Now the most obvious thing about time is that it strikes us as some kind of‘ passing along ’ and changing; 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.]
5185 Kal πανταχοῦ καὶ mapa πᾶσιν. ἔτι δὲ μεταβολὴ 16 μὲν ἔστι πᾶσα θάττων καὶ βραδυτέρα, χρόνος δ᾽ re - 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 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 movement. Thus the standard unit for the measurement of movemeyt would naturally be: that movement which covers the standard unit of length.
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 movement: 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 moreor-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. Similarly the ‘ station’ has the double function of being the final limit of the-movement-before and the initial limit of themovement-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 different; for time flowed on continuously during the pause; the-movement-after-the-pause did not begur when the-movement-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 movement 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 movement in Bk. V. chup. iv. throws much light on this passage, 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 cirenmstances 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 distinguish 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 movement 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 pertains 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 Apollodorus ii. 7. 6).—C.]
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 underwe 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 movement 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 significance 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 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,᾽ 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 isolation, 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-andafterness.
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-andlessness by number; so, since we estimate all moreor-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’ 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 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 everywhere, 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 inasmuch 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 movement 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 distinguish 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.
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 indivisible. 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.
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 beforeand-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 beforeand-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 translated 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 whatever ticks off the position of the one ticks off the other. Tor time is the dimension proper to movement, 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 extension, 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.
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 endpoint 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.
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, regarding 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, 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 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 magnitudes, 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 particular 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 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.