 The assumption that a definite value (1 or 0) is to be assigned to each projector on the system’s Hilbert space, with the condition that values assigned to commuting projectors be additive, is a weakening of the assumption of the von Neumann no-go theorem (von Neumann 1932), which assumes that the quantum mechanical additivity of expectation values of all observables, whether represented by commuting operators or not, extends to the hypothetical dispersion-free states (see section 2 of entry on  the Kochen-Specker Theorem).  Despite the prima facie plausibility of this assumption, Bell regards it, too, as physically unmotivated, and therefore, unlike Kochen and Specker, does not regard the Bell-Kochen-Specker theorem as a no-go theorem for hidden-variables theories. The reason for this is that the assumption embodies a condition that was later to be known as  noncontextuality.[1]  In a Hilbert space of dimension greater than two, any projection operator will be a member of more than one complete set of commuting projections. For each of these complete sets, there will be an experiment whose outcomes correspond to the projections in the set. The assumption of noncontextuality amounts to the assumption that a value can be assigned to a projection operator that is independent of which of these experiments is to be performed, or as Bell puts it, that “measurement of an observable must yield the same value independently of what other measurements may be made simultaneously.” The assumption need not hold; “[t]he result of an observation may reasonably depend not only on the state of the system (including hidden variables) but also on the complete disposition of the apparatus” (Bell 1966, 451; 1987b and 2004, 9 ).