Authors/Aristotle/priora/Liber 2/C15

Chapter 15

Greek	Latin	English
	(PL 64 0701B) CAPUT XV. De ratiocinatione ex oppositis.	15
63b22 Ἐν ποίωι δὲ σχήματι ἔστιν ἐξ ἀντικειμένων προτάσεων συλλογίσασθαι καὶ ἐν ποίωι οὐκ ἔστιν, ὧδ᾽ ἔσται φανερόν. λέγω δ᾽ ἀντικειμένας εἶναι προτάσεις κατὰ μὲν τὴν λέξιν τέτταρας, οἷον τὸ παντὶ τῶι οὐδενί, καὶ τὸ παντὶ τῶι οὐ παντί, καὶ τὸ τινὶ τῶι οὐδενί, καὶ τὸ τινὶ τῶι οὐ τινί, κατ᾽ ἀλήθειαν δὲ τρεῖς· τὸ γὰρ τινὶ τῶι οὐ τινὶ κατὰ τὴν λέξιν ἀντίκειται μόνον. τούτων δ᾽ ἐναντίας μὲν τὰς καθόλου, τὸ παντὶ τῶι μηδενὶ ὑπάρχειν, οἷον τὸ πᾶσαν ἐπιστήμην εἶναι σπουδαίαν τῶι μηδεμίαν εἶναι σπουδαίαν, τὰς δ᾽ ἄλλας ἀντικειμένας.	In qua autem figura est ex oppositis propositionibus syllogizare, et in qua non est, sic erit manifestum. (0701C) Dico autem oppositas esse propositiones, secundum locutionem quidem quatuor, ut omni et nulli, et omni et non omni, et alicui et nulli, et alicui et non alicui inesse; secundum veritatem autem tres, nam alicui et non alicui secundum locutionem opponuntur solum; harum autem contrarias quidem universales, omni nulli inesse, ut omnem disciplinam esse studiosam, nullam esse studiosam, alias vero oppositas.	In what figure it is possible to draw a conclusion from premisses which are opposed, and in what figure this is not possible, will be made clear in this way. Verbally four kinds of opposition are possible, viz. universal affirmative to universal negative, universal affirmative to particular negative, particular affirmative to universal negative, and particular affirmative to particular negative: but really there are only three: for the particular affirmative is only verbally opposed to the particular negative. Of the genuine opposites I call those which are universal contraries, the universal affirmative and the universal negative, e.g. ‘every science is good’, ‘no science is good’; the others I call contradictories.
Ἐν μὲν οὖν τῶι πρώτωι σχήματι οὐκ ἔστιν ἐξ ἀντικειμένων προτάσεων συλλογισμός, οὔτε καταφατικὸς οὔτε ἀποφατικός, καταφατικὸς μὲν ὅτι ἀμφοτέρας δεῖ καταφατικὰς εἶναι τὰς προτάσεις, αἱ δ᾽ ἀντικείμεναι φάσις καὶ ἀπόφασις, στερητικὸς δὲ ὅτι αἱ μὲν ἀντικείμεναι τὸ αὐτὸ τοῦ αὐτοῦ κατηγοροῦσι καὶ ἀπαρνοῦνται, τὸ δ᾽ ἐν τῶι πρώτωι μέσον οὐ λέγεται κατ᾽ ἀμφοῖν, ἀλλ᾽ ἐκείνου μὲν ἄλλο ἀπαρνεῖται, αὐτὸ δὲ ἄλλου κατηγορεῖται· αὗται δ᾽ οὐκ ἀντίκεινται.	In prima igitur figura non est ex oppositis propositionibus syllogismus, neque affirmativus, neque negativus; affirmativus quidem, quoniam oportet utrasque affirmativas esse propositiones, oppositae autem affirmatio et negatio; privativus autem, quoniam oppositae quidem idem de eodem praedicant et negant, in prima autem medium non dicitur de utrisque, sed de illo quidem aliud negatur, idem autem de alio praedicatur, hae vero non opponuntur.	In the first figure no syllogism whether affirmative or negative can be made out of opposed premisses: no affirmative syllogism is possible because both premisses must be affirmative, but opposites are, the one affirmative, the other negative: no negative syllogism is possible because opposites affirm and deny the same predicate of the same subject, and the middle term in the first figure is not predicated of both extremes, but one thing is denied of it, and it is affirmed of something else: but such premisses are not opposed.
