'Frege' on the Trinity

Peter Lupu writes,

The following are some recent thoughts about the Trinity. Let me know what you think.

The three expressions of the Trinity: ‘The Father’, ‘The Son’, and ‘The Holy Spirit’ all refer to the same divine being namely God. Thus, with respect to reference, each pair of expressions forms a true identity. However, they have different senses in Frege’s sense. The three senses are as follows:

1) The sense of ‘The Father’ is the will of the divine being to love, atone, and forgive. Call this the divine-will.  

2) The sense of ‘The Holy Spirit’ is the will of a non-divine being when and only when it genuinely aspires to be like the divine with respect to its moral identity and worth. Call this the inspired-will.

3) The sense of ‘The Son’ (i.e., the person of Jesus) is when the divine-will and the inspired-will coincide in a human person such as Jesus. Thus, Jesus is a moral-exemplar (Steven’s term) of a case when the divine-will and the inspired-will seamlessly coincide.

The senses of the three expressions of the Trinity are different. Therefore, while identities among each pair with respect to their senses are false, identities with respect to their referents are true.

It warms my heart that  a Jew should speculate on the Trinity on Good Friday.   Rather than comment specifically on the senses that Peter  attaches to 'the Father,' 'the Son,' and 'the Holy Spirit,' I will  address the deeper question of whether the logical problem of the orthodox doctrine of the Trinity can be solved by means of Gottlob Frege's distinction between the sense and the reference of expressions.

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 and by the Necessity of Identity).  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.  Here I consider only one, the Fregean way.  (Of course, Frege himself did not address the Trinity; but we may address it using his nomenclature and conceptuality.) 

The Fregean solution is to say that 'Father,' 'Son,' and 'Holy Spirit, are expressions that differ in sense (Sinn) but coincide in reference (Bedeutung).  Frege famously gave the example of 'The morning star is the evening star.'  This is an identity statement that is both true and informative.  But how, Frege asked, could it be both?  If it says of one thing that it is identical to itself, then it is true but not informative because tautological.  If it says of two things that they  are one thing, then it is false, and uninformative for this reason.  How can it be both true and nontautological? 

Frege solved his puzzle by distinguishing between sense and reference and by maintaining that reference is not direct but routed through sense.  'Morning star' and 'evening star' differ in sense, but coincide in reference.  The terms flanking the identity sign refer to the same entity, the planet Venus, but the reference is mediated by two numerically distinct senses.  The distinction allows us to account for both the truth and the informativeness of the identity statement.  The statement is true because the two terms have the same referent; the statement is informative because the two terms have different senses.  They are different modes of presentation of the same object.

Now let's apply this basic idea to the Trinity.  To keep the discussion simple we can restrict ourselves to the Father and the Son.  If we can figure out the Binity, then we can figure out the Trinity.  And if we restrict ourselves to the Binity, then we get a nice neat parallel to the Fregean example.  The Frege puzzle can be put like this:

a. The Morning Star is Venus
b. The Evening Star is Venus
c. The Morning Star is not the Evening Star. 

This parallels

2. The Father is God
3. The Son is God
5. The Father is not the Son.

Both triads are inconsistent.  The solution to the Fregean triad is to replace (c) with
c'.  The sense Morning Star is not the sense Evening Star.

The suggestion, then, is to solve the Binity triad by replacing (5) with
5'. The sense Father is not the sense Son.

The idea, then, is that the persons of the Trinity are Fregean senses.  To say that the three persons are one God is to say that the three senses, Father, Son, Holy Spirit, are three distinct modes of presentation (Darstellungsweisen) of the same entity, God.

Why the Fregean Solution Doesn't Work

Bear in mind that we are laboring under the constraint of preserving orthodoxy.  So, while the Fregan approach is not incoherent, it fails to preserve the orthodox doctrine.  One reason is this.  Senses are abstract (causally inert) objects while the persons of the Trinity are concrete (causally efficacious).  Thus the Holy Spirit inspires people, causing them to to be in this or that state of mind.  The Father begets the Son.  Begetting is a kind of causing, though unlike empirical causing.  The Son loves the Father, etc.  Therefore, the persons cannot be Fregean senses.

