selfcontradictory

Self-contradictory is an adjective used in logic and philosophy to describe a statement, theory, or set of assertions that cannot be true without contradicting itself. In formal logic, a self-contradictory proposition is one that entails both a statement and its negation, typically expressed as p ∧ ¬p. Under classical logic, such a sentence is false in every interpretation, making it necessarily false.

Examples include the canonical sentence "It is raining and it is not raining" and, in a broader sense, the sentence "This sentence is false" (the Liar Paradox) which challenges notions of truth rather than fitting p ∧ ¬p exactly. Self-contradiction can also arise from inconsistent definitions or conflicting assertions within a theory.

Implications in logic are significant. In a system that obeys the principle of explosion, from a contradiction any proposition can be deduced, which collapses deductive usefulness. For this reason standard deductive frameworks aim to avoid inconsistent premises. By contrast, paraconsistent logics allow some contradictions to be true without exploding into triviality, modeling real-world reasoning where conflicting information can coexist.

In everyday language, self-contradictory statements may reflect vagueness, ambiguity, or rhetorical devices rather than strict logical conflict. Distinguishing between self-contradictions in language and formal contradictions in logic is essential for analysis across philosophy, mathematics, and linguistics.