Abstract
Probabilistic phenomena are often perceived as being problematic targets for contrastive explanation. It is usually thought that the possibility of contrastive explanation hinges on whether or not the probabilistic behaviour is irreducibly indeterministic, and that the possible remaining contrastive explananda are token event probabilities or complete probability distributions over such token outcomes. This paper uses the invariance-under-interventions account of contrastive explanation to argue against both ideas. First, the problem of contrastive explanation also arises in cases in which the probabilistic behaviour of the explanandum is due to unobserved causal heterogeneity. Second, it turns out that, in contrast to the case of pure indeterminism, the plausible contrastive explananda under causal heterogeneity are not token event probabilities, but population-level statistical facts.
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Notes
Percival (2000) makes a distinction between strongly chancy events that have a non-trivial objective probability of occurring for all times in their causal history, and weakly chancy events that are truly chancy only for some parts of their causal history. This distinction is rarely, if ever, empirically determinable and therefore cannot be used to solve the problem of contrastive explanation under indeterminism.
The fact that Hempel had to resort to the requirement of maximal specificity to deal with the problems of ambiguity and epistemic relativity (see, e.g., Niiniluoto 2000) should be seen as an argument against the broader Hempelian framework, not as an argument for maximal specificity.
Note that this is a non-standard way of formulating the quantum-physical problem. I have no idea whether such a function can be given a closed-form expression. In general, such functional dependencies are often harder to determine compared to the joint distribution of the variables and this difficulty may be seen as one facet of the general problematic of probabilities and contrastive explanation.
do(X = x) indicates, in the usual manner, that the value of X variable was set to x by an intervention. Since this expression is here used merely to remind the reader of the intended interpretation of the conditioning event and no formal work is done with it, no rigorous definitions are offered.
Granted, sometimes these kinds of counterfactual evaluations are precisely the point of causal language. For example, sometimes the heritability measure H 2 (which is just R 2 with H for heritability) is used as if to gauge the causal contribution of the genome for a trait in a population. What this purported causal factor expressing the contribution of the genome is supposed to tell us is how the traits would have developed, if we indeed had reshuffled all the environmental factors during the development. However, even this usage is usually seen as very problematic (Lewontin 1974).
There are important differences in the conditions under which average treatment effects can be consistently estimated for different sub-populations. However, since these differences are not important for the philosophical points developed here, they are not discussed further.
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The author would like to thank the reviewers and the audience of the Philosophy of Science Seminar at the University of Helsinki for their valuable comments. This research has been supported by the Academy of Finland.
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Kuorikoski, J. Contrastive statistical explanation and causal heterogeneity. Euro Jnl Phil Sci 2, 435–452 (2012). https://doi.org/10.1007/s13194-012-0050-1
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DOI: https://doi.org/10.1007/s13194-012-0050-1