Quine and Slater on Paraconsistency and Deviance

ISSN： 0022-3611

Source： Journal of Philosophical Logic, Vol.32, Iss.5, 2003-10, pp. : 531-548

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Abstract

In a famous and controversial paper, B. H. Slater has argued against the possibility of paraconsistent logics. Our reply is centred on the distinction between two aspects of the meaning of a logical constant ^*c^* in a given logic: its operational meaning, given by the operational rules for ^*c^* in a cut-free sequent calculus for the logic at issue, and its global meaning, specified by the sequents containing ^*c^* which can be proved in the same calculus. Subsequently, we use the same strategy to counter Quine's meaning variance argument against deviant logics. In a nutshell, we claim that genuine rivalry between (similar) logics ^*L^* and ^*L′^* is possible whenever each constant in ^*L^* has the same operational meaning as its counterpart in ^*L′^* although differences in global meaning arise in at least one case.