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Aristotle · Physics §1.4#2

Limits of Size and the Critique of Anaxagoras

Passage 7 of 113 · Greek

Summary

Aristotle argues that living things and their parts have upper and lower limits of size, criticizing Anaxagoras' theory of infinite division and the mixture of all things in all things on both quantitative and qualitative grounds, concluding that principles should be finite.

§1.4#2ἔτι δʼ εἰ ἀνάγκη, οὗ τὸ μόριον ἐνδέχεται ὀπηλικονοῦν εἶναι κατὰ μέγεθος καὶ μικρότητα, καὶ αὐτὸ ἐνδέχεσθαι (λέγω δὲ τῶν τοιούτων τι μορίων, εἰς ὃ ἐνυπάρχον διαιρεῖται τὸ ὅλον), εἰ δὴ ἀδύνατον ζῷον ἢ φυτὸν ὁπηλικονοῦν εἶναι κατὰ μέγεθος καὶ μικρότητα, φανερὸν ὅτι οὐδὲ τῶν μορίων ὁτιοῦν· ἔσται γὰρ καὶ τὸ ὅλον ὁμοίως.
Furthermore, if it is necessary that, of whatever the part can be of any size whatsoever in magnitude and smallness, the whole itself can also be so (and I mean by 'part' of such things, that which is present in the whole and into which the whole is divided); if, then, it is impossible for an animal or a plant to be of any size whatsoever in magnitude and smallness, it is clear that neither can any of its parts be so; for the whole too will be likewise.
σὰρξ δὲ καὶ ὀστοῦν καὶ τὰ τοιαῦτα μόρια ζῴου, καὶ οἱ καρποὶ τῶν φυτῶν.
But flesh and bone and such things are parts of an animal, and fruits are parts of plants.
δῆλον τοίνυν ὅτι ἀδύνατον σάρκα ἢ ὀστοῦν ἢ ἄλλο τι ὁπηλικονοῦν εἶναι τὸ μέγεθος ἢ ἐπὶ τὸ μεῖζον ἢ ἐπὶ τὸ ἔλαττον.
It is clear, therefore, that it is impossible for flesh or bone or anything else to be of any size whatsoever, either in the direction of the greater or of the less.
ἔτι εἰ πάντα μὲν ἐνυπάρχει τὰ τοιαῦτα ἐν ἀλλήλοις, καὶ μὴ γίγνεται ἀλλʼ ἐκκρίνεται ἐνόντα, λέγεται δὲ ἀπὸ τοῦ πλείονος, γίγνεται δὲ ἐξ ὁτουοῦν ὁτιοῦν (οἷον ἐκ σαρκὸς ὕδωρ ἐκκρινόμενον καὶ σὰρξ ἐξ ὕδατος), ἅπαν δὲ σῶμα πεπερασμένον ἀναιρεῖται ὑπὸ σώματος πεπερασμένου, φανερὸν ὅτι οὐκ ἐνδέχεται ἐν ἑκάστῳ ἕκαστον ὑπάρχειν.
Furthermore, if all such things are present in one another, and they do not come to be but are separated out from what is present, and a thing is named after that which is more abundant, and anything comes to be from anything (as water is separated out from flesh and flesh from water), and every finite body is exhausted by a finite body, it is clear that it is not possible for everything to be present in everything.
ἀφαιρεθείσης γὰρ ἐκ τοῦ ὕδατος σαρκός, καὶ πάλιν ἄλλης γενομένης ἐκ τοῦ λοιποῦ ἀποκρίσει, εἰ καὶ ἀεὶ ἐλάττων ἔσται ἡ ἐκκρινομένη, ἀλλʼ ὅμως οὐχ ὑπερβαλεῖ μέγεθός τι τῇ μικρότητι.
For if flesh is subtracted from the water, and again another portion is produced from the remainder by separation, even if the portion separated is always smaller, yet it will not exceed a certain magnitude in its smallness.
ὥστʼ εἰ μὲν στήσεται ἡ ἔκκρισις, οὐχ ἅπαν ἐν παντὶ ἐνέσται (ἐν γὰρ τῷ λοιπῷ ὕδατι οὐκ ἐνυπάρξει σάρξ), εἰ δὲ μὴ στήσεται ἀλλʼ ἀεὶ ἕξει ἀφαίρεσιν, ἐν πεπερασμένῳ μεγέθει ἴσα πεπερασμένα ἐνέσται ἄπειρα τὸ πλῆθος· τοῦτο δʼ ἀδύνατον.
So that, if the separation is going to stop, not everything will be in everything (for in the remaining water there will be no flesh present); while if it does not stop but will always have a subtraction, there will be present in a finite magnitude an infinite number of equal finite parts; but this is impossible.
πρὸς δὲ τούτοις, εἰ ἅπαν μὲν σῶμα ἀφαιρεθέντος τινὸς ἔλαττον ἀνάγκη γίγνεσθαι, τῆς δὲ σαρκὸς ὥρισται τὸ ποσὸν καὶ μεγέθει καὶ μικρότητι, φανερὸν ὅτι ἐκ τῆς ἐλαχίστης σαρκὸς οὐθὲν ἐκκριθήσεται σῶμα· ἔσται γὰρ ἐλάττων τῆς ἐλαχίστης.
In addition to these, if every body, when something is subtracted from it, must become smaller, and the quantity of flesh is limited both in magnitude and smallness, it is clear that from the smallest flesh no body will be separated out; for it would be smaller than the smallest.
ἔτι δʼ ἐν τοῖς ἀπείροις σώμασιν ἐνυπάρχοι ἂν ἤδη σὰρξ ἄπειρος καὶ οἷμα καὶ ἐγκέφαλος, κεχωρισμένα μέντοι ἀπʼ ἀλλήλων οὔ, οὐθὲν δʼ ἧττον ὄντα, καὶ ἄπειρον ἕκαστον· τοῦτο δʼ ἄλογον.
Furthermore, in those infinite bodies there would already be present infinite flesh and blood and brain, not indeed separated from each other, but nonetheless existing, and each infinite in quantity; but this is irrational.
τὸ δὲ μηδέποτε διακριθήσεσθαι οὐκ εἰδότως μὲν λέγεται, ὀρθῶς δὲ λέγεται· τὰ γὰρ πάθη ἀχώριστα· εἰ οὖν μέμικται τὰ χρώματα καὶ αἱ ἕξεις, ἐὰν διακριθῶσιν, ἔσται τι λευκὸν καὶ ὑγιεινὸν οὐχ ἕτερόν τι ὂν οὐδὲ καθʼ ὑποκειμένου.
And the statement that they will never be completely separated, though said without knowledge of the reason, is said correctly; for affections are inseparable; if, then, the colours and states are mixed, if they should be separated, there will be something 'white' and 'healthy' which is not anything else nor belonging to any subject.
ὥστε ἄτοπος τὰ ἀδύνατα ζητῶν ὁ νοῦς, εἶπερ βούλεται μὲν διακρῖναι, τοῦτο δὲ ποιῆσαι ἀδύνατον καὶ κατὰ τὸ ποσὸν καὶ κατὰ τὸ ποιόν, κατὰ μὲν τὸ ποσὸν ὅτι οὐκ ἔστιν ἐλάχιστον μέγεθος, κατὰ δὲ τὸ ποιὸν ὅτι ἀχώριστα τὰ πάθη.
So that the mind is absurd in seeking the impossible, if it indeed wants to separate them, but to do this is impossible both in quantity and in quality—in quantity because there is no least magnitude, and in quality because affections are inseparable.
οὐκ ὀρθῶς δὲ οὐδὲ τὴν γένεσιν λαμβάνει τῶν ὁμοειδῶν.
Nor does he correctly understand the coming to be of things of the same kind.
ἔστι μὲν γὰρ ὡς ὁ πηλὸς εἰς πηλοὺς διαιρεῖται, ἔστι δʼ ὡς οὕ.
For there is a sense in which clay is divided into clays, but there is also a sense in which it is not.
καὶ οὐχ ὁ αὐτὸς τρόπος, ὡς πλίνθοι ἐξ οἰκίας καὶ οἰκία ἐκ πλίνθων, οὕτω καὶ ὕδωρ καὶ ἀὴρ ἐξ ἀλλήλων καὶ εἰσὶ καὶ γίγνονται.
And it is not the same way as bricks come from a house and a house from bricks, that water and air both exist and come to be from each other.
βέλτιόν τε ἐλάττω καὶ πεπερασμένα λαβεῖν, ὅπερ ποιεῖ Ἐμπεδοκλῆς.
And it is better to assume fewer and finite principles, which is what Empedocles does.

