Local reduction in physics

Joshua Rosaler

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

A conventional wisdom about the progress of physics holds that successive theories wholly encompass the domains of their predecessors through a process that is often called "reduction." While certain influential accounts of inter-theory reduction in physics take reduction to require a single "global" derivation of one theory[U+05F3]s laws from those of another, I show that global reductions are not available in all cases where the conventional wisdom requires reduction to hold. However, I argue that a weaker "local" form of reduction, which defines reduction between theories in terms of a more fundamental notion of reduction between models of a single fixed system, is available in such cases and moreover suffices to uphold the conventional wisdom. To illustrate the sort of fixed-system, inter-model reduction that grounds inter-theoretic reduction on this picture, I specialize to a particular class of cases in which both models are dynamical systems. I show that reduction in these cases is underwritten by a mathematical relationship that follows a certain liberalized construal of Nagel/Schaffner reduction, and support this claim with several examples. Moreover, I show that this broadly Nagelian analysis of inter-model reduction encompasses several cases that are sometimes cited as instances of the "physicist[U+05F3]s" limit-based notion of reduction.

Original languageEnglish (US)
Pages (from-to)54-69
Number of pages16
JournalStudies in History and Philosophy of Science Part B - Studies in History and Philosophy of Modern Physics
Volume50
DOIs
StatePublished - May 1 2015

Bibliographical note

Publisher Copyright:
© 2015 Elsevier Ltd.

Keywords

  • Dynamical systems
  • Limits
  • Local reduction
  • Models
  • Nagel
  • Reduction

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