Authors/Thomas Aquinas/metaphysics/liber11/lect10

Lecture 10

Latin	English
lib. 11 l. 10 n. 1 Postquam philosophus determinavit de motu, hic determinat de infinito, quod est passio motus et cuiuslibet quanti universalis. Et circa hoc tria facit. Primo distinguit quot modis dicitur infinitum. Secundo ostendit quod non est infinitum actu, ibi, separabile quidem. Tertio quomodo infinitum invenitur in diversis, ibi, infinitum autem. Circa primum duo facit. Primo ostendit quot modis dicitur infinitum in actu. Secundo quot modus dicitur infinitum in potentia, ibi, adhuc autem appositione. Circa primum considerandum est, quod omne finitum dividendo pertransitur. Unde infinitum proprie est, quod mensurando pertransiri non potest. Tot ergo modis dicitur infinitum, quot modis dicitur intransibile.	2314. Having given his views about motion, here the Philosopher deals with the infinite, which is an attribute of motion and of any quantity in general. In regard to this he does three things. First (989)C 2314), he distinguishes the various senses in which the term infinite is used. Second (991:C 2322), he shows that the actually infinite does not exist (“That the infinite”). Third (1004:C 2354), he explains how the infinite is found in different things (“And the infinite”). In regard to the first he does two things. First, he explains the different senses in which the term infinite is used; and second (990:C 2319), the various senses in which things are said to be potentially infinite (“Further, a thing”). In regard to the first (989) part it should be borne in mind that every finite thing may be spanned by division. Hence the infinite, properly speaking, is what cannot be spanned by measurement; and therefore the term infinite is used in the same number of senses as the term untraversable.
lib. 11 l. 10 n. 2 Utrumque autem dicitur quatuor modis: quorum primus est secundum quod infinitum sive intransibile dicitur quod non potest transiri mensurando, eo quod non est natum secundum suum genus pertransiri, sicut dicimus punctum, aut unitatem, aut aliquid quod non est quantum et mensurabile, esse infinitum seu intransibile; per quem modum vox dicitur invisibilis, quia non est de genere visibilium.	2315. Now each of these is used in four ways. First, the infinite or untraversable means what cannot be spanned by measurement because it does not belong to the class of things which are naturally fitted to be spanned; for example, we say that the point or the unit or something which is not a quantity and is not measurable is infinite or untraversable; and in this sense the spoken word is said to be invisible because it does not belong to the class of things which are visible.
lib. 11 l. 10 n. 3 Secundo modo dicitur infinitum vel intransibile quod nondum est pertransitum, licet inceptum sit pertransiri: hoc enim est quod dicit habens transitionem imperfectam.	2316. Second, the infinite or untraversable means what has not yet been spanned although it has begun to be spanned. This is his meaning in saying “what is imperfectly spanned.”
lib. 11 l. 10 n. 4 Tertius modus est secundum quod dicitur infinitum vel intransibile quod vix transitur. Ut si dicamus profunditatem maris infinitam, vel altitudinem caeli, vel aliquam viam longam immensurabilem seu intransibilem seu infinitam: quia excedit vires mensurantis, licet in se sit transibilis.	2317. Third, the infinite or untraversable means what is spanned with difficulty. Thus we may say that the depth of the sea or the height of the sky is infinite, or that any long distance is immeasurable or untraversable or infinite, because it surpasses our powers of measurement although in itself it is capable of being spanned.
lib. 11 l. 10 n. 5 Quartus modus est secundum quod dicitur infinitum illud quod natum est habere transitionem aut terminum secundum suum genus, sed non habet. Puta si sit linea aliqua interminata. Et hoc est vere et proprie infinitum.	2318. Fourth, the infinite or untraversable means what belongs to the class of things which are naturally fitted to be spanned, or to have some limit set to them, but are not actually spanned; for example, if a line is limitless. This sense of the infinite is the true and proper one.
lib. 11 l. 10 n. 6 Secundo ibi, adhuc appositione ostendit quot modis dicitur infinitum in potentia; et dicit quod dicitur infinitum uno modo appositione sicut numerus. Semper enim cuilibet numero dato est apponere unitatem, et sic numerus est augmentabilis in infinitum.	2319. Further, a thing (990). Second, he explains the various senses in which things are said to be potentially infinite. He says that in one sense a thing is said to be infinite by addition, as a number; for it is always possible to add a unit to any number, and in this respect number is capable of infinite increase.
lib. 11 l. 10 n. 7 Alius modus secundum quod infinitum dicitur ablatione et divisione, secundum quod magnitudo dicitur divisibilis in infinitum.	2320. In another sense a thing is said to be infinite by subtraction or division inasmuch as a continuous quantity is said to be infinitely divisible.
lib. 11 l. 10 n. 8 Tertius modus contingit utrinque; sicut tempus dicitur infinitum et divisione, quia continuum est, et appositione, quia numerus est. Et similiter etiam in motu infinitum est.	2321. In a third sense it is possible for a thing to be infinite from both points of view; for example, time is said to be infinite both as regards division, because it is continuous, and as regards addition, because it is a number. It is in a similar way that the infinite is found in motion.
