In this ambitious study, David Corfield attacks the widely held view that it is the nature of mathematical knowledge which has shaped the way in which mathematics is treated philosophically and claims that contingent factors have brought us to the present thematically limited discipline. Illustrating his discussion with a wealth of examples, he sets out a variety of approaches to new thinking about the philosophy of mathematics, ranging from an exploration of whether computers producing mathematical proofs or conjectures are doing real mathematics, to the use of analogy, the prospects for a Bayesian confirmation theory, the notion of a mathematical research programme and the ways in which new concepts are justified. His inspiring book challenges both philosophers and mathematicians to develop the broadest and richest philosophical resources for work in their disciplines and points clearly to the ways in which this can be done.
Towards a Philosophy of Real Mathematics
and over 1.5 million other books are available for Amazon Kindle . Learn more
| ||||||||||||||||||||
Did you know you can trade in your old books for an Amazon.co.uk Gift Card to spend on the things you want? Visit the Books Trade-In Store for more details. Learn more. |
Book Description
Product details
Would you like to update product info or give feedback on images?
|
More About the Author
Discover books, learn about writers, and more.
Product Description
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
'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.
Inside This Book
(Learn More)
Browse and search another edition of this book.
Browse and search another edition of this book.
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
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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
Explore More
Concordance
Browse Sample PagesConcordance
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
Customer Reviews
Most Helpful Customer Reviews
1 of 1 people found the following review helpful
4.0 out of 5 stars
Don't expect this book to blow your mind: That task is left up to you
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.
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.
Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com:
5.0 out of 5 stars
1 review
14 of 14 people found the following review helpful
5.0 out of 5 stars
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.
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
›
Go to Amazon.com to see the review
5.0 out of 5 stars
Was this review helpful?
Let us know
Customer Discussions
|
This product's forum
Active discussions in related forums
Search Customer Discussions
|
Related forums
|
Listmania!
Look for similar items by category
Feedback
- Would you like to update product info or give feedback on images?
- I am the Author, and I want to comment on my book.
- I am the Publisher, and I want to comment on this book.
|
