Paraconsistent Logic

[Revised entry by Graham Priest, Koji Tanaka, and Zach Weber on December 1, 2016. Changes to: Main text] The contemporary logical orthodoxy has it that, from contradictory premises, anything can
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[Revised entry by Graham Priest, Koji Tanaka, and Zach Weber on December 1, 2016. Changes to: Main text] The contemporary logical orthodoxy has it that, from contradictory premises, anything can be inferred. Let ⊨ be a relation of logical consequence, defined either semantically or proof-theoretically. Call ⊨ explosive if it validates {A , nA} ⊨ B for every A and B (ex contradictione quodlibet (ECQ)). Classical logic, and most standard 'non-classical' logics too such as intuitionist logic, are explosive. Inconsistency,...

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News source: Stanford Encyclopedia of Philosophy

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