It should be noted how Kant’s proposal for connecting the
sensible and the conceptual, though superficially straightforward, is at another level extremely
perplexing. Is a transcendental schema a thought about time, or is it time as thought in a certain
way? Our ways of referring to transcendental schemata inevitably assimilate them, it would
seem, to one side or the other of the concept/intuition divide. Moreover, it appears necessary to
do exactly this, if we are to answer the question of what they are, or say anything contentful
about them. The cost of the assimilation, however, in either direction, is to make them
apparently unfit for their designated mediating role: if they are either concepts with a special
relation to intuition, or intuitions as formed conceptually, then they seem to presuppose the very
possibility of connecting the sensible and the conceptual which transcendental schematism is
invoked to explain.

Kant may declare that transcendental schemata are irreducibly sensible-and-intellectual, and
that this is how the question of their identity should be answered. If so, Kant’s original division of
our representations into intuitions and concepts is not exhaustive, for there is a third class,
about which we can say very little, other than that it is dependent on and somehow derivative
from the others. We can specify it in terms of the transcendental role to which the problem of
relating concepts and intuitions gives rise, but the manner of its derivation, and the nature of
schemata, we cannot specify. Note, it is not just that we can say relatively less about schemata
than we can about intuitions and concepts, and that we cannot identify their ultimate source; we
are equally ignorant of the grounds of our faculties of sensibility and understanding.
Transcendental schemata remain in a special sense hard to grasp, because they are required to
combine in themselves two kinds of property, or representational functions, the seeming
immiscibility of which is precisely what made us introduce them in the first place. That this is
nevertheless Kant’s own view of the matter is, plausibly, what is suggested by his statement that
schematism is ‘an art concealed in the depths of the human soul, whose real modes of activity
nature is hardly likely ever to allow us to discover’ (A141/B180-1).

Sebastian Gardner

I’ve been accused of obsession with the schematism, but the intuition-concept gap is for me the core problem that Kant runs into, and I have never been able to find an adequate solution in Kant for it. Here’s Paul Guyer’s unsatisfactory explanation:

Thus, in the case of
the categories our concepts are not “homogeneous” with our objects, and
some intermediary has to be found in order to make them so.
But this is
not the case with our other concepts, which are inherently homo-
geneous with their objects. A pure mathematical concept like circle is
homogeneous with our experience, because it describes its object in terms
of properties that can be directly presented in experience – that something
is a curved, closed line every point of which is equidistant from its center
is the kind of thing we can observe because the pure form of all our outer
intuition is spatial. And an empirical concept like plate or dog is already
homogeneous with its object because it includes predicates that correspond immediately to observable properties of objects, whether those
properties are pure, like the circularity of a plate, or empirical, like its non-
porousness or like the furriness or noisiness of a typical dog.

If you’re willing to accept that Platonic concepts like “plate” and “dog” have exact referents in the real world, then fine. But Kant doesn’t (since he thinks the application of all concepts is normative and prescriptive and subjective) and his whole project is to figure out a way to salvage conceptual mental content out of a non-conceptual world.

Anyway, I mention this because I was just thinking about how much of modern philosophy grows out of exactly this particular problem. Kant wasn’t the first to come up with it, but I think it’s his formulation of it and failed solution to it that echoes in Russell (who tries to pull the same trick solution), Heidegger (who tries to punt the problem away), and many others.

And ultimately there’s something a little pleasing in Kant’s ceding of this problem to “art,” which is a rare concession on his part.