Here’s a simplified criticism of the Aristotelian theory of substance. For Aristotle, a substance has three components: matter, form, and accidents, each playing a different explanatory role. Consider a tree. It’s one thing, but also a member of a particular natural kind, and the subject of various changes through its existence. “Form” answers the question, “What is this?” For a substance to have the form of a tree is just for it to be a tree, by virtue of possessing a certain repeatable, intelligible structure (“software,” as James Ross put it). That form is what abides through the many changes of state undergone by the tree, changes reflected in the various predicates attaching to the tree. Those predicates are the tree’s “accidents,” and while they come in various kinds (e.g., some are “proper accidents,” such as being able to carry out photosynthesis, whereas others are incidental, such as being a certain height, or situated in a particular spatio-temporal location), they’re all united in being distinct from the form, in that whether they obtain or not doesn’t affect the tree’s tree-hood.
Now, it’s important to note that neither form nor accidents can account for the individuality of a particular substance: form can’t, because it’s repeated across every token of the type, and accidents can’t, because they’re so defined as to be incidental to the identity of the substance (the substance isn’t reconstituted every time its accidents change). Rather, a substance’s individuating principle (principium individuationis) is matter; “matter,” on this scheme, answers the question, “Which one?”
What is it about matter that allows it to individuate substances? This is where things get murky for the Aristotelian theory. Imagine that we’re trying to tell if some tree is the same tree that we admired last week on our walk. We do so, invariably, by attending to its accidents — its location, a distinctive branch, a heart with initials carved on its trunk. We can’t know its matter — matter, in abstraction from form, is completely unknowable, for the Aristotelian. Our ability to distinguish out one member of kind from others doesn’t have much to do, in the order of knowing, with matter after all.
Maybe things are different in the order of being, though. The Aristotelian might grant that accidents are the only way for us to individuate substances, but deny that those accidents are what truly constitute the individuality of the substance. After all, he’ll point out, you might individuate me by saying that I’m your college friend who went to Duke Divinity, but we wouldn’t want to say that my individuality as such depends on that contingent fact. In the order of being, then, perhaps matter is just the irreducible thisness (haecceitas, as Scotus put it) that allows us to pick out one thing as distinct from another. But this seems a little strange, too, since by definition matter has no attributes until informed, and indiscernibles are identical. Perhaps matter is simply the condition of possibility for having the kinds of attributes (e.g., spatio-temporal location) that allow us to be individuated? (This locates matter in a kind of Kantian noumenal realm — we have to live as if it existed, even though we can’t say much about it.) But that begs the question of whether we in fact need something called “matter” to make sense of spatio-temporal location, or any other sensible attribute. And anyway, far from being a constant amid change in the manner of form, an individual’s matter seems to be in constant change too. If we identify matter with whatever possesses mass — again, hardly a self-evident claim, but let’s consider it for the sake of argument — then surely we’d have to say that the tree, in its course from seedling to sapling to full-grown specimen undergoes many changes of underlying matter. What questions does an appeal to matter actually answer?
What are the alternatives to matter as the individuating principle, though? An extreme alternative is the one adopted by Leibniz, who bit the bullet and denied that are any accidents — every substance is four-dimensional, a-temporally possessing all of its predicates. (He denies that this negates freedom in ordinary usage — we a-temporally possess some predicates freely and some by necessity.) Here, what the Aristotelian hoped to divide between the orders of being and knowing are combined — what individuates a substance for us is just what individuates it tout court. Another alternative is Hegel’s notion of the “concrete universal,” e.g., a substance kind every one of whose tokens is a distinct individual.