Are Deterministic Descriptions And Indeterministic Descriptions Observationally Equivalent?

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 philosoph