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Thinking about Mathematics: The Philosophy of Mathematics 1st Edition

4.2 out of 5 stars 17 customer reviews
ISBN-13: 978-0192893062
ISBN-10: 0192893068
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  • Thinking about Mathematics: The Philosophy of Mathematics
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Editorial Reviews

Review

"Stewart Shapiro admirably provides an accessible introduction to contemporary thinking in mathematics, while avoiding caricature of the technicalities. His ease with the subject and lucid style makes this book a succinct introduction to a fascinating intellectual discipline." Times Literary Supplement

About the Author


Stewart Shapiro is Professor of Philosophy at Ohio State University at Newark and Professorial Fellow in the Department of Logic and Metaphysics at the University of St Andrews, Scotland.
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Product Details

  • Paperback: 328 pages
  • Publisher: Oxford University Press; 1 edition (October 5, 2000)
  • Language: English
  • ISBN-10: 0192893068
  • ISBN-13: 978-0192893062
  • Product Dimensions: 8.2 x 0.7 x 5.2 inches
  • Shipping Weight: 1.1 pounds (View shipping rates and policies)
  • Average Customer Review: 4.2 out of 5 stars  See all reviews (17 customer reviews)
  • Amazon Best Sellers Rank: #419,047 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

Format: Paperback
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.
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Format: Paperback
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!
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By A Customer on October 5, 2002
Format: Paperback Verified Purchase
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.
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I am a reader with some basic background in logic and philosophy of language. Despite this background, I find Shapiro terribly difficult to read. For example, I read the section on Kant three times and am still not sure whether I understood anything. There must be simpler ways of explaining the material he presents.

So this might be a great book for someone with a solid backgrounds in both philosophy and mathematics who wants to know more about questions at the crossroads of both fields. However, I absolutely do not recommend it as an introduction to these ideas.
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Format: Paperback Verified Purchase
This is a great book. It gives a comprehensive view of what math is really about, not about how to do math. It covers the fundamental issues as to the nature of mathematical entities and related problems all the way from ancient times to the present. It also engages some thorny problems concerning the discipline, all in fluent unobtrusive language that makes understanding easier than usual, without sacrificing depth or breath. I recommend it to anyone who, like myself, has struggled for a long time to grasp the significance, importance and limitations of math. As far as my needs are concerned, this is the best book on the subject that I have come across.
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Format: Paperback
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.
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Format: Paperback
The amazing thing about the little handful of books on Mathematical Philosophy--2 by Shapiro, Frege, Russell and of course Benacerraf and Putnam's classic, is the paucity of literature in this key field!
Some will say that mathematical philosophy, or the closely related philosophy of mathematics, only began in the 1980's in earnest. But reading the "big 5" shows threads going back to antiquity. The field is far from settled, and the two aspects--the philosophy of math itself, and the closely related field of applying math and logic TO other branches of philosophy, has enough active journalized information in the mid 2014+ years to fill 50 volumes. Since thousands have been written in mainline philosophy, and even the philosophy of science as well as logic, this is not without surprise and mystery.

The good news is that an invested, energetic reader can pick up this handful of keys and be in the top percent of folks on the planet with a good foundation! This is hardly true of any other field. I'd start with Shapiro's Oxford Encylopedia, study Benacerraf and Putnam's classic collection of essays, then finish with Shapiro's deep and difficult "Thinking about" and of course Russell and Frege for historic and specialized puzzle pieces.
One "sleeper" I'd like to recommend that is not usually included in comparisons of books in this field is Steinhart: More Precisely: The Math You Need to Do Philosophy.

Eric helps with both math within philosophy (the basics) and tangentially helps with the math used as examples within the philosophy OF math. Beyond the issues of categorization, discovery, math as model vs.
Read more ›
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