DOCSLIB.ORG

Bayes Or Bust? a Critical Examination of Bayesian Confirmation Theory

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Bayes Or Bust? a Critical Examination of Bayesian Confirmation Theory Bayesor Bust? A Critical Examination of Bayesian Confirmation Theory John Earman A Bradford Book The MIT Press Cambridge, Massachusetts London, England Second printing. 1996 © 1992 Massachusetts Institute of Technology For Peter Hempel, teacher extraordinaire, All rights reserved. No part of this book may be reproduced in any form by any electronic And Grover Maxwell, a gentleman who left his mark on an or mechanical means (including photocopying, recording, or information storage and ungentlemanly world retrieval) without permission in writing from the publisher. This book was set in Times Roman by Asco Trade Typesetting Ltd., Hong Kong, and was printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Earman, John. Bayes or bust? : a critical examination of Bayesian confirmation theory I John Earman. p. em. "A Bradford book." Includes bibliographical references and index. ISBN 0-262-05046-3 1.Science-Philosophy. 2. Science-Methodology. 3. Bayesian statistical decision theory. I. Title. Q175.E23 1992 502.8-dc20 91-35623 CIP Contents Preface xi Notation xiii Introduction 1 1 Bayes's Bayesianism 7 1 Bayes's Problem 7 2 Bayes's Two Concepts of Probability 8 3 Bayes's Attempt to Demonstrate the Principles of Probability 9 4 Bayes's Princip1e-of-Insufficient-Reason Argument 14 5 Choosing a Prior Distribution 16 6 Proxy Events and the Billiard-Table Model 20 7 Applications of Bayes's Results 24 8 Conclusion 26 Appendix: Bayes's Definitions and Propositions 27 2 TheMachinery of Modern Bayesianism 33 1 The Elements of Modern Bayesianism 33 2 The Probability Axioms 35 3 Dutch Book and the Axioms of Probability 38 4 Difficulties with the Dutch Book Argument 40 5 Non-Dutch Book Justifications of the Probability Axioms 44 6 Justifications for Conditionalization 46 7 Lewis's Principal Principle 51 8 Descriptive versus Normative Interpretations of Bayesianism 56 9 Prior Probabilities 57 10 Conclusion 59 Appendix 1: Conditional Probability 59 Appendix 2: Laws of Large Numbers 61 3 Success Stories 63 1 Qualitative Confirmation: The Hypotheticodeductive Method 63 2 Hempel's Instance Confirmation 65 Contents ix viii Contents 3 The Washing Out of Priors: Some Bayesian Folklore 141 3 The Ravens Paradox 69 4 Convergence to Certainty and Merger of Opinion as a 4 Bootstrapping and Relevance Relations 73 Consequence of Martingale Convergence 144 5 Variety of Evidence and the Limited Variety of Nature 77 5 The Results of Gaifman and Snir 145 6 Putnam and Hempel on theIndispensability of 6 Evaluation ofthe Convergence-to-Certainty and Theories 79 Merger-of-Opinion Results 147 7 The Quine and Duhem Problem 83 7 Underdetermination and Antirealism 149 8 Conclusion 86 8 Confirmability and Cognitive Meaningfulness 153 9 Alternative Explanations of Objectivity 154 4 Challenges Met 87 10 The Evolutionary Solution 155 1 The Problem of Zero Priors: Carnap's Version 87 11 Modest but Realistic Solutions 156 2 The Problem ofZero Priors: Jeffrey's Version 90 12 Non-Bayesian Solutions 158 3 The Problem of Zero Priors: Popper's Versions 92 13 Retrenchment 158 4 The Popper and Miller Challenge 95 14 Conclusion 160 5 Richard Miller and the Return to Adhocness 98 6 Griinbaum's Worries 102 7 A Plea for Eliminative Induction 163 7 Goodman's New Problem of Induction 104 1 Teaching Dr. Watson to Do Induction 163 8 Novelty of Prediction and Severity ofTest 113 2 The Necessity ofthe Eliminative Element in Induction 163 9 Conclusion 117 3 Salmon's Retreat from Bayesian Inductivism 171 4 Twentieth-Century Gravitational Theories: A Case The Problem of Old Evidence 119 S Study 173 1 Old Evidence as a Challenge to Bayesian Confirmation 5 Conclusion 180 Theory 119 2 Preliminary Attempts to Solve or Dissolve the Old- 8 Normal Science, Scientific Revolntions, and All That: Evidence Problem 120 Thomas Bayes versus Thomas Kuhn 187 3 Garber's Approach 123 1 Kuhn's Structure of Scientific Revolutions 187 4 Jeffrey's Demonstration 126 2 Theory-Ladenness of Observation and the Incommen- 5 The Inadequacy ofthe Garber, Jeffrey, and Niiniluoto surability ofTheories 189 Solution 130 3 Tom Bayes and Tom Kuhn: Incommensurability? 