The estimation of magnitude by means of concepts of number (or their signs in algebra) is mathematical, but that in mere intuition (by the eye) is aesthetic.Now we can only get definite concepts of how great anything is by having recourse to numbers (or, at any rate, by getting approximate measurements by means of numerical series progressing ad infinitum), the unit being the measure; and to this extent all logical estimation of magnitude is mathematical.But, as the magnitude of the measure has to be assumed as a known quantity, if, to form an estimate of this, we must again have recourse to numbers involving another standard for their unit, and consequently must again proceed mathematically, we can never arrive at a first or fundamental measure, and so cannot get any definite concept of a given magnitude.The estimation of the magnitude of the fundamental measure must, therefore, consist merely in the immediate grasp which we can get of it in intuition, and the use to which our imagination can put this in presenting the numerical concepts: i.e., all estimation of the magnitude of objects of nature is in the last resort aesthetic (i.e., subjectively and not objectively determined).
Now for the mathematical estimation of magnitude there is, of course, no greatest possible (for the power of numbers extends to infinity), but for the aesthetic estimation there certainly is and of it I say that where it is considered an absolute measure beyond which no greater is possible subjectively (i.e., for the judging subject), it then conveys the idea of the sublime and calls forth that emotion which no mathematical estimation of magnitudes by numbers can evoke (unless in so far as the fundamental aesthetic measure is kept vividly present to the imagination): because the latter presents only the relative magnitude due to comparison with others of a like kind, whereas the former presents magnitude absolutely, so far as the mind can grasp it in an intuition.
To take in a quantum intuitively in the imagination so as to be able to use it as a measure, or unit for estimating magnitude by numbers, involves two operations of this faculty: apprehension (apprehensio)and comprehension (comprehension aesthetica).Apprehension presents no difficulty: for this process can be carried on ad infinitum; but with the advance of apprehension comprehension becomes more difficult at every step and soon attains its maximum, and this is the aesthetically greatest fundamental measure for the estimation of magnitude.For if the apprehension has reached a point beyond which the representations of sensuous intuition in the case of the parts first apprehended begin to disappear from the imagination as this advances to the apprehension of yet others, as much, then, is lost at one end as is gained at the other, and for comprehension we get a maximum which the imagination cannot exceed.
This explains Savary's observations in his account of Egypt, that in order to get the full emotional effect of the size of the Pyramids we must avoid coming too near just as much as remaining too far away.For in the latter case the representation of the apprehended parts (the tiers of stones) is but obscure, and produces no effect upon the aesthetic judgement of the Subject.In the former, however, it takes the eye some time to complete the apprehension from the base to the summit; but in this interval the first tiers always in part disappear before the imagination has taken in the last, and so the comprehension is never complete.The same explanation may also sufficiently account for the bewilderment, or sort of perplexity, which, as is said, seizes the visitor on first entering St.Peter's in Rome.For here a feeling comes home to him of the inadequacy of his imagination for presenting the idea of a whole within which that imagination attains its maximum, and, in its fruitless efforts to extend this limit, recoils upon itself, but in so doing succumbs to an emotional delight.
At present I am not disposed to deal with the ground of this delight, connected, as it is, with a representation in which we would least of all look for it-a representation, namely, that lets us see its own inadequacy, and consequently its subjective want of finality for our judgement in the estimation of magnitude-but confine myself to the remark that if the aesthetic judgement is to be pure (unmixed with any teleological judgement which, as such, belongs to reason), and if we are to give a suitable example of it for the Critique of aesthetic judgement, we must not point to the sublime in works of art, e.g., buildings, statues and the like, where a human end determines the form as well as the magnitude, nor yet in things of nature, that in their very concept import a definite end, e.g., animals of a recognized natural order, but in rude nature merely as involving magnitude (and only in this so far as it does not convey any charm or any emotion arising from actual danger).For, in a representation of this kind, nature contains nothing monstrous (nor what is either magnificent or horrible)-the magnitude apprehended may be increased to any extent provided imagination is able to grasp it all in one whole.An object is monstrous where by its size it defeats the end that forms its concept.
The colossal is the mere presentation of a concept which is almost too great for presentation, i.e., borders on the relatively monstrous; for the end to be attained by the presentation of a concept is made harder to realize 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 end belonging to the object as its determining ground, if it is to be aesthetic and not to be tainted with any judgement of understanding or reason.
