Intuitionism and the Anti-Justification of Bivalence

Abstract

Dag Prawitz has argued [12] that it is possible intuitionistically to prove the validity of ’ A → there is a proof of ⌌A⌍’ by induction over formula complexity, provided we observe an object language/meta-language distinction. In the present paper I mainly argue that if the object language with its axioms and rules can be represented as a formal system, then the proof fails. I also argue that if this restriction is lifted, at each level of the language hierarchy, then the proof can go through, but at the expense of virtually reducing the concept of a proof to that of truth in a non-constructive sense.