  Under a standard set of assumptions for a hidden-variables model for quantum
events, we show that all observables must commute simultaneously. And, despite
Bell's complaint that a key condition of von Neumann's was quite unrealistic,
we show these these conditions are entirely equivalent to those later
introduced by Bell, Kochen and Specker. As is it known that these conditions
are also equivalent to those under which the Bell-Clauser-Horne inequalities
are derived, we see that any experimental violations of the inequalities
demonstrate only that quantum observables do not commute.The same conclusion
applies to the collection of elegant inequality-free no-go proofs of
Greenberger-Horne-Zeilinger, Mermin and Peres. Otherwise expressed, the usual
hidden-variable models have assumptions that are collectively too strong to be
interesting, and hence need modification or deletion.
