Authors/Thomas Aquinas/physics/L6/lect12

Lecture 12 What is indivisible according to quantity is moved only per accidens

Latin	English
	Lecture 12 What is indivisible according to quantity is moved only per accidens
lib. 6 l. 12 n. 1 Postquam philosophus solvit rationes Zenonis improbantis motum, hic intendit ostendere quod impartibile non movetur. Per quod destruitur opinio Democriti, ponentis atomos per se mobiles. Et circa hoc duo facit: primo proponit intentionem; secundo probat propositum, ibi: mutetur enim ex ab in bc et cetera. Dicit ergo primo, quod suppositis his quae supra ostensa sunt, dicendum est quod impartibile non potest moveri, nisi forte per accidens, sicut punctum movetur in toto corpore, vel quacumque alia magnitudine in qua est punctum, scilicet linea vel superficie.	872. After answering the arguments of Zeno who tried to disprove motion, the Philosopher now intends to show that a thing incapable of being divided into parts cannot be moved. This will answer the opinion of Democritus, who posited atoms that are per se mobile. About this he does two things: First he proposes his intention; Secondly, he proves his proposition, at 876. He says therefore first (669 240 b8) that assuming what we have proved above, it must be said that a thing incapable of being divided into parts cannot be moved, except perchance per accidens, as a point is moved in a whole body in which there is a point, for example, in a line or a surface.
lib. 6 l. 12 n. 2 Moveri autem ad motum alterius contingit dupliciter. Uno modo quando illud quod movetur ad motum alterius, non est aliqua pars eius; sicut illud quod est in navi movetur ad motum navis, et albedo etiam movetur ad motum corporis, cum non sit pars eius: alio modo sicut pars movetur ad motum totius. Et quia impartibile dicitur multipliciter, sicut et partibile, ostendit quomodo accipiat hic impartibile: et dicit quod impartibile hic dicitur illud quod est indivisibile secundum quantitatem. Dicitur enim et aliquid impartibile secundum speciem, sicut si dicamus ignem impartibilem aut aerem, quia non potest resolvi in plura corpora specie diversa. Sed tale impartibile nihil prohibet moveri: intendit ergo excludere motum ab impartibili secundum quantitatem.	873. To be in motion as a result of something else being in motion can occur in two ways. In one way, when what is moved as the result of something else being moved is not part of the latter, as what is on a ship is being moved when the ship is being moved, and as whiteness is moved with the motion of body, since it is not of the body. In a second way, as a part is moved when the whole is moved. And because “what is incapable of being divided into parts” has many senses, just as what is capable of being divided into parts” has, he shows how he uses the phrase here and says that here it means what is indivisible in respect of quantity. For some things are indivisible according to species, as when we say that fire or air are indivisible, because they cannot be further resolved into several bodies that differ in species. But in regard to such an indivisible there is nothing to prevent it from being moved. Consequently, Aristotle intends to exclude motion from what is indivisible according to quantity.
lib. 6 l. 12 n. 3 Et quia dixerat quod pars movetur ad motum totius, et aliquis posset dicere quod pars nullo modo movetur, subiungit quod sunt aliqui motus partium, inquantum sunt partes, qui sunt diversi a motu totius, inquantum est motus totius. Et hanc differentiam aliquis maxime potest considerare in motu sphaerico: quia non est eadem velocitas partium quae moventur circa centrum, et partium quae sunt extra, idest versus superficiem exteriorem sphaerae, et quae est etiam velocitas totius: ac si motus iste non sit unius sed diversorum. Manifestum est enim quod velocius est, quod in aequali tempore pertransit maiorem magnitudinem. Dum autem sphaera movetur, manifestum est quod maiorem circulum pertransit pars exterior sphaerae quam pars interior; unde maior est velocitas partis exterioris quam interioris. Tamen velocitas totius est eadem cum velocitate interioris et exterioris partis. Ista autem diversitas motuum intelligenda est secundum quod partibus continui convenit moveri, scilicet in potentia. Unde actu est unus motus totius et partium: sed potentia sunt diversi motus partium, et ad invicem, et a motu totius. Et sic cum dicitur pars moveri per accidens ad motum totius, est tale per accidens, quod est in potentia per se: quod non est de motu per accidens, secundum quod dicuntur accidentia vel formae per accidens moveri.	874. Because he had said that the part is being moved when the whole is, and someone might say that the part is not moved at all, he adds that there are some motions of parts precisely as parts, that are diverse from the motion of the whole, as a motion of the whole. This difference is particularly clear in the motion of a sphere, because the speed of the parts near the center is not the same as that of those outside, i.e., on the exterior surface of the sphere, the speed of whose parts is considered to be the speed of the whole. It is as if there is not just one motion but the motions of many parts involved. For it is evident that whatever traverses a larger magnitude in an equal time is faster. Now, while the sphere is rotating, it is clear that an external part describes a larger circle than an interior part; hence the velocity of the external part is greater than that of an interior part. Yet the velocity of the whole sphere is the same as the velocity of the interior and exterior part. But this diversity of motions is to be understood in the sense in which motion is ascribed to parts of a continuum, i.e., in a potential sense, Hence, actually there is one motion of the whole and of the parts, but potentially there are diverse motions: those of the parts being different from one another and from the motion of the whole. And so, when it is said that a part is being moved per accidens with the motion of the whole, it is a per accidens which is in potency per se—which is something not true of motion per accidens, when it is taken in the sense that accidents or forms are said to be moved per accidens.
