Can the world be shown to be indeterministic after all?

This essay considers and evaluates recent results and arguments from classical chaotic systems theory and non-relativistic quantum mechanics that pertain to the question of whether our world is deterministic or indeterministic. While the classical results are inconclusive, quantum mechanics is often assumed to establish indeterminism insofar as the measurement process involves an ineliminable stochastic element, even though the dynamics between two measurements is considered fully deterministic. While this latter claim concerning the Schrödinger evolution must be qualified, the former fully depends on a resolution of the measurement problem. Two alleged proofs that nature is indeterministic, relying, in turn, on Gleason’s theorem and Conway and Kochen’s recent ‘free will theorem’, are shown to be wanting qua proofs of indeterminism. We are thus left with the conclusion that the determinism question remains open. Do probabilities exist out there in the world, independently of our epistemic situation in it; or are they mere indications of our imperfect knowledge of matters of fact? This old question has recently, and very recently, been enriched by new results. The purpose of this paper is to introduce and discuss these results, as well as to appraise the status of probabilities as objective or subjective in a world that is either deterministic or indeterministic. But first and foremost, this essay addresses the dual issues of whether our world is deterministic or indeterministic and of whether we can ever know this. There are at least two roles that probabilities can play in a dynamical theory. First, they may codify a distribution over initial or boundary conditions. Second, probabilities may concern the dynamical evolution given a certain initial state of the physical system at stake. Orthogonally, probabilities in either role may be objectively in the world, i.e. real world chances, or they may be subjective and arise only due to our ignorance of the exact state of affairs in the world. A subjective probability distribution over initial conditions would simply mean that although it is the case that the world was in some particular initial state, we don’t know which and the probability distribution encodes our best guess concerning the likelihoods with which the different initial states obtained. It is somewhat less straightforward to say what objective probabilities on initial conditions might be. They may be generated by a random process, but as we turn to the initial conditions of the whole universe, this approach no longer succeeds. One way to get them may be via a multiverse, perhaps of non-denumerably many universes, where the probabilities over initial states capture the (measure-theoretic) frequency of the particular initial states. Note that in this case, we may have objective and subjective probabilities, where the latter need not coincide with the objective ones, but rather result from our limited knowledge about the objective distribution. Another way, following Barry Loewer (2001), would be to argue that a Humean best-system analysis entails that the probability distribution over initial states in statistical mechanics is objective. For the probabilities pertaining to the dynamical evolution, the dynamical probabilities, the existence, at the fundamental level, of objective and subjective probabilities seems to line up neatly with indeterministic and deterministic worlds, respectively. If the world is deterministic, then one would expect that the (non-trivial) dynamical probabilities that feature in physical theories are nothing but reflections of our incomplete knowledge of the dynamics in that world. Objective