# Law of Excluded Middle/Explanation

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## Proof Rule

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

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)