This article reconstructs Jean-François Lyotard’s theory of the sublime in contemporary art, focusing on his claim that such art ‘presents’ the unpresentable, and tracing its origins in Kant’s account of the sublime. I propose that Lyotard identifies a difficulty concerning Kant’s account: to understand why the disparate elements in the experience of the sublime (idea of reason, sensible representation) should be synthesized to form that experience. Lyotard recasts this difficulty as a pragmatic problem for artistic practice – how to ‘testify’ to the absolute in a non-absolute, sensibly perceivable object (the artwork) – that can be understood to drive avant-garde artistic experimentation.