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Are deterministic descriptions and indeterministic descriptions observationally equivalent?

Werndl, Charlotte (2009) Are deterministic descriptions and indeterministic descriptions observationally equivalent? Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 40 (3). pp. 232-242. ISSN 1355-2198

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Abstract

The central question of this paper is: are deterministic and indeterministic descriptions observationally equivalent in the sense that they give the same predictions? I tackle this question for measure-theoretic deterministic systems and stochastic processes, both of which are ubiquitous in science. I first show that for many measure-theoretic deterministic systems there is a stochastic process which is observationally equivalent to the deterministic system. Conversely, I show that for all stochastic processes there is a measure-theoretic deterministic system which is observationally equivalent to the stochastic process. Still, one might guess that the measure-theoretic deterministic systems which are observationally equivalent to stochastic processes used in science do not include any deterministic systems used in science. I argue that this is not so because deterministic systems used in science even give rise to Bernoulli processes. Despite this, one might guess that measure-theoretic deterministic systems used in science cannot give the same predictions at every observation level as stochastic processes used in science. By proving results in ergodic theory, I show that also this guess is misguided: there are several deterministic systems used in science which give the same predictions at every observation level as Markov processes. All these results show that measure-theoretic deterministic systems and stochastic processes are observationally equivalent more often than one might perhaps expect. Furthermore, I criticize the claims of some previous philosophy papers on observational equivalence.

Item Type: Article
Official URL: http://www.elsevier.com/wps/find/journaldescriptio...
Additional Information: © 2009 Elsevier Ltd.
Library of Congress subject classification: B Philosophy. Psychology. Religion > B Philosophy (General)
Q Science > QA Mathematics
Sets: Departments > Philosophy, Logic and Scientific Method
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 04 Jan 2011 13:37
URL: http://eprints.lse.ac.uk/31094/

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