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

Arnold Koslow


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
ar-gued 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
condi-tions of extensionality of the classical logical operators.

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