In St. Thomas' Disputed Questions on Truth, the end of his argument that God knows singulars involves him saying that God has within Him an immaterial likeness of matter. Delving into the meaning of this will shed much light on the nature of cognition.
Knowledge comes to be, not when the knower is the same as what's known, but when there is some likeness or representation of the known within the knower. Aristotle's De Anima seems to go back to the principle many times, from the initial dialectical considerations of the first book, to his definition of sensation, to his accounts about the operation of the intellect.
His response to Empedocles shows why something like this must be true. He says that if like is known by like, it would be the case that God would be ignorant of the elements, but that he would make him most foolish of all. Certainly not a position to be held.
The whole consideration of sensation in book two makes it clear that some likeness must enter in. The eye does not become the color that it sees, yet somehow the color appears to it or is represented to it. And this, without matter.
Any body, insofar as it is a body, is capable of receiving sensible forms. This does not require any degree of life or knowledge. (Berkeley would beg to differ, but that's another story.) Knowledge seems to begin when forms exist in an immaterial way. This may present a difficulty with sensation: For doesn't sensation always happen with a corporeal organ? Sensation certainly takes place apart from an organ; and, in some cases, that organ cannot help but to materially receive the sensible form (as being near hot things makes us hot), yet it is not in this that sensation consists. It is only when the form is received apart from matter.
Another difficulty arises: Isn't the intellect, when it abstracts, knowing the form without the matter? How does this differ? Since the sense powers are seated in corporeal organ, sensation always happens with material conditions, yet these are on the part of the organ, not on the part of what is being received. For this reason, sensation is always of the particular (as Aristotle says in book one of the Physics). Our organs have their own here and now, and these are what cause sensation always to be of the particular.
But wait: What about the imagination or the other interior senses? Don't these remove the here and now? Otherwise, how could I imagine something that isn't actually happening? I don't have a complete answer to this, especially as regards the interior senses related more immediately to instinct. Yet at least with imagination, it is the case that our organ (some part of the brain) is corporeal, and therefore its use will have material conditions. The other powers are more difficult, on account of the obscurity of their objects. Aristotle himself does not give any extended consideration to these higher sense powers, so it is only with the developments by the Arabs and the Medievals (perhaps also some ancient commentators) that an understanding of these have been appended to Aristotle's account of the powers of the soul.
Not only are these powers (these being the memorative and the estimative/cogitative powers) not part of De Anima, but they are not part of the current curriculum at Thomas Aquinas College, so that it seems a thesis considering how a representation of the known is needed for knowledge, will also need to give an account of these powers and the kind of abstraction that is done by them, and how it exceeds what the other sense power do, and yet falls short of what the intellect does.
After this, a consideration of the intellect will be in order. Here it will be fitting to give the argument that our intellect is incapable of receiving a likeness of matter, and therefore that we are only able to consider by some kind of analogy. From here, we must ascend even higher.
Higher, unto God Himself and His knowledge. Here it will be fitting to consider briefly that He is the proper object of His own thought. Then how it is that He knows all things. Then how it is that matter is a thing, and how it is thus known by God.
St. Thomas, in his consideration on God's creation of matter (Summa, I.44.2) and on whether God has an idea of prime matter (De Veritate, 3.5), St. Thomas makes clear that matter is somehow included under the notion of being, and as such falls under the universal scope of God's knowledge and causality. This will be the place to address what seems incongruous about an immaterial likeness of matter, but then also how such a likeness or representation is possible. And further in what way this compares to the analogous knowledge we have of matter.
Very little has been attended to above about the nature of matter itself as a being in potency. There many places where it comes up (such as the argument that our intellect does not know it), but perhaps it may be God to give a preliminary account of Aristotle's argument for its existence and that it is wholly a being in potency.
This looks pretty good. I'm now at peace about the direction of my thesis. A lot of blanks to fill in, but at least I know where they are, and there's some order. Also, I'll be able to make use of a lot of the research I did this summer on the Medieval/Arabic theories on how individuals are cognized.