When people lecture on Aristotle's De Anima, it is common, I think, that they say something like this:
Aristotle takes a hylomorphic view of the relationship between soul and body. That is, he thinks that soul stands to body as form to matter. But forms depend on the matter which they inform: when the bronze is melted, the statue is destroyed at the same time. Thus, Aristotle's hylomorphism places him generally at odds with Plato. Hylomorphism is inherently incompatible with dualism. It is true that Aristotle leaves open the possibility that some souls, or some functions of some souls, exist independently of a body. And possibly he even believes that himself. But, if he does, this looks like a strange and perhaps even unaccountable divergence from what is the basic outlook of his philosophy of mind.Yet when they lecture on the Metaphysics, they might say something like the following:
The central books of Aristotle's Metaphysics are a careful examination of substance as form. In these books, Aristotle looks largely at 'sensible' substances, that is, substances that have matter. Yet he thinks that Metaphysics in the proper sense is 'first philosophy', which is concerned with, as he puts it, non-sensible and unchangeable substances. His discussion of sensible substances is meant to prepare the way for his examination in book Lambda of separately existing, non-sensible substances. These are pure forms, which exist without matter.That is, these lecturers ascribe to Aristotle the incompatible view that (i) forms can exist without matter, and that the most important substances are like that (those which, from the point of view of knowledge and explanation, are most basic); yet (ii) forms depend on matter for their existence, and it would be strange and unaccountable to regard some forms as independent of matter.
Chris Shields, in his SEP article, is not so crude as the lecturer I imagine above:
In a fairly direct way, though, the question of whether soul and body are one loses its force when it is allowed that it contains no implications beyond those we establish for any other hylomorphic compound, including houses and other ordinary artifacts.Yet even Shields' discussion leaves something to be desired, because he writes as if the independence of mind from body is a special exception to the doctrine of hylomorphism, pressed upon us, perhaps, by attention to human psychology. There is no suggestion in the above paragraph--as there should be--that Aristotle thought that a careful examination of hylomorphism itself would show that forms could in principle exist independently of matter. (The sentence, "At the same time, Aristotle does not appear to think that his hylomorphism somehow refutes all possible forms of dualism", is misleading through understatement.)
One way of appreciating this is to consider a second general moral Aristotle derives from hylomorphism. This concerns the question of the separability of the soul from the body, a possibility embraced by substance dualists from the time of Plato onward. Aristotle's hylomorphism commends the following attitude: if we do not think that the Hermes-shape persists after the bronze is melted and recast, we should not think that the soul survives the demise of the body. So, Aristotle claims, “It is not unclear that the soul -- or certain parts of it, if it naturally has parts -- is not separable from the body” (De Anima ii 1, 413a3-5). So, unless we are prepared to treat forms in general as capable of existing without their material bases, we should not be inclined to treat souls as exceptional cases. Hylomorphism, by itself, gives us no reason to treat souls as separable from bodies, even if we think of them as distinct from their material bases. At the same time, Aristotle does not appear to think that his hylomorphism somehow refutes all possible forms of dualism. For he appends to his denial of the soul's separability the observation that some parts of the soul may in the end be separable after all, since they are not the actualities of any part of the body (De Anima ii 1, 413a6-7). Aristotle here prefigures his complex attitude toward mind (nous), a faculty he repeatedly describes as exceptional among capacities of the soul.