28: On the Conversion of de contingenti Propositions through Opposite Qualities
Conversion through Opposite Qualities etc. Hence, if nothing is white, then in the proposition 'A white thing is possibly a man' the subject cannot be taken for what is white, since nothing is white. But it can still be asserted that it is taken for what is white. Therefore, if nothing is white, then the proposition is false, since something false is asserted by means of it. For by means of that proposition it is asserted, in the sense in question, that something is white, even though nothing is white.
28: On the Conversion of de contingenti Propositions through Opposite Qualities Next we will look into the conversion of de contingenti propositions through opposite qualities. It should be noted that every proposition, which contains the mode of contingency with respect to truth and falsity, is converted through opposite qualities if it is taken in the sense of division. That is, an affirmative proposition is converted into a negative proposition, and vice versa. For example, this follows: 'B is contingently A; therefore B is contingently not A'. Likewise, this follows: 'Every man contingently runs; therefore every man contingently does not run'.
It should be noted that when a proposition, which contains the mode of contingency with respect to truth and falsity, is converted through opposite qualities, then in both propositions the mode should be affirmed and not denied. Therefore, this does not follow: 'Every man contingently runs; therefore no man contingently runs'. Nor does this follow: 'No man contingently runs;' therefore every man contingently runs'. Rather this follows: 'Every man contingently runs; therefore every man contingently does not run'. Similarly, this follows: Every man contingently does not tun; therefore every man contingently runs'.
The conversion just mentioned is obvious. For this follows formally: 'A man contingently runs; therefore a man possibly runs',
Conversion through Opposite Qualities Likewise, this follows: 'Every man contingently runs; therefore it is not necessary that every man mn'—from which this follows:
'Some man possibly does not run'. But then from the two propositions 'Some man possibly does not run' and 'He possibly runs' it follows that some man contingently does not run. Therefore, this last proposition follows from the first one alluded to above in accord with the rule: 'Whatever follows from the consequent follows from the antecedent'. This rule is always true.
Now for the sake of certain perverse people it should be noted that whenever I use a proposition like 'A man contingently runs' or 'A man contingently does not run' I mean the following: 'It is contingent that a man runs' and 'It is contingent that a man does not run'.!
I mention this lest someone impudently argue against me by claiming that the following is valid: 'A man contingently runs; therefore a man runs'.
Thus, it is manifestly clear how such a de contingenti proposition in the sense of division or an equivalent proposition is converted through opposite qualities. But such a proposition in the sense of composition is not converted through opposite qualities. For in such a case one would be arguing in accord with one of the following rules: 'One of two contrary propositions is contingent; therefore the other is contingent', or 'One of two subcontrary propositions is contingent; therefore the other is contingent'. But these rules are false. And thus this does not follow:
'That no existing being is a man is contingent; therefore that every existing being is a man is contingent'. Nor does this follow:
'That every existing being is God is contingent; therefore that no existing being is God is contingent'. Similarly, this does not follow: 'That some existing being is a man is contingent; therefore that some existing being is not a man is contingent'. For in all these examples the antecedent is true and the consequent false, if all the propositions are taken in the sense of composition.