Authors/Ockham/Summa Logicae/Book II/Chapter 28

Latin	English
[2.28 DE CONVERSIONE PROPOSITIONUM DE CONTINGENTI PER OPPOSITAS QUALITATES]	Chapter 28. On the Conversion of Propositions of Contingency through Opposite Qualities.
Sequitur videre de conversione propositionum de contingenti per oppositas qualitates. Et est sciendum quod quaelibet propositio de contingenti ad utrumlibet, si sumatur in sensu divisionis, convertitur per oppositas qualitates; hoc est, affirmativa convertitur in negativam et e converso, sicut sequitur 'contingit b esse a, igitur contingit b non esse a'. Similiter sequitur 'omnis homo contingenter currit, igitur omnis homo contingenter non currit'.	It follows to see about the conversion of propositions of contingency by opposite qualities. And it should be known that any proposition of contingency to the opposite, if taken in the sense of division, is converted by opposite qualities; that is, an affirmative is converted into a negative and vice versa, as follows 'it happens that b is a, therefore it happens that b is not a'. Similarly it follows 'every man runs contingently, therefore every man does not run contingently'.
Et est advertendum quod quando propositio de contingenti ad utrumlibet convertitur per oppositas qualitates, in utraque propositione modus debet esse affirmatus et non negatus. Et ideo non sequitur 'omnis homo contingenter currit, igitur nullus homo contingenter currit', nec sequitur 'nullus homo contingenter currit, igitur omnis homo contingenter currit', sed bene sequitur 'omnis homo contingenter currit, igitur omnis homo contingenter non currit'. Similiter sequitur 'omnis homo contingenter non currit, igitur omnis homo contingenter currit'.	And it should be noted that when a proposition is converted by opposite qualities from contingent to non-contingent, in both propositions the mode must be affirmed and not denied. And therefore, it does not follow 'every man runs contingently, therefore no man runs contingently', nor does it follow 'no man runs contingently, therefore every man runs contingently', but it does follow 'every man runs contingently, therefore every man does not run contingently'. Similarly, it follows 'every man does not run contingently, therefore every man runs contingently'.
Praedicta conversio patet, nam sequitur formaliter 'homo contingenter currit, igitur homo potest currere'. Similiter sequitur 'omnis homo contingenter currit, igitur non necesse est omnem hominem currere'; ex qua sequitur ista 'aliquis homo potest non currere'. Nunc autem ex istis duabus 'aliquis homo potest non currere' et 'ille potest currere' sequitur quod aliquis homo contingenter non currit. Igitur ex prima sequitur ista per illam regulam 'quidquid sequitur ad consequens, sequitur ad antecedens', quae semper vera est.	The aforementioned conversion is clear, for it follows formally that 'a man runs contingently, therefore a man can run'. Similarly, it follows that 'every man runs contingently, therefore it is not necessary for every man to run'; from which follows that 'some man is able to not run'. Now, however, from these two 'some man may not run' and 'he may run' it follows that some man does not run contingently. Therefore from the first follows that by the rule 'whatever follows to the consequent, follows to the antecedent', which is always true.
Propter protervos autem est sciendum quod quandocumque dico talem propositionem 'homo contingenter currit', 'homo contingenter non currit' intelligo talem 'contingit hominem currere', 'contingit hominem non currere', ne proterviatur contra me, dicendo quod sequitur 'homo contingenter currit, igitur homo currit'.	But for the sake of the stubborn, it should be known that whenever I say such a proposition as 'a man runs contingently', 'a man does not run contingently', I understand such a proposition as 'it is contingent for a man to run', 'it is contingent for a man not to run', lest he be stubborn against me, saying that what follows is 'a man runs contingently, therefore a man runs'.
Sic igitur patet manifeste quomodo quaelibet talis propositio de contingenti in sensu divisionis et aequivalens ei convertitur per oppositas qualitates. Sed talis propositio in sensu compositionis non convertitur per oppositas qualitates, nam tunc argueretur per aliquam istarum regularum 'una contrariarum est contingens, igitur reliqua est contingens', 'una subcontrariarum est contingens, igitur reliqua est contingens'; quae falsae sunt. Et ideo non sequitur 'nullum exsistens esse hominem est contingens, igitur omne exsistens esse hominem est contingens'; nec sequitur 'omne exsistens esse Deum est contingens, igitur nullum exsistens esse Deum est contingens'. Similiter non sequitur 'aliquod exsistens esse hominem est contingens, igitur aliquod exsistens non esse hominem est contingens', quia in omnibus praedictis exemplis antecedens est verum et consequens falsum, si sumantur omnes propositiones in sensu compositionis.	Thus, therefore, it is clearly evident how any such proposition of contingency in the sense of division and equivalent to it is converted by opposite qualities. But such a proposition in the sense of composition is not converted by opposite qualities, for then it would be argued by one of these rules 'one of the contraries is contingent, therefore the rest is contingent', 'one of the subcontraries is contingent, therefore the rest is contingent'; which are false. And therefore, it does not follow that 'for no existing thing to be a man is contingent, therefore tor every existing thing to be a man is contingent'; nor does it follow 'for every existing thing to be God is contingent, therefore for nothing existing to be God is contingent'. Similarly, it does not follow 'for something existing to be a man is contingent, therefore for something existing not to be a man is contingent', because in all the aforementioned examples the antecedent is true and the consequent false, if all the propositions are taken in the sense of composition.