contradictio

Contradictio, Latin for "opposition" or "speaking against," is a term used in logic, philosophy, and rhetoric to denote a state or proposition that essentially opposes itself. In English scholarship the form contradictio is uncommon; the standard term is contradiction. The word derives from the Latin contra- "against" and dictio "speaking, utterance."

In logic, a contradiction is a statement that cannot be true and false at the same time. A classic formulation is p and not-p, a proposition together with its negation. The principle of non-contradiction holds that such a conjunction cannot be true in a consistent theory. In classical logic, from a contradiction, anything follows (ex contradicitone quodlibet). Some non-classical logics—paraconsistent logics—allow limited contradictions without explosion.

In rhetoric, contradictio can refer to a figure of speech where two incompatible terms co-occur, notably in the Latin phrase contradicto in adjecto—a pair of adjectives that negate one another within the same phrase (for example, "deafening silence" or "bitter-sweet"). The term is related to, but distinct from, the oxymoron, which is a broader category of paradoxical phrases.

Historically, the concept has been central in scholastic philosophy and medieval logic, where contradictions were discussed in relation to the principles of logic, truth, and entailment.

See also: contradiction, paradox, law of non-contradiction, principle of explosion, ex contradictione quodlibet, paraconsistent logic.