Towards a Philosophy of Real Mathematics by David Corfield (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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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