lib. 11 l. 10 n. 9 Deinde cum dicit separabile quidem ostendit, quod non sit infinitum in actu. Circa quod sciendum est, quod Platonici posuerunt infinitum separatum a sensibilibus, et posuerunt ipsum esse principium. Naturales autem philosophi posuerunt infinitum in rebus sensibilibus; non ita quod ipsum infinitum esset substantia, sed quod esset accidens alicui corpori sensibili. Primo ergo ostendit quod non est infinitum separatum. Secundo, quod non est infinitum actu in sensibilibus, ibi, quod autem in sensibilibus. Circa primum ponit tres rationes. Quarum prima est: quod si ipsum infinitum est quaedam substantia per se existens, et non accidens alicui subiecto, oportet quod ipsum infinitum sit absque magnitudine et multitudine, quia magnitudo et numerus sunt subiectum infiniti. Si autem est sine magnitudine et multitudine, oportet quod sit indivisibile; quia omne divisibile, aut est magnitudo, aut multitudo. Si autem est indivisibile, non est infinitum nisi primo modo, sicut vox dicitur invisibilis: quo modo non inquirimus nos nunc, nec ipsi; sed de infinito intransibili secundum quartum modum. Ergo, de primo ad ultimum, si infinitum sit substantia separata per se existens, non erit vere infinitum. Et sic ista positio destruit seipsam.	2322. That the infinite (991). Then he shows that the actually infinite does not exist; and in regard to this it should be noted that the Platonists held that the infinite is separate from sensible things and is a principle of them, whereas the philosophers of nature held that the infinite exists in sensible things, not in the sense that it is a substance, but rather in the sense that it is an accident of some sensible body. He therefore shows, first (991:C 2322), that the infinite is not a separate entity; and second (994:C 2327), that the actually infinite does not exist in sensible things (“That the infinite does not”). In treating the first member of this division he gives three arguments. The first is as follows: if the infinite is a substance which exists of itself and is not an accident of some subject, the infinite must lack continuous quantity and plurality, because continuous quantity and number constitute the subject of the infinite. But if it lacks continuous quantity and plurality, it must be indivisible, because everything divisible is either a continuous quantity or a plurality. But if it is indivisible, it is infinite only in the first sense of the term, as a spoken word is said to be invisible. However, we are not investigating this sense of the term here, nor did they use the term in this sense; but we are considering the fourth sense, i.e., what is untraversable. Therefore, all things considered, if the infinite were an independently existing substance, it would not be truly infinite. This position destroys itself in this way.
lib. 11 l. 10 n. 10 Secundam rationem ponit ibi, adhuc quomodo quae talis est. Infinitum est passio numeri et magnitudinis. Sed numerus et magnitudo non sunt per se existentia separata, ut in primo ostensum est, et infra ostendetur: ergo multo minus infinitum separatum est.	2323. Further, how can (992). Then he gives the second argument, which runs thus: infinity is an attribute of number and of continuous quantity. But number and continuous quantity are not things which have separate existence, as has been shown in Book I (122:C 239) and will be shown below (993:C 2324). Therefore much less is the infinite a separate substance.
lib. 11 l. 10 n. 11 Tertiam rationem ponit ibi, adhuc si quae talis est. Si infinitum ponitur separatum a sensibilibus, aut ponitur ut substantia per se existens, aut ut accidens inhaerens alicui subiecto separato, puta magnitudini, aut numero, quae sunt separata secundum Platonicos. Si autem ponatur esse accidens, tunc ipsum infinitum non erit principium entium inquantum hoc est infinitum, sed magis subiectum infiniti. Sicut principium locutionis non dicitur invisibile, sed vox, quamvis vox sit sic invisibilis.	2324. Again, if the infinite (993). Here he gives the third argument, which runs as follows. Let us suppose that the infinite is either a substance which is separate from sensible things or an accident belonging to some separate subject, for example, to continuous quantity or to number-which are separate according to the Platonists. Now if the infinite is assumed to be an accident, it cannot be the infinite as infinite that is a principle of existing things, but rather the subject of the infinite; just as what is invisible is not said to be a principle of speech, but the spoken word, although the spoken word is invisible in this sense.
lib. 11 l. 10 n. 12 Si autem infinitum sit substantia, et non praedicetur de aliquo subiecto, etiam manifestum est quod non potest esse actu infinitum. Aut enim est divisibile, aut indivisibile. Si autem est divisibile, et infinitum hoc ipsum quod est infinitum est substantia, oportet quod quaelibet pars eius accepta sit infinita, quia idem est infinito esse et infinitum, si infinitum est substantia, id est si infinitum praedicat propriam rationem eius quod est infinitum. Unde, sicut quaelibet pars aquae est aqua, et quaelibet pars aeris est aer, ita quaelibet pars infiniti est infinita, si infinitum est substantia divisibilis. Quare oportet dicere, quod aut sit indivisibile infinitum, aut sit divisibile in multa infinita. Sed hoc est impossibile, quod multa infinita constituant unum infinitum: quia infinitum non est maius infinito: omne autem totum maius est sua parte.	2325. And if the infinite is assumed to be a substance and is not predicated of a subject, it is also evident that it cannot be actually infinite; for it is either divisible or indivisible. But if the infinite itself as infinite is a substance and is divisible, any part of it which might be taken would necessarily be infinite; because infinity and the infinite are the same “if the infinite is a substance,” i.e., if infinity expresses the proper intelligible structure of the infinite. Hence, just as a part of water is water and a part of air is air, so too any part of the infinite is infinite if the infinite is a divisible substance. We must say, then, that the infinite is either indivisible or divisible into many infinites. But many infinite things cannot possibly constitute one finite thing; for the infinite is not greater than the infinite, but every whole is greater than any of its parts.
