Abstract
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. 1. Introduction2. Exposition3. Examination I: Claims (1) and (2), asymptotic explanation and reference4. Examination II: Claim (3), reduction and singular asymptotics5. Examination III: Claim (4), emergence and multiple realisability6. Conclusion
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