This book is concerned with `the problem of existence in mathematics'. It develops a mathematical system in which there are no existence assertions but only assertions of the constructibility of certain sorts of things. It explores the philosophical implications of such an approach through an examination of the writings of Field, Burgess, Maddy, Kitcher, and others.
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
Brian Vickers, Zurich; founding President of the International Society for the History of Rhetoric) Vickers, Brian (Professor of English and Renaissance Literature, Professor of English and Renaissance Literature, Swiss Federal Institute of Technology
H. C. G. Matthew, Oxford) Matthew, H. C. G. (late Professor of Modern History, University of Oxford, and Fellow, late Professor of Modern History, University of Oxford, and Fellow, St Hugh's College
J. L. Austin, University of Oxford) Austin, J. L. (late White's Professor of Moral Philosophy, late White's Professor of Moral Philosophy, J. I. Austin, J. O. Urmson, G. J. Warnock, Geoffrey J. Warnock, James O. Urmson
Ellen T. Harris, University of Chicago) Harris, Ellen T. (Chairman of the Music Department and Professor of Music, Chairman of the Music Department and Professor of Music