lib. 11 l. 10 n. 13 Relinquitur igitur, quod infinitum sit indivisibile. Sed impossibile est quod id quod est indivisibile sit actu infinitum, quia infinitum oportet esse quantum. Relinquitur igitur quod non sit substantia, sed accidens. Sed si est accidens, non est principium ipsum infinitum, sed illud cui accidit, ut dictum est, sive sit aer, ut quidam naturales posuerunt, sive sit par, ut posuerunt Pythagorici. Relinquitur igitur quod infinitum non possit esse substantia simul et principium entium. Et ultimo concludit quod haec inquisitio est universalis excedens naturalium considerationem.	2326. It follows, then, that the infinite is indivisible. But that any indivisible thing should be actually infinite is impossible, because the infinite must be a quantity. Therefore it remains that it is not a substance but an accident. But if the infinite is an accident, it is not the infinite that is a principle, but the subject of which it is an accident (as was said above), whether it be air, as some of the natural philosophers claimed, or the even, as the Pythagoreans claimed. Thus it follows that the infinite cannot be both a substance and a principle of beings at the same time. Last, he concludes that this investigation is a general one which goes beyond the study of natural things.
lib. 11 l. 10 n. 14 Deinde cum dicit quod autem probat quod infinitum actu non sit in sensibilibus. Et primo probat hoc per rationes probabiles. Secundo per rationes naturales, ibi, naturaliter autem. Dicit ergo primo, quod manifestum est quod infinitum actu non est in sensibilibus. Et ostendit duo. Dicit ergo primo, quod in sensibilibus non est corpus infinitum. De ratione enim corporis est, quod sit superficie determinatum. Sed nullum corpus determinatum superficie est infinitum: ergo nullum corpus est infinitum, neque sensibile, idest naturale, neque intellectuale, idest mathematicum.	2327. That the infinite does not exist (994). Then he proves that the actually infinite does not exist in sensible things. First (994:C 2327), he proves this by probable arguments; and second (996:C 2330), by arguments drawn from nature (“This is evident”). He accordingly says, first (994), that it is obvious that the actually infinite is not found in sensible things; and he proves two points. First, he says that there is no infinite body in the sensible world, for it is the nature of a body to be bounded by surfaces. But no body with a definite surface is infinite. Therefore no body is infinite, “whether it be perceptible,” i.e., a natural body, “or intelligible,” i.e., a mathematical one.
lib. 11 l. 10 n. 15 Secundo ibi, neque numerus dicit quod in sensibilibus non est numerus infinitus hoc modo. Omnis numerus et omne habens numerum est numerale. Sed nullum numerale est infinitum, quia numerale est pertransibile numerando: ergo nullus numerus est infinitus.	2328. Nor can there be (995). Second, he shows in the following way that there is no infinite number in sensible things. Every number and everything which has a number is numerable. But nothing numerable is infinite, because what is numerable can be spanned by numeration. Therefore no number is infinite.
lib. 11 l. 10 n. 16 Hae autem rationes non sunt naturales, quia non sumuntur ex principiis corporis naturalis, sed ex quibusdam principiis communibus et probabilibus, non ex necessariis: quia qui poneret corpus infinitum, non poneret ipsum terminari superficie. Hoc enim est de ratione corporis finiti. Et qui poneret multitudinem infinitorum, non poneret eam numerum, quia numerus est multitudo mensurata per unum, ut in decimo habitum est. Nullum autem mensuratum infinitum est.	2329. Now these arguments do not pertain to natural philosophy, because they are not based on the principles of a natural body but on certain principles which are common and probable and not necessary. For anyone who would claim that a body is infinite would not maintain that its surface has limits, for this characteristic belongs to the nature of a finite body. And anyone who would claim that there is an infinite multitude would not hold that it is a number, because number is multitude measured by one, as has been explained in Book X (875-C 2090). But nothing measured is infinite.
lib. 11 l. 10 n. 17 Deinde cum dicit naturaliter autem ostendit quod non sit infinitum in actu in sensibilibus, per rationes naturales. Et primo ex parte activi et passivi. Secundo ex parte loci et locati, ibi, adhuc sensibile. Activum autem et passivum, locus et locatum sunt proprietates corporis naturalis, inquantum huiusmodi. Et ideo dicit, quod istae rationes sunt naturales. Dicit ergo primo, quod si corpus aliquod sensibile et infinitum, aut erit corpus simplex, aut erit corpus compositum, sive mixtum.	2330. This is evident (996). Next, he proves that the actually infinite does not exist within sensible things, by using arguments drawn from nature. He does this, first (996:C 2330), with reference to the active and passive powers of bodies; and second (998:C 2339), with reference to place and the thing in place (“Again, a sensible body”). Now active and passive powers, Place and thing in place are proper to natural bodies as such; and therefore he says that these arguments are drawn from nature. He accordingly says, first (996), that, if a body is perceptible and infinite, it wilt be either a simple body or a composite body or compound.
