Plausibly, a fusion of extended objects is extended. Also, plausibly, an extended object has a size. Now suppose, as is surely possible, that there are two universes that aren't spatiotemporally connected, and an extended object A in one and another extended object B in another. Then the fusion of A and B would be an extended object that has no size, since there is no meaningful distance between a part of A and a part of B. Hence, given our assumptions about extended objects, mereological universalism--the thesis that necessarily all pluralities have a fusion--is false.

## 4 comments:

Plausibly, the size (magnitude, volume) of an object is the sum of the sizes (magnitudes, volumes) of its disjoint parts. So the fusion of A and B would have a size, namely the sum of the size of A and the size of B. That is, we can still apply (Jordan, Lebesgue or Borel) measure theory.

If the particles we are made of turn out to be point particles, then by this account our size is zero. But that seems false.

Sure, but in your example A and B are both extended. So, just substitute 'extended object' for 'object' and 'extended parts' for 'parts' in my previous comment - and the point I made is still valid.

Suppose that it turns out that elementary particles are extended, but very tiny as compared to the empty space between them. Then on your definition of size, we are much smaller than intuitively we are.

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