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

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 mathematical objects 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.