A Survey of Responses to the Three-In-One Paradox

Philosophers love a paradox, but hate a contradiction. Paradoxes drive inquiry while contradictions stop it dead in its tracks. The doctrine of the Trinity is a paradox threatening to collapse into one  or more contradictions. Put starkly, and abstracting from the complexity of the creedal formulations, the doctrine says that God is one, and yet God is three. Now this is, or rather entails, an apparent contradiction since if God is three, then God is not one, which contradicts God's being one. But not every apparent contradiction is a real one. Hence it is a mistake to reject the doctrine due to its  initial appearance of being self-contradictory. To put it another way, the doctrine is not obviously self-contradictory as some appear to believe. It is not obviously self-contradictory since it is not obvious that God is one and three in the same respect. To see contradictions that are not there is just as much of an intellectual mistake as to fail to see ones that are there.

I should say that I am interested in the general problem of apparent contradictions both in philosophy and out, what contradictions signify, and how we ought to deal with them. My interest in the Trinity is a special case of this general interest. Herewith, a preliminary attempt at cataloging some ways of dealing with apparent contradictions, taking the Trinity as my chief example.

The following catalog divides into two parts. The first five entries treat the three-in-one contradiction as merely apparent, unreal, unproblematic, while the remaining entries treat it as real or unavoidable. But what do I mean when I say that a contradiction is  unavoidable? Let us say that a contradiction has limbs. For example, I am sitting now and I am not sitting now is a contradiction assuming that 'now'  denotes the same time in both of its occurrences. I am sitting now is the first limb; I am not sitting now is the second  limb. A contradiction is unavoidable (avoidable) if we have (do not have) good reasons for accepting both limbs. The example just cited is an example of an avoidable contradiction since there is no good reason to accept both limbs.

But some contradictions seem unavoidable. For example, there is reason to think that a set exists if and only if it has members. But there is  also reason to think that a set -- the null set -- can exist without members. This apparent contradiction is quite different from the one concerning my being seated/unseated. It is not obviously avoidable if it is avoidable at all. I am not saying that this is genuine contradiction; I am saying that it is a plausible candidate for such status.

The Contradiction as Merely Apparent

1. Deny the first limb. In God is one and God is three, God is one is  the first limb. The contradiction is easily dismissed if we simply  deny this limb and embrace tri-theism. This is of course unacceptable to the Christian and indeed to any sophisticated theist. A defensible theism must be a monotheism.

2. Deny the second limb, and embrace radical monotheism along Jewish or Islamic lines.

3. Reject both limbs by rejecting the presupposition on which both rest, namely, that God exists, or that 'God' has a referent. If this presupposition is not satisfied, then the question lapses.

4. Make a distinction between the respect in which God is one and the respect in which God is three. Alphonse Gratry, for example,  distinguishing between nature and person says that God is one nature
 in three persons. (Logic, p. 336) Drawing a distinction between respects is the standard way to defuse a contradiction. But in the case of the Trinity it accomplishes little unless one can explain how the distinguished items are related. Suppose one is told that a certain ball is both red and green at the same time. This is easily  seen to be true if the ball is red in one hemisphere and green in the other. In this case it is clear without further ado how the two  hemispheres are related. Not so in the case of the Trinity.

5. A more sophisticated strategy is to locate an uncontroversial phenomenon in nature that exhibits a trinitarian or binitarian structure. Suppose there is a two-in-one ( binity) in nature. If   uncontroversially actual, then uncontroversially possible, even if we cannot understand how exactly it is possible. The possibility of a binitarian or trinitarian phenomenon in nature could then be used as a model to show, or begin to show, the possibility of the Trinity.

A putative example of a two-in-one is a statue. The statue S and the lump L of matter it is composed of are two things in that L can exist  without S. If S is made of bronze, and the bronze is melted down, then  L will exist without S existing. Even if the lump of bronze and the statue come into existence at the same time, and pass out of existence at the same later time, they are two.  For they are modally discernible: the lump has a property the statue lacks, the property of being possibly such as not to be a statue.  So, for both temporal and modal reasons, lump and statue are not strictly identical.  They are two.

But they are also one thing in that S  just is formed matter. If S and L come into existence at the same time, and pass out of existence at the same later time, then they are spatiotemporally coincident and composed of exactly the same matter arranged in exactly the same way.  That strongly suggests that S and L are the same. 

On the one hand, it seems we must say that S and L are two and not one.  On the other, it seems we must say that they are one and not two.

