Note 497 — Chapter III

The application of this rule again leaves us with a proposition equivalent to our original proposition. The following rule, which may be regarded as a corollary from the above rule, or which may be arrived at independently, does not necessarily leave us with an equivalent: If a new determinant is introduced into the subject of a universal affirmative proposition (see section 449) every alternant in the predicate which contains the contradictory of the determinant may be omitted. Thus, from Whatever is A or B is C or DX or Ex, we may infer Whatever is AX or BX is C or D.

The application of this rule may sometimes result in the disappearance of all the alternants from the predicate; and the meaning of such a result is that we now have a non-existent subject.

Thus, given All P is ABCD or Abcd or aBCd, if we particularise the subject by making it PbC, we find that all the alternants in the predicate disappear. The interpretation is that the class PbC is non-existent, that is, No P is bC ; a conclusion which might of course have been obtained directly from the given proposition.