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 language||English (US)|
|Number of pages||16|
|Journal||Studies in History and Philosophy of Science Part B - Studies in History and Philosophy of Modern Physics|
|State||Published - May 1 2015|
Bibliographical noteFunding Information:
I would like to thank David Wallace, Simon Saunders, Christopher Timpson, Jeremy Butterfield, John Norton and an anonymous referee for invaluable comments on earlier drafts of this work, and Jos Uffink, Cian Dorr and David Albert for helpful discussions. Thanks also to audiences in Munich, Pittsburgh, Amersfoort and Minnesota, where earlier versions of this article were presented. This work was supported by the University of Pittsburgh's Center for Philosophy of Science.
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- Dynamical systems
- Local reduction