., the former union of the elements; or the year or hate returns to a full bond, because by a certain ability and hidden power it returns to predominate over things.
lib. 3 l. 11 n. 15 Post quae verba Empedoclis Aristoteles faciens vim in hoc quod dixerat mutabilis, subiungit exponens quasi necessarium ens transmutari: quasi dicat: sic praedicta dixit Empedocles ac si necessarium sit esse transmutationem odii et amoris: sed nullam causam ostendit huius necessitatis. In uno enim animali est manifesta causa transmutationis et odii et amoris, propter motum caeli, qui causat generationem et corruptionem in rebus. Sed talis causa non potest assignari totius universi sic transmutati per amicitiam et litem. Unde patet, quod eius ratio fuit insufficiens.	480. After these words of Empedodes, Aristotle, in giving the meaning of the word “changeable” which he used, adds the explanation as though change were necessary; for he says that Empedocles made the foregoing statements as though it were necessary that there should be an alternation of hate and love, but he gives no reason for this necessity. For in the case of this one living thing it is evident that what causes the alternation of hate and love is the motion of the heavens which causes generation and corruption in the world. But no such cause can be assigned why the whole should be changed in this way by love and hate. Hence it is clear that his argument was inadequate.
lib. 3 l. 11 n. 16 Deinde cum dicit attamen tantum ostendit quod praedicta ratio Empedoclis non est ad propositum: et dicit quod hoc solum videtur dicere confesse, idest manifeste, quod non ponit quaedam existentium ex principiis esse corruptibilia, et quaedam non corruptibilia, sed omnia ponit esse corruptibilia praeter sola elementa. Et ita videtur evadere praedictam dubitationem, qua dubitabatur, quare quaedam sunt corruptibilia et quaedam non, si sunt ex eisdem principiis? Unde etiam patet, quod eius ratio non est ad propositum, quia interemit id de quo est dubitatio.	481. Yet he alone (263). Here he shows that this argument of Empedocles is not to the point. He says that Empedocles seems to say 11 expressly,” i.e., clearly, only that he does not hold that some of the things derived from these principles are corruptible and others incorruptible, but he holds that all things are corruptible with the exception of the elements alone. Thus he seems to avoid the foregoing problem inasmuch as the question remains why some things are corruptible and some not, if they come from the same principles. Hence it is also clear that his argument is not to the point, because he neglects the very point that requires explanation.
lib. 3 l. 11 n. 17 Sed potest quaeri quomodo hic dicit, quod Empedocles ponebat omnia esse corruptibilia praeter elementa, cum supra dixerit unum esse Deum, scilicet ex aliis principiis compositum praeter quam ex odio? Sed dicendum, quod Empedocles ponebat duplicem corruptionem in rebus, sicut ex praedictis patet. Unam quidem secundum confusionem totius universi, quam faciebat amor; et ab hac corruptione nec ipsum Deum faciebat immunem, cum in eo poneret amorem, qui alia ei commiscebat. Aliam autem corruptionem ponebat singularium rerum, quarum principium est odium. Et hanc corruptionem excludebat a Deo per hoc, quod in eo odium non ponebat. Sic igitur Aristoteles epilogando concludit tot dicta esse ad ostendendum, quod non sunt eadem principia corruptibilium et incorruptibilium.	482. But it can be asked how he can say here that Empedocles held all things to be corruptible except the elements, since Empedocles has said above that the one is God, i.e., what is composed of the other principles except hate. It must be noted, however, that Empedocles posited two processes of corruption in the world, as is clear from what was said above. He posited one with respect to the blending of the whole universe, which was brought about by love; and from this process he did not make even God immune, because in God he placed love, which caused other things to be mixed with God. And he posited another process of corruption for singular things, and the principle of this process is hate. But he excluded this kind of corruption from God, seeing that he did not posit hate in God. In summing up, then, Aristotle concludes that this much has been said for the purpose of showing that corruptible and incorruptible things do not have the same principles.
lib. 3 l. 11 n. 18 Deinde cum dicit si vero obiicit ad contrariam partem per duas rationes: quarum prima est: si non sint eadem principia corruptibilium et incorruptibilium, relinquitur quaestio, utrum principia corruptibilium sint corruptibilia, an incorruptibilia. Si dicatur quod sint corruptibilia, ostendit hoc esse falsum duplici ratione. Quarum prima est: omne corruptibile corrumpitur in ea ex quibus est: si igitur principia corruptibilium sunt corruptibilia, oportet iterum ponere alia principia ex quibus sint. Et hoc inconveniens est, nisi ponantur principia procedere in infinitum. Ostensum autem est in secundo quod secundum nullum genus causae contingit in principiis procedere in infinitum. Similiter etiam est inconveniens si dicatur, quod fit status in principiis corruptibilibus; cum corruptio videatur esse per resolutionem in aliqua priora.	483. But if the principles (264) Here he argues the other side of the question, with two arguments. The first is this: if the principles of corruptible and incorruptible things are not the same, the question arises whether the principles of corruptible things are corruptible or incorruptible. If one says that they are corruptible, he proves that this is false by two arguments. The first runs thus: every corruptible thing is dissolved into the principles of which it is composed. If, then, the principles of corruptible things are corruptible, it will be necessary to hold also that there are other principles from which they are derived. But this is untenable, unless an infinite regress is posited. Now it was shown in Book II (152:C 299) that it is impossible to have an infinite regress in principles in any class of cause. And it would be just as untenable for someone to say that this condition applies in the case of corruptible principles, since corruption seems to come about as a result of something being dissolved into prior principles.
lib. 3 l. 11 n. 19 Secunda ratio est, quia si principia corruptibilium sint corruptibilia, oportet quod corrumpantur, quia omne corruptibile corrumpetur. Sed postquam sunt corrupta non possunt esse principia; quia quod corrumpitur vel corruptum est, non potest causare aliquid. Cum ergo corruptibilia semper causentur per successionem, non potest dici, quod principia corruptibilium sint corruptibilia.	484. The second argument runs thus. If the principles of corruptible things are corruptible, they must be corrupted, because every corruptible thing will be corrupted. But after they have been corrupted they cannot be principles, for what is corrupted or has been corrupted cannot cause anything. Therefore, since corruptible things are always caused in succession, the principles of corruptible things cannot be said to be corruptible.
