tag:blogger.com,1999:blog-3891434218564545511.post5252710415945194082..comments2018-01-17T20:47:48.227-06:00Comments on Alexander Pruss's Blog: Substantivalism about space is a kind of relationalismAlexander R Prusshttp://www.blogger.com/profile/05989277655934827117noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-3891434218564545511.post-24322336166123111072017-02-05T22:49:05.926-06:002017-02-05T22:49:05.926-06:00That's a very good point. So, it's hard to...That's a very good point. So, it's hard to escape some sort of relationalism about space.<br /><br />So the pure relationalist has a significant advantage: everybody else has spatial relations plus something else, but the relationalist just has the spatial relations.<br /><br />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.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-60919650694141524992017-02-04T16:32:02.307-06:002017-02-04T16:32:02.307-06:00"Moreover, a substantivalist theory couched i..."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."<br /><br />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.Brian Cutterhttps://www.blogger.com/profile/17059155559949747916noreply@blogger.com