History & Philosophy of Modern Mathematics

An Opinionated Introduction . . . 3
Philip Kitcher and William Aspray

I. Logic and the Foundations of Mathematics

• Poincaré against the Logicists . . . 61
  Warren Goldfarb
• Logical Truth and Analyticity in Carnap's "Logical Syntax of Language" . . . 82
  Michael Friedman
• The Emergence of First-Order Logic . . . 95
  Gregory H. Moore

II. Reinterpretations in the History of Mathematics

• Kronecker's Place in History . . . 139
  Harold Fdwards
• Felix Klein and His "Erlanger Programm" . . . 145
  Garrett Birkhoff and M. K. Bennett
• Abraham Robinson and Nonstandard Analysis: History, Philosophy, and Foundations of Mathematics . . . 177
  Joseph W. Dauben
• How Can Mathematicians and Mathematical Historians
  Help Each Other? . . . 201
  Richard Askey

III. Case Studies in the History and Philosophy of Mathematics

• Fitting Numbers to the World: The Case of Probability Theory . . . 221
  Lorraine J. Daston
• Logos, Logic, and Logistike: Some Philosophical Remarks on Nineteenth-Century Transformation of Mathematics . . . 238
  Howard Stein
• Ten Misconceptions about Mathematics and Its History . . . 260
  Michael J. Crowe
• Mathematics and the Sciences . . . 278
  Felix E. Browder
• Mathematical Naturalism . . . 293
  Philip Kitcher

IV. The Social Context of Modern Mathematics

• Partisans and Critics of a New Science: The Case of Artificial Intelligence and Some Historical Parallels . . . 329
  Judith V. Grabiner
• The Emergence of Princeton as a World Center for Mathematical Research, 1896-1939 . . . 346
  William Aspray

Index . . . 371