• PART I: THE CONSTRUCTIBILITY THEORY: The Problem of Existence in Mathematics; The Constructibility Quantifiers; Constructibility and Open-Sentences; The Deductive System; Cardinality and Number Theory; Measurable Quantities and Analysis. PART II: PHILOSOPHICAL DEVELOPMENTS: Mathematical Structuralism; Science Without Numbers; Why Burgess is a Moderate Realist; Maddy's Solution to the Problem of Reference; Kitcher's Ideal Agents; Deflationism and Mathematical Truth. Appendix; Field's Nominalistic Logical Theory.

`More than half of this important book is devoted to extended, largely informal discussions of just about everybody engaged in post-Quinean philosophy of mathematics ... Especially delightful are Chihara's exchanges with all or almost all of these philosophers in the form of personal correspondence.'Review of Metaphysics