The Bell 1964 theorem states that nonlocality is a necessary feature of hidden variable theories that reproduce the statistical predictions of quantum mechanics. In view of the no-go theorems for non-contextual hidden variable theories already existing up to 1964, and due to Gleason and Bell, one is forced to acknowledge the contextual character of the hidden variable theory which the Bell 1964 theorem refers to. Both the mathematical and the physical justifications of this contextualism are reconsidered. Consequently, the role of (...) contextualism in recent no-hidden-variables proofs and the import of these proofs are investigated. With reference to the physical intuition underlying contextualism, the possibility is considered whether a context-dependence of individual measurement results is compatible with context-independence of the statistics of measurement results. (shrink)

Let A 1 , A 2 , A 3 A 4 be four observables, the compatible observables among them being (A 1 , A 3 ), (A 1 , A 4 ), (A 2 , A 3 ), (A 2 , A 4 ). In order that the empirical data be reproducible by a quantum or a classical theory, the two-point correlation functions $$\{ C_{ij} = \left\langle {A_i A_j } \right\rangle :i,j a compatible pair\} $$ must necessarily satisfy $$|X_{13} X_{14} (...) - X_{23} X_{24} | \leqslant \left( {1 - X_{13} ^2 } \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \left( {1 - X_{14} ^2 } \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} + \left( {1 - X_{23} ^2 } \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \left( {1 - X_{24} ^2 } \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} (*)$$ where Xij=CijC ii −1/2 C jj −1/2 . In the case ofGaussian data, this inequality is alsosufficient; If (*) holds, there is a Gaussian joint distribution for A 1 , A 2 , A 3 , A 4 which reproduces the Gaussian data for compatible pairs. It follows that Bell's inequality is satisfied by all true-false propositions about the Gaussian data. A further consequence of the analysis is thatquantum Gaussian fields satisfy Bell's inequality for all true-false propositions aboutfield measurements.The maximum violation of (*) corresponds to Rastall's example in the case of two-valued observables. (shrink)

The Bell/CHSH inequalities of quantum physics are identical with the inequalities derived in mathematical psychology for the problem of selective influences in cases involving two binary experimental factors and two binary random variables recorded in response to them. The following points are made regarding cognitive science applications: (1) compliance of data with these inequalities is informative only if the data satisfy the requirement known as marginal selectivity; (2) both violations of marginal selectivity and violations of the Bell/CHSH inequalities are interpretable (...) as indicating that at least one of the two responses is influenced by both experimental factors. (shrink)