Authors/Thomas Aquinas/physics/L4/lect19

Lecture 19 From the definition of time certain things are clarified

Latin	English
	Lecture 19 From the definition of time certain things are clarified
lib. 4 l. 19 n. 1 Postquam philosophus definivit tempus, hic ex definitione data reddit rationem eorum quae dicuntur de tempore. Et circa hoc quatuor facit: primo ostendit quomodo in tempore invenitur minimum, et quomodo non; secundo quare tempus dicitur multum et paucum, breve et longum, non autem velox et tardum, ibi: manifestum est autem propter quid etc.; tertio quomodo tempus sit idem, et quomodo non, ibi: et idem autem ubique etc.; quarto quomodo tempus cognoscitur motu et e converso, ibi: non solum autem motum et cetera.	593. Having defined time, the Philosopher now, in the light of the definition which he has given, gives an explanation of those things that are said about time. About which he does four things: First, he shows in what sense there to found in time a smallest part, and in what sense there is not; Secondly, why time is said to be “much” and “little,” “short” and “long”, but not “fast” and “slow,” at no. 595; Thirdly, in what sense time is the saw, and in what sense it is not [ever the same again] at no. 596; Fourthly, how time to known through motion and vice-versa, at no. 597.
lib. 4 l. 19 n. 2 Dicit ergo primo quod manifestum est ex definitione temporis prius data, quod tempus est numerus motus secundum prius et posterius, ut supra expositum est; et iterum manifestum est ex praemissis, quod tempus est quoddam continuum. Licet enim non habeat continuitatem ex eo quod est numerus, habet tamen continuitatem ex eo cuius est numerus: quia est numerus continui, scilicet motus, ut etiam supra dictum est. Non enim est tempus numerus simpliciter, sed numerus numeratus. In numero autem simpliciter est omnino invenire aliquem minimum numerum, scilicet dualitatem. Sed si accipiamus numerum quendam, scilicet numerum alicuius rei continuae, quodammodo est invenire minimum, et quodammodo non; quia secundum multitudinem est invenire minimum, non autem secundum magnitudinem. Sicut in multis lineis secundum multitudinem quidem est minimum, ut una linea vel duae lineae; una quidem si accipiatur id quod est minimum simpliciter in numero; duae autem si accipiatur id quod est minimum in genere numeri, habens rationem numeri. Sed in lineis non est invenire minimum secundum magnitudinem, ut sit scilicet aliqua linea minima; quia semper est dividere quamcumque lineam. Et similiter dicendum est de tempore: quia est invenire in eo minimum secundum multitudinem, scilicet unum vel duo, ut puta aut unum annum aut duos annos, aut duos dies aut horas. Sed minimum secundum magnitudinem non est invenire in tempore; quia cuiuslibet temporis dati est accipere partes in quas dividitur.	594. He says therefore first [420 220 a24] that the previously given definition of time makes clear that time is “the number of motion according to before and after,” as was expounded above, and that time is a type of continuum, as is likewise manifest from what has gone before. For although it does not have continuity insofar as it is a number, yet it has continuity by reason of that of which it is the number: for it is the number of a continuum, namely, of motion, as was said above. For time to not a number absolutely but a number of something numbered. Among absolute numbers there is unequivocally a least to be found, namely, two. But if we consider owe certain number, namely, the number of something that is continuous, then there is in one sense a minimum and in one sense no minimum, because in the order of multitude [plurality] there is a least, but not in the order of magnitude. For example, in a plurality of lines there is a minimum according to plurality, i.e., one line or two lines (one if you consider what is the minimum in number absolutely; two if you mean that which is least in the genus of number, having the notion of number). But in respect of magnitude there is no minimum in lines, so that there would be namely, some smallest lines—because it is always possible to divide any line whatsoever. A parallel situation is found in time, for there is a minimum according to multitude, namely, one or two, for example, one year or two years or two days or two hours. But in the order of magnitude there is no minimum, because of any given time there are parts into which it may be divided.
