Two conceptions of infinity in Kant's mathematical sublime

Abstract

The Kantian theory of the mathematical sublime can be studied from the point of view of the concept of the infinite, which admits a double perspective. On the one hand, we have the notion of sensible infinity (which must be understood as the capacity to always add a new unit to a previously given sensible magnitude). On the other hand, we find the infinite as something absolutely given. This latter conception of the infinite demands that we situate ourselves on the suprasensible realm. I argue that in the Kantian theory of the sublime both notions of the infinite coexist, for it is a kind of aesthetic judgment that takes as its point of departure the estimation of objects which, because of their large size, suggest the idea of sensible infinity. And in turn, the latter rests on the infinite as something absolutely given, which can only be explained if we understand the absolutely infinite as a suprasensible magnitude.