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By David Corfield
Publisher: Cambridge University Press
Print Publication Year:2003
Online Publication Date:September 2009
Online ISBN:9780511487576
Hardback ISBN:9780521817226
Paperback ISBN:9780521035255
Book DOI: http://dx.doi.org/10.1017/CBO9780511487576
Subjects: Philosophy: general interest , Recreational mathematics
David Corfield provides a variety of innovative approaches to research in the philosophy of mathematics. His study ranges 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 program; and the ways in which new concepts are justified. This highly original book will challenge philosophers as well as mathematicians to develop the broadest and most complete philosophical resources for research in their disciplines.
Reviews:
pp. i-vi
pp. vii-viii
pp. ix-x
1 - Introduction: a role for history: Read PDF
pp. 1-34
PART I - HUMAN AND ARTIFICIAL MATHEMATICIANS: Read PDF
pp. 35-36
2 - Communicating with automated theorem provers: Read PDF
pp. 37-56
3 - Automated conjecture formation: Read PDF
pp. 57-79
4 - The role of analogy in mathematics: Read PDF
pp. 80-100
PART II - PLAUSIBILITY, UNCERTAINTY AND PROBABILITY: Read PDF
pp. 101-102
5 - Bayesianism in mathematics: Read PDF
pp. 103-129
6 - Uncertainty in mathematics and science: Read PDF
pp. 130-148
PART III - THE GROWTH OF MATHEMATICS: Read PDF
pp. 149-150
7 - Lakatos's philosophy of mathematics: Read PDF
pp. 151-174
8 - Beyond the methodology of mathematical research programmes: Read PDF
pp. 175-203
9 - The importance of mathematical conceptualisation: Read PDF
pp. 204-232
PART IV - THE INTERPRETATION OF MATHEMATICS: Read PDF
pp. 233-236
10 - Higher-dimensional algebra: Read PDF
pp. 237-270
pp. 271-273
pp. 274-285
pp. 286-288