191 6 New Theories and Doubly Counting Evidence 132 4 Revolutions and New Theories 195 7 Conclusion: A Pessimistic Resolution of the Old- 5 Objectivity, Rationality, and the Problem of Consensus 198 133 Evidence Problem 6 A Partial Resolution of the Problem of Consensus 201 7 Conclusion 203 6 The Rationality and Objectivity of Scientific Inference 137 1 Introduction 137 2 Constraining Priors 139 x Contents Preface 9 Bayesianism versns Formal-Learning Theory 207 Philosophers of science can be justifiably proud of the progress achieved 1 Putnam's Diagonalization Argument 207 in their discipline since the early days of logical positivism. A glaring 2 Taking Stock 209 exception concerns the analysis of the testing of scientific hypotheses and 3 Formal-Learning Theory 210 theories, an exception that threatens to block further progress toward a 4 Bayesian Learning Theory versus Formal-Learning central goal not only of the logical positivists but also of their predecessors Theory 211 and heirs. That goal is the understanding of "the scientific method." What­ 5 Does Formal Learning Have an Edge over Bayesian ever else this method involves, its principal concern is with the issue of how Learning? 212 the results of observation and experiment serve to support or undermine scientific conjectures. Not only does contemporary philosophy of science 6 The Dogmatism of Bayesianism 215 fail to provide a persuasive analysis of this issue, there are even rumblings 7 In What Sense Does a Formal Learner Learn? 218 to the effect that a search for an "inductive logic" or "theory of confirma­ 8 Putnam's Argument Revisited 220 tion" is a fruitless quest for a nonexistent philosopher's stone. The princi­ 9 Conclusion 222 pal difficulty here, it should be emphasized, does not derive from Kuhnian incommensurability and its fellow travelers, for the issue has resisted reso­ 10 A Dialogue 225 lution even for cases that do not stray near the frontiers of scientific revolutions, Notes 237 This work explores one dimension of this impasse by providing a critical References 253 evaluation of the approach I take to provide the best good hope for a Index 265 comprehensive and unified treatment of induction, confirmation, and sci­ entific inference: Bayesianism. It is intended for students of the philosophy of scientific methodology, where 'student' is used in the broad sense to include advanced undergraduates, graduate students, and professional phi­ losophers. It is also intended to annoy both the pro- and contra-Bayesians, To fling down the gauntlet, the critics of Bayesianism have generally failed to get the proper measure of the doctrine, while the Bayesians themselves have failed to appreciate the pitfalls and limitations of their approach. And to add insult to insult, neither side has appreciated the source of the doctrine-the Reverend Bayes's essay. Nor is there much appreciation of what the new discipline of formal learning theory has to tell us about the latent assumptions responsible for the apparent reliability of Bayesian methods. Ifthe annoyance serves as a spur to further progress, I will count this book a success. I want to emphasize as strongly as I can that this work is not intended as a comprehensive review of the pros and cons of Bayesianism. Issues and points of views on issues have been selected with an eye to giving the reader a sense of the strengths and weaknesses of the Bayesian approach to confirmation, and my selections should be judged on that basis. xii Preface Notation The reader who penetrates very far into this work may begin to experi­ Logic ence a topsy-turvy feeling. Those who complain will in: effect be crying, Stop the world, I want to get off! For the world of confirmation is a (Vx) universal quantifier topsy-turvy world. (3x) existential quantifier My intellectual debts are too numerous to recount here. But I would be & conjunction, A & B (A and B) remiss ifI did not acknowledge the many helpful suggestions I received on earlier drafts of this book. Thank you Jeremy Butterfield, Charles Chihara, A l &A2 & ... &A. Alan Franklin, Donald Gillies, Clark Glymour, David Hillman, Colin disjunction, A v B (A or B or both) Howson, Richard Jeffrey, Cory Juhl, Kevin Kelly, Philip Kitcher, Tim Al v A z v ... v An Maudlin, John Norton, Teddy Seiden:feld, Elliott Sober, Paul Teller, Jan material implication, A -->B (if A then B) von Plato, Bas van Fraassen, and Sandy Zabell. With all of this help, the biconditional, A ....B (A if and only ifB) book should be better than it is. The material in chapter 1 appeared as "Bayes' Bayesianism," Studies in negation, I A (not A) the History and Philosophy of Science 21 (1990): 351-370. A version of definition chapter 5 appeared as "Old Evidence, New Theories: Two Unsolved Prob­ I=A A is valid (i.e., A is true in every possible world or model) lems in Bayesian Con:firmation Theory," Pacific Philosophical Quarterly70 AI=B A semantically implies B (i.e., B is true in every possible (1989): 323-340. I am grateful to the editors of these journals for their world or model in which A is true) permission to reprint this material. The excerpts from Bayes's essay found in the appendix to chapter 1 are reproduced with the kind-permission of the editors of Biometrika. Mathematics XEX x is an element of X XsY X is a subset of Y XnY the intersection of X and Y XuY the union of X and Y L' summation over the index i J integral N natural numbers D1I real line f: X --> Y fmaps x E X tof(x) E Y supremum the limit as n approaches in:finity xiv Notation Bayes or Bust? Probability andStatistics Pr(A) the (unconditional) prohability of A Pr(A/B) the conditional probability of A on B E(X) the expectation value of the random variable X (:) n!/[m!(n - m)!] Introduction The Reverend Thomas Bayes died in 1761, leaving a not inconsiderable estate.
Load more

Recommended publications
  • The Open Handbook of Formal Epistemology
    THEOPENHANDBOOKOFFORMALEPISTEMOLOGY Richard Pettigrew &Jonathan Weisberg,Eds. THEOPENHANDBOOKOFFORMAL EPISTEMOLOGY Richard Pettigrew &Jonathan Weisberg,Eds. Published open access by PhilPapers, 2019 All entries copyright © their respective authors and licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. LISTOFCONTRIBUTORS R. A. Briggs Stanford University Michael Caie University of Toronto Kenny Easwaran Texas A&M University Konstantin Genin University of Toronto Franz Huber University of Toronto Jason Konek University of Bristol Hanti Lin University of California, Davis Anna Mahtani London School of Economics Johanna Thoma London School of Economics Michael G. Titelbaum University of Wisconsin, Madison Sylvia Wenmackers Katholieke Universiteit Leuven iii For our teachers Overall, and ultimately, mathematical methods are necessary for philosophical progress. — Hannes Leitgeb There is no mathematical substitute for philosophy. — Saul Kripke PREFACE In formal epistemology, we use mathematical methods to explore the questions of epistemology and rational choice. What can we know? What should we believe and how strongly? How should we act based on our beliefs and values? We begin by modelling phenomena like knowledge, belief, and desire using mathematical machinery, just as a biologist might model the fluc- tuations of a pair of competing populations, or a physicist might model the turbulence of a fluid passing through a small aperture. Then, we ex- plore, discover, and justify the laws governing those phenomena, using the precision that mathematical machinery affords. For example, we might represent a person by the strengths of their beliefs, and we might measure these using real numbers, which we call credences. Having done this, we might ask what the norms are that govern that person when we represent them in that way.
