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Aristotle · Metaphysics §11.10#2

Impossibility of Infinite Sensible Bodies from Place and Motion

Passage 119 of 159 · Greek

Summary

In the second half of this chapter, the existence of an infinite sensible body is rejected from various physical standpoints, including the nature of elements, the concept of place and directions, and the conceptual dependency of the infinite in motion and time upon magnitude.

§11.10#2ἅπαν γάρ, ἐξ οὗ ἐστί, καὶ διαλύεται εἰς τοῦτο, οὐ φαίνεται δὲ τοῦτο παρὰ τὰ ἁπλᾶ σώματα), οὐδὲ πῦρ οὐδʼ ἄλλο τῶν στοιχείων οὐθέν· χωρὶς γὰρ τοῦ ἄπειρον εἶναί τι αὐτῶν, ἀδύνατον τὸ ἅπαν, κἂν ᾖ πεπερασμένον, ἢ εἶναι ἢ γίγνεσθαι ἕν τι αὐτῶν, ὥσπερ Ἡράκλειτός φησιν ἅπαντα γίγνεσθαί ποτε πῦρ.
(for everything is dissolved into that of which it consists, and no such thing appears apart from the simple bodies). Nor is it fire or any other of the elements; for apart from any of them being infinite, it is impossible for the whole, even if it is finite, either to be or to become any one of them, as Heraclitus says that all things at some time become fire.
ὁ δʼ αὐτὸς λόγος καὶ ἐπὶ τοῦ ἑνὸς ὃ ποιοῦσι παρὰ τὰ στοιχεῖα οἱ φυσικοί· πᾶν γὰρ μεταβάλλει ἐξ ἐναντίου, οἷον ἐκ θερμοῦ εἰς ψυχρόν. —ἔτι τὸ αἰσθητὸν σῶμα πού, καὶ ὁ αὐτὸς τόπος ὅλου καὶ μορίου, οἷον τῆς γῆς, ὥστʼ εἰ μὲν ὁμοειδές, ἀκίνητον ἔσται ἢ ἀεὶ οἰσθήσεται, τοῦτο δὲ ἀδύνατον (τί γὰρ μᾶλλον κάτω ἢ ἄνω ἢ ὁπουοῦν;
The same argument applies also to the one which the physicists posit apart from the elements; for everything changes from the contrary, as from hot to cold. —Further, a sensible body is somewhere, and the place of the whole and of the part is the same (for instance, of earth); so that if it is homogeneous, it will be either motionless or always in motion. But this is impossible (for why should it move down rather than up, or anywhere else?
οἷον εἰ βῶλος εἴη, ποῦ αὕτη κινήσεται ἢ μενεῖ;
For instance, if there were a clod of earth, where will it move or remain?
ὁ γὰρ τόπος τοῦ συγγενοῦς αὐτῇ σώματος ἄπειρος·
For the place of the body akin to it is infinite.
καθέξει οὖν τὸν ὅλον τόπον;
Will it then occupy the whole place?
καὶ πῶς;
And how?
τίς οὖν ἡ μονὴ καὶ ἡ κίνησις;
What then is its rest and its motion?
ἢ πανταχοῦ μενεῖ—οὐ κινηθήσεται ἄρα, ἢ πανταχοῦ κινηθήσεται —οὐκ ἄρα στήσεται)·
Or will it remain everywhere—and so not move, or move everywhere —and so not stop?).
εἰ δʼ ἀνόμοιον τὸ πᾶν, ἀνόμοιοι καὶ οἱ τόποι, καὶ πρῶτον μὲν οὐχ ἓν τὸ σῶμα τοῦ παντὸς ἀλλʼ ἢ τῷ ἅπτεσθαι, εἶτα ἢ πεπερασμένα ταῦτʼ ἔσται ἢ ἄπειρα εἴδει.
And if the whole is heterogeneous, the places are also heterogeneous, and first, the body of the whole is not one except by contact, and next, these will be either finite or infinite in species.
πεπερασμένα μὲν οὖν οὐχ οἷόν τε (ἔσται γὰρ τὰ μὲν ἄπειρα τὰ δʼ οὔ, εἰ τὸ πᾶν ἄπειρον, οἷον πῦρ ἢ ὕδωρ· φθορὰ δὲ τὸ τοιοῦτον τοῖς ἐναντίοις)·
Now they cannot be finite (for some will be infinite and others not, if the whole is infinite, such as fire or water; but such a state is destruction to their contraries).
εἰ δʼ ἄπειρα καὶ ἁπλᾶ, καὶ οἱ τόποι ἄπειροι καὶ ἔσται ἄπειρα στοιχεῖα·
And if they are infinite and simple, the places are also infinite and there will be infinitely many elements.
εἰ δὲ τοῦτʼ ἀδύνατον καὶ οἱ τόποι πεπερασμένοι, καὶ τὸ πᾶν ἀνάγκη πεπεράνθαι.
But if this is impossible and the places are finite, the whole must also be finite.
ὅλως δʼ ἀδύνατον ἄπειρον εἶναι σῶμα καὶ τόπον τοῖς σώμασιν, εἰ πᾶν σῶμα αἰσθητὸν ἢ βάρος ἔχει ἢ κουφότητα· ἢ γὰρ ἐπὶ τὸ μέσον ἢ ἄνω οἰσθήσεται, ἀδύνατον δὲ τὸ ἄπειρον ἢ πᾶν ἢ τὸ ἥμισυ ὁποτερονοῦν πεπονθέναι·
In general, it is impossible for there to be an infinite body and a place for bodies, if every sensible body has either weight or lightness; for it will move either toward the center or upward, but it is impossible for the infinite, whether as a whole or as a half, to be affected in either way.
πῶς γὰρ διελεῖς;
For how will you divide it?
ἢ πῶς τοῦ ἀπείρου ἔσται τὸ μὲν κάτω τὸ δʼ ἄνω, ἢ ἔσχατον καὶ μέσον;
Or how can there be a down and an up, or an extremity and a center, in the infinite?
ἔτι πᾶν σῶμα αἰσθητὸν ἐν τόπῳ, τόπου δὲ εἴδη ἕξ, ἀδύνατον δʼ ἐν τῷ ἀπείρῳ σώματι ταῦτʼ εἶναι.
Further, every sensible body is in a place, and there are six kinds of place, but it is impossible for these to exist in an infinite body.
ὅλως δʼ εἰ ἀδύνατον τόπον ἄπειρον εἶναι, καὶ σῶμα ἀδύνατον· τὸ γὰρ ἐν τόπῳ πού, τοῦτο δὲ σημαίνει ἢ ἄνω ἢ κάτω ἢ τῶν λοιπῶν τι, τούτων δʼ ἕκαστον πέρας τι.
In general, if it is impossible for place to be infinite, it is also impossible for body to be so; for that which is in a place is somewhere, and this means either up or down or some of the other directions, and each of these is a limit.
τὸ δʼ ἄπειρον οὐ ταὐτὸν ἐν μεγέθει καὶ κινήσει καὶ χρόνῳ ὡς μία τις φύσις, ἀλλὰ τὸ ὕστερον λέγεται κατὰ τὸ πρότερον, οἷον κίνησις κατὰ τὸ μέγεθος ἐφʼ οὗ κινεῖται ἢ ἀλλοιοῦται ἢ αὔξεται, χρόνος δὲ διὰ τὴν κίνησιν.
But the infinite is not the same in magnitude, motion, and time, as if it were a single nature; rather, the posterior is so called in virtue of the prior, for instance, motion is called infinite in virtue of the magnitude over which it moves or alters or increases, and time in virtue of the motion.

