§7.12νῦν δὲ λέγωμεν πρῶτον ἐφʼ ὅσον ἐν τοῖς ἀναλυτικοῖς περὶ ὁρισμοῦ μὴ εἴρηται· ἡ γὰρ ἐν ἐκείνοις ἀπορία λεχθεῖσα πρὸ ἔργου τοῖς περὶ τῆς οὐσίας ἐστὶ λόγοις.
Now let us speak first in so far as it has not been discussed in the Analytics concerning definition; for the difficulty stated in them is useful for the inquiries concerning substance.
λέγω δὲ ταύτην τὴν ἀπορίαν, διὰ τί ποτε ἕν ἐστιν οὗ τὸν λόγον ὁρισμὸν εἶναί φαμεν, οἷον τοῦ ἀνθρώπου τὸ ζῷον δίπουν· ἔστω γὰρ οὗτος αὐτοῦ λόγος.
And I mean this difficulty: why on earth is that one, whose formula we say is a definition—for example, 'two-footed animal' of man; for let this be his formula?
διὰ τί δὴ τοῦτο ἕν ἐστιν ἀλλʼ οὐ πολλά, ζῷον καὶ δίπουν·
Why, then, is this one and not many, namely, 'animal' and 'two-footed'?
ἐπὶ μὲν γὰρ τοῦ ἄνθρωπος καὶ λευκὸν πολλὰ μέν ἐστιν ὅταν μὴ ὑπάρχῃ θατέρῳ θάτερον, ἓν δὲ ὅταν ὑπάρχῃ καὶ πάθῃ τι τὸ ὑποκείμενον, ὁ ἄνθρωπος (τότε γὰρ ἓν γίγνεται καὶ ἔστιν ὁ λευκὸς ἄνθρωπος)· ἐνταῦθα δʼ οὐ μετέχει θατέρου θάτερον· τὸ γὰρ γένος οὐ δοκεῖ μετέχειν τῶν διαφορῶν (ἅμα γὰρ ἂν τῶν ἐναντίων τὸ αὐτὸ μετεῖχεν· αἱ γὰρ διαφοραὶ ἐναντίαι αἷς διαφέρει τὸ γένος).
For in the case of 'man' and 'pale', they are many when the one does not belong to the other, but one when it does belong and the subject, 'man', is affected in some way (for then 'pale man' becomes and is one); but here the one does not participate in the other; for the genus is not thought to participate in its differences (for then the same thing would participate in contraries at the same time, since the differences by which the genus differs are contraries).
εἰ δὲ καὶ μετέχει, ὁ αὐτὸς λόγος, εἴπερ εἰσὶν αἱ διαφοραὶ πλείους, οἷον πεζὸν δίπουν ἄπτερον.
And even if it does participate, the same argument holds, if the differences are several, as 'pedestrian, two-footed, wingless'.
διὰ τί γὰρ ταῦθʼ ἓν ἀλλʼ οὐ πολλά;
For why are these one and not many?
οὐ γὰρ ὅτι ἐνυπάρχει· οὕτω μὲν γὰρ ἐξ ἁπάντων ἔσται ἕν.
For it is not because they are present in the subject; for in that way one thing will be made out of all.
δεῖ δέ γε ἓν εἶναι ὅσα ἐν τῷ ὁρισμῷ· ὁ γὰρ ὁρισμὸς λόγος τίς ἐστιν εἷς καὶ οὐσίας, ὥστε ἑνός τινος δεῖ αὐτὸν εἶναι λόγον· καὶ γὰρ ἡ οὐσία ἕν τι καὶ τόδε τι σημαίνει, ὡς φαμέν. —δεῖ δὲ ἐπισκοπεῖν πρῶτον περὶ τῶν κατὰ τὰς διαιρέσεις ὁρισμῶν.
