Authors/Aristotle/priora/Liber 1/C5

Chapter 5

Greek	Latin	English
	(PL 64 0643B) CAPUT V. De syllogismis absolutis in secunda figura.	5
26b34 Ὅταν δὲ τὸ αὐτὸ τῶι μὲν παντὶ τῶι δὲ μηδενὶ ὑπάρχηι, ἢ ἑκατέρωι παντὶ ἢ μηδενί, τὸ μὲν σχῆμα τὸ τοιοῦτον καλῶ δεύτερον, μέσον δὲ ἐν αὐτῶι λέγω τὸ κατηγορούμενον ἀμφοῖν, ἄκρα δὲ καθ᾽ ὧν λέγεται τοῦτο, μεῖζον δὲ ἄκρον τὸ πρὸς τῶι μέσωι κείμενον· ἔλαττον δὲ τὸ πορρωτέρω τοῦ μέσου. τίθεται δὲ τὸ μέσον ἔξω μὲν τῶν ἄκρων, πρῶτον δὲ τῆι θέσει. ↵ τέλειος μὲν οὖν οὐκ ἔσται συλλογισμὸς οὐδαμῶς ἐν τούτωι τῶι σχήματι, δυνατὸς δ᾽ ἔσται καὶ καθόλου καὶ μὴ καθόλου τῶν ὅρων ὄντων.	Quando vero idem huic omni quidem, illi vero nulli inest, vel utique omni, vel nulli, figuram quidem huiusmodi voco secundam. (0643C) Medium autem in hac dico quod de utraque praedicatur; extremitates vero de quibus dicitur hoc, maiorem quidem extremitatem, quae iuxta medium posita est, minorem vero, quae longius sita est A medio. Ponitur autem medium foras quidem extremitatum, primum vero positione. Perfectus igitur non erit syllogismus nullo modo in hac figura, possibile vero erit et universalibus, et non universalibus existentibus terminis.	Whenever the same thing belongs to all of one subject, and to none of another, or to all of each subject or to none of either, I call such a figure the second; by middle term in it I mean that which is predicated of both subjects, by extremes the terms of which this is said, by major extreme that which lies near the middle, by minor that which is further away from the middle. The middle term stands outside the extremes, and is first in position. A syllogism cannot be perfect anyhow in this figure, but it may be valid whether the terms are related universally or not.
καθόλου μὲν οὖν ὄντων ἔσται συλλογισμὸς ὅταν τὸ μέσον τῶι μὲν παντὶ τῶι δὲ μηδενὶ ὑπάρχηι, ἂν πρὸς ὁποτερωιοῦν ἦι τὸ στερητικόν· ἄλλως δ᾽ οὐδαμῶς. κατηγορείσθω γὰρ τὸ Μ τοῦ μὲν Ν μηδενός, τοῦ δὲ Ξ παντός. ἐπεὶ οὖν ἀντιστρέφει τὸ στερητικόν, οὐδενὶ τῶι Μ ὑπάρξει τὸ Ν· τὸ δέ γε Μ παντὶ τῶι Ξ ὑπέκειτο· ὥστε τὸ Ν οὐδενὶ τῶι Ξ· τοῦτο γὰρ δέδεικται πρότερον.	Universalibus igitur terminis erit syllogismus, quando medium huic quidem omni, illi vero nulli inerit, etsi ad utrumvis sit privativum, aliter vero nullo modo. Praedicetur enim M de N quidem nullo, de O vero omni, quoniam igitur convertitur privativa, nulli M inerit N, at M omni O supponebatur, quare N nulli O inerit: hoc enim ostensum est prius.	If then the terms are related universally a syllogism will be possible, whenever the middle belongs to all of one subject and to none of another (it does not matter which has the negative relation), but in no other way. Let M be predicated of no N, but of all O. Since, then, the negative relation is convertible, N will belong to no M: but M was assumed to belong to all O: consequently N will belong to no O. This has already been proved.
