Philosophies of Mathematics / Edition 1

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Overview

This book provides an accessible, critical introduction to the three main approaches that dominated work in the philosophy of mathematics during the twentieth century: logicism, intuitionism and formalism.

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Editorial Reviews

From the Publisher

"George and Velleman manage to accomplish a difficult feat: on the one hand, they explain, clearly and rigorously, a number of highly technical accomplishments of twentieth-century mathematical logic, making plain the relevance of the mathematical work for philosophy; yet, on the other, they presuppose little more from their readers than a first course in basic logic. The examples they choose to explicate their points are carefully selected and illuminating. This is a splendid book." William Ewald, University of Pennsylvania

"This book includes just the right mix of helpful historical exposition and clear, tight philosophical argument. It is extremely well written and does an excellent job of making difficult material accessible. There is nothing else currently available that discusses in a single volume such a wide range of important material. The authors are to be commended for a job well done." Andrew Irvine, University of British Columbia

"This is a well-written, informative and innovative introduction to philosophies of mathematics. It is a very valuable addition to the existing literature." Wilfried Sieg, Carnegie Mellon University

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Product Details

  • ISBN-13: 9780631195443
  • Publisher: Wiley, John & Sons, Incorporated
  • Publication date: 12/11/2001
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 244
  • Sales rank: 1,363,238
  • Product dimensions: 6.00 (w) x 9.00 (h) x 0.68 (d)

Meet the Author

Alexander George is Associate Professor of Philosophy at Amherst College. He is editor of Reflections on Chomsky (1989) Western State Terrorism (1991) and Mathematics and Mind (1994).

Daniel J. Velleman is Professor of Mathematics at Amherst College. He is author of How to Prove It: A Structured Approach (1994) and co-author of Which Way Did the Bicycle Go? And Other Intriguing Mathematical Mysteries (with Joseph Konhauser and Stan Wagon, 1996).

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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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Customer Reviews

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  • Anonymous

    Posted January 9, 2006

    Great reading for a limited audience

    George and Velleman do an excellent job explaining various schools of thought, with each separate school explained in terms of the historical problems that motivated its foundation. Of particular interest is a chapter on what intuitionist analysis might look like, and a very clear proof of Godel's incompleteness theorem. Each chapter ends with interesting but entirely optional exercises. My one complaint would be that the authors presume a rather peculiar audience: they expect readers to be completely familiar with first-order logic notation, but introduce very basic concepts from analysis to motivate most of the examples in the book. Most math students will be far more comfortable with the latter than the former, I imagine. This suggests that the book is targeted primarily at philosophy students, but if so, why spend so much time on the theorems of intuitionistic mathematics?

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