Logicality and meaning

Research output: Contribution to journalArticlepeer-review


In standard model-Theoretic semantics, the meaning of logical terms is said to be fixed in the system while that of nonlogical terms remains variable. Much effort has been devoted to characterizing logical terms, those terms that should be fixed, but little has been said on their role in logical systems: on what fixing their meaning precisely amounts to. My proposal is that when a term is considered logical in model theory, what gets fixed is its intension rather than its extension. I provide a rigorous way of spelling out this idea, and show that it leads to a graded account of logicality: The less structure a term requires in order for its intension to be fixed, the more logical it is. Finally, I focus on the class of terms that are invariant under isomorphisms, as they render themselves more easily to mathematical treatment. I propose a mathematical measure for the logicality of such terms based on their associated Löwenheim numbers.

Original languageEnglish
Pages (from-to)133-159
Number of pages27
JournalReview of Symbolic Logic
Issue number1
StatePublished - 1 Mar 2018

Bibliographical note

Publisher Copyright:
© Association for Symbolic Logic 2018.


  • Löwenheim numbers
  • invariance criteria
  • meaning
  • model theory
  • phraseslogical constants

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Philosophy
  • Logic


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