lib. 11 l. 10 n. 18 Et primo ostendit, quod corpus compositum non possit esse infinitum, supposito quod corpora simplicia, quae sunt elementa corporum compositorum, sunt finita multitudine. Quod ita probat: quia oportebit quod vel omnia sint infinita in quantitate, aut quod unum sit infinitum, alia finita. Aliter enim non posset componi corpus infinitum ex elementis multitudine finitis.	2331. First, he shows that a composite body cannot be infinite, if we assume that simple bodies, which are the elements of composite bodies, are finite in number. He proves this as follows: either all the elements must be infinite in quantity, or one must be infinite and the others finite, otherwise an infinite body could not be composed of elements which are finite in number.
lib. 11 l. 10 n. 19 Non autem potest esse quod unum eorum sit infinitum et alia finita; quia in corpore mixto oportebit aliqualiter adaequari contraria, ad hoc, quod corpus mixtum conservetur. Aliter enim unum eorum quod esset excedens, corrumperet alia. Si autem unum sit infinitum, et alia finita, non est aequalitas, cum non sit proportio infiniti ad finitum. Unde corpus mixtum non poterit consistere, sed infinitum corrumpet alia.	2332. But that one of the elements should be infinite and the rest finite is impossible; because in the case of a compound contraries must somehow be equalized in order that the compound may be preserved in being, for otherwise that contrary which exceeds the others will destroy them. But if one contrary is infinite and the rest finite, no equality will be established, since there is no proportion between the infinite and the finite. A compound, then, could not exist, for the infinite element would destroy the others.
lib. 11 l. 10 n. 20 Sed quia posset aliquis dicere, quod corpus quod est finitum quantitate est potentius virtute, et ita fit aequalitas; puta si quis dicat quod in corpore mixto sit aer infinitus et ignis finitus: ideo subiungit, quod quamvis virtus unius corporis quod ponitur infinitum, deficiat a virtute alterius cuiuscumque, quod ponitur finitum, nihilominus finitum corrumperetur ab infinito. Corporis enim finiti necesse est esse virtutem finitam; et ita ignis finitus habebit virtutem finitam. Si ergo abscindatur ab aere infinito, aer aequalis igni habebit minorem virtutem, quam habeat totus aer infinitus, proportionatam tamen virtuti ignis. Sit ergo virtus ignis centupla virtuti aeris. Si ergo accipiamus centuplum de aere ab aere infinito, habebit aequalem virtutem cum igne; et ita totus aer infinitus habebit maiorem virtutem infinitam quam ignis, et corrumpet ipsum. Non est ergo possibile quod in corpore mixto sit unum elementum infinitum, et alia finita.	2333. And since someone might say that a body which is finite in quantity has greater power, and that equality is achieved in this way (for example, if someone were to say that in a cornpound air is infinite and fire finite), he therefore adds that, even if we suppose that the active power of one body which is assumed to be infinite falls short of the active power of any one of the others, because these are assumed to be finite, the finite element will be destroyed by the infinite one; for a finite body must have a finite power, and then finite fire will have a finite power. Hence, if from infinite air a portion of air equal to the fire is taken out, its power will be less than that of the whole infinite air, but proportioned to the power of fire. Let us suppose, then, that the power of fire is a hundred times greater than that of air. Hence, if we take away a hundredfold of air from infinite air it will be equal to fire in power; and thus the whole infinite air will have a greater infinite power than fire and will destroy it. It is impossible, then, that one element of a compound should be infinite and the rest finite.
lib. 11 l. 10 n. 21 Similiter non est possibile quod omnia sint infinita; quia corpus est quod distenditur in omnem dimensionem. Infinitum autem est quod habet dimensionem infinitam. Unde oportet quod corpus infinitum habeat ex omni parte dimensionem infinitam. Duo autem corpora non possunt esse simul. Sic ergo duo infinita non possunt coniungi in unum.	2334. Similarly, it is impossible that all should be infinite, because a body is what is extended in every dimension. But the infinite is what is infinite in dimension. Hence an infinite body must have an infinite dimension in every direction. But two bodies cannot be in the same place. Therefore two infinite bodies cannot be combined into one.
lib. 11 l. 10 n. 22 Secundo ibi, neque unum ostendit, quod non potest esse aliquod corpus simplex infinitum. Non enim est possibile, quod sit corpus simplex praeter elementa, ex quo omnia generantur, sicut quidam posuerunt vaporem: quia unumquodque resolvitur in ea ex quibus componitur: in nullis autem videmus resolvi corpora mixta nisi in quatuor elementa: non est ergo aliquod corpus simplex praeter quatuor elementa.	2335. Nor can the infinite (997). Second, he proves that the infinite cannot be a simple body. There cannot be a simple body apart from the elements, from which all of them are generated, as some claimed air to be, because each thing is dissolved into the elements of which it is composed. But we see that compounds are dissolved only into the four elements; and therefore there cannot be a simple body apart from the four elements.
