Bell's theorem in an indeterministic universe

Donald Bedford

Henry Stapp

pp. 139-164

in: Synthese 102 (1), 1995.

Abstract

A variation of Bell's theorem that deals with the indeterministic case is formulated and proved within the logical framework of Lewis's theory of counterfactuals. The no-faster-than-light-influence condition is expressed in terms of Lewis ‘would’ counterfactual conditionals. Objections to this procedure raised by certain philosophers of science are examined and answered. The theorem shows that the incompatibility between the predictions of quantum theory and the idea of no faster-than-light influence cannot be ascribed to any auxiliary or tacit assumption of either determinism or the related idea that outcomes of unperformed measurements are determinate within nature. In addition, the theorem provides an example of an application of Lewis's theory of counterfactuals in a rigorous scientific context.