Tuesday, June 5, 2007

Critique of I Am a Strange Loop's Central Premise

Posted by Jeff Lipshaw

First, l love this book.  There, I've said it.  It is deeply personal and idiosyncratic and touching and hopeful. I also think Douglas Hofstadter's image of perception and consciousness is a powerful one:  the mind as inordinately complex universal machine capable of considering its own existence.  But I have Dughof also gotten to the point where Hofstadter's use of the Godelian analogy as a theory of everything does not work for me.  In Chapter 20, he creates a dialogue between Strange Loop #641 ("a believer in the ideas of I Am a Strange Loop") and Strange Loop #642 ("a doubter of the ideas of I Am a Strange Loop.")  Hofstadter is a close friend of Daniel Dennett, and the cross-influence is apparent here.  Hence, he is committed to the idea that consciousness must be subordinate to physical law - there's no transcendental anything.  Nevertheless, the complex universal machine that is the human brain has evolved to the point that it is capable of considering itself and creating what seems to be a very real, yet in fact an illusory, "I".

To Hofstadter, the power of Godel's proof is its mapping of meta-arithmetic within arithmetic itself, creating a system in which mathematics can think about itself in the language of mathematics.  Moreover, the system is recursive and infinite.  And computer language has the capability of being infinite and universal, almost but not quite human.  And I don't have any issue with Hofstadter's characterization of the way each "I" may contain parts of another "I."  Indeed, SL #642, the skeptic, is a straw man, and is not posing the right questions.

It's clear now that Hofstadter is committed to the idea that physics must trump any notion of Kantian autonomy.  We are free only in the same way that chess only seems like a game and not a calculation:  it's too complex to fathom all the moves.  That's notwithstanding Hofstadter's own contagious energy and sparkle and sense of mystery.  But more troubling is that he ignores one of the more significant parts of the analogy to Godel.  SL #641, Hofstadter's alter ego, says:

One thing that gives people a sneaking suspicion that something about this "I" notion might be mythical is precisely what you've been troubled about through our discussion - namely, that there seems to be something incompatible between the hard laws of physics and the existence of vague, shadowy things called "I"'s.  How could experiencers come to exist in a world where there are just inanimate things moving around?  It seems as if perception, sensation, and experience are something extra, above and beyond physics.

But what did we spend much of the book considering?  Godel proved, using the logic of Principia Mathematica itself, that there could be a true formula within the formal logical system of PM that was not decidable (i.e., neither the formula nor its negation was provable).  Hence, the formal system was not complete; indeed, no consistent formal logic system could be complete, and no formal system could provide proof of its own consistency.  To paraphrase Hofstadter, "how could an undecidable but true formula of PM come to exist in a world where, by axiom, true formulas were the result of derivation only by rules of inference from axioms or other provable formulas?"  The answer is:  we don't know.  All we know is that paradox is something that seems to be part of our world, and even if we get everything just about complete and consistent, there's still another turtle at the end of some infinite regress somewhere.  Why not transcendental or metaphysical?  I'm willing to stay agnostic on the question.

I'm afraid there's nothing new under the sun.  Hofstadter says:  "[F]or a few people the battle starts to rage:  physics versus 'I'.  And various escape hatches have been proposed, including the notion that consciousness is a novel kind of quantum phenomenon, or the idea that consciousness resides uniformly in all matter, and so on.  My proposal for a truce to end this battle is to see the 'I' as a hallucination perceived by a hallucination, which sounds pretty strange, or perhaps even stranger:  the 'I' as a hallucination hallucinated by a hallucination."  Therein lies the giveaway.  He proposes to end the battle that started when Kant observed there did seem to be an autonomy within the person apart from and able to act upon physical cause, and a fundamental dualism to the way the world is organized that will never be the subject of a truce, all by the nature of reason itself.  The Gordian knot is that we have a world in which even formal logic has an unresolvable paradox in its midst.  A truce is precisely what we'd get:  a cessation of hostilities but no resolution to an unresolvable battle.  Unlike SL #642, I'm not all that troubled about whether my "I" exists and does so solely within me.  I'm more troubled Professor Hofstadter (who I admire deeply) failed to account for the reality that Godel demonstrated but did not explain the very existence of paradox.

UPDATE:  An Aussie by the name of Darby Higgs has let me know that he is collecting commentary on IAASL.

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Comments

You do realize that it was this sort of thing that sent Phaedrus in Pirsig's _Zen And The Art Of Motorcycle Maintenance_ round the bend, yes?

Posted by: simon Pride | Jun 5, 2007 6:32:34 PM

As you point out, there is a lesson to be learned here from Godel when it comes to the mind/body duality. The reductionist view of consciousness is analogous to the attempt in Principia Mathematica to reduce mathematical truth to the mere formal manipulation of symbols. The existence of Godel's self-referential formula showed that this is a permanent duality - truth and formalism cannot be unified. Similarly, the self-referential nature of our subjective experience at least suggests this split between the subjective and objective worlds. Hofstadter does not provide the needed proof for the reductionist case; I remain agnostic as well.

Posted by: Matt Pulver | Jun 16, 2007 11:12:25 AM

Matt, I'm drawing to the end of IAASL, and Hofstadter's antipathy to dualism really only shows up in the second half of the book.

As you point out, there's no proof. Certainly not in the formal logical sense. And not in the scientific sense of a falsifiable theory. To "prove," as H asserts, that the "I" is a powerful, but necessarily illusion, he would have to provide a TESTABLE theory about the appearance of self-referential consciousness through complexity (extremely high huneker, as he puts it). So he is in this instance a philosopher, not a scientist, albeit a touching and affecting one, trying to push the round peg of his mysterious soul - particularly after the death of his wife - into the square hole of reductionist science.

The fact is we are all looking for a satisfactory way to make sense of the world. H is assuming an Ockham's Razor preference to unitary theories over "dual theories," but as you point out, even unitary theories have this (minute) point of inexplicable or unprovable or undecidable paradox. H has not turned self-reference on himself to ask the question why he is so sure the explanation has to be unitary. So it's not clear to me that unitary theory has it over dual theory even from a simplicity standpoint. I think Kant's dualism is just as elegant as H's unitary theory, and does a better job of dealing with our own consciousness than, say, Manicheanism.

But he is a lot of fun. (I sent him a link to my critique and got a nice response that said he read and would love to debate it, but doesn't have time.)

Posted by: Jeff Lipshaw | Jun 17, 2007 4:54:54 AM

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