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The Theory of Indistinguishables

A Search for Explanatory Principles Below the Level of Physics

  • Book
  • © 1981

Overview

Authors:
  1. A. F. Parker-Rhodes
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Part of the book series: Synthese Library (SYLI, volume 150)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Theory

    1. Front Matter

      Pages 1-1
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    2. Introduction

      • A. F. Parker-Rhodes
      Pages 3-17

    3. Semantic Theory of the Notation F

      • A. F. Parker-Rhodes
      Pages 18-38

    4. The Physical Relevance of Indistinguishables

      • A. F. Parker-Rhodes
      Pages 39-55

    5. Sort Theory — Axioms and Definitions

      • A. F. Parker-Rhodes
      Pages 56-74

    6. Sort Theory — Mappings

      • A. F. Parker-Rhodes
      Pages 75-92

    7. Representations of Initial Sorts

      • A. F. Parker-Rhodes
      Pages 93-105

    8. Representation of Superstruct Sorts

      • A. F. Parker-Rhodes
      Pages 106-126

  3. Application

    1. Front Matter

      Pages 127-127
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    2. Hypothesis and Principles

      • A. F. Parker-Rhodes
      Pages 129-138

    3. Events in the Void

      • A. F. Parker-Rhodes
      Pages 139-148

    4. The Texture of Space-Time

      • A. F. Parker-Rhodes
      Pages 149-166

    5. The Constitution of Matter

      • A. F. Parker-Rhodes
      Pages 167-179

    6. States of Particles

      • A. F. Parker-Rhodes
      Pages 180-196

    7. General Assessment

      • A. F. Parker-Rhodes
      Pages 197-210

  4. Back Matter

    Pages 211-216
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Keywords

About this book

It is widely assumed that there exist certain objects which can in no way be distinguished from each other, unless by their location in space or other reference-system. Some of these are, in a broad sense, 'empirical objects', such as electrons. Their case would seem to be similar to that of certain mathematical 'objects', such as the minimum set of manifolds defining the dimensionality of an R -space. It is therefore at first sight surprising that there exists no branch of mathematics, in which a third parity-relation, besides equality and inequality, is admitted; for this would seem to furnish an appropriate model for application to such instances as these. I hope, in this work, to show that such a mathematics in feasible, and could have useful applications if only in a limited field. The concept of what I here call 'indistinguishability' is not unknown in logic, albeit much neglected. It is mentioned, for example, by F. P. Ramsey [1] who criticizes Whitehead and Russell [2] for defining 'identity' in such a way as to make indistinguishables identical. But, so far as I can discover, no one has made any systematic attempt to open up the territory which lies behind these ideas. What we find, on doing so, is a body of mathematics, offering only a limited prospect of practical usefulness, but which on the theoretical side presents a strong challenge to conventional ideas.

Bibliographic Information

  • Book Title: The Theory of Indistinguishables

  • Book Subtitle: A Search for Explanatory Principles Below the Level of Physics

  • Authors: A. F. Parker-Rhodes

  • Series Title: Synthese Library

  • DOI: https://doi.org/10.1007/978-94-009-8401-1

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: D. Reidel Publishing Company, Dordrecht, Holland 1981

  • Hardcover ISBN: 978-90-277-1214-1Published: 30 November 1981

  • Softcover ISBN: 978-94-009-8403-5Published: 13 October 2011

  • eBook ISBN: 978-94-009-8401-1Published: 06 December 2012

  • Series ISSN: 0166-6991

  • Series E-ISSN: 2542-8292

  • Edition Number: 1

  • Number of Pages: XIV, 216

  • Topics: Philosophy of Science, Mathematical Logic and Foundations

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