(1) Some of it is past and no longer exists, and the rest is future and does not yet exist; and all time, whether in its limitless totality or any given length of time we take, is entirely made up of the no- longer and the not-yet; and how can we conceive of that which is composed of non-existents sharing in existence in any way?
(2) Moreover, if anything divisible exists, then, so long as it is in existence, either allits parts or some of them mus} exist. Now time is divisible into parts, and some of these were in the past and some will be in the future, but none of them exists. The present ‘now’ is not part of time at all, for a part measures the whole, and the whole must be made up of the 10 ARISTOTLE ὅλοι; ἐϊς τῶν pepdv ὁ δὲ χρόνος od δοκεῖ ovy- κεῖσθαι ἐκ τῶν νῦν.
"Ert δὲ τὸ νῦν, ὃ φαίνεται διορίζειν τὸ παρελθὸν καὶ τὸ μέλλον, πότερον ἕν καὶ ταὐτὸν ἀεὶ διαμένει ἢ ἄλλο καὶ ἄλλο, οὐ ῥᾷδιον ἰδεῖν.
Ei μὲν γὰρ ἀεὶ ἕτερον καὶ ἕτερον, μηδὲν δ᾽ ἐστὶ τῶν ἐν τῷ χρόνῳ ἄλλο καὶ ἄλλο μέρος ἅμα (ὃ μὴ περιέχει, τὸ δὲ περιέχεται, ὥσπερ 6 ἐλάττων χρόνος ὑπὸ τοῦ πλείονος), τὸ δὲ νῦν μὴ ὃν πρότερον δὲ ὃν ἀνάγκη η ἐφθάρθαι ποτέ, καὶ τὰ νῦν ἅμα μ μὲν ἀλλήλοις οὐκ ἔσται, ἐφθάρ θαι δὲ ἀνάγκη ἀεὶ τὸ πρότερον. ἐν ἑαυτῷ μὲν οὖν ἐφθάρ θαι οὐχ οἷόν τε, διὰ τὸ εἶναι τότε, ἐν ἄλλῳ δὲ νῦν ἐφθάρθαι τὸ πρότερον νῦν οὐκ ἐνδέχεται. ἔστω “γὰρ ἀδύνατον ἐχόμενα εἶναι ἀλλήλων τὰ νῦν ὥσπερ στιγμὴ στιγμῆς. εἴπερ οὖν ἐν τῷ ἐφεξῆς οὐκ ἔφθαρται ἀλλ' ἐν ἄλλῳ, ἐν τοῖς μεταξὺ τοῖς νῦν ἀπείροις οὖσιν ἅμα ἂν εἴη" τοῦτο δ᾽ ἀδύνατον.
᾿Αλλὰ μὴν οὐδ᾽ ἀεὶ τὸ αὐτὸ διαμένειν, δυνατόν. οὐδενὸς γὰρ διαιρετοῦ πεπερασμένου ἕν πέρας ἐστίν, οὔτ᾽ ἂν ἐφ᾽ ἕν ἢ,»συνεχὲς οὔτ᾽ ἂν ἐπὶ πλείω" τὸ δὲ νῦν πέρας ἐστί, καὶ χρόνον ἔστι λαβεῖν πεπερασμένον. ἔτι εἰ τὸ ἅμα εἷναι κατὰ χρόνον καὶ μήτε πρότερον μήτε ὕστερον τὸ ἐν τῷ αὐτῷ εἶναι καὶ ἐν τῷ νῦν ἐστιν, εἰ τά τε πρότερον καὶ τὰ ὕστερον ἐν τῷ νῦν τῳδί ἐστιν, ἅμα ἂν εἴη n * {Or ‘and if anything that does not exist now, but formerly did exist, must have perished αἱ some moment,’— ® This is proved in Book VI, chap. i, PIAYSLUS, LV. Χ.
parts, but we cannot say that time is made up of “nows.’
(3) Nor is it easy to see whether the ‘now’ that appears to divide the past and the future (a) is always one and the same or (6) is continuously changing.
(b) For if it is always changing, and if no two sectional parts of time can exist at once (unless one includes the other, the longer the shorter), and if the ‘now’ that is not, but was, must have ceased to be at some time or other, so also no two ‘ nows’' can exist to- gether, but the past ‘ now’ must have perished before there was any other‘ now.’ Now it cannot have ceased to be when it was itself the ‘ now,’ for that is just when it existed; but it is mpossible that the past ‘ now’ should have perished in any other ‘ now’ but itself, For we must lay it down as an axiom that there can be no next ‘now’ to a given ‘now’, any more than a next point to a given point. So that if it did not perish in the next ‘now,’ but im some subsequent one, it would have been in existence coincidently with the countless ‘nows’ that lie between the ‘ now’ in which it was and the subsequent ‘ now ’ in which we are supposing it to perish; which is impossible.
(a) But neither can it continuously persist in its identity. For nothing which is finite and divisible is bounded by a single limit, whether it be continuous in one dimension only or in more than one; but the ‘now’ is a time limit, and if we take any limited period of time, it must be determined by two limits, which canpot be identical. Again, if simultaneity in time, and not being before or after, means coinciding and being in the very ‘now’ wherein they coincide, then, if the before and the after were both in the per- sistenfly identical ‘now’ we are discussing, what 80 10 ARISTOTLE τὰ εἰς Eros γενόμενα μυριοστὸν τοῖς γενομένοις τήμερον, καὶ οὔτε πρότερον οὔθ᾽ ὕστερον οὐδὲν ἄλλο ἄλλου.
