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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

Funding Information:
Material from this paper was presented in Bergen, Jerusalem, Munich, and at the 2016 Annual Meeting of the Association for Symbolic Logic?I thank the audiences there for comments and feedback. I?d also like to thank Eli Dresner, Ran Lanzet, Sam Lebens, Hannes Leitgeb, Oron Shagrir, Stewart Shapiro, and Jack Woods for comments and discussion. This research was supported by the ISRAEL SCIENCE FOUNDATION (grant no. 1954/17).

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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