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David Atkinson Jeanne Peijnenburg Probability and the Regress Problem Synthese Library 383 Studies in Epistemology, Logic, Methodology, and Philosophy of Science David Atkinson Jeanne Peijnenburg Fading Foundations Probability and the Regress Problem Synthese Library Studies in Epistemology, Logic, Methodology, and Philosophy of Science Volume 383 Editor-in-Chief Otávio Bueno, University of Miami, Department of Philosophy, USA Editors Berit Brogaard, University of Miami, USA Anjan Chakravartty, University of Notre Dame, USA Steven French, University of Leeds, UK Catarina Dutilh Novaes, University of Groningen, The Netherlands More information about this series at http://www.springer.com/series/6607 David Atkinson • Jeanne Peijnenburg Fading Foundations Probability and the Regress Problem David Atkinson Jeanne Peijnenburg University of Groningen University of Groningen Groningen, The Netherlands Groningen, The Netherlands Synthese Library ISBN 978-3-319-58294-8 ISBN 978-3-319-58295-5 (eBook) DOI 10.1007/978-3-319-58295-5 Library of Congress Control Number: 2017941185 © The Editor(s) (if applicable) and The Author(s) 2017. This book is an open access publication Open Access This book is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, duplication, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made. The images or other third party material in this book are included in the work’s Creative Commons license, unless indicated otherwise in the credit line; if such material is not included in the work’s Creative Commons license and the respective action is not permitted by statutory regulation, users will need to obtain permission from the license holder to duplicate, adapt or reproduce the material. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Tief ist der Brunnen der Vergangenheit. Sollte man ihn nicht unergrundlich¨ nennen? (Deep is the well of the past. Should one not call it unfathomable?) Thomas Mann — Joseph und seine Bruder¨ Preface This book is the result of ten years on and off thinking about infinite regresses in epistemology. It draws on several of our papers, which, partly because of the development of our thoughts, are not always well connected. Our overall purpose here is to show how our understanding of infinite epistemic chains benefits from an analysis of justification in terms of prob- ability theory. It has been often assumed that epistemic justification is prob- abilistic in character, but we think that the consequences of this assumption for the epistemic regress problem have been insufficiently taken into account. The book has eight chapters, detailed calculations having been relegated to appendices. Chapter 1 contains an introduction to the epistemological regress problem, giving some historical background, and recalling its three attempted solutions, foundationalism, coherentism and infinitism. Chapter 2 discusses different views on epistemic justification, since they bear on both the framing of the problem and its proposed solution. Chapters 3 and 4 form the core of the book. Taking as our point of departure a debate between Clarence Irving Lewis and Hans Reichenbach, we introduce the concept of a probabilistic regress, and we explain how it leads to a phenomenon that we call fading foundations: the importance of a foundational proposition dwin- dles away as the epistemic chain lengthens. In Chapters 5 and 6 we describe how a probabilistic regress resists the traditional objections to infinite epis- temic chains, and we reply to objections that have been raised against prob- abilistic regresses themselves. Chapter 7 compares a probabilistic regress to an endless hierarchy of probability statements about probability statements; it is demonstrated that the two are formally equivalent. In the final chapter we leave one-dimensional chains behind and turn to multi-dimensional net- works. We show that what we have found for linear chains applies equally vii viii Preface to networks that stretch out in many directions: the effect of foundational propositions fades away as the network expands. Epistemic regresses are not the only regresses about which philosophers have wracked their brains. The ancient Greeks and the mediaeval scholastics worried a lot about infinite causal chains, and more recently philosopers have shown interest in the phenomenon of grounding. Although we remain silent about the latter, and only tangentially touch upon the former, we believe that our analysis could shed light on causal regresses — on condition that causality is interpreted probabilistically. We owe much to others who have concurrently been thinking about epis- temic regresses, notably Peter D. Klein and Scott F. Aikin. Peter Klein de- serves the credit for being the first to set the cat among the pigeons by sup- posing that infinite regresses in epistemology are not prima facie absurd. With Scott Aikin one of us organized a workshop on infinite regresses in October 2013 at Vanderbilt University. This resulted in a special issue of Metaphilosophy (2014, vol. 45 no. 3), which was soon followed by a special issue of Synthese (2014, vol. 191 no. 4), co-edited with Sylvia Wenmackers. The writing of this book has been made possible by financial support from the Dutch Organization for Scientific Research (Nederlandse Organ- isatie voor Wetenschappelijk Onderzoek, NWO), grant number 360-20-280. Our colleagues at the Faculty of Philosophy of the University of Groningen provided support of many different kinds. This has meant a lot to us and we thank them very much. Aix-en-Provence, October 2015 David Atkinson and Jeanne Peijnenburg Contents 1 The Regress Problem ..................................... 1 1.1 Reasons for Reasons: Agrippa’s Trilemma . ............... 1 1.2 Coherentism and Infinitism ............................. 8 1.3 Vicious Versus Innocuous Regress . .................... 14 2 Epistemic Justification .................................... 25 2.1 Making a Concept Clear. ............................. 25 2.2 Two Questions . ...................................... 29 2.3 Entailment ........................................... 33 2.4 Probabilistic Support . ................................. 36 2.5 Smith’s Normic Support . ............................. 45 2.6 Alston’s Epistemic Probability . ........................ 51 3 The Probabilistic Regress.................................. 59 3.1 A New Twist . ...................................... 59 3.2 The Lewis-Reichenbach Dispute . ........................ 61 3.3 Lewis’s Argument . .................................. 65 3.4 A Counterexample . ................................. 69 3.5 A Nonuniform Probabilistic Regress . .................... 72 3.6 Usual and Exceptional Classes . ........................ 74 3.7 Barbara Bacterium . ................................. 78 4 Fading Foundations and the Emergence of Justification ....... 83 4.1 Fading Foundations . .................................. 83 4.2 Propositions versus Beliefs ............................. 86 4.3 Emergence of Justification . ............................. 90 4.4 Where Does the Justification Come From? . ............... 94 4.5 Tour d’horizon . ...................................... 98 ix x Contents 5 Finite Minds .............................................101 5.1 Ought-Implies-Can . .................................101 5.2 Completion and Computation . ........................105 5.3 Probabilistic Justification as a Trade-Off . ...............107 5.4 Carl the Calculator . .................................115 6 Conceptual Objections ....................................119 6.1 The No Starting Point Objection . ........................119 6.2 A Probabilistic Regress Needs No Starting Point ...........124 6.3 The Reductio Argument . .............................128 6.4 How the Probabilistic Regress Avoids the Reductio . ......131 6.5 Threshold and Closure Constraints . ....................134 6.6 Symmetry and Nontransitivity . ........................139 7 Higher-Order Probabilities ................................143 7.1 Two Probabilistic Regresses ............................143 7.2 Second- and Higher-Order Probabilities...................145 7.3 Rescher’s Argument . .................................150 7.4 The Two Regresses Are Isomorphic . ....................156 7.5 Making Coins . ......................................160 8 Loops and Networks ......................................167 8.1 Tortoises and Serpents .................................167
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