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Philosophy of Mathematics: A Contemporary Introduction to the World of Proofs and Pictures (Routledge Contemporary Introductions to Philosophy) [Paperback]

James Robert Brown
4.0 out of 5 stars  See all reviews (1 customer review)
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Book Description

31 Mar 2008 0415960479 978-0415960472 2

In his long-awaited new edition of Philosophy of Mathematics, James Robert Brown tackles important new as well as enduring questions in the mathematical sciences. Can pictures go beyond being merely suggestive and actually prove anything? Are mathematical results certain? Are experiments of any real value?  

This clear and engaging book takes a unique approach, encompassing non-standard topics such as the role of visual reasoning, the importance of notation, and the place of computers in mathematics, as well as traditional topics such as formalism, Platonism, and constructivism. The combination of topics and clarity of presentation make it suitable for beginners and experts alike. The revised and updated second edition of Philosophy of Mathematics contains more examples, suggestions for further reading, and expanded material on several topics including a novel approach to the continuum hypothesis.

Product details

  • Paperback: 264 pages
  • Publisher: Routledge; 2 edition (31 Mar 2008)
  • Language: English
  • ISBN-10: 0415960479
  • ISBN-13: 978-0415960472
  • Product Dimensions: 23 x 16 x 1 cm
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Bestsellers Rank: 505,482 in Books (See Top 100 in Books)
  • See Complete Table of Contents

Product Description


"Extraordinary! A brilliant, important book. Summing up: Highly recommended."
—M. Schiff, CHOICE

"…The book has been written in a very clear, lively way, it is a pleasure to read. It is very accessible, even entertaining, and the author is very good in explaining issues without technicalities. … Summarizing: a very elegant, accessible and up-to-date book on the philosophy of mathematics, not only very appropriate for beginners, but also a must for experts."
—H.C.M. de Swart, Zentralblatt MATH 1171

Praise for the First Edition:

"This book is a breath of fresh air for undergraduate philosophy of mathematics.  Very accessible and even entertaining, Brown explains most of the issues without technicalities. "
—Janet Folina, Macalester College

"A wonderful introduction to the philosophy of mathematics. It's lively, accessible, and, above all, a terrific read. It would make an ideal text for an undergraduate course on the philosophy of mathematics; indeed, I recommend it to anyone interested in the philosophy of mathematics — even specialists in the area can learn from this book."
—Mark Colyvan, University of Sydney


From the Back Cover

Philosophy of Mathematics is an excellent introductory text for philosophy of mathematics. Clear and engaging, it moves at a good pace, is easy to use and student friendly. The book discusses the great philosophers and the importance of mathematics to their thought. Philosophy of Mathematics covers the following topics:
* the mathematical image
* platonism
* picture-proofs
* applied mathematics
* Hilbert and Godel
* knots and nations
* definitions
* picture-proofs and Wittgenstein
* computation, proof and conjecture
The author Smoke and Mirrors and The Laboratory of the Mind, James Robert Brown introduces one of the newer issues in the philosophy of mathematics, namely those associated with computers, 'experimentation', and visualization, and presents a controversial account of how picture-proofs work. Philosophy of Mathematics raises problems that are truly worthy of attention. --This text refers to an out of print or unavailable edition of this title.

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Most Helpful Customer Reviews
4 of 4 people found the following review helpful
4.0 out of 5 stars Platonism rules O.K. 8 Jun 2010
Format:Paperback|Verified Purchase
I am neither an undergraduate philosophy student nor a logician so the second half of this book was lost on me.However the first half was a suprisingly entertaining and to me somewhat iconoclastic defence of Platonism in mathematics and a suprisingly informative and convincing demonstration that diagrams can be more than heuristic devices as I have been taught but can be used to create valid general proofs.
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Most Helpful Customer Reviews on (beta) 2.5 out of 5 stars  2 reviews
7 of 7 people found the following review helpful
4.0 out of 5 stars I may becoming a Platonist... 11 Aug 2010
By Massimo Pigliucci - Published on
Format:Kindle Edition|Verified Purchase
I've always had trouble with the idea that mathematicians discover things, as opposed to inventing them. You see, if you discover something, the implication is that that something is, in some sense, out there. But where would mathematical entities reside, if not inside human brains and thought processes? I must say, reading this book has if not changed my mind at least made me seriously question my positions - which is really what you want from any good book. Brown's treatment is relatively accessible, but of course you will be in for a good amount of philosophy, and some not so easily digestible math. Still, the attentive reader can get the gist of the arguments without having to follow every proof presented by the author. I am a little less convinced, though still intrigued, by Brown's claim that pictures can - in some circumstances - do the work of formal proofs. Then again, that notion does appeal to my generally pluralistic attitude about methods of inquiry, and it does fit very well with the author's overall contention that mathematics is - surprisingly - a lot more like the natural sciences than one might think at first. Of course, all of this leaves completely unanswered the underlying question of the ontological status of mathematical objects. Oh well, can't get everything out of a single book.
7 of 12 people found the following review helpful
1.0 out of 5 stars Not an Introduction 2 Nov 2009
By Anax Andron - Published on
I second the objections to this book raised by the previous 1 star review. I further wish to rant about the tone of the entire book...I must be honest, I have not finished the book. I am considering not doing so. The Platonist biased is too strong for a simple introduction.

In that this is pegged as an introduction the demographic is presumably those who are not familiar with the arguments for the positions philosophers of mathematics hold. In this regard I feel it is bad form to produce an introduction that is so obviously skewed. It is reassuring that the author is up front concerning his position and bias. However, when the author off handedly rejects arguments by some of the giants in the field as non-sequiturs, he is doing a diservice to his readers who are as much his students. This is bias affecting argumentation that is bad form in philosophy, as far as I am concerned.
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