Mystery, Trinity, and symmetry

I'm going to post some things I said in a recent email exchange. Quotations are italicized.

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i) In general, I think the only justification we need to invoke a paradox is just in case we have good, independent reasons for affirming both relata of the paradoxical relation.

Put another way, does the problematic nature of the paradox outweigh the evidence for the respective relata which generate the paradox?

I don’t see that there’s any standing presumption to that effect.

And, by the same token, I don’t see that this is distinctive to theological propositions. Surely there are examples in science, mathematics, and logic where one is warranted in affirming a paradox if one has good, independent reasons for affirming the relata.

And that doesn’t justify a willy-nilly appeal to paradox. A paradox would have to meet the precondition of well-attested relata (“attested” by reason or evidence).

ii) Turning to specifics, I realize that it sounds like special pleading or a cop-out for Christians to justify a theological paradox on the grounds that our finite minds can’t grasp the infinite nature of God.

Yet if, ad arguendo, the mode of divine existence really is sui generis, or if the divine nature really is (in some sense) “infinite,” or if the hypostatic union really is sui generis, then it’s not surprising if that would be somewhat impenetrable to human understanding.

Sure, it sounds a little too convenient to say that, but it follows from the nature of the proposition, does it not?

Even if, from an atheistic standpoint, we’re just discussing this for the sake of argument, then I still don’t see that this is even implausible.

They may think the existence of God is implausible, but if such a God exists, then is this paradoxical situation implausible?

Of course, speaking for myself, I prefer to gloss the numerical identity of the Trinity enantiomorphically. And that doesn't generate a prima facie contradiction between singularity and multiplicity.

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I grant you that if I have good grounds for believing both limbs of an apparaent contradiction, then I have good grounds for thinking that the apparent contradiction is merely apparent. (You make roughly this point against Tuggy in your excellent article.) And so I seem entitled to suppose that there is a point of view from which the apparent contradiction will be resolved. Thus when the Flatlander gets to 3D heaven and sees cones for the first time, then he grasps how circles and triangles can coexist.

But the problem for me and Peter is the identity of the Trinitarian proposition that will resolve the apparent contradictoriness of the Trinitarian propositions that we have before our minds here below. Which proposition is that? You cannot specify it. You can only gesture toward it in a general sort of way. How can I accept a proposition that I cannot get before my mind in proprie persona? How can I be required to believe something I know not what?

How can I believe a proposition the identity of which is unknown to me?

Posted by: Bill Vallicella | Tuesday, February 23, 2010 at 06:50 PM

http://maverickphilosopher.typepad.com/maverick_philosopher/2010/02/another-look-at-andersons-trinitarian-mysterianism-peter-lupu.html?cid=6a010535ce1cf6970c01310f3231e5970c#comment-6a010535ce1cf6970c01310f3231e5970c

At the risk of being simple-minded, it seems to me that he answered his own question when he said "I grant you that if I have good grounds for believing both limbs of an apparaent contradiction, then I have good grounds for thinking that the apparent contradiction is merely apparent."

If belief in the Trinity involves belief in several individually intelligible propositions, then you can know what you believe by believing the individually intelligible propositions which comprise belief in the Trinity.

His objection seems to be that unless you can understand how the propositional relata are logically related, then you can't believe the relation.

Well, in a sense that's true. If the propositional relation is unintelligible or apparently incoherent, then, in that sense, it is not an object of belief.

However, that admits two qualifications.

i) The relation is not entirely opaque, for even if the specific proposition surpasses comprehension, the general idea of what constitutes a contradiction is intelligible, and if we know what it means to recognize and affirm a contradiction, we also know what it means to recognize an apparent contradiction and/or disaffirm a real contradiction.

ii) There's a difference between believing something because I can see it for myself, and believing something because it is vouched for by a reliable second party.

We believe many things on authority which we are in no position to see for ourselves.

That's an indirect belief in the proposition. I believe in the person who says it. Therefore, I believe what he says.

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Okay, call this Problem A. The logical problem I address in my book
(call it Problem B) is how to reconcile the following statements, all
of which appear to be essential to the doctrine of the Trinity (and
taught in Scripture):

(1) There is only one God.
(2) The Father is God.
(3) The Son is God.
(4) The Spirit is God.
(5) The Father is not the Son.
(6) The Father is not the Spirit.
(7) The Son is not the Spirit.

I think that formulation suffers from a fallacy of equivocation since "God" doesn't have the same meaning in (1) that it has in (2-4). In (1) it's being used to single out the particular entity who is God. In (2-4) it's being used as a synonym for "divine."

Strictly speaking, the Trinity is "God" whereas the persons of the Trinity are "divine."

Mind you, I'm not so naive that I confuse a linguistic harmonization with a logical or conceptual harmonization.

But it seems to be that this formulation conceals some conceptual ambiguities. If the Trinity is apparently contradictory, then the contradiction is more subtle than the 7-point formulation successfully captures, for I think we can reformulate that statement in a way that's superficially consistent.

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But the problem remains however you
disambiguate it. For if there is only one divine entity (the 'God' of
(1)) and the Father is divine -- that is, a divine entity -- then it
seems the Father must be identical to God. But the same goes, mutatis
mutandis, for the Son and the Spirit. Yet according to (5-7) the
Father, Son, and Spirit are distinct entities. Hence the problem. In
short, we want to say both that there is only one divine entity but
also that there are three divine entities.

But it seems to me that this simply shifts the ambiguity to another equivocal formulation. If we use "divine entity/ies in each case, yet when we try to unpack the term as it applies in each case, then wouldn't the sense of (1) amount to something like: "there is only one unique set of divine entities who share the same attributes"?–whereas, in (2-4), it would mean something like "the Father (Son, Spirit) has all and only those divine attributes which make him a member of the unique set of divine entities"?

