Evidence for the Deterministic or the Indeterministic Description? A Critique of the Literature About Classical Dynamical Systems

Abstract

It can be shown that certain kinds of classical deterministic descriptions and indeterministic descriptions are observationally equivalent. In these cases there is a choice between deterministic and indeterministic 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 paper comments on Winnie's (1998) analogy between his argument for the deterministic description and his argument against the prevalence of Bernoulli randomness in deterministic descriptions. It is argued that while there is indeed an analogy, it is also important to see that the arguments are disanalogous in another sense.

Complexity–entropy analysis of daily stream flow time series in the continental United States

“…Our results contribute from an empirical point of view to the discussion about the observational equivalence between measure-theoretic deterministic systems and stochastic processes, in which observational equivalence means that deterministic description, when observed, and indeterministic descriptions gives the same predictions (Werndl 2009). Moreover, if the evidence equally supports a deterministic and a stochastic description, there is underdetermination concerning which description is preferable relative to evidence (Werndl 2012). Indeed, Werndl (2009) showed that every stochastic process is observationally equivalent to a deterministic system and many deterministic systems are observationally equivalent to stochastic processes.…”