---
tag: 0RYYK8PG4S
kind: statement
role: theorem
name: Law of excluded middle
aliases: [excluded-middle, tertium-non-datur]
msc: [03B05]
uses: [0H5GKDTB01, 0XR7A7RSXB]
sources:
  - url: https://en.wikipedia.org/wiki/Law_of_excluded_middle
    locator: lead section
same_as:
  wikidata: Q468422
  wikipedia: Law of excluded middle
---

## Statement

In classical logic, for each [[proposition|0ZGC7ZESYN]] $p$, the proposition $p \lor \neg p$ is true.

## Remarks

The formula $p \lor \neg p$ is a [[tautology|0D1AHYPM8N]].
Some systems take the law as an axiom.
Intuitionistic logic does not accept the law in general.
The law is the basis of [[proof by cases|0WCP0PVET6]] on $p$ and $\neg p$.

## Explanations

### L1 human

The law says that there is no third option: a statement is true, or its negation is true.
For example, each natural number $n$ is even or not even.