Contradiction

A relation among claims that cannot all be true under the same interpretation and conditions. In classical logic, a contradiction is a statement and its negation.

Negation: A logical operation that forms a statement denying the truth of another statement. Contradiction arises when a claim and its negation are both asserted.
Proposition: A declarative content that can be evaluated as true or false. Contradiction is a relation between propositions or claims.
Proof by contradiction: A proof method that establishes a claim by deriving an impossibility from its negation. It uses contradiction as evidence that an assumption must be rejected.
Dialetheism: The view that some contradictions are true. It rejects the assumption that every contradiction must be false.
Law of noncontradiction: The principle that a proposition and its negation cannot both be true in the same sense and at the same time. It states the classical constraint that contradictory claims violate.
Logical consistency: The property of a set of statements having a model in which all are true. Its absence is inconsistency, which may arise from contradictory claims.
Inconsistent system: A formal theory whose axioms and rules allow a contradiction to be derived. It is a system in which contradictory consequences can be proved.
Paraconsistent logic: A logic in which contradictions do not entail every proposition. Its systems contain inconsistency without classical explosion.
Satisfiability: The property of a logical formula having at least one interpretation that makes it true. A set of claims is contradictory when no interpretation satisfies them all.
Contrariety: A relation between claims that cannot both be true but may both be false. Unlike contradictories, contraries can fail together without either being true.

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