Authors/Ockham/Summa Logicae/Book III-1/Chapter 36

Latin	English
Cap. 36. De mixtione de inesse et possibilis in tertia figura	Chapter 36. On the mixture of assertoric and possible propositions in the third figure.
Si autem in. tertia figura illa de possibili sumatur in semu compositionis, sive fuerit affirmativa sive negativa, non sequitur universaliter aliqua conclusio de possibili in sensu compositionis. Unde non sequitur ‘omnem hominem esse album est possibile; omnis homo est niger; igitur aliquod nigrum esse album est possibile’. Quando tamen utraque est affirmativa, sequitur conclusio de possibili sumpta in sensu divisionis, sic ‘possibile est omnem hominem esse album; omnis homo est niger; igitur aliquod nigrum potest esse album’, quia si possibile est omnem hominem esse album, aliqua singularis est possibilis. Tunc haec est possibilis ‘hoc est album’, et per consequens hoc potest esse album, quia dictum est prius quod talis singularis in sensu compositionis et in sensu divisionis convertuntur. Nunc sequitur 'hoc potest esse album; hoc est nigrum; igitur nigrum potest esse album'.	But if in the third figure a premise de possibili is taken in the seminal part of the composition, whether it is affirmative or negative, no conclusion de possibili in the sense of composition universally follows. Hence it does not follow that ‘it is possible for every man to be white; every man is black; therefore it is possible for something black to be white’. However, when both are affirmative, a conclusion of possibility taken in the sense of division follows, thus ‘it is possible for every man to be white; every man is black; therefore something black can be white’, because if it is possible for every man to be white, some singular is possible. Then this is possible ‘this is white’, and consequently this can be white, because it was said before that such singulars are convertible in the sense of the composition and in the sense of the division. Now it follows that ‘this can be white; this is black; therefore a black thing can be white’.
Si autem illa de possibili sit negativa, nulla sequitur conclusio. Non enim sequitur 'possibile est nullum hominem esse Deum; omnis homo est Pater; igitur possibile est nullum Patrem esse Deum'.	But if the proposition de possibili is negative, no conclusion follows. For it does not follow that 'it is possible for no man to be God; every man is the Father; therefore it is possible for no Father to be God'.
Si autem illa de possibili sumatur in sensu divisionis, tunc si maior sit de possibili, qualitercumque subiectum sumatur, sequitur conclusio de possibili, quia potest reduci in primam figuram per conversionem minoris, vel per conversionem maioris in illam de inesse et per transpositionem propositionum, inferendo unam de inesse, quae est conversa primae conclusionis de possibili.	But if the premise de possibili is taken in the sense of division, then if the major is de possibili, no matter how the subject is taken, the conclusion de possibili follows, because it can be reduced to the first figure by converting the minor, or by converting the major into that assertoric and by transposing the propositions, inferring one assertoric, which is the converse of the first conclusion de possibili.
Si autem maior sit de inesse et minor de possibili, si subiectum sumatur pro his quae sunt, bene valet mixtio si utraque fuerit universalis. Bene enim sequitur 'omnis homo est albus; omnis homo potest esse niger; igitur nigrum potest esse album', sumpto subiecto conclusionis pro his quae possunt esse, non pro his quae sunt. Similiter sequitur 'nullus homo est asinus; omnis homo potest esse albus; igitur aliquod album potest non esse asinus'. ƿ	But if the major is assertoric and the minor de possibili, if the subject is taken for things that are, the mixture is valid if both are universal. For it follows well that 'every man is white; every man can be black; therefore a black thing can be white', taking the subject of the conclusion for things that can be, not for things that are. Similarly, it follows that 'no man is a donkey; every man can be white; therefore it is possible for something white to not be a donkey'.
Si autem minor de possibili fuerit particularis et subiectum sumatur pro his quae possunt esse, non valet mixtio, sicut non sequitur 'omne album est homo; aliquod album potest esse asinus; igitur aliquis asinus potest esse homo'. Nec sequitur 'nullus homo est Deus; aliquis homo potest esse Pater vel Verbum; igitur Pater vel Verbum potest non esse Deus'.	But if the minor de possibili is particular and the subject is taken for those things that can be, the mixture is not valid, just as it does not follow that 'every white thing is a man; some white thing can be a donkey; therefore some donkey can be a man'. Nor does it follow that 'no man is God; some man can be the Father or the Word; therefore it is possible for the Father or the Word not to be God'.
Prima mixtio probatur per syllogismum expositorium si maior sit particularis, quia si aliquis homo est albus et omnis homo potest esse niger, detur ille homo qui est albus. Tunc ille est albus et ille potest esse niger, igitur aliquid, quod potest esse nigrum, est album; et per consequens potest esse album.	The first mixture is proven by an expository syllogism if the major is particular, because if any man is white and every man can be black, let there be that man who is white. Then that man is white and that man can be black, therefore something that can be black is white; and consequently it can be white.
Si dicatur quod consimiliter potest probari si minor sit particularis de possibili, sic 'omne album est homo; aliquod album potest esse asinus; igitur' etc. Quia si haec minor sit vera, detur. Sit illud a; nunc sequitur 'a est homo; a potest esse asinus; igitur aliquid, quod potest esse asinus, est homo', et per consequens potest esse homo:	If it is said that it can be similarly proven if the minor is particular de possibili, thus 'every white is a man; some white thing can be a donkey; therefore' etc. Because if this minor is true, let it be given. Let that be a; now it follows 'a is a man; a can be a donkey; therefore something that can be a donkey is a man', and consequently can be a man.
Dicendum est quod talis probatio non valet in isto casu. Nam dato quod a potest esse asinus, non habetur per maiorem quod a est homo, quia subiectum non supponit pro a, quamvis in minore supponat pro a. Hoc autem requiritur ad hoc quod talis probatio valeret per syllogismum expositorium., quo modo est in aliis, sicut dictum est.	It must be said that such a proof is not valid in this case. For given that a can be a donkey, it is not held by the major that a is a man, because the subject does not supposit for a, although in the minor it supposits for a. This is required for such a proof to be valid by an expository syllogism, as it is in the others, as was said in the penultimate paragraph.