§1.1.46#1διαφέρει δέ τι ἐν τῷ κατασκευάζειν ἢ ἀνασκευάειν τὸ ὑπολαμβάνειν ἢ ταὐτὸν ἢ ἕτερον σημαίνειν τὸ μὴ εἶναι τοδὶ καὶ εἶναι μὴ τοῦτο, οἷον τὸ μὴ εἶναι λευκὸν τῷ εἶναι μὴ λευκόν.
Whether we suppose "not to be this" and "to be not-this" to signify the same or something different—for example, "not to be white" and "to be not-white"—makes some difference in establishing or refuting a thesis.
οὐ γὰρ ταὐτὸν σημαίνει, οὐδʼ ἔστιν ἀπόφασις τοῦ εἶναι λευκὸν τὸ εἶναι μὴ λευκόν, ἀλλὰ τὸ μὴ εἶναι λευκόν.
For they do not signify the same, nor is "to be not-white" the negation of "to be white," but rather "not to be white" is.
λόγος δὲ τούτου ὅδε.
The reason for this is as follows.
ὁμοίως γὰρ ἔχει τὸ δύναται βαδίζειν πρὸς τὸ δύναται οὐ βαδίζειν τῷ ἔστι λευκόν πρὸς τὸ ἔστιν οὐ λευκόν, καὶ ἐπίσταται τἀγαθόν πρὸς τὸ ἐπίσταται τὸ οὐκ ἀγαθόν.
For the relation of "it is able to walk" to "it is able not to walk" is similar to that of "it is white" to "it is not-white", and of "it knows the good" to "it knows the not-good".
τὸ γὰρ ἐπίσταται τἀγαθόν ἢ ἔστιν ἐπιστάμενος τἀγαθόν οὐδὲν διαφέρει, οὐδὲ τὸ δύναται βαδίζειν ἢ ἔστι δυνάμενος βαδίζειν· ὥστε καὶ τὰ ἀντικείμενα, οὐ δύναται βαδίζειν—οὐκ ἔστι δυνάμενος βαδίζειν.
For "it knows the good" or "it is knowing the good" does not differ at all, nor does "it is able to walk" or "it is capable of walking"; so that their opposites also, "it is not able to walk" [and] "it is not capable of walking" [do not differ].
εἰ οὖν τὸ οὐκ ἔστι δυνάμενος βαδίζειν ταὐτὸ σημαίνει καὶ ἔστι δυνάμενος οὐ βαδίζειν ἢ μὴ βαδίζειν, ταῦτά γε ἅμα ὑπάρξει ταὐτῷ (ὁ γὰρ αὐτὸς δύναται καὶ βαδίζειν καὶ μὴ βαδίζειν, καὶ ἐπιστήμων τἀγαθοῦ καὶ τοῦ μὴ ἀγαθοῦ ἐστί), φάσις δὲ καὶ ἀπόφασις οὐχ ὑπάρχουσιν αἱ ἀντικείμεναι ἅμα τῷ αὐτῷ.
If, then, "it is not capable of walking" signifies the same as "it is capable of not walking" or "of not-walking", these at least will belong to the same thing at the same time (for the same person is able both to walk and not to walk, and has knowledge both of the good and of the not-good); but opposite affirmation and negation do not belong to the same thing at the same time.
ὥσπερ οὖν οὐ ταὐτό ἐστι τὸ μὴ ἐπίστασθαι τἀγαθὸν καὶ ἐπίστασθαι τὸ μὴ ἀγαθόν, οὐδʼ εἶναι μὴ ἀγαθὸν καὶ μὴ εἶναι ἀγαθὸν ταὐτόν.
Just as, therefore, "not to know the good" and "to know the not-good" are not the same, so "to be not-good" and "not to be good" are not the same.
τῶν γὰρ ἀνάλογον ἐὰν θάτερα ἕτερα, καὶ θάτερα.
For of analogical things, if one pair are different, the other pair are also different.
οὐδὲ τὸ εἶναι μὴ ἴσον καὶ τὸ μὴ εἶναι ἴσον· τῷ μὲν γὰρ ὑπόκειταί τι, τῷ ὄντι μὴ ἴσῳ, καὶ τοῦτʼ ἔστι τὸ ἄνισον, τῷ δʼ οὐδέν.
Nor are "to be not-equal" and "not to be equal" [the same]; for to the one, namely, "that which is not-equal", some subject underlies, and this is the unequal, whereas to the other, nothing underlies.
διόπερ ἴσον μὲν ἢ ἄνισον οὐ πᾶν, ἴσον δʼ ἢ οὐκ ἴσον πᾶν.
Therefore, not everything is equal or unequal, but everything is equal or not equal.
ἔτι τὸ ἔστιν οὐ λευκὸν ξύλον καὶ οὐκ ἔστι λευκὸν ξύλον οὐχ ἅμα ὑπάρχει.
Furthermore, "it is a not-white wood" and "it is not a white wood" do not belong to a thing at the same time.
εἰ γάρ ἐστι ξύλον οὐ λευκόν, ἔσται ξύλον· τὸ δὲ μὴ ὂν λευκόν ξύλον οὐκ ἀνάγκη ξύλον εἶναι.
For if it is "a not-white wood", it will be "wood"; but that which is "not a white wood" is not necessarily "wood".
