Law of Excluded Middle/Explanation

Proof Rule

The law of (the) excluded middle can be expressed in natural language as:

Every statement is either true or false.

This is one of the Aristotelian principles upon which rests the whole of classical logic, and the majority of mainstream mathematics.

The LEM is rejected by the intuitionistic school, which rejects the existence of an object unless it can be constructed within an axiomatic framework which does not include the LEM.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): excluded middle
• 1988: Alan G. Hamilton: Logic for Mathematicians (2nd ed.) ... (previous) ... (next): $\S 1$: Informal statement calculus: $\S 1.1$: Statements and connectives (in passing)