A Structural Account of Mathematics

Paperback | May 17, 2007

byCharles S. Chihara

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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 areapplied 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 howsuch 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 nominalisticoutlook 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.

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From the Publisher

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 areapplied in science and everyday life, it is n...

Charles S. Chihara is in the Department of Philosophy, University of California, Berkeley.

other books by Charles S. Chihara

Format:PaperbackDimensions:400 pages, 9.21 × 6.14 × 0.83 inPublished:May 17, 2007Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199228078

ISBN - 13:9780199228072

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Table of Contents

Introduction1. Five Puzzles in Search of an Explanation2. Geometry and Mathematical Existence3. The Van Inwagen Puzzle4. Structuralism5. Platonism6. Minimal Anti-Nominalism7. The Constructibility Theory8. Constructible Structures9. Applications10. If-Thenism11. Field's Account of Mathematics and MetalogicAppendix A: Some Doubts about Hellman's ViewsAppendix B: Balaguer's Fictionalism

Editorial Reviews

`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 andapplied mathematics.'Colin McLarty, Notre Dame Philosophical Reviews