A Structural Account of Mathematics
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A Structural Account of Mathematics

 Taschenbuch
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ISBN-13:
9780199228072
Einband:
Taschenbuch
Erscheinungsdatum:
01.07.2007
Seiten:
394
Autor:
Charles S. Chihara
Gewicht:
553 g
Format:
234x156x21 mm
Sprache:
Englisch
Beschreibung:

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 presents 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 ofundermining the Platonic view of mathematics. Anyone working in the field will find much to reward and stimulate them here.