ὥστε φανερὸν ὅτι οὐκ ἔστι τοῦ ἔστιν ἀγαθόν τὸ ἔστιν οὐκ ἀγαθόν ἀπόφασις.
So it is clear that "it is not-good" is not the negation of "it is good".
εἰ οὖν κατὰ παντὸς ἑνὸς ἢ φάσις ἢ ἀπόφασις ἀληθής, εἰ μὴ ἔστιν ἀπόφασις, δῆλον ὡς κατάφασις ἄν· πως εἴη.
If, then, of every single thing either the affirmation or the negation is true, and if this is not the negation, it is clear that it must in a way be an affirmation.
καταφάσεως δὲ πάσης ἀπόφασις ἔστιν· καὶ ταύτης ἄρα τὸ οὐκ ἔσ0τιν οὐκ ἀγαθόν.
But of every affirmation there is a negation; therefore, of this one also, the negation is "it is not not-good".
Ἔχει δὲ τάξιν τήνδε πρὸς ἄλληλα.
They have the following order in relation to one another.
ἔστω τὸ εἶναι ἀγαθὸν ἐφʼ οὗ Α, τὸ δὲ μὴ εἶναι ἀγαθὸν ἐφʼ οὗ Β, τὸ δὲ εἶναι μὴ ἀγαθὸν ἐφʼ οὗ Γ, ὑπὸ τὸ Β, τὸ δὲ μὴ εἶναι μὴ ἀγαθὸν ἐφʼ οὗ Δ, ὑπὸ τὸ Α. παντὶ δὴ ὑπάρξει ἢ τὸ Α ἢ τὸ Β, καὶ οὐδενὶ τῷ αὐτῷ·
Let "to be good" be represented by A, "not to be good" by B, "to be not-good" by C (which is under B), and "not to be not-good" by D (which is under A).
καὶ ἢ τὸ Γ ἢ τὸ Δ, καὶ οὐδενὶ τῷ αὐτῷ.
To everything, then, either A or B will belong, and to nothing both of them; and either C or D, and to nothing both of them.
καὶ ᾧ τὸ Γ, ἀνάγκη τὸ Β παντὶ ὑπάρχειν (εἰ γὰρ ἀληθὲς εἰπεῖν ὅτι ἐστὶν οὐ λευκόν, καὶ ὅτι οὐκ ἔστι λευκὸν ἀληθές· ἀδύνατον γὰρ ἅμα εἶναι λευκὸν καὶ εἶναι μὴ λευκόν, ἢ εἶναι ξύλον οὐ λευκὸν καὶ εἶναι ξύλον λευκόν, ὥστʼ εἰ μὴ ἡ κατάφασις, ἡ ἀπόφασις ὑπάρξει), τῷ δὲ Β τὸ Γ οὐκ ἀεί (ὃ γὰρ ὅλως μὴ ξύλον, οὐδὲ ξύλον ἔσται οὐ λευκόν).
And to whatever C belongs, B must belong to all of it (for if it is true to say "it is not-white", it is also true that "it is not white"; for it is impossible at the same time to be white and to be not-white, or to be a not-white wood and to be a white wood, so that if the affirmation does not belong, the negation will); but C does not always belong to B (for that which is not wood at all will not be not-white wood either).
ἀνάπαλιν τοίνυν, ᾧ τὸ Α, τὸ Δ παντί (ἢ γὰρ τὸ Γ ἢ τὸ Δ· ἐπεὶ δʼ οὐχ οἷόν τε ἅμα εἶναι μὴ λευκὸν καὶ λευκόν, τὸ Δ ὑπάρξει· κατὰ γὰρ τοῦ ὄντος λευκοῦ ἀληθές εἰπεῖν ὅτι οὐκ ἔστιν οὐ λευκόν), κατὰ δὲ τοῦ Δ οὐ παντὸς τὸ Α (κατὰ γὰρ τοῦ ὅλως μὴ ὄντος ξύλου οὐκ ἀληθὲς τὸ Α εἰπεῖν, ὡς ἔστι ξύλον λευκόν, ὥστε τὸ Δ ἀληθές, τὸ δʼ οὐκ ἀληθές, ὅτι ξύλον λευκόν).
Conversely, then, to whatever A belongs, D belongs to all of it (for either C or D must belong; and since it is not possible to be at once not-white and white, D will belong; for of that which is white it is true to say that it is not not-white), but A does not belong to all of D (for of that which is not wood at all, it is not true to say A, i.e., that it is white wood, so that D is true of it, but it is not true that it is white wood).
δῆλον δʼ ὅτι καὶ τὸ Α Γ οὐδενὶ τῷ αὐτῷ καὶ τὸ Β καὶ τὸ Δ ἐνδέχεται τινὶ τῷ αὐτῷ ὑπάρξαι.
It is clear also that A and C belong to nothing at the same time, but B and D can belong to some same thing.
Ὁμοίως δʼ ἔχουσι καὶ αἰ στερήσεις πρὸς τὰς κατηγορίας ταύτῃ τῇ θέσει.
Privations also have the same relation to predications in this arrangement.
ἴσον ἐφʼ οὗ τὸ Α, οὐκ ἴσον ἐφʼ οὗ Β, ἄνισον ἐφʼ οὗ Γ, οὐκ ἄνισον ἐφʼ οὗ Δ.
Let "equal" be represented by A, "not equal" by B, "unequal" by C, "not unequal" by D.