Authors/Thomas Aquinas/physics/L8/lect18

Lecture 18 Dialectical reasons to show reflex motion is not continuous

Latin	English
	Lecture 18 Dialectical reasons to show reflex motion is not continuous
lib. 8 l. 18 n. 1 Postquam philosophus ostendit rationibus propriis quod motus reflexus non est continuus, hic ostendit idem rationibus communibus et logicis. Et circa hoc duo facit: primo dicit de quo est intentio; secundo probat propositum, ibi: omne enim quod movetur et cetera. Dicit ergo primo, quod si aliquis velit rationabiliter, idest logice, intendere ad propositum ostendendum, videbitur hoc idem sequi, scilicet quod motus reflexus non est continuus, ex rationibus quae ponentur.	1123. After proving with proper reasons that reflex motion is not continuous, the Philosopher now proves the same with common and logical reasons. About this he does two things: First he expresses his intention; Secondly, he proves his proposition, at 1124. He says therefore first that if someone wishes to prove “reasonably,” i.e., logically, the proposition in question, it will be seen from the reasons to be given that the same thing follows, namely, that reflex motion is not continuous.
lib. 8 l. 18 n. 2 Deinde cum dicit: omne enim quod movetur etc., ostendit propositum: et primo solum in motu reflexo locali; secundo communiter in omnibus motibus, ibi: amplius et ex his manifestum et cetera. Prima ratio talis est. Omne quod movetur continue, a principio sui motus ferebatur sicut in finem ad hoc ad quod pervenit secundum loci mutationem, nisi fuerit aliquid prohibens (quia a prohibente potuisset in aliam partem deflecti). Exemplificat autem hanc propositionem, dicens quod si aliquid per motum localem pervenit ad b, non solum quando propinquum erat, sed statim quando incepit moveri, movebatur ad b: non est enim aliqua ratio quare magis moveatur ad b nunc quam prius. Et simile est in aliis motibus. Si autem ita sit quod motus reflexus sit continuus, verum erit dicere quod id quod movetur ab a in c, et iterum reflectitur in a, continue movetur. Ergo in prima parte motus qui est ab a in c, movebatur ad terminum ultimae partis qui est a; et sic dum movetur ab a, movetur ad a. Sequitur ergo quod simul moveatur contrariis motibus: quia in motibus rectis contrarium est moveri ab eodem et in idem; in motibus autem circularibus non est contrarium. Hoc autem est impossibile, quod aliquid simul moveatur contrariis motibus: ergo impossibile est quod motus reflexus sit continuus.	1124. Then at (885 264 a9) he proves the proposition. First, for reflex local motion only; Secondly, in common for all motions, at 1126. The first argument is this: Everything in continuous motion has been, from the very beginning of its motion, in the process of being carried, as toward an end, to that at which it arrives according to change of place, unless there is some obstacle (because an obstacle could deflect it in another direction). He exemplifies this by saying that if something in local motion has arrived at B, it was being moved toward B not only when it was near B but at soon as it began to be moved. For there is no reason why it should be tending more toward B now than before. And the same is true in other motions. But if a reflex motion should be continuous, it will be true to say that what is in motion from A to C, and is then reflected back to A, is in a continuous motion. Therefore, in the very first part of the motion from A to C it was being moved to its final terminus in the part A; in this way, while it is being moved from A, it is being moved toward A. It follows, therefore, that it is being simultaneously moved with contrary motions, because in the sphere of rectilinear motions, to be moved from a thing and to be moved toward the same are contrary. But in circular motions this is not contrary. Now it is impossible for something to be moved simultaneously with contrary motions. Therefore, it is impossible for a reflex motion to be continuous.
lib. 8 l. 18 n. 3 Deinde cum dicit: simul autem et ex hoc etc., ex eodem medio ducit ad aliud inconveniens. Si enim aliquid, dum movetur ab a, movetur ad a; non autem potest moveri ad a nisi ex aliquo contraposito, quod sit c, in quo mobile nondum fuit cum incipit moveri ab a: sequitur quod aliquid movetur ex illo termino in quo non est; quod est impossibile. Non enim potest aliquid recedere a loco in quo non est. Sic ergo impossibile est quod motus reflexus sit continuus. Et si hoc est impossibile, necesse est quod in puncto reflexionis mobile quiescat, scilicet in c. Ex quo patet quod non est unus motus; quia motus qui distinguitur per interpositionem quietis, non est unus.	1125. Then at (886 264 a18) from the same middle he leads to another impossibility. For if something, while it is being moved from A, is being moved toward A, it cannot be moved toward A except from a counter-point C, in which the mobile was not yet present when it began to be moved from A. It follows, then, that something is being moved from a terminus at which it is not present—which is impossible. For it cannot leave a place in which it is not. Thus, it is impossible for a reflex motion to be continuous. And if this is impossible, then it is necessary that at the point of reflexion the mobile be at rest, i.e., in C. From which it is plain that it is not one motion, because a motion interrupted by rest is not one.
