Kant's Critique of Judgement

by Immanuel Kant

The estimation of magnitude by means of concepts of number (or their signs in Algebra) is mathematical; but that in mere intuition (by the measurement of the eye) is aesthetical. Now we can come by definite concepts of how great a thing is, [only][44] by numbers, of which the unit is the measure (at all events by series of numbers progressing to infinity); and so far all logical estimation of magnitude is mathematical. But since the magnitude of the measure must then be assumed known, and this again is only to be estimated mathematically by means of numbers,—the unit of which must be another [smaller] measure,—we can never have a first or fundamental measure, and therefore can never have a definite concept of a given magnitude. So the estimation of the magnitude of the fundamental measure must consist in this, that we can immediately apprehend it in intuition and use it by the Imagination for the presentation of concepts of number. That is, all estimation of the magnitude of the objects of nature is in the end aesthetical (i.e. subjectively and not objectively determined).

Now for the mathematical estimation of magnitude there is, indeed, no maximum (for the power of numbers extends to infinity); but for its aesthetical estimation there is always a maximum, and of this I say that if it is judged as the absolute measure than which no greater is possible subjectively (for the judging subject), it brings with it the Idea of the sublime and produces that emotion which no mathematical estimation of its magnitude by means of numbers can bring about (except so far as the aesthetical fundamental measure remains vividly in the Imagination). For the former only presents relative magnitude by means of comparison with others of the same kind; but the latter presents magnitude absolutely, so far as the mind can grasp it in an intuition.

In receiving a quantum into the Imagination by intuition, in order to be able to use it for a measure or as a unit for the estimation of magnitude by means of numbers, there are two operations of the Imagination involved: apprehension (apprehensio) and comprehension (comprehensio aesthetica). As to apprehension there is no difficulty, for it can go on ad infinitum; but comprehension becomes harder the further apprehension advances, and soon attains to its maximum, viz. the aesthetically greatest fundamental measure for the estimation of magnitude. For when apprehension has gone so far that the partial representations of sensuous intuition at first apprehended begin to vanish in the Imagination, whilst this ever proceeds to the apprehension of others, then it loses as much on the one side as it gains on the other; and in comprehension there is a maximum beyond which it cannot go.

Hence can be explained what Savary[45] remarks in his account of Egypt, viz. that we must keep from going very near the Pyramids just as much as we keep from going too far from them, in order to get the full emotional effect from their size. For if we are too far away, the parts to be apprehended (the stones lying one over the other) are only obscurely represented, and the representation of them produces no effect upon the aesthetical judgement of the subject. But if we are very near, the eye requires some time to complete the apprehension of the tiers from the bottom up to the apex; and then the first tiers are always partly forgotten before the Imagination has taken in the last, and so the comprehension of them is never complete.—The same thing may sufficiently explain the bewilderment or, as it were, perplexity which, it is said, seizes the spectator on his first entrance into St. Peter’s at Rome. For there is here a feeling of the inadequacy of his Imagination for presenting the Ideas of a whole, wherein the Imagination reaches its maximum, and, in striving to surpass it, sinks back into itself, by which, however, a kind of emotional satisfaction is produced.

I do not wish to speak as yet of the ground of this satisfaction, which is bound up with a representation from which we should least of all expect it, viz. a representation which lets us remark its inadequacy and consequently its subjective want of purposiveness for the Judgement in the estimation of magnitude. I only remark that if the aesthetical judgement is pure (i.e. mingled with no teleological judgement or judgement of Reason) and is to be given as a completely suitable example of the Critique of the aesthetical Judgement, we must not exhibit the sublime in products of art (e.g. buildings, pillars, etc.) where human purpose determines the form as well as the size; nor yet in things of nature the concepts of which bring with them a definite purpose (e.g. animals with a known natural destination); but in rude nature (and in this only in so far as it does not bring with it any charm or emotion produced by actual danger) merely as containing magnitude. For in this kind of representation nature contains nothing monstrous (either magnificent or horrible); the magnitude that is apprehended may be increased as much as you wish provided it can be comprehended in a whole by the Imagination. An object is monstrous if by its size it destroys the purpose which constitutes the concept of it. But the mere presentation of a concept is called colossal, which is almost too great for any presentation (bordering on the relatively monstrous); because the purpose of the presentation of a concept is made harder [to realise] by the intuition of the object being almost too great for our faculty of apprehension.—A pure judgement upon the sublime must, however, have no purpose of the Object as its determining ground, if it is to be aesthetical and not mixed up with any judgement of Understanding or Reason.

