§10.5ἐπεὶ δὲ ἓν ἑνὶ ἐναντίον, ἀπορήσειεν ἄν τις πῶς ἀντίκειται τὸ ἓν καὶ τὰ πολλά, καὶ τὸ ἴσον τῷ μεγάλῳ καὶ τῷ μικρῷ.
Since one thing is contrary to one thing, one might puzzle how the one and the many are opposed, and also the equal to the great and the small.
εἰ γὰρ τὸ πότερον ἀεὶ ἐν ἀντιθέσει λέγομεν, οἷον πότερον λευκὸν ἢ μέλαν, καὶ πότερον λευκὸν ἢ οὐ λευκόν (πότερον δὲ ἄνθρωπος ἢ λευκὸν οὐ λέγομεν, ἐὰν μὴ ἐξ ὑποθέσεως καὶ ζητοῦντες οἷον πότερον ἦλθε Κλέων ἢ Σωκράτης—ἀλλʼ οὐκ ἀνάγκη ἐν οὐδενὶ γένει τοῦτο· ἀλλὰ καὶ τοῦτο ἐκεῖθεν ἐλήλυθεν· τὰ γὰρ ἀντικείμενα μόνα οὐκ ἐνδέχεται ἅμα ὑπάρχειν, ᾧ καὶ ἐνταῦθα χρῆται ἐν τῷ πότερος ἦλθεν· εἰ γὰρ ἅμα ἐνεδέχετο, γελοῖον τὸ ἐρώτημα· εἰ δέ, καὶ οὕτως ὁμοίως ἐμπίπτει εἰς ἀντίθεσιν, εἰς τὸ ἓν ἢ πολλά, οἷον πότερον ἀμφότεροι ἦλθον ἢ ἅτερος)· —εἰ δὴ ἐν τοῖς ἀντικειμένοις ἀεὶ τοῦ ποτέρου ἡ ζήτησις, λέγεται δὲ πότερον μεῖζον ἢ ἔλαττον ἢ ἴσον, τίς ἐστιν ἡ ἀντίθεσις πρὸς ταῦτα τοῦ ἴσου;
For if we always speak of "which of the two" in an opposition, as for instance "which of the two, white or black," and "which of the two, white or not-white" (but we do not say "which of the two, a man or white," unless under some hypothesis and when inquiring, as for instance "which of the two came, Cleon or Socrates?"—but this is not necessary in any genus; yet even this has come from there: for only opposed things cannot be present together, which is what is used here too in "which of the two came"; for if it were possible for them to be together, the question would be ridiculous; but if not, even so it similarly falls into an opposition, into the one or the many, as for instance "which of the two, did both come or one of them?")— if, then, the inquiry of "which of the two" is always in opposed things, and we speak of "which of the two, greater or less or equal," what is the opposition of the equal to these?
οὔτε γὰρ θατέρῳ μόνῳ ἐναντίον οὔτʼ ἀμφοῖν· τί γὰρ μᾶλλον τῷ μείζονι ἢ τῷ ἐλάττονι;
For it is contrary neither to one of them alone nor to both; for why to the greater rather than to the less?
ἔτι τῷ ἀνίσῳ ἐναντίον τὸ ἴσον, ὥστε πλείοσιν ἔσται ἢ ἑνί.
Furthermore, the equal is contrary to the unequal, so that it will be contrary to more than one thing.
εἰ δὲ τὸ ἄνισον σημαίνει τὸ αὐτὸ ἅμα ἀμφοῖν, εἴη μὲν ἂν ἀντικείμενον ἀμφοῖν (καὶ ἡ ἀπορία βοηθεῖ τοῖς φάσκουσι τὸ ἄνισον δυάδα εἶναι), ἀλλὰ συμβαίνει ἓν δυοῖν ἐναντίον· ὅπερ ἀδύνατον.
But if the unequal signifies the same thing at the same time for both, it would be opposed to both (and this difficulty helps those who assert that the unequal is a dyad), but the result is that one thing is contrary to two things, which is impossible.
ἔτι τὸ μὲν ἴσον μεταξὺ φαίνεται μεγάλου καὶ μικροῦ, ἐναντίωσις δὲ μεταξὺ οὐδεμία οὔτε φαίνεται οὔτε ἐκ τοῦ ὁρισμοῦ δυνατόν· οὐ γὰρ ἂν εἴη τελεία μεταξύ τινος οὖσα, ἀλλὰ μᾶλλον ἔχει ἀεὶ ἑαυτῆς τι μεταξύ.
Furthermore, the equal appears to be intermediate between the great and the small, but no contrariety is intermediate, nor is it possible from the definition; for it would not be complete if it were intermediate between something, but rather it always has some intermediate of its own.
