respect also the analogy with the translation and the object translated holds good; for the movement or translation is one-and-continuous in virtue of the identity of the translated object—not its identity qua object (for it would preserve that if it stopped) but its unbroken identity qua ‘the thing that is being moved’; and it is this that also marks the division between the movement before and the movement after. And there is an analogy also between such a ‘ body that is being moved’ and a point; for it is a point that both constitutes (by its movement) the continuity of the line it traces and also marks the end of the line that is behind and the beginning of the line in front. If, however, one asenbes the latter function to it, re- garding the one point in two capacitics—as the end of one section of the line and the beginning of another—-it must have been arrested, since its identity in this ‘ statical ’ relation must be preserved. But the ‘now,’ as it follows the object in motion, is continuously marking a continuously changing position, so that time is not counted as if by one and the same point, since each point in it so counted is a double point, being end and beginning at once, but rather as the two extremities of the same line, and not as parts of it, for the reason already stated (that, if one were to count the dividing point in its two capacities, that would involve a pause), and because it is obvious that the ‘now’ is not a portion οἷν time, just as the division of motion is not part of motion any more than points are of a line; it is the two sections that are parts of the one line.» The ‘ now’ therefore, as a limit is not time, ARISTOTLE 220a πέρας τὸ viv, οὐ χρόνος ἀλλὰ συμβέβηκεν, ἧ δ᾽ ἀριθμεῖ, ἀριθμός" τὰ μὲν γὰρ πέρατα ἐκείνου μόνον ἐστὶν οὗ ἐστι πέρατα, 6 δ᾽ ἀριθμὸς ὁ τῶνδε τῶν ἵππων---ἡ δεκάς.--καὶ ἄλλοθι.
95 TL μὲν τοίνυν ὁ χρόνος ἀριθμός ἐστι κινήσεως κατὰ τὸ igri καὶ ὕστερον, καὶ συνεχής (συνεχοῦς γάρ), φανερόν.
CHAPTER XII ARGUMENT There is no smallest unit of a continuous magnitude, and therefore not of time (220 a 27-32 ).
Time rs‘ much’ or ΚΟ according to tha number of its unite, and ‘long’ or ‘ short’ as a continuous magnitude. But it is not‘ quick’ or ‘ slow,’ any more than other magni- tudes, or than numbers, are in themselves quick or slow Any given period of time is the same everywhere, and any given ‘now’ cuts across all changes ‘ every ywhere’ and ‘ at once, ’ for the * now’ of each change is the same ὁ now "and ig the‘ now’ of time. And though every‘ now’ divides the past and the future, whether of time or change, the past and the future that it divides are always changing, so that although ‘now’ is the same everywhere taken ‘ across’ changes, it 18 always different at every-when taken ‘ along’ @ change or changes or time as a dimension, and any period of time is different from one that comes before or after it Mutual determinations of time and movemené (Ὁ 14-82).
Time is a dimension of movement itself (since one mobile moving faster than another means that ut covers the same Ἔλάχιστος δὲ ἀριθμὸς ὁ μὲν ἁπλῶς ἐστιν ἡ δυάς" τὶς δ᾽ ἀριθμὸς ἔστι μὲν ὡς ἔστιν, ἔστι δ᾽ ὡς PHYSICS, IV. xe.—-x11.
bul is incidental to time, while as the numerator it is a number; for limits are limits ouly of the par- ticular thing they limit, whereas the number 10, for instance, pertains equally to the ten horses (say) the sum of which it has defined, and to anything else numerable.
That time, then, is the dimension of movement in its before-and-afterncss, and is continuous (because movement is so), is evident.
CHAPTER XII ARGUMENT (continued) distance in lesa tume) and also of the duration of movement. But in this second sense it also measures the duration of everything else that begins and ceases to be. And it is in this sense of being embraced or bounded by ut that things in general (including movements) are most properly said to be “in tame,’ on the analogy of the wine which, being embraced or bounded by the flask (in space), is sard to be‘ in the flask.’ Another sense of ‘ having existence in time,’ that must not be allowed to mislead us (Ὁ 82-221 a 26).
Development of the meaning of being ‘ embraced by time,’ and being ‘ affected by time’ (a 20- 8).
Things eternal (b 3-7).
Time, in directly measuring the duration of motion, incidentally measures the duration of cessation of motion, but not of * all that does not move’; for what cannot move cannot cease to move and so has no beginning or end of its non-movemgnt (Ὁ 7-23).
