An argument against four-dimensional mereological sums

Say that x is a four-dimensional mereological sum provided that x is a mereological sum with the property that not all of its parts exist at all the same times, i.e., x has parts a and b such that a exists at some time at which b does not. Mereological sums of stages will, typically, be four-dimensional mereological sums. Plausibly, a four-dimensional mereological sum exists at t provided that it overlaps the spacetime region of time t (times are spacelike hypersurfaces, I suppose).

1. Without backwards causation, it is not possible to make it the case that an object did not exist yesterday.
2. If there are four-dimensional mereological sums, then it is possible to make it the case that an object did not exist yesterday.
3. Hence, there are no four-dimensional mereological sums.

The argument for (2) is simple. If four-dimensional mereological sums exist, then there could be a four-dimensional mereological sum that existed prior to t₀ but that contains a particle a that comes into existence after t₀. Then at t₀ it would be possible, without backwards causation to make the sum not have existed by preventing the coming-into-existence of a—for if one prevented that, then the four-dimensional mereological sum would never have existed.