  The well known Bell experiment with two actors Alice and Bob is considered.
First the simple deduction leading to the CHSH inequality under local realism
is reviewed, and some arguments from the literature are recapitulated. Then I
take up certain background themes before I enter a discussion of Alice's
analysis of the situation. An important point is that her mind is limited by
the fact that her Hilbert space in this context is two-dimensional. General
statements about a mind's limitation during a decision process are derived from
recent results on the reconstruction of quantum theory from conceptual
variables. These results apply to any decision situation. Let all the data from
the Bell experiment be handed over to a new actor Charlie, who performs a data
analysis. But his mind is also limited: He has a four-dimensional Hilbert space
in the context determined by the experiment. I show that this implies that
neither Alice nor Charlie can have the argument leading to the CHSH inequality
as a background for making decisions related to the experiment. Charlie may be
any data analyst, and he may communicate with any person. It is argued that no
rational person can be convinced by the CHSH argument when making empirical
decisions on the Bell situation.
