The second part of the Prolegomena concerns itself with the question, "how is pure natural science possible?" "Natural science" is what nowadays we would simply call "science": it is the systematic body of knowledge that deals with nature. Kant remarks first of all that when we talk about nature we are not talking about things in themselves, which, as he has already claimed, we can know nothing about. Rather, we are talking about the objects of experience as they appear to us. For our study of nature to be a science, these experiences must conform to universal and necessary laws. Kant observes that we do indeed study natural science and make use of universal and necessary laws. There is some kind of pattern or regularity in our experience, but how is this possible?
Kant draws a distinction between judgments of perception and judgments of experience. Judgments of perception bring together several empirical intuitions and are only subjectively valid. For instance, I may see the sun shining brightly and feel that a rock under the sun's rays is warm, and judge that the rock grows warm under the sun. This judgment draws together the intuitions that the sun is shining and the rock is warm, but it is still valid only for me and only at that particular time.
Judgments of experience apply pure concepts of the understanding to judgments of perception, turning them into objective, universally valid laws. For instance, I can apply the concept of cause to my earlier judgment that the rock grows warm under the sun and judge that the sun caused the rock to grow warm. We do not find pure concepts of the understanding in experience. Rather, they are concepts we use to structure our understanding of experience. They are a priori concepts we use to draw together and make sense of our various judgments of perception. Because these concepts are a priori, they are also universal and necessary. Thus, judgments of experience are the synthetic a priori laws that make natural science possible.
Essentially, the distinction is that judgments of perception deal only with what we sense, or intuit, while judgments of experience deal with what we infer from our perceptions. We cannot dispute judgments of perception because they are wholly subjective: you cannot tell me the car didn't seem red to me. We can dispute judgments of experience because they are meant to be objective: you can tell me the car wasn't red.
Section twenty-one categorizes the different kinds of judgments, concepts of the understanding, and universal principles of natural science into three separate tables. These tables are reproduced in a special section in this SparkNote entitled "Kant's Tables of Categories."
The table of judgments divides judgments into their logical parts. Every judgment must have one of the three kinds of quantity, quality, relation, and modality. For instance, the judgment "the sky is blue" is singular (it deals with the sky), affirmative (it affirms that the sky is blue), categorical (it is a simple subject-predicate sentence), and assertoric (it makes an assertion).
The table of the concepts of the understanding lists the concepts that correspond to the logical parts of judgments. By applying a concept to the corresponding judgment, we can turn a judgment of perception into a judgment of experience. For instance, the concept that corresponds to an assertoric judgment is "existence," so we can make the objective judgment that a blue sky exists.
The table of universal principles classifies four different kinds of law that correspond to the four different kinds of concepts of the understanding.
Kant is complicated, but there is a very clear structure hiding underneath all this difficult vocabulary. Essentially, Kant is building a complex system to explain how we make sense of the world.
At a very basic level, Kant distinguishes between things in themselves, and our perceiving mind. The first question is how can we perceive things in themselves? How does our mind make contact with anything outside it? Kant answers that we cannot perceive things in themselves directly; all we can perceive are sensations, the impression things in themselves make upon our senses.
Our mind perceives sensations, but must impose some sort of form on these sensations for them to be intelligible. This form is our intuition of space and time. By subjecting the sensations we perceive to the intuitions of space and time, we get empirical intuitions. Empirical intuitions are what we might refer to as "sense-data": they are what I see, hear, or feel at any given moment.
If all I had were empirical intuitions, life would be a meaningless blur of unintelligible sensations. In order to make sense of experience, we must first draw connections between empirical intuitions. Judgments of perception join two or more intuitions, associating them with one another. Seeing the bright, shining sun and feeling the warm rock are two separate empirical intuitions: a judgment of perception makes a connection between the two.
Judgments of perception are subjective. I can draw a connection between the sun and the warm rock, but I can't relate that connection to any of my past or future experience, and I can't relate it to anyone else's experience. Empirical intuitions and judgments of perception come from our faculty of sensibility, which deals with our senses and what they tell us. To give objectivity or universality to our experience, we must subject it to our faculty of understanding, which deals with our capacity for thought and concept formation.
Kant infers that we must use concepts of pure understanding to turn judgments of perception into judgments of experience because empirical intuitions in themselves cannot be generalized. Judgments of perception are particular and subjective: only a priori concepts can be universal and objective. As Hume was right to observe, we cannot find universal concepts like "every event is caused" in experience. Kant concludes that such concepts are a part of the understanding: we do not find them in experience; we apply them to experience.
Kant has a two-step schema that explains how we come to see the world. In the first step, which deals with our faculty of sensibility, we have things in themselves providing sensations that are then given subjective form by our pure intuitions of space and time. Sensations combined with pure intuitions make empirical intuitions. In the second step, which deals with our faculty of understanding, these empirical intuitions are given objective form by the pure concepts of the understanding. Empirical intuitions combined with pure concepts of the understanding make the appearances that constitute experience.
We should not mistake Kant's system for elaborate psychology. He is not giving a map of the human mind, or explaining how it is that we come to cognize things. Rather, he is examining what we find in experience, and analyzing its parts. His procedure is logical rather than psychological. He recognizes, for instance, that we have a concept of cause and effect, but that that concept cannot possibly be derived from experience. Thus, he concludes that we must have some faculty that leads us to see the world in terms of cause and effect. Similarly, he argues that our understanding of time and space cannot itself be found in experience, and so must also rely on our intuition.
Ultimately, mere sensations constitute very little of what we consider to be our experience of the world. A great deal of our experience comes from our inner faculties. Though none of these faculties can actually "say" anything themselves, they give shape and form to our sensations, and thus deeply influence how we experience them.