Authors/Thomas Aquinas/physics/L3/lect9

Lecture 9 No infinite body shown absolutely

Latin	English
	LECTURE 9 No infinite body shown absolutely
lib. 3 l. 9 n. 1 Postquam philosophus ostendit non esse corpus sensibile infinitum, facta suppositione quod sint elementa finita, hic ostendit idem simpliciter absque omni suppositione. Et primo dicit de quo est intentio; secundo exequitur propositum, ibi: aptum enim natum est et cetera. Dicit ergo primo quod ex iis quae sequuntur oportet considerare de omni corpore universaliter, nulla suppositione facta, si contingat quodcumque corpus naturale esse infinitum. Et ex sequentibus rationibus manifestum fiet quod non. Deinde cum dicit: aptum enim natum est etc., ostendit propositum quatuor rationibus. Secunda incipit ibi: omnino autem manifestum etc.; tertia ibi: amplius omne corpus sensibile etc.; quarta ibi: simpliciter autem si impossibile et cetera. Circa primam rationem tria facit: primo praesupponit quaedam necessaria ad rationem; secundo ponit rationem ibi: quare si quidem sit eiusdem speciei etc.; tertio excludit quandam falsam opinionem, ibi: Anaxagoras autem inconvenienter et cetera.	358. After showing that there is no infinite sensible body on the assumption that the elements are finite, the Philosopher here shows the same absolutely, without assumptions of any kind. First he declares his intention; Secondly he carries out his proposal, at 359. He says therefore first [239 205 a7] that in what follows it is necessary to consider every body universally, without any suppositions, and ask whether any natural body can be infinite. And from the following reasons it will be clear that none can. Then, he proves his proposition with four reasons, beginning at 359. The second reason begins at 367; the third at 368; the fourth at 369. In regard to the first reason he does three things: First he lays down certain facts presupposed to his reasoning; Secondly he gives the reasoning itself, at 360. Thirdly, he excludes a false opinion, at 364.
lib. 3 l. 9 n. 2 Praemittit ergo tria. Quorum primum est quod omne corpus sensibile habet aptitudinem naturalem ut sit in aliquo loco. Secundum est quod cuilibet corpori naturali convenit aliquis locus locorum qui sunt. Tertium est quod idem est locus naturalis totius et partis, sicut totius terrae et unius glebae, et totius ignis et unius scintillae: et huius signum est, quod in quacumque parte loci totius ponatur pars corporis, quiescit ibi.	359. Therefore [240 205 a9] he lays down three presuppositions. The first of these is that every sensible body has a natural aptitude to be in some definite place. Secondly, that every natural body has, among available places, some place that befits it. Thirdly, that the natural place of the whole and of the part is the same, i.e., of all earth and each clod, of all fire and each spark. A sign of this is that in whatever part of the place of the whole there is placed a part of some body, it is at rest there.
