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Towards a Philosophy of Real Mathematics

$38.00 USD

  • Date Published: January 2005
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9780511030604

$ 38.00 USD
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About the Authors
  • 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.

    • Accessibly and engagingly written
    • Uses many examples and case studies as illustrations
    • Shows alternative ways in which mathematics can be studied philosophically
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    Reviews & endorsements

    '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

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    Product details

    • Date Published: January 2005
    • format: Adobe eBook Reader
    • isbn: 9780511030604
    • contains: 1 table
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • Table of Contents

    Preface
    1. Introduction: a role for history
    Part I. Human and Artificial Mathematicians:
    2. Communicating with automated theorem provers
    3. Automated conjecture formation
    4. The role of analogy in mathematics
    Part II. Plausibility, Uncertainty and Probability:
    5. Bayesianism in mathematics
    6. Uncertainty in mathematics and science
    Part III. The Growth of Mathematics:
    7. Lakatos's philosophy of mathematics
    8. Beyond the methodology of mathematical research programmes
    9. The importance of mathematical conceptualisation
    Part IV. The Interpretation of Mathematics:
    10. Higher dimensional algebra
    Appendix
    Bibliography
    Index.

  • Author

    David Corfield, University of Oxford
    David Corfield holds a Junior Lectureship in Philosophy of Science at the University of Oxford.

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