Single Idea 17925

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

Full Idea

In intuitionist logic double negation elimination fails. After all, proving that there is no proof that there can't be a proof of S is not the same thing as having a proof of S.

Gist of Idea

Showing a disproof is impossible is not a proof, so don't eliminate double negation

Source

Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.3)

Book Reference

Colyvan,Mark: 'An Introduction to the Philosophy of Mathematics' [CUP 2012], p.7


A Reaction

I do like people like Colyvan who explain things clearly. All of this difficult stuff is understandable, if only someone makes the effort to explain it properly.