Semantic pollution and syntactic purity

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Logical inferentialism claims that the meaning of the logical constants should be given, not model-theoretically, but by the rules of inference of a suitable calculus.
It has been claimed that certain proof-theoretical systems, most particularly, labelled deductive systems for modal logic, are unsuitable, on the grounds that they are semantically polluted and suffer from an untoward intrusion of semantics into syntax. The charge is shown to be mistaken. It is argued on inferentialist grounds that labelled deductive systems are as syntactically pure as any formal system in which the rules define the meanings of the logical constants.
Original languageEnglish
Pages (from-to)649-661
Number of pages13
JournalThe Review of Symbolic Logic
Issue number4
Early online date7 Aug 2015
Publication statusPublished - Dec 2015


  • Modal logic
  • Inferentialism
  • Model theory
  • Kripke semantics
  • Labelled deductive systems
  • Tree-hypersequents
  • Gentzen
  • Poggiolesi
  • Restall


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