Of existents and non-exrstents as subject or not to time Tue dyad is the smallest possible abstract number. In one sense there is no smallest possible concrete ARISTOTLE 220. οὐκ ἔστιν' οἷον γραμμῆς ἐλάχιστος πλήθει μὲν 0 ἔστιν at δύο ἢ ἡ μία, μεγέθει δ᾽ οὐκ ἔστιν ἐλά- χιστος" ἀεὶ γὰρ διαιρεῖται πᾶσα γραμμή. ὥσθ᾽ ὁμοίως καὶ ὁ χρόνος: ἐλάχιστος γὰρ κατὰ μὲν ἀριθμόν ἐστιν ὁ εἷς ἢ οἱ δύο, κατὰ μέγεθος ὃ οὐκ ἔστιν. 220b (Φανερὸν δὲ καὶ ὅτι ταχὺς μὲν καὶ βραδὺς οὐ λέγεται, πολὺς δὲ Kat ὀλίγος καὶ μακρὸς καὶ βραχύς. ἧ μὲν γὰρ συνεχής, μακρὸς καὶ βραχύς, μὰ δ᾽ > 6 / λὺ ‘ λί ΒἹ ἣ δὲ \ A ἀριθμός, πολὺς καὶ ὀλίγος: ταχὺς δὲ καὶ 5 βραδὺς οὐκ ἔστιν: οὐδὲ γὰρ ἀριθμὸς ᾧ ἀριθμοῦμεν ταχὺς καὶ βραδὺς οὐδείς. Kat ὁ αὐτὸς δὴ πανταχοῦ ἅμα' πρότερον δὲ καὶ ὕστερον οὐχ ὁ αὐτός, ὅτι καὶ ἡ μεταβολὴ ἡ μὲν παροῦσα μία, ἡ δὲ γεγενημένη καὶ ἡ μέλλουσα ἑτέρα. ὃ δὲ χρόνος ἀριθμός ἐστιν οὐχ ᾧ ἀριθ- μοῦμεν GAN’ ὁ ἀριθμούμενος" οὗτος δὲ συμβαίνει 10 πρότερον καὶ ὕστερον ἀεὶ ἕτερος" τὰ γὰρ νῦν ἕτερα" *'The Greek text gives ‘two or one’ as the smallest number in concrete numbers, though it gives no alternative to the dvad as the smallest abstract number (abstract number being defined as a ‘ plurality of ones,’ the unit itself is not a number). Themistius does not seem to have read ἣ ἡ ula or ὁ εἷς ἢ in 1, 32), Philoponus finds it embarrassing. Alexander, quoted with approval by Simplic. 730. 18, suggests that Aristotle might speak of ‘one kne’ or ‘one unit of time’ as a minimum aumber, if using words popularly.—-C.]
Which smaller lines could he taken for the units instead of the larger one, and these again could be divided. up into slill smaller units, and so on without end. ‘lhe smaller the PHYSICS, IV. xu.
number, but in another sense there is; for, whatever line you take for the unit, two is the smallesL number of such units, but in magnitude there is no minimum, for any linc whatever may itself be divided into smaller lines.2 So too with time, ‘two’ is the smallest possible number of time units, but there is no smallest possible time unit itself that may be selected.
Observe too that we do not speak of time itself as ‘ swift or slow,’ but as consisting of ‘ many or few’ of the units in which it is counted, or as‘ long and short’ when we regard it as a continuum. It would not be swift or slow, even if we supposed it to be the counter that counts, not the dimension that is counted (which it really is); for abstract numbers are in no case swift or slow, though the counting of them may be.
Moreover, though time is identical everywhere simultaneously, it is not identical if taken twice successively;° for the change it measures, likewise, is one when considered as present, but not one if considered as partly past and partly future. And time considered numerically is concrete, not abstract; whereby follows that it changes from the former to the latter ‘ now,’ ὦ inasmuch as these ‘ nows’ themunit is, the smaller will a given aggregate of those units be, and as there ia no limit to the conceptual smallness of a unit, so neither is there a limit to the conceptual smallness of a given ageregate of them. In this sense ‘there is no smallest possible concrete number.’
¢ What time measures is not the nature of the change, but its before-and-afterness, Therefore it is not differentiated by the specific nature of the several contemporaneous changes, but it is by 1ts very definition differentiated by the before-and-afterness that it counts.
