Against a Minimalist Reading of Bell's Theorem: Lessons from Fine

Since the validity of Bell’s inequalities implies the existence of joint probabilities for non-commuting observables, there is no universal consensus as to what the violation of these inequalities signifies. While the majority view is that the violation teaches us an important lesson about the possibility of explanations, if not about metaphysical issues, there is also a minimalist position claiming that the violation is to be expected from simple facts about probability theory. This minimalist position is backed by theorems due to A. Fine and I. Pitowsky. Our paper shows that the minimalist position cannot be sustained. To this end, we give a formally rigorous interpretation of joint probabilities in the combined modal and spatiotemporal framework of ‘stochastic outcomes in branching space-time’ (SOBST) (Kowalski and Placek, 1999; Placek, 2000). We show in this framework that the claim that there can be no joint probabilities for non-commuting observables is incorrect. The lesson from Fine’s theorem is not that Bell’s inequalities will be violated anyhow, but that an adequate model for the Bell/Aspect experiment must not define global joint probabilities. Thus we investigate the class of stochastic hidden variable models, which prima facie do not define such joint probabilities. The reason why these models fail supports the majority view: Bell’s inequalities are not just a mathematical artifact.