History and Philosophy of Modern Mathematics
Publication Year: 1988
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.
Published by: University of Minnesota Press
Title Page, Copyright
...The purpose of this volume is to bring together a number of different perspectives on modern mathematics, with the aim of understanding how the work of historians, philosophers, and mathematicians can be integrated in an interdisciplinary study of...
An Opinionated Introduction
Philip Kitcher and William Aspray
...Each of the essays that follow could be sent forth as an orphan, with only the most perfunctory comment, to make its own solitary way in the world, and some of them would undoubtedly do well. However, we believe...
I: Logic and the Foundations of Mathematics
Poincaré against the Logicists
...Although the great French mathematician Henri Poincare wrote on topics in the philosophy of mathematics from as early as 1893, he did not come to consider the subject of modern logic until 1905. The attitude...
Logical Truth and Analyticity in Carnap's "Logical Syntax of Language"
...Throughout his philosophical career, Carnap places the foundations of logic and mathematics at the center of his inquiries: he is concerned above all with the Kantian question...
The Emergence of First-Order Logic
Gregory H. Moore
...To most mathematical logicians working in the 1980s, first-order logic is the proper and natural framework for mathematics. Yet it was not always so. In 1923, when a young Norwegian mathematician...
II: Reinterpretations in the History of Mathematics
Kronecker's Place in History
...At a conference on the history and philosophy of mathematics, it seems especially appropriate to talk about Kronecker's place in history. My objective is to show that the prevalence...
Felix Klein and His "Erlanger Programm"
Garrett Birkhoff and M. K. Bennett
...Felix Klein's "Erlanger Programm" (E.P.), listed in our references as (Klein 1872), is generally accepted as a major landmark in the mathematics of the nineteenth century. In his obituary biography...
Abraham Robinson and Nonstandard Analysis: History, Philosophy, and Foundations of Mathematics
Joseph W Dauben
...Historically, the dual concepts of infinitesimals and infinities have always been at the center of crises and foundations in mathematics, from the first "foundational crisis" that some, at least, have associated...
How Can Mathematicians and Mathematical Historians Help Each Other?
...dropped, but I could argue both sides of that question. The present title presumes the optimistic answer, and while we all hope that this is the correct answer, the present time may not be the right one for this answer. The history of mathematics is not an easy field...
III: Case Studies in the History and Philosophy of Mathematics
Fitting Numbers to the World: The Case of Probability Theory
Lorraine J. Daston
...mathematics is a perpetual miracle. Neither formalist nor logicist nor Platonist (at least of the latter-day dilute variety) can provide a plausible explanation of why numbers should...
Logos, Logic, and Logistiké: Some Philosophical Remarks on Nineteenth-Century Transformation of Mathematics
...so profound that it is not too much to call it a second birth of the subject— its first birth having occurred among the ancient Greeks, say from the sixth through the fourth century...
Ten Misconceptions about Mathematics and Its History
Michael J. Crowe
...teaching, and writing history of mathematics. During those decades, I have become convinced that ten claims I formerly accepted concerning mathematics and its development are both seriously wrong and a hindrance to the historical study of...
Mathematics and the Sciences
Felix E. Browder
...interaction between mathematics and the sciences and to relate the trends to the historical development of mathematics as an intellectual discipline and of the sciences as they have developed since the seventeenth century. This story is interesting...
...century has been concerned with the enterprise of providing a foundation for mathematics. There is no doubt that this enterprise has often been mathematically fruitful. Indeed, the growth of logic as an important field within mathematics owes much to the pioneering...
IV: The Social Context of Modern Mathematics
Partisans and Critics of a New Science: The Case of Artificial Intelligence and Some Historical Parallels
Judith V Grabiner
...in mathematics courses—we see the presence of the computer. We are told that we are entering a new age, that of the Computer Revolution, and that the field known as Artificial Intelligence is at the forefront of that revolution. Its practitioners have...
The Emergence of Princeton as a World Center for Mathematical Research, 1896-1939
...University, reflecting its ambitions for graduate education and research. At the time, Princeton, like other American universities, was primarily a teaching institution that made few significant contributions...
...Richard Askey, Professor of Mathematics, University of Wisconsin at Madison William Aspray, Associate Director, Charles Babbage Institute for the History of Information Processing, University of Minnesota M. K. Bennett, Professor of Mathematics, University of Massachusetts at Amherst...
About the Author
...Currently a professor of philosophy at the University of California, San Diego, Philip Kitcher has also taught at Vassar College, the University of Vermont, and the University of Minnesota, where he served...
Page Count: 396
Publication Year: 1988
Series Title: Minnesota Studies in the Philosophy of Science
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