Maverick Philosopher

Footnotes to Plato from the foothills of the Superstition Mountains

The Logical Problem of the Trinity

Our question concerns the logical consistency of the following septad, each limb of which is a commitment of orthodoxy.  See here for details.  How can the following propositions all be
true?

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

If we assume that in (2)-(7), the 'is' expresses absolute numerical identity, then it is clear that the septad is inconsistent.  (Identity has the following properties: it is reflexive, symmetric, transitive, governed by the Indiscernibility of Identicals).  For example, from (2) and (3) taken together it follows that the Father is the Son by Transitivity of Identity.  But this contradicts (5).

So we have an inconsistent septad each limb of which is a commitment of orthodoxy.  The task is to remove the contradiction without abandoning orthodoxy.  There are different ways to proceed.

In a paper he sent me, Chad M. seems to adopt the following approach.  Distinguish between the 'is' of identity and the 'is' of predication, and construe (2), (3), and (4) as predications.  Well, suppose we do this.  We get:

2*. The Father is divine
3*. The Son is divine
4*. The Holy Spirit is divine.

But this implies that there are three Gods, which contradicts (1).  The trick is to retain real distinctness of Persons while avoiding tritheism.

Chad also blends the above strategy wth a mereological one. Following W. L. Craig, he thinks of the Persons as (proper) parts of God/Godhead.  Each is God in that each is a (proper) part of God/Godhead.  The idea, I take it, is that Persons are really distinct in virtue of being really distinct proper parts of God, but that there is only one God because there is only one whole of these parts.  Each Person is divine in that each is a part of the one God.  The parts of God are divine but not God in the way that the proper parts of a cat are not cats but are feline.  Thus the skeleton of a cat is not a cat but is feline.  The skeleton is feline without being a feline.

But I have a question for Chad.  On orthodoxy as I understand it, God is one, not merely in number, but in a deeper metaphysical sense.  Roughly, God is a unity whose unity is 'tighter' than the unity of other sorts of unity.  Indeed, as befits an absolute, his unity is that than which no tighter can be conceived.  The unity of mathematical sets and mereological sums is fairly loose, and the same goes for such concrete aggregates as Kerouac holding his cat.  Although we are not forced to take the whole-part relation in the strict sense of classical mereology, I think it remains the case that the unity of anything that could be called a  whole of parts will be too loose to capture the divine unity. 

For one thing, wholes depend on their parts for their existence, and not vice versa.  (Unless you thought of parts as abstractions from the whole, which the Persons could not be.)  Parts are ontologically prior to the wholes of which they are the parts.  This holds even in the cases in which the whole is a necessary being and each part is as well.  The mathematical set of all primes greater than 1 and less than 8 is a necessary being, but so is each element of this set: 3, 5, and 7 are each necessary beings.  Still, the existence of the set is metaphysically grounded in the existence of the elements, and not vice versa.  The divine aseity, however, rules out God's being dependent on anything.

So my question for Chad is this: does the view that God is a whole of parts do justice to the divine unity?

 

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19 responses to “The Logical Problem of the Trinity”

  1. Bilbo Avatar
    Bilbo

    I’m not sure if this analogy will help, and it’s probably bad theology, but what if we think of the Father has being the mind; the Son as being the thoughts (words) of the Father; and the Holy Spirit as being the emotions of the Father? The advantage of this analogy is that we can understand how both the Son and the Holy Spirit would be ontologically dependent upon the Father; in a very tight unity with the Father; yet somehow separate from the Father. The problem would be trying to understand how the Son and Holy Spirit are distinct persons from the Father.

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  2. Peter Lupu Avatar
    Peter Lupu

    Bill,
    Could chad construe the part-whole relationship when it applies to substances such as water?
    For instance: one gallon of water is distinct from another, while both are in some sense “parts” of ten gallons from which they were extracted. So construed, both one-gallon poetions when extracted from the whole are distinct; but they are also “parts” of the ten gallon and when the former are mixed in the later, the parts and the whole are indistinguishable.

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  3. Luther Flint Avatar
    Luther Flint

    I’ve always thought the relationship between chapters in a book provides a reasonable analogy for a unity and separateness of parts – an analogy I thought resolved some similar difficulties with regard to Plato’s tripartite notion of soul.

    Reply
  4. Peter Lupu Avatar
    Peter Lupu

    Luther,
    One trouble with the Book-Chapter analogy is that a chapter of a book is not itself a book (unless the book is a collection of books). Yet in the case of the Trinity, each Person is allegedly identical to God.

