Constructibility and Mathematical Existence

by Charles S. Chihara

Overview

This book is concerned with 'the problem of existence in mathematics'. It develops a mathematical system in which there are no existence assertions but only assertions of the constructibility of certain sorts of things. It explores the philosophical implications of such an approach in an examination of the writings of Field, Burgess, Maddy, Kitcher, and others.

Product Details

ISBN-13:	9780191520006
Publisher:	Oxford University Press
Publication date:	04/12/1990
Series:	Clarendon Paperbacks
Sold by:	Barnes & Noble
Format:	eBook
File size:	571 KB

About the Author

University of California, Berkeley

Table of Contents

PART I: THE CONSTRUCTIBILITY THEORY: The Problem of Existence in Mathematics; The Constructibility Quantifiers; Constructibility and Open-Sentences; The Deductive System; Cardinality and Number Theory; Measurable Quantities and Analysis. PART II: PHILOSOPHICAL DEVELOPMENTS: Mathematical Structuralism; Science Without Numbers; Why Burgess is a Moderate Realist; Maddy's Solution to the Problem of Reference; Kitcher's Ideal Agents; Deflationism and Mathematical Truth. Appendix; Field's Nominalistic Logical Theory.

Editorial Reviews

"Written in a lively, engaging style and is filled with penetrating analyses and careful thought. I recommend it to anyone with a serious interest in the philosophy of mathematics."—Mind

"An important book....It helps sharpen and deepen our understanding of some of the most interesting issues in the philosophy of mathematics, and it thereby pushes our subject forward."—Philosophia Mathematica

From the Publisher