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The Language of Nature

Reassessing the Mathematization of Natural Philosophy in the Seventeenth Century

2016

Geoffrey Gorham, Benjamin Hill, Edward Slowik, and C. Kenneth Waters, Editors

Minnesota Center for Philosophy of Science

The Language of Nature

Reassessing how the integration of mathematics and natural philosophy contributed to the scientific revolution

Although the mathematization of nature is a distinctive and crucial feature of the emergence of modern science in the seventeenth century, this volume shows that it was a far more complex, contested, and context-dependent phenomenon than the received historiography has indicated.

Galileo’s dictum that the book of nature “is written in the language of mathematics” is emblematic of the accepted view that the scientific revolution hinged on the conceptual and methodological integration of mathematics and natural philosophy. Although the mathematization of nature is a distinctive and crucial feature of the emergence of modern science in the seventeenth century, this volume shows that it was a far more complex, contested, and context-dependent phenomenon than the received historiography has indicated, and that philosophical controversies about the implications of mathematization cannot be understood in isolation from broader social developments related to the status and practice of mathematics in various commercial, political, and academic institutions.

Contributors: Roger Ariew, U of South Florida; Richard T. W. Arthur, McMaster U; Lesley B. Cormack, U of Alberta; Daniel Garber, Princeton U; Ursula Goldenbaum, Emory U; Dana Jalobeanu, U of Bucharest; Douglas Jesseph, U of South Florida; Carla Rita Palmerino, Radboud U, Nijmegen and Open U of the Netherlands; Eileen Reeves, Princeton U; Christopher Smeenk, Western U; Justin E. H. Smith, U of Paris 7; Kurt Smith, Bloomsburg U of Pennsylvania.

The Language of Nature

Geoffrey Gorham is associate professor of philosophy at Macalester College.

Benjamin Hill is associate professor of philosophy at the University of Western Ontario.

Edward Slowik is associate professor of philosophy at Winona State University.

C. Kenneth Waters is professor of philosophy at the University of Calgary.

The Language of Nature

Contents

Introduction
Geoffrey Gorham, Benjamin Hill, and Edward Slowik

1. Reading the Book of Nature: The Ontological and Epistemological Underpinnings of Galileo’s Mathematical Realism
Carla Rita Palmerino

2. “The Marriage of Physics with Mathematics”: Francis Bacon on Measurement, Mathematics and the Construction of a Mathematical Physics
Dana Jalobeanu

3. On the Mathematization of Free Fall: Galileo, Descartes, and a History of Misconstrual
Richard T. W. Arthur

4. The Mathematization of Nature in Descartes and the First Cartesians
Roger Ariew

5. Laws of Nature and the Mathematics of Motion
Daniel Garber

6. Ratios, Quotients, and the Language of Nature
Douglas Jesseph

7. Color By Numbers: The Harmonious Palette in Early Modern Painting
Eileen Reeves

8. The Role of Mathematical Practitioners and Mathematical Practice in Developing Mathematics as the Language of Nature
Lesley B. Cormack

9. Leibniz on Order and the Notion of Substance: Mathematizing the Sciences of Metaphysics and Physics
Kurt Smith

10. Leibniz’s Harlequinade: Nature, Infinity, and the Limits of Mathematization
Justin E. H. Smith

11. The Geometrical Method as a New Standard of Truth, Based on the Mathematization of Nature
Ursula Goldenbaum

12. Philosophical Geometers and Geometrical Philosophers
Christopher Smeenk

Contributors

Index