Carnap's Problem: What is it Like to be a Normal Interpretation of Classical Logic?

Abstract

Carnap in the 1930s discovered that there were non-normal interpretations of classical logic - ones for which negation and conjunction are not truth-functional so that a statement and its negation could have the same truth value, and a disjunction of two false sentences could be true. Church argued that this did not call for a revision of classical logic. More recent writers seem to disa-gree. We provide a definition of "non-normal interpretation" and argue that Church was right, and in fact, the existence of non-normal interpretations tells us something important about the conditions of extensionality of the classical logical operators.