The Routledge Handbook of the Philosophy of Evidence 1138943177, 9781138943179

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THE ROUTLEDGE HANDBOOK OF THE PHILOSOPHY OF EVIDENCE

What one can know depends on one’s evidence. Good scientific theories are supported by evidence. Our experiences provide us with evidence. Any sort of inquiry involves the seeking of evidence. It is irrational to believe contrary to your evidence. For these reasons and more, evidence is one of the most fundamental notions in the field of epistemology and is emerging as a crucial topic across academic disciplines. The Routledge Handbook of the Philosophy of Evidence is an outstanding reference source to the key topics, problems, and debates in this exciting subject and is the first major volume of its kind. Comprising forty chapters by an international team of contributors the handbook is divided into six clear parts: • • • • • •

The Nature of Evidence Evidence and Probability The Social Epistemology of Evidence Sources of Evidence Evidence and Justification Evidence in the Disciplines

The Routledge Handbook of the Philosophy of Evidence is essential reading for students and researchers in philosophy of science and epistemology, and will also be of interest to those in related disciplines across the humanities and social sciences, such as law, religion, and history. Maria Lasonen-Aarnio is Professor of Theoretical Philosophy at the University of Helsinki, Finland. She has published on a wide range of topics within epistemology, philosophy of mind, and the study of normality. Her book The Good, the Bad, and the Feasible (2024) defends a novel normative framework and applies it to various problems and puzzles in epistemology and beyond. Clayton Littlejohn is Professor of Philosophy at the Dianoia Institute of Philosophy at the Australian Catholic University in Melbourne, Australia. He has written extensively on epistemic justification, reasons, and evidence.

ROUTLEDGE HANDBOOKS IN PHILOSOPHY

Routledge Handbooks in Philosophy are state-of-the-art surveys of emerging, newly refreshed, and important fields in philosophy, providing accessible yet thorough assessments of key problems, themes, thinkers, and recent developments in research. All chapters for each volume are specially commissioned, and written by leading scholars in the field. Carefully edited and organized, Routledge Handbooks in Philosophy provide indispensable reference tools for students and researchers seeking a comprehensive overview of new and exciting topics in philosophy. They are also valuable teaching resources as accompaniments to textbooks, anthologies, and research-orientated publications. ALSO AVAILABLE: THE ROUTLEDGE HANDBOOK OF WOMEN AND EARLY MODERN PHILOSOPHY Edited by Karen Detlefsen and Lisa Shapiro THE ROUTLEDGE HANDBOOK OF PHILOSOPHY OF RESPONSIBILITY Edited by Maximilian Kiener THE ROUTLEDGE HANDBOOK OF WOMEN AND ANCIENT GREEK PHILOSOPHY Edited by Sara Brill and Catherine McKeen THE ROUTLEDGE HANDBOOK OF PROPERTIES Edited by A.R.J. Fisher and Anna-Sofia Maurin THE ROUTLEDGE HANDBOOK OF THE PHILOSOPHY OF EVIDENCE Edited by Maria Lasonen-Aarnio and Clayton Littlejohn For more information about this series, please visit: www.routledge.com/RoutledgeHandbooks-in-Philosophy/book-series/RHP

THE ROUTLEDGE HANDBOOK OF THE PHILOSOPHY OF EVIDENCE

Edited by Maria Lasonen-Aarnio and Clayton Littlejohn

Cover image: © Getty Images First published 2024 by Routledge 4 Park Square, Milton Park, Abingdon, Oxon OX14 4RN and by Routledge 605 Third Avenue, New York, NY 10158 Routledge is an imprint of the Taylor & Francis Group, an informa business © 2024 selection and editorial matter Maria Lasonen-Aarnio and Clayton Littlejohn; individual chapters, the contributors The right of Maria Lasonen-Aarnio and Clayton Littlejohn to be identified as the authors of the editorial material, and of the authors for their individual chapters, has been asserted in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data Names: Lasonen-Aarnio, Maria, 1979– editor. | Littlejohn, Clayton, editor. Title: The Routledge handbook of the philosophy of evidence / edited by Maria Lasonen-Aarnio, Clayton Littlejohn. Description: Abingdon, Oxon ; New York, NY : Routledge, 2024. | Series: Routledge handbooks in philosophy | Includes bibliographical references and index. Identifiers: LCCN 2023032319 (print) | LCCN 2023032320 (ebook) | ISBN 9781138943179 (hardback) | ISBN 9781032632285 (paperback) | ISBN 9781315672687 (ebook) Subjects: LCSH: Evidence. Classification: LCC BC173 .R68 2024 (print) | LCC BC173 (ebook) | DDC 121/.65—dc23/eng/20231019 LC record available at https://lccn.loc.gov/2023032319 LC ebook record available at https://lccn.loc.gov/2023032320 ISBN: 978-1-138-94317-9 (hbk) ISBN: 978-1-032-63228-5 (pbk) ISBN: 978-1-315-67268-7 (ebk) DOI: 10.4324/9781315672687 Typeset in Sabon by Apex CoVantage, LLC

CONTENTS

Notes on Contributors

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Introduction Maria Lasonen-Aarnio and Clayton Littlejohn

1

PART 1

The Nature of Evidence

17

  1 Experience as Evidence Chris Tucker

19

  2 E = K, but What About R? Timothy Williamson

30

  3 Epistemological Disjunctivism and Evidence Duncan Pritchard

40

  4 Evidential Internalism and Evidential Externalism Giada Fratantonio

51

  5 The Evidential Support Relation of Evidentialism T. Ryan Byerly

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  6 How Can “Evidence” be Normative? Ralph Wedgwood

74

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Contents PART 2

Evidence and Probability

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  7 Varieties of Measures of Evidential Support Peter Brössel

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  8 Positive Relevance Peter Achinstein

104

  9 The Paradoxes of Confirmation Jan Sprenger

113

10 Good Predictions and Bad Accommodations Eric Christian Barnes

124

11 Bayesian Norms and Non-Ideal Agents Julia Staffel

135

12 The Value of Evidence Bernhard Salow

148

13 Sleeping Beauty’s Evidence Jeffrey Sanford Russell

163

14 Higher-Order Evidence Kevin Dorst

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PART 3

The Social Epistemology of Evidence

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15 Evidence and Power: Feminist Empiricist Approaches to Evidence Kristen Intemann

197

16 Evidence, Relativism and Progress in Feminist Standpoint Theory Natalie Alana Ashton

209

17 Epistemic Injustice in Collecting and Appraising Evidence David Schraub and Joel Sati

221

18 Prejudiced Belief: Evidential Considerations Endre Begby

232

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Contents

19 Evidence and Bias Nick Hughes

243

20 Disagreement and Higher-Order Evidence Jonathan Matheson

256

PART 4

Sources of Evidence

273

21 Intuitions as Evidence Marc A. Moffett

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22 The Evidence in Perception Ali Hasan

292

23 Testimony and Evidence Nick Leonard

307

24 Introspection and Evidence Alex Byrne

318

25 Explanation and Evidence Kevin McCain and Ted Poston

329

PART 5

Evidence and Justification

343

26 Prospects for Evidentialism Bob Beddor

345

27 Permissivism, Underdetermination, and Evidence Elizabeth Jackson and Greta LaFore

358

28 Moral Encroachment and Evidence Jessica Brown

371

29 Evidence and Virtue (and Beyond) Kurt L. Sylvan

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30 Propositional Justification and Doxastic Justification Paul Silva Jr. and Luis R.G. Oliveira

395

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Contents

31 Evidence and Epistemic Reasons Errol Lord

408

32 Fallibilism and a Guarantee of Truth Charity Anderson

426

33 Evidence and Inductive Inference Nevin Climenhaga

435

PART 6

Evidence in the Disciplines

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34 Legal Evidence and Knowledge Georgi Gardiner

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35 Evidence in Logic Ben Martin and Ole Thomassen Hjortland

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36 Evidence: From Science to Policy Eleonora Montuschi

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37 Theory and Evidence in Economics Julian Reiss

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38 Evidence-Based Medicine and Evidence-Based Public Health Benjamin Smart

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39 Evidence in Classical Statistics Samuel C. Fletcher and Conor Mayo-Wilson

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40 Scientific Evidence Alexander Bird

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Index537

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NOTES ON CONTRIBUTORS

Peter Achinstein is Krieger-Eisenhower Professor at Johns Hopkins University. He is the author of eight books in the philosophy of science, including these that discuss the concept of evidence: Particles and Waves (which received the Lakatos Award in 1993), The Book of Evidence (2001), Evidence and Method (2013), and Speculation (2018). Charity Anderson is an Associate Professor of Philosophy at Baylor University. Her research is in epistemology and philosophy of religion, with a focus on issues concerning fallibilism, evidence, epistemic modals, invariantism, and knowledge norms. Her current research projects include the topics of wishful thinking, evidential uptake, and divine hiddenness. Natalie Alana Ashton is a Postdoctoral Researcher at Vrije University, Amsterdam. Previously she worked at the University of Stirling and the University of Vienna. She completed her PhD at the University of Edinburgh. Her research concerns the political and social aspects of epistemology—specifically the effects of oppression and power on epistemic justification—and she has published on feminist standpoint theory and relativism. Her latest work is on knowledge-producing communities in the online sphere. Eric Christian Barnes is Professor of Philosophy at Southern Methodist University. He has published papers on a variety of topics in the philosophy of science, including explanation theory, confirmation theory, the realist-antirealist debate, and artificial intelligence. His 2008 book, The Paradox of Predictivism (Cambridge University Press), offers a comprehensive account of the claim that novel predictions carry special epistemic weight in theory confirmation. His more recent writings focus on free will and moral responsibility, action theory, and metaethics. Bob Beddor is currently an Associate Professor of Philosophy at the National University of Singapore, and he will be joining the Philosophy Department at the University of Florida in the fall of 2023. He received his PhD from Rutgers University in 2016. Most of his research falls at the intersection of epistemology, philosophy of language, and metaethics. He is particularly interested in the nature of certainty, theories of justification, noncognitivist ix

