Gödel: What could it mean for a statement to be “true but not provable”? Is this just because there are some statements such that neither P nor not-P can be proven, yet one of them must be true? If so, I would (stubbornly) contest that perhaps P and not-P really are both non-true.
“P and not-P really are both non-true” is classically false, and Gödel holds in classical mathematics, so Sunny’s response isn’t available in that case.
Sunny’s sense that “perhaps P and not-P really are both non-true” might be a reason for him to endorse intuitionism as “more correct” than classical math in some sense.
Ike is responding to this:
“P and not-P really are both non-true” is classically false, and Gödel holds in classical mathematics, so Sunny’s response isn’t available in that case.
Sunny’s sense that “perhaps P and not-P really are both non-true” might be a reason for him to endorse intuitionism as “more correct” than classical math in some sense.