    [Show full text]
  • University of Oklahoma Graduate College The
    UNIVERSITY OF OKLAHOMA GRADUATE COLLEGE THE VIRTUES OF BAYESIAN EPISTEMOLOGY A DISSERTATION SUBMITTED TO THE GRADUATE FACULTY in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY By MARY FRANCES GWIN Norman, Oklahoma 2011 THE VIRTUES OF BAYESIAN EPISTEMOLOGY A DISSERTATION APPROVED FOR THE DEPARTMENT OF PHILOSOPHY BY ______________________________ Dr. James Hawthorne, Chair ______________________________ Dr. Chris Swoyer ______________________________ Dr. Wayne Riggs ______________________________ Dr. Steve Ellis ______________________________ Dr. Peter Barker © Copyright by MARY GWIN 2011 All Rights Reserved. For Ted How I wish you were here. Acknowledgements I would like to thank Dr. James Hawthorne for his help in seeing me through the process of writing my dissertation. Without his help and encouragement, I am not sure that I would have been able to complete my dissertation. Jim is an excellent logician, scholar, and dissertation director. He is also a kind person. I am very lucky to have had the opportunity to work with him. I cannot thank him enough for all that he has given me. I would also like to thank my friends Patty, Liz, Doren, Murry, Becky, Jim, Rebecca, Mike, Barb, Susanne, Blythe, Eric, Ty, Rosie, Bob, Judy, Lorraine, Paulo, Lawrence, Scott, Kyle, Pat, Carole, Joseph, Ken, Karen, Jerry, Ray, and Daniel. Without their encouragement, none of this would have been possible. iv Table of Contents Acknowledgments iv Abstract vi Chapter 1: Introduction 1 Chapter 2: Bayesian Confirmation Theory 9 Chapter 3: Rational Analysis: Bayesian Logic and the Human Agent 40 Chapter 4: Why Virtue Epistemology? 82 Chapter 5: Reliability, Credit, Virtue 122 Chapter 6: Epistemic Virtues, Prior Probabilities, and Norms for Human Performance 145 Bibliography 171 v Abstract The aim of this dissertation is to address the intersection of two normative epistemologies, Bayesian confirmation theory (BCT) and virtue epistemology (VE).
    [Show full text]
  • Inference to the Best Explanation, Bayesianism, and Knowledge
    Inference to the Best Explanation, Bayesianism, and Knowledge Alexander Bird Abstract How do we reconcile the claim of Bayesianism to be a correct normative the- ory of scientific reasoning with the explanationists’ claim that Inference to the Best Explanation provides a correct description of our inferential practices? I first develop Peter Lipton’s approach to compatibilism and then argue that three challenges remain, focusing in particular on the idea that IBE can lead to knowl- edge. Answering those challenges requires renouncing standard Bayesianism’s commitment to personalism, while also going beyond objective Bayesianism regarding the constraints on good priors. The result is a non-standard, super- objective Bayesianism that identifies probabilities with evaluations of plausibil- ity in the light of the evidence, conforming to Williamson’s account of evidential probability. Keywords explanationism, IBE, Bayesianism, evidential probability, knowledge, plausibility, credences. 1 Introduction How do scientists reason? How ought they reason? These two questions, the first descriptive and the second normative, are very different. However, if one thinks, as a scientific realist might, that scientists on the whole reason as they ought to then one will expect the two questions to have very similar answers. That fact bears on debates between Bayesians and explanationists. When we evaluate a scientific hypothesis, we may find that the evidence supports the hypoth- esis to some degree, but not to such a degree that we would be willing to assert out-
    [Show full text]
  • Evidential Probability and Objective Bayesian Epistemology
    Evidential Probability and Objective Bayesian Epistemology Gregory Wheeler, CENTRIA, New University of Lisbon Jon Williamson, Philosophy, University of Kent To appear in Prasanta S. Bandyopadhyay and Malcolm Forster (eds): Handbook of the Philosophy of Statistics, Elsevier Draft of July 16, 2010 Abstract In this chapter we draw connections between two seemingly opposing approaches to probability and statistics: evidential probability on the one hand and objective Bayesian epistemology on the other. Contents 1 Introduction2 2 Evidential Probability2 2.1 Motivation..............................2 2.2 Calculating Evidential Probability.................6 3 Second-order Evidential Probability9 3.1 Motivation..............................9 3.2 Calculating Second-order EP.................... 11 4 Objective Bayesian Epistemology 15 4.1 Motivation.............................. 15 4.2 Calculating Objective Bayesian Degrees of Belief......... 18 5 EP-Calibrated Objective Bayesianism 19 5.1 Motivation.............................. 19 5.2 Calculating EP-Calibrated Objective Bayesian Probabilities... 21 6 Conclusion 22 1 1 Introduction Evidential probability (EP), developed by Henry Kyburg, offers an account of the impact of statistical evidence on single-case probability. According to this theory, observed frequencies of repeatable outcomes determine a probability interval that can be associated with a proposition. After giving a comprehensive introduction to EP in x2, in x3 we describe a recent variant of this approach, second-order evidential probability (2oEP). This variant, introduced in Haenni et al.(2008), interprets a probability interval of EP as bounds on the sharp probability of the corresponding proposition. In turn, this sharp probability can itself be interpreted as the degree to which one ought to believe the proposition in question. At this stage we introduce objective Bayesian epistemology (OBE), a theory of how evidence helps determine appropriate degrees of belief (x4).