Notes on Contributors

treatments of normative judgment, the semantics of modals, and the connections between epistemology and action theory. Endre Begby is Professor of Philosophy at Simon Fraser University. He specializes in epistemology, the philosophy of language, and social and political philosophy. Among his recent publications is Prejudice: A  Study in Non-Ideal Epistemology (Oxford University Press, 2021). His current work is aimed at further developing the concept of non-ideal epistemology in several directions at once, tracing its impact on our understanding of everyday epistemic agency, on scientific inquiry, as well as on collective deliberation and information sharing. Alexander Bird is the Bertrand Russell Professor of Philosophy at Cambridge, and a Fellow at St. John’s College, Cambridge. He was previously Peter Sowerby Professor of Philosophy and Medicine at King’s College London and before that the Professor of Philosophy at the University of Bristol. He also taught at the University of Edinburgh, Dartmouth College, and Saint Louis University. His published works include Philosophy of Science (1998), Thomas Kuhn (2000), Knowing Science (2002), and Nature’s Metaphysics (2007). Jessica Brown is Professor of Philosophy in the Arché Philosophical Research Centre at St. Andrews University. She has worked on a wide range of topics within philosophy of mind, epistemology, the methodology of philosophy, and blame and responsibility. She has published two monographs (Anti-Individualism and Knowledge, and Fallibilism) and co-edited several collections (Assertion; Knowledge Ascriptions; and Reasons, Justification and Defeat). She is an Associate Editor of the Stanford Encyclopedia of Philosophy and Fellow of the Royal Society of Edinburgh. During 2022–24, she was a recipient of a Leverhulme Major Research Fellowship to write a monograph on group epistemology. Peter Brössel is a Junior Professor of Philosophy at the Institute of Philosophy II of the Ruhr University Bochum. His research focuses on epistemology and philosophy of science (including social epistemology) and, within the philosophy of language and philosophy of mind, on topics fundamental to human cognition, perception, and action. T. Ryan Byerly is Senior Lecturer in the Philosophy Department at the University of Sheffield. He works on epistemology, virtue theory, and the philosophy of religion. His most recent book is Intellectual Dependability: A  Virtue Theory of the Epistemic and Educational Ideal (Routledge, 2021). Alex Byrne is Professor of Philosophy at the Massachusetts Institute of Technology. His interests include epistemology (especially self-knowledge) and the philosophy of mind. He is the author of Transparency and Self-Knowledge (Oxford, 2018), and Trouble with Gender: Sex Facts, Gender Fictions (Polity, 2023). His co-edited volumes include The Norton Introduction to Philosophy (Norton, 2018). Nevin Climenhaga (PhD, University of Notre Dame) is a Senior Research Fellow in the Dianoia Institute of Philosophy at Australian Catholic University. His research interests include knowledge, probability, explanation, evidence, inference, rationality, science,

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Notes on Contributors

goodness, and God. His publications have appeared in Mind, Noûs, Journal of Philosophy, Philosophy and Phenomenological Research, Philosophical Studies, Philosophy of Science, Journal of Biblical Literature, The Monist, and Oxford Studies in Philosophy of Religion. Kevin Dorst is an Assistant Professor in the Department of Linguistics and Philosophy at MIT. He works mainly in epistemology and its border with cognitive science, focusing on questions about rationality: what it is, why it matters, and whether we have it. Samuel C. Fletcher is an Associate Professor in the Department of Philosophy at the University of Minnesota, Twin Cities, a Resident Fellow of the Minnesota Center for Philosophy of Science, and an External Member of the Munich Center for Mathematical Philosophy, Ludwig-Maximilians-Universität. Much of his work so far has concerned the foundations of physics and of statistics and how problems in these fields inform and are informed by broader issues in the philosophy of science. He also has interests in the conceptual and physical basis of computation, metaphilosophy, and the history of physics and philosophy of science. Giada Fratantonio is a Postdoctoral Research Fellow working at the Cogito Epistemology Research Centre, at the University of Glasgow. She previously held research fellowships at Lingnan University in Hong Kong, University of Edinburgh, Harvard University, and University of Helsinki. She has published on various topics on the nature and normativity of evidence and on how these topics interact with various issues in epistemology, ethics, and the law. Georgi Gardiner is an Associate Professor of Philosophy and a Humanities Center Research Fellow at the University of Tennessee. Before that she was a Fellow of the American Council for Learned Societies (ACLS) and the Andrew Fraser Junior Research Fellow at St. John’s College, Oxford University. She focuses on social and applied epistemology, including the epistemology of law, statistics, trauma, attention, and love. Her research received the Royal Institute of Philosophy’s Annual Essay Prize, Canada’s Killam Fellowship, Rutgers University’s Distinguished Scholarly Achievement Award, and the University of Tennessee’s Chancellor’s Notable Woman Award and the Provost’s Early Career Research Award. Ali Hasan is Associate Professor of Philosophy at the University of Iowa, where he currently serves as Chair of the Philosophy Department. He has very broad interests, including epistemology, philosophy of mind, ethical theory, and philosophy of technology (especially epistemology and ethics of AI). He is author of A Critical Introduction to the Epistemology of Perception (Bloomsbury Academic, 2017), and published several shorter works in various places, including in the Stanford Encyclopedia of Philosophy, Episteme, Philosophical Studies, International Journal for the Study of Skepticism, Res Philosophica, and Big Data and Society. Ole Hjortland is a Professor in Philosophy at the University of Bergen and an external member of the Munich Center for Mathematical Philosophy. He has published on a number of topics in the philosophy of logic, including logical pluralism, inferentialism, proof-theoretic

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semantics, paradoxes, and anti-exceptionalism. Together with Colin Caret, he is the editor of The Nature of Logical Consequence (Oxford University Press, 2015). Nick Hughes is Associate Professor of Philosophy at the University of Oslo. His research interests lie primarily within epistemology and ethics. Most of his work to date has focused on the nature and limits of normative guidance, ‘ought-implies-can’ principles, cognitive biases, questions about what normative and metaphysical roles knowledge plays, and the relationship between knowledge and rationality. Recently he has published a number of papers about the possibility, nature, and scope of epistemic dilemmas: situations in which one faces conflicting, and so jointly unsatisfiable, epistemic requirements. He is currently working on a new project about non-ideal epistemic rationality. Kristen Intemann is a Professor of Philosophy and Director of the Center for Science, Technology, Ethics & Society at Montana State University. Her research focuses on feminist philosophy of science, particularly on issues such as objectivity and values in science, epistemic trust, and diversity in epistemic communities. Elizabeth Jackson is an Assistant Professor at Toronto Metropolitan University. Her research focuses on epistemology and philosophy of religion. She has recently published work on the belief–credence connection, epistemic permissivism, and pragmatic and moral encroachment. Her research interests also include social epistemology, decision theory, and the rationality of religious commitment. She completed her PhD in Philosophy at the University of Notre Dame. Greta LaFore is Assistant Professor of Philosophy at Gonzaga University. Her interests are in social epistemology and philosophy of science, and her current research projects surround the social epistemology of public allegations of abuse. She has published work on underdetermination and disagreement, especially disagreement within paleobiology. She is an advocate and architect of trauma-informed, gameful, and role-playing pedagogies that empower students to take ownership of their own learning with enthusiasm. At Gonzaga, she teaches philosophy in the University Core and Honors programs. Nick Leonard is an Assistant Professor of Philosophy at the University of San Francisco. His research interests lie primarily in epistemology, cognitive science, and some topics at the intersection of the two. Errol Lord is an Associate Professor of Philosophy at the University of Pennsylvania. He works on ethical theory, epistemology, aesthetics, and the philosophies of mind and action. His first monograph, The Importance of Being Rational, appeared with Oxford University Press in 2018. Ben Martin is an Assistant Professor in Logic and the Philosophy of Science at the University of Padua. Before that, he was a Marie Skłodowska-Curie Fellow at the University of Bergen and the Principal Investigator for the European Union Horizon2020–funded project The Unknown Science: Understanding the Epistemology of Logic through Practice. He works mainly in the philosophy of logic and epistemology, publishing articles on these

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topics in journals such as the Australasian Journal of Philosophy, Journal of Philosophical Logic, and Synthese. Jonathan Matheson is a Professor of Philosophy at the University of North Florida. His research is primarily in epistemology with a focus on the epistemology of disagreement and epistemic autonomy. He is the author of The Epistemic Significance of Disagreement (Palgrave, 2015) and Why It’s OK Not to Think for Yourself (Routledge, 2023). Conor Mayo-Wilson is an Associate Professor at the University of Washington, where he has worked since 2014. Prior to 2014, he was an Assistant Professor at the Munich Center for Mathematical Philosophy, where he worked directly after earning his PhD in 2012 from Carnegie Mellon University. Mayo-Wilson specializes in epistemology (esp. formal and social), decision theory, and causal modeling. Kevin McCain is Professor of Philosophy at the University of Alabama at Birmingham. His primary research interests are in epistemology and philosophy of science, primarily where the two intersect. He is especially interested in the nature of explanatory reasoning and how such reasoning generates knowledge in both ordinary and scientific contexts. Marc A. Moffett is an Associate Professor of Philosophy at the University of Texas, El Paso. He is co-editor (with John Bengson) of Know How: Essays on Knowledge, Mind, and Action (Oxford, 2011) and has published broadly on issues in philosophy of language, philosophy of mind, and epistemology. He is currently completing a manuscript, The Indispensability of Intuition, for the Cambridge Elements in Epistemology Series. Eleonora Montuschi is Professor of Philosophy of Science at the Department of Philosophy  and Cultural Heritage at the University Ca’ Foscari of Venice. She works on scientific  objectivity, the theory and practice of evidence, and science and expertise in public debate.  She is an associate fellow at CPNSS-London School of Economics and Political Science (research project: Evidence for Use). She is currently the PI/coordinator of the Horizon 2020 project “Inclusive Science and European Democracies” (https://iseedeurope.eu/). Luis R.G. Oliveira is Associate Professor of Philosophy at the University of Houston. He works mainly on epistemic normativity and the philosophy of religion. He has edited or coedited three volumes, has published articles in Philosophical Studies, Australasian Journal of Philosophy, Pacific Philosophical Quarterly, European Journal of Philosophy, and British Journal of Aesthetics, and has contributed many chapters to academic volumes. Ted Poston is Professor of Philosophy at the University of Alabama and Inaugural Director of the McCollough Institute for Pre-Medical Scholars. His research interests are in epistemology, philosophy of medicine, and philosophy of religion. His research focuses on inference to the best explanation, its relationship to Bayesian inference, and the applications of IBE in medical and religious contexts. Duncan Pritchard is UC Distinguished Professor of Philosophy and Director of the Center for Knowledge, Technology & Society at the University of California, Irvine. His monographs

