The Sublime, Entry Directory

by Corry Shores
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Entry Directory for the Topic of
The Sublime

Hegel

Hegel's Sublime in Lectures on Aesthetics, partial summary

Longinus

Musical Arrangement of Words in Longinus' Sublime

Lyotard. Jean-François Lyotard

Lyotard, "The Sublime and the Avant-Garde," summary

Kant

Kant's Mathematical Sublime (§25)

Kant's Mathematical Sublime (§26)

Mathematical Sublime (§27)

Schiller

Schiller "Of the Sublime: Toward the Further Elaboration of Some Kantian Ideas"

Schiller "On the Sublime" summary and text

Schiller, "On the Tragic Art," 1st part summary

Schiller, "Of the Cause of the Pleasure We Derive from Tragic Objects," 1st part summary

Schiller, "Reflections on the Use of the Vulgar and Low Elements in Works of Art"

Achilles' Shield (Shield of Achilles) as Illustration to Schiller's Aesthetical Essays

Schlegel

Schlegel, On the Study of Greek Poetry, Selective Summary

Barnet Newman

Barnett Newman's "The Sublime is Now," partial summary

Bergson, Time and Free Will, Chapter 2, §70 "The Common Confusion between Motion and the Space Traversed Gives Rise to the Paradoxes of the Eleatics"

by Corry Shores
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[The following is summary; my commentary is in brackets.]

Bergson, Time and Free Will

Chapter II, "The Multiplicity of Conscious States," "The Idea of Duration"

Part XXIII: The Eleatic Paradox

§70 "The Common Confusion between Motion and the Space Traversed Gives Rise to the Paradoxes of the Eleatics"

Previously we saw how we confuse motion with the space that a body traverses. We know that space is infinitely divisible. So if we confuse motion with space, we conclude that motion is divisible as well. But, if space is infinitely divisible, then there are an infinite number of intervals to cross in a finite area. So motion across a finite extent could never be completed. Hence when we confuse space and motion, we obtain Zeno's paradoxes. (112-113)

This confusion forms the basis of Zeno's paradox of Achilles and the Tortoise. The two race. The Tortoise starts further down the track. But they begin at the same time. Before Achilles can overtake the Tortoise, he must first reach the spot where the Tortoise began. Quickly Achilles arrives there. But, the Tortoise has been moving continuously since then. So by the time Achilles arrives at the Tortoise's starting spot, the Tortoise has already advanced a bit down the track. So now for Achilles to overtake the Tortoise, he must first cross the Tortoise's more advanced position. But again, as soon as Achilles arrives, the Tortoise has advance and created a new spot that Achilles must cross. So long as the Tortoise continues moving, there will aways be points in advance for Achilles to cross. Hence Achilles can never overtake the Tortoise.

Bergson explains that indeed space is infinitely divisible. But the motion through it is an act. And acts are indivisible. So "each of Achilles' steps is a simple indivisible act." (113a) After so many of these acts, Achilles will pass the tortoise. Zeno's mistake is that he believes motion to be as homogeneous and divisible as space is. Rather, in motion there is a heterogeneous series of indivisible acts.

Zeno and the Eleatics homogenize the movement of Achilles and the Tortoise. So in the end, each step of Achilles is equal to each of the Tortoise's step. In a way, Zeno really is comparing the movement of two tortoises who "agree to make the same kind of steps or simultaneous acts, so as never to catch one another." (113bc)

To help us better understand the problem, Bergson has us make a distinction.

1) As motions, the steps of both Achilles and the Tortoise are indivisible acts.

2) As spatial motions, the steps of both racers have extensive magnitudes. So their movements are made up of discrete simple motions. Now, the extensive magnitude of each of Achilles' steps is greater than the lengths of the Tortoise's steps. So even if the Tortoise has a head start, eventually Achilles' longer strides will allow him to pass the Tortoise.

To visualize, consider each discrete movement-act of Achilles and the Tortoise as having disproportionate extensive magnitudes.

