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Philosophy of Mathematics: A Contemporary Introduction to the World of Proofs and Pictures Paperback – Mar 31 2008

by James Robert Brown (Author)

9 reviews from Amazon.com |

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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.

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Product details

Paperback: 264 pages
Publisher: Routledge; 2 edition (Jan. 15 2008)
Language: English
ISBN-10: 0415960479
ISBN-13: 978-0415960472
Product Dimensions: 15.6 x 1.5 x 23.4 cm
Shipping Weight: 481 g
Average Customer Review: Be the first to review this item
Amazon Bestsellers Rank: #527,561 in Books (See Top 100 in Books)
- #3319 in Books > Textbooks > Sciences > Mathematics
- #4039 in Books > Textbooks > Humanities > Philosophy
- #6884 in Books > Science & Math > Mathematics

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Review

"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

About the Author

James Robert Brown is Professor of Philosophy at the University of Toronto.

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Amazon.com: 9 reviews

10 people found this helpful.

I may becoming a Platonist...

ByMassimo Pigliuccion August 11, 2010 - Published on Amazon.com

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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.

Five Stars

ByKay Mon June 26, 2017 - Published on Amazon.com

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Great for potential philosophers who aren't that great at maths

Good and thorough coverage of the major subjects with plenty ...

ByEdward H. Alexanderon September 14, 2015 - Published on Amazon.com

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Good and thorough coverage of the major subjects with plenty of references. Clearly written with lots of examples. Highly recommended.

For the mathematical and philosophical mind, as the title shows.

Bymomomo58on April 7, 2011 - Published on Amazon.com

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I graduated with a bachelor's in philosophy, but was pursuing mathematics pretty hard before that. This book is genius! It certainly engages the mind and shows the beauty of mathematics never taught in a typical mathematics class. It's not an easy read though, so be warned!

15 people found this helpful.

Good Defense of Platonism in Phil. of Mathematics

ByPedro M. Rosario Barbosaon May 9, 2002 - Published on Amazon.com

James Robert Brown has exposed with excellence in his book a very good defense of Platonism in Philosophy of Mathematics. He shows the basic premises that are shared more or less by all Platonists, including Frege, Godel, and many others.
He shows why philosophers argue against Platonism, and which are the biases and confusions they make that apparently they show a rejection to it.
It discusses subjects such as numbers, sets, geometrical objects, graphs, and even fractals, and how Platonism can recognize all of them as abstract objects, and how pictures can help us psychologically to grasp these abstract objects.
However, with all of this I have only one problem. He proposes a kind of "mind's eye" by which we are able to "grasp" these abstract objects. Although he presents a very keen argument for refuting the argument that only through sensible experience we are able to know anything about the world, I still feel uneasy and not satisfied about his epistemological account. The hypothesis of this "mind's eye" is the reason why most philosophers find the Platonist proposal so objectionable. In order to account for our knowledge of abstract objects, we must posit a kind of myserious mystic faculty of the "mind's eye".
I think that Husserl's categorial intuition and categorial abstraction (which he proposes in his "Logical Investigations") or Katz proposal of intellectual intuition (in his "Realistic Rationalism") are much more acceptable proposals than Brown's "mind's eye".
Despite this difference, I highly recommend this book, along with Jerrold Katz's "Realistic Rationalism", as a great and serious exposition of the Platonist proposal in philosophy of mathematics that I have ever found. It also serves as a good introduction to philosophy of mathematics.

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