πάλιν εἰ τὸ Μ τῶι μὲν Ν παντὶ τῶι δὲ Ξ μηδενί, οὐδὲ τὸ Ξ τῶι Ν οὐδενὶ ὑπάρξει (εἰ γὰρ τὸ Μ οὐδενὶ τῶι Ξ, οὐδὲ τὸ Ξ οὐδενὶ τῶι Μ· τὸ δέ γε Μ παντὶ τῶι Ν ὑπῆρχεν· τὸ ἄρα Ξ οὐδενὶ τῶι Ν ὑπάρξει· γεγένηται γὰρ πάλιν τὸ πρῶτον σχῆμα)· ἐπεὶ δὲ ἀντιστρέφει τὸ στερητικόν, οὐδὲ τὸ Ν οὐδενὶ τῶι Ξ ὑπάρξει, ὥστ᾽ ἔσται ὁ αὐτὸς συλλογισμός. ἔστι δὲ δεικνύναι ταῦτα καὶ εἰς τὸ ἀδύνατον ἄγοντας.	(0643D) Rursum si M N quidem omni inest, O vero nulli, neque N O nulli inerit. Nam si M nulli O, neque O nulli N inerit, at vero M omni N inerat, quare O nulli inerit. Facta est enim rursum prima figura. Quoniam autem convertitur privativum, neque N nulli O inerit, quare erit idem syllogismus, est autem ostendere haec et ad impossibile ducentes.	Again if M belongs to all N, but to no O, then N will belong to no O. For if M belongs to no O, O belongs to no M: but M (as was said) belongs to all N: O then will belong to no N: for the first figure has again been formed. But since the negative relation is convertible, N will belong to no O. Thus it will be the same syllogism that proves both conclusions. It is possible to prove these results also by reductio ad impossibile.
ὅτι μὲν οὖν γίνεται συλλογισμὸς οὕτως ἐχόντων τῶν ὅρων, φανερόν, ἀλλ᾽ οὐ τέλειος· οὐ γὰρ μόνον ἐκ τῶν ἐξ ἀρχῆς ἀλλὰ καὶ ἐξ ἄλλων ἐπιτελεῖται τὸ ἀναγκαῖον.	Quoniam ergo fit syllogismus sic se habentibus terminis manifestum, sed non perfectus, non enim solum ex iis quae ab initio sumpta sunt, sed ex aliis perficitur necessarium.	It is clear then that a syllogism is formed when the terms are so related, but not a perfect syllogism; for necessity is not perfectly established merely from the original premisses; others also are needed.
ἐὰν δὲ τὸ Μ παντὸς τοῦ Ν καὶ τοῦ Ξ κατηγορῆται, οὐκ ἔσται συλλογισμός. ὅροι τοῦ ὑπάρχειν οὐσία - ζῶιον - ἄνθρωπος, τοῦ μὴ ὑπάρχειν οὐσία - ζῶιον - ἀριθμός· μέσον οὐσία.	Si autem M de omni N et O praedicetur, non erit syllogismus. Termini inesse, substantia, animal, ratio; non inesse, substantia, animal, lapis, medium, substantia.	But if M is predicated of every N and O, there cannot be a syllogism. Terms to illustrate a positive relation between the extremes are substance, animal, man; a negative relation, substance, animal, number-substance being the middle term.
οὐδ᾽ ὅταν μήτε τοῦ Ν μήτε τοῦ Ξ μηδενὸς κατηγορῆται τὸ Μ. ὅροι τοῦ ὑπάρχειν γραμμή – ζῶιον – ἄνθρωπος, τοῦ μὴ ὑπάρχειν γραμμή – ζῶιον – λίθος.	Nec quando de N nec de O nullo praedicatur M. (0644A) Termini inesse, linea, animal, homo; non inesse, linea, animal, lapis.	Nor is a syllogism possible when M is predicated neither of any N nor of any O. Terms to illustrate a positive relation are line, animal, man: a negative relation, line, animal, stone.
