Authors/Thomas Aquinas/physics/L3/lect13

Lecture 13 Solution of arguments in favor of existence of the infinite

Latin	English
	LECTURE 13 Solution of arguments in favor of existence of the infinite
lib. 3 l. 13 n. 1 Postquam philosophus per definitionem infiniti assignavit rationes eorum quae de infinito dicuntur, hic solvit rationes quae supra positae sunt ad ostendendum infinitum esse. Et primo dicit de quo est intentio; secundo exequitur propositum, ibi: neque enim ut generatio et cetera. Dicit ergo primo quod post ea quae dicta sunt de infinito, reliquum est solvere rationes secundum quas videbatur ostendi quod infinitum sit non solum in potentia, sicut supra determinavimus, sed quod sit in actu, sicut ea quae sunt finita et determinata. Aliquae enim illarum rationum non concludunt ex necessitate, sed sunt totaliter falsae; aliquae autem earum ex aliqua parte verum concludunt.	400. After the Philosopher has used the definition of the infinite to explain the things attributed to it he now solves the argument presented above (l.7) to show the infinite existed. First, he proposes his intention; Then he follows it out, at 401. He says therefore first [271 208 a5] that after speaking of the nature of the it remains to settle the arguments which appeared to show that the infinite is not only something in potency, as we determined above (l. 10), but that was in act, as things are that are finite and determined. For some of the arguments do not conclude necessarily but are entirely false, while others are partially true.
lib. 3 l. 13 n. 2 Deinde cum dicit: neque enim ut generatio etc., solvit quinque rationes quae supra positae sunt ad ostendendum infinitum esse. Et primo solvit eam quae sumebatur ex parte generationis. Concludebatur enim quod si generatio non deficit, quod oporteat esse infinitum. Sed haec ratio quantum ad hoc verum concludit, quod infinitum sit in potentia, quae successive in actum reducatur, sicut supra dictum est. Sed non est necessarium quod sit aliquod corpus sensibile infinitum in actu, ad hoc quod generatio non deficiat, sicut antiqui aestimaverunt, ponentes in infinitum conservari generationem, ac si semper generatio fieret per extractionem ex aliquo corpore; quod in infinitum fieri non posset nisi illud corpus esset infinitum. Sed hoc non est necessarium; cum toto corpore sensibili existente finito, generatio in infinitum durare possit per hoc quod corruptio unius est generatio alterius.	401. Then [272 208 a8] he solves the five reasons cited above (l.7) as proving that the infinite exists. And first he solves the one based on the fact of generation. For it concluded that if generation does not cease, then the infinite must be. Now this argument concludes truly insofar as the infinite is in a potency that is successively reduced to act. But it is not necessary that there be some sensible body which is infinite in act, in order to account for generation not ceasing, as the earlier philosophers supposed when they said that generation continues to infinity, supposing it to take place by extracting from some body, with the consequence that the process could not be infinite unless that body were infinite. But this is not necessary: for even supposing the whole of sensible body as finite, generation can endure ad infinitum by the fact that the corruption of one thing is the generation of another.
lib. 3 l. 13 n. 3 Deinde cum dicit: amplius tangi et includi etc., solvit rationem quae sumebatur ex parte contactus; ac si necessarium sit omne corpus finitum tangere quoddam aliud; et sic oporteat in infinitum procedere. Sed ipse solvit, quod alterum est tangi et finiri: quia tangi et includi dicitur respectu alterius; omne enim tangens tangit aliquid: sed finitum dicitur absolute, et non ad aliud, inquantum per proprios terminos aliquid finitum est in seipso. Accidit enim alicui finito quod tangat. Non tamen oportet quod omne tactum ab uno tangat aliud; ut sic in infinitum procedatur. Unde manifestum est quod haec ratio omnino nihil ex necessitate concludit.	402. Then [273 208 a11] he solves the argument based on the principle of contact, as though it were necessary for every finite body to touch some other body and so on to infinity. But he solves this by saying that it is one thing to be “touched” and another to be “terminated”, because to be “touched” and “enclosed” are said in respect to something else, for whatever touches, touches something else. To be “terminated,” however, is said absolutely and does not imply a relationship to something else, because a thing is made finite in itself by its own terminations. For it is incidental to the finite that it be touching something. Nevertheless, neither is it necessary that everything touched by something should touch something else and that this go on to infinity. Hence it is evident that this argument does not conclude anything of necessity.
