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Avoiding Late Preemption with the Right Kind of Influence


David Lewis championed a counterfactual account of causation, but counterfactual accounts have a notoriously difficult time handling cases of late preemption. These are cases in which we still count one event as the cause of another although the effect does not depend on the cause in the way taken to be necessary by the account. Lewis recognized these cases, but they have been shown to be problematic even for his final analysis of causation, the Influence Account. In this paper, I show how these cases led to and remain a problem for Lewis’s Influence Account, and I give a new counterfactual account available to a Lewisian that can handle late preemption cases. What is crucial to my account is that a cause not merely has counterfactual influence over its effects, but that the cause has influence of the right kind. I conclude by arguing that even if problems remain with this account, they will not be problems of late preemption, and the problems stemming from other kinds of cases will be no worse for my account than for other counterfactual accounts.

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  1. Hall (2004) makes the case for even claiming that we have two distinct concepts of causation – one that is focused on production, and one that is focused on dependence.

  2. Since this is my aim, I will not address other reductive accounts of causation or other traditions in the causation literature that were in part motivated by late preemption cases. For example, although there has been a torrent of important work on causal modeling and causation as involving the notion of intervention, my aim here is to show that purely Lewisian tools can be used to solve the problem of late preemption cases.

  3. That is, we are understanding Causation to be the ancestral of dependence, where, for two events E1 and E2, E2 depends on E1 just in case in the closest world in where E1 does not occur, E2 does not occur. Taking the ancestral of dependence was essential for Lewis to maintain that causation is invariably transitive, and we will see how a commitment to transitivity is helpful below in examining cases of early preemption.

  4. One could bite the bullet and say that that which we judge to be the cause in this case actually isn’t, because it doesn’t satisfy the analysis, though this feels pretty implausible. Or one might take up a view like that found in Coady (2004) on which we treat events as more or less fragile based on the context so that we can say that it’s true that E would not have occurred if C hadn’t, as E wouldn’t have occurred at all if it hadn’t occurred exactly as it did. Though this is an interesting view, I think it saves the original account at the dual expense of having to say unpalatable things about events and not respecting the extent of dependence as much as Lewis’s later view.

  5. Although, Lewis himself leaves it open whether or not the alterations of an event are identical to the event that actually occurs.

  6. There is the mention of ‘significance’ in the characterization of influence, but little has been done to quantify what it means for a cause to have more or less influence over an effect. I do not have any suggestions here for the best way to do this. Instead, I will spot that there is such a way of quantifying being a more significant or bigger cause, but the account that I give below will not require this notion or knowing how best to quantify it.

  7. Though my example is inspired by and modeled after the case in Schaffer (2001a:12), I have avoided using Schaffer’s example itself. In his case, the event which supposedly has the most influence is the event of a third party’s actively watching one event cause another. However, we want a case of late preemption here, where the preempted back-up works independently from the actual cause. The difficulties of this example are brought to the fore in Noordhof (2001). Collins 2004:114) also offers a version of a trumping case that is similarly modified to be an objection specifically to the Influence Account, and we will discuss trumping cases more at length below.

  8. We will discuss this possibility below.

  9. Of course, there are plenty of non-counterfactual tools that the opponents are quick to point out could help with these cases. For instance, we might think that what is needed is something that recognizes that the cause produces the effect, or that there is some causal process that leads to the effect. Towards this end, Schaffer (2001a) suggests that some kind of effluence is required to get the cases right.

  10. We will see below how keeping this in mind might also help us think about spurious causation.

  11. It is worth acknowledging that this is a backtracking counterfactual we are evaluating – since Billy’s throw would have only broken the window on the assumption that the past would have included his throwing – and we might worry that Lewis himself specifically prohibits backtracking counterfactuals. There are a few things to say about this. First, Lewis (1979) argues that counterfactuals are vague but that in most contexts are evaluated on a non-backtracking reading, not that there can be no true backtracking counterfactuals. Second, it is Lewis’s account that requires these counterfactuals, not mine, since his view requires events having when/when influence. My view only requires evaluating if the effect would have been different had the event in question not occurred at all, not if it had occurred earlier. I follow Lewis in recognizing the possibility of having when/when influence, but my account crucially does not rely on it.