lib. 11 l. 10 n. 23 Sed neque ignis, neque aliquod aliud elementorum potest esse infinitum: quia impossibile esset aliquod elementorum esse, praeter id quod esset infinitum, quia illud repleret totum undique. Et etiam si esset aliquod finitum, oporteret quod converteretur in illud infinitum, propter excessum ipsius virtutis; sicut Heraclitus manifeste posuit quod aliquando omnia sint convertenda in elementum ignis, propter nimium excessum virtutis eius.	2336. Nor can fire or any of the other elements be infinite, because no element could possibly exist except the one which is infinite, since it would fill every place. Again, if there were some finite element it would have to be changed into that infinite element because of the very great power of the latter; just as Heraclitus claimed that at some time all things must be changed into the element fire because of its very great power.
lib. 11 l. 10 n. 24 Et eadem ergo ratio est de uno corpore simplici, quod quidem faciunt naturales praeter ipsa elementa. Oportet enim quod habeat quamdam contrariam repugnantiam in ordine ad alia elementa, cum permutatio fiat ex illo uno solo corpore ad alia. Omnis autem rerum permutatio fit ex contrario in contrarium. Cum igitur unum contrariorum corrumpat alterum, sequitur quod si illud corpus quod ponitur praeter elementa sit infinitum, quod corrumpat alia.	2337. And the same argument therefore applies to the one simple body which the natural philosophers posited as an entity over and above the elements themselves; for it would have to be opposed to the other elements as a kind of contrary, since according to them there is change from that one body alone into the others. But every change in things is from one contrary to another. Therefore, since one of two contraries destroys the other, it follows that, if that body which is supposed to exist apart from the elements is infinite, it will destroy the others.
lib. 11 l. 10 n. 25 Praetermittit autem hic philosophus de corpore caelesti, quod est praeter ipsa quatuor elementa, non tamen habet aliquam contrarietatem sive repugnantiam ad ea, nec constituuntur ex eo naturaliter corpora. Non enim naturales philosophi ponentes corpus infinitum actu, pervenerunt in notitiam huius quintae essentiae vel naturae. Sed tamen in libro de caelo Aristoteles probat etiam de corpore caeli quod circulariter movetur, quod non sit infinitum actu.	2338. The philosopher omits the celestial body here, because, while it is something apart from the four elements, it is not contrary or repugnant to them in any way, nor are these bodies naturally derived from it. For the philosophers of nature who posited an actually infinite body did not attain any knowledge of this fifth essence or nature. Yet in The Heavens Aristotle proves that even a celestial body, which moves circularly, is not actually infinite.
lib. 11 l. 10 n. 26 Deinde cum dicit adhuc sensibile ostendit quod non est corpus sensibile infinitum, rationibus acceptis ex parte ipsius loci et locati: et ponit tres. Circa quarum primam praemittit duo necessaria. Quorum primum est, quod omne corpus sensibile est in loco. Et dicit notanter, sensibile, ad differentiam corporis mathematici, cui non attribuitur locus et tactus nisi per similitudinem.	2339. Again, a sensible body (998). Then he proves that a sensible body is not infinite; and he does this by means of arguments based upon place and a thing in place. He gives three arguments. As a sort of preamble to the first he considers two points necessary for its development. The first is that every sensible body is in a place. He emphasizes sensible in order to distinguish this kind of body from a mathematical one, to which place and contact are attributed only figuratively.
lib. 11 l. 10 n. 27 Aliud est quod idem est locus naturalis totius et partis, scilicet in quo naturaliter quiescit, et ad quod, scilicet naturaliter movetur. Sicut patet de terra et parte terrae. Utriusque enim locus naturalis est deorsum.	2340. The second point is that the natural place of a whole and that of a part are the same, i.e., the place in which it naturally rests and to which it is naturally moved. This is clear, for instance, in the case of earth and of any part of it, for the natural place of each is down.
lib. 11 l. 10 n. 28 His autem duobus positis proponit rationem, ibi, quare siquidem. Et est ratio talis. Si ponatur corpus sensibile infinitum, aut est totum unius speciei, sicut corpora similium partium, sicut aer et terra et sanguis et huiusmodi. Aut erit diversarum specierum in partibus.	2341. Hence, if the infinite (999). After giving these two points he states his argument, which runs as follows. If a sensible body is assumed to be infinite, either its parts will all be specifically the same, as is the case with bodies having like parts, such as air, earth, blood, and so on, or they will be specifically different.
lib. 11 l. 10 n. 29 Si autem est eiusdem speciei quantum ad omnes partes, sequetur, quod aut totum erit immobile et semper quiescens, aut totum semper movebitur. Quorum utrumque est impossibile et repugnans sensui.	2342. But if all of its parts are specifically the same, it will follow that the whole will always be at rest or always in motion. Each one of these is impossible and incompatible with the facts of sensory perception.
lib. 11 l. 10 n. 30 Sed quod oporteat alterum sequi, ostendit cum dicit, quid enim magis deorsum. Iam enim suppositum est quod idem est locus naturalis totius et partis. Manifestum est etiam quod unumquodque corpus, cum est in loco suo naturali, quiescit. Cum autem est extra naturalem locum suum, naturaliter movetur ad ipsum. Si igitur totus locus in quo est corpus similium partium infinitum, est ei naturalis, oportet quod sit naturalis cuilibet parti; et ita ipsum totum et quaelibet pars quiescit. Si vero non est ei naturalis, ergo et totum et pars erunt extra proprium locum. Et ita totum et quaelibet pars eius movebitur semper.	2343. For why should it (ibid.). Then he shows that the other alternative has to be accepted; for it has already been assumed that the natural place of a whole and that of a part are the same. And it is evident that every body is at rest when it is in its natural place, and that it naturally moves to its natural place when it is outside of it. If, then, the whole place occupied by a body having an infinite number of like parts is natural to it, this place must be natural to each part, and thus the whole and each of its parts will be at rest. But if it is not natural to it, the whole and each of its parts will then be outside their proper place; and thus the whole and any part of it will always be in motion.
