§1.1.32ἐκ τῶν εἰρημένων·
[is clear] from what has been said.
πῶς δʼ ἀνάξομεν τοὺς συλλογισμούς εἰς τὰ προειρημένα σχήματα, λεκτέον ἂν εἴη μετὰ ταῦτα· λοιπὸν γάρ ἔτι τοῦτο τῆς σκέψεως.
But how we shall reduce syllogisms to the aforementioned figures, we must say after this; for this is still the remaining part of our inquiry.
εἰ γάρ τήν τε γένεσιν τῶν συλλογισμῶν θεωροῖμεν καὶ τοῦ εὑρίσκειν ἔχοιμεν δύναμιν, ἔτι δὲ τοὺς γεγενημένους ἀναλύοιμεν εἰς τὰ προειρημένα σχήματα, τέλος αν ἔχοι ἡ ἐξ ἀρχῆς πρόθεσις.
For if we should contemplate the generation of syllogisms and have the power of discovering them, and further analyze those already produced into the aforementioned figures, our original project would have its end.
συμβήσεται δʼ ἅμα καὶ τὰ πρότερον εἰρημένα ἐπιβεβαιοῦσθαι καὶ φανερώτερα εἶναι ὅτι οὕτως ἔχει, διὰ τῶν νῦν λεχθησομένων· δεῖ γὰρ πᾶν τὸ ἀληθές αὐτὸ ἑαυτῷ ὁμολογούμενον εἶναι πάντῃ.
And at the same time, what was said before will be confirmed and be more manifest that it is so, through what will now be said; for everything that is true must be in agreement with itself in every way.
Πρῶτον μὲν οὖν δεῖ πειρᾶσθαι τὰς δύο προτάσεις ἐκλαμβάνειν τοῦ συλλογισμοῦ (ῥᾷον γὰρ εἰς τὰ μείζω διελεῖν ἢ τὰ ἐλάττω, μείω δὲ τὰ συγκείμενα ἢ ἐξ ὧν), εἶτα σκοπεῖν ποτέρα ἐν ὅλῳ καὶ ποτέρα ἐν μέρει, καί, εἰ μὴ ἄμφω εἰλημμέναι εἶεν, αὐτὸν τιθέναι τὴν ἑτέραν.
First, then, one must try to extract the two premises of the syllogism (for it is easier to divide into larger parts than into smaller, and composite things are larger than those from which they are composed), then observe which of them is universal and which is particular, and, if both have not been taken, one must posit the other oneself.
ἐνίοτε γὰρ τὴν καθόλου προτείναντες τὴν ἐν ταύτη οὐ λαμβάνουσιν, οὔτε γράφοντες οὔτʼ ἐρωτῶντες· ἢ ταύτας μὲν προτεί νουσι, διʼ ὧν δʼ αὗται περαίνονται, παραλείπουσιν, ἄλλα δὲ μάτην ἐρωτῶσιν.
For sometimes they propose the universal premise but do not take the one contained in it, either in writing or in questioning; or they propose these premises, but omit those through which these are concluded, and ask other things in vain.
σκεπτέον οὖν εἴ τι περίεργον εἴληπτα καὶ εἴ τι τῶν ἀναγκαίων παραλέλειπται, καὶ τὸ μὲν θετέον τὸ δʼ ἀφαιρετέον, ἕως ἂν ἔλθῃ εἰς τὰς δύο ἄνευ γὰρ τούτων οὐκ ἕστιν ἀναγαγεῖν τοὺς οὕτως ἠρωτημένους λόγους.
Therefore, we must examine whether anything redundant has been taken, and whether any of the necessary things has been omitted, and we must posit the one and remove the other, until we arrive at the two premises; for without these it is not possible to reduce arguments that have been questioned in this way.
ἐνίων μὲν οὖν ῥᾴδιον ἰδεῖν τὸ ἐνδεές, ἔνιοι δὲ λανθάνουσι καὶ δοκοῦσι συλλογίζεσθαι διὰ τὸ ἀναγκαῖόν τι συμβαίνειν ἐκ τῶν κειμένων, οἶον εἰ ληφθείη μὴ οὐσίας ἀναιρουμένης μὴ ἀναιρεῖσθαι οὐσίαν, ἐξ ὧν δʼ ἐστὶν ἀναιρουμένων, καὶ τὸ ἐκ τούτων φθείρεσθαι· τούτων γὰρ τεθέντων ἀναγκαῖον μὲν τὸ οὐσίας μέρος εἶναι οὐσίαν, οὐ μὴν συλλελόγισται διὰ τῶν εἰλημμένων ἀλλʼ ἐλλείπουσι προτάσεις.
In some cases indeed it is easy to see what is lacking, but in others it escapes notice and they seem to syllogize because something necessary results from what is laid down, as, for example, if it were taken that when a non-substance is destroyed, a substance is not destroyed, but when those things from which it is composed are destroyed, that which is composed of them is also destroyed; for when these are posited, it is necessary that a part of a substance is a substance, yet it has not been syllogized through the taken premises, but premises are lacking.
