Authors/Thomas Aquinas/physics/L6/lect13

Lecture 13 By nature, no change is infinite. How motion may be infinite in time

Latin	English
	Lecture 13 By nature, no change is infinite. How motion may be infinite in time
lib. 6 l. 13 n. 1 Postquam philosophus ostendit quod impartibile non movetur, hic intendit ostendere quod nulla mutatio est infinita; quod est contra Heraclitum, qui posuit omnia moveri semper. Et circa hoc duo facit: primo ostendit quod nulla mutatio est infinita secundum propriam speciem; secundo ostendit quomodo possit esse infinita tempore, ibi: sed si sic contingit et cetera. Circa primum duo facit: primo ostendit quod mutatio non est infinita secundum speciem in aliis mutationibus praeter motum localem; secundo ostendit idem in motu locali, ibi: loci autem mutatio et cetera.	878. After showing that things which cannot be divided into parts are not moved, the Philosopher now intends to show that no change is infinite, This is against Heraclitus, who supposed that things are always in motion. About this he does two things: First he shows that no change is infinite according to its own species; Secondly, how there can be infinites in time, at 883, About the first he does two things: First he shows for all changes except local motion that no change is infinite according to its species; Secondly, he shows the same thing for local motion, at 881.
lib. 6 l. 13 n. 2 Prima ratio talis est. Supra dictum est quod omnis mutatio est ex quodam in quiddam. Et in quibusdam quidem mutationibus, quae scilicet sunt inter contradictorie opposita, ut generatio et corruptio, vel inter contraria, ut alteratio, et augmentum et decrementum, manifestum est quod habent praefixos terminos. Unde in his mutationibus quae sunt inter contradictorie opposita, terminus est vel affirmatio vel negatio, sicut terminus generationis est esse, corruptionis vero non esse. Similiter illarum mutationum quae sunt inter contraria, ipsa contraria sunt termini ad quos, sicut ad quaedam ultima, mutationes huiusmodi terminantur. Unde sequitur quod, cum omnis alteratio sit de contrario in contrarium, quod omnis alteratio habeat aliquem terminum. Et similiter dicendum est in augmento et decremento: quia terminus augmenti est perfecta magnitudo (et dico perfectam secundum conditionem propriae naturae: alia enim perfectio magnitudinis competit homini et alia equo); terminus autem decrementi est id quod contingit esse in tali natura maxime remotum a perfecta magnitudine. Et sic patet quod quaelibet praedictarum mutationum habet aliquid ultimum in quod terminatur: nihil autem tale est infinitum: ergo nulla praedictarum mutationum potest esse infinita.	880. The first reason is this: Every change is from something to something. Indeed, in some changes, namely, those which occur between contradictories, as do generation and ceasing-to-be, or between contraries, as do alteration and growing and decreasing, it is evident that they have pre-defined termini. Hence in changes that occur between contradictory termini, the terminus is either affirmation or negation, as the terminus of generation is a being, and that of ceasing-to-be, non-being. Likewise, in regard to changes that are between contraries, the contraries are termini at which, as at ultimate goals, changes of this kind are terminated. Hence it follows, since every alteration is from contrary to contrary, that every alteration has some terminus. The same must be said for growth and decrease, for the terminus of growth is perfect magnitude (and I say “perfect” in respect of the nature, for a different perfection of magnitude befits man from the one that befits a horse), and the terminus of decrease is the one that happens to a definite nature to be most removed from perfect magnitude. Consequently, it is evident that each of the above-mentioned changes has a goal at which it is terminated. But such a situation precludes the infinite. Therefore, none of these changes can be infinite.
lib. 6 l. 13 n. 3 Deinde cum dicit: loci autem mutatio etc., procedit ad loci mutationem. Et primo ostendit quod non est similis ratio de loci mutatione et aliis mutationibus. Non enim potest sic probari quod loci mutatio sit finita, sicut probatum est de aliis mutationibus, per hoc quod terminantur ad aliqua contraria, vel contradictorie opposita: quia non omnis loci mutatio est inter contraria simpliciter. Dicuntur enim contraria quae maxime distant. Maxime autem distantia simpliciter accipitur quidem in motibus naturalibus gravium et levium: locus enim ignis a centro terrae habet maximam distantiam, secundum distantias determinatas talibus corporibus in natura. Unde tales mutationes sunt inter contraria simpliciter. Unde de huiusmodi mutationibus posset ostendi quod non sunt infinitae, sicut et de aliis. Sed maxima distantia in motibus violentis aut voluntariis, non accipitur simpliciter secundum aliquos terminos certos; sed secundum propositum aut violentiam moventis, qui aut non vult, aut non potest ad maiorem distantiam movere. Unde est ibi secundum quid maxima distantia, et per consequens contrarietas, non autem simpliciter. Et ideo non poterat ostendi per terminos, quod nulla mutatio localis esset infinita.	881. Then at (674 241 b2) he proceeds to local motion. And first he shows that the argument in regard to local motion is not the same as for the other changes. For it cannot be proved that local motion is finite (as we have proved other motions are finite), because it is terminated at something contrary or contradictory, for not every local motion is between strict contraries, where contraries refer to things most distant. There is a maximum distance in the strict sense in the natural motions of heavy and light bodies, for the place of fire is at a maximum distance from the center of the earth, in accordance with the distance that nature determines for such bodies. Hence, such changes are between strict contraries, Hence, it can be proved of such changes that they are not infinite any more than the others were. But maximum distance in compulsory or voluntary motions does not depend strictly on certain definite termini but on the intention or energy of the one causing the motion, who either does not desire to or cannot physically move something any farther. Hence, it is only in a qualified sense., ere is maximum distance and a consequent contrariety. Hence, if you stick with the termini, it cannot be proved that no local motion is infinite.
