Charles Chihara's new book develops and defends a structural view of the nature of mathematics, and uses it to explain a number of striking features of mathematics that have puzzled philosophers for centuries. The view is used to show that, in order to understand how mathematical systems are applied in science and everyday life, it is not necessary to assume that its theorems either presuppose mathematical objects or are even true. Chihara builds upon his previous work, in which he presented a new system of mathematics, the constructibility theory, which did not make reference to, or presuppose, mathematical objects. Now he develops the project further by analysing mathematical systems currently used by scientists to show how such systems are compatible with this nominalistic outlook. He advances several new ways of undermining the heavily discussed indispensability argument for the existence of mathematical objects made famous by W. V. Quine and Hilary Putnam. And Chihara presents a rationale for the nominalistic outlook that is quite different from those generally put forward, which he maintains have led to serious misunderstandings. A Structural Account of Mathematics will be required reading for anyone working in this field.

Introduction 1. Five Puzzles in Search of an Explanation 2. Geometry and Mathematical Existence 3. The Van Inwagen Puzzle 4. Structuralism 5. Platonism 6. Minimal Anti-Nominalism 7. The Constructibility Theory 8. Constructible Structures 9. Applications 10. If-Thenism 11. Field's Account of Mathematics and Metalogic Appendix A: Some Doubts about Hellman's Views Appendix B: Balaguer's Fictionalism

Charles S. Chihara , Department of Philosophy, University of California, Berkeley

`Review from previous edition This terrific contribution will promote discussion for and against its views. It has unusually full discussion of what makes "philosophy" of mathematics. It engages in extensive debates with other philosophers. And it has a wide range of examples from pure and applied mathematics.' Colin McLarty, Notre Dame Philosophical Reviews |d 02/09/2004