Mathematics

Mathematics and Scientific Representation

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This book discusses the contributions that mathematics makes to the success of science. This topic falls between the philosophy of mathematics and the philosophy of science as they are currently practiced, and this may account for its relative neglect in contemporary philosophy. Despite this situation, I believe that the presence of mathematics in much of science has significant philosophical implications for our understanding of both mathematics and science. Though many readers will find much to disagree with in this book, I hope to place the topic of applications on the agenda of philosophy of science and mathematics. For those who reject the particular approach I have taken to this problem, I look forward to other proposals that my efforts might generate.
This project began as my dissertation, which was completed in the spring of 2002 under the supervision of Paolo Mancosu. I am extremely grateful to him for his continuing encouragement and critical suggestions over the many years since then. I have been strongly influenced by his many articles and his overall approach to the philosophy of mathematics, as reflected in the anthology he recently edited, The Philosophy of Mathematical Practice (Mancosu 2008c). I hope that my book will be a step in the right direction toward reconnecting philosophers of mathematics with the philosophy of science and scientific practice.
Shortly after 2002 I became convinced that issues connected with applications of mathematics are best pursued by focusing on the epistemic contributions which mathematics makes. This approach is first reflected in Pincock (2007). The philoso- phers most responsible for this shift in my thinking are Robert Batterman and Mark Wilson. A reader of their work will find their influence throughout this book, from the choice of examples to the selection of the issues most deserving of extended dis- cussion. While I expect that both Batterman and Wilson will find much to criticize in this book, I would like to express my gratitude to both for their work on these topics and for their many discussions and expressions of support.
The writing of this book began in earnest while I was a visiting fellow at the Center for the Philosophy of Science at the University of Pittsburgh in the 2008–2009 academic year. I thank John Norton, the director of that center, along with the other fellows, Hanne Andersen, Claus Beisbart, Erik Curiel, Laura Felline, Ulrich Krohs, Flavia Padovani, Daniel Parker and Federica Russo for a stimulating and engaging atmosphere. Additional support for this project came in the form of a National Endowment for the Humanities fellowship. I am thankful to the NEH for supporting a project of this kind. Finally, Purdue University provided generous leave and sabbatical support, and I am thankful to the Philosophy Department and my colleagues for their help in completing this book manuscript.

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English

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978-0-19-975710-7

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