The Reality of Numbers: A Physicalist's Philosophy of Mathematics

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Overview

Challenging the myth that mathematical objects can be defined into existence, Bigelow here employs Armstrong's metaphysical materialism to cast new light on mathematics. He identifies natural, real, and imaginary numbers and sets with specified physical properties and relations and, by so doing, draws mathematics back from its sterile, abstract exile into the midst of the physical world.

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Product Details

  • ISBN-13: 9780198249573
  • Publisher: Oxford University Press, USA
  • Publication date: 12/28/1994
  • Pages: 202
  • Product dimensions: 5.60 (w) x 8.60 (h) x 0.80 (d)

Table of Contents

Introduction 1
Part I Metaphysics
1. Mathematics and universals 11
2. Recurrence 18
Part II Mathematics
II(a) Natural Numbers
3. Pebbles and Pythagoras 31
4. Numbers as properties 38
5. Numbers as paradigms 45
6. Numbers as relations 48
7. Numbering sets 55
II(b) Real Numbers
8. Approximations 58
9. Arithmetic and geometry 62
10. Proportions 66
11. Ratios 71
12. Real numbers 76
II(c) Complex Numbers
13. Imaginary numbers 81
14. Complex proportions 89
II(d) Sets
15. From universals to sets 101
16. Sets and essences 105
17. Sets and consistency 110
Part III Truth And Existence
III(a) The Problem
18. Functions and arguments 121
19. Truth and essence 128
20. The Fox paradox 135
III(b) Wholes and Parts
21. Counterparts and accidents 139
22. Property-instances 143
23. Robinson's merger 149
24. States of affairs 154
III(c) Anyhow to Something
25. Categories of being 158
26. The second-order Fox 166
27. Platonism and necessity 174
Bibliography 179
Index 189
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