4 πρότερον καὶ ὕστερον here (rather misleadingly) used for γεγενημένον καὶ μέλλον, ARISTOTLE 220b ἔστι δὲ 6 ἀριθμὸς εἷς μὲν καὶ ὁ αὐτὸς ὁ τῶν ἑκατὸν ἵππων καὶ ὁ τῶν ἑκατὸν ἀνθρώπων, ὧν δ᾽ ἀριθμὸς ἕτερα, οἱ ἵπποι τῶν ἀνθρώπων. ἔτι ὡς ἐνδέχεται κίνησιν εἶναι τὴν αὐτὴν καὶ μίαν πάλιν καὶ πάλιν, οὕτω καὶ χρόνον, οἷον ἐνιαυτὸν ἢ ἔαρ ἢ μετόπωρον. w Οὐ μόνον͵ δὲ τὴν κίνησιν τῷ χρόνῳ μετροῦμεν, ἀλλὰ καὶ τῇ κινήσει τὸν χρόνον, διὰ τὸ ὁρίζεσθαι ὑπ᾽ ἀλλή ἤλων' ὁ μὲν γὰρ χρόνος ὁρίζει τὴν κίνησιν anaes ὧν αὐτῆς, ἡ ἡ δὲ κίνησις τὸν χρόνον. καὶ λέγομεν πολὺν ἢ ὀλίγον. χρόνον τῇ κινήσει με- τροῦντες, καθάπερ καὶ τῷ ἀριθμητῷ τὸν ἀριθμόν, 20 οἷον τῷ ἑνὶ ἵππῳ τὸν τῶν ἵππων ἀριθμόν. τῷ μὲν γὰρ ἀριθμῷ τὸ τῶν ἵππων ’ πλῆθος γνωρίζομεν, πάλιν δὲ τῷ ἑνὶ ἵππῳ τὸν τῶν ἵππων ἀριθμὸν αὐτόν. ὁμοίως δὲ καὶ ἐπὶ τοῦ χρόνου καὶ τῆς κινήσεως" τῷ μὲν γὰρ χρόνῳ τὴν κίνησιν, τῇ δὲ κινήσει τὸν χρόνον μετροῦμεν. καὶ τοῦτ᾽ εὐλόγως συμβέβηκεν' ἀκο- ag λουθεῖ γὰρ τῷ μὲν μεγέθει ἡ ἡ κίνησις, τῇ δὲ κινήσει 6 χρόνος, τῷ καὶ ποσὰ καὶ συνεχῆ καὶ διαιρετὰ εἶναι" διὰ μὲν γὰρ τὸ τὸ μέγεθος εἶναι τοιοῦτον ἡ κίνησις ταῦτα πέπονθεν, διὰ δὲ τὴν κίνησιν ὄ χρόνος. καὶ μετροῦμεν καὶ τὸ μέγεθος τῇ κινήσει καὶ τὴν κίνησιν τῷ μεγέθει: πολλὴν γὰρ εἶναί 80 φαμεν τὴν ὁδόν, ἂν ἢ ἡ πορεία πολλή, καὶ ταύτην “ This leads up to the selection of the rotation of the starry sphere as the standard for measuring time. It in- dicates that evenly flowing time can be ent fip into pre- sumably equal periods (years), or may present us with a recognizable recurrence of experiences or phenomena. But time itself must not he thought of as ‘ moving in a circle’ any more than ‘inaline.’ ‘This and the following parallels are technically imperfect, for in one case the unit of what PHYSICS, IV. χη.
selves are different; just as the number of a hundred horses is identical with that of a hundred men, but the horses enumerated are different from the men enumerated. Now note further that as there may be movement (of rotation to wit) that covers the same course over and over again, in like manner we mark off time by the year or by spring or autumn.@ And not only do we measure the length of uniform movement by time, but also the length of time by uniform movement, since they mutually determine each other®; for the time taken determines the length moved over(the time units corresponding to the space units), and the length moved over determines the time taken. And when we call time ‘ much’ or ‘little’ we are estimating it in units of uniform motion, as we measure the ‘number’ of anything we count by the units we count it in—the number of horses, for example, by taking one horse as our unit. For when we are told the number of horses, we know how many there are in the troop; and by counting how many there are, horse by horse, we know their number. And so too with time and uniform motion, for we measure them by each other either way. And this is only natural, for movement corresponds to linear magnitude, and time to movement, in being a quantity, in being continuous, and in being divisible; for it is from near magnitude that motion takes on these qualities, and from motion that time does, That we do measure linear magnitude by movement, and vice verga, is evidenced from our saying that it is is measured is itself a magnitude of the same order as what it measures (line measurig line), in the other it is proportional to it but not identical with it.
» V being countant, 8 (which is proportional to V) and T determine each other.
10 18 ARISTOTLE πολλήν, ἂν ἡ ὁδὸς ἢ i) πολλή. καὶ τὸν χρόνον, ἂν ς κίνησις, καὶ τὴν «κίνησιν, ἂν ὁ χρόνος.
᾿Ἐπεὶ & ἐστὶν ὁ χρόνος μέτρον κινήσεως καὶ τοῦ κινεῖσθαι, “μετρεῖ δ᾽ οὗτος τὴν κίνησιν τῷ ὁρίσαι τινὰ κίνησιν ἣ καταμετρήσει σὴν ὅλην (ὥσπερ καὶ τὸ μῆκος ὁ πῆχυς τῷ ὡρίσθαι τι μέγεθος ὃ ἀναμετρήσει πὸ ὅλον), ᾿καὶ ἔστι τῇ κινήσει τὸ ἐν χρόνῳ εἶναι τὸ μετρεῖσθαι τῷ χρόνῳ͵ καὶ αὐτὴν καὶ τὸ εἶναι αὐτῆς--ἅμα γὰρ τὴν κίνησιν καὶ τὸ εἶναι τῇ κινήσει μετρεῖ, καὶ τοῦτ᾽ ἔστιν αὐτῇ τὸ ἐν χρόνῳ εἶναι, τὸ μετρεῖσθαι αὐτῆς τὸ εἶναι---δῆλον' ὅτι καὶ τοῖς ἄλλοις τοῦτ᾽ ἔστι τὸ ἐν χρόνῳ εἶναι, τὸ μετρεῖσθαι αὐτῶν τὸ εἶναι ὑπὸ τοῦ χρόνου.
To γὰρ ἐν χρόνῳ εἶναι δυοῖν ἐστι θάτερον, ἕν μὲν τὸ εἶναι τότε ὅτε 6 χρόνος ἔστιν, ἕν δὲ τὸ ὥσπερ ἔνια λέγομεν ὁ ὅτι ἐν ἀριθμῷ ἐ ἐστιν’ τοῦτο δὲ σημαίνει ἤτοι ὡς μέρος ἀριθμοῦ καὶ πάθος, καὶ ὅλως ὅτυ τοῦ ἀριθμοῦ τι, 7 ὅτι ἔστιν αὐτοῦ ἀριθμός.
