§2.5#2Περὶ μὲν οὖν τούτων εἴρηται πρότερον· ὅτι δ᾿ ἐπειδὴ μεταβάλλουσιν εἰς ἄλληλα, ἀδύνατον ἀρχήν τινα εἶναι αὐτῶν ἢ ἐπὶ τῷ ἄκρῳ ἢ μέσῳ, ἐκ τῶνδε δῆλον.
So, about these things it has been said before; but that, since they change into one another, it is impossible for some principle of them to be either at the extreme or in the middle, is clear from the following.
ἐπὶ μὲν οὖν τοῖς ἄκροις οὐκ ἔσται, ὅτι πῦρ ἔσται ἢ γῆ πάντα· καὶ ὁ αὐτὸς λόγος τῷ φάναι ἐκ πυρὸς ἢ γῆς εἶναι πάντα·
On the one hand, then, at the extremes it will not be, because all things would be fire or earth; and this is the same argument as saying that all things are from fire or earth.
ὅτι δ᾿ οὐδὲ μέσον, ὥσπερ δοκεῖ τισὶν ἀὴρ μὲν καὶ εἰς πῦρ μεταβάλλειν καὶ εἰς ὕδωρ, ὕδωρ δὲ καὶ εἰς ἀέρα καὶ εἰς γῆν, τὰ δ᾿ ἔσχατα οὐκέτι εἰς ἄλληλα ἐκ τῶνδε δῆλον1 δεῖ μὲν γὰρ στῆναι καὶ μὴ εἰς ἄπειρον τοῦτο ἰέναι ἐπ᾿ εὐθείας ἐφ᾿ ἑκάτερα· ἄπειροι γὰρ αἱ ἐναντιότητες ἐπὶ τοῦ ἑνὸς ἔσονται.
But that neither is it in the middle, as it seems to some that air indeed changes both into fire and into water, and water both into air and into earth, but the extremes no longer into one another, is clear from the following1; for on the one hand, it is necessary to stop and not for this to go into infinity in a straight line in either direction; for infinite contrarieties will belong to the one.
γῆ ἐφ᾿ ᾧ Γ, ὕδωρ ἐφ᾿ ᾧ Υ, ἀὴρ ἐφ᾿ ᾧ Α, πῦρ ἐφ᾿ ᾧ Π. εἰ δὴ τὸ A μεταβάλλει εἰς τὸ Π καὶ Υ, ἐναντιότης ἔσται τῶν ΑΠ. ἔστω ταῦτα λευκότης καὶ μελανία.
Let earth be represented by Γ, water by Υ, air by Α, fire by Π. If indeed A changes into Π and Y, there will be a contrariety of the ΑΠ. Let these be whiteness and blackness.
πάλιν εἰ εἰς τὸ Υ τὸ Α, ἔσται ἄλλη· οὐ γὰρ ταὐτὸ τὸ καὶ Π. ἔστω δὲ ξηρότης καὶ ὑγρότης, τὸ μὲν Ξ ξηρότης, τὸ δὲ Υ ὑγρότης.
Again, if A changes into Υ, there will be another; for Υ and Π are not the same. Let [them] be dryness and wetness, on the one hand Ξ being dryness, and Υ being wetness.
οὐκοῦν εἰ μὲν μένει τὸ λευκόν, ὑπάρξει τὸ ὕδωρ ὑγρὸν καὶ λευκόν, εἰ δὲ μή, μέλαν ἔσται τὸ ὕδωρ· εἰς τἀναντία γὰρ ἡ μεταβολή.
Therefore, if on the one hand the white remains, the water will be wet and white, but if not, the water will be black; for change is into contraries.
ἀνάγκη ἄρα ἢ λευκὸν ἢ μέλαν εἶναι τὸ ὕδωρ.
It is necessary, therefore, for the water to be either white or black.
ἔστω δὴ τὸ πρῶτον.
Let it indeed be the first.
ὁμοίως τοίνυν καὶ τῷ Π τὸ Ξ ὑπάρξει ἡ ξηρότης.
Likewise, then, also to Π, Ξ (dryness) will belong.
ἔσται ἄρα καὶ τῷ Π τῷ πυρὶ μεταβολὴ εἰς τὸ ὕδωρ· ἐναντία γὰρ ὑπάρχει· τὸ μὲν γὰρ πῦρ τὸ πρῶτον μέλαν ἦν, ἔπειτα δὲ ξηρόν, τὸ δ᾿ ὕδωρ ὑγρόν, ἔπειτα δὲ λευκόν.
Therefore, there will be also for Π (fire) a change into water; for contrary qualities belong; for on the one hand, fire was first black, and then dry; while water was wet, and then white.
