Monday, November 16, 2009

Steven E. Landsburg's "The Big Questions"

Steven E. Landsburg is a Professor of Economics at the University of Rochester, where students recently elected him Professor of the Year. He is the author of The Armchair Economist, Fair Play, More Sex is Safer Sex, The Big Questions: Tackling the Problems of Philosophy with Ideas from Mathematics, Economics and Physics, two textbooks in economics, a forthcoming textbook on general relativity and cosmology, and over 30 journal articles in mathematics, economics and philosophy.

He applied the “Page 99 Test” to The Big Questions and reported the following:
In partial penance for killing his wife and children, Hercules agreed to slay the many-headed hydra. But each time Hercules severed a head, two grew back in its place.

On page 99 of The Big Questions, I describe a far more insidious sort of hydra, one that grows vast numbers of new heads almost every time Hercules cuts one off. But they grow back in patterns that a sufficiently clever Hercules can exploit and win the day.

What's more astonishing is that even a very unclever Hercules is guaranteed to win, provided he plays long enough. What's most astonishing is that while Hercules is guaranteed to win, that fact cannot be proven.

Or more precisely, it can be proven only if you assume the consistency of arithmetic (that is, a given arithmetic problem can't have two correct answers) -- something which in turn is unprovable (unless you assume something else equally strong). But we know that Hercules always wins, because we know that arithmetic is consistent -- even though we can't prove it.

We know arithmetic is consistent because arithmetic is not just the manipulation of meaningless symbols -- those symbols are *about* something, and the something they are about is the system of natural numbers, which exists and has properties quite independent of what we can or cannot prove.

I believe that the natural numbers are the starting point for all existence, and there is a sense in which everything is made of arithmetic. In The Big Questions, I've tried to explain what I mean by that, and why I believe it's true.

I'm not sure I'm right, of course -- who but a lunatic could be sure he was right about this sort of thing? But I hope I've shown how ideas from mathematics can potentially illuminate the biggest question in philosophy, namely: Why is there something instead of nothing?

Philosophy poses a lot of other interesting questions, too: questions about the sources of our knowledge and beliefs, the difference between right and wrong, and the best way to live our lives. I've tried to tackle all of these questions with ideas from other disciplines, especially economics, mathematics and physics. And I've resisted no opportunity for an interesting digression along the way.
Read an argument introduced on Page 29 of The Big Questions and peruse the index.

Learn more about the book at The Big Questions website and blog.

--Marshal Zeringue