View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by D-Scholarship@Pitt STUDIES IN THE LOGIC OF EXPLANATORY POWER by Jonah N. Schupbach M. A., Philosophy of Religion, Denver Seminary, 2004 M. A., Philosophy, Western Michigan University, 2006 Submitted to the Graduate Faculty of Arts and Sciences in partial fulfillment of the requirements for the degree of Ph. D. in History and Philosophy of Science University of Pittsburgh 2011 UNIVERSITY OF PITTSBURGH ARTS AND SCIENCES This dissertation was presented by Jonah N. Schupbach It was defended on June 14, 2011 and approved by John Earman, Pittsburgh, HPS Edouard Machery, Pittsburgh, HPS David Danks, Carnegie Mellon University, Philosophy Stephan Hartmann, Tilburg University, Philosophy John Norton, Pittsburgh, HPS Dissertation Advisors: John Earman, Pittsburgh, HPS, Edouard Machery, Pittsburgh, HPS ii Copyright c by Jonah N. Schupbach 2011 iii STUDIES IN THE LOGIC OF EXPLANATORY POWER Jonah N. Schupbach, PhD University of Pittsburgh, 2011 Human reasoning often involves explanation. In everyday affairs, people reason to hypotheses based on the explanatory power these hypotheses afford; I might, for example, surmise that my toddler has been playing in my office because I judge that this hypothesis delivers a good explanation of the disarranged state of the books on my shelves. But such explanatory reasoning also has relevance far beyond the commonplace. Indeed, explanatory reasoning plays an important role in such varied fields as the sciences, philosophy, theology, medicine, forensics, and law. This dissertation provides an extended study into the logic of explanatory reasoning via two general questions. First, I approach the question of what exactly we have in mind when we make judgments pertaining to the explanatory power that a hypothesis has over some evidence. This question is important to this study because these are the sorts of judgments that we constantly rely on when we use explanations to reason about the world. Ultimately, I introduce and defend an explication of the concept of explanatory power in the form of a probabilistic measure E. This formal explication allows us to articulate precisely some of the various ways in which we might reason explanatorily. The second question this dissertation examines is whether explanatory reasoning con- stitutes an epistemically respectable means of gaining knowledge. I defend the following ideas: The probability theory can be used to describe the logic of explanatory reasoning, the normative standard to which such reasoning attains. Explanatory judgments, on the other hand, constitute heuristics that allow us to approximate reasoning in accordance with this logical standard while staying within our human bounds. The most well known model of iv explanatory reasoning, Inference to the Best Explanation, describes a cogent, nondeductive inference form. And reasoning by Inference to the Best Explanation approximates reasoning directly via the probability theory in the real world. Finally, I respond to some possible objections to my work, and then to some more general, classic criticisms of Inference to the Best Explanation. In the end, this dissertation puts forward a clearer articulation and novel defense of explanatory reasoning. Keywords: abduction, Bayesian explanationism, Bayesianism, bounded rationality, Car- nap, epistemology, explanation, explanatory power, explanatory reasoning, explication, formal epistemology, formal methods, formal philosophy, heuristics, human reasoning, inductive logic, Inference to the Best Explanation, Peirce, probability theory. v TABLE OF CONTENTS PREFACE ......................................... xi 1.0 INTRODUCTION .................................1 1.1 What Paley and Darwin Have in Common...................1 1.2 Toward an Epistemology of Explanation....................6 1.3 Objective of the Study.............................. 11 1.4 Preview...................................... 13 2.0 THE LOGIC OF EXPLANATORY POWER ................ 17 2.1 Introduction................................... 17 2.2 Conceptual Analysis and Carnapian Explication................ 18 2.3 Our Explicandum: Clarifying \Explanatory Power".............. 25 2.3.1 Examples: Paley and Darwin Revisited................. 26 2.3.2 Examples: Murder on the London Underground............ 27 2.3.3 Examples: No Miracles Allowed..................... 28 2.3.4 Informal Description............................ 29 2.4 Toward an Explicatum.............................. 30 2.4.1 Carnap's Desiderata Revisited...................... 30 2.4.2 Conditions for an Explication of Explanatory Power.......... 31 2.5 The Measure of Explanatory Power E ..................... 35 2.5.1 Uniqueness, Version 1........................... 