An Inferentialist Approach to Paraconsistency

James Trafford

Abstract


This paper develops and motivates a paraconsistent approach to semantic paradox from within a modest inferentialist framework. I begin from the bilateralist theory developed by Greg Restall, which uses constraints on assertions and denials to motivate a multiple-conclusion sequent calculus for classical logic, and, via which, classical semantics can be determined. I then use the addition of a transparent truth-predicate to motivate an intermediate speech-act. On this approach, a liar-like sentence should be “weakly asserted”, involving a commitment to the sentence and its negation, without rejecting the sentence. From this, I develop a proof-theory, which both determines a typical paraconsistent model theory, and also gives us a nice way to understand classical recapture.


Keywords


Bilateralism; Inferentialism; Paraconsistent logic; Recapture; Multiple-conclusion

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