18 Unconventional Essays on the Nature of Mathematics
Springer-Verlag New York Inc.
978-0-387-25717-4 (ISBN)
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 w- ners. ) None are historians, I regret to say, but there are two historically o- ented articles. These essays don’t share any common program or ideology. The standard for admission was: Nothing boring! Nothing trite, nothing tr- ial! Every essay is challenging, thought-provoking, and original. Back in the 1970s 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 en- tled “Introducing Imre Lakatos” in the Mathematical Intelligencer in 1978.
REUBEN HERSH is professor emeritus at the University of New Mexico, Albuquerque. He is the recipient (with Martin Davis) of the Chauvenet Prize and (with Edgar Lorch) the Ford Prize. Hersh is the author (with Philip J. Davis) of The Mathematical Experience and Descartes' Dream, which won the National Book Award in l983, and What is Mathematics, Really?
A Socratic Dialogue on Mathematics.- “Introduction” to Filosofia e matematica.- On Proof and Progress in Mathematics.- The Informal Logic of Mathematical Proof.- Philosophical Problems of Mathematics in the Light of Evolutionary Epistemology.- Towards a Semiotics of Mathematics.- Computers and the Sociology of Mathematical Proof.- From G.H.H. and Littlewood to XML and Maple: Changing Needs and Expectations in Mathematical Knowledge Management.- Do Real Numbers Really Move? Language, Thought, and Gesture: The Embodied Cognitive Foundations of Mathematics.- Does Mathematics Need a Philosophy?.- How and Why Mathematics Is Unique as a Social Practice.- The Pernicious Influence of Mathematics upon Philosophy.- The Pernicious Influence of Mathematics on Science.- What Is Philosophy of Mathematics Looking for?.- Concepts and the Mangle of Practice Constructing Quaternions.- Mathematics as Objective Knowledge and as Human Practice.- The Locus of Mathematical Reality: An Anthropological Footnote.- Inner Vision, Outer Truth.
| Zusatzinfo | 10 Illustrations, black and white; XXII, 326 p. 10 illus. |
|---|---|
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika |
| Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
| ISBN-10 | 0-387-25717-9 / 0387257179 |
| ISBN-13 | 978-0-387-25717-4 / 9780387257174 |
| Zustand | Neuware |
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