The Theory of Indistinguishables

A Search for Explanatory Principles Below the Level of Physics

  • Authors
  • A. F. Parker-Rhodes

Part of the Synthese Library book series (SYLI, volume 150)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Theory

    1. Front Matter
      Pages 1-1
    2. A. F. Parker-Rhodes
      Pages 3-17
    3. A. F. Parker-Rhodes
      Pages 18-38
    4. A. F. Parker-Rhodes
      Pages 39-55
    5. A. F. Parker-Rhodes
      Pages 56-74
    6. A. F. Parker-Rhodes
      Pages 75-92
    7. A. F. Parker-Rhodes
      Pages 93-105
    8. A. F. Parker-Rhodes
      Pages 106-126
  3. Application

    1. Front Matter
      Pages 127-127
    2. A. F. Parker-Rhodes
      Pages 129-138
    3. A. F. Parker-Rhodes
      Pages 139-148
    4. A. F. Parker-Rhodes
      Pages 149-166
    5. A. F. Parker-Rhodes
      Pages 167-179
    6. A. F. Parker-Rhodes
      Pages 180-196
    7. A. F. Parker-Rhodes
      Pages 197-210
  4. Back Matter
    Pages 211-216

About this book

Introduction

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.

Keywords

Bertrand Russell Interpretation cardinality classification coherence conditional corpus model nature notation opera physics reconstruction space time

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-009-8401-1
  • Copyright Information Springer Science+Business Media B.V. 1981
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-009-8403-5
  • Online ISBN 978-94-009-8401-1
  • About this book