Kant's Mathematical Sublime (§25)

by Corry Shores
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The mathematical sublime is absolutely great.

A magnitude is a multitude of homogeneous elements that together constitute a unity, and magnitudes can be cognized by themselves alone. However, the greatness of something depends on judging not only the multitude or number of homogeneous elements in the object’s magnitude, but also the magnitude of each unity, and this magnitude requires a common measure, although no absolute concept of magnitude is possible (on account of an infinite regress: each magnitude derives its value by relating to some other, and hence there can be no first one. This is why numerical estimation of magnitude – no matter how abstractly computed – is grounded in aesthetic apprehension) (132b). The common measure is aesthetic and presumed subjectively universal, and may be empirical, as in the case of average magnitude, or a priori, which are given in concreto, such as the “magnitude of a certain virtue” or “the magnitude of the accuracy or inaccuracy of an observation or measurement” (133b).

But when something is absolutely great, that is, sublime, then there is no standard of measurement outside it, only one within it. “It is a magnitude that is equal only to itself,” and thus the sublime is not found in nature but rather only in ideas (133-134).

On account of its self-relative absolute magnitude: “that is sublime in comparison with which everything else is small” (134a).

We can use microscopes and telescopes to see continually smaller-and-smaller or larger-and-larger objects, but our imagination strives to attain-to the infinite scope, and our reason contains a real idea of absolute totality, thus “the very inadequacy of our faculty for estimating the magnitude of the things of the sensible world awakens the feeling of a supersensible faculty in us” (134b-c). [For Deleuze, it is not the imagination’s concordant efforts with reason to attain to the absolute scope that constitutes the “supersensible;” rather it is the detection of irreducible difference resulting when the faculties jointly perceive something differently and communicate their differences to one another.]

Hence as well: “that is sublime which even to be able to think of demonstrates a faculty of the mind that surpasses every measure of the senses” (134c).

Kant, Immanuel. Critique of the Power of Judgment. Transls. & Eds. Paul Guyer & Eric Matthews. Cambridge: Cambridge University Press, 2000.