nLab
law of double negation

Definition

The law of double negation is the statement that the double negation of a proposition implies that proposition

$$\not \not A \Rightarrow A \,.$$

In classical logic, this is simply true. In constructive logic, it is equivalent to the law of excluded middle (because $\not \not (P \vee \not P)$ is a constructive theorem), and is not assertable in general.

Related concepts

• excluded middle

• closed subspace

References

• eomDouble negation, law of