lib. 3 l. 11 n. 20 Si autem dicatur, quod principia corruptibilium sunt incorruptibilia, manifestum est quod principia incorruptibilium sunt incorruptibilia. Relinquitur ergo quaestio, quare ex quibusdam incorruptibilibus principiis producantur effectus corruptibiles, et ex quibusdam effectus incorruptibiles. Hoc enim non videtur esse rationabile; sed aut est impossibile, aut indiget multa manifestatione.	485. Again, if it is said that the principles of corruptible things are incorruptible, evidently the principles of incorruptible things are incorruptible. Therefore the question remains why it is that from certain incorruptible principles corruptible effects are produced, and from certain others incorruptible effects are produced; for this seems to be unreasonable and is either impossible or requires considerable explanation.
lib. 3 l. 11 n. 21 Deinde cum dicit amplius autem secundam rationem ad principale propositum ponit, quae sumitur ex communi opinione omnium. Nullus enim conatus est hoc dicere, quod sint diversa principia corruptibilium et incorruptibilium; sed omnes dicunt eadem esse principia omnium. Et tamen id quod primo obiectum est, scilicet pro prima parte, ac si esset aliquid modicum omnes leviter transeunt, quod est concedere. Unde litera Boetii habet, sed primum obiectum deglutiunt, sicut hoc parvum quoddam opinantes.	486. Further, no one (265). Then relative to his main thesis he gives his second argument, which is drawn from the common opinions of all men. For no one has attempted to say that corruptible and incorruptible things have different principles, but all say that all things have the, same principles. Yet the first argument, given in favor of the first part of the question, all pass over lightly, as though it were of little importance; but this is to acknowledge its truth. Hence the text of Boethius says: “But they swallow the first argument as though they considered it a minor matter.”
lib. 3 l. 11 n. 22 Huius autem dubitationis solutio ponitur in duodecimo: ubi philosophus ostendit prima quidem principia activa vel motiva esse eadem omnium sed quodam ordine. Nam prima quidem sunt principia simpliciter incorruptibilia et immobilia. Sunt autem secunda incorruptibilia et mobilia, scilicet caelestia corpora, quae per sui motum causant generationem et corruptionem in rebus. Principia autem intrinseca non sunt eadem numero corruptibilium et incorruptibilium, sed secundum analogiam. Nec tamen principia intrinseca corruptibilium, quae sunt materia et forma, sunt corruptibilia per se, sed solum per accidens. Sic enim corrumpitur materia et forma corruptibilium, ut habetur in primo physicorum.	487. Now the solution to this problem is given in Book XII (2553), where the Philosopher shows that the first active or motive principles of all things are the same but in a certain sequence. For the first principles of things are unqualifiedly incorruptible and immobile, whereas the second are incorruptible and mobile, i.e., the celestial bodies, which cause generation and corruption in the world as a result of their motion. Now the intrinsic principles of corruptible and of incorruptible things are the same, not numerically but analogically. Still the intrinsic principles of corruptible things, which are matter and form, are not corruptible in themselves but only in reference to something else. For it is in this way that the matter and form of corruptible things are corrupted, as is stated in Book I of the Physics.

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.

Lecture 13

Latin	English
lib. 3 l. 13 n. 1 Postquam philosophus inquisivit utrum unum et ens sint substantia rerum, hic inquirit utrum numerus et magnitudo sint substantia rerum: et circa hoc tria facit. Primo movet dubitationem. Secundo obiicit pro una parte, ibi, nam si non sunt et cetera. Tertio obiicit ad contraria, ibi, at vero si hoc quidem confessum est et cetera. Dicit ergo primo, quod dubitatio habita, idest consequens ad praemissam, est, utrum numeri et magnitudines, scilicet corpora et superficies et termini eorum, ut puncta, sint aliquae substantiae vel a rebus separatae, vel etiam sint substantiae ipsorum sensibilium, aut non. Dicit autem hanc dubitationem esse consequentem ad praemissam; quia in praemissa dubitatione quaerebatur utrum unum sit substantia rerum; unum autem est principium numeri; numerus autem videtur esse substantia magnitudinis; sicut et punctum, quod est principium magnitudinis, nihil aliud videtur quam unitas positionem habens, et linea dualitas positionem habens. Prima autem superficies est ternarius positionem habens, corpus autem quaternarius positionem habens.	502. Having inquired whether unity and being are the substances of sensible things, the Philosopher now asks whether numbers and continuous quantities are the substances of sensible things; and in regard to this he does three things. First (502), he presents the question. Second (503), he argues in support of one side of the question (“For if they are not”). Third (507), he argues on the other side (“But if it is admitted”). Accordingly he says, first, that “connected with these,” i.e., following from the foregoing problem, there is the question whether numbers and continuous quantities, i.e., bodies, surfaces, and their extremities, such as points, are either substances that are separate from sensible things, or are the substances of sensible things themselves, or not. He says that this problem is a result of the foregoing one, because in the foregoing problem it was asked whether unity is the substance of things. Now unity is the principle of number. But number seems to be the substance of continuous quantity inasmuch as a point, which is a principle of continuous quantity, seems to be merely the number one having position, and a line to be the number two having position, and the primary kind of surface to be the number three having position, and a body the number four having position.