lib. 11 l. 10 n. 31 Non enim potest dici quod aliqua pars loci sit naturalis toti et partibus eius, et aliqua pars innaturalis: quia si corpus esset infinitum, et omne corpus esset in loco, oportet quod locus etiam sit infinitus. In loco autem infinito non potest inveniri ratio divisionis, quare aliquid eius sit naturalis locus corporis, et aliud non naturalis locus: quia oportet esse aliquam determinatam proportionem et distantiam loci naturalis ad non naturalem: quod in loco infinito non potest inveniri. Hoc est ergo quod dicit, quod non magis movebitur corpus infinitum aut pars eius, deorsum quam sursum, vel versus quamcumque aliam partem; quia in loco infinito non potest sumi aliqua determinata proportio harum partium.	2344. For it cannot be said that some part of a place is natural to the whole and to its parts, and that some part of a place is not; because, if a body were infinite and every body were in a place, its place would also have to be infinite. But in infinite place there is no dividedness by reason of which one part of it is the natural place of the body and another is not, because there must be some fixed proportion and distance between a place which is natural and one which is not, and this cannot apply to an infinite place. This is what he means when he says that an infinite body or one of its parts will not be moved downwards rather than upwards or in some other direction, because in an infinite place it is impossible to find any fixed proportion between these parts.
lib. 11 l. 10 n. 32 Et ponit exemplum: ut si ponamus terram esse infinitam, non erit assignare rationem, quare magis moveatur vel quiescat hic quam ibi: quia totus locus infinitus est connaturalis similiter ipsius corporis infiniti, quod est in loco. Unde si aliqua pars loci est connaturalis glebae, et similiter alia pars; et si una non est connaturalis, nec alia. Si igitur corpus infinitum sit in loco, obtinebit totum locum infinitum. Et quomodo poterit simul esse quies et motus? Quia si ubique quiescit, non movebitur; aut si movebitur ubique, sequitur quod nihil quiescat.	2345. He gives an example of this. If we assume that the earth is infinite, it will be impossible to give any reason why it should be in motion or at rest in one place rather than in another, because the whole infinite place will be equally fitted by nature to the infinite body which occupies this place. Hence, if some part of a place is naturally fitted to a clod of earth, the same will apply to another part; and if one part is not naturally fitted to a Place, neither will another be. If, then, an infinite body is in a place, it will fill the whole of that infinite place. Yet how can it be at rest and in motion at the same time? For if it rests everywhere, it will not be in motion ; or if it is in motion everywhere, it follows that no part of it will be at rest.
lib. 11 l. 10 n. 33 Deinde cum dicit si autem prosequitur philosophus alteram partem disiunctivae, scilicet si totum non est similium partium: dicens, quod primo sequitur, quod corpus omnis, idest totius, si sit partium dissimilium specie, non sit unum nisi in tangendo, sicut acervus lapidum est unus. Quae autem sunt diversarum specierum, non possunt esse continua, sicut ignis et aer et aqua. Et hoc non est esse unum simpliciter.	2346. And if the whole (1000). Then the Philosopher examines the other alternative, namely, the supposition that the whole is not composed of like parts. He says that it follows, first, that, if “the body of the whole,” i.e., of the universe, is composed of specifically unlike parts, it will be one only by contact, as a pile of stones is one. But things specifically different, such as fire, air and water, cannot be continuous; and this is not to be one in an absolute sense.
lib. 11 l. 10 n. 34 Item si istud totum constat ex dissimilibus partibus specie, aut essent infinita specie, ita scilicet quod sint infinitae species diversae partes totius; aut essent finita specie, ita scilicet quod diversitas specierum quae est in partibus, aliquo certo numero concludatur.	2347. Again, if this whole is composed of parts which are specifically unlike, they will be either infinite in species, i.e., so that the different parts of the whole are infinite in species; or they will be finite in species, i.e., so that the diversity of species found among the parts amount to some fixed number.
lib. 11 l. 10 n. 35 Sed quod impossibile sit esse finita elementa secundum speciem, patet ex eo quod in praecedenti ratione est positum. Non enim esset possibile ex partibus numero finitis constitui totum infinitum, nisi vel omnes partes essent infinitae quantitate, quod est impossibile, cum corpus infinitum oporteat ad quamlibet partem infinitum esse, vel saltem quod aliqua pars vel aliquae partes infinitatem habeant. Sequitur igitur quod, si totum est infinitum et partes specie diversae infinitae numero, quod quaedam earum sint infinitae in quantitate, et quaedam finitae: puta si poneretur quod aqua esset infinita, et ignis finitus. Sed hoc ponere inducit corruptionem in contrariis: quia id quod est infinitum, corrumpet alia, ut supra ostensum est. Non est igitur possibile, quod sint finita numero.	2348. But that the elements cannot be finite in species is clear from what was proposed in the preceding argument; for it would be impossible for an infinite whole to be composed of parts which are finite in number, unless either all parts were infinite in quantity, which is impossible, since an infinite body must be infinite in any of its parts, or at least unless some part or parts were infinite. Therefore, if a whole were infinite and its parts were different species infinite in number, it would follow that some of them would be infinite and some finite in quantity—for example, if one were to assume that water is infinite and fire finite. But this position introduces corruption among contraries, because an infinite contrary would destroy other contraries, as has been shown above (996:C 2332). Therefore they cannot be finite in number.
