Defending Chaos: An Examination and Defense of the Models Used in Chaos Theory

Dissertation, The Ohio State University (1997)

Authors
Jeffrey Koperski
Saginaw Valley State University
Abstract
The indispensable role of models in science has long been recognized by philosophers. In contemporary dynamics, the models are often simply sets of equations. Bridging the gap between pure mathematics and real-world phenomenon is especially difficult when the model is chaotic. I address the charge that this bridge has not, in fact, been built and that chaos remains "just math." Although the problems discussed have become acute with the rise of modern chaos theory, their roots were recognized nearly a century ago by Pierre Duhem. The skeptical attacks are both foundational and epistemic. ;Targeting the foundations of chaos theory, the skeptic claims that the geometry instantiated by some chaotic models cannot be representative of real-world processes. Specifically, mathematical fractals are said to have more complexity than can be captured in a material world of discrete atoms. Furthermore, there is what physicists call "the problem of quantum chaos:" quantum mechanics appears to forbid full-blown chaotic evolutions. I argue that the counterfactual nature of chaotic models can be used to resolve these tensions. Moreover, I show that the skeptic cannot attack the foundations of chaos theory without calling into question unproblematic areas of mathematical science. ;The epistemological problems are driven by an essential property of chaotic dynamics, viz., sensitive dependence on initial conditions. This sensitivity confounds the confirmation schemes familiar to philosophers by precluding future predictions of the state of a system. The skeptic argues that without such predictions, the models cannot be tested. I show how researchers in chaos theory can overcome these skeptical objections via a recently developed method of model construction. This new method not only yields a decisive answer to the skeptic, but reveals a lacuna in the philosophical literature on models in science. I present a new taxonomy of models that incorporates these recent discoveries and conforms more closely to contemporary scientific practice than do previous classifications
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 61,089
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Has Chaos Been Explained?Jeffrey Koperski - 2001 - British Journal for the Philosophy of Science 52 (4):683-700.
Nonseparability and Quantum Chaos.Fred Kronz - 1998 - Philosophy of Science 65 (1):50-75.
Models, Confirmation, and Chaos.Jeffrey Koperski - 1998 - Philosophy of Science 65 (4):624-648.
The Construction of Chaos Theory.Yvon Gauthier - 2009 - Foundations of Science 14 (3):153-165.
A Philosophical Evaluation of the Chaos Theory "Revolution".Stephen H. Kellert - 1992 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:33 - 49.
Chaos in a Model of an Open Quantum System.Frederick M. Kronz - 2000 - Philosophy of Science 67 (3):453.
Deterministisches Chaos: Einige Wissenschaftstheoretisch Interessante Aspekte. [REVIEW]Klaus Jürgen Düsberg - 1995 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 26 (1):11 - 24.

Analytics

Added to PP index
2015-02-05

Total views
0

Recent downloads (6 months)
0

How can I increase my downloads?

Downloads

Sorry, there are not enough data points to plot this chart.

My notes