That subject heading sounds like a title for a post on cutting-edge Trinitarian theology. Not so. Following Richard Cross, Holmes points out (The Quest for the Trinity: The Doctrine of God in Scripture, History and Modernity, 136-7) that Augustine was suspicious of substance as a category for speaking about God. He is explaining Augustine’s famous admission in The Trinity, Book 5, that he doesn’t understand the Greek distinction between ousia and hypostasis. His reasons are philosophical:
“God can never be merely one example of a broader kind of thing [because if he were, the genus of which he was a member would be greater than he, as being God plus other things, and nothing can be greater than God]; ‘substance’ [along with, inter alia, 'essence' and 'person'] is the name of a genus, and so Augustine is profoundly doubtful about language which defines God as substance, or as anything else.”
Holmes doesn’t think there’s an substantive difference between Augustine and the Greeks, since the Greeks would invoke the Creator-creature distinction to distinguish between divine and creaturely ousia, and would stress the “ineffability of the divine ousia.”
Lewis Ayres (Augustine and the Trinity) makes much of this same point in Augustine, arguing (again following Richard Cross) that “Augustine’s idiosyncrasy and theological fruitfulness stem in part from the manner in which he rejects the usefulness of genus and species terminologies for describing the relations between the divine three” (3).
Cross suggests that Augustine assumes the “tree” of Porphyry in his discussion of genus and species. According to Porphyry: “Substance is itself a genus. Under it is body, and under body, animate body, under which is animal; under animal is rational animal, under which is man, and under man are Socrates and Plato and particular men. Of these items, substance is the most general and is only a genus, while man is the most special and is only a species. Body is a species of substance and genus of animate body. Animate body is a species of body, and a genus of rational animal . . . man is a species of rational animal, but not a genus of particular men – only a species. Everything which is proximate before the individuals will be only a species and not also a genus.”
None of this works when explaining the term “person.” It cannot be a genus term, because the Persons have the same nature. Essence is not genus either, of which the persons are a genus, nor is essence a species of which the persons are individuals. The first doesn’t fit because we cannot infer from “three persons” that there are “three essences”; the second doesn’t work because we cannot reason from many individuals to many members of a species to many members of a genus. Species are problematic because a species is divisible into individuals. In each case, “the inherited principles of Trinitarian faith demand patterns of speech that defeat any attempt to interpret these terms according to Porphyry’s logic” (219).
The result is that Augustine introduces genus and species not to do any real Trinitarian lifting but mainly to highlight the difference between God and creatures: “While, when its material and temporal associations are abstracted, this analogy is largely consonant with the account of the Father’s giving rise to Son and Spirit from his own essence that Augustine develops, it is not one that plays any significant role in his Trinitarian discussions here or elsewhere. Its function seems to be primarily rhetorical, emphasizing how far we must depart from genus and species concepts if we are to see the traditional terminology as logically coherent. We have already seen some hints towards a conception of the divine three existing eternally in non-accidental relation; these hints will not, however, be developed by extensive discussion of genus/species terminologies, but by further reflection on what it means for the Son to be ‘God from God’ and ‘Wisdom from Wisdom’ (220).