Journal Article

Asymptotics, Reduction and Emergence

C. A. Hooker

in The British Journal for the Philosophy of Science

Published on behalf of British Society for the Philosophy of Science

Volume 55, issue 3, pages 435-479
Published in print September 2004 | ISSN: 0007-0882
Published online September 2004 | e-ISSN: 1464-3537 | DOI: http://dx.doi.org/10.1093/bjps/55.3.435
Asymptotics, Reduction and Emergence

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All the major inter-theoretic relations of fundamental science are asymptotic ones, e.g. quantum theory as Planck's constant h → 0, yielding (roughly) Newtonian mechanics. Thus asymptotics ultimately grounds claims about inter-theoretic explanation, reduction and emergence. This paper examines four recent, central claims by Batterman concerning asymptotics and reduction. While these claims are criticised, the discussion is used to develop an enriched, dynamically-based account of reduction and emergence, to show its capacity to illuminate the complex variety of inter-theory relationships in physics, and to provide a principled resolution to such persistent philosophical problems as multiple realisability and the nature of the special sciences.

Introduction

Exposition

Examination I: Claims (1) and (2), asymptotic explanation and reference

Examination II: Claim (3), reduction and singular asymptotics

Examination III: Claim (4), emergence and multiple realisability

Conclusion

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Subjects: Philosophy of Science ; Science and Mathematics

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