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.

3 comments:

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.

Tim

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". :-)

江仁趙雲虹昆 said...

嗯~蠻不錯耶~~我喜歡 ∩ 3∩............................................................