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Contrary to a common assumption, I argue that there is full agreement between East and West on the issue of the relation between the divine essence and the divine persons. I defend this claim by using the understanding of universals found in D. M. Armstrong to cast light on the theories. Taking Gregory of Nyssa and John of Damascus as representatives of the Eastern tradition, I show that this tradition sees the divine essence as a numerically singular object that is wholly present in each divine person. The Eastern tradition explicitly sees this object as a universal. The Western tradition – exemplified in Augustine and Aquinas – likewise sees the divine essence as a numerically singular object that is wholly present in each divine person. But this tradition customarily denies that such an object could be a universal, on the merely philosophical grounds that universals are divided amongst the particulars that share them, and thus cannot be numerically one. Having shown the fundamental consonance of the two traditions, I argue by way of conclusion that differences between social and non–social theories of the Trinity depend entirely on the nature and extent of the features that are supposed to distinguish the persons from each other.