§6.6#1Πάλιν ἐπὶ τῶν διαφορῶν ὁμοίως σκεπτέον εἰ καὶ τὰς διαφορὰς εἶπε τὰς τοῦ γένους.
Again, regarding the differences, one must likewise examine whether he has stated the differences of the genus.
Εἰ γὰρ μὴ ταῖς τοῦ πράγματος ἰδίαις ὥρισται διαφοραῖς, ἢ καὶ παντελῶς τοιοῦτον εἴρηκεν ὃ μηδενὸς ἐνδέχεται διαφορὰν εἶναι, οἷον τὸ ζῷον ἢ τὴν οὐσίαν, δῆλον ὅτι οὐχ ὥρισται· οὐδενὸς γὰρ διαφοραὶ τὰ εἰρημένα.
For if he has not defined the thing by its own proper differences, or if he has spoken of something entirely of such a kind as cannot be a difference of anything, for example, 'animal' or 'substance', it is clear that he has not defined it; for the things mentioned are differences of nothing.
Ὁρᾶν δὲ καὶ εἰ ἔστιν ἀντιδιῃρημένον τι τῇ εἰρημένῃ διαφορᾷ.
One must also see if there is any contrary division to the mentioned difference.
Εἰ γὰρ μή ἐστι, δῆλον ὅτι οὐκ ἂν εἴη ἡ εἰρημένη τοῦ γένους διαφορά· πᾶν γὰρ γένος ταῖς ἀντιδιῃρημέναις διαφοραῖς διαιρεῖται, καθάπερ τὸ ζῷον τῷ πεζῷ καὶ τῷ πτηνῷ καὶ τῷ ἐνύδρῳ καὶ τῷ δίποδι.
For if there is not, it is clear that the mentioned difference would not be a difference of the genus; for every genus is divided by contrarily divided differences, just as 'animal' is divided by 'terrestrial', 'winged', 'aquatic', and 'biped'.
Ἣ εἰ ἔστι μὲν ἡ ἀντιδιῃρημένη διαφορά, μὴ ἀληθεύεται δὲ κατὰ τοῦ γένους.
Or if the contrarily divided difference exists, but is not true of the genus.
Δῆλον γὰρ ὅτι οὐδετέρα ἂν εἴη τοῦ γένους διαφορά· πᾶσαι γὰρ αἱ ἀντιδιῃρημέναι διαφοραὶ ἀληθεύονται κατὰ τοῦ οἰκείου γένους.
For it is clear that neither would be a difference of the genus; for all contrarily divided differences are true of their proper genus.
Ὁμοίως δὲ καὶ εἰ ἀληθεύεται μέν, μὴ ποιεῖ δὲ προστιθεμένη τῷ γένει εἶδος.
Likewise, if it is true, but does not, when added to the genus, make a species.
Δῆλον γὰρ ὅτι οὐκ ἂν εἴη αὕτη εἰδοποιὸς διαφορὰ τοῦ γένους· πᾶσα γὰρ εἰδοποιὸς διαφορὰ μετὰ τοῦ γένους εἶδος ποιεῖ.
For it is clear that this would not be a specific difference of the genus; for every specific difference, along with the genus, makes a species.
Εἰ δ᾿ αὕτη μή ἐστι διαφορά, οὐδ᾿ ἡ λεχθεῖσα, ἐπεὶ ταύτῃ ἀντιδιῄρηται.
But if this is not a difference, neither is the one mentioned, since it is contrarily divided against this.
Ἔτι ἐὰν ἀποφάσει διαιρῇ τὸ γένος, καθάπερ οἱ τὴν γραμμὴν ὁριζόμενοι μῆκος ἀπλατὲς εἶναι.
Moreover, if he divides the genus by negation, as those who define a line as 'a length without breadth'.
Οὐδὲν γὰρ ἄλλο σημαίνει ἢ ὅτι οὐκ ἔχει πλάτος.
For it signifies nothing else than that it does not have breadth.
Συμβήσεται οὖν τὸ γένος μετέχειν τοῦ εἴδους· πᾶν γὰρ μῆκος ἢ ἀπλατὲς ἢ πλάτος ἔχον ἐστίν, ἐπεὶ κατὰ παντὸς ἢ ἡ κατάφασις ἢ ἡ ἀπόφασις ἀληθεύεται, ὥστε καὶ τὸ γένος τῆς γραμμῆς μῆκος ὂν ἢ ἀπλατὲς ἢ πλάτος ἔχον ἔσται.
It will follow, then, that the genus participates in the species; for every length is either without breadth or having breadth, since of everything either the affirmation or the negation is true, so that the genus of line, being length, will be either without breadth or having breadth.
Μῆκος δ᾿ ἀπλατὲς εἴδους ἐστὶ λόγος, ὁμοίως δὲ καὶ μῆκος πλάτος ἔχον· τὸ γὰρ ἀπλατὲς καὶ πλάτος ἔχον διαφοραί εἰσιν, ἐκ δὲ τῆς διαφορᾶς καὶ τοῦ γένους ὁ τοῦ εἴδους ἐστὶ λόγος, ὥστε τὸ γένος ἐπιδέχοιτ᾿ ἂν τὸν τοῦ εἴδους λόγον.
But 'length without breadth' is the definition of a species, and likewise 'length having breadth'; for 'without breadth' and 'having breadth' are differences, and from the difference and the genus is the definition of the species, so that the genus would admit the definition of the species.
Ὁμοίως δὲ καὶ τὸν τῆς διαφορᾶς, ἐπειδὴ ἡ ἑτέρα τῶν εἰρημένων διαφορῶν ἐξ ἀνάγκης κατηγορεῖται τοῦ γένους.
Likewise also that of the difference, since one of the mentioned differences is of necessity predicated of the genus.
