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The British Journal for the Philosophy of Science Advance Access originally published online on May 18, 2007
The British Journal for the Philosophy of Science 2007 58(2):263-286; doi:10.1093/bjps/axm007
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Copyright © The Author 2007. Published by Oxford University Press on behalf of British Society for the Philosophy of Science.

On the Specialness of Special Functions (The Nonrandom Effusions of the Divine Mathematician)

Robert W. Batterman

University of Western Ontario, Department of Philosophy, Talbot College, London, Ontario N6A 3K7, Canada

rbatterm{at}uwo.ca


  Abstract

This article attempts to address the problem of the applicability of mathematics in physics by considering the (narrower) question of what make the so-called special functions of mathematical physics special. It surveys a number of answers to this question and argues that neither simple pragmatic answers, nor purely mathematical classificatory schemes are sufficient. What is required is some connection between the world and the way investigators are forced to represent the world.

1 Introduction
2 Some responses to the question
3 Idealization
4 Airy's equation
5 Stokes on the Airy integral
6 Asymptotic expansions and special functions
7 Special functions and the world
8 Conclusion: special functions and the philosophy of mathematics


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