Note 220 — Chapter VIII

Jevons remarks that he does not see how there can be in deductive logic any question about existence, and observes, with reference to the opposite view taken by De Morgan, that “this is one of the few points in which it is possible to suspect him of unsoundness “ (Studies in Deductive Logic, p. 141). It is, however, impossible to attach any meaning to Jevons’s own “Criterion of Consistency,” unless it has some reference to “existence.” “It is assumed as a necessary law that every term must have its negative. Thence arises what I propose to call the Criterion of Consistency, stated as follows:—Any two or more propositions are contradictory when, and only when, after all possible substitutions are made, they occasion the total disappearance of any term, positive or negative, from the Logical Alphabet” (p. 181). What can this mean but that although we may deny the existence of the combination AB, we cannot without contradiction deny the existence of A itself, or not-A, or B, or not-B? This assumption regarding the existential implication of propositions runs through the whole of Jevons’s equational logic. The following passage, for example, is taken almost at random: “There remain four combinations, ABC, aBC, abC, abc. But these do not stand on the same logical footing, because if we were to remove ABC, there would be no such thing as A left; and if we were to remove abc there would be no such thing as c left. Now it is the criterion or condition of logical consistency that every separate term and its negative shall remain. Hence there must exist some things which are described by ABC, and other things described by abc” (p. 216).