Friday, February 18, 2011

On Gödel himself

We have seen, throughout history, and perhaps especially of late, the phenomenon of the monomaniac, the homo unius notionis, with his One Big Idea.  He rides it through all the talk shows, he remolds it and reworks it, and sends it out to do battle with the issues of the day, as they crop up; however distant they might be to his central conception.  (“`Soft power’, anyone?  ‘Soft power’?”)
            Had Gödel been a small man, he might have become Mr. Undecidability, after his most famous result.  “So, professor, what about this Iraq business?” “Y’know, Bob, it’s like I said in my famous paper.  The situation on the ground is like, just plain --undecidable!”  (Chuckles all around;  cut to commercial break.)  But instead, Gödel maintained (as summarized in HaoWang ,  Reflections on Kurt Gödel (1987), p. 193), that “there exist no number-theoretical questions undecidable for the human mind.  Hence, the human mind surpasses all machines.”
            That stance is part of what Wang calls Gödel’s optimism.  Again, given Gödel’s status as the discoverer of mathematics’ most celebrated negative result, and the slayer of the Hilbert program, one might intellectually expect the opposite; and, given the dreadful psychological cross he had to bear, which eventually led to his death by inanition, a more Kierckegaardian view might have been anticipated. Yet he embraces an intellectual optimism, not because of his intensely reticulated logical constitution, but to some extent despite it. As Wang puts it (op.cit, p. 193): “I find these propitious projections   a strange piece of inductive generalization … mov[ing] from accidental successes in very limited areas  to an anticipation of universal success.”

God rest his soul.

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