lib. 3 l. 13 n. 2 Deinde cum dicit nam si non obiicit ad ostendendum quod praedicta sint substantiae rerum: et circa hoc duo facit. Primo obiicit ad ostendendum quod praedicta sunt substantiae rerum. Secundo ostendit quomodo philosophi praecedentes secuti fuerunt rationes primas, ibi, propter quod multi. Circa primum duo facit. Primo enim obiicit ad ostendendum quod corpus sit substantia rerum. Secundo quod multo magis alia, ibi, at vero corpus et cetera. Dicit ergo primo, quod si praedicta non sunt substantiae quaedam, fugiet a nobis quid sit substantialiter ens, et quae sunt substantiae entium. Manifestum est enim quod passiones et motus, et relationes, et dispositiones seu ordines, et orationes secundum quod voce proferuntur, prout ponuntur in genere quantitatis, non videntur alicuius significare substantiam, quia omnia huiusmodi videntur dici de aliquo subiecto, et nihil eorum significare hoc aliquid, idest aliquid absolutum et per se subsistens. Et hoc specialiter manifestum est in praemissis, qui non dicuntur absolute, sed eorum ratio in quadam relatione consistit. Inter omnia vero, quae maxime videntur significare substantiam, sunt ignis et terra et aqua, ex quibus componuntur corpora multa. Praetermittit autem aerem, quia minus est sensibilis, unde aliqui opinati sunt aerem nihil esse. In his autem corporibus inveniuntur quaedam dispositiones, scilicet calor et frigus et aliae huiusmodi passiones vel passibiles qualitates, quae non sunt substantiae secundum praedicta. Unde relinquitur quod solum corpus sit substantia.	503. For if they are not (276). Then he advances an argument to show that these are the substances of sensible things; and in regard to this he does two things. First (276:C 503), he introduces an argument to show that these are the substances of sensible things. Second (278:C 506), he shows how the early philosophers followed out the first arguments (“For this reason”). In regard to the first he does two things. For, first, he advances an argument to show that body is the substance of things; and second (277:C 504), to show that many other things are substances to an even greater degree (“Yet a body”). He says, first (276), that if these things are not substances, we are in a quandary as to what being is essentially, and what the substances of beings are. For it is evident that affections and motions and relations and dispositions or arrangements, and their complex conceptions ‘ according as they are put into words, do not seem to signify the substance of anything; because all things of this kind seem to be predicated of a subject as something belonging to the genus of quantity, and no one of them seems to signify “this particular thing,” i.e., something that is complete and subsists of itself. This is especially evident in regard to the foregoing things, which are not said to be complete things but things whose nature consists in a kind of relation. But of all things those which especially seem to signify substance are fire, earth, and water, of which many bodies are composed. But he omits air, because it is less perceptible; and this is the reason why some thought air to be nothing. But in these bodies there are found certain dispositions, namely, hot and cold and other affections and passible qualities of this kind, which are not substances according to what has been said. It follows, then, that body alone is substance.
lib. 3 l. 13 n. 3 Deinde cum dicit at vero, procedit ulterius ad alia, quae etiam videntur magis esse substantia quam corpus: et dicit, quod corpus videtur minus esse substantia quam superficies, et superficies minus quam linea, et linea minus quam punctus aut unitas. Et hoc probat per duo media: quorum unum est; quia id, per quod aliquid definitur, videtur esse substantia eius: nam definitio significat substantiam. Sed corpus definitur per superficiem, et superficies per lineam, et linea per punctum, et punctus per unitatem, quia dicunt quod punctus est unitas positionem habens: ergo superficies est substantia corporis, et sic de aliis.	504. Yet a body (277) Here he proceeds to examine those things which appear to be substance to an even greater degree than a body. He says that a body seems to be a substance to a lesser degree than a surface, and a surface than a line, and a line than a point or a unit. He proves this in two ways, of which the first is as follows. That by which a thing is defined seems to be its substance, for a definition signifies substance. But a body is defined by a surface, a surface by a line, a line by a point, and a point by a unit, because they say that a point is a unit having position. Therefore surface is the substance of body, and so on for the others.
lib. 3 l. 13 n. 4 Secundum medium est, quia cum substantia sit primum in entibus, illud quod est prius, videtur esse magis substantia: sed superficies natura prior est corpore, quia superficies potest esse sine corpore non autem corpus sine superficie: ergo superficies est magis substantia quam corpus. Et idem potest argui de omnibus aliis per ordinem.	505. The second argument runs as follows. Since substance is the primary kind of being, whatever is prior seems to be substance to a greater degree. But a surface is naturally prior to a body, because a surface can exist without a body but not a body without a surface. Therefore a surface is substance to a greater degree than a body. The same reasoning can be applied to all the others in turn.
lib. 3 l. 13 n. 5 Deinde cum dicit propter quod ostendit quomodo philosophi praecedentes secuti fuerunt praedictas rationes; et dicit, quod propter praedictas rationes multi antiquorum philosophorum, et maxime illi, qui fuerunt priores, nihil opinabantur esse ens et substantiam nisi corpus, omnia vero alia esse quaedam accidentia corporis. Et inde est, quod quando volebant inquirere principia entium, inquirebant principia corporum, ut supra in primo circa opiniones antiquorum naturalium habitum est. Alii vero posteriores philosophi, qui reputabantur sapientiores praedictis philosophis, quasi altius attingentes ad principia rerum, scilicet Pythagorici et Platonici, opinati sunt numeros esse rerum substantias, inquantum scilicet numeri componuntur ex unitatibus. Unum autem videtur esse una substantia rerum. Sic ergo videtur secundum praemissas rationes et philosophorum opiniones, quod si praedicta non sunt substantiae rerum, scilicet numeri et lineae et superficies et corpora, nihil erit ens. Non est enim dignum ut, si ista non sunt entia, quod accidentia eorum entia vocentur.	506. For this reason (278). Then he shows how the earlier philosophers followed out the foregoing arguments. He says that it was because of the foregoing arguments that many of the ancient philosophers, especially the first, thought that body alone was being and substance, and that all other things were accidents of bodies. Hence when they wanted to study the principles of beings, they studied the principles of bodies, as was stated above in Book I (36:C 74) with regard to the positions of the ancient natural philosophers. But the other philosophers who came later, and were reputed to be wiser than the aforesaid philosophers inasmuch as they dealt more profoundly with the principles of things, i.e., the Pythagoreans and Platonists, were of the opinion that numbers are the substances of sensible things inasmuch as numbers are composed of units. And the unit seems to be one substance of things. Hence, according to the foregoing arguments and opinions of the philosophers, it seems that if these things—numbers, lines, surfaces, and bodies—are not the substances of things, there will be no being at all. For if these are not beings, it is unfitting that their accidents should be called beings.
lib. 3 l. 13 n. 6 Deinde cum dicit at vero obiicit in contrarium: et ponit quatuor rationes: quarum prima talis est. Si quis confitetur, quod longitudines et puncta sint magis substantiae quam corpora, sequetur quod, si huiusmodi non sint substantiae, et corpora non sint substantiae; et per consequens nihil erit substantia, quia accidentia corporum non sunt substantiae, ut supra dictum est. Sed puncta et linea et superficies non sunt substantiae. Haec enim oportet aliquorum corporum esse terminos; nam punctus est terminus lineae, linea superficiei, et superficies corporis. Non autem videtur qualium corporum sint illae superficies, quae sunt substantiae, vel lineae, vel puncta. Manifestum enim est, quod lineae et superficies sensibilium corporum non sunt substantiae; variantur enim per modum aliorum accidentium circa idem subiectum. Sequetur ergo quod nihil erit substantia.	507. But if it is (279). Then he argues in support of the other side of the question; and he gives four arguments, the first of which is as follows. If anyone were to admit that lengths and points are substances to a greater degree than bodies, then supposing that things of this sort are not substances, it also follows that bodies are not substances. Consequently, no substance will exist, because the accidents of bodies are not substances, as has been stated above (C 503). But points,’lines and surfaces are not substances. For these must be the limits of some bodies, because a point is the limit of a line, a line the limit of a surface, and a surface the limit of a body. But it is not evident to what sort of bodies these surfaces, lines and points, which are substances, belong. For it is evident that the lines and surfaces of sensible bodies are not substances, because they are altered in the same way as the other accidents in reference to the same subject. Therefore it follows that there will be no substance whatever.
