In the Third Part, Kant discusses the various ideas of reason, and how they mislead the understanding into posing insoluble metaphysical questions. In this section, he hopes to determine the value of reason and the precise bounds within which it can operate. While we can never know more about an object than what experience teaches us, the concepts of our understanding help us to pose metaphysical questions that experience cannot answer. It is only natural, then, that we should consult reason when experience lets us down.
Kant distinguishes metaphysics from mathematics and science by saying that the former has bounds while the latter two have only limits. Both math and science are complete in and of themselves: there are no insoluble problems in these fields, no questions that cannot be answered given enough time, insight, and progress. They are limited only in that their scope is not absolutely general. Math cannot answer metaphysical or moral questions, and science cannot give us insight into things in themselves. However, morality and metaphysics are not needed in mathematical explanations and the nature of things in themselves does not affect the progress of science, which deals only with the objects of experience. What these fields don't know can't hurt them.
Metaphysics, on the other hand, is bounded: reason poses questions for itself that it cannot answer. In investigating metaphysical questions, reason bumps up against boundaries that it cannot press beyond. That is, metaphysics asks questions about the nature of things in themselves, but we cannot gain definite knowledge of anything outside experience.
However, these bounds can be useful. While we cannot know what is beyond them, we can infer from the existence of these bounds that there is something beyond them (i.e. things in themselves) and we can infer the connection these things in themselves must have with the perceptible world. While we cannot reach beyond experience to things in themselves, we can examine the relation between things in themselves and our experience.
Kant has already dismissed any attempt to prove the existence of God or to learn anything positive about God's nature. Our knowledge is structured by categories and concepts that are applicable only to experience, so we cannot apply these categories and concepts in any meaningful way to things beyond experience. For instance, it would be a mistake to attribute supreme rational powers to a Supreme Being, since we can't attribute anything to something beyond experience. What we can do, however, is attribute the rational order of the experienced world to a Supreme Being that sits outside the experienced world. This is not to say anything about a Supreme Being, but only about the relation that Being has with the world. If we see the world as structured in a rational way, we find a unity in experience by stretching our powers of reason right to the bounds of experience.
Though there is no way of knowing the reason why we have reason, Kant offers some speculation. He suggests that perhaps reason, in showing us the bounds of experience, also teaches us that there is something beyond experience that we cannot know, thereby giving us a more balanced perspective. Without the idea of a soul, we might think psychology can fully explain human behavior; without the cosmological ideas, we might think nature is sufficient unto itself; without the idea of God, we might become fatalists, doubting the possibility of free will.
In the Third Part, Kant dismisses standard metaphysical questions and debates as pointless. He argues that these questions arise from a failure to distinguish between appearances and things in themselves, and from trying to apply the concepts of the understanding to something other than the objects of experience. In this conclusion, he shows us that reason and metaphysics do in fact have a very important value—just not the value we normally think of them as having.
The distinction between math and science on the one hand, and metaphysics on the other, rests on the important distinction Kant makes between limits and bounds. Math and science are limited, meaning that they cannot tell us everything. No mathematical equation can tell me whether cloning is wrong, and no scientific experiment can tell me whether or not God exists. (These limits, incidentally, become all the more important in an age when scientific advances pose increasingly complicated moral dilemmas.) However, there is no boundary to what math or science can solve within their particular realms. This is not to say we have solved or can solve all the problems in these fields, but just to say that there is no external constraint on what can be learned. There may be puzzles we will never solve, but they will nonetheless have solutions—just solutions we are incapable of finding. Neither math nor science will ever confront us with a puzzle to which there is no solution.
While math and science are limited, metaphysics is bounded. That means that there are metaphysical puzzles to which there is no solution. The ideas of reason deal with precisely that. "What is the nature of the soul?" is a question, says Kant, to which we cannot give an answer—not because we do not know the answer, but because there is no answer to give. Metaphysics tries to deal with things in themselves, but all our concepts and intuitions are suited only to dealing with appearances. Our reason poses riddles for us for which there is no answer. Metaphysics is an attempt to reach for things that are beyond our grasp.
If metaphysics is bounded in such a way that we can never answer any of the questions it poses, we might think of it as a useless discipline. Kant suggests, on the contrary, that its value lies precisely in the establishment of these bounds. We cannot know what is beyond experience, but in reaching for it, we know there is something beyond experience. If something is bounded, that suggests there is something outside those bounds. Limits do not teach us this.
If all we had were our faculties of sensibility and understanding without reason, and all we had was math and science without metaphysics, we would have no awareness of things in themselves. We would pursue math and science with the assumption that we were learning everything there is to learn. We would assume that the concepts of science can explain all natural phenomena, and that whatever science can't explain doesn't exist. For instance, we would assume that a mind is nothing more than a brain, and that thought is nothing more than the firing of neurons.
Though reason cannot teach us anything about things in themselves, it gives us an awareness that there are things in themselves, and thus gives us an awareness of the bounds placed upon our learning. Metaphysics is important to us precisely because it is bounded. It gives us perspective, something that none of the more complete sciences can give us. While math and science teach us what we can know, metaphysics teaches us what we can't know.