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9780521035255

Towards a Philosophy of Real Mathematics

by
  • ISBN13:

    9780521035255

  • ISBN10:

    0521035252

  • Edition: 1st
  • Format: Paperback
  • Copyright: 2006-12-14
  • Publisher: Cambridge University Press

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Summary

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.

Table of Contents

Preface
Introduction: a role for history
Human and Artificial Mathematicians
Communicating with automated theorem provers
Automated conjecture formation
The role of analogy in mathematics
Plausibility, Uncertainty and Probability
Bayesianism in mathematics
Uncertainty in mathematics and science
The Growth of Mathematics
Lakatos's philosophy of mathematics
Beyond the methodology of mathematical research programmes
The importance of mathematical conceptualisation
The Interpretation of Mathematics
Higher dimensional algebra
Appendix
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

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