lib. 3 l. 13 n. 7 Secundam rationem ponit ibi, amplius autem quae talis est. Omnia praedicta videntur esse quaedam corporis dimensiones: vel secundum latitudinem, ut superficies: vel secundum profunditatem, ut corpus: vel secundum longitudinem, ut linea. Sed dimensiones corporis non sunt substantiae: ergo huiusmodi non sunt substantiae.	508. Further, all of these (280). Here he gives the second argument, which is as follows. All of the abovementioned things seem to be certain dimensions of bodies, either according to width, as a surface, or according to depth, as a solid, or according to length, as a line. But the dimensions of a body are not substances. Therefore things of this kind are not substances.
lib. 3 l. 13 n. 8 Tertiam rationem ponit ibi, adhuc autem quae talis est. In corpore solido simili modo inest, scilicet potentialiter, quaelibet figura, quae potest protrahi ex illo solido per aliquam dimensionem. Sed manifestum est quod in quodam magno lapide nondum secto non inest Mercurius idest figura Mercurii, in actu, sed solum in potentia: ergo similiter in cubo, idest in corpore habente sex superficies quadratas, non inest medietas cubi, quae est quaedam alia figura, actu. Sed hoc modo est actu, quando iam cubus dividitur in duas medietates. Et quia omnis protractio novae figurae in solido exciso fit secundum aliquam superficiem, quae terminat figuram, manifestum est quod nec etiam superficies talis erit in corpore in actu, sed solum in potentia: quia si quaecumque superficies praeter exteriorem essent in actu in corpore solido, pari ratione esset in actu superficies, quae terminat medietatem figurae. Quod autem dictum est de superficie, intelligendum est in linea, puncto, unitate. Haec enim in continuo non sunt in actu, nisi solum quantum ad illa quae terminant continuum, quae manifestum est non esse substantiam corporis. Aliae vero superficies vel lineae non possunt esse corporis substantiae, quia non sunt actu in ipso. Substantia autem actu est in eo cuius est substantia. Unde concludit quod inter omnia, maxime videtur esse substantia corpus; superficies autem et lineae magis videntur esse substantia quam corpus. Haec autem si non sunt entia in actu, nec sunt aliquae substantiae, videtur effugere cognitionem nostram, quid sit ens, et quae sit rerum substantia.	509. And, similarly (281). Here he gives a third argument, which is as follows. Any figure which can be educed from a solid body according to some dimension is present in that body in the same way, i.e., potentially. But in the case of a large piece of stone which has not yet been cut, it is evident that “Mercury,” i.e., the figure of Mercury, is not present in it actually but only potentially. Therefore, in like manner, “in a cube,” i.e., in a body having six square surfaces, one half of the cube, which is another figure, is not present actually; but it becomes actual in this way when a cube has already been divided into two halves. And since every eduction of a new figure in a solid which has been cut is made according to some surface which limits a figure, it is also evident that such a surface will not be present in a body actually but only potentially. For if each surface besides the external one were actually present in a solid body, then for the same reason the surface which limits one half of the figure would also be actually present in it. But what has been said of a surface must also be understood of a line, a point, and a unit; for these are actually present in the continuum only insofar as they limit the continuum, and it is evident that these are not the substance of a body. But the other surfaces and lines cannot be the substance of a body, because they are not actually present in it; for a substance is actually present in the thing whose substance it is. Hence he concludes that of all of these body especially seems to be substance, and that surfaces and lines seem to be substance to a great degree than bodies. Now if these are not actual beings or substances, it seems to escape our comprehension as to what being is and what the substances of things are.
lib. 3 l. 13 n. 9 Quartam rationem ponit ibi nam cum et primo ponit ipsam. Secundo manifestat eam in quodam simili, ibi, similiter autem se habet et cetera. Dicit ergo primo, quod cum dictis inconvenientibus etiam irrationabilia accidunt ex parte generationis et corruptionis, ponentibus lineas et superficies esse substantias rerum. Omnis enim substantia, quae prius non fuit et postea est, aut prius fuit et postea non est, videtur hoc pati cum generatione et corruptione. Et hoc manifeste apparet in omnibus his quae per motum causantur. Puncta autem et lineae et superficies quandoque quidem sunt, quandoque vero non sunt, et tamen non generantur nec corrumpuntur; ergo nec sunt substantiae.	510. For along with (282). Here he gives the fourth argument. First, he states it, and second (283:C 513), he clarifies it by using a similar case (“And it is similar”). Accordingly, he says, first (282), that along with the other untenable consequences mentioned there also happen to be certain unreasonable views about generation and corruption on the part of those who hold that lines and surfaces are the substances of sensible things. For every substance which at first did not exist and later does exist, or which first was and afterwards is not, seems to suffer this change by way of generation and corruption. This is most evident in the case of all those things which are caused by way of motion. But points and lines and surfaces sometimes are and sometimes are not. Yet they are not generated or corrupted. Neither, then, are they substances.