Περὶ μὲν οὖν τῶν ὑπαρχόντων αὐτῷ τοσαῦτ᾽ ἔστω ἘΠΕ be Τί ὃ ἐστὶν ὁ χρόνος καὶ τίς αὐτοῦ ἡ φύσις, ὁμοίως ἔκ τε τῶν παραδεδομένων ἄδηλόν ἐστι καὶ περὶ ὧν τυγχάνομεν διεληλυθότες πρότερον. οἱ μὲν γὰρ τὴν τοῦ ὅλου κίνησιν εἶναί φασιν, οἱ δὲ τὴν σφαῖραν αὐτήν. καίτοι τῆς περιφορᾶς καὶ τὸ μέρος χρόνος τίς ἐστι, περιφορὰ δέ γε οὔ' μέρος γὰρ περιφορᾶς τὸ ληφθέν, ἀλλ᾽ οὐ περιφορά. ἔτι δ᾽ εἰ πλείους ἦσαν οἱ οὐρανοί, ὁμοίως ἂν ἣν ὃ χρόνος ἡ ὁτουοῦν αὐτῶν κίνησις, ὥστε πολλοὶ χρόνοι ἅμα. ἡ δὲ τοῦ ὅλου σφαῖρα ἔδοξε μὲν τοῖς εἰποῦσιν εἶναι 6 χρόνος ὅτι ἔν τε τῷ χρόνῳ πάντα ἐστὶ καὶ ἐν τῇ τοῦ ὅλου σφαίρᾳ" ἔστι δ᾽ εὐηθικώ- τερον τὸ εἰρημένον 7) ὥστε περὶ αὐτοῦ τὰ sacar ἐπισκοπεῖν.
*Eret. δὲ δοκεῖ μάλιστα κίνησις εἶναι καὶ μετα- βολή͵ τι ὃ χρόνος, τοῦτ᾽ ἂν εἴη σκεπτέον. ἡ μὲν οὖν ἑκάστου μεταβολὴ καὶ κίνησις ἐν αὐτῷ τῷ μεταβάλλοντι μόνον ἐστίν, ἢ οὗ ἂν τύχῃ ὃν αὐτὸ τὸ κινούμενον καὶ μεταβάλλον' 6 δὲ χρόνος ὁμοίως α [Plato, according to Eudemus and Theophrastus (Simpl. > (Pythagoreans, Diels, Fors 45 Β 88.--[ὐ] ” he characteristic motion of the heavens is re-entrant ‘circumlation.’ But part of a 1e-entrant circumlation is not re-entrant, whereas time (in addition to not being re- entrant, it might have been added, and therefore having no PHYSICS, IV. x.
happened ten thousand years ago would be simul- taneous with what is happening to-day, and nothing would be before or after anything else.
Let this suffice as to the problems raised by con- sidering the properties of time.
But what time really is and under what category it falls, is no more revealed by anything that has come down to us from earlier thinkers than it is by the considerations that have just been urged. For (a) some ὁ have identified time with the revolution of the all-embracing heaven, and (6) some ® with that heavenly sphere itself. But (a) a partial revolution is time just as much as a whole one is, but it is not just as much a revolution; for any finite portion of time is a portion of a revolution, but is not a revolution.¢ Moreover, if there were more universes than one, the re-cntrant cirenmlation of each of them would be time, so that several different times would exist at once. And (ὁ) as to those who declare the heavenly sphere itself to be time, their only reason was that all things are contained ‘in the celestial sphere ’ and also take place ‘in time,’ which is too childish to be worth reducing to absurdities more obvious than itself.
Now the most obvious thing about time is that it strikes us as some kind of‘ passing along ’ and chang- ing; but if we follow this clue, we find that, when any particular thing changes or moves, the movement or change is in the moving or changing thing itself or takes place only where that thing is; whereas ‘ the natural unity is such that any portion of it (a day, for instance) is time just as truly and completely as any other portion (a day and night, for instance). So the Greek commentators understand this obscure and apparently not very significant passage. [If time is actually idendified with the diurnal revolution, there is no time of [ess duration than a day.—C.]
ARISTOTLE 5185 Kal πανταχοῦ καὶ mapa πᾶσιν. ἔτι δὲ μεταβολὴ 16 μὲν ἔστι πᾶσα θάττων καὶ βραδυτέρα, χρόνος δ᾽ re 2 - οὐκ ἔστιν" τὸ γὰρ βραδὺ καὶ ταχὺ χρόνῳ ὥρισται, ταχὺ μὲν τὸ ἐν ὀλίγῳ πολὺ κινούμενον, βραδὺ δὲ τὸ ἐν πολλῷ ὀλίγον: ὁ δὲ χρόνος οὐχ ὥρισται χρόνῳ, οὔτε τῷ ποσός τις εἶναι οὔτε τῷ ποιός. ὅτι μὲν τοίνυν οὐκ ἔστι κίνησις, φανερόν' μηδὲν δὲ διαφερέτω λέγειν ἡμῖν ἐν τῷ παρόντι κίνησιν ἢ μεταβολήν.
