De Trinitate: The Statue/Lump Analogy and the 'Is' of Composition

Thanks to Bill Clinton, it is now widely appreciated that much rides on what the meaning of ‘is’ is. Time was, when only philosophers were aware of this. The fact that Clinton made the point to save his hide rather than to advance philosophical logic is irrelevant.  Credit where credit is due.  But enough joking around.

In our recent Trinitarian explorations we have thus far discussed the ‘is’ of identity and the ‘is’ of predication. We saw that ‘The Father is God’ could be construed as

1. The Father is identical to God

or as

2. The Father is divine.

Both construals left us with logical trouble. If each of the Persons is identical to God, and there is exactly one God, then (given the transitivity and symmetry of identity) there is exactly one Person.  On the other hand, if each of the Persons is divine, where ‘is’ is the 'is' of predication,  then there are three Gods and tri-theism is the upshot. Either way, we end up contradicting a central Trinitarian tenet.

We explored the mereological way out and we found it wanting, or at least I found it wanting.  God is not a whole whose proper parts are the Persons.

But there is also the ‘is’ of composition as when we say, ‘This countertop is marble,’ or in my house, ‘This countertop is faux marble.’ ‘Is’ here is elliptical for ‘is composed of.’ Compare: ‘That jacket is leather,’ and ‘This beverage is whisky.’ To say that a jacket is leather is not to say that it is identical to leather – otherwise it would be an extremely large jacket – or that it has leather as a property: leather is not a property. A jacket is leather by being made out of leather.

Suppose you have a statue S made out for some lump L of material, whether marble, bronze, clay, or whatever. How is S related to L? It seems clear that L can exist without S existing. Thus one could melt the bronze down, or re-shape the clay. In either case, the statue would cease to exist, while the quantity of matter would continue to exist.  If S ceases to exist while L continues to exist, then S is not identical to L. They are not identical because something is true of L that is not true of S: it is true of L that it can exist without S existing, but it is not true of S that it can exist without S existing.   I am relying upon the following principle, one that seems utterly beyond reproach:

(InId)  If x = y, whatever is true of x is true of y, and vice versa.

(This is a rough formulation of the Indiscenibility of Identicals.  A more careful formulation would block 
such apparent counterexamples  as:  Maynard G. Krebs believes that the morning star is a planet but does not believe that the evening star is a planet.)

Returning to the statue and the lump, although S is not identical to L, S is not wholly distinct, or wholly
diverse, from L either. This is because S cannot exist unless L exists. Note also that while S exists it occupies exactly the same space as does L.  As long as S exists, S and L are spatiotemporally coincident.  What's more, they are composed of exactly the same matter arranged in exactly the same way.  And yet they are not identical!  Very curious.  How could there be two physical things in the same place at the same time?  But I have just shown that they cannot be identical.  Suppose that the statue and the lump come into existence at the same time t and pass out of existence at the same later time t*.  At all times they share the same matter, and at no time are they not spatiotemporally coincident. And yet they are not identical because modally discernible.  In our world, L composes S now, but there are possible worlds at which L does not not compose S now.

The fact that there are bronze statues and that the statue and its matter are neither strictly identical nor strictly distinct  suggests the following analogy: The Father is to God as the statue is to the lump of matter out of which it is sculpted. And the same goes for the other Persons. Each Person is to God as the statue is to the lump.  Schematically, P is to G as S to L. The Persons are like hylomorphic compounds where the hyle in question is the divine substance.

Thus the Persons are not each identical to God, which would have the consequence that they are identical to one another. Nor are the persons instances of divinity which would entail tri-theism. It is rather that the persons are composed of God as of a common  substance. Thus we avoid a unitarianism in which there is no room for distinctness of Persons, and we avoid tri-theism. So far, so good.

Something like this approach is advocated by Jeffrey Brower and Michael Rea, here.

But does the statue/lump analogy avoid the problems we faced with the water analogy? Aren’t the two analogies so closely analogous that they share the same problems?   Water occurs in three distinct states, the gaseous, the liquid, and the solid. One and and the same quantity of water can assume any of these three states. Distinctness of states is compatible with oneness of substance. On the water analogy, the Persons are to God as the three states of water are to water. 

Liquid, solid, and gaseous are states of water. Similarly, a statue is a state of a lump of matter.  The main problem with both analogies is as follows.  God is not a substance in the sense in which clay and water are substances. Thus God is not a stuff or hyle, but a substance in the sense of a hypostasis or hypokeimenon.  Beware of equivocating on 'substance.'  And it does no good to say that God is an immaterial or nonphysical stuff.  God is an immaterila being, but he cannot be or be composed of an immaterial stuff.  Besides, 'immaterial stuff' smacks of a contradictio in adjecto.  It sounds like 'immaterial matter.'  Furthermore, the divine unity must be accommodated. The ground of divine unity cannot be amorphous matter whether physical or nonphysical.

In addition, one and the same quantity of H₂0 cannot be simultaneously and throughout liquid, solid, and gaseous. Similarly, one and the same quantity of bronze cannot be simultaneously and throughout three different statues. Connected with this is how God could be a hylomorphic compound, or any sort of compound, given the divine simplicity which rules out all composition in God.

In sum, the statue/lump analogy is not better than the water/state analogy. Neither explains how we can secure both unity of the divine nature and distinctness of Persons.

