§10#1Ἐπεὶ δέ ἐστί τι κατά τινος ἡ κατάφασις σημαίνουσα, τοῦτο δέ ἐστιν ἢ ὄνομα ἢ τὸ ἀνώνυμον, ἓν δὲ δεῖ εἶναι καὶ καθ᾿ ἑνὸς τὸ ἐν τῇ καταφάσει (τὸ δὲ ὄνομα εἴρηται καὶ τὸ ἀνώνυμον πρότερον· τὸ γὰρ οὐκ ἄνθρωπος ὄνομα μὲν οὐ λέγω ἀλλ᾿ ἀόριστον ὄνομα· ἓν γάρ πως σημαίνει καὶ τὸ ἀόριστον· ὥσπερ καὶ τὸ οὐχ ὑγιαίνει οὐ ῥῆμα ἀλλ᾿ ἀόριστον ῥῆμα), ἔσται πᾶσα κατάφασις καὶ ἀπόφασις ἢ ἐξ ὀνόματος καὶ ῥήματος ἢ ἐξ ἀορίστου ὀνόματος καὶ ῥήματος.
Since an affirmation is something signifying something of something, and this is either a noun or an indefinite noun, and what is in the affirmation must be one and of one (and we have already spoken of the noun and the indefinite noun before; for I do not call "not-man" a noun but an indefinite noun; for an indefinite noun too in a way signifies one thing, just as "not-healthy" is not a verb but an indefinite verb), every affirmation and negation will consist either of a noun and a verb or of an indefinite noun and a verb.
Ἄνευ δὲ ῥήματος οὐδεμία κατάφασις οὐδὲ ἀπόφασις· τὸ γὰρ ἔστιν ἢ ἔσται ἢ ἦν ἢ γίνεται, ἢ ὅσα ἄλλα τοιαῦτα, ῥήματα ἐκ τῶν κειμένων ἐστί· προσσημαίνει γὰρ χρόνον.
Without a verb there is no affirmation or negation; for "is," "will be," "was," "becomes," or any other such, are verbs from among those established; for they additionally signify time.
Ὥστε πρώτη ἔσται κατάφασις καὶ ἀπόφασις τὸ ἔστιν ἄνθρωπος — οὐκ ἔστιν ἄνθρωπος, εἶτα ἔστιν οὐκ ἄνθρωπος — οὐκ ἔστιν οὐκ ἄνθρωπος, πάλιν ἔστι πᾶς ἄνθρωπος — οὐκ ἔστι πᾶς ἄνθρωπος, ἔστι πᾶς οὐκ ἄνθρωπος — οὐκ ἔστι πᾶς οὐκ ἄνθρωπος. Καὶ ἐπὶ τῶν ἐκτὸς δὲ χρόνων ὁ αὐτὸς λόγος.
Consequently, the first affirmation and negation will be: "a man is"—"a man is not"; next, "a not-man is"—"a not-man is not"; again, "every man is"—"not every man is"; "every not-man is"—"not every not-man is." And the same account holds also for times outside the present.
Ὅταν δὲ τὸ ἔστι τρίτον προσκατηγορῆται, ἤδη διχῶς λέγονται αἱ ἀντιθέσεις.
But when "is" is predicated as a third element, the oppositions are already spoken of in two ways.
Λέγω δὲ οἷον ἔστι δίκαιος ἄνθρωπος· τὸ ἔστι τρίτον φημὶ συγκεῖσθαι ὄνομα ἢ ῥῆμα ἐν τῇ καταφάσει.
I mean, for example, "a man is just"; I say that "is" is combined as a third element, whether noun or verb, in the affirmation.
Ὥστε διὰ τοῦτο τέτταρα ἔσται ταῦτα, ὧν τὰ μὲν δύο πρὸς τὴν κατάφασιν καὶ ἀπόφασιν ἕξει κατὰ τὸ στοιχοῦν ὡς αἱ στερήσεις, τὰ δὲ δύο οὔ.
Consequently, because of this, these will be four, of which two will hold in relation to the affirmation and negation according to the order as privations, while the other two will not.
Λέγω δ᾿ ὅτι τὸ ἔστιν ἢ τῷ δικαίῳ προσκείσεται ἢ τῷ οὐ δικαίῳ, ὥστε καὶ ἡ ἀπόφασις.
I mean that "is" will be added either to "just" or to "not-just," and so too for the negation.
Τέτταρα οὖν ἔσται.
Thus there will be four.
Νοοῦμεν δὲ τὸ λεγόμενον ἐκ τῶν ὑπογεγραμμένων.
And we understand what is said from the list below.
Ἔστι δίκαιος ἄνθρωπος· ἀπόφασις τούτου, οὐκ ἔστι δίκαιος ἄνθρωπος. Ἔστιν οὐ δίκαιος ἄνθρωπος· τούτου ἀπόφασις, οὐκ ἔστιν οὐ δίκαιος ἄνθρωπος. Τὸ γὰρ ἔστιν ἐνταῦθα καὶ τὸ οὐκ ἔστι τῷ δικαίῳ προσκείσεται καὶ τῷ οὐ δικαίῳ. Ταῦτα μὲν οὖν, ὥσπερ ἐν τοῖς Ἀναλυτικοῖς λέγεται, οὕτω τέτακται.