® Τῇ more or less change can take place in the same time, time itself cannot be identical with change. For if it were, equal portions of lime would coincide with more or less of time itself.
CHAPTER XI ARGUMENT Ag to time, Aristotle enters into no profound metaphysical speculations as to its essential nature. He is content with attempting to bring precision into the thoughts of the plain man, who may eastly fall into confusions and contradictions when he tries to give himself an account of what he really means by it.
He finds that we are aware of what we call the passage of time if, and only if, we are aware of some hind of change or movement; but it need not be spatial movement or change; a mental experience, though it came to us in darkness and silence, when we were aware of nothing outside our own consciousness, would make us aware of the passage of time, no less than an objective change which came to us through the senses.
Now movement or change implies interval, and therefore some kind of magnitude. dnd magnitude is continuous, PHYSICS, IV. x—x1.
passage of time’ is current everywhere alike and is in relation with everything. And further, all changes may be faster or slower, but not so time; for fast and slow are defined by time, ‘ faster ’ being more change in less time, and ‘ slower’ less in more. But time cannot measure time thus, as though it were a distance (like the space passed through in motion) or a qualitive modification, as in other kinds of change. It is evident, therefore, that time is not identical with movement; nor, in this connexion, need we distinguish between movement and other kinds of change.
CHAPTER XI ARGUMENT (continued) therefore movement or change, and time (which leeps pace with chunge) must also be continuous.
As local movement, or change of local position, is the simplest and most obvious form of change, we will begin by examining wt. Suppose A, B, CO, D, ete. ta be successive points ona line. If we say that C comes after B and before D we mean that the distance from A to U ig more than the distance from A to B and less than the distance from A to D. Ifa point D has moved atong the line (starting at A) we say that when it reached C it had moved more than when it reached B and less than when it reached D because C comes after B and before D.
This more-or-lessnese, or before-or-afterness is primarily a@ measure of space, and derivatively of movement; for rt is the change of relative position that makes us aware of move- ment. Thus the standard unit for the measurement of movemeyt would naturally be: that movement which covers the standard unit of length.
ARISTOTLE ARGUMENT (continued) Now let us examine spatial movement in its relation to time, Time is the same everywhere, and more than ane movement goes on αὐ the same time, and the relation af time to movement is different in different cases.
For suppose P and P’ to be two points which begin ta moue from A simultaneously, and suppose P reaches B and P’ reaches D simultaneously, then 2’ has moved more than P in the interval between the initial and the final ‘ now’ of the interval.
This lends us to another kind of more-or-lessness in move- ment: the more-or-lessness of intensity or concentration of the motion itself, or, as we should say, the speed of the motion. or if Οἱ comes after B in space, but the arrival 4. at C comes before the arrival of P at B in time, then the motion of P’ is faster (i.e. more concentrated) than the motion of P.
Now that by which we count the more-or-lessness of motion itself (i.e. its rapidity or slowness) is precisely what we mean by Time; and if we fix a unit of time, we shall say that the faster movement covers a given distance rn less time than the slower one.
The precise relation, then, of time to movement is that Time is the measure; the counting, or the dimension, of movement which is primary to motion itself. It determines the speed of a movement with a test that is not identical with the atatical or local more-or-lessness of the distance covered. Aristotle expresses this by saying that time is the ‘ number’ (that is, system of units) which measures the kind of more- or-lessness which is peculiar to motion, as distinct from that which is determined by distances covered.
Again, if the moving point P makes ἃ pause at the point B and then continues its movement, then the ‘ station’ divides the motion, as a point divides a line. The whole of the movement takes place cither before or after the‘ station ’; juat as the whole of the line comes either before or after the point of division B, the point itself being no part of the line. The point of division B has a double function: ut marks the PHYSICS, IV. χε, ARGUMENT (continued) end of ‘ the before’ and the beginning of ‘ the after.’ Tt is therefore called a ‘ double point’; not in the sense of being two separate points, but as having a double function. Simi- larly the ‘ station’ has the double function of being the final limit of the-movement-before and the initial limit of the- movement-after, bué is not itself any part of the motion. And with respect to space; the-~-movement-after-the-pause began where the movement-before-the-pause ended; there was no space between them, and the sanie where has the double function af marking the beginning af the one and the end of the other. But with respect to time, the case 15 differ- ent; for time flowed on continuously during the pause; the-movement-after-the-pause did not begur when the-move- ment-before-the-pause ended, but there was an tnterval of time between the beginning of the one and the end of the other, and other changes were yong on during this interval, and the limits of the interval were marked by two separate ‘ nows.’
So that, though the ‘ station’ is marked tn Space by one point, which is eteelf no part of space, rt is marked in Time by an interval, which is itself a part of time, and whose initial and final limits ware marked by two separate ‘ nows’ (analogous to two distinct points).* When we come to the question how the unite of movement in this sense are to be established, we shall find that it can only be done by fiving on some standard of re-entrant move- ment assumed to be uniform. This rs the condition which the diurnal revolution af the starry heavens coniplies with. We may assume ἐξ to be uniform; the return of a given star to an identical positron with reference tv the (supposed stable) earth may be regarded as the natural unit of this motion, und any convenient fraction of it may be taken for any speciag purpose. We shall then say that one mavenent is faster than another according as it covers a given space coincidently with the movement of the stur through a smaller angular distance.
