I’ve been reading up on Lewis on causation, and in particular on the account of events he uses. The big thing that his metaphysics of events delivers is a way of getting rid of spurious causal dependence. I say hello, in the course of saying hello abruptly and loudly. I go for a walk, in the course of myself and my girlfriend going for a walk. These patterns of events arise not because one event causes the other, but because one event is part of the other. Pairs of events like these can stand in relations of counterfactual dependence. Suppose I say hello abruptly and loudly. Had I not said hello, then I wouldn’t have said hello abruptly and loudly. So Lewis says: causal dependence between events is not just a matter of counterfactual dependence: it’s counterfactual dependence between distinct events (events that don’t share a part).
When you dig into his metaphysics of events, you see that two notions of parthood are in play. One is broadly logical: event E is a logical part of event F if E occurring in region R entails that F occurs in region R.
A second notion of parthood he uses is spatio-temporal: event E is a st-part of event F if, necessarily, if F occurs in region R, then E occurs some subregion of R. Saying hello abruptly is an l-part of saying hello; my walking is an st-part of myself and my girlfriend walking.
But this still doesn’t cover all cases. Consider Trafalgar and the Napoleonic war. Intuitively, that battle is part of the wars (and not caused by the war, though caused by its earlier parts). But it’s not an l-part, since the region in which the war occurs is more extensive than the region in which the battle occurs. And it’s not an st-part, since the war could have been completed before Trafalgar happened. So Lewis defines up an “accidental” variant of spatio-temporal parthood between occurrent events: E is an a-part of F iff E and F are occurrent, and there’s an occurrent l-part x of E, which is a st-part of some occurrent y which is an l-part of F. I take it the idea is that as well as the Napoleonic wars, there’s another event, the Napoleonic-war-as-it-happened, that is a l-part of the Napoleonic wars; and there’s also Trafalgar-as-it-happened, which is an l-part of Trafalgar. And the latter is an st-part of the former; hence, derivatively, Trafalgar is an st-part of the war.
(Some notes on the interrelation of these notions: if E and F are occurrent, and E is an l-part of F, then it’s an a-part of F (take x=E, y=E). And if E is an st-part of F, then it’s an a-part of F (take x=E, y=F). Rather weirdly, note that when E is an l-part of F, then wherever E occurs, F occurs in an (improper) subregion. Hence F is an st-part of E. And so by the above, if they’re occurrent, we’ll have F an a-part of E. That is, when E is an l-part of F, and both are occurrent, then E and F are a-parts of each other (though of course they may still be distinct).)
Lewis’s requirement that events be “distinct” in order to be candidates for causing one another is that they don’t share a common part in any of these senses.
Lewis notes several times that this would be way too strong a constraint if we allowed events with very rich essences—I’m interested in what this tells us about what sorts of events we can think are hanging around.
Ok: so here is my puzzle. Here’s a first shot—an objection which is plausible but mistaken. Right now, a ball drops, and hits the floor. Consider the conjunctive event or “process” of the ball dropping and hitting the floor. Now (here comes the fallacy) doesn’t this event imply that the ball drops? And so doesn’t that mean the process is an l-part of the ball dropping, and likewise of the ball hitting the floor? But if so, then these two events wouldn’t be distinct, and so couldn’t stand in causal relations. It would be impossible to have a conjunctive process, whose constituents were causally interrelated.
That worried me for a bit but I reckon it’s not a problem. Necessarily, the region *in* which the dropping-and-hitting the floor is a region *within* which the dropping occurs; but it’s not a region *in* which the dropping occurs. “in” is like exact location; an event is then *within* any region it is “in”. But it’s only when every region in which the first occurs is a region *in* which the second occurs, that we have implication or l-parthood. What we have here is just st-parthood, running in the direction you’d have imagined—from constituents to process rather than vice versa.
So that exact puzzle isn’t an objection to Lewis; but I suspect he’s escaped on a technicality, and the underlying trouble with processes will rearise if we tweak the example. Lewis allows for colocated events—and allows they may stand in causal relations. He contemplates a battle of invisible goblins having causal influence on the progress of the AAP conference with which it’s colocated. More seriously, he thinks the presence of an electron in a electric field might cause its acceleration. But the location of the electron, and its acceleration, are colocated events. But in examples of this kind, we really are in trouble if we allow for the conjunctive “process”—the electron-being-so-located-and-accelerating. For necessarily, wherever we have that process in a given region, we have the accelaration *in that region*. So the process is an l-part of the acceleration. Likewise for the locatedness of the electron. But then the two events share a part, and are not distinct—so they couldn’t cause one another!
The trouble for Lewis will arise if we both allow (i) cause and effect to be located in the same region; and (ii) the existence of a “process” encompassing both cause and effect. Lewis says he wants to allow (i); and denying the existence of conjunctive events/processes in (ii) looks unprincipled if we allow them in parallel cases (where the ball drops to the floor). So I conclude there’s pressure on Lewis to rule out conjunctive events/processes across the board.