# Sound and Fury

Signifying nothing

## Lewis’ semantics of counterfactuals entails determinism

Here’s a tired old subject that I’m going to have a go at. First, a confession: I’ve never read Lewis’ Counterfactuals. So maybe the following thrown together worries are easily dealt with. But here goes. I am going to argue that the existence of what I call “as-if” possible worlds mean that Lewis is committed to determinism: all and only the counterfactuals with true consequents are true. That is, only if the consequent is true in the actual world is the counterfactual true.

Take your favourite counterfactual: I’ll be using “If Oswald hadn’t shot Kennedy, he would still be alive”. (Linguistic point: this is ambiguous. Is the “he” Kennedy or Oswald? I’m pretending it means Kennedy.) What we want is a false antecedent, a false conclusion, but a true counterfactual. (We’ll come back to counterfactuals with true consequents later.) We want $A \to B$ where $A$ and $B$ are both false, but the conditional is true. [Wordpress’ LaTeX features don’t extend to \boxright …]

Your typical Lewis semantics for counterfactuals go like this: find the nearest possible world where $A$ is true. If this is also a world where $B$ is true, then the conditional is true. And, for our Oswald/Kennedy case, the story goes like this: Find the nearest possible world where Oswald didn’t shoot Kennedy. In this possible world, Kennedy didn’t get shot, and so he is still alive. So the conditional is true.

But here’s another possible world. Oswald didn’t shoot Kennedy, but a bullet spontaneously appeared right outside the window where Oswald would have been, and this bullet has just the right velocity and so on that it hits and kills Kennedy, just like Oswald’s bullet does in the actual world. Now, this is also a world where the antecedent of the conditional is true. But this is a world where Kennedy dies. But which world is closer to the actual? Well, I claim that the “bullet appears as if Oswald had shot” world is closer. Why? Because it is exactly the same as the other world except in one crucial respect (the bullet) and that in this respect it is closer to the actual world, because the thing that is different is what happens in the actual world.

So the counterfactual is false. And we can easily generalise to any counterfactual whose components are both false. Take any $A \to B$ which we intuitively think is true. Any claim like “If A had been true, things would have been different in the way B describes”. Now I let Lewis tell the intuitive possible world story that makes this seem right. Lewis says: “Take the nearest A world: it is also a B world. QED”. But I reply: “But what about the world where everything happens just as you say such that A is true, but everything else happens as if B were false”. This has to be a closer possible world, since B is false in the actual world.

One might object that I’m just misunderstanding what closeness of possible worlds amounts to. Worlds where bullets just spontaneously appear, where things are As, but everything else happens just as if not-B? These are not plausible worlds. So it seems that there’s a way out if you interpret possible worlds in terms of intuitive likelihood, rather than intuitive similarity. But our intuitions about how likely something is are tied to our notions of how the laws of nature work.

So if you want to take this route out, you need to have pre-existing ideas about laws of nature to hang your similarity relation on. And you’re welcome to do that. But then what you’re doing isn’t really Lewis’ semantics any more. Why’s that?

Lewis was a systematic philosopher. He wanted all his ideas to work together. So Lewis would want to appeal to his account of laws of nature. But Lewis’ view on laws made them supervene on the non-modal properties of spacetime points. So any similarity relation in terms of Lewis-laws is going to supervene on a relation among spacetime points across worlds.

Now, if we’re comparing worlds at this level, then the worlds where bullets spontaneously appear just at the end of where Oswald’s gun barrel would have been are closer worlds to the actual world: more of the spacetime points are the same as the actual in that world than in the “intuitively” close world where our laws of physics apply. So it seems if you want to stay close to the idea of Lewis’ project, then you can’t take this “similarity on the level of the laws of nature” route out of the problem.

I’m not totally sure about this “laws of nature” stuff, so let’s ignore that for now and go back to the original problem. The basic problem is that a certain kind of possible world: “A, but everything happens as if not-B”-worlds seem to make any counterfactual with an actually false consequent false. So if this analysis of counterfactuals is right, the conclusion is that things could not have been otherwise: all and only counterfactuals with true consequents are true. Determinism.

Another attitude you might adopt is to just take the “possible worlds” semantics of counterfactuals as a way of talking about counterfactuals. “There aren’t really concrete possible worlds, the whole approach is just a façon de parler. And so what matters are not those weird “A, but as if not-B” worlds, but the intuitively nearby worlds that we started with.” This seems a perfectly reasonable way out, and it’s one I endorse. But again, it’s not an escape route that Lewis can endorse. He does seem committed to this idea that there are concrete possible worlds with a genuine similarity relation between them: there is a fact of the matter about which worlds are closer. So again, this route is closed to Lewis.

Alan Hájek has a paper about Lewis’ semantics of counterfactuals where he ends up concluding that “most counterfactuals are false”. He does this by using some odd looking “might counterfactuals” to defeat any intuitively plausible counterfactual claim. I think my approach is relevantly different. Hájek’s might-counterfactuals say at-best-controversial things about possibilities left open in quantum mechanics: “this glass might just hover in the air”. That is, this possibility has non-zero probability. I guess he’s trying to give some sort of gloss of plausibility to the “A but as if not-B”-worlds that I talk about. I don’t think that’s necessary for the argument: you don’t need to make things fit with our (actual) laws of nature to undermine the truth of the counterfactuals. Also, it looks like Hájek wants to make “Even if not-A, B still would have happened”-style counterfactuals false too, while I make them all come out true. (Disclaimer: I’m basing this on vague memories of Hájek’s paper. I guess I should reread it before making these claims “in print”, but life’s too short for fact-checking blog posts).

What have I shown? That Lewis’ actual view on possible world semantics is crazy? But we all knew that already. That the idea of “similarity” of possible worlds is very tricky. Again, we all knew that already. So I don’t think the above comments are all that interesting in the sense of furthering our understanding of anything, but it does seem like there’s an oddity there that I don’t believe has been addressed.