It’s just occurred to me that substantivalist views of space or spacetime are actually relationalist: they define location by relations between objects. It’s just that they introduce one or more additional objects—say, points or space or spacetime—to fill out the theory. An entity’s being located is then a matter of the entity standing in a certain relation to one or more of these additional objects.
Moreover, a substantivalist theory couched in terms of points may have to be even closer to relationalism, in that it may need to say that what makes the points be points of the kind of space or spacetime they are points of are their mutual spatial or spatiotemporal relations.
What has a hope of being a more radical alternative to relationalist theories are property theories, on which being in a location is a property very much like having a certain electric charge—the only difference being that the location properties have a three- or four-dimensional structure while the charge properties have a one-dimensional structure. Of course, having properties will be a matter of relation on heavy-weight Platonism and on trope theories, but these relations are not special spatial or spatiotemporal relations, but just general-purpose relations like instantiation or inherence.
Of course, maybe we don’t want an alternative to relationalism because we like relationalism.
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"Moreover, a substantivalist theory couched in terms of points may have to be even closer to relationalism, in that it may need to say that what makes the points be points of the kind of space or spacetime they are points of are their mutual spatial or spatiotemporal relations."
Doesn't this point apply to the property theory too? Here I assume the relevant location properties would have a 3- or 4-dimensional structure that mirrors the structure the substantivalist takes to hold among points of space/spacetime. So wouldn't this just replace first-order spatial relations among points with second-order quasi-spatial relations among properties? If that's right, then maybe relationism of some kind is inescapable.
That's a very good point. So, it's hard to escape some sort of relationalism about space.
So the pure relationalist has a significant advantage: everybody else has spatial relations plus something else, but the relationalist just has the spatial relations.
Well, maybe with one exception. If you're a mathematical Platonist, you could hold that many physical properties are relations to mathematical objects. Thus, charge is constituted by a charge-relation to a real number, mass is constituted by a mass-relation to a real number, momentum is constituted by a mass-relation to a 3-vector, etc. Perhaps, then, position is constitution by a position-relation to a 3-vector (in a non-relativistic setting). Of course, that 3-vector stands in mathematical relations to other 3-vectors. But these relations are not posited to explain spatiality--they are just there in the mathematical world. Moreover, the 3-vectors and their relations constituting position could (in a non-relativistic setting) be the very same 3-vectors and relations constituting momentum. I think that if one is a mathematical Platonism, this is a very elegant and parsimonious view: one gets so much structure just by positing a few contingent relations between the physical and the mathematical. But Platonism is probably false.
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