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INVARIANCE CRITERIA AS META-CONSTRAINTS

Part of: Model theory Philosophical aspects of logic and foundations

Published online by Cambridge University Press:  02 December 2021

GIL SAGI
GIL SAGI*
Affiliation:
DEPARTMENT OF PHILOSOPHY UNIVERSITY OF HAIFA 199 ABA KHOUSHY AVE MT. CARMEL, HAIFA 3498838, ISRAEL E-mail: [email protected]
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Abstract

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.

Keywords

logical consequencelogical constantsinvariance criteriasemantic constraints

MSC classification

Primary: 03A05: Philosophical and critical
Secondary: 03C99: None of the above, but in this section
Type
Articles
Information
Bulletin of Symbolic Logic , Volume 28 , Issue 1 , March 2022 , pp. 104 - 132
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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