λείπεται δὴ ἢ ὡς ἀπόφασιν ἀντικεῖσθαι ἢ ὡς στέρησιν.
It remains, then, that it is opposed either as a negation or as a privation.
θατέρου μὲν δὴ οὐκ ἐνδέχεται (τί γὰρ μᾶλλον τοῦ μεγάλου ἢ μικροῦ; )· ἀμφοῖν ἄρα ἀπόφασις στερητική, διὸ καὶ πρὸς ἀμφότερα τὸ πότερον λέγεται, πρὸς δὲ θάτερον οὔ (οἷον πότερον μεῖζον ἢ ἴσον, ἢ πότερον ἴσον ἢ ἔλαττον), ἀλλʼ ἀεὶ τρία.
Now it is not possible for it to be opposed to one of them alone (for why to the great rather than to the small?); it is, therefore, a privative negation of both, which is why "which of the two" is spoken of in relation to both, but not to one of them alone (as for instance "which of the two, greater or equal," or "which of the two, equal or less"), but always three.
οὐ στέρησις δὲ ἐξ ἀνάγκης· οὐ γὰρ πᾶν ἴσον ὃ μὴ μεῖζον ἢ ἔλαττον, ἀλλʼ ἐν οἷς πέφυκεν ἐκεῖνα. —ἔστι δὴ τὸ ἴσον τὸ μήτε μέγα μήτε μικρόν, πεφυκὸς δὲ ἢ μέγα ἢ μικρὸν εἶναι· καὶ ἀντίκειται ἀμφοῖν ὡς ἀπόφασις στερητική, διὸ καὶ μεταξύ ἐστιν.
But it is not a privation of necessity; for not everything that is neither greater nor less is equal, but only those things in which these are by nature present. —The equal, then, is that which is neither great nor small, but is by nature capable of being great or small; and it is opposed to both as a privative negation, which is why it is also intermediate.
καὶ τὸ μήτε ἀγαθὸν μήτε κακὸν ἀντίκειται ἀμφοῖν, ἀλλʼ ἀνώνυμον· πολλαχῶς γὰρ λέγεται ἑκάτερον καὶ οὐκ ἔστιν ἓν τὸ δεκτικόν, ἀλλὰ μᾶλλον τὸ μήτε λευκὸν μήτε μέλαν.
And that which is neither good nor bad is opposed to both, but is nameless; for each of these is spoken of in many ways and their receptive recipient is not one, but rather that which is neither white nor black.
ἓν δὲ οὐδὲ τοῦτο λέγεται, ἀλλʼ ὡρισμένα πως ἐφʼ ὧν λέγεται στερητικῶς ἡ ἀπόφασις αὕτη· ἀνάγκη γὰρ ἢ φαιὸν ἢ ὠχρὸν εἶναι ἢ τοιοῦτόν τι ἄλλο.
But even this is not spoken of as one thing, but those things of which this negation is spoken privatively are determined in a way; for it is necessary to be either grey or pale yellow or some other such thing.
ὥστε οὐκ ὀρθῶς ἐπιτιμῶσιν οἱ νομίζοντες ὁμοίως λέγεσθαι πάντα, ὥστε ἔσεσθαι ὑποδήματος καὶ χειρὸς μεταξὺ τὸ μήτε ὑπόδημα μήτε χεῖρα, ἔπειπερ καὶ τὸ μήτε ἀγαθὸν μήτε κακὸν τοῦ ἀγαθοῦ καὶ τοῦ κακοῦ, ὡς πάντων ἐσομένου τινὸς μεταξύ.
So those who believe that all things are spoken of similarly are not right in their criticism, so that there would be an intermediate between a shoe and a hand, namely that which is neither a shoe nor a hand, since that which is neither good nor bad is intermediate between the good and the bad, as though there would be some intermediate of all things.
οὐκ ἀνάγκη δὲ τοῦτο συμβαίνειν.
But it is not necessary for this to happen.
ἡ μὲν γὰρ ἀντικειμένων συναπόφασίς ἐστιν ὧν ἔστι μεταξύ τι καὶ διάστημά τι πέφυκεν εἶναι· τῶν δʼ οὐκ ἔστι διαφορά· ἐν ἄλλῳ γὰρ γένει ὧν αἱ συναποφάσεις, ὥστʼ οὐχ ἓν τὸ ὑποκείμενον.
For the co-negation of opposites is of things between which there is some intermediate and some interval is by nature present; but of those other things there is no difference; for those things of which they are co-negations are in different genera, so that the subject is not one.