· The Kid, the Clerk, and the Gambler · Critical Studies in Statistics and Cognitive Science Mathias Winther Madsen · The Kid, the Clerk, and the Gambler · Critical Studies in Statistics and Cognitive Science ILLC Dissertation Series DS-2015-02 For further information about ILLC-publications, please contact Institute for Logic, Language and Computation Universiteit van Amsterdam Science Park 107 1098 XG Amsterdam phone: +31-20-525 6051 e-mail: [email protected] homepage: http://www.illc.uva.nl/ Copyright (cid:13)c 2015 by Mathias Winther Madsen Cover design by Julie Cetti and Marie-Anne Soyez after a watercolor by Mathias Winther Madsen. Printed and bound by Ipskamp Drukkers, Enschede. ISBN: 978-94-6259-947-5 · The Kid, the Clerk, and the Gambler · Critical Studies in Statistics and Cognitive Science Academisch Proefschrift ter verkrijging van de graad van doctor aan de Universiteit van Amsterdam op gezag van de Rector Magnificus prof.dr. D.C. van den Boom ten overstaan van een door het college voor promoties ingestelde commissie, in het openbaar te verdedigen in de Agnietenkapel op diensdag 1 december 2015, te 10:00 uur door Mathias Winther Madsen geboren te Kopenhagen, Denemarken. Promotores: Prof. dr. M.J.B. Stokhof Prof. dr. M. van Lambalgen Overige leden: Prof. dr. A. Betti, Unversiteit van Amsterdam Prof. dr. G.J. Steen, Unversiteit van Amsterdam Dr. W.H. Zuidema, Unversiteit van Amsterdam Prof. dr. J.W. Romeijn, Rijksunversiteit Groningen Prof. dr. R.A. Zwaan, Erasmus Unversiteit Rotterdam Dr. D.H. Lassiter, Stanford University Faculteit der Geesteswetenschappen v Contents Acknowledgments and Sources ix 1 Introduction 1 2 Cognitive Metaphor Theory and the Metaphysics of Immediacy 5 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Reliability Issues in Metaphor Identification . . . . . . . . . . . . 11 2.3 Further Problems for Word Sense Ordering . . . . . . . . . . . . . 19 2.4 Differences in Immediacy . . . . . . . . . . . . . . . . . . . . . . . 23 2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.6 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3 Back in Time is Not Back in Space: New Evidence from Spontaneous Gesture 35 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.3 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.7 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4 Brain Potentials and the Syntax-Semantics Distinction 53 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.2 The N400 and the P600 . . . . . . . . . . . . . . . . . . . . . . . 54 4.3 The Frayed Ends of Syntax . . . . . . . . . . . . . . . . . . . . . 57 4.4 The Statistics of Decoding . . . . . . . . . . . . . . . . . . . . . . 62 4.5 An Application to Locally Noisy Strings . . . . . . . . . . . . . . 69 4.6 Linguistic Plausibility . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.7 Physiological Plausibility . . . . . . . . . . . . . . . . . . . . . . . 81 4.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 vi 5 A Quantitative Measure of Relevance Based on Kelly Gambling Theory 87 5.1 Doubling Rates and Kelly Gambling . . . . . . . . . . . . . . . . 88 5.2 Relevant Information and Relevance Rates . . . . . . . . . . . . . 92 5.3 Examples of Relevance Measurements . . . . . . . . . . . . . . . . 96 5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 6 Multi-Agent Probability Models of Social Cognition 107 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 6.2 Multi-Agent Uncertainty Representation . . . . . . . . . . . . . . 109 6.3 Example 1: Preference Attribution . . . . . . . . . . . . . . . . . 116 6.4 Example 2: The Sally-Anne Task . . . . . . . . . . . . . . . . . . 120 6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 7 On the Consistency of Approximate Multi-Agent Probability Theory 131 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 7.2 Probabilistic Reasoning in Church . . . . . . . . . . . . . . . . . . 132 7.3 Multi-Agent Probability Theory . . . . . . . . . . . . . . . . . . . 135 7.4 Aymptotic Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . 142 7.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 8 An Epistemological Meditation on the Bias-Variance Trade-off 147 8.1 The Bias-Variance Trade-off . . . . . . . . . . . . . . . . . . . . . 148 8.2 Example: Beta Estimators . . . . . . . . . . . . . . . . . . . . . . 149 8.3 The Frequentist Dilemma . . . . . . . . . . . . . . . . . . . . . . 150 8.4 Two Examples with “Gaps” . . . . . . . . . . . . . . . . . . . . . 152 8.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 9 Fear and Loathing in Statistics 155 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 9.2 Mathematical Background . . . . . . . . . . . . . . . . . . . . . . 156 9.3 Aftermath . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 9.4 A History of Rationality . . . . . . . . . . . . . . . . . . . . . . . 169 9.5 Two Paradigms of Rationality . . . . . . . . . . . . . . . . . . . . 176 9.6 Estimates and Estimators . . . . . . . . . . . . . . . . . . . . . . 182 9.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 Summary 193 Samenvatting 195 vii