Edward Ockham: Created page with "==Chapter 20== {| 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 0662C..."

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==Chapter 20==
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|(PL 64 0662C) CAPUT XIX/XX. De syllogismis ex ambabus contingentibus in tertia figura.

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|{{a|bk39a4|39a4}}Ἐν δὲ τῶι τελευταίωι σχήματι καὶ ἀμφοτέρων ἐν δεχομένων καὶ τῆς ἑτέρας ἔσται συλλογισμός. ὅταν μὲν οὖν ἐνδέχεσθαι σημαίνωσιν αἱ προτάσεις, καὶ τὸ συμπέρασμα ἔσται ἐνδεχόμενον· καὶ ὅταν ἡ μὲν ἐνδέχεσθαι ἡ δ᾽ ὑπάρχειν. ὅταν δ᾽ ἡ ἑτέρα τεθῆι ἀναγκαία, ἐὰν μὲν ἦι καταφατική, οὐκ ἔσται τὸ συμπέρασμα οὔτε ἀναγκαῖον οὔθ᾽ ὑπάρχον, ἐὰν δ᾽ ἦι στερητική, τοῦ μὴ ὑπάρχειν ἔσται συλλογισμός, καθάπερ καὶ ἐν τοῖς πρότερον· ληπτέον δὲ καὶ ἐν τούτοις ὁμοίως τὸ ἐν τοῖς συμπεράσμασιν ἐνδεχόμενον.

|In postrema autem figura, et utrisque contingentibus, et altera, erit syllogismus. (0662D) Quando ergo contingere significant propositiones, et conclusio erit contingens. Et quando haec quidem contingere, illa vero inesse, similiter erit syllogismus. Quando autem altera ponitur necessaria, si affirmativa quidem non erit conclusio, neque necessaria, neque inesse. Si autem privativa, eius quod est non inesse erit syllogismus, quemadmodum in prioribus.

|In the last figure a syllogism is possible whether both or only one of the premisses is problematic. When the premisses are problematic the conclusion will be problematic; and also when one premiss is problematic, the other assertoric. But when the other premiss is necessary, if it is affirmative the conclusion will be neither necessary or assertoric; but if it is negative the syllogism will result in a negative assertoric proposition, as above. In these also we must understand the expression ‘possible’ in the conclusion in the same way as before.

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|Ἔστωσαν δὴ πρῶτον ἐνδεχόμεναι, καὶ τὸ Α καὶ τὸ Β παντὶ τῶι Γ ἐνδεχέσθω ὑπάρχειν. ἐπεὶ οὖν ἀντιστρέφει τὸ καταφατικὸν ἐπὶ μέρους, τὸ δὲ Β παντὶ τῶι Γ ἐνδέχεται, καὶ τὸ Γ τινὶ τῶι Β ἐνδέχοιτ᾽ ἄν. ὥστ᾽ εἰ τὸ μὲν Α παντὶ τῶι Γ ἐνδέχεται, τὸ δὲ Γ τινὶ τῶι Β, ἀνάγκη καὶ τὸ Α τινὶ τῶι Β ἐνδέχεσθαι· γίγνεται γὰρ τὸ πρῶτον σχῆμα.

|Sumendum autem et in his similiter, quod est in conclusionibus contingens. Sint ergo primum contingentes, et A et B contingant omni C inesse, quoniam ergo convertitur affirmativa particulariter, B autem omni C contingit, et C alicui B contingit, quare si A quidem omni C contingit, C autem alicui B, et A alicui B contingit, fit enim prima figura.

|First let the premisses be problematic and suppose that both A and B may possibly belong to every C. Since then the affirmative proposition is convertible into a particular, and B may possibly belong to every C, it follows that C may possibly belong to some B. So, if A is possible for every C, and C is possible for some of the Bs, then A is possible for some of the Bs. For we have got the first figure.

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|καὶ εἰ τὸ μὲν Α ἐνδέχεται μηδενὶ τῶι Γ ὑπάρχειν, τὸ δὲ Β παντὶ τῶι Γ, ἀνάγκη τὸ Α τινὶ τῶι Β ἐνδέχεσθαι μὴ ὑπάρχειν· ἔσται γὰρ πάλιν τὸ πρῶτον σχῆμα διὰ τῆς ἀντιστροφῆς. εἰ δ᾽ ἀμφότεραι στερητικαὶ τεθείησαν, ἐξ αὐτῶν μὲν τῶν εἰλημμένων οὐκ ἔσται τὸ ἀναγκαῖον, ἀντιστραφει σῶν δὲ τῶν προτάσεων ἔσται συλλογισμός, καθάπερ ἐν τοῖς πρότερον.

|(0663A) Et si A quidem contingit nulli C inesse, B autem omni C contingat, necesse est A alicui cui B contingere non inesse, erit enim rursum prima figura per conversionem. Si autem utraeque privativae ponantur, ex his quidem quae sumpta sunt non erit necessarium, conversis autem propositionibus erit syllogismus, quemadmodum in prioribus.

|And A if may possibly belong to no C, but B may possibly belong to all C, it follows that A may possibly not belong to some B: for we shall have the first figure again by conversion. But if both premisses should be negative no necessary consequence will follow from them as they are stated, but if the premisses are converted into their corresponding affirmatives there will be a syllogism as before.

