This is a paper I wrote for a collection on probability in physics, edited by Claus Beisbart and Stephan Hartmann. A preprint can be found at the Pitt PhilSci Archive.
Here’s the 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.
Bibliographic reference: To appear in Claus Beisbart and Stephan Hartmann (eds.), Probabilities in Physics, Oxford: Oxford University Press.