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9780203932964

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

by
  • ISBN13:

    9780203932964

  • ISBN10:

    020393296X

  • Edition: 2nd
  • Copyright: 2008-01-15
  • Publisher: Taylor & Francis

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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.

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