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|εἰ γὰρ τὸ Α καὶ τὸ Β τῶι Γ ἐνδέχεται μὴ ὑπάρχειν, ἐὰν μεταληφθῆι τὸ ἐνδέχεσθαι ὑπάρχειν, πάλιν ἔσται τὸ πρῶτον σχῆμα διὰ τῆς ἀντιστροφῆς.

|Si enim A et B contingunt C non inesse, si transmutatur contingere non inesse, rursum erit prima figura per conversionem.

|For if A and B may possibly not belong to C, if ‘may possibly belong’ is substituted we shall again have the first figure by means of conversion.

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|εἰ δ᾽ ὁ μέν ἐστι καθόλου τῶν ὅρων ὁ δ᾽ ἐν μέρει, τὸν αὐτὸν τρόπον ἐχόντων τῶν ὅρων ὅνπερ ἐπὶ τοῦ ὑπάρχειν, ἔσται τε καὶ οὐκ ἔσται συλλογισμός. ἐνδεχέσθω γὰρ τὸ μὲν Α παντὶ τῶι Γ, τὸ δὲ Β τινὶ τῶι Γ ὑπάρχειν. ἔσται δὴ πάλιν τὸ πρῶτον σχῆμα τῆς ἐν μέρει προτάσεως ἀντιστραφείσης· εἰ γὰρ τὸ Α παντὶ τῶι Γ, τὸ δὲ Γ τινὶ τῶι Β, τὸ Α τινὶ τῶι Β ἐνδέχεται. καὶ εἰ πρὸς τῶι Β Γ τεθείη τὸ καθόλου, ὡσαύτως.

|Si autem hic quidem terminorum est universalis, ille vero particularis, eodem modo se habentibus terminis quo inesse, et erit, et non erit syllogismus. Contingat enim A quidem omni C, B autem alicui C inesse, erit ergo rursum prima figura particulari propositione conversa, nam si A omni C, C autem alicui B, et A alicui B contingit. Et si ad B C ponatur universale, similiter.

|But if one of the premisses is universal, the other particular, a syllogism will be possible, or not, under the arrangement of the terms as in the case of assertoric propositions. Suppose that A may possibly belong to all C, and B to some C. We shall have the first figure again if the particular premiss is converted. For if A is possible for all C, and C for some of the Bs, then A is possible for some of the Bs. Similarly if the proposition BC is universal.

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|ὁμοίως δὲ καὶ εἰ τὸ μὲν Α Γ στερητικὸν εἴη, τὸ δὲ Β Γ καταφατικόν· ἔσται γὰρ πάλιν τὸ πρῶτον σχῆμα διὰ τῆς ἀντιστροφῆς. εἰ δ᾽ ἀμφότεραι στερητικαὶ τεθείησαν, ἡ μὲν καθόλου ἡ δ᾽ ἐν μέρει, δι᾽ αὐτῶν μὲν τῶν εἰλημ {{ln|bk39b1}} μένων οὐκ ἔσται συλλογισμός, ἀντιστραφεισῶν δ᾽ ἔσται, καθάπερ ἐν τοῖς πρότερον. ὅταν δὲ ἀμφότεραι ἀδιόριστοι ἢ ἐν μέρει ληφθῶσιν, οὐκ ἔσται συλλογισμός· καὶ γὰρ παντὶ ἀνάγκη τὸ Α τῶι Β καὶ μηδενὶ ὑπάρχειν. ὅροι τοῦ ὑπάρ χειν ζῶιον – ἄνθρωπος – λευκόν, τοῦ μὴ ὑπάρχειν ἵππος – ἄνθρωπος – λευκόν, μέσον λευκόν.

|(0663B) Similiter autem et si A C quidem privativa sit, B C autem affirmativa, erit unum rursum prima figura per conversionem, si autem utraeque privativae ponantur, haec quidem universaliter, illa vero particulariter, per ea quidem quae sumpta sunt non erit syllogismus, conversis autem propositionibus erit quemadmodum in prioribus. Quando autem utraeque indefinitae vel particulares sumuntur, non erit syllogismus, etenim necesse est A omni B, et nulli inesse. Termini inesse, animal, homo, album: non inesse, equus, homo, medium album.

|Likewise also if the proposition AC is negative, and the proposition BC affirmative: for we shall again have the first figure by conversion. But if both premisses should be negative-the one universal and the other particular-although no syllogistic conclusion will follow from the premisses as they are put, it will follow if they are converted, as above. But when both premisses are indefinite or particular, no syllogism can be formed: for A must belong sometimes to all B and sometimes to no B. To illustrate the affirmative relation take the terms animal-man-white; to illustrate the negative, take the terms horse-man-white — white being the middle term.

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==Notes==
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Authors/Aristotle/priora/Liber 1/C20 - Revision history

Edward Ockham: Created page with "==Chapter 20== {| 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 0662C..."