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Aristotle · Physics §6.10#2

Finiteness of Change and Infinite Circular Motion

Passage 83 of 113 · Greek

Summary

The author demonstrates again that indivisible things cannot move because time is divisible, and argues that while all changes are finite as they possess opposing limits, circular motion is the only single motion that can be infinite in time.

§6.10#2ἔτι δʼ εἰ ἅπαν ἐν χρόνῳ κινεῖται, ἐν δὲ τῷ νῦν μηθέν, ἅπας δὲ χρόνος διαιρετός, εἴη ἄν τις χρόνος ἐλάττων ὁτῳοῦν τῶν κινουμένων ἢ ἐν ᾧ κινεῖται ὅσον αὐτό.
Furthermore, if everything moves in time, and nothing in the 'now', and all time is divisible, there would be some time smaller than that in which any whatever of the things in motion moves a distance equal to itself.
οὗτος μὲν γὰρ ἔσται χρόνος ἐν κινεῖται διὰ τὸ πᾶν ἐν χρόνῳ κινεῖσθαι, χρόνος δὲ πᾶς διαιρετὸς δέδεικται πρότερον.
For this will be a time in which it moves, because everything moves in time, and it has been shown before that all time is divisible.
εἰ δʼ ἄρα στιγμὴ κινεῖται, ἔσται τις χρόνος ἐλάττων ἢ ἐν ᾧ αὑτὴν ἐκινήθη.
But if, then, a point moves, there will be some time smaller than that in which it moved itself.
ἀλλὰ ἀδύνατον· ἐν γὰρ τῷ ἐλάττονι ἔλαττον ἀνάγκη κινεῖσθαι.
But this is impossible; for in the smaller time it is necessary to move a smaller distance.
ὥστε ἔσται διαιρετὸν τὸ ἀδιαίρετον εἰς τὸ ἔλαττον, ὥσπερ καὶ ὁ χρόνος εἰς τὸν χρόνον.
Consequently, the indivisible will be divisible into the smaller, just as time is divisible into time.
μοναχῶς γὰρ ἂν κινοῖτο τὸ ἀμερὲς καὶ ἀδιαίρετον, εἰ ἦν ἐν τῷ νῦν κινεῖσθαι δυνατὸν τῷ ἀτόμῳ· τοῦ γὰρ αὐτοῦ λόγου ἐν τῷ νῦν κινεῖσθαι καὶ ἀδιαίρετόν τι κινεῖσθαι.
For the partless and indivisible could move in only one way: if it were possible for the indivisible to move in the 'now'; for to move in the 'now' and for some indivisible thing to move belong to the same argument.
μεταβολὴ δʼ οὐκ ἔστιν οὐδεμία ἄπειρος· ἅποσα γὰρ ἦν ἔκ τινος εἴς τι, καὶ ἡ ἐν ἀντιφάσει καὶ ἡ ἐν ἐναντίοις.
And no change is infinite; for every change was from something to something, both that in contradiction and that in contraries.
ὥστε τῶν μὲν κατʼ ἀντίφασιν ἡ φάσις καὶ ἡ ἀπόφασις πέρας (οἷον γενέσεως μὲν τὸ ὄν, φθορᾶς δὲ τὸ μὴ ὄν), τῶν δʼ ἐν τοῖς ἐναντίοις τὰ ἐναντία·
So that of those in contradiction, affirmation and negation are the limit (for example, of generation, 'being', and of destruction, 'non-being'), and of those in contraries, the contraries are the limit; for these are the extremes of change.
ταῦτα γὰρ ἄκρα τῆς μεταβολῆς, ὥστε καὶ ἀλλοιώσεως πάσης (ἐξ ἐναντίων γάρ τινων ἡ ἀλλοίωσις, ὁμοίως δὲ καὶ αὐξήσεως καὶ φθίσεως· αὐξήσεως μὲν γὰρ τὸ πέρας τοῦ κατὰ τὴν οἰκείαν φύσιν τελείου μεγέθους, φθίσεως δὲ ἡ τούτου ἔκστασις.
Consequently, this is so for all alteration too (for alteration is from certain contraries); and similarly for growth and decay; for the limit of growth is the complete magnitude according to its proper nature, and of decay, the departure from this.
ἡ δὲ φορὰ οὕτω μὲν οὐκ ἔσται πεπερασμένη· οὐ γὰρ πᾶσα ἐν ἐναντίοις·
But locomotion will not be limited in this way; for not all locomotion is between contraries.
ἀλλʼ ἐπειδὴ τὸ ἀδύνατον τμηθῆναι οὕτω, τῷ μὴ ἐνδέχεσθαι τμηθῆναι (πλεοναχῶς γὰρ λέγεται τὸ ἀδύνατον), οὐκ ἐνδέχεται τὸ οὕτως ἀδύνατον τέμνεσθαι, οὐδὲ ὅλως τὸ ἀδύνατον γενέσθαι γίγνεσθαι, οὐδὲ τὸ μεταβαλεῖν ἀδύνατον ἐνδέχοιτʼ ἂν μεταβάλλειν εἰς ὃ ἀδύνατον μεταβαλεῖν.
But since that which is impossible to be cut is impossible in this way, namely by its not being capable of being cut (for 'impossible' is used in several senses), it is not possible for what is impossible in this way to be cut, nor in general for what is impossible to become to be in process of becoming, nor could that which is impossible to change be in process of changing into that into which it is impossible to change.
εἰ οὖν τὸ φερόμενον μεταβάλλοι εἴς τι, καὶ δυνατὸν ἔσται μεταβαλεῖν.
If, then, that which is in locomotion changes into something, it will also be possible for it to change.
ὥστ᾿ οὐκ ἄπειρος ἡ κίνησις, οὐδʼ οἰσθήσεται τὴν ἄπειρον· ἀδύνατον γὰρ δικλθεῖν αὐτήν.
Therefore, its motion is not infinite, nor will it move through an infinite distance; for it is impossible to traverse it.
ὅτι μὲν οὖν οὕτως οὐκ ἔστιν ἄπειρος μεταβολὴ ὥστε μὴ ὡρίσθαι πέρασι, φανερόν.
That, then, change is not infinite in such a way as not to be bounded by limits is clear.
ἀλλʼ εἰ οὕτως ἐνδέχεται ὥστε τῷ χρόνῳ εἶναι ἄπειρον τὴν αὐτὴν οὖσαν καὶ μίαν, σκεπτέον.
But whether it is possible in such a way that the same and single change is infinite in time, must be considered.
μὴ μιᾶς μὲν γὰρ γιγνομένης οὐθὲν ἴσως κωλύει, οἷον εἰ μετὰ τὴν φορὰν ἀλλοίωσις εἴη καὶ μετὰ τὴν ἀλλοίωσιν αὔξησις καὶ πάλιν γένεσις· οὕτω γὰρ αἰεὶ μὲν ἔσται τῷ χρόνῳ κίνησις, ἀλλʼ οὐ μία διὰ τὸ μὴ εἶναι μίαν ἐξ ἁπασῶν.
For if it does not become a single change, nothing perhaps prevents it, as for example if after locomotion there should be alteration, and after alteration growth, and again generation; for in this way there will always be motion in time, but it will not be one motion because there is not a single motion composed of them all.
ὥστε δὲ γίγνεσθαι μίαν, οὐκ ἐνδέχεται ἄπειρον εἶναι τῷ χρόνῳ πλὴν μιᾶς· αὕτη δʼ ἐστὶν ἡ κύκλῳ φορά.
But so as to become a single motion, it is not possible for it to be infinite in time, except for one; and this is locomotion in a circle.

