The Epistemology of Measurement: A Model-Based Account by Eran Tal A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Graduate Department of Philosophy University of Toronto © Copyright by Eran Tal 2012 The Epistemology of Measurement: A Model-Based Account Eran Tal, Doctor of Philosophy Department of Philosophy, University of Toronto, 2012 Thesis abstract Measurement is an indispensable part of physical science as well as of commerce, industry, and daily life. Measuring activities appear unproblematic when performed with familiar instruments such as thermometers and clocks, but a closer examination reveals a host of epistemological questions, including: 1. How is it possible to tell whether an instrument measures the quantity it is intended to? 2. What do claims to measurement accuracy amount to, and how might such claims be justified? 3. When is disagreement among instruments a sign of error, and when does it imply that instruments measure different quantities? Currently, these questions are almost completely ignored by philosophers of science, who view them as methodological concerns to be settled by scientists. This dissertation shows that these questions are not only philosophically worthy, but that their exploration has the potential to challenge fundamental assumptions in philosophy of science, including the distinction between measurement and prediction. ii The thesis outlines a model-based epistemology of physical measurement and uses it to address the questions above. To measure, I argue, is to estimate the value of a parameter in an idealized model of a physical process. Such estimation involves inference from the final state (‘indication’) of a process to the value range of a parameter (‘outcome’) in light of theoretical and statistical assumptions. Idealizations are necessary preconditions for the possibility of justifying such inferences. Similarly, claims to accuracy, error and quantity individuation can only be adjudicated against the background of an idealized representation of the measurement process. Chapters 1-3 develop this framework and use it to analyze the inferential structure of standardization procedures performed by contemporary standardization bureaus. Standardizing time, for example, is a matter of constructing idealized models of multiple atomic clocks in a way that allows consistent estimates of duration to be inferred from clock indications. Chapter 4 shows that calibration is a special sort of modeling activity, i.e. the activity of constructing and testing models of measurement processes. Contrary to contemporary philosophical views, the accuracy of measurement outcomes is properly evaluated by comparing model predictions to each other, rather than by comparing observations. iii Acknowledgements In the course of writing this dissertation I have benefited time and again from the knowledge, advice and support of teachers, colleagues and friends. I am deeply indebted to Margie Morrison for being everything a supervisor should be and more: generous with her time and precise in her feedback, unfailingly responsive and relentlessly committed to my success. I thank Ian Hacking for his constant encouragement, for never ceasing to challenge me, and for teaching me to respect the science and scientists of whom I write. I owe many thanks to Anjan Chakravartty, who commented on several early proposals and many sketchy drafts; this thesis owes its clarity to his meticulous feedback. My teaching mentor, Jim Brown, has been a constant source of friendly advice on all academic matters since my very first day in Toronto, for which I am very grateful. In addition to my formal advisors, I have been fortunate enough to meet faculty members in other institutions who have taken an active interest in my work. I am grateful to Stephan Hartmann for the three wonderful months I spent as a visiting researcher at Tilburg University; to Allan Franklin for ongoing feedback and assistance during my visit to the University of Colorado; to Paul Teller for insightful and detailed comments on virtually the entire dissertation; and to Marcel Boumans, Wendy Parker, Léna Soler, Alfred Nordmann and Leah McClimans for informal mentorship and fruitful research collaborations. Many other colleagues and friends provided useful comments on this thesis at various stages of writing, of which I can only mention a few. I owe thanks to Giora Hon, Paul Humphreys, Michela Massimi, Luca Mari, Carlo Martini, Ave Mets, Boaz Miller, Mary Morgan, Thomas Müller, John Norton, Isaac Record, Jan Sprenger, Jacob Stegenga, Jonathan Weisberg, Michael Weisberg, Eric Winsberg, and Jim Woodward, among many others. I am especially thankful to Hasok Chang for writing a thoughtful and detailed appraisal of this dissertation, and to Joseph Berkovitz and Denis Walsh for serving on my examination committee. iv The work presented here depended on numerous physicists who were kind enough to meet with me, show me around their labs and answer my often naive questions. I am grateful to members of the Time and Frequency Division at the US National Institute of Standards and Technology (NIST) and JILA labs in Boulder, Colorado for their helpful cooperation. The long hours I spent in conversation with Judah Levine introduced me to the fascinating world of atomic clocks and ultimately gave rise to the central case studies reported in this thesis. David Wineland’s invitation to visit the laboratories of the Ion Storage Group at NIST in summer 2009 resulted in a wealth of materials for this dissertation. I am also indebted to Eric Cornell, Till Rosenband, Scott Diddams, Tom Parker and Tom Heavner for their time and patience in answering my questions. Special thanks go to Chris Ellenor and Rockson Chang, who, as graduate students in Aephraim Steinberg’s laboratory in Toronto, spent countless hours explaining to me the technicalities of Bose-Einstein Condensation. My research for this dissertation was supported by several grants, including three Ontario Graduate Scholarships, a Chancellor Jackman Graduate Fellowship in the Humanities, a School of Graduate Studies Travel Grant (the latter two from the University of Toronto), and a Junior Visiting Fellowship at Tilburg University. I am indebted to Gideon Freudenthal, my MA thesis supervisor, whose enthusiasm for teaching and attention to detail inspired me to pursue a career in philosophy. My mother, Ruth Tal, has been extremely supportive and encouraging throughout my graduate studies. I deeply thank her for enduring my infrequent visits home and the occasional cold Toronto winter. Finally, to my partner, Cheryl Dipede, for suffering through my long hours of study with only support and love, and for obligingly jumping into the unknown with me, thanks for being you. v Table of Contents Introduction ...................................................................................................... 1 1. Measurement and knowledge........................................................................... 1 2. The epistemology of measurement................................................................. 3 3. Three epistemological problems...................................................................... 5 The problem of coordination.................................................................... 8 The problem of accuracy .........................................................................11 The problem of quantity individuation..................................................12 Epistemic entanglement...........................................................................14 4. The challenge from practice...........................................................................15 5. The model-based account...............................................................................17 6. Methodology.....................................................................................................21 7. Plan of thesis ....................................................................................................24 1. How Accurate is the Standard Second? ................................................... 26 1.1. Introduction......................................................................................................26 1.2. Five notions of measurement accuracy ........................................................29 1.3. The multiple realizability of unit definitions................................................33 1.4. Uncertainty and de-idealization .....................................................................37 1.5. A robustness condition for accuracy ............................................................40 1.6. Future definitions of the second ...................................................................44 1.7. Implications and conclusions.........................................................................46 2. Systematic Error and the Problem of Quantity Individuation ................ 48 2.1. Introduction......................................................................................................48 2.2. The problem of quantity individuation ........................................................51 2.2.1. Agreement and error...................................................................51 2.2.2. The model-relativity of systematic error..................................55 2.2.3. Establishing agreement: a threefold condition........................59 2.2.4. Underdetermination....................................................................62