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Philosophies of Mathematics

ISBN: 978-0-631-19543-6
240 pages
December 2001, Wiley-Blackwell
Philosophies of Mathematics (0631195432) cover image
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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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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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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  • Systematically presents both philosophical and mathematical aspects of the three central approaches to mathematics: logicism, intuitionism, and formalism.

  • Requires only that students have a basic familiarity with quantificational logic and very fundamental parts of set theory and analysis.

  • Comprehensive and accessible.
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"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 <!--end-->

"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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