In a recent paper, Robert Griffiths has argued, based on the consistent
histories interpretation, that Hilbert space quantum mechanics (QM) is non-contextual.
According to Griffiths, the problem of contextuality disappears if the apparatus is
“designed and operated by a competent experimentalist” and we accept the Single
Framework Rule (SFR). In the present paper we will argue that Griffiths’ conclusion is
untenable. Firstly, we will argue that Kochen-Specker (KS) type contextuality has
nothing to do with the measurement processes nor the measurement problem – solving
this problem does not necessarily remove contextuality. Secondly, that the
consideration of counterfactual situations is endemic when reasoning by means of
physics. Griffiths’ SFR amounts to an unprincipled (or impractical) denial of this fact.
Thirdly, that Griffiths’ demonstration implies, as a direct consequence, that QM allows
a Global Valuation for all properties independently of the context. This would mean not
only that KS theorem is false, but also that the SFR is completely unnecessary. Finally,
we will argue that quantum contextuality should be reconsidered – instead of as a
problem that we need to escape – as a main feature of the formalism which must be
positively taken into account in order to provide a coherent representation of physical
reality and explain what QM is talking about.

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