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These contentions about the connection between causal claims and statistical relevance relations are consequences of a more general principle called the Causal Markov condition which has been extensively discussed in the recent literature on causation.[ 10 ] A set of variables standing in a causal relationship and an associated probability distribution over those variables satisfy the Causal Markov condition if and only if conditional on its direct causes every variable is independent of every other variable except possibly Scientific software for its effects. Two relevant points have emerged from discussion of this condition. The first, which was in effect noted by Salmon himself in work subsequent to his (1971), is that there are circumstances in which the Causal Markov condition fails and hence in which causal claims do not imply the screening off relationships described above. This can happen, for example, if the variables to which the condition is applied are characterized in an insufficiently fine-grained way.[ 11 ] The second and more fundamental observation is that, depending on the details of the case, many different sets of causal relationships may be compatible with the same statistical relevance relationships. For example, a structure in which B causes mathlab A which in turn causes S will, if we assume the Causal Markov condition (that is, make assumptions like Salmon's connecting causation and statistical relevance relationships), lead to exactly the same statistical relevance relationships as in the example in which A is a common cause of B and S. Similarly if S causes A which in turn causes B. In structures with more variables, this underdetermination of causal relationships by statistical relevance relationships may be far more extreme. Thus a list of statistical relevance relationships, which is what the SR model provides, need not tell us which causal relationships are operative. To the extent that explanation has to do with the identification of the causal relationships on which an explanandum-outcome depends, the SR model fails to fully capture these.
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