Causation and Preemption


David Lewis thinks that causation can be reduced to a relation of counterfactual dependence between events. One objection to his view comes from cases of preemption which purport to show that counterfactual dependence is not necessary for causation. If these cases do involve genuine causation, then Lewis’ theory is in trouble. To understand what preemption is and why it is relevant to evaluating his theory, consider the following example.

Imagine that Thomas and Liz are both holding bricks in their hands and aiming them at an expensive glass window. As Liz is about launch her brick, Thomas reasons that one brick will suffice to break the glass so he refrains from throwing his at the very moment that Liz releases hers. Thomas would have thrown his brick had Liz failed to release hers, but he doesn’t need to. So he preempts his own throw. As it turns out, Liz’s brick hits the glass and it shatters into pieces.

Lewis would have us believe that this case of preemption has a counterfactual analysis, such that if Liz had refrained from throwing, the glass would not have shattered. Unfortunately, his analysis is false because had Liz refrained, Thomas would have shattered the glass with his brick instead. If the glass would have shattered without Liz’s throw, then clearly there is no counterfactual dependence between the two.


Lewis could reply to the preemption problem in at least two ways.[1] First, he could argue that upon closer inspection, the shattering does indeed depend on Liz rather than Thomas because her brick produces a slightly different shattering than Thomas’ brick would have. If Liz’s produces 20 shards of glass, but Thomas’ would have only produced 16 shards, then Liz and Thomas are causing distinct effects. So it remains the case that had Liz refrained from throwing, the glass would not have shattered in exactly the same way, which ensures that the effect depends on Liz after all.

In my view, the appeal to small differences is a bit a stretch. Even if Liz’s and Thomas’ throws would result in slightly different shatterings, we are hard pressed to conclude that all cases of preemption are like this. It’s a pretty tall order to assume that precision will always reveal differences between effects. However, since there is no knock-down argument against that assumption, this solution to the preemption problem is always available as a kind of last resort.

A second way for Lewis to address the preemption problem is by fixing (or holding constant) certain facts about Liz’ situation. Suppose Lewis holds as constant the fact that Thomas preempts his throw. When this fact is taken as a given, it follows once more that if Liz had refrained, then the glass would not have shattered.

To see why this follows, we need to revisit Lewis’ analysis of causation. His analysis states that Liz is the cause of the shattered glass if and only if the glass would not have broken, had Liz failed to throw her brick in a similar situation. Clearly, the similar situation in which she fails is going to be different in certain respects from the one in which she throws. For instance, different neural pathways will be activated in her brain just prior to her failure. But for the most part, everything else remains constant, including Thomas’ choice to preempt his throw just moments before Liz fails. If so, then it follows that the glass would not have shattered in the situation of failure, which on Lewis’ analysis implies that Liz’s throw caused the shattering.

But does this reply even work? In my view, Thomas’ choice to preempt is a fact about the situations in which Liz succeeds or fails to throw her brick, but I find it hard to understand why it should be considered a relevant fact – that is, a fact used to determine whether Liz’s brick is a cause. I say this because Thomas’ choice has little or no relevance to whether her brick shatters the glass; it only has relevance to whether some brick(s) shatter the glass. To see why, considering the following outcomes: if Liz fails and Thomas preempts, the glass stays in tact; if Liz succeeds and Thomas preempts, the glass shatters; if Liz succeeds and Thomas throws, then once again the glass shatters. But in none of these scenarios does Thomas’ choice affect Liz’s actions. Thus, if only relevant facts should be used to determine whether Liz’s brick is a cause, then Thomas’ choice is not among them, and so this second strategy for addressing the preemption problem fails.

Someone might object to my criticism by arguing that Thomas’s choice is a relevant feature of Liz’s situation. Why? Because his decision to preempt (or not) issues from his observations of her body in motion, e.g. presumably he is watching to see if she is about to execute her throw successfully. Moreover, Thomas’ decision could trigger a sequence of events that interacts with Liz’s brick in flight, e.g. photons reflecting off his body might intersect (even if ever so slightly) with the flight path of the airborne brick. But again, I find it hard to see how these interactions between Thomas and Liz are significant enough to be relevant. Nevertheless, those who disagree with me and who see these interactions as relevant have not managed to escape the problem of preemption just yet; at least not if Jonathan Schaffer (2007) has anything to say about it!


In The Metaphysics of Causation (2007), Schaffer claims we can imagine cases of preemption that are immune to the replies in the previous section which appeal to slight differences in effects, hold certain facts about a situation constant, or viewing tiny interactions as causally relevant. He invites us to imagine a world in which wizards cast spells that have identical effects, are produced directly, and are governed by laws of magic. He writes,

“Suppose that the laws of magic say that the first spell cast on a given day matches [an] enchantment that midnight. Merlin casts a spell (the first that day) to turn the prince into a frog, Morgana casts a spell (the second that day) to turn the prince into a frog, and at midnight the prince turns into a frog. It seems that Merlin’s spell caused the prince to turn into a frog — his spell was the first cast that day, and that’s what the laws of magic identify as the relevant feature. … It does not need to be the case that there are any intermediary events at all in the story — the magic might as well work directly. And it does not need to be the case that there would have been any differences in what befalls the prince had Merlin left it to Morgana.” [2]

This counterexample is brilliantly formulated because it effectively neutralizes two of the replies that Lewis could give to it. First, unlike the brick example where Liz’s throw and Thomas’ decision to preempt interact in subtle ways, the spells cast by Merlin and Morgana are causally independent of each other. Merlin and Morgana could be isolated on different planets for all we know, but the laws of magic still guarantee that the first spell will trump (and therefore preempt) the second one. And because their spells work directly, there are no intermediate effects prior to the enfrogging that can causally interact in subtle ways. Second, unlike the brick example where Liz’s and Thomas’ throws are likely to cause slightly different shatterings of the glass, the spells cast by the two magicians are too direct and precise to cause different enfroggings. So any reply based on small differences in effects fails.

But what about the third reply, i.e. holding certain facts about Merlin’s spell constant? Lewis could argue that when we take as constant the fact that Morgana’s spell happens after Merlin’s, the enfrogging ends up depending on Merlin, just as the counterfactual analysis requires. But unfortunately for Lewis, this reply doesn’t work. Even if the timing of Morgana’s spell is a fixed fact about Merlin’s situation, it still does not follow that the enfrogging would not have happened had Merlin not cast his spell. Why? Because if Merlin had refrained, then the laws of magic would have determined that Morgana’s spell worked instead! But if the enfrogging would still happen without Merlin, then the enfrogging does not counterfactually depend on Merlin, and so Lewis’ analysis fails. In other words, Schaffer’s example of trumping preemption shows us that the enfrogging can be caused by Merlin’s spell without it being counterfactually dependent on the spell, as Lewis’ view requires.

[1] I am indebted to Jonathan Schaffer’s The Metaphysics of Causation (2007) for these replies and for my subsequent reflections on trumping preemption.

[2] Schaffer (2007).

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