Authors/Aristotle/priora/Liber 1/C4

Chapter 4

Greek	Latin	English
	(PL 64 0641C) CAPUT IV. De modis syllogisticis et asyllogistis absolutis primae figurae.	4
25b26 Διωρισμένων δὲ τούτων λέγωμεν ἤδη διὰ τίνων καὶ πότε καὶ πῶς γίνεται πᾶς συλλογισμός· ὕστερον δὲ λεκτέον περὶ ἀποδείξεως. πρότερον δὲ περὶ συλλογισμοῦ λεκτέον ἢ περὶ ἀποδείξεως διὰ τὸ καθόλου μᾶλλον εἶναι τὸν συλλογισμόν· ἡ μὲν γὰρ ἀπόδειξις συλλογισμός τις, ὁ συλλογισμὸς δὲ οὐ πᾶς ἀπόδειξις.	His vero determinatis dicemus iam per quae et quando et quomodo fit omnis syllogismus, postea vero dicendum de demonstratione. (0641D) Prius enim de syllogismo dicendum quam de demonstratione, eo quod universalior est syllogismus, nam demonstratio quidem syllogismus quidam est; syllogismus vero non omnis demonstratio.	After these distinctions we now state by what means, when, and how every syllogism is produced; subsequently we must speak of demonstration. Syllogism should be discussed before demonstration because syllogism is the general: the demonstration is a sort of syllogism, but not every syllogism is a demonstration.
Ὅταν οὖν ὅροι τρεῖς οὕτως ἔχωσι πρὸς ἀλλήλους ὥστε τὸν ἔσχατον ἐν ὅλωι εἶναι τῶι μέσωι καὶ τὸν μέσον ἐν ὅλωι τῶι πρώτωι ἢ εἶναι ἢ μὴ εἶναι, ἀνάγκη τῶν ἄκρων εἶναι συλλογισμὸν τέλειον. καλῶ δὲ μέσον μὲν ὁ καὶ αὐτὸ ἐν ἄλλωι καὶ ἄλλο ἐν τούτωι ἐστίν, ὁ καὶ τῆι θέσει γίνεται μέσον· ἄκρα δὲ τὸ αὐτό τε ἐν ἄλλωι ὂν καὶ ἐν ὧι ἄλλο ἐστίν. εἰ γὰρ τὸ Α κατὰ παντὸς τοῦ Β καὶ τὸ Β κατὰ παντὸς τοῦ Γ, ἀνάγκη τὸ Α κατὰ παντὸς τοῦ Γ κατηγορεῖσθαι· πρότερον γὰρ εἴρηται πῶς τὸ κατὰ παντὸς λέγομεν. ὁμοίως δὲ καὶ εἰ τὸ μὲν Α κατὰ μη ↵ δενὸς τοῦ Β, τὸ δὲ Β κατὰ παντὸς τοῦ Γ, ὅτι τὸ Α οὐδενὶ τῶι Γ ὑπάρξει.	Quando igitur tres termini sic se habent ad invicem, ut et postremus sit in toto medio, et medius in toto primo vel sit, vel non sit, necesse est extremitatum perfectum esse syllogismum. Voco autem medium quod et ipsum in alio, et aliud in ipso est, quod et positione medium est; extrema vero quod et ipsum in alio, et in quo aliud est. Si enim A de omni B, et B de omni C, necesse est A de omni C praedicari. Prius enim dictum est quomodo de omni dicimus. Similiter autem et si A de nullo B, B autem de omni C, quoniam A nulli C inerit.	Whenever three terms are so related to one another that the last is contained in the middle as in a whole, and the middle is either contained in, or excluded from, the first as in or from a whole, the extremes must be related by a perfect syllogism. I call that term middle which is itself contained in another and contains another in itself: in position also this comes in the middle. By extremes I mean both that term which is itself contained in another and that in which another is contained. If A is predicated of all B, and B of all C, A must be predicated of all C: we have already explained what we mean by ‘predicated of all’. Similarly also, if A is predicated of no B, and B of all C, it is necessary that no C will be A.
