Monday, April 29, 2013

A cardinality argument against five-dimensional universalism

Five-dimensional universalism (hereby stipulated) holds that if f is a partially defined mapping f from worlds to regions such that (a) if f(w) is defined, then f(w) is a nonempty region of w's spacetime and (b) f(w) is nonempty for some w, there is an object Of that exists in every world w for which f(w) is defined and occupies precisely f(w) at w. We will call a function f with the above properties a "modal profile", indeed the modal profile of Of.

I think that to do justice to the vast flexibility of our language about artifacts, if we want to be realists about artifacts, we will need to be five-dimensional universalists. Mere four-dimensionalism mereological universalism is insufficient, because there can be always coincident artifacts with different modal properties.


  1. There is a set of all actual concrete objects.
  2. There is no set of all modal profiles.
  3. If there is no set of all modal profiles and five-dimensional universalism is true, there is no set of all actual concrete objects.
  4. So, five-dimensional universalism is not true.

The argument for (2) is that there are way too many possible worlds with spacetimes to make up a set[note 1], and for each such world w there is a different modal profile[note 2], so there is no set of all modal profiles.

1 comment:

Richard Davis said...

Sir Alexander, thy mountain of formalism is too steep for my tender young hoofs to climb. Couldst aid me in surmounting the definition of 5D Mereological Universalism? Perhaps point me at least to a piedmont from which I might better view yon high peak?