In his long-awaited new edition of Philosophy of Mathematics, James Robert Brown tackles important new as well as enduring questions in the mathematical sciences. Can pictures go beyond being merely suggestive and actually prove anything? Are mathematical results certain? Are experiments of any real value?
This clear and engaging book takes a unique approach, encompassing non-standard topics such as the role of visual reasoning, the importance of notation, and the place of computers in mathematics, as well as traditional topics such as formalism, Platonism, and constructivism. The combination of topics and clarity of presentation make it suitable for beginners and experts alike. The revised and updated second edition of Philosophy of Mathematics contains more examples, suggestions for further reading, and expanded material on several topics including a novel approach to the continuum hypothesis.
Table of Contents
Preface and Acknowledgements 1. Introduction: The Mathematical Image 2. Platonism 3. Picture-Proofs and Platonism 4. What is Applied Mathematics? 5. Hilbert and Gödel 6. Knots and Notation 7. What is a Definition? 8. Constructive Approaches 9. Proofs, Pictures and Procedures in Wittgenstein 10. Computation, Proof and Conjecture 11. How to Refute the Continuum Hypothesis 12. Calling the Bluff. Notes. Bibliography. Index
"Extraordinary! A brilliant, important book. Summing up: Highly recommended."
—M. Schiff, CHOICE
"…The book has been written in a very clear, lively way, it is a pleasure to read. It is very accessible, even entertaining, and the author is very good in explaining issues without technicalities. … Summarizing: a very elegant, accessible and up-to-date book on the philosophy of mathematics, not only very appropriate for beginners, but also a must for experts."
—H.C.M. de Swart, Zentralblatt MATH 1171
Praise for the First Edition:
"This book is a breath of fresh air for undergraduate philosophy of mathematics. Very accessible and even entertaining, Brown explains most of the issues without technicalities. "
—Janet Folina, Macalester College
"A wonderful introduction to the philosophy of mathematics. It's lively, accessible, and, above all, a terrific read. It would make an ideal text for an undergraduate course on the philosophy of mathematics; indeed, I recommend it to anyone interested in the philosophy of mathematics — even specialists in the area can learn from this book."
—Mark Colyvan, University of Sydney