Authors/Thomas Aquinas/physics/L4/lect17

Lecture 17 The definition of time, given and explained

Latin	English
	Lecture 17 The definition of time, given and explained
lib. 4 l. 17 n. 1 Postquam philosophus disputative inquisivit de tempore, hic incipit determinare veritatem. Et primo determinat veritatem de tempore; secundo movet quasdam dubitationes circa veritatem determinatam, et solvit eas, ibi: dignum autem et cetera. Circa primum duo facit: primo determinat de tempore secundum se; secundo per comparationem ad ea quae tempore mensurantur, ibi: quoniam autem est tempus et cetera. Circa primum tria facit: primo manifestat quid sit tempus; secundo quid sit nunc temporis, ibi: et sicut motus semper etc.; tertio ex definitione motus assignata, assignat rationes eorum quae dicuntur de tempore, ibi: quod quidem igitur tempus et cetera. Circa primum duo facit: primo ponit definitionem temporis; secundo manifestat eam, ibi: signum est autem et cetera. Prima pars dividitur in tres, secundum tres particulas definitionis temporis quas investigat; secunda pars incipit ibi: quoniam autem quod movetur etc.; tertia ibi: determinamus autem et cetera.	571. After treating of time dialectically, the Philosopher here begins to determine the truth. First, he determines the truth concerning time; Secondly, he brings up and solves some objections concerning the truth determined, at no. 625 (L.23). In regard to the first he does two things: First he determines concerning time absolutely. Secondly, in relation to things measured by time, at no. 600 (L.20). As to the first he does three things: First he makes clear what time is; Secondly, what the “now” of time is, at no. 582 (L.18); Thirdly, from the definition he gives of time, he explains the things said about time, at no. 593 (L.19). About the first he does two things: First he gives the definition of time; Secondly, he explains it, at no. 581. The first point is divided into three parts according to the three parts which he investigates of the definition; The second part begins at no. 575; The third part at no. 580.
lib. 4 l. 17 n. 2 Primo ergo investigat hanc particulam, quod tempus est aliquid motus. Unde dicit quod quia inquirimus quid sit tempus, hinc incipiendum est, ut accipiamus quid motus sit tempus. Et quod tempus sit aliquid motus, per hoc manifestum est, quod simul sentimus motum et tempus. Contingit enim quandoque quod percipimus fluxum temporis, quamvis nullum motum particularem sensibilem sentiamus; utpote si simus in tenebris, et sic visu non sentimus motum alicuius corporis exterioris. Et si nos non patiamur aliquam alterationem in corporibus nostris ab aliquo exteriori agente, nullum motum corporis sensibilis sentiemus: et tamen si fiat aliquis motus in anima nostra, puta secundum successionem cogitationum et imaginationum, subito videtur nobis quod fiat aliquod tempus. Et sic percipiendo quemcumque motum, percipimus tempus: et similiter e converso, cum percipimus tempus, simul percipimus motum. Unde cum non sit ipse motus, ut probatum est, relinquitur quod sit aliquid motus.	572. First [404 219 a1] therefore he investigates this part: that time is “something of motion.” He says that since we are investigating what time is, we must begin by understanding what aspect of motion time is. That time is something of motion is manifested by the very fact that we sense motion and time together. For it happens that we perceive the flow of time even though we are not sensing any particular sensible motion; for example, if we are in the dark and do not see any external object moving. And if while we are in this situation, we are not undergoing any bodily changes brought about by an external agent, then we are not sensing any motion of a sensible body. Yet if there is a motion within our soul, such as a succession of thoughts and imaginings, suddenly it appears to us that some time is elapsing. Thus by perceiving any sort of motion we perceive time and, vice-versa, when we perceive time we are simultaneously perceiving a motion. Hence, although time is not a motion, as we have already shown, yet it is somehow connected with motion.
lib. 4 l. 17 n. 3 Habet autem dubitationem quod hic dicitur de perceptione temporis et motus. Si enim tempus consequatur aliquem motum sensibilem extra animam existentem, sequitur quod qui non sentit illum motum, non sentiat tempus; cuius contrarium hic dicitur. Si autem tempus consequatur motum animae, sequetur quod res non comparentur ad tempus nisi mediante anima; et sic tempus erit non res naturae, sed intentio animae, ad modum intentionis generis et speciei. Si autem consequatur universaliter omnem motum, sequetur quod quot sunt motus, tot sint tempora: quod est impossibile, quia duo tempora non sunt simul, ut supra habitum est.	573. What has been just said about the perceiving of time and of motion raises a difficulty. For if time follows upon some sensible motion outside the mind, it follows that whosoever does not sense that motion, does not sense time; whereas the opposite of that is said here. And if time depends upon some motion of the mind, it follows that things are not connected to time except through the medium of the mind: thus time will not be a thing of nature but a notion in the mind like the intention of genus and species. But if time follows upon any and every motion, then there are as many times as there are motions—which is impossible, for there cannot be two times together as we said above.
