introduction to “18 unconventional essays on the nature of.docVIP

Introduction to “18 Unconventional Essays on the Nature of Mathematics” Reuben Hersh This book comes from the Internet. Browsing the Web, I stumbled on philosophers, cognitive scientists, sociologists, computer scientists, even mathematicians!—saying original, provocative things about mathematics. And many of these people had probably never heard of each other! So I have collected them here. This way, they can read each other’s work. I also bring back a few provocative oldies that deserve publicity. The authors are philosophers, mathematicians, a cognitive scientist, an anthropologist, a computer scientist, and a couple of sociologists. (Among the mathematicians are two Fields Prize winners and two Steele Prize winners.) None are historians, I regret to say, but there are two historically oriented articles. These essays don’t share any common program or ideology. The standard for admission was: Nothing boring! Nothing trite, nothing trivial! Every essay is challenging, thought-provoking, and original. Back in the 70’s when I started writing about mathematics (instead of just doing mathematics), I had to complain about the literature. Philosophy of science was already well into its modern revival (largely stimulated by the book of Thomas Kuhn). But philosophy of mathematics still seemed to be mostly foundationist ping-pong, in the ancient style of Rudolf Carnap or Willard Van Ormond Quine. The great exception was Proofs and Refutations by Imre Lakatos. But that exciting book was still virtually unknown and unread, by either mathematicians or philosophers. (I wrote an article entitled “Introducing Imre Lakatos” in the Mathematical Intelligencer in 1978.) Since then, what a change! In the last few years newcomers— linguists, neuroscientists, cognitive scientists, computer scientists, sociologists--are bringing new ideas, studying mathematics with new tools. (George Lakoff-Rafael Nunez, Stanislas Dehaene, Brian Butterworth, Keith D