Philosophies of Mathematics
December 2001, Wiley-Blackwell
3. Set Theory.
5. Intuitionistic Mathematics.
7. The Incompleteness Theorems.
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
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).
- 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.
"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