Law of Excluded Middle

Discipline: Philosophy

One of the traditional three laws of thought (along with the laws of identity and contradiction).

Every proposition is either true or not true.

This is weaker than the law of bivalence (every proposition is true or false), since if there is a third truth value excluded middle can still hold, though bivalence will fail. (However, bivalence is sometimes treated as a version of excluded middle).

For classical logic, excluded middle follows from the law of contradiction. Intuitionist logic accepts the latter but not excluded middle (also see: double negation), for reasons connected with the 'Jones was brave' example (see bivalence).

P T Geach and W F Bednarowski, "The Law of Excluded Middle' (symposium), Proceedings of the Aristotelian Society, supplementary volume (1956)


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