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Information to Users INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. University Microfilms International A Bell & Howell Information Company 30 0 North Z eeb Road. Ann Arbor, Ml 48106-1346 USA 313/761-4700 800/521-0600 Order Number 9427800 Newton’s “De gravitatione” argument: Cartesian relationalist dynamics and the structure of space and time Slowik, Edward Steven, Ph.D. The Ohio State University, 1994 Copyright ©1994 by Slowik, Edward Steven. All rights reserved. 300 N. Zeeb Rd. Ann Arbor, MI 48106 NEWTON'S "DE GRAVITATIONE" ARGUMENT: CARTESIAN RELATIONALIST DYNAMICS AND THE STRUCTURE OF SPACE AND TIME DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Edward Steven Slowik, B.A., M.A. The Ohio State University 1994 Dissertation Committee: Approved by Mark Wilson Calvin Normore Ronald Laymon Advisor Department of Philosophy Copyright by Edward Steven Slowik 1994 To Emily Slowik and Christine King ii ACKNOWLEDGMENTS I express my sincere appreciation to Prof. Mark Wilson for his guidance and support over the past several years, both as an undergraduate and graduate student. I have had the considerable fortune during this time to experience and partake of Prof. Wilson's vast knowledge of philosophy and science, and my understanding of these disciplines will continue to be a reflection of his deep insights. I would also like to thank Profs. Ronald Laymon and Calvin Normore for their generous assistance in the research of this dissertation: the success of this entire project owes a great deal to their efforts. In addition, I would also like to express my sincere thanks to Prof. Normore for his kind help and encouragement over the many years of my graduate career, and in the many courses that have constituted such an important part of my education. Finally, I owe a great debt of gratitude to my family and friends for their continued support and backing. Without them, I would certainly not have been able to pursue my degree. VITA May 12,1963 .............................................................. Bom-Addison, Illinois 1988............................................................................. B.A., The University of Illinois at Chicago 1991............................................................................. M.A., The Ohio State University, Columbus, Ohio 1991-Present.............................................................. Teaching Associate, The Ohio State University FIELDS OF STUDY Major Field: Philosophy Areas of Specialization: History and Philosophy of Science, History of Early Modem Philosophy, Metaphysics Areas of Competence: Ethics, Logic, Analytic Philosophy, Epistemology TABLE OF CONTENTS DEDICATION......................................................................................................................ii ACKNOWLEDGMENTS...................................................................................................iii VITA......................................................................................................................................iv LIST OF FIGURES............................................................................................................. viii INTRODUCTION................................................................................................................I CHAPTER I NEWTONIAN SPACE-TIME AND NEWTON'S ARGUMENT AGAINST CARTESIAN DYNAMICS................................................................6 1.1. The Two Trends in Cartesian Natural Philosophy........................... 7 1.2. Newton's argument against Cartesian Relationalism........................ 10 1.3. Newtonian Space and Time.................................................................15 1.4. Connecting Newtonian Space and Time.............................................22 1.5. A Frame-Independent Interpretation of Neo-Newtonian Space- Time ..............................................................................................................28 1.6. Conclusions........................................................................................... 33 Endnotes....................................................................................................... 39 CHAPTER H THE CARTESIAN SCIENTIFIC PROJECT....................................................... 41 n. 1. The Cartesian Laws of Nature............................................................41 H.2. The Role of Force in Cartesian Natural Philosophy........................ 49 D.3. The Cartesian Natural Laws and Relational Space-Time...............59 ENDNOTES.................................................................................................64 CHAPTER m CONSTRUCTING A CARTESIAN DYNAMICS WITHOUT "FIXED" REFERENCE FRAMES: COLLISIONS IN THE CENTER-OF-MASS FRAME..................................................................................................................... 66 ELI. Descartes, Huygens, and The Center-of-Mass Reference Fram e............................................................................................................67 v m.2. Huygen's on Conservation Laws, Impact, and Force...................... 73 m.3. Evaluating Huygens' Center-of-Mass Reference Frame................. 80 m.4. Constructing a Center-of-Mass Reference Frame............................85 m.5. Conclusion.......................................................................................... 90 ENDNOTES..................................................................................................91 CHAPTER IV THE STATUS OF THE CARTESIAN NATURAL LAWS IN A PLENUM..................................................................................................................93 IV. 1. "Perfect Solidity" and The Cartesian Natural Law s ....................... 93 IV. 1.1. What Does Descartes mean by Perfectly Solid?..............94 IV. 1.2. The Phenomena of Density and the Three Elements of Matter...........................................................................................95 IV. 1.3. Volume, Quantity of Matter, and the Agitation Force................................................................................................. 98 IV. 1.4. Surface Area and the Agitation Force............................... 99 IV. 1.5. Agitation and Solidity: Towards a Synthesis .................102 IV. 1.6. Perfect Solidity and the Natural Laws: A Proposal...... 104 IV.2. "Rigidity" and Size Invariance ..... ,..................... 105 IV.3. Motion and Individuation ....... ............................ ....................111 IV.4. Additional Constraints on the Application of the Collision Rules..............................................................................................................114 IV.4.1. Restriction to Two Bodies................................................. 114 IV.4.2. Ignoring the Plenum........................................................... 115 IV.4.3. Further Idealized Conditions ............................................. 117 IV.5. Concluding Remarks ..........................................................................119 ENDNOTES................................................................................................ 120 CHAPTER V CONSTRUCTING A CARTESIAN DYNAMICS WITH "FIXED" REFERENCE FRAMES: THE "KINEMATICS OF MECHANISMS" THEORY................................................................................................................... 122 V. 1. The Cartesian Vortex and Newton'sDe gravitatione Argument...................................................................................................... 123 V.2. The "Kinematics of Mechanisms" and Cartesian Space-Time 127 V.2.1. The Details of the "Kinematics of Mechanisms" Theory................................................................................................128 V.2.2. Developing a Cartesian Space-Time Using Fixed Landmarks .........................................................................................130 V.2.3. A Newtonian Reply...............................................................134 V.3. Locating Fixed Landmarks in the Cartesian Plenum ........................136
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