φανερὸν δὴ ὅτι πᾶσιν ἐξ ἀλλήλων ἔσται ἡ μεταβολή, καὶ ἐπί γε τούτων, ὅτι καὶ ἐν τῷ Γ τῇ γῇ ὑπάρξει τὰ λοιπὰ καὶ δύο σύμβολα, τὸ μέλαν καὶ τὸ ὑγρόν· ταῦτα γὰρ οὐ συνδεδύασταί πως.
So it is clear that for all there will be change from one another, and indeed in the case of these, that also in Γ (earth) there will belong the remaining and two symbols, the black and the wet; for these have not been coupled in any way.
Ὅτι δ᾿ εἰς ἄπειρον οὐχ οἷόν τ᾿ ἰέναι, ὅπερ μελλήσαντες δείξειν ἐπὶ τοῦτο ἔμπροσθεν ἤλθομεν, δῆλον ἐκ τῶνδε.
But that it is not possible to go to infinity, which we approached previously when we were about to show it, is clear from the following.
εἰ γὰρ πάλιν τὸ πῦρ, ἐφ᾿ Π, εἰς ἄλλο μεταβαλεῖ καὶ μὴ ἀνακάμψει, οἷον εἰς τὸ Ψ, ἐναντιότης τις τῷ πυρὶ καὶ τῷ Ψ ἄλλ ὑπάρξει τῶν εἰρημένων· οὐδενὶ γὰρ τὸ αὐτὸ ὑπόκειται τῶν Γ Υ Α Π τὸ Ψ. ἔστω δὴ τῷ μὲν Π τὸ Κ, τῷ δὲ Ψ τὸ Φ. τὸ δὴ Κ πᾶσιν ὑπάρξει τοῖς Γ Υ Α Π· μεταβάλλουσι γὰρ εἰς ἄλληλα.
For if again the fire, represented by Π, changes into another and does not return, for example into Ψ, some other contrariety besides the ones mentioned will belong to the fire and to Ψ; for to none of the Γ, Υ, Α, Π is Ψ underlying as the same. Let indeed Κ belong to Π, and Φ to Ψ. So indeed Κ will belong to all Γ, Υ, Α, Π; for they change into one another.
ἀλλὰ γὰρ τοῦτο μὲν ἔστω μήπω δεδειγμένον ἀλλ᾿ ἐκεῖνο δῆλον, ὅτι εἰ πάλιν τὸ Ψ εἰς ἄλλο, ἄλλη ἐναντιότης καὶ τῷ Ψ ὑπάρξει καὶ τῷ πυρὶ τῷ Π. ὁμοίως δ᾿ ἀεὶ μετὰ τοῦ προστιθεμένου ἐναντιότης τις ὑπάρξει τοῖς ἔμπροσθεν, ὥστ᾿ εἰ ἄπειρα, καὶ ἐναντιότητες ἄπειροι τῷ ἑνὶ ὑπάρξουσιν.
But indeed, let this on the one hand be not yet shown, but that other thing is clear, that if again Ψ changes into another, another contrariety will belong both to Ψ and to the fire Π. And likewise always, along with the element being added, some contrariety will belong to the preceding ones, so that if they are infinite, infinite contrarieties will also belong to the one.
εἰ δὲ τοῦτο, οὐκ ἔσται οὔτε ὁρίσασθαι οὐδὲν οὔτε γενέσθαι· δεήσει γάρ, εἰ ἄλλο ἔσται ἐξ ἄλλου, τοσαύτας διεξελθεῖν ἐναντιότητας, καὶ ἔτι πλείους, ὥστ᾿ εἰς ἔνια μὲν οὐδέποτ᾿ ἔσται μεταβολή, οἷον εἰ ἄπειρα τὰ μεταξύ· ἀνάγκη δ᾿, εἴπερ ἄπειρα τὰ στοιχεῖα· ἔτι δ᾿ οὐδ᾿ ἐξ ἀέρος εἰς πῦρ, εἰ ἄπειροι αἱ ἐναντιότητες.
And if this is so, it will be possible neither to define anything nor to be generated; for it will be necessary, if one thing is to be from another, to pass through so many contrarieties, and still more, so that for some indeed there will never be change, for instance if the intermediates are infinite; and this is necessary, if indeed the elements are infinite; and furthermore, neither will there be change from air into fire, if the contrarieties are infinite.
γίνεται δὲ καὶ πάντα ἕν· ἀνάγκη γὰρ πάσας ὑπάρχειν τοῖς μὲν κάτω τοῦ Π τὰς τῶν ἄνωθεν, τούτοις δὲ τὰς τῶν κάτωθεν, ὥστε πάντα ἓν ἔσται.
And all things also become one; for it is necessary for all contrarieties of those below Π to belong to those above Π, and to these those of below, so that all things will be one.