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Summary
Kant takes it as self-evident that it is in everyone's interests to establish metaphysics as a science that proceeds according to agreed-upon and well-grounded principles. Kant's work proposes to do just that, so he feels he is only open to criticism if he has failed to do so, or if he is mistaken in claiming that metaphysics until now has been unproductive. If someone wishes to make the latter accusation, he challenges them to show him one metaphysical truth that is grounded with certainty and agreed upon by all.
The second, and longest, appendix deals primarily with an unfavorable review of Kant's Critique of Pure Reason published in a journal of metaphysics. The reviewer dismisses Kant's work as unclear and unoriginal metaphysical idealism. He makes no mention of Kant's central project of trying to make metaphysics scientific, and does not once refer to Kant's important category of the synthetic a priori. Though this reviewer clearly misunderstood Kant entirely, Kant takes this opportunity to clarify what he means by "transcendental" or "critical" idealism.
Traditional idealists, like Berkeley, assert that all the objects of experience are illusory, and that only pure concepts contain truth. Berkeley claims we have only a posteriori knowledge of space and all the objects in it, and that we therefore cannot be certain of this knowledge. Kant, on the other hand, asserts that we can know about space and time a priori, and that we can have certainty with regard to our experience. Contrary to Berkeley, Kant asserts that our pure concepts are illusory and that only experience contains truth.
Kant's motive for writing his Critique of Pure Reason was that there is no standard for agreement on judgments in metaphysics. This being the case, he does not feel his reviewer's judgment has any solid basis. He challenges his reviewer to produce one metaphysical synthetic a priori principle that can be used to contradict what Kant has written. Better yet, he offers his reviewer the choice of any one of the eight metaphysical propositions listed in his discussion of cosmological ideas. Kant wagers that he could provide a "proof" of the contrary position that his reviewer would not be able to dislodge. He suggests further that he could then provide a similar "proof" of the reviewer's own position, in order to show what dire straits metaphysics stands in.
If people acknowledge the problems in contemporary metaphysics, and study his work as a possible alternative, Kant is confident that much headway can be made, not only in metaphysics, but in other fields as well. For instance, it could free theology from dogmatism and speculation, as well as from the shallow mysticism that masks itself with dogmatic metaphysics.
Analysis
Kant's Critique of Pure Reason was met mostly with bewilderment when it was first published in 1781. The Prolegomena, published in 1783, was primarily intended to clarify and simplify what was said in the Critique in order to make it accessible. A second, largely revised, edition of the Critique was published in 1787.
Readers and reviewers generally failed to appreciate the originality of Kant's ideas. Readers interpreted Kant as saying something more familiar to them than what he was actually saying. The idea that rationalist metaphysics, which was the main occupation of philosophers in Germany at the time, could be dismissed entirely was too revolutionary a concept to catch on easily.
One of Kant's main troubles, it seems, was that he was taken for an idealist. Idealism is the doctrine that reality is dependent upon the mind. A common idealistic argument suggests that everything I know about the world I learn through the senses, and so the things I "know" are not external objects and phenomena, but just the report of my senses. My concept of the world, an idealist would argue, is based entirely on sensory images that exist only in my mind, and has at best a dubious connection with the things in themselves that exist in the world.
A famous proponent of this position is George Berkeley, an Irish bishop who argues that esse est percipi—"being is being perceived." He asserts that chairs and tables and the like have no independent existence, that they only exist in the mind of someone who is perceiving them. He evades the odd claim that these things cease to exist when no one is perceiving them by positing the existence of God as a being who is perpetually perceiving everything.
Kant's philosophy is very firm in asserting that we can know only about appearances, and that we can know nothing about things in themselves. This assertion is enough to make Kant an idealist of sorts, but he wants to qualify this title of "idealism." He is not, like Berkeley, saying that only appearances exist: though we can know nothing about things in themselves, they are still a crucial part of his philosophy.
Kant calls his philosophy "transcendental" or "critical" idealism. The "transcendent" world of things in themselves is contrasted with the "immanent" world of appearances. Because he believes that things in themselves exist, his idealism believes in the existence of a "transcendent" world that is behind the world of appearances.
His idealism is "critical" because it is directed toward what we can know, not toward what exists. He is not saying that only appearances exist, but that appearances are all we can know. Kant's critical philosophy questions how we can come to know what we know, so he is an idealist only in saying that we cannot know things in themselves.
The concept of the thing in itself is one of the most controversial aspects of Kant's philosophy. In Germany, Kant's successors—most notably Hegel—criticized this concept, and advanced a pure form of idealism that did away with things in themselves entirely. It is unclear what sort of relation things in themselves are supposed to bear to appearances if categories such as space, time, and causality do not apply to them. For instance, suppose we see Frank hit John, and then John hit Frank back, we must assume that these appearances are somehow related to things in themselves. But how can there be actions and reactions in things in themselves without the concept of time?
Because he says that they are unknowable, Kant cannot say anything about the nature of things in themselves, but his silence in this regard leaves us with a number of mystifying puzzles. How can appearances in space and time be related to things in themselves outside of space and time? Those who are dissatisfied with Kant generally identify their dissatisfaction with the unanswered questions raised by Kant's doctrine of things in themselves. Idealists generally deny that things in themselves exist, and realists generally assert that categories like space and time have more than just a subjective existence.