* The discussion of unity and continuity of time and move- ment in Bk. V. chup. iv. throws much light on this passage, ARISTOTLE ARGUMENT (continued) All this can be expressed in more modern language by saying that tume is the non-spatial dimension of movement. Ever since Fourrier this has been symbolically expressed by saying that the dimensions of vate uf movement are space entering positively and time entering negatively, or the dimensions of Rare SI'-*. To realize this is to realize the greatness of Aristotie’s achievement, and to see how directly it opens the way to the four-dimensronal algebra to which so much attention has recently been directed in connexion with the doctrine of relativity.
21ab ᾿Αλλὰ μὴν οὐδ᾽ ἄνευ γε εταβολῆς' ὅταν γὰρ μηδὲν αὐτοὶ μεταβάλλωμεν τὴν διάνοιαν ἢ ἢ λάθωμεν μεταβάλλοντες, οὐ δοκεῖ ἡμῖν γεγονέναι χρόνος, καθάπερ οὐδὲ τοῖς ἐν Σαρδοῖ μυθολογουμένοις 36 καθεύδειν παρὰ τοῖς ἥρωσιν, ὅταν,ἐγερθῶσιν" συνάπτουσι γὰρ τὸ πρότερον νῦν τῷ ὕστερον νῦν καὶ ἕν ποιοῦσιν, ἐξαιροῦντες διὰ τὴν ἀναισθησίαν τὸ μεταξύ. ὥσπερ οὖν εἰ μὴ ἦν ἕτερον τὸ νῦν ἀλλὰ ταὐτὸ καὶ ἕν, οὐκ ἂν ἦν χρόνος, οὕτως καὶ ἐπεὶ λανθάνει ὁ ἕτερον ὄν, οὐ δοκεῖ εἶναι τὸ μεταξὺ 80 χρόνος. εἰ δὴ τὸ μὴ οἴεσθαι εἶναι χρόνον τότε συμβαίνει ἡμῖν ὅταν μὴ ὁρίζωμεν μηδεμίαν, μετα- βολὴν ἀλλ᾽ ἐν ἑνὶ καὶ ἀδιαιρέτῳ φαίνηται ἡ ψυχὴ μένειν, ὅταν δ᾽ αἰσθώμεθα καὶ ὁρίσωμεν, τότε φαμὲν γεγονέναι “Χρόνον, φανερὸν ὅτι οὐκ ἔστιν 319. ἄνευ κινήσεως καὶ μεταβολῆς χρόνος. Ὅτι μὲν οὖν οὔτε κίνησις οὔτ᾽ ἄνευ κινήσεως ὁ χρόνος ἐστί, φανερόν. Ληπτέον δέ, ἐπεὶ ζητοῦμεν τί ἐστιν ὁ χρόνος, ἐντεῦθεν ἀρχομένοις, τί τῆς κινήσεώς ἐστιν. ἅμα PHYSICS, IV. xt.
ARGUMENT (continued) Aristotle, however, carries his investigation no further than the comparison of movements, each of which is uniform with wtself. He is aware of the fact of acceleration (in which T enters twice as ἃ dimension symbolized as T-*), but he does not carry his investigations into this further reguon.
On the other hand, time cannot be disconnected from change; for when we experience no changes of consciousness, or, if we do, are not aware of them, no time seems to have passed, any more than it did to the men in the fable who ‘ slept with the heroes ’ 4 in Sardinia, when they awoke; for under such cirenm- stances we fit the former ‘now’ on to the later, making them one and the same and eliminating the interval between them, because we did not perceive it. So, just as there would be no time if there were no distinction between this ‘now’ and that ‘now,’ but it were always the same‘ now’; in the same way there appears to be no time between two ‘ nows’ when we fail to distinguish between them. Since, then, we are not aware of time when we do not dis- tinguish any change (the mind appearing to abide in a single indivisible and undifferentiated state), whereas if we perceive and distinguish changes, then we say that time has elapsed, it is clear that time cannot be disconnected from motion and change.
Plainly, then, time is neither identical with move- ment nor capable of being separated from it.
In our attempt to find out what time is, therefore, we must start from the question, in what ay it per- tains to motion. For when we are aware of motion α [Sons of Herakles and of the daughters of Thespius, who were said to have colonized Sardinia (see Frazer on Apollo- dorus ii. 7. 6).—C.]
