In Treatise 1.4.3, Hume gives his account of broadly Aristotelian and scholastic philosophy, and it's an interesting insight into early modern views of the 'schools'. (Early modern philosophers often don't really elaborate much on what they see as the problems with the schoolmen, so it's nice to have an actual account.)
Hume takes Peripatetic philosophy to be fundamentally motivated by two problems.
(1) the problem of how a composite thing can be one (simplicity)
(2) the problem of how a changing thing can be the same (identity)
These are not minor problems; Hume thinks they are genuine and quite serious, and that there is no easy solution to them. We do in fact face apparent contradictions in both these cases, since we psychologically tend to elide similar and related perceptions but are at the same time able to recognize them as distinct. The 'ancient' way of handling this has at least an initial promise, although Hume thinks it ultimately fails: "feign something unknown and invisible" which remains the same through the variations and one in the composition. 'Feign' is a semi-technical term for Hume; the result of feigning is a fiction in something much like the sense of a 'legal fiction' and the original meaning of the Latin term: a thing made, a construct. We construct this unknown invisible something and suppose it to exist. This unknown invisible something is substance or prime matter. (Hume is not alone among early modern critics of scholastic philosophy in not making a sharp distinction between substance and matter.) This does have the apparent advantage of navigating the contradiction:
The peripatetic philosophy asserts the original matter to be perfectly homogeneous in all bodies, and considers fire, water, earth, and air, as of the very same substance; on account of their gradual revolutions and changes into each other. At the same time it assigns to each of these species of objects a distinct substantial form, which it supposes to be the source of all those different qualities they possess, and to be a new foundation of simplicity and identity to each particular species. (T 1.4.3.6, SBN 221)
This line of thought naturally leads to the notion of 'accidents'. We never find colors, sounds, tastes, shapes, and the like in isolation, which means that, if we are supposing substances, we always find them associated with substances, and "The same habit, which makes us infer a connexion betwixt cause and effect", that is, on Hume's account custom based on constant connection, "makes us here infer a dependance of every quality on the unknown substance" (T 1.4.3.7, SBN 222). Once we have accidents, though, we have room for 'occult qualities' and 'faculties' or causal powers, which are accidents that are themselves only supposed and not known or ever experienced. And the tendency to attribute human psychological movements to the world around us leads from there to things like 'sympathy' and 'horror vacui' to top it all off.
All of this, on Hume's basic empiricist principles, is untenable. We get unknown somethings piled on unknown somethings. Because of the copy principle, if we don't ever have any experience of something, we have no actual idea of it. Assigning words to these unknown somethings gives us the illusion that we know what we are talking about when in reality, we don't. And by the separability principle, anything that can be conceived of distinctly can exist separately, so the entire justification of substance and accidents, and the notion of 'inherence in a substance' becomes completely unworkable.
Hume's actual criticisms depend almost entirely on these two principles, so rejecting them both (which any Aristotelian would) will evade the objections he specifically identifies. It is, however, an interesting (and unusual) attempt actually to give an account of basic ideas in Aristotelian philosophy and explain why they would be initially attractive.
