Authors/Aristotle/priora/Liber 2/C1

Chapter 1

Greek	Latin	English
	(PL 64 0685) CAPUT PRIMUM.	1
52b38 Ἐν πόσοις μὲν οὖν σχήμασι καὶ διὰ ποίων καὶ πόσων προτάσεων καὶ πότε καὶ πῶς γίνεται συλλογισμός, ἔτι δ᾽ εἰς ποῖα βλεπτέον ἀνασκευάζοντι καὶ κατασκευά↵ ζοντι, καὶ πῶς δεῖ ζητεῖν περὶ τοῦ προκειμένου καθ᾽ ὁποιανοῦν μέθοδον, ἔτι δὲ διὰ ποίας ὁδοῦ ληψόμεθα τὰς περὶ ἕκαστον ἀρχάς, ἤδη διεληλύθαμεν.	(0685A) In quot ergo figuris, et per quales, et quot propositiones, et quando, et quomodo fit syllogismus, amplius autem ad quae perspiciendum construenti et destruenti, et quomodo oporteat quaerere de proposito secundum unamquamque artem, amplius autem per quam viam sumemus, quae in singulis sunt principia iam pertransivimus.	WE have already explained the number of the figures, the character and number of the premisses, when and how a syllogism is formed; further what we must look for when a refuting and establishing propositions, and how we should investigate a given problem in any branch of inquiry, also by what means we shall obtain principles appropriate to each subject.
ἐπεὶ δ᾽ οἱ μὲν καθόλου τῶν συλλογισμῶν εἰσὶν οἱ δὲ κατὰ μέρος, οἱ μὲν καθόλου πάντες αἰεὶ πλείω συλλογίζονται, τῶν δ᾽ ἐν μέρει οἱ μὲν κατηγορικοὶ πλείω, οἱ δ᾽ ἀποφατικοὶ τὸ συμπέρασμα μόνον. αἱ μὲν γὰρ ἄλλαι προτάσεις ἀντιστρέφουσιν, ἡ δὲ στερητικὴ οὐκ ἀντιστρέφει. τὸ δὲ συμπέρασμα τὶ κατά τινός ἐστιν, ὥσθ᾽ οἱ μὲν ἄλλοι συλλογισμοὶ πλείω συλλογίζον- ται, οἷον εἰ τὸ Α δέδεικται παντὶ τῶι Β ἢ τινί, καὶ τὸ Β τινὶ τῶι Α ἀναγκαῖον ὑπάρχειν, καὶ εἰ μηδενὶ τῶι Β τὸ Α, οὐδὲ τὸ Β οὐδενὶ τῶι Α, τοῦτο δ᾽ ἕτερον τοῦ ἔμπροσθεν· εἰ δὲ τινὶ μὴ ὑπάρχει, οὐκ ἀνάγκη καὶ τὸ Β τινὶ τῶι Α μὴ ὑπάρχειν· ἐνδέχεται γὰρ παντὶ ὑπάρχειν.	Quoniam autem alii quidem syllogismorum sunt universales, alii vero particulares: universales quidem omnes semper plura syllogizant, particularium autem praedicativi quidem plura, negativi vero conclusionem solam. Nam aliae quidem propositiones convertuntur, privativa vero non convertitur. Conclusio vero aliquid de aliquo est, quare alii quidem syllogismi plura syllogizant: ut si A ostensum sit omni aut alicui B inesse, et B alicui A necessarium est inesse, et si nulli B inesse A, et B nulli A, hoc autem aliud est A priore. (0685C) Si autem A alicui B non insit, non necesse est et B alicui A non inesse; contingit enim omni A inesse.	Since some syllogisms are universal, others particular, all the universal syllogisms give more than one result, and of particular syllogisms the affirmative yield more than one, the negative yield only the stated conclusion. For all propositions are convertible save only the particular negative: and the conclusion states one definite thing about another definite thing. Consequently all syllogisms save the particular negative yield more than one conclusion, e.g. if A has been proved to to all or to some B, then B must belong to some A: and if A has been proved to belong to no B, then B belongs to no A. This is a different conclusion from the former. But if A does not belong to some B, it is not necessary that B should not belong to some A: for it may possibly belong to all A.
