I am currently reading through Immanuel Kant: Key Concepts, edited by Dudley and Engelhard, in preparation for tackling the Prolomegna and (possibly) the Critique of Pure Reason, and I am a bit stuck on exactly how Kant thinks about cognition. Is the following a correct (albeit incomplete) sketch?
We receive through the senses a "manifold" of sensations, which is all of the sights, sounds, etc. outside of us, as well as the internal sensations (like, I guess, the sensation of having emotions or having thoughts). Without the aid of the understanding, this manifold is an incoherent blob of these sensations, such as the image in this article: https://www.mirror.co.uk/science/viral-image-unrecognisable-objects-creepy-14705067 Nevertheless, these sensations are still arranged spacio-temporally, and must be from the moment I begin having sensations. For example, I can tell in the above picture that there is a sensation of "white" and, elsewhere, a different sensation of "red," even if I have no further perception of specific objects. This suggests that I cannot acquire awareness of space from experience, since all my (outer) sensations are already bound up in it. (Is this along the lines of what Kant means when he says space is the "form of all appearances of outer sense"? - A26/B42, quoted in Key Concepts, 33) If this is so, then my awareness (=representation?) of space is presupposed by my awareness of all outer sensations, even just as they are presented as the undifferentiated manifold. Moreover, my awareness of space is independent of this latter awareness, since I can conceive of space devoid of objects/the manifold sensation. Thus my awareness of space is a priori. This awareness, in particular, is of space considered singularly, not of a space or spaces, so by its singularity it cannot be a concept (by Kant's definition of concepts as general). Therefore, awareness of space is an a priori intuition. I (or any other cognizing subject) must have this intuition within my own makeup as a cognizing subject, since I could not have gotten it any other way.
As for understanding, my comprehension gets more sketchy. As I understand it, we have concepts of specific features that objects might share (being the same color, being made of wood, being happy/sad feelings, etc.) Our understanding, by means of the rules of judgement, sorts objects under their respective categories using their sensible component. However, to do this at all we need to, I guess, "pick out" the objects from the manifold of sensation, which (I guess...) we do by the pure concepts of understanding. By pick out I mean, have an awareness that some specific set of sensations (this swatch of white, or that loud noise) belongs to a specific object. Are these concepts are a priori because otherwise we could make no sense of the manifold of sensation in order to learn them? Anyways, sorry if my language is imprecise. Kant uses a lot of the words that I would use to describe my understanding in his own technical way, so I have tried to find other ways around it while still conveying where I am shaky in my... understanding.
EDIT: I think one thing complicating my attempt to comprehend understanding is the following question: does sensibility give us objects in its own right? That is, if I am looking at two chairs, those chairs are objects of my cognition. Does sensibility itself give me the two different packets of sensations as two different objects? Or is my above belief correct in that sensibility just gives me the sensation of the visual image of both chairs together, and my understanding sorts the sensations and belonging to two different objects, namely, the different chairs?