There does not seem to be any formal contradiction either way. Let's assume that there is a form of cognising which is not done, or supported, or caused, by something else, material or otherwise. So presumably all that the cognising process would know would be itself. So, how would that be a problem at all?
Of course, people tend to also believe things, i.e. beyond what they actually know, and we do tend to believe that, in the material world, some specific material support needs to exists for knowledge to exist too.
EB
" Let's assume that there is a form of cognising which is not done, or supported, or caused, by something else, material or otherwise. So presumably all that the cognising process would know would be itself" But that is the point that can there be such a cognizing.
When you are sitting alone and thinking, some insight may come to you which was not there in your mind before. Do you mean something like that? Can you give any actual example?
"some specific material support needs to exists for knowledge to exist too."
Perhaps it is not quite right to say that knowledge, "exists". I tend to think that knowledge is made by the cognizer and is not already present there ; and what exists there is something which that particular cognizer can cognize. Another cognizer may not find any knowledge in the same thing.