law of noncontradiction

In logic, the law of noncontradiction judges as false any proposition P asserting that both proposition Q and its denial, proposition not-Q, are true at the same time and "in the same respect". In the words of Aristotle, "One cannot say of something that it is and that it is not in the same respect and at the same time." More tersely, for any proposition P, it is not both the case that P and not-P. Symbolically, this is expressed as

\neg (P \wedge \neg P).

Bivalence and related laws examines how the law of non-contradiction is related to similar laws, such as the principle of bivalence, with which it should not be confused. See also: Contradiction; Principle of explosion

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