ARISTOTLE 2188 γὰρ κινήσεως αἰσθανόμεθα καὶ,χρόνου" καὶ γὰρ δ ἐὰν ἦ σκότος καὶ μηδὲν διὰ τοῦ σώματος πάσχωμεν, κίνησις δέ τις ἐν τῇ ψυχῇ ἐνῇ, εὐθὺς ὁ ἅμα δοκεῖ τις γεγονέναι καὶ χρόνος. ἀλλὰ μὴν καὶ ὅταν γε χρόνος δοκῇ γεγονέναι. τις, ἅμα καὶ κίνησίς τις φαίνεται γεγονέναι. ὥστε ἦτοι κίνησις ὴ τῆς κινήσεώς τί ἐστιν ὁ χρόνος" ἐπεὶ οὖν οὐ κίνησις, 10 ἀνάγκη τῆς κινήσεις τι εἶναι αὐτόν. ᾿Ιπεὶ δὲ τὸ κινούμενον κινεῖται ἔκ τινος εἴς τι καὶ πᾶν μέγεθος συνεχές, ἀκολουθεῖ τῷ μεγέθει ἡ κίνησις" διὰ γὰρ τὸ τὸ μέγεθος εἶναι συνεχὲς καὶ ἡ κίνησίς. ἐστι συνεχής" διὰ δὲ τὴν κίνησιν ὁ _xpdvos: ὅση yap ἡ κίνησις, τοσοῦτος καὶ ὁ χρόνος ἀεὶ 16 δοκεῖ γεγονέναι. τὸ δὲ δὴ πρότερον καὶ ὕστερον ἐν τόπῳ πρῶτόν ἐστιν. ἐνταῦθα μὲν δὴ 7 θέσει" ἐπεὶ δ᾽ ἐν τῷ μεγέθει ἐ ἐστὶ τὸ πρότερον καὶ ὕστερον, ἀνάγ yen καὶ ἐν κινήσει εἶναι τὸ πρότερον καὶ ὕστερον, ἀνάλογον τοῖς ἐκεῖ. ἀλλὰ μὴν καὶ ἐν χρόνῳ ἐστὶ τὸ πρότερον καὶ ὕστερον διὰ τὸ ἀκο- 20 λουθεῖν ἀεὶ θατέρῳ θάτερον αὐτῶν. ἔστι δὲ τὸ πρότερον καὶ ὕστερον αὐτῶν' ἐν τῇ κινήσει, ὃ μέν ποτε ὃν κίνησίς ἐστιν" τὸ μέντοι. εἶναι αὐτῷ ἕτερον καὶ οὐ κίνησις. ἀλλὰ μὴν καὶ τὸν χρόνον γε 1 [αὐτῶν om. H: αὐτῶν ἐν τῇ κινήσει om, Philop. 720. 24 (lemma).—C,] @ * From here to there ἡ implies an interval between them, and this implies some kind of magnitude, Ὁ [Philop. 720, 26 paraphrases: ‘This before-and-after, when obseryed in motion and in time, in r€spect of the substrate (iroxeluevov)—that is the meaning of ὃ μέν wore ὅν —is nothing but the motion, but in respect of its definition is distinct; as ascent and descent in respect of their substrate are a ladder, but in definition distinct from it.’ Cf. De gen. et corp. 319 Ὁ 2 ἢ ἔστι μὲν ὡς (ea. ἡ ὕλη, the matter under- PHYSICS, IV. x1.
we are thereby aware of time, since, even if it were dark and we were conscious of no bodily sensations, but something were ‘ going on’ in our minds, we should, from that very experience, recognize the passage of time. And conversely, whenever we recognize that there has been a lapse of time, we by that act recognize that something ‘has been going on.’ So time must either itself be motion, or if not, must pertain to motion; and since we have seen that it is not identical with motion, it must pertain to it in some way.
Well then, since anything that moves moves from a ‘here’ to a ‘there,’* and magnitude as such is continuous, movement is dependent on magnitude; for it is because magnitude is continuous that move- ment is so also, and because movement is continuous so is time; for (excluding differences of velocity) the time occupied is conceived as proportionate to the distance moved over. Now, the primary signific- ance of before-and-afterness is the local one of ‘in front of ’ and ‘ behind.’ There it is applied to order of position; but since there is a before-and-after in magnitude, there must also be a before-and-after in movement in analogy with them. But there is also a before-and-after in time, in virtue of the dependence of time upon motion. Movement, then, is the objective seat of before-and-afterness both in movement and in time; but conceptually the before-and-afterness is distinguishable from movement,? Now, when we determine a movement lying the four simple bodies) 4 αὐτή, ἔστι δὲ ὡς ἑτέρα; ὃ μὲν γάρ ποτε ὃν ὑπόκειται, τὸ αὐτό, τὸ δ᾽ εἶναι οὐ τὸ αὐτό, ‘for that which underlies them, whatever its nature may be qua underlying them, is the same, but its actual being is not the same’ (Joachim).