Affirmations, Denials, and Contradictions
Aristotle takes some pains in On Interpretation to argue that to every affirmation there corresponds exactly one denial such that that denial denies exactly what that affirmation affirms.
The pair consisting of an affirmation and its corresponding denial is a contradiction (antiphasis).
In general, Aristotle holds, exactly one member of any contradiction is true and one false:
– they cannot both be true, and they cannot both be false.
However, he appears to make an exception for propositions about future events, though interpreters have debated extensively what this exception might be (see further discussion below [http://plato.stanford.edu/entries/aristotle-logic/#TimNecSea]).
The principle that contradictories cannot both be true has fundamental importance in Aristotle’s metaphysics (see further discussion below [http://plato.stanford.edu/entries/aristotle-logic/#DiaRhe]).