lib. 8 l. 18 n. 4 Deinde cum dicit: amplius et ex his etc., probat idem universalius in quolibet genere motus, tribus rationibus. Quarum prima talis est. Omne quod movetur, movetur aliqua specierum motus supra assignatarum: et similiter omne quod quiescit oportet quod quiescat aliqua quietum oppositarum praedictis motibus. Ostensum est enim supra in quinto, quod non potest esse alius motus praeter assignatos. Accipiamus ergo aliquem motum distinctum ab aliis motibus hoc modo, quod sit differens specie ab aliis, sicut dealbatio differt a denigratione; non autem sic quod motus qui accipitur distinguatur ab aliis sicut una pars motus ab aliis partibus eiusdem motus, ut una pars dealbationis distinguitur ab aliis partibus dealbationis eiusdem. Accepto ergo uno tali motu sicut dictum est, verum est dicere quod illud quod non semper movetur hoc motu, ex necessitate prius quiescebat opposita quiete: sicut quod non semper dealbatur, aliquando quiescebat quiete opposita dealbationi. Sed haec propositio non esset vera, si aliqua pars determinata motus acciperetur: non enim est necesse ut id quod non semper movebatur hac parte dealbationis, quod antea quiesceret quiete opposita; quia antea etiam dealbabatur alia parte dealbationis. Et propter hoc signanter dixit: et non si aliqua pars est totius. Hanc autem propositionem sic probat. Duorum privative oppositorum necesse est, cum unum non inest, alterum inesse susceptibili: quies autem opponitur motui privative: ergo si mobile erat quando sibi motus non inerat, ex necessitate sequitur quod tunc quies sibi inesset. Hac ergo propositione probata, ex ratione supra posita assumit minorem, dicens quod si motus recti contrarii sunt qui est ab a ad c, et qui est a c ad a; et non contingit simul esse motus contrarios: manifestum est quod quando movebatur ab a ad c, non movebatur tunc a c ad a; et sic isto motu qui est a c ad a non semper movebatur. Unde secundum propositionem praemissam, necesse est quod mobile prius quiesceret quiete opposita. Ostensum est autem in quinto, quod motui qui est a c, opponitur quies quae est in c: ergo quiescebat in c. Non ergo motus reflexus erat unus et continuus, cum distinguatur per interpositionem quietis.	1126. Then at (887 264 a21) he proves the same thing in a more universal way for every genus of motion, with three arguments. The first of them is this: Whatever is in motion is being moved with respect to one of the species of motion listed previously. In like manner, whatever is at. rest is so with respect to a rest that is opposite to one of the aforesaid species of motion. For it was shown above in Book V that no motions other than the ones listed are possible. Let us, therefore, take a motion that is distinct from other motions, in the sense of being specifically distinct from others, as whitening is distinct from blackening—but not distinct in the way that one part of a motion is distinct from other parts of the same motion, as one part of the motion of whitening is distinct from other parts of the same whitening. Taking, therefore, one motion in the way described, it is true to say that whatever is not forever being moved with this motion, was before of necessity at rest with an opposite rest, as whatever is not being forever whitened was at some time at rest with a rest opposite to whitening. But this proposition would not be true if some definite part of the motion should be taken, for it is not necessary that what was not forever being moved in this part of the whitening was previously at rest with an opposite rest, because before the thing was becoming white in some other part of the whitening. And because of this he states significantly: “...not some particular part of the whole.” This proposition he now proves: When one of two things that are in privative opposition is not in its recipient, the other must be. But rest is opposed to motion privatively. Therefore, if a mobile was existing at a time when motion was not in it, it follows of necessity that rest would then have been in it. Accordingly, since this proposition has been proved, he takes the minor from the argument already presented above and says that, if rectilinear motions from A to C and from C to A are contrary, and contrary motions cannot coexist, it is plain that when something was being moved from A to C, it was not at the same time being moved from C to A. Consequently, it was not forever being moved with respect to the motion from C to A. Hence, according to the previous proposition, it is necessary that the mobile first rest with an opposite rest. For it has been shown in Book V that to a motion from C is opposed rest in C. Therefore, it was at rest in C, Therefore the reflex motion was not one and continuous, since it was interrupted by the interposition of rest.
