The concluding chapter of the Analytic of Principles, “On the Basis of the Distinction of All Objects As Such into Phenomena and Noumena,” examines the ancient distinction between phenomena, beings of sense, and noumena, beings of the understanding or reason. In the Aesthetic, Kant had made a distinction from the standpoint of sensible intuition between appearances and things in themselves: things considered in relation to the forms of human sensibility and things considered in abstraction from that relation, respectively. In the Analytic, that distinction is treated from the standpoint of concepts and is related to the distinction between phenomena and noumena.
Although not formally divided, the chapter consists of two distinct parts. The first part, from A235/B295 to A248/B305, concerns the limits of the use of the pure concepts of the understanding or categories. The second part is concerned with phenomena and noumena. There are two passages from the first (A) edition of the Critique that are omitted from the first part. Both have to do with the question of whether the categories can be defined, and they will not be treated here. In the second part, a long passage from the first edition is replaced by four paragraphs in the second (B) edition.
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. “Whatever contradicts these rules is false, because the understanding is then in conflict with its own universal laws of thought, and hence with itself” (A59/B84).
In the present chapter, Kant states that the principles of the understanding “are even the source of all truth, i.e., the source of our cognition’s agreement with objects” (A237/B296). But these principles 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.” One uses a concept in a principle trancendentally when “it is referred to things as such and in themselves” (A238/B298). It is used empirically when “it is referred merely to appearances, i.e., to objects of a possible experience” (A238-9/B298).
The reason for the limitation of the use of the categories to objects of a possible experience lies in the fact that pure concepts of the human understanding have no reference to objects except through empirical intuition, which in humans is sensible. 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 [Sinn], i.e., without signification [Bedeutung]” (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 the categories can do is is to play a logical role in judgment. For example, the concept of a substance is the concept of a thing which can occur 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 pure concepts of the understanding and their associated principles have an application 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 things in themselves must give way to the modest name of a mere analytic of the understanding” (A246/B303).
Kant describes his negative result in terms of the legitimate use of the categories. This use is empirical, not transcendental. As noted above, the empirical use of the categories is their application to appearances. A transcendental use would be application to an object from which abstraction is made from the relation of the object 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 [Bedeutung]” (A248/B305). This signification is that of providing “the unity of thought of a manifold as such” (A247/B304). That is, it is the unity provided by the act of judging. The categories 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 range of application than merely 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 a manifold that is given in sensible intuition.
At this point, Kant turns his discussion away from the categories and introduces the terms “phenomena” and “noumena.” We will here follow the presentation of these notions as given in the second edition. Before so doing, we will first note how Kant used these terms in his 1770 Inaugural Dissertation, On the Form and Principles of the Sensible and Intelligible World.
Sensibility is the receptivity of a subject in virtue of which it is possible for the subject’s own representative state to be affected in a definite way by the presence of some object. Intelligence (rationality) is the faculty of a subject in virtue of which it has the power to represent things which cannot by their own quality come before the senses of that subject. The object of sensibility is the sensible; that which contains nothing but what is to be cognized through the intelligence is intelligible. In the schools of the ancients, the former was called a phenomenon and the latter a noumenon. Cognition, in so far as it is subject to the laws of sensibility is sensitive, and, in so far as it is subject to the laws of intelligence, it is intellectual or rational. (§3, Ak 2:392).Kant goes on to claim that there is a form of the intelligible world, an objective principle, which is “some cause in virtue of which there is a combining together of the things which exist in themselves” (§13, Ak 2:398). This cause is a unitary being on which all substances depend, a creator and architect of the world. Thus, Kant makes what he would later call a “transcendental” use of the pure concept of cause (or that from which something is derived) in principles like the following: “The substances which constitute the world are beings which derive from another being, though not from a number of different beings; they all derive from the same being” (§20, Ak 2:408).
In the Critique, Kant took a different approach. The distinction made in the Aesthetic between appearances and things in themselves is now said to yield 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, there 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 special kind of object, a being of the understanding or noumenon. Such an object either would have the character of objects of the senses, considered in themselves, or might 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 apply concepts to such an object in itself. The concepts that might apply to an object in itself 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 (since to determine an object just is to apply a concept to it). And to determine the noumenon by categories 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—sensible intuition.
Thus, there are two problems with applying the categories to a supposed noumenon: the categories themselves are only rules for judging objects given in intuition, and the alleged noumenon is nothing more than an abstraction from all the forms space and time that could make application of the categories possible.
The heart of the problems lies in the fact that there are two distinct ways of thinking about noumena. A positive notion of a noumenon would be that of a determinate object, and such an object would have to be given to the understanding itself in an intuition that is not sensible, but intellectual. Since intellectual intuition “lies absolutely outside our cognitive power” (A253/B308), Kant concludes that there is no basis for applying categories to noumena. On the other hand, the notion as such of a noumenon is not illegitimate: only the positive notion is. “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.”
One way of thinking about the distinction between negative and positive noumena is to distinguish between the possible extension of the categories and the sphere of objects which they determine. Kant states that the categories extend farther than sensible intuitions, because “they think objects as such without yet taking account of the special way (viz., sensibility) in which they may be given” (A254/B309). It is possible that they apply to objects that might be given in another way than in space and time. On the other hand, there is no evidence that such objects are actual, since we have no other kind of intuition besides the specific sensible intuition we have.
Thus, the categories “do not thereby determine a larger sphere of objects” (A254/B309). We might say that the categories have a potentially larger sphere of objects, and hence extend further than to sensible objects, but we cannot tell whether they have an actually larger sphere. The concept of an object occupying a sphere beyond that of the sensible is “problematic” because “its objective reality cannot be cognized in any way” (A254/B310). Our concepts extend farther than sensible objects, but they do so only problematically: “We have an understanding that problematically extends further than [the] sphere [of appearances]” (A255/B310). In the Metaphysical Deduction, Kant had stated that “Problematic judgments are those where the affirmation or negation is taken as merely possible (optional)” (A74/B100).
In the excised passage from the A edition of the Critique, Kant restricted the use of ‘noumenon’ to what in the B edition he called the “positive” sense of the term. “If I assume things that are objects merely of the understanding and that, as such, can nonetheless be given to an intuition—even if not a sensible intuition . . . —then such things would be called noumena (intelligibila)” (A249). He explained that the concept of a noumenon arises from the fact that we must refer appearances to an object that appears, by abstracting from the forms of sensible intuition. This something is the “substratum of sensibility” or “transcendental object,” “the wholly indeterminate concept of something as such” (A253). But the transcendental object must not itself be called a noumenon. (The notion of the transcendental object appears first in the A Deduction at A109, and it plays a diminished role in the second edition.)
In the Prolegomena, which was written between the first and second editions of the Critique, Kant uses ‘noumena’ in the positive sense, and he often uses it interchangeably with ‘things in themselves,’ e.g. in §30, Ak 4:312, and §45, Ak 4:332. He gives as examples of “beings of understanding” an immaterial being, a world of the understanding, and a supreme being, “all mere noumena” (§57, Ak 4:354).
According to Kant, some philosophers of recent vintage had proposed a division between a “sensible” and “intellectual” world, corresponding to a distinction we might now make between the worlds
of 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 here concerns whether the understanding has a transcendental use. As we have seen, Kant had himself made a distinction between a sensible and intelligible world in the Inaugural Dissertation. 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 prove his proposition; indeed, what is still more, he will never be able to 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 [sinnenfreien] judgment” (A259/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 preceding chapter, which laid out the principles themselves. 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 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 such an object has a character in itself (B306).
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.
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