Strange Loops and Theology, Part 1: The Gödelian Swirl of Self

One of my favorite authors is Douglas Hofstadter. I first encountered his work when I picked up his 1979 Pulitzer-Prize winning Gödel, Escher, Bach: An Eternal Golden Braid (henceforth, GEB). In GEB, Hofstadter meditates on the idea of self-reference and how it seems central to consciousness and meaning.

In his recent book I Am a Strange Loop Hofstadter picks up those themes he left off in 1979. I'd like to take a few posts to theologically ruminate on I Am a Strange Loop.

First, my apologies to Dr. Hofstadter. From what I can tell from his writings Dr. Hofstadter is not a religious person, so he may object to his ideas being borrowed for a theological purpose. If, however, Dr. Hoftadter does find his way to this page I hope he finds my interaction with his ideas a deep form of compliment. Again, I am a big fan of his books.

GEB is mainly a reflection on Kurt Gödel's famous incompleteness theorem. Simplifying greatly, Gödel was able to embed self-reference in what what then considered to be a mathematical system of iron-clad logical rigor, Russell and Whitehead's Principia Mathematica. Today, Gödel's theorem is considered to be one of the most important logical, philosophical, and epistemological breakthroughs in the history of world. I encourage you to explore it further. Pecs' recommendation of Rebecca Goldstein's Incompleteness: The Proof and Paradox of Kurt Godel is a good place to start.

The idea of self-reference is common enough. It even has biblical roots. Paul in Titus 1:12 says,

Even one of their own prophets has said, "Cretans are always liars..."
Given ancient sources we know the person Paul is referring to: The Cretan philosopher Epimenides. Consequently, the self-referential paradox surrounding Epimedides' statement is called The Epimedides Paradox or The Liar Paradox.

The paradox is easy to see. If Epimenides is a Cretan and he utters the statement p--"Cretans are always liars"--then what is that truth-status of p?
If p is true then Cretans are not always liars which means p is false: A contradiction.
The contradiction is due to self-reference. The simplest way to see this is in the old-standby:
This sentence is false.
You see the paradox. If the sentence is false then it's true. If it's true then it is false.

Again, the paradox is due to self-reference, the sentence points to itself. The point about Gödel's theorem was that Gödel was able to embed self-reference into the system of Principia Mathematica, making the PM-system speak about its own truth/proof status.

But Gödel's breakthrough was not just simply about self-reference. Rather, Gödel's proof was able to create a new level of analysis. That is, Gödel's paradox came via a higher-order coding system, a new level of meaning, which could "speak about" a lower level of meaning. The outcome was still paradoxical and self-referential, but it came via a higher-order, nested structure. A structure, Gödel later proved, that would continue on Ad infinitum. Kind of like logical Russian dolls.

What does all this have to do with us?

Well, Hofstadter contends that this idea of nested self-reference is what gives rise to human consciousness, our symbols, and our sense of self. It is our ability to reflect on reflections that pulls us up, cognitively speaking, from being simply stimulus-response creatures. That is, I can have a thought, then wonder about that thought, then wonder about that wondering... Emotionally, I can feel guilty and then feel guilty about feeling guilty and then feel stupid for feeling guilty about feeling guilty... It's like Gödel's self-referential Russian Dolls, with new meanings produced at each new level of nested self-reference. Hofstadter has some great labels for this process. He calls it the "Gödelian swirl of self." But mainly he calls us Strange Loops: Self-reference looping back on itself to create new meaning. In the words of Hofstadter we Strange Loops are "self-perceiving, self-inventing, locked-in, mirages [which] are little miracles of self-reference."

How all this relates to theology will take some unpacking. More to come. In the meantime, think of loops, Russian Dolls, and the miracle of your self-referential mind.

BTW, psychologists are always liars and this blog post is false.

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7 thoughts on “Strange Loops and Theology, Part 1: The Gödelian Swirl of Self”

  1. I love reading things which stretch my imagination, cause me to step out into thin air and see what happens.

    Your blog is like that for me.

    However, I probably should save my reading for when I don't have the flu :)


  2. I'm back to reading your blog. I had a brief hiatus between defending and starting my new job. One comment on incompleteness: Maybe you are going to make a similar move as Stephen Hawking in using incompleteness to argue against unifying theories tieing gravity with quantum theory? That our formulations of reality will always be incomplete?

  3. Richard,

    Alas! We meet ourselves coming and going. Hofstadter's strange loops and nested self-reference sounds a lot like self-contained bio-feedback. This kind of self-reflection, in my opinion, can work in isolation but actually works better in community. Theologically it is phrased this way: "we are members of one another."

    What's the difference between solipsism and self-reference? Much of the theological individualism we see around us and which is actually stimulated and shaped by commercial nihilism is actually solipsistic and dissociative. My take on Hofstadter is that his thinking is not solipsistic.

    Psychologists are not always
    liars. After all, Freud said:
    "Sometimes a cigar is just a cigar." And sometimes it isn't.


    George C.

  4. Hofstader is great, his AI stuff is really cool.

    Have you read Metamagical Themas? A friend in college read me the story written by self-referential sentences and I was hooked.

  5. Sue,
    Get well soon!

    Welcome back. I don't think I'll being doing anything more with Godel, but I was unaware of the connection with GUTs.

    Actually, this whole series is going to move in the communal direction in a very interesting way.

    I have read Metamagical Themas. Regarding AI, the most intersting book of Hoftadter's in that area, IMHO, is Fluid Concepts and Creative Analogies. That book has more of his technical work in AI so it's not for the faint of heart. But you, being a computer guy, might like it.

  6. This reminds me of the lyrics of mewithoutYou's "Wolf Am I (And Shadow)!":

    "She was graceful and green as a stem,
    But I walk heavy on delicate ground
    (Oh, there I go, showing off again,
    Self-impressed by how well I can put myself down!
    And there I go again, to the next further removed level
    Of that same exact
    Feigned humility!)

    (And this for me goes on and on to the point of nausea...)"

    Though, I would perhaps contend that we cannot observe ourselves in COMPLETENESS, or that is, we cannot observe the part, at the very least, that is currently observing - or can we? I would think that Gödel's theorem would imply this as well.

    This is probably why we require the input of others and are typically so deceived about ourselves - and why God's view of us is the most important one to have.

  7. In fact, it seems to me that we only observe the version of ourselves that existed but a slight moment ago - perhaps a "planck length" of time before, or however that is measured?

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