Abstract

Maddy’s book is an examination of an important question for the philosophy of mathematics: what justifies the axioms of set theory? In part 1, entitled “The Problem,” Maddy provides a summary of the philosophical and mathematical beginnings of set theory and highlights the importance that certain questions play in current debates about the foundations of the theory. Part 2, “Realism,” reviews three versions of mathematical realism and gives reasons for abandoning these views. Part 3, “Naturalism,” furnishes a look at Maddy’s new philosophy of mathematics, Mathematical Naturalism, and explains the way it diagnoses the problem of justifying new axioms.