lib. 4 l. 19 n. 3 Deinde cum dicit: manifestum est autem etc., assignat rationem quare tempus non dicitur tardum aut velox, sed dicitur multum et paucum, breve et longum. Iam enim ostensum est quod tempus et numerus est, et continuum est. Inquantum ergo est continuum, dicitur tempus et longum et breve, sicut et linea; inquantum autem numerus est, dicitur et multum et paucum. Esse autem velox et tardum, nullo modo competit numero: neque numero simpliciter, ut manifestum est; neque etiam potest convenire numero alicuius rei. Nam esse velox vel tardum, dicitur de aliquo secundum quod est numeratum: dicitur enim velox motus, eo quod parvo tempore numeratur; tardum autem e converso. Unde manifestum est quod tempus nullo modo potest dici velox vel tardum.	595. Then [421 220 a32] he gives a reason why time is not said to be slow or fast, but great and small, short and long. For it has already been shown that time is both a number and a continuum. Insofar, therefore, as it is the latter, time, is said to be “long” and “short”, insofar as it is a number, it is said to be “great” and “small.” But to be “fast” and “slow” in no wise belongs to number, neither to number absolutely, as is plain, not to the number of some things. For to be “fast” or “slow” is said of something accordingly as it is numbered: for a motion is called “fast” insofar as it is counted off in a short time—and “slow” conversely. Hence it is clear that in no sense can time be called “fast” or “slow.”
lib. 4 l. 19 n. 4 Deinde cum dicit: et idem autem etc., ostendit quomodo tempus sit idem, et quomodo non idem. Et primo quomodo sit idem vel non idem simpliciter; secundo quomodo sit idem secundum quid, ibi: amplius sicut contingit et cetera. Dicit ergo primo quod tempus simul existens, est idem ubique, idest respectu omnium quae moventur ubicumque. Non enim diversificatur secundum diversa mobilia; sed diversificatur secundum diversas partes eiusdem motus. Et ideo tempus prius et tempus posterius non est idem. Et hoc ideo, quia prima mutatio praesens, cuius primo et principaliter numerus tempus est, una est; sed huius mutationis altera pars est, quae iam facta est et pertransiit, et altera, quae futura est. Unde et tempus alterum est quod prius fuit, et alterum quod futurum est. Et hoc ideo, quia tempus non est numerus simpliciter, sed numerus alicuius rei numeratae, scilicet prioris et posterioris in motu; et huic numero semper accidit esse alterum, et prius et posterius, propter hoc quod ipsa nunc, secundum quod se habent prius et posterius, semper sunt altera. Si autem esset numerus simpliciter, tunc esset idem tempus et mutationis quae praeteriit, et eius quae futura est; quia numerus simpliciter est unus et idem diversorum numeratorum, ut centum equorum et centum hominum. Sed numerus numeratus est alius diversorum: centum enim equi sunt aliud quid a centum hominibus. Et quia tempus est numerus prioris et posterioris in motu; quia alia sunt quae in motu se habent prius et posterius secundum id quod praeteriit de motu, et alia secundum id quod sequitur; propter hoc est aliud tempus praeteritum, et aliud futurum.	596. Then [422 220 b5] he shows how time is the same and how not the same. First, how it is the same or not the same absolutely; Secondly, how it is the same in a certain respect, at no. 597. He says therefore first that the time existing at a given moment is the same everywhere, i.e., it is the same in respect to everything that is being moved anywhere. For it is not diversified by reason of the diverse mobiles, but by reason of the diverse parts of the same motion. For which reason a prior time and a later time are not the same. Why? Because the first and present motion, of which time is primarily and principally the number, is one; but one part of this motion has already taken place and is past, and another will be in the future. Hence there is one time which is past, and another time which is future. This is so because time is not number absolutely but the number of something numbered; namely, of the “before” and “after” in motion. And this number always varies and is “before” and “after,” because the “now’s,” as before and after, are always other. But if time were number absolutely, then the time corresponding to the change which is past and the time corresponding to the change which is to come would be the same, for number absolutely is one and the same of different things counted as, for example, in the case of 100 horses and 100 men. But number numbered varies with different things. For 100 horses are not the same as 100 men. Since time is the number of “before’s and “after” in motion; and since the “before” and “after” of a past motion are not the same as those of that which follow, therefore the past time and the future time are other and other.