But indeed, all the things in the definition must be one; since the definition is a certain single formula and a formula of substance, so that it must be a formula of some one thing; for indeed substance signifies a certain one thing and a 'this', as we say.—And we must first examine concerning the definitions made by divisions.
οὐδὲν γὰρ ἕτερόν ἐστιν ἐν τῷ ὁρισμῷ πλὴν τὸ πρῶτον λεγόμενον γένος καὶ αἱ διαφοραί· τὰ δʼ ἄλλα γένη ἐστὶ τό τε πρῶτον καὶ μετὰ τούτου αἱ συλλαμβανόμεναι διαφοραί, οἷον τὸ πρῶτον ζῷον, τὸ δὲ ἐχόμενον ζῷον δίπουν, καὶ πάλιν ζῷον δίπουν ἄπτερον· ὁμοίως δὲ κἂν διὰ πλειόνων λέγηται.
For there is nothing else in the definition except the primary genus mentioned and the differences; and the other genera are the primary genus and the differences taken together with it, as, the primary genus is 'animal', the next 'two-footed animal', and again 'wingless two-footed animal'; and similarly even if it is stated through more terms.
ὅλως δʼ οὐδὲν διαφέρει διὰ πολλῶν ἢ διʼ ὀλίγων λέγεσθαι, ὥστʼ οὐδὲ διʼ ὀλίγων ἢ διὰ δυοῖν· τοῖν δυοῖν δὲ τὸ μὲν διαφορὰ τὸ δὲ γένος, οἷον τοῦ ζῷον δίπουν τὸ μὲν ζῷον γένος διαφορὰ δὲ θάτερον.
And in general it makes no difference whether it is stated through many or few terms, and so neither through few or two; but of the two, the one is difference and the other genus, as in 'two-footed animal', 'animal' is genus and the other is difference.
εἰ οὖν τὸ γένος ἁπλῶς μὴ ἔστι παρὰ τὰ ὡς γένους εἴδη, ἢ εἰ ἔστι μὲν ὡς ὕλη δʼ ἐστίν (ἡ μὲν γὰρ φωνὴ γένος καὶ ὕλη, αἱ δὲ διαφοραὶ τὰ εἴδη καὶ τὰ στοιχεῖα ἐκ ταύτης ποιοῦσιν), φανερὸν ὅτι ὁ ὁρισμός ἐστιν ὁ ἐκ τῶν διαφορῶν λόγος.
If, then, the genus simply does not exist apart from the species of the genus, or if it does exist but exists as matter (for voice is genus and matter, and the differences make the species and the letters out of this), it is clear that the definition is the formula derived from the differences.
ἀλλὰ μὴν καὶ δεῖ γε διαιρεῖσθαι τῇ τῆς διαφορᾶς διαφορᾷ, οἷον ζῴου διαφορὰ τὸ ὑπόπουν· πάλιν τοῦ ζῴου τοῦ ὑπόποδος τὴν διαφορὰν δεῖ εἶναι ᾗ ὑπόπουν, ὥστʼ οὐ λεκτέον τοῦ ὑπόποδος τὸ μὲν πτερωτὸν τὸ δὲ ἄπτερον, ἐάνπερ λέγῃ καλῶς (ἀλλὰ διὰ τὸ ἀδυνατεῖν ποιήσει τοῦτο), ἀλλʼ ἢ τὸ μὲν σχιζόπουν τὸ δʼ ἄσχιστον· αὗται γὰρ διαφοραὶ ποδός· ἡ γὰρ σχιζοποδία ποδότης τις.
But indeed, one must also divide by the difference of the difference, as, 'having feet' is a difference of animal; again, one must find the difference of 'animal having feet' in so far as it has feet, so that one must not say of 'that which has feet' that one is 'winged' and the other 'wingless', if one is to speak properly (though one will do this through inability), but rather that one is 'cloven-footed' and the other 'not cloven'; for these are differences of foot, since having cloven feet is a kind of footedness.
