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The Limits of Understanding

The main result of the Analytic is that the understanding, through its pure concepts, provides rules which apply to all objects of experience because they make experience possible. At the beginning of the Analytic, Kant had noted that agreement with the a priori principles of the understanding can serve as a negative criterion of truth, in the sense that what does not agree with the principles is false. Here he states that "they are even the source of all truth, i.e., the source of our cognition's agreement with objects" (A237/B296).

But the principles of the understanding are valid only for the objects of experience. So Kant asks whether we have to settle for truth in the limited realm of experience, at the expense of frustrating our desire to know of things beyond that realm. If not, then what is the point of the laborious inquiry into the a priori? The principles that are justified are principles that would be assumed to hold in empirical investigation anyway.

There is, however, a vital negative use of the investigation. The understanding is not capable of judging its own limits, "knowing what may lie inside or outside its entire sphere" (A238/B297). Only the "deep inquiries that we have performed" will do that job. Because of the failure of the understanding to recognize its bounds, those inquiries can save it from the inevitable embarrassment it faces when it leaps beyond its bounds in experience and uses its principles "transcendentally."

The reason for this limitation lies in the fact that pure concepts of the understanding have no reference to objects except through intuition. They must refer to objects through empirical intuition, since even if they are made more specific by their relation to pure intuition (space and time), they would still not refer to objects except insofar as pure intuition is related to empirical intuition. "Without this reference they have no objective validity whatever, but are mere play, whether by the imagination or by the understanding, with their respective presentations" (A239/B298). Unless a concept is "made sensible" it is "without sense, i.e., without signification" (A240/B299).

For example, the concept of magnitude gets its sense from the concept of number, which in turn requires empirical intuition to be presented, since "how-many-times" can be only understood through succession. In general, the categories cannot be defined except through reference to possible intuition. All we can do is indicate the logical role it plays in judgment. So the concept of a substance is the concept of a thing which can exist only as subject. From this one does "not know any conditions at all under which some thing will possess this logical superiority" (A243/B301). Thus a definition of a concept for Kant must give the conditions under which it is applicable.

Kant goes through the list of categories to show their particular limitations. Perhaps the most important limitation lies with the category of causality. The pure concept is that of "something from which the existence of something can be inferred" (A243/B301). Without reference to time and succession in time, the concept is totally useless: "the concept would have no determination whatever as to how it fits any object" (A243/B301). This is the source of the problem noted in the last lecture with the assertion that some transcendental object is the basis for appearances.

The conclusion is that the positive results of the Analytic apply only to objects of experience and therefore (since such objects are connected appearances) only to appearances. Since appearances are relative to the forms of human sensibility, the results hold only within the limits of sensibility. This is why "the proud name of an ontology that pretends to provide, in a systematic doctrine, synthetic a priori cognitions (e.g., the principle of causality) for thing in themselves must give way to the modest name of a mere analytic of the understanding" (A246/B303).

Transcendental Use

Kant describes his negative result in terms of the legitimate use of the categories. This use is empirical, not transcendental. The empirical use of the categories is their application to appearances. A transcendental use would be to an object from which abstraction is made of the relation to sensibility. But if this abstraction is made, the conditions for applying the category to an object (the schemata) would be missing, and no application can be made, "for nothing is then given that can be subsumed under the concept" (A247/B304).

Although categories cannot be said to have transcendental use, they still have "merely transcendental signification" (A248/B305). This signification is that of providing "the unity of thought of a manifold as such" (BA247/B304). That is, it is the unity provided by the act of judging. They are "forms of thought" analogous to the forms of intuition (B305). But the use of the act of judging requires that reference already be made to objects, and no reference can be made to objects thought in abstraction from the conditions of sensibility.

It may be thought that because the categories have their origins in the understanding, they have wider application than to the objects of sensibility. But this is a delusion, as has been shown. If we try to widen the scope of their application by abstracting from the a priori contributions of sensibility, we instead just empty them of content. They are in this respect unlike space and time, which still are given as objects in sensibility. Because we lack intellectual intuition, nothing is given through categories. Their only function is to unify what is already intuited.

Noumena

Kant now introduces the terms "phenomena" and "noumena." We will here follow the presentation of these notions as given in the second edition. The distinction made in the Aesthetic between appearances and things in themselves yields the notion of "beings of sense," phenomena. An appearance is a thing considered with respect to the way in which it is intuited. If we classify an appearance as a special kind of object, then we consider it as a phenomenon.

