§10#2Ἐπεὶ δὲ ἐναντία ἀπόφασίς ἐστι τῇ ἅπαν ἐστὶ ζῷον δίκαιον ἡ σημαίνουσα ὅτι οὐδέν ἐστι ζῷον δίκαιον, αὗται μὲν φανερὸν ὅτι οὐδέποτε ἔσονται οὔτε ἀληθεῖς ἅμα οὔτε ἐπὶ τοῦ αὐτοῦ, αἱ δὲ ἀντικείμεναι ταύταις ἔσονταί ποτε, οἷον οὐ πᾶν ζῷον δίκαιον καὶ ἔστι τι ζῷον δίκαιον. Ἀκολουθοῦσι δὲ αὗται, τῇ μὲν πᾶς ἄνθρωπος οὐ δίκαιός ἐστιν ἡ οὐδείς ἐστιν ἄνθρωπος δίκαιος, τῇ δὲ ἔστι τις ἄνθρωπος δίκαιος ἡ ἀντικειμένη ὅτι οὐ πᾶς ἄνθρωπός ἐστιν οὐ δίκαιος· ἀνάγκη γὰρ εἶναί τινα.
Since the contrary negation to "every animal is just" is the one signifying that "no animal is just," it is clear that these will never be true at the same time or of the same subject, while those opposed to these will sometimes be so, as for example, "not every animal is just" and "some animal is just." And these follow in this way: "no man is just" follows "every man is not-just," while the opposite, "not every man is not-just," follows "some man is just"; for there must be some.
Φανερὸν δὲ καὶ ὅτι ἐπὶ μὲν τῶν καθ᾿ ἕκαστον, εἰ ἀληθὲς ἐρωτηθέντα ἀποφῆσαι, ὅτι καὶ καταφῆσαι ἀληθές· οἷον ἆρά γε Σωκράτης σοφός; οὔ. Σωκράτης ἄρα οὐ σοφός. Ἐπὶ δὲ τῶν καθόλου οὐκ ἀληθὴς ἡ ὁμοίως λεγομένη, ἀληθὴς δὲ ἡ ἀπόφασις, οἷον ἆρά γε πᾶς ἄνθρωπος σοφός; οὔ. Πᾶς ἄρα ἄνθρωπος οὐ σοφός· τοῦτο γὰρ ψεῦδος.
It is also clear that in the case of particulars, if it is true to deny when asked, it is also true to affirm; as for example, "Is Socrates wise?" "No." "Then Socrates is not-wise." But in the case of universals, the one spoken of in a similar way is not true, but the negation is true; as for example, "Is every man wise?" "No." "Then every man is not-wise"; for this is false.
Ἀλλὰ τὸ οὐ πᾶς ἄρα ἄνθρωπος σοφός ἀληθές· αὕτη δέ ἐστιν ἡ ἀντικειμένη, ἐκείνη δὲ ἡ ἐναντία.
Rather, "Then not every man is wise" is true; and this is the opposite, while that is the contrary.
Αἱ δὲ κατὰ τὰ ἀόριστα ἀντικείμεναι ὀνόματα καὶ ῥήματα, οἷον ἐπὶ τοῦ μὴ ἄνθρωπος καὶ μὴ δίκαιος, ὥσπερ ἀποφάσεις ἄνευ ὀνόματος καὶ ῥήματος δόξειαν ἂν εἶναι.
On the other hand, oppositions according to indefinite nouns and verbs, as for example in the case of "not-man" and "not-just," might seem to be negations without a noun and a verb.
Οὐκ εἰσὶ δέ· ἀεὶ γὰρ ἀληθεύειν ἀνάγκη ἢ ψεύδεσθαι τὴν ἀπόφασιν, ὁ δ᾿ εἰπὼν οὐκ ἄνθρωπος οὐδὲν μᾶλλον τοῦ εἰπόντος ἄνθρωπος ἀλλὰ καὶ ἧττον ἠλήθευκέ τι ἢ ἔψευσται, ἐὰν μήτι προστεθῇ.
But they are not; for a negation must always be true or false, but one who says "not-man" has no more spoken truly or falsely than one who says "man"—indeed, even less so—unless something is added.
Σημαίνει δὲ τὸ ἔστι πᾶς οὐκ ἄνθρωπος δίκαιος οὐδεμιᾷ ἐκείνων ταὐτόν, οὐδὲ ἡ ἀντικειμένη ταύτῃ ἡ οὐκ ἔστι πᾶς οὐκ ἄνθρωπος δίκαιος· τὸ δὲ πᾶς οὐ δίκαιος οὐκ ἄνθρωπος τῷ οὐδεὶς δίκαιος οὐκ ἄνθρωπος ταὐτὸν σημαίνει. Μετατιθέμενα δὲ τὰ ὀνόματα καὶ τὰ ῥήματα ταὐτὸν σημαίνει, οἷον ἔστι λευκὸς ἄνθρωπος, ἔστιν ἄνθρωπος λευκός. Εἰ γὰρ μὴ τοῦτό ἐστι, τοῦ αὐτοῦ πλείους ἔσονται ἀποφάσεις.
And "every not-man is just" does not signify the same as any of those, nor does the one opposed to this, "not every not-man is just"; but "every not-man is not-just" signifies the same as "no not-man is just." Furthermore, nouns and verbs when transposed signify the same; for example, "a man is white" and "a white man is." For if this were not so, there would be more than one negation of the same.
Ἀλλ᾿ ἐδέδεικτο ὅτι μία μιᾶς.
But it has been shown that there is one negation for one affirmation.
Τοῦ μὲν γὰρ ἔστι λευκὸς ἄνθρωπος ἀπόφασις τὸ οὐκ ἔστι λευκὸς ἄνθρωπος· τοῦ δὲ ἔστιν ἄνθρωπος λευκός, εἰ μὴ ἡ αὐτή ἐστι τῇ ἔστι λευκὸς ἄνθρωπος, ἔσται ἀπόφασις ἤτοι τὸ οὐκ ἔστιν οὐκ ἄνθρωπος λευκός ἢ τὸ οὐκ ἔστιν ἄνθρωπος λευκός. Ἀλλ᾿ ἡ ἑτέρα μέν ἐστιν ἀπόφασις τοῦ ἔστιν οὐκ ἄνθρωπος λευκός, ἡ ἑτέρα δὲ τοῦ ἔστι λευκὸς ἄνθρωπος, ὥστε ἔσονται δύο μιᾶς.
For the negation of "a man is white" is "a man is not white"; while for "a white man is," if it is not the same as "a man is white," its negation will be either "not-man is not white" or "a man is not white." But the former is the negation of "a not-man is white," while the latter is the negation of "a man is white," so that there would be two negations for one affirmation.
Ὅτι μὲν οὖν μετατιθεμένου τοῦ ὀνόματος καὶ τοῦ ῥήματος ἡ αὐτὴ γίνεται κατάφασις καὶ ἀπόφασις, δῆλον.
Consequently, it is clear that when the noun and the verb are transposed, the same affirmation and negation result.