A Structural Account of Mathematics

Első borító
Clarendon, 2004 - 380 oldal
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 Willard 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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Tartalomjegyzék

Introduction
1
1 Five Puzzles in Search of an Explanation
8
2 Geometry and Mathematical Existence
27
3 The van Inwagen Puzzle
49
4 Structuralism
62
5 Platonism
99
6 Minimal AntiNominalism
151
7 The Constructibility Theory
169
9 Applications
229
10 IfThenism
293
11 Fields Account of Mathematics and Metalogic
317
Appendix A Some Doubts About Hellmans Views
349
Appendix B Balaguers Fictionalism
356
Bibliography
363
Index
373
Copyright

8 Constructible Structures
218

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A szerzőről (2004)

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

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