The homogeneous spinning disc

People like me who like Humean supervenience, four-dimensionalism and things like that probably ought to pay more attention to the homogeneous spinning disc argument. It gets attributed to Kripke and Armstrong in the 1970s and CD Broad earlier than that. (Broad had currents in a homogeneous liquid.) The argument means to show that how the world is qualitatively at each time doesn’t determine how it is qualitatively overall, because a world containing only a disc of homogeneous matter would be the same at each time whether the disc was spinning or not. Katherine Hawley seems to have fairly similar inclinations to me, but she still responds to the argument by rejecting Humean supervenience, saying that there are non-supervenient relations holding between instantaneous bits of the disc at different times, in virtue of which an instantaneous bit at one time is a future stage of an instantaneous bit at another. It seems to work. I don’t have a big problem with the very idea of immanent causation grounding temporal counterpart relations, but I don’t generally think of it as fundamental, because violations of Humean supervenience are odd. The spinning disc argument is powerful though, and I should have a response. I think Hawley’s arguments against the responses she considers look pretty good, but lately I’ve been wondering about a different one. I don’t know if it’s already out there, but I’ve not seen it before.

The difference between the spinning disc and the stationary disc is supposed to ground counterfactuals about things like what would have happened if some paint or a volleyball had landed on the disc. I’m wondering whether a homogeneous disc really would do different things to some paint or a volleyball when they landed on it. If a homogeneous disc would interact with its surroundings in exactly the same way whether or not it was spinning, it’s easier to deny that it makes sense to say that a homogeneous thing is spinning or not. One way of thinking about it is that when something is internally moving like when a disc spins or there are currents in a liquid what’s really moving are the inhomogeneities. Now, in the actual particulate world a particle can be looked at as an inhomogeneity, especially if you’re a supersubstantivalist. So on this way of thinking, particles still move. But to say that the contents of a homogeneous region of space was moving internally wouldn’t make sense, for the banal reason that inhomogeneities are what moves, and it doesn’t contain any of those.

So why will the disc interact in the same way with the volleyball or the paint whether it’s moving or not? We don’t have a true theory of physics for homogeneous matter, so we have to think about it in an intuitive way, or at best in a Newtonian way. Essentially the idea is that the disc is perfectly smooth, and that means it won’t have any friction and won’t exert an angular force on the volleyball. It’ll just spin smoothly underneath it. The paint is a bit harder to picture, but I’m not sure the paint will properly stick to the disc. If the disc is smooth it’ll exert no angular force on the paint and just spin underneath it without affecting the circular puddle that forms. At least, I don’t know that that’s wrong.

I’m not sure how to make the case that the disc would behave the same way whether or not it was spinning if you drilled a hole in it, but I can believe there’s a case to be made. Perhaps a spinning disc would just flow around the drillbit. I don’t have a brilliant grip on the difference between a homogeneous liquid and a homogeneous solid. There’s an intuitive way of thinking about it, where the liquid disc would flow around the drillbit and the solid disc would get an arc-shaped hole in it, but that doesn’t fit well with the Newtonian picture in which under the microscope all matter is in the same state of being composed of tiny indestructible billiard balls. Would a piece of homogeneous matter behave like a giant impenetrable indestructible billiard ball, or more like a gas? I don’t know how to settle a question like that. I’m suggesting that to get homogeneous matter to behave anything like normal matter behaves we may already need the non-supervenient properties or relations, like non-supervenient frictional properties of smooth surfaces and cohesion properties of homogeneous substances. If that’s the case, it isn’t that the counterfactuals are there and the Humean can’t explain them; the counterfactuals aren’t there in the first place unless the non-supervenient properties and relations are introduced. This is because inhomogeneities aren't just the things the move; they're also the things that act. The Humean can say that non-particulate matter would have to be metaphysically weird to behave anything like normal matter does, so pieces of homogeneous matter would have to behave like big particles, and particles don't internally move. I suspect that showing whether or not they'd be right would take some hard work.