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| Douglas Hofstadter's I Am a Strange Loop |
A lot of prior discussion led up to that conclusion. In that previous post and in its three predecessors from this, my "God Is a Strange Loop" series, I leveraged ideas laid out by Douglas Hofstadter in his book I Am a Strange Loop, ideas concerning how a human brain produces a self-referential "I" symbol, into the basis for a theology.
The gist of Hofstadter's notion of the "I" is that it is analogous to the self-referential, externally knowable-as-true propositions lurking in supposedly purely mechanical systems that do nothing but extend a handful of basic axioms into a cornucopia of provable theorems. They do so by means of applying one rule after another, each rule aptly chosen from a small set of rules of inference.
Hofstadter shows that emergent self-referentiality in such "axiomatic systems," as they are called, mirrors the same phenomenon in the brain, which at some level is just an elaborate machine. Hence a brain is just like an axiomatic system in its basic operation, with the system's "theorems" being replaced by the brain's "thoughts."
But certain of the system's self-referential, manifestly true propositions, such as "I am not provable," are not capable of being derived in any systematic, bottom-up way. We see the truth of them, but only from above, as it were. The system itself is blind to their truth.
In the series' previous post, I called this top-down phenomenon "truth bestowal," while Hofstadter calls it by the less grandiose name "downward causation." In that earlier post I glossed over the fact that these two phrases are not really perfect synonyms. For Hofstadter, "downward causation" is only "real" to a limited, nuanced degree, while to me, "truth bestowal" is much more "real" than that — it implies there is a God.
In short, exactly here is where you can begin to see a sliver of daylight coming between my worldview and Hofstadter's.
For Hofstadter, the "reality" of many things that we know about, such as, for example, a rainbow, is due to how our brains evolved. We simply see the world as fundamentally organized into high-level objects, causal patterns, and meaningful categories. A rainbow is a real object, to our brain's way of looking at things, even if it is just a collection of water droplets refracting sunlight into organized hues of color.
To take another example, even though the image on a TV screen is just a bunch of colored pixels, we see in it faces and trees, blue skies and white clouds and the like. Those identifiable, meaningful splotches and blobs in the image are real to us, as long as they behave coherently in the ways we associate with the symbols we have long since built up in our brains for ... well, for faces, trees, blue skies, clouds, and so on.
The categories we viewers impose on the TV image have no causal effect on how the scene develops. But for the creators of the TV program, it is a different story. Imagine the program is a cartoon. The cartoonist imposes order and meaning on the moving picture according to some preconceived mental notion of how the characters and objects represented by the moving blobs and splotches ought to behave. From this perspective, Mickey Mouse or Homer Simpson is much more real to the cartoonist than just a bunch of screen pixels. Their behavior is imbued by the creator with order and meaning.
We, too, impose order and meaning upon our own behavior. We do this in accordance with our idea of how we as individuals — as the special persons we each refer to as "I" — ought to behave. Our brain's internal "I" symbol has "causal potency," says Hofstadter. If our "I" calls for us to, for instance, shake somebody's hand, it arranges for our body to make the proper muscular movements in order to accomplish that. In other words, the ephemeral high-level symbol called our "I" somehow "pushes stuff around" at the lower, physical levels of bodily organization, so that they do its bidding.
I haven't finished reading I Am a Strange Loop yet, but as of chapter 14, it is not clear exactly how Hofstadter thinks the "I" pushes stuff around at lower, more physical levels.
I gather he thinks that the top-down symbols (including the "I") by which a brain comprehends its body and its surrounding world it exists in are genuinely real, but with an asterisk. The asterisk points to, in effect, a footnote which says, "These high-level things of the mind are 'real' only to the extent that they map what's really going on at the lower level of neurons and the chemicals they squirt back and forth at one another millions of times each second."
I think they are "realer" than that. To show why, I'm hoping to concoct an argument that I derive from Hofstadter's own presentation concerning the nature of the "I". It is an argument that answers a question that Hofstadter himself seems to sidestep. Unfortunately, however, it is also an argument that undermines one of my own basic assumptions in this series of posts.
The argument I would like to concoct runs something like this. Hofstadter shows that an axiomatic system that is ostensibly about the truths of number theory — "4 is not a prime number," for example — contains unsuspected self-referential propositions that can be interpreted on another level entirely.
