## More on Causation

June 4, 2008

Say that an event, e1 is weirder than an event e2 just in case every world in which e2 doesn’t occur, there is a closer world where e1 doesn’t occur. e1’s failing to happen accords better with our laws and whatever else determines similarity, than e2’s failing to happen. Basically things would be more normal if e1 hadn’t happened, more normal than if e2 hadn’t happened.

Secondly suppose that for any two events, x and y, there is a fusion of those events, which occurs just in case x and y both occur.

• (1) $\Box(O(x + y) \leftrightarrow (O(x) \wedge O(y)))$

With this machinery in place, I think we can run a kind of triviality result for Lewis’s account of causation. Suppose that e2 is weirder than e1. Then we get the following counterfactual

• (2) $(\neg (O(e_1) \wedge O(e_2)) \Box\!\!\!\rightarrow \neg O(e_2))$

Why’s that? Suppose w is a closest world in which $(\neg O(e_1) \vee \neg O(e_2))$ holds. We want to show that $\neg O(e_2)$ holds at w. Suppose it doesn’t. Then $\neg O(e_1)$ must hold to make the disjunction true. Since e2 happening is weirder, there must be a closer world where e2 fails to happen. Thus there is a world v such that $(\neg O(e_1) \vee \neg O(e_2))$ holds, and v is closer than w. This contradicts the assumption that w was closest.

Now here is the problem for Lewis. By (1) we get the strict conditional $\Box (\neg O(e_1) \rightarrow \neg O(e_1 + e_2))$ which gives us the counterfactual

• (3) $(\neg O(e_1) \Box\!\!\!\rightarrow \neg O(e_1 + e_2))$

Substituting $O(e_1 + e_2)$ (by (1)) into the antecedent of (2) we get

• (4) $(\neg O(e_1 + e_2)) \Box\!\!\!\rightarrow \neg O(e_2))$

But (3) and (4) just constitutes a chain of causal dependence between e1 and e2.

But this is intolerable! An event causes every event weirder than it!

This was all a little abstract, so lets take a more down to earth example to fix ideas. Suppose we have two events, with one weirder than the other. For an uncontroversial example, the event that I sneeze, and the event that it rains down frogs (this occasionally happens when tornados suck them up out of the water.) The idea is that if I hadn’t sneezed, then the joint event of my sneezing and it raining frogs would not have occurred. But if at least one of the following obtained: (a) it hadn’t rained frogs or (b) I hadn’t sneezed, then it would have been the former that obtained: (a) it wouldn’t have rained frogs, because that is closer to normality. Thus, it seems as if my sneezing caused it to rain frogs.

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### 2 comments

1. For those, like me, who reject transitivity while staying within a (broadly) counterfactual approach to causation, the solution is straightforward. But I think I’d want to resist it anyway, for the simple reason that neither (3) nor (4) express a causal relationship, because they don’t relate DISTICT events. Think of what Lewis says to a different kind of counterexample: ‘Such exceptions as this, however, do not involve any sort of dependence among distinct particular events. The hope remains that causal dependence among events, at least, may be analysed simply as counterfactual dependence.’ (p. 562 in the original). Later on that same page, in the offical definition of causal dependence among pairs of events, the events c and e are required to be ‘distinct possible particular events’ (562–3).

I guess you might finess this issue; O(e1+e2) is clearly not identical to O(e1), and hence distinct from O(e1). But that hardly accords with the Humean intuition moving Lewis, which is just that there should be no necessary connections (like causation) between ‘distinct existences’; entites which stand in a part-whole relation do stand in such connections, so cannot be distinct existences. Lewis is pretty consistent on this point.

2. I see. When I read Lewis, I took the stipulation that they be distinct to be just that (i.e. that they were non-identical) the motivation being to rule out events causing themselves by definition.

I’m just worried if we went for the more stringent constraint that overlapping events couldn’t stand in any causal relations we’d be ruling out too much. The event of my falling over presumably overlapped with the slipping on the banana skin – or the breaking of the window overlapped with it’s being hit with a hammer. That these kinds of events overlap seem to me quite plausible to me, if we are conceiving of them as spatio-temporal regions.

You might reply: sure, you can have overlapping events standing in causal relations, but the whole event can still occur when the parts don’t. We can deny (1) and (3) by denying mereological essentialism for *any* events. e.g. my falling might have happened, even without the slipping component. I guess I’m not hostile to this kind or response. I just feel that the events we end up talking about are quite sensitive to how they are described. The event that’s described as the fusion of two events, seems to have both those event as parts essentially. Maybe we can just restrict our attention to those events that don’t have their parts essentially. But if so, I’d like to see how that would pan out. Surely they are allowed to have *some* of their part essentially?