Authors/Aristotle/priora/Liber 1/C32

Chapter 32

Greek	Latin	English
	(PL 64 0675C) CAPUT XXXIII. De resolutione syllogismorum in propositiones.	32
46b38 Ἐκ τίνων μὲν οὖν αἱ ἀποδείξεις γίνονται καὶ πῶς, καὶ εἰς ὁποῖα βλεπτέον καθ᾽ ἕκαστον πρόβλημα, φανερὸν ἐκ τῶν εἰρημένων· πῶς δ᾽ ἀνάξομεν τοὺς συλλογισμοὺς εἰς ↵ τὰ προειρημένα σχήματα, λεκτέον ἂν εἴη μετὰ ταῦτα· λοιπὸν γὰρ ἔτι τοῦτο τῆς σκέψεως. εἰ γὰρ τήν τε γένεσιν τῶν συλλογισμῶν θεωροῖμεν καὶ τοῦ εὑρίσκειν ἔχοιμεν δύναμιν, ἔτι δὲ τοὺς γεγενημένους ἀναλύοιμεν εἰς τὰ προειρημένα σχήματα, τέλος ἂν ἔχοι ἡ ἐξ ἀρχῆς πρόθεσις. συμβήσεται δ᾽ ἅμα καὶ τὰ πρότερον εἰρημένα ἐπιβεβαιοῦσθαι καὶ φανερώτερα εἶναι ὅτι οὕτως ἔχει, διὰ τῶν νῦν λεχθησομένων· δεῖ γὰρ πᾶν τὸ ἀληθὲς αὐτὸ ἑαυτῶι ὁμολογούμενον εἶναι πάντηι.	(0675D) Quomodo autem reducemus syllogismos in praedictas figuras, dicendum erit post haec, restat enim consideratio haec, si enim et generationem syllogismorum inspiciamus, et inveniendi habeamus potestatem, amplius autem factos reducamus praedictas figuras, finem habebit quod ex principio propositum est, accidet etiam simul quae praedicta sunt confirmari et manifestiora esse, quoniam sic se habent per ea quae nunc dicenda sunt. Oportet enim omne quod verum est, ipsum sibi ipsi manifestum esse omnino.	Our next business is to state how we can reduce syllogisms to the aforementioned figures: for this part of the inquiry still remains. If we should investigate the production of the syllogisms and had the power of discovering them, and further if we could resolve the syllogisms produced into the aforementioned figures, our original problem would be brought to a conclusion. It will happen at the same time that what has been already said will be confirmed and its truth made clearer by what we are about to say. For everything that is true must in every respect agree with itself.
Πρῶτον μὲν οὖν δεῖ πειρᾶσθαι τὰς δύο προτάσεις ἐκλαμβάνειν τοῦ συλλογισμοῦ (ῥᾶιον γὰρ εἰς τὰ μείζω διελεῖν ἢ τὰ ἐλάττω, μείζω δὲ τὰ συγκείμενα ἢ ἐξ ὧν), εἶτα σκοπεῖν ποτέρα ἐν ὅλωι καὶ ποτέρα ἐν μέρει, καί, εἰ μὴ ἄμφω εἰλημμέναι εἶεν, αὐτὸν τιθέναι τὴν ἑτέραν.	Primum ergo oportet tentare duas propositiones accipere syllogismi, facilius enim in maiora dividere quam in minora: maiora autem compositiora sunt quam ea ex quibus componuntur. Deinde considerare utra in toto, et utra in parte. Et si non ambae sumptae sint, eum qui ponit alteram.	First then we must attempt to select the two premisses of the syllogism (for it is easier to divide into large parts than into small, and the composite parts are larger than the elements out of which they are made); next we must inquire which are universal and which particular, and if both premisses have not been stated, we must ourselves assume the one which is missing.
