§1.1.15#2Διωρισμένων δὴ τούτων ὑπαρχέτω τὸ Α παντὶ τῷ Β, τὸ δὲ Β παντὶ τῷ Γ ἐνδεγέσθω·
These being defined, let A belong to all B, and let B be possible to belong to all Γ.
ἀνάγκη οὖν τὸ παντὶ τῷ Γ ἐνδέχεσθαι ὑπάρχειν.
Therefore it is necessary for [A] to be possible to belong to all Γ.
μὴ γὰρ ἐνδεχέσθω, τὸ δὲ Β παντὶ τῷ Γ κείσθω ὡς ὑπάρχον· τοῦτο δὲ ψεῦδος μέν, οὐ μέντοι ἀδύνατον.
For let it not be possible, and let B be assumed to belong to all Γ; this is indeed false, but not impossible.
εἰ οὖν τὸ μὲν Α μὴ ἐνδέχεται παντὶ τῷ Γ, τὸ δὲ Β παντὶ ὑπάρχει τῷ Γ τὸ οὐ παντὶ τῷ Β ἐνδέχεται· γίνεται γὰρ συλλογισμὸς διὰ τοῦ τρίτου σχήματος.
If, then, A is not possible for all Γ, and B belongs to all Γ, [A] is not possible for all B; for a syllogism comes about through the third figure.
ἀλλʼ ὑπέκειτο παντὶ ἐνδέχεσθαι ὑπάρχειν.
But it was assumed to be possible to belong to all [B].
ἀνάγκη ἄρα τὸ Α παντὶ τῷ Γ ἐνδέχεσθαι· ψεύδους γὰρ τεθέντος καὶ οὐκ ἀδυνάτου τὸ συμβαῖνόν ἐστιν ἀδύνατον.
Therefore it is necessary for A to be possible for all Γ; for when a falsehood and not an impossible thing is assumed, the result is impossible.
Δεῖ δὲ λαμβάνειν τὸ παντὶ ὑπάρχον μὴ κατὰ χρόνον ὁρίσαντας, οἷον νῦν ἢ ἐν τῷδε τῷ χρόνῳ, ἀλλʼ ἁπλῶς·
But we must assume belonging to all not by defining it by time, such as "now" or "at this time," but absolutely.
διὰ τοιούτων γὰρ προτάσεων καὶ τοὺς συλλογισμούς ποιοῦμεν, ἐπεὶ κατά γε τὸ νῦν λαμβανομένης τῆς προτάσεως οὐκ ἔσται συλλογισμός·
For it is through such premises that we also make syllogisms, since if the premise is assumed at least with respect to the "now," there will be no syllogism.
οὐδὲν γὰρ ἴσως κωλύει ποτὲ καὶ παντὶ κινουμένῳ ἄνθρωπον ὑπάρχειν, οἷον εἰ μηδὲν ἄλλο κινοῖτο·
For perhaps nothing prevents, at some time, man from belonging to everything that is moving, for example, if nothing else were moving.
τὸ δὲ κινούμενον ἐνδέχεται παντὶ ἵππῳ· ἀλλʼ ἄνθρωπον οὐδενὶ ἵππῳ ἐνδέχεται.
And that which is moving is possible to all horses; but man is possible to no horse.
ἔτι ἔστω τὸ μὲν πρῶτον ζῷον, τὸ δὲ μέσον κινούμενον, τὸ δʼ ἔσχατον ἄνθρωπος. αἱ μὲν οὖν προτάσεις ὁμοίως ἕξουσι, τὸ δὲ συμπέρασμα ἀναγκαῖον, οὐκ ἐνδεχόμενον· ἐξ ἀνάγκης γὰρ ὁ ἄνθρωπος ζῷον.
Further, let the first be "animal," the middle "moving," and the last "man." Then the premises will be in the same relation, but the conclusion is necessary, not possible; for of necessity man is animal.
φανερὸν οὖν ὅτι τὸ καθόλου ληπτέον ἀπλῶς, καὶ οὐ χρόνῳ διορίζοντας.
It is clear, then, that the universal must be assumed absolutely, and not by defining it by time.
Πάλιν ἔστω στερητικὴ πρότασις καθόλου ἡ Α Β, καὶ εἰλήφθω τὸ μὲν Α μηδενὶ τῷ Β ὑπάρχειν, τὸ δὲ Β παντὶ ἐνδεχέσθω ὑπάρχειν τῷ Γ. τούτων οὖν τεθέντων ἀνάγκη τὸ ἐνδέχεσθαι μηδενὶ τῷ Γ ὑπάρχειν.
