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Are deterministic descriptions and indeterministic descriptions observationally equivalent
 Studies in the History and Philosophy of Modern Physics
, 2009
"... 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 measuretheoretic deterministic systems and stochastic processes, both of which are ubiquitous in science ..."
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Cited by 17 (6 self)
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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 measuretheoretic deterministic systems and stochastic processes, both of which are ubiquitous in science. I first show that for many measuretheoretic 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 measuretheoretic deterministic system which is observationally equivalent to the stochastic process. Still, one might guess that the measuretheoretic 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 measuretheoretic 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 measuretheoretic deterministic systems and stochastic processes are observationally equivalent more often than one might perhaps expect. Furthermore, I criticise the claims of the previous philosophy
Evidence for the Deterministic or the Indeterministic Description? – A Critique of the Literature about Classical Dynamical Systems
"... It can be shown that certain kinds of classical deterministic descriptions and indeterministic descriptions are observationally equivalent. In these cases there is a choice between deterministic and indeterministic descriptions. Therefore, the question arises of which description, if any, is prefe ..."
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It can be shown that certain kinds of classical deterministic descriptions and indeterministic descriptions are observationally equivalent. In these cases there is a choice between deterministic and indeterministic descriptions. Therefore, the question arises of which description, if any, is preferable relative to evidence. This paper looks at the main argument in the literature (by Winnie, 1998) that the deterministic description is preferable. It will be shown that this argument yields the desired conclusion relative to in principle possible observations where there are no limits, in principle, on observational accuracy. Yet relative to the currently possible observations (the kind of choice of relevance in practice), relative to the actual observations, or relative to in principle observations where there are limits, in principle, on observational accuracy the argument fails because it also applies to situations where the indeterministic description is preferable. Then
Are Deterministic Descriptions And Indeterministic Descriptions Observationally Equivalent?
, 2009
"... 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 measuretheoretic deterministic systems and stochastic processes, both of which are ubiquitous in science ..."
Abstract
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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 measuretheoretic deterministic systems and stochastic processes, both of which are ubiquitous in science. I first show that for many measuretheoretic 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 measuretheoretic deterministic system which is observationally equivalent to the stochastic process. Still, one might guess that the measuretheoretic 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 measuretheoretic 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 measuretheoretic deterministic systems and stochastic processes are observationally equivalent more often than one might perhaps expect. Furthermore, I criticise the claims of the previous philosophy
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"... Deterministic versus indeterministic descriptions: not that different after all? ..."
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Deterministic versus indeterministic descriptions: not that different after all?