Title: Sets as fusions of materially-equivalent rigid embodiments

Abstract: Albeit having some initial plausibility, most philosophers today would reject the thesis that members of sets are parts of sets, instead following Lewis (1991, 1993) in taking sets and classes more generally to have only their subclasses as parts, with singletons being mereologically atomic. Against this background, Caplan et. al (2010) attempt to maintain that sets have their members as parts, in the framework of Fine’s (1999, 2010) theory of rigid embodiments. Their view, however, is committed to a rejection of classical mereology as it very directly entails failures of the principle of strong supplementation. In this talk I will attempt to motivate a (work-in-progress) view of the mereology of sets based on Fine’s theory of rigid embodiments in which: (i) the members of sets are parts of sets; and (ii) no principle of classical mereology is violated. The resulting view is that sets just are fusions of rigid embodiments sharing the same material parts. Throughout the talk I will also consider how this theory may help justify some of the restrictions on set construction from standard set theory.