lib. 8 l. 18 n. 5 Secundam rationem ponit ibi: amplius autem et haec ratio etc.: quae talis est. Simul corrumpitur non album et generatur album: et e contrario simul corrumpitur album et fit non album. Sed si motus reflexus in quolibet genere sit continuus, sequetur quod continue alteratio terminetur ad album, et incipiat ex albo recedere, et quod non quiescet ibi aliquo tempore: alioquin non esset continua alteratio, si interponeretur quies. Sed sicut dictum est, cum fit album, corrumpitur non album; et cum receditur ab albo, fit non album. Sequetur ergo quod simul corrumpatur non album, et fiat non album: quia ista tria sunt in eodem tempore, scilicet fieri album, et corrumpi non album, et iterum fieri non album: si tamen continuetur reflexio absque interpositione quietis. Hoc autem est manifeste impossibile, quod simul fiat non album et corrumpatur non album. Non ergo est possibile quod motus reflexus sit continuus. Haec autem ratio ad generationem et corruptionem pertinere videtur. Et propter hoc, hanc rationem dicit esse magis propriam quam praemissas, quia in contradictoriis magis apparet quod non possunt esse simul vera. Et tamen quod dicitur in generatione et corruptione, extenditur ad omnes motus; quia in quolibet motu est quaedam generatio et corruptio. Sicut enim in alteratione generatur et corrumpitur album vel non album, ita et in quolibet alio motu.	1127. He presents the second argument at (888 264 b1), and it is this: Non-white ceases to be and white comes to be simultaneously; similarly, white ceases to be and non-white comes to be simultaneously. But if reflex motion in every genus is continuous, it will follow that an alteration is terminated at whiteness, and begins to depart from whiteness, in such a way as to form a continuous motion, and that it does not rest there for any time; for if rest should intervene, the alteration would not be continuous. But, as has been said, when the white comes to be, the non-white ceases to be, and when departure from white occurs, non-white comes to be. Therefore, it will follow that non-white is ceasing to be and coming to be at the same time, for these three things are present at the same time, namely, the coming-to-be of white, the ceasing-to-be of non-white and the coming-to-be of non-white—that is, if the reflex motion is continuous without any interval of rest. This, however, is plainly impossible, namely, that non-white should be coming to be, and ceasing to be, at the same time. Therefore, a reflex motion cannot be continuous. Now, this argument is seen to refer to generation and ceasing-to-be. For this reason he says that this argument is more proper than the previous ones, because it is more apparent in contradictories that they cannot be true at the same time. And yet, what is said in generation and ceasing-to-be applies to all motions, since in every motion there is a kind of generation and ceasing-to-be. For just as in the case of alteration, white is generated, and non-white ceases to be, so too in every other motion.
lib. 8 l. 18 n. 6 Tertiam rationem ponit ibi: amplius non si continuum etc.: quae talis est. Sicut supra in quinto habitum est, non est necessarium si continuum est tempus, quod propter hoc motus sit continuus. Motus enim diversarum specierum, etsi succedant sibi in tempore continuo, non tamen sunt continui, sed consequenter se habentes; eo quod oportet continuorum esse unum communem terminum; contrariorum autem et specie differentium, ut albedinis et nigredinis, non potest esse unus communis terminus. Cum igitur motus qui est ab a in c, sit contrarius motui qui est a c in a in quocumque genere motus, ut supra in quinto ostensum est, impossibile est quod isti duo motus sint continui ad invicem, etiam si tempus eorum sit continuum, nulla interposita quiete. Relinquitur ergo quod motus reflexus nullo modo potest esse continuus. Est autem considerandum quod rationes praemissae dicuntur logicae, quia procedunt ex quibusdam communibus, scilicet ex proprietate contrariorum.	1128. At (889 264 b6) he gives the third argument, which is this: As was had in Book V, it is not necessary, if the time is continuous, that a motion be on that account continuous. For motions of diverse kinds, even though they succeed one another in continuous time, are not on that account continuous, but are, rather, consequent upon one another, for continua must have one common terminus. But there cannot be one common terminus in things that are contrary and specifically different, such as whiteness and blackness. Since, therefore, a motion from A to C is contrary to one from C to A in any genus of motion, as was shown in Book V, it is impossible that those two motions be continuous one to the other—even though the time be continuous—with no intervening rest. It remains, therefore, that a reflex motion can in no way be continuous. It should be noted that the foregoing arguments are called “logical” because they proceed from certain common things, namely, from the property of contraries.