UNDERDETERMINATION AND INDIRECT MEASUREMENT A DISSERTATION SUBMITTED TO THE DEPARTMENT OF PHILOSOPHY AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Teru Miyake June 2011 © 2011 by Teru Miyake. All Rights Reserved. Re-distributed by Stanford University under license with the author. This work is licensed under a Creative Commons Attribution- Noncommercial 3.0 United States License. http://creativecommons.org/licenses/by-nc/3.0/us/ This dissertation is online at: http://purl.stanford.edu/cs884mb1574 ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Michael Friedman, Primary Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Helen Longino I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Patrick Suppes I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. George Smith Approved for the Stanford University Committee on Graduate Studies. Patricia J. Gumport, Vice Provost Graduate Education This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file in University Archives. iii Abstract We have been astonishingly successful in gathering knowledge about certain objects or systems to which we seemingly have extremely limited access. Perhaps the most difficult problem in the investigation of such systems is that they are extremely underdetermined. What are the methods through which these cases of underdetermination are resolved? I argue in Chapter 1 that these methods are best understood by thinking of what scientists are doing as gaining access to the previously inaccessible parts of these systems through a series of indirect measurements. I then discuss two central problems with such indirect measurements, theory mediation and the combining of effects, and ways in which these difficulties can be dealt with. In chapter 2, I examine the indirect measurement of planetary distances in the solar system in the sixteenth and seventeenth centuries by Copernicus and Kepler. In this case, there was an underdetermination between three different theories about the motions of the planets, which can be partly resolved by the measurement of distances between the planets. The measurement of these distances was enabled by making certain assumptions about the motions of the planets. I argue that part of the iv justification for making these assumptions comes from decompositional success in playing off measurements of the earth‘s orbit and the Mars orbit against each other. In chapter 3, I examine the indirect measurement of mechanical properties such as mass and forces in the solar system by Newton. In this case, there were two underdeterminations, the first an underdetermination between two theories about the true motion of the sun and the earth, and the second an underdetermination between various theories for calculating planetary orbits. Newton resolves these two problems of underdetermination through a research program where the various sources of force are identified and accounted for. This program crucially requires the third law of motion to apply between celestial objects, an issue about which Newton was criticized by his contemporaries. I examine the justification for the application of the third law of motion through its successful use for decomposition of forces in the solar system in a long-term research program. I further discuss comments by Kant on the role of the third law of motion for Newton, in which Kant recognizes its indispensability for a long-term program for determining the center of mass of the solar system and thus defining a reference point relative to which forces can be identified. Chapter 4 covers the indirect measurement of density in the earth‘s interior using observations of seismic waves. One of the difficult problems in this case is that we can think of the interior density of the earth as a continuous function of radius—in order to determine this radius function, you are in effect making a measurement of an infinite number of points. The natural question to ask here is how much resolution the observations give you. I will focus on the work of geophysicists who were concerned with this problem, out of which a standard model for the earth‘s density was developed. v Acknowledgments I am incredibly lucky to have been able to take two extraordinary seminars in which the seeds for the ideas set forth in this dissertation were sown. The first is a seminar on Newton‘s Principia that George Smith taught at Tufts University that I took when I was an MA student. George‘s unwavering attention to the details that make a difference, his way of identifying and trying to answer truly deep and interesting questions about science, and above all his kindness and dedication to his students, all made a deep impression on me. I sat in on this seminar again when George taught a version of it when he visited Stanford University a few years later. I would like to sit in on it many more times if I could—I‘m sure I would get more out of it every time. The one other seminar that made a similarly deep impression on me was Michael Friedman‘s seminar on Kant‘s Metaphysical Foundations of Natural Science that I took at Stanford. I found Michael to be a thinker of a completely different sort from George, but I also saw a very similar uncompromising attitude with regard to the study of Kant and the sciences of his time, and Michael‘s warm personality made it easy for me to work with him as my advisor at Stanford. George and Michael are a pair of mentors who, each in his own unique way, sets the highest standards in his area of research. I only hope my own work could approach those standards someday. vi The rest of the dissertation committee is no less distinguished. Pat Suppes is, of course, in a league of his own. When I first talked to Pat, I have to admit that it was with a mixture of awe and apprehension, but I grew to really enjoy walking out to visit him at Ventura Hall. Helen Longino was always very helpful and encouraging, even during a very busy stint as department chair. Tom Ryckman was not an official member of the committee, but he was certainly a committee member in my eyes. I have had countless discussions with him about the topics covered in this dissertation, and he was the most dependable source of advice and support during my years at Stanford. As I have already mentioned, I got my MA in philosophy at Tufts University, and besides George I would like to thank Dan Dennett, Jody Azzouni, Kathrin Koslicki, David Denby, and the members of my cohort. At Stanford, I would like to thank the following faculty: Brian Skyrms, David Hills, Krista Lawlor, Lanier Anderson, Chris Bobonich, Mark Crimmins, Nadeem Hussain, Marc Pauly, John Perry, and Dagfinn Follesdal. Grad students and visiting scholars who have contributed to the development of the ideas in this dissertation include Quayshawn Spencer, Angela Potochnik, Joel Velasco, Alistair Isaac, Johanna Wolff, Tomohiro Hoshi, Sally Riordan, Ben Wolfson, Dan Halliday, Danny Elstein, Shawn Burns, Micah Lewin, and Samuel Kahn. Part of this dissertation was given as a talk at the UC Irvine LPS department, and I thank the audience for their comments, and Jeff Barrett and Kyle Stanford in particular for their hospitality. I wrote much of this dissertation at the Max Planck Institute for the History of Science in Berlin, where I was a Predoctoral Fellow. The Max Planck Institute provided a perfect environment for writing this dissertation, and I would especially like to thank vii Raine Daston and the scholars in Department II. Financial support for the years during which I was working on this dissertation was provided by the Whiting Foundation and the Ric Weiland Fellowship. In addition, I am proud to say that I was the very first Pat Suppes Fellow at Stanford, for which I would like to thank Pat a second time. I could not have had better preparation for the work I had to do for this dissertation than my undergraduate experience at Caltech. I want to thank all of my friends throughout those four very tough but ultimately rewarding years. Finally, all the members of my family know that the roots of my philosophical education began with long arguments over pretty much anything with my twin brother Kay. I would like to thank Dad, Mom, Yochan, June, and Kay for their support. viii Table of Contents Chapter 1: Underdetermination and Indirect Measurement .................................................. 1 Chapter 2: Copernicus, Kepler, and Decomposition .............................................................. 35 Chapter 3: Newton and Kant on the Third Law of Motion ................................................... 68 Chapter 4: Underdetermination in the Indirect Measurement of the Density Distribution of the Earth’s Interior............................................................................................................... 102 Epilogue ..................................................................................................................................... 136 Bibliography .............................................................................................................................. 141 ix -1- Underdetermination and Indirect Measurement 1 Prelude Suppose one day archeologists unearth a mysterious artifact—a perfect black cube, 10 centimeters on a side, cool to the touch, made of what looks like the blackest possible steel. They decide, rather unimaginatively, to call the artifact ―Cube‖. It‘s a mere curiosity at first, but scientists soon find that it has some mystifying features.