lib. 4 l. 19 n. 5 Deinde cum dicit: amplius sicut contingit etc., ostendit quomodo tempus reiteratur idem secundum quid. Et dicit quod sicut reiterari unum et eundem motum contingit, sic contingit reiterari unum et idem tempus. Reiteratur enim unus et idem motus specie, sed non numero: quia ab eodem signo arietis, a quo primo movebatur sol, et postea movebitur; et ideo sicut fuit hiems aut ver aut aestas aut autumnus, ita erit, non quidem unum numero, sed specie.	597. Then [423 220 b12] he shows how the same time returns in a certain respect. And he says that in the same way that one and the same motion may be repeated, so may one and the same time. For one and the same motion can be duplicated specifically, but not numerically; for it is from the same sign of the Ram that the sun first moves [at the vernal equinox] and later will move the following year; therefore, just as there has been winter or spring or summer or fall, so also there will be, not, indeed, the same one in number, but in species.
lib. 4 l. 19 n. 6 Deinde cum dicit: non solum autem motum tempore etc., ostendit quod sicut motum cognoscimus tempore, ita et tempus motu: et hoc primo ex ratione numeri et numerati; secundo ex similitudine magnitudinis et motus, ibi: et hoc rationabiliter et cetera. Dicit ergo primo quod non solum mensuramus motum per tempus, sed etiam mensuramus tempus per motum, propter hoc quod ad invicem definiuntur. Oportet enim accipere quantitatem unius secundum quantitatem alterius. Quod enim tempus determinet motum, ex hoc contingit, quia est numerus ipsius; sed e converso motus determinat tempus quoad nos. Percipimus enim interdum quantitatem temporis ex motu, utpote cum dicimus tempus esse multum vel paucum, secundum mensuram motus nobis certam: quia et ipsum numerum aliquando per numerabilia cognoscimus, et e converso. Cognoscimus enim numero equorum multitudinem, et iterum uno equo cognoscimus numerum equorum. Non enim sciremus quot sunt milliaria, nisi sciremus quid est milliare. Et similiter est in tempore et motu. Quia cum est nobis certa quantitas temporis, quantitas autem motus ignota, tunc tempore mensuramus motum; e converso autem, quando motus est notus et tempus ignotum.	598. Then [424 220 b14] he shows that just as we know motion from time, so also time from motion. First, by reason of number and the thing numbered; Secondly, from the likeness existing between magnitude and motion, at no. 599. He says therefore first that we not only measure time by motion but motion by time, because each is defined in terms of the other. For one must take the quantity of the one according to the quantity of the other. Now that time should determine motion comes about because it is the number of motion; but conversely, as to us, motion determines time. For we sometimes perceive a quantity of time by means of motion, as when we declare a time to be long or short according to a measure of motion, certain to us; because sometimes we know a number through the things that can be counted, and conversely. For we know by this number a multitude of horses and likewise by one horse we know the number of horses. For we would not know how many thousands there were unless we know what a thousand was. The same holds for time and motion. For when a quantity of time is certain to us, but the quantity of motion unknown, then by the time we measure the motion; but we do the opposite when the motion is known and the time unknown.
lib. 4 l. 19 n. 7 Deinde cum dicit: et hoc rationabiliter etc., ostendit idem ex comparatione motus ad magnitudinem. Et dicit quod rationabiliter accidit quod dictum est de tempore et motu: quia sicut motus magnitudinem imitatur in quantitate et continuitate et divisibilitate, ita et tempus imitatur motum; haec enim in motu inveniuntur propter magnitudinem, et in tempore propter motum. Mensuramus autem et magnitudinem per motum, et motum per magnitudinem. Dicimus enim multam esse viam, quando percipimus motum nostrum fuisse multum: et e converso, quando consideramus magnitudinem viae, dicimus motum nostrum fuisse multum. Et ita etiam est de tempore et motu, ut supra dictum est.	599. Then [425 220 b24] he shows the same thing by comparing motion and magnitude. And he says that what has been just said of time and motion happens reasonably because just as motion imitates magnitude in quantity and continuity and divisibility, so also does time imitate motion; for the latter [quantity, continuity and divisibility] are found in motion on account of their presence in magnitude, and they are found in time on account of their presence in motion. For we measure magnitude by means of motion, and motion by means of magnitude. For we say that a road is long when we notice that our motion over it was long; and conversely, when we consider the magnitude of the road, we say that our motion was long. The same holds when relating time and motion, “ we said above.