    Reply
  5. Chad McIntosh Avatar
    Chad McIntosh

    I should qualify my earlier statement that the mereological view consistent with the creeds. There are some creeds a primia facie reading of which is inconsistent with the view. For example, Eleventh Council of Toledo (675) and the Anathasian Creed (8th century) both seem to affirm that each person is “wholly God” himself, and “by himself to be God and Lord,” respectively. If these are understood as identity statements, then inconsistency seems unavoidable.
    I’d be eager to see whether another reading is plausible. But if not, then I say so much for these creeds. What matters most is whether the model is consistent with the Biblical data. Second in line is the Nicene Creed (of 325). And it is consistent with, if not quite congenial to, both. In my mind, only the Councils of Nicea and Chalcedon are non-negotiables for orthodoxy. Much of what comes afterward gets progressively less concerned with systematizing raw Biblical data and testimony and more philosophically speculatory. Though I see them as important and informative, I feel little compulsion to treat them as normative.

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  6. Chad McIntosh Avatar
    Chad McIntosh

    I typed up a long-ish response and submitted it as a comment prior to the one above. I’m assuming it didn’t go through? Sigh…

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  7. Bill Vallicella Avatar
    Bill Vallicella

    Chad,
    I didn’t receive it. If you take a long time composing a response, it is always a good idea to make a copy before trying to upload it.
    Luther,
    Peter’s response to you is correct.
    Peter,
    The skeleton-cat analogy is better. Although the skeleton of a cat is not a cat, it is feline. Analogously, the Persons are not Gods but divine.
    My problem with the mereological approah is that it is not adequate to the divine unity.

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  8. Bill Vallicella Avatar
    Bill Vallicella

    Bilbo,
    Wouldn’t all three Persons have to be minds?

    Reply
  9. Luther Flint Avatar
    Luther Flint

    The are several points that might be made. One might say that trying to find an exact analogy for God/the Trinity is a fool’s errand. How could there be a thing in the world exactly analogous with God? Thus we might say the best that can be done is to offer various analogies, each of which offers something to counter some particular doubt/error or other. And by doing so we might show that doubts about the Trinity are based on crudely thinking of God/the Trinity in terms of things which are quite unlike God and the analogies might be used to show the limitations in that thinking.
    With that in mind, then, we might offer the following three analogies to counter various doubts/errors: a) the same book written in three different languages; b) the same book as written, as read to oneself and as spoken aloud; and c) the Mandelbrot set viewed from three “locations”.

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  10. John A. Avatar
    John A.

    Chad’s proposal approximates to what I have sometimes heard from Eastern Orthodox: viz., the creed’s unity of essence is generic, not numerical; it means each person of the Trinity is divine.
    As you observe, that creates a tension with proposition (1). They answer that there is one God because the Father is one; and the Father is the eternal cause of the Son and the Spirit, and therefore the ultimate cause of all that exists. “God” is not univocal; there is a sense referring to causation in which it applies only to the first person of the Trinity.
    The “one God” is then strictly speaking the Father, not the Godhead or the Trinity (cf. how the creed opens, “I believe in one God, the Father Almighty…”, and the usage of the NT, where God almost always refers to the Father). The Son and the Spirit are subordinate to the Father in respect of deriving their existence from Him; but equal to Him in respect of essence, being divine as he is. The idea at work here is that being uncaused, as well as generating and spirating, are “personal properties” of the Father, not “attributes” belonging to the divine nature as such.
    That way of thinking is rather foreign to St. Augustine’s theology, which the West has generally followed, but arguably it is what the Cappadocian fathers taught. A good resource is Christopher Beeley’s Gregory of Nazianzus on the Trinity and the Knowledge of God (Oxford, 2008).

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  11. John A. Avatar
    John A.