37 2.5.2 Uniqueness, Version 2........................... 40 2.6 Theorems of E .................................. 44 2.6.1 Addition of Irrelevant Evidence...................... 45 vi 2.6.2 Addition of Relevant Evidence...................... 46 2.6.3 Conjunction of Independently Explained Evidence........... 48 2.7 A Misguided Objection............................. 50 3.0 AN EMPIRICAL DEFENSE OF THE EXPLICATION E ........ 52 3.1 Introduction................................... 52 3.2 Candidate Measures of Explanatory Power................... 53 3.3 Experimental Design............................... 57 3.3.1 Materials and Procedure......................... 57 3.3.2 Participants................................ 60 3.4 Results...................................... 60 3.4.1 Preparing the Measures for Comparison................. 60 3.4.2 Comparing the Measures......................... 64 3.5 Discussion..................................... 71 4.0 HOW TO BE (AND HOW NOT TO BE) A BAYESIAN EXPLANA- TIONIST ....................................... 75 4.1 Explanatory Reasoning, Peircean Abduction, and Inference to the Best Ex- planation..................................... 76 4.2 The Bayesian and the Explanationist...................... 79 4.3 How Not to Be a Bayesian Explanationist................... 81 4.3.1 Pluralism I: van Fraassen's Target.................... 83 4.3.2 Pluralism II: Weisberg's Principle.................... 85 4.4 How to Be a Bayesian Explanationist...................... 89 4.4.1 The Heuristic Approach.......................... 90 4.4.2 Okasha, Lipton, and McGrew on Bayesian Explanationism...... 93 4.4.3 Carnapian Explication and the Heuristic Approach........... 96 4.4.4 A Recent Critique of the Heuristic Approach.............. 98 4.4.4.1 Criticism 1............................. 98 4.4.4.2 Criticism 2............................. 106 5.0 INFERENCE TO THE BEST EXPLANATION, CLEANED UP AND MADE RESPECTABLE ............................. 110 vii 5.1 Introduction................................... 110 5.2 Inference to the Best Explanation, Cleaned Up................ 113 5.3 ... And Made Respectable: Implications of Explanatory Power........ 114 5.4 ... And Made Respectable: What Computers Teach us about Inference to the Best Explanation............................... 117 5.5 Conclusion.................................... 124 6.0 OBJECTIONS ................................... 127 6.1 Objections to this Work............................. 127 6.1.1 Objection 1: Explanation without Explanatory Power?........ 127 6.1.2 Objection 2: Priors and Explanatory Power............... 131 6.2 General Objections to Inference to the Best Explanation........... 134 6.2.1 Objection 1: Affirming the Consequent................. 134 6.2.2 Objection 2: Best of a Bad Lot...................... 136 7.0 EPILOGUE ..................................... 143 APPENDIX A. PROOF OF THEOREM 1 (UNIQUENESS OF E) ..... 146 APPENDIX B. PROOF OF THEOREM 2 AND COROLLARY 1 ..... 150 APPENDIX C. PROOF OF THEOREM 3 .................... 154 APPENDIX D. PROOF OF THEOREM 4 .................... 156 APPENDIX E. PROOF OF THEOREMS 5 AND 6 .............. 159 APPENDIX F. PROOF OF THEOREM 7 .................... 161 APPENDIX G. PROOF OF THEOREM 8 .................... 163 BIBLIOGRAPHY .................................... 167 viii LIST OF TABLES 3.1 Candidate Measures of Explanatory Power.................... 54 3.2 Respective Contents of Urns A and B....................... 58 3.3 Distances between participant judgments and measures (subjective probabilities). 65 3.4 Distances between participant judgments and measures (objective probabilities). 66 3.5 Sample statistics (using subjective probabilities)................. 69 3.6 Sample statistics (using objective probabilities)................. 69 3.7 Comparison of E with other measures (using subjective probabilities on top and objective probabilities on bottom). Note: Each cell reports the results of a paired t-test between residuals obtained with E and those obtained with the measure in the associated column. For each test, N = 520, corresponding to the total number of participant judgments.................... 70 5.1 Relative percentage accuracies of Inference to the Best Explanation (percentage accuracy of Inference to the Best Explanation / percentage accuracy of IMP). 125 ix LIST OF FIGURES 3.1 E(d; h) perfectly correlated with J(d; h) but giving vastly different values... 62 3.2 Three members of the Lα family.......................... 65 3.3 Distances of members of Lα versus that of EP (dotted line) and E (solid line) { calculated using subjective probabilities..................... 68 3.4 Distances of members of Lα versus that of EP (dotted line) and E (solid line) { calculated using objective probabilities....................