A theology of the possible, part 3
Ross sets forth to establish five major claims in “God, Creator of Kinds and Possibilities,” the first three of which are in refutation of the traditional, theological exemplarism, and the final two in defense of his voluntaristic alternative. His first, anti-exemplarist claim is that “[t]here is not a universal domain of kinds and universal domain of things of the kinds (or a universal domain of exemplar ideas) determined by God’s nature, from which God must choose what to create, nor are there exemplars for empty kind and things” (319). As Ross explains, “[t]he usual explanation of how God comes to have universal exemplars is that God knows, exhaustively, every way in which the divine being can be finitely imitated and finitely participated. these intensional objects form a universal domain of exemplars” (320). The strength of this notion, mistaken though it may be, is that its denial would seem to imply the existence or possibility of “some finite imitation of God that God does not represent to himself, even though it is possible only if he knows it—a contradiction.” For Ross, however, it simply doesn’t make any sense to speak of there being an “every way infinite being can be finitely imitated,” and though he doesn’t himself develop the point further, he says that “[w]e have to deny that God’s self-knowledge is by finite REPRESENTATION to himself” (emphasis original). (Ross’s claim here might be augmented by the phenomenological critique of representationalism of Husserl and Heidegger.)
Instead, Ross focuses on the incoherence of there being “every way infinite being can be finitely imitated,” which he associates with the “ancient idea that the perfection of God can be exhaustively participated by an extensional multitude or even exhaustively represented to God in that way.” Ross quickly traces this idea from Plato forward through Augustine to Leibniz and Spinoza, citing Aquinas as the only “notable exception” to this tradition, notwithstanding the prevalent interpretation of Aquinas to the contrary. Ross gives three distinct reasons why he thinks exemplars, understood as “exhaustive and replete domains,” are incoherent. The first is that they are formally inconsistent, running afoul of certain prohibitions (which Ross doesn’t take the time to elaborate) established in set theory against the possibility of maximal sets (316), obstacles, moreover, that he claims that present-day modal actualists, with all their “universal domains of essences, propositions, states of affairs, and even divine ideas,” have yet to overcome (317).
The second objection to there being a universal domain of divine exemplars lies in its defective understanding and explanation of being. Ross offers two distinct lines of argument here, the first of which is the inconsistency involved in making the “external real relation of participation or ‘exemplification’” responsible for “mak[ing] a thing to be of its kind or to be the individual that it is.” He gives the example of Socrates who, on the exemplarist account, is a human being by virtue of his relation of participation in or being exemplified by the form or divine idea of “being a human.” Yet this is to suggest that there is some initial, pre-human substance, a “bare particular,” that is the subject of this relation, in which the relation of “being a human” is said to inhere and by which relation that bare particular is able to be a human. But Socrates isn’t first a generic, bare particular who afterward gains its status of “being human” by participating in the exemplar “being a human.” If the particular entity that is Socrates were not human from the very beginning of its being, there would be no thing at all that could enter into the relation of “being a human.” Things, consequently, cannot be constituted as the things that they are by some supposed external relation of participation or exemplification to something else.
 For further investigation, however, Ross directs his reader to Loux, ed., The Possible and the Actual, 53, and Fraenkel, “Set Theory,” in Encyclopedia of Philosophy.