    PS The most relevant section of Beeley’s work consists of pp. 201-217

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  12. Chad McIntosh Avatar
    Chad McIntosh

    Dr. Vallicella,
    At the heart of your post is really three questions. First, does model present a tight enough unity to be orthodox? Second, there is the Anselmian question: is a unity less than “that than which no tighter can be conceived” appropriate for divinity? Third, does the part/whole relationship introduce a dependence relation in the Godhead that’s anathema to aseity?
    Long comments rarely inspire readership, so I’ll only take a stab at the first question in this comment, and reserve comment on the latter two.
    I should say first that the model is wholly consistent with the Biblical understanding of God’s oneness, the defining feature of the Judaic monotheism from which NT and early Christian monotheism is derived.
    As Thomas McCall belabors to show, Biblical scholars are agreed that the Shema (Hear, O Israel, the Lord your God is one”) is “not centered on numerical oneness, nor does it obviously dictate that there is at most one divine person” (Which Trinity? Whse Monotheism?, p. 60). Rather, it is primarily about exclusive devotion to the only uncreated being on whom the rest of creation depends. Ruchard Bauckham: “For Jewish monotheism, tis insistence on the one God’s exclusive right to religious worship was far more important than metaphysical notions of the unity of the divine nature” (The Climax of Prophecy, p. 118). The Jews were monotheistic, to be sure (at least since the period known as “Second Temple Judaism”); but they were not so fiercely Unitarian that Paul, the Jewiest of Jews, had no difficulty including Jesus in the Shema (1 Cor 8:1-6) without compromising its meaning or abandoning monotheism (seen. T. Wright, Climax and Covenant, p. 94, 129; Bauckham, “Biblical Theology and the Problems of Monotheism,” p. 224-229). McCall summarizes: “For the original formulation of the Shema (Deut. 6:4) is not bout the number of tropes of divinity any more than Paul’s reformulation; its primary purpose is to call the children of the covenant to exclusive devotion to the only God there is” (Which Trinity? Whose Monotheism? , p. 63). Tellingly, the same Hebrew word for “one” in the Shema is used to describe the unity between man and wife as “one flesh.” This does not mean God’s oneness is no tighter or deeper than oneness in marriage; rather, God’s oneness serves as the model toward which marriage and communal relationships should strive to emulate).
    This was the concept of God’s oneness at play in early Christian monotheism, and the concept any model of the Trinity should minimally display. And clearly, the model under discussion passes.

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  13. Chad McIntosh Avatar
    Chad McIntosh

    The cat analogy is not being offered as an analogy for the Trinity. It only illustrates how there could be more than one way of being divine (by showing how there is more than one way of being feline).

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  14. Chad McIntosh Avatar
    Chad McIntosh

    Here and below I’ll try to say a few things in response to the Anselmian question: is a unity less than “that than which no tighter can be conceived” appropriate for divinity?
    My short answer is: I’m not sure. The greatest conceivable form of unity is that which is the greatest conceivable form of unity compossible with other divine perfections. If there is a ‘stronger’ form of unity conceivable all by itself, it is not properly a divine perfection, and so is not the greatest. This is why I don’t see divine simplicity as a divine perfection (or at least versions of simplicity that are incompatible with Trinitarianism). The reasoning is straightforward: the Christian God is the most perfect being, exhibiting all the divine perfections there are. The Christian God is not absolutely simple. Therefore, absolute simplicity is not a divine perfection.
    Moreover, absolute divine simplicity is not unity at all. A “unity” by definition unites, or is a uniting of, individuals into a whole. And that is not an illicit use of ‘by definition.’ Absolute divine simplicity, by contrast, unites nothing because it denies of God anything unite-able. There is nothing, no thing(s), to unite into a one, or whole; definitely not things with enough integrity to be considered “persons”.

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  15. Chad McIntosh Avatar
    Chad McIntosh

    Continuing the above thought: “Tightness” is degree of unity between distinct things. I don’t know exactly what maximally-great (i.e., most perfect) tightness between things would be like. But maybe a good place to start thinking about such a relation might be Robert Nozick’s “organic unities.”
    According to Nozick, the degree to which some whole is valuable depends on how intimately and harmoniously related it is with its parts, and how intimately and harmoniously related each of its parts are with the themselves: “the greater the diversity gets unified, the greater the organic unity; and also the tighter the unity to which the diversity is brought, the greater the organic unity” (Nozick, The Examined Life, p. 164). In a very striking passage, Nozick considers the value of persons conceived as organic unities:
    Consciousness and the mind not only enable an organism to unify its activities over time; at any given moment, consciousness is tightly unified with the physical/biological processes then occurring. What we have, then, is an apparently enormous diversity which is unified to a very high degree—that is, we have an extremely high degree of organic unity, hence something extremely valuable. If (degree of) value is (degree of) organic unity, the mind-body problem shows that people are very valuable (The Examined Life, p. 165).
    Obviously nothing turns on whether we think of the organic unity of a person in terms the relation between mind and body or between, say, mind and substance generally (actually, the indivisible unity between nous and immaterial substance would be tighter, and hence greater, than the divisable unity between nous and body). Now apply these insights to a substance in which there are three divine persons, or centers of will and intellect. Not only would the substance of which the persons are parts bring a tight unity to their diversity, each being omniscient and omnipotent, there would be a maximally intimate union of intellect and will between them. It’s hard to conceive of a greater unity than that. But maybe I have a dull imagination!

