## Abstract

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.

Original language | English |
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Pages (from-to) | 1-12 |

Number of pages | 12 |

Journal | Synthese |

DOIs | |

Publication status | Accepted/In press - 16 Jun 2017 |

## Keywords

- Classical logic
- Complementary system
- Consequence relation
- Decidability
- Paraconsistency
- Unprovability