lib. 11 l. 10 n. 36 Sed si sunt infinitae secundum speciem primae partes universi, quas oportet ponere partes simplices, sequitur quod loca erunt infinita, et quod elementa erunt infinita. Quorum utrumque est impossibile. Cum enim unumquodque corpus simplex habeat locum sibi connaturalem diversum a loco corporis alterius secundum speciem, si sint infinita corpora simplicia secundum speciem diversa, sequitur quod etiam sint infinita loca diversa specie. Quod patet esse falsum. Nam species locorum sunt sub aliquo numero determinato, quae sunt sursum et deorsum et huiusmodi. Elementa etiam esse infinita impossibile est; quia sic sequeretur quod essent ignota, et eis ignotis omnia ignorarentur. Si ergo impossibile est elementa esse infinita, necesse est quod loca sint finita, et per consequens quod totum sit finitum.	2349. But if the parts of the universe were infinite in species, and these must be assumed to be simple, it would follow that places would be infinite and that the elements would be infinite. But both of these are impossible; for since each simple body has a place naturally fitted to it which is specifically different from the place of another body, if there were an infinite number of simple bodies which are different in species, it would also follow that there are an infinite number of places which are different in species. This is obviously false; for the species of places are limited in number, and these are up and down, and so on. It is also impossible that the elements should be infinite in number, because it would then follow that they would remain unknown; and if they were unknown, all things would be unknown. Therefore, if the elements cannot be infinite, places must be finite, and consequently the whole must be finite.
lib. 11 l. 10 n. 37 Deinde cum dicit totaliter autem secundam rationem ponit; dicens, quod cum omne corpus sensibile habeat locum, impossibile est quod aliquod corpus sensibile sit infinitum: hac positione facta, quod omne corpus sensibile habeat gravitatem aut levitatem. Quod quidem verum erat secundum opinionem antiquorum naturalium ponentium corpus infinitum actu: sed ipse opinatur quod sit aliquod corpus sensibile, non habens gravitatem neque levitatem, scilicet corpus caeleste, ut probavit in libro de caelo et mundo. Et ideo hoc induxit sub conditione, quasi ab adversariis concessum, sed non simpliciter verum. Si ergo omne corpus sensibile est grave vel leve, et est aliquod corpus sensibile infinitum, oportet quod sit grave vel leve, et per consequens quod feratur sursum vel ad medium. Definitur enim leve quod fertur sursum, et grave quod fertur ad medium. Sed hoc est impossibile invenire in infinito, neque in toto neque in parte. Non enim invenitur medium in aliquo corpore nisi proportione habita ad extrema in dividendo totum. Infinitum vero non potest dividi secundum aliquam proportionem. Unde non potest ibi inveniri sursum et deorsum, nec extremum et medium.	2350. And in general (1001). Here he gives the second argument. He says that, since every sensible body has a place, it is impossible for any sensible body to be infinite, granted the assumption that every sensible body has heaviness and lightness-which would be true according to the opinion of the ancient natural philosophers, who claimed that bodies are actually infinite. Aristotle, however, is of the opinion that there is a sensible body which does not have heaviness or lightness, namely, a celestial body, as he proved in The Heavens. He introduces this circumstantially, as admitted by his opponents, but not in the sense that it is unqualifiedly true. If every sensible body, then, is either heavy or light and some sensible body is infinite, it must be heavy or light; and therefore it must be moved upwards or towards the center; for a light thing is defined as one that rises upwards, and a heavy thing as one that tends towards the center. But this cannot apply to the infinite, either to the whole of it or to a part; for the center of a body is found only when a proportion is established between the boundaries by dividing the whole. But the infinite cannot be divided according to any proportion; and therefore neither up and down nor boundary and center can be found there.
lib. 11 l. 10 n. 38 Considerandum autem quod haec ratio valet etiam si ponatur corpus tertium, quod neque est grave neque leve. Tale enim corpus naturaliter movetur circa medium, quod non potest in corpore infinito inveniri.	2351. This argument must be understood to apply even if one assumes that there is a third kind of body which is neither heavy nor light; for such a body is naturally moved around the center, and this could not be the case with an infinite body.