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Because everything which is to give disinterested pleasure to the merely reflective Judgement must bring with the representation of it, subjective and, as subjective, universally valid purposiveness—although no purposiveness of the form of the object lies (as in the case of the Beautiful) at the ground of the judgement—the question arises “what is this subjective purposiveness?” And how does it come to be prescribed as the norm by which a ground for universally valid satisfaction is supplied in the mere estimation of magnitude, even in that which is forced up to the point where our faculty of Imagination is inadequate for the presentation of the concept of magnitude?

In the process of combination requisite for the estimation of magnitude, the Imagination proceeds of itself to infinity without anything hindering it; but the Understanding guides it by means of concepts of number, for which the Imagination must furnish the schema. And in this procedure, as belonging to the logical estimation of magnitude, there is indeed something objectively purposive,—in accordance with the concept of a purpose (as all measurement is),—but nothing purposive and pleasing for the aesthetical Judgement. There is also in this designed purposiveness nothing which would force us to push the magnitude of the measure, and consequently the comprehension of the manifold in an intuition, to the bounds of the faculty of Imagination, or as far as ever this can reach in its presentations. For in the estimation of magnitude by the Understanding (Arithmetic) we only go to a certain point whether we push the comprehension of the units up to the number 10 (as in the decimal scale) or only up to 4 (as in the quaternary scale); the further production of magnitude proceeds by combination or, if the quantum is given in intuition, by apprehension, but merely by way of progression (not of comprehension) in accordance with an assumed principle of progression. In this mathematical estimation of magnitude the Understanding is equally served and contented whether the Imagination chooses for unit a magnitude that we can take in in a glance, e.g. a foot or rod, or a German mile or even the earth’s diameter,—of which the apprehension is indeed possible, but not the comprehension in an intuition of the Imagination (not possible by comprehensio aesthetica, although quite possible by comprehensio logica in a concept of number). In both cases the logical estimation of magnitude goes on without hindrance to infinity.

But now the mind listens to the voice of Reason which, for every given magnitude,—even for those that can never be entirely apprehended, although (in sensible representation) they are judged as entirely given,—requires totality. Reason consequently desires comprehension in one intuition, and so the presentation of all these members of a progressively increasing series. It does not even exempt the infinite (space and past time) from this requirement; it rather renders it unavoidable to think the infinite (in the judgement of common Reason) as entirely given (according to its totality).

But the infinite is absolutely (not merely comparatively) great. Compared with it everything else (of the same kind of magnitudes) is small. And what is most important is that to be able only to think it as a whole indicates a faculty of mind which surpasses every standard of Sense. For [to represent it sensibly] would require a comprehension having for unit a standard bearing a definite relation, expressible in numbers, to the infinite; which is impossible. Nevertheless, the bare capability of thinking this infinite without contradiction requires in the human mind a faculty itself supersensible. For it is only by means of this faculty and its Idea of a noumenon,—which admits of no intuition, but which yet serves as the substrate for the intuition of the world, as a mere phenomenon,—that the infinite of the world of sense, in the pure intellectual estimation of magnitude, can be completely comprehended under a concept, although in the mathematical estimation of magnitude by means of concepts of number it can never be completely thought. The faculty of being able to think the infinite of supersensible intuition as given (in its intelligible substrate), surpasses every standard of sensibility, and is great beyond all comparison even with the faculty of mathematical estimation; not of course in a theoretical point of view and on behalf of the cognitive faculty, but as an extension of the mind which feels itself able in another (practical) point of view to go beyond the limit of sensibility.