Tuesday, October 25, 2011

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.

Heath White said...

I am not entirely sure I am following, but…

It seems plausible to me that ‘law-bounded’ is just a species of ‘functional’. That is, I am inclined to say, if a determinable is law-bounded then it is functional, just because it is defined by its role in the relevant laws. Any formally similar set of laws would, ipso facto, contain the same law-bounded determinables.

Location, not being law-bound (I don’t think; location does not figure in any natural laws I know of, unless we count things like velocity or acceleration, which seem to presuppose a notion of location) lacks at least this argument for being functional.

Secondly, I want to tell this dualist that they are supposed to be DUALists, not mentalists with a veneer of physics. If awareness is going to be a non-functional relation, then there is a pleasing symmetry if we claim that embodiment (entailing having a location) is a non-functional relation. Moreover, it seems intuitively correct to me.

Alexander R Pruss said...

1. I think there is a difference between being law bounded and being functional. Fness is law bounded roughly just in there are no Fs in worlds whose laws differ significantly in respect of F. This does not mean that Fness is defined by its role in the laws.

Now, one explanation of Fness's being law bounded would be that Fness is functional and its functionality requires such-and-such laws. But there could be another explanation. For instance, it could be that the laws governing Fness are grounded in things' instantiating of Fness. I actually like the account of laws that the latter leads to: the lawmakers for gravity are objects that have mass (deeming mass zero a kind of mass).

2. That said, you're likely right that my carving up of the territory may not be the best way. I don't know of any discussion of this material, and I am just doing my best to try to divide things up as best I can.

3. In classical physics, acceleration is the second derivative of location. So there are differential equations governing location. Moreover, the laws of gravity and electromagnetism concern distances. (On absolutism, location is prior to distances; on relationism, it could be the other way around.)

4. This sounds to me like the folks who say that Leibniz's monads aren't really in spacetime. But I think there is an important intuition in what you say. I am not sure, however, that location is fundamental to embodiment. Aristotle identifies materiality with some kind of passive potentiality. I don't understand this, but if one could make sense of it, it would be an account of materiality on which location is not fundamental to it.

Heath White said...

Aristotle identifies materiality with some kind of passive potentiality. I don't understand this, but if one could make sense of it, it would be an account of materiality on which location is not fundamental to it.

Here’s an idea. “Passive” = “acted upon”; “potentiality” = “determinable”.

If I can telepathically send you messages, then your mind has passive potentiality, in that it can become aware of various propositions through my agency. And that could happen even if we are disembodied spirits.

In the Aristotelian sense, then, your mind would be “material.” I am much less clear that this is what the rest of us mean by “material.”

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