Edward Ockham: Created page with "==Chapter 10== {| border=1 cellpadding=10 !valign = top width=33.33%|Greek !valign = top width=33.33%|Latin !valign = top width=33.33%|English |- valign = top | |(PL 64 0649A..."

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==Chapter 10==
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|(PL 64 0649A) CAPUT X. De mixtis ex una necessaria et altera absoluta in secunda figura.

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|{{a|bk30b7|30b7}} Ἐπὶ δὲ τοῦ δευτέρου σχήματος, εἰ μὲν ἡ στερητικὴ πρότασίς ἐστιν ἀναγκαία, καὶ τὸ συμπέρασμα ἔσται ἀναγκαῖον, εἰ δ᾽ ἡ κατηγορική, οὐκ ἀναγκαῖον. ἔστω γὰρ πρῶτον ἡ στερητικὴ ἀναγκαία, καὶ τὸ Α τῶι μὲν Β μηδενὶ ἐνδεχέσθω, τῶι δὲ Γ ὑπαρχέτω μόνον. ἐπεὶ οὖν ἀντιστρέφει τὸ στερητικόν, οὐδὲ τὸ Β τῶι Α οὐδενὶ ἐνδέχεται· τὸ δὲ Α παντὶ τῶι Γ ὑπάρχει, ὥστ᾽ οὐδενὶ τῶι Γ τὸ Β ἐνδέχεται· τὸ γὰρ Γ ὑπὸ τὸ Α ἐστίν. ὡσαύτως δὲ καὶ εἰ πρὸς τῶι Γ τεθείη τὸ στερητικόν· εἰ γὰρ τὸ Α μηδενὶ τῶι Γ ἐνδέχεται, οὐδὲ τὸ Γ οὐδενὶ τῶι Α ἐγχωρεῖ· τὸ δὲ Α παντὶ τῶι Β ὑπάρχει, ὥστ᾽ οὐδενὶ τῶι Β τὸ Γ ἐνδέχεται· γίνεται γὰρ τὸ πρῶτον σχῆμα πάλιν. οὐκ ἄρα οὐδὲ τὸ Β τῶι Γ· ἀντιστρέφει γὰρ ὁμοίως.

|(0649B) In secunda autem figura si privativa quidem propositio universalis sit et necessaria, conclusio erit necessaria. Si autem praedicativa, non necessaria. Sit enim primum privativa necessaria, et A B quidem nulli contingat, C autem insit tantum; quoniam ergo convertitur privativa, et B nulli A contingit, A autem omni C inest, quare nulli C contingit B, nam C sub A est. Similiter autem et si ad C ponatur privativum, nam si A C nulli contingit, et C nulli A poterit inesse, A autem omni B inest. Quare nulli eorum quae sunt B contingit C, fit enim prima figura. Rursum non ergo neque B ipsi C, convertitur enim similiter.

|In the second figure, if the negative premiss is necessary, then the conclusion will be necessary, but if the affirmative, not necessary. First let the negative be necessary; let A be possible of no B, and simply belong to C. Since then the negative statement is convertible, B is possible of no A. But A belongs to all C; consequently B is possible of no C. For C falls under A. The same result would be obtained if the minor premiss were negative: for if A is possible be of no C, C is possible of no A: but A belongs to all B, consequently C is possible of none of the Bs: for again we have obtained the first figure. Neither then is B possible of C: for conversion is possible without modifying the relation.

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|Εἰ δὲ ἡ κατηγορικὴ πρότασίς ἐστιν ἀναγκαία, οὐκ ἔσται τὸ συμπέρασμα ἀναγκαῖον. ὑπαρχέτω γὰρ τὸ Α παντὶ τῶι Β ἐξ ἀνάγκης, τῶι δὲ Γ μηδενὶ ὑπαρχέτω μόνον. ἀντιστραφέντος οὖν τοῦ στερητικοῦ τὸ πρῶτον γίνεται σχῆμα· δέδεικται δ᾽ ἐν τῶι πρώτωι ὅτι μὴ ἀναγκαίας οὔσης τῆς πρὸς τὸ μεῖζον στερητικῆς οὐδὲ τὸ συμπέρασμα ἔσται ἀναγκαῖον, ὥστ᾽ οὐδ᾽ ἐπὶ τούτων ἔσται ἐξ ἀνάγκης.

|Si autem praedicativa propositio est necessaria, non erit conclusio necessaria, insit enim A omni B ex necessitate, C autem nulli insit tantum, conversa ergo privativa, fit prima figura. (0649C) Ostensum est autem in prima quoniam cum non est necessaria quae ad maiorem est privativa, nec conclusio erit necessaria, quare nec in his erit ex necessitate.

|But if the affirmative premiss is necessary, the conclusion will not be necessary. Let A belong to all B necessarily, but to no C simply. If then the negative premiss is converted, the first figure results. But it has been proved in the case of the first figure that if the negative major premiss is not necessary the conclusion will not be necessary either. Therefore the same result will obtain here.

