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Philosophy of Mathematics: A Contemporary Introduction to the World of Proofs and Pictures (Routledge Contemporary Introductions to Philoso
Free Ebook Philosophy of Mathematics: A Contemporary Introduction to the World of Proofs and Pictures (Routledge Contemporary Introductions to Philoso
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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.
- Sales Rank: #1310993 in Books
- Published on: 2008-01-17
- Released on: 2008-03-31
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x .60" w x 6.14" l, .84 pounds
- Binding: Paperback
- 264 pages
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.
Most helpful customer reviews
10 of 10 people found the following review helpful.
I may becoming a Platonist...
By Massimo Pigliucci
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.
0 of 0 people found the following review helpful.
Good and thorough coverage of the major subjects with plenty ...
By Edward H. Alexander
Good and thorough coverage of the major subjects with plenty of references. Clearly written with lots of examples. Highly recommended.
4 of 8 people found the following review helpful.
Intermediate value theorem
By J. R. G. Mendonca
I didn't read this book, but I'd like to share with the other customers the "review" by Thomas William Körner, a mathematician from Cambridge University (winner of the Salem Prize 1972) that I appreciate so much for his vastly erudite, instructive, and entertaining books on mathematics. In chapter 1 of his "A Companion to Analysis," Professor Körner states: "A good example of this [that people are easily fooled by intuition and ignorance of mathematics] is given in the book [9] [J. R. Brown, "Philosophy of Mathematics]. The author cannot understand the problems involved in proving results like the intermediate value theorem and has written his book to share his lack of understanding with a wider audience."
What else can I say?
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