Notes

  1. ¦15¦ἔτι δʼ εἰ ἀνάγκη, οὗ τὸ μόριον ἐνδέχεται ὀπηλικονοῦν εἶναι κατὰ μέγεθος καὶ μικρότητα, καὶ αὐτὸ ἐνδέχεσθαι — A double conditional structure meaning "if it is necessary that, of whatever the part can be of any size in magnitude and smallness, the whole itself also can be so". Here `οὗ` is a genitive relative pronoun referring to the implied antecedent of `αὐτό` (the whole itself), and `ἐνδέχεσθαι` is an infinitive depending on `ἀνάγκη`.
  2. ¦30¦οὐχ ὑπερβαλεῖ μέγεθός τι τῇ μικρότητι — The phrase "will not exceed a certain magnitude in its smallness". `τῇ μικρότητι` is a dative of respect. Literally, "it will not exceed a certain magnitude in respect of smallness," which means that no matter how small the separated parts become, they cannot go beyond a certain minimum size (i.e., there is a physical limit below which they cannot decrease).
  3. ¦5¦τὸ δὲ μηδέποτε διακριθήσεσθαι οὐκ εἰδότως μὲν λέγεται, ὀρθῶς δὲ λέγεται — The subject of the sentence is the articular future infinitive clause `τὸ ... διακριθήσεσθαι` ("the statement that they will never be completely separated"). The contrast between `οὐκ εἰδότως` ("without knowing the reason" or "unconsciously") and `ὀρθῶς` ("correctly") shows Aristotle's critical evaluation: Anaxagoras' conclusion that complete separation is impossible is correct, but he himself did not understand the true ontological reason (that affections cannot be separated from substance).

Cite this passage

Aristotle, Physics §1.4#2. Humanitext Reader, https://reader.humanitext.ai/en/text/urn:cts:greekLit:tlg0086.tlg031.humanitext-grc1:1.4%232

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