Validity, Sense and Denotation in the Face of Paradoxes

Which modifications does the account of PTS developed in the second chapter need to undergo for it to be applicable to languages containing paradoxical expressions? We argue that one of the basic tenets of Prawitz-DummettDummett, Michael PTS—namely, the definition of the correctness of an inference as validity preservation—must be given up. As a result, the proposed account of PTS is enriched by introducing a notion of sense alongside the one of denotation. Paradoxical derivations are shown to act as the proof-theoretic analog of singular terms endowed with sense but lacking a denotation. The question of which class of derivations should be regarded as having a denotation is reconsidered, and we show the consequences of the choice of different criteria of identity of proofs for the analysis of languages containing paradoxical expressions.