φανερὸν οὖν ὅτι ἂν ἦι συλλογισμὸς καθόλου τῶν ὅρων ὄντων, ἀνάγκη τοὺς ὅρους ἔχειν ὡς ἐν ἀρχῆι εἴπομεν· ἄλλως γὰρ ἐχόντων οὐ γίνεται τὸ ἀναγκαῖον.	Manifestum ergo quoniam si fit syllogismus ex universalibus terminis, necesse est terminos sic se habere, ut in principio diximus. Aliter enim se habentibus terminis non fit conclusio necessaria.	It is clear then that if a syllogism is formed when the terms are universally related, the terms must be related as we stated at the outset: for if they are otherwise related no necessary consequence follows.
Ἐὰν δὲ πρὸς τὸν ἕτερον ἦι καθόλου τὸ μέσον, ὅταν μὲν πρὸς τὸν μείζω γένηται καθόλου ἢ κατηγορικῶς ἢ στερητικῶς, πρὸς δὲ τὸν ἐλάττω κατὰ μέρος καὶ ἀντικειμένως τῶι καθόλου (λέγω δὲ τὸ ἀντικειμένως, εἰ μὲν τὸ καθόλου στερητικόν, τὸ ἐν μέρει καταφατικόν· εἰ δὲ κατηγορικὸν τὸ καθόλου, τὸ ἐν μέρει στερητικόν), ἀνάγκη γίνεσθαι συλλογισμὸν στερητικὸν κατὰ μέρος.	Si autem ad alterum sit universaliter medium, quando ad maius quidem fuerit universaliter vel praedicative, vel privative, ad minus autem et particulariter, et oppositae universali (dico autem oppositae, si universale quidem privativum particulare praedicativum, vel si universale praedicativum, particulare privativum), necesse est syllogismum fieri privativum particulariter.	If the middle term is related universally to one of the extremes, a particular negative syllogism must result whenever the middle term is related universally to the major whether positively or negatively, and particularly to the minor and in a manner opposite to that of the universal statement: by ‘an opposite manner’ I mean, if the universal statement is negative, the particular is affirmative: if the universal is affirmative, the particular is negative.
εἰ γὰρ τὸ Μ τῶι μὲν Ν μηδενὶ τῶι δὲ Ξ τινὶ ὑπάρχει, ἀνάγκη τὸ Ν τινὶ τῶι Ξ μὴ ὑπάρχειν. ἐπεὶ γὰρ ἀντιστρέφει τὸ στερητικόν, οὐδενὶ τῶι Μ ὑπάρξει τὸ Ν· τὸ δέ γε Μ ὑπέκειτο τινὶ τῶι Ξ ὑπάρχειν· ὥστε τὸ Ν τινὶ τῶι Ξ οὐχ ὑπάρξει· γίνεται γὰρ συλλογισμὸς διὰ τοῦ πρώτου σχήματος. πάλιν εἰ τῶι μὲν Ν παντὶ τὸ Μ, τῶι δὲ Ξ τινὶ μὴ ὑπάρχει, ἀνάγκη τὸ Ν τινὶ τῶι Ξ μὴ ὑπάρχειν· εἰ γὰρ παντὶ ὑπάρχει, κατηγορεῖται δὲ καὶ τὸ Μ παντὸς τοῦ Ν, ἀνάγκη τὸ Μ ↵ παντὶ τῶι Ξ ὑπάρχειν· ὑπέκειτο δὲ τινὶ μὴ ὑπάρχειν. καὶ εἰ τὸ Μ τῶι μὲν Ν παντὶ ὑπάρχει τῶι δὲ Ξ μὴ παντί, ἔσται συλλογισμὸς ὅτι οὐ παντὶ τῶι Ξ τὸ Ν· ἀπόδειξις δ᾽ ἡ αὐτή. ἐὰν δὲ τοῦ μὲν Ξ παντὸς τοῦ δὲ Ν μὴ παντὸς κατηγορῆται, οὐκ ἔσται συλλογισμός. ὅροι ζῶιον – οὐσία – κόραξ, ζῶιον – λευκόν – κόραξ. οὐδ᾽ ὅταν τοῦ μὲν Ξ μηδενός, τοῦ δὲ Ν τινός. ὅροι τοῦ ὑπάρχειν ζῶιον – οὐσία – μονάς, τοῦ μὴ ὑπάρχειν ζῶιον – οὐσία – ἐπιστήμη.	Nam si M nulli quidem N, O autem alicui inest, necesse est N alicui O non inesse. (0644B) Quoniam enim convertitur privativum, nulli M inerit, N M vero supponebatur alicui O inesse, quare N alicui eorum quae sunt O non inerit. Fit enim syllogismus per primam figuram. Rursus si N quidem omni M, O vero alicui non inest, necesse est N alicui O non inesse. Nam si O omni inest N, praedicatur autem et M de omni N, necesse est M omni O inesse, supponebatur autem alicui non inesse. Et si M N omni quidem inest, O autem non omni, erit syllogismus, quoniam non omni O inest N. Demonstratio autem eadem. Si autem de O quidem omni, de N vero non omni praedicatur M, non erit syllogismus. Termini inesse, animal, substantia, corvus. Non inesse, animal, album, corvus. Nec quando de O quidem nullo, de N vero aliquo. Termini inesse, animal, substantia, lapis. Non inesse, animal, substantia, scientia.	