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Thinking about Mathematics: The Philosophy of Mathematics Paperback – October 5, 2000

ISBN-13: 978-0192893062 ISBN-10: 0192893068 Edition: 0th

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Thinking about Mathematics: The Philosophy of Mathematics + Philosophy of Mathematics: Selected Readings + The Oxford Handbook of Philosophy of Mathematics and Logic (Oxford Handbooks)
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Product Details

  • Paperback: 328 pages
  • Publisher: Oxford University Press (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: 13.6 ounces (View shipping rates and policies)
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (12 customer reviews)
  • Amazon Best Sellers Rank: #306,920 in Books (See Top 100 in Books)

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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Customer Reviews

4.3 out of 5 stars
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Most Helpful Customer Reviews

30 of 30 people found the following review helpful By N on August 22, 2005
Format: Paperback Verified Purchase
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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27 of 30 people found the following review helpful By A Customer on February 27, 2001
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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16 of 19 people found the following review helpful By A Customer on October 5, 2002
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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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8 of 9 people found the following review helpful By M. Le Corre on November 24, 2009
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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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5 of 6 people found the following review helpful By Amazon Customer on April 29, 2008
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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2 of 3 people found the following review helpful By Jordan Bell on February 27, 2014
Format: Paperback
This is not a great work, but it is probably worth reading for undergraduate students of philosophy. You need some knowledge of mathematics to understand this book, but if you know too much mathematics you may feel that it is not talking about the questions that you care about. For example, I don't find categorizing statements as a priori, a posteriori, analytic and synthetic to be useful distinctions for talking about mathematics.

What does it mean to understand a mathematical statement? What makes a mathematician believe that something is true before they have written a proof of it? Shapiro talks about the existence of mathematical objects and the truth of mathematical statements, but gives much less room to talking about how these things get into our minds or what it means for them to be in our minds. To me the process of learning is making more processes unconscious, so you can move your attention to harder things without having to keep conscious track of other things.

Or what do we mean when we say "why is something true?". It's possible to check something line by line and still to have the feeling that you don't understand why something is true.

My thinking about the relation between mathematics and the physical world is the following: mathematics does not say anything directly about the physical world. We build mathematical models, and the better a model satisfies the phenomena we observe the more we like the model. Now, it is indeed a good question why we can make models that do such a good job, and I would have liked to read more about this.

I think that the mathematically informed reader would also benefit from some discussion of category theory. For example, I would enjoy reading a nontechnical discussion of what it means to define something using a universal property. This would come closer to what a mathematician does than talking about type theory (although in fact I liked the discussion of type theory).
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