European Journal for Philosophy of Science
, Volume 1, Issue 2, pp 193225
First online:
On the observational equivalence of continuoustime deterministic and indeterministic descriptions
 Charlotte WerndlAffiliated withDepartment of Philosophy, Logic and Scientific Method, London School of Economics Email author
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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.
Keywords
Observational equivalence Determinism Indeterminism Continuoustime descriptions Classical physics Stochastic processes Ergodic theory 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
 201105
 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