—C. ] VoL. I Qc 385 ARISTOTLE 2198 γνωρίζομεν, ὅταν ὁρίσωμεν τὴν κίνησιν τὸ πρό- τερον καὶ ὕστερον ὁρίζοντες" καὶ τότε φαμὲν yeyo- νέναι χρόνον, ὅταν τοῦ προτέρου καὶ ὑστέρου ἐν TH ame 4 ~ 85 κινήσει αἴσθησιν λάβωμεν. ὁρίζομεν δὲ τῷ ἄλλο καὶ ἄλλο ὑπολαβεῖν αὐτὰ καὶ μεταξύ τι αὐτῶν ἕτερον" ὅταν yap ἕτερα τὰ ἄκρα τοῦ μέσου νοήσωμεν καὶ δύο εἴπῃ ἡ ψυχὴ τὰ νῦν---τὸ μὲν πρότερον τὸ δ᾽ ὕστερον---τότε καὶ τοῦτό φαμεν εἶναι χρόνον' τὸ 80 γὰρ ὁριζόμενον τῷ νῦν χρόνος εἶναι δοκεῖ" καὶ ‘4 ὑποκείσθω. Ὅταν μὲν οὖν ὡς ἕν τὸ νῦν αἰσθανώμεθα καὶ μὴ ἤτοι ὡς πρότερον καὶ ὕστερον ἐν τῇ κινήσει ἢ ὡς τὸ αὐτὸ μὲν προτέρου δὲ καὶ ὑστέρου τινός, οὐ δοκεῖ χρόνος γεγονέναι οὐθείς, ὅτι οὐδὲ κίνησις. 2igh ὅταν δὲ τὸ πρότερον καὶ ὕστερον, τότε λέγομεν χρόνον' τοῦτο γάρ ἐστιν ὁ χρόνος, ἀριθμὸς κινήσεως κατὰ τὸ πρότερον καὶ ὕστερον. Οὐκ dpa κίνησις ὁ χρόνος, GAN ἢ ἀριθμὸν ἔχει ἡ ra a ΓΑ 4 < ‘ ζω \ow κίνησις. σημεῖον δέ: τὸ μὲν γὰρ πλεῖον καὶ ἔλαττον υ Κρίνομεν ἀριθμῷ, κίνησιν δὲ πλείω καὶ ἐλάττω χρόνῳ" ἀριθμὸς ἄρα τις ὁ χρόνος. ἐπεὶ δ᾽ ἀριθμός ἐστι διχῶς (καὶ γὰρ τὸ ἀριθμούμενον καὶ τὸ ἀριθ- 4 That is, ‘ whose beginning and end are each a “ ποιν,᾽ PHYSICS, IV. x1.
by defining its first and last limit, we also recognize a lapse of me; for it is when we are aware of the measuring vf movement by a prior and posterior limit that we may say time has passed. And our determination consists in distingmshing between the initial limit and the final one, and seeing that what lies between them is distinct from both; for when we distinguish between the extremes and what is between them, and the mind pronounces the “nows’ to be two—an sitial and a final one—xt is then that we say that a certain time has passed; for that which is determined either way by a ‘ now ’# seems to be what we mean by time. And let this be accepted and laid down.
Accordingly, when we perceive ἃ ‘ now’ in isola- tion, that is to say not as one of two, an initial and a final one in the movement, nor yet as being a final ‘now’ of one period and at the same time the initial ‘now’ of a succeeding period, then no time seems to have elapsed, for neither has there been any corresponding movement. But when we perceive a distinct before and after, then we speak of time; for this is just what time is, the calculable measure or dimension of motion with respect to before-and- afterness.
Time, then, is not movement, but that by which movement can be numerically estimated, To see this, reflect that we estimate any kind of more-and- lessness by number; so, since we estimate all more- or-lessness» on some numerical scale and estimate the more-or-lessness of motion by time, time is a seale on which something (to wit movement) can be numerically estimated. But now, since ‘ number’ has two meanings (for we speak of the ‘numbers’ ARISTOTLE 819} μητὸν ἀριθμὸν λέγομεν, καὶ ᾧ ἀριθμοῦμεν), ὁ det χρόνος ἐστὶ τὸ ἀριθμούμενον καὶ οὐχ ᾧ ἀριθμοῦμεν. ἔστι δ᾽ ἕτερον ᾧ ἀριθμοῦμεν καὶ τὸ ἀριθμούμενον.
τ Καὶ ὥσπερ ἡ κῴησις ἀεὶ ἄλλη καὶ ἄλλη, καὶ ὃ χρόνος. ὁ δ᾽ ἅμα πᾶς χρόνος ὁ αὐτός: τὸ γὰρ νῦν τὸ αὐτὸ ὅ ποτ᾽ ἦν, τὸ δ᾽ εἶναι αὐτῷ Ere ον" τὸ δὲ νῦν τὸν χρόνον μετρεῖ, ἣ πρότερον καὶ ὕστερον. τὸ δὲ νῦν ἔστι μὲν ὡς τὸ αὖτό, ἔστι δ᾽ ὡς οὐ τὸ αὐτό" ἣ μὲν γὰρ ἐν ἄλλῳ καὶ ἄλλῳ, ἕτερον (τοῦτο 16 δ᾽ ἦν ee τὸ viv"), # δὲ 6 ποτε ὄν ἐστι τὸ νῦν, τὸ αὐτό. ἀκολουθεῖ γάρ, ὡς ἐλέχθη, τῷ μὲν μεγέθει ἡ ἡ κίνησις, ταύτῃ δ᾽ ὁ χρόνος, ὥς φαμεν: καὶ ὁμοίως δὴ τῇ στιγμῇ τὸ φερόμενον, ᾧ ᾧ τὴν κίνησιν γνωρίομεν καὶ τὸ πρότερον ἐν αὐτῇ καὶ τὸ ὕστερον. τοῦτο δὲ ὃ μέν ποτε ὃν τὸ αὐτό (ἢ στιγμὴ γὰρ ἢ 20 λίθος ἢ τι ἄλλο τοιοῦτόν ἐστὶ), τῷ λόγῳ δὲ dAdo: ὥσπερ οἱ σοφισταὶ λαμβάνουσιν ἕ ἕτερον τὸ Κορίσκον ἐν Λυκείῳ εἶναι καὶ τὸ Κορίσκον ἐν ἀγορᾷ, καὶ τοῦτο δὴ τῷ ἄλλοθι καὶ ἄλλοθι εἶναι ἕ ἕτερον. τῷ δὲ μεν ἐμὰ ἀκολουθεῖ τὸ νῦν, ὥσπερ 6 χρόνος τῇ ne!
