Since whatever is to be a source of pleasure, apart from interest, to the merely reflective judgement must involve in its representation subjective, and, as such, universally valid finality-though here, however, no finality of the form of the object underlies our estimate of it (as it does in the case of the beautiful)-the question arises: What is the subjective finality, and what enables it to be prescribed as a norm so as to yield a ground for universally valid delight in the mere estimation of magnitude, and that, too, in a case where it is pushed to the point at which faculty of imagination breaks down in presenting the concept of a magnitude, and proves unequal to its task?
In the successive aggregation of units requisite for the representation of magnitudes, the imagination of itself advances ad infinitum without let or hindrance-understanding, however, conducting it by means of concepts of number for which the former must supply the schema.This procedure belongs to the logical estimation of magnitude, and, as such, is doubtless something objectively final according to the concept of an end (as all measurement is), but it is hot anything which for the aesthetic judgement is final or pleasing.Further, in this intentional finality there is nothing compelling us to tax the utmost powers of the imagination, and drive it as far as ever it can reach in its presentations, so as to enlarge the size of the measure, and thus make the single intuition holding the many in one (the comprehension) as great as possible.For, in the estimation of magnitude by the understanding (arithmetic), we get just as far, whether the comprehension of the units is pushed to the number 10 (as in the decimal scale) or only to 4 (as in the quaternary); the further production of magnitude being carried out by the successive aggregation of units, or, if the quantum is given in intuition, by apprehension, merely progressively (not comprehensively), according to an adopted principle of progression.In this mathematical estimation of magnitude, understanding is as well served and as satisfied whether imagination selects for the unit a magnitude which one can take in at a glance, e.g., a foot, or a perch, or else a German mile, or even the earth's diameter, the apprehension of which is indeed possible, but not its comprehension in, sit intuition of the imagination (i.e., it is not possible by means of a comprehension aesthetica, thought quite so by means of a comprehension logica in a numerical concept).In each case the logical estimation of magnitude advances ad infinitum with nothing to stop it.
The mind, however, hearkens now to the voice of reason, which for all given magnitudes-even for those which can never be completely apprehended, though (in sensuous representation) estimated as completely given-requires totality, and consequently comprehension in one intuition, and which calls for a presentation answering to all the above members of a progressively increasing numerical series, and does not exempt even the infinite (space and time past)from this requirement, but rather renders it inevitable for us to regard this infinite (in the judgement of common reason) as completely given (i.e., given in its totality).
But the infinite is absolutely (not merely comparatively) great.
In comparison with this all else (in the way of magnitudes of the same order) is small.But the point of capital importance is that the mere ability even to think it as a whole indicates a faculty of mind transcending every standard of sense.For the latter would entail a comprehension yielding as unit a standard bearing to the infinite ratio expressible in numbers, which is impossible.Still the mere ability even to think the given infinite without contradiction, is something that requires the presence in the human mind of a faculty that is itself supersensible.For it is only through this faculty and its idea of a noumenon, which latter, while not itself admitting of any intuition, is yet introduced as substrate underlying the intuition of the world as mere phenomenon, that the infinite of the world of sense, in the pure intellectual estimation of magnitude, is completely comprehended under a concept, although in the mathematical estimation by means of numerical concepts it can never be completely thought.Even a faculty enabling the infinite of supersensible intuition to be regarded as given (in its intelligible substrate), transcends every standard of sensibility and is great beyond all comparison even with the faculty of mathematical estimation: not, of course, from a theoretical point of view that looks to the interests of our faculty of knowledge, but as a broadening of the mind that from another (the practical) point of view feels itself empowered to pass beyond the narrow confines of sensibility.