lib. 3 l. 9 n. 3 Deinde cum dicit: quare si quidem sit eiusdem speciei etc., ponit rationem, quae talis est. Si ponatur aliquod corpus infinitum, aut oportet quod totum sit unius speciei cum suis partibus, sicut aqua vel aer; aut quod habeat partes dissimilium specierum, ut homo aut planta. Si habet omnes partes unius speciei, sequitur secundum praemissa, quod vel sit totaliter immobile et nunquam moveatur, aut quod semper moveatur. Quorum utrumque est impossibile: quia per alterum horum excluditur quies, et per alterum motus a rebus naturalibus, et utroque modo tollitur ratio naturae, cum natura sit principium motus et quietis. Quod autem sequatur quod sit vel totaliter mobile vel totaliter quietum, probat consequenter per hoc, quod non esset assignare rationem quare aliquid magis sursum aut deorsum moveretur, aut in quamcumque partem. Et hoc manifestat per exemplum: ponamus enim quod totum illud corpus infinitum simile in partibus sit terra; non erit assignare ubi aliqua gleba terrae moveatur vel ubi quiescat; quia quamlibet partem loci infiniti occupabit aliquod corpus sibi cognatum, idest eiusdem speciei. Numquid igitur potest dici quod una gleba moveatur ad hoc quod contineat, idest quod occupet, successive totum locum infinitum, sicut sol movetur ut sit in qualibet parte circuli zodiaci? Et quomodo poterit hoc esse, ut una gleba terrae pertranseat per omnes partes infiniti loci? Nihil autem movetur ad impossibile: si igitur impossibile est quod gleba moveatur ad occupandum totum locum infinitum, ubi erit quies eius, et ubi motus eius? Aut enim oportet quod semper quiescat, et sic nunquam moveatur: aut quod semper moveatur, et sic nunquam quiescat.	360. Then [241 205 a12] he gives the [first] reason, which is this. If an infinite body be supposed, it must have parts either of the same species, as water or air, of parts of varying species, as a man or a plant has. If all its parts are of the same species, it follows according to our pre-suppositions (no. 359) that it is either entirely immobile and is never moved, or is always being moved. But both of these are impossible: for in the second case, rest is excluded; and in the other, motion is excluded from natural things. Thus, in both cases there is denied the notion of nature, for nature is a principle of motion and of rest. He proves that this body would be either entirely mobile or entirely at rest by the fact that no reason can be given for its being moved either up or down or in any direction whatsoever. He manifesto this by an example: for let us suppose that the entire infinite body which is similar throughout is earth. Then it will be impossible to say where any clod of earth should move or be at rest, because each part of infinite place would be occupied by some body related to it, i.e., of the same species. Can it be said that one clod of earth would be moved so as to occupy successively all the infinite places, as the sun is moved so as to be in each part of the zodiacal circle? And how could one clod of earth pass through all the parts of infinite place? Now nothing is moved toward the impossible: if therefore it is impossible for a clod of earth to be moved so as to occupy all the infinite places, in which place will it rest and in which will it be in motion? it will either always be at rest and thus never in motion or it will always be in motion and thus never at rest.
lib. 3 l. 9 n. 4 Si autem detur alia pars divisionis, scilicet quod corpus infinitum habeat partes dissimiles secundum speciem; sequitur etiam quod dissimilia sint loca diversarum partium: alius est enim locus naturalis aquae, et alius terrae. Sed ex hac positione sequitur primo, quod corpus totius infiniti non sit unum simpliciter sed secundum quid, scilicet secundum contactum; et sic non erit unum corpus infinitum ut ponebatur.	361. If we suppose the other possibility, namely, that the infinite body has parts that are unlike in species, it will then follow that there would be unlike places for the unlike parts, for the natural place of water is one thing and that of earth is another, But on this supposition it follows at once that the body of this infinite whole would not be one body simply but one through contact; and thus there will not be one infinite body as our supposition granted.
lib. 3 l. 9 n. 5 Et quia posset aliquis non reputare hoc inconveniens, subiungit aliam rationem contra hoc: et dicit quod si totum infinitum componitur ex dissimilibus partibus, necesse est quod huiusmodi partes dissimiles secundum speciem, aut sint specierum finitarum, aut infinitarum secundum numerum. Non autem potest esse quod sint finitarum specierum, quia oportebit, si totum est infinitum, quod quaedam sint finita secundum quantitatem, et quaedam infinita; aliter enim ex finitis numero posset componi infinitum: hoc autem posito, sequitur quod illa quae sunt infinita, corrumpant alia propter contrarietatem, ut prius dictum est in praecedenti ratione. Et ideo etiam nullus antiquorum naturalium philosophorum unum principium, quod dixit esse infinitum, posuit ignem vel terram, quae sunt extrema, sed magis aquam vel aerem vel aliquod medium, quia loca istorum erant manifesta et determinata, scilicet sursum et deorsum; non sic autem est de aliis, sed terra est deorsum respectu eorum, et ignis sursum.	362. Because someone might not consider this impossible [i.e., an infinite body of dissimilar parts], he adds another reason against this, saying that if the infinite whole is composed of unlike parts, these parts will be either of a finite number of species or of an infinite number. It will not be the first, because it then follows that if the whole is infinite, then some of the parts will be finite and some infinite; otherwise we would be able to get an infinite composed all of finites. On this assumption it follows that those which are infinite will corrupt the others, on account of contrariety, as was said in previous reasoning (nos. 354, 356). For this reason, no one of the early philosophers who posited one infinite principle, posited it to be fire or earth, which are extremes; rather they posited water or air or some medium between them, because the places of the former were evident, i.e., above and below, but it is not the same with the others, for earth is below in respect of them and fire above.
