Classical Logic and the Liar

Abstract

The liar and kindred paradoxes show that we can derive contradictions when we reason in accordance with classical logic from the schema (T) about truth: S is true iff p, where ‘p’ is to be replaced with a sentence and ‘S’ with a name of that sentence. The paper presents two arguments to the effect that the blame lies not with (T) but with classical logic. The arguments derive contradictions using classical logic, but instead of appealing to (T), they invoke semantic claims that seem even harder to reject. The first argument relies on two standard semantic principles that are not disquotational and on the claim that if there is such a thing as the property of being true, then ‘true’ expresses that property. The second argument relies on a schema about meaning: S means that p, where ‘S’ and ‘p’ are to be replaced as before.