§11.10#1τὸ δʼ ἄπειρον ἢ τὸ ἀδύνατον διελθεῖν τῷ μὴ πεφυκέναι διιέναι, καθάπερ ἡ φωνὴ ἀόρατος, ἢ τὸ διέξοδον ἔχον ἀτελεύτητον, ἢ ὃ μόλις, ἢ ὃ πεφυκὸς ἔχειν μὴ ἔχει διέξοδον ἢ πέρας·
The infinite is either that which is impossible to go through because it is not its nature to be gone through (just as voice is invisible), or that which has a passage that is endless, or that which is scarcely gone through, or that which, though having a nature to have a passage or limit, does not have one.
ἔτι προσθέσει ἢ ἀφαιρέσει ἢ ἄμφω.
Further, it is so by addition or by subtraction or by both.
χωριστὸν μὲν δὴ αὐτό τι ὂν οὐχ οἷόν τʼ εἶναι·
Now, it is impossible for the infinite to exist as something separate, itself being a certain entity.
εἰ γὰρ μήτε μέγεθος μήτε πλῆθος, οὐσία δʼ αὐτὸ τὸ ἄπειρον καὶ μὴ συμβεβηκός, ἀδιαίρετον ἔσται (τὸ γὰρ διαιρετὸν ἢ μέγεθος ἢ πλῆθος), εἰ δὲ ἀδιαίρετον, οὐκ ἄπειρον, εἰ μὴ καθάπερ ἡ φωνὴ ἀόρατος·
For if it is neither a magnitude nor a plurality, but the infinite itself is a substance and not an accident, it will be indivisible (for that which is divisible is either a magnitude or a plurality); but if it is indivisible, it is not infinite, except in the way that voice is invisible.
ἀλλʼ οὐχ οὕτω λέγουσιν οὐδʼ ἡμεῖς ζητοῦμεν, ἀλλʼ ὡς ἀδιέξοδον.
But this is not what people mean by it, nor what we are investigating, but rather as that which cannot be gone through.
ἔτι πῶς ἐνδέχεται καθʼ αὑτὸ εἶναι ἄπειρον, εἰ μὴ καὶ ἀριθμὸς καὶ μέγεθος, ὧν πάθος τὸ ἄπειρον;
Further, how is it possible for the infinite to exist in itself, if number and magnitude (of which the infinite is an attribute) do not also exist so?
ἔτι εἰ κατὰ συμβεβηκός, οὐκ ἂν εἴη στοιχεῖον τῶν ὄντων ᾗ ἄπειρον, ὥσπερ οὐδὲ τὸ ἀόρατον τῆς διαλέκτου, καίτοι ἡ φωνὴ ἀόρατος.
Further, if it exists by accident, it would not be an element of existing things insofar as it is infinite, just as the invisible is not an element of speech, although voice is invisible.
καὶ ὅτι οὐκ ἔστιν ἐνεργείᾳ εἶναι τὸ ἄπειρον, δῆλον.
And that the infinite cannot exist in actuality is clear.
ἔσται γὰρ ὁτιοῦν αὐτοῦ ἄπειρον μέρος τὸ λαμβανόμενον (τὸ γὰρ ἀπείρῳ εἶναι καὶ ἄπειρον τὸ αὐτό, εἴπερ οὐσία τὸ ἄπειρον καὶ μὴ καθʼ ὑποκειμένου), ὥστε ἢ ἀδιαίρετον, ἢ εἰς ἄπειρα διαιρετόν, εἰ μεριστόν·
For any part of it that is taken will be infinite (for to be infinite and the infinite are the same, if the infinite is a substance and is not predicated of a substrate); so that it is either indivisible, or divisible into infinites, if it is divisible into parts.
πολλὰ δʼ εἶναι τὸ αὐτὸ ἀδύνατον ἄπειρα (ὥσπερ γὰρ ἀέρος ἀὴρ μέρος, οὕτως ἄπειρον ἀπείρου, εἰ ἔστιν οὐσία καὶ ἀρχή)· ἀμέριστον ἄρα καὶ ἀδιαίρετον.
