Has Chaos Been Explained?

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Reference

Jeffrey Koperski: Has Chaos Been Explained? In: Brit. J. Phil. Sci. 52 (2001), 683-700.

DOI

Abstract

In his recent book, Explaining Chaos, Peter Smith presents a new problem in the foundations of chaos theory. Speci®cally, he argues that the standard ways of justifying idealizations in mathematical models fail when it comes to the in®nite intricacy found in strange attractors. I argue that Smith's analysis undermines much of the explanatory power of chaos theory. A better approach is developed by drawing analogies from the models found in continuum mechanics.

Extended Abstract

Bibtex

Used References

Abraham, R. and Shaw, C. [1992]: Dynamics: The Geometry of Behavior, 2nd edn, Redwood City, California: Addison-Wesley.

Arnold, V. I. [1983]: Geometrical Methods in the Theory of Ordinary Diff€erential Equations, Berlin: Springer.

Batterman, R. [1995]: `Theories Between Theories: Asymptotic Limiting Intertheoretic Relations', Synthese, 103, pp. 171±201.

Cartwright, N. [1983]: How the Laws of Physics Lie, New York: Clarendon Press. Diacu, F. and Holmes, P. [1996]: Celestial Encounters: The Origin of Chaos and Stability, Princeton: Princeton University Press.

Devaney, R. [1989]: An Introduction to Chaotic Dynamical Systems, 2nd edn, Redwood City: Addison-Wesley.

Devaney, R. [1992]: A First Course in Chaotic Dynamical Systems, Redwood City: Addison-Wesley.

Kaplan, J. L. and Yorke, J. A. [1979]: `The onset of chaos in a ̄fluid ̄flow model of Lorenz', Annals of the New York Academy of Sciences, 316, p. 400.

Koperski, J. [1998]: `Models, Confirmation, and Chaos', Philosophy of Science, 65, pp. 624±48.

Laymon, R. [1989]: `Cartwright and the Lying Laws of Physics', The Journal of Philosophy, 86, pp. 353±72.

Lorenz, E. [1993]: The Essence of Chaos, Seattle: University of Washington Press. Poston, T. and Stewart, I. [1978]: Catastrophe Theory and its Applications, London: Pitman Press.700

Prigogine, I. [1996]: The End of Certainty, New York: Free Press. Smith, P. [1991]: `The Butter ̄y E€ect', Proceedings of the Aristotelian Society, 91, pp. 247±67.

Smith, P. [1998]: Explaining Chaos, Cambridge: Cambridge University Press. Tabor, M. [1989]: Chaos and Integrability in Nonlinear Dynamics: An Introduction, New York: John Wiley & Sons.

Teller, P. [1979]: `Quantum Mechanics and the Nature of Continuous Physical Quantities', The Journal of Philosophy, 76, pp. 345±61.

Truesdell, C. and Muncaster, R. G. [1980]: Fundamentals of Maxwell's Kinetic Theory of a Simple Monatomic Gas, New York: Academic Press.

Truesdell, C. [1984]: An Idiot's Fugitive Essays on Science, New York: Springer-Verlag. Williams, R. F. [1979]: `The structure of Lorenz attractors', Publications MatheÂmatiques de l'Institut des Hautes EÂtudes Scienti®ques, 50, p. 321.

Wilson, M. [1991]: `Law Along the Frontier: Di€erential Equations and Their Boundary Conditions', in A. Fine (ed.), PSA 1990, Vol. 2, East Lansing: Philosophy of Science Association, pp. 565±75.

Wimsatt, W. C. [1987]: `False Models as Means to Truer Theories', in M. Nitecki and A. Ho€mann (eds), Neutral Models in Biology, New York: Oxford University Press, pp. 23±55.


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