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(2018) Synthese 195 (12).
Classical propositional logic can be characterized, indirectly, by means of a complementary formal system whose theorems are exactly those formulas that are not classical tautologies, i.e., contradictions and truth-functional contingencies. Since a formula is contingent if and only if its negation is also contingent, the system in question is paraconsistent. Hence classical propositional logic itself admits of a paraconsistent characterization, albeit "in the negative". More generally, any decidable logic with a syntactically incomplete proof theory allows for a paraconsistent characterization of its set of theorems. This, we note, has important bearing on the very nature of paraconsistency as standardly characterized.
Publication details
DOI: 10.1007/s11229-017-1458-0
Full citation:
Pulcini, G. , Varzi, A.C. (2018). Paraconsistency in classical logic. Synthese 195 (12), pp. 5485-5496.
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