§1.2.23Πῶς μὲν οὖν ἔχουσιν οἱ ὅροι κατὰ τὰς ἀντιστροφὰς καὶ τὸ αἱρετώτεροι ἢ φευκτότεροι εἶναι, φανερόν·
It is therefore clear how the terms are related with respect to conversions and to being more desirable or more to be avoided.
ὅτι δʼ οὐ μόνον οἱ διαλεκτικοὶ καὶ ἀποδεικτικοὶ συλλογισμοὶ διὰ τῶν προειρημένων γίνονται σχημάτων, ἀλλὰ καὶ οἱ ῥητορικοὶ καὶ ἀπλῶς ἡτισοῦν πίστις καὶ ἡ καθʼ ὁποιανοῦν μέθοδον, νῦν ἄν εἴη λεκτέον.
But we must now state that not only dialectical and demonstrative syllogisms are formed through the aforementioned figures, but also rhetorical ones, and in short any belief whatsoever and that which is according to any method whatsoever.
ἅπαντα γὰρ πιστεύομεν ἢ διὰ συλλογισμοῦ ἢ ἐξ ἐπαγωγῆς.
For we believe everything either through syllogism or from induction.
Ἐπαγωγὴ μὲν οὖν ἐστι καὶ ὁ ἐξ ἐπαγωγῆς συλλογισμὸς τὸ διὰ τοῦ ἑτέρου θάτερον ἄκρον τῷ μέσῳ συλλογίσασθαι, οἷον εἰ τῶν Α Γ μέσον τὸ Β, διὰ τοῦ Γ θεῖξαι τὸ Α τῷ Β ὑπάρχον· οὕτω γὰρ ποιούμεθα τὰς ἐπαγωγάς.
Induction, then, and the syllogism from induction, consists in syllogistically establishing one extreme to belong to the middle through the other extreme; for example, if B is the middle of A and Γ, demonstrating through Γ that A belongs to B; for it is in this way that we produce inductions.
οἷον ἔστω τὸ Α μακρόβιον, τὸ δʼ ἐφʼ ᾧ Β τὸ χολὴν μὴ ἔχον, ἐφʼ δὲ Γ τὸ καθʼ ἕκαστον μακρόβιον, οἶον ἄνθρωπος καὶ ἵππος καὶ ἡμίονος.
For example, let A be long-lived, B be that which has no gall, and Γ be the individual long-lived things, such as man, horse, and mule.
τῷ δὴ ἅλῳ ὑπάρχει τὸ Α (πᾶν γὰρ τὸ Γ μακρόβιον)· ἀλλὰ καὶ τὸ Β, τὸ μὴ ἔχειν χολήν, παντὶ ὑπάρχει τῷ Γ. εἰ οὖν ἀντιστρέφει τὸ Γ τῷ Β καὶ μὴ ὑπερτείνει τὸ μέσον, ἀνάγκη τὸ Α τῷ Β ὑπάρχειν.
Indeed, A belongs to the whole of Γ (for every Γ is long-lived); but B, not having gall, also belongs to every Γ. If therefore Γ converts with B and the middle does not exceed it, it is necessary that A belongs to B.
δέδεικται γὰρ πρότερον ὅτι ἂν δύο ἄττα τῷ αὐτῷ ὑπάρχῃ καὶ πρὸς θάτερον αὐτῶν ἀντιστρέφῃ τό ἄκρον, ὅτι τῷ ἀντιστρέφοντι καὶ θάτερον ὑπάρξει τῶν κατηγορουμένων.
For it has been shown previously that if any two things belong to the same thing, and the extreme converts with one of them, then the other of the predicated terms will also belong to the converting term.
δεῖ δὲ νοεῖν τὸ Γ ὁ ἐξ ἀπάντων τῶν καθʼ ἕκαστον συγκείμενον· ἡ γὰρ ἐπαγωγὴ διὰ πάντων.
But one must understand Γ as being composed of all the particulars; for induction is through all.
Ἔστι δʼ ὁ τοιοῦτος συλλογισμός τῆς πρώτης καὶ ἀμέσου προτάσεως· ὧν μὲν γὰρ ἔστι μέσον, διὰ τοῦ μέσου ὁ συλλογισμός, ὧν δὲ μὴ ἔστι, διʼ ἐπαγωγῆς.
And this kind of syllogism is of the first and immediate premise; for in those cases where there is a middle, the syllogism is through the middle, but where there is not, it is through induction.
καὶ τρόπον τινὰ ἀντίκειται ἡ ἐπαγωγὴ τῷ συλλογισμῷ· ὁ μὲν γὰρ διὰ τοῦ μέσου τὸ ἄκρον τῷ τρίτῳ δείκνυσιν, ἡ δὲ διὰ τοῦ τρίτου τὸ ἄκρον τῷ μέσῳ.
And in a way, induction is opposed to syllogism; for the latter demonstrates the extreme to belong to the third term through the middle, whereas the former demonstrates the extreme to belong to the middle through the third term.
