§1.2.15#2Ἐν δὲ τῷ τρίτῳ σχήματι καταφατικός μὲν συλλογισμὸς οὐδέποτʼ ἔσται ἐξ ἀντικειμένων προτάσεων διὰ τὴν εἰρημέντην αἰτίαν καὶ ἐπὶ τοῦ πρώτου σχήματος, ἀποφατικὸς δʼ ἔσται, καὶ καθόλου καὶ μὴ καθόλου τῶν ὅρων ὄντων.
But in the third figure, an affirmative syllogism will never arise from opposite premises, for the same reason as was stated in the case of the first figure; but a negative one will, both when the terms are universal and when they are not universal.
ἔστω γὰρ ἐπιστήμη ἐφʼ οὗ τὸ Β καὶ Γ, ἰατρικὴ δʼ ἐφʼ οὗ Α. εἰ οὖν λάβοι πᾶσαν ἰατρικὴν ἐπιστήμην καὶ μηδεμίαν ἰατρικὴν ἐπιστήμην, τὸ Β παντὶ τῷ Α εἴληφε καὶ τὸ οὐδενί, ὥστʼ ἔσται τις ἐπιστήμη οὐκ ἐπιστήμη.
For let B and Γ be "science", and A "medicine". If, then, one assumes every medicine to be science and no medicine to be science, one has assumed B to belong to all A and to no [A], so that a certain science will not be science.
ὁμοίως δὲ καὶ ἂν μὴ καθόλου ληφθῇ ἡ Β Α πρότασις· εἰ γάρ ἐστί τις ἰατρικὴ ἐπιστήμη καὶ πάλιν μηδεμία ἰατρικὴ ἐπιστήμη, συμβαίνει ἐπιστήμην τινὰ μὴ εἶναι ἐπιστήμην.
And similarly also if the BA premise is assumed not to be universal; for if a certain medicine is science and again no medicine is science, it results that a certain science is not science.
εἰσὶ δὲ καθόλου μὲν τῶν ὅρων λαμβανομένων ἐναντίαι αἱ προτάσεις, ἐὰν δʼ ἐν μέρει ἅτερος, ἀντικείμεναι.
And the premises are contraries when the terms are assumed universally, but opposites when one of them is in part.
Δεῖ δὲ κατανοεῖν ὅτι ἐνδέχεται μὲν οὕτω τὰ ἀντικείμενα λαμβάνειν ὥσπερ εἴπομεν πᾶσαν ἐπιστήμην σπουδαίαν εἶναι καὶ πάλιν μηδεμίαν, ἢ τινὰ μὴ ὅπερ οὐκ εἴωθε λανθάνειν.
But we must understand that it is possible to assume opposites in the way we have said, as that every science is excellent and again that none is, or that some is not, which is not usually overlooked.
ἔστι δὲ διʼ ἄλλων ἐρωτημάτων συλλογίσασθαι θάτερον, ἢ ὡς ἐν τοῖς Τοπικοῖς ἐλέχθη λαβεῖν.
But it is possible to syllogize one of them through other questions, or to assume them as was stated in the Topics.
ἐπεὶ δὲ τῶν καταφάσεων αἱ ἀντιθέσεις τρεῖς, ἑξαχῶς συμβαίνει τὰ ἀντικείμενα λαμβάνειν, ἢ παντὶ καὶ μηδενί, ἢ παντὶ καὶ μὴ παντί, ἢ τινὶ καὶ μηδενί, καὶ τοῦτο ἀντιστρέψοι ἐπὶ τῶν ὅρων, οἷον τὸ Α παντὶ τῷ Β, τῷ δὲ Γ μηδενί, ἢ τῷ Γ παντί, τῷ δὲ Β μηδενί, ἢ τῷ μὲν παντί, τῷ δὲ μὴ παντί, καὶ πάλιν τοῦτο ἀντιστρέψαι κατὰ τοὺς ὅρους.
And since the oppositions to affirmations are three, it happens that opposites are assumed in six ways: either "all" and "none", or "all" and "not all", or "some" and "none"; and this can be converted with respect to the terms, for example, A to all B and to no Γ, or to all Γ and to no B, or to one "all" and to the other "not all", and again this can be converted according to the terms.