εἰ δὲ τὸ μὲν πρῶτον παντὶ τῶι μέσωι ἀκολουθεῖ, τὸ δὲ μέσον μηδενὶ τῶι ἐσχάτωι ὑπάρχει, οὐκ ἔσται συλλογισμὸς τῶν ἄκρων· οὐδὲν γὰρ ἀναγκαῖον συμβαίνει τῶι ταῦτα εἶναι· καὶ γὰρ παντὶ καὶ μηδενὶ ἐνδέχεται τὸ πρῶτον τῶι ἐσχάτωι ὑπάρχειν, ὥστε οὔτε τὸ κατὰ μέρος οὔτε τὸ καθόλου γίνεται ἀναγκαῖον·	(0642A) Si autem primum quidem omni medio consequens est, medium vero nulli postremo, non erit syllogismus extremitatum. Nihil enim necessarium accidit, eo quod haec sunt, nam et omni et nulli contingit primum postremo inesse, quare neque particulare, neque universale fit necessarium.	But if the first term belongs to all the middle, but the middle to none of the last term, there will be no syllogism in respect of the extremes; for nothing necessary follows from the terms being so related; for it is possible that the first should belong either to all or to none of the last, so that neither a particular nor a universal conclusion is necessary.
μηδενὸς δὲ ὄντος ἀναγκαίου διὰ τούτων οὐκ ἔσται συλλογισμός. ὅροι τοῦ παντὶ ὑπάρχειν ζῶιον – ἄνθρωπος – ἵππος, τοῦ μηδενὶ ζῶιον – ἄνθρωπος – λίθος. οὐδ᾽ ὅταν μήτε τὸ πρῶτον τῶι μέσωι μήτε τὸ μέσον τῶι ἐσχάτωι μηδενὶ ὑπάρχηι, οὐδ᾽ οὕτως ἔσται συλλογισμός. ὅροι τοῦ ὑπάρχειν ἐπιστήμη – γραμμή – ἰατρική, τοῦ μὴ ὑπάρχειν ἐπιστήμη – γραμμή – μονάς.	Cum autem nihil est necessarium, per haec non erit syllogismus. Termini vero eius quod est omni inesse, animal, homo, equus; eius vero quod est nulli, animal, homo, lapis. Quando vero nec primum medio, nec medium postremo ulli inest, nec sic erit syllogismus. Termini vero ut inesse, scientia, linea, medicina; ut non inesse, scientia, linea, unitas.	But if there is no necessary consequence, there cannot be a syllogism by means of these premisses. As an example of a universal affirmative relation between the extremes we may take the terms animal, man, horse; of a universal negative relation, the terms animal, man, stone. Nor again can syllogism be formed when neither the first term belongs to any of the middle, nor the middle to any of the last. As an example of a positive relation between the extremes take the terms science, line, medicine: of a negative relation science, line, unit.
καθόλου μὲν οὖν ὄντων τῶν ὅρων, δῆλον ἐν τούτωι τῶι σχήματι πότε ἔσται καὶ πότε οὐκ ἔσται συλλογισμός, καὶ ὅτι ὄντος τε συλλογισμοῦ τοὺς ὅρους ἀναγκαῖον ἔχειν ὡς εἴπομεν, ἄν θ᾽ οὕτως ἔχωσιν, ὅτι ἔσται συλλογισμός.	(0642B) Universalibus igitur existentibus terminis, manifestum est in hac figura quando erit, et quando non erit syllogismus, et quoniam cum est syllogismus, necessarium est terminos sic se habere, ut diximus, et sic se habens manifestum quoniam erit syllogismus.	If then the terms are universally related, it is clear in this figure when a syllogism will be possible and when not, and that if a syllogism is possible the terms must be related as described, and if they are so related there will be a syllogism.
Εἰ δ᾽ ὁ μὲν καθόλου τῶν ὅρων ὁ δ᾽ ἐν μέρει πρὸς τὸν ἕτερον, ὅταν μὲν τὸ καθόλου τεθῆι πρὸς τὸ μεῖζον ἄκρον ἢ κατηγορικὸν ἢ στερητικόν, τὸ δὲ ἐν μέρει πρὸς τὸ ἔλαττον κατηγορικόν, ἀνάγκη συλλογισμὸν εἶναι τέλειον, ὅταν δὲ πρὸς τὸ ἔλαττον ἢ καὶ ἄλλως πως ἔχωσιν οἱ ὅροι, ἀδύνατον. λέγω δὲ μεῖζον μὲν ἄκρον ἐν ὧι τὸ μέσον ἐστίν, ἔλαττον δὲ τὸ ὑπὸ τὸ μέσον ὄν.	Si autem hic quidem terminorum universaliter, alius vero particulariter ad alium, quando universale quidem ponitur ad maiorem extremitatem vel praedicativum, vel privativum, particulare vero ad minorem praedicativum, necesse est syllogismum esse perfectum. Quando vero ad minorem vel quolibet modo aliter se habeant termini, impossibile est. Dico autem maiorem extremitatem quidem in qua medium est, minorem vero, quae sub medio est.	But if one term is related universally, the other in part only, to its subject, there must be a perfect syllogism whenever universality is posited with reference to the major term either affirmatively or negatively, and particularity with reference to the minor term affirmatively: but whenever the universality is posited in relation to the minor term, or the terms are related in any other way, a syllogism is impossible. I call that term the major in which the middle is contained and that term the minor which comes under the middle.
