Kant on Imagination and Basic Measure

In the analysis of the mathemtical sublime, Kant gives a peculiar argument that the judgment of the mathematical sublime involves the faculty of reason, because the faculty of imagination is inadequate for giving a basic measure for an indefinite magnitude (5:254-256). I fail to see how this argument work. While I do not dispute that the judgment of the mathematical sublime involves the inadequacy of the imagination to unify an indefinite magnitude under one singular form (hence its appeal to the faculty of reason), I believe that this has nothing to do with the basic measure argument, and that the basic measure argument fails to cohere.

Motivating my skepticism is Kant’s granting that imagination is adequate for mathematical estimation of magnitude: “the imagination is adequate for the mathematical estimation of every object, that is, for giving an adequate measure for it, because the numerical concepts of the understanding, by means of progression, can make any measure adequate for any given magnitude. (5: 254)” Throughout the analysis of the mathematical sublime, it appears consistant that the mathematical measurement of a magnitude involves three components. 1), the pure numerical concepts provided a priori by the Understanding. 2), the empirical concepts of unit: cm, mile, foot, inch, etc. These unit-concepts are obviously empirical concepts given their conventional nature: they are only defined by human beings a posteriori. With these, and 3), the imagination’s capacity of comprehension gives a unity of an intuitive manifold in accordance with the empirical concepts, which functions as the basic measure. The enumeration of basic measures, i.e. the subsumption of basic measures under the pure numerical concepts, eventually yields the mathematical measure of a magnitude. .

For example, when mathematically measuring an indefinitely long road, we must have at our disposal both the pure numerical concepts (1, 2, 3…) and the empirical concepts of unit (mile); in accordance with these concepts at our disposal, our imagination comprehends a manifold and subsumes it under the empirical concept of unit (1 mile of road), which our Understanding then subsumes under various numerical concepts and thereby enumerates (so we have 1 mile of road, 2 miles road … .)

What this suggests is that the comprehending ability of imagination, on its own, is supposed to be able to isolate parts of an indefinite magnitude and combine these parts under a unity, even though this unity 1) does not have to conform to the empirical concepts of unit and 2) does not have to be subsumed under pure numerical concepts. In the above example, the comprehension should be able to unify manifold into a single piece of the road, which does not have to be exactly 1 mile or the multiplication of 1 mile. And if we only preclude the participation of pure concepts and allow the participation of empirical concepts, it follows that imagination, if we have at our disposal the empirical concepts of unit, can still unify an intuitive manifold in accordance with empirical concepts, 1 mile of road for example, without enumerating multiple such unities with numerical concepts. But such a unity is already a basic measure, even though it is not further enumerated and multiplied.

It is of course possible that in the context, Kant is blocking the participation of the empirical concepts as well. Since a basic measure is by definition subsumed under empirical concepts of unit, forbidding the participation of empirical concepts entails the failure of imagination to give a unity as basic measure. So, even if imagination can isolate parts of the indefinite magnitude and bring it under a unity (a single piece of an indefinitely long road), it will not be a basic measure. So, when Kant in the text speaks of the imagination’s constant search for basic measure, he does not mean the search for the unity that can be potentially subsumed under an empirical concept of unity, but the search for an empirical concept of unit under which the unity can be subsumed.

But a case can be made that imagination as a faculty in its own has the potential to generate empirical concepts; for elsewhere, Kant has said that imagination, in its ability to compare and abstract, is the source of all empirical concepts (whereas understanding simply supplies the pure concepts a priori). So, all particular unities brought out by imagination are potentially basic measures, if the same faculty of imagination that brings the unites out has not yet generated the empirical concepts of unit. Accordingly, all arbitrarily unities brought out by imagination and not accorded to any empirical concept of unit at our disposal can potentially count as a basic measure, pending on imagination’s ability to produce a fitting concept. In other words, imagination can arbitrarily unify a piece of road of some a specific length; even if we do not have an explicit empirical concept of unit to subsume this specific length, once imagination’s ability to compare and abstract gives one, we can comfortably use it as a unit for enumeration. Thus, when we are in front of a sublime object which is indefinitely big/great, only with our imaginative comprehension without any other higher faculties, we can 1) isolate parts of this object into a unity, which is a potential basic measure; and 2) generates an empirical concept of unity by comparison and abstraction, which makes the potential basic measure an actual one. In this vein, it is unclear why Kant insists that imagination cannot find any basic measure.

All of these, of course, does not contradict the basic claim about the judgment of the mathematical sublime and that such judgment is formless, as long as we abandon Kant’s particular argument in terms of basic measure. The unity that imagination fails to produce is that of the sublime object as a whole, not the unity as either potential or actual basic measure.

A Conceptualist Solution?

There might be a solution to this problematic argument under the conceptualist reading, according to which the particular intuitions/unity of intuition undertaken by the non-conceptual faculty must involve particular concepts given by conceptual faculties. So, imagination cannot give a unity of basic measure at all, without presuming the pure numerical concepts by Understanding under which the former unity is subsumed. Since the unity of basic measure is teleological service of the numerical concepts, without the latter, the former is not possible.

There are two challenges to this solution. The first is specific to the judgment of the beautiful. There, the subjective purposiveness is attributed to the form of the object, without any concept of the end. A particular unity is possible, even without presuming a particular concept. This clearly contradicts the conceptualist reading.

The second challenge is at the strategic level. Kant in the 3rd Critique grounds purposiveness and the validity of aesthetic and teleological judgments not in intrinsic relatedness of particular concepts/intuitions, but in the intrinsic harmony of capacities themselves. Hence, even if we accept a possible reading that the non-conceptual faculties must in themselves involve conceptual, higher faculties, and vice versa, it does not entail that particular intuitions/unities in themselves involve particular concepts. A conceptualist reading described above runs contrary to Kant’s general strategy and aim in this work.