{
  "id": "1408.1672",
  "version": "v2",
  "published": "2014-08-07T18:14:09.000Z",
  "updated": "2015-06-12T13:28:55.000Z",
  "title": "Grades of Discrimination: Indiscernibility, symmetry, and relativity",
  "authors": [
    "Tim Button"
  ],
  "comment": "Minor changes: a table has been added to section 2 (for user reference), and the identity-free version of Beth-Svenonius in section 6 gets a slightly nicer treatment",
  "categories": [
    "math.LO"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-07T18:14:09.000Z",
      "abstract": "Grades of discrimination may fall short of genuine identity, but they behave like identity in important respects. Philosophers of mathematics and physics have recently investigated these grades of discrimination from a philosophical and technical perspective. This paper aims to complete the 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 (see Casanovas et al. 1996). 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 Svenonius's Theorem and related results.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-06-12T13:28:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "00A30",
      "03C07",
      "03C40",
      "03A10"
    ],
    "keywords": [
      "discrimination",
      "relativity",
      "indiscernibility",
      "first-order formulas",
      "paper aims"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.1672B"
    }
  }
}