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include Epistemic Luck (Oxford University Press, 2005), The Nature and Value of Knowledge (co-authored, Oxford University Press, 2010), Epistemological Disjunctivism (Oxford University Press, 2012), and Epistemic Angst (Princeton University Press, 2015). Julian Reiss is Professor and Head of the Institute of Philosophy and Scientific Method at Johannes Kepler University Linz. He is the author of Error in Economics (2008); Philosophy of Economics (2013); Causation, Evidence, and Inference (2015); and over seventy journal articles and book chapters on topics in general philosophy of science and philosophy of the biomedical and social sciences. He is a past President of the International Network for Economic Method (INEM) and a member of the German National Academy of Sciences Leopoldina. Jeffrey Sanford Russell is a Professor of Philosophy at the University of Southern California. He works on a wide range of topics, including metaphysics, epistemology, decision theory, ethics, and philosophy of religion. Bernhard Salow is an Associate Professor at the University of Oxford and a Tutorial Fellow at Magdalen College. He studied in Oxford and at MIT and has previously worked at Trinity College Cambridge. His primary research interests concern the structural principles governing knowledge and evidence and questions about when and how to look for further information. Joel Sati is an Assistant Professor of Law at the University of Oregon School of Law. His research interests are in criminal law, immigration law, crimmigration, privacy law, and jurisprudence. His dissertation project, titled A Punishment of the Severest Kind: Immigration Enforcement, Social Degradation, and the Harm of Illegalization, develops an account of illegalization, defined as state practices of criminalization that use immigration enforcement as the central mechanism of social degradation.  Sati  has been published by  Duke University Press, University of California Press, Social Epistemology Research and Reply Collective, and the Washington Post. Sati holds a BA from the City University of New York, a JD from Yale Law School, and a PhD from the University of California, Berkeley. Sati is also a 2018 Paul and Daisy Soros Fellow and a 2019 recipient of the FOUNDATIONS FOR CHANGE Thomas I. Yamashita Prize. David Schraub is an Assistant Professor of Law at Lewis & Clark Law School, where his research concentrates on constitutional and anti-discrimination law, political theory, and contemporary issues of racism and antisemitism. His articles have appeared in a wide range of publications, including Social Theory & Practice, the American Political Science Review, the California Law Review, and The Association of Jewish Studies (AJS) Review. He holds a BA from Carleton College, a JD from the University of Chicago Law School, and an MA and PhD in Political Science from the University of California, Berkeley. Paul Silva Jr. is a Junior Professor at the University of Cologne. He previously held positions at Monash University and the University of Pennsylvania, and he took his PhD from the University of Connecticut. His work centers on issues in the theory of knowledge and rationality. He is the author of Awareness and the Substructure of Knowledge (Oxford

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University Press, 2022), and he has published numerous papers in leading international journals, such as Noûs, Philosophy and Phenomenological Research, Philosophical Studies, Australasian Journal of Philosophy, Synthese, Erkenntnis, and the Pacific Philosophical Quarterly. Professor Benjamin Smart is Co-founder and Director of the University of Johannesburg’s Centre for Philosophy of Epidemiology, Medicine and Public Health. He received his PhD from the University of Nottingham in 2012 and has published widely on philosophy of medicine, philosophy of public health, and metaphysics, including monographs entitled “Concepts and Causes in Philosophy of Disease” and (with Professor Olaf Dammann) “Causation in Population Health Informatics and Data Science”. Jan Sprenger is Professor of Logic and Philosophy of Science at the University of Turin in Italy. He obtained his PhD from the University of Bonn (2008) and worked afterwards at Tilburg University in the Netherlands (2008–2017). His main research topics are statistical inference, probabilistic reasoning, causality, and scientific objectivity. Together with Stephan Hartmann, he recently published the monograph “Bayesian Philosophy of Science” (Oxford University Press, 2019). Julia Staffel is an Associate Professor of philosophy at the University of Colorado at Boulder. Her main research areas are epistemology and formal epistemology. Her book Unsettled Thoughts: A Theory of Degrees of Rationality was published with Oxford University Press in 2019. She is currently working on a new book that explores the nature of complex deliberation. Kurt L. Sylvan is Associate Professor of Philosophy at the University of Southampton. He specializes in epistemology, philosophy of practical reason, and philosophy of mind. His papers have appeared in Philosophical Review, Mind, and Philosophy and Phenomenological Research. He was co-editor (with Ruth Chang) of the Routledge Handbook of Practical Reason. Chris Tucker  is the Francis S. Haserot Professor of Philosophy at William  & Mary. He specializes in epistemology, ethics, and philosophy of religion. He loves his children almost as much as he loves coffee and chocolate. Ralph Wedgwood is Professor of Philosophy and Director of the School of Philosophy at the University of Southern California. Before moving to California, he was educated at Magdalen College, Oxford, at King’s College London, and at Cornell University, and taught at the Massachusetts Institute of Technology and at Merton College, Oxford. His primary interests are in epistemology and ethics (including metaethics, ethical theory, and the history of ethics). He has published more than sixty articles and three books, The Nature of Normativity (Oxford University Press, 2007), The Value of Rationality (Oxford University Press, 2017), and Rationality and Belief (Oxford University Press, 2023). Timothy Williamson became Wykeham Professor of Logic at Oxford University in 2000 and Whitney Griswold Visiting Professor at Yale in 2018. His books include Identity and

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Discrimination, Vagueness, Knowledge and Its Limits, The Philosophy of Philosophy, Modal Logic as Metaphysics, Tetralogue, Doing Philosophy, Suppose and Tell: The Semantics and Heuristics of Conditionals, and (with Paul Boghossian) Debating the A Priori. He is a Fellow of the British Academy and of the Royal Society of Edinburgh, Member of the Academia Europaea, International Honorary Member of the American Academy of Arts and Sciences, and Honorary Member of the Royal Irish Academy.

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INTRODUCTION Maria Lasonen-Aarnio and Clayton Littlejohn

It is easy to think of claims about evidence that sound almost platitudinous. What one can know at any one time depends on one’s evidence. Good scientific theories are supported by evidence. Our experiences provide us with evidence. Any sort of inquiry involves the seeking of evidence. It is irrational to believe contrary to one’s evidence. Indeed, it seems that all rationally evaluable responses—whether doxastic states, choices, emotional responses, or reactive attitudes such as blame—should be sensitive to evidence. However, once we try to give an account of the exact role that evidence plays in a theory of justified belief or knowledge, a theory of fitting emotions and reactive attitudes, or a theory of rational choice, things start looking less platitudinous. The same is true when attempting to say just what evidence is in the first place and what it is for a doxastic state such as a belief to be supported by the evidence. Platitudes about evidence often point to highly debated views. Consider, for instance, the seeming connection between justified (rational, reasonable) belief and evidence, or the connection between knowledge and evidence. According to evidentialism facts about justification are fixed by one’s evidence: a subject has justification to believe a proposition p just in case p is supported by her evidence (Conee and Feldman, 1985, 2004). Justification, in turn, is necessary for knowledge. Evidentialism is a substantive and controversial view. There are plenty of alternative theories of justification. For instance, according to process reliabilists justification is produced by reliable belief-forming processes (Goldman 1986). Virtue epistemology grounds epistemic normativity in competences or epistemically virtuous character traits, not evidence (e.g., Sosa 2007). Anscombe (1962) claimed that we can know the position of our limbs without needing evidence: you don’t need evidence in order to know that your legs are crossed. Austin (1962) proposed that we can know without evidence that a pig is in a pen or on the path provided that we had the sight of one. And as Beddor argues in this handbook, it is not clear whether the evidentialist can cash out their core notions of evidence and evidential support in ways that don’t assume the notion of justification. If a permissivist view is correct, then a single body of evidence does not uniquely fix facts about what one is justified in believing—non-evidential features of one’s epistemic situation might be needed to fix such facts (Jackson and LaFore). It is not clear how evidentialism is to be reconciled with phenomena like moral encroachment (Brown). And numerous authors 1 DOI: 10.4324/9781315672687-1

