Quine and Slater on paraconsistency and deviance

Journal of Philosophical Logic 32 (5):531-548 (2003)
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
Keywords deviant logics  logical pluralism  paraconsistent logics  proof-theoretic semantics  Quine  substructural logics
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DOI 10.1023/A:1025648722188
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Patrick Allo (2007). Logical Pluralism and Semantic Information. Journal of Philosophical Logic 36 (6):659 - 694.
Patrick Allo (2014). Synonymy and Intra-Theoretical Pluralism. Australasian Journal of Philosophy 93 (1):77-91.

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