Is the Trinity brute fact?

1. I suspect many Christians affirm and defend the Trinity because they're supposed to, but not because they find any intrinsic value in the doctrine. The Trinity is often presented as an impenetrable paradox. You have a pious duty to check that box, but it it wasn't a revealed truth, how many Christians would miss it, or even breathe a sign of relief that they no longer had to defend it. Is the Trinity a chore, a nuisance, and intellectual embarrassment? In this post I'll offer a few philosophical musings. 

2. In historical theology there are different models of the Trinity:

i) In Greek Orthodox theology, the Trinity is like a tree trunk with two branches. The Father is the trunk, while the Son and Spirit are offshoots. The Father directly causes the Son and Spirit to exist (albeit eternally and necessarily).

ii) In Latin theology, the Father causes the Son directly and the Spirit indirectly via the Son (the Filioque). So that's a linear conception. Greek Orthodox theologians complain that the Filioque destroys the unity of the Trinity by positing two causes for the Spirit rather than a unified cause for Son and Spirit alike. 

iii) Those are pre-Reformation paradigms. A more recent position repudiates the hierarchical model. Instead it posits that each person is autotheos or God in himself. In Latin and Greek Orthodoxy theology, by contrast, only the Father is autotheos. 

3. Proponents of the Nicene paradigm claim it protects the unity of the Godhead. The Son and Spirit share a common essence with the Father. However, that by itself doesn't have much explanatory value:

i) At best it amounts to generic unity rather than numerical unity. Human beings share a common nature, yet they are separate entities. 

ii) In addition, if the Father can generate at least one divine person, additional to himself, why is there any upper limit on how many he can generate? How does that select for a total of three persons rather than two or four or forty?

4. To contend that each person is autotheos doesn't mean the persons exist independent of each other. Just that one doesn't cause the other two. These don't represent three different points of origin. On this model, they have no causal origin. So they aren't separate in that regard. 

5. Is it a brute fact that God is three persons, no more and no less? It might be an epistemological brute fact. Perhaps the explanation for why there are just three persons is way over our heads. 

Even if that's the case, it doesn't imply that the Trinity is a metaphysical brute fact, in the sense that it's arbitrary. Rather, it's a brute fact in the qualified sense that nothing outside of God explains what God is like. Indeed, we could argue that God is not a brute fact:

i) The existence of a creature is arbitrary because creatures are contingent. A creature could exist or not exist. There could be one more creature or one less creature. In that respect, creatures have a brute factuality that God does not. God's nonexistence is impossible. Moreover, one thing must exist necessarily for anything else to exist. 

ii) Another angle is the perfection of God. God is the way he is because God is perfect, so anything different would be less perfect or imperfect. That's not arbitrary, but represents the culmination of an axiological principle.  

6. These (admittedly) sketchy explanations operate at a higher, more generic level. But do they explain why God is a trinity rather than a binity or quadrinity? Again, this may be out of reach of human reason, but it's worth exploring the question to see how far we can take it. 

7. In physics and ancient philosophy, there's a strong bias towards reductionism. Where the most fundamental component of reality is one. Monadic units. You get down to something ultimately simple and discrete. Absolute unicity is the philosophical ideal.

The Trinity challenges that prejudice. According to the Trinity, relations are more fundamental than units. According to the Trinity, ultimate reality already has structure. It's not organizing isolated units into structures. Rather, reality has structure at rock bottom. So one is not the most fundamental reality. Three is fundamental. 

8. Considered strictly as a number, 3 has some striking properties: 

3 is the only integer which is the sum of the preceding positive integers (1+2=3) and the only number which is the sum of the factorials of the preceding positive integers (1!+2!=3). It is also the first odd prime. A quantity taken to the power 3 is said to be cubed.

http://mathworld.wolfram.com/3.html

To be sure, that's a pure number rather than a numbed object,  but it's still interesting to consider. 

9. A relation is conceptually richer than a unit. And a trinary relation is richer than a binary relation. A binary relation is more elementary. 

10. Thus far the analysis is rather abstract, but suppose we try to visualize it. A reflection is a relation. It takes at least two elements to generate a mirror-image. 

Consider three mirrors arranged in a triangle. They reflect each other. They contain each other.  You couldn't tell which is a reflection of which without a frame of reference. And the mirror images are self-enclosed within the triangle. Internal to that configuration. 

Compare that to arranging four mirrors in a square. In one respect that's more complex because it has an added element, a fourth element. Yet the reflection pattern is simpler because the mirrors stand at right angles to each other, so the reflections are only generated by mirrors directly facing each other. Even though there are four mirrors, they only generate paired reflections, wheres three mirrors capture all three, in a circular reflection. Three mirrors can reflect each other in a way that four mirrors can't. 

So the trinary relation is more ontologically parsimonious, yet more conceptually fecund. Which constitutes a more elegant pattern because it combines superior economy with superior complexity. Hence, there is a containment principle for why more is less and less is more. The binary relation is both ontologically and conceptually simpler. The trinary relation gives you more with less while the quaternarian relation gives you less with more. In that respect the trinary relation is more perfect than a fewer or greater number of constituents.