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  16. Bill Vallicella Avatar
    Bill Vallicella

    >>The cat analogy is not being offered as an analogy for the Trinity. It only illustrates how there could be more than one way of being divine (by showing how there is more than one way of being feline). << Well, then I didn't understand what you were saying in that portion of your paper. I thought you were trying to show that the Trinity doctrine is coherent along these lines: 1. God is a whole of parts. 2. The Persons are proper parts of God. 3. The Persons are distinct in the way the proper parts of a whole are distinct among themselves. 4. To say that, e.g., the Father is God is not to say that the Father is identical to God, but that God is divine. 5. But the Persons are not divine in that each is a God, but they are divine in that each is a part of God. 6. To support (5),the skeleton-cat analogy is given: the skeleton of a cat is not a cat but it is feline. That, I take it, is the argument. Or am I mistaken?

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  17. Chad McIntosh Avatar
    Chad McIntosh

    Dr. Vallicella,
    Your reconstruction of the argument is exactly right. When I think of an “analogy for the Trinity” (both bad and better) I think of things like “water in three states” or “an actor with three roles” or “egg as shell, yolk, and albumen” or “three in one shampoo” or equilateral triangle” or “Cerberus the three-headed dog” or “mas as father, son, and husband” or “lover, beloved, and the shared love,’ etc.
    But the cat analogy, as you rightly note, is being used to offer support for the key claim in the argument. So I wasn’t thinking of it per se as an analogy of for the Trinity in the way the ones mentioned above are. But it’s a minor point, and I have no real qualms with thinking about it that way.

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  18. Bill Vallicella Avatar
    Bill Vallicella

    Chad,
    There is a typo is what I said. In (4), replace the last occurrence of ‘God’ with ‘the Father.’
    But I see we are on the same page re: the mereological approach. Is it primarily due to W . L. Craig?
    My printer crapped out after printing only four pages of your paper, so I didn’t get to the part about the inconsistency of Trinity and simplicity. But I take it that the mereological model you endorse entails that God cannot be absolutely simple.
    I don’t see why a unity must be a uniting of individuals into a whole. You could define ‘unity’that way, but that would be arbitrary. Consider an instant of time or a an extensionaless point. Are they not unities? Some unities are unities of disparate elements. Why must all be?

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  19. Chad McIntosh Avatar
    Chad McIntosh

    Yes, I read (4) as you intended.
    I was aware of arguments that entail that the Persons must be part of God qua Trinity before I discovered explicitly mereological models of the Trintiy, and so I found it quite attractive. The model I summarize in the paper is primarily due to Craig. It has affinities to models Shieva Kleinschmidt considers, but criticizes (“Composition as Identity and the Trinity”) and to the model Keith Yandell defends in several unpublished papers (e.g., “A Metaphysical Structure for the Doctrine of the Trinity”). But Craig’s is by far the most developed.
    Interestingly, I don’t think the model entails that God cannot be absolutely simple. As Craig explains, Trinity Monotheism is “open to various mereological construals, leaving it up to the metaphysician to choose that construal which best accords with his views.” And surely he is right: one need not be a realist about parts and wholes to favor the model. One could maintain, as Craig apparently does, that there really are no such things as parts and wholes; talk of such is merely an indispensable façon de parler. But in the paper–the section that crapped out–I aim to explore whether a mereological model according to which God really does have parts (or, at least, really is a composite) can be harmonized with divine aseity. In other words, whether a mereological model that does entails that God cannot be absolutely simple is consistent with aseity.
    Is an instant of time or an extensionaless point a unity? I would prefer to call them units, or better, simples (simpletons?). But you’re right—my preferred terminology is somewhat arbitrary. I suppose a unit could just as well be defined as a set of disparate elements. Still, something seems conceptually wrong about a “unity” that does not unite—more or less tightly—disparate elements. But if “unity” is neither definitionally composite or simple, your question is the right one: what kind of unity is appropriate for a maximally great being? What do you think of the Nozickian considerations?

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