§6.9Ἔτι ἐὰν μὲν ᾖ τῆς ἕξεως ὁ ὁρισμός, σκοπεῖν ἐπὶ τοῦ ἔχοντος, ἐὰν δὲ τοῦ ἔχοντος, ἐπὶ τῆς ἕξεως· ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων τῶν τοιούτων.
Moreover, if the definition is of a habit, one must examine it in relation to the possessor, and if of the possessor, in relation to the habit; and likewise also in the case of other such things.
Οἷον εἰ τὸ ἡδὺ ὅπερ ὠφέλιμον, καὶ ὁ ἡδόμενος ὠφελούμενος.
For example, if the pleasant is that which is beneficial, then also he who enjoys himself is being benefited.
Καθόλου δ᾿ εἰπεῖν, ἐν τοῖς τοιούτοις ὁρισμοῖς τρόπον τινὰ πλείω ἑνὸς συμβαίνει τὸν ὁριζόμενον ὁρίζεσθαι· ὁ γὰρ τὴν ἐπιστήμην ὁριζόμενος τρόπον τινὰ καὶ τὴν ἄγνοιαν ὁρίζεται, ὁμοίως δὲ καὶ τὸ ἐπιστῆμον καὶ τὸ ἀνεπιστῆμον καὶ τὸ ἐπίστασθαι καὶ τὸ ἀγνοεῖν· τοῦ γὰρ πρώτου δήλου γενομένου τρόπον τινὰ καὶ τὰ λοιπὰ δῆλα γίνονται.
Generally speaking, in such definitions it happens that the definer in some way defines more than one thing; for he who defines knowledge also in some way defines ignorance, and likewise also the knower and the ignorant, and knowing and being ignorant; for when the first is made clear, in some way the rest also become clear.
Σκεπτέον οὖν ἐπὶ πάντων τῶν τοιούτων μή τι διαφωνῇ, στοιχείοις χρώμενον τοῖς ἐκ τῶν ἐναντίων καὶ τῶν συστοίχων.
One must therefore examine in the case of all such things whether there is any discrepancy, using elements derived from contraries and co-ordinates.
Ἔτι ἐπὶ τῶν πρός τι σκοπεῖν εἰ πρὸς ὃ τὸ γένος ἀποδίδοται, τὸ εἶδος πρὸς ἐκεῖνό τι ἀποδίδοται, οἷον εἰ ἡ ὑπόληψις πρὸς ὑποληπτόν, ἡ τὶς ὑπόληψις πρός τι ὑποληπτόν, καὶ εἰ τὸ πολλαπλάσιον πρὸς τὸ πολλοστημόριον, τὸ τὶ πολλαπλάσιον πρὸς τὸ τὶ πολλοστημόριον· εἰ γὰρ μὴ οὕτως ἀποδίδοται, δῆλον ὅτι ἡμάρτηται.
Moreover, in the case of relatives, one must examine whether, if the genus is rendered in relation to something, the species also is rendered in relation to a particular thing; for example, if belief is in relation to what is believable, a particular belief is in relation to a particular believable thing; and if the multiple is in relation to the fraction, a particular multiple is in relation to a particular fraction; for if it is not rendered in this way, it is clear that a mistake has been made.
Ὁρᾶν δὲ καὶ εἰ τοῦ ἀντικειμένου ὁ ἀντικείμενος λόγος, οἷον τοῦ ἡμίσεος ὁ ἀντικείμενος τῷ τοῦ διπλασίου·
One must also see whether the definition of the opposite corresponds to the opposite; for example, whether the definition of the half is opposite to that of the double.
εἰ γὰρ διπλάσιον τὸ ἴσῳ ὑπερέχον, ἥμισυ τὸ ἴσῳ ὑπερεχόμενον.
For if the double is that which exceeds by an equal amount, the half is that which is exceeded by an equal amount.
Καὶ ἐπὶ τῶν ἐναντίων δ᾿ ὡσαύτως.
And likewise also in the case of contraries.
Ὁ γὰρ ἐναντίος τοῦ ἐναντίου λόγος ἔσται κατὰ μίαν τινὰ συμπλοκὴν τῶν ἐναντίων, οἷον εἰ ὠφέλιμον τὸ ποιητικὸν ἀγαθοῦ, βλαβερὸν τὸ ποιητικὸν κακοῦ ἢ τὸ φθαρτικὸν ἀγαθοῦ· θάτερον γὰρ τούτων ἀναγκαῖον ἐναντίον εἶναι τῷ ἐξ ἀρχῆς ῥηθέντι.
