This article contains a review of Nelson's analysis of Bell's theorem. It
shows that Bell's inequalities can be violated with a theory of local random
variables if one accepts that the outcomes of these variables are not
predetermined prior to measurement. The article describes the relation between
Bell's theorem and the Strong Free Will theorem of Conway and Kochen. Then, the
original articles of Bell are analyzed in detail. Following an article of
Faris, it is explained that Bell's work on the hidden variable question in fact
describes two separate theorems. Bell's first theorem says that there can be no
model for the singlet state where an outcome does not depend locally on the
settings of the detector where the outcome was measured. Bell's second theorem
shows that Bell's inequalities can be violated by a theory that is either not
deterministic, or violates causality in the sense of relativity or the free
will assumption of the experimenters. It is shown in detail where Bell
implicitly makes the various locality assumptions that Nelson has shown to be
necessary for deriving Bell's inequality. The article closes by relating the
various assumptions needed to derive Bell's theorem with the reality criterion
of EPRComment: 19 pages, section added where Bell's original articles are analyzed
and compared in detail with Nelson's wor