᾿Επεὶ δ᾽ ἀριθμὸς ὁ χρόνος, τὸ μὲν νῦν καὶ τὸ πρότερον καὶ ὅσα τοιαῦτα οὕτως ἐν Χρόνῳ ὡς ἐν ἀριθμῷ μονὰς καὶ τὸ περιττὸν καὶ ἄρτιον (τὰ μὲν 1 [δῆλον Themist. 154. 10, Simplic. 735. 8, Philop. 749, 20: δῆλον δὲ EFGI, Philop. 749. 24: δὲ δῆλον ἘΠ, ae j @ (Literally, ‘ Since time is a measure of movement and of the movement’s actually taking place, and this measure- ment of movement by time is effected by determining a certain unit of movement which shall serve t¢ measure off the whole movement (as the cnbit serves to measure length by being fixed upon as a unit of magnitude which will serve to measure off the whole length), and for movement to be ‘in time ’ means that both the movement itself and its existence (or taking place) are measured by time—for in measuring the PHYSICS, IV. χη.
a great ‘ way ’if it is a great ‘ walk,’ or vice versa. So too with time and movement: we spcak of a ‘long walk’ taking a ‘long time,’ or vice versa.
It¢ is by reference to the standard unit of time that we determine the relative velocity of two several movements. For we ask what distance either move- ment has covered during the lapse of the standard unit of time, and pronounce the movement itself fast or slow in proportion as that distance is great or small. But that same standard unit of time measures the duration of movement. So the way in which movement exists in time is by both itself and its duration being measured by time. For time measures both the movement and its duration by the same act, and its duration being so measured con- stitutes it as existing in time. But it is obvious that other things as well as movement exist in time, because their existence too is measured by time.
For this phrase ‘ existing in time’ is ambiguous. It may mean (1) existing when time also exists, or (2) it may mean ‘ in time ’ in a sense analogous to that in which we say that certain things exist ‘in number’; and this phrase again is ambiguous, for it may mean (a) that they exist in number as parts or affections of it, or generally that they pertain to it in some way or other, or (6) it may mean that they themselves can be counted.
Now (2) taking time as a number scale, (a) the ‘now’ and the ‘ before’ and suchlike exist in time as the mongd and the odd and even exist in number movement time does also measure the movement’s existence, and this fact that its existence 1s measured is what it means for a movement to be ‘in time ’—evidently for all other things also to be ‘in time ’ means that their existence 1s measured by time.’—C.]
ARISTOTLE 2214 γὰρ τοῦ ἀριθμοῦ τι, τὰ δὲ τοῦ χρόνου τί ἐστὺὴ, τὰ δὲ πράγματα ws ἐν ἀριθμῷ τῷ χρόνῳ ἐστίν" εἰ δὲ τοῦτο, περιέχεται ὑπ᾽ ἀριθμοῦ ὥσπερ Kal τὰ ἐν τόπῳ ὑπὸ τόπου.. Φανερὸν δὲ καὶ ὅτι οὐκ ἔστι τὸ ἐν χρόνῳ εἶναι ο τὸ εἶναι ὅτε ὁ χρόνος ἔστιν, ὥσπερ οὐδὲ TO ἐν fd ΕΝ 4 > τ Lg ε Fy < κινήσει εἶναι οὐδὲ TO ἐν τόπῳ ὅτε ἡ κίνησις καὶ ὃ τόπος ἔστιν. εἰ γὰρ ἔσται τὸ ἔν Tut οὕτως, πάντα τὰ πράγματα ἐν ὁτῳοῦν ἔσται, καὶ ὁ οὐρανὸς ἐν τῇ κέγχρῳ’ ὅτε γὰρ ἡ κέγχρος ἔστιν ἔστι καὶ ὁ οὐρανός. ἀλλὰ τοῦτο μὲν συμβέβηκεν, a ἐκεῖνο δ᾽ ἀνάγκη παρακολουθεῖν---καὶ τῷ ὄντι ἐν n χρόνῳ εἶναί τινα χρόνον ὅτε κἀκεῖνο ἔστι, Kal τῷ ἐν κινήσει ὄντι εἶναι τότε κίνησιν. πεὶ ἐστὶν ὡς ἐν ἀριθμῷ τὸ ἐν χρόνῳ, ληφθήσεταί τις πλείων χρόνος παντὸς τοῦ ἐν χρόνῳ ὄντος" διὸ ἀνάγκη πάντα τὰ ἐν χρόνῳ ὄντα περιέχεσθαι ὑπὸ χρόνου, ὥσπερ καὶ τἄλλα ὅσα 80 ἔν τινί ἐστιν, οἷον τὰ ἐν τόπῳ ὑπὸ τοῦ τόπου, Kal πάσχειν δή τι ὑπὸ τοῦ χρόνου, καθάπερ Kal λέγειν εἰώθαμεν ὅτι κατατήκει ὃ χρόνος, καὶ γηράσκει πάνθ᾽ ὑπὸ τοῦ χρόνου καὶ ἐπιλανθάνεται διὰ τὸν > gat b Χρόνον, ἀλλ᾽ οὐ μεμάθηκεν, οὐδὲ νέον γέγονεν οὐδὲ PHYSICS, IV. xm.
