may be reduced to a conjunctive
If A is not B, C is D,
and so to a simple proposition with a negative term for subject.
All cases of A not being B are cases of C being D.
(Every not-AB is a CD.)
§ 708. It is true that the disjunctive proposition, more than any other form, except U, seems to convey two statements in one breath. Yet it ought not, any more than the E proposition, to be regarded as conveying both with equal directness. The proposition 'No A is B' is not considered to assert directly, but only implicitly, that 'No B is A.' In the same way the form 'Either A is B or C is D' ought to be interpreted as meaning directly no more than this, 'If A is not B, C is D.' It asserts indeed by implication also that 'If C is not D, A is B.' But this is an immediate inference, being, as we shall presently see, the contrapositive of the original. When we say 'So and so is either a knave or a fool,' what we are directly asserting is that, if he be not found to be a knave, he will be found to be a fool. By implication we make the further statement that, if he be not cleared of folly, he will stand condemned of knavery. This inference is so immediate that it seems indistinguishable from the former proposition: but since the two members of a complex proposition play the part of subject and predicate, to say that the two statements are identical would amount to asserting that the same proposition can have two subjects and two predicates. From this point of view it becomes clear that there is no difference but one of expression between the disjunctive and the conjunctive proposition. The disjunctive is merely a peculiar way of stating a conjunctive proposition with a negative antecedent.
§ 709. Conversion of Complex Propositions.
A / If A is B, C is always D.
\ .'. If C is D, A is sometimes B.
E / If A is B, C is never D.
\ .'. If C is D, A is never B.
I / If A is S, C is sometimes D.
\ .'. If C is D, A is sometimes B.
§ 710. Exactly the same rules of conversion apply to conjunctive as to simple propositions.