Ἔστι δ᾿ ὁ εἰρημένος τόπος χρήσιμος πρὸς τοὺς τιθεμένους ἰδέας εἶναι.
And the mentioned topic is useful against those who posit that there are ideas.
Εἰ γάρ ἐστιν αὐτὸ μῆκος, πῶς κατηγορηθήσεται κατὰ τοῦ γένους ὅτι πλάτος ἔχον ἐστὶν ἢ ἀπλατές ἐστιν;
For if there is length itself, how will it be predicated of the genus that it is having breadth or is without breadth?
δεῖ γὰρ κατὰ παντὸς μήκους τὸ ἕτερον αὐτῶν ἀληθεύεσθαι, εἴπερ κατὰ τοῦ γένους ἀληθεύεσθαι μέλλει.
For one of them must be true of every length, if it is to be true of the genus.
Τοῦτο δ᾿ οὐ συμβαίνει· ἔστι γὰρ ἀπλατῆ καὶ πλάτος ἔχοντα μήκη.
But this does not happen; for there are lengths without breadth and lengths having breadth.
Ὥστε πρὸς ἐκείνους μόνους χρήσιμος ὁ τόπος, οἳ τὸ γένος ἓν ἀριθμῷ φασὶν εἶναι.
So that the topic is useful only against those who say that the genus is one in number.
Τοῦτο δὲ ποιοῦσιν οἱ τὰς ἰδέας τιθέμενοι· αὐτὸ γὰρ μῆκος καὶ αὐτὸ ζῷον γένος φασὶν εἶναι.
And this is what those who posit the ideas do; for they say that length itself and animal itself are genera.
Ἴσως δ᾿ ἐπ᾿ ἐνίων ἀναγκαῖον καὶ ἀποφάσει χρῆσθαι τὸν ὁριζόμενον, οἷον ἐπὶ τῶν στερήσεων· τυφλὸν γάρ ἐστι τὸ μὴ ἔχον ὄψιν, ὅτε πέφυκεν ἔχειν.
But perhaps in some cases it is necessary for the definer to use negation as well, as in the case of privations; for 'blind' is that which does not have sight when it is natural to have it.
Διαφέρει δ᾿ οὐδὲν ἀποφάσει διελεῖν τὸ γένος, ἢ τοιαύτῃ καταφάσει ᾗ ἀπόφασιν ἀναγκαῖον ἀντιδιαιρεῖσθαι, οἷον εἰ μῆκος πλάτος ἔχον ὥρισται· τῷ γὰρ πλάτος ἔχοντι τὸ μὴ ἔχον πλάτος ἀντιδιῄρηται, ἄλλο δ᾿ οὐδέν, ὥστε ἀποφάσει πάλιν διαιρεῖται τὸ γένος.
And it makes no difference to divide the genus by negation, or by such an affirmation to which it is necessary for a negation to be contrarily divided, for example, if length is defined as having breadth; for to 'having breadth', 'not having breadth' is contrarily divided, and nothing else, so that the genus is divided by negation again.
Πάλιν εἰ τὸ εἶδος ὡς διαφορὰν ἀπέδωκε, καθάπερ οἱ τὸν προπηλακισμὸν ὕβριν μετὰ χλευασίας ὁριζόμενοι· ἡ γὰρ χλευασία ὕβρις τις, ὥστ᾿ οὐ διαφορὰ ἀλλ᾿ εἶδος ἡ χλευασία.
Again, if he has rendered the species as a difference, as those who define insult as 'outrage accompanied by mockery'; for mockery is a kind of outrage, so that mockery is not a difference but a species.
Ἔτι εἰ τὸ γένος ὡς διαφορὰν εἴρηκεν, οἷον τὴν ἀρετὴν ἕξιν ἀγαθὴν ἢ σπουδαίαν· γένος γὰρ τἀγαθὸν τῆς ἀρετῆς ἐστίν.
Moreover, if he has stated the genus as a difference, for example, defining virtue as a 'good' or 'excellent' state; for the good is the genus of virtue.
Ἢ οὐ γένος τἀγαθόν, ἀλλὰ διαφορά, εἴπερ ἀληθὲς ὅτι οὐκ ἐνδέχεται ταὐτὸν ἐν δύο γένεσιν εἶναι μὴ περιέχουσιν ἄλληλα.
Or, if the good is not the genus but a difference, this is true if indeed it is true that the same thing cannot be in two genera that do not contain one another.
Οὔτε γὰρ τἀγαθὸν τὴν ἕξιν περιέχει οὔθ᾿ ἡ ἕξις τἀγαθόν· οὐ γὰρ πᾶσα ἕξις ἀγαθόν, οὐδὲ πᾶν ἀγαθὸν ἕξις, ὥστ᾿ οὐκ ἂν εἴη γένη ἀμφότερα.
For neither does the good contain the state, nor does the state contain the good; for not every state is a good, nor is every good a state, so that both would not be genera.
Εἰ οὖν ἡ ἕξις τῆς ἀρετῆς γένος, δῆλον ὅτι τἀγαθὸν οὐ γένος, ἀλλὰ μᾶλλον διαφορά.
If, then, the state is the genus of virtue, it is clear that the good is not the genus, but rather a difference.
Ἔτι ἡ μὲν ἕξις τί ἐστι σημαίνει ἡ ἀρετή, τὸ δ᾿ ἀγαθὸν οὐ τί ἐστιν ἀλλὰ ποιόν· δοκεῖ δ᾿ ἡ διαφορὰ ποῖόν τι σημαίνειν.
Moreover, the state signifies the 'what it is' of virtue, but the good signifies not 'what it is' but 'of what kind'; and the difference seems to signify 'of what kind'.