Authors/Ockham/Summa Logicae/Book II/Chapter 26

Latin	English
[2.26 DE CONVERSIONE PROPOSITIONUM DE IMPOSSIBILI]	Chapter 26. On the Conversion of Propositions of Impossibility.
Circa conversionem propositionum de impossibili est sciendum quod propositiones de impossibili, acceptae in sensu compositionis, convertuntur sicut suae de inesse, quando illae de inesse convertuntur simpliciter, quia tunc arguitur per istam regulam 'si unum convertibilium est impossibile, reliquum est impossibile'; quae regula vera est. Sed quando sua de inesse non convertitur simpliciter sed tantum per accidens, tunc illa de impossibili in sensu compositionis [non est convertibilis] nec aliqua sibi aequivalens est convertibilis. Et hoc quia non posset tenere talis conversio nisi per istam regulam 'si antecedens est impossibile, consequens est impossibile'; quae regula falsa est, nam aliquando antecedens est impossibile et consequens necessarium.	Regarding the conversion of propositions of impossibility, it should be known that propositions of impossibility, taken in the sense of composition, are converted as their propositions of inherence, when those of inherence are converted simply, because then it is argued by this rule 'if one of the convertibles is impossible, the rest is impossible'; which rule is true. But when its proposition of inherence is not converted simply but only accidentally, then that of inherence in the sense of composition [is not convertible] nor is any equivalent to it convertible. And this because such a conversion could not hold except by this rule 'if the antecedent is impossible, the consequent is impossible'; which rule is false, for sometimes the antecedent is impossible and the consequent necessary.
Et ideo tales consequentiae sunt bonae 'nullum hominem esse animal est impossibile, igitur nullum animal esse hominem est impossibile'; 'aliquem hominem esse asinum est impossibile, igitur aliquem asinum esse hominem est impossibile'; 'Deum esse corpus est impossibile, igitur corpus esse Deum est impossibile'. Sed tales consequentiae 'omne animal esse hominem est impossibile, igitur aliquem hominem esse animal est impossibile'; omne ens in actu vel in potentia esse Deum est impossibile, igitur Deum esse ens in actu vel in potentia est impossibile' et huiusmodi non valent.	And therefore such consequences are good as 'for no man to be an animal is impossible, therefore it is impossible for no animal to be a man'; 'it is impossible for any man to be a donkey, therefore it is impossible for any ass to be a man'; 'it is impossible for God to be a body, therefore it is impossible for a body to be God'. But such consequences as 'it is impossible for every animal to be a man, therefore it is impossible for any man to be an animal'; it is impossible for any being actually or potentiality to be God, therefore it is impossible for God to be a being actually or potentiality' and the like are not valid.
Si autem talis propositio de impossibili sumatur in sensu divisionis vel aequivalens sibi, tunc convertibilis est sicut illa de necessario. Unde ista consequentia non valet 'aliquod album impossibiliter est homo, igitur aliquis homo impossibiliter est albus', nam antecedens est verum et consequens falsum; sed debet sic converti 'igitur aliquid, quod impossibiliter est homo, est album'. [Similiter ista 'nullum album potest esse homo' non convertitur sic 'igitur nullus homo potest esse albus' sed sic 'igitur aliquid, quod non potest esse homo, est album'.]	But if such a proposition of impossibility is taken in the sense of division or its equivalent, then it is convertible like that of necessity. Hence this consequence is not valid 'something white is impossibly a man, therefore some man is impossibly white', for the antecedent is true and the consequent false; but it must be converted thus 'therefore something that is impossibly a man is white'. [Similarly, this 'no white thing can be a man' is not converted thus 'therefore no man can be white' but thus 'therefore something that cannot be a man is white'.]
[Istud cancellavit ipsc Occkam. Est autem sciendum quod quando negatio praecedit modum, mutat modum, ut non dicatur propositio de tali modo. Et ideo ista 'nullus homo potest esse albus' non est de possibili sed magis de impossibili. Sicut ista 'nullus homo de necessitate est albus' non est proprie et stricte de necessario sed magis de possibili, quia aequivalet isti 'omnis homo potest non esse albus'. Et ideo quia tales propositiones in quibus negantur modi aequivalent propositionibus affirmativis de aliis modis, ideo non convertuntur simpliciter sed per accidens tantum. Unde ista 'nullum ens de necessitate creat' non convertitur in istam 'igitur nullum creans de necessitate est ens', quia falsa est, cum sua contradictoria sit vera, scilicet 'aliquod creans de necessitate est ens', quia hoc creans de necessitate est ens, demonstrando Deum; nec in istam nihil quod non de necessitate creat est ens', nam non sequitur, quia antecedens est verum et consequens falsum; sed sequitur ista 'igitur aliquid, quod non de necessitate creat, est ens'.]	[This was cancelled by Occam. But it should be known that when negation precedes a mode, it changes the mode, so that the proposition is not said to be of such a mode. And therefore this 'no man can be white' is not of the possible but rather of the impossible. Just as this 'no man of necessity is white' is not properly and strictly of necessity but rather of possibility, because it is equivalent to this: 'every man can be not white'. And therefore, because such propositions in which modes are denied are equivalent to affirmative propositions of other modes, they are therefore not converted simply but only accidentally. Hence this 'no being of necessity creates' is not converted into this 'therefore no creator of necessity is a being', because it is false, since its contradictory is true, namely 'something that creates of necessity is a being', because this creator of necessity is a being, demonstrating God; nor into this 'nothing that does not create of necessity is a being', for it does not follow, because the antecedent is true and the consequent false; but this follows 'therefore something that does not create of necessity is a being'.]