From Natural Philosophy to Natural Science: the Entrenchment of Newton's Ideal of Empirical Success

From Natural Philosophy to Natural Science: The Entrenchment of Newton's Ideal of Empirical Success Pierre J. Boulos Graduate Pro gram in Philosophy Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Faculty of Graduate Studies The Universly of Western Ontario London, Ontario April 1999 O Pierre J- Boulos 1999 National Library Bibliotheque nationale of Canada du Canada Acquisitions and Acquisitions et Bibliographic Services services bibliographiques 395 Wellington Street 395, rue Wellington Ottawa ON KIA ON4 Ottawa ON KIA ON4 Canada Canada Your Me Voue reference Our file Notre rddrence The author has granted a non- L'auteur a accorde me licence non exclusive licence dowing the exclusive pennettant a la National Library of Canada to Bibliotheque nationale du Canada de reproduce, loan, distribute or sell reproduire, preter, distribuer ou copies of this thesis in microform, vendre des copies de cette these sous paper or electronic formats. la forme de microfiche/£ih, de reproduction sur papier ou sur format electronique. The author retains ownership of the L'auteur conserve la propriete du copyright in this thesis. Neither the droit d'auteur qui protege cette these. thesis nor substantial extracts &om it Ni la these ni des extraits substantieis may be printed or otherwise de celle-ci ne doivent Stre imprimes reproduced without the author's ou autrement reproduits sans son permission. autorisation. ABSTRACT William Harper has recently proposed that Newton's ideal of empirical success as exempli£ied in his deductions fiom phenomena informs the transition fiom natural philosophy to natural science. This dissertation examines a number of methodological themes arising fiom the Principia and that purport to exemplifjr Newton's ideal of empirical success. Among these themes is the method of answering important theoretical questions empirically by measurement f?om phenomena According to Newton's ideal, a successll theory has its parameters measured by the phenomena it purports to explain. The ideal of empirical success is not limited to prediction, but also generates reliable measurements of the parameters of the phenomena. Newton's Principiu exempliiies deductions fiom phenomena where a higher level theoretical claim is inferred f?om certain other high level theoretical principles along with phenomena. Newton established that a measure of the rate of orbital precession could sensitively measure the exponent of the force law. In the moon-test, Newton turned the theoretical question regarding the measure of the force holding the moon m her orbit into an empirical question of measurement of the length of a seconds pendulum on earth. Two different phenomena are giving agreeing measurements of the same inverse-square centripetal force field. The agreement in measured vahres is a higher level phenomenon which relates the two phenomena in quest ion Newton's model of evidential reasoning exploits these agreements in such a way that the stakes are raised for rival theories. The work done on the bar perturbation problem forms the focus of this project. In considering the effect of the sun on the moon m her orbit, Newton was able to account for only half of the observed lunar precession. The solution to this problem came in the late 1740s and early 1750s through the work of Clairaut, d1Alembert. and Euler. The zero precession left over after the effect of the sun on the lunar orbit had been correctly solved removed impediments to the acceptance of Newton's system The solution exhibited Newton's stronger ideal. Newton's ideal of empirical success did not immediately become part of the practice of natural philosophy. When one traces the developments of Euler, Clairaut, and others working on lunar precession and perturbat ion theory, these developments exhibit a better realization of Newton's ideal. Thus a good candidate for exploring the entrenchment of Newton's ideal is the solution ofthe lunar perturbation problem. The question is "when did it occur?" We will examine whether Euler had m mind this stronger ideal after he first denounced the Newtonian system for failing to solve the lunar problem (and the n-body problem in general) arid then accepted it largely based on Clairaut's solution to the problem. Although this stronger ideal is exemplified in the solution to the lunar perturbation problem, it is not clear that Euler exhibits an understanding and an awareness of the kind of evidential reasoning which drives Newton in his own work. Newton's ideal suggests that a priori metaphysical commitments ought not to drive scientific investigations. Although Euler is willing to bracket an a priuri metaphysical commitment to an aether theory, he nonetheless seems to accept the inverse-square law on hypothetico-deductive grounds. Keywords: Newton, Principia, Ideal of Empirical Success, Hypothetico-Deduct ivism, Measurement, Phenomena, Lunar Theory, Precession, Perturbation, Universal Gravitation, Clairaut, dlAlembert, and