The Reality of Numbers A Physicalist's Philosophy of Mathematics

by Bigelow, John

• ISBN13: 9780198249573
• ISBN10: 0198249578
• Format: Hardcover
• Copyright: 1988-09-01
• Publisher: Clarendon Press

Summary

This book casts new light on mathematics through its consideration of metaphysical materialism. The author identifies natural, real and imaginary numbers and sets with specified physical properties and relations. However sets are construed numbers are not sets. Sets are important simply because they instantiate all the numbers and all the other properties and relations studied in mathematics. Set theory tempts us into misunderstanding the nature of mathematics; Bigelow challenges the myth that mathematicalobjects can be defined into existence. By reconstruing numbers as real, non-linguistic, physical properties or relations, mathematics can be drawn back from its sterile, abstract exile into the midst of the physical world to which we belong.

Table of Contents

Introduction	p. 1
Metaphysics
Mathematics and universals	p. 11
Recurrence	p. 18
Mathematics
Natural Numbers
Pebbles and Pythagoras	p. 31
Numbers as properties	p. 38
Numbers as paradigms	p. 45
Numbers as relations	p. 48
Numbering sets	p. 55
Real Numbers
Approximations	p. 58
Arithmetic and geometry	p. 62
Proportions	p. 66
Ratios	p. 71
Real numbers	p. 76
Complex Numbers
Imaginary numbers	p. 81
Complex proportions	p. 89
Sets
From universals to sets	p. 101
Sets and essences	p. 105
Sets and consistency	p. 110
Truth And Existence
The Problem
Functions and arguments	p. 121
Truth and essence	p. 128
The Fox paradox	p. 135
Wholes and Parts
Counterparts and accidents	p. 139
Property-instances	p. 143
Robinson's merger	p. 149
States of affairs	p. 154
Anyhow to Something
Categories of being	p. 158
The second-order Fox	p. 166
Platonism and necessity	p. 174
Bibliography	p. 179
Index	p. 189
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