Short version of the argument: Necessary knowablity entails exhaustive conceptual constitution. Phenomenal experience is necessarily knowable. Therefore phenomenal experience is exhaustively constituted by conceptual content.
Long version of the argument: Suppose that there is a rock that is heavy, lumpy and igneous. Suppose that George has the concepts of lumpiness and heaviness, but no concept of being igneous. Suppose further that at no point does George acquire the concept of being igneous. What, then, can George know about the rock? He may know that it is lumpy and heavy, but barring acquisition of the concept of being igneous bars George from knowing that the rock is igneous. That the rock is igneous is, relative to George, un-conceptualized residue. Since idealism about rocks is false, rocks are the sorts of things that can have lots and lots of un-conceptualized residue. In worlds with rocks but no knowers, rocks are 100% un-conceptualized residue.
Letâ€™s turn from rocks to phenomenal experiences and ask whether they can be, in whole or part, unconceptualized residue. One important thing to note about phenomenal experience is its first-person necessary knowablity. This means that if a person has phenomenal experience then that person is necessarily able to know that they have phenomenal experience. I take it that not only am I not a zombie, but I know that I am not a zombie. I may not be able to know whether or not you are a zombie, but that would simply be a failure of third-person knowability. If phenomenal experiences are the sorts of things that might even be beyond the knowability of the persons that have them, then for all that person knows, they are a zombie, which I take to be absurd. If a phenomenal experience has any phenomenal quality, q, that is beyond the knowability of the person having the experience, then for all that person knows, they lack experiences with q. They would be a q-zombie for all they know. Again, I take that to be absurd. Since non-zombies can know of themselves that they are non-zombies, phenomenal experiences can have no phenomenal qualities that are necessarily unknowable from the first-person point of view. If something is necessarily knowable by me in that every aspect of it is necessarily knowable by me, then it can have no aspect that outstrips my concepts. If there were such an aspect it would inaccessible from the first person point of view.
So far this seems to show only that there must be a correlation between phenomenal characteristics and phenomenal concepts. Why make the further step of identifying phenomenal character with the contents of phenomenal concepts? Hereâ€™s why: If, with regards to the phenomenal, character is distinct from conceptual content, then it would be possible for me to be in two different phenomenal states even though I had the same doxastic state. That is, I could believe that I had an experience with quality q on both occasions but in one case the belief would be true and the other case it would be false. However, if this is possible, then there would be states that are phenomenally distinct but subjectively indiscernible. I would be unable to know, from the first person point of view, whether I was in a state with quality q or not. I could, for all I know, be a q-zombie. I take this to be absurd. It follows, then, that with respect to the phenomenal, character is not distinct from conceptual content.
So, what about the widely attributed non-conceptual contents of the perceptual states of babies and nonhuman animals? They can allegedly phenomenally experience colors etc that outstrip their conceptual repertoire. If their experience has content, then the content must be non-conceptual content. But guess what? I am neither a baby nor a non-human animal (I swear!). While I know that I am not a zombie, for all I know, those cute critters are zombies. Further, they are zombies for all they know too. Not only am I not in a position to know whether they are zombies, neither are they. Whatever it is that is going on in babies and nonhuman animals it canâ€™t be the sort of thing thatâ€™s going on in me, because the sort of thing thatâ€™s going on in me is such that I know that I am not a zombie.