lib. 3 l. 9 n. 6 Si vero aliquis accipiat aliam partem, scilicet quod corpora partialia sint infinita secundum speciem, sequitur quod etiam loca sint infinita secundum speciem, et quod elementa sint infinita. Si autem hoc est impossibile, quod elementa sint infinita, ut in primo probatum est, et quod loca etiam sint infinita, cum non sit possibile invenire infinitas species locorum; necesse est quod totum corpus sit finitum. Et quia concluserat ex infinitate corporum infinitatem locorum subiungit quod impossibile est non aequari corpus ad locum; quia non potest esse quod sit locus maior quam quantum contingit esse corpus, neque corpus potest esse infinitum si locus non est infinitus, et neque corpus potest esse maius quam locus quocumque modo. Quia si locus sit maior quam corpus, sequitur quod sit vacuum alicubi: aut si corpus sit maius quam locus, sequitur quod aliqua pars corporis non sit in aliquo loco.	363. But if someone admits the other alternative, namely, that the parts of the body are infinite in species, it follows that their places also are infinite in species, and that the elements are infinite. But if it is impossible that the elements be infinite, as was already proved in Book I (l.11), and that places be infinite, since it is not possible to find infinite species of place, it is necessary to admit that the whole body is finite. And because he had concluded to an infinity of places from the infinite of bodies, he adds that it is impossible not to equate body with place; for no place is greater than the body it contains, nor can a body be infinite if its place is not infinite, nor can in any way a body be greater than its place. This is so because if the place is greater than the body, there will be some empty place; if the body is greater than its place, then some part of the body is in no place.
lib. 3 l. 9 n. 7 Deinde cum dicit: Anaxagoras autem etc., excludit quendam errorem. Et primo ponit ipsum: et dicit quod Anaxagoras dixit infinitum quiescere, sed inconvenienter assignavit rationem quietis eius. Dixit enim quod fulcit, idest sustentat, infinitum seipsum, quia est in se et non in alio, cum nihil ipsum contineat; et sic non possit extra se moveri.	364. Then [242 205 b1] he excludes an error. First, he cites the error and says that Anaxagoras claimed that the infinite is at rest but gave an invalid reason for its rest. For he said that the infinite bears up, i.e., sustains itself since it exists in itself and not in something else, for nothing contains it. And thus it could not be moved outside itself.
