Corrigendum to: On translating between logics

Abstract

The proof in Dewar 2018 that classical and intuitionistic logic are not intertranslatable is defective. The proof claims that up to logical equivalence, there are only three non-trivial one-place schemata in intuitionistic logic (λφ.φ, λφ.¬φ and λφ.¬¬φ). This is false, for two reasons. First, we could include arbitrary further propositional constants in a one-place schema: for instance, the schema λφ.(φ∨P) is still a one-place schema. Second, even if we restrict our attention to one-place schemata that do not include any propositional constants, there are still infinitely many (logically inequivalent) schemata: this follows from the result of Nishimura (1960) that for any propositional constant, there are infinitely many intuitionistically inequivalent formulae containing only that propositional constant. However, the result still stands, as the following proof demonstrates.