Authors/Aristotle/priora/Liber 1/C31

Chapter 31

Greek	Latin	English
	(PL 64 0674C) CAPUT XXXII. De divisione et eius syllogismo.	31
46a31 Ὅτι δ᾽ ἡ διὰ τῶν γενῶν διαίρεσις μικρόν τι μόριόν ἐστι τῆς εἰρημένης μεθόδου, ῥάιδιον ἰδεῖν· ἔστι γὰρ ἡ διαίρεσις οἷον ἀσθενὴς συλλογισμός· ὁ μὲν γὰρ δεῖ δεῖξαι αἰτεῖται, συλλογίζεται δ᾽ ἀεί τι τῶν ἄνωθεν.	Quoniam autem divisio per genera parva quaedam particula est dictae methodi facile videre: est enim divisio velut infirmus syllogismus, nam quod oporteat quidem ostendere petitur, syllogizatur vero semper aliquid superiorum.	It is easy to see that division into classes is a small part of the method we have described: for division is, so to speak, a weak syllogism; for what it ought to prove, it begs, and it always establishes something more general than the attribute in question.
πρῶτον δ᾽ αὐτὸ τοῦτο ἐλελήθει τοὺς χρωμένους αὐτῆι πάντας, καὶ πείθειν ἐπεχείρουν ὡς ὄντος δυνατοῦ περὶ οὐσίας ἀπόδειξιν γενέσθαι καὶ τοῦ τί ἐστιν. ὥστ᾽ οὔτε ὅ τι ἐνδέχεται συλλογίσασθαι διαιρουμένοις ξυνίεσαν, οὔτε ὅτι οὕτως ἐνεδέχετο ὥσπερ εἰρήκαμεν. ἐν μὲν οὖν ταῖς ἀποδείξεσιν, ὅταν δέηι τι συλλογίσασθαι ὑπάρχειν, δεῖ τὸ μέσον, δι᾽ οὗ γίνεται ὁ συλλο ↵ γισμός, καὶ ἧττον ἀεὶ εἶναι καὶ μὴ καθόλου τοῦ πρώτου τῶν ἄκρων· ἡ δὲ διαίρεσις τοὐναντίον βούλεται· τὸ γὰρ καθόλου λαμβάνει μέσον.	(0674D) Primum autem idem hoc latuit omnes utentes ea, et suadere conati sunt quoniam esset possibile de substantia demonstrationem fieri, et de eo quod est quid; quare neque quoniam contingebat syllogizare eos qui dividunt, intellexerunt, neque quoniam contingebat sic quemadmodum diximus. Ergo in demonstrationibus quidem cum oporteat quid syllogizare, oportet medium per quod fit syllogismus minus semper esse, et non universaliter de prima extremitate. Divisio autem contrarium vult, nam universalius sumit medium.	First, this very point had escaped all those who used the method of division; and they attempted to persuade men that it was possible to make a demonstration of substance and essence. Consequently they did not understand what it is possible to prove syllogistically by division, nor did they understand that it was possible to prove syllogistically in the manner we have described. In demonstrations, when there is a need to prove a positive statement, the middle term through which the syllogism is formed must always be inferior to and not comprehend the first of the extremes. But division has a contrary intention: for it takes the universal as middle.
ἔστω γὰρ ζῶιον ἐφ᾽ οὗ Α, τὸ δὲ θνητὸν ἐφ᾽ οὗ Β, καὶ ἀθάνατον ἐφ᾽ οὗ Γ, ὁ δ᾽ ἄνθρω πος, οὗ τὸν λόγον δεῖ λαβεῖν, ἐφ᾽ οὗ τὸ Δ. ἅπαν δὴ ζῶιον λαμβάνει ἢ θνητὸν ἢ ἀθάνατον· τοῦτο δ᾽ ἐστίν, ὁ ἂν ἦι Α, ἅπαν εἶναι ἢ Β ἢ Γ.	Sit enim animal quidem in quo A, mortale autem in quo B, et immortale in quo C, homo vero cuius terminum oportet sumere in quo D, omne ergo animal accipit aut mortale, aut immortale: hoc autem est quidquid erat, omne esse aut B, aut C.	Let animal be the term signified by A, mortal by B, and immortal by C, and let man, whose definition is to be got, be signified by D. The man who divides assumes that every animal is either mortal or immortal: i.e. whatever is A is all either B or C.
