Causation and Overdetermination


In a previous post entitled Causation and Preemption, I argued against David Lewis’ counterfactual analysis of causation by citing examples of “trumping.” Trumping happens when two causes each suffice to bring about the same effect, but one cause overrides the other somehow. We can only speculate about why this might occur. Perhaps one cause is slightly faster than the other (as in cases of late preemption); or maybe a law of nature requires that one override the other after both causes have been initiated.

For example, imagine a world in which two atomic clocks are independently set to remotely detonate a nuclear bomb. The first clock goes off before the second clock does and thereby detonates the bomb. The first clock is the cause because it trumps the second, but either would have sufficed. In other words, the second clock would have succeeded had the first one failed. The bomb detonation still would have occurred without the first clock, even though it was the cause. So here we have an example of causation without counterfactual dependence – a result that is difficult to square with Lewis’ theory.


The focus of today’s post is a bit different. Instead of exploring examples of trumping, we will be looking at cases of “symmetrical overdetermination.” These cases happen when two causes (C1 & C2) suffice for the very same effect (E1). Each cause by itself determines the effect, but instead of one trumping the other, both causes end up contributing to the effect. Because the effect is determined by both causes, even though one was enough, we can properly say that the effect was over-determined. [see figure 1 below]

Overdetermination1 x 672

To make this explanation more concrete, let’s change our trumping example into a case of overdetermination. Imagine that our atomic clocks (C1 & C2) are independently set to remotely detonate a nuclear bomb (E1) at exactly the same time. Each clock is by itself sufficient to trigger the bomb (so each clock by itself determines its effect) but as a matter of fact, both clocks go off simultaneously. Unlike the example of trumping where one clock goes off before the other, this case of overdetermination has both clocks contributing to the bomb detonation, even though one was enough [see figure 1 above]. But if each clock succeeds in determining the same detonation, it follows that detonation still would have occurred if one clock had failed. So yet again, we have a case of causation without counterfactual dependence – a result which Lewis’ theory cannot allow for.


As with any philosophical objection, there are always loopholes that can be exploited to evade it– and the problem of overdetermination is no different. However, if those loopholes come at too high a price for the theory in question (in this case, Lewis’), then they can serve to undercut that theory and call for an alternative view. As I see it, there are at least three ways Lewis can evade the overdetermination objection. [Note: I do not claim that Lewis actually exploits these loopholes in the philosophical literature]

First, Lewis could deny that each cause by itself determines (or is sufficient for) its own effect, but the effects are slightly different. Perhaps one clock (C1) activates the trigger switch on the bomb (E1) in a slightly different way than the other clock (C2) happens to activate it (E2). Or maybe the blast radius of the nuclear explosion is slightly larger depending on which clock detonates the bomb. In either case, the causes (C1 & C2) determine different effects (E1 & E2). [See figure 2]

Overdetermination2 x 672

This first loophole preserves Lewis’ theory quite nicely because he can still claim that one of the detonations (E1) was counterfactually dependent on one of the causes (C1). And had C1 not occurred, then E1 would not have either – E2 would have instead. As it stands, I have nothing to say about this loophole except that, as in a previous post, the counterexample can be modified to guarantee identical effects.

Second, Lewis could avoid speculation about the effects of the clocks acting separately, and simply deny that the clocks would yield the same effect when acting together. Maybe each clock separately determines the same detonation, say, by sending the same number of radio waves to the trigger switch on the bomb. Or maybe they determine different detonations? Who knows! What matters is that both clocks (C1 & C2) working together yield a unique effect (E3), perhaps by flooding the trigger switch with twice as many radio waves as a single clock would have; or by issuing in a nuclear explosion with a larger blast radius than otherwise. [See figure 2]

As it stands, this response to the overdetermination objection is more plausible than the previous one because it is much simpler. The first loophole assumes that the reason why C1 and C2 yield a new effect E3 together is because they yield different effects (E1 or E2) separately. The second loophole makes no such assumption. It simply leaves the question unresolved as to why C1 and C2 yield a different effect together (E3) than they would have on their own. And that’s much simpler.

But is it reasonable? At first blush, this loophole is a tough pill to swallow: it makes it impossible for C1 and C2 to yield the same effect together and separately, as is required for overdetermination in the sense I have defined. Whether this consequence is tolerable will depend on whether one believes it is inherent to multiple causes that they generate differences in effects, and I for one have firm opinion either way.

Third, Lewis could deny that cases of overdetermination genuinely involve multiple causes. He could argue that C1 determines E1; C2 determines E1; but when C1 and C2 together determine E1, they function as one determining cause, not two. This loophole is rather clever because it allows Lewis to preserve the relation of counterfactual dependence between cause and effect. If both of our atomic clocks detonate the nuclear bomb together, but as two causes, then the counterfactual relation is threatened because the detonation would still have occurred in the absence of one or the other clock. But if they detonate as one combined caused, then no such consequence follows. It remains the case that had the combination of the two clocks failed to activate the bomb, it would not have exploded. So Lewis’ analysis has been saved.

As clever as this loophole is, however, it comes at the price of making Lewis’ analysis unnecessarily complicated. It is much simpler to suppose that the clocks contribute to the nuclear explosion as two causes, than it is to suppose that they combine into one cause on special occasions. Perhaps this is a price that Lewis is willing to pay, but in the absence of independent reasons for combining causes in exceptional cases, Lewis’ loophole looks more like an ad hoc evasion than a reasoned response.

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