  12. Paul (1998) provides an emended counterfactual analysis that captures this insight along the dimension of time. To judge whether some event is a cause, she suggests that we look to see whether the effect would have occurred or whether it would have occurred later had that event not occurred. Lewis (2004:87) uses this account as a jumping-off point to considering influence more generally, but the crucial idea I am using is that what really matters is what would have been different had the cause not occurred.

  13. We can see that we still need to think of causation as the ancestral here easily enough. Suzy’s button-pushing has whether/when influence over window-breaking, and suppose that the window-breaking has whether/whether influence over the event of the occupant of the house seeing the broken window and getting upset. The window would have been broken regardless of Suzy’s pushing, so the occupant would have been upset regardless, and, if the occupant walks in and gets upset at a later time, then he would have gotten upset just when and how he does regardless of Suzy’s pushing. So, Suzy’s pushing seems to lack all influence over this further effect, though her button-pushing is still clearly the cause.

    However, I should note that though I’m keeping causation as the ancestral of exercised influence to stay close to Lewis’s original thinking, one could identify causation simply with exercised influence if one had become convinced (contra Lewis) that causation is not a transitive relation. Stone (2009) even uses a modified version of a possible counterexample to the transitivity of causation against the influence account in particular.

  14. I thus take causation to be the ancestral of a certain dependence relation, just as Lewis did. This will come in handy when we consider early preemption cases again below.

  15. Counting surprisingly small or distant events as causes is a standard upshot for counterfactual accounts of causation, although it is worth noting that Lewis’s Influence Account actually has a way around admitting them. On that account, any influence at all is not sufficient for causation; instead, causes must have a ‘substantial range’ of alterations that co-vary. This idea of requiring more influence is attractive, but my account internalizes the thought that what really matters is having influence of the right kind, rather than the right amount.

  16. And I am in good company. Not only are counterfactual accounts of causation generally taken to imply a multitude of causes, but Schaffer (2001b) points out that probability-raising and process-linkage views of causation also have the result of counting many apparent non-causes as causes.

  17. This defense may be convincing if we keep talking in terms of ‘causing,’ but it may be less convincing if instead we consider other causal verbs. For example, if instead of throwing rocks at a window, Billy and Suzy were throwing rocks at a man’s head, we would count Suzy and not Billy as murdering the man. This is suggestive, but it would be a stronger objection if ‘murder’ really meant ‘cause to die.’ Then our reticence for calling Billy a murderer would tell against his throw being a cause. But murder requires more. Murder seems to require a match between the murderer’s intention and how the murderer causes the death as well as that the action of the murderer is the primary cause of the death. Neither of these elements are present in the morbid Billy and Suzy case. If, however, we instead consider some other verb such as ‘kill’ that is closer to meaning ‘cause to die,’ then I find that it is not as unintuitive to say that Billy does partially kill the man at least insofar as he influences the way that the man dies. If this still feels unintuitive, however, then this may be because ‘kill’ also does not quite mean ‘cause to die,’ as both Fodor (1970) and Morreall (1976) argue.

  18. Notice that in order to get a case where the cause truly has no influence (where it doesn’t make even the slightest difference in how or when the effect occurs), we seem to have to move to a magical case. The best example of a genuine ‘no influence’ case in the real world that I can think of is given as the primary example of Strevens (2003). However, his case (of a ricochet) strikes me as both only approximating no influence and also a case of joint causation. Choi (2005) gives some good reasons to think that the Influence Account already has the resources to deal with this specific objection, though I’m less confident.

  19. Hall and Paul (2013:138) identify the trumping case as corresponding to one of virulent late preemption, and Lewis himself took the trumping case to decisively show that his original counterfactual analysis could not answer late preemption.

