Bottle breaking and counterfactuals: the importance of clear questions

David Lewis defined causation as:

“something that makes a difference, and the difference it makes must be a difference from what would have happened without it. Had it been absent, its effects – some of them, at least, and usually all – would have been absent as well”
Source: Stanford Encyclopedia of Philosophy

But, to keep a long story short, a lot of people had problems with this definition. One of these problems was that of preemption which is explained using this short thought experiment:

Billy and Suzy throw rocks at a bottle. Suzy throws first so that her rock arrives first and shatters the glass; Billy’s rock sails through the air where the bottle had stood moments earlier. Without Suzy’s throw, Billy’s throw would have shattered the bottle. However, Suzy’s throw caused the bottle to shatter, while Billy’s throw is merely a preempted potential cause. This is a case of late preemption because the alternative process (Billy’s throw) is cut short by the main process (Suzy’s throw) running to completion.

Lewis’s theory cannot explain the judgement that Suzy’s throw caused the shattering of the bottle. For there is no causal dependence between Suzy’s throw and the shattering, since even if Suzy had not thrown her rock, the bottle would have shattered due to Billy’s throw. Nor is there a chain of stepwise dependences running cause to effect, because there is no event intermediate between Suzy’s throw and the shattering that links them up into a chain of dependences. Take, for instance, Suzy’s rock in mid-trajectory. This event depends on Suzy’s initial throw, but the problem is that the shattering of the bottle does not depend on it, because even without it the bottle would still have shattered because of Billy’s throw.
Source: Stanford Encyclopedia of Philosophy

To me there are two different causal questions being asked, each of which has a different answer. If you don’t bother to clearly think through your causal question(s), you can easily think there is only one question with two contradictory answers.

The first causal question is, once all the rock-throwing is said and done, let’s say 10 seconds after the bottle breaks, did Suzy’s throw make a difference to the state of the bottle at that point in time. The answer to this question is no it did not because the counterfactual state of the bottle had Suzy thrown the rock or had Suzy not thrown the rock is the same: the bottle is broken. So the answer to this causal question is that Suzy did not cause the bottle to be broken at time $t=10$ seconds after the bottle was broken.

The second causal question is, did Suzy’s rock cause the bottle to go from unbroken at some time $t$ to broken at time $t+$ sometime fraction of a second later. The answer to this causal question is that, Suzy’s throw did cause the bottle to go from unbroken to broken at time $t$. Had she not throw her rock, the bottle would have gone from broken to unbroken at a different time $t^*$.

So if you keep your causal questions clear, realizing that our seemingly contradictory intuitions in this example as simply the correct answer to two different, equally valid, causal questions, the problem of preemption disappears.

Jeremy A. Labrecque
Assistant professor, Epidemiology and causal inference

My research is on how we know what we know.