Mathematical logic and foundations Constructive mathematics Theorem

Law of excluded middle

Statement

In classical logic, for each proposition $p$ , the proposition $p \lor \neg p$ is true.

Remarks

The formula $p \lor \neg p$ is a tautology. 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 on $p$ and $\neg p$ .

Reading path

To understand this page from the ground up, read these 4 pages in order. The foundations come first.

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Proposition concept
Disjunction definition
Negation definition
Law of excluded middle statement

Where this leads

15 pages build on this one.

Tag	`0RYYK8PG4S`
URI	`m2://0RYYK8PG4S`
Aliases	`excluded-middle`, `tertium-non-datur`
Kind	statement, theorem
Writing	W1 stated
MSC	03B05
Status	This copy of the site has no build data. Run `m2 status 0RYYK8PG4S`.
Uses	Disjunction, Negation
Same as	Wikidata Q468422 Wikipedia Law of excluded middle

Law of excluded middle

Statement

Remarks

Reading path

Where this leads

Further reading

What this page needs for W2

What links here

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