Αὕτη μὲν οὖν κοινὴ πάντων αἰτία, τῶν τε καθόλου καὶ τῶν κατὰ μέρος· ἔστι δὲ περὶ τῶν καθόλου καὶ ἄλλως εἰπεῖν. ὅσα γὰρ ἢ ὑπὸ τὸ μέσον ἢ ὑπὸ τὸ συμπέρασμά ἐστιν, ἁπάντων ἔσται ὁ αὐτὸς συλλογισμός, ἐὰν τὰ μὲν ἐν τῶι μέσωι τὰ δ᾽ ἐν τῶι συμπεράσματι τεθῆι, οἷον εἰ τὸ Α Β συμπέρασμα διὰ τοῦ Γ, ὅσα ὑπὸ τὸ Β ἢ τὸ Γ ἐστίν, ἀνάγκη κατὰ πάντων λέγεσθαι τὸ Α· εἰ γὰρ τὸ Δ ἐν ὅλωι τῶι Β, τὸ δὲ Β ἐν τῶι Α, καὶ τὸ Δ ἔσται ἐν τῶι Α· πάλιν εἰ τὸ Ε ἐν ὅλωι τῶι Γ, τὸ δὲ Γ ἐν τῶι Α, καὶ τὸ Ε ἐν τῶι Α ἔσται.	Haec ergo communis omnium causa universalium et particularium. Est autem de universalibus, et aliter dicere, quaecunque enim aut sub medio aut sub conclusione sunt, omnium erit idem syllogismus, si illa quidem in medio, haec vero in conclusione ponantur, ut si A B conclusio per C, quaecunque sub B aut sub C sunt, necesse est de omnibus dici A, nam D si in toto B, et B in A, et D erit in A. Rursum si E in toto C, et C in toto A, et E in toto A erit.	This then is the reason common to all syllogisms whether universal or particular. But it is possible to give another reason concerning those which are universal. For all the things that are subordinate to the middle term or to the conclusion may be proved by the same syllogism, if the former are placed in the middle, the latter in the conclusion; e.g. if the conclusion AB is proved through C, whatever is subordinate to B or C must accept the predicate A: for if D is included in B as in a whole, and B is included in A, then D will be included in A. Again if E is included in C as in a whole, and C is included in A, then E will be included in A.
ὁμοίως δὲ καὶ εἰ στερητικὸς ὁ συλλογισμός. ἐπὶ δὲ τοῦ δευτέρου σχήματος τὸ ὑπὸ τὸ συμπέρασμα μόνον ἔσται συλλογίσασθαι, οἷον εἰ τὸ Α τῶι Β μηδενί, τῶι δὲ Γ παντί· συμπέρασμα ὅτι οὐδενὶ τῶι Γ τὸ Β. εἰ δὴ τὸ Δ ὑπὸ τὸ Γ ἐστί, φανερὸν ὅτι οὐχ ὑπάρχει αὐτῶι τὸ Β· τοῖς δ᾽ ὑπὸ τὸ Α ὅτι οὐχ ὑπάρχει, οὐ δῆλον διὰ τοῦ συλλογισμοῦ. καίτοι οὐχ ὑπάρχει τῶι Ε, εἰ ἔστιν ὑπὸ τὸ Α· ἀλλὰ τὸ μὲν τῶι Γ μηδενὶ ὑπάρχειν τὸ Β διὰ τοῦ συλλογισμοῦ δέδεικται, τὸ δὲ τῶι Α μὴ ὑπάρχειν ἀναπόδεικτον εἴληπται, ὥστ᾽ οὐ διὰ τὸν συλλογισμὸν συμβαίνει τὸ Β τῶι Ε μὴ ὑπάρχειν.	Similiter autem et si privativus sit syllogismus. (0685D) In secunda autem figura quod sub conclusione erit, solum erit syllogizare, ut si A insit nulli B, et omni C, conclusio quoniam nulli C inest B; si autem D sub C est, manifestum quoniam non inest ei B, iis autem quae sunt sub A, quoniam B non inest, non palam est per syllogismum, et si non inest B ei quod est E, si est E sub A, sed inesse quidem B nulli C per syllogismum ostensum est, non inesse vero A hoc quod est B, indemonstratum sumptum est, quare nec per syllogismum accidit B non inesse E.	Similarly if the syllogism is negative. In the second figure it will be possible to infer only that which is subordinate to the conclusion, e.g. if A belongs to no B and to all C; we conclude that B belongs to no C. If then D is subordinate to C, clearly B does not belong to it. But that B does not belong to what is subordinate to A is not clear by means of the syllogism. And yet B does not belong to E, if E is subordinate to A. But while it has been proved through the syllogism that B belongs to no C, it has been assumed without proof that B does not belong to A, consequently it does not result through the syllogism that B does not belong to E.