For the definition of the contrary will be of the contrary according to a certain combination of contraries; for example, if the beneficial is that which is productive of good, the harmful is that which is productive of evil, or that which is destructive of good; for one of these must be contrary to what was stated at the beginning.
Εἰ οὖν μηδέτερον ἐναντίον τῷ ἐξ ἀρχῆς ῥηθέντι, δῆλον ὅτι οὐδέτερος ἂν εἴη τῶν ὕστερον ἀποδοθέντων τοῦ ἐναντίου λόγος, ὥστ᾿ οὐδ᾿ ὁ ἐξ ἀρχῆς ἀποδοθεὶς ὀρθῶς ἀποδέδοται.
If, then, neither of them is contrary to what was stated at the beginning, it is clear that neither of the definitions rendered later would be the definition of the contrary, so that not even the one rendered at the beginning has been correctly rendered.
Ἐπεὶ δ᾿ ἔνια τῶν ἐναντίων στερήσει θατέρου λέγεται, οἷον ἡ ἀνισότης στέρησις ἰσότητος δοκεῖ εἶναι (ἄνισα γὰρ τὰ μὴ ἴσα λέγεται), δῆλον ὅτι τὸ μὲν κατὰ στέρησιν λεγόμενον ἐναντίον ἀναγκαῖον ὁρίζεσθαι διὰ θατέρου, τὸ δὲ λοιπὸν οὐκέτι διὰ τοῦ κατὰ στέρησιν λεγομένου· συμβαίνοι γὰρ ἂν ἑκάτερον δι᾿ ἑκατέρου γνωρίζεσθαι.
But since some contraries are spoken of by the privation of the other, as inequality seems to be a privation of equality (for things that are not equal are called unequal), it is clear that the contrary which is spoken of by privation must be defined through the other, but the other no longer through the one spoken of by privation; for otherwise it would happen that each is known through the other.
Ἐπισκεπτέον οὖν ἐν τοῖς ἐναντίοις τὴν τοιαύτην ἁμαρτίαν, οἷον εἴ τις ὁρίσαιτο τὴν ἰσότητα εἶναι τὸ ἐναντίον ἀνισότητι· διὰ γὰρ τοῦ κατὰ στέρησιν λεγομένου ὁρίζεται.
One must therefore examine such a mistake in the case of contraries, for example, if someone should define equality as the contrary to inequality; for he defines it through the one spoken of by privation.
Ἔτι τὸν οὕτως ὁριζόμενον ἀναγκαῖον αὐτῷ τῷ ὁριζομένῳ χρῆσθαι.
Moreover, he who defines in this way must necessarily use the very thing to be defined.
Δῆλον δὲ τοῦτο, ἐὰν μεταληφθῇ ἀντὶ τοῦ ὀνόματος ὁ λόγος· εἰπεῖν γὰρ ἢ ἀνισότητα οὐδὲν διαφέρει ἢ στέρησιν ἰσότητος, ἔσται οὖν ἡ ἰσότης τὸ ἐναντίον στερήσει ἰσότητος, ὥστ᾿ αὐτῷ ἂν εἴη κεχρημένος.
This becomes clear if the definition is substituted for the name; for to say 'inequality' or 'privation of equality' makes no difference, so that equality will be the contrary to the privation of equality, so that he would be using it itself.
Ἂν δὲ μηδέτερον τῶν ἐναντίων κατὰ στέρησιν λέγηται, ἀποδοθῇ δ᾿ ὁ λόγος ὁμοίως, οἷον ἀγαθὸν τὸ ἐναντίον κακῷ, δῆλον ὅτι κακὸν τὸ ἐναντίον ἀγαθῷ ἔσται· τῶν γὰρ οὕτως ἐναντίων ὁμοίως ὁ λόγος ἀποδοτέος.
But if neither of the contraries is spoken of by privation, but the definition is rendered in a similar way, for example, the good is the contrary to the evil, it is clear that the evil will be the contrary to the good; for the definition of such contraries must be rendered in a similar way.
Ὥστε πάλιν αὐτῷ τῷ ὁριζομένῳ συμβαίνει χρῆσθαι· ἐνυπάρχει γὰρ ἐν τῷ τοῦ κακοῦ λόγῳ τὸ ἀγαθόν.
