This will be a talk for the Conference on Infinity, a collaborative meeting of logicians and specialists in Chinese philosophy here at Peking University, 24 June 2025, in the philosophy department.

Abstract.  I shall lay out a spectrum of fundamentally different potentialist conceptions of infinity. The differences in these potentialist ideas become especially clear when adopting a modal perspective on potentialism, grounded in the ideas of modal logic. I shall argue that some forms of potentialism, the “convergent” forms, are implicitly actualist, whereas the radical branching form of potentialism is more truly potentialist in nature.