Authors/Ockham/Summa Logicae/Book III-1/Chapter 40

Latin	English
Cap. 40. De mixtione ex propositione de inesse et de impossibili	On the mixture of assertoric (of inherence) and impossible propositions.
Post praedicta videndum est an ex illa de inesse et de impossibili possit fieri syllogismus mixtus. Et est primo sciendum quod semper illa de impossibili aequivalet alicui propositioni de necessario, et ideo ex praedictis circa mixtionem necessarii et inesse potest patere quomodo potest argui ex propositionc de inesse et propositione de impossibili. ƿ	After the above, we must see whether a mixed syllogism can be made from that of inherence and that of impossibility. And it must first be known that that of impossibility is always equivalent to some proposition of necessity, and therefore from the above about the mixture of necessity and inherence it can be clear how it can be argued from a proposition of inherence and a proposition of impossibility.
Propter quod sciendum quod in prima figura ex maiore de impossibili, aequivalente universali de necessario, sumpta in sensu compositionis et minore de inesse simpliciter sequitur conclusio de impossibili in eodem sensu, si minor sit de inesse simpliciter, et aliter non. Et ideo non sequitur 'omne falsum esse verum est impossibile; te sedere est falsum; igitur te sedere esse verum est impossibile'. Tum quia maior aequivalet particulari de necessario, scilicet isti 'aliquod falsum non esse verum est necessarium', et ita syllogismus non valet, quia maior est particulatis aequipollenter; tum quia minor est de inesse ut nunc, et manifestum est quod praemissae sunt verae et conclusio falsa. Similiter non sequitur 'omne verum esse necessarium est impossibile; Deum esse est verum; igitur Deum esse esse necessarium est impossibile, quia non obstante quod minor sit de inesse simpliciter, tamen maior aequivalet uni particulari de necessario, et ideo non valet discursus. Sed iste discursus est bonus 'aliquod verum esse falsum est impossibile; Deum esse est verum; igitur Deum esse esse falsum est impossibile', quia minor est de inesse simpliciter. Sed iste non valet 'aliquod verum esse falsum est impossibile; te sedere est verum; igitur te sedere esse falsum est impossibile', et hoc quia minor est de inesse ut nunc. Primus discursus est bonus, quia maior aequivalet isti 'nullum verum esse falsum est necessarium' et conclusio aequipollet isti 'Deum esse non esse falsum est necessarium'. Et patet quod ex illa de necessario et minore de inesse simpliciter sequitur conclusio de necessario. Et per idem patet quod secundus discursus non valet. Et ita in istis necessarium est scire aequipollentiam propositionis de impossibili ad propositionem de necessario. Et hoc sufficit.	Because of which it should be known that in the first figure from the major of impossibility, the universal equivalent of necessary, taken in the sense of composition and the minor of inherence simply, the conclusion of impossibility follows in the same sense, if the minor is of inherence simply, and not otherwise. And therefore it does not follow 'for every false thing to be true is impossible; that you are sitting is false; therefore that 'you are sitting is true' is impossible'. Both because the major is equivalent to the particular of necessity, namely 'something false not being true is necessary', and so the syllogism is not valid, because the major is equivalent to the particulars; also because the minor is of inherence as of now, and it is clear that the premises are true and the conclusion false. Similarly, it does not follow that 'for every true thing to be necessary is impossible; that God exists is true; therefore, for God's existence to be necessary is impossible', because despite the minor being of inherence simply, the major is still equivalent to one particular of necessity, and therefore the discourse is not valid. But this discourse is good: 'For some true thing to be false is impossible; that God exists is true; therefore for God's existence to be false is impossible', because the minor is of inherence simply. But this discourse is not valid: 'For some true thing to be false is impossible; you are sitting is true; therefore for you to be sitting to be false is impossible', and this because the minor is of inherence as of now. The first discourse is good, because the major is equivalent to 'that no true thing is false is necessary' and the conclusion is equivalent to 'God's existence not being false is necessary'. And it is clear that from the premise of necessity and the minor of inherence simply, the conclusion of necessity follows. And by the same token, it is clear that the second discourse is not valid. And so in these it is necessary to know the equivalence of the proposition of impossibility to the proposition of necessity. And this is sufficient.
Si autem. illa de impossibili sumatur in sensu divisionis et minor de inesse simpliciter, semper sequitur conclusio de impossibili in sensu divisionis, retentis principiis communibus primae figurae, per syllogismum regulatum per dici de omni vel de nullo. Unde bene sequitur 'omnis homo non potest esse asinus; album est homo; igitur album non potest esse asinus'. Hic tamen sciendum est quod quando arguitur ex proposiƿtione de impossibili in qua modus possibilitatis negatur, semper termini	If, however, the proposition of impossibility is taken in the sense of division and the minor of inherence simply, the conclusion of impossibility in the sense of division always follows, retaining the common principles of the first figure, by a syllogism governed by 'to be said of all or none'. Whence it follows well 'every man cannot be a donkey; a white thing is a man; therefore a white thing cannot be a donkey'. Here, however, it should be known that when an argument is made from a proposition of impossibility in which the mode of possibility is denied, the terms always
debent supponere pro his quae sunt, quia in illis syllogismis universalibus si terminus conclusionis supponeret pro his quae possunt esse, syllogismus non valeret. Unde non sequitur 'omnis homo non potest esse asinus; omne album est homo; igitur omne quod potest esse album non potest esse asinus'.	must supposit for things that are, because in those universal syllogisms if the term of the conclusion supposited for things that can be, the syllogism would not be valid. Hence it does not follow that 'every man cannot be a donkey; everything white is a man; therefore everything that can be white cannot be a donkey'.
Et sicut dictum est de ista mixtione in prima figura, ita consimiliter dicendum est in aliis figuris sicut dictum est prius de mixtione necessarii et inesse. Nec oportet aliquid scire nisi aequipollentiam inter propositionem de necessario et de impossibili.	And as was said about this mixture in the first figure, so must be said similarly in the other figures, as was said before about the mixture of necessity and inherence. Nor is it necessary to know anything except the equivalence between the proposition of necessity and of impossibility.