lib. 3 l. 9 n. 8 Secundo, ibi: tanquam ubi utique etc., improbat duabus rationibus quod dictum est. Quarum prima est quod Anaxagoras sic assignavit rationem de quiete infiniti, ac si ubi aliquid sit, ibi sit aptum natum esse: quia ex hac sola ratione dixit infinitum quiescere, quia est in seipso. Sed hoc non est verum quod ubi aliquid est, ibi semper aptum natum sit esse: quia aliquid est alicubi per violentiam, et non naturaliter. Quamvis igitur hoc maxime verum sit, quod totum infinitum non movetur, quia sustentatur et manet in seipso, et sic est immobile: sed tamen dicendum erat quare non est aptum natum moveri. Non enim potest aliquis evadere sic, dicens quod non movetur infinitum: quia eadem ratione et de quolibet alio nihil prohibet quod non moveatur; sed sit aptum natum moveri. Quia et si terra esset infinita, sicut nunc non fertur quando est in medio, ita et tunc non ferretur quantum ad partem quae esset in medio: sed hoc non esset quia non haberet aliquid aliud ubi sustentaretur nisi in medio, sed quia non habet aptitudinem naturalem ut a medio moveatur. Si ergo ita est in terra, quod non est causa quare quiescat in medio, quia est infinita, sed quia gravitatem habet ex qua nata est manere in medio; similiter de quocumque alio infinito assignanda est causa quare quiescat; et non quia est infinitum, vel quia fulcit seipsum.	365. Secondly [243 205 b4] he disproves this statement with two reasons. The first of which is that Anaxagoras so assigned his reason for the rest of the infinite as to suppose that wherever a thing is, that is its natural place, for the only reason he gave for saying that the infinite is at rest, is that it exists in itself. But it is not true that where a thing is, there it is always naturally disposed to be, because some things are somewhere by force and not by nature. Now although it is true that an infinite whole is not moved, because it is sustained and remains in itself and for that reason is immobile, yet a reason should be given why it is not naturally disposed to be moved. one cannot evade this simply by saying that the infinite is not moved, since by the same reasoning there is nothing to prevent any other body from not being moved while it might be naturally disposed to be moved. Because oven if earth were infinite, just as now it will not be carried further when it is in the center, so even then no part in the center would move further: but this would not be because it had no other natural place except the center where it could be sustained but because it does not have a natural aptitude to be moved from the center. If, therefore, this is the case with earth, that the reason why it rests at the center is not that it is infinite but that it has gravity which accounts for its remaining in the center; similarly, in the case of any other infinite, the reason why it rests should be given, and this is not simply because it is infinite or that it supports itself.
lib. 3 l. 9 n. 9 Aliam autem rationem ponit ibi: similiter autem manifestum et cetera. Et dicit quod si totum infinitum quiescit quia manet in seipso, sequitur quod quaelibet pars ex necessitate quiescat quia manet in seipsa. Idem enim est locus totius et partis, ut dictum est, ut ignis et scintillae sursum, et terrae et glebae deorsum. Si ergo totius infiniti locus est ipsummet, sequitur quod quaelibet pars infiniti maneat in seipsa sicut in proprio loco.	366. He lays down another argument [244 205 b18]. Thus he states that if the whole infinite is in repose because it remains within itself, it follows that any part thereof necessarily is necessarily at rest since it remains within itself. For the place of the whole and the part is the same, as was said (no. 359), e.g., that of fire and a spark upwards, that of earth and a clod of earth downward. If, therefore, the place of the whole infinite is itself, it follows that any part of the infinite will remain at rest within itself as in its proper place.
lib. 3 l. 9 n. 10 Secundam rationem ponit ibi: omnino autem manifestum est et cetera. Et dicit quod omnino manifestum est quod impossibile est dicere esse infinitum corpus in actu, et quod cuiuslibet corporis est aliquis locus, si omne corpus sensibile aut habet gravitatem aut levitatem, sicut antiqui dixerunt ponentes infinitum. Quia si sit corpus grave, oportet quod naturaliter feratur ad medium: si autem sit leve, necesse est quod feratur sursum. Si ergo sit aliquod infinitum corpus sensibile, necesse est quod etiam in corpore infinito sit sursum et medium: sed impossibile est quod totum infinitum sustineat in se utrumlibet horum, scilicet vel sursum vel medium; vel etiam quod sustineat utrumque secundum diversas medietates. Quomodo enim infinitum poterit dividi, ut una pars eius sit sursum et alia deorsum, vel quod in infinito sit ultimum aut medium? Non est igitur corpus sensibile infinitum.	367. He gives a second reason against Anaxagoras [245 205 b24] saying that it is clearly impossible to say that there is an actually infinite body and that there is some place for each body, if every sensible body is either heavy or light, as the ancients said who posited the infinite. Because if the body is heavy, it will be naturally carried to the center; if it is light, it will be carried upward. If, therefore, there be an infinite sensible body, there must be in it an “up” and a center. But it is impossible that the infinite body should sustain in itself either of these, i.e., either an “up” or a center, or even that it sustain both according to different centers. For how could the infinite be divided so that one part would be “up” and another “down” or how can there be in the infinite a boundary or a center? Therefore there is no infinite sensible body.
