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Invariance criteria are widely accepted as a means to demarcate the logical vocabulary of a language. In previous work, I proposed a framework of semantic constraints for model-theoretic consequence which does not rely on a strict distinction between logical and nonlogical terms, but rather on a range of constraints on models restricting the interpretations of terms in the language in different ways. In this paper I show how invariance criteria can be generalized so as to apply to semantic constraints on models. Some obviously unpalatable semantic constraints turn out to be invariant under isomorphisms. I shall connect the discussion to known counter-examples to invariance criteria for logical terms, and so the generalization will also shed light on the current existing debate on logicality. I analyse the failure of invariance to fulfil its role as a criterion for logicality, and argue that invariance conditions should best be thought of as merely methodological meta-constraints restricting the ways the model-theoretic apparatus should be used.

Original languageEnglish
Pages (from-to)104-132
Number of pages29
JournalBulletin of Symbolic Logic
Issue number1
StatePublished - 2 Mar 2022

Bibliographical note

Publisher Copyright:
© The Author(s), 2021. Published by Cambridge University Press on behalf of The Association for Symbolic Logic.


  • invariance criteria
  • logical consequence
  • logical constants
  • semantic constraints

ASJC Scopus subject areas

  • Philosophy
  • Logic


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