Maria Lasonen-Aarnio and Clayton Littlejohn

have argued that non-evidential considerations can sometimes provide epistemic reasons to believe (Lord). Many of the articles in this collection evaluate evidentialism as a theory of justified belief and critically discuss the seeming platitude that evidence and evidence alone determines what it is justified or rational to believe. Philosophers have invoked evidence to play various theoretical roles. Indeed, it is somewhat standard practice to begin with a view of what evidence is seen as doing, and to then give an account of evidence and its metaphysics informed by this role. The articles in this handbook describe some of the main theoretical roles that evidence has been assigned. It is widely agreed that evidence can support beliefs, hypotheses, and theories. It is debatable whether, for instance, material objects, as opposed to propositions, can enter into such support-relations. Perhaps the most prominent role that evidence has been given is connected to the epistemic status of justification (rationality, reasonableness) of doxastic states such as belief. Evidence, according to many, is whatever justifies our beliefs, or makes certain degrees of confidence reasonable or rational. This is just the role that evidentialism assigns to evidence. If one thinks that facts about justification depend on one’s evidence, and that justified beliefs are based on reasons, then it is natural to think that evidence, and only evidence, provides reasons to believe (Lord assesses such a view). And there are further claims to be discussed in this handbook. There is the claim discussed and criticized by Wedgwood that evidence is whatever is evident or given. Bird discusses the empiricists’ hope that evidence provides a neutral arbiter for choosing amongst different scientific theories. Sylvan argues that evidence consists in facts that are potential inputs in good reasoning. Additionally, the contributions to this handbook tackle some of the difficult questions that arise when we try to say what it is for evidence to support (believing) a proposition. We might initially think that evidence supports a proposition by increasing its probability. This approach has much to be said for it, as our contributors note, but has not won over everyone. Some are troubled by the idea that something might constitute evidence for a hypothesis when it only marginally increases its probability or stands in no explanatory connection to the hypothesis it is thought to confirm. Moreover, there are difficult questions about how evidential support is to be measured. Finally, both naive and sophisticated theories of evidential support face a host of difficult paradoxes and puzzles. Our contributors also discuss a wide range of philosophical issues that have to do with the application of evidence in practices or in disciplines. As we have noted, evidence seems to matter in theoretical and practical settings. There are difficult questions about how we should use evidence in settings like the political arena or a courtroom. For example, should we look to the canons of good scientific reasoning to understand how evidence should be used in a criminal trial or in the course of deciding between competing policy initiatives? There are also difficult questions about how evidence should be used in particular theoretical settings. Our contributors discuss the role that evidence plays in social sciences, applied sciences, and the natural sciences. Our aim is to give interested readers the widest introduction to philosophical issues having to do with our reliance on evidence feasible, one that both provides readers with a thorough understanding of the background that informs current philosophical debate as well as some ideas about where future conversations might take us.

Part 1: The Nature of Evidence The notion of evidence plays a central role in our thinking about all rationally evaluable responses. We rely on it when trying to decide what to believe for ourselves or in evaluating 2

Introduction

the beliefs and doubts of others. It provides our basis for choosing between theories. Evidence matters, too, to non-doxastic attitudes. The fittingness of our emotional responses and the appropriateness of our reactive attitudes depends, inter alia, upon our evidence or information. When it comes to choice, evidence plays a vital role in determining what we should choose in light of our ignorance and uncertainty. A philosophical account of evidence must identify the things that constitute evidence in these different settings. Our first set of chapters discusses the most recent work on the nature of evidence. Much of our ordinary talk suggests that among the things that constitute evidence are ordinary objects. Think of the pistols, pottery, fossils, or manuscripts that can be put in boxes or bags, lost and later found, or created and destroyed. Most philosophers seem to favour an understanding of evidence that either excludes these kinds of objects or stresses the importance of things more intimately connected to the perspective of thinkers who use their evidence to revise their beliefs. A piece of pottery or a fossil, if unobserved, has no rational bearing on our attitudes or actions. Once observed, however, something bears rationally on our actions and attitudes. Two tempting lines of argument suggest that it is our experiences of these objects, not the objects themselves, that bear rationally on our actions and attitudes. First, some are struck by the thought that when we compare two subjectively similar experiences, it seems they have the same impact on the rationality of the relevant individual’s actions and attitudes even if one experience is veridical and the other is hallucinatory. In essence, the worry seems to be that if we thought of the fossil as the evidence, we would struggle to explain why a certain kind of experience had in the presence of the fossil and a similar experience had in the absence of the fossil seem to do equally well in terms of providing rational support for belief. Second, some are struck by the thought that when we pair the fossil with all of the various ways that things might appear when an individual sees a fossil, only some of these experiences make it rational to believe things about that fossil or about the significance of that fossil for questions that interest us. We can see a fossil well or badly, say, by seeing it under good lighting conditions or seeing it at too great a distance to recognise what it is. This suggests that it is the way things appear to us that bears most directly on the rationality of our attitudes. In his contribution, Chris Tucker explores the idea that a thinker’s experiences play this rational role in constraining which attitudes would be rational. He focuses on the view that identifies a thinker’s evidence with the experiences that she has. He evaluates attempts to show that certain experiences (e.g., seeming to see an apple in a certain way) might always be evidence that supports to some extent believing that things are the way that our experiences represent. We have seen how an argument from error might be used to criticise the view that ordinary material objects constitute evidence. Such arguments can also be used to argue that (a) the conscious experiences we have when we perceive are the same kind of experiences we might have if we were to hallucinate and that (b) the evidence a thinker has depends upon the conscious character of her experiences and not upon whether those experiences are veridical. This suggests that a thinker’s evidence generally supervenes upon the internal conditions that determine what mental states we’re in and does not depend upon what external conditions might be like or how these external conditions are connected to our mental lives. Giada Frantantonio’s chapter addresses the debate between internalists and externalists about evidence, arguing that evidential externalism is a more promising view. On the externalist view, it might be possible for two thinkers to be internally as similar as you like, but it would not follow that they had the same evidence. 3

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In their contributions, Duncan Pritchard and Timothy Williamson discuss two externalist accounts of evidence. Pritchard’s focus is on epistemological disjunctivism, a view that implies that the kind of rational support perception provides when, say, we see that it is a pig on the path differs from the kind of rational support hallucination can provide: the perception gives us evidence that entails and guarantees that there is indeed a pig on the path. This view has the surprising consequence that when we consider sceptical scenarios in which thinkers internally similar to us are deceived by Cartesian demons, we’re imagining situations in which thinkers lack the kind of evidence that we have when we know how things are in our surroundings via perception. Whilst our deceived counterparts might entertain the possibility that their evidence for beliefs about the external world includes facts about external objects and their properties (e.g., that I have a hand that I can plainly see), only our evidence includes such facts. Williamson’s view differs in that he thinks that a thinker’s evidence consists of her knowledge. Whereas the epistemological disjunctivist thinks that our evidence, ultimately, is provided by experience and does not require a thinker to believe or to know in order to possess that evidence, on Williamson’s we cannot have a fact or true proposition as part of our evidence unless we know it to be true. A familiar objection to these views is that they conflict with the idea that if two thinkers are in similar enough mental states, the very same beliefs will be rational for them. Williamson critically evaluates this kind of objection. Whilst these discussions focus on questions about what constitutes evidence, the contributions of T. Ryan Byerly and Ralph Wedgwood are more concerned with questions about the function of evidence. Whatever our evidence consists of, it seems that it must be suited to do things like support hypotheses, hunches, guesses, and beliefs. How should we understand the support relation? Byerly surveys a variety of different accounts of support (e.g., explanatory, probabilistic, and attitudinal) and evaluates objections to each proposal. Wedgwood sounds a sceptical note about the significance of evidence, taken in the sense the word has in everyday English, for individualistic epistemology (i.e., attempts to explain why it might be rational for some thinker in isolation to believe some things and not to believe others). Wedgwood argues that while we should understand justification in terms of facts that are “given” to an agent at a time, what is thus given cannot be identified with one’s evidence. He suggests instead that evidence might be useful for thinking about issues in social epistemology where we are interested in how it is that a believer is able to justify their beliefs to others: evidence is what makes it evident in a social or public sense that something is the case.

Part 2: Evidence and Probability What is it for a belief, or for an entire scientific theory, to fit the evidence? What is it for a particular piece of evidence to confirm a theory? These questions concern the evidential support relation. In a Cartesian dream world: evidential support is a matter of logical entailment, and we frequently acquire evidence that logically entails our beliefs and theories. But we do not live in such a dream: we hardly ever have evidence that affords our beliefs or theories such maximal, truth-guaranteeing support. It has become common to use the term confirmation for non-deductive relations of evidential support. Though Bayesian views of confirmation are not the only game in town, it is widely accepted that confirmation has to do with probability. Hence, the framework of Bayesian

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Introduction

epistemology is standardly used to give an account of evidential or confirmational support. Bayesianism provides a mathematically powerful framework that allows quantifying confirmation. Confirmation does, after all, come in degrees: while two pieces of evidence might both provide confirmation for a hypothesis h, one might confirm h more strongly than the other. Some of the entries in this section explore Bayesian measures of confirmation (Peter Brössel) and the potential limits of the Bayesian account (Peter Achinstein). Jan Sprenger’s entry discusses some well-known paradoxes that arise for various accounts of confirmation, including Bayesian ones. Julia Staffel asks how Bayesian norms of ideal rationality apply to non-ideal beings like ourselves. Eric Christian Barnes discusses two ways in which a theory might be supported by its empirical consequences: either through prediction or accommodation. Other entries in this section deploy Bayesian tools to answer various questions relating to evidence. Bernhard Salow asks whether more evidence is always better. Kevin Dorst explores the nature and rational impact of higher-order evidence, evidence regarding what opinions are rationalized by one’s evidence. Jeffrey Sanford Russell discusses the socalled Sleeping Beauty problem. Bayesians distinguish between two notions of confirmation, an absolute and an incremental one. Absolute support or confirmation as firmness is a matter of how likely some evidence E makes a hypothesis h in absolute terms, relative to some probability function (and possible background information). For instance, one might take E to confirm h in this sense just in case h is likelier than not-h conditional on E—and hence, above .5 likely. Incremental support is a matter of probabilistic relevance, of the conditional probability of h on E being higher than the unconditional probability of h, again relative to some probability function (and possible background information). There are debates, however, about how to quantify incremental degrees of support—there is a plurality of alternative probabilistic measures of relevance confirmation—and about what kinds of probabilities are at issue. Peter Brössell’s contribution discusses the different measures of incremental support and the different interpretations of the underlying probabilities. After surveying the main proposals in the literature and identifying key desiderata for choosing between them, he recommends using two measures. One measure is meant to capture actualised support and tell us something informative about the belief-worthiness of hypotheses. One is meant to indicate something about the potential that evidence has for changing the probability assigned to hypotheses. Though a positive relevance view of incremental evidential support or confirmation is quite popular, Peter Achinstein argues that the fact that E is positively probabilistically relevant for h does not suffice for E to (incrementally) support h. He points to cases where E is probabilistically relevant to h where he thinks it would be a mistake to say that E is evidence for h since the probability of h on the evidence is quite small. For example, if we learn that Alice purchases 1% of the lottery tickets and Binh purchases the remaining tickets, we have acquired information that is probabilistically relevant to the hypothesis that Alice wins (i.e., it is more likely that Alice will win given that she purchased a ticket), but Achinstein believes that it is not evidence that Alice will win given that Binh will almost certainly win. He additionally argues that there should be an explanatory connection between the evidence that confirms a hypothesis and that hypothesis, something that can go missing when some evidence is probabilistically relevant to a hypothesis. Theories have empirical consequences, and the support enjoyed by a theory—how probable the theory is—depends on these consequences. It is uncontroversial that a scientific theory should accord with or fit the evidence. But we should distinguish two ways in which