For if M belongs to no N, but to some O, it is necessary that N does not belong to some O. For since the negative statement is convertible, N will belong to no M: but M was admitted to belong to some O: therefore N will not belong to some O: for the result is reached by means of the first figure. Again if M belongs to all N, but not to some O, it is necessary that N does not belong to some O: for if N belongs to all O, and M is predicated also of all N, M must belong to all O: but we assumed that M does not belong to some O. And if M belongs to all N but not to all O, we shall conclude that N does not belong to all O: the proof is the same as the above. But if M is predicated of all O, but not of all N, there will be no syllogism. Take the terms animal, substance, raven; animal, white, raven. Nor will there be a conclusion when M is predicated of no O, but of some N. Terms to illustrate a positive relation between the extremes are animal, substance, unit: a negative relation, animal, substance, science.
Ὅταν μὲν οὖν ἀντικείμενον ἦι τὸ καθόλου τῶι κατὰ μέρος, εἴρηται πότ᾽ ἔσται καὶ πότ᾽ οὐκ ἔσται συλλογισμός· ὅταν δὲ ὁμοιοσχήμονες ὦσιν αἱ προτάσεις, οἷον ἀμφότεραι στερητικαὶ ἢ καταφατικαί, οὐδαμῶς ἔσται συλλογισμός. ἔστωσαν γὰρ πρῶτον στερητικαί, καὶ τὸ καθόλου κείσθω πρὸς τὸ μεῖζον ἄκρον, οἷον τὸ Μ τῶι μὲν Ν μηδενὶ τῶι δὲ Ξ τινὶ μὴ ὑπαρχέτω· ἐνδέχεται δὴ καὶ παντὶ καὶ μηδενὶ τῶι Ξ τὸ Ν ὑπάρχειν. ὅροι τοῦ μὲν μὴ ὑπάρχειν μέλαν – χιών – ζῶιον· τοῦ δὲ παντὶ ὑπάρχειν οὐκ ἔστι λαβεῖν, εἰ τὸ Μ τῶι Ξ τινὶ μὲν ὑπάρχει τινὶ δὲ μή. εἰ γὰρ παντὶ τῶι Ξ τὸ Ν, τὸ δὲ Μ μηδενὶ τῶι Ν, τὸ Μ οὐδενὶ τῶι Ξ ὑπάρξει· ἀλλ᾽ ὑπέκειτο τινὶ ὑπάρχειν. οὕτω μὲν οὖν οὐκ ἐγχωρεῖ λαβεῖν ὅρους, ἐκ δὲ τοῦ ἀδιορίστου δεικτέον· ἐπεὶ γὰρ ἀληθεύεται τὸ τινὶ μὴ ὑπάρχειν τὸ Μ τῶι Ξ καὶ εἰ μηδενὶ ὑπάρχει, μηδενὶ δὲ ὑπάρχοντος οὐκ ἦν συλλογισμός, φανερὸν ὅτι οὐδὲ νῦν ἔσται.	(0644C) Quando igitur oppositum est universale particulari, dictum est quando erit, et quando non erit syllogismus. Quando autem similis figurae fuerint propositiones, ut ambae privativae vel affirmativae, nullo modo erit syllogismus. Sint enim primum privativae, et universale ponatur ad maiorem extremitatem, ut M N quidem nulli, O autem alicui non insit: contingit ergo et omni, et nulli O inesse N. Termini quidem nulli inesse, nigrum, nix, animal. Omni vero inesse, non est sumere, si M alicui quidem O inest, alicui autem non. Nam si omni O inest N, et M nulli, N etiam M nulli O inerit; sed positum erat alicui inesse, non igitur sic sumere contingit terminos. Ex indefinito autem ostendendum est. (0644D) Quoniam enim verum est M non inesse alicui O, et si nulli inest, nulli vero cum insit non erit syllogismus, manifestum quoniam neque nunc erit.	