φύσει μὲν οὖν πρότερος καὶ γνωριμώτερος ὁ διὰ τοῦ μέσου συλλογισμός, ἡμῖν δʼ ἐναργέστερος ὁ διὰ τῆς ἐπαγωγῆς.
By nature, then, the syllogism through the middle is prior and more knowable, but to us, the one through induction is more vivid.
§1.2.24Παράδειγμα δʼ ἐστὶν ὅταν τῷ μέσῳ τὸ ἄκρον ὑπάρχον δειχθῇ διὰ τοῦ ὁμοίου τῷ τρίτῳ.
An example is when the extreme is shown to belong to the middle through what is similar to the third term.
δεῖ δὲ καὶ τὸ μέσον τῷ τρίτῳ καὶ τὸ πρῶτον τῷ ὁμοίῳ γνώριμον εἶναι ὑπάρχον.
But it must be known both that the middle belongs to the third term and that the first belongs to the similar term.
οἷον ἔστω τὸ κακόν, τὸ δὲ Β πρὸς ὁμόρους ἀναιρεῖσθαι 69a πόλεμον, ἐφʼ ᾧ δὲ Γ τὸ Ἀθηναίους πρὸς Θηβαίους, τὸ δʼ ἐφʼ ᾧ Δ Θηβαίους πρὸς Φωκεῖς.
For example, let [A] be bad, B be initiating war against neighbors, 69a Γ be Athenians against Thebans, and Δ be Thebans against Phocians.
ἐὰν οὖν βουλώμεθα δέξαι ὅτι τὸ Θηβαίοις πολεμεῖν κακόν ἐστι, ληπτέον ὅτι τὸ πρὸς τοὺς ὁμόρους πολεμεῖν κακόν.
If, then, we wish to demonstrate that to wage war against the Thebans is bad, we must take as a premise that to wage war against neighbors is bad.
τούτου δὲ πίστις ἐκ τῶν ὁμοίων, οἷον ὅτι Θηβαίοις ὁ πρὸς Φωκεῖς.
The belief of this is obtained from similar cases, as for instance that for the Thebans, the war against the Phocians was bad.
ἐπεὶ οὖν τὸ πρὸς τοὺς ὁμόρους κακόν, τὸ δὲ πρὸς Θηβαίους πρὸς ὁμόρους ἐστί, φανερὸν ὅτι τὸ πρὸς Θηβαίους πολεμεῖν κακόν.
Since, therefore, war against neighbors is bad, and war against the Thebans is against neighbors, it is clear that to wage war against the Thebans is bad.
ὅτι μὲν οὖν τὸ Β τῷ Γ καὶ τῷ Δ ὑπάρχει, φανερόν (ἄμφω γάρ ἐστι πρός τοὺς ὁμόρους ἀναιρεῖσθαι πόλεμον), καὶ ὅτι τὸ Α τῷ Δ (Θηβαίοις γὰρ οὐ συνήνεγκεν ὁ πρὸς Φωκεῖς πόλεμος)· ὅτι δὲ τὸ Α τῷ Β ὑπάρχει, διὰ τοῦ Δ δειχθήσεται.
That B, then, belongs to Γ and to Δ is clear (for both are initiating war against neighbors), and that A belongs to Δ (for the war against the Phocians was not beneficial to the Thebans); and that A belongs to B will be demonstrated through Δ.
τὸν αὐτὸν δὲ τρόπον κἂν εἰ διὰ πλειόνων τῶν ὁμοίων ἡ πίστις γένοιτο τοῦ μέσου πρὸς τὸ ἄκρον.
And in the same way also if the belief of the middle's belonging to the extreme should be produced through several similar cases.
φανερὸν οὖν ὅτι τὸ παράδειγμά ἐστιν οὔτε ὡς μέρος πρὸς ὅλον οὔτε ὡς ὅλον πρός μέρος, ἄλλʼ ὡς μέρος πρὸς μέρος, ὅταν ἄμφω μὲν ᾖ ὑπὸ ταὐτό, γνώριμον δὲ θάτερον.
It is clear, then, that an example is related neither as part to whole nor as whole to part, but rather as part to part, when both are under the same term, and one of them is known.
καὶ διαφέρει τῆς ἐπαγωγῆς, ὅτι ἡ μὲν ἐξ ἀπάντων τῶν ἀτόμων τὸ ἄκρον ἐδείκνυεν ὑπάρχειν τῷ μέσῳ καὶ πρὸς τὸ ἄκρον οὐ συνῆπτε τὸν συλλογισμόν, τὸ δὲ καὶ συνάπτει καὶ οὐκ ἐξ ἀπάντων δείκνυσιν.
And it differs from induction because induction demonstrated the extreme to belong to the middle from all the individual cases and did not connect the syllogism to the other extreme, whereas the example both connects it and does not demonstrate from all cases.