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 theconcept of the infinite, which admits a double perspective. On the one hand, we have thenotion of sensible infinity (which must be understood as the capacity to always add a newunit to a previously given sensible magnitude). On the other hand, we find the infinite assomething absolutely given. This latter conception of the infinite demands that we situateourselves on the suprasensible realm. I argue that in the Kantian theory of the sublime bothnotions of the infinite coexist, for it is a kind of aesthetic judgment that takes as its point ofdeparture the estimation of objects which, because of their large size, suggest the idea ofsensible 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 suprasensiblemagnitude.