Can a contradiction prove anything?Sourced
Classical logic has a surprising problem when a claim and its denial are both assumed.
Under the principle of explosion, classical inference rules allow any unrelated conclusion from a proposition together with its negation. Paraconsistent logics change the rules so contradictions can be handled without that result.
How a system handles conflict depends on its rules.
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Rule of inference · Wikimedia contributors
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Reviewed: 2026-10-02