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a theory’s empirical consequences might be seen to accord with the evidence. On the one hand, the theory might predict some consequence that had not been observed when the theory was constructed. On the other, the theory might be formulated so that it accommodates empirical consequences that had been observed prior to the formulation of the theory. Predictions, to many, seem to provide much stronger evidence for a theory than accommodations. In his contribution, Eric Christian Barnes explores attempts to explain this (or to explain this appearance away). In addition to evaluating defences of predictivism (i.e., the view that predictions provide much stronger confirmation for a theory than accommodating), Barnes distinguishes between different kinds of predictivist views. Not all accounts of confirmation are Bayesian or probabilistic. There is the instantial relevance view on which hypotheses are confirmed by observing their instances: for instance, the hypothesis that all ravens are black is confirmed by an observation of a black raven. There is the hypothetico-deductive, “deduction-in-reverse” account on which evidence E confirms a hypothesis h just in case h, together with auxiliary hypotheses and assumptions, entails E. And there is, of course, the Bayesian positive relevance view of confirmation mentioned earlier. All of these accounts of evidential support or confirmation give rise to well-known paradoxes. In his contribution, Jan Sprenger discusses some of the paradoxes that arise when we try to incorporate plausible assumptions about confirmation into a larger theory. The discussion focuses on Hempel’s raven paradox, Goodman’s new riddle of induction, and the paradox of tacking by conjunction. Sprenger evaluates potential solutions to these paradoxes. Bayesian epistemologists and philosophers of science often see Bayesianism as giving us norms of ideal rationality. At any time the credences or degrees of belief of a rational agent satisfy the probability axioms. And they evolve by some form of conditionalization on new evidence. Julia Staffel spells out the core commitments of a Bayesian epistemology, as well as various additional principles the Bayesian might adopt. But irrespective of what sort of Bayesian view one chooses, it is clear that we human beings are not ideal Bayesian agents. How, then, do Bayesian norms apply to non-ideal agents like ourselves? Staffel critically evaluates a common answer, which is that such norms are ideals we can approximate, and that the closer we come to conforming to these ideals, the better. In what sense is it better to be closer to ideal rationality? And how is such closeness measured in the first place? Different distance measures yield different verdicts about which credence functions are closer to the ideal, and it is not clear which distance measure we should use. Staffel draws on a value-based conception of rationality to answer these questions. It is intuitive to think that on balance, more evidence is always better. For instance, it’s a good idea to find out whether a house contains asbestos before buying it. Bernhard Salow builds an intuitive argument for the claim that in an interesting set of circumstances we should always think that acquiring additional evidence would improve our decisions and opinions. The argument builds in much less background theory than Good’s (1967) well-known argument for a similar conclusion, and applies not only to decisions, but also to beliefs. Salow discusses decision-theoretic and epistemological objections to his argument, concluding that the question whether more evidence is always better remains open. Kevin Dorst’s chapter discusses the nature and rational impact of higher-order evidence. Dorst characterises higher-order evidence as evidence regarding what opinions are rationalised by one’s evidence. His starting point is that it is possible to acquire misleading higherorder evidence: even if my confidence that it will rain today is perfectly rational, I  can 6

Introduction

acquire misleading evidence that it is way too low. Such evidence can take many forms: it might consist in learning that an epistemic peer disagrees, that one is subject to a cognitive bias, or that one is sleep-deprived. It seems that such evidence can make us higher-order uncertain—that is, uncertain about what opinions are rational. But the rationality of such higher-order uncertainty has various puzzling consequences. Avoiding such consequences would seem to require defending some sort of systematic bridge principles that connect first- and higher-order opinions, ruling out the seemingly problematic kinds of higher-order uncertainty. Dorst outlines a rigorous model-based methodology for investigating these issues that draws on probabilistic epistemic logic, and he uses this methodology to investigate various natural principles restricting higher-order uncertainty. He also connects the issue of higher-order uncertainty with various other debates and issues, such as internalism versus externalism, the value of evidence (discussed by Salow), ambiguous evidence, and hindsight and confirmation bias. The so-called Sleeping Beauty problem (Elga 2000) has evoked a large debate that intersects with fundamental questions concerning evidence. Sleeping Beauty knows that upon her being put to sleep for two days on Sunday, some researchers will flip a fair coin. If it lands Heads, they will wake her just once, on Monday; if it lands Tails, they will also wake her up on Tuesday. After each waking she will be put back to sleep with a drug that causes her to forget that waking. As she wakes up for the first time, how confident ought she to be that the coin landed Heads? According to ‘Halfers’, she should still be ½ confident; according to ‘Thirders’, she should now be 1/3 confident in Heads. Jeffrey Russell presents the standard arguments in favour of each position, connecting the puzzle with some general questions about evidence. For instance, can I gain evidence for a hypothesis h even in a situation in which I know that it is impossible for me to gain evidence against it? Is the evidence I have fixed by my present qualitative phenomenal state—this is a form of internalism about evidence—or can it include facts about the world that I observe and remember, as externalists about evidence think it can? Russell deploys externalist reasoning to arrive at a striking argument in favour of a position on which Sleeping Beauty’s confidence in heads should be ½ upon waking up on Monday, but—were she to wake up on Tuesday—it should be 1/3. He also connects the puzzle with questions in the epistemology of cosmology.

Part 3: The Social Epistemology of Evidence Individualistic approaches to epistemology that have been dominant in the Western philosophical tradition focus on the solitary investigator and knower. In contrast, social epistemologists emphasise the importance of the social environments in which individuals are embedded, seeing social interactions and systems as having epistemic relevance. The entries in this section touch upon some central topics in social epistemology such as peer disagreement, epistemic injustice and privilege, and social prejudice and bias. Several entries highlight the social dimensions of acquiring and assessing evidence. Among the social dimensions that affect how we acquire and assess evidence are power dynamics. Feminist epistemologists highlight ways in which power dynamics influence the production of knowledge. Kristen Intemann discusses feminist approaches to evidence. How do gender and intersecting categories, such as race and class, affect what we consider to be evidence in the first place (e.g., whether we consider someone’s testimony credible in the first place), its strength, and how much evidence is needed for believing a particular claim? And how should epistemic communities be structured in order to prevent gendered 7

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norms and relations from leading to problematic bias? Intemann discusses these questions by focusing on feminist empiricist approaches. A core insight of feminist standpoint epistemology is that being oppressed due to social factors can enable occupying an epistemically privileged standpoint regarding relevant social facts, and that occupying such a standpoint can enable making distinctive contributions to inquiry. One understanding and explanation of this epistemic advantage is in terms of having access to evidence provided by experiences that are distinctive of positions of oppression. Natalie Alana Ashton discusses two challenges that standpoint epistemology faces. First, how can this claim of epistemic privilege be reconciled with the standpoint epistemologist’s commitment to the claim that standards of epistemic progress depend on socially situated perspectives? The second difficulty is that if the claimed epistemic privilege is just possessing certain evidence, it is not clear what is distinctive or even controversial about the standpoint epistemologist’s thesis. Ashton sketches a form of feminist hinge epistemology on which standpoints are understood as sets of hinge commitments (à la Wittgenstein), arguing that it can overcome these two challenges. As a response to the first challenge, Ashton argues that the standpoint theorist should adopt a relativist notion of epistemic and scientific progress. And second, she argues that the epistemic advantage in question should be interpreted in terms of redefining evidential standards. Miranda Fricker (2007) has influentially coined the term epistemic injustice to refer to the wrongs people suffer in their capacity as knower—though similar issues and notions have been explored in the Black feminist tradition. A paradigm example of epistemic injustice is discounting someone’s testimony due to a bias against the speaker. David Schraub and Joel Sati’s discussion highlights the social dimensions of acquiring and assessing evidence. After offering an overview of epistemic injustice, they consider the topic in connection with inquiry and evidence-gathering. They deploy the notion of epistemic injustice to analyse cases of police misconduct and failure on the part of law enforcement to properly investigate a matter. Several of the entries in this section assess how various phenomena relate to evidentialism. Endre Begby provides an overview of the epistemology of prejudice, which he understands as predominantly negative stereotypes attaching to particular social groups and their members. Begby’s starting point is an evidentialist view on which a belief is justified or rational insofar as it is supported by one’s evidence. According to a tempting and often voiced view, acquiring and maintaining prejudiced belief is always epistemically irrational. Drawing on a social conception of evidence, Begby argues that prejudiced beliefs can be supported by the evidence and hence, be rational. This is so especially if our aim is to do so-called non-ideal epistemology, epistemology that takes into account human cognitive limitations. Where Begby uses an evidentialist view to argue that that prejudiced belief can be rational, Nick Hughes argues against evidentialism on the basis that beliefs produced by cognitive biases are irrational. Hughes argues that whether or not a belief results from a cognitive bias, or is based on evidence gathered in a selective way as a result of the influence of a bias, can affect its rational standing. This is so despite the fact that cognitive biases often operate at a sub-personal level introspectively inaccessible to the subject. This creates trouble for internalism, Hughes argues, including internalist versions of evidentialism. Externalist evidentialists can accommodate the irrationality of