lib. 3 l. 13 n. 10 Probat autem utrumque suppositorum. Primo quidem, quod quandoque sint et quandoque non sint. Contingit enim corpora prius divisa copulari in unum aut prius copulata dividi. Quando autem corpora primum divisa copulantur, fit una superficies duorum corporum, quia partes corporis continui copulantur ad unum communem terminum, qui est superficies una. Quando vero corpus unum dividitur in duo, efficiuntur duae superficies. Quia non potest dici quod quando corpora duo componuntur, quod duae superficies eorum maneant, sed utraeque corrumpuntur, idest desinunt esse. Similiter quando corpora dividuntur, incipiunt esse de novo duae superficies prius non existentes. Non enim potest dici quod superficies quae est indivisibilis secundum profunditatem, dividatur in superficies duas secundum profunditatem: aut linea, quae est indivisibilis secundum latitudinem, dividatur secundum latitudinem: aut punctum, quod omnino est indivisibile, quocumque modo dividatur. Et sic patet quod ex uno non possent fieri duo in via divisionis: nec ex duobus praedictorum potest fieri unum in via compositionis. Unde relinquitur quod puncta et linea et superficies quandoque esse incipiant, et quandoque esse deficiant.	511. He then proves each assumption. The first of these, is that they sometimes are and sometimes are not. For it happens that bodies which were at first distinct are afterwards united, and that those which were at first united are afterwards divided. For when bodies which were initially separated are united, one surface is produced for the two of them, because the parts of a continuous body are united in having one common boundary, which is one surface. But when one body is divided into two, two surfaces are produced, because it cannot be said that when two bodies are brought together their surfaces remain intact, but that both “perish,” i.e., cease to be. In like manner, when bodies are divided there begin to exist for the first time two surfaces which previously did not exist. For it cannot be said that a surface, which is indivisible according to depth, is divided into two surfaces according to depth; or that a line, which is indivisible according to width, is divided according to width; or that a point, which is indivisible in every respect, is divided in any respect whatsoever. Thus it is clear that two things cannot be produced from one thing by way of division, and that one thing cannot be produced from two of these things by way of combination. Hence it follows that points, lines and surfaces sometimes begin to be and sometimes cease to be.
lib. 3 l. 13 n. 11 Consequenter probat secundum quod supponebatur, scilicet quod ista non generantur nec corrumpuntur. Omne enim quod generatur, ex aliquo generatur: et omne quod corrumpitur, in aliquid corrumpitur sicut in materiam. Sed non est dare aliquam materiam, ex qua ista generentur et in qua corrumpantur, propter eorum simplicitatem; ergo non generantur nec corrumpuntur.	512. After having proved this, he proves the second assumption, namely, that these things are neither generated nor corrupted. For everything that is generated is generated from something, and everything that is corrupted is dissolved into something as its matter. But it is impossible to assign any matter whatever from which these things are generated and into which they are dissolved, because they are simple. Therefore they are neither generated nor corrupted.
lib. 3 l. 13 n. 12 Deinde cum dicit similiter autem manifestat praedictam rationem in simili. Ita enim se habet nunc in tempore, sicut punctus in linea. Nunc autem non videtur generari et corrumpi: quia si generaretur vel corrumperetur, oporteret quod generatio et corruptio ipsius mensurarentur aliquo tempore vel instanti. Et sic mensura ipsius nunc, esset vel aliud nunc in infinitum, vel tempus, quod est impossibile. Et licet nunc non generetur et corrumpatur, tamen videtur semper esse aliud et aliud nunc: non quidem quod differant secundum substantiam, sed secundum esse. Quia substantia ipsius nunc, respondet subiecto mobili. Variatio autem ipsius nunc secundum esse, respondet variationi motus, ut ostenditur in quarto physicorum. Similiter ergo videtur se habere de puncto in comparatione ad lineam, et de linea in comparatione ad superficiem, et de superficie in comparatione ad corpus; scilicet quod non corrumpantur nec generentur, et tamen aliqua variatio attendatur circa huiusmodi. Eadem enim ratio est de omnibus his: omnia enim huiusmodi similiter sunt termini, secundum quod in extremo considerantur, vel divisiones secundum quod sunt in medio. Unde, sicut secundum defluxum motus variatur nunc secundum esse, licet maneat idem secundum substantiam propter identitatem mobilis, ita etiam variatur punctus, nec fit aliud et aliud propter divisionem lineae, licet non corrumpatur nec generetur simpliciter. Et eadem ratio est de aliis.	513. And it is similar (283). Then he makes the foregoing argument clear by using a similar case. For the now in time stands to time as a point to a line. But the now in time does not seem to be generated and corrupted, because if it were its generation and corruption would have to be measured by some particular time or instant. Thus the measure of this now either would be another now and so on to infinity, or would be time itself. But this is impossible. And even though the now is not generated or corrupted, still each now always seems to differ, not substantially but existentially, because the substance of the now corresponds to the mobile subject. But the difference of the now in terms of existence corresponds to the variation in motion, as is shown in Book IV of the Physics. Therefore the same thing seems to be true of a point in relation to a line, and of a line in relation to a surface, and of a surface in relation to a body, namely, that they are neither corrupted nor generated, although some variation is observable in things of this kind. For the same holds true of all of these, because all things of this kind are, in like manner, limits if regarded as at the extremities, or divisions if they are found in between. Hence, just as the now varies existentially as motion flows by, although it remains substantially the same because the mobile subject remains the same, so also does the point vary. And it does not become different because of the division of a line, even though it is not corrupted or generated in an absolute sense. The same holds true of the others.
lib. 3 l. 13 n. 13 Hanc autem quaestionem philosophus pertractat in decimotertio et decimoquarto. Et veritas quaestionis huius est, quod huiusmodi mathematica non sunt substantiae rerum, sed sunt accidentia supervenientia substantiis. Deceptio autem quantum ad magnitudines provenit ex hoc, quod non distinguitur de corpore secundum quod est in genere substantiae, et secundum quod est in genere quantitatis. In genere enim substantiae est secundum quod componitur ex materia et forma, quam consequuntur dimensiones in materia corporali. Ipsae autem dimensiones pertinent ad genus quantitatis, quae non sunt substantiae, sed accidentia, quibus subiicitur substantia composita ex materia et forma. Sicut etiam supra dictum est, quod deceptio ponentium numeros esse substantias rerum, proveniebat ex hoc quod non distinguebant inter unum quod est principium numeri, et unum quod convertitur cum ente.	514. But the Philosopher will treat this question in Books XIII and XIV. And the truth of the matter is that mathematical entities of this kind are not the substances of things, but are accidents which accrue to substances. But this mistake about continuous quantities is due to the fact that no distinction is made between the sort of body which/belongs to the genus of substance and the sort which belongs to the genus of quantity. For body belongs to the genus of substance according as it is composed of matter and form; and dimensions are a natural consequence of these in corporeal matter. But dimensions themselves belong to the genus of quantity, and are not substances but accidents whose subject is a body composed of matter and form. The same thing too was said above (500) about those who held that numbers are the substances of things; for their mistake came from not distinguishing between the one which is the principle of number and that which is interchangeable with being.

