As we move on to the Second Analogy, we enter a different section of the Critique, so this is perhaps a good place to say a few things about the overlapping and somewhat incompatible principles on which the book is organized. Kant wasn't kidding when he said that he thought he had handled every major question in philosophy. There is so much going on in the Critique that some system of organization is needed, and Kant being Kant, he gave us about four.
First of all, Kant distinguishes between the elements of knowledge and the method of employing those elements. So the book is divided into the Transcendental Doctrine of Elements ["transcendental," remember, meaning roughly "epistemological"] and the Transcendental Doctrine of Method. But the Doctrine of Method is just an afterthought, and though there are some interesting things in it, such as Kant's remarks about mathematics, we can safely ignore it. Since Kant has deliberately charted a middle course between the Rationalists, who say that all knowledge rests on reason alone, and the Empiricists, who trace all knowledge back to perception, he says that there are two "elements" of knowledge: Sensibility and Understanding. So the Doctrine of Elements has two parts: The Transcendental Aesthetic and the Transcendental Logic. The Aesthetic deals with sensibility, the Logic with the intellect. Strictly speaking, of course, one needs the cooperation of the two elements to have knowledge. Hence, one ought not to be able to arrive at any definitive conclusions about any body of knowledge solely on the basis of the arguments in the Aesthetic,. But Kant, ever busy with pigeon-holing, decides that the Aesthetic grounds mathematics and the Logic grounds science. He knows better, of course, and half-heartedly tries to make amends in the part of the Logic known as the Anticipations of Perception, but by the time he came to write the Critique, his attention was focused on Hume's challenge to physics, and since he was pretty happy with what he had said about mathematics in the Dissertation, he just it carried over into the Aesthetic almost unaltered and let it go at that. Not surprisingly, the Aesthetic is tiny compared to the Logic -- in the Kemp-Smith translation, 27 pages versus 471. All the good stuff is in the Transcendental Logic.
How to organize that? Well, Kant had two separate incompatible ideas, and he used both of them. First of all, he wanted to distinguish between what we can genuinely know to be true, and what previous philosophers have mistakenly and confusedly thought they could know. So he divides the Transcendental Logic into a Logic of Truth, which he calls the Transcendental Analytic, and a Logic of Illusion, which he calls the Transcendental Dialectic. Note that the Dialectic is a logic of illusion, not simply of error, like the fallacies of traditional logical theory. The beliefs Kant is attacking -- that we can have knowledge of the existence and nature of God, that we can have knowledge of the existence and nature of the self in itself, that we can have knowledge of the Infinite -- are illusions, he thinks, which is to say beliefs that we find it terribly difficult to give up even after we see that they are groundless. It is in the Dialectic that he is going to trot out the notion of antinomies he had already broached in the Dissertation.
Entirely separate from all this is the standard, old-fashioned organization of logic textbooks, which Kant decides he can use for his classificatory purposes. The customary understanding of the subject in Kant's day [and remember that during his many years as a privatdozent, he lectured regularly on Logic at Kőnigsberg] was that the fundamental elements of logic are concepts, judgments, and inferences. Concepts are class notions, formed by uniting several "notes" or characteristics in a single thought. So we unite the characteristics of "being a man" and "being unmarried" to form the concept "bachelor." Judgments, or propositions, are formed out of concepts by uniting them by means of the copula, "is." So we form the judgment, "A bachelor is unmarried," or "A bachelor is unhappy." [Never mind truth at this point.] Finally, we form inferences by putting together propositions into syllogisms.
Kant liked that way of arranging things, even though, as should now be clear [I will explain why in a moment], his arguments in the Deduction completely undermine this principle of organization. So he divided the Transcendental Logic into: The Analytic of Concepts, The Analytic of Principles [or judgments], and The Dialectical Inferences of Pure Reason. Except that he needed someplace to talk about the notion of the Unconditioned, which is the root of all the trouble in traditional metaphysics, so he sticks in an extra chapter in the Dialectic called "The Concepts of Pure Reason."
Organizationally speaking, this whole thing is a godawful mess. But you can see what Kant was getting at. My old professor, Clarence Irving Lewis, in his great course on the Critique, actually used as a question on the final exam [which was most definitely not open book!] "Reproduce as much as you can of the Table of Contents of the Critique of Pure Reason." It turns out that the better you understand the book, the finer the detail in which you can conjure up the Table of Contents. There are not many books of philosophy that you could examine in that way!
The central, underlying problem, once we get past the three or four overlapping principles of organization, is this: Both the principle of organization of the Transcendental Logic and Kant's resolution of the conflict between Free Will and Determinism depend on the claim that we can form concepts prior to attempting to unite them into judgments. The idea is that we can then legitimately use the concepts to form judgments about things that lie beyond the limits of experience -- judgments that are, as Kant would say, problematic, or as we might say hypothetical. So, on this view, we can form the empty concept of an unconditioned being, or of a free will, or of a thing in itself. With such concepts, or Ideas as Kant calls them, we can form judgments that conform to the canons of logic -- judgments that are not self-contradictory. But since the component Ideas are empty, inasmuch as no sense experience is adequate to them, we can never ascertain whether the judgments we form with them are true or false. Any claim otherwise is an illusion.
However, in the depths of the Deduction [in A], as Kant is wrestling with the explication of the notion of synthesis, he concludes that concepts are actually rules. As he tells us, "a concept is always, as regards its form, something universal which serves as a rule." Thus, a concept has a propositional form. So concepts are not the basic building blocks of thought; propositions are. What is even worse, for his future architectonic plans, concepts are rules for doing something with a manifold of sensibility, which means that we cannot even hypothetically form judgments about things that could never appear in intuition [which is to say, about things as they are in themselves.] It is at least possible that there might be creatures whose forms of sensible intuition are different from mine, and hence who would, using the same rules, organize a different realm of appearances. But those rules, the Categories, could never, even hypothetically, apply to things in themselves, which are not manifolds of sensibility.
I am going to return to all of these problems, and some others besides, when I come to talk briefly about Kant's ethical theory [if I ever get out of the First Critique!]. Now it is time to see how Kant completes the argument of the Analytic, using the deeper understanding of synthesis as a rule-governed reproduction in imagination that he has arrived at in the Subjective Deduction.