ὑπαρχέτω γὰρ τὸ μὲν Α παντὶ τῶι Β, τὸ δὲ Β τινὶ τῶι Γ. οὐκοῦν εἰ ἔστι παντὸς κατηγορεῖσθαι τὸ ἐν ἀρχῆι λεχθέν, ἀνάγκη τὸ Α τινὶ τῶι Γ ὑπάρχειν. καὶ εἰ τὸ μὲν Α μηδενὶ τῶι Β ὑπάρχει, τὸ δὲ Β τινὶ τῶι Γ, ἀνάγκη τὸ Α τινὶ τῶι Γ μὴ ὑπάρχειν· ὥρισται γὰρ καὶ τὸ κατὰ μηδενὸς πῶς λέγομεν· ὥστε ἔσται συλλογισμὸς τέλειος. ὁμοίως δὲ καὶ εἰ ἀδιόριστον εἴη τὸ Β Γ, κατηγορικὸν ὄν· ὁ γὰρ αὐτὸς ἔσται συλλογισμὸς ἀδιορίστου τε καὶ ἐν μέρει ληφθέντος.	Insit enim A quidem omni B, B autem alicui C, ergo si est de omni praedicari, quod in principio dictum est, necesse est A alicui C inesse. (0642C) Et si A quidem nulli B inest, B vero alicui C, necesse est A alicui C non inesse, determinatum est enim et de nullo, quomodo dicimus, quare erit syllogismus perfectus. Similiter autem et si indefinitum sit B C praedicativum, nam idem erit syllogismus indefinito et particulari sumpto.	Let all B be A and some C be B. Then if ‘predicated of all’ means what was said above, it is necessary that some C is A. And if no B is A but some C is B, it is necessary that some C is not A. The meaning of ‘predicated of none’ has also been defined. So there will be a perfect syllogism. This holds good also if the premiss BC should be indefinite, provided that it is affirmative: for we shall have the same syllogism whether the premiss is indefinite or particular.
Ἐὰν δὲ πρὸς τὸ ἔλαττον ἄκρον τὸ καθόλου τεθῆι ἢ κατηγορικὸν ἢ στερητικόν, οὐκ ἔσται συλλογισμός, οὔτε καταφατικοῦ οὔτε ἀποφατικοῦ τοῦ ἀδιορίστου ἢ κατὰ μέρος ὄντος, οἷον εἰ τὸ μὲν Α τινὶ τῶι Β ὑπάρχει ἢ μὴ ὑπάρχει, τὸ δὲ Β παντὶ τῶι Γ ὑπάρχει· ὅροι τοῦ ὑπάρχειν ἀγαθόν – ἕξις – φρόνησις, τοῦ μὴ ὑπάρχειν ἀγαθόν – ἕξις – ἀμαθία. πάλιν εἰ τὸ μὲν Β μηδενὶ τῶι Γ, τὸ δὲ Α τινὶ τῶι Β ἢ ὑπάρχει ἢ μὴ ὑπάρχει ἢ μὴ παντὶ ὑπάρχει, οὐδ᾽ οὕτως ἔσται συλλογισμός. ὅροι λευκόν – ἵππος – κύκνος, λευκόν – ἵππος – κόραξ. οἱ αὐτοὶ δὲ καὶ εἰ τὸ Α Β ἀδιόριστον.	Si autem ad minorem extremitatem universale ponatur vel praedicativum, vel privativum, non erit syllogismus neque cum affirmativa, neque negativa, neque indefinita, neque particularis sit, ut si A quidem alicui B inest, vel non inest, B autem omni C inest. Termini ut inesse, bonum, habitus, prudentia; ubi non inesse, bonum, habitus, indisciplina. Rursum si B quidem nulli C, A vero alicui B inest, vel non inest, vel non omni inest, nec sic erit syllogismus. Termini omni inesse, album, equus, cygnus; nulli inesse, album, equus, corvus. Idem autem et si A B indefinitum sit.	But if the universality is posited with respect to the minor term either affirmatively or negatively, a syllogism will not be possible, whether the major premiss is positive or negative, indefinite or particular: e.g. if some B is or is not A, and all C is B. As an example of a positive relation between the extremes take the terms good, state, wisdom: of a negative relation, good, state, ignorance. Again if no C is B, but some B is or is not A or not every B is A, there cannot be a syllogism. Take the terms white, horse, swan: white, horse, raven. The same terms may be taken also if the premiss BA is indefinite.
