§1.1.28#2Δῆλον δὲ καὶ ὅτι διὰ τῶν τριῶν ὅρων καὶ τῶν δύο προτασεων ἡ σκέψις, καὶ διὰ τῶν προειρημένων σχημάτων οἱ συλλογισμοὶ πάντες.
It is also clear that the inquiry is through three terms and two premises, and that all syllogisms are through the aforementioned figures.
δείκνυται γὰρ ὑπάρχειν μὲν παντὶ τῷ Ε τὸ Α, ὅταν τῶν Γ καὶ Ζ ταὐτόν τι ληφθῇ.
For it is shown that A belongs to every E when some one of the Γ and Z is taken as the same.
τοῦτο δʼ ἔσται μέσον, ἄκρα δὲ τὸ Α καὶ Ε· γίνεται οὖν τὸ πρῶτον σχῆμα.
This will be the middle, and the extremes will be A and E; thus the first figure is produced.
τινὶ δέ, ὅταν τὸ Γ καὶ τὸ Η ληφθῇ ταὐτόν.
And to some, when Γ and H are taken as the same.
τοῦτο δὲ τὸ ἔσχατον σχῆμα· μέσον γὰρ τὸ γίνεται.
This is the last figure; for the [term followed] becomes the middle.
μηδενὶ δέ, ὅταν τὸ Δ καὶ Ζ ταὐτόν.
And to none, when Δ and Z are the same.
οὕτω δὲ καὶ τὸ πρῶτον σχῆμα καὶ τὸ μέσον, τὸ μὲν πρῶτον ὅτι οὐδενὶ τῷ Ζ ὑπάρχει τὸ Α (εἴπερ ἀντιστρέφει τὸ στερητικόν), τὸ δὲ Ζ παντὶ τῷ Ε, τὸ δὲ μέσον ὅτι τὸ Δ τῷ μὲν Α οὐδενὶ τῷ δὲ Ε παντὶ ὑπάρχει.
In this way both the first figure and the middle are produced: the first, because A belongs to no Z (if indeed the negative proposition is convertible), and Z belongs to every E; and the middle, because Δ belongs to no A, but to every E.
τινὶ δὲ μὴ ὑπάρχειν, ὅταν τὸ Δ καὶ Η ταὐτὸν ᾖ.
And not to belong to some, when Δ and H are the same.
τοῦτο δὲ τὸ ἔσχατον σχῆμα· τὸ μὲν γὰρ οὐδενὶ τῷ Η ὑπάρξει, τὸ δὲ παντὶ τῷ Η. φανερὸν οὖν ὅτι διὰ τῶν προειρημένων σχημάτων οἱ συλλογισμοὶ πάντες, καὶ ὅτι οὐκ ἐκλεκτέον ὅσα πᾶσιν ἕπεται, διὰ τὸ μηδένα γίγνεσθαι συλλογισμὸν ἐξ αὐτῶν.
This is the last figure; for the one will belong to no H, and the other to every H. It is clear, then, that all syllogisms are through the aforementioned figures, and that we must not select things that follow all, because no syllogism is produced from them.
κατασκευάζειν μὲν γὰρ ὅλως οὐκ ἦν ἐκ τῶν ἑπομένων, ἀποστερεῖν δʼ οὐκ ἐνδέχεται διὰ τοῦ πᾶσιν ἑπομένου· δεῖ γὰρ τῷ μὲν ὑπάρχειν τῷ δὲ μὴ ὑπάρχειν.
For establishing universally was not possible at all from consequents, nor is it possible to deny through what follows all; for it must belong to the one and not belong to the other.
Φανερὸν δὲ καὶ ὅτι αἱ ἄλλαι σκέψεις τῶν κατὰ τὰς ἐκλογὰς ἄχρειοι πρὸς τὸ ποιεῖν συλλογισμόν, οἷον εἰ τὰ ἑπόμενα ἑκατέρῳ ταὐτά ἐστιν, ἢ εἰ οἷς ἕπεται τὸ Α καὶ ἃ μὴ ἐνδέχεται τῷ Ε, ἢ ὅσα πάλιν μὴ ἐγχωρεῖ ἑκατέρῳ ὑπάρχειν· οὐ γὰρ γίνεται συλλογισμὸς διὰ τούτων.
It is also clear that the other inquiries concerning the selections are useless for producing a syllogism, as, for example, if the consequents to each are the same, or if those things which A follows and those which cannot belong to E [are the same], or, again, if those things which cannot belong to either are the same; for no syllogism is produced through these.
