§1.1.33Πολλάκις μὲν οὖν ἀπατᾶσθαι συμβαίνει περὶ τοὺς συλλογισμοὺς διὰ τὸ ἀναγκαῖον, ὥσπερ εἴρητας πρότερον, ἐνίοτεδὲ παρὰ τὴν ὁμοιότητα τῆς τῶν ὅρων θέσεως· ὅπερ οὐ χρὴ λανθάνειν ἡμᾶς.
So, it often happens that we are deceived about syllogisms because of the necessary, as was said before, but sometimes because of the similarity in the position of the terms; which must not escape our notice.
οἷον εἰ τὸ Α κατὰ τοῦ Β λέγεται καὶ τὸ Β κατὰ τοῦ δόξειε γὰρ ἂν οὕτως ἐχόντων τῶν ὅρων εἶναι συλλογισμός, οὐ γίνεται δʼ οὔτʼ ἀναγκαῖον οὐδὲν οὔτε συλλογισμός.
For example, if A is said of B, and B is said of C. For if the terms are related in this way, it might seem that there is a syllogism, but nothing necessary results, nor does a syllogism come about.
ἔστω γὰρ ἐφʼ ᾧ Α τὸ ἀεὶ εἶναι, ἐφʼ ᾧ δὲ Β διανοητὸς Ἀριστομένης, τὸ δʼ ἐφ᾿ ᾧ Γ Ἀριστομένης.
For let A be 'to be always', B 'Aristomenes as thought of', and C 'Aristomenes'.
ἀληθὲς δὴ τὸ. τῷ Β ὑπάρχειν· ἀεὶ γάρ ἐστι διανοητὸς Ἀριστομένης.
It is true then that B belongs to C; for Aristomenes is Aristomenes as thought of.
ἀλλὰ καὶ τὸ Β τῷ Γ ὁ γὰρ Ἀριστομένης ἐστὶ διανοητός Ἀριστομένης.
But it is also true that A belongs to B; for Aristomenes as thought of always is.
τὸ δʼ τῷ Γ οὐχ ὑπάρχει· φθαρτὸς γάρ ἐστιν ὁ Ἀριστομένης.
But A does not belong to C; for Aristomenes is perishable.
οὐ γὰρ ἐγίνετο συλλογισμὸς οὕτως ἐχόντων τῶν ὅρων, ἀλλʼ ἔδει καθόλου τὴν Α Β ληφθῆναι πρότασιν.
For a syllogism did not come about when the terms were related in this way, but the premise AB should have been taken as universal.
τοῦτο δὲ ψεῦδος, τὸ ἀξιοῦν πάντα τὸν διανοητὸν Ἀριστομένην ἀεὶ εἶναι, φθαρτοῦ ὄντος Ἀριστομένους.
But this is false, to claim that every Aristomenes as thought of always is, since Aristomenes is perishable.
πάλιν ἔστω τὸ μὲν ἐφʼ ᾧ Γ Μίκκαλος τὸ δʼ ἐφʼ ᾧ Β μουσικὸς Μίκκαλος, ἐφʼ ᾧ δὲ τὸ Α τὸ φθείρεσθαι αὔριον.
Again, let C be 'Mikkalos', B 'musical Mikkalos', and A 'to be destroyed tomorrow'.
ἀληθές δὴ τὸ τοῦ Γ κατηγορεῖν· ὁ γὰρ Μίκκαλός ἐστι μουσικὸς Μίκκαλος ἀλλὰ καὶ τὸ Α τοῦ Β· φθείροιτο γὰρ ἂν αὔριον μουσικὸς Μίκκαλος.
It is true then to predicate B of C; for Mikkalos is musical Mikkalos. But it is also true to predicate A of B; for musical Mikkalos might be destroyed tomorrow.
τὸ δέ γε Α τοῦ Γ ψεῦδος.
But to predicate A of C is false.
τοῦτο δὴ ταὐτόν ἐστι τῷ πρότερον· οὐ γὰρ ἀληθὲς καθόλου, Μίκκαλος μουσικὸς ὅτι φθείρεται αὔριον· τούτου δὲ μὴ ληφθέντος οὐκ ἦν συλλογισμός.
This indeed is the same as the previous case; for it is not universally true that a musical Mikkalos is destroyed tomorrow, and unless this was taken, there was no syllogism.
Αὕτη μὲν οὖν ἡ ἀπάτη γίνεται ἐν τῷ παρὰ μικρόν· ὡς γὰρ οὐδὲν διαφέρον εἰπεῖν τόδε τῷδε ὑπάρχειν ἢ τόδε §1.1.34τῷδε παντὶ ὑπάρχειν, συγχωροῦμεν.
This deception, then, comes about through what is close; for we concede as if it makes no difference to say that this belongs to that, or that this belongs to all of that.
