Observational Equivalence of Deterministic and Indeterministic Descriptions and the Role of Different Observations

Conference paper
Part of the The European Philosophy of Science Association Proceedings book series (EPSP, volume 1)

Abstract

Recently some results have been presented which show that certain kinds of deterministic descriptions and indeterministic descriptions are observationally equivalent (Werndl 2009a, 2011). These results prompt interesting philosophical questions, such as what exactly they show or whether the deterministic or indeterministic description is preferable. There is hardly any philosophical discussion about these questions, and this paper contributes to filling this gap. More specifically, first, I discuss the philosophical comments made by mathematicians about observational equivalence, in particular Ornstein and Weiss (1991). Their comments are vague, and I argue that, according to a reasonable interpretation, they are misguided. Second, the results on observational equivalence raise the question of whether the deterministic or indeterministic description is preferable relative to evidence. If the deterministic and indeterministic description are equally well supported by evidence, there is underdetermination. I criticise Winnie’s (1998) argument that, by appealing to different observations, one finds that the deterministic description is preferable. In particular, I clarify a confusion in this argument. Furthermore, I show that the argument delivers the desired conclusion relative to in principle possible observations, but that the argument fails relative to currently possible observations.

References

  1. Chernov, Nikolai, and Roberto Markarian. 2006. Chaotic billiards. Providence: American Mathematical Society.Google Scholar
  2. Janssen, Jacques, and Nikolaos Limnios. 1999. Semi-Markov models and applications. Dordrecht: Kluwer.CrossRefGoogle Scholar
  3. Laudan, Larry. 1995, Damn the consequences! Proceedings and Addresses of the American Philosophical Association 69: 27–34.CrossRefGoogle Scholar
  4. Laudan, Larry, and Jarrett Leplin. 1991. Empirical equivalence and underdetermination. The Journal of Philosophy 88: 449–472.CrossRefGoogle Scholar
  5. Luzzatto, Stefano, Ian Melbourne, and Frederic Paccaut. 2005. The Lorenz attractor is mixing. Communications in Mathematical Physics 260: 393–401.CrossRefGoogle Scholar
  6. Okasha, Samir. 2002. Underdetermination, holism and the theory/data distinction. The Philosophical Quarterly 208: 303–319.CrossRefGoogle Scholar
  7. Ornstein, D. 1970. Imbedding Bernoulli shifts in flows. In Contributions to ergodic theory and probability, eds. Albrecht Dold and Beno Eckmann, 178–218. Berlin: Springer.CrossRefGoogle Scholar
  8. Ornstein, Dan, and Benjamin Weiss. 1991. Statistical properties of chaotic systems. Bulletin of the American Mathematical Society 24: 11–116.CrossRefGoogle Scholar
  9. Simanyi, Nandor. 1999. Ergodicity of hard spheres in a box. Ergodic Theory and Dynamical Systems 19: 741–766.CrossRefGoogle Scholar
  10. Simanyi, Nandor. 2003. Proof of the Boltzmann-Sinai ergodic hypothesis for typical hard disk systems. Inventiones Mathematicae 154: 123–178.CrossRefGoogle Scholar
  11. Suppes, Patrick. 1993. The transcendental character of determinism. Midwest Studies in Philosophy 18: 242–257.CrossRefGoogle Scholar
  12. Werndl, Charlotte. 2009a. Are deterministic descriptions and indeterministic descriptions observationally equivalent? Studies in History and Philosophy of Modern Physics 40: 232–242.CrossRefGoogle Scholar
  13. Werndl, Charlotte. 2009b. What are the new implications of chaos for unpredictability? The British Journal for the Philosophy of Science 60: 195–220.CrossRefGoogle Scholar
  14. Werndl, Charlotte. 2011a. On the observational equivalence of continuous-time deterministic and indeterministic descriptions. European Journal for the Philosophy of Science 1(2): 193–225.CrossRefGoogle Scholar
  15. Werndl, Charlotte. 2011b. On choosing between deterministic and indeterministic models: Underdetermination and Indirect Evidence. Synthese. doi: 10.1007/S1122901199669.Google Scholar
  16. Winnie, J. 1998. Deterministic chaos and the nature of chance. In The cosmos of science – essays of exploration, eds. John Earman and John Norton, 299–324. Pittsburgh, PA: Pittsburgh University Press.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of Philosophy, Logic and Scientific MethodLondon School of Economics and Political ScienceLondonUK

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