Our question concerns the logical consistency of the following septad, each limb of which is a commitment of orthodoxy. See here for details. How can the following propositions all be
1. There is only one God.
2. The Father is God.
3. The Son is God.
4. The Holy Spirit is God.
5. The Father is not the Son.
6. The Son is not the Holy Spirit.
7. The Father is not the Holy Spirit.
If we assume that in (2)-(7), the 'is' expresses absolute numerical identity, then it is clear that the septad is inconsistent. (Identity has the following properties: it is reflexive, symmetric, transitive, governed by the Indiscernibility of Identicals). For example, from (2) and (3) taken together it follows that the Father is the Son by Transitivity of Identity. But this contradicts (5).
So we have an inconsistent septad each limb of which is a commitment of orthodoxy. The task is to remove the contradiction without abandoning orthodoxy. There are different ways to proceed.
In a paper he sent me, Chad M. seems to adopt the following approach. Distinguish between the 'is' of identity and the 'is' of predication, and construe (2), (3), and (4) as predications. Well, suppose we do this. We get:
2*. The Father is divine
3*. The Son is divine
4*. The Holy Spirit is divine.
But this implies that there are three Gods, which contradicts (1). The trick is to retain real distinctness of Persons while avoiding tritheism.
Chad also blends the above strategy wth a mereological one. Following W. L. Craig, he thinks of the Persons as (proper) parts of God/Godhead. Each is God in that each is a (proper) part of God/Godhead. The idea, I take it, is that Persons are really distinct in virtue of being really distinct proper parts of God, but that there is only one God because there is only one whole of these parts. Each Person is divine in that each is a part of the one God. The parts of God are divine but not God in the way that the proper parts of a cat are not cats but are feline. Thus the skeleton of a cat is not a cat but is feline. The skeleton is feline without being a feline.
But I have a question for Chad. On orthodoxy as I understand it, God is one, not merely in number, but in a deeper metaphysical sense. Roughly, God is a unity whose unity is 'tighter' than the unity of other sorts of unity. Indeed, as befits an absolute, his unity is that than which no tighter can be conceived. The unity of mathematical sets and mereological sums is fairly loose, and the same goes for such concrete aggregates as Kerouac holding his cat. Although we are not forced to take the whole-part relation in the strict sense of classical mereology, I think it remains the case that the unity of anything that could be called a whole of parts will be too loose to capture the divine unity.
For one thing, wholes depend on their parts for their existence, and not vice versa. (Unless you thought of parts as abstractions from the whole, which the Persons could not be.) Parts are ontologically prior to the wholes of which they are the parts. This holds even in the cases in which the whole is a necessary being and each part is as well. The mathematical set of all primes greater than 1 and less than 8 is a necessary being, but so is each element of this set: 3, 5, and 7 are each necessary beings. Still, the existence of the set is metaphysically grounded in the existence of the elements, and not vice versa. The divine aseity, however, rules out God's being dependent on anything.
So my question for Chad is this: does the view that God is a whole of parts do justice to the divine unity?