12. REDUCTION OF THE DISJUNCTIVE ARGUMENT TO THE HYPOTHETICAL AND THEN TO THE CATEGORICAL.
It would seem that the laws of the disjunctive contradict those of the categorical syllogism; for we apparently derive from two affirmatives a negative conclusion, and we also derive an affirmative conclusion when one premise is negative. This objection is seen to be nugatory when the disjunctive is reduced to the categorical form. The reduction involves the two steps of first changing the disjunctive to the hypothetical form and then to the categorical form. The following illustrations will suffice to make the matter clear:
(1) Disjunctive.
A is either B or C
A is B
∴ A is not C
Hypothetical.
If A is B, then A is not C
A is B
∴ A is not C