Werndl, Charlotte (2009) Are Deterministic Descriptions And Indeterministic Descriptions Observationally Equivalent? [Preprint]

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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 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 papers Suppes (1993, 1999), Suppes and de Barros (1996) and Winnie (1998) on observational equivalence.
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Item Type:  Preprint  

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Additional Information:  Forthcoming in Studies in History and Philosophy of Modern Physics  
Keywords:  Determinism, Indeterminism, Observational Equivalence, Prediction, Ergodic Theory, Stochastic Processes, Chaos  
Subjects:  Specific Sciences > Physics > Classical Physics General Issues > Determinism/Indeterminism Specific Sciences > Physics > Statistical Mechanics/Thermodynamics 

Depositing User:  Charlotte Werndl  
Date Deposited:  01 Oct 2009  
Last Modified:  06 Jun 2011 11:02  
Item ID:  4924  
Subjects:  Specific Sciences > Physics > Classical Physics General Issues > Determinism/Indeterminism Specific Sciences > Physics > Statistical Mechanics/Thermodynamics 

Date:  August 2009  
URI:  http://philsciarchive.pitt.edu/id/eprint/4924 
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