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|ἔτι δ᾽ εἰ τὸ συμπέρασμά ἐστιν ἀναγκαῖον, συμβαίνει τὸ Γ τινὶ τῶι Α μὴ ὑπάρχειν ἐξ ἀνάγκης. εἰ γὰρ τὸ Β τῶι Γ μηδενὶ ὑπάρχει ἐξ ἀνάγκης, οὐδὲ τὸ Γ τῶι Β οὐδενὶ ὑπάρξει ἐξ ἀνάγκης. τὸ δέ γε Β τινὶ τῶι Α ἀνάγκη ὑπάρχειν, εἴπερ καὶ τὸ Α παντὶ τῶι Β ἐξ ἀνάγκης ὑπῆρχεν. ὥστε τὸ Γ ἀνάγκη τινὶ τῶι Α μὴ ὑπάρχειν. ἀλλ᾽ οὐδὲν κωλύει τὸ Α τοιοῦτον λη- φθῆναι ὧι παντὶ τὸ Γ ἐνδέχεται ὑπάρχειν.

|Amplius autem si conclusio est necessaria, accidit C alicui A non inesse ex necessitate, si enim B nulli C inest ex necessitate, neque C nulli B inerit ex necessitate, B autem alicui A necesse est inesse, siquidem et A omni B ex necessitate inerat, quare C necesse est alicui A non inesse, sed nihil prohibet A huiusmodi accipere, cui omni C contingat inesse.

|Further, if the conclusion is necessary, it follows that C necessarily does not belong to some A. For if B necessarily belongs to no C, C will necessarily belong to no B. But B at any rate must belong to some A, if it is true (as was assumed) that A necessarily belongs to all B. Consequently it is necessary that C does not belong to some A. But nothing prevents such an A being taken that it is possible for C to belong to all of it.

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|ἔτι κἂν ὅρους ἐκθέμενον εἴη δεῖξαι ὅτι τὸ συμπέρασμα οὐκ ἔστιν ἀναγκαῖον ἁπλῶς, ἀλλὰ τούτων ὄντων ἀναγκαῖον. οἷον ἔστω τὸ Α ζῶιον, τὸ δὲ Β ἄνθρωπος, τὸ δὲ Γ λευκόν, καὶ αἱ προτάσεις ὁμοίως εἰλήφθωσαν· ἐνδέχεται γὰρ τὸ ζῶιον μηδενὶ λευκῶι ὑπάρχειν. οὐχ ὑπάρξει δὴ οὐδ᾽ ὁ ἄνθρωπος οὐδενὶ λευκῶι, ἀλλ᾽ οὐκ ἐξ ἀνάγκης· ἐνδέχεται γὰρ ἄνθρωπον γενέσθαι λευκόν, οὐ μέντοι ἕως ἂν ζῶιον μηδενὶ λευκῶι ὑπάρχηι. ὥστε τούτων μὲν ὄντων ἀναγκαῖον ἔσται τὸ συμπέρασμα, ἁπλῶς δ᾽ οὐκ ἀναγκαῖον.

|Amplius et si terminos ponentes sit ostendere, quoniam conclusio non est necessaria simpliciter. (0649D) Et his existentibus, necessarium ut sit A animal, B vero homo, C autem album, et similiter propositiones sumptae sint, contingit enim animal nulli albo inesse, non inerit ergo nec homo nulli albo, sed non ex necessitate. Contingit enim hominem fieri album, non tamen donec animal nulli albo insit, quare cum haec sint, necessaria erit conclusio, simpliciter autem non necessaria.

|Further one might show by an exposition of terms that the conclusion is not necessary without qualification, though it is a necessary conclusion from the premisses. For example let A be animal, B man, C white, and let the premisses be assumed to correspond to what we had before: it is possible that animal should belong to nothing white. Man then will not belong to anything white, but not necessarily: for it is possible for man to be born white, not however so long as animal belongs to nothing white. Consequently under these conditions the conclusion will be necessary, but it is not necessary without qualification.

