Law of the excluded middle

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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. For example, "Ginger is a cat" affirms 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]

In mathematics, the law of the excluded middle is a key presupposition behind a proof technique called 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]

Related pages[change | change source]

Notes[change | change source]

  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.