Notes

  1. 1067a1χωρὶς γὰρ τοῦ ἄπειρον εἶναί τι αὐτῶν — The preposition χωρίς governs the genitive articular infinitive phrase τοῦ ἄπειρον εἶναί τι αὐτῶν. τι serves as the subject accusative of the infinitive εἶναι, expressing a conditional reservation, i.e., 'independently of any of them being infinite.'
  2. 1067a8ὥστʼ εἰ μὲν ὁμοειδές, ἀκίνητον ἔσται ἢ ἀεὶ οἰσθήσεται — In the conditional clause εἰ μὲν ὁμοειδές, the subject σῶμα (or τὸ πᾶν) is omitted. In a homogeneous infinite body, since the proper place of a part is identical with that of the whole, all directions are equal, leading to the dilemma that it must either remain entirely motionless (ἀκίνητον) or be in perpetual motion (ἀεὶ οἰσθήσεται).
  3. 1067a25ἀδύνατον δὲ τὸ ἄπειρον ἢ πᾶν ἢ τὸ ἥμισυ ὁποτερονοῦν πεπονθέναι — The subject of the infinitive πεπονθέναι (perfect of πάσχω) is the accusative τὸ ἄπειρον, with ἢ πᾶν ἢ τὸ ἥμισυ ὁποτερονοῦν ('either as a whole or as a half') inserted in apposition. It shows the logical structure that it is impossible for an infinite entity to undergo or possess directional motions under either of these descriptions.
  4. 1067a33τὸ δʼ ἄπειρον οὐ ταὐτὸν... ἀλλὰ τὸ ὕστερον λέγεται κατὰ τὸ πρότερον — The 'prior' (πρότερον) in the prepositional phrase κατὰ τὸ πρότερον refers to 'magnitude' (μέγεθος), while the 'posterior' (ὕστερον) refers to 'motion' (κίνησις) and 'time' (χρόνος). This explains the dependency (κατά) where infinity belongs primarily to magnitude, and is only secondarily or derivatively predicated of motion and time.

Cite this passage

Aristotle, Metaphysics §11.10#2. Humanitext Reader, https://reader.humanitext.ai/en/text/urn:cts:greekLit:tlg0086.tlg025.humanitext-grc2:11.10%232

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