	(PL 64 0701C) CAPUT XVI. De ratiocinatione ex oppositis in secunda figura.
Ἐν δὲ τῶι μέσωι σχήματι καὶ ἐκ τῶν ἀντικειμένων καὶ ἐκ τῶν ἐναντίων ἐνδέχεται γίγνεσθαι συλλογισμόν. ἔστω γὰρ ↵ ἀγαθὸν μὲν ἐφ᾽ οὗ Α, ἐπιστήμη δὲ ἐφ᾽ οὗ Β καὶ Γ. εἰ δὴ πᾶσαν ἐπιστήμην σπουδαίαν ἔλαβε καὶ μηδεμίαν, τὸ Α τῶι Β παντὶ ὑπάρχει καὶ τῶι Γ οὐδενί, ὥστε τὸ Β τῶι Γ οὐδενί· οὐδεμία ἄρα ἐπιστήμη ἐπιστήμη ἐστίν. ὁμοίως δὲ καὶ εἰ πᾶσαν λαβὼν σπουδαίαν τὴν ἰατρικὴν μὴ σπουδαίαν ἔλαβε· τῶι μὲν γὰρ Β παντὶ τὸ Α, τῶι δὲ Γ οὐδενί, ὥστε ἡ τὶς ἐπιστήμη οὐκ ἔσται ἐπιστήμη. καὶ εἰ τῶι μὲν Γ παντὶ τὸ Α, τῶι δὲ Β μηδενί, ἔστι δὲ τὸ μὲν Β ἐπιστήμη, τὸ δὲ Γ ἰατρική, τὸ δὲ Α ὑπόληψις· οὐδεμίαν γὰρ ἐπιστήμην ὑπόληψιν λαβὼν εἴληφε τινὰ εἶναι ὑπόληψιν.	(0701D) In media autem figura, et ex oppositis, et ex contrariis contingit fieri syllogismum. Sit enim bonum quidem in quo A, disciplina autem in quo B et C; si ergo omnem disciplinam studiosam sumpsit, et nullam, A inest omni B, et nulli C, quare B nulli C, nulla ergo disciplina disciplina est. Similiter autem et si omnem sumens studiosam disciplinam, medicinam vero non studiosam sumpsit, nam A B quidem omni, C autem nulli, quare aliqua disciplina non erit disciplina. Et si A C quidem omni, B autem nulli, est autem B quidem disciplina, C autem medicina, A vero opinio, nullam enim disciplinam opinionem sumens, sumpsit aliquam disciplinam esse opinionem.	In the middle figure a syllogism can be made both oLcontradictories and of contraries. Let A stand for good, let B and C stand for science. If then one assumes that every science is good, and no science is good, A belongs to all B and to no C, so that B belongs to no C: no science then is a science. Similarly if after taking ‘every science is good’ one took ‘the science of medicine is not good’; for A belongs to all B but to no C, so that a particular science will not be a science. Again, a particular science will not be a science if A belongs to all C but to no B, and B is science, C medicine, and A supposition: for after taking ‘no science is supposition’, one has assumed that a particular science is supposition.
