In this paper, I will discuss a certain conception of matter that Aristotle introduces in Metaphysics Z3. It is often assumed that Aristotle came to distinguish between matter and form only in his physical writings, and that this lead to a conflict with the doctrine of primary substances in the Categories that he tries to resolve in Z3. I will argue that there is no such conflict. In Z3, Aristotle seems to suggest that matter is what is left over when we strip a thing of all its properties. I take it that he does not want us to strip away these properties by physical means or in our imagination. Rather, we are asked to strip a referring noun phrase of all its predicative parts. We are thus not supposed to be able to refer to something that has no qualities whatsoever, but to construct a phrase that refers to something that has properties without referring to its having them, and without implying which properties it has. The idea that there might be a way of referring to something definite without mentioning any of its qualities is platonic and it still underlies modern predicate logic. In Z3, Aristotle argues against this conception and thus against the basic idea of predicate logic. According to him, matter is at best an inseparable aspect of a primary substance, which substance is best referred to as a compound τóδε τι (“this such”). Matter is what the τóδε refers to as part of this phrase. But it cannot exist in separation from form, and we cannot refer to it by a separated term, without also referring to the substantial form of the substance of which it is an aspect.