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).