3 [τὸ νῦν εἶναι Philop. 726. 21 (paraphr.), Bonitz, Prantl.—C,] 4 The contrast is between the numeri numerati and the numeri numeranies and between the ‘concrete’ and ‘abstract’ of modern arithmetical terminology, In counting the successive ἡ nows,’ we are counting sections of continuous time; but we are counting them in abstract numbers. Time, then, is a concrete numerable, not ‘an abstract numerator.
Ὁ [The following paragraph points out ‘ that as movement is oo by observing a single moving body successively at different points, the passage of time is recognized by noting that the single character of ‘‘ nowness”’ has been PHYSICS, IV. x1.
that are counted in the thing in question, and also of the ‘numbers’ by which we count them and in which we calculate), we are to note that time is the countable thing that we are counting, not the numbers we count in—which two things are different.* And ® as movement is a continuous flux, so is time; but at any given moment time is the same every- where, for the ‘ now’ itself is identical in its essence, but the relations into which it enters differ in different connexions, and it is the ‘ now ἡ that marks of time as before and after. But this ‘now,’ which 15 identical everywhere, itsclf retains its identity in one sense, but is continually changing in another; for inasmuch as the point in the flux of time which it marks is changing (and so to mark it is its essential function) the ‘now’ too keeps changing, but inas- much as at every moment it 1s performing its essential function of dividing the past and future it retains its identity. For there is a dependent sequence, as we have shown, of movement upon magnitude and (we may add) of time upon movement; and the moving body, by which we become aware of move- ment and its before-and-afterness, may be regarded as a point;’ and throughout its course this— whether point or stone or what you like—retains its identity, but its relations alter: as the Sophists distin- guish between Koriscos in the Lyceum and Koriscos in the market-place, so this moving body also is different in so far as it is constantly in a different place. Apd as time follows the analogy of movement, so does the ‘ now’ of time follow the analogy of the attached to more than one experienced event’ (Ross, Aristotle, Ὁ. 90).—C.]
°* As a point,’ that is, as a mere indicator of movement, in abstraction from all its other properties.
ARISTOTLE 249 b 0 κινήσει" τῷ γὰρ φερομένῳ γνωρίζομεν τὸ πρότερον καὶ ὕστερον ἐν κινήσει" ἡ δ᾽ ἀριθμητὸν τὸ πρότερον καὶ ὕστερον, τὸ νῦν ἐστιν" ὥστε καὶ ἐν τούτοις, ὃ μέν ποτε ὃν νῦν ἐστι, τὸ αὐτό (τὸ πρότερον γὰρ καὶ ὕστερόν ἐστιν ἐν κινήσει), τὸ δ᾽ εἶναι ἕτερον" a ἀριθμητὸν yap τὸ πρότερον καὶ ὕστερον, τὸ νῦν ἐστιν. καὶ γνώριμον δὲ μάλιστα τοῦτ᾽ ἔστιν" καὶ 80 γὰρ ἡ κίνησις διὰ τὸ κινούμενον καὶ ἡ φορὰ διὰ τὸ pep ὄμενον' τόδε γάρ τι τὸ φερόμενον, ὴ δὲ κίνησις οὔ. ἔστι μὲν οὖν, ὡς τὸ αὐτὸ τὸ νῦν ἀεί, ἔστι δ᾽ ὡς οὐ τὸ αὐτό: καὶ γὰρ τὸ φερόμενον. “Φανερὸν δὲ καὶ ὅτι εἴτε χρόνος μὴ εἴη, τὸ νῦν 280 οὐκ ἂν εἴη, εἴτε τὸ νῦν μὴ εἴη, χρόνος οὐκ ἂν εἴη! ἅμα γὰρ ὥσπερ, τὸ φερόμενον καὶ ἡ φορά, οὕτως καὶ ὁ ἀριθμὸς ὃ τοῦ φερομένου καὶ ὁ τῆς φορᾶς. χρόνος μὲν γὰρ ὁ τῆς φορᾶς ἀριθμός, τὸ νῦν δὲ ὡς τὸ φερόμενον οἷον μονὰς ἀριθμοῦ. ε Kal συνεχής τε δὴ ὁ χρόνος τῷ νῦν, καὶ διήρηται 9 [Or, * the “" now” is the before and after, gua countable.’ Themist. 150, 23 τὸ δὲ ἀριθμούμενον πρότερόν re καὶ ὕστερον τὸ νῦν ἐστιν, Simplic. 723, 29 καθύσον δὲ ἀριθμητὸν τὸ πρότερον τοῦτο καὶ ὕστερον, κατὰ τοσοῦτον, φησί, viv δείκνυται.---( 1 δῚ understand this to be a reference to the general principle of the more easy apprehensibility of the concrete and the greatcr intellectual juminosity of, the abstract. (Themistius, 150. 27 explains: The ‘now,’ as a sort of particular existent, is more cognizable than time (γνωριμώ- τερον τοῦ χρόνου), just as the moving body is more so than its motion,—C.]
