Direct and Indirect Causes

Everybody agrees that the distinction between direct and indirect causation is important. And it seems easy to draw, i f an analysis of causation in general is available. The causal influence of one event on another is direct, if it is not mediated by other events in between; otherwise it is indirect. The trouble is with the proviso. Indeed, I contend that the order of analysis must be reversed because the distinction is required for a successful analysis of causation. Such an analysis perhaps proceeds best in two steps: the first analyses direct causation, and the second extends the analysis to indirect causation and thus to causation in general. Such a strategy is at least plausible. For direct causation is a very special case and so may be supposed to be more easily explicable. Then, one might say that the relation "A is a cause of B" is just the transitive closure of the relation "A is a direct cause of B", thus completing the full analysis of causation. 1 The complete story is not so simple; but the idea will turn out to be right. In (1983a), I dealt mainly with the first step direct causation. Here, I deal mainly with indirect causation. Section 2 introduces the conceptual machinery required throughout the paper. Section 3 recapitulates my 1983 explication of direct causes. Section 4 considers the circumstances of direct causal relations in greater detail. Section 5 presents the main difficulties with indirect causes. Section 6, finally, proposes a strategy for dealing with these difficulties and shows that it will work. The whole enterprise is subject to two major constraints. First, I shall discuss only causation of single events. The hope, of course, is that it will emerge from knowledge of causation in the single case what causal laws are. This procedure seems to me to be more likely to succeed than the reverse strategy endorsed by several philosophers$ though I shall not argue the point here. Secondly, I am concerned here only with probabilistic causation because this is the context in which all the problems dealt with here have been raised and have been discussed most extensively. It should be mentioned, however, that each consideration, definition, and theorem of the present paper can routinely be extended to deterministic causation with the help of the theory of ordinal conditional functions (OCFs) I proposed in (1988); only some marginal adjustments may be needed. This follows because deterministic conditional independence defined for OCFs obeys essentially the same laws as probabilistic conditional independence. 3 It is thus possible to unify the deterministic and the probabilistic approach. 4