καὶ οὕτως ἀεὶ βούλεται βαδίζειν ἕως ἂν ἔλθῃ εἰς τὰ ἀδιάφορα· τότε δʼ ἔσονται τοσαῦτα εἴδη ποδὸς ὅσαιπερ αἱ διαφοραί, καὶ τὰ ὑπόποδα ζῷα ἴσα ταῖς διαφοραῖς.
And in this way one always wishes to proceed until one comes to the things which have no further differences; and then there will be as many species of foot as there are differences, and the animals having feet will be equal in number to the differences.
εἰ δὴ ταῦτα οὕτως ἔχει, φανερὸν ὅτι ἡ τελευταία διαφορὰ ἡ οὐσία τοῦ πράγματος ἔσται καὶ ὁ ὁρισμός, εἴπερ μὴ δεῖ πολλάκις ταὐτὰ λέγειν ἐν τοῖς ὅροις· περίεργον γάρ.
If, then, these things are so, it is clear that the ultimate difference will be the substance of the thing and its definition, if indeed we must not say the same things many times in definitions; for that is superfluous.
συμβαίνει δέ γε τοῦτο· ὅταν γὰρ εἴπῃ ζῷον ὑπόπουν δίπουν, οὐδὲν ἄλλο εἴρηκεν ἢ ζῷον πόδας ἔχον, δύο πόδας ἔχον· κἂν τοῦτο διαιρῇ τῇ οἰκείᾳ διαιρέσει, πλεονάκις ἐρεῖ καὶ ἰσάκις ταῖς διαφοραῖς.
Yet this does happen; for when one says 'animal having feet, two-footed', one has said nothing other than 'animal having feet, having two feet'; and if one divides this by its proper division, one will speak many times, indeed as many times as there are differences.
ἐὰν μὲν δὴ διαφορᾶς διαφορὰ γίγνηται, μία ἔσται ἡ τελευταία τὸ εἶδος καὶ ἡ οὐσία· ἐὰν δὲ κατὰ συμβεβηκός, οἷον εἰ διαιροῖ τοῦ ὑπόποδος τὸ μὲν λευκὸν τὸ δὲ μέλαν, τοσαῦται ὅσαι ἂν αἱ τομαὶ ὦσιν.
If, then, a difference of a difference is made, the ultimate one will be single, and this will be the form and the substance; but if it is according to accident, as if one were to divide 'that which has feet' into 'white' and 'black', there will be as many differences as there are cuts.
ὥστε φανερὸν ὅτι ὁ ὁρισμὸς λόγος ἐστὶν ὁ ἐκ τῶν διαφορῶν, καὶ τούτων τῆς τελευταίας κατά γε τὸ ὀρθόν.
So that it is clear that the definition is the formula derived from the differences, and, at least if it is correct, from the ultimate of these.
δῆλον δʼ ἂν εἴη, εἴ τις μετατάξειε τοὺς τοιούτους ὁρισμούς, οἷον τὸν τοῦ ἀνθρώπου, λέγων ζῷον δίπουν ὑπόπουν· περίεργον γὰρ τὸ ὑπόπουν εἰρημένου τοῦ δίποδος.
And this would be clear if one were to transpose such definitions, for example that of man, saying 'two-footed animal having feet'; for 'having feet' is superfluous when 'two-footed' has been said.
τάξις δʼ οὐκ ἔστιν ἐν τῇ οὐσίᾳ· πῶς γὰρ δεῖ νοῆσαι τὸ μὲν ὕστερον τὸ δὲ πρότερον;
But there is no order in the substance; for how must one conceive one part as posterior and another as prior?
περὶ μὲν οὖν τῶν κατὰ τὰς διαιρέσεις ὁρισμῶν τοσαῦτα εἰρήσθω τὴν πρώτην, ποῖοί τινές εἰσιν.
Therefore, concerning the definitions made by divisions, let so much be said for a first attempt, as to what kind of things they are.