lib. 6 l. 12 n. 4 Posita igitur distinctione eius quod movetur, explicat suam intentionem. Et dicit quod id quod est impartibile secundum quantitatem, potest moveri quidem ad motum corporis per accidens: non tanquam pars, quia nulla magnitudo componitur ex indivisibilibus, ut ostensum est; sed sicut movetur aliquid ad motum alterius quod non est pars eius, sicut sedens in navi movetur ad motum navis. Sed per se non contingit impartibile moveri. Hoc autem idem supra probavit, non ex principali intentione, sed incidenter. Unde praeter rationem supra positam, hic magis explicat veritatem, et rationes addit efficaces ad propositum ostendendum.	875. Having made a distinction among things that are moved, he explains his intention. And he says that what is indivisible in respect of quantity can indeed be moved per accidens when something else is moved, but it is not moved as a part, for no magnitude is made up of indivisibles, as we have proved. Now, something not a part of another is moved along with the other in the same way that one sitting in a ship is moved along with the motion of a ship. But per se the indivisible cannot be moved. He had proved this point previously, not as a main proposition but incidentally. Hence, in addition to the reason cited earlier, he now gives a further explanation of the truth and adds reasons that are strong enough to prove the proposition.
lib. 6 l. 12 n. 5 Deinde cum dicit: mutetur enim etc., probat propositum tribus rationibus. Quarum prima talis est. Si ponatur quod impartibile movetur, moveatur ex ab in bc. Nec differt quantum ad hanc rationem, utrum ista duo, scilicet ab et bc, sint duae magnitudines, sive duo loca, ut in motu locali et augmenti et decrementi; vel duae species, idest duae qualitates, sicut in motu alterationis; vel sint duo contradictorie opposita, ut in generatione et corruptione. Et sit tempus ed in quo aliquid mutatur de uno termino in alterum primo, idest non ratione partis. In hoc ergo tempore necesse est quod id quod mutatur, aut sit in ab, idest in termino a quo; aut in bc, idest in termino ad quem; aut aliquid eius est in uno termino, alia vero pars eius est in altero. Omne enim quod mutatur, oportet quod aliquo horum trium modorum se habeat, sicut supra dictum est. Non autem potest dari tertium membrum, scilicet quod sit in utroque secundum diversas partes sui: quia sic sequeretur quod esset partibile, et positum erat quod esset impartibile. Sed similiter non potest dari secundum membrum, scilicet quod sit in bc, idest in termino ad quem: quia quando est in termino ad quem, tunc iam est mutatum, ut ex superioribus patet; ponebatur autem quod in hoc tempore mutaretur. Relinquitur ergo quod in toto tempore in quo mutatur indivisibile, sit in ab, idest in termino a quo. Ex quo sequitur quod quiescat: nihil enim est aliud quiescere, quam quod aliquid sit in uno et eodem per totum aliquod tempus. Cum enim in quolibet tempore sit prius et posterius, si tempus est divisibile, quidquid per aliquod tempus est in uno et eodem, similiter se habet nunc et prius; quod est quiescere. Sed hoc est impossibile, quod aliquid dum mutatur quiescat. Relinquitur ergo quod non contingit impartibile moveri, neque aliquo modo mutari. Hoc enim solo modo posset esse aliquis motus rei indivisibilis, si tempus componeretur ex ipsis nunc: quia in nunc semper est motum esse vel mutatum. Et quia quod motum est, inquantum huiusmodi, non movetur, sequitur quod in nunc nihil movetur, sed sit motum. Sic igitur posset poni indivisibile moveri in aliquo tempore, si tempus ex ipsis nunc componeretur: quia posset dari quod in quolibet ipsorum nunc ex quibus componitur tempus, esset in uno, et in toto tempore, idest in omnibus nunc, esset in multis; et sic in toto tempore moveretur, non autem in aliquo nunc. Sed quod hoc sit impossibile, scilicet tempus componi ex ipsis nunc, ostensum est prius. Ostensum est enim supra quod neque tempus componitur ex ipsis nunc, neque linea ex ipsis punctis, neque motus componitur ex momentis (ut per momentum intelligamus hoc quod est mutatum esse). Qui enim hoc dicit, quod indivisibile movetur, aut quod motus componatur ex indivisibilibus, nihil aliud facit quam quod tempus componatur ex nunc, aut magnitudo ex punctis; quod est impossibile. Ergo et impossibile est impartibile moveri.	