This is a talk for the Actualism and Potentialism Conference at the University of Konstanz, 28-29 September 2023. Also on Zoom: 928 0804 3434.

Abstract. What is or should be the potentialist account of classes? It turns out that 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.