Authors/Ockham/Summa Logicae/Book III-1/Chapter 54

Latin	English
Cap. 54. De mixtione possibilis et contingentis in prima figura	Chapter 54. On the mixture of possible and contingent in the first figure.
Viso quomodo valet mixtio ex propositionibus de necessario et ceteris modalibus, videndum est quomodo valet mixtio ex propositione de possibili et ceteris modalibus. Et primo de mixtione possibilis et contingentis, et primo in prima figura.	Having seen how the mixture is valid from propositions of necessity and other modals, we must see how the mixture is valid from propositions about possibility and other modals. And first about the mixture of possibility and contingency, and first in the first figure.
Et est primo sciendum quod si utraque sumatur in sensu compositionis, nulla sequitur conclusio. Non enim sequitur 'omnem hominem esse album est possibile; omne nigrum esse hominem est contingens; igitur omne nigrum esse album est possible'. Nec sequitur 'omnem hominem esse album est contingens; omne nigrum esse hominem est possibile; igitur omne nigrum esse album est contingens vel etiam possibile'.	And it must first be known that if both are taken in the sense of composition, no conclusion follows. For it does not follow that 'it is possible for every man to be white; it is contingent for every black man to be a man; therefore it is possible for every black man to be white'. Nor does it follow that 'it is contingent for every man to be white; it is possible for every black man to be a man; therefore it is contingent or possible for every black man to be white'.
Nec etiam valet si altera sumatur in sensu compositionis et altera in sensu divisionis. Sicut non sequitur 'omne album esse hominem est contingens; omnis asinus potest esse albus; igitur omnis asinus potest esse homo’. Nec sequitur 'omne album potest esse homo; omnem asinum esse album est contingens; igitur omnis asinus potest esse homo’. Sicut nec sequitur 'omnis homo potest ridere; omne animal esse hominem est contingens; igitur omne animal potest ridere’, nam praemissae sunt verae et conclusio falsa, qualitercumque supponat subiectum. Nec etiam sequitur 'omnis homo potest esse albus; omne nigrum esse hominem est contingens; igitur omne nigrum esse album est contingens’. Nec sequitur 'omne album esse hominem est possibile; contingit omnem asinum esse album; igitur contingit omnem asinum esse hominem'.	Nor is it valid if one is taken in the sense of composition and the other in the sense of division. Just as it does not follow that 'every white thing being a man is contingent; every donkey can be white; therefore every donkey can be a man'. Nor does it follow that 'every white thing being a man is contingent; every donkey can be white; therefore every donkey can be a man'. Just as it does not follow that 'every man can laugh; every animal being a man is contingent; therefore every animal can laugh', for the premises are true and the conclusion false, no matter how the subject supposits. Nor does it follow that 'every man can be white; every black thing being a man is contingent; therefore every black being white is contingent'. Nor does it follow that 'every white thing being a man is possible; it is contingent that every donkey is white; therefore it is contingent that every donkey is a man'.
Secundo videndum est quando utraque sumitur in sensu divisionis vel aequivalens ei. Et est primo sciendum quod si maior sit de possibili et minor de contingenti, si subiectum maioris supponat pro his quae possunt esse et subiectum minoris pro his quae sunt, vel tam pro his quae sunt quam pro his quae contingunt, sequitur conclusio de possibili. Sicut sequitur omne quod potest esse homo, potest esse album; omne ƿ quod est risibile, vel contingit esse risible, contingit esse hominem; igitur omne risibile potest esse album'. Si autem subiectum niaioris supponat pro his quae sunt praecise, non valet mixtio; sicut non sequitur 'omne album potest esse homo; contingit omnem asinum esse album; igitur omnis asinus potest esse homo'.	Secondly, we must see when both are taken in the sense of division or equivalent to it. And it must first be known that if the major is of possibility and the minor of contingency, if the subject of the major supposits for things that can be and the subject of the minor for things that are, or both for things that are and for things that are contingent, the conclusion of possibility follows. Just as it follows that: everything that can be a man can be white; everything that can laugh, or happens to be able to laugh, happens to be a man; therefore everything that can laugh can be white'. But if the subject of the major supposits for things that are precise, the mixture is not valid; just as it does not follow that 'every white thing can be a man; it happens to be that every donkey is white; therefore every donkey can be a man'.
Si autem maior sit de contingenti et minor de possibili, si subiectum maioris supponat tam pro his quae sunt quam pro his quae contingent, valet syllogismus respectu conclusionis de contingenti; si autem, supponat pro his quae sunt, non valet. Hoc patet per eosdem terminos.	But if the major is of contingency and the minor of possibility, if the subject of the major supposits both for things that are and for things that are contingent, the syllogism is valid with respect to a conclusion of contingency; but if it supposits for things that are, it is not valid. This is clear from the same terms.