Details
18 Unconventional Essays on the Nature of Mathematics
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96,29 € |
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| Verlag: | Springer |
| Format: | |
| Veröffentl.: | 16.01.2006 |
| ISBN/EAN: | 9780387298313 |
| Sprache: | englisch |
| Anzahl Seiten: | 326 |
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Beschreibungen
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.
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.
<P>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?</P>
<P>Advance praise for 18 Unconventional Essays on the Nature of Mathematics:</P>
<P>"I was pleasantly surprised to find that this book does not treat mathematics as dessicated formal logic but as a living organism, immediately recognizable to any working mathematician."</P>
<P>- Sir Michael Atiyah, University of Edinburgh</P>
<P>"A wonderful collection of essays on the philosophy of mathematics, some by mathematicians, others by philosophers, and all having significant things to say. Most readers will be informed, some will be infuriated, but all will be stimulated."</P>
<P>- John H. Conway, John von Neumann Distinguished Professor of Mathematics, Princeton University</P>
<P> </P>
<P>This startling 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.</P>
<P>The following essays are included:</P>
<P>* Alfred Renyi: Socratic Dialogue</P>
<P>* Carlo Cellucci: Filosofia e Matematica, introduction</P>
<P>* William Thurston: On Proof and Progress in Mathematics</P>
<P>* Andrew Aberdein: The Informal Logic of Mathematical Proof</P>
<P>* Yehuda Rav: Philosophical Problems of Mathematics in Light of Evolutionary Epistemology</P>
<P>* Brian Rotman: Towards a Semiotics of Mathematics</P>
<P>* Donald Mackenzie: Computers and the Sociology of Mathematical Proof</P>
<P>* Terry Stanway: From G.H.H. and Littlewood to XML and Maple: Changing Needs and Expectations in Mathematical Knowledge Management</P>
<P>* Rafael Nunez: Do Numbers Really Move?</P>
<P>* Timothy Gowers: Does Mathematics Need a Philosophy?</P>
<P>* Jody Azzouni: How and Why Mathematics is a Social Practice</P>
* Gian-Carlo Rota: The Pernicious Influence of Mathematics Upon Philosophy</P>
<P>* Jack Schwartz: The Pernicious Influence of Mathematics on Science</P>
<P>* Alfonso Avila del Palacio: What is Philosophy of Mathematics Looking For?</P>
<P>* Andrew Pickering: Concepts and the Mangle of Practice: Constructing Quaternions</P>
<P>* Eduard Glas: Mathematics as Objective Knowledge and as Human Practice</P>
<P>* Leslie White: The Locus of Mathematical Reality: An Anthropological Footnote</P>
<P>* Reuben Hersh: Inner Vision, Outer Truth</P>
<P>"I was pleasantly surprised to find that this book does not treat mathematics as dessicated formal logic but as a living organism, immediately recognizable to any working mathematician."</P>
<P>- Sir Michael Atiyah, University of Edinburgh</P>
<P>"A wonderful collection of essays on the philosophy of mathematics, some by mathematicians, others by philosophers, and all having significant things to say. Most readers will be informed, some will be infuriated, but all will be stimulated."</P>
<P>- John H. Conway, John von Neumann Distinguished Professor of Mathematics, Princeton University</P>
<P> </P>
<P>This startling 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.</P>
<P>The following essays are included:</P>
<P>* Alfred Renyi: Socratic Dialogue</P>
<P>* Carlo Cellucci: Filosofia e Matematica, introduction</P>
<P>* William Thurston: On Proof and Progress in Mathematics</P>
<P>* Andrew Aberdein: The Informal Logic of Mathematical Proof</P>
<P>* Yehuda Rav: Philosophical Problems of Mathematics in Light of Evolutionary Epistemology</P>
<P>* Brian Rotman: Towards a Semiotics of Mathematics</P>
<P>* Donald Mackenzie: Computers and the Sociology of Mathematical Proof</P>
<P>* Terry Stanway: From G.H.H. and Littlewood to XML and Maple: Changing Needs and Expectations in Mathematical Knowledge Management</P>
<P>* Rafael Nunez: Do Numbers Really Move?</P>
<P>* Timothy Gowers: Does Mathematics Need a Philosophy?</P>
<P>* Jody Azzouni: How and Why Mathematics is a Social Practice</P>
* Gian-Carlo Rota: The Pernicious Influence of Mathematics Upon Philosophy</P>
<P>* Jack Schwartz: The Pernicious Influence of Mathematics on Science</P>
<P>* Alfonso Avila del Palacio: What is Philosophy of Mathematics Looking For?</P>
<P>* Andrew Pickering: Concepts and the Mangle of Practice: Constructing Quaternions</P>
<P>* Eduard Glas: Mathematics as Objective Knowledge and as Human Practice</P>
<P>* Leslie White: The Locus of Mathematical Reality: An Anthropological Footnote</P>
<P>* Reuben Hersh: Inner Vision, Outer Truth</P>
Collection of the most interesting recent writings on the philosophy of mathematics written by highly respected researchers from philosophy, mathematics, physics, and chemistry Interdisciplinary book that will be useful in several fields—with a cross-disciplinary subject area, and contributions from researchers of various disciplines Includes supplementary material: sn.pub/extras
<P>This book collects some of the most interesting recent writings tackling the problem of giving an account of the nature, purpose, and justification of mathematics as actually done by real live mathematicians. What is the nature of the objects being studied? What determines the directions and styles in which mathematics progresses (or, perhaps, degenerates)? What certifies its claim to certainty, or to a priori status, to independence of experience? Why is mathematics the same for all times and places, or is it really the same, or in what senses is it the same and in what senses different? </P>
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