876. Then at (670 240 b20) he proves his point with three arguments. The first of which is this: If it is insisted that an indivisible can be moved, let it be moved from AB into BC. (In this argument it makes no difference whether AB and BC are two magnitudes or two places, as in local motion and growth and decrease, or whether they are two qualities, as in the motion of alteration, or two things that are contradictorily opposed, as in generation and ceasing-to-be.) Let ED be the time in which something is changed from one terminus to the other first, i.e., not by reason of a part. In this time, then, it is necessary that what is being moved be either in AB, i.e., in the terminus a quo, or in BC, i.e., in the terminus ad quem; or else a part is in one terminus and a part in the other. For anything being moved must be in one of these three ways, as was said above. Now the third situation is impossible; namely, that it be in each term according to its various parts, because then, the mobile would be divided into parts, and we have assumed that it is an indivisible mobile. Likewise, it cannot be the second alternative, i.e., that it be in BC, i.e., in the terminus ad quem, for when it is in the terminus ad quem, it has been already changed (as is clear from what we have said above), whereas we are assuming that it is being changed. What remains, therefore, is that in the entire time that the indivisible is being changed it remains at AB, i.e., in the terminus a quo, From which it follows that it is at rest, for resting is nothing more than to be in one and the same state throughout a definite period of time. For since there is a prior and a subsequent in time, if time is divisible, whatever for a period of time is in one and the same state keeps itself the same; namely, as it was previously—which is to rest. But it is impossible that a thing is at rest while it is being changed. Therefore, it cannot be that an indivisible is moved or changed in any way whatsoever. The only way in which there could be motion of an indivisible thing is to have the time composed of “now’s”, because in the “now” there is always a condition called “having been moved” or “having been changed”. And because what has been moved, precisely as such is not now being moved, it follows that in the “now” nothing is being moved, but has been moved. But if time were made up of “now’s”, there would be a way in which motion could be posited in an indivisible, because it could be granted that in each of those “now’s” of which time is composed, it would be in one, and in the whole time, i.e., in all the “now’s”, it would be in many. And thus it would be in motion throughout the entire time, but not in one “now”. But it has been proved above that it is impossible for time to be made up of “now’s”. Indeed, we have proved that neither is time composed of now’s nor a line of points, nor a motion of moments (where “moments” refers to states called “having been changed”). For anyone who says that an indivisible is being moved or that motion is composed of indivisibles is making time be composed of “now’s” or a magnitude of points—which is impossible. Therefore, it is also impossible that a thing incapable of being divided into parts be moved.
