Law of noncontradiction

For the Fargo episode, see The Law of Non-Contradiction.
This article uses forms of logical notation. For a concise description of the symbols used in this notation, see List of logic symbols.

In logic, the law of noncontradiction (LNC; also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that for any given proposition, the proposition and its negation cannot both be simultaneously true, e.g., the proposition "the house is white" and its negation "the house is not white" are mutually exclusive.

To express the fact that the law is tenseless and to avoid equivocation, sometimes the law is amended to say "contradictory propositions cannot both be true 'at the same time and in the same sense'".

Formally, the law is expressed as the tautology ¬(p ∧ ¬p). One reason to have this law is the principle of explosion, which states that anything follows from a contradiction, resulting in trivialism. The law is employed in a reductio ad absurdum proof. Paraconsistent logics are those logics which deny explosion.

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