I have been bugged for a long time by EPR-Bell's hidden function "lambda" (Bell1964: lambda is a hidden 'variable or a set, or even a set of functions'). Here's my latest problem with it. Triggered by some recent discussions which brought up papers, in which is argued (and claimed to be proved) that Bell's inequality is equally applicable to non-local as to local influences, I suddenly remembered the following remarks by Bell: BERTLMANN'S SOCKS AND THE NATURE OF REALITY "It is important to note that to the limited degree to which determinism plays a role in the EPR argument, it is not assumed but inferred. What is held sacred is the principle of "local causality" - or "no action at a distance." [..] Let us suppose then that the correlations between A and B in the EPR experiment are likewise "locally explicable". That is to say we suppose that there are variables λ, which, if only we knew them, would allow decoupling of the fluctuations: P(A,B¦a,b,λ) = P1(A¦a,λ) P2(B¦b,λ) ...(11) [..] It is notable that in this argument nothing is said about the locality, or even localizability, of the variables λ. These variables could well include, for example, quantum mechanical state vectors, which have no particular localization in ordinary space time. It is assumed only that the outputs A and B, and the particular inputs a and b, are well localized." Indeed, as Bell stated, λ itself is not necessarily local and could well include parameters of QM; and it may be similarly stochastic, as long as it predicts with certainty the outcomes for certain settings. But then his theorem should be equally valid for NON-local "quantum" influences: His same argument can be given for a probabilistic "quantum function" λ that fully determines the QM predictions, such that P(A|aλ) is not different from P(A|Bbaλ). If not, why not??