lib. 6 l. 12 n. 6 Secundam rationem ponit ibi: amplius autem ex his etc.: et dicit quod ex his quae sequuntur, potest esse manifestum quod neque punctum, neque aliud quodcumque indivisibile potest moveri. Et ista ratio specialis est de motu locali. Omne enim quod movetur secundum locum, impossibile est quod prius pertranseat maiorem magnitudinem ipso mobili, quam aequalem vel minorem; sed semper mobile prius pertransit magnitudinem aequalem sibi aut minorem, quam maiorem. Si ergo hoc ita se habet, manifestum est quod et punctum, si movetur, prius pertransibit aliquid minus se aut aequale sibi, quam longitudinem maiorem se. Sed impossibile est quod pertranseat aliquid minus se, quia est indivisibile. Relinquitur ergo quod pertransibit aliquid aequale sibi. Et ita oportet quod numeret omnia puncta quae sunt in linea: quia semper punctum, cum moveatur motu aequali lineae, propter hoc quod movetur per totam lineam, sequitur quod totam lineam mensuret; hoc autem facit numerando omnia puncta. Ergo sequitur quod linea sit ex punctis. Si ergo hoc est impossibile, impossibile est quod indivisibile moveatur.	877. The second argument is given at (671 241 a6). He says that if we look at the consequences, it is clear that neither a point nor any indivisible can be moved. And this special argument applies to local motion. For whatever is being moved according to place cannot traverse a distance greater than the mobile itself before traversing one that is equal to or less than it; rather, a mobile always traverses a magnitude equal to itself or less than itself before one greater than itself. If this is so, then it is clear that a point, if it is being moved will first traverse a length less than or equal to itself, before it traverses one greater than itself. But it is impossible for it to traverse something less than itself, since it is indivisible. So it has to traverse a length equal to itself. Consequently, it must number all the points in the line; for the point, since it is being moved through a motion equal to a line, is by that very fact being moved through the whole line, and, consequently, is always measuring the whole line—and this it does by counting all the points. Therefore, it follows that a line arises from points. Therefore, if this is impossible, it is impossible for an indivisible to be moved.
lib. 6 l. 12 n. 7 Tertiam rationem ponit ibi: amplius autem si omne etc.: quae talis est. Omne quod movetur, movetur in tempore, et nihil movetur in ipso nunc, ut supra probatum est. Ostensum est autem supra quod omne tempus est divisibile. Ergo in quolibet tempore in quo aliquid movetur, erit accipere minus tempus, in quo movetur aliquod minus mobile: quia manifestum est quod supposita eadem velocitate, in minori tempore pertransit minus mobile aliquod signum datum, quam mobile maius, sicut in minori tempore pars quam totum, ut ex superioribus patet. Si ergo punctum movetur, erit accipere aliquod tempus minus tempore in quo ipsum movetur. Sed hoc est impossibile: quia sequeretur quod in illo minori tempore moveretur aliquid minus quam punctum; et sic indivisibile esset divisibile in aliquod minus, sicut tempus dividitur in tempus. Hoc enim solo modo posset moveri indivisibile, si esset possibile aliquid moveri in nunc indivisibili: quia sicut non esset accipere aliquod minus ipso nunc in quo movetur, ita non oporteret accipere aliquod minus mobili. Et sic patet quod eiusdem rationis est, quod fiat motus in nunc, et quod indivisibile aliquod moveatur. Hoc autem est impossibile, quod in nunc fiat motus. Ergo impossibile est quod indivisibile moveatur.	878. The third argument is at (672 241 a15) and is this: Since motion is always in a period of time and never in a “now”, and since all time is divisible, as was shown above, then in every time in which something is . moved, there must be a lesser time in which a lesser mobile is moved. For, supposing the same speed, it is plain that in a lesser time the lesser mobile crosses a given mark than does a greater mobile, as in a lesser time the part than the whole, as is evident from what is above. If, therefore, a point is in motion, there must be a time less than that in which it is moved. But this is impossible, for it would follow that in that lesser time something less than a point would be moved, and thus the indivisible would be divisible into something less, just as time is divisible. This would be the only condition under which the indivisible could be in motion, namely, if it were possible for something to be moved in an indivisible “now”, for just as there is nothing smaller than the “now” in time, so one cannot take a smaller mobile. And so it is evident that in the two questions—that of motion in a “now” and that of an indivisible being moved—the same principle is involved. But it is impossible for motion to occur in a “now”. Therefore, it is impossible for an indivisible to be moved.