πάλιν εἰ ἀνθρώπου ὄντος ἀνάγκη ζῷον εἶναι καὶ ζῴου οὐσίαν, ἀνθρώπου ὄντος ἀνάγκη οὐσίαν εἶναι· ἀλλʼ οὔπω συλλελόγισται· οὐ γὰρ ἔχουσιν αἱ προτάσεις ὡς εἴπομεν.
Again, if when man is, it is necessary for animal to be, and when animal is, for substance to be, then when man is, it is necessary for substance to be; but it has not yet been syllogized; for the premises do not stand as we said.
Ἀπατώμεθα δʼ ἐν τοῖς τοιούτοις διὰ τὸ ἀναγκαῖόν τι συμβαίνειν ἐκ τῶν κειμένων, ὅτι καὶ ὁ συλλογισμὸς ἀναγκαῖόν ἐστιν.
We are deceived in such cases because something necessary results from what is laid down, and because the syllogism is also something necessary.
ἐπὶ πλέον δὲ τὸ ἀναγκαῖον ἢ ὁ συλλογισμός· ὁ μὲν γὰρ συλλογισμὸς πᾶς ἀναγκαῖον, τὸ δʼ ἀναγκαῖον οὐ πᾶν συλλογισμός.
But the necessary is of wider extent than the syllogism; for every syllogism is necessary, but not everything necessary is a syllogism.
ὥστʼ οὐκ εἴ τι συμβαίνει τεθέντων τινῶν, πειρατέον ἀνάγειν εὐθύς, ἀλλὰ πρῶτον ληπτέον τὰς δύο προτάσεις, εἶθʼ οὕτω διαιρετέον εἰς τοὺς ὅρους, μέσον δὲ θετέον τῶν ὅρων τὸν ἐν ἀμφοτέραις ταῖς προτάσεσι λεγόμενον· ἀνάγκη γὰρ τὸ μέσον ἐν ἀμφοτέραις ὑπάρχειν ἐν ἅπασι τοῖς σχήμασιν.
So, not because something results when certain things are posited, should we try to reduce immediately, but we must first take the two premises, and then divide them into terms, and we must posit as the middle of the terms the one spoken of in both premises; for it is necessary for the middle to belong to both premises in all figures.
Ἐὰν μὲν οὖν κατηγορῇ καὶ κατηγορῆται τὸ μέσον, ἢ αὐτὸ μὲν κατηγορῇ, ἄλλο δʼ ἐκείνου ἀπαρνῆται, τὸ πρῶτον ἔσται σχῆμα· ἐὰν δὲ καὶ κατηγορῇ καὶ ἀπαρνῆται ἀπό τινος, τὸ μέσον· ἐάν δʼ ἄλλα ἐκείνου κατηγορῆται, ἢ τὸ μὲν ἀπαρνῆται τὸ δὲ κατηγορῆται, τὸ ἔσχατον.
If, then, the middle both attributes and is attributed, or itself attributes while another is denied of it, it will be the first figure; but if it both attributes and is denied of something, it will be the middle figure; and if other things are attributed to it, or one is denied and the other attributed, it will be the last figure.
οὕτω γὰρ εἶχεν ἐν ἑκάστῳ σχήματι τὸ μέσον.
For in each figure the middle stood in this way.
ὁμοίως δὲ καὶ ἐὰν μὴ καθόλου ὦσιν αἰ προτάσεις· ὁ γάρ αὐτὸς διορισμός τοῦ μέσου.
And similarly if the premises are not universal; for the definition of the middle is the same.
φανερὸν οὖν ὡς ἐν ᾧ λόγῳ μὴ λέγεται ταὐτὸ πλεονάκις, ὅτι οὐ γίνεται συλλογισμός· οὐ γὰρ εἴλτηπται μέσον.
It is clear, then, that in whichever argument the same thing is not said more than once, a syllogism does not come about; for a middle has not been taken.
ἐπεὶ δʼ ἔχομεν ποῖον ἐν ἑκάστῳ σχήματι περαίνεται τῶν προβλημάτων, καὶ ἐν τίνι τὸ καθόλου καὶ ἐν ποίῳ τὸ ἐν μέρει, φανερόν ὡς οὐκ εἰς ἅπόντα τὰ σχήματα βλεπτέον, ἀλλʼ ἑκάστου προβλήματος εἰς τὸ οἰκεῖον.
And since we know what kind of problem is concluded in each figure, and in which the universal and in which the particular, it is clear that we must not look to all the figures, but to the one appropriate to each problem.
ὅσα δʼ ἐν πλείοσι περαίνεται, τῇ τοῦ μέσου θέσει γνωριοῦμεν τὸ σχῆμα.
And as many as are concluded in more than one figure, we shall recognize the figure by the position of the middle.