This paper presents and philosophically assesses three types of results onthe observational equivalence of continuous-time measure-theoreticdeterministic and indeterministic descriptions. The first results establishobservational equivalence to abstract mathematical descriptions. The secondresults are stronger because they show observational equivalence betweendeterministic and indeterministic descriptions found in science. Here I alsodiscuss Kolmogorov's contribution. For the third results I introduce two newmeanings of `observational equivalence at every observation level'. Then I showthe even stronger result of observational equivalence at every (and not justsome) observation level between deterministic and indeterministic descriptionsfound in science. These results imply the following. Suppose one wants to findout whether a phenomenon is best modeled as deterministic or indeterministic.Then one cannot appeal to differences in the probability distributions ofdeterministic and indeterministic descriptions found in science to argue thatone of the descriptions is preferable because there is no such difference.Finally, I criticise the extant claims of philosophers and mathematicians onobservational equivalence.
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