On the observational equivalence of continuous-time deterministic and indeterministic descriptions

Abstract. This paper presents and philosophically assesses three types of results on the observational equivalence of continuous-time measure-theoretic deterministic and indeter-mathematical descriptions. The second results are stronger because they show observa-tional 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 im-ply 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 crit-icise the extant claims of philosophers and mathematicians on observational equivalence. This article has been published in the European Journal for the Philosophy of Science