On the observational equivalence of continuoustime deterministic and indeterministic descriptions
 Charlotte Werndl
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This paper presents and philosophically assesses three types of results on the observational equivalence of continuoustime measuretheoretic deterministic and indeterministic descriptions. The first results establish observational equivalence to abstract mathematical descriptions. The second results are stronger because they show observational equivalence between deterministic and indeterministic descriptions found in science. Here I also discuss Kolmogorov’s contribution. For the third results I introduce two new meanings of ‘observational equivalence at every observation level’. Then I show the even stronger result of observational equivalence at every (and not just some) observation level between deterministic and indeterministic descriptions found in science. These results imply the following. Suppose one wants to find out whether a phenomenon is best modeled as deterministic or indeterministic. Then one cannot appeal to differences in the probability distributions of deterministic and indeterministic descriptions found in science to argue that one of the descriptions is preferable because there is no such difference. Finally, I criticise the extant claims of philosophers and mathematicians on observational equivalence.
 Berkovitz, J., Frigg, R., & Kronz, F. (2006). The Ergodic Hierarchy, Randomness and Hamiltonian Chaos. Studies in History and Philosophy of Modern Physics, 37, 661–691. CrossRef
 Butterfield, J. (2005). Determinism and indeterminism. Routledge Encyclopaedia of Philosophy Online.
 Cornfeld, I. P., Fomin, S. V., & Sinai, Y. G. (1982). Ergodic theory. Berlin: Springer.
 Doob, J. L. (1953). Stochastic processes. New York: John Wiley & Sons.
 Eagle, A. (2005). Randomness is unpredictability. The British Journal for the Philosophy of Science, 56, 749–790. CrossRef
 Eckmann, J.P., & Ruelle, D. (1985). Ergodic theory of chaos and strange attractors. Reviews of Modern Physics, 57, 617–654. CrossRef
 Feldman, J., & Smorodinksy, M. (1971). Bernoulli flows with infinite entropy. The Annals of Mathematical Statistics, 42, 381–382. CrossRef
 Halmos, P. (1944). In general a measurepreserving transformation is mixing. The Annals of Mathematics, 45, 786–792. CrossRef
 Halmos, P. (1949). Measurable transformations. Bulletin of the American Mathematical Society, 55, 1015–1043. CrossRef
 Hopf, E. (1932). Proof of Gibbs’ hypothesis on the tendency toward statistical equilibrium. Proceedings of the National Academy of Sciences of the United States of America, 18, 333–340. CrossRef
 Janssen, J., & Limnios, N. (1999). SemiMarkov models and applications. Dotrecht: Kluwer Academic Publishers.
 Krieger, W. (1970). On entropy and generators of measurepreserving transformations. Transactions of the American Mathematical Society, 149, 453–456. CrossRef
 Lorenz, E. (1963). Deterministic nonperiodic flow. Journal of the Atmospheric Sciences, 20, 130–141. CrossRef
 Luzzatto, S., Melbourne, I., & Paccaut, F. (2005). The Lorenz attractor is mixing. Communications in Mathematical Physics, 260, 393–401. CrossRef
 Ornstein, D. (1970). Imbedding Bernoulli shifts in flows. In A. Dold, & B. Eckmann (Eds.), Contributions to Ergodic theory and probability, proceedings of the first Midwestern conference on Ergodic theory (pp. 178–218). Berlin: Springer.
 Ornstein, D. (1974). Ergodic theory, randomness, and dynamical systems. New Haven and London: Yale University Press.
 Ornstein, D., & Galavotti, G. (1974). Billiards and Bernoulli schemes. Communications in Mathematical Physics, 38, 83–101. CrossRef
 Ornstein, D., & Weiss, B. (1991). Statistical properties of chaotic systems. Bulletin of the American Mathematical Society, 24, 11–116. CrossRef
 Park, K. (1982). A special family of Ergodic flows and their \(\bar{d}\) limits. Israel Journal of Mathematics, 42, 343–353. CrossRef
 Petersen, K. (1983). Ergodic theory, Cambridge: Cambridge University Press.
 Radunskaya, A. (1992). Statistical properties of deterministic Bernoulli flows. Ph.D. Dissertation, Stanford: University of Stanford.
 Simányi, N. (2003). Proof of the BoltzmannSinai Ergodic hypothesis for typical hard disk systems. Inventiones Mathematicae, 154, 123–178. CrossRef
 Sinai, Y. G. (1989). Kolmogorov’s work on Ergodic theory. The Annals of Probability, 17, 833–839. CrossRef
 Strogatz, S. H. (1994). Nonlinear dynamics and chaos, with applications to physics, biology, chemistry, and engineering. New York: Addison Wesley.
 Suppes, P. (1999). The noninvariance of deterministic causal models. Synthese, 121, 181–198. CrossRef
 Suppes, P., & de Barros, A. (1996). Photons, billiards and chaos. In P. Weingartner, & G. Schurz (Eds.), Law and prediction in the light of chaos research (pp. 189–207). Berlin: Springer. CrossRef
 Uffink, J. (2007). Compendium to the foundations of classical statistical physics. In J. Butterfield, & J. Earman (Eds.), Philosophy of physics (handbooks of the philosophy of science B) (pp. 923–1074). Amsterdam: NorthHolland.
 Werndl, C. (2009a). Are deterministic descriptions and indeterministic descriptions observationally equivalent? Studies in History and Philosophy of Modern Physics, 40, 232–242. CrossRef
 Werndl, C. (2009b). What are the new implications of chaos for unpredictability? The British Journal for the Philosophy of Science, 60, 195–220. CrossRef
 Werndl, C. (2011). On choosing between deterministic and indeterministic descriptions: underdetermination and indirect evidence (unpublished manuscript).
 Winnie, J. (1998). Deterministic chaos and the nature of chance. In J. Earman, & J. Norton (Eds.), The cosmos of science—essays of exploration (pp. 299–324). Pittsburgh: Pittsburgh University Press.
 Title
 On the observational equivalence of continuoustime deterministic and indeterministic descriptions
 Journal

European Journal for Philosophy of Science
Volume 1, Issue 2 , pp 193225
 Cover Date
 20110501
 DOI
 10.1007/s1319401000115
 Print ISSN
 18794912
 Online ISSN
 18794920
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Observational equivalence
 Determinism
 Indeterminism
 Continuoustime descriptions
 Classical physics
 Stochastic processes
 Ergodic theory
 Authors

 Charlotte Werndl ^{(1)}
 Author Affiliations

 1. Department of Philosophy, Logic and Scientific Method, London School of Economics, Houghton Street, London, WC2A 2AE, UK