  20. Hitchcock (2011) argues that the trumping case is best understood as overdetermination, rather than late preemption. He does this by arguing that the magical law, however it’s construed, cannot rule out a law that has both Merlin and Morgana’s spell-casting as causing the enfrogging. Bernstein (2014, 2015) goes further by arguing that the trumping cases will collapse into either cases of overdetermination or early preemption depending on the mechanism of trumping (or how the law privileges the cause). These arguments are difficult to assess when considering the magical case, because the nature of the magical law is left unclear (Is it a mere regularity? Is it a non-Humean law that makes Merlin’s spell cause the enfrogging?). I focus here on the military case to avoid this confusion and show how easily the trumping collapses into other kinds of cases.

  21. Kvart (2001) offers a case of early preemption that he argues is a problem for Lewis’s Influence Account and cannot be solved by thinking about the ancestral. However, the problem that Kvart points to is not that there is not an unbroken chain of influence from the event we take to be the cause to the effect; rather, it is that, just like in the Modified Window-Breaking Case, there is a non-cause with more influence than the actual cause. This is a problem for the Influence Account, but as long as we focus on the influence that is exercised (the whether/whatever influence that is had), this will not be an objection to the Exercising Influence Account. So this is another advantage of the Exercising Influence Account.

  22. This approach will not work for the magical trumping case. Even if we can read it as a case of early preemption (where Merlin’s spell-casting prevents Morgana’s spell-casting from beginning a causal process that eventuates in the effect), there will be no intermediary event that we can point to between Merlin’s spell-casting and the enfrogging that exercises influence over the enfrogging. Merlin’s spell-casting directly causes the enfrogging at midnight when he casts it, and not via a long causal chain. This provides an objection to the Exercising Influence Account (as well as to both of Lewis’s accounts), but it is only persuasive insofar as we take causation across a temporal gap such as this to be possible. And I do not think that it is possible. We may be able to conceive of this kind of causation, but we do not seem to see any real-world cases. There may nevertheless be arguments for the possibility of these cases, but considering them goes beyond the scope of this paper.

  23. Cases of overdetermination can be just as problematic for the Influence Account, if not worse. Suppose the snipers must fire when and how they do if they are to fire at all. Then they will lack all influence over the death, and so will both be judged as non-causes on the Influence Account. Or worse, we might imagine a case of overdetermination where we still judge only one of the causes to have all of the influence. Stone (2009) presents a case of this kind as a counterexample to the Influence Account. In this case, the Exercising Influence Account fares better than the Influence Account, since at least on the former account the two causes are judged on a par – since they both lack whether/(when/how/whether) influence.

  24. Although cases of pure overdetermination seem to be rare, if they occur at all, Schaffer (2003) has argued that overdetermination of this kind is in fact ubiquitous in our world. He gives examples of effects that are overdetermined by objects and their parts. However, this kind of ubiquitous case can be shown to be misdiagnosed as overdetermination if wholes are able to share in the singular causation of effects with their parts. See Paul (2007) and Hall and Paul (2013:160) for this approach.

  25. This is similar to the ‘spoils to the victor’ approach taken in Lewis (1986). There, he leaves the view we should take of overdetermination cases open to what is said of them by whatever theory best aligns with our intuitions of easier cases. I am suggesting that getting these cases intuitively wrong is acceptable if there is reason enough to undermine our intuitions in these cases. See Hall and Paul (2013:152-3) for concerns with this approach.


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I would like to thank Kadri Vihvelin for extensive feedback and discussion on this topic. I would also like to thank Scott Soames, Jake Ross, Nicholas Laskowski, Ryan Walsh, Julian Stone-Kronberg, and the audience for a presentation on this topic for the University of Southern California’s Speculative Society.

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Correspondence to Kenneth Silver.

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Silver, K. Avoiding Late Preemption with the Right Kind of Influence. Philosophia 47, 1297–1312 (2019).

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