The Theory of Indistinguishables

1. Front Matter

   Pages i-xiv

   PDF

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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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.

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

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