In a sense, Kant is quite at one with Hume in that he believes that we never actually experience the self; or, in Kant’s terms, the “soul” (or the “substance of our thinking being”). This is because the soul is the mode through which we experience and is not, therefore, an object of experience. Perhaps it would be like a dog trying to catch its own tail. We can, of course, experience the “cognitions” of the soul; though we can’t experience the soul which has the cognitions. Like all other substances, including the substances of objects, the “substantial itself remains unknown” (978). We can, however, prove “the actuality of the soul” through the “appearances of the internal sense”. This is a proof of the soul, however, not an experience of it.
The Antinomies and Experience
What are the “antinomies”? They are subjects of philosophical dispute that have “equally clear, evident, and irresistible proof”(982) on both sides of the argument. That is, a proposition and its negation are both equally believable and acceptable in terms of rational inquiry.
Kant gives an example of such an argument with two equally weighty sides. One is whether or not the world had a beginning or as existed for eternity. The other is whether or not “matter is infinitely divisible or consists of simple parts” (982). What unites these arguments is that none of them can be solved with the help of experience. In a sense, this is an argument of an empiricist. In addition, according to the empiricism of the logical positivists, these arguments would have been considered non-arguments precisely because they can't be settled or solved by experience. As Kant puts it, such “concepts cannot be given in any experience” (982). It follows that such issues are transcendent to us.
Kant goes into further detail about experience-transcendent (or even evidence-transcendent) facts or possibilities. We can't know, through experience, whether or not the “world” (i.e., the universe) is infinite or finite in magnitude. Similarly, infinite time can't “be contained in experience” (983). Kant also talks about the intelligibility of talking about space beyond universal space or time before universal time. If there were a time before time it would not actually be a time “before” time because time is continuous. And if there were a space beyond universal space, it wouldn’t be “beyond” universal space because there can be no space beyond space itself.
The Unperceived Tree in Space and Time
This is very much like Berkeley’s argument.
Thus, when we imagine a tree unperceived, we are, in fact, imagining it as it is perceived; though perceived by some kind of disembodied mind. Or, as Kant puts it, to represent “to ourselves that experience actually exists apart from experience or prior to it” (983). Thus when we imagine the objects of the senses existing in a “self-subsisting” manner, we are, in fact, imagining them as they would be as they are experienced. That isn't surprising because there's no other way to imagine the objects of the senses.
Space and time, on the other hand, are “modes” through which we represent external objects of the senses. As Bertrand Russell put it, we wear spatial and temporal glasses through which we perceive the world. If we take the glasses off, then, quite simply, space and time would simply disappear. They have no actuality apart from our minds. Appearances must be given up to us in the containers we call “space and time”. Space and time are the vehicles of our experiences of the objects of the senses. In a sense, it seems like a pretty banal truism to say that “objects of the senses therefore exist only in experience” because quite evidently there are no experiences without the senses and our senses themselves determine those experiences.
Freedom and Causal Necessity
“…if natural necessity is referred merely to appearances and freedom merely to things in themselves…” 
Thus Kant manages to solve a very difficult problem: the problem of determinism. That is, “nature and freedom” can exist together. Nature is not free. However, things-in-themselves (including the mind’s substance) are free. The same things can “be attributed to the very same thing”. That is, human beings are beings of experience and also beings-in-themselves. The experiential side of human nature is therefore subject to causal laws; whereas the mind transcends causal necessitation. We are, therefore, partly free and partly unfree.
Kant has a particular way of expressing what he calls “the causality of reason”. Because reason is free, its cognitions and acts of will can be seen as examples of “first beginnings” (986). A single cognition or act of will is a “first cause”. It's not one of the links in a causal chain. If they were links in such a possibly infinite causal chain, then there would be no true freedom. First beginnings guarantee us freedom of the will and self-generated (or self-caused) cognitions. In contemporary literature, such “first beginnings” are called “originations” and what a strange notion it is! What does it mean to say that something just happens ex nihilo? Would such originations therefore be arbitrary or even chaotic – sudden jolts in the dark of our minds? They would be like the quantum fluctuations in which particles suddenly appear out of the void. Why would such things guarantee us freedom rather than make us the victims of chance?
Knowledge of Things-in-Themselves
Kant both says that we can't know anything about things in themselves, yet he also says that “we are not at liberty to abstain entirely from inquiring into them” (989). So which one is it to be? Can we have knowledge of things-in-themselves or not? Perhaps Kant means that although we can indeed inquire into things in themselves, nevertheless it will be a fruitless endeavour. Or perhaps it's the psychological need to inquire because “experience never satisfies reason fully” (989). Alternatively, though our inquiries into things-in-themselves won't give us knowledge, we can still offer, nevertheless, conjectures or suppositions about such things. That is, we can speculate about the true nature of things-in-themselves; though we'll never have knowledge (in the strict sense) of them.
There are questions that will press upon us despite the fact that answers to them may never be forthcoming. Kant, again, gives his earlier examples of evidence- or experience-transcendent issues such as “the duration and magnitude of the world, of freedom or of natural necessity” (989). However, experience lets us down on these issues. Reason shows us, according to Kant, “the insufficiency of all physical modes of explanation” (989). Can reason truly offer us more?
Again, Kant tells us that we can't be satisfied by the appearances. The
“chain of appearances…has…no subsistence by itself…and consequently must point to that which contains the basis of these appearances”. .