Influence and Backwards Causation
About half a minute ago, I've poured tea into this cup. In a few seconds, I will take a sip. What if I had taken a sip a minute earlier? I wouldn't have taken a sip of tea from an empty cup: that is impossible. So there would have been tea in the cup a minute ago. How did it get there? Maybe I would have poured it in earlier. Or maybe it would have tunnelled directly from the pot into the cup. Or maybe the tea would have just materialized out of thin air. Some of these counterfactuals do not sound very plausible, but let's assume that for the kind of counterfactuals relevant to causation, they are all equally good so that there is no fact of the matter about how the tea got into the cup at the closest world where I take the sip a minute earlier: it does so differently at different worlds that are equally close. (See Lewis, "Counterfactual Dependence and Time's Arrow" for the standards of evaluating such counterfactuals, and "Are we free to break the laws?" for the indeterminacy of divergence miracles.)
But now consider the event of the tea being there in the cup right now. Call this event E. E is rich in aspects and properties: The tea has a certain temperature, say 73 degrees Celsius, a certain volume, say 184 cm^2; the cup is located 7.9 cm from the edge of the table, has certain finger prints on it, and so on. That these are aspects or properties of E does not mean that E would not have occurred if they had been different. Not all properties are essential properties. Some counterfactual events in other worlds are just like E in our world, except that the tea is a little hotter or colder, the cup a little closer to the edge, etc. Call these alterations of E "E1", "E2", etc. It doesn't matter whether they are variations or counterparts of E itself or entirely different events.
Let C be my taking a sip from the cup of tea in a few seconds. (Yes, I'm writing this entry instantaneously!). Just like E, C has many aspects and properties: the temperature of the tea, the size of the sip, the exact place and time at which I take it, and so on. Again, there are all kinds of alterations of C in other possible worlds, with different temperatures, sizes, places and times of the sip. Let C1, C2, etc. be alterations of my sip that all occur around 1 minute earlier than the actual C.
In all the C1, C2, ... worlds, some divergance miracle has occured that assured that tea was already in the cup a minute ago. But it is, we assumed, indeterminate just what miracle that is. (So strictly speaking, I shouldn't say "the C1 world".) How do these worlds progress afterwards? What happens after I've taken the counterfactual sip about 50 seconds ago in the C1 world? Presumably I put the cup down again. So a little later, one of E1, E2, ... will take place: the cup of tea will stand there -- not exactly where it actually stands, and with slightly different finger prints, a slightly different volume of tea, etc. Which of E1, E2, ... takes place largely depends on what exactly C1 looks like. Suppose it is an event where I take a sip of 5 cm^3 from a cup with 165 cm^3 tea of temperature 69°C. Then the corresponding E-alteration will be one with a tea volume of 160 cm^3 and a temperature somewhat below 69°C. If we consider a slightly different C-alteration, C2, where the original volume was 170 cm^3, the corresponding E-alteration will be one with 165 cm^3 and minutely higher temperature.
In "Causation as Influence" (in the Collins, Hall, Paul volume on Causation and Counterfactuals, 2004), Lewis defines causation in terms of influence:
C influences E if and only if there is a substantial range C1, C2, ... of different not-too-distant alterations of C (including the actual alteration of C) and there is a range E1, E2, ... of alterations of E, at least some of which differ, such that if C1 had occurred, E1 would have occurred, and if C2 had occurred, E2 would have occurred, and so on. [...] C causes E if there is a chain of stepwise influence from C to E. (p.91)
So my taking a sip in a few seconds causes the tea to be in the cup now!
I see three lines of response, none of which look satisfactory.
1. One might say that my candidates for C1, C2, ... are too distant from C. Intuitively, that seems incredible. They could be complete intrinsic duplicates of the actual C. And why should occuring a minute earlier make such a big difference? Of course, my alterations also have very different causal origins than C: they are caused by divergence miracles. But that is equally true for the alterations in ordinary cases of causation. Moreover, Lewis even counts the complete absence of C as a "not-too-distant alteration" of C. Still, we could stipulate that even small differences in temporal location make for too big a distance between the alterations and C. But that sounds quite ad hoc.
2. One might say that it is not true that if C1 had occurred, E1 had occurred, because the occurrence of C1 leaves open just which divergence miracle happened earlier. And what happens after C1 depends on this. It makes a difference whether I myself poured in the tea two minutes earlier or whether it got there by quantum tunneling. That might actually be true. But if it is, it undermines all ordinary cases of causation as well.
3. One might grant that my taking a sip later influences the tea being in the cup now, but that the influence and thus the causal relevance is negligible. After all, most alterations of C leave E completely unchanged. Only C-alterations that occur at least a few seconds earlier than the actual C make a difference to E. This is Lewis's response to other cases where his account implies causal relevance where intuitively there is none: the moon orbiting the earth influences the flooding of New Orleans, but surely that isn't the cause of the flooding! -- It is, says Lewis, at least it is a causally relevent factor, though a negligible and obvious factor, which is why we normally ignore it. I think this response is fair and correct. But I don't think it works in my case. The moon orbiting the earth indeed has negligible causal influence on the flooding of New Orleans, but my taking a sip later has no causal influence at all on the tea being here now.