More about functionalism about location

Functionalism about location holds that any sufficiently natural relation, say between objects and points in a topological space, that has the right formal properties (and, maybe, interacts the right way with causation) is a location relation.

Here is an argument against functionalism. Functionalism is false for other fundamental physical determinables: it is false for mass, charge, charm, etc. There is a possible world where some force other than electromagnetic is based on a determinable other than charge, but where the force and determinable follow structurally the same laws. By induction, functionalism is probably false for location.

Some will reject this argument precisely because they accept something like functionalism for the other physical determinables, and hence deny the thought experiment about the non-electromagnetic force--they will say that if the laws are structurally the same, the properties are literally the same.

I think there is a way to counter the above argument by pointing out a disanalogy between location and other fundamental physical determinables (this disanalogy goes against the spirit of this post, alas). Let's say we live in an Einsteinian world. A Newtonian world still might have been actual. But, plausibly, the Newtonian world's "mass" is a different determinable from our world's mass. Here's why. In our world, mass is the very same determinable as energy (one could deny this by making it a nomic coextensiveness, but I like the way of identity here). In the Newtonian world "mass" is a different determinable from "energy". Therefore either (a) Newtonian "mass" is a different determinable from mass, or (b) Newtonian "energy" is a different determinable from energy, or (c) both (a) and (b). Of these, the symmetry of (c) is pleasing. More generally, it is very plausible that fundamental physical determinables like mass-energy, charge, charm or wavefunction are all law bound: you change the relevant laws (namely, those that make reference to these determinables) significantly, and you don't have instances of these determinables.

But location does not appear to be law bound. "Location" in a Newtonian spacetime and a relativistic spacetime are used univocally. You can have a set of really weird laws, with a really weird 2.478-dimensional space (for fractional dimensions, see, e.g., here), and yet still have location. Maybe there are some formal constraints on the laws needed for locations to be instantiated, but intuitively these are lax.

Plausibly, natural (in the David Lewis sense of not being gerrymandered) physical determinables that are not law bound are functional. If location is a natural physical determinable, which is very plausible on an absolutist view of spacetime, then it is, plausibly, functional. I think an analogous argument can be run on relationism, except that the fundamentality constraint is a bit less plausible there.

One might question the claim that natural physical determinables that are not law bound are functional. After all, if the claim is plausible with the "physical", isn't it equally plausible without "physical"? But the dualist denies the claim that natural determinables that are not law bound are functional. For instance, awareness seems to be a natural determinable (whose determinates are of a form like being aware of/that ..., and nothing else), but the dualist is apt to deny that it's functional.

In any case, one interesting result transpires from the above. It is an important question whether location is law bound. If we could resolve that, we would be some ways towards a good account of spacetime (if it is law bound, proposals like this one might have some hope, if based on a better physics). The account I give above of law boundedness is rather provisory, and a better account is also needed.