## Notre Dame Journal of Formal Logic

### Grades of Discrimination: Indiscernibility, Symmetry, and Relativity

Tim Button

#### Abstract

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.

#### Article information

Source
Notre Dame J. Formal Logic, Volume 58, Number 4 (2017), 527-553.

Dates
Accepted: 20 March 2015
First available in Project Euclid: 25 April 2017

https://projecteuclid.org/euclid.ndjfl/1493085740

Digital Object Identifier
doi:10.1215/00294527-2017-0007

Mathematical Reviews number (MathSciNet)
MR3707650

Zentralblatt MATH identifier
06803186

#### Citation

Button, Tim. Grades of Discrimination: Indiscernibility, Symmetry, and Relativity. Notre Dame J. Formal Logic 58 (2017), no. 4, 527--553. doi:10.1215/00294527-2017-0007. https://projecteuclid.org/euclid.ndjfl/1493085740

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