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.