In this Book

University of Minnesota Press
summary

History and Philosophy of Modern Mathematics was first published in 1988. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions.

The fourteen essays in this volume build on the pioneering effort of Garrett Birkhoff, professor of mathematics at Harvard University, who in 1974 organized a conference of mathematicians and historians of modern mathematics to examine how the two disciplines approach the history of mathematics. In History and Philosophy of Modern Mathematics, William Aspray and Philip Kitcher bring together distinguished scholars from mathematics, history, and philosophy to assess the current state of the field. Their essays, which grow out of a 1985 conference at the University of Minnesota, develop the basic premise that mathematical thought needs to be studied from an interdisciplinary perspective.

The opening essays study issues arising within logic and the foundations of mathematics, a traditional area of interest to historians and philosophers. The second section examines issues in the history of mathematics within the framework of established historical periods and questions. Next come case studies that illustrate the power of an interdisciplinary approach to the study of mathematics. The collection closes with a look at mathematics from a sociohistorical perspective, including the way institutions affect what constitutes mathematical knowledge.

Table of Contents

  1. Cover
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  1. Title Page, Copyright
  2. pp. i-iv
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  1. Contents
  2. pp. v-vi
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  1. Preface
  2. pp. vii-x
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  1. An Opinionated Introduction
  2. Philip Kitcher and William Aspray
  3. pp. 3-58
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  1. I: Logic and the Foundations of Mathematics
  2. pp. 59-60
  1. Poincaré against the Logicists
  2. Warren Goldfarb
  3. pp. 61-81
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  1. Logical Truth and Analyticity in Carnap's "Logical Syntax of Language"
  2. Michael Friedman
  3. pp. 82-94
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  1. The Emergence of First-Order Logic
  2. Gregory H. Moore
  3. pp. 95-136
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  1. II: Reinterpretations in the History of Mathematics
  2. pp. 137-138
  1. Kronecker's Place in History
  2. Harold Edwards
  3. pp. 139-144
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  1. Felix Klein and His "Erlanger Programm"
  2. Garrett Birkhoff and M. K. Bennett
  3. pp. 145-176
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  1. Abraham Robinson and Nonstandard Analysis: History, Philosophy, and Foundations of Mathematics
  2. Joseph W Dauben
  3. pp. 177-200
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  1. How Can Mathematicians and Mathematical Historians Help Each Other?
  2. Richard Askey
  3. pp. 201-218
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  1. III: Case Studies in the History and Philosophy of Mathematics
  2. pp. 219-220
  1. Fitting Numbers to the World: The Case of Probability Theory
  2. Lorraine J. Daston
  3. pp. 221-237
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  1. Logos, Logic, and Logistiké: Some Philosophical Remarks on Nineteenth-Century Transformation of Mathematics
  2. Howard Stein
  3. pp. 238-259
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  1. Ten Misconceptions about Mathematics and Its History
  2. Michael J. Crowe
  3. pp. 260-277
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  1. Mathematics and the Sciences
  2. Felix E. Browder
  3. pp. 278-292
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  1. Mathematical Naturalism
  2. Philip Kitcher
  3. pp. 293-326
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  1. IV: The Social Context of Modern Mathematics
  2. pp. 327-328
  1. Partisans and Critics of a New Science: The Case of Artificial Intelligence and Some Historical Parallels
  2. Judith V Grabiner
  3. pp. 329-345
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  1. The Emergence of Princeton as a World Center for Mathematical Research, 1896-1939
  2. William Aspray
  3. pp. 346-366
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  1. Contributors
  2. pp. 367-370
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  1. Index
  2. pp. 371-386
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  1. About the Author
  2. pp. 387-387
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