Lewis and the Grounding of Intermediate Causes — Epoche B2
Transitivity, not the intermediate event, is what Lewis's chains are for The question, and a frame it does not fit Take a chain in which one event brings about a second and the second brings about a third: a throw, an impact, a shattering. The impact sits in the middle. It is caused, and it causes. A natural question is whether the middle event contributes anything of its own, or whether it is a conduit through which the throw reaches the window. The question is sometimes put using the vocabulary of grounding, and that is a mistake worth clearing away before anything else. Grounding, as the term is used in metaphysics since about 2000, is defined by contrast with causation: it is non-causal determination, the relation that holds when a fact obtains in virtue of another rather than because of it. Asking whether a cause grounds its effect therefore runs two relations together, and asking it of a paper published in 1973 asks a theory to answer a question posed a generation later. Reformulated in David Lewis's own terms the question is sharp and answerable. Does the intermediate event do work in his analysis that the analysis could not do without it? This essay argues that it does, and that the work is of a particular kind: the middle link is where the analysis stores what counterfactual dependence alone cannot capture. It is a repair, not a discovery. That is why the middle link is also where every serious counterexample has struck, and why Lewis changed twice what his chains are made of while never giving up the way they are strung together. The claim is deniable, and the final section says by whom. The analysis in three steps In "Causation" (1973 [1] ) Lewis builds his account in three moves, and it matters that they are separate. First, counterfactual dependence: for distinct actual events, e depends causally on c when, had c not occurred, e would not have occurred. The conditional is read on the possible-worlds semantics Lewis had set out in Counterfactuals , published the same year [2] : it holds when e fails to occur in the closest worlds where c does not. The requirement that the events be distinct is doing quiet work here, since without it the analysis counts a thing's parts as its causes, but that is another argument. Second, the chain: a finite sequence of actual events in which each depends causally on its predecessor. Third, and this is the step under examination, causation is defined as the existence of such a chain. Causation is thus the ancestral of causal dependence, which is to say its transitive closure. Whatever else follows, transitivity follows immediately: if there is a chain from c to d and one from d to e, there is one from c to e. Why the third step is there Lewis did not take the ancestral for elegance. He took it because dependence alone gives the wrong answer in cases of preemption, and it is worth walking through one. An assassin poisons a cup of coffee. A second assassin stands ready and would have poisoned it had the first failed; seeing the first succeed, he does nothing. The victim drinks and dies. Ask whether the death depends counterfactually on the first assassin's act. It does not: had he not acted, the second would have, and the victim would have died anyway. By the first step alone, the first assassin did not cause the death, which is absurd. The ancestral rescues the verdict, and it rescues it through the middle. Take the intermediate event: the poison being in the victim's stomach. That event does depend on the first assassin's act, because had he not acted, the second would have poisoned the cup later and a different intermediate event would have occurred. And the death depends on that intermediate event. Two links, each a genuine dependence, and the chain joins them. The intermediate event is what makes the difference between an outcome that would have happened anyway and one that happened by this route. So the middle link is a device Now the point of the whole exercise. The intermediate event earns its place in the analysis by absorbing a distinction the first step cannot express: the difference between the effect being secured and the effect being secured this way. Dependence is a relation between two events and is blind to routes. Chains recover routes by putting the route into the sequence. That is a considerable achievement, and it is also a warning. A feature introduced to absorb what a theory cannot otherwise say is the feature that will fail first, because it is carrying more than its official job description. Ask what the intermediate event contributes and the answer, in Lewis's framework, is not that it has metaphysical standing of its own. The answer is that it is the adjustable part. It broke twice, and Lewis adjusted the same part The adjustments are the best evidence for the claim. Late preemption came first. Suppose the backup process is cut off not before it acts but by the effect itself: two rocks fly at a bottle, the first shatters it, the second sails through where the glass had been. Here there is no suitable intermediate event on the first rock's route that the shattering depends on, because at every stage the second rock stands ready to take over. The chain has nothing to be a chain of. In the postscripts collected with his papers in 1986 [3] , Lewis replaced dependence in the links with quasi-dependence, defined through the intrinsic character of the process together with its surroundings: a process counts if a duplicate of it, suitably surrounded, is one the effect depends on. Note what changed. The links changed. The ancestral did not. Trumping came second [4] . Jonathan Schaffer's cases, published in 2000, involve two processes intrinsically alike, one of which nonetheless does the causing: a major and a sergeant both give the order to advance, the soldiers obey the major because he outranks the sergeant. Since the processes are intrinsically alike, quasi-dependence cannot separate them. Lewis's response, in "Causation as