(for these latler pertain to number just in the same way in which the former pertain to time); but (0) events have their placcs in time in a sense analogous to that in which any numbered group of things exist in number (2.¢., in such and such a definite number), and such things as these are embraced in number (e.,in time) as things that have locality are embraced in their places.
And it is further evident (1) that to be in existence while time is in existence docs not constitute being ‘in time,’ just as neither is a thing constituted as in movement or in a place because movement and place exist while it does. For if this constitutes being ‘zn’ a thing, everything would be in anything, and the universe in a grain of millet, because a grain of millet exists while the universe is in exislence. But this latter is an incidental coincidence; whereas when a thing is said to exist in time, it follows of necessity that there should be time while this thing exisLs, and if it exists in motion, it follows of necessity that there should be motion while it exists.
And since what exists in time exists in it as number (that is to say, as countable), you can take a time longer than anything that exists in time. So we must add that for things to exist in time they must be embraced by time, just as with other cases of being ‘in’ something; for instance, things that are in places are embraced by place. And it will follow that they are in some respect affected by time, just as we are wont to say that time crumbles things, and that everything grows old under the power of time and is forgotten through the lapse of time. But we do not say that we have learnt, or that anything is made uew or beautiful, by the mere lapse of time; ARISTOTLE ARISTOTLE 581} καλόν! φθορᾶς γὰρ αἴτιος καθ᾽ αὑτὸν μᾶλλον ὄ χρόνος" ἀριθμὸς γὰρ κινήσεως, ἡ δὲ κίνησις ἐξίστησι τ ὑπάρχον. ὥστε avepov ὅτι τὰ ἀεὶ ὄντα, ἡ ἀεὶ ὄντα, οὐκ ἔστιν ἐν χρόνῳ' οὐ γὰρ b περιέχεται ὑπὸ χρόνου, οὐδὲ μετρεῖται τὸ εἶναι αὐτῶν ὑπὸ του χρόνου' σημεῖον δὲ τούτου ότι os πάσχει οὐδὲν ὑπὸ τοῦ χρόνου ὡς οὐκ ὄντα ν χρόνῳ. “πε δ᾽ ἐστὶν ὁ χρόνος μέτρον κινήσεως, ἔοται κα t ἠρεμίας μέτρον κατὰ συμβεβηκός" πᾶσα γὰρ ἠρεμία ἐν χρόνῳ. οὐ γὰρ ὥσπερ τὸ ἐν κινήσει ὃν 10 ἀνάγκη κινεῖσθαι, οὕτω καὶ τὸ ἐν χρόνῳ" οὐ γὰρ κίνησις ὁ χρόνος, ἀλλ’ ἀριθμὸς κινήσεως" ἐν ἀριθμῷ δὲ κινήσεως ἐνδέχεται εἶναι καὶ τὸ ἠρεμοῦν. οὐ γὰρ πᾶν τὸ ἀκίνητον ἠρεμεῖ, ἀλλὰ τὸ ἐστερημένον κινήσεως πεφυκὸς δὲ κινεῖσθαι, καθάπερ εἴρηται ἐν τοῖς πρότερον. τὸ δ᾽ εἶναι 15 ἐν ἀριθμῷ ἐστι τὸ εἶναί, τινα ἀριθμὸν τοῦ πράγ- ματος καὶ μετρεῖσθαι τὸ εἶναι αὐτοῦ τῷ ἀριθμῷ ἐν ᾧ ἐστιν" ὥστ' εἰ ἐν χρόνῳ, ὑπὸ χρόνου. με- τρήσει δ᾽ ὁ χρόνος τὸ κινούμενον καὶ τὸ ἠρεμοῦν, ἧ͵ τὸ μὲν κινούμενον τὸ δὲ ἠρεμοῦν',τὴν γὰρ κίνησιν αὐτῶν μετρήσει καὶ τὴν ἠρεμίαν, πόση τις. ὥστε τὸ κινούμενον οὐχ ἁπλῶς ἔσται μετρητὸν 80 ὑπὸ χρόνου ἢ «ποσόν τί ἐστιν, ἀλλ᾽ ἧ ἡ κίνησις αὐτοῦ ποσή. dor’ ὅσα “μήτε κινεῦται μήτ᾽ ἠρεμεῖ οὐκ ἔστιν ἐν χρόνῳ" τὸ μὲν γὰρ ἐν χρόνῳ εἶναι τὸ ᾿μετρεῖσθαί ἐστι χρόνῳ, ὁ δὲ χρόνος κινήσεως καὶ ἠρεμίας μέτρον. Φανερὸν οὖν ὅτι οὐδὲ τὸ μὴ ὃν ἔσται πᾶν ἐν PHYSICS, IV. xu.
PHYSICS, IV. xu.
for we regard time in itself as destroying rather than producing, for what is counted in time is movement, and movement dislodges whatever it affects from its present state. From all this it is clear that things which exist eternally, as such, are not in time; for they are not embraced by time, nor is their duration measured by time. This is indicated by their not suffering anything undcr the action of time as though they were within its scope.
