This book investigates the ontological and epistemological status of mathematical objects, questioning how mathematical realism can be reconciled with the physical sciences. Penelope Maddy, a prominent philosopher of mathematics, utilizes her expertise in set theory and mathematical practice to construct a framework that addresses the traditional challenges of realism. She argues for a naturalistic approach that bridges the gap between abstract mathematical entities and their empirical applications, ultimately proposing a novel perspective on how mathematicians interact with their subject matter.

Experts frequently cite this work as a significant contribution to the philosophy of mathematics, particularly for its attempt to ground abstract concepts in actual mathematical practice. Readers often note the academic density of the prose, which requires a foundational understanding of both set theory and contemporary philosophical discourse.