Contradiction in the Trinity?

Dr Vallicella has another post about the Trinity, here:

I don't assert, but I suspect that it's directed at least partially at me. He writes:

5. Is the doctrine thinkable (conceivable) without contradiction? . . . It is difficult to get some people to appreciate the force and importance of (5) because they are dogmatists who accept the Trinity doctrine as true simply because they were brought up to believe it, or because it is something their church teaches. Since they accept it as true, no question of its logical coherence arises for them. And so they think that anyone who questions the doctrine must not understand it. To 'set the objector straight' they then repeat the very verbal formulas the logical coherence of which is in question. "What's the problem? There is one God in three divine Persons!" They think that if they only repeat the formulas often enough, then the objector will 'get it.' But it is they who do not get it, since they do not understand the logical problems to which the doctrinal formulations give rise.

I suspect that this is directed at me, or at least that he thinks I'm one of these people. In his reply to my first letter to him he wrote As you no doubt will grant, the mere repetition of verbal formulas is not the same as an exposition of those formulas that shows them to be intelligible. After my response to his reply he wrote off the discussion as not worthwhile, then writes the above. I infer that he thinks my response was nothing more than a repetition of verbal formulas and that I don't understand the logical problem involved. Now I think that my response indicated no such thing. What I was attempting to do, at least, was to clarify the true sense that the verbal formulas hold, rather than a false and plainly contradictory sense. Now this is indeed different from directly showing that the doctrine is coherent. But, as I've already said, analyzing the doctrine must only come after getting the doctrine right. Now I suggest that the reformulations of the doctrine by Dr Vallicella and his sources distort it through the lens of a metaphysics not designed to accommodate it, so that the "logical problem" takes on the character of a petitio principii. I believe that the very way that Dr Vallicella presents the problem begs the question.

Now Dr Vallicella writes that "the gist of the Trinity doctrine is as follows:"

1. Monotheism: There is exactly one God.

2. Divinity of Persons: The Father is God; the Son is God; the Holy Ghost is God.

3. Distinctness of Persons: The Father is not the Son; and the Holy Ghost is not the Father or the Son.

And he follows this up with:

The problem is to show how these propositions are logically consistent, that is, how they can all be true, but without falling into heresy. If you cannot see the problem, you are not paying attention, or you lack intelligence, or your thought-processes are being distorted by ideological commitments.

So, presumably, Dr Vallicella thinks that responses such as the one I gave are not worth responding since I fall under one or all three of these deficiencies. Well, I wouldn't presume to make claims about my intelligence, and if my thought-processes were being distorted by ideological commitments I may well fail to observe it, but the problem is certainly not that I am not paying attention, since I have been studying Latin Trinitarian theology for many years now.

Now it's not that I "cannot see the problem," since there is a prima facie difficulty. How is God both one and three? How are the three identical with the one but not with each other? But the logic of the solution is not very difficult, hardly more difficult than the formulation of the problem. The key is to properly define the terms and distinguish the kinds of identity involved. But once this is done there is no logical problem at all, because the doctrine does not affirm and deny the same thing and in the same respect:

2. Divinity of Persons: The Father is God; the Son is God; the Holy Ghost is God.

It is orthodox to reformulate this as:

2a. Divinity of Persons: The Father, Son, and Holy Ghost are identical with respect to the divine essence.

And now:

3. Distinctness of Persons: The Father is not the Son; and the Holy Ghost is not the Father or the Son.

It is orthodox to reformulate this as:

3a. The Father, Son, and Holy Ghost are distinct with respect to their personally constitutive relations of origin.

So: The divine persons are identical in one respect and distinct in another respect. This is very different from saying "3=1" or "~(things which are equal to the same thing are also equal to each other)".

As far as I'm concerned this dispenses with, at least, any obvious contradiction. The only way to make the contradiction reappear is by importing some such question-begging premise as the one I quoted in an earlier comment thread by Cartwright, from an article cited with approval by Dr Vallicella:

The heretical conclusion [tritheism] follows, by the general principle that if every A is a B then there cannot be fewer B's than A's.

Cartwright claims that this principle "is evident to the natural light of reason," but the examples he gives are not analogous to the case of the Trinity: "Thus, if every cat is an animal, there cannot be fewer animals than cats; if every senator from Massachusetts is a Democrat, there cannot be fewer Democrats than senators from Massachusetts. Just so, if every Divine Person is a God, there cannot be fewer Gods than Divine Persons." But these examples all presuppose a paradigm of the relation of essence to supposit which is explicitly denied in the doctrine of the Trinity, for reasons explained in my last post. In a quote from St Bonaventure I have already pointed out the difference between humanity in Peter and Paul, for instance, and divinity in the Father and the Son. In the first case Cartwright's principle is correct: If every apostle is a man, then there cannot be fewer men than apostles. But the multiplication of apostles involves necessarily the multiplication of individual instances of humanity. On the other hand since deity is not a common nature like humanity, the multiplication of divine supposits cannot be presumed to involve the multiplication of individual instances of deity. Furthermore it should be clear that the claim is not that "The Father is a God," and "The Son is a God, for this formulation, again, presupposes that "God" is a universal and "divinity" a common nature, a "multiply instantiable entity," which I have already denied.*

One may decide that the way that Catholic theology explains the relation of the essence to the divine persons, and their distinction from one another solely according to their personally constitutive relations of origin, is incoherent or otherwise unsatisfying. But in order to do so one must engage this problem and locate the contradiction somewhere further back than where Dr Vallicella does so.

As it stands Dr Vallicella's attempts to grapple with the Trinity are not as off the mark as Dawkins' flying spaghetti monsters or his absurd attempts to refute arguments to a First Cause by resorting to a childish infinite regress argument. The difference, however, is one of degree, not of kind. If Dr Vallicella's aim really is, as stated, to discover whether the doctrine is thinkable without contradiction, then he must attempt to think it as it is thought, without importing foreign premises.

*There is so little danger of Catholic doctrine falling into tritheism or affirming any multiplication of the divine essence that I would be more sympathetic to an objection claiming that the three persons could not be really distinct at all than to this one claiming that they are too distinct to preserve divine unity. After all the word person does not signify a substance at all, but a relation! And the divine persons are defined as internal relations in the one God. Just look at Aquinas, Summa I q.29 a.4: "Distinctio autem in divinis non fit nisi per relationes originis, ut dictum est supra. Relatio autem in divinis non est sicut accidens inhaerens subiecto, sed est ipsa divina essentia: unde est subsistens, sicut essentia divina subsistit. Sicut ergo deitas est Deus, ita paternitas divina est Deus Pater, qui est persona divina. Persona igitur divina significat relationem ut subistentem. Et hoc est significare relationem per modum substantiae quae est hypostasis subsistens in natura divina; licet subsistens in natura divina non sit aliud quam natura divina. Based on texts like this I could give more credence to an objection that there were not really three at all than to the objection that according to this doctrine God is not really one.