    [Show full text]
  • Quantitative Epidemiology: a Bayesian Perspective
    Quantitative Epidemiology: A Bayesian Perspective Alexander Eugene Zarebski ORCID 0000-0003-1824-7653 Doctor of Philosophy August 2019 Department of School of Mathematics and Statistics The thesis is being submitted in total fulfilment of the degree. The degree is not being completed under a jointly awarded degree. ii © Alexander Eugene Zarebski, 2019. iii Except where acknowledged in the allowed manner, the ma- terial presented in this thesis is, to the best of my knowledge, original and has not been submitted in whole or part for another degree in any university. Alexander Eugene Zarebski iv Abstract Influenza inflicts a substantial burden on society but accurate and timely forecasts of seasonal epidemics can help mitigate this burden by informing interventions to reduce transmission. Recently, both statistical (correlative) and mechanistic (causal) models have been used to forecast epidemics. However, since mechanistic models are based on the causal process underlying the epidemic they are poised to be more useful in the design of intervention strate- gies. This study investigate approaches to improve epidemic forecasting using mechanistic models. In particular, it reports on efforts to improve a forecasting system targeting seasonal influenza epidemics in major cities across Australia. To improve the forecasting system we first needed a way to benchmark its performance. We investigate model selection in the context of forecasting, deriving a novel method which extends the notion of Bayes factors to a predictive setting. Applying this methodology we found that accounting for seasonal variation in absolute humidity improves forecasts of seasonal influenza in Melbourne, Australia. This result holds even when accounting for the uncertainty in predicting seasonal variation in absolute humidity.
    [Show full text]
  • Bayesan Epistemology
    Bayesian Epistemology Olsson, Erik J Published in: Introduction to Formal Philosophy 2018 Document Version: Peer reviewed version (aka post-print) Link to publication Citation for published version (APA): Olsson, E. J. (2018). Bayesian Epistemology. In S. O. Hansson, & V. F. Hendricks (Eds.), Introduction to Formal Philosophy (pp. 431-442). (Springer undergraduate texts in philosophy). Springer. Total number of authors: 1 General rights Unless other specific re-use rights are stated the following general rights apply: Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal Read more about Creative commons licenses: https://creativecommons.org/licenses/ Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. LUND UNIVERSITY PO Box 117 221 00 Lund +46 46-222 00 00 Bayesian Epistemology Erik J. Olsson Abstract: Bayesian epistemology provides a formal framework within which concepts in traditional epistemology, in particular concepts relating to the justification of our beliefs, can be given precise definitions in terms of probability.
    [Show full text]
  • Reasons As Causes in Bayesian Epistemology Author(S): Clark Glymour and David Danks Source: the Journal of Philosophy, Vol
    Journal of Philosophy, Inc. Reasons as Causes in Bayesian Epistemology Author(s): Clark Glymour and David Danks Source: The Journal of Philosophy, Vol. 104, No. 9 (Sep., 2007), pp. 464-474 Published by: Journal of Philosophy, Inc. Stable URL: http://www.jstor.org/stable/20620044 . Accessed: 01/10/2013 12:24 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Journal of Philosophy, Inc. is collaborating with JSTOR to digitize, preserve and extend access to The Journal of Philosophy. http://www.jstor.org This content downloaded from 128.237.147.56 on Tue, 1 Oct 2013 12:24:32 PM All use subject to JSTOR Terms and Conditions 464 THE JOURNAL OF PHILOSOPHY REASONS AS CAUSES IN BAYESIAN EPISTEMOLOGY* In everyday matters, as well as in law, we allow that someone's reasons can be causes of her actions, and often are. That correct reasoning accords with Bayesian principles is now so widely held in philosophy, psychology, computer science, and elsewhere that the contrary is beginning to seem obtuse, or at best quaint. And that rational agents should learn about the world from energies striking sensory inputs?nerves in people?seems beyond question.