ἐνίοτε γὰρ τὴν καθόλου προτείναντες τὴν ἐν ταύτηι οὐ λαμβάνουσιν, οὔτε γράφοντες οὔτ᾽ ἐρωτῶντες· ἢ ταύτας μὲν προτείνουσι, δι᾽ ὧν δ᾽ αὗται περαίνονται, παραλείπουσιν, ἄλλα δὲ μάτην ἐρωτῶσιν. σκεπτέον οὖν εἴ τι περίεργον εἴληπται καὶ εἴ τι τῶν ἀναγκαίων παραλέλειπται, καὶ τὸ μὲν θετέον τὸ δ᾽ ἀφαιρετέον, ἕως ἂν ἔλθηι εἰς τὰς δύο προτάσεις· ἄνευ γὰρ τούτων οὐκ ἔστιν ἀναγαγεῖν τοὺς οὕτως ἠρωτημένους λόγους.	(0676A) Aliquoties enim universalem protendentes, eam quae in hac est non sumunt, neque scribentes, neque interrogantes, aut has quidem protendunt, per quas autem hae concluduntur, omittunt, alia vero vane interrogant. Considerandum autem si quid superfluum sumptum sit, et si quid necessariorum omissum, et hoc quidem ponendum, illud vero auferendum, donec veniat quis ad duas propositiones, sine his enim non est reducere sic interrogatas orationes.	For sometimes men put forward the universal premiss, but do not posit the premiss which is contained in it, either in writing or in discussion: or men put forward the premisses of the principal syllogism, but omit those through which they are inferred, and invite the concession of others to no purpose. We must inquire then whether anything unnecessary has been assumed, or anything necessary has been omitted, and we must posit the one and take away the other, until we have reached the two premisses: for unless we have these, we cannot reduce arguments put forward in the way described.
ἐνίων μὲν οὖν ῥάιδιον ἰδεῖν τὸ ἐνδεές, ἔνιοι δὲ λανθάνουσι καὶ δοκοῦσι συλλογίζεσθαι διὰ τὸ ἀναγκαῖόν τι συμβαίνειν ἐκ τῶν κειμένων, οἷον εἰ ληφθείη μὴ οὐσίας ἀναιρουμέ νης μὴ ἀναιρεῖσθαι οὐσίαν, ἐξ ὧν δ᾽ ἐστὶν ἀναιρουμένων, καὶ τὸ ἐκ τούτων φθείρεσθαι·	In aliquibus ergo facile est videre quod minus est, aliqui vero latent, et videntur quidem syllogizare, eo quod necessarium quid accidit ex iis quae posita sunt. Ut si sumatur, non substantia interempta substantiam non interimi, ex quibus autem est, interemptis, et quod ex eis est corrumpi.	In some arguments it is easy to see what is wanting, but some escape us, and appear to be syllogisms, because something necessary results from what has been laid down, e.g. if the assumptions were made that substance is not annihilated by the annihilation of what is not substance, and that if the elements out of which a thing is made are annihilated, then that which is made out of them is destroyed:
τούτων γὰρ τεθέντων ἀναγκαῖον μὲν τὸ οὐσίας μέρος εἶναι οὐσίαν, οὐ μὴν συλλελόγισται διὰ τῶν εἰλημμένων, ἀλλ᾽ ἐλλείπουσι προτάσεις. πάλιν εἰ ἀνθρώπου ὄντος ἀνάγκη ζῶιον εἶναι καὶ ζώιου οὐσίαν, ἀνθρώπου ὄντος ἀνάγκη οὐσίαν εἶναι· ἀλλ᾽ οὔπω συλλελόγισται· οὐ γὰρ ἔχουσιν αἱ προτάσεις ὡς εἴπομεν.	(0676B) His enim positis, necessarium est substantiae partem esse substantiam, non tamen syllogizatum est quod ea quae sumpta sunt, sed desunt, propositiones. Rursum si cum est homo, necesse est esse animal, et cum est animal, substantiam, et cum est homo, necesse est esse substantiam, sed nondum syllogizatum est, non enim se habent propositiones ut diximus.	these propositions being laid down, it is necessary that any part of substance is substance; this has not however been drawn by syllogism from the propositions assumed, but premisses are wanting. Again if it is necessary that animal should exist, if man does, and that substance should exist, if animal does, it is necessary that substance should exist if man does: but as yet the conclusion has not been drawn syllogistically: for the premisses are not in the shape we required.
Ἀπατώμεθα δ᾽ ἐν τοῖς τοιούτοις διὰ τὸ ἀναγκαῖόν τι συμβαίνειν ἐκ τῶν κειμένων, ὅτι καὶ ὁ συλλογισμὸς ἀναγκαῖόν ἐστιν. ἐπὶ πλέον δὲ τὸ ἀναγ καῖον ἢ ὁ συλλογισμός· ὁ μὲν γὰρ συλλογισμὸς πᾶς ἀναγκαῖον, τὸ δ᾽ ἀναγκαῖον οὐ πᾶν συλλογισμός. ὥστ᾽ οὐκ εἴ τι συμβαίνει τεθέντων τινῶν, πειρατέον ἀνάγειν εὐθύς, ἀλλὰ πρῶτον ληπτέον τὰς δύο προτάσεις,	Fallimur autem in talibus eo quod necessarium quiddam accidat ex his quae posita sunt, quam et syllogismus, necessarium est, in plus autem est necessarium quam syllogismus, nam omnis syllogismus, necessarium, necessarium autem non omne syllogismus. Quare non (si quid accidat positis quibusdam) statim tentandum est reducere, sed primum secundum est duas propositiones.	We are deceived in such cases because something necessary results from what is assumed, since the syllogism also is necessary. But that which is necessary is wider than the syllogism: for every syllogism is necessary, but not everything which is necessary is a syllogism. Consequently, though something results when certain propositions are assumed, we must not try to reduce it directly, but must first state the two premisses,
	(PL 64 0676B) CAPUT XXXIV. De resolutione in terminos.