lib. 3 l. 9 n. 11 Tertiam rationem ponit ibi: amplius omne corpus sensibile in loco est et cetera. Et dicit quod omne corpus sensibile est in loco. Differentiae autem loci sunt sex: sursum, deorsum, ante et retro, dextrorsum et sinistrorsum; quae quidem sunt determinata non solum quoad nos, sed etiam in ipso toto universo. Determinantur enim secundum se huiusmodi positiones, in quibus sunt determinata principia et termini motus. Unde in animatis determinantur sursum et deorsum secundum motum alimenti; ante et retro secundum motum sensus; dextrorsum et sinistrorsum secundum motum processivum, cuius principium est a parte dextra. In rebus autem inanimatis, in quibus non sunt principia determinata horum motuum, dicitur dextrorsum et sinistrorsum per comparationem ad nos: dicitur enim columna dextra, quae est ad dextram hominis, et sinistra quae est ad sinistram. Sed in toto universo determinatur sursum et deorsum secundum motum gravium et levium: secundum autem motum caeli determinatur dextrum oriens, sinistrum occidens; ante vero hemisphaerium superius, retro vero hemisphaerium inferius; sursum vero meridies, deorsum vero Septentrio. Haec autem non possunt determinari in corpore infinito: impossibile est ergo totum universum esse infinitum.	368. He gives the third reason [246 205 b31] saying that every sensible body is in place. But the differences of place are six: above, and below, before and behind, to the right and to the left—and these are determined not only in relation to us but even in the whole universe itself. For such positions are determined in themselves in those things in which there are determinate principles and terms of motion. Whence in living things “up” and “down” are determined according to the movement of food; “front” and “rear” according to the movement of sense; “right” and “left” according to forward motion, which begins from the right. But in inanimate things, in which there are no determinate principles of such motions, “right” and “left” are said with respect to us—for a column is said to be “at the right” which is to the right of a man, and “at the left” which is at his left. But in the whole universe “up” and “down” are determined according to the movement of heavy and light things; while according to the motion of the heavens the rising sun determines “right,” the setting sun, “left”; “front” is determined by the upper hemisphere, “rear” by the lower hemisphere; “above” by the south, “below” by the north. Now such things cannot be determined in an infinite body. It is therefore impossible for the whole universe to be infinite.
lib. 3 l. 9 n. 12 Quartam rationem ponit ibi: simpliciter autem si impossibile est et cetera. Et dicit quod si impossibile est esse locum infinitum, cum omne corpus sit in loco, sequitur quod impossibile sit esse aliquod corpus infinitum. Sed quod impossibile sit esse locum infinitum, sic probat: quia haec duo convertuntur, esse in loco et esse in aliquo loco; sicut et esse hominem et esse aliquem hominem, et esse quantitatem et esse aliquam quantitatem. Sicut igitur impossibile est esse quantitatem infinitam, quia sequeretur aliquam quantitatem esse infinitam, ut bicubitum et tricubitum, quod est impossibile; ita impossibile est esse locum infinitum, quia sequeretur aliquem locum infinitum esse, vel sursum vel deorsum et huiusmodi: quod est impossibile, cum quodlibet eorum significet quendam terminum, ut dictum est. Sic igitur nullum corpus sensibile est infinitum.	369. Then [247 205 b35] he gives the fourth reason, saying that if it is impossible that there be an infinite place because every body is in a place, it follows that there can be no infinite body. That an infinite place is impossible be proves thus: To be in place and to be in some place are convertible, just as to be man and to be some man or to be quantity and to be some quantity. Therefore, just as it is impossible that there be infinite quantity, because then it would follow that some quantity is infinite, e.g., two cubits or three cubits, which is impossible, so infinite place is impossible , because it would follow that some place is infinite (either up or down or some other place), which is impossible—since each of these implies a definite term as was said (in 368). Therefore no sensible body is infinite.