The metaphysics of previous generations, which Kant discusses in the Third Part, is dialectical nonsense: debates as to the nature of the soul or the possibility of freedom can go on and on and back and forth forever without reaching any satisfying conclusions. He cannot deny that metaphysics exists as a disposition of human reason (we are naturally drawn to metaphysical questions), but he does deny that metaphysics as it has been conducted can lead to any real knowledge.
Kant is now finally ready to answer what he posed as the general question of this book: "How is metaphysics possible as a science?" His answer, effectively, is one word: "critique." Our faculty of reason cannot teach us anything about what lies beyond experience or about things in themselves, but it can help us to categorize and classify the various concepts of our faculties of sensibility, understanding, and reason. Rather than use reason to look outward, we should turn it inward and direct it toward itself.
Kant considers science to be a body of synthetic a priori knowledge. The faculty of reason has no power to gain a priori knowledge of things outside experience, or even outside the intellect. What it can do is survey the mind in its entirety and gain knowledge a priori about the nature and variety of our many concepts and faculties.
Kant is confident that anyone who has read the Prolegomena will conclude with him that nothing to date has advanced metaphysics in the slightest, and that metaphysics as it has been conducted to date is useless. Nevertheless, Kant remarks, we are naturally drawn to metaphysics and cannot just abandon it. For this reason, he expects formerly dogmatic metaphysicians to begin advancing the critical philosophy he envisions with great vigor.
Kant challenges anyone who disagrees with his dismissal of dogmatic metaphysics to provide one example of a metaphysical synthetic a priori judgment that has been proved with certainty. Such a judgment cannot be based on probability or conjecture, since a priori truths are necessary, and it cannot be based on common sense, since we derive common sense from experience. While common sense is useful for practical purposes, it cannot advance metaphysics as a science.
Kant uses the term "metaphysics" to talk about two very different things. On one hand, he talks about the "dogmatic" metaphysics that he attributes to his rationalist predecessors, and on the other hand, he talks about the critical metaphysics he intends to set up in its place. In examining this distinction, we should also get a clearer sense of what a "critique" is, and why Kant thinks "dogmatic" metaphysics is not a science but that his critical metaphysics is.
"Dogmatic" metaphysics pursues the kinds of questions outlined in the Third Part as prompted by ideas of reason. These questions ask about the nature of the soul, the possibility of freedom, the ultimate constituents of matter, the existence of God, and so on. Metaphysics relies entirely on the faculty of reason, and Kant tries to show us that reason cannot get us any closer to answering these questions. The faculty of reason cannot connect with anything outside the mind, and certainly not with things in themselves.
If we recall, a science is a body of synthetic a priori knowledge. That is, it is a field of study that makes interesting, non- analytic judgments, but does so without any reference to experience. In order to make synthetic judgments without reference to experience, our mental faculties must be able to make significant connections within their own pure concepts. Our faculty of sensibility can use its pure intuitions of space and time to make mathematics and geometry. Our faculty of understanding can use its pure concepts to make natural science possible. Our faculty of reason has ideas, so the pressing question is what kind of synthetic judgments can these ideas produce?
We have seen that the ideas of reason pose all sorts of metaphysical questions that reason cannot answer. We have also seen that in doing so, reason pushes itself to the bounds of human knowledge, giving a sense of completeness and unity as to what we can know. Reason, then, has a sense of what kind of knowledge is possible, and so is ideally suited to examining the different mental faculties and determining precisely how knowledge is structured. The Prolegomena itself has essentially employed this technique: throughout, Kant has been investigating the different kinds of knowledge we have and the grounds on which this knowledge is justified. His conclusions that there are three mental faculties (sensibility, understanding, and reason), that the faculty of sensibility contains pure intuitions of time and space, or that the faculty of understanding is structured according to the concepts listed in his table of categories, are all conclusions reached through a critical investigation of the structure of knowledge.
While "dogmatic" metaphysics asks what we can know, Kant's critical metaphysics asks how we can know. A "critique" is an investigation that looks inward rather than outward, that investigates knowledge itself rather than the objects of knowledge. The Prolegomena is a shortened version of Kant's great work, the Critique of Pure Reason, which is an attempt to investigate how and what our faculty of reason is capable of.
Kant is not doing psychology. He is not trying to figure out how the mind works or anything like that. Rather, he is trying to figure out how knowledge works, and any claims he makes about the workings of the mind are based on his conclusions as to how knowledge must be structured in the mind.
One of the most significant conclusions of Kant's critical philosophy is that many concepts we think of as objective—like space, time, or causation—are in fact part of the way we structure knowledge. These concepts, as Kant shows in the Third Part, are often the source of perplexing metaphysical conundrums. In showing that these concepts are not to be found in the world, but rather in our own faculties, Kant is essentially redirecting metaphysics. He is telling us that we should not apply metaphysical concepts to the world but to our own faculties. All metaphysics can do for us is tell us how we know what we know. It cannot tell us what we cannot know.