Authors/Thomas Aquinas/metaphysics/liber3/lect13

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.