Proof and other dilemmas : mathematics and philosophy

著者

• Gold, Bonnie
• Simons, Roger A.

書誌事項

Proof and other dilemmas : mathematics and philosophy

edited by Bonnie Gold and Roger A. Simons

（MAA spectrum）

Mathematical Association of America, c2008

タイトル別名

Proof & other dilemmas : mathematics and philosophy

注記

Includes bibliographical references

内容説明・目次

内容説明

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.

目次

• Acknowledgments
• Introduction
• Part I. Proof and How it is Changing: 1. Proof: its nature and significance Michael Detlefsen
• 2. Implications of experimental mathematics for the philosophy of mathematics Jonathan Borwein
• 3. On the roles of proof in mathematics Joseph Auslander
• Part II. Social Constructivist Views of Mathematics: 4. When is a problem solved? Philip J. Davis
• 5. Mathematical practice as a scientific problem Reuben Hersh
• 6. Mathematical domains: social constructs? Julian Cole
• Part III. The Nature of Mathematical Objects and Mathematical Knowledge: 7. The existence of mathematical objects Charles Chihara
• 8. Mathematical objects Stewart Shapiro
• 9. Mathematical Platonism Mark Balaguer
• 10. The nature of mathematical objects Oystein Linnebo
• 11. When is one thing equal to some other thing? Barry Mazur
• Part IV. The Nature of Mathematics and its Applications: 12. Extreme science: mathematics as the science of relations as such R. S. D. Thomas
• 13. What is mathematics? A pedagogical answer to a philosophical question Guershon Harel
• 14. What will count as mathematics in 2100? Keith Devlin
• 15. Mathematics applied: the case of addition Mark Steiner
• 16. Probability - a philosophical overview Alan Hajek
• Glossary of common philosophical terms
• About the editors.

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詳細情報

• NII書誌ID(NCID): BA88042938
• ISBN:
  • 9780883855676
• LCCN: 2008922718
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: [Washington, D.C.]
• ページ数/冊数: xxxii, 346 p.
• 大きさ: 26 cm
• 親書誌ID:
  • BA17084268