§3.5#3Ἀναξαγόρας δʼ
ἀτόπως λέγει περὶ τῆς τοῦ ἀπείρου μονῆς·
Anaxagoras speaks absurdly about the immobility of the infinite; for he says that the infinite itself supports itself.
στηρίζειν γὰρ αὐτὸ αὐτ ό φησιν τὸ ἄπειρον· τοῦτο δέ, ὅτι ἐν αὐτῷ (ἄλλο γὰρ οὐδὲν περιέχειν, ὡς ὅπου ἄν τι ᾖ, πεφυκὸς ἐνταῦθα εἶ.
And this [it does] because it is in itself (for nothing else contains it), on the assumption that wherever anything is, it is by nature to be there.
ναι. τοῦτο δʼ οὐκ ἀληθές· εἴη γὰρ ἄν τί που βιᾶ καὶ οὐχ οὗ πέφυκεν.
But this is not true; for a thing might be somewhere by force and not where it is by nature.
εἰ οὖν ὅτι μάλιστα μὴ κινεῖται τὸ ὅλον (τὸ γὰρ αὐτῷ στηριζόμενον καὶ ἐν αὐτῷ ὄν ἀκίνητον εἶναι ἀνάγκη), ἀλλὰ διὰ τί οὐ πέφυκε κινεῖσθαι, λεκτέον.
Therefore, even if it is ever so true that the whole does not move (for that which is supported by itself and is in itself must be motionless), yet why it is not by nature disposed to move must be explained.
οὐ γὰρ ἱκανὸν τὸ οὕτως εἰπόντα ἀπηλλάχθαι· εἴη γὰρ ἂν καὶ ὅτι οὐκ ἔχει ἀλλαχῆ κινεῖσθαι οὐ κινούμενον, ἀλλὰ πεφυκέναι οὐδὲν κωλύει·
For it is not sufficient to get off by merely speaking thus; for a thing might be not moving also because it has nowhere else to move, but nothing prevents it from having a nature [to move].
ἐπεὶ καὶ ἡ γῇ οὐ φέρεται, οὐδʼ εἰ ἄπειρος ἦν, εἰργμένη μέντοι ὑπὸ τοῦ μέσου ἀλλʼ οὐχ ὅτι οὐκ ἔστιν ἄλλο οὗ ἐνεχθήσεται, μείνειεν ἄν, ἀλλʼ ὅτι πέφυκεν οὕτω.
Since indeed the earth does not travel, not even if it were infinite, being restrained, however, by the center; but it would remain not because there is no other place to which it will be carried, but because it is by nature so.
καίτοι ἐξείη) ἂν λέγειν ὅτι στηρίζει αὐτήν.
And yet it would be open to say that it supports itself.
εἰ οὖν μηδʼ ἐπὶ τῆς γῆς τοῦτο αἴτιον ἀπείρου οὔσης, ἀλλʼ ὅτι βάρος ἔχει, τὸ δὲ βαρὺ μένει ἐπὶ τοῦ μέσου, ἡ δὲ γῆ ἐπὶ τοῦ μέσου, ὁμοίως ἂν καὶ τὸ ἄπει. ρον μένοι ἐν αὐτῷ διά τινʼ ἄλλην αἰτίαν, καὶ οὐχ ὅτι ἄπει. ρον καὶ στηρίζει αὐτὸ ἑαυτό.
If then, not even in the case of the earth, if it were infinite, would this be the cause, but because it has weight, and what is heavy remains at the center, and the earth is at the center, likewise also the infinite would remain in itself because of some other cause, and not because it is infinite and supports itself.
ἅμα δὲ δῆλον ὅτι κἂν ὁτιοῦν μέρος δέοι μένειν· ὡς γὰρ τὸ ἄπειρον ἐν ἑαυτῷ μένει στηρίζον, οὕτως κἂν ὁτιοῦν ληφθῇ μέρος ἐν ἑαυτῷ μενεῖ· τοῦ γὰρ ὅλου καὶ τοῦ μέρους ὁμοειδεῖς οἱ τόποι, οἶον ὅλης γῆς καὶ βώλου κάτω καὶ παντὸς πυρὸς καὶ σπινθῆρος ἄνω.
And at the same time it is clear that any part whatever ought to remain; for as the infinite remains in itself supporting [itself], so also any part whatever that is taken will remain in itself; for the places of the whole and of the part are of uniform kind, for instance, of the whole earth and of a clod down, and of all fire and of a spark up.