Again, let the universal privative premise be AB, and let A be assumed to belong to no B, and B be possible to belong to all Γ. When these are assumed, it is necessary for [A] to be possible to belong to no Γ.
μὴ γὰρ ἐνδεχέσθω, τὸ δὲ Β τῷ Γ κείσθω ὑπάρχον, καθάπερ πρότερον.
For let it not be possible, and let B be assumed to belong to Γ, just as before.
ἀνάγκη δὴ τὸ Α τινὶ τῷ Β ὑπάρχειν· γίνεται γὰρ συλλογισμός διὰ τοῦ τρίτου σχήματος· τοῦτο δὲ ἀδύνατον.
Then it is necessary for A to belong to some B; for a syllogism comes about through the third figure; but this is impossible.
ὥστʼ ἐνδέχοιτʼ ἂφν τὸ Α μηδενὶ τῷ Γ· ψεύδους γὰρ τεθέντος ἀδύνατον τὸ συμβαῖνον.
Therefore, A would be possible to belong to no Γ; for when a falsehood is assumed, the result is impossible.
οὗτος οὖν ὁ συλλογισμὸς οὐκ ἔστι τοῦ κατὰ τὸν διορισμὸν ἐνδεχομένου, ἀλλὰ τοῦ μηδενὶ ἐξ ἀνάγκης (αὕτη γάρ ἐστιν ἡ ἀντίφασις τῆς γενομένης ὑποθέσεως· ἐτέθη γὰρ ἐξ ἀνάγκης τὸ Α τινὶ τῷ Γ ὑπάρχειν, ὁ δὲ διὰ τοῦ ἀδυνάτου συλλογισμὸς τῆς ἀντικειμένης ἐστὶν φάσεως).
This syllogism, then, is not of the possible according to the definition, but of belonging of necessity to none (for this is the contradiction of the hypothesis that was made; for A was assumed to belong of necessity to some Γ, and the syllogism through the impossible is of the opposite assertion).
ἔτι δὲ καὶ ἐκ τῶν ὅρων φανερὸν ὅτι οὐκ ἔσται τὸ συμπέρασμα ἐνδεχόμενον.
Further, it is also clear from the terms that the conclusion will not be possible.
ἔστω γὰρ τὸ μὲν Α κόραξ, τὸ δʼ ἐφʼ ᾧ Β διανοούμενον, ἐφʼ ᾧ δὲ Γ ἄνθρωπος. οὐδενὶ δὴ τῷ Β τὸ ὑπάρχει· οὐδὲν γὰρ διανοούμενον κόραξ.
For let A be "crow," B "thinking," and Γ "man." Then A belongs to no B; for nothing thinking is a crow.
τὸ δὲ Β παντὶ ἐνδέχεται τῷ Γ· παντὶ γὰρ ἀνθρώπῳ τὸ διανοεῖσθαι.
And B is possible to all Γ; for thinking is possible to all man.
ἀλλὰ τὸ ἐξ ἀνάγκης οὐδενὶ σῷ Γ· οὐκ ἄρα τὸ συμπέρασμα ἐνδεχόμενον.
But A belongs of necessity to no Γ; therefore the conclusion is not possible.
ἀλλʼ οὐδʼ ἀνακαῖονγ ἀεί.
But neither is it always necessary.
ἔστω γὰρ τὸ μὲν Α κινούμενον, τὸ δὲ Β ἐπιστήμη, τὸ δʼ ἐφʼ ᾧ Γ ἄνθρωπος. τὸ μὲν οὖν οὐδενὶ τῷ Β ὑπάρξει, τὸ δὲ Β παντὶ τῷ Γ ἐνδέχεται, καὶ οὐκ ἔσται τὸ συμπέρασμα ἀναγκαἱον· οὐ γὰρ ἀνάγκη μηδένα κινεῖσθαι ἄνθρωπον, ἀλλʼ οὐκ ἀνάγκη τινά.
For let A be "moving," B "knowledge," and Γ "man." Then A will belong to no B, and B is possible to all Γ, and the conclusion will not be necessary; for it is not necessary for no man to move, nor is it necessary for some to move.
δῆλον οὖν ὅτι τὸ συμπέρασμά ἐστι τοῦ μηδενὶ ἐξ ἀνάγκης ὑπάρχειν.
It is clear, then, that the conclusion is of belonging of necessity to no thing.
ληπτέον δὲ βέλτιον τοὺς ὅρους.
But better terms must be assumed.