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History & Philosophy of Modern Mathematics

Volume 11: Minnesota Studies in Philosophy of Science

Table of Contents

Preface…vii

An Opinionated Introduction…3
Philip Kitcher and William Aspray

I. Logic and the Foundations of Mathematics

PoincarĂ© 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

Contributors…367

Index…481

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