Because our intellect, Aristotle maintains at III.4.429a18-20 of the De Anima, potentially cognizes all (corporeal) things, it cannot be “mixed” with – that is, composed out of – anything corporeal. In his commentary on this terse passage, Aquinas explicates it by teasing out from it the following argument:
What is in potentiality to something is lacking in that to which it is in potentiality
The intellect is in potentiality to cognizing anything corporeal
Therefore, the intellect is lacking in anything corporeal
Now if a thing lacks anything that is corporeal, then that thing must be incorporeal. Our intellect, then, since it is in potency to cognizing, i.e., can come to have knowledge of, all corporeal natures, is itself an incorporeal faculty (quwwa).
Omitting Aquinas’ proof (by way of an analogy with the senses) for the major premise (which self-evident in any case), the above I think is the gist of his intention. He doesn’t seem to offer any proof for the minor premise in the text which, as we’ll see below, leaves room for disputing it.
I grant the major. But, I think, since the minor is ambiguous, I first distinguish it in (at least) 4 ways, all of which will then be rejected. Consequently, the argument as a whole will be rejected as well.
Now, the minor can mean either:
(a) That the intellect can cognize all corporeal things in the sense that its perceptual act is not limited to only one individual of its proper perceptual object (i.e., the intelligible) without also being able to perceive another such individual (intelligible) object;
(b) That the intellect can cognize all corporeal things in the sense that its perceptual act is not limited to any species of perceptual objects. In other words, that it, in addition to grasping (individual) intelligibles (one at a time), it can also grasp imaginables qua imaginable and sensibles qua sensible in the same way;
(c) That the intellect can cognize all corporeal things, whether its own proper objects (as in (a)) or not (as in (b)), all at once;
(d) That the intellect can cognize all corporeal things in the sense that it can perceive their different (intelligible) forms without itself becoming a corporeal object of the relevant kind (in the way, e.g., a parcel of matter does so).
Regarding (a), the power of imagination can also perceive all corporeal things in that sense; for its not the case, as is plain from experience, that its perceptual act is limited to only one proper object without being able to grasp another individual proper object beyond that. But that fact, in the case of the imagination, does not entail that it is incorporeal; therefore, the same reasoning applies to the intellect.
Regarding (b), it is evidently false; the intellect, like any other cognitive power, has proper objects (i.e., intelligibles) and as such cannot grasp other kinds of perceptibles, namely, those that are the proper objects of the other faculties. But since in the case of the other faculties this fact does not entail they are incorporeal, the same will be the case for the intellect.
Regarding (c), it is also plainly false. Its falsity is evident, from among other things, common experience; we cannot, try as we might, perceive more than one intelligible, let alone more than one kind of cognitive object – nay, let alone all intelligibles and all cognitive objects(!) simultaneously or at the same time.
Regarding (d), the response to this is similar to the one in (a), namely, the fact that the intellect can perceive different (intelligible) forms without itself becoming a corporeal object of the relevant kind is no less true for the faculty of imagination or even one of the senses, like the faculty of sight. The imagination perceives some (imaginal) form, say of a horse, but neither it nor the corporeal organ in which it is located and of which it is the actuality, becomes a horse. And sight perceives the color green, but neither it nor the corporeal organ of which it is the actuality becomes green as a result. But, again, since in the case of these latter corporeal faculties this fact does not entail they are incorporeal, the same will be the case for the intellect.
I conclude, then, that either there is some other sense of the minor which can salvage the argument or it is not demonstrative (burhani). From the above, I opt for the latter.