A Structural Account of Mathematics
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A Structural Account of Mathematics

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ISBN-13:
9780199267538
Einband:
Buch
Erscheinungsdatum:
01.11.2003
Seiten:
400
Autor:
Charles S. Chihara
Gewicht:
721 g
Format:
242x168x26 mm
Sprache:
Englisch
Beschreibung:

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 waysof undermining the Platonic view of mathematics. Anyone working in the field will find much to reward and stimulate them here.
Charles Chihara's 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. He also advances several new ways of undermining the Platonic view of mathematics.
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 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 Willard 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.