Title: Partial identity and mereotopology

Abstract: How should we think about the ways in which identity and parthood interact? One important line of thought comes from the joint influence of the two Davids: Armstrong and Lewis. The underlying idea is that mereological overlap is a kind of identity – namely, partial identity. The aim of this paper is to ask whether there may be principled reasons to doubt that two partially identical objects must share some part. We wish to explore a notion of partial identity that does not require the existence of some separate part of both. We then provide a formal theory of such a relation drawn from mereotopology. We then consider an application in the philosophy of mathematics.