Here’s an argument that poses a problem for developing a theory of the Trinity:
- For polytheism to be true is for it to be the case that there is an x and there is a y such that (i) x is god (i.e., the predicate “god” applies to x), (ii) y is god (i.e., the predicate “god” applies to y), and (iii) x is not identical to y. In other words, there are at least two gods
- The Son is god (i.e., the predicate “god” applies to the Son)
- The Father is god (i.e., the predicate “god” applies to the Father)
- The Son is not identical to the Father
Therefore, via conjunction introduction and existential generalization on (2), (3), and (4):
- There is an x and there is a y such that (i) x is god (i.e., the predicate “god” applies to x), (ii) y is god (i.e., the predicate “god” applies to y), and (iii) x is not identical to y
- Therefore, polytheism is true
Question: why hasn’t anyone rejected (2) and (3) and introduced a non-distributive plural predicate “(are) god” that applies to a plurality of things taken together without applying to any of them individually (or understood “god” to be a “multigrade” predicate that can be used in such a way)?
Compare: Jones, Smith, and Mary are such that they are carrying the casket, but none of them is individually such that they are carrying the casket.
This needn’t incur an ontological commitment to a fourth divine thing (a “group”) so long as plural logic is irreducible to singular logic.
NOTE: I submitted this draft post unintentionally, but since it already generated some discussion in the comments, I decided to leave it up.
Great argument. Going to be thinking about this one all day.
Here’s a very preliminary response. Deny 1 by saying that your two ways of phrasing 1 are not equivalent unless you assume that if there are two individuals that exemplify F, then there are two Fs. That’s a metaphysical claim about individuation of attributes, not just a logical one. It seems to usually be the case, but unless it can be proven, the Trinitarian can just deny that it applies to the predicate “God.”
William of Auxerre considers a similar problem, and that’s roughly his answer. I’m on the phone or else I’d quote the text. It’s in the second part of the Prologue to the Summary Aurea. In his own terms, he says that among created things distinct individuals make for distinct instances of a nature, but this can simply be denied for uncreated things.
Another response, more likely to be heretical: deny that the Persons are individuals in a strictly logical sense, while somehow maintaining that they are persons in a meatier sense of the term that satisfies orthodoxy.
As to your question: This is very close to the view called Partialism. But orthodox Trinitarian theology affirms that the Father is God and the Son is God (and so considers Partialism heretical). So that wouldn’t solve the problem for the orthodox view.
There is a similar strategy in the literature which says that the composite of the three persons is god. This is one way of construing Craig’s view, though if I remember correctly he’s cagey about whether the persons are parts of God. See also Daniel Spencer’s paper “Social Trinitarianism and the Tripartite God.”
I guess I should clarify that Spencer doesn’t defend the view I described, but his paper is relevant.
First, the Trinity theorist ought to simply deny the first premise, because according to the Trinity theorist (1) polytheism is false, and (2) the Father is God, the Son is God, and the Father and the Son are not identical. As far as I can tell, (1) and (2) are unavoidable, and so there’s already a premise in the argument that the Trinity theorist will have to reject – a naive characterization of polytheism.
But second, once we consider a non-distributive plural predicate “are God”, such that “the Father and the Son are God” is true, we have to consider a new naive characterization of polytheism. Here’s the naive, plurality-theoretic characterization of polytheism:
This characterization of polytheism is no less plausible than the first one. But given this characterization of polytheism, the pair of claims
(a) the Father and the Son are God, and
(b) the Father is not identical to the Son
entail (plural) polytheism. So I think the problem resurfaces once we adopt your recommended solution to the argument.