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==Chapter 9==
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|(PL 64 0648C) CAPUT IX. De mixtis ex una necessaria et altera absoluta in prima figura.

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|{{a|bk30a15|30a15}} Συμβαίνει δέ ποτε καὶ τῆς ἑτέρας προτάσεως ἀναγκαίας οὔσης ἀναγκαῖον γίνεσθαι τὸν συλλογισμόν, πλὴν οὐχ ὁποτέρας ἔτυχεν, ἀλλὰ τῆς πρὸς τὸ μεῖζον ἄκρον, οἷον εἰ τὸ μὲν Α τῶι Β ἐξ ἀνάγκης εἴληπται ὑπάρχον ἢ μὴ ὑπάρχον, τὸ δὲ Β τῶι Γ ὑπάρχον μόνον· οὕτως γὰρ εἰλημμένων τῶν προτάσεων ἐξ ἀνάγκης τὸ Α τῶι Γ ὑπάρξει ἢ οὐχ ὑπάρξει.

|Accidit autem quandoque et altera propositione necessaria, necessarium fieri syllogismum, verum non utralibet, sed quae ad maiorem extremitatem est, ut si A quidem, B ex necessitate sumptum est inesse, vel non inesse, B autem C inesse tantum; sic enim sumptis propositionibus ex necessitate A inerit C, vel non erit.

|It happens sometimes also that when one premiss is necessary the conclusion is necessary, not however when either premiss is necessary, but only when the major is, e.g. if A is taken as necessarily belonging or not belonging to B, but B is taken as simply belonging to C: for if the premisses are taken in this way, A will necessarily belong or not belong to C.

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|ἐπεὶ γὰρ παντὶ τῶι Β ἐξ ἀνάγκης ὑπάρχει ἢ οὐχ ὑπάρχει τὸ Α, τὸ δὲ Γ τι τῶν Β ἐστί, φανερὸν ὅτι καὶ τῶι Γ ἐξ ἀνάγκης ἔσται θάτερον τούτων. εἰ δὲ τὸ μὲν Α Β μὴ ἔστιν ἀναγκαῖον, τὸ δὲ Β Γ ἀναγκαῖον, οὐκ ἔσται τὸ συμπέρασμα ἀναγκαῖον. εἰ γὰρ ἔστι, συμβήσεται τὸ Α τινὶ τῶι Β ὑπάρχειν ἐξ ἀνάγκης διά τε τοῦ πρώτου καὶ διὰ τοῦ τρίτου σχήματος. τοῦτο δὲ ψεῦδος· ἐνδέχεται γὰρ τοιοῦτον εἶναι τὸ Β ὧι ἐγχωρεῖ τὸ Α μηδενὶ ὑπάρχειν. ἔτι καὶ ἐκ τῶν ὅρων φανερὸν ὅτι οὐκ ἔσται τὸ συμπέρασμα ἀναγκαῖον, οἷον εἰ τὸ μὲν Α εἴη κίνησις, τὸ δὲ Β ζῶιον, ἐφ᾽ ὧι δὲ τὸ Γ ἄνθρωπος· ζῶιον μὲν γὰρ ὁ ἄνθρωπος ἐξ ἀνάγκης ἐστί, κινεῖται δὲ τὸ ζῶιον οὐκ ἐξ ἀνάγκης, οὐδ᾽ ὁ ἄνθρωπος. ὁμοίως δὲ καὶ εἰ στερητικὸν εἴη τὸ Α Β· ἡ γὰρ αὐτὴ ἀπόδειξις.

| (0648D) Nam quoniam omni B ex necessitate inest, vel non inest A, C autem aliquid eorum quae sunt B, est manifestum quoniam et C ex necessitate erit alterum horum. Si autem A B quidem non necessaria, B C autem necessaria, non erit conclusio necessaria. Nam si est, accidit A alicui B inesse ex necessitate, per primam et tertiam figuram, hoc autem falsum, contingit enim tale esse B cui possibile est A nulli inesse. Amplius autem et ex terminis manifestum quoniam non erit conclusio necessaria; ut si A quidem sit motus, B autem sit animal, in que autem C homo, namque homo animal est ex necessitate, movetur autem animal non ex necessitate, quare nec homo. Similiter autem et si privativa sit A B; nam eadem demonstratio.

