 The theory requires more than the relation of (absolute) numerical sameness or identity. In addition, Koons defines a relation of “real” sameness. Like identity, this relation is reflexive and symmetrical, but unlike identity it is neither transitive nor Euclidian (such that if any x is related to some y and to some z then this implies that y and z are related in that same way). Thus, real sameness is not an equivalence relation (348, 357 n. 5) According to this theory each Person is really the same as the divine nature (God), but not identical to him. But no Person here is really the same as any other Person; all three are really distinct from one another. To summarize: there are four divine realities on this model of the Trinity. The three Persons are so many qua-objects, while God is not. None of these four is really distinct from God; all are really the same as him. Yet none of the four is identical to any of the others (348).