A Structural Account of Mathematics [Hardcover]

Charles Chihara's new book develops 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. In particular, this perspective allows Chihara to show that, in order to understand how mathematical systems are applied in science, it is not necessary to assume that its theorems either presuppose mathematical objects or are even true. He also advances several new ways of undermining the Platonic view of mathematics. Anyone working in the field will find much to reward and stimulate them here.

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

The book has a clear structure and is very well written. Apart from the themes described here, the book contains a wealth of material. Throughout the book many positions relevant to the debate between realists and anti-realists are discussed. It is impossible in a short space to do justice to all the points made in this book. Suffice it to say that it certainly makes a substantial contribution to the debate on realism in mathematics and is a 'must read' for anyone interested in this debate. --International Studies in the Philosophy of Science