    [Show full text]
  • Evidential Probability and Objective Bayesian Epistemology
    EVIDENTIAL PROBABILITY AND OBJECTIVE BAYESIAN EPISTEMOLOGY Gregory Wheeler and Jon Williamson 1 INTRODUCTION Evidential probability (EP), developed by Henry Kyburg, offers an account of the impact of statistical evidence on single-case probability. According to this theory, observed frequencies of repeatable outcomes determine a probability interval that can be associated with a proposition. After giving a comprehensive introduction to EP in 2, in 3 we describe a recent variant of this approach, second-order evidential§ probability§ (2oEP). This variant, introduced in [Haenni et al., 2010], interprets a probability interval of EP as bounds on the sharp probability of the corresponding proposition. In turn, this sharp probability can itself be interpreted as the degree to which one ought to believe the proposition in question. At this stage we introduce objective Bayesian epistemology (OBE), a theory of how evidence helps determine appropriate degrees of belief ( 4). OBE might be thought of as a rival to the evidential probability approaches.§ However, we show in 5 that they can be viewed as complimentary: one can use the rules of EP to narrow§ down the degree to which one should believe a proposition to an interval, and then use the rules of OBE to help determine an appropriate degree of belief from within this interval. Hence bridges can be built between evidential probability and objective Bayesian epistemology. 2 EVIDENTIAL PROBABILITY 2.1 Motivation Rudolf Carnap [Carnap, 1962] drew a distinction between probability1, which concerned rational degrees of belief, and probability2, which concerned statistical regularities. Although he claimed that both notions of probability were crucial to scientific inference, Carnap practically ignored probability2 in the development of his systems of inductive logic.
    [Show full text]
  • The Role of Bayesian Philosophy Within Bayesian Model Selection
    The Role of Bayesian Philosophy within Bayesian Model Selection Jan Sprenger∗ 13 July 2012 Abstract Bayesian model selection has frequently been the focus of philosoph- ical inquiry (e.g., Forster 1995; Bandyopadhyay and Boik 1999; Dowe et al. 2007). This paper argues that Bayesian model selection procedures are very diverse in their inferential target and their justification, and substan- tiates this claim by means of case studies on three selected procedures: MML, BIC and DIC. Hence, there is no tight link between Bayesian model selection and Bayesian philosophy. Consequently, arguments for or against Bayesian reasoning based on properties of Bayesian model selection pro- cedures should be treated with great caution. 1. Introduction Model selection is a relatively young subfield of statistics that compares sta- tistical models on the basis of their structural properties and their fit to the data. The goal of model selection consists in comparing and appraising various candidate models on the basis of observed data.1 Following up on Forster and Sober's seminal (1994) paper, the problem of model selection attracted much attention in philosophy of science. The properties of various model selection procedures have been used to argue for general theses in philosophy of science, such as the replacement of truth by predictive accuracy as an achievable goal of science (Forster 2002), the predic- tion/accommodation problem (Hitchcock and Sober 2004), the realism/instrumentalism dichotomy (Mikkelson 2006; Sober 2008), and the aptness of Bayesian reasoning for statistical inference (Forster 1995; Bandyopadhyay et al. 1996; Bandyopad- hyay and Boik 1999; Dowe et al. 2007). This paper explores the extent to which Bayesian model selection procedures are anchored within Bayesian philosophy, and in particular their philosophical ∗Contact information: Tilburg Center for Logic and Philosophy of Science, Tilburg Univer- sity, P.O.
