Monday, April 4, 2016

Spacetime: Beyond substantivalism and relationalism

According to substantivalism, spacetime or its points or regions is a substance, and location is a relation between material things and spacetime or its points or regions. According to relationalism, location is constituted by relations between material things. Often, the two views are treated as an exhaustive division of the territory.

But they're not. Lately, I've found myself attracted to a tertium quid which I know is not original (it's a story other people, too, have come to by thinking about the analogy between location and physical qualities like charge or mass). On a simplified version of this view, being located is a determinable unary property. Locations are simply determinates of being located. This picture is natural for other physical qualities like charge. Having charge of 7 coulombs is not a matter of being related to some other substances--whether other charged substances or some kind of substantial "chargespace" or its points or regions. It's just a determinate of the determinable having charge.

This determinate-property view is more like the absolutism of substantivalism, but differs from substantivalism by not positing any "spacetime substance", or by making the locations into substances. Locations are determinates of a property, and hence are properties rather than substances. If nominalism is tenable for things like charge or mass, the theory won't even require realism about locations.


Unknown said...

This is interesting. It seems like this view might have interesting consequences for debates about mereological harmony and persistence debates.

So it seems true that no object can have two determinate properties of the same determinable. We might then think that extended simples require having multiple distinct location determinate properties and so are impossible. Same goes for multiple location. If multi-location is impossible, then enduring through time is impossible, and so on.

It doesn't seem clear what would make co-location impossible though. And that seems to be an interesting result.

I know that was all really hand-waivey but it seems like a line thought someone that held this view might want to take.

Alexander R Pruss said...

I don't need to insist on the locations being determinates, just properties. That's enough to generate a tertium quid. I should have gone with that.
That said, locations can be region-like rather than point-like. In that case there is problem with extended simples. An extended complex thing is one that has location and is such that a part has a proper sublocation.
I also suspect that it's possible to have multiple determinates, but that's a different story.

Alexander R Pruss said...

Here's a potential difficulty for the view. The locations either are tied to a particular four-dimensional manifold or they are not. If they are not, then the Hole Argument for substantivalism works against the theory: the locations of the particles may not be enough to determine the whole geometry of spacetime. If they are tied to a particular manifold, then the geometry of all of spacetime can be recovered from the location of a *single* particle, and that seems wrong.

Alexander R Pruss said...

Here's another way to think about the last difficulty. The metric relations between locations are either contingent or not. If they are not contingent, then all spacetime geometry can be recovered from the location of a single particle. If they are contingent, however, then causal processes in the physical world cause contingent and apparently non-Cambridge relations between Platonic entities.