lib. 4 l. 17 n. 4 Ad huius igitur evidentiam sciendum est, quod est unus primus motus, qui est causa omnis alterius motus. Unde quaecumque sunt in esse transmutabili, habent hoc ex illo primo motu, qui est motus primi mobilis. Quicumque autem percipit quemcumque motum, sive in rebus sensibilibus existentem, sive in anima, percipit esse transmutabile, et per consequens percipit primum motum quem sequitur tempus. Unde quicumque percipit quemcumque motum, percipit tempus: licet tempus non consequatur nisi unum primum motum, a quo omnes alii causantur et mensurantur: et sic remanet tantum unum tempus.	574. In order to clear up this difficulty it must be remembered that there is one first motion which is the cause of every other motion. Hence whatever is in a transmutable state possesses that state on account of the first motion, which is the motion of the first mobile being. Whosoever, therefore, perceives any motion, whether it exists in sensible things or in the mind, is perceiving transmutable being and consequently is perceiving the first motion, which time follows. Thus anyone who perceives any motion whatsoever is perceiving time, although time follows upon just the one first motion by which all other motions are caused and measured. Consequently, there remains only one time.
lib. 4 l. 17 n. 5 Deinde cum dicit: quoniam autem quod movetur etc., investigat secundam particulam positam in definitione temporis. Supposito enim quod tempus sit aliquid motus, consequens scilicet ipsum, restat investigandum secundum quid tempus consequatur motum, quia secundum prius et posterius. Circa hoc ergo tria facit: primo ostendit quomodo in motu inveniatur prius et posterius; secundo quomodo prius et posterius se habeant ad motum, ibi: est autem prius et posterius etc.; tertio quod tempus sequitur motum secundum prius et posterius, ibi: at vero et tempus et cetera. Circa primum duo facit: primo ostendit quod continuitas est in tempore ex motu et magnitudine; secundo quod etiam prius et posterius, ibi: prius autem et posterius et cetera.	575. Then [405 219 a10] he investigates the second particle placed in the definition of time. For supposing that time is something of motion, namely, that it follows upon motion, there still remains the task of investigating according to what does time follow upon motion; the answer being that it follows upon motion “according to before and after.” As to this then he does three things: First he shows how “before and after” are found in motion; Secondly, how they are related to motion, at no. 578; Thirdly, he shows that time follows motion according to “before and after,” at no. 579. About the first he does two things: First he shows that the continuity of time is due to the continuity of motion and magnitude; Secondly, that the same is true of the “before and after” of time, at no.577.
lib. 4 l. 17 n. 6 Dicit ergo primo quod omne quod movetur, movetur ex quodam in quiddam. Sed inter alios motus, primus est motus localis, qui est a loco in locum secundum aliquam magnitudinem. Primum autem motum consequitur tempus; et ideo ad investigandum de tempore oportet accipere motum secundum locum. Quia ergo motus secundum locum, est secundum magnitudinem ex quodam in quiddam et omnis magnitudo est continua; oportet quod motus consequatur magnitudinem in continuitate, ut, quia magnitudo continua est, et motus continuus sit. Et per consequens etiam tempus continuum est: quia quantus est motus primus, tantum videtur fieri tempus. Non autem tempus mensuratur secundum quantitatem cuiuscumque motus, quia tardum movetur secundum paucum spatium in multo tempore, velox autem e converso; sed solum quantitatem primi motus sequitur tempus.	576. He says therefore first that everything that is being moved is being moved. from something to something. But of motions the first is local motion, which is from place to place along a magnitude. But it is the first motion that time follows upon, and therefore, to investigate time, one must take local motion. Since, then, motion according to place is motion according to a magnitude from one place to another, and since every magnitude is continuous, motion must follow magnitude in regard to its continuity, so that, just as magnitude is continuous, so also is motion. Consequently time also is continuous: for the quantity of the first motion and the quantity of time correspond. For time is not measured according to the quantity of just any motion, since something is being moved over a small distance In a large amount of time, and a fast object, vice-versa. Time however corresponds only to the quantity of the first motion.
