Consider for instance claims like the following that many mereologists like:
- If R is any region all the points of which are occupied by x, and R* is any sub-region, then there is a part of x that occupies all and only the points in R*.
(We can also talk without invoking points, but points will be convenient.) Consider now some parallels for other relations:
- If R is a set of propositions all the members of which are believed by x (think of belief as epistemic occupation!), and R* is any subset, then there is a part of x that believes all and only the propositions in R*.
- If R is a set of people all members of which x is a friend to, and R* is any subset, then there is a part of x such that that part is a friend to all and only the people in R*.
These are absurd, though we may non-literally talk that way. "The part of Josh that is friends with Trent likes epistemology."
Or consider some claim that nothing can be in two places at once. Make the claim precise, for instance in the following way:
- It is not possible that there is an object x and disjoint regions R and R* such that every part of x occupies some point (perhaps different points for different parts) in R and every part of x occupies some point (ditto) in R*.
But why think that the occupation relation satisfies this kind of an axiom?
Here's a broad sweeping thought: Otherwise Humean philosophers who believe in all sorts of very general rearrangement principles for fundamental relations do not extend the same courtesy to the occupation relation.
Ironically, while I am not happy with general recombination principles (that say that any recombination of possible objects makes for a possible scenario), I am happy to allow for wild and crazy rearrangements of the occupation relation--objects being in more than one place at a time, objects occupying spatiotemporally disconnected regions, etc. If I thought there were such things as parts, I might even be open to such options as composite objects occupying locations that none of their proper parts occupy, parts occupying locations that the whole does not occupy, etc.