26: On the Conversion of de impossibili Propositions
Conversion of de impossibili Propositions those things which are actually creators or for those things which are possibly creators.
From what has been said it is clear that consequences such as the following are not valid: 'A being with sight is possibly blind; therefore a blind being is possibly with sight'; 'Something true is possibly impossible; therefore something impossible is possibly true'; 'Nothing necessary is possibly false; therefore nothing false is possibly necessary'. They are invalid, that is, if the subject of the consequent is taken for those things which are actually suchand-such. Otherwise these consequences are valid.
26: On the Conversion of de impossibili Propositions As far as the conversion of de impossibili propositions is concerned, it should be noted that de impossibili propositions, taken in the sense of composition, are converted just as their non-modal counterparts are converted, as long as those non-modal counterparts are converted simply. For in such cases one argues in accord with the rule 'If one of two interchangeable propositions is impossible, the other is impossible'. This rule is true. However, when its non-modal counterpart is converted only accidentally and not simply, then a de impossibili proposition in the sense of composition is not converted—nor is any proposition equivalent to such a proposition converted. The reason is that such a conversion could not hold except in accord with the following rule: 'If the antecedent is impossible, the consequent is impossible'. But this rule is false, for sometimes the antecedent is impossible and the consequent is necessary.
Thus, consequences such as the following are valid: 'That no man is an animal is impossible; therefore that no animal is a mein is impossible'; 'That some man is a donkey is impossible; there-fore that some donkey is a man is impossible'; 'That God is a Conversion of de impossibili Propositions corporeal being is impossible; therefore that a corporeal being is God is impossible'. However, consequences such as the following are not valid: 'That every animal is a man is impossible; therefore that some man is an animal is impossible'; 'That every being in act or in potency is God is impossible; therefore that God is a being in act or in potency is impossible'; and so on.
On the other hand, if such a de impossibili proposition is taken in the sense of division or is equivalent to a proposition so taken, then it is converted just as its de necessario counterpart is 'converted. Hence, this consequence is not valid: 'Some white thing is not possibly a man; therefore some man is not possibly white'.
For the antecedent is true and the consequent false. Rather, the antecedent should be converted into 'therefore something which is not possibly a man is white'. (Similarly, the proposition 'No white thing is possibly a man' is not converted into 'therefore no man is possibly white'. Rather, it is converted into 'therefore something which is not possibly a man is white'.)
[Ockham himself crossed out the following.
Now it should be noted that when a negation precedes the mode, it changes the mode in such a way that the proposition should not be called one of that mode. Therefore, the proposition 'No man is possibly white' is a de impossibili proposition rather than a de possibili proposition. In the same way, the proposition 'No man is necessarily white' is not, properly and strictly speaking, a de necessario proposition. Rather, it is a de possibili proposition, since it is equivalent to 'Every man is possibly not white'. Thus, since propositions in which the modes are negated are equivalent to affirmative propositions of other modes, such propositions are converted only accidentally and not simply.
Hence, the proposition 'No being necessarily creates' is not converted into 'therefore no being which creates is necessarily a being'. For the latter is false, since its contradictory, namely, 'Some being which creates is necessarily a being', is true. For this being vwhich creates, referring to God, is necessarily a being. Nor is the P.toposition in question converted into 'Nothing which does not ne:cessarily create is a being'. This does not follow, since the antecedent is true and the consequent false. Rather, the proposition in question is converted into 'therefore something which does not necessarily create is a being'.