lib. 6 l. 13 n. 4 Unde consequenter hoc ostendit alia ratione, quae talis est. Illud quod impossibile est esse decisum, non contingit decidi. Et quia multipliciter dicitur aliquid impossibile, scilicet quod omnino non contingit esse, et quod non de facili potest esse; ideo interponit de quo impossibile hic intelligat. Intelligit enim de eo quod sic est impossibile, quod nullo modo contingit esse. Et eadem ratione id quod est impossibile factum esse, impossibile est fieri; sicut si impossibile est contradictoria esse simul, impossibile est hoc fieri. Et pari ratione illud quod impossibile est mutatum esse in aliquid, impossibile est quod mutetur in illud; quia nihil tendit ad impossibile. Sed omne quod mutatur secundum locum, mutatur in aliquid. Ergo possibile est per motum pervenire in illud. Sed infinitum non potest pertransiri. Non ergo fertur aliquid localiter per infinitum. Sic ergo nullus motus localis est infinitus. Et ita universaliter patet quod nulla mutatio potest esse sic infinita, ut non finiatur certis terminis, a quibus speciem habet.	882. Consequently, this must be proved by another argument, which is this: What is impossible to exist divided cannot be divided, And because things are said to be impossible in many senses, name, what never can occur or what cannot occur except with great difficulty, he therefore explains his meaning of “impossible” here. And he means it in the sense of that which cannot happen at all. For the same reason, what is impossible to have been made, is impossible to make; for example, if it is impossible that contradictories be together, it is impossible that this be brought about. For the same reason, what is impossible to have been changed into something cannot be changed into it, because nothing tends toward the impossible. But everything that is being changed according to place is being changed into something. Therefore, it is possible through that motion to arrive at something. But the infinite cannot be gone through. Therefore, nothing is moved through the infinite. Thus, therefore, no local motion is infinite. And so it is universally evident that no change can be infinite in such a way that it be not terminated by definite termini from which it derives its species.
lib. 6 l. 13 n. 5 Deinde cum dicit: sed si sic contingit etc., ostendit quomodo motus possit esse infinitus tempore. Et dicit quod considerandum est utrum sic contingat motum esse infinitum tempore, ut semper maneat unus et idem numero. Quod enim motus duret per infinitum tempus, non existente uno ipso motu, nihil prohibet: quod sub dubitatione dicit, addens forte, quia posterius de hoc inquiret. Et ponit exemplum: sicut si dicamus quod post loci mutationem est alteratio, et post alterationem est augmentum, et post augmentum iterum generatio, et sic in infinitum. Sic enim semper posset motus durare tempore infinito. Sed non esset unus secundum numerum; quia ex huiusmodi motibus non fit unum numero, ut in quinto ostensum est. Sed quod motus duret tempore infinito, ita quod semper maneat unus numero, hoc non contingit nisi in una specie motus: motus enim circularis potest durare unus et continuus tempore infinito, ut in octavo ostendetur.	883. Then at (675 241 b12) he shows how motion can be infinite in time. And he says that we must consider whether motion can be infinite in time in such a way that it remains numerically one and the same motion. For there is nothing to prevent motion from enduring through infinite time as long as it is not one and the same motion. But he leaves that matter in doubt when he adds “perhaps”, because he will settle the matter later. And he gives an example: Let us say that after a local motion there is an alteration, and after that a growing, and after that generation, and so on ad infinitum. In this way motion could always endure throughout infinite time. And it would not be one and the same numerical motion, because a series of such motions as are given in the example do not form one numerical motion, as we have proved in Book V. But that motion endure throughout infinite time in such a way that it remain one numerical motion can occur in only one species of motion, for a circular motion can endure as one and continuous throughout infinite time, as will be proved in Book VIII.