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Introduction

biased belief, but only at the cost of denying the common assumption that false beliefs can be rational. In his contribution, Jonathan Matheson discusses some of the puzzles raised by cases of peer disagreement. It is not surprising that thinkers with different information might end up with different opinions – say, when a jury relying on the evidence presented in trial believes a defendant to be guilty but this defendant knows full well that they are innocent. An interesting case is one in which equally capable thinkers discover that they disagree despite sharing the same relevant evidence. On the one hand, one of these thinkers might have responded appropriately to the (initial) evidence. Given an evidentialist view according to which it is rational to believe when our beliefs are appropriate to the evidence, it might seem that this thinker may or should continue to believe as they do. On the other hand, when discovering that an epistemic peer with the same relevant evidence disagrees, shouldn’t one think they are no more likely to have erred? That suggests there is some rational pressure on both peers to revisit the issue, weaken their stance, and perhaps suspend judgment on the matter until they acquire additional evidence or discover where precisely one of them processed the evidence incorrectly. Views that encourage disagreeing peers to suspend might be difficult to reconcile with the evidentialist idea just mentioned, but evidentialists might also argue that this tension is merely apparent: there is higherorder evidence that also needs to be taken into account when the peers disagree. Matheson explores the norms that govern disagreement and those that tell us how higher-order evidence might matter to the rationality of our beliefs given a broadly evidentialist approach to epistemic rationality.

Part 4: Sources of Evidence In recent philosophical work on evidence, there has been considerable discussion of the sources of evidence. The evidence that you possess might overlap with the evidence possessed by others, but we expect this overlap to be partial. We also expect that your evidence will change over time as you learn new things and have new experiences. Should we recognise many different potential sources of evidence or just one? How do we decide whether something is a source of evidence? The chapters in this section explore these kinds of foundational questions with special focus on different potential sources. Davidson somewhat infamously declared that the only thing that could be a reason to believe is another belief. This suggestion does not sit well with many foundationalists who believe that there are sources of evidence that can provide evidential support for our beliefs without requiring any belief to possess this support. In his contribution, Ali Hasan discusses the possibility that some of our beliefs might be justified thanks to the ‘evidence of the senses’. One of the challenges faced by such a view is providing a satisfactory account of just what such evidence is. Should we say that, via perceptual experience, our evidence might include facts about things external to us, or should we conceive of our evidence as constituted by appearances that do not constitutively depend upon the existence of external objects? Hasan discusses the challenges that arise when we try to answer this question. Whilst it might have been a presupposition of some traditional epistemological projects that an individual thinker can only rely on their own resources, there has been increased interest in the ways in which our connections to other thinkers helps to determine our epistemic

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predicament. Nick Leonard discusses the role that testimony plays in the justification of our beliefs. Whilst it might seem to be a bit of commonsense that testimony matters to justification, there is considerable philosophical controversy about how it matters. Does the testimony provided by a friend, a stranger, or an expert provide justification by providing evidence? How should we understand the transmission of evidence provided by testimony? Does testimony transmit justification by transmitting evidence, by generating a new kind of evidence, or by some other means? In choosing between philosophically controversial positions, we seem to rely on something besides or beyond perceptual experience, testimony, and introspection. We might say, if pressed, that we are inclined to think that ordinary objects are distinct from the matter that composes them because that’s how it seems to us, having reflected on various thought experiments. We might say that we are attracted to certain views about the rational force of disagreement because they seem intuitive. In his contribution, Marc A. Moffett discusses the connection between intuition and evidence. His discussion is primarily concerned with evaluating a rationalist view according to which there are capacities that go beyond experience and our grasp of definitions that provide evidence by means of intellectual appearances. Moffett discusses important challenges from experimental philosophy and the role that expertise might play in understanding the evidential force of intuition. Evidence is related to explanation, but in what way? In particular, do explanatory facts provide evidence—are explanatory considerations linked to the truth? Kevin McCain and Ted Poston ask whether the fact that h explains some data better than competing hypotheses itself provide evidence for h. Is it reasonable to infer that h is true on the basis of its providing the best explanation of some data? McCain and Poston clarify the nature of inference to the best explanation (IBE) and offer a critical discussion of its merits and problems. We seem to have a peculiar way of finding out about our own mental states. For instance, to know that you are feeling tired you would have to tell me, or I would have to observe your droopy eyes, but my own tiredness I can introspect in a seemingly special way. Alex Byrne characterises introspection as the unaided and direct means by which we know about our own present mental states. He discusses various accounts of introspection as well as its connection to evidence—in particular, to what extent the deliverances of introspection are based on evidence. Byrne argues that some of our knowledge of our present mental lives is acquired without evidence. Hence, the deliverances of introspection are not always based on evidence.

Part 5: Evidence and Justification: General Considerations According to evidentialism, which doxastic attitudes are rational or justified for a subject to have supervenes or is fixed by her evidence (Conee and Feldman 1985, 2004). Many think that the rational or justified attitudes are the ones the subject epistemically ought to have. Hence, an important set of epistemic normative facts depends on nothing but one’s evidence. Evidentialism has been a highly influential view, and even those who reject it tend to think that evidence has some central role to play in epistemology. For instance, even if facts about what doxastic attitudes are rational or justified are not fully determined by one’s evidence, evidence at least constrains such facts. Most of the articles in this section focus on assessing the evidentialist view of justification and epistemic normativity, as well as its compatibility with other views. Evidentialism itself faces challenges, and its basic notions are in need of clarification. What makes for a subject’s evidence in the first place, and how is evidential support to be 10

Introduction

understood? Evidentialism is first and foremost a theory of so-called propositional justification, of what propositions a subject is justified in believing. How, then, should doxastic justification be understood? Bob Beddor assesses evidentialism, asking whether the evidentialist can provide accounts of their key notions without appeal to the notion of justification. Many of the articles in this section discuss the prospects for evidentialism assuming various other views or theses that have gained support in epistemology. Kurt L. Sylvan asks whether evidentialism can be reconciled with virtue epistemology. Liz Jackson and Greta LaFore assess its compatibility with a permissivist view on which several different attitudes regarding a proposition p may be rational given a body of evidence. Jessica Brown asks whether evidentialism is compatible with moral encroachment, the claim that moral considerations can affect the epistemic status of a given doxastic state. The question regarding how evidentialism relates to the thought that what doxastic attitudes we epistemically ought to be in depends on our normative epistemic reasons comes up in Errol Lord’s chapter. Charity Anderson discusses the fallibilism-infallibilism debate. While the debate is roughly about how strong an epistemic position one must be in in order to know, the debate intersects in many places with questions about evidence and knowledge. Nevin Climenhaga shows how questions about which inductive inferences are rational intersects with questions about evidence. It is worth noting that ‘evidentialism’ is used in epistemology in a slightly different, though closely related sense in the debate between so-called evidentialists and pragmatists. This debate is about normative reasons for belief and, more generally, reasons for adopting doxastic states. Do all reasons to believe consist of evidence? Can pragmatic considerations like incentives or facts about the costs of being wrong provide reasons? Note that evidentialism in this sense does not entail evidentialism in the other sense—the thesis that which doxastic attitudes are rational or justified for a subject supervenes or is fixed by her evidence. As Errol Lord notes in his contribution, the claim that only evidence provides epistemic reasons is compatible with the claim that facts about what doxastic states it is rational (or justified) for one to be in can depend on non-evidential considerations like the practical or moral stakes of being wrong. One might hold, for instance, that only evidence provides epistemic reasons, but that how strong one’s reasons must be in order to rationalise belief can depend on practical and/or moral stakes. Bob Beddor assesses evidentialism as a thesis of justification, discussing an often ignored, fundamental challenge for the view. An account of what evidence is does not yet tell us what it takes for a subject to possess an item of evidence. And of course, the evidentialist must also provide an account of evidential support. Can the evidentialist give an account of these notions without helping themselves to the notion of justification? Beddor outlines and critically evaluates the space of options open to the evidentialist. It is commonplace to distinguish between doxastic and propositional justification: between having justification to believe a proposition p and justifiably believing p. For instance, evidentialism is first and foremost a theory of propositional justification: one has propositional justification to believe p just in case p is sufficiently supported by one’s evidence. Paul Silva and Luis R.G. Oliveira discuss the propositional/doxastic distinction and why it matters. They discuss different ways of understanding the basing relation in terms of which doxastic justification is commonly understood. After surveying some arguments that appeal to an understanding of doxastic justification in terms of basing, they critically evaluate such views. They discuss three challenges for a view on which basing a belief on good reasons or evidence suffices for doxastic justification. According to the first not all basing 11