διαφέρει δὲ τοῦ πάλαι τῶι ἐπὶ τῶν ὅρων ἀντιστρέφεσθαι· πρότερον μὲν γὰρ πρὸς τῶι Β, νῦν δὲ πρὸς τῶι Γ τὸ καταφατικόν. καὶ ἂν ἦι δὲ μὴ καθόλου ἡ ἑτέρα πρότασις, ὡσαύτως· ἀεὶ γὰρ τὸ μέσον ἐστὶν ὁ ἀπὸ θατέρου μὲν ἀποφατικῶς λέγεται, κατὰ θατέρου δὲ καταφατικῶς. ὥστ᾽ ἐνδέχεται τἀντικείμενα περαίνεσθαι, πλὴν οὐκ ἀεὶ οὐδὲ πάντως, ἀλλ᾽ ἐὰν οὕτως ἔχηι τὰ ὑπὸ τὸ μέσον ὥστ᾽ ἢ ταὐτὰ εἶναι ἢ ὅλον πρὸς μέρος. ἄλλως δ᾽ ἀδύνατον· οὐ γὰρ ἔσονται οὐδαμῶς αἱ προτάσεις οὔτ᾽ ἐναντίαι οὔτ᾽ ἀντικείμεναι.	(0702A) Differt autem A priore in terminis converti, nam prius quidem ad B, nunc autem ad C affirmativum. Et si sit non universalis altera propositio, similiter; semper enim medium est, quod ab altero quidem negative dicitur, de altero vero affirmative. Quare contingit opposita quidem perfici, non autem semper, neque omnino, sed sic se habeant, quae sunt sub medio, ut vel eadem sint, vel totum ad partem; aliter autem impossibile, non enim erunt propositiones ullo modo, neque contrariae, neque oppositae.	This syllogism differs from the preceding because the relations between the terms are reversed: before, the affirmative statement concerned B, now it concerns C. Similarly if one premiss is not universal: for the middle term is always that which is stated negatively of one extreme, and affirmatively of the other. Consequently it is possible that contradictories may lead to a conclusion, though not always or in every mood, but only if the terms subordinate to the middle are such that they are either identical or related as whole to part. Otherwise it is impossible: for the premisses cannot anyhow be either contraries or contradictories.
	(PL 64 0702A) CAPUT XVII. De syllogismo ex oppositis in tertia figura.
Ἐν δὲ τῶι τρίτωι σχήματι καταφατικὸς μὲν συλλογισμὸς οὐδέποτ᾽ ἔσται ἐξ ἀντικειμένων προτάσεων διὰ τὴν εἰρημένην αἰτίαν καὶ ἐπὶ τοῦ πρώτου σχήματος, ἀποφατικὸς δ᾽ ἔσται, καὶ καθόλου καὶ μὴ καθόλου τῶν ὅρων ὄντων. ἔστω γὰρ ἐπιστήμη ἐφ᾽ οὗ τὸ Β καὶ Γ, ἰατρικὴ δ᾽ ἐφ᾽ οὗ Α. εἰ οὖν λάβοι πᾶσαν ἰατρικὴν ἐπιστήμην καὶ μηδεμίαν ἰατρικὴν ἐπιστήμην, τὸ Β παντὶ τῶι Α εἴληφε καὶ τὸ Γ οὐδενί, ὥστ᾽ ἔσται τις ἐπιστήμη οὐκ ἐπιστήμη. ὁμοίως δὲ καὶ ἂν μὴ καθόλου ληφθῆι ἡ Β Α πρότασις· εἰ γάρ ἐστί τις ἰατρικὴ ἐπιστήμη καὶ πάλιν μηδεμία ἰατρικὴ ἐπιστήμη, συμβαίνει ἐπιστήμην τινὰ μὴ εἶναι ἐπιστήμην. εἰσὶ δὲ καθόλου μὲν τῶν ὅρων λαμβανομένων ἐναντίαι αἱ προτάσεις, ἐὰν δ᾽ ἐν μέρει ἅτερος, ἀντικείμεναι.	In tertia vero figura affirmativus quidem syllogismus nunquam erit ex oppositis propositionibus propter causam dictam, et in prima figura. (0702B) Negativus autem erit syllogismus, et universalibus, et non universalibus terminis. Sit enim disciplina in quo B et C, medicina autem in quo A; si ergo sumat omnem medicinam disciplinam, et nullam medicinam disciplinam, B omni A sumpsit, et C nulli A, quare erit aliqua disciplina non disciplina. Similiter autem et si non universaliter sumpta sit A B propositio, nam si est aliqua medicina disciplina, et rursum nulla medicina disciplina, accidit disciplinam aliquam non esse disciplinam. Sunt autem universaliter quidem sumptis terminis contrariae propositiones, si autem particularis altera sit, oppositae.	In the third figure an affirmative syllogism can never be made out of opposite premisses, for the reason given in reference to the first figure; but a negative syllogism is possible whether the terms are universal or not. Let B and C stand for science, A for medicine. If then one should assume that all medicine is science and that no medicine is science, he has assumed that B belongs to all A and C to no A, so that a particular science will not be a science. Similarly if the premiss BA is not assumed universally. For if some medicine is science and again no medicine is science, it results that some science is not science, The premisses are contrary if the terms are taken universally; if one is particular, they are contradictory.
