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Towards a Philosophy of Real Mathematics Paperback – 14 Dec 2006


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Product details

  • Paperback: 300 pages
  • Publisher: Cambridge University Press; 1 edition (14 Dec. 2006)
  • Language: English
  • ISBN-10: 0521035252
  • ISBN-13: 978-0521035255
  • Product Dimensions: 15.2 x 1.7 x 22.8 cm
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Bestsellers Rank: 2,331,029 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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Review

'Corfield's book as a whole is itself a fine specimen of a philosophical approach to mathematics that takes its questions and its resources from 'real' mathematics, showing convincingly the richness and fruitfulness of such an approach.' Philosophia Mathematica

'I found this book interesting and it is certainly worth looking at if only to increase one's sense of the possibilities for the philosophy of mathematics.' Metascience

'What is really special about the book under review is that it demonstrates a philosopher struggling to grapple with modern mathematics as it is actually carried out by practitioners. This is what the author means by 'real mathematics' as quoted in the book title.' Zentralblatt MATH

Book Description

In this ambitious study, David Corfield sets out a variety of approaches to new thinking about the philosophy of mathematics, and challenges both philosophers and mathematicians to develop the broadest and richest philosophical resources for work in their disciplines.

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First Sentence
To allay any concerns for my mental health which the reader may be feeling if they have come to understand from the book's title that I believe mathematics based on the real numbers deserves singling out for philosophical treatment, let me reassure them that I mean no such thing. Read the first page
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1 of 1 people found the following review helpful By Mr. S. T. Hughes on 15 Jun. 2009
Format: Paperback
Highly recommended for those that are interested in the philosophy of maths and also recommended for pure mathematicians and more advanced students.

This book is an early step in the attempt to redirect the lines of inquiry of the philosophy of mathematics. Corfield has been labelled as one of the forerunners in what has been described as a 'maverick' movement in the philosophy of maths. For Corfield, philosophy of maths should no longer be a question of the logical consequences of a set of axioms preceeded and precluded by strange epistomological questions like : 'Do numbers really exist?', but should be redirected "towards a better grounding in mathematical practice".

Corfield is very aware that what he's doing is very ambitious and difficult. In this sense it becomes hard to criticise him for the way in which some of his thoughts are not entirely polished. He is only starting the dialogue and there is *very* little for him work with. This accounts for most of the shortcomings of the book and some sense also tells us that Corfield is not to blame. It explains why the section on the works of Lakatos is the best in the book, explains the brevity of some of the sections and the feeling that some of his arguements lack weight (if nothing has been said on a topic until now, any initial thoughts can just look like a stab in the dark).

You might find a thread which could lead you somewhere incredible, but don't expect this book to blow your mind: That task is left up to you. This book is only a starting point for you to criticise and from which to grow.
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Most Helpful Customer Reviews on Amazon.com (beta)

Amazon.com: 1 review
15 of 15 people found the following review helpful
A philosopher with a real interest in mathematics 19 Jan. 2004
By B - Published on Amazon.com
Format: Hardcover
Philosophy of math has long been obsessed with questions like the existence of numbers and the set-theoretic or logical foundation of the discipline. A century ago, top level mathematicians like Weyl, Hilbert, and Brouwer were engaged in some of these problems. But today's mathematics has largely moved on to other issues. This book is an attempt for philosophy to catch up with these developments.
I have to admit that I was less interested in the chapters on automated theorem proving and conjecture formation. So I read the introductory chapter (which should be comprehensible for a general audience) and then jumped to the later chapters which I find particularly intriguing. In these chapters, Corfield touches several modern areas of mathematics (such as algebraic topology, category theory). These are fields that do not lend themselves well to armchair philosophy, and it is reassuring to know that Corfield has a degree in math from Cambridge University. At times, the book gets technical, not in terms of formulas, but in terms of advanced mathematical concepts that are being discussed. Still, the gist gets conveyed. This makes the book an excellent read.
For those interested, there is a long review of the book on John Baez' home page, under "This Week's Finds in Mathematical Physics (Week 198)".
B. Schölkopf
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