ἐπὶ δὲ τῶν ἐν μέρει τῶν μὲν ὑπὸ τὸ συμπέρασμα οὐκ ἔσται τὸ ἀναγκαῖον (οὐ γὰρ γίνεται συλλογισμός, ὅταν αὕτη ληφθῆι ἐν μέρει), τῶν δ᾽ ὑπὸ τὸ μέσον ἔσται πάντων, πλὴν οὐ διὰ τὸν συλλογισμόν· οἷον εἰ τὸ Α παντὶ τῶι Β, τὸ δὲ Β τινὶ τῶι Γ· τοῦ μὲν γὰρ ὑπὸ τὸ Γ τεθέντος οὐκ ἔσται συλλογισμός, τοῦ δ᾽ ὑπὸ τὸ Β ἔσται, ἀλλ᾽ οὐ διὰ τὸν προγεγενημένον. ὁμοίως δὲ κἀπὶ τῶν ἄλλων σχημάτων· τοῦ μὲν γὰρ ὑπὸ τὸ συμπέρασμα οὐκ ἔσται, ↵ θατέρου δ᾽ ἔσται, πλὴν οὐ διὰ τὸν συλλογισμόν, ἧι καὶ ἐν τοῖς καθόλου ἐξ ἀναποδείκτου τῆς προτάσεως τὰ ὑπὸ τὸ μέσον ἐδείκνυτο· ὥστ᾽ ἢ οὐδ᾽ ἐκεῖ ἔσται ἢ καὶ ἐπὶ τούτων.	In particularibus autem, eorum quidem quae sub conclusione sunt, non erit necessarium. Non enim fit syllogismus, quando ea sumpta fuerit particularis, eorum autem quae sunt sub medio, erit omnium, verumtamen non per syllogismum, ut si A omni B, et B alicui C: nam eius quod sub C est positum, non erit syllogismus, eius vero quod sub B erit, sed non propter eum qui prius factus est syllogismum. (0686A) Similiter autem et in aliis figuris, nam eius quidem quod sub conclusione est non erit, alterius vero erit, verum non per syllogismum, eo quod et in universalibus ex indemonstrata propositione quae sunt sub medio ostendebantur; quare neque hic erit, vel et in illis.	But in particular syllogisms there will be no necessity of inferring what is subordinate to the conclusion (for a syllogism does not result when this premiss is particular), but whatever is subordinate to the middle term may be inferred, not however through the syllogism, e.g. if A belongs to all B and B to some C. Nothing can be inferred about that which is subordinate to C; something can be inferred about that which is subordinate to B, but not through the preceding syllogism. Similarly in the other figures. That which is subordinate to the conclusion cannot be proved; the other subordinate can be proved, only not through the syllogism, just as in the universal syllogisms what is subordinate to the middle term is proved (as we saw) from a premiss which is not demonstrated: consequently either a conclusion is not possible in the case of universal syllogisms or else it is possible also in the case of particular syllogisms.