What Exactly Are the Intra-Trinitarian Relations?

The core of a Trinitarian model is the internal layout of intra-Trinitarian relations. Depending on different metaphysical interpretations of the nature of the relations, various patristic authors have produced different and oftentimes incompatible Trinitarian models, and, consequently, conflicting expositions of the doctrine of the Trinity. In order to elucidate the differences in their Trinitarian theologies, I demonstrate the divergence in their understanding of the divine relations using the contemporary philosophical taxonomy of relations. I analyze the models of Basil of Caesarea, Gregory Nazianzen, and Boethius, and their attempted synthesis by Thomas Aquinas. Each of the patristic Trinitarian models, in spite of being fully orthodox, uses completely different types of relations, which makes them incompatible. One of the results of this incompatibility is the problem of the filioque, which cannot be resolved without addressing the metaphysics of relations.