§4.7ἀλλὰ μὴν οὐδὲ μεταξὺ ἀντιφάσεως ἐνδέχεται εἶναι οὐθέν, ἀλλʼ ἀνάγκη ἢ φάναι ἢ ἀποφάναι ἓν καθʼ ἑνὸς ὁτιοῦν.
Moreover, there cannot be anything between a contradiction, but it is necessary either to assert or to deny any one thing of another.
δῆλον δὲ πρῶτον μὲν ὁρισαμένοις τί τὸ ἀληθὲς καὶ ψεῦδος.
This is clear, in the first place, to those who define what is true and false.
τὸ μὲν γὰρ λέγειν τὸ ὂν μὴ εἶναι ἢ τὸ μὴ ὂν εἶναι ψεῦδος, τὸ δὲ τὸ ὂν εἶναι καὶ τὸ μὴ ὂν μὴ εἶναι ἀληθές, ὥστε καὶ ὁ λέγων εἶναι ἢ μὴ ἀληθεύσει ἢ ψεύσεται·
For to say of that which is that it is not, or of that which is not that it is, is false, while to say of that which is that it is, and of that which is not that it is not, is true; so that he who says that anything is or is not will either speak truly or falsely.
ἀλλʼ οὔτε τὸ ὂν λέγεται μὴ εἶναι ἢ εἶναι οὔτε τὸ μὴ ὄν.
But it is not the case that either that which is is said not to be or to be, or that which is not.
ἔτι ἤτοι μεταξὺ ἔσται τῆς ἀντιφάσεως ὥσπερ τὸ φαιὸν μέλανος καὶ λευκοῦ, ἢ ὡς τὸ μηδέτερον ἀνθρώπου καὶ ἵππου.
Furthermore, either it will be a middle of the contradiction in the way that grey is between black and white, or in the way that what is neither is between man and horse.
εἰ μὲν οὖν οὕτως, οὐκ ἂν μεταβάλλοι (ἐκ μὴ ἀγαθοῦ γὰρ εἰς ἀγαθὸν μεταβάλλει ἢ ἐκ τούτου εἰς μὴ ἀγαθόν), νῦν δʼ ἀεὶ φαίνεται (οὐ γὰρ ἔστι μεταβολὴ ἀλλʼ ἢ εἰς τὰ ἀντικείμενα καὶ μεταξύ)·
If indeed it were in the former way, it would not change (for a thing changes from what is not-good to good, or from this to what is not-good); but as it is, it is always seen to change (for there is no change except to opposites and to the middle).
εἰ δʼ ἔστι μεταξύ, καὶ οὕτως εἴη ἄν τις εἰς λευκὸν οὐκ ἐκ μὴ λευκοῦ γένεσις, νῦν δʼ οὐχ ὁρᾶται.
But if there is a middle, in this way too there would be a generation into white not from not-white, but as it is, this is not seen.
ἔτι πᾶν τὸ διανοητὸν καὶ νοητὸν ἡ διάνοια ἢ κατάφησιν ἢ ἀπόφησιν—τοῦτο δʼ ἐξ ὁρισμοῦ δῆλον—ὅταν ἀληθεύῃ ἢ ψεύδηται· ὅταν μὲν ὡδὶ συνθῇ φᾶσα ἢ ἀποφᾶσα, ἀληθεύει, ὅταν δὲ ὡδί, ψεύδεται.
Furthermore, the mind either affirms or denies everything that is thinkable and intelligible—and this is clear from the definition—whenever it speaks truly or falsely: when it connects them in this way, by affirming or denying, it speaks truly, and when in that way, it speaks falsely.
ἔτι παρὰ πάσας δεῖ εἶναι τὰς ἀντιφάσεις, εἰ μὴ λόγου ἕνεκα λέγεται· ὥστε καὶ οὔτε ἀληθεύσει τις οὔτʼ οὐκ ἀληθεύσει, καὶ παρὰ τὸ ὂν καὶ τὸ μὴ ὂν ἔσται, ὥστε καὶ παρὰ γένεσιν καὶ φθορὰν μεταβολή τις ἔσται.
