Does mathematics exist as an abstract realm, or can mathematical objects be grounded in the physical properties of the material world? John Bigelow, a philosopher known for his work in metaphysics, utilizes the framework of Armstrong's materialism to argue against the traditional view that mathematical entities are purely abstract or defined into existence. By identifying numbers and sets with concrete physical properties and relations, Bigelow attempts to bridge the gap between abstract mathematical theory and the observable physical universe.

Experts in the philosophy of mathematics recognize this text as a significant contribution to physicalist accounts of mathematical objects. Readers frequently note the technical density of the prose, which requires a strong background in both metaphysical theory and mathematical logic to fully appreciate the author's arguments.