    [Show full text]
  • Computational Epistemology and the Limits of Rationality for Finite Reasoners by Danilo Fraga Dantas B.A
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by PhilPapers ALMOST IDEAL: Computational Epistemology and the Limits of Rationality for Finite Reasoners By Danilo Fraga Dantas B.A. (Universidade Federal da Bahia) 2005 M.A. (Universidade Federal da Bahia) 2007 M.A. (Universidade Federal do Rio Grande do Sul) 2010 M.A. (University of California Davis) 2013 Dissertation Submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Philosophy in the Office of Graduate Studies of the University of California Davis Approved: Bernard Molyneux, Chair Hanti Lin Adam Sennet George J. Mattey II Almerindo Ojeda Committee in Charge 2016 -i- Para Emilly. -ii- Contents List of Figures . .v List of Tables . viii Abstract . ix Acknowledgments . xi Introduction 1 1 The limits of finite reasoning 14 1.1 Definitions . 17 1.2 Classical reasoners . 21 1.3 Nonmonotonic reasoners . 25 1.4 Stable beliefs . 31 1.5 Conclusions . 34 2 Ideal reasoners don't believe in zombies 35 2.1 Ideal negative conceivability . 37 2.2 Conclusive ideal conceiver . 41 2.3 Defeasible ideal conceiver . 47 2.4 Someone is conscious! . 51 2.5 Conclusions . 55 3 Achilles and the truth-goal 57 3.1 The truth-goal . 59 3.1.1 Truth-goal as the maximization of function g ............ 63 3.2 Maximum epistemic rationality . 67 3.2.1 Features of the function g model . 70 3.3 Discussion . 72 4 Computational epistemology 81 4.1 Efficient reasoning . 84 -iii- 4.2 Computational epistemology . 91 4.2.1 Class of problems .
    [Show full text]
  • Parameterizing Developmental Changes in Epistemic Trust
    Parameterizing developmental changes in epistemic trust Baxter S. Eaves Jr. Rutgers University–Newark Patrick Shafto Rutgers University–Newark Abstract Children rely on others for much of what they learn, and therefore must track who to trust for information. Researchers have debated whether to interpret children’s be- havior as inferences about informants’ knowledgeability only or as inferences about both knowledgeability and intent. We introduce a novel framework for integrating results across heterogeneous ages and methods. The framework allows application of a recent computational model to a set of results that span ages 8 months to adulthood and a variety of methods. The results show strong fits to specific find- ings in the literature trust, and correctly fails to fit one representative result from an adjacent literature. In the aggregate, the results show a clear development in children’s reasoning about informants’ intent and no appreciable changes in rea- soning about informants’ knowledgeability, confirming previous results. The results extend previous findings by modeling development over a much wider age range and identifying and explaining differences across methods. Keywords: Bayesian models, social learning, selective trust, epistemic trust Children face a difficult problem in learning about the world. There is much to learn and little time in which to learn it. In this context, the benefits of social learning are self-evident. Self-directed strategies are slow and cannot be used to acquire some knowledge (e.g. language). It is quicker to call upon on the knowledge of others. However, people do not always produce reliable data. A person may have inaccurate knowledge or may wish to deceive.
    [Show full text]
  • Being Realist About Bayes, and the Predictive Processing Theory of Mind
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by PhilSci Archive Being Realist about Bayes, and the Predictive Processing Theory of Mind Matteo Colombo∗ Lee Elkiny Stephan Hartmannz July 19, 2018 Forthcoming in The British Journal for the Philosophy of Science Abstract Some naturalistic philosophers of mind subscribing to the predictive processing theory of mind have adopted a realist attitude towards the results of Bayesian cognitive science. In this paper, we argue that this realist attitude is unwarranted. The Bayesian research program in cognitive science does not possess special epistemic virtues over alternative approaches for explaining mental phenomena involving uncertainty. In particular, the Bayesian approach is not simpler, more unifying, or more rational than alternatives. It is also contentious that the Bayesian approach is overall better supported by the empirical evidence. So, to develop philosophical theories of mind on the basis of a realist interpretation of results from Bayesian cognitive science is unwarranted. Naturalistic philosophers of mind should instead adopt an anti-realist attitude towards these results and remain agnostic as to whether Bayesian models are true. For continuing on with an exclusive focus and praise of Bayes within debates about the predictive processing theory will impede progress in philosophical understanding of scientific practice in computational cognitive science as well as of the architecture of the mind. Keywords: Bayesian cognitive science, predictive processing, representing uncertainty, naturalistic philosophy of mind, scientific realism, underdetermination thesis 1. Introduction 2. From Uncertainty to Bayesian Brains ∗Tilburg Center for Logic, Ethics, and Philosophy of Science, Tilburg University, 5037 AB Tilburg (The Netherlands) – https://mteocolphi.wordpress.com – [email protected].
    [Show full text]