ὥστε εἰ τοῦ ἀπείρου τόπος τὸ ἐν αὐτῷ, καὶ τοῦ μέρους ὁ αὐτός.
Consequently, if the place of the infinite is 'in itself', the place of the part is also the same.
μενεῖ ἄρα ἐν ἑαυτῶ.
It will therefore remain in itself.
ὅλως δὲ φανερὸν ὅτι ἀδύνατον ἄπειρον
ἅμα λέγειν σῶμα καὶ τόπον τινὰ εἶναι τοῖς σώμασιν, εἰ πᾶν σῶμα αἰσθητὸν ἢ βάρος ἔχει ἢ κουφότητα, καὶ εἰ μὲν βαρύ, ἐπὶ τὸ μέσον ἔχει τὴν φορὰν φύσει, εἰ δὲ κοῦφον, ἄνω·
And in general it is clear that it is impossible to say at the same time that there is an infinite body and that there is a certain place for bodies, if indeed every sensible body has either weight or lightness, and if heavy, it has its motion naturally toward the center, and if light, upward.
ἀνάγκη γὰρ καὶ τὸ ἄπειρον, ἀδύνατον δὲ ἢ ἅπαν ὁποτερονοῦν ἢ τὸ ἥμισυ ἑκάτερον πεπονθέναι·
For it is necessary that the infinite also [should have this], but it is impossible for either the whole of it to be one of the two, or for each half to have experienced each of the two.
πῶς γὰρ διελεῖς;
For how will you divide it?
ἢ πῶς τοῦ ἀπείρου ἔσται τὸ μὲν ἄνω τὸ δὲ κάτω, ἢ ἔσχατον καὶ μέσον;
Or how will there be of the infinite one part up and another down, or extreme and center?
ἔτι πᾶν σῶμα αἰσθητὸν ἐν τόπῳ, τόπου δὲ εἴδη καὶ διαφοραὶ τἄνω καὶ κάτω καὶ ἔμπροσθεν καὶ ὄπισθεν καὶ δεξιὸν καὶ ἀριστερόν· καὶ ταῦτα οὐ μόνον πρὸς ἡμᾶς καὶ θέσει, ἀλλὰ καὶ ἐν αὐτῷ τῷ ὅλῳ διώρισται.
Furthermore, every sensible body is in a place, and the kinds and differences of place are up and down, and before and behind, and right and left; and these are determined not only in relation to us and by position, but also in the universe itself.
ἀδύνατον δʼ ἐν τῷ ἀπείρῳ εἶναι ταῦτα.
But it is impossible for these to exist in the infinite.
ἀπλῶς δʼ εἰ ἀδύνατον τόπον ἄπειρον εἶναι, ἐν τόπῳ δὲ πᾶν σῶμα, ἀδύνατον ἄπειρον εἶναι σῶμα.
And simply, if it is impossible for place to be infinite, and every body is in a place, it is impossible for a body to be infinite.
ἀλλὰ μὴν τό γε ποὺ ἐν τόπῳ, καὶ τὸ ἐν τόπῳ πού.
But indeed, that which is 'somewhere' is in a place, and that which is in a place is 'somewhere'.
εἰ οὖν μηδὲ ποσὸν οἶόν τʼ εἶναι τὸ ἄπειρον—ποσὸν γὰρ τὶ ἔσται, οἷον δίπηχυ ἢ τρίπηχυ· ταῦτα γὰρ σημαίνει τὸ ποσόν—οὕτω καὶ τὸ ἐν τόπῳ ὅτι πού, τοῦτο δὲ ἢ ἄνω ἢ κάτω ἢ ἐν ἄλλη τινὶ διαστάσει τῶν ἕξ, τούτων δʼ ἕκαστον πέρας τί ἐστιν.
If then, the infinite cannot even be a quantity—for it would be some particular quantity, such as of two cubits or three cubits; for these signify quantity—so also that which is in a place [is signified by] 'somewhere', and this is either up or down or in some other of the six dimensions, and each of these is a certain limit.
ὅτι μὲν οὖν ἐνεργείᾳ οὐκ ἔστι σῶμα ἄπειρον, φανερὸν ἐκ τούτων.
That therefore there is no actually infinite body is clear from these.