Submitted December 11th, 2013. Supervisors: Prof. dr. Joke Meheus, Universiteit Gent Dr. Bert Leuridan, Universiteit Gent Reading Committee: Prof. dr. Atocha Aliseda, Universidad Nacional Autonoma´ de M´exico Prof. dr. Igor Douven, Rijksuniversiteit Groningen Dr. Michela Massimi, The University of Edinburgh Prof. dr. Maarten Van Dyck, Universiteit Gent Prof. dr. Erik Weber, Universiteit Gent This thesis was typeset in LATEX. Cover Image: Daya Bay Neutrino Experiment (Courtesy of Brookhaven National Laboratory) Cover Design: Gitte Callaert Faculteit Letteren en Wijsbegeerte Tjerk Gauderis Patterns of Hypothesis Formation At the crossroads of Philosophy of Science, Logic, Epistemology, Artificial Intelligence and Physics Proefschrift voorgelegd tot het behalen van de graad van Doctor in de Wijsbegeerte Promotoren: Prof. Dr. Joke Meheus en Dr. Bert Leuridan to my daughter Ada, who explains it all acknowledgments This piece of work would never have emerged in its present form, were it not for the support of many. In particular, I want to thank my love Nel, for being there and complementing me; my daughter Ada for bringing her liveliness into our home: her look on the world was and is a con- stant inspiration; my supervisor Joke for allow- ing me to pursue my own path in these muddy waters; my co-supervisor Bert for his detailed and constructive remarks on every part of this thesis; the Centre for Logic and Philosophy of Science for giving me a four years grant; its cur- rent and former employees for their many useful comments and ideas over the years; my friends, they mean more to me than they realize; and finally, the world itself, for being such an intrigu- ing and fascinating place to dwell in. Contents 1 Introduction 1 1.1 General Topic of the Dissertation . 2 1.2 Overview of the Literature . 3 1.3 Four Parts, Four Approaches . 8 1.4 ‘Scientific Discovery’ and ‘Abductive Reasoning’ . 9 1.5 Some Common Themes . 13 1.6 A Note on the Structure . 15 I Epistemological Considerations 17 2 Two Distinct Doxastic Attitudes 23 2.1 The Notion ‘Doxastic Attitude’ . 23 2.2 Doxastic Attitudes and Doxastic Concepts . 26 2.3 The Theoretical and the Practical Doxastic Attitude . 27 2.4 Three Categories of Doxastic Concepts . 31 2.5 Belief and Acceptance . 33 2.6 Belief, Degrees of Belief and the Bayesian Challenge . 37 2.7 Conclusion . 40 3 The Attitude of Entertaining a Hypothesis 43 3.1 Uncertainties and Doxastic Attitudes . 43 3.2 Hypotheses and Beliefs . 48 3.3 The Doxastic Attitude of Entertaining a Hypothesis . 57 3.4 Hypotheses and Science, Rationality and Skepticism . 59 II Logical Patterns 65 4 Singular Fact Abduction in Science 83 4.1 Introduction . 83 ii CONTENTS 4.2 General Characterization of Adaptive Logics . 86 4.3 The Deductive Framework . 89 s 4.4 Informal Presentation of the Logic MLAs . 90 s 4.5 Formal Presentation of the Logic MLAs . 96 4.6 Modeling Human Reasoning and Consequence Sets . 97 4.7 Case Study: The Origin of the Moon . 99 4.8 Conclusion . 103 5 Singular Fact Abduction in AI 105 5.1 A Set-based Formulation of Adaptive Logics Syntax . 106 5.2 Other Conditional Approaches in AI . 109 5.3 The Problem of Multiple Explanatory Hypotheses . 109 s 5.4 A Set-based Formulation of the Logic MLAs . 112 5.5 An Elaborate Example: a Bird called Tweety . 116 5.6 Conclusion . 119 6 Abduction of Generalizations 121 6.1 Introduction . 121 6.2 Abduction of a Generalization . 123 6.3 Introducing the Formal Framework . 129 6.4 Presentation of The Logic LAr . 134 6.5 A New Problem for the Logic 8LAr . 140 6.6 Conclusion . .8 . 142 III A Historical Case 143 7 The Curious β spectrum 151 7.1 Introduction . 152 7.2 The β puzzle in 1927 . 155 7.3 Charles Ellis and William Wooster . 162 7.4 Ernest Rutherford and James Chadwick . 165 7.5 George Paget Thomson . 169 7.6 Niels Bohr . 174 7.7 Werner Heisenberg . 182 7.8 Wolfgang Pauli . 184 7.9 Summary and Conclusions . 192 CONTENTS iii IV Thinking about Models 197 8 The Adaptation of Old Ideas 203 8.1 The Heuristic Role of Models in Science . 204 8.2 Models and Scientific Discovery in Physics . 205 8.3 Case Study A: Rutherford’s idea of the Neutron . 209 8.4 Case Study B: Pauli’s idea of the Neutrino . 212 8.5 Conclusion . 216 9 Models and Hypotheses 217 9.1 Introduction . 217 9.2 Some Conceptual Issues . 219 9.3 Four Stances on their Relation . 223 9.4 Three Case Studies from Astrophysics . 230 9.5 Heuristic and Fully Interpretable Hypotheses . 237 9.6 Hypotheses in Model-Based Scientific Practice . 240 9.7 Conclusion . 