Towards a Philosophy of Real Mathematics [Hardcover]

David Corfield (Author)

Book Description

ISBN-10: 0521817226 | ISBN-13: 978-0521817226 | Publication Date: June 16, 2003

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.

Editorial Reviews

Review

"...this is a fine book. Recommended." Choice

"This is an important book that I would recommend to anybody interested in practice-oriented philosophy of mathematics." Mathematical Reviews

"...Corfield's book can be greeted as a welcome addition to an emerging discussion." MAA Reviews, Dennis Lomas

Book Description

In this ambitious study, David Corfield sets out a variety of approaches to new thinking about the philosophy of mathematics, ranging 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 programme, and the ways in which new concepts are justified. His highly original book challenges both philosophers and mathematicians to develop the broadest and richest philosophical resources for work in their disciplines.

See all Editorial Reviews

Product Details

• Hardcover: 300 pages
• Publisher: Cambridge University Press (June 16, 2003)
• Language: English
• ISBN-10: 0521817226
• ISBN-13: 978-0521817226
• Product Dimensions: 9.3 x 6.4 x 0.9 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #3,928,786 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

14 of 14 people found the following review helpful:

5.0 out of 5 stars A philosopher with a real interest in mathematics, January 19, 2004

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"bernhard_schoelkopf" - See all my reviews

This review is from: Towards a Philosophy of Real Mathematics (Hardcover)

Philosophy of math has long been obsessed with questions like the existence of numbers and the set-theoretic or logical foundation of the discipline. A century ago, top level mathematicians like Weyl, Hilbert, and Brouwer were engaged in some of these problems. But today's mathematics has largely moved on to other issues. This book is an attempt for philosophy to catch up with these developments.
I have to admit that I was less interested in the chapters on automated theorem proving and conjecture formation. So I read the introductory chapter (which should be comprehensible for a general audience) and then jumped to the later chapters which I find particularly intriguing. In these chapters, Corfield touches several modern areas of mathematics (such as algebraic topology, category theory). These are fields that do not lend themselves well to armchair philosophy, and it is reassuring to know that Corfield has a degree in math from Cambridge University. At times, the book gets technical, not in terms of formulas, but in terms of advanced mathematical concepts that are being discussed. Still, the gist gets conveyed. This makes the book an excellent read.

For those interested, there is a long review of the book on John Baez' home page, under "This Week's Finds in Mathematical Physics (Week 198)".

B. Schölkopf