ὁμοίως δὲ καὶ ἐπὶ τοῦ τρίτου σχήματος.
And similarly also in the case of the third figure.
ὥστε φανερὸν ὁσαχῶς τε καὶ ἐν ποίοις σχήμασιν ἐνδέχεται διὰ τῶν ἀντικειμένων προτάσεων γενέσθαι συλλογισμόν.
So that it is clear in how many ways and in which figures it is possible for a syllogism to arise through opposite premises.
Φανερὸν δὲ καὶ ὅτι ἐκ ψευδῶν μὲν ἔστιν ἀληθὲς συλλογίσασθαι, καθάπερ εἴρηται πρότερον, ἐκ δὲ τῶν ἀντικειμένων οὐκ ἔστιν· ἀεὶ γὰρ ἐναντίος ὁ συλλογισμὸς γίνεται τῷ πράγματι, οἷον εἰ ἔστιν ἀγαθόν, μὴ εἶναι ἀγαθόν, ἢ εἰ ζῷον, μὴ ζῷον, διὰ τὸ ἐξ ἀντιφάσεως εἶναι τὸν συλλογισμὸν καὶ τοὺς ὑποκειμένους ὄρους ἢ τοὺς αὐτοὺς εἶναι ἢ τὸν μὲν ὅλον τὸν δὲ μέρος.
And it is also clear that while it is possible to syllogize truth from falsehoods, as has been said before, from opposites it is not; for the syllogism is always contrary to the fact, for example, if it is good, [the conclusion is] that it is not good, or if it is an animal, that it is not an animal, because the syllogism is from a contradiction and the underlying terms are either the same or one is whole and the other part.
δῆλον δὲ καὶ ὅτι ἐν τοῖς παραλογισμοῖς οὐδὲν κωλύει γίνεσθαι τῆς ὑποθέσεως ἀντίφασιν, οἶον εἰ ἔστι περιττόν, μὴ εἶναι περιττόν. ἐκ γάρ τῶν ἀντικειμένων· προτάσεων ἐναντίος ἦν ὁ συλλογισμός·
And it is clear also that in paralogisms nothing prevents a contradiction of the hypothesis from arising, for example, if it is odd, that it is not odd; for the syllogism from opposite premises was contrary.
ἐὰν οὖν λάβη τοιαύτας, ἔσται τῆς ὑποθέσεως ἀντίφασις, δεῖ δὲ κατανοεῖν ὅτι οὕτω μὲν οὐκ ἔστιν ἐναντία συμπεράνασθαι ἐξ ἑνὸς συλλογισμοῦ ὥστʼ εἶναι τὸ συμπέρασμα τὸ μὴ ὃν ἀγαθὸν ἀγαθὸν ἢ ἄλλο τι τοιοῦτον, ἐὰν μὴ εὐθὺς ἡ πρότασις τοιαύτη ληφθῇ (οἷον πᾶν ζῷον λευκὸν εἶναι καὶ μὴ λευκόν, τὸν δʼ ἄνθρωπον ζῷον), ἄλλʼ ἢ προσλαβεῖν δεῖ τὴν ἀντίφασιν (οἷον ὅτι πᾶσα ἐπιστήμη ὑπόληφις, εἰτα λαβεῖν ὅτι ἡ ἰατρικὴ ἐπιστήμη μέν ἐστιν, οὐδεμία δʼ ὑπόληψις, ὥσπερ οἱ ἔλεγχοι γίνονται), ἢ ἐκ δύο συλλογισμῶν.
If, then, one assumes such premises, there will be a contradiction of the hypothesis. But we must understand that it is not possible to conclude contraries from a single syllogism in such a way that the conclusion is that what is not good is good or something else of this kind, unless the premise is assumed in this way right from the start (for example, that every animal is white and not white, and that man is an animal); rather, either one must assume in addition the contradiction (for example, that all science is belief, and then assume that medicine is science but no [medicine] is belief, just as refutations occur), or from two syllogisms.
ὥστε δʼ εἶναι ἐναντία κατʼ ἀλήθειαν τὰ εἰλημμένα, οὐκ ἔστιν ἄλλον τρόπον ἢ τοῦτον, καθάπερ εἴρηται πρότερον.
But for the assumed premises to be contraries in truth, there is no other way than this, as has been said before.