Accounts of the immateriality of intellect need to do more than appeal to the fact that we have no idea what it would mean for matter to think, since to leave it at this would leave one powerless against the obvious fact that we have no better idea of what it would be for a non-material thing to think. We can’t see thought coming out of Leibniz’s mill, but this is just as true of the Platonic form of the mill. Disembodied existence is not obviously cognitive any more than physical existence.
The Greeks saw knowledge as the cognitive grasp of form. This was more a definition than a finding, since “form” meant whatever was intelligible about a thing. Plato, so the story goes, put what was intelligible about things separate from the things themselves, whereas Aristotle put the intelligible structures of material things into matter. Now Plato’s account makes intelligence pretty strightforwardly non-material: if what is intelligible about things is outside the material cosmos, then in knowing we occupy a state outside the cosmos. Aristotle’s account leads to immateriality by a more subtle but just as direct inference: if knowledge means having the intelligible structure of something, it must have it in a way other than the material thing with that structure. But it is precisely by having that structure that it is material, and so cognitive powers possess forms in a way that does not make them material things. This gives cognition a sort of immateriality, though we’d need additional premises to establish that some intellect was immaterial simply speaking, and not just with respect to the material things it knows.
So if we wanted a theory of knowledge that made no use of the immaterial, we’d need to say either that knowledge does not consist in possessing some intelligible structure in things, or that this structure was neither within or without the things themselves.