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Luca Tranchini, Proof-theoretic semantics, paradoxes and the distinction between sense and denotation, Journal of Logic and Computation, Volume 26, Issue 2, April 2016, Pages 495–512, https://doi.org/10.1093/logcom/exu028
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Abstract
In this paper we show how Dummett-Prawitz-style proof-theoretic semantics has to be modified in order to cope with paradoxical phenomena. It will turn out that one of its basic tenets has to be given up, namely the definition of the correctness of an inference as validity preservation. As a result, the notions of an argument being valid and of an argument being constituted by correct inference rules will no more coincide. The gap between the two notions is accounted for by introducing the distinction between sense and denotation in the proof-theoretic-semantic setting.
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