Proof and Other Dilemmas: Mathematics and Philosophy

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Bonnie Gold, Roger A. Simons
MAA, 2008 - Mathematics - 346 pages
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For the majority of the twentieth century, philosophers of mathematics focused their attention on foundational questions. However, in the last quarter of the century they began to return to basics, and two new schools of thought were created: social constructivism and structuralism. The advent of the computer also led to proofs and development of mathematics assisted by computer, and to questions concerning the role of the computer in mathematics. This book of sixteen original essays is the first to explore this range of new developments in the philosophy of mathematics, in a language accessible to mathematicians. Approximately half the essays were written by mathematicians, and consider questions that philosophers have not yet discussed. The other half, written by philosophers of mathematics, summarise the discussion in that community during the last 35 years. A connection is made in each case to issues relevant to the teaching of mathematics.
  

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A collection of essays by mathematicians (Ms) and philosophers of math (PMs) on proof and how it is changing, social constructivist views of math, the nature of math objects and math knowledge, and ... Read full review

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Contents

Proof and How it is Changing
1
Its Nature and Significance Michael Detlefsen
3
Implications of Experimental Mathematics for the Philosophy of Mathematics Jonathan Borwein
33
On the Roles of Proof in Mathematics Joseph Auslander
61
U SocialConstructivist Views of Mathematics
79
When Is a Problem Solved? Philip J Davis
81
Mathematical Practice as a Scientific Problem Reuben Hersh
95
Social Constructs? Julian Cole
109
The Nature of Mathematical Objects 0ystein Linnebo
205
When is One Thing Equal to Some Other Thing? Barry Mazur
221
TV The Nature of Mathematics and its Applications
243
Mathematics as the Science of Relations as Such R S D Thomas
245
What is Mathematics? A Pedagogical Answer to a Philosophical Question Guershon Harel
265
What Will Count as Mathematics in 2100? Keith Devlin
291
The Case of Addition Mark Steiner
313
ProbabilityA Philosophical Overview Alan Hdjek
323

The Nature of Mathematical Objects and Mathematical Knowledge
129
The Existence of Mathematical Objects Charles Chihara
131
Mathematical Objects Stewart Shapiro
157
Mathematical Platonism Mark Balaguer
179
Glossary of Common Philosophical Terms
341
About the Editors
345
Copyright

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About the author (2008)

Bonnie Gold is a Professor in the Mathematics Department at Monmouth University, New Jersey.

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