(5-7) would refer to non-identity at the level of the subset, which is compatible with identity at the level of the set, viz., "Each member of the set is not identical to another member of the set, but all members collectively (and necessarily) constitute the set of members."

I hope I'm not being pedantic. But in order to posit an apparent contradiction, the formulation has to be unequivocal.

Now, perhaps we could say that my set/subset formulation fails to capture everything we need to say about the intraTrinitarian relations, but, if so, then that underscores the difficulty with any simple formulation of the Trinity. And to the extent that any thorough and accurate formulation of the Trinity will be complicated and highly qualified, that, in turn, complicates the appearance of a contradiction.

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One of the problems is that, in Trinitarian jargon, "being," "nature," "essence," and "substance," tend to be used interchangeably.

But "being" is ambiguous since I think, it ordinary usage, we're more likely to use "being" as a synonym for "subsistence" rather than "substance."

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Daniel Howard-Snyder wrote a good article explaining why social
trinitarian models are unsatisfactory (he's targeting in particular
the version offered by Moreland and Craig):

http://www.ac.wwu.edu/~howardd/trinitymonotheismpc.pdf

Section 4.3 nails the problem, in my view. In fact, the argument
could be further strengthened by an examination of the way the OT
consistently speaks about Yahweh. But let me know what you think.

It’s a repetitious article. For now I’ll concentrate on two issues:

“Consequently, the property of being triune is an essential property of God, in which case it is a property of the divine nature. But if the property of being triune is a property of the divine nature, then none of the Persons exemplifies the divine nature; for none of them exemplifies the property of being triune.”

i) I don’t think we can avoid saying that while the property of triunity is a divine property, this is not a property which any one person has in his possession–although I think there is another way to capture that property (see below).

For isn’t this just another way of saying the Father lacks the property of sonship, the Son lacks the property of fatherhood, and so on (for the Spirit)? No one person is the Trinity (without further qualification).

It seems to me that this is a primitive datum of the Trinity. It’s not a result of our formulation. Rather, it’s a datum which our formulation must take into account.

ii) At the same time, I also don’t think it’s accurate to speak of each person as an “exemplification” of a divine nature. Poythress makes the same mistaken when he speaks of the persons as “instances.”

That treats the divine nature as something over and above the persons. A generic, ulterior universal. I think that’s the wrong model for the Godhead. Rather, that applies to the Creator/creature (exemplar/exemplum) relation.

“For on their view, there exists exactly one God, namely the Trinity ‘as a whole,’ and no Person is absolutely identical with the Trinity ‘as a whole.’ Rather, each Person is a proper part of the Trinity ‘as a whole.’”

i) There’s an obvious problem with explicating the Trinity as a part/whole relation.

ii) Mind you, we have to make allowance for the limitations of ordinary language at this point.

iii) It might be objected that my set/subset comparison does the same thing. However, I wasn’t using that as a full-blown model of the Trinity. I was merely using that to illustrate the ambiguities of identity.

iv) I think it would be preferable to view the persons as analogous to mutual permutations. In that sense, each permutation “contains” the corresponding permutations. Each permutation is mirrored in the other–as symmetrical (but incongruous) iterations.

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1.One of the issues is how we conceptualize the Trinity when we try to make sense of the Trinity.

For example, many people find it hard to consider pure abstractions. They need concrete illustrations. They need to “visualize” the idea.

But to picture something is to picture a spatial object. And in the nature of the case, any such object will tend to have discrete boundaries and surfaces. So three such objects will be external to each other. Even if they share a common boundary at one point, they are still apart from each other in terms of spatial relations. They are “beings,” individuals, or particulars in that sense.

2.But if God subsists outside of time and space, then the persons of the Godhead can’t be external to each other in that sense.

3.This raises the question of what kinds of analogues we should use to model the Trinity. The obvious candidates are abstract objects and mental entities. Abstract objects are necessary “things” which subsist outside time and space. Thoughts are personal and immaterial.

And, indeed, as you know, there’s a sense in which thoughts and abstract objects are mutually defining. Abstract objects are best understood as mental entities, but mental in a timeless and necessary mode of subsistence.

4.Let’s use the term “abstract structure.” Take the Mandelbrot set.

People find that fascinating in several respects. In one sense, it’s a simple object. For it consists of self-similar figures. Yet, in another respect, this is a complex object inasmuch as the permutations are infinite.

5.There is also a difference between the way we display the Mandelbrot set (i.e. a graphic computer simulation), and the way it exists in itself.

6.The Mandelbrot set embodies an internal set of mathematically logical relations. These internal relations are necessarily given.

Each permutation is logically implicit in the others. I don’t mean “implicit” in the sense of “latent.” Rather, each permutation “images” the other. And for any permutation to obtain, they must all obtain–given their mutual entailments.

7. One limitation with this particular analogue is that, to my knowledge, the self-similar relations of the Mandelbrot set are congruous. In that respect they lack any distinctive property to distinguish one permutation from another–other than pure replication. However, it’s different with mirror symmetries.

Keep in mind that I’m not a mathematician or crystallographer. So there could be some inaccuracies in the way I’m putting this, or in the specific illustrations I’m using. But I think the general principles are true.

8.If we conceptualize the Trinity as an abstract structure or abstract symmetry, of the right type, and if by “abstract” we include “mental,” then it seems to me that this model is not reducible to a group or set of “beings” in the crude sense.

The persons are not external to each other. Rather, the persons are like logical permutations of each other. Self-similar, but incongruous (in the technical sense).