Principle of non-contradiction

The qualifications matter. A body being warm today but not yesterday concerns different times; one side being warm and the other not concerns different parts. Neither asserts contradictory properties in the same respect.

The subject and the meaning of the predicate must also remain fixed. Using one word for different things can create a verbal appearance of contradiction without contradictory claims about one and the same fact.

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Book IV argues that proving every principle from earlier propositions would produce a regress. Aristotle instead asks an opponent to make a meaningful assertion and examines the distinctions that assertion already requires.

This refutative strategy differs from an ordinary derivation from agreed premises. It seeks to show that removing determinate distinctions also undermines the definite content of the opponent’s own assertion.

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Applying the principle begins with checking subject, time, conditions and terminology. Evaluations can concern different respects, so disagreement alone does not establish both a proposition and its negation.

This account concerns the classical argument in Metaphysics. It does not settle every later logical theory or replace investigation of historical context and evidence with a slogan.

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