The central question of this paper is: are deterministic and inde-terministic descriptions observationally equivalent in the sense that they give the same predictions? I tackle this question for measure-theoretic deterministic systems and stochastic processes, both of which are ubiquitous in science. I first show that for many measure-theoretic deterministic systems there is a stochastic process which is observa-tionally equivalent to the deterministic system. Conversely, I show that for all stochastic processes there is a measure-theoretic deter-ministic system which is observationally equivalent to the stochastic process. Still, one might guess that the measure-theoretic determin-istic systems which are observationally equivalent to stochastic pro-cesses 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 measure-theoretic 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 de-terministic systems used in science which give the same predictions at every observation level as Markov processes. All these results show that measure-theoretic deterministic systems and stochastic processes are observationally equivalent more often than one might perhaps ex-pect. Furthermore, I criticise the claims of the previous philosophy

Deterministic versus indeterministic descriptions: not that

It can be shown that certain kinds of classical deterministic descrip-tions and indeterministic descriptions are observationally equivalent. In these cases there is a choice between deterministic and indetermin-istic 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

The central question of this paper is: are deterministic and inde-terministic descriptions observationally equivalent in the sense that they give the same predictions? I tackle this question for measure-theoretic deterministic systems and stochastic processes, both of which are ubiquitous in science. I first show that for many measure-theoretic deterministic systems there is a stochastic process which is observa-tionally equivalent to the deterministic system. Conversely, I show that for all stochastic processes there is a measure-theoretic deter-ministic system which is observationally equivalent to the stochastic process. Still, one might guess that the measure-theoretic determin-istic systems which are observationally equivalent to stochastic pro-cesses 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 measure-theoretic 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 de-terministic systems used in science which give the same predictions at every observation level as Markov processes. All these results show that measure-theoretic deterministic systems and stochastic processes are observationally equivalent more often than one might perhaps ex-pect. Furthermore, I criticise the claims of the previous philosophy

Deterministic versus indeterministic descriptions: not that different after all?