Οὐδ᾽ ὅταν τὸ μὲν πρὸς ↵ τῶι μείζονι ἄκρωι καθόλου γένηται ἢ κατηγορικὸν ἢ στερητικόν, τὸ δὲ πρὸς τῶι ἐλάττονι στερητικὸν κατὰ μέρος, οὐκ ἔσται συλλογισμός [ἀδιορίστου τε καὶ ἐν μέρει ληφθέντοσ], οἷον εἰ τὸ μὲν Α παντὶ τῶι Β ὑπάρχει, τὸ δὲ Β τινὶ τῶι Γ μή, ἢ εἰ μὴ παντὶ ὑπάρχει· ὧι γὰρ ἄν τινι μὴ ὑπάρχηι τὸ μέσον, τούτωι καὶ παντὶ καὶ οὐδενὶ ἀκολουθήσει τὸ πρῶτον.	(0642D) Nec quando ad maiorem extremitatem quidem universale ponatur vel praedicativum, vel privativum, ad minorem vero particulare privativum, non erit syllogismus vel indefinito, vel particulari sumpto. Velut si A quidem omni B inest, B autem alicui C non inest, vel non omni inest. Cui enim alicui non inest medium, hoc omne et nullum sequatur primum.	Nor when the major premiss is universal, whether affirmative or negative, and the minor premiss is negative and particular, can there be a syllogism, whether the minor premiss be indefinite or particular: e.g. if all B is A and some C is not B, or if not all C is B. For the major term may be predicable both of all and of none of the minor, to some of which the middle term cannot be attributed.
ὑποκείσθωσαν γὰρ οἱ ὅροι ζῶιον – ἄνθρωπος – λευκόν· εἶτα καὶ ὧν μὴ κατηγορεῖται λευκῶν ὁ ἄνθρωπος, εἰλήφθω κύκνος καὶ χιών· οὐκοῦν τὸ ζῶιον τοῦ μὲν παντὸς κατηγορεῖται, τοῦ δὲ οὐδενός, ὥστε οὐκ ἔσται συλλογισμός. πάλιν τὸ μὲν Α μηδενὶ τῶι Β ὑπαρχέτω, τὸ δὲ Β τινὶ τῶι Γ μὴ ὑπαρχέτω· καὶ οἱ ὅροι ἔστωσαν ἄψυχον – ἄνθρωπος – λευκόν· εἶτα εἰλήφθωσαν, ὧν μὴ κατηγορεῖται λευκῶν ὁ ἄνθρωπος, κύκνος καὶ χιών· τὸ γὰρ ἄψυχον τοῦ μὲν παντὸς κατηγορεῖται, τοῦ δὲ οὐδενός.	Ponantur enim termini, animal, homo, album, deinde et de quibus albis non praedicatur homo, sumantur cygnus et nix; ergo animal de uno quidem omni praedicatur, de altero vero nullo, quare non erit syllogismus. (0643A) Rursum A quidem nulli B insit, B autem alicui C non insit, et sint termini, inanimatum, homo, album, deinde sumantur alba, de quibus non praedicatur homo, cygnus et nix; nam inanimatum de hoc quidem omni praedicatur, de illo vero nullo.	Suppose the terms are animal, man, white: next take some of the white things of which man is not predicated-swan and snow: animal is predicated of all of the one, but of none of the other. Consequently there cannot be a syllogism. Again let no B be A, but let some C not be B. Take the terms inanimate, man, white: then take some white things of which man is not predicated-swan and snow: the term inanimate is predicated of all of the one, of none of the other.