But it is impossible for the same thing to be many infinites (for just as a part of air is air, so a part of the infinite would be infinite, if it is a substance and a principle); therefore it is partless and indivisible.
ἀλλὰ ἀδύνατον τὸ ἐντελεχείᾳ ὂν ἄπειρον (ποσὸν γὰρ εἶναι ἀνάγκη)· κατὰ συμβεβηκὸς ἄρα ὑπάρχει.
But the infinite existing in complete reality is impossible (for it must be a quantity); therefore it exists by accident.
ἀλλʼ εἰ οὕτως, εἴρηται ὅτι οὐκ ἐνδέχεται εἶναι ἀρχήν, ἀλλʼ ἐκεῖνο ᾧ συμβέβηκε, τὸν ἀέρα ἢ τὸ ἄρτιον. —αὕτη μὲν οὖν ἡ ζήτησις καθόλου, ὅτι δʼ ἐν τοῖς αἰσθητοῖς οὐκ ἔστιν, ἐνθένδε δῆλον· εἰ γὰρ σώματος λόγος τὸ ἐπιπέδοις ὡρισμένον, οὐκ εἴη ἂν ἄπειρον σῶμα οὔτʼ αἰσθητὸν οὔτε νοητόν, οὐδʼ ἀριθμὸς ὡς κεχωρισμένος καὶ ἄπειρος· ἀριθμητὸν γὰρ ὁ ἀριθμὸς ἢ τὸ ἔχον ἀριθμόν.
But if so, it has been said that it cannot be a principle, but rather that to which it is accidental, such as air or the even.— This inquiry, then, is universal; but that the infinite is not among sensible things is clear from this: for if the definition of a body is that which is bounded by surfaces, there could not be an infinite body, whether sensible or intelligible, nor a number as separate and infinite; for number is that which is countable or that which has number.
φυσικῶς δὲ ἐκ τῶνδε δῆλον· οὔτε γὰρ σύνθετον οἷόν τʼ εἶναι οὔθʼ ἁπλοῦν.
And from a physical point of view, it is clear from the following: for it can be neither composite nor simple.
σύνθετον μὲν γὰρ οὐκ ἔσται σῶμα, εἰ πεπέρανται τῷ πλήθει τὰ στοιχεῖα (δεῖ γὰρ ἰσάζειν τὰ ἐναντία καὶ μὴ εἶναι ἓν αὐτῶν ἄπειρον· εἰ γὰρ ὁτῳοῦν λείπεται ἡ θατέρου σώματος δύναμις, φθαρήσεται ὑπὸ τοῦ ἀπείρου τὸ πεπερασμένον· ἕκαστον δʼ ἄπειρον εἶναι ἀδύνατον, σῶμα γάρ ἐστι τὸ πάντῃ ἔχον διάστασιν, ἄπειρον δὲ τὸ ἀπεράντως διεστηκός, ὥστʼ εἰ τὸ ἄπειρον σῶμα, πάντῃ ἔσται ἄπειρον)· οὐδὲ ἓν δὲ καὶ ἁπλοῦν ἐνδέχεται τὸ ἄπειρον εἶναι σῶμα, οὔθʼ ὡς λέγουσί τινες, παρὰ τὰ στοιχεῖα ἐξ οὗ γεννῶσι ταῦτα (οὐκ ἔστι γὰρ τοιοῦτο σῶμα παρὰ τὰ στοιχεῖα·
For it will not be a composite body if the elements are limited in multitude (for the contraries must be equalized and one of them must not be infinite; for if the power of one of the bodies is in any way deficient, the finite will be destroyed by the infinite; and it is impossible for each to be infinite, for a body is that which has dimension in every direction, and the infinite is that which is infinitely extended, so that if the body is infinite, it will be infinite in every direction); nor is it possible for the infinite body to be one and simple, nor, as some say, that which is apart from the elements, from which they generate these (for there is no such body apart from the elements).