Law of Excluded Middle

Context
This is one of the axioms of natural deduction.

The rule
For any statement $$p$$, either $$p$$ is true or $$p$$ is false:

$$\vdash p \lor \lnot p$$

Otherwise known as "tertium non datur" (Latin for "third is not given", that is, a third possibility is not possible).


 * Abbreviation: $$\textrm{LEM}$$
 * Deduced from: Nothing.
 * Depends on: Nothing.

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

This rule is denied by the intuitionist school.