Title:
Constructibility and mathematical existence
Personal Author:
Publication Information:
Oxford : Clarendon Press, 1990
ISBN:
9780198248170
Available:*
Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000000655377 | QA8.4 C45 1090 | Open Access Book | Book | Searching... |
On Order
Summary
Summary
Chihara here develops a mathematical system in which there are no existence assertions but only assertions of the constructibility of certain sorts of things. He utilizes this system in the analysis of the nature of mathematics, and discusses many recent works in the philosophy of mathematics from the viewpoint of the constructibility theory developed. This innovative analysis will appeal to mathematicians and philosophers of logic, mathematics, and science.
Author Notes
Charles S. Chihara is a Professor of Philosophy at University of California at Berkeley.
Table of Contents
| constructibility And Mathematical Existence | p. i |
| Constructibility and Mathematical Existence | p. iii |
| Preface | p. vii |
| Acknowledgements | p. xi |
| Part I the Constructibility Theory | p. 1 |
| 1 The Problem of Existence in Mathematics | p. 3 |
| 2 The Constructibility Quantifiers | p. 24 |
| 3 Constructibility and Open-Sentences | p. 40 |
| 4 The Deductive System | p. 55 |
| 5 Cardinality and Number Theory | p. 80 |
| 6 Measurable Quantities and Analysis | p. 95 |
| Part II Philosophical Developments | p. 122 |
| 7 Mathematical Structuralism | p. 125 |
| 8 Science Without Numbers | p. 146 |
| 9 Why Burgess is a Moderate Realist | p. 181 |
| 10 Maddy's Solution to the Problem of Reference | p. 194 |
| 11 Kitcher's Ideal Agents | p. 216 |
| 12 Deflationism and Mathematical Truth | p. 251 |
| Appendix Field's Nominalistic Logical Theory | p. 261 |
| Bibliography | p. 273 |
| Index | p. 279 |
