Our crisis of foundations: what Tom Wolfe's novel, among other things, brings to mind

National Review, Dec 13, 2004 by John Derbyshire

   ... Great God! I'd rather be
   A Pagan suckled in a creed outworn;
   So might I, standing on this pleasant lea,
   Have glimpses that would make me less forlorn;
   Have sight of Proteus rising from the sea;
   Or hear old Triton blow his wreathed horn.

For all that, I am not quite ready yet to give up belief in the conscious self. Although the neuroscientists are chasing the self through ever narrower and darker passageways of the brain, they have not caught it yet, and there are good reasons to believe they never will. Roger Penrose's book about fundamental physics offers one of those reasons. Physicists have been pursuing matter for much longer, and with much more fruitful consequences, than neuroscientists have been pursuing mind, yet still the nature of physical reality eludes us. What is the physical world composed of? If you make it through the 1,000-odd pages of Penrose's book, through the explanations of tensor calculus, Clifford algebras, spinors, twistors, Riemann surfaces, and Feynman propagators, you may have an inkling, but that is all you will have. If you can't hack all that heavy-duty math, you won't even have an inkling, ever.

Perhaps, for a few decades at least, we can continue to ignore the scientists sapping away at our vulgar metaphysic. Perhaps Hume's prescription of "carelessness and in-attention" will see us through for a while longer. Math professor Michael Harris tells a true story about a conversation held in his presence during a conference in Munster, Germany, last year. Over a restaurant dinner, three professional mathematicians resurrected an issue from the great "crisis of foundations" that racked mathematics in the early 20th century--during roughly the period from Russell's paradox (1901) to Godel's theorem (1931). This crisis arose because mathematicians had begun inquiring into the logical and philosophical underpinnings of their subject, trying to find the fundamental axioms underlying all of math, seeking unshakably firm foundations for the process of mathematical proof.

Well, the three diners all expressed different opinions on the issue in question, which is a very crucial one. ("The ontological status of the continuum"--but you don't need to know this to understand my point.) Harris sought to pursue the discussion down into deeper matters ... but found that his colleagues did not have the necessary knowledge, and didn't actually care. These foundational issues, though interesting in their own right, and fine for a few casual conversational exchanges over the dinner table, do not really matter in the day-to-day work of most mathematicians.

We Americans are heading into a "crisis of foundations" of our own right now. Our judicial elites, with politicians and pundits close behind, are already at work deconstructing our most fundamental institutions--marriage, the family, religion, equality under the law. The human sciences are showing human nature in a strange new light. Yet perhaps all this will matter as little in the daily lives of Americans a few decades from now as Russell's paradox and Godel's theorem matter to working mathematicians today. Perhaps we shall come to our senses and stop trying to analyze and deconstruct our humanity down to the bitter end. Perhaps we shall realize that in order to get on properly with life, as with mathematics, a great many things just need to be taken for granted. What will our new metaphysic be? Perhaps the one that sustained Bertrand Russell's grandmother: "What is mind? No matter. What is matter? Never mind."