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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).
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