Furthermore, there must be something besides all contradictions, unless it is said merely for the sake of argument; so that someone will neither speak truly nor not speak truly, and there will be something besides that which is and that which is not, so that there will be some change besides generation and destruction.
ἔτι ἐν ὅσοις γένεσιν ἡ ἀπόφασις τὸ ἐναντίον ἐπιφέρει, καὶ ἐν τούτοις ἔσται, οἷον ἐν ἀριθμοῖς οὔτε περιττὸς οὔτε οὐ περιττὸς ἀριθμός·
Furthermore, in all classes in which negation brings about the contrary, this will also occur; for example, in numbers, there will be a number that is neither odd nor not-odd.
ἀλλʼ ἀδύνατον· ἐκ τοῦ ὁρισμοῦ δὲ δῆλον.
But this is impossible, and it is clear from the definition.
ἔτι εἰς ἄπειρον βαδιεῖται, καὶ οὐ μόνον ἡμιόλια τὰ ὄντα ἔσται ἀλλὰ πλείω.
Furthermore, it will go on to infinity, and existing things will not only be half as many again but more.
πάλιν γὰρ ἔσται ἀποφῆσαι τοῦτο πρὸς τὴν φάσιν καὶ τὴν ἀπόφασιν, καὶ τοῦτʼ ἔσται τι· ἡ γὰρ οὐσία ἐστί τις αὐτοῦ ἄλλη.
For it will be possible again to deny this in relation to the assertion and negation, and this will be something; for its substance is some other.
ἔτι ὅταν ἐρομένου εἰ λευκόν ἐστιν εἴπῃ ὅτι οὔ, οὐθὲν ἄλλο ἀποπέφηκεν ἢ τὸ εἶναι· ἀπόφασις δὲ τὸ μὴ εἶναι.
Furthermore, when, someone asking if it is white, one says no, one has denied nothing other than being; and negation is not-being.
ἐλήλυθε δʼ ἐνίοις αὕτη ἡ δόξα ὥσπερ καὶ ἄλλαι τῶν παραδόξων· ὅταν γὰρ λύειν μὴ δύνωνται λόγους ἐριστικούς, ἐνδόντες τῷ λόγῳ σύμφασιν ἀληθὲς εἶναι τὸ συλλογισθέν.
But this opinion has come to some people as indeed other paradoxical opinions have; for when they are unable to solve eristic arguments, they yield to the argument and agree that the concluded is true.
οἱ μὲν οὖν διὰ τοιαύτην αἰτίαν λέγουσιν, οἱ δὲ διὰ τὸ πάντων ζητεῖν λόγον.
Some, then, speak for this sort of reason, and others because they seek a reason for everything.
ἀρχὴ δὲ πρὸς ἅπαντας τούτους ἐξ ὁρισμοῦ.
The starting-point against all these people is from definition.
ὁρισμὸς δὲ γίγνεται ἐκ τοῦ σημαίνειν τι ἀναγκαῖον εἶναι αὐτούς· ὁ γὰρ λόγος οὗ τὸ ὄνομα σημεῖον ὁρισμὸς ἔσται.
And definition arises from the necessity that they mean something; for the formula of which the name is a sign will be the definition.
ἔοικε δʼ ὁ μὲν Ἡρακλείτου λόγος, λέγων πάντα εἶναι καὶ μὴ εἶναι, ἅπαντα ἀληθῆ ποιεῖν, ὁ δʼ Ἀναξαγόρου, εἶναί τι μεταξὺ τῆς ἀντιφάσεως, πάντα ψευδῆ· ὅταν γὰρ μιχθῇ, οὔτε ἀγαθὸν οὔτε οὐκ ἀγαθὸν τὸ μῖγμα, ὥστʼ οὐδὲν εἰπεῖν ἀληθές.
And the argument of Heraclitus, which says that all things are and are not, seems to make all things true, while that of Anaxagoras, that there is something between a contradiction, seems to make all things false; for when all things are mixed, the mixture is neither good nor not-good, so that nothing can be said truly.