Mereological Sums via Abstraction Principles

An object is said to be thin when its existence makes no demands on reality beyond those already made by the existence of certain other objects. Mereological sums are often taken to be thin in this sense, since many metaphysicians have maintained that a sum is nothing over an above the objects that compose it. In this paper, I develop an abstractionist account of the existence and thinness of mereological sums. Specifically, I show that Classical Extensional Mereology and Universalist Mereology, a much weaker non-extensional system that does not prove any supplementation principle, can both be axiomatized via appropriate abstraction principles for sums. I conclude by commenting on the philosophical significance of this result.