When we abstract from the way in which objects are intuited, their remains the notion of the "character that they have in themselves" (B306). Since appearances are thought of as special kinds of objects, there is a temptation to think that there is a contrasting kind of object, a being of the understanding or noumenon. Such an object would either have the character that objects of the senses have in themselves, or even not be an object of the senses at all.

Now if we can frame a notion of "an object in itself" (B306) in this way, we are tempted to think that we can frame concepts of an object in itself. These could only be the categories, since the categories are the only concepts provided by the pure understanding. But if the categories apply to the noumenon, then they determine it. And this is a mistake, because the notion of noumenon is completely indeterminate. It is a negative notion, formed by abstraction from the only thing that would allow us to determine it.

A positive notion a noumenon would be that of a determinate object, and such an object would have to be given in an intellectual intuition to the understanding itself. Since intellectual intuition "lies absolutely outside our cognitive power," Kant concludes that there is no basis for applying categories to noumena. "Hence what is called noumenon by us must be meant as such only in the negative signification" (A253/B309). We can still think of "objects as such" by abstraction from intuition, but this is not to think of "beings of the understanding."

We have to say that noumena are possible in order to articulate the fact that sensibility does not extend to things in themselves. But the sphere of such noumena is empty for the human understanding. It is possible that an understanding could intuit such beings and thereby make them subject to its pure concepts, in that there is no contradiction in supposing this. So there is no contradiction in the concept of a (positive) noumenon.

Yet it is a "problematic" concept because "its objective reality cannot be cognized in any way" (A254/B310). We cannot assertorically say anything substantive about noumena, though, "We have an understanding that problematically extends further than [the] sphere [of appearances]" (A255/B310). The problem is how it is possible for the understanding to intuit an object rather than merely to bring it under concepts, even though we must acknowledge that it is possible.

An Intelligible World

According to Kant, some philosophers of recent vintage (presumably Leibniz and Wolff) had proposed a division between a "sensible" and "intellectual" world, corresponding to a distinction we might now make between observation and theory. Kant objected on grammatical grounds that "intellectual" is applied properly only to cognitions, so the correct contrast would be with an "intelligible" world.

While there is nothing wrong with making this kind of distinction, it does no good. It evades the issue of whether there is an "intellectual" world of noumena. All the use of the understanding in the intellectual world of science is merely empirical, and the issue concerns whether the understanding has a transcendental use.

Kant had himself made a distinction between a sensible and intelligible world in the Inaugural Dissertation. There, he had claimed that we have a symbolic knowledge of the intelligible world, understood in what in the Critique he would call the transcendental sense. The abandonment of this claim is one of the most important differences between the pre-Critical and Critical periods.

Kant concludes this chapter by challenging any partisan of positive noumena to produce any synthetic principles which apply to them. He claims that this cannot be done, because what unites the concepts in a synthetic judgment is some aspect or condition of experience. "That reader will never be able to to prove his proposition; indeed, what is still more, he will never be able ot offer justification for the possibility of such a pure assertion without taking into account the empirical use of understanding and thereby forgoing entirely the pure and sense-free judgment" (BA259/B315). This seems to have been the challenge Kant applied to his own pre-critical doctrine. The notion of a noumenon is then compared with that of an empty space which serves as a limit to a space that is filled.

For the most part, Chapter III of the Analytic of Principles summarizes positions set out in the earlier chapter. The key point is that the categories cannot be used to refer to objects other than those of experience. This means that they cannot determine things in themselves. So things considered in themselves cannot be taken as beings of the understanding to which our pure categories apply.

This raises an interpretive issue. It would seem that we cannot give the notion of a thing in itself any positive content at all. Space, time, and all properties depending on them have been abstracted away to arrive at the notion. The categories cannot be used to determine them. We are left with the notion an indeterminate transcendental object, and yet Kant seems to have wanted to make this notion do some work for him, as signifying the thing that stands in relation to sensibility. In the present chapter, he says that they have a character of their own.

But how is Kant entitled to say even this, given that none of the categories can be used to determine things in themselves? What concepts is he using when he writes of the "character" of these things? Perhaps "character" is a purely logical concept. If so, then by the argument of this chapter, it makes no reference to objects without some connection to the way the object is intuited. But this is precisely what we strip away in arriving at the notion of things in themselves.