§2.8Ἐπεὶ δ᾿ αἱ ἀντιθέσεις τέτταρες, σκοπεῖν ἐκ μὲν τῶν ἀντιφάσεων ἀνάπαλιν ἐκ τῆς ἀκολουθήσεως καὶ ἀναιροῦντι καὶ κατασκευάζοντι, λαμβάνειν δ᾿ ἐξ ἐπαγωγῆς, οἷον εἰ ὁ ἄνθρωπος ζῷον, τὸ μὴ ζῷον οὐκ ἄνθρωπος.
Since oppositions are four, one must examine, from contradictories, the consequence in reverse, both for refuting and for establishing, and grasp them from induction, for example, if man is an animal, what is not an animal is not a man.
Ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων.
Similarly also in other cases.
Ἐνταῦθα γὰρ ἀνάπαλιν ἡ ἀκολούθησις· τῷ μὲν γὰρ ἀνθρώπῳ τὸ ζῷον ἕπεται, τῷ δὲ μὴ ἀνθρώπῳ τὸ μὴ ζῷον οὔ, ἀλλ᾿ ἀνάπαλιν τῷ μὴ ζῴῳ τὸ οὐκ ἄνθρωπος.
For here the consequence is in reverse; for 'animal' follows 'man', but 'not-animal' does not follow 'not-man', but conversely, 'not-man' follows 'not-animal'.
Ἐπὶ πάντων οὖν τὸ τοιοῦτον ἀξιωτέον, οἷον εἰ τὸ καλὸν ἡδύ, καὶ τὸ μὴ ἡδὺ οὐ καλόν· εἰ δὲ μὴ τοῦτο, οὐδ᾿ ἐκεῖνο.
One should therefore claim this to be so in all cases, for example, if the beautiful is pleasant, what is not pleasant is not beautiful; and if the latter is not, neither is the former.
Ὁμοίως δὲ καὶ εἰ τὸ μὴ ἡδὺ οὐ καλόν, τὸ καλὸν ἡδύ.
Similarly also, if what is not pleasant is not beautiful, the beautiful is pleasant.
Δῆλον οὖν ὅτι πρὸς ἄμφω ἀντιστρέφει ἡ κατὰ τὴν ἀντίφασιν ἀκολούθησις ἀνάπαλιν γινομένη.
It is clear, then, that the consequence according to contradiction, when made in reverse, converts for both.
Ἐπὶ δὲ τῶν ἐναντίων σκοπεῖν εἰ τῷ ἐναντίῳ τὸ ἐναντίον ἕπεται, ἢ ἐπὶ ταὐτὰ ἢ ἀνάπαλιν, καὶ ἀναιροῦντι καὶ κατασκευάζοντι· λαμβάνειν δὲ καὶ τὰ τοιαῦτα ἐξ ἐπαγωγῆς, ἐφ᾿ ὅσον χρήσιμον.
And in the case of contraries, one must examine whether the contrary follows the contrary, either in the same direction or in reverse, both for refuting and for establishing; and one must also grasp such things from induction, as far as it is useful.
Ἐπὶ ταὐτὰ μὲν οὖν ἡ ἀκολούθησις, οἷον τῇ ἀνδρίᾳ καὶ τῇ δειλίᾳ· τῇ μὲν γὰρ ἀρετὴ ἀκολουθεῖ, τῇ δὲ κακία, καὶ τῇ μὲν ἀκολουθεῖ τὸ αἱρετόν, τῇ δὲ τὸ φευκτόν.
Now, the consequence in the same direction is, for example, in the case of courage and cowardice; for virtue follows the former, and vice the latter, and what is to be chosen follows the former, and what is to be avoided the latter.
Ἐπὶ ταὐτὰ οὖν καὶ ἡ τούτων ἀκολούθησις· ἐναντίον γὰρ τὸ αἱρετὸν τῷ φευκτῷ.
Therefore, the consequence of these also is in the same direction; for what is to be chosen is contrary to what is to be avoided.
Ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων.
Similarly also in other cases.
Ἀνάπαλιν δὲ ἡ ἀκολούθησις, οἷον εὐεξίᾳ μὲν ἡ ὑγίεια ἀκολουθεῖ, καχεξίᾳ δὲ νόσος οὔ, ἀλλὰ νόσῳ καχεξία.
But the consequence is in reverse, for example, health follows good condition, but disease does not follow bad condition, but bad condition follows disease.
Δῆλον οὖν ὅτι ἀνάπαλιν ἐπὶ τούτων ἡ ἀκολούθησις.
It is clear, then, that in these cases the consequence is in reverse.
Σπάνιον δὲ τὸ ἀνάπαλιν ἐπὶ τῶν ἐναντίων συμβαίνει, ἀλλὰ τοῖς πλείστοις ἐπὶ ταὐτὰ ἡ ἀκολούθησις.
