Jul 9, 2022

west coast math for romantics

Stephen Budiansky, in Journey to the End of Reason: A Life of Kurt Gödel:

Gödel’s public renown continued to grow after his death, notably boosted by the improbable 1979 bestseller Gödel, Escher, Bach by Douglas Hofstadter, which sought to weave Gödel’s proof into an exploration of self-referential form in art, music, and ideas, but which contained not a word about the man himself. The general idea that there are truths that cannot be proved had an irresistible appeal that far outran Gödel’s actual proof, helping to secure him a place, as the American mathematician and writer Jordan Ellenberg put it, as “the romantic’s favorite mathematician.”

Well—it me. Busted. When I encountered the Incompleteness Theorem, I was just blown over by its sheer beauty as an idea. I’m not alone, seems like, and not always to good effect:

Like Heisenberg’s Uncertainty Principle and Einstein’s Theory of Relativity, Gödel’s Incompleteness Theorem has provided what Alan Sokal and Jean Bricmont, in their takedown of postmodernism, called “an inexhaustible source of intellectual abuse,” invoked by theologians, literary theorists, architects, photographers, academic deconstructionists, pop philosophers, and mystics of all kinds to prove everything from the existence of God to the nature of free will, the structure of poetry, and the phenomenon of human misery.”


Gödel himself, to be sure, was not always quite as scornful as his fellow logicians have since been of such interpretations. “It was to be expected after all that my proof would be made useful for religion sooner or later,” he wrote his mother in 1963, “for that is doubtlessly supportable in a certain sense.” But probably more wrong things have been said about his proof than any other mathematical theorem in history, a dubious distinction—if perhaps an inevitable consequence of popular fame in a field such as mathematics.

In the end, it comes down to this:

The fact that there might exist truths forever beyond human reach is…not necessarily the cause for philosophical alarm and despair it was taken to be by some. As the philosopher Robert Fogelin observed, skeptics about the extent of human knowledge come in two types, facetiously categorized as East Coast skeptics and West Coast skeptics, according to their relative degree of laid-backness. “East Coast skeptics recognize that their knowledge is limited,” Fogelin said, “and this troubles them deeply. West Coast skeptics recognize the same thing but find it liberating.”