Δεῖ δὲ κατανοεῖν ὅτι ἐνδέχεται μὲν οὕτω τὰ ἀντικείμενα λαμβάνειν ὥσπερ εἴπομεν πᾶσαν ἐπιστήμην σπουδαίαν εἶναι καὶ πάλιν μηδεμίαν, ἢ τινὰ μὴ σπουδαίαν· ὅπερ οὐκ εἴωθε λανθάνειν. ἔστι δὲ δι᾽ ἄλλων ἐρωτημάτων συλλογίσασθαι θάτερον, ἢ ὡς ἐν τοῖς Τοπικοῖς ἐλέχθη λαβεῖν.	(0702C) Oportet autem scire quoniam contingit opposita sic sumere quemadmodum diximus, omnem disciplinam studiosam esse, et rursum nullam aut aliquam non esse studiosam, quod non solet latere; erit autem per alias interrogationes syllogizare alteram, et quemadmodum in Topicis dictum est, sumere.	We must recognize that it is possible to take opposites in the way we said, viz. ‘all science is good’ and ‘no science is good’ or ‘some science is not good’. This does not usually escape notice. But it is possible to establish one part of a contradiction through other premisses, or to assume it in the way suggested in the Topics.
ἐπεὶ δὲ τῶν καταφάσεων αἱ ἀντιθέσεις τρεῖς, ἑξαχῶς συμβαίνει τὰ ἀντικείμενα λαμβάνειν, ἢ παντὶ καὶ μηδενί, ἢ παντὶ καὶ μὴ παντί, ἢ τινὶ καὶ μηδενί, καὶ τοῦτο ἀντιστρέψαι ἐπὶ ↵ τῶν ὅρων, οἷον τὸ Α παντὶ τῶι Β, τῶι δὲ Γ μηδενί, ἢ τῶι Γ παντί, τῶι δὲ Β μηδενί, ἢ τῶι μὲν παντί, τῶι δὲ μὴ παντί, καὶ πάλιν τοῦτο ἀντιστρέψαι κατὰ τοὺς ὅρους. ὁμοίως δὲ καὶ ἐπὶ τοῦ τρίτου σχήματος. ὥστε φανερὸν ὁσαχῶς τε καὶ ἐν ποίοις σχήμασιν ἐνδέχεται διὰ τῶν ἀντικειμένων προτάσεων γενέσθαι συλλογισμόν.	Quoniam autem affirmationum oppositiones sunt tres, sexies accidit opposita sumere, aut omni et nulli, aut omni et non omni, aut alicui et nulli; et hoc converti in terminis, ut A omni B et nulli C, aut omni C et nulli B, aut huic quidem omni, illi vero non omni, et rursum hoc converti secundum terminos; similiter autem et in tertia figura. Quare manifestum est et quoties et in quibus figuris contingit per oppositas propositiones fieri syllogismum.	Since there are three oppositions to affirmative statements, it follows that opposite statements may be assumed as premisses in six ways; we may have either universal affirmative and negative, or universal affirmative and particular negative, or particular affirmative and universal negative, and the relations between the terms may be reversed; e.g. A may belong to all B and to no C, or to all C and to no B, or to all of the one, not to all of the other; here too the relation between the terms may be reversed. Similarly in the third figure. So it is clear in how many ways and in what figures a syllogism can be made by means of premisses which are opposed.
