Can the World Beshown to be Indeterministic after all?

Abstract

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.

An Operationalist Perspective on Setting Dependence

“…Its (in)famous reformulation with an emphasis on "free will" is due to Conway and Kochen [6,7]. 15 See [5,14,43] for discussion on the distinction between the philosophical implications of Bell's theorem and the free will theorem and further discussion. 16 Bohmian mechanics, for example, is usually taken not to suffer from a free will problem.…”

Did the Universe Have a Chance?

“…A second contrast to consider concerns how chances are implemented in a probabilistic physical theory, namely as initial chances or dynamical chances. This is a context class that is emphasized by, among others, (Maudlin, 2011;Wüthrich, 2011), taking as a model the idea that dynamical theories explain via two things: laws of evolution and initial conditions (Hempel, 1965). So, on the one hand, probabilities may all have their source in initial chances, as in the accounts of Loewer and Demarest described above, while having an otherwise deterministic dynamics; on the other hand, probabilities may by dynamical, in the sense that the laws of evolution are probabilistic laws, specifying only probabilities for state transitions.…”

Metaphysics of Science as Naturalized Metaphysics

“…The socalled free will theorem by Kochen (2006 and does not show anything standing up to scrutiny that is not already given by Bell's theorem. See notably Tumulka (2009), Goldstein et al (2010) and Wüthrich (2011). foliation of space-time into three-dimensional, spatial hypersurfaces that are ordered in time (general relativity).…”