lib. 4 l. 17 n. 7 Deinde cum dicit: prius autem et posterius etc., ostendit etiam, quod idem ordo consideratur in priori et posteriori: et dicit quod prius et posterius sunt prius in loco sive in magnitudine. Et hoc ideo, quia magnitudo est quantitas positionem habens: de ratione autem positionis est prius et posterius: unde ex ipsa positione, locus habet prius et posterius. Et quia in magnitudine est prius et posterius, necesse est quod in motu sit prius et posterius proportionaliter his quae sunt ibi, scilicet in magnitudine et in loco. Et per consequens etiam in tempore est prius et posterius; quia motus et tempus ita se habent, quod semper alterum eorum sequitur ad alterum.	577. Then [406 219 a14] he shows that the same order prevails in respect to “before and after,” saying that “before and after” are first of all in a place or in a magnitude. This is so, because a magnitude is a quantity having position; position, however, implies “before and after.” Hence from its position place has “before and after.” And because there is “before and after” in magnitude, it follows that there is a “before and after” in motion corresponding to the things which are there, i.e., in magnitude and place. Consequently, there is a prior and subsequent also in time: for motion and time are so related that the one always follows the other.
lib. 4 l. 17 n. 8 Deinde cum dicit: est autem prius et posterius ipsorum etc., ostendit quomodo prius et posterius se habeant ad motum. Et dicit quod prius et posterius ipsorum, scilicet temporis et motus, quantum ad id quod est, motus est: tamen secundum rationem est alterum a motu, et non est motus. De ratione enim motus est, quod sit actus existentis in potentia: sed quod in motu sit prius et posterius, hoc contingit motui ex ordine partium magnitudinis. Sic igitur prius et posterius sunt idem subiecto cum motu, sed differunt ratione. Unde restat inquirendum, cum tempus sequatur motum, sicut supra ostensum est, utrum sequatur ipsum inquantum est motus, an inquantum habet prius et posterius.	578. Then [407 219 a19] he shows how “before and after” are related to motion. And he says that the “before and after” of these, namely, of time and of motion is, as to what it is, motion; yet in conception, it is distinct from motion and not motion. For it is the notion of motion that it be the act of a being in potency; but that there be in motion a “before and after” occurs in it by reason of the order of the parts of the magnitude. Accordingly, “before and after” are the same as motion as to subject but they differ from it as to notion. Hence the task remains to inquire, since time follows motion, whether it follows upon it inasmuch as it is motion, or inasmuch as it has a “before and after.”
lib. 4 l. 17 n. 9 Deinde cum dicit: at vero et tempus cognoscimus etc., ostendit quod tempus sequatur motum ratione prioris et posterioris. Propter hoc enim ostensum est quod tempus sequitur motum, quia simul cognoscimus tempus et motum. Secundum illud ergo tempus sequitur motum, quo cognito in motu cognoscitur tempus: sed tunc cognoscimus tempus, cum distinguimus motum determinando prius et posterius; et tunc dicimus fieri tempus, quando accipimus sensum prioris et posterioris in motu. Relinquitur ergo quod tempus sequitur motum secundum prius et posterius.	579. Then [408 219 a22] he shows that motion follows upon time by reason of “before and after.” For it has been shown that the reason why time follows motion is that we recognize both simultaneously. Therefore time follows motion according to that which, when it is perceived in motion, time is perceived. But it is then that we perceive time, when we distinguish a “before” and “after” in motion; and it is then that we say time is passing when we have a sense of the “before” and “after” in motion. Consequently time follows motion according to “before and after.”
