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Several preliminary conclusions are suggested by these observations.
First, it is far from obvious that we should try to construct a
single, unified model of statistical explanation that applies to both
quantum mechanics and macroscopic phenomena like delinquency or
recovery from infection. Second, and relatedly, while explanation in
*QM* satisfies the objective homogeneity condition, it is
dubious that the sorts of “statistical explanations” found
in the social and biomedical sciences do so. In other words, if an
objective homogeneity condition is imposed on statistical explanation,
it is not clear that there will mathlab be any examples of successful
statistical explanation outside of quantum mechanics.

With these observations in mind, let us revisit the question of what
is explained by statistical theories, whether quantum mechanical or
macroscopic. As we have seen, both Hempel and Salmon, as well as most
subsequent contributors to the literature on statistical explanation,
have tended to assume that statistical theories that assign a
probability to some outcome strictly between 0 and 1 should
nonetheless be interpreted as explaining that outcome. Given this
common starting point, Salmon is quite persuasive in arguing that it
is arbitrary to hold, as Hempel does, that only individual outcomes
with high probability can be explained. But why should we accept the
starting point? Why not take Salmon's argument instead to be a reason
for rejecting the LaTeX editor idea that statistical theories explain individual
outcomes, whether of high or low probability? If we take this view, we
need not conclude that a theory like *QM* is unexplanatory.
Instead, we may take the explananda of *QM* to be facts about
the probabilities or expectation values of outcomes rather than
individual outcomes themselves. On this view, the explananda that are
explained by *QM* are a (proper) subset of those that can be
derived from it — at least in this respect, the explanations
provided by *QM* are like *DS* explanations in
structure. Woodward (1989) argues that this construal allows us to say
all that we might legitimately wish to say about the explanatory
virtues of *QM*. If this is correct, there is no obvious need
for a separate theory of statistical explanation of individual
outcomes of the sort that Hempel and Salmon sought to devise (But see
footnote 7).