This book is a cultural phenomenology of doing physics. It describes the ways physicists actually do their work--their motives, and their ways of making sense of the world--so that outsiders can understand it. Martin H. Krieger explains that physicists employ a small number of everyday notions to get at the world experimentally and conceptually.

Throughout, this book questions our accepted definitions and biases, showing the self-reflective nature of scientific activity within society.

We shall argue that the attempt carried out by certain philosophers in this century to parrot the language, the method, and the results of mathematics has harmed philosophy. Such an attempt results from a misunderstanding of both mathematics and philosophy, and has harmed both subjects.

The first part of the essay describes how mathematics, in particular mathematical concepts, are applicable to nature. mathematical constructs have turned out to correspond to physical reality. this correlation between the world and mathematical concepts, it is argued, is a true phenomenon. the second part of this essay argues that the applicability of mathematics to nature is mysterious, in that not only is there no known explanation for the correlation between mathematics and physical reality, but there is a good reason (...) to except no such correlation. it is argued that there is a subjective element in the decision as to what constitutes a mathematical concept. a number of purported solutions to the mystery of the applicability of mathematics to nature are discarded, until we are left with eugene wigner's thesis that we are here confronted with a "miracle that we neither understand nor deserve.". (shrink)

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. (shrink)

This is arguably the seminal work in historical andphilosophical analysis of the twentieth century.