Authors/Ockham/Summa Logicae/Book III-1/Chapter 25

Latin	English
Cap. 25. De uniformi de possibili in tertia figura	On uniform syllogisms from de possibili propositions in the third figure.
In tertia figura si utraque sumatur in sensu divisionis et subiectum utriusque supponat pro his quae sunt, sequitur conclusio de possibili, sumpto subiecto pro eo quod potest esse. Sequitur enim ‘omnis homo potest esse albus; aliquis homo potest esse niger; igitur quod potest esse nigrum potest esse album’. Similiter sequitur ‘omnis homo potest non esse albus; aliquis homo potest esse niger; igitur aliquod nigrum potest non esse album’. Hoc probatur: quia dictum est quod talis minor convertitur in illam de inesse, sic ‘aliquis homo potest esse niger, igitur aliquid, quod potest esse nigrum, est homo’. Nunc autem sequitur per syllogismum regulatum per dici de omni ‘omnis homo potest esse albus; aliquid, quod potest esse nigrum, est homo; igitur aliquid, quod potest esse nigrum, potest esse album’. Sic igitur talis syllogismus probatur per conversionem.	In the third figure, if both are taken in the sense of division and the subject of both supposits for things that are, a conclusion of the possible follows, taking the subject for that which can be. For it follows ‘every man can be white; some man can be black; therefore what can be black can be white’. Similarly it follows ‘every man can be not white; some man can be black; therefore something black can be not white’. This is proven: because it was said that such a minor is converted into that of inherence, thus ‘some man can be black, therefore something that can be black is a man’. Now however it follows by a syllogism regulated by to say of all, ‘every man can be white; something that can be black is a man; therefore something that can be black can be white’. Thus therefore such a syllogism is proven by conversion.
Similiter, si subiectum utriusque supponat pro his quae possunt esse, sequitur conclusio de possibili, sumpto subiecto pro eo quod potest esse, quia illa de possibili, sumpto subiecto pro eo quod est, semper sequitur ad illam de possibili, sumpto subiecto pro eo quod potest esse. Sed uniformis ex illis in quibus subiectum supponit pro his quae sunt, ƿ tenet; igitur ex aliis tenet, quia quidquid sequitur ad consequens, sequitur ad antecedens. Potest etiam probari per conversionem, sicut prior uniformis.	Similarly, if the subject of both supposits for things that can be, the conclusion of the possible follows, taking the subject for what can be, because the one of possibility, taking the subject for what is, always follows from the other of possibility, taking the subject for what can be. But the uniform holds from those in which the subject supposits for things that are; therefore it holds from others, because whatever follows from the consequent, follows from the antecedent. It can also be proved by conversion, as from the prior uniform.
Si autem subiectum in maiore sumatur pro eo quod est et in minore pro eo quod potest esse, tenet syllogismus; et similiter e converso. Et uterque probatur per hoc quod ad illam de possibili, sumpto subiecto pro eo quod potest esse, sequitur illa de possibili, sumpto subiecto pro eo quod est. Sed conclusio de possibili, sumpto subiecto pro eo quod est, non sequitur; sicut non sequitur ‘omnis homo potest esse albus; omnis homo potest esse intelligens; igitur quod est intelligens, potest esse album’, quia si nullus homo esset intelligens sed angelus, praemissae essent verae et conclusio falsa.	But if the subject in the major is taken for that which is and in the minor for that which can be, the syllogism holds; and similarly vice versa. And both are proven by the fact that to the proposition of possibility, taking the subject for that which can be, the conclusion of possibility follows, taking the subject for that which is. But the conclusion of possibility, taking the subject for that which is, does not follow; just as it does not follow that ‘every man can be white; every man can be intelligent; therefore that which is intelligent can be white’, because if no man were intelligent except an angel, the premises would be true and the conclusion false.
Si autem maior sumatur in sensu divisionis et subiectum supponat pro eo quod potest esse, et minor sit de possibili in sensu compositionis, sequitur conclusio de possibili in sensu divisionis, non in sensu compositionis. Quod enim sequatur in sensu divisionis, patet, nam sequitur ‘omne quod potest esse homo, potest esse album; haec est possibilis: omnis homo est niger; igitur aliquid, quod potest esse nigrum, potest esse album’. Et ratio istius est, quia semper illa de possibili singularis in sensu compositionis et in sensu divisionis convertuntur si in praemissis supponat pronomen demonstrativum vel nomen proprium. Et quia quidquid sequitur ad quamlibet singularem alicuius particularis cum aliquo, sequitur ad illam particularem cum eodem, per istam regulam ‘quidquid sequitur ad quodlibet antecedens alicuius consequentis, sequitur ad illud consequens. Et virtute istius regulae tenet probatio syllogismorum quando probantur per syllogismum expositorium, de quo dictum est prius. Et ita in ista probationc nun arguitur per illud medium ‘quidquid sequitur ad singularem, sequitur ad particularem’, quia hoc est falsum, sed per illud medium ‘quidquid sequitur ad quodlibet antecedens alicuius consequentis, sequitur ad illud conseƿquens . Probatur igitur talis syllogismus ‘omne quod potest esse homo, potest esse album; haec est possibilis: aliquis homo est niger; igitur aliquid, quod potest esse nigrum, potest esse album’. Quia si haec sit possibilis ‘aliquis homo est niger’, aliqua singularis erit possibilis: sit illa a; tunc haec est possibilis ‘a est nigrum et a est homo, igitur a potest esse album’, per universalem primam. Modo sequitur ‘haec est possibilis: a est nigrum; igitur a potest esse nigrum’, sicut dictum est prius. Nunc autem iste syllogismus est bonus ‘a potest esse album; a potest esse nigrum; igitur nigrum potest esse album’. Igitur primus syllogismus fuit bonus.	But if the major is taken in the sense of division and the subject supposits for that which can be, and the minor is of possibility in the sense of composition, the conclusion follows of possibility in the sense of division, not in the sense of composition. For that which follows in the sense of division is clear, for it follows ‘everything that can be a man can be white; this is possible: every man is black; therefore something that can be black can be white’. And the reason for this is that those possible singulars in the sense of composition and in the sense of division are always converted if in the premises it supposits a demonstrative pronoun or a proper name. And because whatever follows to any singular of some particular with something, follows to that particular with the same, by this rule ‘whatever follows to any antecedent of some consequent, follows to that consequent. And by virtue of this rule the proof of syllogisms holds when they are proved by the expository syllogism, of which we have spoken before . And so in this proof it is not argued by that means ‘whatever follows to the singular, follows to the particular’, because this is false, but by the means ‘whatever follows to any antecedent of any consequent, follows to that consequent’. Therefore, such a syllogism is proved ‘everything that can be a man can be white; this is possible: some man is black; therefore something that can be black can be white’. For if this is possible ‘some man is black’, some singular will be possible: let that be ‘a’; then this is possible ‘a’ is black and ‘a’ is a man, therefore ‘a’ can be white’, by the first universal. Now it follows ‘this is possible: ‘a’ is black; therefore ‘a’ can be black’, as was said before. Now however, this syllogism is good ‘a’ can be a white thing; ‘a’ can be a black thing; therefore a black thing can be a white thing’. Therefore the first syllogism was good.
Similiter, si maior sumatur in sensu compositionis et minor in sensu divisionis, bene sequitur per eundem modum respectu conclusionis de possibili in sensu divisionis.	Similarly, if the major is taken in the sense of composition and the minor in the sense of division, it follows well in the same way with respect to the conclusion of possibility in the sense of division.