Rosaler, Joshua
(2013)
Theory Reduction in Physics: A ModelBased, Dynamical Systems Approach.
[Preprint]
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Abstract
In 1973, Nickles identified two senses in which the term `reduction' is used to describe the relationship between physical theories: namely, the sense based on Nagel's seminal account of reduction in the sciences, and the sense that seeks to extract one physical theory as a mathematical limit of another. These two approaches have since been the focus of most literature on the subject, as evidenced by recent work of Batterman and Butterfield, among others. In this paper, I discuss a third sense in which one physical theory may be said to reduce to another. This approach, which I call `dynamical systems (DS) reduction,' concerns the reduction of individual models of physical theories rather than the wholesale reduction of entire theories, and specifically reduction between models that can be formulated as dynamical systems. DS reduction is based on the requirement that there exist a function from the state space of the lowlevel (more encompassing) model to that of the highlevel (less encompassing) model that satisfies certain general constraints and thereby serves to identify quantities in the lowlevel model that mimic the behavior of those in the highlevel model  but typically only when restricted to a certain domain of parameters and states within the lowlevel model. I discuss the relationship of this account of reduction to the Nagelian and limitbased accounts, arguing that it is distinct from both but exhibits strong parallels with a particular version of Nagelian reduction, and that the domain restrictions employed by the DS approach may, but need not, be specified in a manner characteristic of the limitbased approach. Finally, I consider some limitations of the account of reduction that I propose and suggest ways in which it might be generalised. I offer a simple, idealised example to illustrate application of this approach; a series of more realistic case studies of DS reduction is presented in another paper.
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