Definition of double negation in English:
The result of negating the negation of a proposition, and the principle (not admitted in intuitionist logic) that this is equivalent to the proposition itself.
- Thus, the double negation nPn is established when one shows that an assumption nPn is contradictory.
- One reason has to do with the common (natural language) reasoning involving counter-logicals, including, for example, sentences such as ‘If intuitionistic logic is correct, then double negation elimination is invalid’.
- And so, classical logic is seen to be a fragment of intuitionist logic and obtains a legitimate, if virtual, existence, in the shadow world of double negations, a compelling picture.