But for the consequence to be in reverse in the case of contraries happens rarely, but in most cases the consequence is in the same direction.
Εἰ οὖν μήτ᾿ ἐπὶ ταὐτὰ τῷ ἐναντίῳ τὸ ἐναντίον ἀκολουθεῖ μήτε ἀνάπαλιν, δῆλον ὅτι οὐδ᾿ ἐπὶ τῶν ῥηθέντων ἀκολουθεῖ τὸ ἕτερον τῷ ἑτέρῳ.
If, therefore, the contrary follows the contrary neither in the same direction nor in reverse, it is clear that neither does one of the things spoken of follow the other.
Εἰ δ᾿ ἐπὶ τῶν ἐναντίων, καὶ ἐπὶ τῶν ῥηθέντων ἀναγκαῖον τὸ ἕτερον τῷ ἑτέρῳ ἀκολουθεῖν.
But if it does in the case of the contraries, it is necessary that one of the things spoken of should follow the other.
Ὁμοίως δὲ τοῖς ἐναντίοις καὶ ἐπὶ τῶν στερήσεων καὶ ἕξεων σκεπτέον.
In the same way as with contraries, one must also examine in the case of privations and states.
Πλὴν οὐκ ἔστιν ἐπὶ τῶν στερήσεων τὸ ἀνάπαλιν, ἀλλ᾿ ἐπὶ ταὐτὰ τὴν ἀκολούθησιν ἀναγκαῖον ἀεὶ γίνεσθαι, καθάπερ ὄψει μὲν αἴσθησιν, τυφλότητι δ᾿ ἀναισθησίαν.
Except that in the case of privations the reverse does not occur, but it is necessary that the consequence always be in the same direction, just as sensation follows sight, and insensibility follows blindness.
Ἀντίκειται γὰρ ἡ αἴσθησις τῇ ἀναισθησίᾳ ὡς ἕξις καὶ στέρησις· τὸ μὲν γὰρ ἕξις αὐτῶν, τὸ δὲ στέρησίς ἐστιν.
For sensation is opposed to insensibility as a state and a privation; for the former of them is a state, and the latter is a privation.
Ὁμοίως δὲ τῇ ἕξει καὶ τῇ στερήσει καὶ ἐπὶ τῶν πρός τι χρηστέον· ἐπὶ ταὐτὰ γὰρ καὶ τούτων ἡ ἀκολούθησις.
Similarly to the state and privation, one should also apply this to relative terms; for of these too the consequence is in the same direction.
Οἷον εἰ τὸ τριπλάσιον πολλαπλάσιον, καὶ τὸ τριτημόριον πολλοστημόριον· λέγεται γὰρ τὸ μὲν τριπλάσιον πρὸς τὸ τριτημόριον, τὸ δὲ πολλαπλάσιον πρὸς τὸ πολλοστημόριον.
For example, if the triple is a multiple, the third part is also a fraction; for the triple is spoken of in relation to the third part, and the multiple in relation to the fraction.
πάλιν εἰ ἡ ἐπιστήμη ὑπόληψις, καὶ τὸ ἐπιστητὸν ὑποληπτόν· καὶ εἰ ἡ ὅρασις αἴσθησις, καὶ τὸ ὁρατὸν αἰσθητόν.
Again, if knowledge is a belief, the knowable is also believable; and if sight is sensation, the visible is also sensible.
Ἔνστασις ὅτι οὐκ ἀνάγκη ἐπὶ τῶν πρός τι τὴν ἀκολούθησιν γίνεσθαι, καθάπερ εἴρηται· τὸ γὰρ αἰσθητὸν ἐπιστητόν ἐστιν, ἡ δ᾿ αἴσθησις οὐκ ἐπιστήμη.
An objection is that it is not necessary for the consequence to occur in the case of relative terms, as has been said; for the sensible is knowable, but sensation is not knowledge.
Οὐ μὴν ἀληθής γε ἡ ἔνστασις δοκεῖ εἶναι· πολλοὶ γὰρ οὔ φασι τῶν αἰσθητῶν ἐπιστήμην εἶναι.
Yet the objection does not seem to be true; for many deny that there is knowledge of sensible things.
Ἔτι πρὸς τοὐναντίον οὐχ ἧττον χρήσιμον τὸ ῥηθέν, οἷον ὅτι τὸ αἰσθητὸν οὐκ ἔστιν ἐπιστητόν· οὐδὲ γὰρ ἡ αἴσθησις ἐπιστήμη.
Furthermore, what has been said is no less useful for the contrary, for example, that the sensible is not knowable; for neither is sensation knowledge.