Wednesday, November 18, 2009

A theory of spacetime

I am not saying this theory is correct—it's too platonic for my taste. But it's suggestive. There are special properties called "locators". Moreover, as it happens, the collection of all locators forms a topological space (one can think of the open sets as corresponding to certain distinguished properties of locators). This space we can call the Receptacle. The Receptacle partitions into topologically connected subspaces. Each of these we can call a spacetime. Thus, a spacetime is a maximal connected set of locators. Some spacetimes have an additional structure, say a metric or manifold one.

The points of a spacetime are simply the locators that make it up. They are, thus, Platonic entities. An entity x occupies a point P if and only if x has the property P. Occupation, then, is simply exemplification. A spacetime is said to be actualized if and only if some point in it is occupied.

Question: Wherein do locators differ from other properties, like mass-properties (having mass x grams), that also have a topological (and even metric) structure?

6 comments:

Jonathan D. Jacobs said...

I was chatting with Jonathan Lowe this summer, and he seemed to hope that a similar view could be made out, but where the locators were location tropes. (Locations would then be sets of exactly similar tropes, I take it.) Would it really make a difference if the theory weren't Platonic?

Alexander R Pruss said...

If it weren't Platonic, it would have the consequence that there are no empty places. I think that's a plus. However, sets are already Platonic!

PFS said...

So, on Lowe's view the locators would be concrete instantiations of universal attributes (non-kind). In his Four-Category Ontology he calls them modes. I don't see why they would have to be Platonic entities in that the modes stand in an instantiation relation to the universal attributes, and these locator modes would characterize the objects or substances that are located. I think that Platonism only arises if no distinction is made between a universal property and a concrete property.

Alexander R Pruss said...

If locations are sets of exactly similar locators then we have a paradox. Suppose George (mayhep a ghost) and Patrick are in the same place in w1, and nobody else is. Then they have exactly similar locator tropes, and the place they are in is a set of two locator tropes. Suppose that in w2 that only George is there. Then, in w2, George has numerically the same locator trope as he does in w1. But in w2, George is at a different location from the one he is at in w1, because in w1 he is at a location which is a set of two tropes while in w2 he is at a location which is a singleton.

I suppose a counterpart theory might help. But I think that if we work out the details, then we lose the transitivity of sameness of location.

I don't think biting the bullet here is so bad.

If one could have sets of merely possible tropes, that would solve that.

Jonathan D. Jacobs said...

First, I should have been clear that I was giving my take on what was a rather short conversation. Any faults are, of course, mine.

Second, the set talk was too quick, and it was my own addition. I should have some something like, one thing occupies the same location as another iff they have exactly similar location tropes. (Alternatively, something that Jonathan toys with, they might share the same trope.) Locations might be Jonathan's universals, or you might just go for a two category ontology and think that there are no locations, only located substances.

For the most part, the second point should take care of Alex's worry about sameness of location.

Alexander R Pruss said...

The trope version would do the job I want this theory to do--namely, to make temporal (and spatial) location properties be no different in kind from charge and mass properties, thereby undercutting any temptations towards an A-theory. :-)