Furthermore, senses reside in Frege's World 3 which houses all the Platonica necessary for the semantic mediation of mental contents (ideas, Vorstellungen, etc.) in World 2 and primary referents in World 1.  Now God is in World 1.  But if the persons are senses, then they are in World 3.  But this entails the shattering of the divine unity.  God is one, three-in-one, yet still one.  But on the Fregean approach what we have is a disjointed quaternity: God in World 1, and the three persons in World 3.  That won't do, if the task is to preserve orthodoxy.

At this point, someone might suggest the following.  "Suppose we think of senses, not as semantic intermediaries, but as constituents of the entity in World 1.  Thus the morning star and the evening star are ontological parts of Venus somewhat along the lines of Hector Castaneda's Guise Theory.   To say that a sense S is of its referent R is to say  that S is an ontologcal part or constitutent of R.  And then we can interpret 'The Morning Star is the Evening Star' to mean that the MS-sense is 'consubstantiated' (to borrow a term from Castaneda) with the ES-sense.  Thus we would not have the chorismos, separation, of senses in Worldf3 from the primary referents in World 1: the senses would be where the primary referents are, as ontological parts of them. 

But this suggestion also violates orthodoxy.  The persons of the Trinity are not parts of God; each is (identically) God.  No proper part of a whole is identical to the whole.  But each person is identical to God.

I conclude that there is no Fregean way out of the logical difficulties of the orthodox Trinity doctrine.  If so, then Peter's specific suggestion above lapses.

 

Comments

[Leo Carton Mollica]

Thanks for the post.

"If we assume that in (2)-(7), the 'is' expresses absolute numerical identity, then it is clear that the septad is inconsistent."

What, though, if we say that it expresses relative identity, so that we get

8. The Father and the Son are the same God, and
9. The Father and the Son are not the same Person?

Would this help matters, or would it just confuse them?

[Leo Carton Mollica]

Also, would nor Mr. Lupu more immediately be guilty of the heresy of Modalism?

[Bill Vallicella]

Leo,

Thanks for the comments.

I think you are right about Peter being a modalist heretic. It occurred to me that the Fregean approach is a version of modalism, but I'll have to review modalism to be sure.

The topic of relative identity is a huge separate topic which ought to be discussed separately. Peter Geach favors the rel. identity approach.

[Account Deleted]

Of course I am a heretic: isn't that obvious! But a modalist? No!

Modalism is the view that the three persons of the Trinity are aspects, modes, or some other manifestations of the one God. Fregean senses, for better or worst, are not merely aspects inherent in an object. They have independent existence, albeit not of the same kind as the referent. They serve as propositional constituents quite apart from the state of affairs that house the referent. They are the material from which truths (not necessarily truth-makers) are made.

The Fregean suggestion about the Trinity is that the three persons of the Trinity are the stuff (senses) from which true *propositions* about the one God are made. Yet the only truth maker of these propositions is one God, not three anything.

Of course, I have no clue whether the Fregean approach satisfies all elements of the orthodox creed. I do not know whether any suggestion would do so. In light of such a possibility, a very real one, something must give, perhaps slightly nudge the orthodoxy. The question is: What?

[Richard E. Hennessey]

You said, Bill, "Bear in mind that we are laboring under the constraint of preserving orthodoxy." Why so labor? Would we so labor in the case of, shall we call it, orthodox Venusology?

To give up the orthodox view of the Trinity, rather than preserve it, is not even to give up Christianity. The heterodox view that sees the Son as the first creature, and so not identical with with the Father as the creator, is yet, for all its heterodoxy, a Christianity.

[Bill Vallicella]

Peter,

I grant that you can reasonably claim not to be a modalist. (But it depends on what exactly modalism is, which is a large separate discussion. Tuggy at his blog has a lot to say about it.)