εἰ μὲν γὰρ τὰ ἑπόμενα ταὐτά, οἷον τὸ Β καὶ τὸ Ζ, τὸ μέσον γίνεται σχῆμα κατηγορικὰς ἔχον τὰς προτάσεις· εἰ δʼ οἷς ἕπεται τὸ Α καὶ ἃ μὴ ἐνδέχεται τῷ Ε, οἷον τὸ Γ καὶ τὸ Θ, τὸ πρῶτον σχῆμα στερητικὴν ἔχον τὴν πρὸς τὸ ἔλατ ἄκρον πρότασιν.
For if the consequents are the same, such as B and Z, the middle figure is produced having affirmative premises; but if those things which A follows and those which cannot belong to E, such as Γ and Θ, the first figure is produced having a negative premise in relation to the minor extreme.
εἰ δʼ ὅσα μὴ ἐνδέχεται ἑκατέρῳ, οἷοντον τὸ Δ καὶ τὸ Θ, στερητικαὶ ἀμφότεραι αἱ προτάσεις, ἢ ἐν τῷ πρώτῳ ἢ ἐν τῷ μέσῳ σχήματι.
And if those things which cannot belong to either, such as Δ and Θ, both premises are negative, either in the first or in the middle figure.
οὕτως δʼ οὐδαμῶς συλλογισμός.
But in this way, there is by no means a syllogism.
Δῆλον δὲ καὶ ὅτι ὁποῖα ταὐτὰ ληπτέον τὰ κατὰ τὴν ἐπίσκεψιν, καὶ οὐχ ὁποῖα ἕτερα ἢ ἐναντία, πρῶτον μὲν ὅτι τοῦ μέσου χάριν ἡ ἐπίβλεφις, τὸ δὲ μέσον οὐχ ἕτερον ἀλλὰ ταὐτὸν δεῖ λαβεῖν.
It is also clear what sort of identical things must be taken in the inquiry, and not what sort of different or contrary things; first, because the inspection is for the sake of the middle, and the middle must be taken not as different but as the same.
εἶτα ἐν ὅσοις καὶ συμβαίνει γίνεσθαι συλλογισμὸν τῷ ληφθῆναι ἐναντία ἢ μὴ ἐνδεχόμενα τῷ αὐτῷ ὑπάρχειν, εἰς τοὺς προειρημένους ἅπαντα ἀναχθήσεται τρόπους, οἷον εἰ τὸ Β καὶ τὸ Ζ ἐναντία ἢ μὴ ἐνδέχεται τῷ αὐτῷ ὑπάρχειν· ἔσται μὲν γὰρ τούτων ληφθέντων συλλογισμὸς ὅτι οὐδενὶ τῶν τὸ Α ὑπάρχει, ἀλλʼ οὐκ ἐξ αὐτῶν ἀλλʼ ἐκ τοῦ προειρημένου τρόπου· τὸ γὰρ Β τῷ μὲν Α παντὶ τῷ δὲ Ε οὐδενὶ ὑπάρξει· ὥστʼ ἀνάγκη ταὐτὸ εἶναι τὸ Β τινὶ τῷ Θ.
Φανερὸν οὖν ὅτι ἐξ αὐτῶν μὲν τούτων τῶν ἐπιβλέψεων οὐδεὶς γίνεται συλλογισμός, ἀνάγκη δʼ εἰ τὸ Β καὶ τὸ Ζ ἐναντία, ταὐτόν τινι εἶναι τὸ Β τῶν Θ καὶ τὸν συλλογισμὸν γίγνεσθαι διὰ τούτων.
Secondly, in all cases where a syllogism happens to be produced by taking contraries or things that cannot belong to the same thing, they will all be reduced to the aforementioned modes; as, for example, if B and Z are contraries or cannot belong to the same thing; for if these are taken, there will be a syllogism that A belongs to no E, but not from them, but from the aforementioned mode; for B will belong to every A, but to no E; so that it is necessary that B is the same as some one of the Θ. It is clear, then, that from these inspections themselves no syllogism is produced, but it is necessary, if B and Z are contraries, that B is the same as some one of the Θ, and that the syllogism is produced through these.
συμβαίνει δὴ τοῖς οὕτως ἐπισκοποῦσι προσεπιβλέπειν ἄλλην ὁδὸν τῆς ἀναγκαίας διὰ τὸ λανθάνειν τὴν ταὐτότητα τῶν Β καὶ τῶν Θ.
Thus it happens that those who inquire in this way look additionally to another way than the necessary one, because the identity of the B and of the Θ is overlooked.