A Trinitarian Trilemma for Deniers of Divine Simplicity

The doctrine of Divine simplicity is closely tied to the doctrine of Divine aseity, and proponents of DDS regularly claim that the doctrine of Divine aseity entails the DDS, for if God had parts, these parts would ground Him, and He would not be a se. Deniers of DDS often reply that God grounds His parts and not vice versa, and so the denial of DDS poses no problem for Divine aseity. But they face the following argument:

1. If God has parts, then the Divine Persons have parts.
2. If the Divine Persons have parts, then they share at least some of those parts with each of the other Divine Persons.
3. If the Divine Persons share at least some of their parts with each of the other Divine Persons, then either (i) those parts are fully grounded by more than one thing or (ii) at least one of the Divine Persons is at least partially grounded by some of that Person's parts.
4. Therefore, if God has parts, then either (i) those parts are fully grounded by more than one thing or (ii) at least one of the Divine Persons is at least partially grounded by some of that Person's parts.

(1) is true because the Divine Persons cannot be simpler than God. The whole force of arguments against DDS is that it is incoherent for anything to be absolutely metaphysically simple. So the denier of DDS can't admit that the Divine Persons are simple while insisting that God is not. (2) is true because if the Persons do have parts, at least some of those parts will be properties that all three of the Persons share in common, such as Their power, or Their knowledge, or Their will. This is confirmed by professions of faith concerning the Trinity in which it is emphasized that although there are three Persons who are omnipotent, there are not three omnipotents (Denzinger §39). And (3) exhausts the possibilities of what could ground what between the Persons and their common parts: for any common part (let's call it O, for concreteness), either more than one Person fully grounds O, or O partially grounds at least one Person. This assumes that grounding is irreflexive and transitive, as commonly believed. One might object here that the each of the Persons might partially ground O, but this certainly can't be the story with some Divine attributes, such as power or knowledge. What would such partial grounding look like? The Divine Persons obviously don't contribute some part of the Divine power or knowledge to God.

(4) can be restated as a trilemma. One of the following must be true:

1. The common parts of the Divine Persons are fully grounded by more than one thing (i.e. there is grounding overdetermination).
2. At least one of the Divine Persons is at least partially grounded by some of that Person's parts.
3. God is simple.

Grounding overdetermination (other than in logical grounding, such as the grounding of a true disjunction in both of its true disjuncts) is bad, and allowing that some of the Divine Persons are grounded by Their parts returns the denier of DDS to the same problem he was trying to escape by claiming that God grounds His parts. So we should accept (iii) and affirm DDS.