Pluralism and proofs

Greg Restall*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Beall and Restall's Logical Pluralism (2006) characterises pluralism about logical consequence in terms of the different ways cases can be selected in the analysis of logical consequence as preservation of truth over a class of cases. This is not the only way to understand or to motivate pluralism about logical consequence. Here, I will examine pluralism about logical consequence in terms of different standards of proof. We will focus on sequent derivations for classical logic, imposing two different restrictions on classical derivations to produce derivations for intuitionistic logic and for dual intuitionistic logic. The result is another way to understand the manner in whichwe can have different consequence relations in the same language. Furthermore, the proof-theoretic perspective gives us a different explanation of how the one concept of negation can have three different truth conditions, those in classical, intuitionistic and dual-intuitionistic models.

Original languageEnglish
Pages (from-to)279-291
Number of pages13
Early online date20 Mar 2014
Publication statusPublished - Mar 2014


  • Logical consequence
  • Classical logic
  • Kripke model
  • Proof theory


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