If then the universal statement is opposed to the particular, we have stated when a syllogism will be possible and when not: but if the premisses are similar in form, I mean both negative or both affirmative, a syllogism will not be possible anyhow. First let them be negative, and let the major premiss be universal, e.g. let M belong to no N, and not to some O. It is possible then for N to belong either to all O or to no O. Terms to illustrate the negative relation are black, snow, animal. But it is not possible to find terms of which the extremes are related positively and universally, if M belongs to some O, and does not belong to some O. For if N belonged to all O, but M to no N, then M would belong to no O: but we assumed that it belongs to some O. In this way then it is not admissible to take terms: our point must be proved from the indefinite nature of the particular statement. For since it is true that M does not belong to some O, even if it belongs to no O, and since if it belongs to no O a syllogism is (as we have seen) not possible, clearly it will not be possible now either.
πάλιν ἔστωσαν κατηγορικαί, καὶ τὸ καθόλου κείσθω ὁμοίως, οἷον τὸ Μ τῶι μὲν Ν παντὶ τῶι δὲ Ξ τινὶ ὑπαρχέτω. ἐνδέχεται δὴ τὸ Ν τῶι Ξ καὶ παντὶ καὶ μηδενὶ ὑπάρχειν. ὅροι τοῦ μηδενὶ ὑπάρχειν λευκόν – κύκνος – λίθος τοῦ δὲ παντὶ οὐκ ἔσται λαβεῖν διὰ τὴν αὐτὴν αἰτίαν ἥνπερ πρότερον, ἀλλ᾽ ἐκ τοῦ ἀδιορίστου δεικτέον. εἰ δὲ τὸ καθόλου πρὸς τὸ ἔλαττον ἄκρον ἐστί, καὶ τὸ Μ τῶι μὲν Ξ μηδενὶ τῶι δὲ Ν τινὶ μὴ ὑπάρχει, ἐνδέχεται τὸ Ν τῶι Ξ καὶ παντὶ καὶ μηδενὶ ὑπάρχειν. ὅροι τοῦ ὑπάρχειν λευκόν – ζῶιον – κόραξ, τοῦ μὴ ὑπάρχειν λευκόν – λίθος – κόραξ. εἰ δὲ κατηγορικαὶ αἱ προτάσεις, ὅροι τοῦ μὴ ὑπάρχειν λευκόν – ζῶιον – χιών, τοῦ ὑπάρχειν λευκόν – ζῶιον – κύκνος.	Rursum si praedicativae, et universale ponatur similiter, ut M omni quidem N, O autem alicui insit, contingit ergo et omni, et nulli O inesse. Termini nulli inesse, album, cygnus, lapis. Omni vero non erit sumere terminos, propter eamdem causam quam et prius, sed ex indefinito monstrandum est. Si autem universale ad minorem extremitatem est, et M O quidem nulli, N vero alicui non inest, contingit N, et omni et nulli O inesse. Termini inesse, album, animal, corvus; non inesse, album, lapis, corvus. Similiter autem et si praedicativae fuerint propositiones. Termini non inesse, album, animal, nix; inesse, album, animal, cygnus. (0645A)	Again let the premisses be affirmative, and let the major premiss as before be universal, e.g. let M belong to all N and to some O. It is possible then for N to belong to all O or to no O. Terms to illustrate the negative relation are white, swan, stone. But it is not possible to take terms to illustrate the universal affirmative relation, for the reason already stated: the point must be proved from the indefinite nature of the particular statement. But if the minor premiss is universal, and M belongs to no O, and not to some N, it is possible for N to belong either to all O or to no O. Terms for the positive relation are white, animal, raven: for the negative relation, white, stone, raven. If the premisses are affirmative, terms for the negative relation are white, animal, snow; for the positive relation, white, animal, swan.