° A monad is not a ‘unit’ but a ‘ unity," ie. an in- divisible. The ‘ numbers’ we count with, and by which we cut up any continuous magnitude into parts (which parts we can also count) are not themselves magnitudes, and do not themselves add to or subtract from magnitudes, Nor can they be continuous by contact.
PHYSICS, IV. x1.
PHYSICS, IV. x1.
moving body, since it is by the moving body that we come to know the before-and-after in movement, and it is in virtue of the countableness of its before- and-afters that the ‘now’ exists;* so that the ‘now,’ wherever found in the before-and-afters, is identical (for it is simply the mark of the before- and-afters in motion), but the before-and-afternesses it marks differ; though the nature of the ‘now’ depends on the markableness of any before-and-~ after in general, not on the specific before-and-after marked by it. And it is this specifically related ‘now’ that is nearest to our apprehension,’ just as motion-change is apprehended through the changing object, and translation through the trans- lated object, for this object is a concrete thing, which motion is not. There is a sense, then, in which what we mean when we say ‘now’ is always the same, and a sense in which it is not, just as is the case with anything that is in motion.
It is evident, too, that neither would time be if there were no ‘ now,’ nor would ‘ now’ be if there were no time; for they belong to each other as the moving thing and the motion do, so that what- ever ticks off the position of the one ticks off the other. Tor time is the dimension proper to move- ment, and the ‘now’ corresponds to the moving object as the numerical monad.° So, too, time owes its continuity to the ‘ now,’ and yet is divided by reference to it, since in this Here the moving object is not regarded as having ex- tension, but only as having position. It is, therefore, for this purpose, ‘ monadic.’ Its ‘ positions’ can be counted, but sitch a position 1s not a ‘ part’ of the ‘ distance’ the moving thing has passed or is passing over.
ARISTOTLE 220 a κατὰ τὸ νῦν" ἀκολουθεῖ “γὰρ καὶ τοῦτο τῇ φορᾷ καὶ τῷ φερομένῳ' καὶ γὰρ ἡ κίνησις καὶ ἡ φορὰ μία τῷ φερομένῳ, ὅτι ἕν, καὶ οὐχ ὅ TOTE ov (καὶ γὰρ ἂν διαλίποι) ἀλλὰ τῷ λόγῳ" καὶ ὁρίζει δὴ τὴν πρό- 10 Tepov καὶ ὕστερον κίνησιν τοῦτο. ἀκολουθεῖ δὲ καὶ τοῦτό πως τῇ στιγμῇ" καὶ γὰρ ἡ στιγμὴ καὶ συνέχει τὸ μῆκος καὶ ὁρίζει" ἔστι γὰρ τοῦ μὲν ἀρχὴ τοῦ δὲ τελευτή. ἀλλ᾽ ὅταν μὲν οὕτω λαμβάνῃ τις ὡς δυσὶ χρώμενος τῇ μιᾷ, ἀνάγκη ἵστασθαι, εἰ ἔσται ἀρχὴ καὶ τελευτὴ ἡ αὐτὴ στιγμή" τὸ δὲ νῦν, διὰ τὸ κινεῖσθαι τὸ φερόμενον, ἀεὶ ἕτερον" ὥσθ᾽ 6 15 χρόνος ἀριθμὸς οὐχ ὡς τῆς αὐτῆς στιγμῆς, ὅτι ἀρχὴ καὶ τελευτή, ἀλλ᾽ ὡς τὰ ἔσχατα τῆς αὐτῆς μᾶλλον, καὶ οὐχ ὡς τὰ μέρη, διά τε τὸ εἰρημένον (τῇ γὰρ μέσῃ στιγμῇ ὡς δυσὶ χρήσεται, ὥστε ἠρεμεῖν συμβήσεται), καὶ ἔτι φανερὸν ὅτι οὐδὲ μόριον τὸ νῦν τοῦ χρόνου, οὐδ᾽ ἡ διαίρεσις τῆς 20 κινήσεως, ὥσπερ οὐδ᾽ αἱ στιγμαὶ τῆς γραμμῆς" αἱ δὲ γραμμαὶ αἱ δύο τῆς μιᾶς μόρια. ἢ μὲν οὖν 1 [καὶ ὁρίζει δὴ HI, Philop. 133. 12. (lemma): καὶ γὰρ ὁρίζει cett. The moving ‘body both constitutes the continuity of the motion and at any moment marks the boundary (division) between the motion that has taken place and that which will follow. (Cf. Themist. 151. 11 (τὸ φερόμενον) καὶ διορίζει τὴν προτέραν καὶ ὑστέραν κίνησιν καὶ πάλιν cuvéxer. \—C, * [The ‘now’ is analogous to the dividing point in a bisected line, in so far as either can be regarded as the end- point of what comes before and also the starting-point of what comes after. But the ‘now’ is not stdiionary; 80 when time 1s counted, we do not take the same ‘ now > twice as we took the dividing point), but different ‘ nows,’ like the two extremities of the line—two different points.—C.]
> [If the line AB is divided at the point C, the two lines AC, CB are parts of AB; the point Cis not a part of AB.—C.]
PITYSICS, IV, x1.