Authors/Thomas Aquinas/metaphysics/liber3/lect7

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.