This will be talk for the workshop Philosophy of Set Theory held at the University of Konstanz, 3 – 4 December 2021 — in person!
Update: Unfortunately, the workshop has been cancelled (perhaps postponed to next year) in light of the Covid resurgence.
Abstract. I shall analyze the roles and interaction of reflection and urelements in second-order set theory. Second-order reflection already exhibits large cardinal strength even without urelements, but recent work shows that in the presence of abundant urelements, second-order reflection is considerably stronger than might have been expected—at the level of supercompact cardinals. This is joint work with Bokai Yao (Notre Dame).