International Journal of Theoretical Physics, Vol. 37, No. 1, 1998 Context Independence as a Statistical Property of Hidden Variable Theories Federico Laudisa 1 Received July 4, 1997 The context dependence of Bell local hidden variable theory is reconsidered both in its mathematical and physical justification. The compatibility of the context dependence of individual measurement results with the context independence of the statistics of measurement results is shown to warrant the consistency of the Bell framework with respect to the Gleason no-hidden-variables theorem. Finally, a sharp distinction between context dependence and (any form of) nonlocal dependence is defended on the background of some recent algebraic proofs of nonlocality. 1. BELL LOCAL CAUSAL THEORIES AND CONTEXTUALISM In his fundamental paper, ªOn the problem of hidden variables in quan- tum mechanics,º John Bell (1966) proved the nonexistence of dispersion- free states in quantum mechanics to follow from less questionable premises with respect to von Neumann’s no-hidden-variable theorem. Two proofs were actually provided, one relying and one not relying on Gleason’s theorem. However, Bell also argued that Gleason’s theorem actually rules out only noncontextual hidden variable theoriesÐaccording to which the result of a measurement of an observable depends only on the state of the system, and not also on the set of (compatible) observables that are measured with itÐand it is as irrelevant as von Neumann’s theorem with respect to contextual hidden variable theories (as is the case with Bohm’s causal interpretation of quantum mechanics). However, in his later formulation of local causal theory, suitable for the derivation of his celebrated inequality, Bell did not explicitly address the problem of contextualism for his own local hidden variable formulation, and 1 Dipartimento di Filosofia, UniversitaÁ di Firenze, 50139 Florence, Italy. 443 0020-7748/98/0100-044 3$15.00/0 q 1998 Plenum Publishing Corporation