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Aristotle · Physics §8.8#3

Dividing Points of Time and the Necessity of a Stop

Passage 109 of 113 · Greek

Summary

The text argues that the dividing point of time must belong to the posterior state of a changing thing, thereby rejecting the theory of indivisible times, and demonstrates logically that a continuous turning-back motion must involve a stop.

§8.8#3δῆλον δὲ καὶ ὅτι ἐὰν μή τις ποιῇ τοῦ χρόνου τὸ διαιροῦν σημεῖον τὸ πρότερον καὶ ὕστερον ἀεὶ τοῦ ὑστέρου τῷ πράγματι, ἔσται ἅμα τὸ αὐτὸ ὂν καὶ οὐκ ὄν, καὶ ὅτε γέγονεν οὐκ ὄν.
It is also clear that unless one makes the point of time which divides the prior and the posterior always belong to the posterior in respect of the thing, the same thing will at the same time be and not be, and [it will] not be when it has become [it].
τὸ σημεῖον μὲν οὖν ἀμφοῖν κοινόν, καὶ τοῦ προτέρου καὶ τοῦ ὑστέρου, καὶ ταὐτὸν καὶ ἓν ἀριθμῷ, λόγῳ δʼ οὐ ταὐτόν (τοῦ μὲν γὰρ τελευτή, τοῦ δʼ ἀρχή)· τῷ δὲ πράγματι ἀεὶ τοῦ ὑστέρου πάθους ἐστίν.
Now the point is common to both, both the prior and the posterior, and is the same and one in number, but not the same in definition (for it is the end of the one, and the beginning of the other); but in respect of the thing, it always belongs to the posterior affection.
χρόνος ἐφʼ ΑΓΒ. πρᾶγμα ἐφʼ ᾧ Δ. τοῦτο ἐν μὲν τῷ Α χρόνῳ λευκόν, ἐν δὲ τῷ Β οὐ λευκόν· ἐν τῷ ἄρα Γ λευκὸν καὶ οὐ λευκόν.
Let time be ACB; the thing, D. This is white in time A, and not white in B; therefore, in C it is white and not white.
ἐν ὁτῳοῦν γὰρ τοῦ Α λευκὸν ἀληθὲς εἰπεῖν, εἰ πάντα τὸν χρόνον τοῦτον ἦν λευκόν, καὶ ἐν τῷ Β οὐ λευκόν· τὸ δὲ Γ ἐν ἀμφοῖν.
For in any part of A it is true to say that it is white, if it was white during all this time, and in B it is not white; and C is in both.
οὐκ ἄρα δοτέον ἐν παντί, ἀλλὰ πλὴν τοῦ τελευταίου νῦν ἐφʼ οὗ τὸ Γ· τοῦτο δʼ ἤδη τοῦ ὑστέρου.
Therefore it must not be granted [that it is white] in all [of A], but except for the last 'now' C; and this already belongs to the posterior.
καὶ εἰ ἐγίγνετο οὐ λευκὸν καὶ ἐφθείρετο ⟨τὸ⟩ λευκὸν ἐν τῷ Α παντί, γέγονεν ἢ ἔφθαρται ἐν τῷ Γ. ὥστε λευκὸν ἢ μὴ λευκὸν ἐν ἐκείνῳ πρῶτον ἀληθὲς εἰπεῖν, ἢ ὅτε γέγονεν οὐκ ἔσται, καὶ ὅτε ἔφθαρται ἔσται, ἢ ἅμα λευκὸν καὶ οὐ λευκὸν καὶ ὅλως ὂν καὶ μὴ ὂν ἀνάγκη εἶναι.
And if it was becoming not-white and the white was perishing in the whole of A, it has become [not-white] or has perished in C. Thus, it must be true to say first in that [C] that it is white or not-white, or else when it has become it will not be, and when it has perished it will be, or it is necessary that it be at the same time white and not-white, and in general being and non-being at the same time.
εἰ δʼ ὁ ἂν ᾖ πρότερον μὴ ὄν, ἀνάγκη γίγνεσθαι ὄν, καὶ ὅτε γίγνεται μὴ ἔστιν, οὐχ οἷόν τε εἰς ἀτόμους χρόνους διαιρεῖσθαι τὸν χρόνον.
And if that which, having previously not been, must necessarily become being, and when it is becoming it is not, it is not possible for time to be divided into indivisible times.
εἰ γὰρ ἐν τῷ Α τὸ Δ ἐγίγνετο λευκόν, γέγονε δʼ ἅμα καὶ ἔστιν ἐν ἑτέρῳ ἀτόμῳ χρόνῳ ἐχομένῳ δʼ, ἐν τῷ Β—εἰ ἐν τῷ Α ἐγίγνετο, οὐκ ἦν, ἐν δὲ τῷ Β ἐστί—, γένεσιν δεῖ τινὰ εἶναι μεταξύ, ὥστε καὶ χρόνον ἐν ᾧ ἐγίγνετο.
For if in A, D was becoming white, and has become and is so at the same time in another, adjacent indivisible time B—if it was becoming in A, it was not, but in B it is—there must be some becoming between them, and therefore also a time in which it was becoming.
οὐ γὰρ ὁ αὐτὸς ἔσται λόγος καὶ τοῖς μὴ ἄτομα λέγουσιν, ἀλλʼ αὐτοῦ τοῦ χρόνου, ἐν ᾧ ἐγίγνετο, γέγονε καὶ ἔστιν ἐν τῷ ἐσχάτῳ σημείῳ, οὗ οὐδὲν ἐχόμενόν ἐστιν οὐδʼ ἐφεξῆς· οἱ δὲ ἄτομοι χρόνοι ἐφεξῆς.
For the argument will not be the same for those who do not speak of indivisible [times], but rather, of the time itself in which it was becoming, it has become and is in the last point, to which nothing is adjacent or next; but indivisible times are next [to each other].
φανερὸν δʼ ὅτι εἰ ἐν τῷ Α ὅλῳ χρόνῳ ἐγίγνετο, οὐκ ἔστιν πλείων χρόνος ἐν ᾧ γέγονεν καὶ ἐγίγνετο ἢ ἐν ᾧ ἐγίγνετο μόνον παντί.
And it is clear that if it was becoming in the whole time A, the time in which it has become and was becoming is not greater than that in all of which it was only becoming.
οἶς μὲν οὖν ἄν τις ὡς οἰκείοις πιστεύσειε λόγοις, οὗτοι καὶ τοιοῦτοί τινές εἰσιν· λογικῶς δʼ ἐπισκοποῦσι κἂν ἐκ τῶνδε δόξειέ τῳ ταὐτὸ τοῦτο συμβαίνειν.
These, then, and such as these are the arguments which one might trust as appropriate; but to those who examine the matter logically, this same thing would seem to follow from the following.
ἅπαν γὰρ τὸ κινούμενον συνεχῶς, ἂν ὑπὸ μηδενὸς ἐκκρούηται, εἰς ὅπερ ἦλθεν κατὰ τὴν φοράν, εἰς τοῦτο καὶ ἐφέρετο πρότερον, οἷον εἰ ἐπὶ τὸ Β ἦλθε, καὶ ἐφέρετο ἐπὶ τὸ Β, καὶ οὐχ ὅτε πλησίον ἦν, ἀλλʼ εὐθὺς ὡς ἤρξατο κινεῖσθαι· τί γὰρ μᾶλλον νῦν ἢ πρότερον;
For everything that is in continuous motion, if it is not deflected by anything, was also previously being carried toward that which it has reached in its locomotion; for instance, if it has reached B, it was also being carried toward B, and not [only] when it was near, but from the very beginning of its motion; for why now rather than previously?
ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων.
And similarly in other cases too.
τὸ δὴ ἀπὸ τοῦ Α φερόμενον, ὅταν ἐπὶ τὸ Γ ἔλθῃ, πάλιν ἥξει ἐπὶ τὸ Α συνεχῶς κινούμενον.
Therefore, that which is carried from A, when it reaches C, will come back to A, moving continuously.
ὅτε ἄρα ἀπὸ τοῦ Α φέρεται πρὸς τὸ Γ, τότε καὶ εἰς τὸ Α φέρεται τὴν ἀπὸ τοῦ Γ κίνησιν, ὥσθʼ ἅμα τὰς ἐναντίας· ἐναντίαι γὰρ αἱ κατʼ εὐθεῖαν.
Therefore, when it is carried from A toward C, it is at that time also carried to A with the motion from C, so that opposite motions [occur] at the same time; for motions along a straight line are opposite.
ἅμα δὲ καὶ ἐκ τούτου μεταβάλλει ἐν οὐκ ἔστιν.
And at the same time, from this, it changes into that in which it is not.
εἰ οὖν τοῦτʼ ἀδύνατον, ἀνάγκη ἵστασθαι ἐπὶ τοῦ Γ. οὐκ ἄρα μία ἡ κίνησις·
If, then, this is impossible, it must necessarily stop at C.
ἡ γὰρ διαλαμβανομένη στάσει σὐ μία.
Therefore, the motion is not one; for a motion interrupted by a stop is not one.
ἔτι καὶ ἐκ τῶνδε φανερὸν καθόλου μᾶλλον περὶ πάσης κινήσεως.
Furthermore, this is clear more generally concerning all motion from the following.

