The conjunction of a proposition and its negation. The law of non-contradiction provides that no such conjunction can be true: not (p & not-p). The standard proof of the inconsistency of a set of propositions or sentences is to show that a contradiction may be derived from them.

In Hegelian and Marxist writing the term is used more widely. A contradiction may be a pair of features that together produce an unstable tension in a political or social system: a ‘contradiction’ of capitalism might be the arousal of expectations in the workers that the system cannot requite. For Hegel the gap between this and genuine contradiction is not as wide as it is for other thinkers, given the equation between systems of thought and their historical embodiments.