πάλιν τὸν ἄνθρωπον ἀεὶ διαιρούμενος τίθεται ζῶιον εἶναι, ὥστε κατὰ τοῦ Δ τὸ Α λαμβάνει ὑπάρχειν. ὁ μὲν οὖν συλλογισμός ἐστιν ὅτι τὸ Δ ἢ Β ἢ Γ ἅπαν ἔσται, ὥστε τὸν ἄνθρωπον ἢ θνητὸν μὲν ἢ ἀθάνατον ἀναγκαῖον εἶναι, ζῶιον θνητὸν δὲ οὐκ ἀναγκαῖον, ἀλλ᾽ αἰτεῖται· τοῦτο δ᾽ ἦν ὁ ἔδει συλλογίσασθαι.	(0675A) Rursus hominem semper qui dividit, ponit animal esse, quare de D sumit A esse, ergo syllogismus quidem est, quoniam D, aut B, aut C omne erit, quare hominem aut mortalem, aut immortalem oportet sumere, nam mortale quidem, aut immortale esse necessarium est animal, mortale autem non necessarium est, sed petitur. Hoc autem erat quod oportebat syllogizare.	Again, always dividing, he lays it down that man is an animal, so he assumes A of D as belonging to it. Now the true conclusion is that every D is either B or C, consequently man must be either mortal or immortal, but it is not necessary that man should be a mortal animal-this is begged: and this is what ought to have been proved syllogistically.
καὶ πάλιν θέμενος τὸ μὲν Α ζῶιον θνητόν, ἐφ᾽ οὗ δὲ τὸ Β ὑπόπουν, ἐφ᾽ οὗ δὲ τὸ Γ ἄπουν, τὸν δ᾽ ἄνθρωπον τὸ Δ, ὡσαύτως λαμβάνει τὸ μὲν Α ἤτοι ἐν τῶι Β ἢ ἐν τῶι Γ εἶναι (ἅπαν γὰρ ζῶιον θνητὸν ἢ ὑπόπουν ἢ ἄπουν ἐστί), κατὰ δὲ τοῦ Δ τὸ Α (τὸν γὰρ ἄνθρωπον ζῶιον θνητὸν εἶναι ἔλαβεν)· ὥσθ᾽ ὑπόπουν μὲν ἢ ἄπουν εἶναι ζῶιον ἀνάγκη τὸν ἄνθρωπον, ὑπόπουν δ᾽ οὐκ ἀνάγκη, ἀλλὰ λαμβάνει· τοῦτο δ᾽ ἦν ὁ ἔδει πάλιν δεῖξαι.	Et rursus qui ponit A quidem animal mortale in quo autem B pedes habens, in quo autem C, non habens pedes, hominem vero D, similiter sumit A quidem, aut in B, aut in C esse. Omne enim animal mortale aut pedes habens, aut pedes non habens est, de D autem A, nam hominem animal mortale sumpsit esse, quare habens pedes, vel non habens pedes esse animal, necesse est hominem, pedes autem habens non necesse est, sed sumit, hoc autem erat quod oportebat rursum ostendere.	And again, taking A as mortal animal, B as footed, C as footless, and D as man, he assumes in the same way that A inheres either in B or in C (for every mortal animal is either footed or footless), and he assumes A of D (for he assumed man, as we saw, to be a mortal animal); consequently it is necessary that man should be either a footed or a footless animal; but it is not necessary that man should be footed: this he assumes: and it is just this again which he ought to have demonstrated.
