Philosophies of Mathematics / Edition 1

Philosophies of Mathematics / Edition 1

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by Alexander L. George, Daniel Velleman
     
 

During the first few decades of the twentieth century, philosophers and mathematicians mounted a sustained effort to clarify the nature of mathematics. This led to considerable discord, even enmity, and yielded fascinating and fruitful work of both a mathematical and a philosophical nature. It was one of the most exhilarating intellectual adventures of the century,

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Overview

During the first few decades of the twentieth century, philosophers and mathematicians mounted a sustained effort to clarify the nature of mathematics. This led to considerable discord, even enmity, and yielded fascinating and fruitful work of both a mathematical and a philosophical nature. It was one of the most exhilarating intellectual adventures of the century, pursued at an extraordinarily high level of acuity and imagination. Its legacy principally consists of three original and finely articulated programs that seek to view mathematics in the proper light: logicism, intuitionism, and finitism. Each is notable for its symbiotic melding together of philosophical vision and mathematical work: the philosophical ideas are given their substance by specific mathematical developments, which are in turn given their point by philosophical reflection.

This book provides an accessible, critical introduction to these three projects as it describes and investigates both their philosophical and their mathematical components.

Solutions manual is available upon request.

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Product Details

ISBN-13:
9780631195443
Publisher:
Wiley
Publication date:
12/11/2001
Edition description:
New Edition
Pages:
244
Product dimensions:
6.00(w) x 9.00(h) x 0.68(d)

Table of Contents

Preface.

1. Introduction.

2. Logicism.

3. Set Theory.

4. Intuitionism.

5. Intuitionistic Mathematics.

6. Finitism.

7. The Incompleteness Theorems.

8. Coda.

References.

Index.

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