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is of the sort that makes for doxastic justification. The second challenge comes from views (such as Alvin Goldman’s 1986 process reliabilism) that define propositional justification in terms of doxastic justification, rather than vice-versa. The third has to do with an analogy between moral assessment of action and epistemic assessment of belief. Assuming the rationality or justification of doxastic attitudes to depend on the evidence one has, the following question arises: does a body of evidence determine a unique rational doxastic attitude for every proposition p that it bears on? According to uniqueness it does. According to permissivism at least sometimes a body of evidence can make rational different doxastic attitudes to a proposition p. Liz Jackson and Greta LaFore clarify both positions, and outline some of the main arguments for each side. They also spell out some of the implications of the debate for issues like peer disagreement. They then argue that understanding permissivism as an underdetermination thesis strengthens the case for permissivism, moving the debate forward. A version of permissivism on which sometimes one’s evidence (but not all potentially relevant facts about one’s epistemic situation) underdetermines the rational attitude to take toward a proposition p avoids various objections that have been raised. However, this version of permissivism is not consistent with evidentialism. Virtue epistemology has been a highly influential research program. At first sight it looks to be incompatible with evidentialism: virtue epistemology grounds epistemic normativity in competences or epistemically virtuous character traits, not evidence. Recently, however, there has been much interest in combining the two approaches. Kurt L. Sylvan identifies two places where evidentialists could acknowledge virtue-epistemological conditions: in the possession of evidence and proper basing of belief and other doxastic states on evidence. Sylvan argues that the most promising approach treats neither virtue epistemology nor evidentialism as fundamental, attempting to derive one theory from the other, but derives both from a unified third theory. Sylvan’s preferred theory grounding and explaining the insights of both evidentialism and virtue epistemology is rationalist. Central to a rationalist approach is the notion of reason, understood as a fundamental mental capacity. Sylvan argues that a rationalist account of evidence can avoid some of the main problems encountered by evidentialism, and that a rationalist account of competence or virtue is able to avoid some of the main problems faced by virtue epistemology. Recently some have defended so-called moral encroachment, a view on which epistemic statuses such as justification can depend on moral factors. It has been argued, for instance, that certain profiling beliefs are not justified even if they are highly likely on the evidence, due to the fact that they morally wrong others in virtue of their contents (e.g., Basu and Schroeder 2019). Jessica Brown discusses moral encroachment as a challenge to evidentialism, the thesis that what one is justified in believing is solely a function of one’s evidence. Brown critically examines several arguments in favour of moral encroachment, also relating moral encroachment to debates about moral responsibility. Errol Lord explores the debate between evidentialism and pragmatism, which he frames as a debate about normative epistemic reasons. Evidentialism here is the view that only evidence provides such reasons. It is widely accepted that if E is evidence for p, then E is a normative epistemic reason to believe p. But the claim that only evidence provides reasons is much more controversial. In particular, some pragmatists of either the Pascalian or encroachment sort claim that non-epistemic considerations, he claims, can provide epistemic reasons for belief. Lord argues against evidentialism: non-evidential considerations can provide epistemic reasons. In particular, reasons to suspend judgment need not

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Introduction

be evidential. The fact that the practical costs of being wrong are high can be a reason to suspend. Such encroachment pragmatism, however, is compatible with maintaining that only evidence can provide reasons for belief. We gain new knowledge and justified belief from our evidence by drawing inferences. And on some accounts of evidence, we can also gain new evidence through inference. Most everyday and scientific inferences are inductive or non-deductive: the truth of the premises of these inferences does not guarantee the truth of the conclusion. Nevin Climenhaga discusses the kinds of good inductive inferences there are. He presents a principled typology for such inferences based on the explanatory relationship between the evidence (premises of the inference) and the conclusion. Inferences, Climenhaga argues, can proceed downwards, from cause to effect; upwards, from effect to cause; or sideways, from effect to cause to additional effect. After presenting the typology, Climenhaga shows how canonical forms of inductive inference—inference to the best explanation, enumerative induction, and analogical inference—can be subsumed under it. Climenhaga’s discussion shows how questions regarding evidence and inference are closely related: which inferences we deem rational or irrational depends on our views of what it takes for something to be part of a subject’s evidence. Most epistemologists these days are fallibilists about knowledge: knowing does not require a maximally strong epistemic position. But just how should we understand this claim—should it, for instance, be understood as the claim that knowing does not require maximally strong evidence? Charity Anderson canvasses and critically assesses several ways of understanding fallibilism. She then argues that we should understand infallible knowledge as involving a guarantee of truth: infallible knowledge is irresistible and both positively and negatively introspected. This, Anderson argues, yields a substantive division between fallible and infallible knowledge.

Part 6: Evidence in the Disciplines The chapters in this section are concerned with evidence as it figures in practices and disciplines. There are philosophically interesting questions about the kinds of evidence that should guide reasoning in, say, our legal practices, the practice of medicine, and in various theoretical disciplines. Georgi Gardiner discusses whether bare statistical evidence can satisfy legal standards of proof. She motivates and defends that claim that it cannot, and discusses various explanations of this fact. Recently several authors have defended a natural, knowledge-centric explanation: legal proof requires knowledge of culpability, but it is not possible to have knowledge on the basis of bare statistical evidence. Gardiner argues, however, that legal proof does not require knowledge. For instance, she argues that the beyond reasonable doubt standard that governs criminal proceedings in many countries is both less demanding than knowledge—since knowledge is factive, but the legal standard is not—and more demanding, since many everyday instances of knowledge would not pass the standard. Instead, Gardiner suggests that we explain the inadequacy of bare statistical evidence by appealing to desirable features of knowledge. Benjamin Smart discusses evidence in medicine with a special focus on evidence-based medicine (EBM) and evidence-based public health (EBPH). In EBM, clinical decisions are supposed to be guided by ‘best evidence’, and here proponents of EBM will say that

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this evidence should come from randomised control trials (RCTs). Smart looks at the philosophical justifications for EBM and the role that EBM has played in the adoption of EBPH. Eleonora Montuschi’s contribution discusses the recent trend of trying to emulate the evidence-based methods of science in policymaking and governance. The benefits of an evidence-based approach to policy and governance are supposed to be that it optimizes policy decisions, helps us hold policymakers accountable, and should help reduce bias. Montuschi uses cases studies to identify the strengths and limits of this attempt to use our understanding of good scientific practice in non-scientific practices. In their contribution, Ben Martin and Ole Thomassen Hjortland discuss the role that evidence in logic. Unlike the empirical sciences that rely heavily on observation, logic is often described as an a priori discipline. On this view, the evidence that would be used to advance our understanding of logic might consist of analytic truths or the deliverances of rational intuition. This picture is often supported by the suggestion that we always need to presuppose some logical knowledge in order to use any empirical observations to support a theory, something that seems to rule out the possibility that such empirical observations might be a basic form of evidence used by logicians. Martin and Hjortland think this picture is not true to the history of the discipline and that the evidence used in logic is quite similar to the evidence used in scientific theorizing. Samuel C. Fletcher and Conor Mayo-Wilson discuss a puzzle that arises when we think about the role that evidence plays in classical statistics. Science is a paradigmatic source of good evidence and knowledge. Quantitative experimental science is often described in classical statistical terms. What is puzzling about this is that many philosophers, statisticians, and scientists interested in the foundations of statistics reject the hybrid of Fisherian and Neyman-Pearsonian techniques. Because of this, we might wonder why the use of classical statistics in quantitative experimental science is successful. It is possible that classical measures of evidence do not track anything of epistemic significance, but that makes the puzzle all the more puzzling. Fletcher and Mayo-Wilson examine strategies for trying to solve this puzzle that appeal to analogies with the use of the kinds of modal principles that figure in tracking theories of knowledge. Julian Reiss discusses the evidence used to confirm or disconfirm economic theories. He focuses on a series of historical debates that concern the proper methodology of economic theorizing. He examines the debates about the role of empirical evidence in economic theorizing that began with Adam Smith and continued well until the 1960s. He then continues with a discussion of more recent disagreements about the role that theory-laden evidence might play in the field. These debates continue without resolution, and Reiss speculates about the ways they might develop in the future. Alexander Bird discusses the nature of scientific evidence, providing a historical overview of the debate. Since scientific evidence has standardly been assumed to be observational, questions about the nature of scientific evidence largely concern the nature of observation. While an empiricist conception of observation as perceptual has often been taken for granted, it is challenged by the theory-ladenness of observation: typical observation statements in science are laden with scientific theory. If observation is indeed theory-laden, it is not epistemologically prior to theory, and can not serve as the neutral arbiter that empiricists had hoped it would be. Bird discusses non-empiricist conceptions of observation and evidence to see whether they might be suitable for giving an adequate philosophical account of scientific evidence. 14

Introduction

References Anscombe, G. E. M. 1962. On Sensations of Position. Analysis 22: 55–58. Austin, J. L. 1962. Sense and Sensibilia. Oxford University Press. Basu, R. and Schroeder, M. 2019. “Doxastic wronging”. In Brian Kim and Matthew McGrath (eds.), Pragmatic Encroachment in Epistemology. New York: Routledge, 181–205. Conee, E. and Feldman, R. 1985. Evidentialism. Philosophical Studies 48(1): 15–34. Elga, A. 2000. Self-Locating Belief and the Sleeping Beauty Problem. Analysis 60: 143–147. Fricker, M. 2007. Epistemic Injustice. Oxford: Oxford University Press. Goldman, A. 1986. Epistemology and Cognition. Harvard University Press. Good, I. J. 1967. On the Principle of Total Evidence. British Journal for the Philosophy of Science 17: 319–321. Sosa, E. 2007. A Virtue Epistemology: Apt Belief and Reflective Knowledge: Volume I. Oxford University Press.

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PART 1

The Nature of Evidence

1 EXPERIENCE AS EVIDENCE Chris Tucker

1 Introduction This chapter explores whether and when experience can be evidence. In Sections 2 and 3, I clarify “experience” and “evidence”, respectively. In Section 4, I argue that sometimes experience is evidence. In Section 5, I consider at length whether certain kinds of experience are always evidence.

2  What Is Experience? Three-time pro-bowlers have a lot of experience playing NFL football. Someone who drives a campervan across New Zealand will have a wonderful experience. These notions of experience are not the one I am concerned with, though they are probably related. Here experiences are in the same broad category as beliefs, desires, moods, and thoughts. Experiences are “in the mind”.1 They are mental states, mental events, mental modes, or something along those lines. They also have phenomenal character. To have phenomenal character is to have a conscious “feel”, for there to be something it is like to have it in one’s consciousness. Consider the pains associated with a headache. There is something it is like to have such a pain. There is also something it is like when you seem to see a squirrel ripping its way into your screen porch. Let me tell you, it’s not pleasant. As an approximation, experience is a mental state or event that has phenomenal character.2 In addition to pains, perceptual experiences are paradigmatic kinds of experiences, e.g., seeming to see or hear something. They often have rich phenomenal character. The squirrel will seem to have a specific shape and shade of gray. The sound of the screen ripping will ingrain itself in your memory. Memory often involves experiences with rather rich phenomenal character. When you seem to remember the squirrel ripping into your porch, you may get imagery that is essentially a degraded version of the original perceptual experience. Other experiences have more subtle kinds of phenomenal character, including plainer memorial seemings and intellectual intuitions. You seem to remember that the Declaration of Independence was signed in 1776 and that atoms are composed of electrons, but such memorial seemings are probably not associated with rich sensory phenomenal character.