And since time is the measure of movement, it will also incidentally be the measure of rest; for all rest isin time. For a thing being in movement necessi- tates that it should be moving, but its being in time does not; for time is not identical with movement, but is that in terms of which movement is counted; and even if a thing is at rest, it may be countable by the same count as motion. For not everything that is unmoved is at rest, but that only which by its nature is capable of moving but now lacks its actual move- ment, as we have already noted. But a thing existing in number means that it ‘has’ a number and that its existence is measured by that number; and so too in the case of time. And time will measure that which is in motion and that which is at rest, as such; for it is their movement and their rest of which it determines the amount. So that the thing in motion is not measured by time in all respects in its capacity of a quantum, but in so far as its movement is defined in quantity; hence that which is neither in movement nor at rest is not in time, since to be ‘in time” means to be measured by time, and it is movement and rest of which time is the measure.
Clearly, then, not all non-existents are in time, 25 80 ARISTOTLE χρόνῳ, οἷον ὅσα μὴ ἐνδέχεται ἄλλως, ὥσπερ τὸ τὴν διάμετρον εἶναι τῇ πλευρᾷ σύμμετρον. ὅλως γάρ, εἰ μέτρον μὲν ἔστι κινήσεως ὁ χρόνος καθ᾽ αὑτό, τῶν δ' ἄλλων κατὰ συμβεβηκός, δῆλον ὅτι ὧν τὸ εἶναι μετρεῖ, τούτοις ἅπασιν ἔσται τὸ εἶναι ἐν τῷ ἠρεμεῖν ἢ κινεῖσθαι. ὅσα μὲν οὖν φθαρτὰ καὶ γενητὰ καὶ ὅλως ὁτὲ μὲν ὄντα ὁτὲ δὲ μή, ἀνάγκη ἐν χρόνῳ εἶναι" ἔστι γὰρ χρόνος τις πλείων, ὃς ὑπερέξει τοῦ τε εἶναι αὐτῶν καὶ τοῦ μετροῦντος τὴν οὐσίαν. τῶν δὲ μὴ ὄντων ὅσα μὲν περιέχει χρόνος, τὰ μὲν ἦν (οἷον δε τὶ ποτε ἢν) τὰ δὲ ἔσται (οἷον τῶν μελλόντων tt), ἐφ᾽ ὁπότερα περιέχει, καὶ εἰ ἐπ᾽ ἄμφω, ἀμφότερα καὶ ἦν καὶ ἔσται: ὅσα δὲ μὴ περιέχει μηδαμῇ, οὔτ᾽ ἣν our’ ἔστιν οὐτ᾽ ἔσται. ἔστι δὲ τὰ τοιαῦτα τῶν μὴ ὄντων, ὅσων τἀντικείμενα ἀεὶ ἔστιν, οἷον τὸ ἀσύμμετρον εἷναι τὴν διάμετρον ἀεὶ ἔστι, καὶ οὐκ ἔσται τοῦτ᾽ ἐν χρόνῳ. οὐ τοίνυν οὐδὲ τὸ σύμ- μετρον' διὸ ἀεὶ οὐκ ἔστιν, ὅτι ἐναντίον τῷ ἀεὶ ὄντι' ὅσων δὲ τὸ ἐναντίον μὴ ἀεί, ταῦτα δὲ δύναται καὶ εἶναι καὶ μή, καὶ ἔστι γένεσις καὶ φθορὰ αὐτῶν.
α fal, ἐφ᾽ ὁπότερα περιέχει κτὰ,, ‘ according as they are embraced by a stretch of time lying wholly on one or the other side of the present moment; or, if they are embraced by time extending on both sides of the present moment, they can be either past or future.’"—C,] PHYSICS, IV. xr.
but only such as might exist; for instance, the comimensurability of the diagonal and the side does not exist, but its non-existence is not temporal. For, as a general proposition, if time is the measure of movement, on its own account and of anything else only by incidental coincidence, obviously every~ thing whose existence it measures must have its existence at rest or in motion. Accordingly, what~ ever is destructible or generable, or (more broadly) sometimes existing and sometimes not, must be embraced by time; for there must be some time great enough to exceed the time of their duration and therefore the time which measures their being. Among non-existents, on the other hand, those which are embraced by time either once were (as Homer once existed) or will be (e.g.,some future event), according as they are embraced by time on one or the other side of the present moment, or, if they are embraced in both directions, they can be either past or future*; whereas those which are not in any way embraced by time neither were nor are nor will be. Non-existents of this latter kind are all those things whose opposites eternally exist; for instance, the incommensurability of the diagonal eternally exists, and therefore is not in time. And it follows that neither is its commensurability in time; hence it is edernally non-existent, inasmuch as it is a contradiction of what is eternally existent; whereas things of which the opposite does not exist eternally way either be or not be, and so they can come into existence and vanish from it.
ARISTOTLE CHAPTER XIII ARGUMENT Analogy between a point and a‘ now,’ as uniters in their unity and dvuiders in ther plurality (222 a 10-20).
Opening of an examination of vaguer meanings aitached to the word ‘ now’ and to other adverbs of time (a 20-28).
