In a previous blog post, we looked at how the counterfactual analysis of causation is superior to the regularity analysis because it is able to distinguish a true cause from a mere regularity. It makes this distinction on the basis of what would have happened in very similar circumstances, had the supposed cause been absent. Thus, to say that A causes B just is to say that B would not have occurred if A had not occurred, given very similar conditions. But the counterfactual analysis leaves us with some important questions: how should we understand these “very similar circumstances”? And what makes it true that B would not have occurred if A had not? To address these questions, we need to reframe them using the Lewis-Stalnaker theory of counterfactuals.
The Lewis-Stalnaker Theory of Counterfactuals
Roughly speaking, a world is a set of circumstances. Some circumstances can happen; some must happen, and still others can’t happen. The difference, then, between the actual world and a merely possible world consists in a distinction between the set of circumstances that happens in our world and all the other sets of circumstances that do not.
Possible worlds have the important feature of containing their own truths and falsehoods. A statement can be true in some worlds but false in others depending on the circumstances that make up that world. It is actually true that gunpowder explodes when ignited by a flaming match, but this may not be true in other worlds. Perhaps they involve circumstances with different physical laws that prevent gunpowder from exploding when lit with a match. Thus, whether it is true that ignitions of gunpowder cause explosions depends on which world we are talking about.
Now, if we limit our discussion to the actual world, how are we to interpret the following statement (S) that “the explosion would not have happened under similar circumstances, had the ignition failed to occur”? Lewis has at least two replies to this question:
First, Lewis would interpret the words “under similar circumstances” as just another way of talking about possible worlds quite like our own. Such worlds presumably have the very same history, atmospheric conditions, oxygen levels, and laws of combustion as the actual world does – except that in those worlds, the explosion fails to occur because the gunpowder has not been ignited. This is just a roundabout way of saying that S is true in similar worlds.
Second, Lewis would analyze the truth of S in terms of how similar other worlds are in comparison to our own. His analysis would go something like this: S is true in our world if and only if (1) the circumstances of S occur in another world and (2) such a world turns out to be more similar to ours than any other world in which the circumstances of S fail to happen.
What does this analysis mean? It means that S is true because some worlds be more similar (or closer) to ours than other ones. But what would a closer world have to look like, according to Lewis? At the very least, it would need to have the two features outlined in the above analysis. Namely, it must be a world where (1) the gunpowder fails to explode without being ignited, and which (2) is closer to ours than any other world where the gunpowder still explodes without being ignited. In other words, S is made true by the fact that the “fails to explode” world is closer to ours than any “still explodes” world. The closeness of that world to ours is what make S true.
What do you, the reader, think of David Lewis’ analysis of counterfactuals? Can you think of an exception to his analysis – such that a “still explodes” world ends up being closer (or as close) to ours as any “fails to explode” world? Which features should we consider most relevant to world similarity anyway? These questions will be the subject of my next blog post!
 We need not concern ourselves with situations in which counterfactuals with impossible antecedents are vacuously true.
 As I understand him, Stalnaker’s original theory of counterfactuals required that there be a world closest to ours in which the circumstances of S occur. Lewis relaxes this requirement by allowing multiple worlds to be equally close to ours, or even just closer and closer without any limit. For more on Lewis’ modification of Stalnaker’s theory, click here.