Authors/Aristotle/priora/Liber 1/C44

Chapter 44

Greek	Latin	English
	(PL 64 0681A) CAPUT XL. De resolutione syllogismorum ad impossibile et ex hypothesi.	44
50a16 Ἔτι δὲ τοὺς ἐξ ὑποθέσεως συλλογισμοὺς οὐ πειρατέον ἀνάγειν· οὐ γὰρ ἔστιν ἐκ τῶν κειμένων ἀνάγειν. οὐ γὰρ διὰ συλλογισμοῦ δεδειγμένοι εἰσίν, ἀλλὰ διὰ συνθήκης ὡμολογημένοι πάντες. οἷον εἰ ὑποθέμενος, ἂν δύναμίς τις μία μὴ ἦι τῶν ἐναντίων, μηδ᾽ ἐπιστήμην μίαν εἶναι, εἶτα διαλεχθείη ὅτι οὐκ ἔστι πᾶσα δύναμις τῶν ἐναντίων, οἱονεὶ τοῦ ὑγιεινοῦ καὶ τοῦ νοσώδους· ἅμα γὰρ ἔσται τὸ αὐτὸ ὑγιεινὸν καὶ νοσῶδες. ὅτι μὲν οὖν οὐκ ἔστι μία πάντων τῶν ἐναντίων δύναμις, ἐπιδέδεικται, ὅτι δ᾽ ἐπιστήμη οὐκ ἔστιν, οὐ δέδεικται. καίτοι ὁμολογεῖν ἀναγκαῖον· ἀλλ᾽ οὐκ ἐκ συλλογισμοῦ, ἀλλ᾽ ἐξ ὑποθέσεως. τοῦτον μὲν οὖν οὐκ ἔστιν ἀναγαγεῖν, ὅτι δ᾽ οὐ μία δύναμις, ἔστιν· οὗτος γὰρ ἴσως καὶ ἦν συλλογισμός, ἐκεῖνο δ᾽ ὑπόθεσις.	Amplius autem ex hypothesi syllogismos non est tentandum reducere, nam non est ex iis quae posita sunt reducere; non enim per syllogismum ostensi sunt, sed ad placitum concessi sunt omnes. Ut si quis ponat, si una quaedam potestas non sit contrariorum, neque disciplinam esse unam; deinde disputet quoniam non est una potestas contrariorum, ut sanativi et aegrotativi, simul enim idem erit sanativum et aegrotativum. (0681B) Quoniam autem non est omnium contrariorum una potestas, ostensum est, sed quoniam disciplina non una, non est ostensum; quamvis confiteri sit necesse, at non ex syllogismo, verum ex hypothesi; hoc igitur non est reducere, quoniam non una potestas est: hic enim fortassee erat syllogismus, illud autem hypothesis.	Further we must not try to reduce hypothetical syllogisms; for with the given premisses it is not possible to reduce them. For they have not been proved by syllogism, but assented to by agreement. For instance if a man should suppose that unless there is one faculty of contraries, there cannot be one science, and should then argue that not every faculty is of contraries, e.g. of what is healthy and what is sickly: for the same thing will then be at the same time healthy and sickly. He has shown that there is not one faculty of all contraries, but he has not proved that there is not a science. And yet one must agree. But the agreement does not come from a syllogism, but from an hypothesis. This argument cannot be reduced: but the proof that there is not a single faculty can. The latter argument perhaps was a syllogism: but the former was an hypothesis.
Ὁμοίως δὲ καὶ ἐπὶ τῶν διὰ τοῦ ἀδυνάτου περαινομένων· οὐδὲ γὰρ τούτους οὐκ ἔστιν ἀναλύειν, ἀλλὰ τὴν μὲν εἰς τὸ ἀδύνατον ἀπαγωγὴν ἔστι (συλλογισμῶι γὰρ δείκνυται), θάτερον δ᾽ οὐκ ἔστιν· ἐξ ὑποθέσεως γὰρ περαίνεται. διαφέρουσι δὲ τῶν προειρημένων ὅτι ἐν ἐκείνοις μὲν δεῖ προδιομολογήσασθαι, εἰ μέλλει συμφήσειν, οἷον ἂν δειχθῆι μία δύναμις τῶν ἐναντίων, καὶ ἐπιστήμην εἶναι τὴν αὐτήν· ἐνταῦθα δὲ καὶ μὴ προδιομολογησάμενοι συγχωροῦσι διὰ τὸ φανερὸν εἶναι τὸ ψεῦδος, οἷον τεθείσης τῆς διαμέτρου συμμέτρου τὸ τὰ περιττὰ ἴσα εἶναι τοῖς ἀρτίοις.	Similiter autem in his qui per impossibile concluduntur, nam neque hoc est resolvere, sed ad impossibile quidem reductio est; syllogismo enim monstratur; alterum autem non est, nam ex hypothesi concluditur. Differunt autem A praedictis quoniam in illis quidem oportet prius confiteri, si debet concedere, ut si ostendatur una potestas contrariorum, et disciplinam es E eamdem; hic autem et non prius confessi concedunt, eo quod manifestum sit falsum, ut posita dian etro symetro, eo quod imparia esse aequalia paribus. (0681C) Plures autem et diversi terminantur ex conditione, quos prospicere oportet, et notare apte.	The same holds good of arguments which are brought to a conclusion per impossibile. These cannot be analysed either; but the reduction to what is impossible can be analysed since it is proved by syllogism, though the rest of the argument cannot, because the conclusion is reached from an hypothesis. But these differ from the previous arguments: for in the former a preliminary agreement must be reached if one is to accept the conclusion; e.g. an agreement that if there is proved to be one faculty of contraries, then contraries fall under the same science; whereas in the latter, even if no preliminary agreement has been made, men still accept the reasoning, because the falsity is patent, e.g. the falsity of what follows from the assumption that the diagonal is commensurate, viz. that then odd numbers are equal to evens.
Πολλοὶ δὲ καὶ ἕτεροι περαίνονται ἐξ ὑποθέσεως, οὓς ἐπισκέψασθαι δεῖ καὶ διασημῆναι καθαρῶς. τίνες μὲν οὖν αἱ ↵ διαφοραὶ τούτων, καὶ ποσαχῶς γίνεται τὸ ἐξ ὑποθέσεως, ὕστερον ἐροῦμεν· νῦν δὲ τοσοῦτον ἡμῖν ἔστω φανερόν, ὅτι οὐκ ἔστιν ἀναλύειν εἰς τὰ σχήματα τοὺς τοιούτους συλλογισμούς. καὶ δι᾽ ἣν αἰτίαν, εἰρήκαμεν.	Quae ergo horum differentiae, et quoties fiunt, qui sunt ex hypothesi, postea dicemus. Nunc autem tantum sit nobis manifestum quoniam non est resolvere in figuras huiusmodi syllogismos, et ob quam causam diximus.	Many other arguments are brought to a conclusion by the help of an hypothesis; these we ought to consider and mark out clearly. We shall describe in the sequel their differences, and the various ways in which hypothetical arguments are formed: but at present this much must be clear, that it is not possible to resolve such arguments into the figures. And we have explained the reason.