We have therefore wanted to say that all our intuition is nothing but the representation of appearance; that the things that we intuit are not in themselves what we intuit them to be, nor are their relations so constituted in themselves as they appear to us; and that if we remove our own subject or even only the subjective constitution of the senses in general, then all constitution, all relations of objects in space and time, indeed space and time themselves would disappear, and as appearances they cannot exist in themselves, but only in us. What may be the case with objects in themselves and abstracted from all this receptivity of our sensibility remains entirely unknown to us. We are acquainted with nothing except our way of perceiving them, which is peculiar to us, and which therefore does not necessarily pertain to every being, though to be sure it pertains to every human being. We are concerned solely with this. Space and time are its pure forms, sensation in general its matter. We can cognize only the former a priori, i.e., prior to all actual perception, and they are therefore called pure intuition; the latter, however, is that in our cognition that is responsible for its being called a posteriori cognition, i.e., empirical intuition. The former adheres to our sensibility absolutely necessarily, whatever sort of sensations we may have; the latter can be very different. (A42/B59–60)OK; and here's the Stanford Encyclopedia of Philosophy:
Kant introduces transcendental idealism in the part of the Critique called the Transcendental Aesthetic, and scholars generally agree that for Kant transcendental idealism encompasses at least the following claims:
 In some sense, human beings experience only appearances, not things in themselves.
 Space and time are not things in themselves, or determinations of things in themselves that would remain if one abstracted from all subjective conditions of human intuition. [Kant labels this conclusion a) at A26/B42 and again at A32–33/B49. It is at least a crucial part of what he means by calling space and time transcendentally ideal (A28/B44, A35–36/B52)].
 Space and time are nothing other than the subjective forms of human sensible intuition. [Kant labels this conclusion b) at A26/B42 and again at A33/B49–50].
 Space and time are empirically real, which means that “everything that can come before us externally as an object” is in both space and time, and that our internal intuitions of ourselves are in time (A28/B44, A34–35/B51–51).Right, so: I'm less interested for the moment in the question of whether the relationship between representations and things-in-themselves can be resolved, or whether the latter are necessary to Kant's theory. I'm interested in what K. says about the a priori forms of our sensible intuition. Wikipedia quotes John Watson's The philosophy of Kant Explained (1908), 62–72., so you can see how up to date my engagement is:
[Kant's] most influential contribution to metaphysics: the abandonment of the quest to try to know the world as it is "in itself" independent of sense experience. He demonstrated this with a thought experiment, showing that it is not possible to meaningfully conceive of an object that exists outside of time and has no spatial components and is not structured in accordance with the categories of the understanding, such as substance and causality. Although such an object cannot be conceived, Kant argues, there is no way of showing that such an object does not exist. Therefore, Kant says, the science of metaphysics must not attempt to reach beyond the limits of possible experience but must discuss only those limits, thus furthering the understanding of ourselves as thinking beings. The human mind is incapable of going beyond experience so as to obtain a knowledge of ultimate reality, because no direct advance can be made from pure ideas to objective existence.There's a rightness about this; it has a common-sense-y 'an eyeball can see lots of things but not itself' vibe to it. But I don't think it is right. Let's replicate Kant's thought experiment.
Kant's argument is that space and time are not 'things'; they are forms of perceiving. The Wikipedia article I quote there goes on: 'both space and time and conceptual principles and processes pre-structure experience.' So in other words, Kant's point is that we see space and time when we look around us because (I read this analogy somewhere, but can't remember where) we are in effect wearing 'space and time spectacles' over our eyes. A parallel case would be a man who had his corneas tinted yellow, and who accordingly would see a yellowish world. We can prove this, says Kant, because it is not possible to imagine a spaceless or timeless object, or entity, or whatever. So: I can think of a cube, in space; and I can imagine that the cube has vanished, but I can't imagine that the space in which I had previously imagined the cube has vanished. This appears to have persuaded many people.
My problem is that Kant takes these 'categories' as absolutes. What I mean is: he says, in effect, 'we can imagine lots of objects that have spatial dimensions and that exist in time; but we cannot imagine no space and no time.' I don't disagree: I, personally, cannot imagine no space. But I can imagine more or less space.
