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Title: Thinking About Mathematics: The Philosophy of Mathematics by Stewart Shapiro ISBN: 0-19-289306-8 Publisher: Oxford University Press Pub. Date: 01 August, 2000 Format: Paperback Volumes: 1 List Price(USD): $24.00 |
Average Customer Rating: 4.6 (5 reviews)
Rating: 3
Summary: Excellent introduction to the philosophy of mathematics
Comment: I finished my Maths degree in 1975, so many of the more recent developments (references are made right up to 1997) were not always comprehensible to me, but I still got enjoyment out of dipping through this book.
If these 2 examples don't spark any interest for you in the discussion that followed, then this book is not for you :
Kant : The concept expressed by the English word 'triangle' contains the concept of being 'three-angled'. Does it also contain the concept of 'three-sided'? The German word for 'triangle' is 'Dreieck', or 'three-cornered'. Presumably, that concept includes 'three-angled', but, again, does it include 'three-sided'?
Formalism : Consider the equation 0=0. If you print this out, you cannot say that the equation says that the leftmost hunk of ink shaped like an oval is identical to the rightmost hunk of ink also shaped like an oval. Clearly, those are two different hunks of ink.
Rating: 5
Summary: 5 Stars for Stain on Tie!
Comment: I found this book gave an excellent and amazingly evenhanded overview of the history and contemporary state of PhiMath. Since any discussion of the Philosphy of Science usually takes only 5 minutes before getting into PhiMath, this book will also interest PhiSci-ers as well. The presentation was clear without being simplistic and without any waste. As an electrical engineer with a strong interest in PhiSci this book was the best general intro to the subject I've come across. I especially liked the large coffee stain on the author's tie on the front cover.
Rating: 5
Summary: Incredibly clear
Comment: 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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Title: Philosophy of Mathematics: Structure and Ontology by Stewart Shapiro ISBN: 0195139305 Publisher: Oxford University Press Pub. Date: 01 August, 2000 List Price(USD): $25.00 |
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Title: Foundations and Fundamental Concepts of Mathematics by Howard Eves ISBN: 048669609X Publisher: Dover Publications Pub. Date: 20 May, 1997 List Price(USD): $16.95 |
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Title: New Directions in the Philosophy of Mathematics by Thomas Tymoczko ISBN: 0691034982 Publisher: Princeton University Press Pub. Date: 12 January, 1998 List Price(USD): $35.00 |
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Title: Philosophy of Mathematics by Paul Benacerraf, Hilary Putnam ISBN: 052129648X Publisher: Cambridge University Press Pub. Date: 01 June, 1984 List Price(USD): $47.00 |
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Title: Realism in Mathematics (Clarendon Paperbacks) by Penelope Maddy ISBN: 019824035X Publisher: Oxford University Press Pub. Date: 01 July, 1992 List Price(USD): $40.00 |
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