(I became dissatisfied with STA’s account of the agent and possible intellects around six or seven years ago and have been trying to come to some conclusion about the matter since then. The two posts of this series are the closest I’ve come to an answer)
0.) Approach De anima 3.5 with the assumption that it is an attempt to respond to the question of how mind is the same as its object but does not always think (raised at 430a 4-7).
1.) This explains why this is the question posed two sentences before 3:5 begins and is not answered.
2.) It explains why 3:5 concludes by establishing a sense in which mind does always think and which it cannot always think.
3.) The rival position is one made canonical by St. Thomas, namely that 3:4 is an attempt to speak of the passive intellect and 3:5 speaks of the active one. This reading fails to account for the facts we pointed out in #1 and #2 and fails to account for the things discussed in the chapters. C. 4 and c. 5 are not attempts to speak of principles of mind but of mind as such. Neither a passive or active intellect thinks, but the entities described in chapters 4 and 5 do think.
4.) Still, it is very reasonable to read 3:5 in the way that I’ve just argued is mistaken:
Since in every class of things, as in nature as a whole, we find two factors involved, (1) a matter which is potentially all the particulars included in the class, (2) a cause which is productive in the sense that it makes them all (the latter standing to the former, as e.g. an art to its material), these distinct elements must likewise be found within the soul.
And in fact mind as we have described it is what it is what it is by virtue of becoming all things, while there is another which is what it is by virtue of making all things: this is a sort of positive state like light; for in a sense light makes potential colours into actual colours.
5.) “Mind as we’ve described it” is one reading of toioutos nous, but it need not refer to 3:4. The sense could be “mind in light of the distinction just given”. So how do we read this as describing minds and not principles of mind?
6.) Aristotle’s claim is that since everything in nature has material and an agent, so too mind in nature has material and an agent. But “material” means mind so far as it strives to become all things but is incapable of being more than a few of them. It is hemmed in by physical limitations or the ways “in which human nature is in many ways a slave”. This is why Aristotle opens 3:5 with a claim about all things in nature (en apase te phusei, etc.) Mind so far as it enters nature has to be characterized by “matter” i.e. limitation and desire for forms that can never be completely acquired.
7.) Mind as maker or agent is present in nature in a completely different way, since to be an agent in nature does not require being a natural agent. The first unmoved mover, for example, acts in nature without being a natural being. Aristotle’s point in speaking of an agent intellect is to describe that there is something about it which, can act in nature without itself being natural.
8.) If we wanted to speak of “agent intellects” and “possible intellect” we would say this: Mind in itself is not natural but is capable of acting in nature. Considered in this way it is “agent intellect”. So far as we view it in nature it is “possible intellect”, i.e. it takes part in the limitation and desire for being that characterizes all natural things. These two elements are “present in the soul” because the soul is both natural thing and source of life, which latter need not be natural.
9.) This makes the traditional Thomistic teaching on passive and agent intellect largely superfluous, but there is an element in the controversy which was crucial to keep in mind, sc. the essential personality of intellect. Personality as present in nature is a limitation, largely subconscious, hemming in freedom, and in a large part of the population incapable of even rising to literacy. Personality as separate from nature (as “agent intellect” in our sense) is simply a self, which is always seeking to break out in nature but is frustrated by the strictures of embodiment. The Christian doctrine of resurrection cannot be understood as some sort of return to corporality in this sense of frustration, possible retardation, corruption, hemmed in freedom, etc. Christ’s resurrected body is not even properly historical.