contradictory

Contradictory is an adjective used to describe statements, ideas, or propositions that oppose each other in such a way that they cannot both be true in the same sense at the same time. In ordinary language, a contradictory claim directly conflicts with another claim or with itself.

In logic, a proposition and its negation form a contradictory pair. The law of non-contradiction holds that a statement cannot be both true and false simultaneously in classical logic. When a theory proves both a statement and its negation, it is called inconsistent, and from such a contradiction the principle of explosion can follow, allowing any conclusion to be inferred.

In traditional syllogistic, the term is used to describe pairs of propositions that cannot both be true: universal affirmative (A) contradicts universal negative (E), and particular affirmative (I) contradicts particular negative (O). A and O are contradictories; E and I are contradictories. In everyday use, contradictions are distinguished from mere disagreements or ambiguities; paradoxes like “This sentence is false” illustrate self-referential contradictions that challenge straightforward truth evaluation.

Contradictory as a concept is related to inconsistency, paradox, and dispute. Some non-classical logics, such as paraconsistent logic, tolerate certain contradictions without collapsing into triviality. Etymologically, the term derives from Latin contra- “against” and dicere “to say,” signifying statements that say opposite things.