Single Idea 8708

[catalogued under 4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic]

Full Idea

In intuitionist logic, if we do not know that we do not know A, it does not follow that we know A, so the inference (and, in general, double negation elimination) is not intuitionistically valid.

Gist of Idea

Double negation elimination is not valid in intuitionist logic

Source

Michèle Friend (Introducing the Philosophy of Mathematics [2007], 5.2)

Book Reference

Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.107


A Reaction

That inference had better not be valid in any logic! I am unaware of not knowing the birthday of someone I have never heard of. Propositional attitudes such as 'know' are notoriously difficult to explain in formal logic.