Notes

  1. 263bτοῦ ὑστέρου πάθους ἐστίν — The genitive `τοῦ ὑστέρου πάθους` denotes possession or belonging ('belongs to the posterior affection'). In this context, it determines which state of the changing thing (e.g., white or not-white) the dividing point of time belongs to.
  2. 263bεἰ δʼ ὃ ἂν ᾖ πρότερον μὴ ὄν — The relative pronoun with the particle `ἄν` followed by the subjunctive `ᾖ` (`ὃ ἂν ᾖ`) forms a conditional relative clause denoting a general assumption ('whatever is...'). Combined with the main clause `ἀνάγκη γίγνεσθαι`, it states a general principle that whatever becomes being must be becoming.
  3. 264aοὐ γὰρ ὁ αὐτὸς ἔσται λόγος καὶ τοῖς μὴ ἄτομα λέγουσιν — The construction `ὁ αὐτός ... καί` expresses identity or similarity ('the same as...'). Connected with the dative `τοῖς μὴ ἄτομα λέγουσιν` ('those who do not speak of indivisible times'), it means 'the same argument will not hold for those who do not speak of indivisibles.'

Cite this passage

Aristotle, Physics §8.8#3. Humanitext Reader, https://reader.humanitext.ai/en/text/urn:cts:greekLit:tlg0086.tlg031.humanitext-grc1:8.8%233

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