18 Unconventional Essays on the Nature of Mathematics

by Hersh, Reuben

• ISBN13: 9780387257174
• ISBN10: 0387257179
• Format: Paperback
• Copyright: 2005-11-08
• Publisher: Springer Verlag

Summary

"This new collection of essays edited by Reuben Hersh contains frank facts and opinions from leading mathematicians, philosophers, sociologists, cognitive scientists, and even an anthropologist. Each essay provides a challenging and thought-provoking look at recent advances in the philosophy of mathematics, demonstrating the possibilities of thinking fresh, sticking close to actual practice, and fearlessly letting go of standard shibboleths."--BOOK JACKET.

Author Biography

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?

Table of Contents

Introduction	vii
Reuben Hersh
About the Authors	xvii
A Socratic Dialogue on Mathematics	1	(16)
Alfred Renyi
``Introduction'' to Filosofia e matematica	17	(20)
Carlo Cellucci
On Proof and Progress in Mathematics	37	(19)
William P. Thurston
The Informal Logic of Mathematical Proof	56	(15)
Andrew Aberdein
Philosophical Problems of Mathematics in the Light of Evolutionary Epistemology	71	(26)
Yehuda Rav
Towards a Semiotics of Mathematics	97	(31)
Brian Rotman
Computers and the Sociology of Mathematical Proof	128	(19)
Donald MacKenzie
From G.H.H. and Littlewood to XML and Maple: Changing Needs and Expectations in Mathematical Knowledge Management	147	(13)
Terry Stanway
Do Real Numbers Really Move? Language, Thought, and Gesture: The Embodied Cognitive Foundations of Mathematics	160	(22)
Rafael Nunez
Does Mathematics Need a Philosophy?	182	(19)
William Timothy Gowers
How and Why Mathematics Is Unique as a Social Practice	201	(19)
Jody Azzouni
The Pernicious Influence of Mathematics upon Philosophy	220	(11)
Gian-Carlo Rota
The Pernicious Influence of Mathematics on Science	231	(5)
Jack Schwartz
What Is Philosophy of Mathematics Looking for?	236	(14)
Alfonso C. Avila del Palacio
Concepts and the Mangle of Practice Constructing Quaternions	250	(39)
Andrew Pickering
Mathematics as Objective Knowledge and as Human Practice	289	(15)
Eduard Glas
The Locus of Mathematical Reality: An Anthropological Footnote	304	(16)
Leslie A. White
Inner Vision, Outer Truth	320
Reuben Hersh