Synopses & Reviews
David Corfield provides a variety of innovative approaches to research in the philosophy of mathematics. His study ranges from an exploration of whether computers producing mathematical proofs or conjectures are doing real mathematics to the use of analogy; the prospects for a Bayesian confirmation theory; the notion of a mathematical research program; and the ways in which new concepts are justified. This highly original book will challenge philosophers as well as mathematicians to develop the broadest and most complete philosophical resources for research in their disciplines.
Review
"...this is a fine book. Recommended." Choice
Review
"This is an important book that I would recommend to anybody interested in practice-oriented philosophy of mathematics." Mathematical Reviews
Review
"...Corfield's book can be greeted as a welcome addition to an emerging discussion." MAA Reviews, Dennis Lomas
Synopsis
In this ambitious study, David Corfield sets out a variety of approaches to new thinking about the philosophy of mathematics, and challenges both philosophers and mathematicians to develop the broadest and richest philosophical resources for work in their disciplines.
Synopsis
Corfield sets out a variety of approaches to new thinking about the philosophy of mathematics.
About the Author
David Corfield holds a Junior Lectureship in Philosophy of Science at the University of Oxford.
Table of Contents
Preface; 1. Introduction: a role for history; Part I. Human and Artificial Mathematicians: 2. Communicating with automated theorem provers; 3. Automated conjecture formation; 4. The role of analogy in mathematics; Part II. Plausibility, Uncertainty and Probability: 5. Bayesianism in mathematics; 6. Uncertainty in mathematics and science; Part III. The Growth of Mathematics: 7. Lakatos's philosophy of mathematics; 8. Beyond the methodology of mathematical research programmes; 9. The importance of mathematical conceptualisation; Part IV. The Interpretation of Mathematics: 10. Higher dimensional algebra; Appendix; Bibliography; Index.