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.