A Note on Unrestricted Composition

I discuss a general limitative consequence of the unrestricted mereological composition thesis. The unrestricted composition thesis, which is roughly the assertion that every plurality of objects possesses a fusion or sum, is shown to be in conflict with general existence-conditions for certain categories of mereologically non-composite objects. The conclusion is that the unrestricted composition thesis, which is a maximizing principle about what aggregates exist, places sharp limits on what unaggregated items can exist.