selfcontradiction

Self-contradiction refers to a statement or set of statements that contain mutually incompatible claims, such that a proposition and its negation are both endorsed or implied. In classical logic, this makes it impossible to assign a consistent truth value, because the content cannot be true and false at the same time. Self-contradiction can arise from faulty reasoning, ambiguous language, or genuine self-reference.

Common examples include semantic paradoxes such as the liar paradox: “This sentence is false.” If the sentence is true, then it is false, but if it is false, then it is true. Other self-referential cases include the barber paradox, which involves a rule about who shaves whom and leads to a contradiction when applied to the barber himself. Such cases illustrate how self-reference can generate inconsistency even from seemingly simple statements.

In formal logic, a single self-contradictory statement (a proposition and its negation both holding) leads to explosion: from a contradiction, any statement can be derived, making the system trivial. To avoid this, most mathematical and scientific theories are required to be consistent. Some logical frameworks, known as paraconsistent logics, allow controlled contradictions without producing explosion, and dialetheism accepts that some contradictions can be true simultaneously.

In everyday use, self-contradiction often signals confusion, ambiguity, or faulty argumentation rather than a strict logical inconsistency. Related concepts include the law of non-contradiction, paradox, and theories of truth and reference.

See also: logic, paradox, law of noncontradiction, inconsistency, paraconsistent logic.