New Directions in the Philosophy of Mathematics (Paperback)

~ Thomas Tymoczko (Editor) "We are still in the aftermath of the great foundationist controversies of the early twentieth century..." (more)
Key Phrases: simple empiricist picture, surveyable proof, heuristic falsifier, New York, Imre Lakatos, Bertrand Russell (more...)

Editorial Reviews

Product Description

The traditional debate among philosophers of mathematics is whether there is an external mathematical reality, something out there to be discovered, or whether mathematics is the product of the human mind. This provocative book, now available in a revised and expanded paperback edition, goes beyond foundationalist questions to offer what has been called a "postmodern" assessment of the philosophy of mathematics--one that addresses issues of theoretical importance in terms of mathematical experience. By bringing together essays of leading philosophers, mathematicians, logicians, and computer scientists, Thomas Tymoczko reveals an evolving effort to account for the nature of mathematics in relation to other human activities. These accounts include such topics as the history of mathematics as a field of study, predictions about how computers will influence the future organization of mathematics, and what processes a proof undergoes before it reaches publishable form.

This expanded edition now contains essays by Penelope Maddy, Michael D. Resnik, and William P. Thurston that address the nature of mathematical proofs. The editor has provided a new afterword and a supplemental bibliography of recent work.

Product Details

• Paperback: 448 pages
• Publisher: Princeton University Press; Rev Sub edition (January 12, 1998)
• Language: English
• ISBN-10: 0691034982
• ISBN-13: 978-0691034980
• Product Dimensions: 9 x 6.5 x 1.1 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (3 customer reviews)
• Amazon.com Sales Rank: #523,909 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

20 of 21 people found the following review helpful:

5.0 out of 5 stars provides insight into how mathematicians think, November 1, 2000

By A Customer

To most people, "philosophy of mathematics" probably sounds like the driest subject in the world. I admit that a typical person in the street would probably never want to read this book, but many people who would be put off by the title would find it fascinating.

The basic question is how we should think about mathematics. When we do mathematics, are we describing an independent reality, following arbitrary rules, building a social construct? One can ultimately say only so much about this particular question, but it leads off in many wonderful directions. To me, the highlight of this book is the article by Thurston, which provides a beautiful description of how mathematicians actually think about and do mathematics. It really rings true to me (I'm a mathematician too), and is much better than any other account I've ever seen.

In general, whenever people seriously discuss the philosophy of mathematics, they are likely to make revealing comments about their approach to the field. People who are curious about this (e.g., students considering studying mathematics, or anyone who has heard about the results of mathematics and wonders about the mindset behind them) should read the book. As a bonus, once they start reading the essays they'll rapidly start caring about the philosophical issues as well, even if they've never thought about them before.

15 of 17 people found the following review helpful:

5.0 out of 5 stars Philosophy of mathematics reconsidered, September 11, 2000

By	Gary L. Herstein (Prescott, AZ USA) - See all my reviews

After almost a century in which the attempt was made to reduce philosophy of mathematics to set theory, philosophers have begun to reconsider the traditional approaches. The Tymoczko volume provides a solid intro to these new approaches, that is both readable and insightful. A background in formal logic, or traditional philosophy of mathematics, is not presupposed, as there are basic essays that should get the reader up to speed on the terminology. Nor does one have to be a mathematician to appreciate the thoughts presented. At the same time, I don't believe any mathematician would be offended or alarmed by the presentations of this book.

Ultimately, there is no final consensus offered. Rather, the topic is reinvigorated with a collection of fresh approaches that do not falsify the experience of mathematics by trying to reduce it to something else.

11 of 40 people found the following review helpful:

5.0 out of 5 stars I suggest a closely related book, January 26, 1998

By	G. J. Chaitin (Yorktown Heights, NY USA) - See all my reviews (REAL NAME)

Hi, I'm one of the contributors to Tymoczko's anthology, and I would like to suggest a related book on the quasi-empirical view of mathematics. That's my book "The Limits of Mathematics" just published by Springer Verlag. Together these two books make a nice set. Greg Chaitin, IBM Research