So that again it happens that he uses the very thing to be defined; for the good is present in the definition of the evil.
Ὥστ᾿ εἰ ἀγαθόν ἐστι τὸ κακῷ ἐναντίον, τὸ δὲ κακὸν οὐδὲν διαφέρει ἢ τὸ τῷ ἀγαθῷ ἐναντίον, ἔσται ἀγαθὸν τὸ ἐναντίον τῷ τοῦ ἀγαθοῦ ἐναντίῳ.
So that if the good is the contrary to the evil, and the evil is no different from the contrary to the good, the good will be the contrary to the contrary of the good.
Δῆλον οὖν ὅτι αὐτῷ κέχρηται.
It is clear, then, that he has used it itself.
Ἔτι εἰ τὸ κατὰ στέρησιν λεγόμενον ἀποδιδοὺς μὴ ἀποδέδωκεν οὗ ἐστὶ στέρησις, οἷον τῆς ἕξεως ἢ τοῦ ἐναντίου ἢ ὁτουοῦν ἐστὶν ἡ στέρησις· καὶ εἰ μὴ ἐν ᾧ πέφυκε γίνεσθαι προσέθηκεν, ἢ ἁπλῶς ἢ ἐν ᾧ πρώτῳ πέφυκε γίνεσθαι, οἷον εἰ τὴν ἄγνοιαν εἰπὼν στέρησιν μὴ ἐπιστήμης στέρησιν εἶπεν, ἢ μὴ προσέθηκεν ἐν ᾧ πέφυκε γίνεσθαι, ἢ προσθεὶς μὴ ἐν ᾧ πρώτῳ ἀπέδωκεν, οἷον ὅτι οὐκ ἐν τῷ λογιστικῷ ἀλλ᾿ ἐν ἀνθρώπῳ ἢ ψυχῇ· ἐὰν γὰρ ὁτιοῦν τούτων μὴ ποιήσῃ, ἡμάρτηκεν.
Moreover, if in rendering what is spoken of by privation, he has not rendered that of which it is a privation, for example, of the habit, or of the contrary, or of whatever it is a privation; and if he has not added that in which it naturally arises, either simply or that in which it primarily naturally arises; for example, if in speaking of ignorance as a privation, he did not say it is a privation of knowledge, or did not add that in which it naturally arises, or having added it, did not render that in which it primarily arises, for example, not in the rational part but in man or in the soul; for if he fails to do any of these things, he has made a mistake.
Ὁμοίως δὲ καὶ εἰ τὴν τυφλότητα μὴ ὄψεως στέρησιν ἐν ὀφθαλμῷ εἶπεν· δεῖ γὰρ τὸν καλῶς ἀποδιδόντα τὸ τί ἐστι, καὶ τίνος ἐστὶν ἡ στέρησις ἀποδοῦναι καὶ τί ἐστι τὸ ἐστερημένον.
Likewise also if he did not say that blindness is a privation of sight in the eye; for he who renders the essence correctly must render both that of which it is a privation and that which is deprived.
Ὁρᾶν δὲ καὶ εἰ μὴ λεγομένου κατὰ στέρησιν στερήσει ὡρίσατο, οἷον καὶ ἐπὶ τῆς ἀγνοίας δόξειεν ἂν ὑπάρχειν ἡ τοιαύτη ἁμαρτία τοῖς μὴ κατ᾿ ἀπόφασιν τὴν ἄγνοιαν λέγουσιν.
One must also see whether, when a thing is not spoken of by privation, he has defined it by privation; as in the case of ignorance, such a mistake might seem to occur to those who do not speak of ignorance by negation.
Τὸ γὰρ μὴ ἔχον ἐπιστήμην οὐ δοκεῖ ἀγνοεῖν, ἀλλὰ μᾶλλον τὸ διηπατημένον, διὸ οὔτε τὰ ἄψυχα οὔτε τὰ παιδία φαμὲν ἀγνοεῖν, ὥστ᾿ οὐ κατὰ στέρησιν ἐπιστήμης ἡ ἄγνοια λέγεται.
For that which does not have knowledge does not seem to be ignorant, but rather that which has been deceived, which is why we say that neither inanimate things nor infants are ignorant, so that ignorance is not spoken of by privation of knowledge.