Now it remains to be seen whether Kant can live with the distinction. In my opinion, the question is severely complicated by the lack of agreement about whether Kant ever articulated a definitive version of the distinction. His position may have been hopelessly ambiguous.
I begin with an etymological point stressed in the early 1970s by Gerold Prauss. Most occurrences of the phrase "things in themselves" are shorthand for the phrase, "things considered in themselves" (Dinge an sich selbest betrachten). The correlative to this is the consideration of things in relation to human sensibility, i.e., in relation to their representation in space and time. So "in themselves" and "as they appear" are two ways of considering "things." Things as they appear are determined by predicates which depend on space and time. The properties of physical things are relational, wholly dependent on space: extension, motion or rest, forces of attraction or repulsion. Apart from these properties there are none to be found.
This led Kant to declare that things considered apart from the conditions of space and time, are not spatial and not temporal. "Now a thing in itself cannot be known through mere relations; and we may therefore conclude that since outer sense gives us nothing but mere relations, this sense can contain in its representation only the relation of an object to the subject, and not the inner properties of the object in itself" (B67). But how could Kant be justified in claiming that things in themselves are not spatial and not temporal? His contemporary Reinhold pointed to a "neglected alternative" between spatial appearances and non-spatial things in themselves, i.e. that things in themselves may be spatial although we could never establish that they are. Is Kant not going too far in saying definitely that things in themselves are not in space and time, that these are nothing but forms of intuition?
Kant made a number of definite claims about things in themselves. We saw in the First Antinomy that for things in themselves, if the conditioned is given, so are all of its conditions. Perhaps Kant took the phrase "in itself" to mean more than the negative "apart from conditions of sensible intuition." He may have thought of them more positively as self-subsistent things. If so, they would have properties which are not relational, something that spatial objects lack. Further, they would not depend on their relations to anything else. Insofar as Kant conceived of objects as depending on space and time, things in themselves could not be in space and time.
Some commentators have found deeper problems with the distinction. An extreme interpretation is that Kant's idealism is a form of phenomenalism, in the sense that the objects of experience are no more than bundles of perceptions. If so, then appearances are nothing more than the way things seem to be to a perceiving being, while things in themselves are the way they really are. But Kant clearly rejected the claim that appearances (Erschinungen) are mere seemings (Schein). The difference between the way things are and the way they seem to be is an empirical difference, akin to that between primary and secondary qualities. Extended objects are empirically real and only transcendentally ideal. (See the Lexicon entry on Idealism.)
On the other hand, Kant frequently described things in themselves using such language as "the real per se." Decribed in this way, things in themselves would seem to have a higher degree of reality than appearances, especially since appearances are frequently characterized as "representations." Now representations are real (as Kant stated in the Aesthetic, we really represent things as in time). Still, we only represent things as in time if there are such things prior to the representation.
Henry Allison has characterized interpretations of this sort as "ontological," and mistaken as well. He claims that the distinction is instead "methodological." That is, characterizing things apart from their relation to sensibility does not characterize them as they really are; it is only an abstraction from conditions of sensible representation. This explains their non-spatiality and non-temporality, since we are considering things explicity apart from space and from time.
One reason for resisting this interpretation lies in Kant's account of the origin of sensible representation. The mind is affected by objects, which affection in turn triggers their representation as in space and time. It would seem that something really existing apart from appearances is required as the stimulus required for the representation of things in space. Something other than appearances supplies the "matter" of outer intuition, to which sensibility adds the form.
This view seems congenial to yet another way of understanding Kant's distinction, i.e., that things in themselves and apperances (as representations) are distinct objects, standing in some sort of "grounding" relation. Things in themselves are the ground of representations of them in space and time. This "two-object" or "double-object" view has plenty of difficulties of its own. One problem is that the categories are said not to apply to things in themselves, which makes the "ground" relation questionable, despite Kant's careless use of the word 'cause' to describe the source of our intuitions. A possible way around this criticism (a prominent advocate of this view is Wilfrid Sellars) is to describe "grounding" as only analogically related to the category of causality. A hint of such a view can be found at A566/B594).
The opposing approach is the "double-object" or "double-aspect" interpretation, according to which things have two "sides," that by which they are intuited as appearances and that by which they are thought in themselves, apart from intuition. Many passages in Kant support this interpretation. I have always wondered, however, what it could mean. Specifically, given the non-spatiality and non-temporality of things in themselves, there are no properties shared in common between appearances and things in themselves. So in what sense could they be said to be the "same things?"
A solution might be sought in the device of possible worlds. Kant language lends itself to this, as he sometimes distinguishes a "sensible world" and an "intelligible world." The same thing, as inhabitants of different worlds could differ with respect to its properties. It has always been a problem to individuate objects across worlds: how different can the inhabitant of one world be from that of another and yet be the same thing? Given that apperances and things in themselves share nothing in common, it seems that there is no grounds for trans-world identity.
My suggestion is that we follow Kripke and say that things in themselves are stipulated to be the same things as appareances. For example, I begin with myself as an object of inner intuition, and then I think that very thing as a thing in itself. As Kripke has stressed, we do not "discover" other possible worlds and their inhabitants; rather, we use the device of possible worlds as a way of thinking differently about objects in this world.
Allison has dismissed this approach as a "ploy," which is based on a mistake. The mistake is that things in themselves are given an ontological, rather than methodological, interpretation. I find it curious that anyone so knowledgeable about Kant would insist that there is only one correct interpretation of this murky distinction. Further, I think Allison may be wrong about my presupposition. There is nothing to prevent the "intelligible world" to be the kind of abstraction he favors on the methodological interpretation. That is, he can think of it in the same way as Kripke thinks of other possible worlds, as useful devices for thinking how things with which we are acquainted would be under different (in this case very different) conditions.