|For since necessarily belongs, or does not belong, to every B, and since C is one of the Bs, it is clear that for C also the positive or the negative relation to A will hold necessarily. But if the major premiss is not necessary, but the minor is necessary, the conclusion will not be necessary. For if it were, it would result both through the first figure and through the third that A belongs necessarily to some B. But this is false; for B may be such that it is possible that A should belong to none of it. Further, an example also makes it clear that the conclusion not be necessary, e.g. if A were movement, B animal, C man: man is an animal necessarily, but an animal does not move necessarily, nor does man. Similarly also if the major premiss is negative; for the proof is the same.

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|ἐπὶ δὲ τῶν ἐν μέρει συλλογισμῶν, εἰ μὲν τὸ καθόλου ἐστὶν ἀναγκαῖον, καὶ τὸ συμπέρασμα ἔσται ἀναγκαῖον, εἰ δὲ τὸ κατὰ μέρος, οὐκ ἀναγκαῖον, οὔτε στερητικῆς οὔτε κατηγορικῆς οὔσης τῆς καθόλου προ- τάσεως.

|(0649A) In particularibus autem syllogismis, si universalis quidem est necessaria, et conclusio erit necessaria; si autem particularis, non necessaria, sive privativa, sive praedicativa fuerit universalis propositio.

|In particular syllogisms, if the universal premiss is necessary, then the conclusion will be necessary; but if the particular, the conclusion will not be necessary, whether the universal premiss is negative or affirmative.

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|ἔστω δὴ πρῶτον τὸ καθόλου ἀναγκαῖον, καὶ τὸ μὲν Α παντὶ τῶι Β ὑπαρχέτω ἐξ ἀνάγκης, τὸ δὲ Β τινὶ τῶι Γ ὑπαρχέτω μόνον· ἀνάγκη δὴ τὸ Α τινὶ τῶι Γ ὑπάρχειν ἐξ ἀνάγκης· τὸ γὰρ Γ ὑπὸ τὸ Β ἐστί, τῶι δὲ Β παντὶ {{ln|bk30b1}} ὑπῆρχεν ἐξ ἀνάγκης, ὁμοίως δὲ καὶ εἰ στερητικὸς εἴη ὁ συλλογισμός· ἡ γὰρ αὐτὴ ἔσται ἀπόδειξις. εἰ δὲ τὸ κατὰ μέρος ἐστὶν ἀναγκαῖον, οὐκ ἔσται τὸ συμπέρασμα ἀναγκαῖον (οὐδὲν γὰρ ἀδύνατον συμπίπτει), καθάπερ οὐδ᾽ ἐν τοῖς καθόλου συλλογισμοῖς. ὁμοίως δὲ κἀπὶ τῶν στερητικῶν. ὅροι κίνησις – ζῶιον – λευκόν.

|Sit autem primo universalis necessaria, et A quidem omni B insit ex necessitate, B autem alicui C insit solum, necesse est ergo A alicui C inesse ex necessitate, nam C sub B est, B autem omni A inerat ex necessitate. Similiter autem et si privativus syllogismus sit, nam eadem erit demonstratio. Si autem particularis est necessaria, non erit conclusio necessaria, nihil enim impossibile evenit, quemadmodum nec in universalibus syllogismis, similiter autem et in privativis. Termini, motus, animal, album.

|First let the universal be necessary, and let A belong to all B necessarily, but let B simply belong to some C: it is necessary then that A belongs to some C necessarily: for C falls under B, and A was assumed to belong necessarily to all B. Similarly also if the syllogism should be negative: for the proof will be the same. But if the particular premiss is necessary, the conclusion will not be necessary: for from the denial of such a conclusion nothing impossible results, just as it does not in the universal syllogisms. The same is true of negative syllogisms. Try the terms movement, animal, white.

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==Notes==
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Authors/Aristotle/priora/Liber 1/C9 - Revision history

Edward Ockham: Created page with "==Chapter 9== {| 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 0648C)..."