Notes

  1. 15ὁτῳοῦν τῶν κινουμένων — The dative ὁτῳοῦν (from the relative pronoun ὅστις) functions as a dative of interest/possession ('for any of the moving things') modified by the comparative ἐλάττων ('shorter time'). The comparative clause beginning with ἤ ('than') shows that the actual comparison is with the implied time, not with the moving entity itself.
  2. 26τοῦ γὰρ αὐτοῦ λόγου — The genitive τοῦ αὐτοῦ λόγου ('of the same argument/account') functions as a predicate genitive of property or characteristic, taking the subsequent infinitive phrase ἐν τῷ νῦν κινεῖσθαι καὶ ἀδιαίρετόν τι κινεῖσθαι as its subject.
  3. 10δικλθεῖν — The form δικλθεῖν in the text is an obvious typographical error for διελθεῖν, the aorist infinitive of διέρχομαι ('to traverse, go through'), and is translated as such.
  4. 10εἰ οὖν τὸ φερόμενον μεταβάλλοι εἴς τι, καὶ δυνατὸν ἔσται μεταβαλεῖν — A mixed conditional sentence using the optative μεταβάλλοι in the protasis and the future indicative ἔσται in the apodosis, employed to draw a highly confident logical conclusion from a hypothetical assumption.

Cite this passage

Aristotle, Physics §6.10#2. Humanitext Reader, https://reader.humanitext.ai/en/text/urn:cts:greekLit:tlg0086.tlg031.humanitext-grc1:6.10%232

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