ἔτι ἐπεὶ ἀδιόριστον τὸ τινὶ τῶι Γ τὸ Β μὴ ὑπάρχειν, ἀληθεύεται δέ, καὶ εἰ μηδενὶ ὑπάρχει καὶ εἰ μὴ παντί, ὅτι τινὶ οὐχ ὑπάρχει, ληφθέντων δὲ τοιούτων ὅρων ὥστε μηδενὶ ὑπάρχειν οὐ γίνεται συλλογισμός (τοῦτο γὰρ εἴρηται πρότερον), φανερὸν οὖν ὅτι τῶι οὕτως ἔχειν τοὺς ὅρους οὐκ ἔσται συλλογισμός· ἦν γὰρ ἂν καὶ ἐπὶ τούτων. ὁμοίως δὲ δειχθήσεται καὶ εἰ τὸ καθόλου τεθείη στερητικόν.	Amplius: quoniam indefinitum est alicui eorum quae sunt C non inesse B, verum est autem et nulli inest, et si non omni, quoniam alicui non inest, sumptis autem his terminis velut nulli inesse, non fit syllogismus (hoc enim dictum est prius) manifestum; ergo est quoniam in eo quod sic se habent termini non erit syllogismus, esset enim et in his. Similiter autem ostendetur, et si universale ponatur privativum.	Further since it is indefinite to say some C is not B, and it is true that some C is not B, whether no C is B, or not all C is B, and since if terms are assumed such that no C is B, no syllogism follows (this has already been stated) it is clear that this arrangement of terms will not afford a syllogism: otherwise one would have been possible with a universal negative minor premiss. A similar proof may also be given if the universal premiss is negative.
Οὐδὲ ἐὰν ἄμφω τὰ διαστήματα κατὰ μέρος ἢ κατηγορικῶς ἢ στερητικῶς, ἢ τὸ μὲν κατηγορικῶς τὸ δὲ στερητικῶς λέγηται, ἢ τὸ μὲν ἀδιόριστον τὸ δὲ διωρισμένον, ἢ ἄμφω ἀδιόριστα, οὐκ ἔσται συλλογισμὸς οὐδαμῶς. ὅροι δὲ κοινοὶ πάντων ζῶιον – λευκόν – ἵππος, ζῶιον – λευκόν – λίθος.	Neque enim si ambo intervalla particularia praedicative, vel privative dicantur, aut hoc quidem praedicativum, illud vero privativum, vel hoc quidem indefinitum, illud vero definitum, vel ambo indefinita, non erit syllogismus nullo modo. (0643B) Termini vero communes omnium, animal, album, equus, animal, album, lapis.	Nor can there in any way be a syllogism if both the relations of subject and predicate are particular, either positively or negatively, or the one negative and the other affirmative, or one indefinite and the other definite, or both indefinite. Terms common to all the above are animal, white, horse: animal, white, stone.
Φανερὸν οὖν ἐκ τῶν εἰρημένων ὡς ἐὰν ἦι συλλογισμὸς ἐν τούτωι τῶι σχήματι κατὰ μέρος, ὅτι ἀνάγκη τοὺς ὅρους οὕτως ἔχειν ὡς εἴπομεν· ἄλλως γὰρ ἐχόντων οὐδαμῶς γίνεται. δῆλον δὲ καὶ ὅτι πάντες οἱ ἐν αὐτῶι συλλογισμοὶ τέλειοί εἰσι· (πάντες γὰρ ἐπιτελοῦνται διὰ τῶν ἐξ ἀρχῆς ληφθέντων), καὶ ὅτι πάντα τὰ προβλήματα δείκνυται διὰ τούτου τοῦ σχήματος· καὶ γὰρ τὸ παντὶ καὶ τὸ μηδενὶ καὶ τὸ τινὶ καὶ τὸ μή τινι ὑπάρχειν. καλῶ δὲ τὸ τοιοῦτον σχῆμα πρῶτον.	Manifestum est igitur ex iis quae dicta sunt quoniam si sit syllogismus in hac figura particularis, quoniam necesse est terminos sic se habere, ut diximus. Aliter enim se habentibus, nullo [modo] fit. Palam autem quoniam omnes qui in hac sunt syllogismi perfecti sunt, omnes enim perficiuntur per ea quae ex principio sumuntur, et quoniam omnia problemata ostenduntur per hanc figuram: etenim omni et nulli, alicui et non alicui inesse. Voco autem huiusmodi figuram, primam.	It is clear then from what has been said that if there is a syllogism in this figure with a particular conclusion, the terms must be related as we have stated: if they are related otherwise, no syllogism is possible anyhow. It is evident also that all the syllogisms in this figure are perfect (for they are all completed by means of the premisses originally taken) and that all conclusions are proved by this figure, viz. universal and particular, affirmative and negative. Such a figure I call the first.