lib. 3 l. 13 n. 4 Deinde cum dicit: intelligentiae autem credere etc., solvit rationem quae sumitur ex parte intellectus et imaginationis, quam antiqui non distinguebant ab intellectu. Per hanc autem rationem supra ostendebatur quod esset spatium infinitum extra caelum, et per consequens locus et corpus. Sed ipse dicit quod inconveniens est credere intelligentiae, ita scilicet quod quidquid apprehenditur intellectu vel imaginatione sit verum, ut quidam antiquorum putaverunt, quorum opinio reprobatur in IV Metaphys. Non enim sequitur, si apprehendo aliquam rem minorem vel maiorem quam sit, quod sit aliqua abundantia vel defectus in re illa, sed solum in apprehensione intellectus vel imaginationis. Potest enim aliquis intelligere quemcumque hominem esse multiplicem eius quod est, idest duplum vel triplum vel qualitercumque augmentans in infinitum: non tamen propter hoc erit aliqua huiusmodi quantitas multiplicata extra intellectum, aut extra determinatam quantitatem aut magnitudinem: sed contingit quod re sic existente, aliquis ita intelligat.	403. Then [274 208 a14] he solves the argument based on the intellect and the imagination, which latter the ancients did not distinguish from the intellect. This argument above (l.7) concluded that there was outside the universe an infinite space, and consequently a place and a body. But it is incorrect to “trust to thought,” i.e., believe that whatever is apprehended by the imagination or intellect is true, as some of the ancients thought, whose opinion is refuted in Metaphysics IV. For if I apprehend a thing as smaller or larger than it is, it does not thereby follow that there is such an abundance or defect in the object itself but only in the apprehension of the intellect or imagination. For one might understand some man to be a multiple of himself, i.e., two or three times larger than he really if, or any other amount to infinity, yet there will not be because of this a corresponding multiplication of him outside the intellect or outside a definite quantity or magnitude.
lib. 3 l. 13 n. 5 Deinde cum dicit: tempus autem et motus etc., solvit rationem acceptam ex tempore et motu. Et dicit quod tempus et motus sunt infinita non in actu, quia nihil est temporis in actu nisi nunc; neque aliquid motus est in actu nisi quoddam indivisibile: sed intellectus apprehendit continuitatem temporis et motus, accipiendo ordinem prioris et posterioris: ita tamen quod id quod primo fuit acceptum de tempore vel motu, non permanet sic. Unde non oportet dicere quod totus motus infinitus sit in actu, vel totum tempus infinitum.	404. But while a thing remains what it is, one can conceive of it in such a manner. Then [275 208 a20] he solves the difficulty based on time and motion. And he says that time and motion are not infinite in act, because nothing of time is actual but the “now,” and nothing of motion is actual except a kind of indivisible. But the intellect apprehends a continuity in time and in motion by apprehending an order of “prior” and “posterior,” in such a way, however, that what was first taken in time or in motion does not remain in the same state. Hence it is not necessary to say that the whole of motion is infinite, or that the whole of time is infinite.
lib. 3 l. 13 n. 6 Deinde cum dicit: magnitudo autem neque divisione etc., solvit rationem sumptam ex parte magnitudinis. Et dicit quod magnitudo non est infinita in actu neque per divisionem neque per augmentationem intelligibilem, sicut ex supra dictis patet. Ultimo autem epilogat quod dictum est de infinito.	405. Then [276 208 a21] he solves the argument based on magnitude, and he says that magnitude is not infinite in act either as a result of division or of an intelligible increase, as is evident from what was said above (ll.8-10). Finally he summarizes by saying that we have completed our study of the infinite.