Related articles

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

Is the Skeleton of a Cat Feline in the Same Sense as a Cat is Feline?

Mereology and Trinity: Response to Wong

A Question About Predication and Identity

Aquinas amongst the analytics

Comments

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I hate being like one of those thickos swinging on their chairs at the back of the classroom who causes everyone to moan when they ask their question. Can you please offer a definition of "person" to help me make sense of the comments you make?

[Bill Vallicella]

In the context of the doctrine of the Trinity, the Persons refer to the Father, Son, and Holy Spirit. The doctrine states that there is one God in three divine Persons. This from the Catholic Catechism:

253 The Trinity is One. We do not confess three Gods, but one God in three persons, the "consubstantial Trinity".83 The divine persons do not share the one divinity among themselves but each of them is God whole and entire: "The Father is that which the Son is, the Son that which the Father is, the Father and the Son that which the Holy Spirit is, i.e. by nature one God."84 In the words of the Fourth Lateran Council (1215), "Each of the persons is that supreme reality, viz., the divine substance, essence or nature."85

Of course, I am a person and so are you. Boethius defined a person as an individual substance with a rational nature.

Nothing in the definition requires that persons be embodied. The God of Christianity is a personal God but wholly immaterial (Incarnation aside).

[Elliott]

Bill,

Thanks for the link. The paper lists some of the better analogies, though I agree with you about the problems with the statue-lump theory. I think it’s best to avoid analogies that use matter. The social and psychological models seem more appropriate. The paper is also a reminder that, although analogies are aids to understanding, analogical reasoning is inductive, hence suggestive and not probative.

It would help to juxtapose definitions of ‘person’ and ‘being' in order to see how three persons could be one being. I am inclined to accept something like the definition of person from Boethius, but I would add free will to rational nature. Why couldn’t one being have three centers of mind and will? In an eerie way, this is almost possible for a human being. Why not possible for God?

[Br. JD]

I think it might be helpful to look at Aquinas' understanding of Persons as "subsistent relations" and I don't know what your thinking on this would be. I agree that we can't treat the Trinity as material substance with Persons as "forms," nor the Persons as proper parts of God. Of course, as you pointed out in an earlier post, the problem is relating "persons" to "nature" in a way that is intelligible. I think the concept of a subsistent relation helps do that in a way that parts or "forms" does not. Aquinas gets to his notion by negating two problematic notions of "processions" found in God - Arius' cause to effect (where the Persons are effects or creatures) or Sabellius' effect to cause (where each Person is merely a different effect of a single cause). Instead, Aquinas notes either of these are processions from internal acts to external acts in matter. However, he uses as exemplary "internal" processions toward internal terms. That's why the psychological analogy is primary - it is a procession from the intellectual agent to an intellectual term (a concept). However, when Aquinas points to the distinction between Person and nature in God, he notes that they aren't really different - whereas in creatures relations are accidental, in God they are essential. So, the subsistent relations are identical with the divine nature (although they have to be separated in our predication because of how we know them - just like other divine perfections being simple in divine simplicity), but they aren't identical with each other. The analogy is the essence or form of something versus its "supposit" or individuation. So, the divine essence is not identical to one Person, but to all three in their mutual relations. Another factor to consider is the lack of distinction between abstract and concrete properties. For Aquinas, the Persons are nothing other than personal properties of God (concrete universals) - the Father *is* paternity, the Son *is* begottenness, and the Spirit *is* procession. Thus each fully is the divine nature, but they are distinct by a kind of relative opposition. The problem is more on the side of our predication, where abstracts cannot stand as substantives. So, it is wrong to say, "Essence begat essence," because that implies that the common properties to all three begat them - which is false. You could say "God begat God" because both are substantives. Aquinas lastly brings this together by making a distinction between relative and absolute properties. The essence of the Godhead is all absolute properties (eternity, wisdom, power, etc.) but the Persons are relative properties and hence not common to all three (although the relative properties are identical with the essence, as we said above). They are subsistent properties mutually distinct by being opposed (as paternity is not the same as filiation or procession, but can only be paternity by having filiation, etc.). Absolute properties are not so opposed, but are really one in divine simplicity. Thus, there aren't an infinity of persons correlated to all absolute properties.

I'd be curious what you think of this kind of solution to the Trinitarian problem.

[Bill Vallicella]

This from the Baltimore Catechism:

24. Is there only one God?

Yes, there is only one God.

I am the Lord, and there is none else: there is no God besides me. (Isaiah 45:5)

25. How many Persons are there in God?

In God there are three Divine Persons – the Father, the Son, and the Holy Ghost.

Going, therefore, teach ye all nations; baptizing them in the name of the Father and of the Son and of the Holy Ghost. (Matthew 28:19)

[Bill Vallicella]

Thanks for your comments, Bro. JD.

I'm afraid I don't see a clear solution to the problem in your remarks. What exactly is a subsistent relation, and how could a person be a relation subsistent or otherwise? Relating what to what?

And then there is the business about supposita, which are brought in to make sense of both Trinity and Incarnation. I find the notion very obscure.

Here is an old post on the topic: http://maverickphilosopher.typepad.com/maverick_philosopher/2010/02/substance-and-suppositum.html

[Bill Vallicella]

Bro JD,

See my latest post for why I have trouble with the Thomist doctrine.