A discussion (episodical in the levicographical context, but Sar outweighing τὲ in importance) of whut may be wnferred from the measurability of any given distance either way in time. Is tume itself limited? No, because motion, as wll be shown more fully later on, is everlasting. Is time ttself, then, α travelling thing analogous to the body in motion that remains the same, or 18 it a medium or dimension analogous to the supreme ‘ place’ in which moving things occupy successive positions with distances between them? Solution —that time (being, as defined, simply movement-change as measured and counted successionally) is analogous to the medium of motion rather than to the moving body—reached a23a10 Τὸ δὲ νῦν ἐστι συνέχεια χρόνου, ὥσπερ ἐλέχθη--- συνέχει γὰρ τὸν χρόνον τὸν παρελθόντα καὶ ἐσόμενον---καὶ πέρας χρόνου ἐστίν! ἔστι γὰρ τοῦ μὲν ἀρχή, τοῦ δὲ τελευτή. ἀλλὰ τοῦτ᾽ οὐχ ὥσπερ ἐπὶ τῆς στιγμῆς μενούσης φανερόν. διαιρεῖ δὲ 15 δυνάμει. καὶ ἣ μὲν τοιοῦτο, ἀεὶ ἕτερον τὸ νῦν, ἧ δὲ συνδεῖ, ἀεὶ τὸ αὐτό, ὥσπερ ἐπὶ τῶν μαθηματι- κῶν γραμμῶν: οὐ γὰρ a αὐτὴ ἀεὶ pia στιγμὴ τῇ νοήσει---διαιρούντων γὰρ ἄλλη-- δὲ μίᾳ, ἡ αὐτὴ πάντῃ. οὕτω καὶ τὸ νῦν τὸ μὲν τοῦ χρόνου διαί- ρεσις κατὰ δύναμιν, τὸ δὲ πέρας ἀμφοῖν καὶ ἑνότης" 1 [καὶ πέρα; EB, Simplic. 748. 18: καὶ ὅλως πέρας cett.—C.]
PHYSICS, IV. xin.
CHAPTER XIII ARGUMENT (continued) by renewed reference to the analogies between a‘ point’ and Linguistic discussion BA aa Provisional conclusion (Note.—The linguistic ates in this chapter cannot be tortured into a discussion of English terms. While finding the best equivalents I could, I have in every case inserted the Greek words in brackets to remind the reader that the definitions (sometimes needing qualification in any case) refer to them and not to the English substitutes, for which laiter they are naturally bad fits, by no fault of the tailor.)
Wr have said that it is through the ‘ now’ that time is continuous, for it holds time past and time present together; and in its general character of ἡ limit’ it is at once the beginning of time to come and the end of time past. But in the case of the ‘ now’ this is not so obvious as in that of the stationary point; for, as well as actually continuing, it potentially divides time. And in this potentiality one ‘now differs from another, but in its actual holding of time continuously together it always remains the game, as in the parallel case of mathematical lines traced by moving points, in which case the point too, if arrested as a divider, is not conceived as re- taining its ἐετωλθι with the tracing point or another arrested point; for if we are dividing the line, the point changes at every division, but if we regard the line as a single undivided one, the point that traces 11 is the same all along. Thus too the ‘ now’ of time is a divider in mental potentiality, but a continuing unifier as the coincident end-term and ARISTOTLE 222420 ἔστι δὲ ταὐτὸ καὶ κατὰ ταὐτὸ ἡ διαίρεσις καὶ ἡ τ ἔνωσις, τὸ δ᾽ εἶναι od ταὐτό.
Τὸ μὲν οὖν οὕτω λέγεται τῶν νῦν, ἄλλο δ᾽ oTaVv O Xpovos Ο TOUTOU eyyus 7)" ἥξει νυν, οτι τήμερον ἥξει" NKEL νυν, OTL ἦλθε τήμερον. τα ὃ ἐν ᾿Ιλίῳ γέγονεν οὐ νῦν, οὐδ᾽ ὁ κατακλυσμὸς γέγονε νῦν" καίτοι συνεχὴς χρόνος εἰς αὐτά, ἀλλ᾽ ὅτι οὐκ ἐγγύς.
To δὲ ‘ore’ χρόνος ὡρισμένος πρὸς TO πρότερον νῦν, οἷον ᾿ποτὲ ἐλήφθη Τροία, καὶ “ποτὲ ἔσται ay ~ AY, AY \ lot κατακλυσμός᾽" δεῖ γὰρ πεπεράνθαι πρὸς τὸ νῦν. Zora, ἄρα ποσός τις ἀπὸ τοῦδε χρόνος καὶ εἰς ἐκεῖνο, καὶ ἦν εἰς τὸ παρελθόν.
ὑ é μη εἰς χρόνος OS οὐ πότε, πὰς AV €t7) 80 χρόνος πεπερασμένος. dp’ οὖν ὑπολείψει; ἢ οὔ, εἴπερ ἀεὶ ἔστι κίνησις. ἄλλος οὖν ἢ 6 αὐτὸς πολλάκις; ϑῆλον ὅτι ὡς ἂν ἡ κίνησις, οὕτω καὶ ὁ χρόνος" εἰ μὲν γὰρ ἡ αὐτὴ Kal μία γίνεταί ποτε, €OTaL καὶ χρόνος εἰς καὶ O QUTOS, εἰ δὲ μη: ουϊς 4 That is to say the ‘now,’ when arrested, divides the same specific past and present which it was dividing in its movement, but differs in the conditions of its functioning.
Ὁ (Or the future flood, mentioned jn the next paragraph. Cf. Plato, Timaeus 22 c—C.]
