Theory Reduction in Physics: A Model-Based, Dynamical Systems Approach

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 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 low-level model to that of the high-level model that satisfies certain general constraints and thereby serves to identify quantities in the low-level model that mimic the behavior of those in the high-level model - but typically only when restricted to a certain domain of parameters and states within the low-level model. I discuss the relationship of this account of reduction to the Nagelian and limit-based 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 limit-based 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.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,616

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

  • Only published works are available at libraries.

Similar books and articles

Local reduction in physics.Joshua Rosaler - 2015 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 50:54-69.
Nagelian Reduction Beyond the Nagel Model.Raphael van Riel - 2011 - Philosophy of Science 78 (3):353-375.
Approaches to reduction.Kenneth F. Schaffner - 1967 - Philosophy of Science 34 (2):137-147.
Why It Is Time To Move Beyond Nagelian Reduction.Marie I. Kaiser - 2012 - In D. Dieks, W. J. Gonzalez, S. Hartmann, M. Stöltzner & M. Weber (eds.), Probabilities, Laws, and Structures. The Philosophy of Science in a European Perspective. Heidelberg, GER: Springer. pp. 255-272.
Beyond reduction: mechanisms, multifield integration and the unity of neuroscience.Carl F. Craver - 2005 - Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences 36 (2):373-395.
From Water to H2O - What Reduction is About.Raphael van Riel - 2008 - 2008 - Reduction in the Special Sciences.
Elements of Physical Reality, Nonlocality and Stochasticity in Relativistic Dynamical Reduction Models.GianCarlo Ghirardi & Philip Pearle - 1990 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1990:35 - 47.
Consciousness and Reduction.Ausonio Marras - 2005 - British Journal for the Philosophy of Science 56 (2):335-361.
Reviewing Reduction in a Preferential Model‐Theoretic Context.Emma Ruttkamp & Johannes Heidema - 2005 - International Studies in the Philosophy of Science 19 (2):123 – 146.

Analytics

Added to PP
2015-09-07

Downloads
41 (#339,996)

6 months
6 (#203,358)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Joshua Rosaler
Oxford University

Citations of this work

No citations found.

Add more citations

References found in this work

Add more references