Perhaps we can say that what we have here is a binity, a two-in-one.  If binities are actual, then they are possible, even if it is not wholly clear how they are possible.  Assuming that the real cannot be contradictory, then the apparent contradiction of a two-in-one must be merely apparent.  If this fifth strategy works, one will come to see that the Trinitarian contradiction is merely apparent, even if one does not achieve full clarity as to how the Trinity is possible. (But of course the transcendence of God ought to insure that much about him will remain beyond the ken of our finite intellects both here below and in  the life to come, if there is one.)

The Contradiction as Unavoidable

6. Take the contradiction to be real or unavoidable -- since both limbs are justifiable -- and as proof that the triune God is impossible and hence   necessarily nonexistent. In other words, adopt the following stance:   (i) there is excellent reason to say that God must be one; (ii) there   is excellent reason to say that God must be three; (iii) it is a   contradiction to maintain that God is both one and three; (iv) therefore, God is impossible, hence nonexistent.

7. Take the contradiction to be unavoidable as in #6 and as proof that God is logically impossible. But instead of inferring from logical impossibility to necessary nonexistence, draw the conclusion that God  exists despite the contradiction. One is reminded of the phrase  attributed to Tertullian: Credo quia absurdum, I believe because it is absurd (logically contradictory). This also appears to be the position  of Kierkegaard. What distinguishes strategy #6 from #7 is that in the former one takes logic as having veto power over reality: one takes the logically impossible, that which cannot be thought without  contradiction, to be really impossible, impossible in reality apart from thought. That is, one takes the finite discursive intellect to be  at least negatively related to extramental reality: nothing can be  real unless it is thinkable by us without contradiction. Strategy #7, however, rests on the assumption that there can be a reality -- the  divine reality -- which is not subject to logical laws which, if this strategy is correct, can only be our laws. What is necessarily false for us can nonetheless be true in reality.

8. Take the contradiction to be real or unavoidable, but also to be true. In both #6 and #7, the contradiction is taken to to be false, indeed necessarily false, but on this dialetheist option, it is a true contradiction.  Accordingly, the Trinity doctrine is a true contradiction!

Are there any other options? Note that the relative identity approach falls under #4.

UPDATE.  Chad comments:

Regarding "are there any other options?" on approaches to the Trinity paradox.

Another option that falls under the 'apparent contradiction' category is mysterianism: the contradiction is apparent only, but the resolution is a mystery, either heretofore or in principle.

Another option, which might stand between the 'apparent contradiction' and 'contradiction' categories, is van Inwagen's relative identity approach: The Trinity is contradictory if the standard logic of identity is correct, apparently contradictory if not.

Yet another option that falls under the 'contradiction' category: To say that a father can beget a son without a mother is a parent [patent?] contradiction.

Chad is right about mysterianism.  That  is a further option under the first category.  I'm surprised I overlooked it.  As for the relative identity approach, this was Peter Geach's before it was van Inwagen's.  But doesn't this approach fall under #4?  I'm not sure why Chad calls his third point a third option.  Furthermore , isn't 'beget' a technical term in Trinitarian theology?  The Son is said to be "begotten not made."  The idea, I take it, is to avoid saying that the Son is created.  If created, then a creature, then not God.  If 'beget' has a technical meaning, why should it be a contradiction to say that the Father begets the Son?

Related articles

The Logical Problem of the Trinity

Comments

[Chad McIntosh]

Dr. Vallicella,

I know of Geach's work on relative identity. But did he ever himself apply it to the doctrine of the Trinity?

I'm still not sure the relative identity response belongs in #4. The strategy in #4 (as well as in the others) still presupposes the standard logic of identity, which is eschewed by relative identity.

Oh oh my third point was a (bad) joke! It trades on a pun between "apparent" and "a parent". Not all of us can make it into Plato and a Platypus Walk into a Bar!

[Bill Vallicella]

Chad,

I think he does somewhere. A quick leaf-through of *Logic Matters* and "God and the Soul,* however, did not turn up anything on the Trinity. I would guess that Geach came to his rel. identity doctrine precisely because he was trying to make sense of the Trinity.

In any case, I'm pretty sure A. P. Martinich's article antedates PvI, but I'd have to check to be sure.

I missed your pun. Thought it was a typo. So you saw the reference to me in the Plato and Platypus book?

[jim]

I am not commenting on the post in question but, for some reason, I couldn't find your email address and I wanted you to respond to a defense of abortion by a philosopher. It's not all the long but interesting and you might want to make use of it as an illustration of a liberal argument for abortion: http://www.assassinationscience.com/abort.html

[Bill Vallicella]

Oh no! Uncle Fetzer, the 9/11 'truther'! I'll take a look at it. Thanks.