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.
One gathers the impression from what is here, that Kant's not terribly compelling, or plausible, whatever his historical importance. I think this is debatable.
About the claim that is made here, that Frege was the first to point out that geometry is not synthetic a priori. Well, this implies that indeed, geometry is not synthetic a priori. However, Some believe that Frege was wrong. I'll note that I'm also reading, here, about how this position 'was given a boost by Einstein's relativity..' That is to say, that Einstein's relativity<... Read more→
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