Invariance and Definability, with and without Equality

Notre Dame Journal of Formal Logic 59 (1):109-133 (2018)
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Abstract

The dual character of invariance under transformations and definability by some operations has been used in classical works by, for example, Galois and Klein. Following Tarski, philosophers of logic have claimed that logical notions themselves could be characterized in terms of invariance. In this article, we generalize a correspondence due to Krasner between invariance under groups of permutations and definability in L∞∞ so as to cover the cases that are of interest in the logicality debates, getting McGee’s theorem about quantifiers invariant under all permutations and definability in pure L∞∞ as a particular case. We also prove some optimality results along the way, regarding the kinds of relations which are needed so that every subgroup of the full permutation group is characterizable as a group of automorphisms.

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Author Profiles

Fredrik Engström
University of Gothenburg
Denis Bonnay
Université Paris Nanterre

Citations of this work

What Are Structural Properties?†.Johannes Korbmacher & Georg Schiemer - 2018 - Philosophia Mathematica 26 (3):295-323.
Grades of Discrimination: Indiscernibility, Symmetry, and Relativity.Tim Button - 2017 - Notre Dame Journal of Formal Logic 58 (4):527-553.

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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.
What Does It Mean to Say That Logic is Formal?John MacFarlane - 2000 - Dissertation, University of Pittsburgh
Logicality and Invariance.Denis Bonnay - 2006 - Bulletin of Symbolic Logic 14 (1):29-68.
Logical operations.Vann McGee - 1996 - Journal of Philosophical Logic 25 (6):567 - 580.

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