Φανερὸν δὲ καὶ ὅτι ἐκ ψευδῶν μὲν ἔστιν ἀληθὲς συλλογίσασθαι, καθάπερ εἴρηται πρότερον, ἐκ δὲ τῶν ἀντικειμέ- νων οὐκ ἔστιν· ἀεὶ γὰρ ἐναντίος ὁ συλλογισμὸς γίνεται τῶι πράγματι, οἷον εἰ ἔστιν ἀγαθόν, μὴ εἶναι ἀγαθόν, ἢ εἰ ζῶιον, μὴ ζῶιον, διὰ τὸ ἐξ ἀντιφάσεως εἶναι τὸν συλλογισμὸν καὶ τοὺς ὑποκειμένους ὅρους ἢ τοὺς αὐτοὺς εἶναι ἢ τὸν μὲν ὅλον τὸν δὲ μέρος. δῆλον δὲ καὶ ὅτι ἐν τοῖς παραλογισμοῖς οὐδὲν κωλύει γίνεσθαι τῆς ὑποθέσεως ἀντίφασιν, οἷον εἰ ἔστι περιττόν, μὴ εἶναι περιττόν. ἐκ γὰρ τῶν ἀντικειμένων προτάσεων ἐναντίος ἦν ὁ συλλογισμός· ἐὰν οὖν λάβηι τοιαύτας, ἔσται τῆς ὑποθέσεως ἀντίφασις,	(0702D) Manifestum est quoniam ex falsis est verum syllogizare, quemadmodum dictum est prius; ex oppositis autem non est, semper enim contrarius syllogismus fit rei (ut si est bonum non esse bonum, aut si animal non animal) eo quod ex contradictione est syllogismus, et subiecti termini aut iidem sunt, aut hic quidem totum, ille autem pars. Palam autem quoniam in paralogismis nihil prohibet fieri hypotheseos contradictionem, ut si est impar non esse impar, nam ex oppositis propositionibus contrarius erit syllogismus; si ergo sumpserit hoc modo, hypotheseos erit contradictio.	It is clear too that from false premisses it is possible to draw a true conclusion, as has been said before, but it is not possible if the premisses are opposed. For the syllogism is always contrary to the fact, e.g. if a thing is good, it is proved that it is not good, if an animal, that it is not an animal because the syllogism springs out of a contradiction and the terms presupposed are either identical or related as whole and part. It is evident also that in fallacious reasonings nothing prevents a contradiction to the hypothesis from resulting, e.g. if something is odd, it is not odd. For the syllogism owed its contrariety to its contradictory premisses; if we assume such premisses we shall get a result that contradicts our hypothesis.
δεῖ δὲ κατανοεῖν ὅτι οὕτω μὲν οὐκ ἔστιν ἐναντία συμπεράνασθαι ἐξ ἑνὸς συλλογισμοῦ ὥστ᾽ εἶναι τὸ συμπέρασμα τὸ μὴ ὂν ἀγαθὸν ἀγαθὸν ἢ ἄλλο τι τοιοῦτον, ἐὰν μὴ εὐθὺς ἡ πρότασις τοιαύτη ληφθῆι (οἷον πᾶν ζῶιον λευκὸν εἶναι καὶ μὴ λευκόν, τὸν δ᾽ ἄνθρωπον ζῶιον), ἀλλ᾽ ἢ προσλαβεῖν δεῖ τὴν ἀντίφασιν (οἷον ὅτι πᾶσα ἐπιστήμη ὑπόληψις [καὶ οὐχ ὑπόληψισ], εἶτα λαβεῖν ὅτι ἡ ἰατρικὴ ἐπιστήμη μέν ἐστιν, οὐδεμία δ᾽ ὑπόληψις, ὥσπερ οἱ ἔλεγχοι γίνονται), ἢ ἐκ δύο συλλογισμῶν. ὥστε δ᾽ εἶναι ἐναντία κατ᾽ ἀλήθειαν τὰ εἰλημμένα, οὐκ ἔστιν ἄλλον τρόπον ἢ τοῦτον, καθάπερ εἴρηται πρότερον.	(0703A) Oportet autem considerare quoniam sic quidem non est contraria concludere ex uno syllogismo (ut sit conclusio quoniam non est bonum, bonum aut aliud quiddam tale), nisi statim huiusmodi propositio sumatur, ut omne animal esse album et non album, hominem autem animal, sed vel assumere oportet contradictionem, ut quoniam omnis disciplina opinio et non opinio, deinde sumere quoniam medicina disciplina quidem est. , nulla autem opinio, quemadmodum redargutiones fiunt, vel ex duobus syllogismis. Quare esse quidem contraria secundum veritatem quae sumpta sunt, non est alio modo quam hoc quemadmodum dictum est prius.	But we must recognize that contraries cannot be inferred from a single syllogism in such a way that we conclude that what is not good is good, or anything of that sort unless a self-contradictory premiss is at once assumed, e.g. ‘every animal is white and not white’, and we proceed ‘man is an animal’. Either we must introduce the contradiction by an additional assumption, assuming, e.g., that every science is supposition, and then assuming ‘Medicine is a science, but none of it is supposition’ (which is the mode in which refutations are made), or we must argue from two syllogisms. In no other way than this, as was said before, is it possible that the premisses should be really contrary.