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