§7.1#2Ἔτι ἐκ τῶν τούτοις συμβεβηκότων, καὶ οἷς ταῦτα συμβέβηκεν, ἐπισκοπεῖν· ὅσα γὰρ θατέρῳ συμβέβηκε, καὶ θατέρῳ δεῖ συμβεβηκέναι, καὶ οἷς θάτερον αὐτῶν συμβέβηκε, καὶ θάτερον δεῖ συμβεβηκέναι.
Again, one must examine from their accidents, and from those things to which these are accidents; for whatever is an accident of the one must also be an accident of the other, and to whatever one of them is an accident, the other must also be an accident.
Εἰ δέ τι τούτων διαφωνεῖ, δῆλον ὅτι οὐ ταὐτά.
If there is any discrepancy in these, it is clear that they are not the same.
Ὁρᾶν δὲ καὶ εἰ μὴ ἐν ἑνὶ γένει κατηγορίας ἀμφότερα, ἀλλὰ τὸ μὲν ποιὸν τὸ δὲ ποσὸν ἢ πρός τι δηλοῖ.
One must also see if both do not belong to one genus of category, but the one signifies quality and the other quantity or relation.
Πάλιν εἰ τὸ γένος ἑκατέρου μὴ ταὐτόν, ἀλλὰ τὸ μὲν ἀγαθὸν τὸ δὲ κακόν, ἢ τὸ μὲν ἀρετὴ τὸ δ᾿ ἐπιστήμη.
Again, see if the genus of each is not the same, but the one is good and the other evil, or the one is virtue and the other knowledge.
Ἢ εἰ τὸ μὲν γένος ταὐτόν, αἱ διαφοραὶ δὲ μὴ αἱ αὐταὶ ἑκατέρου κατηγοροῦνται, ἀλλὰ τοῦ μὲν ὅτι θεωρητικὴ ἐπιστήμη, τοῦ δ᾿ ὅτι πρακτική.
Or if the genus is the same, but the same differences are not predicated of each, but of the one that it is a speculative science, and of the other that it is a practical one.
Ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων.
And similarly in the case of others.
Ἔτι ἐκ τοῦ μᾶλλον, εἰ τὸ μὲν δέχεται τὸ μᾶλλον τὸ δὲ μή, ἢ εἰ ἄμφω μὲν δέχεται, μὴ ἅμα δέ, καθάπερ ὁ μᾶλλον ἐρῶν οὐ μᾶλλον ἐπιθυμεῖ τῆς συνουσίας, ὥστ᾿ οὐ ταὐτὸν ἔρως καὶ ἐπιθυμία συνουσίας.
Further, from the 'more', see if the one admits of 'more' and the other does not, or if both admit of it, but not at the same time; just as he who loves more does not more desire sexual intercourse, so that love and desire for intercourse are not the same.
Ἔτι ἐκ τῆς προσθέσεως, εἰ τῷ αὐτῷ ἑκάτερον προστιθέμενον μὴ ποιεῖ τὸ ὅλον ταὐτόν.
Further, from addition, see if each, when added to the same thing, does not make the whole the same.
Ἢ εἰ τοῦ αὐτοῦ ἀφ᾿ ἑκατέρου ἀφαιρεθέντος τὸ λοιπὸν ἕτερον, οἷον εἰ διπλάσιον ἡμίσεος καὶ πολλαπλάσιον ἡμίσεος ταὐτὸν ἔφησεν εἶναι.
Or if, when the same thing is subtracted from each, the remainder is different; as for example if someone said that 'double of a half' and 'multiple of a half' are the same.
Ἀφαιρεθέντος γὰρ ἀφ᾿ ἑκατέρου τοῦ ἡμίσεος τὰ λοιπὰ ταὐτὸν ἔδει δηλοῦν, οὐ δηλοῖ δέ· τὸ γὰρ διπλάσιον καὶ πολλαπλάσιον οὐ ταὐτὸν δηλοῖ.
For when 'half' is subtracted from each, the remainders ought to signify the same, but they do not; for 'double' and 'multiple' do not signify the same.
Σκοπεῖν δὲ μὴ μόνον εἰ ἤδη τι συμβαίνει ἀδύνατον διὰ τῆς θέσεως, ἀλλὰ καὶ εἰ δυνατὸν ἐξ ὑποθέσεως ὑπάρξαι, καθάπερ τοῖς τὸ κενὸν καὶ τὸ πλῆρες ἀέρος ταὐτὸν φάσκουσιν.
One must examine not only whether some impossibility already results through the thesis, but also whether it is possible for it to occur under a hypothesis, as with those who assert that the void and what is full of air are the same.
Δῆλον γὰρ ὅτι ἐὰν ἐξέλθῃ ὁ ἀήρ, κενὸν μὲν οὐχ ἧσσον ἀλλὰ μᾶλλον ἔσται, πλῆρες δ᾿ ἀέρος οὐκέτι ἔσται.
For it is clear that if the air should go out, the void will be no less but rather more, but it will no longer be full of air.
Ὥστε ὑποτεθέντος τινὸς εἴτε ψευδοῦς εἴτ᾿ ἀληθοῦς (οὐδὲν γὰρ διαφέρει) τὸ μὲν ἕτερον ἀναιρεῖται αὐτῶν, τὸ δ᾿ ἕτερον οὔ.
Thus, when something is hypothesized, whether false or true (for it makes no difference), the one of them is abolished, while the other is not.
Ὥστ᾿ οὐ ταὐτόν.
Therefore, they are not the same.
Καθόλου δ᾿ εἰπεῖν, ἐκ τῶν ὁπωσοῦν ἑκατέρου κατηγορουμένων, καὶ ὧν ταῦτα κατηγορεῖται, σκοπεῖν εἴ που διαφωνεῖ· ὅσα γὰρ θατέρου κατηγορεῖται, καὶ θατέρου κατηγορεῖσθαι δεῖ, καὶ ὧν θάτερον κατηγορεῖται, καὶ θάτερον κατηγορεῖσθαι δεῖ.
To speak generally, one must examine from whatever is predicated in any way of each, and of what these are predicated, to see if they disagree anywhere; for whatever is predicated of the one must also be predicated of the other, and of whatever the one is predicated, the other must also be predicated.
Ἔτι ἐπεὶ πολλαχῶς ταὐτὸν λέγεται, σκοπεῖν εἰ καὶ καθ᾿ ἕτερόν τινα τρόπον ταὐτά ἐστιν· τὰ γὰρ εἴδει ἢ γένει ταὐτὰ ἢ οὐκ ἀνάγκη ἢ οὐκ ἐνδέχεται ἀριθμῷ ταὐτὰ εἶναι, ἐπισκοποῦμεν δὲ πότερον οὕτω ταὐτὰ ἢ οὐχ οὕτως.
Further, since 'the same' is said in many ways, see if they are the same only in some other way; for things that are the same in species or in genus are either not necessarily, or cannot be, the same in number, and we are examining whether they are same in this way or not in this way.
Ἔτι εἰ δυνατὸν θάτερον ἄνευ θατέρου εἶναι· οὐ γὰρ ἂν εἴη ταὐτόν.
Further, if it is possible for the one to exist without the other; for then they would not be the same.