πολλάκις δὲ διαψεύδεσθαι συμπεσεῖται παρὰ τὸ μὴ καλῶς ἐκτίθεσθαι τοὺς κατὰ τὴν πρότασιν ὅρους, οἷον εἰ τὸ μὲν εἴη ὑγίεια, τὸ δʼ ἐφʼ ᾧ Β νόσος, ἐφʼ δὲ Γ ἄνθρωπος.
But it will often happen that we are deceived because the terms in the premise are not set out well, as, for example, if A were 'health', B 'disease', and C 'man'.
ἀληθὲς γὰρ εἰπεῖν ὅτι τὸ οὐδενὶ τῷ ἐνδέχεται ὑπάρχειν (οὐδεμιᾷ γὰρ νόσῳ ὑγίεια ὑπάρχει), καὶ πάλιν ὅτι τὸ Β παντὶ τῷ Γ ὑπάρχει (πᾶς γὰρ ἄνθρωπος δεκτικὸς νόσου).
For it is true to say that A cannot belong to any B (for health belongs to no disease), and again that B belongs to all of C (for every man is receptive of disease).
δόξειεν ἂν οὖν συμβαίνειν μηδενὶ ἀνθρώπῳ ἐνδέχεσθαι ὑγίειαν ὑπάρχειν.
It would seem, then, to result that health cannot belong to any man.
τούτου δʼ αἴτιον τὸ μὴ καλῶς ἐκκεῖσθαι τοὺς ὅρους κατὰ τὴν λέξιν, ἐπεὶ μεταληφθέντων τῶν κατὰ τὰς ἕξεις οὐκ ἔσται συλλογισμός, οἷον ἀντὶ μὲν τῆς ὑγιείας εἰ τεθείη τὸ ὑγιαῖνον, ἀντὶ δὲ τῆς νόσου τὸ νοσοῦν.
But the cause of this is that the terms are not set out well in expression, since if we substitute those that correspond to the states, there will be no syllogism, as, for example, if instead of health we posit 'the healthy', and instead of disease 'the diseased'.
οὐ γὰρ ἀληθὲς εἰπεῖν ὡς οὐκ ἐνδέχεται τῷ νοσοῦντι τὸ ὑγιαίνειν ὑπάρξαι.
For it is not true to say that it is not possible for being healthy to belong to the diseased.
τούτου δὲ μὴ ληφθέντος οὐ γίνεται συλλογισμός, εἰ μὴ τοῦ ἐνδέχεσθαι· τοῦτο δʼ οὐκ ἀδύνατον· ἐνδέχεται γὰρ μηδενὶ ἀνθρώπῳ ὑπάρχειν ὑγίειαν.
And unless this is taken, no syllogism comes about, except of possibility; and this is not impossible, for it is possible for health to belong to no man.
πάλιν ἐπὶ τοῦ μέσου σχήματος ὁμοίως ἔσται τὸ ψεῦδος· τὴν γὰρ ὑγίειαν νόσῳ μὲν οὐδεμιᾷ ἀνθρώπῳ δὲ παντὶ ἐνδέχεται ὑπάρχειν, ὥστʼ οὐδενὶ ἀνθρώπῳ νόσον.
Again, in the middle figure the falsehood will come about in a similar way; for health can belong to no disease, but to every man, so that disease belongs to no man.
ἐν δὲ τῷ τρίτῳ σχήματι κατὰ τὸ ἐνδέχεσθαι συμβαίνει τὸ ψεῦδος, καὶ γὰρ ὑγίειαν καὶ νόσον καὶ ἐπιστήνην καὶ ἄγνοιαν καὶ ὅλως τὰ ἐναντία τῷ αὐτῷ ἐνδέχεται ὑπάρχειν, ἀλλήλοις δʼ ἀδύνατον.
And in the third figure the falsehood comes about concerning possibility; for health and disease, knowledge and ignorance, and generally contraries, can belong to the same thing, but it is impossible for them to belong to each other.
τοῦτο δʼ ἀνομολογούμενον τοῖς προειρημένοις· ὅτε γὰρ τῷ αὐτῷ πλείω ἐνεδέχετο ὑπάρχειν, ἐνεδέχετο καὶ ἀλλήλοις.
But this is in disagreement with what was said before; for when several things could belong to the same thing, they could also belong to each other.
Φανερὸν οὖν ὅτι ἐν ἅπασι τούτοις ἡ ἀπάτη γίνεται παρὰ τὴν τῶν ὅρων ἔκθεσιν· μεταληφθέντων γὰρ τῶν κατὰ τὰς ἕξεις οὐδὲν γίνεται ψεῦδος.
It is clear, then, that in all these cases the deception comes about because of the setting out of the terms; for if those that correspond to the states are substituted, no falsehood comes about.
δῆλον οὖν ὅτι κατὰ τὰς τοιαύτας προτάσεις ἀεὶ τὸ κατὰ τὴν ἕξιν ἀντὶ τῆς ἕξεως μεταληπτέον καὶ θετέον ὅρον.
It is manifest, therefore, that in such premises we must always substitute the term corresponding to the state instead of the state and posit it as the term.