Logic for Equivocators

Abstract

At first the champions of relevance in logic taught that relevance and preservation of truth were two separate merits, equally required of any relation that claims the name of implication. Thus Anderson and Belnap, in [1]: 19-20, cheerfully agree that certain classical implications necessarily preserve truth, but fault them for committing fallacies of relevance. (And there is no hint that necessary truth-preservation might not be truth-preservation enough.) Lately, however, relevance has been praised not-or not only-as a separate merit, but rather as something needed to ensure preservation of truth. The trouble with fallacies of relevance, it turns out, is that they can take us from truth to error. Classical implication does preserve truth, to be sure, so long as sentences divide neatly into those that are true and those with true negations. But when the going gets tough, and we encounter true sentences whose negations also are true, then the relevant logician gets going. Then his relevant implication preserves truth and some classical implication doesn't. Say thatA is true and its negation cA is true as well. Then A & -A is a conjunction of truths, and hence true. LetB be false, and not true. Then the classically valid, but irrelevant, implication ex falso quodlibet