Wolfgang Schwarz

The Problem of Conjunctive Events

This appears to be a problem for Lewis' theories of causation:

Let A,B,C,D be any events such that B depends counterfactually on A, and D on C. Now consider the conjunction (fusion) B+C of B and C. If A had not occurred, B+C would not have occurred. For then B would not have occurred, and presumably B+C can't happen without B. And if B+C had not occurred, C would not have occured either, so (unless the absence of B has some surprising effects on D), D would not have occurred. Hence there is a chain of counterfactual dependence between A and D. But since A,B,C,D were arbitrary, this means that every cause causes every effect.

I can see two possible ways out: First, one could deny the existence of B+C. But unlike disjunctive events, conjunctive events are very common and usually harmless: Many big events, like wars and walks, consist of smaller events, like battles and paces. It's not clear how the bad conjunctions are to be ruled out. Moreover, Lewis often needs rather artificial conjunctions. Thus he solves Frankfurt's case of Jones and the neuroscientist with the help of an event that consists partly of Jones' brain state, partly of the neuroscientist's decision (p.193 of "Causation as Influence").

Second, one could deny that without B+C, C would not have occurred. Maybe the closest possible world without B+C is one where enough of C remains to bring about D? But this is not how we usually evaluate causal counterfactuals, and certainly not what Lewis tells us:

When asked to suppose counterfactually that [B+C] does not occur, we do not really look for the very closest possible world where [B+C]'s conditions of occurrence are not quite satisfied. Rather, we imagine that [B+C] is completely and cleanly excised from history, leaving behind no fragment or approximation of itself. ("Causation as Influence", p.190)

The problem doesn't get easier on the new "Influence" theory: If A influences B, then clearly A also influences B+C. And if C influences D, then B+C influences D.