People made a lot of moves on Tuesday, so I thought it might be good idea to do a bit of a recap.
We mainly talked about the 4D-ist's treatment of the statue/clay problem. Remember that in our original example, Lump began to exist years ago and will continue to exist for many more years. Angel was molded at noon and squished at 6 p.m.One of the theories we discussed was cohabitation theory, a form of 2-ism according to which Lump and Angel are distinct obects that share exactly the same matter and occupy exactly the same spatial region from noon until 6 pm. However, Lump and Angel's distinctness is attested to by their different historical (time of creation/destruction) and modal (e.g., squishability vs. non-squishability) properties. Those who think that modal properties are grounded in physics-y properties will be troubled by the apparent fact that Angel and Lump differ in their modal properties despite possessing exactly the same physics-y properties. They may have to accept the existence of brute modal properties. In addiiton, since statue and lump are not the only possible sortals that apply to our case -- but just the ones for which we have common English descriptors -- we may feel forced to accept gazillionism (not just 2-ism) where many many coincident objects co-exist from noon until 6 pm, distinguished only by their brute modal properties. Check out the very nice discussion of matters related to this stemming from the previous post by Damian.
The 4D-ist enters here to say that if we view Lump and Angel as 4D temporally extended objects then Angel and Lump are clearly distinct. Lump has Angel as a proper part. Angel and Lump share their temporal parts from Noon until 6 pm, but Lump has (and Angel does not) parts outside of the noon - 6 pm interval. Now that seems to account for the historical properties involved in the case we've discussed so far. However, suppose that Lump and Angel came into existence at noon and went out of existence at 6 pm -- via a Lumpl/Goliath scenario (See Wasserman for a description of Lumpl/Goliath) or via the spontaneous creation/destruction of matter. In this case, it seems that we would still want to say that Lump and Angel are distinct objects even though they share exactly the same 4D parts. Haven't we just raised the same problem for 4D-ism that had earlier been raised for Cohabitation theory. Must the 4D-ist accept brute modality to the extent that the 3D-ist does? Why or why not? Does the 4D-ist have tools in her toolbox that the 3D-ist doesn't?