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|{{ln|bk31a1}} Ὁμοίως δ᾽ ἕξει καὶ ἐπὶ τῶν ἐν μέρει συλλογισμῶν. ὅταν μὲν γὰρ ἡ στερητικὴ πρότασις καθόλου τ᾽ ἦι καὶ ἀναγκαία, καὶ τὸ συμπέρασμα ἔσται ἀναγκαῖον· ὅταν δὲ ἡ κατηγορικὴ καθόλου, ἡ δὲ στερητικὴ κατὰ μέρος, οὐκ ἔσται τὸ συμπέρασμα ἀναγκαῖον. ἔστω δὴ πρῶτον ἡ στερητικὴ καθόλου τε καὶ ἀναγκαία, καὶ τὸ Α τῶι μὲν Β μηδενὶ ἐνδεχέσθω ὑπάρχειν, τῶι δὲ Γ τινὶ ὑπαρχέτω. ἐπεὶ οὖν ἀντιστρέφει τὸ στερητικόν, οὐδὲ τὸ Β τῶι Α οὐδενὶ ἐνδέχοιτ᾽ ἂν ὑπάρχειν· τὸ δέ γε Α τινὶ τῶι Γ ὑπάρχει, ὥστ᾽ ἐξ ἀνάγκης τινὶ τῶι Γ οὐχ ὑπάρξει τὸ Β.

|Similiter autem se habebit et in particularibus syllogismis, quando privativa quidem propositio, et universalis fuerit, et necessaria, et conclusio erit necessaria. Quando autem praedicativa universalis fuerit necessaria, privativa vero particularis non necessaria, non erit conclusio necessaria. (0650A) Sit enim primum privativa, et universalis necessaria, et A B quidem nulli contingat inesse, C autem alicui insit, quoniam ergo convertitur privativa, et B nulli A continget inesse, A autem alicui C inest, quare ex necessitate alicui eorum quae sunt, C non inerit B.

|Similar results will obtain also in particular syllogisms. For whenever the negative premiss is both universal and necessary, then the conclusion will be necessary: but whenever the affirmative premiss is universal, the negative particular, the conclusion will not be necessary. First then let the negative premiss be both universal and necessary: let it be possible for no B that A should belong to it, and let A simply belong to some C. Since the negative statement is convertible, it will be possible for no A that B should belong to it: but A belongs to some C; consequently B necessarily does not belong to some of the Cs.

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|πάλιν ἔστω ἡ κατηγορικὴ καθόλου τε καὶ ἀναγκαία, καὶ κείσθω πρὸς τῶι Β τὸ κατηγορικόν. εἰ δὴ τὸ Α παντὶ τῶι Β ἐξ ἀνάγκης ὑπάρχει, τῶι δὲ Γ τινὶ μὴ ὑπάρχει, ὅτι μὲν οὐχ ὑπάρξει τὸ Β τινὶ τῶι Γ, φανερόν, ἀλλ᾽ οὐκ ἐξ ἀνάγκης· οἱ γὰρ αὐτοὶ ὅροι ἔσονται πρὸς τὴν ἀπόδειξιν οἵπερ ἐπὶ τῶν καθόλου συλλογισμῶν. ἀλλ᾽ οὐδ᾽ εἰ τὸ στερητικὸν ἀναγκαῖόν ἐστιν ἐν μέρει ληφθέν, οὐκ ἔσται τὸ συμπέρασμα ἀναγκαῖον· διὰ γὰρ τῶν αὐτῶν ὅρων ἡ ἀπόδειξις.

|Rursum sit praedicativa, et universalis, et necessaria, et ponatur ad B quidem praedicativum, si ergo A omni B ex necessitate inest, C autem alicui non inest, quoniam non inerit B alicui C manifestum, sed non ex necessitate. Nam iidem termini erunt ad demonstrationem, qui in universalibus syllogismis: sed nec si privativa necessaria est particulariter sumpta, erit conclusio necessaria. Nam per eosdem terminos demonstratio.

|Again let the affirmative premiss be both universal and necessary, and let the major premiss be affirmative. If then A necessarily belongs to all B, but does not belong to some C, it is clear that B will not belong to some C, but not necessarily. For the same terms can be used to demonstrate the point, which were used in the universal syllogisms. Nor again, if the negative statement is necessary but particular, will the conclusion be necessary. The point can be demonstrated by means of the same terms.

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==Notes==
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Authors/Aristotle/priora/Liber 1/C10 - Revision history

Edward Ockham: Created page with "==Chapter 10== {| border=1 cellpadding=10 !valign = top width=33.33%|Greek !valign = top width=33.33%|Latin !valign = top width=33.33%|English |- valign = top | |(PL 64 0649A..."