AbstractThe 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 criticise the claims of the previous philosophy papers Suppes (1993, 1999), Suppes and de Barros (1996) and Winnie (1998) on observational equivalence.
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Citations of this work
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Causation as folk science.John D. Norton - 2003 - In Huw Price & Richard Corry (eds.), Philosophers' Imprint. Oxford University Press.
What Are the New Implications of Chaos for Unpredictability?Charlotte Werndl - 2009 - British Journal for the Philosophy of Science 60 (1):195-220.
The ergodic hierarchy, randomness and Hamiltonian chaos.Joseph Berkovitz, Roman Frigg & Fred Kronz - 2006 - Studies in History and Philosophy of Modern Physics 37 (4):661-691.