I've run this argument before. But let's do it again, maybe more clearly. If some things can have non-mereological parts, the following scenario is possible: an entity has m parts to begin with, and then it loses k and is left with n=m−k parts. It would be really weird if this couldn't happen in the case where n=1, but could happen in the case where n=2, say. So, plausibly, this can happen in the case where n=1. Suppose Fred, thus, loses all but one of his parts. The remaining part is not identical with Fred—if it were identical with Fred, then prior to the loss of the other parts, Fred would have been identical with a proper part of himself. So at the end, Fred has one part. But the following two claims seem plausible, too:
- x is a proper part of y if x is a part of y and x is not identical with y
- if x is a proper part of y, then y has at least one other proper part than x.
I take it that the advocate of non-mereological parts will have to deny (2). This introduces a new class of quasi-simples. A quasi-simple is an entity that has at most one proper part. Like a simple, it is not possible to subdivide a quasi-simple any further. But unlike a simple, a quasi-simple is allowed to have a proper part. This is weird indeed.
It is a puzzling question when two or more simples compose a whole. But once one allows quasi-simples, we get the further puzzling question when a simple composes a quasi-simple.