Tuesday, June 5, 2007
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 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.