One of the ways to understand what Humean Supervenience (HS) amounts to is to work out which worlds it is true at. So I want to explore for now whether HS could possibly be true in the worlds of the Harry Potter novels. This requires only a little knowledge of the Harry Potter novels, most of which I’ll explain as I go along. The payoff for this little investigation will be a rather serious problem for Lewis’s theory of laws, but that’s a fair way off.

The first thing to note is that magic itself is not obviously incompatible with HS. We could stipulate that the thesis of HS is that the world is fully determined by the spatiotemporal distribution of actual natural properties. But I think it’s more interesting, and more Lewisian, to define it as the conjunction of the following theses, the first two of which may be analytic.

* All the facts about the world are determined by which natural properties and relations are instantiated
* Natural properties are intrinsic, and intrinsic duplicates can be freely recombined into new possible worlds
* The only natural relations are spatiotemporal relations

Now this is compatible with there being quite a lot of magic in the world. There could be a world where there was a ‘magical ether’ field, and certain kinds of brain patterns caused certain vibrations in that field, which spread out until they hit something at which point certain law-like regularities were instantiated depending on what was hit. That world would be Humean, even though it had magic.

As I read the books, this is how some of the Harry Potter spells work. At least some of the time, a spell seems to ‘travel’ from the end of a wand to its target. In the movies the ‘combat’ spells are always shown as a stream of light going from the end of the wand to the target. And in the books they talk about such spells bouncing off walls, and missing their targets. So it seems the idea of the spells working by causing vibrations in the local field is plausible for these. As we’ll see, I don’t think that all of the Harry Potter world is Humean, but more of it is than you might expect.

The big problem for HS is the unbreakable vow. It seems to be at least a lawlike regularity that if a person makes an unbreakable vow, and breaks it, they die. Could this be explained in a Humean theory of the books? I think not, though it is more complicated than it seems.

Certainly in a Humean world there can be such things as vows with content. After all, this is a Humean world more or less, and this world has vows with content. So there could be a regularity, expressed entirely in Humean terms, that said that anyone who broke an unbreakable vow dies. Since such a regularity seems simple and strong, it could be a law, right?

Not so fast! The regularity is simple when expressed in English, but that’s not the salient simplicity measure for Humean laws. Rather, we have to look at the simplicity of the laws when expressed in terms of perfectly natural properties. And if the world is Humean, then the natural properties have to be local properties. So we have to describe the property of breaking a vow in terms of purely local properties. This can be done in principle, again there are such things as vow breaking in this Humean world, but it won’t be simple. If content externalism is true, the relevant local properties could in principle be local properties of any part of the world, so the description could be very long indeed.

So perhaps there couldn’t be an unbreakable vow laws. But perhaps we could say that it’s just a regularity. There is a Humean world where all the people who break unbreakable vows die. (The principle of recombination guarantees the existence of such a world.) Could the Harry Potter books be set in such a world? Probably not. Not just the regularity, that all breakers of unbreakable laws die, is true in the books, but so is the counterfactual that had someone else broken an unbreakable vow, they would have died. And if it is a brute regularity that unbreakable vow breakers die, that counterfactual won’t be true in the book. So this can’t quite work.

We can, at some cost, get the counterfactuals to turn out right. Posit an omniscient god who makes all the ‘laws’ of magic work. (This is sort of occasionalism for the Harry Potter world.) To make the story Humean we have to lean more heavily on the magical ether, both to get information to the god, and for the god to carry out their wishes. The god observes all the unbreakable vows, and has a standing desire to kill all those who break the unbreakable vows. The desire is counterfactually robust, so anyone who broke an unbreakable vow would be killed. This gets all the counterfactuals in the book right. The problem is that there is no evidence in the book that occasionalism is true in the book, or indeed that there are any kinds of magical gods at all. (The mythological heroes in the book are the very earthly founders of Hogwarts.) So again this can’t really be the book.

So I think there’s probably no way to get the counterfactual dependence into a Humean Harry Potter world. But it’s still interesting to try and figure out how the Harry Potter world looks if we drop the constraint about the only natural relations being spatiotemporal, and just keep the other two constraints. Since Lewis thinks those constraints hold necessarily, and the Harry Potter worlds look to be metaphysically possible (some inadvertent contradictions aside), they should hold in the Harry Potter world.