Lecture 14

Latin	English
lib. 3 l. 14 n. 1 Postquam philosophus inquisivit utrum mathematica sint principia rerum sensibilium, hic inquirit utrum supra mathematica sint aliqua alia principia, puta quae dicuntur species, quae sunt substantiae et principia horum sensibilium. Et circa hoc tria facit. Primo movet dubitationem. Secundo inducit rationem ad unam partem, ibi, nam si ideo. Tertio obiicit ad partem contrariam, ibi, at vero si ponimus et cetera. Dicit ergo primo, quod supposito quod mathematica non sint principia rerum sensibilium et eorum substantia, ulterius aliquis dubitabit quae est ratio quare praeter substantias sensibiles et praeter mathematica quae sunt media inter sensibilia et species, oportet iterum ponere tertium genus, scilicet ipsas species, idest ideas vel formas separatas.	515. Having inquired whether the objects of mathematics are the principles of sensible substances, the Philosopher now inquires whether in addition to the objects of mathematics there are certain other principles, such as those which we call Forms, which are the substances and principles of sensible things. In regard to this he does three things. First, he presents the question. Second (516), he argues one side of the question (“For if it is because”). Third (518), he argues the other side (“But if we hold”). Accordingly, he says, first, that if one assumes that the objects of mathematics are not the principles of sensible things and their substances, one will next have the problem why, in addition to both sensible things and the objects of mathematics (which are an intermediate class between sensible things and the Forms), it is necessary to posit a third class of entities, namely, the specific essences, i.e., the Ideas or separate Forms.
lib. 3 l. 14 n. 2 Deinde cum dicit nam si ideo obiicit ad unam partem: et videtur haec esse ratio quare oportet species ponere praeter sensibilia et mathematica: quia mathematica a praesentibus idest a sensibilibus, quae in universo sunt, differunt quidem in aliquo, quia mathematica abstrahunt a materia sensibili; non tamen differunt in hoc, sed magis conveniunt, quia sicut in sensibilibus inveniuntur plura numero differentia eiusdem speciei, utpote plures homines, aut plures equi, ita etiam in mathematicis inveniuntur plura numero differentia eiusdem speciei, puta plures trianguli aequilateri, et plures lineae aequales. Et si ita est, sequitur quod sicut principia sensibilium non sunt determinata secundum numerum, sed secundum speciem, ita etiam sit in mediis idest in mathematicis. Manifestum est enim quod in sensibilibus propter hoc quod sunt plura individua unius speciei sensibilis, principia sensibilium non sunt determinata numero, sed specie, nisi forte accipiantur principia propria huius individui, quae sunt etiam in numero determinata et individualia. Et ponit exemplum in vocibus. Manifestum est enim quod vocis literatae, literae sunt principia; non tamen sunt aliquo numero determinato individualium literarum, sed solum secundum speciem sunt determinatae literae secundum aliquem numerum, quarum aliae sunt vocales, et aliae consonantes: sed haec determinatio est secundum speciem, non secundum numerum. Non enim unum solum est a sed multa, et sic de aliis literis. Sed si accipiantur hae literae, quae sunt principia huius determinatae syllabae vel dictionis aut orationis, sic sunt determinatae numero. Et eadem ratione, cum sint multa mathematica numero differentia in una specie, non poterunt esse mathematica principia mathematicorum determinata numero, sed determinata specie solum: puta si dicamus quod principia triangulorum sunt tria latera et tres anguli. Sed haec determinatio est secundum speciem: contingit enim quodlibet eorum in infinitum multiplicari. Si igitur nihil esset praeter sensibilia et mathematica; sequeretur quod substantia speciei non esset una secundum numerum, et quod principia entium non essent determinata in aliquo numero, sed erunt determinata solum secundum speciem. Si ergo est necessarium quod sint determinata secundum numerum (alioquin contingeret esse principia rerum infinita numero), sequitur quod necesse sit species esse praeter mathematica et sensibilia.	516. For if it is because (285) Here he argues one side of the question. The reason why it is necessary to posit separate Forms over and above sensible substances and the objects of mathematics seems to be that the objects of mathematics differ in one respect “from the things at hand,” i.e., from sensible things, which exist in the universe; for the objects of mathematics abstract from sensible matter. Yet they do not differ but rather agree in another respect. For just as we find many sensible things which are specifically the same but numerically different, as many men or many horses, in a similar way we find many objects of mathematics which are specifically the same but numerically different, such as many equilateral triangles and many equal lines. And if this is true, it follows that, just as the principles of sensible things are not limited in number but in species, the same thing is true “of the intermediate entities”—the objects of mathematics. For since in the case of sensible things there are many individuals of one sensible. species, it is evident that the principles of sensible things are not limited in number but in species, unless of course we can consider the proper principles of a particular individual thing, which are also limited in number and are individual. He gives as an example words; for in the case of a word expressed in letters it is clear that the letters are its principles, yet there are not a limited number of individual letters taken numerically, but only a limited number taken specifically, some of which are vowels and some consonants. But this limitation is according to species and not according to number. For a is not only one but many, and the same applies to other letters. But if we take those letters which are the principles of a particular syllable, whether written or spoken, then they are limited in number. And for the same reason, since there are many objects of mathematics which are numerically different in one species, the mathematical principles of mathematical science could not be limited in number but only in species. We might say, for example, that the principles of triangles are three sides and three angles; but this limitation is according to species, for any of them can be multiplied to infinity. Therefore, if there were nothing besides sensible things and the objects of mathematics, it would follow that the substance of a Form would be numerically one, and that the principles of beings would not be limited in number but only in species. Therefore, if it is necessary that they be limited in number (otherwise it would happen that the principles of things are infinite in number), it follows that there must be Forms in addition to the objects of mathematics and sensible things.
lib. 3 l. 14 n. 3 Et hoc est quod Platonici volunt dicere, quod sequitur ex necessitate ad positiones eorum quod sit in singularium substantia species aliquid unum, cui non conveniat aliquid secundum accidens. Homini enim individuo convenit aliquid secundum accidens, scilicet album vel nigrum; sed homini separato, qui est species secundum Platonicos, nihil convenit per accidens, sed solum quod pertinet ad rationem speciei. Et quamvis hoc dicere intendant, non tamen bene dearticulant, idest non bene distinguunt.	517. This is what the Platonists wanted to say, because it necessarily follows from the things which they held that in the case of the substance of sensible things there is a single Form to which nothing accidental belongs. For something accidental, such as whiteness or blackness, pertains to an individual man, but to this separate man, who is a Form, according to the Platonists, there pertains nothing accidental but only what belongs to the definition of the species. And although they wanted to say this, they did not “express themselves” clearly; i.e., they did not clearly distinguish things.
