de Anima 3.4 (429a10-429b9) (Understanding)

Turning now to the part of the soul with which the soul knows and (whether this is separable from the others in definition only, or spatially as well) we have to inquire what differentiates this part, and how thinking can take place.
If thinking is like perceiving, it must be either a process in which the soul is acted upon by what is capable of being thought, or a process different from but analogous to that. The thinking part of the soul must therefore be, while impassible, capable of receiving the form of an object; that is, it must be potentially identical in character with its object without being the object. Thought must be related to what is thinkable, as sense is to what is sensible.
Therefore, since everything is a possible object of thought, mind, in order, as Anaxagoras says, to dominate, that is, to know, must be pure from all admixture; for the co-presence of what is alien to its nature is a hindrance and a block: it follows that it can have no nature of its own, other than that of having a certain capacity. Thus that in the soul which is called thought (by thought I mean that whereby the soul thinks and judges) is, before it thinks, not actually any real thing, for this reason it cannot reasonably be regarded as blended with the body; if so, it would acquire some quality, e.g. warmth or cold, or even have an organ like the sensitve faculty: as it is, it has none. It was a good idea to call the soul 'the place of forms', though this description holds only of the thinking soul, and even this is the forms only potentially, not actually.
Observation of the sense organs and their employment reveals a distinction between the impassibility of the sensitive faculty and that of the faculty of thought. After strong stimulation of a sense we are less able to exercise it than before, as e.g. in the case of a loud sound we cannot hear easily immediately after, or in the case of a bright color or a powerful odor we cannot see or smell, but in the case of thought thinking about an object that is highly thinkable renders it more and not less able afterwards to think of objects that are less thinkable; the reason is that while the faculty of sensation is dependent upon the body, thought is separable from it.
De Anima 429a10-429b9

Aristotle thought that in perceiving some perceived object, our perceptive organ receives the form of the perceived object, but not its matter. So when we see white, our sight organs receive the form of white but do not receive white matter. So too, when we use our mind to think about or understand some object, our mind takes on the form of the object. He says that our intellect takes on the quality of the object potentially, but not actually. He does not seem to have thought that there was any organ of the intellect. Whereas sight has eyes, the intellect has no bodily organ.

Because intellect must be able to take on any quality, Aristotle concludes that it itself can have no particular quality. In other words, the intellect cannot actually be anything, but it must potentially be everything it can understand (and yet remain potential!). It cannot be mixed with the body, for then it would have the qualities of the body it was mixed with.

To understand what Aristotle may be talking about, take a house and the blueprint of a house: the house itself has a form, and that form is "the same" as the form present in the blueprint. The blueprint has the form of the house, but none of the matter. In analogous fashion, the mind takes on the form of what it thinks about, but none of the matter. The blueprint has the form of the house, but remains only potentially a house (it is not actually a house). Just so, the mind has the form of the object of thought, but is not actually that object.

Now take a piece of pure white paper: you can depict anything on it that is capable of 2 dimensional depiction except something that is entirely the same color as the paper. I suppose you can depict even that negatively: that is to say, by coloring in everywhere except for the depiction of the object.

There is a problem (only one?) with the theory: when bronze changes from an ingot into a statue, the underlying stuff, bronze, is the sort of stuff that can be an ingot or a statue. Bronze cannot become "the action of batting a baseball" or "watery iridescence" or "father of Sam." In other words, when things change, on Aristotle's version of change, the underlying matter is said to lose one form and acquire another form, but the underlying matter must be such as to acquire that sort of form. What kind of thing must intellect be in order to be capable of acquiring, even merely potentially, absolutely everything that is thinkable (such as "bronze," "watery iridescence," "kick my foot thru that door," "my mummy's mum's mum" or any other thought of whatever form)?

Whatever intellect is, it seems a lot like prime matter. That is, it is psychic prime stuff, because it is not anything in actuality, but it is capable of acquiring every form (in the way that a blueprint acquires the form of a house).

Aristotle does not think that the soul survives the body, nor that the body survives the soul. At most, he may think that the intellect survives the body. But note that there is no good reason to think that Aristotle thinks or should think that whatever survives has anything like a personality: Joe's intellect may survive, but it is no longer identifiable as Joe's. It is rather just intellect in something like the way that the bronze that made up a cannon may be reformed into a porpoise statue and then a bunch of bronze pellets and then...

What is more, human souls qua souls are not different from each other according to Aristotle (well, according to the prevailing view of Aristotle). Thus your soul is the same as my soul. The only difference is a difference "in number," by which is meant that our two souls are two souls, not one soul, and so each one is not the other one (if they were not different in number, there would be only one soul between the two of us).

In all, this chapter highlights some deep problems for Aristotle's theory of knowledge.