The Tortoise begins the race further down the track. They take their first step.

Second:

And then the following:

So Bergson sees movement-actions as descrete units. These may be of different spacial magnitudes. Thus we can see why there really is no paradox.

Bergson then addresses Évellin's similar solution to the Achilles paradox. Both Évellin and Bergson solve the problem by considering Achilles' motion as made up of discrete units. Achille's units are greater than the Tortoise's, so Achilles will overtake him. For Bergson, we experience discrete acts of motion in a non-spatial pure duration. Motions, as durational acts, then, do not extend in time. However, any motion may correspond to a different spatial extent. So this way Achilles' steps are larger. For Bergson, the problem is that we fail to distinguish inextensive duration from extensive time and space. So it does not matter if space is infinitely divisible, for Bergson, because motion-acts are indivisible units corresponding to different extensions in space.

Yet, for Évellin, real space is not infinitely divisible. There are basic discrete units of space and time. But we use our imagination to think geometrically about space. We can imagine any two neighboring points. But no matter how close we picture them to be, we can always imagine another point between them. However, this leads to Zeno's paradoxes. So Évellin argues that there is a real space that is not infinitely divisible. Then, in each common discrete time moment, Achilles will travel more distance-units than the Tortoise. This way, no matter how far ahead the Tortoise begins, Achilles will overtake him, given enough time. So we see that the same diagram that we used for Bergson applies to Évellin as well.

Except now the numbers represent discrete time moments, and not discrete motion-acts.

Bergson thinks it is unnecessary to resort to metaphysical abstractions about the nature of reality. All we need to do is presuppose that motion is qualitative and not quantitative.

But if motion is not quantitative, then what do scientists measure when they calculate velocity? At the start of motion, the object is in one spatial place, and its destination is somewhere else. Eventually, there will be another simulteneity when the object and its destination coincide. Bergson claims that when physicists measure velocity, they are really determining when they can expect the simultaneity during when the object and its destination coincide. So mathematics is perfectly capable of making calculations regarding the starting and ending simulteneities. However, math and physics go beyond their "province" when they try to explain what happens between those simulteneities. (114-115)

So when we looked for a homogeneous medium in duration, we found time, which was really space. But there is no duration in space. Hence what is homogeneous in duration is not durational. And we see now that when we seek something homogeneous in motion, all we find is the line of space traversed. But geometrical lines are motionless. Hence likewise, what is homogeneous in motion is really motionless. (115b)

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Images from the pages summarized above, in the English Translation [click on the image for an enlargement]:

Images from the pages summarized above, in the original French [click on the image for an enlargement]:

Bergson, Henri. Time and Free Will: An Essay on the Immediate Data of Consciousness, Transl. F. L. Pogson, (New York: Dover Publications, Inc., 2001).

Available online at:

http://www.archive.org/details/timeandfreewill00pogsgoog

French text from:

Bergson, Henri. Essai sur les données immédiates de la conscience. Originally published Paris: Les Presses universitaires de France, 1888.

Available online at:

http://www.archive.org/details/essaisurlesdonn00berguoft

Mathematical Sublime (§27)

by Corry Shores
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Reason legislates a law requiring us to judge the great things we sense in nature as small in comparison to reason’s ideas (§27 141b). The feeling of displeasure we feel when encountering the absolutely great object causes displeasure, which then arouses the feeling of our supersensible vocation by which “it is purposive and thus a pleasure to find every standard of sensibility inadequate for the ideas of the understanding” (141c).

The mind is moved during sublime experiences, whereas when judging the beautiful it is calm. Kant likens this movement to vibration, that is, “to a rapidly alternating repulsion from and attraction to one and the same object:” the imagination is fearful of the abyss of reality that lies beyond its comprehensive capacities, but also reason’s notion of the supersensible is what causes the imagination to think there can be more. Our ability to conceive it is something lawful, and hence what is attractive to reason is repulsive to the imagination (141-142).

