This is a talk for the Workshop on Mereology at Shandong University in Jinan, China, a part of the week-long conference Week of Fusion Philosophy, 22-26 June 2026. The mereology talks are on 22 June 2026.

Title: Set-theoretic mereology as a foundation of mathematics?

Speaker: Joel David Hamkins, University of Notre Dame, Peking University

Abstract. Mereology, the study of the relation of part to whole, is often contrasted with set theory and its membership relation, the relation of element to set. Whereas set theory has found success in the foundation of mathematics, since the time of Cantor, Zermelo and Hilbert, nevertheless mereology has been strangely absent. Why is this? In this talk, I shall introduce and discuss set-theoretic mereology, a form of mereology based upon the set-theoretic inclusion relation ⊆ rather than the element-of relation ∈. In particular, we shall investigate the role to be played by set-theoretic mereology in the foundations of mathematics, and come perhaps to an explanation of why it has been absent.