"A man is just"; the negation of this: "a man is not just." "A man is not-just"; the negation of this: "a man is not not-just." For "is" here and "is not" will be added to "just" and to "not-just." These, then, as is said in the *Analytics*, are thus arranged.
Ὁμοίως δὲ ἔχει κἂν καθόλου τοῦ ὀνόματος ᾖ ἡ κατάφασις, οἷον πᾶς ἐστὶν ἄνθρωπος δίκαιος. Ἀπόφασις τούτου, οὐ πᾶς ἐστὶν ἄνθρωπος δίκαιος. Πᾶς ἐστὶν ἄνθρωπος οὐ δίκαιος — οὐ πᾶς ἐστὶν ἄνθρωπος οὐ δίκαιος. Πλὴν οὐχ ὁμοίως τὰς κατὰ διάμετρον ἐνδέχεται συναληθεύειν· ἐνδέχεται δὲ ποτέ.
In like manner also if the affirmation of the noun is universal, for example, "every man is just." The negation of this: "not every man is just." "Every man is not-just"—"not every man is not-just." Except that it is not possible in the same way for those diagonally opposite to be true together; yet it is possible sometimes.
Αὗται μὲν οὖν δύο ἀντίκεινται, ἄλλαι δὲ δύο πρὸς τὸ οὐκ ἄνθρωπος ὡς ὑποκείμενόν τι προστεθέν· ἔστι δίκαιος οὐκ ἄνθρωπος — οὐκ ἔστι δίκαιος οὐκ ἄνθρωπος, ἔστιν οὐ δίκαιος οὐκ ἄνθρωπος — οὐκ ἔστιν οὐ δίκαιος οὐκ ἄνθρωπος. Πλείους δὲ τούτων οὐκ ἔσονται ἀντιθέσεις.
These two, then, are opposed, while another two are in relation to "not-man" added as a kind of subject: "a not-man is just"—"a not-man is not just", "a not-man is not-just"—"a not-man is not not-just." And there will be no more oppositions than these.
Αὗται δὲ χωρὶς ἐκείνων αὐταὶ καθ᾿ ἑαυτὰς ἔσονται, ὡς ὀνόματι τῷ οὐκ ἄνθρωπος χρώμεναι.
These will be on their own, apart from those, as using "not-man" as a noun.
Ἐφ᾿ ὅσων δὲ τὸ ἔστι μὴ ἁρμόττει, οἷον ἐπὶ τοῦ ὑγιαίνει καὶ βαδίζει, ἐπὶ τούτων τὸ αὐτὸ ποιεῖ οὕτω τιθέμενον ὡς ἂν εἰ τὸ ἔστι προσήπτετο, οἷον ὑγιαίνει πᾶς ἄνθρωπος — οὐχ ὑγιαίνει πᾶς ἄνθρωπος, ὑγιαίνει πᾶς οὐκ ἄνθρωπος — οὐχ ὑγιαίνει πᾶς οὐκ ἄνθρωπος. Οὐ γάρ ἐστι τὸ οὐ πᾶς ἄνθρωπος λεκτέον, ἀλλὰ τὸ οὔ, τὴν ἀπόφασιν, τῷ ἄνθρωπος προσθετέον. Τὸ γὰρ πᾶς οὐ τὸ καθόλου σημαίνει, ἀλλ᾿ ὅτι καθόλου.
But in cases where "is" does not fit, as for example in "is healthy" and "walks," in these cases the same is effected by placing it thus, as if "is" were attached, for example, "every man is healthy"—"not every man is healthy", "every not-man is healthy"—"not every not-man is healthy." For one must not say "not every man," but the "not," the negation, must be added to "man." For "every" does not signify the universal, but that it is universal.
Δῆλον δὲ ἐκ τοῦδε, ὑγιαίνει ἄνθρωπος — οὐχ ὑγιαίνει ἄνθρωπος, ὑγιαίνει οὐκ ἄνθρωπος — οὐχ ὑγιαίνει οὐκ ἄνθρωπος. Ταῦτα γὰρ ἐκείνων διαφέρει τῷ μὴ καθόλου εἶναι.
This is clear from the following: "a man is healthy"—"a man is not healthy", "a not-man is healthy"—"a not-man is not healthy." For these differ from those in not being universal.
Ὥστε τὸ πᾶς ἢ οὐδείς οὐδὲν ἄλλο προσσημαίνει ἢ ὅτι καθόλου τοῦ ὀνόματος ἢ κατάφασιν ἢ ἀπόφασιν.
Consequently, "every" or "no" additionally signifies nothing other than that the affirmation or negation is of the noun universally.
Τὰ δὲ ἄλλα τὰ αὐτὰ δεῖ προστιθέναι.
As for the rest, the same must be added.