Open Access
2017 Grades of Discrimination: Indiscernibility, Symmetry, and Relativity
Tim Button
Notre Dame J. Formal Logic 58(4): 527-553 (2017). DOI: 10.1215/00294527-2017-0007


There are several relations which may fall short of genuine identity, but which behave like identity in important respects. Such grades of discrimination have recently been the subject of much philosophical and technical discussion. This paper aims to complete their technical investigation. Grades of indiscernibility are defined in terms of satisfaction of certain first-order formulas. Grades of symmetry are defined in terms of symmetries on a structure. Both of these families of grades of discrimination have been studied in some detail. However, this paper also introduces grades of relativity, defined in terms of relativeness correspondences. This paper explores the relationships between all the grades of discrimination, exhaustively answering several natural questions that have so far received only partial answers. It also establishes which grades can be captured in terms of satisfaction of object-language formulas and draws connections with definability theory.


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Tim Button. "Grades of Discrimination: Indiscernibility, Symmetry, and Relativity." Notre Dame J. Formal Logic 58 (4) 527 - 553, 2017.


Received: 26 July 2013; Accepted: 20 March 2015; Published: 2017
First available in Project Euclid: 25 April 2017

zbMATH: 06803186
MathSciNet: MR3707650
Digital Object Identifier: 10.1215/00294527-2017-0007

Primary: 00A30
Secondary: 03C40 , 03C99

Keywords: equality-free model theory , grades of indiscernibility , grades of relativity , grades of symmetry , identity of indiscernibles , identity-free model theory

Rights: Copyright © 2017 University of Notre Dame

Vol.58 • No. 4 • 2017
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