BELL THEOREM IN AN INDETERMINISTIC UNIVERSE

A variation of Bell's theorem that deals with the indeterministic case is formulated and proved within the logical framework of Lewis's theo ry of counterfactuals. The no-faster-than-light-influence condition is expressed in terms of Lewis 'would' counterfactual conditionals. Obje ctions to this procedure raised by certain philosophers of science are examined and answered. The theorem shows that the incompatibility bet ween the predictions of quantum theory and the idea of no faster-than- light influence cannot be ascribed to any auxiliary or tacit assumptio n of either determinism or the related idea that outcomes of unperform ed measurements are determinate within nature. In addition, the theore m provides an example of an application of Lewis's theory of counterfa ctuals in a rigorous scientific context.