The idea then will be that anyone who makes an unbreakable vow will acquire (or perhaps have) some new perfectly natural property or relation. There will then be a law that anyone with that property who doesn’t carry out their vow dies. What might this property be? I say it’s a new perfectly natural property or relation, an unHumean one that isn’t local. Could it be the property of being disposed to die if you don’t carry out the vow? No; that property couldn’t be perfectly natural in any world. This is for two reasons. First, it isn’t natural here, and naturalness is not world dependent. Second, it violates recombination. Intrinsic duplicates can be recombined any way you like (shape and size permitting). Natural properties are intrinsic properties, so they can be recombined. Hence we could recombine phases of vow-making, phases of vow-breaking, and phases of living into a single continuous phase of vow-making, vow-breaking and living. And we could do it so often that there was no law that vow-breakers died. But then the property of being a vow-maker couldn’t be the property of being disposed to die if vow-breaking. Rather, the property of being a vow-maker must be, or must be lawfully correlated with, the categorical basis of the disposition to die if vow-breaking. In general Lewis thinks there couldn’t be natural dispositional properties, even in worlds where HS is false.

But there’s a deeper problem here. What exactly are the properties and relations that we use in stating the law? To see the problem, consider the following case. Billy makes an unbreakable vow to give Suzy an X-Box 360 for Christmas. Unfortunately, two weeks before Christmas, Billy dies in an unfortunate accident involving Polyjuice Potion and a hair off a corpse. Had he lived, Billy would have gone to Best Buy and bought a box labelled ‘X-Box 360’. Unfortunately, many such boxes have PlayStations inside them, not X-Boxes. Had Billy bought one of those, and given it to Suzy, he would have broken his unbreakable vow, and hence died. Conversely, if he had vowed to give Suzy a PlayStation, then he would have died iff he had bought a box containing an X-Box. It looks like there is a problem here for Lewis.

To make the problem more explicit, note that to get the counterfactuals to turn out right, there have to be laws connecting Billy’s vow to what is inside the box. Now laws can only be stated using perfectly natural properties and relations, so there must be some perfectly natural relation that is instantiated if Billy buys what he vowed to buy, and not if he buys what he didn’t vow to buy. This must be a relation, and it isn’t a spatiotemporal relation, so this is clearly incompatible with Humeanism. (Unless perhaps there are tricky relations to third parties, like the occasionalist god, involved.) The difficulty arises when we try and say what the relation is if it isn’t spatiotemporal.

At one level the solution is simple. The law says that someone who makes an unbreakable vow dies unless the content of the vow accurately represents a salient part of the world. This makes representation the fundamental relation in question. That’s unHumean, but we’ve given up on HS. The problem is that there are two reasons to think that representational relations couldn’t be fundamental relations.

The first reason is somewhat speculative, but having perfectly natural representation relations seems to violate a principle of recombination. Now officially the principle of recombination only talks about intrinsic properties, it says that duplicates can be recombined any spatiotemporal way you like, but it seems it should have something to say about perfectly natural relations. Here’s one way to generate the problem. If R is a perfectly natural relation, then the property of having two parts that stand in R should be intrinsic, just as if F is a perfectly natural property, then the property of having a part that is F is intrinsic. So take the fusion of a representation and what it represents. That fusion should have the property that one part represents the other however the fusion is duplicated. But this won’t be the case. Some of the time there won’t be a causal connection, for instance, between one part and the other. (As we’ll see, Lewis doesn’t think that causal relations between parts are preserved under duplication.) Now maybe causal contact isn’t required for representation, but this kind of reason suggests that there will be problems for a general principle of recombination here.

The second is more straightforward. Lewis says that naturalness is not world-relative. Representation relations are not perfectly natural in this world. So they are not perfectly natural in the Harry Potter world either.

I think there’s something of a problem for Lewis here. I think there could be a world where the laws made essential reference to representation. Indeed, I think a world where there are such things as unbreakable vows as described in the Harry Potter books is such a world. (And I think the Harry Potter world is at least as suitable for use in metaphysical theorising as the magic worlds Lewis discusses in, for example, “Causation as Influence”.) But it’s not clear how to square this with anything like Lewis’s theory of laws.