Thinking about Mathematics: The Philosophy of Mathematics

By Stewart Shapiro

This unique book by Stewart Shapiro looks at a range of philosophical issues and positions concerning mathematics in four comprehensive sections. Part I describes questions and issues about mathematics that have motivated philosophers since the beginning of intellectual history. Part II is an historical survey, discussing the role of mathematics in the thought of such philosophers as Plato, Aristotle, Kant, and Mill. Part III covers the three major positions held throughout the twentieth century: the idea that mathematics is logic (logicism), the view that the essence of mathematics is the rule-governed manipulation of characters (formalism), and a revisionist philosophy that focuses on the mental activity of mathematics (intuitionism). Finally, Part IV brings the reader up-to-date with a look at contemporary developments within the discipline.

This sweeping introductory guide to the philosophy of mathematics makes these fascinating concepts accessible to those with little background in either mathematics or philosophy.

• Format: Paperback
• Language: English
• ISBN: 0192893068
• ISBN13: 9780192893062
• Release Date: October 2000
• Publisher: Oxford University Press
• Length: 328 Pages
• Weight: 0.96 lbs.
• Dimensions: 0.7" x 5.4" x 8.4"

Customer Reviews

Wonderful Book

I recommend this book to all that are interested in the philosophy of mathematics that have only a minimal background in both. It clearly explains all of the debates that exist in the philosophy of mathematics and the major schools of it. Read this book.

Excellent

An excellent book that I recommend to readers interested on mathematical philosophy who are not specialists. A nice difference with other books covering the topic is that no term is considered known so the reader does not have to be accompanied with a philosophy encyclopedia. Needless to say that concepts and ideas are clearly exposed. Congratulations to Prof. Shapiro.

A Solid Introduction

Anybody who's interested in why mathematics might have the least bit to do with philosophy will be interested in this book. To many the philosophy of mathematics may seem too specialized and peripheral to be of much interest. But such is not the case. The philosophy of math is intricately intertwined with many of the classic epistemological questions that I have never seen satisfactory answers to. This book will force you to think about things you have never considered before. Why does mathematics 'just happen' to describe empirical studies so well if mathematics is solely logical and in the head? Or is mathematics empirical and merely charading as necessary logical truth? These questions will be brought up in the book and the different answers given from the different philisophical sides. Some of the book is a little dense and may be skimmed. He does go into detail a bit much in some places and the non technical reader will be lost. But Shapiro usually does do a good job of summarizing complex thoughts. This book whetted my appetite for more and I plan on continuing thinking about these things and hopefully take some classes in mathematical logic and philosophy.

Incredibly clear

This is the best introduction to the philosophy of mathematics I've come across. The concepts presented are clear, up to date, and presented with a minimum of formulas and symbols. The author has an easy going style that will just pull you into this fascinating topic.

Superb introduction to the philosophy of mathematics!

In this introductory level text Prof. Shapiro has presented a thorough introduction to the philosophy of mathematics. Not only does he discuss the three most fundamental positions in the field, but he also provides insight into more recent developments. I would highly suggest this work to anyone interested in having a solid understanding of this issues at stake in the philosophy of mathematics. Along with Paul Benacerraf and Hillary Putnam's book of philosophy of mathematics readings this is a must have!