εἶθ᾽ οὕτω διαιρετέον εἰς τοὺς ὅρους, μέσον δὲ θετέον τῶν ὅρων τὸν ἐν ἀμφοτέραις ταῖς προτάσεσι λεγόμενον· ἀνάγκη γὰρ τὸ μέσον ἐν ἀμφοτέραις ὑπάρχειν ἐν ἅπασι τοῖς σχήμασιν.	(0676C) Deinde sic dividendum in terminos. Medium autem ponendum terminorum, qui utrisque propositionibus dicitur, necesse est enim medium in utrisque esse in omnibus figuris.	then divide them into their terms. We must take that term as middle which is stated in both the remisses: for it is necessary that the middle should be found in both premisses in all the figures.
Ἐὰν μὲν οὖν ↵ κατηγορῆι καὶ κατηγορῆται τὸ μέσον, ἢ αὐτὸ μὲν κατηγορῆι, ἄλλο δ᾽ ἐκείνου ἀπαρνῆται, τὸ πρῶτον ἔσται σχῆμα· ἐὰν δὲ καὶ κατηγορῆι καὶ ἀπαρνῆται ἀπό τινος, τὸ μέσον· ἐὰν δ᾽ ἄλλα ἐκείνου κατηγορῆται, ἢ τὸ μὲν ἀπαρνῆται τὸ δὲ κατηγορῆται, τὸ ἔσχατον. οὕτω γὰρ εἶχεν ἐν ἑκάστωι σχήματι τὸ μέσον. ὁμοίως δὲ καὶ ἐὰν μὴ καθόλου ὦσιν αἱ προτάσεις· ὁ γὰρ αὐτὸς διορισμὸς τοῦ μέσου. φανερὸν οὖν ὡς ἐν ὧι λόγωι μὴ λέγεται ταὐτὸ πλεονάκις, ὅτι οὐ γίνεται συλλογισμός· οὐ γὰρ εἴληπται μέσον. ἐπεὶ δ᾽ ἔχομεν ποῖον ἐν ἑκάστωι σχήματι περαίνεται τῶν προβλημάτων, καὶ ἐν τίνι τὸ καθόλου καὶ ἐν ποίωι τὸ ἐν μέρει, φανερὸν ὡς οὐκ εἰς ἅπαντα τὰ σχήματα βλεπτέον, ἀλλ᾽ ἑκάστου προβλήματος εἰς τὸ οἰκεῖον. ὅσα δ᾽ ἐν πλείοσι περαίνεται, τῆι τοῦ μέσου θέσει γνωριοῦμεν τὸ σχῆμα.	Si ergo subiiciatur et praedicetur medium, aut ipsum quidem praedicetur, aliud vero illo abnegetur, prima erit figura. Si autem et praedicetur, et negetur ab aliquo, media erit figura: si vero alia de illo praedicentur, aut hoc quidem praedicetur, illud vero ab illo negetur, postrema, sic enim se habuit in postrema figura medium, similiter autem etsi non universales sint propositiones, nam est eadem determinatio medii. Manifestum igitur quoniam in qua oratione non dicitur idem frequenter, non fit syllogismus, non enim sumptum est medium. (0676D) Quoniam autem habemus quod propositorum in unaquaque figura clauditur, et in qua universale, et in qua particulare, manifestum est quoniam non ad omnes figuras perspiciendum, sed in unoquoque proposito ad propriam. Quaecunque vero in pluribus concluduntur, medii positione cognoscimus figuram.	If then the middle term is a predicate and a subject of predication, or if it is a predicate, and something else is denied of it, we shall have the first figure: if it both is a predicate and is denied of something, the middle figure: if other things are predicated of it, or one is denied, the other predicated, the last figure. For it was thus that we found the middle term placed in each figure. It is placed similarly too if the premisses are not universal: for the middle term is determined in the same way. Clearly then, if the same term is not stated more than once in the course of an argument, a syllogism cannot be made: for a middle term has not been taken. Since we know what sort of thesis is established in each figure, and in which the universal, in what sort the particular is described, clearly we must not look for all the figures, but for that which is appropriate to the thesis in hand. If the thesis is established in more figures than one, we shall recognize the figure by the position of the middle term.