Euler. Acknowledgements To claim that this project would not have been realised without the support of a number of people is an understatement. I find myselftrying to put into prose an elegant way of saying thank you to all whose support I have found to be priceless. The point is, though, that at the end of the day the best way to show gratitude is with a "thank you." To John Nicholas I owe a debt of gratitude for the helpll comments and LiveIy hallway discussions. Andrea Purvis has been extremely helpfbl in steering me through the various hurdles of graduate studies. Of course, Bill Harper has spent countless hours challenging me and encouraging me m this dissertation Bill has taught me the value of pursuing a project in which one can truly be excited and energetic. There are not words that can capture my gratitude to Biu. To my parents, Victor and Yvette, I would Like to express my appreciation for standing by me f?om the start and for instilling in me a love and thirst for education Wah and Laura, my in-laws, have atways shown me encouragement and support. I do not envy all my siblings, parents, and extended family for having to witness my journey in this dissertation. I do, however, thank them for their unconditional support. Writing a dissertation can take on a life of its own. This one did. Nonetheless, if it were not for the opportunity to witness my children's first steps or to hear their first words, and to share these with a life partner, this dissertation could not have been written. I would like to dedicate this dissertation to Chada& Am, and Andrea whose love, support, and patience have inspired me and motivated me in achieving my dream This is a dream I will always remember. Certificate of Esarnination ,Abstract Acknowledgements Table of Contents List of -1ppendices Chapter 1 Introduction Chapter 2 Lght and Colours Paper (1672) Espedmenm Crucis The Doctrine of Colour Hooke and Huygens: Challenges to Newton a. The Hooke and Newton Debate over &ht b. The Huygens and Newton Debate over Light Newton and E-xpehentd Phdosophy Chapter 3 The Rules Phenomena The Path to Universal Gravitation Chapter 4 Chapter 5 Newon and the Motion of the Lunar Apse: The Setting of the Problem Chapter 6 Euler, Lunar Theory, and the Vindication of Universal Gravitation Clairaut and dlAlembert Sketch of Clairaut's Solution Chapter 7 Newton's Ideal of Empirical Success and Natural Science Euler on the motion of the Lunar Apse Appendix A Appendix B Appendix C Appendix D Bibliography Vita -1ppendis .i Clairaut Translation: Concerning the Orbit of the Moon Appendix B Clairaut Translation: Demonstration of the Fundamental Proposition of bly Lunar Theory .\ppen&x C Detailed Sketch of Clairaut's Proof Appendix D Maple V Workbook: The LUNAR Orbit Chapter 1 Newton the unparaIIelTd,whose Name No Time will wear out of the Book of Fame, Coelestiall Science has promoted more, Than all the Sages that have shone before. Nature compell'd his piercing Mind obeys, And gladly shows him all her secret Ways; 'Gainst Mathematics she has no Defence, And yields t' experimental Consequence; His Tow'ring Genius, fkom its certain Cause Ev'ry Appearance a pion' draws, And shews th' Almighty Architect's der'd Laws. Desaguliers (1 729), I3e N~onianSystem of World, the Best Model of Government, An AIegorical Poem Introduction It is a widely held view that the natural sciences are empirically oriented, and that the progress we have seen in the natural sciences over the past two to three hundred years is due entirely to the decision taken by natural philosophers some centuries back to be concerned strictly with what is known through the senses. One mark of the scientific revolution is that, to this day, science is a leading method by which one understands the world. The revolution in science that took place during the sixteenth and seventeenth centuries facilitated the search for truth in the material world- Sir Isaac Newton (1642472'7) has been characterised by mainstream Anglo- American philosophers of science as a founding practitioner of what we have come to understand as the methods of natural science, and more often than mt, he has been viewed as an outstanding and unique example of the great natural scientist.' On this paradigm scientists and Newton specificdy, are thought to be not at all preoccupied with matters not known empirically. The scientist, under this view, is one whose interests preclude things that are "transcendent" or "metaphysical." Ln the Prefice to the first edition of his Philosophiae Naturalis Principia Mathernatica (1 687)- Newton observes that All the difficulty of philosophy seems to consist in this---fiom the phenomena of motions to investigate the forces of natureT and then hmthese forces to demonstrate other phenomena2 Newton goes on to claim that By the propositions mathematically demonstrated in the former books, we in the third derive from the celestial phenomena the forces of gravity with which bodies tend to the sun and the several planets.3 Not long ago E.A.

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