lib. 4 l. 17 n. 10 Deinde cum dicit: determinamus autem etc., ostendit quid motus tempus sit, quia numerus motus: et hoc etiam ostendit eodem medio, scilicet per cognitionem temporis et motus. Manifestum est enim quod tunc esse tempus determinamus, cum accipimus in motu aliud et aliud, et accipimus aliquid medium inter ea. Cum enim intelligimus extrema diversa alicuius medii, et anima dicat illa esse duo nunc, hoc prius, illud posterius, quasi numerando prius et posterius in motu, tunc hoc dicimus esse tempus. Tempus enim determinari videtur ipso nunc. Et hoc supponatur ad praesens, quia postea erit magis manifestum. Quando igitur sentimus unum nunc, et non discernimus in motu prius et posterius; vel quando discernimus in motu prius et posterius, sed accipimus idem nunc ut finem prioris et principium posterioris; non videtur fieri tempus, quia neque est motus. Sed cum accipimus prius et posterius et numeramus ea, tunc dicimus fieri tempus. Et hoc ideo, quia tempus nihil aliud est quam numerus motus secundum prius et posterius: tempus enim percipimus, ut dictum est, cum numeramus prius et posterius in motu. Manifestum est ergo quod tempus non est motus, sed sequitur motum secundum quod numeratur. Unde est numerus motus. Si quis autem obiiciat contra praedictam definitionem, quod prius et posterius tempore determinantur, et sic definitio est circularis, dicendum est quod prius et posterius ponuntur in definitione temporis, secundum quod causantur in motu ex magnitudine, et non secundum quod mensurantur ex tempore. Et ideo supra Aristoteles ostendit quod prius et posterius prius sunt in magnitudine quam in motu, et in motu quam in tempore, ut haec obiectio excludatur.	580. Then [409 219 a25] he shows what aspect of motion time is, and says that it is “the number of motion.” He explains this by using the same means as before, namely, our knowledge of time and motion. For it is clear that when we take in motion something different from something other and understand that there is something between them, then it is that we determine that time exists. For when we perceive the differing boundaries of something and the mind calls them two “now’s,” one being before and the other after, as though the mind were counting the “before’s” and “after’s” in a motion, that is what we call time. For time seems to be determined by the “now.” (This statement is taken for granted at present, but later it will be explained). When therefore we sense one “now” but do not discern a “before” and “after” of motion, or when we in discerning a “before” and “after” take the same “now” as the end of the prior and the beginning of the subsequent, no time seems to exist because no motion seemed to exist. But when we discern a “before” and “after” and count them, then we say that time is produced. This is so because time is nothing less than “the numbering of motion according to before and after”: for we perceive time, as was said, when we count the “before and after” of motion. it is clear there fore that time is not motion, but accompanies motions inasmuch as it is counted. Hence time is the number of motion. But if someone objects against this definition and says that “before and after” are determined by time, and consequently, that the definition is circular, he should remember that “before and after” are placed in the definition of time inasmuch as they are caused in motion by magnitude, and not inasmuch as they are measured out of time. That is why Aristotle had previously shown that “before and after” are present in magnitude before they are so in motion, and they are in motion before they are in time, to exclude this objection.
lib. 4 l. 17 n. 11 Deinde cum dicit: signum est autem etc., manifestat praedictam definitionem dupliciter. Primo quidem quodam signo. Id enim quo aliquid iudicamus plus et minus, est numerus eius: sed motum iudicamus plurem et minorem tempore: tempus igitur est numerus. Secundo ibi: quoniam autem numerus etc., manifestat quod dictum est per distinctionem numeri; et dicit quod numerus dicitur dupliciter. Uno modo id quod numeratur actu, vel quod est numerabile, ut puta cum dicimus decem homines aut decem equos; qui dicitur numerus numeratus, quia est numerus applicatus rebus numeratis. Alio modo dicitur numerus quo numeramus, idest ipse numerus absolute acceptus, ut duo, tria, quatuor. Tempus autem non est numerus quo numeramus, quia sic sequeretur quod numerus cuiuslibet rei esset tempus: sed est numerus numeratus, quia ipse numerus prioris et posterioris in motu tempus dicitur; vel etiam ipsa quae sunt prius et posterius numerata. Et ideo, licet numerus sit quantitas discreta, tempus tamen est quantitas continua, propter rem numeratam; sicut decem mensurae panni quoddam continuum est, quamvis denarius numerus sit quantitas discreta.	581. Then [410 219 b2] he clarifies the aforesaid definition in two ways, and first by a sign. Now that which is a standard of judging something to be more and less is a number of it. But the standard for judging whether a motion is greater or smaller is time. Therefore, time is a number. Secondly, [411 219 b5] he makes clearer what has been stated by distinguishing number, saying there are two. First there is that which is actually numbered which can be, as when we say ten men or 100 horses, and this is called “number numbered,” because it is a number applied to the things that are numbered. Then there is the number by which we count, i.e., number considered absolutely, such as two, three, four [the counting numbers]. Now time is not a counting number; otherwise the number of anything would be time; rather it is a number numbered, because it is the number of before and after in motion that we call “time,” or else the things that are counted before and after. Therefore, although number is discrete quantity, time is nevertheless a continuous quantity on account of the thing counted, just as ten measures of cloth is a continuous quantity, even though ten is a discrete quantity.