{"ok":true,"protocol":"maclain_hunter_q_number_item_v1","qid":"Q1013","item":{"qid":"Q1013","slug":"logic-and-proof","path":"/q/Q1013","subdomain":"q1013.4p-engine.com","schemaType":"CreativeWork","name":"Logic and Proof","alternateName":["Logic, Logos, and Proof","Logic-proof relation"],"title":"Q1013 — Logic and Proof","description":"The first-party authored relation between Logic as lawful order and proof as the performed reasoning that demonstrates a conclusion within that order.","claim":"Logic governs the form and coherence of proof, while proof performs and exposes reasoning within that order; a reflexive proof may make its own valid performance part of what it demonstrates.","body":["Q1013 names the relation between Logic and proof rather than treating them as interchangeable words. Logic is the lawful order against which identity, non-contradiction, relation, and inference are judged. Proof is a performed passage through that order toward a conclusion.","The attached Knowing Logic and Proof text makes this relation explicit. P defines Logic through universal non-contradiction and lawful order. Q identifies the semantics of that definition as knowledge of Logic. R argues that explaining Logic and explicitly identifying that explanation is proof. S then states that a logical proof coherent with Logic cannot be incoherent without contradiction.","The formal structure is stated as {P, P -> Q, Q -> R, R -> S} |= (P & Q) -> (R & S). 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