Medieval interpretations of hylomorphism, in which substances are conceived as metaphysical composites of prime matter and substantial form, are receiving attention in contemporary philosophy. It has even been suggested that a recovery of Aquinas's conception of prime matter as a ‘pure potentiality’, lacking any actuality apart from substantial form, may be expedient in hylomorphic interpretations of quantum mechanics. In this paper, we consider a recent hylomorphic interpretation of non-relativistic quantum mechanics, the theory of Cosmic Hylomorphism, which does not explicitly invoke (...) any notion of prime matter in its original formulation. We argue that prime matter does in fact play a role in constituting and individuating particles in this theory. However, we demonstrate that the notion of prime matter which features in the extended version of Cosmic Hylomorphism that we propose here is distinct from Aquinas's conception of prime matter, inasmuch as it has discrete metaphysical parts. (shrink)