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Pierre Maupertuis and the Charge of Error Against Fermat and Leibniz" Richard Samuel Lamborn University of South Florida, [email protected]

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Pierre Maupertuis and the Charge of Error Against Fermat and Leibniz University of South Florida Scholar Commons Graduate Theses and Dissertations Graduate School 11-18-2015 Thinking Nature, "Pierre Maupertuis and the Charge of Error Against Fermat and Leibniz" Richard Samuel Lamborn University of South Florida, [email protected] Follow this and additional works at: http://scholarcommons.usf.edu/etd Part of the Philosophy of Science Commons, and the Religious Thought, Theology and Philosophy of Religion Commons Scholar Commons Citation Lamborn, Richard Samuel, "Thinking Nature, "Pierre Maupertuis and the Charge of Error Against Fermat and Leibniz"" (2015). Graduate Theses and Dissertations. http://scholarcommons.usf.edu/etd/5979 This Dissertation is brought to you for free and open access by the Graduate School at Scholar Commons. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Scholar Commons. For more information, please contact [email protected]. Thinking Nature, “Pierre Maupertuis and the Charge of Error Against Fermat and Leibniz” by Richard Lamborn A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Philosophy College of Arts and Sciences University of South Florida Co-Major Professor: Roger Ariew, Ph.D. Co-Major Professor: Douglas Jesseph, Ph.D. Thomas Williams, Ph.D. Alexander Levine, Ph.D. Date of Approval: November 13, 2015 Keywords: Science, Geometry, Physics, Metaphysics, Religion, Light Copyright © 2015, Richard Lamborn Acknowledgments I would like to thank the following persons who walked beside me in life and assisted me in the substantive materialization of this project. From my family, I would like to thank my wife and life partner Sharon Lamborn, a shining example of high quality humanity, whose support made this project possible. I would like to say to my father, Richard S. Lamborn, Sr., his wife Betty, my sisters Esther Huhn and Miriam McNutt, and all other family members, thank you for your emotional support and encouragement throughout this process. I would like to give a special thanks to the following persons who provided research assistance as I pursued this degree: David Garrison, Susan Ariew, Audrey Powers, Ms. LeEtta Schmidt, and Merilyn Burke. I would like to give a very special thanks to my deceased mother Lois Lamborn. America rests on the foundation of women such as her. Table of Contents List of Figures ................................................................................................................................. ii Abstract .......................................................................................................................................... iv Introduction ......................................................................................................................................1 Chapter One: The Context ............................................................................................................13 Chapter Two: Maupertuis’ Position ..............................................................................................31 Chapter Three: Fermat’s Position .................................................................................................68 Chapter Four: Leibniz’s Position ..................................................................................................95 Chapter Five: Critical Analysis ...................................................................................................124 Conclusion ...................................................................................................................................156 Bibliography ................................................................................................................................166 Appendix I: July 6, 1751 Letter From Maupertuis to Johann Bernoulli II .................................177 Appendix II: Email Granting Permission to Use Figure #5 ........................................................183 i List of Figures Figure 1 Snell’s Law of Refraction ........................................................................................7 Figure 2 Problem of Straight Line Route From Air to Water ..............................................10 Figure 3 Lifeguard Analogy .................................................................................................11 Figure 4 Maupertuis’ Geometrical Drawing of Refraction ..................................................47 Figure 5 Pedoe’s Geometrical Illustration............................................................................48 Figure 6 Fermat to de La Chambre Demonstrating Minimum Time ...................................70 Figure 7 Descartes’ Tennis Player, Fig. 6,8, and 9 ..............................................................74 Figure 8 Descartes’ Tennis Racket at Line Segment CBE ...................................................80 Figure 9 Fermat’s 1637 Letter to Mersenne and the Consideration of an Obtuse Angle ......................................................................................................................82 Figure 10 Fermat’s 1637 Letter to Mersenne and Challenge to Descartes Idea of Determination ........................................................................................................83 Figure 11 de La Chambre on Equal Angles and Shortest Distance .......................................89 Figure 12 de La Chambre drawing on Equal Angles but Unequal Line Lengths ..................90 Figure 13 Fermat’s 1657 Letter to de La Chambre and his Idea of Easiest Course ...............91 Figure 14 Fermat’s 1662 Letter to de La Chambre and his Idea of Least Time ....................92 Figure 15 Fermat on Maximum and Minimum ......................................................................93 Figure 16 Leibniz’s 1682 Easiest Path of Beauty ..................................................................98 Figure 17 Leibniz’s 1686 Illustration on the Difference Between Force and Motion .........109 Figure 18 Leibniz’s 1678 – 1680 Assistance Given to Descartes Third Assumption in Efficient Cause in Reflection ...........................................................................117 ii Figure 19 Leibniz’s 1678 – 1680 Argument That Descartes Results Could Be Achieved by Final Cause .....................................................................................117 Figure 20 Leibniz’s 1696 Optics of the Easiest, “Most Determined”, Path .........................118 Figure 21 Leibniz’s 1696 Optics of the Easiest, “Most Determined”, Path .........................120 Figure 22 Leibniz’s 1696 Optics of the Easiest, “Most Determined”, Path .........................121 Figure 23 Mach Drawing .....................................................................................................138 iii Abstract The purpose of this dissertation is to defend Pierre Fermat and Gottfried Wilhelm Leibniz against the charge of error made against them by Pierre Maupertuis that they errantly applied final causes to physics. This charge came in Maupertuis’ 1744 speech to the Paris Academy of Sciences, later published in different versions, entitled Accord Between Different Laws Which at First Seemed Incompatible. It is in this speech that Maupertuis lays claim to one of the most important discoveries in the history of physics and science, The Principle of Least Action. From the date of this speech up until the end of the twentieth century, Maupertuis was credited with this discovery. Fermat discovered least time in optical physics, and Leibniz co-discovered infinitesimal calculus. When the credited discoverer of least action in physics accuses the discoverer of least time in optics and the co-discoverer of infinitesimal calculus of error before and audience of mathematicians, physicists and scientists, it is an event that calls out for investigation. The idea of final causes in physics is the idea that bodies move for an end purpose. During the early modern period, this challenged the intellectual establishment of the day with the idea of thinking in nature. The question which fueled the research for this dissertation is why such a man would accuse two other prominent intellects with such an unprovable metaphysical assumption. The research for this project started with a study of the positions of all three of these men regarding final causes in physics. The second phase was to research the historical context in which Accord Between Different Laws Which at First Seemed Incompatible was iv written and delivered. This context included the life of Maupertuis as member of the Paris Academy of Sciences and as later President of the Berlin Academy of Sciences. It also included the workings of three highly competitive, state funded, academies of science in Berlin, London and Paris. Research showed that no formal positions were held on the subject of final causes by either Maupertuis or Fermat. Only Leibniz demonstrated an established and well thought out position on the subject. Research did reveal the story of an ambitious man in Maupertuis, who made it the fulfillment of his ambition to rise in the ranks of math and science within the academies and establish himself as an intellectual great in European culture. Consequently, the life and career of Maupertuis illustrates the sociological dimension of scientific achievement. Accord Between Different Laws Which at First Seemed Incompatible turned out to be a politically calculated speech delivered
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