lib. 3 l. 14 n. 4 Deinde cum dicit at vero obiicit in contrarium: et dicit, quod si ponamus species separatas esse, et quod principia rerum non sunt solum determinata specie, sed etiam numero, quaedam inconvenientia sequuntur, quae superius in quadam quaestione sunt tacta. Hanc autem dubitationem philosophus determinat duodecimo et quartodecimo huius libri. Et veritas dubitationis est quod sicut mathematica non sunt praeter sensibilia, ita nec species rerum separatae praeter mathematica et sensibilia. Principia autem rerum efficientia et moventia sunt quidem determinata numero; sed principia rerum formalia quorum sunt multa individua unius speciei, non sunt determinata numero, sed solum specie.	518. But if wehold that (286). Then he counters with an argument for the other side of the question. He says that, if we hold that there are separate Forms and that the principles of things are limited not only in species but also in number, certain impossible consequences will follow, which are touched on above in one of the questions (464). But the Philosopher will deal with this problem in Book XII (2450) and Book XIV of this work. And the truth of the matter is that, just as the objects of mathematics do not exist apart from sensible things, neither do Forms exist apart from the objects of mathematics and from sensible substances. And while the efficient and moving principles of things are limited in number, the formal principles of things, of which there are many individuals in one species, are not limited in number but only in species.

Lecture 15

Latin	English
lib. 3 l. 15 n. 1 Postquam philosophus inquisivit quae sunt principia, hic inquirit quomodo sunt. Et primo utrum sint in potentia vel in actu. Secundo utrum sint universalia vel singularia, ibi, et utrum universalia et cetera. Circa primum tria facit. Primo movet dubitationem. Secundo obiicit ad unam partem, ibi, nam si aliter et cetera. Tertio obiicit in contrarium, ibi, si vero potestate et cetera. Quaerit ergo primo, utrum prima principia sint in potentia, vel aliquo alio modo, idest in actu. Et haec dubitatio inducitur propter antiquos naturales, qui ponebant sola principia materialia, quae sunt in potentia. Platonici autem ponentes species quasi principia formalia, ponebant eas esse in actu.	519. Having inquired what the principles are, the Philosopher now asks how they exist. First, he asks whether they exist potentially or actually; and second (523), whether they are universals or singulars (“And there is also the problem”). In regard to the first he does three things. First, he raises the question. Second (520), he argues one side (“If they exist”). Third (501), he argues the opposite side (“But if the elements”). His first question (287), then, is whether first principles exist potentially or “in some other way,” i.e., actually. This problem is introduced because of the ancient philosophers of nature, who held that there are only material principles, which are in potency. But the Platonists, who posited separate Forms as formal principles, claimed that they exist actually.
lib. 3 l. 15 n. 2 Deinde cum dicit nam si aliter probat quod principia sint in potentia. Si enim essent aliter, scilicet in actu, sequeretur quod aliquid esset prius principiis; potentia enim actu prius est. Quod patet ex hoc, quod prius est a quo non convertitur consequentia essendi: sequitur autem si est, quod possit esse; non autem ex necessitate sequitur, si est possibile, quod sit actu. Hoc autem est inconveniens quod aliquid sit prius primo principio; ergo impossibile quod primum principium sit aliter quam in potentia.	520. If they exist (288). He proves that principles exist potentially. For if they were to exist “in some other way,” i.e., actually, it would follow that there would be something prior to principles; for potentiality is prior to actuality. This is clear from the fact that one thing is prior to another when the sequence of their being cannot be reversed; for if a thing exists, it follows that it can be, but it does not necessarily follow that, if a thing is possible, it will exist actually. But it is impossible for anything to be prior to a first principle. Therefore it is impossible for a first principle to exist in any other way than potentially.
lib. 3 l. 15 n. 3 Deinde cum dicit si vero obiicit in contrarium; quia si principia rerum sint in potentia, sequitur quod nihil sit entium in actu; nam illud quod est possibile esse, nondum est ens. Et hoc probat per hoc quod id quod fit, non est ens; quod enim est, non fit. Sed nihil fit nisi quod possibile est esse; ergo omne quod est possibile esse, est non ens. Si igitur principia sint tantum in potentia, erunt non entia. Si autem principia non sint, nec effectus sunt: sequitur ergo quod contingit nihil esse in entibus. Et concludit epilogando quod secundum praedicta necessarium est dubitare de principiis propter praemissas rationes.	521. But if the elements (289). Here he argues the other side of the question. If the principles of things exist potentially, it follows that no beings exist actually; for that which exists potentially does not yet exist actually. He proves this on the grounds that that which is coming to be is not a being. For that which exists is not coming to be; but only that comes to be which exists potentially. Therefore everything that exists potentially is nonbeing. Hence if principles exist only potentially, beings will not exist. But if principles do not exist, neither will their effects. It follows, then, that it is possible for nothing to exist in the order of being. And in summing this tip he concludes that according to what has been said it is necessary to inquire about the principles of things for the reasons given.
lib. 3 l. 15 n. 4 Haec autem quaestio determinabitur in nono huius, ubi ostendetur quod actus est simpliciter prior potentia, sed potentia est prior actu tempore in eo quod movetur de potentia ad actum. Et sic oportet primum principium esse in actu et non in potentia ut ostendit in duodecimo huius.	522. This question will be answered in Book IX (1844) of this work, where it is shown that actuality is prior to potentiality in an unqualified sense, but that in anything moved from potentiality to actuality, potentiality is prior to actuality in time. Hence it is necessary that the first principle exist actually and not potentially, as is shown in Book XII (2500) of this work.
lib. 3 l. 15 n. 5 Deinde cum dicit et utrum inquirit utrum principia sint per modum universalium aut per modum singularium: et circa hoc tria facit. Primo proponit dubitationem. Secundo obiicit ad unam partem, ibi, nam si universalia et cetera. Tertio obiicit ad aliam, ibi, si autem non universalia et cetera. Est ergo dubitatio, utrum principia sint universalia, vel existant per modum quorumdam singularium.	523. And here is also the problem (290). Here he asks whether the principles of things exist as universals or as singular things; and in regard to this he does three things. First, he presents the question. Second (524), he argues one side (“For if they are universals”). Third (527), he argues the other side (“However, if they are not universals”). The problem (290), then, is whether principles are universals or exist in the manner of singular things.
