The Mathematical and Temporal Basis of Judgments of the Sublime

In this paper, I elaborate the difference between the concept of infinity and the idea of infinity through Cantor's diagonalization proof to illuminate a passage in Kant's Critique of Judgment. Taking Lyotard's analysis of aesthetic judgments as the basis for my own project, I focus on the idea of a collapse of temporality required for objective cognition and its concomitant preclusion of cognitive subjectivity. Finally, after borrowing language from Hegel's Phenomenology of Spirit, I show that even though there is not a cognitive subject in judgments of the sublime, there is nevertheless a subjectivity that consciousness is tasked with, even if it never fulfills this task when it is confronted with a mathematically sublime object, and it is an subjectivity that would transcend time in order to know the object in-itself