καὶ τοῦτον δὴ τὸν τρόπον ἀεὶ διαιρουμένοις τὸ μὲν καθόλου συμβαίνει αὐτοῖς μέσον λαμβάνειν, καθ᾽ οὗ δ᾽ ἔδει δεῖξαι καὶ τὰς διαφορὰς ἄκρα. τέλος δέ, ὅτι τοῦτ᾽ ἔστιν ἄνθρωπος ἢ ὅ τι ποτ᾽ ἂν ἦι τὸ ζητούμενον, οὐδὲν λέγουσι σαφὲς ὥστ᾽ ἀναγκαῖον εἶναι· καὶ γὰρ τὴν ἄλλην ὁδὸν ποιοῦνται πᾶσαν, οὐδὲ τὰς ἐνδεχομένας εὐπορίας ὑπολαμβάνοντες ὑπάρχειν. Φανερὸν δ᾽ ὅτι οὔτ᾽ ἀνασκευάσαι ταύτηι τῆι μεθόδωι ἔστιν, οὔτε περὶ συμβεβηκότος ἢ ἰδίου συλλογίσασθαι, οὔτε περὶ γένους, οὔτ᾽ ἐν οἷς ἀγνοεῖται τὸ πότερον ὡδὶ ἢ ὡδὶ ἔχει, οἷον ἆρ᾽ ἡ διάμετρος ἀσύμμετρος ἢ σύμμετρος. ἐὰν γὰρ λάβηι ὅτι ἅπαν μῆκος ἢ σύμμετρον ἢ ἀσύμμετρον, ἡ δὲ διάμετρος μῆκος, συλλελόγισται ὅτι ἀσύμμετρος ἢ σύμμετρος ἡ διάμετρος. εἰ δὲ λήψεται ἀσύμμετρον, ὁ ἔδει συλλογίσασθαι λήψεται. οὐκ ἄρα ἔστι δεῖξαι· ἡ μὲν γὰρ ὁδὸς αὕτη, διὰ ταύτης δ᾽ οὐκ ἔστιν. τὸ ἀσύμμετρον ἢ σύμμετρον ἐφ᾽ οὗ Α, μῆκος Β, διάμετρος Γ. φανερὸν οὖν ὅτι οὔτε πρὸς πᾶσαν σκέψιν ἁρμόζει τῆς ζητήσεως ὁ τρόπος, οὔτ᾽ ἐν οἷς μάλιστα δοκεῖ πρέπειν, ἐν τούτοις ἐστὶ χρήσιμος.	(0675B) Et ad hunc modum semper dividentibus, universale quidem accidit eis medium sumere, de quo oporteat ostendere et differentias et extremitates. In fine autem quoniam hoc est homo, aut quidquid erat quod quaeritur, nihil dicunt manifestum, quare necessarium est esse, etenim aliam viam faciunt omnem, non quidem contingentes idoneitates, opinantes esse. Manifestum est autem quoniam neque destruere hac via est, neque de accidente aliquid, aut de proprio syllogizare, neque de genere, neque de quibus ignoretur utrum hoc modo aut illo se habet, ut putasne diameter est symeter, vel asymeter? si enim sumat quoniam omnis longitudo est symetros vel asymetros, diameter autem longitudo, syllogizatum est quoniam symeter vel asymeter est diameter. (0675C) Si autem sumetur incommensurabile, quod oportebat syllogizare sumetur, non ergo est ostendere, nam via quidem haec, per hanc autem non est ostendere symetrum vel asymetrum, in quo A longitudo, B autem symeter aut asymeter, diameter C. Manifestum est igitur quoniam neque ad omnem considerationem congruit inquisitionis modus, neque in quibus maxime videtur convenire, in his est utilis.	Always dividing then in this way it turns out that these logicians assume as middle the universal term, and as extremes that which ought to have been the subject of demonstration and the differentiae. In conclusion, they do not make it clear, and show it to be necessary, that this is man or whatever the subject of inquiry may be: for they pursue the other method altogether, never even suspecting the presence of the rich supply of evidence which might be used. It is clear that it is neither possible to refute a statement by this method of division, nor to draw a conclusion about an accident or property of a thing, nor about its genus, nor in cases in which it is unknown whether it is thus or thus, e.g. whether the diagonal is incommensurate. For if he assumes that every length is either commensurate or incommensurate, and the diagonal is a length, he has proved that the diagonal is either incommensurate or commensurate. But if he should assume that it is incommensurate, he will have assumed what he ought to have proved. He cannot then prove it: for this is his method, but proof is not possible by this method. Let A stand for ‘incommensurate or commensurate’, B for ‘length’, C for ‘diagonal’. It is clear then that this method of investigation is not suitable for every inquiry, nor is it useful in those cases in which it is thought to be most suitable.
	Ex quibus ergo demonstrationes fiunt, et quomodo, et ad quae perspiciendum secundum unumquodque propositum manifestum ex dictis.	From what has been said it is clear from what elements demonstrations are formed and in what manner, and to what points we must look in each problem.