Apprehensions continue arriving in succession; it is a forward movement. But comprehension is regressive; it is a backward movement, hence “it does violence to the inner sense, which must be all the more marked the greater the quantum is which the imagination comprehends in one intuition.” Because comprehension moves backward, it in this sense seems subjectively contrapurposive, because our purpose is to do as much cognizing as possible, and not to halt the flow. However, it is necessary that we perform such interruptive comprehensions, hence in that way it is also purposive. This is another source of violence inflicted on the subject (142c-d).

But this displeasure from counterpurposivity is also what causes the faculty of reason to provide the idea of the absolute whole, and hence this displeasure comes to be seen as purposive (as a means to rational cognition) and hence is converted into pleasure (143c).

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

Kant's Mathematical Sublime (§26)

by Corry Shores
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When we estimate a magnitude numerically, this is mathematical; when we estimate by mere intuition, ‘measured by the eye,’ this is aesthetic (§26 134d).

But even mathematical estimation relies on an aesthetic estimate of a common measure which may be computed variously (135b). (This aesthetic estimate is obtained by means of averaging).

In mathematical estimation, there can be no greatest magnitude, because numbers succeed to infinity. But on account of the limitations of our faculties, there can be a greatest estimated aesthetic magnitude: if there is a point to which anything greater is beyond our comprehension, it does not matter how much greater, because all will seem absolutely great. This caries with it the idea of the sublime and produces an emotion “which no mathematical estimation of magnitudes by means of numbers can produce” (135bc).

In order to use a quantum in the imagination to estimate a magnitude, there must be two facultative activities: apprehension and comprehension. We apprehend an object when it is given part-by-part in series, and we then comprehend them through synthetic unification. But we have only so much capacity to retain apprehensions, so when a certain quantity has been obtained, we begin to forget those furthest back in our retention. So we cannot comprehend something whose magnitude is beyond our retentional capacities (135c-d).

These aesthetic judgments must be pure, and thus not involve teleology. Hence the sublime is not shown in products of art, which were made with a human end in mind that determines its form and magnitude; nor is the sublime found in natural things whose “concept already brings with it a determinate end,” as for example animals with known natural determinations. Rather, the mathematical sublime can only be found in raw nature merely insofar as it contains magnitudes, and not whether it by itself alone brings charm or the emotion felt in times of danger (136bc).

“An object is monstrous if by its magnitude it annihilates the end which its concept constitutes.” An object is colossal when the mere presentation of its concept is almost too great for all presentation. “A pure judgment on the sublime, however, must have no end of the object as its determining ground if it is to be aesthetic and not mixed-up with any judgment of the understanding or of reason” (136-137).

When magnitudes are estimated conceptually, there is no force that pushes the imagination to comprehend the infinite, because the imagination can schematize in a way that presents the entire magnitude in such a manner that it can be grasped as one abstract quantity (137c-d).

But in aesthetic apprehensions, the “voice of reason” requires that all given magnitudes be comprehended into intuition, and demands that even the infinite be comprehended (138ab). However, the infinite is absolutely great, and cannot be compared to a standard measure, and hence cannot be comprehended into one homogenous quantity. “But what is most important is that even being able to think of it as a whole indicates a faculty of the mind which surpasses every standard of sense;” and “even to be able to think the given infinite without contradiction requires a faculty in the human mind that is itself supersensible” (138b).

“Nature is thus sublime in those of its appearances the intuition of which brings with them the idea of its infinity” (138d).

Normally in aesthetic judgment, the free play of the imagination connects comprehensions to concepts in the understanding: the synthesized representation of a rose is matched with its concept. But we have no concept of the absolute whole, because we have never comprehended it; however, the faculty of reason contains the a priori idea of the absolute whole, and so reason steps-in to restore harmony among the faculties by matching the representation of the faculties’ limitations with this idea of the absolute totality.

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

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.