  After having offered his variant of the argument against HV theories from Gleason’s theorem, Bell proceeds to criticise it. His strategy parallels the one against von Neumann. Bell points out that his own Gleason-type argument against arbitrary closeness of two opposite-valued points presupposes non-trivial relations between values of non-commuting observables, which are only justified given an assumption of noncontextuality (NC). He proposes as an analysis of what went wrong that his own argument “tacitly assumed that measurement of an observable must yield the same value independently of what other measurements may be made simultaneously” (1966: 9). In opposition to von Neumann, the Gleason-type argument derives restrictions on value assignments like (3) only for sets of compatible observables; but still one and the same observable can be a member of different commuting sets, and it is essential to the arguments that the observable gets assigned the same value in both sets, i.e. that the value assignment is not sensitive to a context.