lib. 3 l. 15 n. 6 Deinde cum dicit nam si probat quod principia non sunt universalia tali ratione. Nullum communiter praedicatum de multis significat hoc aliquid, sed significat tale sive quale; non quidem secundum qualitatem accidentalem, sed secundum qualitatem substantialem; est enim quaedam substantialis qualitas, ut infra in quinto huius dicetur. Et ratio huius est quia hoc aliquid dicitur secundum quod in se subsistit; quod autem in se subsistit, non potest esse in multis ens, quod est de ratione communis. Quod enim in multis est, in se subsistens non est; nisi et ipsum esset multa, quod est contra rationem communis. Nam commune est, quod est unum in multis. Sic igitur patet, quod nullum communium significat hoc aliquid, sed significat formam in multis existentem.	524. For if they are (291). Then he proves that principles are not universals, by the following argument. No predicate common to many things signifies a particular thing, but signifies such and such a thing or of what sort a thing is; and it does this not according to accidental quality but according to substantial quality, as is stated below in Book V (487:C 987) of this work. The reason for this is that a particular thing is said to be such insofar as it subsists of itself. But that which subsists of itself cannot be something that exists in many, as belongs to the notion of common. For that which exists in many will not subsist of itself unless it is itself many. But this is contrary to the notion of common, because what is common is what is onein-many. Hence it is clear that a particular thing does not signify anything common, but signifies a form existing in many things.
lib. 3 l. 15 n. 7 Addit autem minorem, scilicet quod substantia significat hoc aliquid. Et hoc quidem verum est quantum ad primas substantias, quae maxime et proprie substantiae dicuntur, ut habetur in praedicamentis: huiusmodi enim substantiae sunt in se subsistentes. Relinquitur ergo quod principia, si sunt universalia, non sunt substantiae. Et ita vel substantiarum non erunt aliqua principia, vel oportebit dicere quod non sint substantiae substantiarum principia.	525. Further, he adds the minor premise, namely, that substance signifies a particular thing. And this is true of first substances, which are said to be substances in the full and proper sense, as is stated in the Categories; “ for substances of this kind are things which subsist of themselves. Thus it follows that, if principles are universals, they are not substances. Hence either there will be no principles of substances, or it will be necessary to say that the principles of substances are not substances.
lib. 3 l. 15 n. 8 Sed quia aliquis posset concedere quod aliquid communiter praedicatum significet hoc aliquid, consequenter diluitur cum dicit sed si est. Ostendit quod inconveniens ex hoc sequitur. Si enim id quod communiter praedicatur sit hoc aliquid, sequeretur quod omne id de quo illud commune praedicatur, sit hoc aliquid quod est commune. Sed planum est, quod de Socrate praedicatur et homo et animal, quorum utrumque, scilicet homo et animal, est quoddam commune praedicatum. Unde si omne commune praedicatum sit hoc aliquid, sequitur quod Socrates sit tria hoc aliquid, quia Socrates est Socrates, quod est hoc aliquid: ipse etiam est homo, quod est secundum praedicta hoc aliquid: ipse etiam est animal, quod similiter est hoc aliquid. Erit ergo tria hoc aliquid. Et ulterius sequitur quod sit tria animalia: nam animal praedicatur de ipso et de homine et de Socrate. Cum ergo hoc sit inconveniens, inconveniens est quod aliquid communiter praedicatum sit hoc aliquid. Haec igitur sunt inconvenientia quae sequuntur, si universalia sunt principia.	526. But since it is possible for someone to affirm that some common predicate might signify this particular thing, he therefore criticizes this when he says “But if it is (292).” He explains the untenable consequence resulting from this. For if a common predicate were a particular thing, it would follow that everything to which that common predicate is applied would be this particular thing which is common. But it is clear that both animal and man are predicated of Socrates, and that each of these—animal and man—is a common predicate. Hence, if every common predicate were a particular thing, it would follow that Socrates would be three particular things; for Socrates is Socrates, which is a particular thing; and he is also a man, which is a particular thing according to the above; and he is also an animal, which is similarly a particular thing. Hence he would be three particular things. Further, it would follow that there would be three animals; for animal is predicated of itself, of man, and of Socrates. Therefore, since this is impossible, it is also impossible for a common predicate to be a particular thing. These, then, will be the impossible consequences which follow if principles are universals.
lib. 3 l. 15 n. 9 Deinde cum dicit si autem obiicit in contrarium. Cum enim omnes scientiae sint universales, non sunt singularium, sed universalium. Si igitur aliqua principia non sint universalia, sed singularia, non erunt scibilia secundum seipsa. Si ergo de eis debet aliqua scientia haberi, oportebit esse aliqua priora principia, quae sunt universalia. Sic igitur oportet prima principia esse universalia, ad hoc quod scientia habeatur de rebus; quia ignoratis principiis necesse est alia ignorare.	527. However, if they are not (293). He argues the other side of the question. Since all sciences are universal, they are not concerned with singulars but with universals. Therefore, if some principles were not universals but were singular things, they would not be knowable in themselves. Hence, if any science were to be had of them, there would have to be certain prior principles, which would be universals. It is necessary, then, that first principles be universals in order that science may be had of things; because if principles remain unknown, other things must remain unknown.
lib. 3 l. 15 n. 10 Haec autem quaestio determinatur in septimo huius; ubi ostenditur quod universalia non sunt substantiae, nec principia rerum. Non autem propter hoc sequitur, quod si principia et substantiae rerum sint singularia, quod eorum non possit esse scientia; tum quia res immateriales etsi sint singulariter subsistentes, sunt tamen etiam intelligibiles; tum etiam quia de singularibus est scientia secundum universales eorum rationes per intellectum apprehensas.	528. This question will be answered in Book VII (1584) of this work, where it is shown that universals are neither substances nor the principles of things. However, it does not follow for this reason that, if the principles and substances of things were singulars, there could be no science of them, both because immaterial things, even though they subsist as singulars, are nevertheless also intelligible, and also because there is science of singulars according to their universal concepts which are apprehended by the intellect.