Logicality and model classes

Bulletin of Symbolic Logic 27 (4):385-414 (2021)
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Abstract

We ask, when is a property of a model a logical property? According to the so-called Tarski–Sher criterion this is the case when the property is preserved by isomorphisms. We relate this to model-theoretic characteristics of abstract logics in which the model class is definable. This results in a graded concept of logicality in the terminology of Sagi [46]. We investigate which characteristics of logics, such as variants of the Löwenheim–Skolem theorem, Completeness theorem, and absoluteness, are relevant from the logicality point of view, continuing earlier work by Bonnay, Feferman, and Sagi. We suggest that a logic is the more logical the closer it is to first order logic. We also offer a refinement of the result of McGee that logical properties of models can be expressed in $L_{\infty \infty }$ if the expression is allowed to depend on the cardinality of the model, based on replacing $L_{\infty \infty }$ by a “tamer” logic.

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Author Profiles

Juliette Kennedy
University of Helsinki
Jouko A Vaananen
University of Helsinki

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References found in this work

What Are Logical Notions?Alfred Tarski - 1986 - History and Philosophy of Logic 7 (2):143-154.
Nominalist Platonism.George Boolos - 1985 - Philosophical Review 94 (3):327-344.
The Higher Infinite.Akihiro Kanamori - 2000 - Studia Logica 65 (3):443-446.
Philosophy of Logic.Willard V. O. Quine - 1986 - Philosophy 17 (3):392-393.

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