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Corrigendum to: On translating between logics

Accepted version
Peer-reviewed

Type

Article

Change log

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.

Description

Keywords

5003 Philosophy, 50 Philosophy and Religious Studies

Journal Title

Analysis

Conference Name

Journal ISSN

0003-2638
1467-8284

Volume Title

Publisher

Oxford University Press (OUP)

Rights

Publisher's own licence