lib. 11 l. 10 n. 39 Deinde cum dicit adhuc omne hic philosophus ponit tertiam rationem, quae talis est. Omne corpus sensibile est in loco. Sed loci species sunt sex; scilicet sursum, deorsum, dextrum, sinistrum, ante et retro. Quae quidem impossibile est attribui corpori infinito, cum sint quaedam extrema distantiarum; et sic corpori infinito impossibile est attribuere locum. Non est igitur aliquod corpus sensibile infinitum. Non autem dicit quod sint sex species loci, asserere intendens quod ista loca distinguantur in elementis; quia motus eorum non distinguunt nisi sursum et deorsum; sed quia, sicut ab infinito corpore removentur sursum et deorsum, ita omnes aliae differentiae loci.	2352. Further, every sensible body (1002). The Philosopher now gives the third argument, which runs thus: every sensible body is in a place. But there are six kinds of place: up and down, right and left, before and behind; and it is impossible to attribute these to an infinite body, since they are ihe limits of distances. Thus it. is impossible that a place should be attributed to an infinite body; and therefore no sensible body is infinite. However, in saying that there are six kinds of place he does not mean that these places are distinguished because of the elements (for their motions are distinguished merely in terms of up and down) but only because, just as up and down are out of the question so far as an infinite body is concerned, so are all the other differences of place.
lib. 11 l. 10 n. 40 Quartam rationem ponit ibi totaliter autem. Quae talis est. Omne corpus sensibile est in loco. Sed impossibile est esse locum infinitum; ergo impossibile est esse corpus infinitum. Quomodo autem impossibile sit locum esse infinitum, ex hoc probatur. De quocumque enim praedicatur commune aliquod, oportet praedicari aliquod eorum quae sunt sub illo communi; sicut quod est animal, oportebit quod sit in aliqua specie animalis. Et quod est homo, oportet quod sit aliquis homo. Et similiter quod est in infinito loco oportet quod sit alicubi, idest in aliquo loco. Esse autem in aliquo loco, est esse vel sursum vel deorsum, vel secundum aliquam aliam speciem: quarum nullam possibile est esse infinitam, quia unumquodque horum est terminus alicuius distantiae; ergo impossibile est esse locum infinitum et similiter corpus.	2353. And in general if (1003). He gives the fourth argument, which is as follows. Every sensible body is in a place; but it is impossible for a place to be infinite; and therefore it is impossible for a body to be infinite. The way in which it is impossible for a place to be infinite he proves thus: whatever has a common term predicated of it must also have predicated of it any of the things which fall under that common term; for example, whatever is an animal must belong to some particular species of animal, and whatever is man must be some particular man. Similarly, whatever occupies an infinite place must be “somewhere,” i.e., it must occupy some place. But to occupy some place is to be up or down or to be in some one of the other kinds of place. However, none of these can be infinite because each is the limit of some distance. It is impossible, then, that a place should be infinite, and the same applies to a body.
lib. 11 l. 10 n. 41 Deinde cum dicit infinitum autem ostendit quomodo infinitum in potentia in diversis inveniatur; et dicit quod invenitur in magnitudine et motu et tempore; et non univoce praedicatur de eis, sed per prius et posterius. Et semper quod est in eis posterius, dicitur infinitum, secundum quod id quod est prius est infinitum, sicut motus secundum magnitudinem, in quam aliquid movetur localiter, aut augetur, aut alteratur. Et tempus dicitur infinitum secundum motum: quod sic intelligendum est. Infinitum enim divisione, attribuitur continuo, quod primo attribuitur magnitudini, ex qua motus habet continuitatem. Quod manifestum est in motu locali; quia partes in motu locali accipiuntur secundum partes magnitudinis. Et similiter manifestum est in motu augmenti; quia secundum additionem magnitudinis, augmentum attenditur. Sed in alteratione non est ita manifestum. Sed tamen etiam ibi aliqualiter verum est; quia qualitas secundum quam fit alteratio, per accidens dividitur ad divisionem magnitudinis. Et iterum intensio et remissio qualitatis attenditur secundum quod subiectum in magnitudine existens, aliquo modo vel perfectiori vel minus perfecto participat qualitatem. Ad continuitatem autem motus, est et tempus continuum. Nam tempus secundum se, cum sit numerus, non habet continuitatem, sed solum in subiecto. Sicut decem mensurae panni continuae sunt, eo quod pannus quoddam continuum est. Eodem igitur ordine oportet quod infinitum de istis tribus dicatur sicut et continuum.	2354. And the infinite (1004). Then he shows how the potentially infinite is found in different things. He says that it is found in continuous quantity, in motion, and in time, and it is not predicated of them univocally but in a primary and a secondary way. And the secondary member among them is always said to be infinite inasmuch as the primary member is; for example, motion is said to be infinite in reference to the continuous quantity in which something is moved locally or increased or altered; and time is said to be infinite in reference to motion. This must be understood as follows: infinite divisibility is attributed to what is continuous, and this is done first with reference to continuous quantity, from which motion derives its continuity. This is evident in the case of local motion because the parts of local motion are considered in relation to the parts of continuous quantity. The same thing is evident in the case of the motion of increase, because increase is noted in terms of the addition of continuous quantity. However, this is not as evident in the case of alteration, although in a sense it also applies there; because quality, which is the realm of alteration, is divided accidentally upon the division of continuous quantity. Again, the intensification and abatement of a quality is also noted inasmuch as its subject, which has continuous quantity, participates in some quality to a greater or lesser degree. And motion is referred to continuity, and so is a continuous time; for since time in itself is a number, it is continuous only in a subject, just as ten measures of cloth are continuous because the cloth is continuous. The term infinite, then, must be used of these three things in the same order of priority as the term continuous is.