There's a parallel, I think, with what Bertrand Russell says about Berkeley in his History of Western Philosophy. Russell challenges Berkeley's 'idealism', the 'argument against matter.' That argument, according to Russell, 'is most persuasively set forth in The Dialogues of Hylas and Philonous (1713); for that is where Berkeley 'advances valid arguments in favour of a certain important conclusion, though not quite in favour of the conclusion that he thinks he is proving.' That's what Russell says, at any rate. 'He thinks he is proving that all reality is mental; what he is proving is that we perceive qualities, not things, and that qualities are relative to the percipient.':
The characters in the Dialogues are two: Hylas, who stands for scientifically educated common sense; and Philonous, who is Berkeley. After a few amiable remarks, Hylas says that he has heard strange reports of the opinions of Philonous, to the effect that he does not believe in material substance. "Can anything," he exclaims, "be more fantastical, more repugnant to Common Sense, or a more manifest piece of Scepticism, than to believe there is no such thing as matter?" Philonous replies that he does not deny the reality of sensible things, i.e. of what is perceived immediately by the senses, but that we do not see the causes of colours or hear the causes of sounds. Both agree that the senses make no inferences. Philonous points out that by sight we perceive only light, colour, and figure; by hearing, only sounds; and so on. Consequently, apart from sensible qualities there is nothing sensible, and sensible things are nothing but sensible qualities or combinations of sensible qualities. Philonous now sets to work to prove that "the reality of sensible things consists in being perceived -- as against the opinion of Hylas -- that "to exist is one thing, and to be perceived is another.' That sense-data are mental is a thesis which Philonous supports by a detailed examination of the various senses. He begins with heat and cold. Great heat, he says, is a pain, and must be in a mind. Therefore heat is mental; and a similar argument applies to cold. This is reinforced by the famous argument about the lukewarm water. When one of your hands is hot and the other cold, you put both into lukewarm water, which feels cold to one hand and hot to the other; but the water cannot be at once hot and cold. This finishes Hylas, who acknowledges that "heat and cold are only sensations existing in our minds." [624-25]Russell has this to say about this famous thought-experiment:
The argument about the hot and cold hands in lukewarm water strictly speaking, would only prove that what we perceive in that experiment is not hot and cold, but hotter and colder. There is nothing to prove that these are subjective. Russell has other arguments against Berkeley but I want to stick with this one. Within the spectrum of human experience, there is no such thing as absolute hot or absolute cold. Of course there is such a thing as absolute zero, and I suppose an object that was so hot the molecules within it were agitated towards the speed of light would be 'absolutely' hot. But we're not talking about such exotic circumstances. 'Hot' and 'cold' describe a spectrum of relative measurements between (say) minus 50 and plus 120 degrees centigrade, because this is how human beings encounter hot and cold in the world. And when we do that encountering, what we actually experience is hotter or colder; which is to say, relative terms.
So, mutatis mutandi, with space and time. I can imagine a three-dimensional object, says Kant, but I cannot imagine an absolute absence of dimension. Perhaps so, but I can imagine a two dimensional object (Abbot's Flatland is an example of somebody imagining such a thing at length and in detail), and I can also imagine a one-dimensional object; not to mention a four- or five-dimensional object. Not that these things actually exist; that's not Kant's point. But that I can imagine them. As with Berkeley's hot and cold, space and time are not proven to be absolutely in the mind by Kant's thought-experiment because space and time figure conceptually as asymptotes towards precisely the situation Kant denies.
There's something similar in Kant's critique of the Descartean cogito. The problem, says Kant, is that 'it is not legitimate to use "I think" as a complete phrase, since it calls for a continuation -- "I think that ... (it will rain, you are right, we shall win ...)" According to Kant, Descartes falls prey to the "subremption of the hypostasized consciousness": he wrongly concludes that, in the empty "I think" which accompanies every representation of an object, we get hold of a positive phenomenal entity, res cogitans, which thinks and is transparent to itself in its capacity to think.' [I'm quoting from here, p.13] Of course I take the point that we don't 'think' in the abstract; that we are always thinking about something. But though it's true that when we think we must think about something and cannot think about nothing, we can nonetheless think about more, or less; and at either end of that spectrum is the asymptote towards which thinking tends, and which returns us to a Descartean purity.