  John Bell once argued that one ought to select, out of the 'observables' of
quantum theory, some subset of 'beables' that can be consistently ascribed
determinate values. Moreover, this subset should be selected so as to guarantee
(among other things) that we can dispense with the orthodox interpretation's
loose talk about 'measurement values': "...the probability of a beable being a
particular value would be calculated just as was formerly calculated the
probability of observing that value". Working in the framework of C*-algebras
(in particular, Segal algebras), I propose an algebraic characterization of
those subsets of bounded observables of a quantum system that can have beable
status with respect to any (fixed) state of the system. It turns out that
observables with beable status in a state need not all commute (a possibility
Bell himself does not consider), but they must at least form a certain kind of
'quasicommutative' subalgebra determined by the state. A virtue of the analysis
is that it applies to beables with continuous spectra, usually neglected in
discussions of the no-hidden-variables theorems. In the (very) special case
where the algebra of observables for a system is representable on a
finite-dimensional Hilbert space, I give a complete characterization of the
maximal beable subalgebras determined by any state of the system; the
infinite-dimensional case remains open. These results are discussed in relation
to previous results of a similar nature, to 'no-collapse' interpretations of
quantum mechanics, and to algebraic relativistic quantum field theory.
