Philosophy of Mathematics: A Contemporary Introduction to the World of Proofs and Pictures

by Brown, James Robert

• ISBN13: 9780203932964
• ISBN10: 020393296X
• eBook ISBN(s): 9781135902384
• Edition: 2nd
• Copyright: 2008-01-15
• Publisher: Taylor & Francis
• More Book Details

Summary

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.

Table of Contents

Preface and Acknowledgements

Introduction: The Mathematical Image

Platonism

Picture-Proofs and Platonism

What is Applied Mathematics?

Hilbert and Gödel

Knots and Notation

What is a Definition?

Constructive Approaches

Proofs, Pictures and Procedures in Wittgenstein

Computation, Proof and Conjecture

How to Refute the Continuum Hypothesis

Calling the Bluff

Notes

Bibliography

Index

Table of Contents provided by Publisher. All Rights Reserved.