When I study the Critique of Pure Reason with new as well as old readers I often encounter questions about 'things-in-themselves.' It is interesting that there always seems to be a crystal clarity as to what is meant by 'things-in-themselves,' but there remains the question: if Kant says we can not know these objects, why does he say so much about them? I hope to clear some of this up briefly, and connect it to some other aspects of the Critique.
I assume most people will agree that we experience ('see') objects, and that we think objects. It will also be agreed that we do not have any other way of dealing with objects except in our representations of them, or thoughts. If we had no representations or thoughts, this would amount to having no concerns at all.
When Kant discusses things-in-themselves, he calls them objects so far as they do not appear to us. Now, when we are concerned with things-in-themselves we are not concerned with things as mere thoughts, but things even standing apart from thought. That is, when we are concerned about the existence of the external world we are not satisfied with saying that it is a mere thought of ours.
Now, things-in-themselves are clearly not seen by us, nor are they thoughts of ours in particular, but only in general: we think an X so far as it is not seen or thought by us, but somehow may relate to what is seen and thought. It should be clear from this that we do not know the conditions that these objects require for either of our modes of cognizing particular objects: appearance and thought.
It is fair to wonder how we become interested in objects that seem to fall outside of our possible concern: not one of them can become directly distinct for us in appearance or thought. Additionally, we may wonder how there could be more than one of these things that we think. This relates to Kant's question in the Introduction to the B edition of the Critique: how is metaphysics as a natural disposition possible?
We can see the answer fairly clearly on our own: it seems the only way we could concern ourselves with things-in-themselves is if we think objects as real that yet contradict some manner of the object appearing to us. If we think an object, but think it as necessarily out of time and space, we find that we no longer have anything distinct to think, yet this contradiction pushes us outside of the field of experience altogether.We may contradict our manner of representation in our thoughts in a number of ways, and this may help us to understand the diversity of things-in-themselves. This is precisely the insight that Kant shares in the Transcendental Dialectic where the conflict of reason with itself tempts us outside of all boundaries of experience.