Heller’s “Temporal Parts of Four Dimensional Objects”

Object = material content of a filled region of spacetime

An object isn’t an enduring spatial hunk of matter but a spatiotemporal hunk of matter.

You can’t say that objects are 3-dimensional and say all of the following:

a) there is such a physical object as my body.

b) there is a physical object in the space that we would typically say is now exactly occupied by all of me other than my left had.

c) a physical object can undergo a loss of parts (in the ordinary sense of ‘parts’).

d) distinct physical objects don’t occupy exactly the same space at the same time.

e) identity is transitive.

a) says Body exists. b) says Body-minus exists. Once we cut off my hand at t, then according to c) Body still exists and must occupy the same space as Body-minus. But by d) this means that after t Body = Body-minus. But Body before t = Body after t, and Body-minus before t = Body-minus after t. So this would mean that Body before t = Body-minus before t, which is clearly false.

Heller wants to say all of a) through e) are true, and thus he appeals to four-dimensionalism with objects having temporal parts.

We say x exists now when, strictly speaking, only part of x exists now, just as we say x is in the drawer when, strictly speaking, only part is.

Objection: How are we to understand something’s location (or any other attribute) at a time? The obvious reply is that a tensed sentence is only talking about the location relative to that time.

Either, “Spatiotemporally, where is (tenseless) it?” or “Spatially, where is (tensed) it?”