Logical Operations and Invariance

Journal of Philosophical Logic 36 (1):33-60 (2007)
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Abstract

I present a notion of invariance under arbitrary surjective mappings for operators on a relational finite type hierarchy generalizing the so-called Tarski-Sher criterion for logicality and I characterize the invariant operators as definable in a fragment of the first-order language. These results are compared with those obtained by Feferman and it is argued that further clarification of the notion of invariance is needed if one wants to use it to characterize logicality.

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Citations of this work

Logicality and Invariance.Denis Bonnay - 2006 - Bulletin of Symbolic Logic 14 (1):29-68.
Logicality and Meaning.Gil Sagi - 2018 - Review of Symbolic Logic 11 (1):133-159.
Tarski's Thesis.Gila Sher - 2008 - In Douglas Patterson (ed.), New Essays on Tarski and Philosophy. Oxford University Press. pp. 300--339.
Isomorphism Invariance and Overgeneration.Owen Griffiths & A. C. Paseau - 2016 - Bulletin of Symbolic Logic 22 (4):482-503.
Applied Logic Without Psychologism.Gregory Wheeler - 2008 - Studia Logica 88 (1):137-156.

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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.
On a Generalization of Quantifiers.Andrzej Mostowski - 1957 - Fundamenta Mathematicae 44 (2):12--36.
Logical Operations.Vann McGee - 1996 - Journal of Philosophical Logic 25 (6):567 - 580.
Logic, Logics, and Logicism.Solomon Feferman - 1999 - Notre Dame Journal of Formal Logic 40 (1):31-54.

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