Boethius's aim was to derive a rational account of the trinity from purely philosophical sources. Using notions of Being, what-is, and participation, he defines a notions of ontological simplicity and essential predication. The notion is then applied to the question of divine simplicity and to that of the divine perfections. He argues that the relative differences among the Persons cannot have any further grounding beyond the Persons themselves, and that consequently the Personal properties of Paternity, Filiation etc must simply be God. He formulates a criterion for substantial predication as what remains true of its subject no matter how the subject is described. In modelling this theory the semantic methods used for Augustine's theory must be supplemented by a device that assigns members of the domain to the abstract of any name. The ontological structure envisaged by Boethius's account then includes everything in Augustine's account. In addition it requires that the divine Substance, as well as being its own abstract, is the Personal properties, and therefore also stands to the Persons as abstract to concrete.
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