Customer Reviews

New Directions in the Philosophy of Mathematics

5 star:		(3)
4 star:		(0)
3 star:		(0)
2 star:		(0)
1 star:		(0)

 

 

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.

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.

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