Wednesday, August 18, 2010

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.


TP said...

Hey Alex,

What do you mean by making it the case that an object didn't exist yesterday? Is this an instance of it?

God promises me that if I push this button today, he will make it such that object O didn't come into existence yesterday. Given this promise, I can make it such that there is no O yesterday by pushing the button. I do so without recourse to backwards causation. My pushing the button isn't backwards causation; God's causing O not to exist isn't backwards causation, and the result is no O yesterday.


Alexander R Pruss said...

I don't know if causation can go through God. Say I pray that you have a good day, and because of this God gives you a good day. Have I caused it? If so, then I will say the same thing about the backwards case, and call it backwards causation.

But if causation can't go through God, then your objection is solid. But then I modify the argument to say: "backwards causation or anything supernatural or otherwise spooky" instead of "backwards causation". :-)

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