# Law of the excluded middle

logical principle stating that for every proposition, either it or its negation is true

The law of the excluded middle is a simple rule of logic. It states that for any proposition,[1] there is no middle ground. Every proposition is either true or false.

## Example

For example, "Ginger is a cat" says the fact that Ginger is a cat. If it is true, then its opposite cannot also be true. If Ginger is a cat, then Ginger is not something else.[2]

## Mathematics

In mathematics, the law of the excluded middle is a presupposition behind the proof by contradiction. Because of that, those who reject the validity of the law of the excluded middle (for example, the intuitionists) must also reject the validity of proof by contradiction as well.[3]

## Notes

1. a proposition is, very roughly, a statement which is claimed to be true
2. Bennett, Deborah Logic Made Easy page 30
3. "The Definitive Glossary of Higher Mathematical Jargon". Math Vault. 2019-08-01. Retrieved 2020-10-08.