Chihara here develops a mathematical system in which there are no existence assertions but only assertions of the constructibility of certain sorts of things. He utilizes this system in the analysis of the nature of mathematics, and discusses many recent works in the philosophy of mathematics from the viewpoint of the constructibility theory developed. This innovative analysis will appeal to mathematicians and philosophers of logic, mathematics, and science.
`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
'the book is written in a lively, engaging style and is filled with penetrating analyses and careful thought ... I recommend it to anyone with a serious interest in the philosophy of mathematics.'
Stewart Shapiro, Ohio State University, Mind, Vol. 101, No. 402, April 1992
'I regard this as an important book, for, in presenting the details of a linguistic modal interpretation of much of scientifically applicable mathematics, it helps sharpen and deepen our understanding of some of the most interesting issues in the philosophy of mathematics, and it thereby pushes our subject forward.
Geoffrey Hellman, Philosophia Mathematica, Series III, 1993
'an important work in the philosophy of mathematics, well deserving of more careful study and analysis than there has been room for here'
John P. Burgess, Princeton University, The Philosophical Review, Vol. 101, No. 4, (October 1992)
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.