Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-25T06:00:23.519Z Has data issue: false hasContentIssue false
  • English
  • Français

Models, Confirmation, and Chaos

Published online by Cambridge University Press:  01 April 2022

Jeffrey Koperski
Jeffrey Koperski*
Affiliation:
Department of Philosophy, Saginaw Valley State University
Get access Rights & Permissions [Opens in a new window]

Abstract

The use of idealized models in science is by now well-documented. Such models are typically constructed in a “top-down” fashion: starting with an intractable theory or law and working down toward the phenomenon. This view of model-building has motivated a family of confirmation schemes based on the convergence of prediction and observation. This paper considers how chaotic dynamics blocks the convergence view of confirmation and has forced experimentalists to take a different approach to model-building. A method known as “phase space reconstruction” not only reveals a lacuna in the philosophical literature on models, it also fails to conform to conventional views about how models are used to confirm a theory.

Type
Research Article
Information
Philosophy of Science , Volume 65 , Issue 4 , December 1998 , pp. 624 - 648
Copyright
Copyright © Philosophy of Science Association 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

†

Send requests for reprints to the author, Department of Philosophy, Saginaw Valley State University, 7400 Bay Road, University Center, MI 48710.

‡

I would like to thank Robert Batterman, Mark Wilson, and Diana Raffman for many helpful comments and guidance through earlier drafts of this paper. Thanks also to two anonymous referees for Philosophy of Science.

References

Abarbanel, H.D.I., Brown, R., and Kadtke, J.B. (1990), “Prediction in Chaotic Nonlinear Systems: Methods for Time-series with Broadband Fourier Spectra”, Physical Review A 41: 1782–1807.CrossRefGoogle Scholar
Abraham, R.H. and Shaw, C.D. (1992), Dynamics: The Geometry of Behavior, 2d ed. Redwood City, CA: Addison-Wesley.Google Scholar
Batterman, R.W. (1993), “Defining Chaos”, Philosophy of Science 60: 43–66.CrossRefGoogle Scholar
Batterman, R.W. (1995), “Theories Between Theories: Asymptotic Limiting Intertheoretic Relations”, Synthese 103: 171–201.CrossRefGoogle Scholar
Cartwright, N. (1983), How the Laws of Physics Lie. New York: Clarendon Press.CrossRefGoogle Scholar
Cartwright, N., Shomar, T., and Suárez, M. (1995), “The Tool Box of Science”, in W. Herfel et al. (eds.), Poznan Studies in the Philosophy of the Sciences and the Humanities 44. Amsterdam: Rodopi, 137–149.Google Scholar
Crutchfield, J.P. and McNamara, B.S. (1987), “Equations of Motion from a Data Series”, Complex Systems 1: 17–45.Google Scholar
Giere, R.N. (1988), Explaining Science. Chicago: University of Chicago Press.CrossRefGoogle Scholar
Glymour, C. (1980), Theory and Evidence. Princeton: Princeton University Press.Google Scholar
Hesse, M. (1966), Models and Analogies in Science. Notre Dame: University of Notre Dame Press.Google Scholar
Hesse, M. (1967), “Models and Analogy in Science”, in The Encyclopedia of Philosophy 5. New York: Macmillan Publishing, 354–358.Google Scholar
Kellert, S.H. (1993), In the Wake of Chaos. Chicago: University of Chicago Press.CrossRefGoogle Scholar
Laymon, R. (1985), “Idealizations and the Testing of Theories by Experimentation”, in P. Achinstein and O. Hanaway (eds.) Observation, Experimentation, and Hypothesis in Modern Physical Science. Cambridge, MA: MIT Press, 147–173.Google Scholar
Laymon, R. (1989), “Cartwright and the Lying Laws of Physics”, The Journal of Philosophy 86: 353–372.CrossRefGoogle Scholar
Lorenz, E. (1963), “Deterministic Nonperiodic Flow”, Journal of the Atmospheric Sciences 20: 130–141. Quoted in S.H. Kellert, In the Wake of Chaos. Chicago: University of Chicago Press.2.0.CO;2>CrossRefGoogle Scholar
McMullin, E. (1967), “What do Physical Models Tell Us?”, in Rootselaar, B. van and Staal, J.F. (eds.), Logic, Methodology, and Philosophy of Science III. Amsterdam: North-Holland Publishing, 385–396.Google Scholar
Morton, A. (1993), “Mathematical Models: Questions of Trustworthiness”, The British Journal for the Philosophy of Science 44: 659–674.CrossRefGoogle Scholar
Ott, E., Sauer, T., and Yorke, J.A. (eds.) (1994), Coping with Chaos. New York: John Wiley & Sons.Google Scholar
Packard, N.H., Crutchfield, J.P., Farmer, J.D., and Shaw, R.S. (1980), “Geometry from a Time-series”, Physical Review Letters 45: 712–716.CrossRefGoogle Scholar
Redhead, M. (1980), “Models in Physics”, The British Journal for the Philosophy of Science 31: 154–163.CrossRefGoogle Scholar
Rueger, A. and Sharp, W.D. (1996), “Simple Theories of a Messy World: Truth and Explanatory Power in Nonlinear Dynamics”, The British Journal for the Philosophy of Science 47: 93–112.CrossRefGoogle Scholar
Sauer, T., Yorke, J.A., and Casdagli, M. (1991), “Embedology”, The Journal of Statistical Physics 65: 579–616.CrossRefGoogle Scholar
Shaw, R.S. (1981), “Modeling Chaotic Systems”, in Haken, H. (ed.), Chaos and Order in Nature. New York: Springer-Verlag, 218–231.CrossRefGoogle Scholar
Shaw, R.S. (1984), The Dripping Faucet as a Model Chaotic System. Santa Cruz: Aerial Press.Google Scholar
Smith, P. (1991), “The Butterfly Effect”, Proceedings of the Aristotelian Society 91: 247–267.CrossRefGoogle Scholar
Tabor, M. (1989), Chaos and Integrability in Nonlinear Dynamics. New York: John Wiley & Sons.Google Scholar
Takens, F. (1981), “Detecting Strange Attractors in Turbulence”, in Rand, D. and Young, L.-S. (eds.), Lecture Notes in Mathematics 898. Berlin: Springer-Verlag.Google Scholar
Tavakol, R.K. (1991), “Fragility and Deterministic Modelling in the Exact Sciences”, The British Journal for the Philosophy of Science 42: 147–156.CrossRefGoogle Scholar
van Fraassen, B.C. (1980), The Scientific Image. New York: Clarendon Press.CrossRefGoogle Scholar
van Fraassen, B.C. (1989), Laws and Symmetry. New York: Clarendon Press.CrossRefGoogle Scholar
Wimsatt, W.C. (1987), “False Models as Means to Truer Theories”, in Nitecki, M. and Hoffmann, A. (eds.), Neutral Models in Biology. New York: Oxford University Press, 3–55.Google Scholar
Wimsatt, W.C. and Schank, J.C. (1992), Modelling—A Primer. University of Maryland Academic Software Development Group.Google Scholar