  Does determinism (or even the incompleteness of quantum mechanics) follow
from locality and perfect correlations? In a 1964 paper John Bell gave the
first demonstration that quantum mechanics is incompatible with local hidden
variables. Since then a vigorous debate has rung out over whether he relied on
an assumption of determinism or instead, as he later claimed in a 1981 paper,
derived determinism from assumptions of locality and perfect correlation. This
paper aims to bring clarity to the debate via simple examples and rigorous
results. It is first recalled, via quantum and classical counterexamples, that
the weakest statistical form of locality consistent with Bell's 1964 paper
(parameter independence) is insufficient for the derivation of determinism.
Attention is then turned to critically assess Bell's appealing to the
Einstein-Rosen-Podolsky incompleteness argument to support his claim. It is
shown this argument is itself incomplete, via counterexamples that expose two
logical gaps. However, closing these gaps via a strong ``counterfactual''
reality criterion enables a rigorous derivation of each of quantum
incompleteness, determinism and parameter independence, and in this sense
justifies Bell's claim. Consequences for quantum interpretations are briefly
discussed.
