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LOGICALITY AND MEANING

Published online by Cambridge University Press:  16 January 2018

GIL SAGI
GIL SAGI*
Affiliation:
Department of Philosophy, University of Haifa
*
*DEPARTMENT OF PHILOSOPHY UNIVERSITY OF HAIFA HAIFA, ISRAEL E-mail: [email protected]
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Abstract

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.

Keywords

03A05logical constantsLöwenheim numbersinvariance criteriamodel theorymeaning
Type
Research Article
Information
The Review of Symbolic Logic , Volume 11 , Issue 1 , March 2018 , pp. 133 - 159
Copyright
Copyright © Association for Symbolic Logic 2018 

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