For instance, take the proposition "I, this very proposition, am not provable." This proposition actually exists, Hofstadter shows, as a well-formed formula of the axiomatic system called PM, after Russell and Whitehead's masterwork Principia Mathematica. The proposition is called, by Hofstadter, KG, after the initials of Kurt Gödel, its discoverer.
Of course, KG has a lower-level, number-theoretical meaning within PM as well — one which, as its higher-level meaning suggests, cannot be derived within PM through the application of its rules of inference to other true propositions.
If KG indeed cannot be proven from the bottom up within PM, as "4 is not a prime number" can, then how can we know it is true? As Hofstadter shows, we can arrive at our certainty of KG's truth by virtue of recognizing that if KG were false — if "this" very proposition were in fact provable — an inconsistency would exist within the axiomatic system as a whole.
Such an inconsistency would be like the one rotten apple that spoils the bunch, for once a lie can be proven within any axiomatic system of mathematical logic, every lie can be proven. Hofstadter shows that much quite well, I think.
But what Hofstadter fails to show, I think, is for what reason KG is true. That question is, I would say, distinct from that of why we prefer to reject the alternative proposition that KG is false. We prefer to reject that alternative proposition in order to avoid turning all of mathematical logic into a cocked hat. But what gives us the right to impose that preference of ours on objective "reality"?
The "KG is true" proposition is, as Hofstadter correctly shows, one whose truth must come from outside PM, since it certainly does not come from within. Ergo, the "I" which emerges from within the bowels of the axiomatic system PM, and which makes it possible to construct well-formed formulas like "I am unprovable," is just as blind as the system as a whole to the truth of KG!
Recognition of that fact does not make me terribly happy. The reason is that I have been trying to show that God could be the "I" which emerges from the world-as-a-whole — if we look at the entire world as a entity that is fully analogous to a mechanical system such as PM — in just the same way as each of our brains is also a PM-equivalent machine.
In other words, if the organ inside the cranium of each of us is, at its lowest levels of operation, just as much of a theorem-deriver (or thought-deriver) as PM is, then Hofstadter is right: an "I" can be expected to arise within it, just as one does in Russell and Whitehead's axiomatic system PM, once Kurt Gödel gets through with it. I have simply been trying to extend that notion to consider the world as a whole as if it, too, is (or has) a PM-equivalent brain.
If the world-as-a-whole somehow can be assumed to be "conscious" and to have an emergent "self" or "I" arising from within it, then perhaps the proper name of that "I" is God. This, at least, is what I have been trying to claim in the present series of posts.
But, I now see, my hopeful claim won't work. Why not? Because any "I" that arises from the operation of the world-as-a-whole as if it were some kind of PM-equivalent axiomatic system will necessarily be a "blind I." It will necessarily be blind, that is, to the truth of any propositions about the world-as-a-system that take the form of KG, "I am unprovable."
Hence, adopting if only for the sake of argument the notion that such a "world I" is capable of being generated at all, as a necessarily "blind I" it would fail to provide an essential reason why the world-as-a-system is not riddled through and through with logical inconsistency.
For, if the "world's KG" is true, the system-internal "world I" is unavoidably blind to the reason why.
That leaves us right where we were before: without a vantage point outside the world system from which "the truth of the 'world's KG'" — the truth that is coherence itself — can be bestowed and known.
There must be a reason why the world "prefers" truth and coherence to lies and logical inconsistency. And — unless you turn a "blind I" to the usual presumption that facts have reasons — that reason must come from outside the world. The basis of all logical coherence, a.k.a. "the truth of the 'world's KG'," cannot be derived from within the world-as-a-system itself.
Which suggests that God does not emerge, as I had been hoping to demonstrate, as a sort of "world I." And we are back to a dualistic scenario in which the "mind" of God is wholly separate from the "body" of the world. This is where I was as of the last post in my "Genesis by Experience" series, which I abandoned out of distaste for the mind-body dualism. Instead of continuing to develop that "GBE" philosophy, I embarked on this, my "God Is a Strange Loop" series. Now I fear I will have to go back to the dualism of GBE.
More later ...
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