The trouble with your comment is that you don't seem to see that I have refuted the Fregean approach. You correctly point out that senses are constituents of Fregean propositions. But then you ignore the two arguments I gave which are contained in the first two paragraphs under *Why the Fregean Solution Does Not Work.*

[Bill Vallicella]

Richard,

The precise question I am addressing is whether the consistency problem posed by the orthodox Athanasian understanding of the Trinity (click on the link to the Richard Cartwright article in the main body of my post) can be solved by invoking Frege's sense-reference distinction. That alone is what the post is about.

But of course one could solve the problem in other ways. One way is by abandoning all or part of the orthodox position. Another way is to hold on to orthodoxy by making some distinction or distinctions that defuse the contradiction.

Your suggestion, according to which the Son is the first creature, might count as a version of Christianity, but then again it might not. Central to and definitive of Xianity is the Incarnation: God becomes man in Jesus of Nazareth. Now if the Son (the 2nd person of the Trinity) is the first creature -- and is therefore NOT "begotten not made" -- then it is not God but a creature who becomes man. And that would not sit well with Christian soteriology according to which man's salvation can be brought about only by God.

[Edward the Ockhamist]

Hello Bill, and happy Easter to you and everyone. If I am not mistaken, this resolution of the problem of the Trinity is one that is discussed, and rejected, by Boethius in his treatise on the Trinity, here http://www.logicmuseum.com/authors/boethius/boethiusdetrinitate.htm#sedhocinterim . He asks whether ‘Father’ and ‘Son’ are different words referring to the same thing in the way that different words for ‘sword’ (Latin: ‘mucro’ and ‘ensis’) refer to the same thing. He says not, for “Father, Son and Holy Ghost are indeed the same, but not identical. For to those asking, "is the Father identical to the Son?" they (i.e. Catholics) say, "not at all." Again, to the question, "is the one the same as the other?" the answer is no.”

It seems to me that he is considering, and rejecting, something similar to the Fregean 'way out'

[Edward the Ockhamist]

PS I discuss Boethius' solution to the problem in a post here http://ocham.blogspot.com/2010/09/boethius-treatise-on-trinity-is-one-of.html . I don't think his own solution is any better, however - see the post for my reasons.

[Account Deleted]

EO,

Good seeing you and happy Easter. Will read the stuff as time permits.

[Bill Vallicella]

Happy Easter, Edward. That is an awful translation full of typos and other mistakes. I skimmed it quickly and found a half-dozen errors.

Some philosophers distinguish between identity and sameness. If one makes such a distinction then one could say that the Father is not identical to the Son but is the same as the Son. That would be a different proposal, distinct from the Fregean one.

Heraclitus said, "The way up and the way down are the same." That makes good sense if you distinguish sameness from identity. The way up and the way down are certainly not identical, but they are the same in the sense of being necessarily co-implicative parts of one whole.

Not that this will rescure Athanasian trinitarianism from the jaws of incoherence.

[Edward the Ockhamist]

Thank you Bill. The translation is by Kenyon. I note a problem with it in the blog posting linked above, together with my own suggested correction.

Geach's 'relative identity' resolution is an interesting one that we could profitably discuss.

[Bill Vallicella]

Edward,

Just took a quick look at your post. You set up the problem very nicely in your opening paragraph: the universal church would appear to demand of us that we accept a logical contradiction on pain of eternal damnation in the case of nonacceptance.

One question: how can one's salvation depend on intellectual assent to a proposition? Second, how can one accept a contradictory proposition? As Peter has said in the past, an uninteliigible proposition is no proposition at all.

Later I hope to address the Boethian way out.

[Account Deleted]

Bill,

I concede your refutation of the Fregean solution to the Trinity in light of orthodoxy. I will ponder the matter further.

[Gian]

Dorothy Sayers found nothing mysterious in Three-Persons-in-One considered as aspects of the Creative Mind. She went as far as claiming that this is intuitive to all creative artists. She also interprets Imageo Dei as man's capacity to create.
So Father is mapped to Idea (of the creative work), Son to Energy or Activity that realizes the work in time and Spirit to the Power of the work. This is not philosophy I suppose but interesting nonetheless.

[Account Deleted]

Gian,

Sayers view is a form of modalism or aspect-theory that contradicts orthodoxy.

[Gian]

She claims to take this analogy from St Augustine, though. .