® [Literally, ‘‘‘ Some time” (or “ one day") means a time determined relatively to the “now” in the former PHYSICS, 1V. xu.
beginning-term of past and future time; and these two capacities of potential divider and actual uniter pertain to the same actual ‘ now’ and on the same count of its being two limits at once, but its essential and defined functioning in the one capacity differs from that in the other.* This is one of the meanings of * now,’ bul it is also used for ‘ not far off in time.’ “He will come now, if he will come to-day; ‘He has come but now,’ if he came to-day. But we do not speak so of the Trojan war or Deucalion’s flood®; though time is continuous between us and these events, they are not near.
‘Sometime’ is used when we wish to be no more definite than that the present ‘now’ comes aftcr it or the reverse. When was Troy taken? ‘ Some- time ’ in the past.¢ When will the flood be? ‘ Some- lime’ in the future. There will be a measurable stretch of time from now onwards to that, or there has been one from that to now.
And since there is no time-ago or time-to-come that was not, or will not be, ‘some time’ off, it would seem that all time is limited. Will it come to an end, then? Surely not; for if motion is everlasting, soistime. Is it, then, always a different stretch of time that continues the succession, or the same stretch of time taken repeatedly? As to this, evidently it must conform to movement; for whichever of these kinds of counting applies to sense’ (i.e. the sense of the present moment, defined in the first paragraph).—C.]
4 ἴῃ the Greek idiom ‘sometime’ {ποτέ)ὺ would not require the addition of past or future, the difference being sufficiently expressed by the tense of the verb.
ARISTOTLE 228 ἔσται. ἐπεὶ δὲ τὸ viv τελευτὴ Kal ἀρχὴ χρόνου, ἀλλ’ οὐ τοῦ αὐτοῦ ἀλλὰ τοῦ μὲν παρήκοντος τελευτὴ ἀρχὴ δὲ τοῦ μέλλοντος, ἔχοι ἂν ὥσπερ ὁ κύκλος ἐν τῷ αὐτῷ πως τὸ κυρτὸν καὶ τὸ κοῖλον, οὕτω καὶ ὁ χρόνος ἀεὶ ἐν ἀρχῇ καὶ τελευτῇ. καὶ διὰ τοῦτο δοκεῖ ἀεὶ ἕτερος" οὐ γὰρ τοῦ αὐτοῦ ἀρχὴ καὶ τελευτὴ τὸ νῦν". ἅμα γὰρ ἂν καὶ κατὰ τὸ αὐτὸ τὰ ἀντικείμενα εἴη. καὶ οὐχ ὑπολείψει δή" ἀεὶ γὰρ ἐν ἀρχῇ.
Τὸ δ᾽ “ἤδη τὸ ἐγγύς ἐστι τοῦ παρόντος νῦν ἀτόμου μέρος τοῦ μέλλοντος χρόνου---' πότε βαδί- ζεις; ᾿ ἤδη, ὅτι ἐγγὺς ὁ χρόνος ἐν ᾧ μέλλει--- 10 καὶ τοῦ παρεληλυθότος χρόνου τὸ μὴ πόρρω τοῦ νῦν" ᾿ πότε βαδίζεις; ᾿ ᾿ἤδη βεβάδικα. τὸ δὲ ἴλιον φάναι ἤδη ἑαλωκέναι οὐ λέγομεν, ὅτι πόρρω λίαν τοῦ νῦν. καὶ τὸ ‘ ἄρτι ᾿ τὸ ἐγγὺς τοῦ παρόντος a Pe 1 n oY), ἐξ t δ ἦλθ Ἢ ’ νῦν pdptov' τοῦ παρελθόντος" ‘ πότε ἦλθες; "ἄρτι, ἐὰν ἦ ὁ χρόνος ἐγγὺς τοῦ ἐνεστῶτος νῦν.
15‘ πάλαι᾽ δὲ τὸ πόρρω. τὸ δ᾽ ‘ ἐξαίφνης ᾿ τὸ ἐν ἀναισθήτῳ χρόνῳ διὰ μικρότητα ἐκστάν.
* Compare Book VIII. chap. ii., where it is shown that the successive repetitions of a recurrent movement are specifically identical but numerically different, so that the ‘now’ of one succeeds the ‘now’ of the other but does not repeat it.
δ The anulogy goes no further than to show that an identical line can be both concave and convex (though it has no breadth) at the same lime, the one withweference to what is inside the circle, the other with reference to what is outside.
¢ (Literally, ‘so also time is always both at a beginning and at an end. And for that reason it seems to be always different...—C.]
ει PHYSICS, IV. χιττ.
motion must apply to time.t And besides, since the ‘now’ is the end and the beginning of time, but not of the same time, but the end of time past and the beginning of time to come, it must present a relation analogous to the kind of identity between the convexity and the concavity of the same circum- ference, which necessitates a difference between that with respect to which it bears the one character and that wrth respect to which it bears the other.’ So too, since every ‘ now’ is at once the beginning and the end of a stretch of time, the two stretches must be different;°* for the same ‘now’ cannot be both the beginning and the end of the same thing, for, if so, it would be both of two contradictories in the same subject at once. Neither, then, will time ever come to an end, for it is always at a beginning.