This will be a talk for the First-order Modal Logic (FoMoLo) Seminar, 12 February 2024. The talk will take place online via Zoom—contact the organizers for access.

Abstract. What is or should be the potentialist account of classes? There are several natural implementations of second-order logic in a modal potentialist setting, which arise from differing philosophical conceptions of the nature of the second-order resources. I shall introduce the proposals, analyze their comparative expressive and interpretative powers, and explain how various philosophical attitudes are fulfilled or not for each proposal. This is joint work in progress with Øystein Linnebo.