242 Conclusion 245 Bibliography 251 1Introduction The Muses love alternatives. — Virgil, Eclogues, Book III How do scientists form new hypotheses? Are there general patterns of hypothesis formation? If so, is the list of patterns humans are capable of limited? Are there better or worse patterns to form new hypotheses? Can we simulate processes of hypothesis formation? How do scientists choose if different patterns are available? How do hypotheses relate to scientific models? How do scientists deal with mutually exclusive hypotheses? Can we rationally endorse mutually exclusive alternatives? Are hypotheses part of our daily life? Can we live with uncertainties? These are the general questions that motivated and led to this disserta- tion, a tour which took me through various philosophical subdisciplines to obtain as rich as possible a view of the topic of hypothesis formation in science. In this general introduction, I will situate my main topic, give an over- view of the existing literature and address some common themes. More specific introductions to the philosophical methods I will use can be found in the separate introductions to the various parts. 2 CHAPTER 1. INTRODUCTION 1.1 General Topic of the Dissertation The topic of this PhD thesis is the formation and use of hypotheses in sci- ence, with a focus on the physical sciences. According to the view I develop, scientific hypotheses can be defined as follows: Scientific hypotheses are statements about the empirical world with an unknown or underdetermined truth status that are ad- vanced as a tentative answer to a particular research question. The different aspects of this definition of scientific hypotheses are argued for and assumed at various places throughout the dissertation, and a full elaboration of this definition can be found in Section 9.2. In the remainder of this section, I want to point out some delineating choices and general features to set the scene. More detailed argumentation will be given in due course. Doxastic Attitude In forming a hypothesis an agent adopts at the same time a specific attitude or cognitive relation towards that hypothesis. As scientific reasoning should not be considered to be isolated from general reasoning in every day life, this attitude, which will be determined as a dox- astic attitude sui generis, can be studied from a more general perspective in the field of epistemology. Truth-purposiveness In this thesis, I deal only with truth-purposive hy- potheses, hypotheses which the agent considers as neither true nor false, but as unknown or even underdetermined. The agent’s main purpose in forming such hypotheses is either to determine their truth value or to use their possible truth for other epistemic purposes. This class of hypotheses has to be sharply distinguished from truth-denying hypotheses, hypotheses the agent considers to be false, but which can be useful for her, for instance, in setting up a thought experiment. Reference to the Empirical World My topic is further limited by the fact that I consider only hypotheses that make reference to the empirical world. In other words, I do not focus on mathematical conjectures or hypothesized conceptual relations. While the analysis of the epistemological and logical parts of this dissertation may probably be extended to include this kind of hypotheses, my analysis of the use of hypotheses in scientific practice is tailored specifically for hypotheses that refer to the empirical world. 1.2. OVERVIEW OF THE LITERATURE 3 The Importance of a Research Question Not just any conjectural state- ment can be considered as a hypothesis. Scientific hypotheses are formed in response to and in relation with a certain research question, which acts as a trigger for them. Although hypotheses are sometimes presented more or less independently at later stages of research, they cannot be fully un- derstood if they are disconnected from their triggers. Hypothesis Formation and Rationality In this thesis I assume through- out the possibility of rational hypothesis formation, both in an absolute and a relative sense. More precisely, I assume that it can be rationally justified to suggest a hypothesis in answer to a particular trigger, and I assume that it can be rationally justified to prefer one method of hypothesis formation above another one in a particular case. Yet I do not assume that there is always a difference: two methods can be (equally) rationally justified in a particular case. Also, rational hypothesis formation does not guar- antee higher truth probabilities for individual hypotheses. It is assumed, however, that rational hypothesis formation serves the agent’s epistemic interests better (largely because of a better understanding and coverage of the space of possibilities). Scientific Discovery and Abductive Reasoning In the literature, hypoth- esis formation in science is generally brought into connection with the con- cepts of ‘scientific discovery’ and ‘abductive reasoning’. However, as the precise meaning of these notions can be ambiguous, I will first give an overview of the literature on hypothesis formation, abduction and scien- tific discovery and clarify how the main questions of this dissertation con- nect to the different research challenges presented in this literature.