φανερὸν οὖν, ὅταν ὁμοιοσχήμονες ὦσιν αἱ προτάσεις καὶ ἡ μὲν καθόλου ἡ δ᾽ ἐν μέρει, ὅτι οὐδαμῶς γίνεται συλλογισμός. ἀλλ᾽ οὐδ᾽ εἰ τινὶ ἑκατέρωι ὑπάρχει ἢ μὴ ὑπάρχει, ἢ τῶι μὲν τῶι δὲ μή, ἢ μηδετέρωι παντί, ἢ ἀδιορίστως. ὅροι δὲ κοινοὶ πάντων λευκόν – ζῶιον – ἄνθρωπος, λευκόν – ζῶιον – ἄψυχον. ↵ Φανερὸν οὖν ἐκ τῶν εἰρημένων ὅτι ἐάν τε οὕτως ἔχωσιν οἱ ὅροι πρὸς ἀλλήλους ὡς ἐλέχθη, γίνεται συλλογισμὸς ἐξ ἀνάγκης, ἄν τ᾽ ἦι συλλογισμός, ἀνάγκη τοὺς ὅρους οὕτως ἔχειν. δῆλον δὲ καὶ ὅτι πάντες ἀτελεῖς εἰσὶν οἱ ἐν τούτωι τῶι σχήματι συλλογισμοί (πάντες γὰρ ἐπιτελοῦνται προσλαμβανομένων τινῶν, ἃ ἢ ἐνυπάρχει τοῖς ὅροις ἐξ ἀνάγκης ἢ τίθενται ὡς ὑποθέσεις, οἷον ὅταν διὰ τοῦ ἀδυνάτου δεικνύωμεν), καὶ ὅτι οὐ γίνεται καταφατικὸς συλλογισμὸς διὰ τούτου τοῦ σχήματος, ἀλλὰ πάντες στερητικοί, καὶ οἱ καθόλου καὶ οἱ κατὰ μέρος.	Manifestum est igitur quoniam si similis figurae sint propositiones, et haec quidem universalis, illa vero particularis, quoniam nullo modo fit syllogismus. Sed nec si alicui, utrique inest, vel non inest, vel huic quidem inest, illi vero non, vel neutri omni, vel indefinitae. Termini autem communes omnium, album, animal, homo, album, animal, inanimatum. Manifestum est igitur ex praedictis quoniam si sic se habent termini ad invicem, ut dictum est, fit syllogismus ex necessitate, et si fit syllogismus, necesse est terminos sic se habere. Palam autem et quoniam omnes imperfecti sunt, qui in hac figura sunt syllogismi; omnes enim perficiuntur assumptis quibusdam, quae vel insunt terminis ex necessitate, vel ponuntur velut hypotheses, ut quando per impossibile ostendimus. (0645B) Et quoniam non fit affirmativus syllogismus per hanc figuram, sed omnes privativi, et universales, et particulares.	Evidently then, whenever the premisses are similar in form, and one is universal, the other particular, a syllogism can, not be formed anyhow. Nor is one possible if the middle term belongs to some of each of the extremes, or does not belong to some of either, or belongs to some of the one, not to some of the other, or belongs to neither universally, or is related to them indefinitely. Common terms for all the above are white, animal, man: white, animal, inanimate. It is clear then from what has been said that if the terms are related to one another in the way stated, a syllogism results of necessity; and if there is a syllogism, the terms must be so related. But it is evident also that all the syllogisms in this figure are imperfect: for all are made perfect by certain supplementary statements, which either are contained in the terms of necessity or are assumed as hypotheses, i.e. when we prove per impossibile. And it is evident that an affirmative conclusion is not attained by means of this figure, but all are negative, whether universal or particular.