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When you remember such things, you don’t typically have “mental images” of people signing a document or electrons orbiting a nucleus. It seems obvious to you that 5 + 5 = 10 and that it is morally wrong to torture for fun. I assume, somewhat controversially, that such memorial and intellectual seemings are indeed kinds of experience. As the previous examples illustrate, experience often has propositional content.3 A proposition is a representation that can be true or false. I seem to see that the squirrel is ripping its way into my screen porch. The italicized phrase can be true or false. Since it is the content of the experience, the experience can truly represent or falsely represent. It is controversial exactly which propositions can serve as the content of experiences. The previous examples include experiences that represent the world around you, historical events, math, and morality. Suppose these examples are genuine. If experience can be evidence, then experience may provide us with evidence on a diverse array of topics. But what exactly is evidence?4

3  What Is Evidence (for the Purposes of This Chapter)? The term “evidence” is ambiguous, which partly explains the importance of this volume. A gloss from Tom Kelly will point us in the right direction: “evidence, whatever else it is, is the kind of thing which can make a difference to what one is justified in believing or . . . what it is reasonable for one to believe” (2014: §1, emphasis in original). (For simplicity, I use “justified”, “reasonable”, “rational”, and their cognates interchangeably.) More specifically, evidence can make at least two kinds of difference: it can make it reasonable to believe something and it can make it unreasonable to believe something. I look out the sliding glass door, and I come to know—and justifiably believe—that the screen is torn in a new place, the porch furniture is chewed, and there is fresh squirrel scat. In the absence of further considerations, these justified beliefs are evidence that makes it reasonable to believe that the abominable squirrel has, yet again, torn its way into my screen porch. To illustrate the second kind of difference, we can embellish the example. After forming the belief that the squirrel did it, I might acquire new evidence that makes this otherwise reasonable belief unreasonable. A guilty confession and video recording of my kids framing the squirrel would make it unreasonable to believe that the squirrel did it. My justified beliefs that there is a new tear, chewed furniture, and fresh squirrel scat still exert power to make it reasonable to believe that the squirrel did it even when other information, such as the confession, neutralizes or overwhelms this power. Analogously, I may be exerting genuine upward force on a bench press bar even if it is overwhelmed by the bar’s weight and the bar is moving down. Evidence’s power to make a difference is more central to what evidence is than its actually making a difference. The justified beliefs about the state of the porch don’t cease to be evidence in favor of believing that the squirrel did it when I acquire new information which, all things considered, makes it unreasonable to believe that the squirrel did it. Something has justifying power with respect to believing P, roughly, when it has some tendency to make it reasonable to believe P. Something has committing power with respect to believing P, roughly, when it has some tendency to make it unreasonable to disbelieve P, withhold judgment about P, or believe any proposition incompatible with P. Since the guilty confession and video recording commit me to believing that my kids framed the squirrel, it is unreasonable for me to believe that the squirrel did it. Justifying power tends to make it 20

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reasonable to do something (e.g., believe P); committing power tends to make it unreasonable to take some range of alternatives (e.g., disbelieve P). Paradigmatic evidence comes with both kinds of power. In other words, the clearest examples of evidence tend to justify believing something exactly to the extent that the evidence makes it unreasonable to disbelieve, withhold judgment about, or believe something incompatible with it. It is controversial whether all evidence fits this paradigm. To my ear— and no worries if you disagree—justifying power is more central to being evidence than is committing power. So I focus on evidence that has justifying power whether or not it also has committing power. I focus more specifically on possessed evidence, or evidence that is had by a subject. It is common for the detective to have evidence in a confidential investigation that I don’t have. And perhaps something can be evidence even if no one possesses it. Something is evidence when it has justificatory power. The evidence is possessed when that power is exerted. While I am resting on the bench, I have the power to put upward force on the bar but I’m not yet exerting that power. That’s the state that unpossessed evidence is in (if there is such a thing). When evidence is possessed, it exerts its justificatory power for whoever possesses it. In what follows, whenever I  talk about evidence, I  have in mind possessed evidence. For simplicity, I’ve been assuming that justified belief (or at least justified belief that is true or counts as knowledge) is often a paradigmatic kind of evidence. This assumption is controversial. For we might debate the ontology of evidence, i.e., exactly which kind of thing evidence is. Is the belief the evidence? The propositional content of the belief? Something else? Similar ontological questions can be raised about any alleged experiential evidence. Would the experience be the evidence? The propositional content of the experience? Something else? Important issues hang in the balance of such ontological questions, but my focus is on evidence’s connection to (un)reasonable belief. If I think that the justified beliefs about the screen porch’s condition are the evidence and you think that it’s really the content of those beliefs, we’ll still generally agree about which further propositions we are justified in and committed to believing.5 I will casually say that justified beliefs are evidence and (eventually) that experiences can be evidence, but most of what I say is compatible with any standard account of evidence’s ontology.

4  Is Experience Ever Evidence? We’ll need to refine the operative notion of “evidence” further in this section, but we have enough on the table to begin considering whether experience is ever evidence. The relatively uncontroversial answer is yes, experience is at least sometimes evidence. Recall that evidence paradigmatically has both justificatory and committing power. It is widely agreed that experience has both kinds of power. You stub your toe and reasonably believe that you are in pain. You don’t need an argument. The pain itself, or perhaps your seeming to be in pain, can make it reasonable to believe you are in pain. You also believe that it is bad to be in pain. You don’t need an argument to reasonably hold such a belief. Its seeming obvious that pain is bad is, arguably, something that makes it reasonable to believe that pain is bad. Apparently, then, experience can have justifying power. Experience can also have committing power. You’ve been told by a credible source that all swans are white. You go to Australia and seem to see a black swan. You keep walking 21

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and you seem to see many more. These experiences make it unreasonable or, at least, less reasonable to believe that all swans are white. Arguably, in each of the previous cases, you get both justifying and committing power. The pain of stubbing one’s toe doesn’t merely justify believing that one is in pain, it also commits one to such a belief: in the absence of further considerations, the pain makes it unreasonable for you to disbelieve or withhold judgment that you are in pain. The experience of a black swan doesn’t just make it unreasonable to believe that all swans are white; it also makes it reasonable to believe some swans aren’t. We need to be careful, though. Evidence paradigmatically has both justificatory and committing power, and we’ve seen that experience often comes with both kinds of power. Yet it doesn’t quite follow that experience is ever evidence. Kelly’s gloss on evidence said that evidence can make a difference to what it’s reasonable to believe. It does not follow that evidence is the only thing that can do so. A contrast between two rival epistemological theories will help us refine our conception of evidence, as well as show us that experience can be evidence even if evidence isn’t the only thing to have justificatory power. Consider evidentialism, roughly, the thesis that evidence is the only thing that makes a difference to what it is reasonable for you to believe. Earl Conee and Richard Feldman are the two most prominent proponents of evidentialism and, in at least one place, they claim that experience can be evidence (2008: 88; cf. my 2011: 56). More generally, if experience does have justificatory or committing power, there is plenty of precedent for thinking of it as evidence. Yet this precedent does not apply universally: not everything that is a candidate for having justificatory power is also a candidate for being evidence. Consider simple (process) reliabilism, the view that a belief is reasonable if and only if it was produced by a reliable process, where a reliable process is one that produces more true beliefs than false ones.6 Such a view holds that a belief’s being produced by a reliable process—whether anyone is aware of the reliable process or not—has the power to justify the belief. Yet no one holds that the mere fact that a belief is produced by a reliable process is evidence that the belief is true—at least, not until the believer has some relevant mental state that brings the fact within the subject’s ken. Facts about reliable processes that are outside your ken may justify your beliefs, but they aren’t “evidential justifiers; they are not pieces of evidence, or reasons” (Goldman and McGrath 2015: 36). At this point, it may seem that reliabilism will deny that even justified beliefs count as evidence. Simple reliabilism holds that process reliability is sufficient for justification (sufficient for exerting justificatory power) and also necessary for justification (necessary for exerting justificatory power). But if process reliability is the only way for justificatory power to be exerted and process reliability is not evidence, can simple reliabilism allow that someone has evidence? Yes. Simple reliabilists generally hold that, most fundamentally, process reliability is the only thing that can exert justificatory power; however, they allow that justified beliefs can derive justificatory power from their role in reliable processes. Take inference, for example. Suppose I infer that I will be sore tomorrow morning from my reasonable belief that I just completed a rigorous, two-hour workout. This inference is a reliable process that, given simple reliabilism, makes its conclusion belief reasonable. The reliable inferential process is not itself evidence, but evidence is still involved. The justified premise belief inherits or derives its justificatory power from its role in the reliable inferential process. Thus, the justified premise belief is considered evidence. The way simple reliabilists make room for evidence helps us better understand what (possessed) evidence is. The mere fact that the belief was produced by a reliable process is 22

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not considered evidence, even if process reliability is what most fundamentally has justificatory power.7 The evidence is the relevant mental state, the justified premise belief. Since we are ignoring disputes about the ontology of evidence, we have arrived at our final definition of evidence: evidence is a mental state or event that exerts justificatory power (cf. Goldman and McGrath 2015: 27).8 The reliabilist can make room for experiences as evidence in the same way that she made room for justified beliefs as evidence. She holds that experiences are often a crucial component in the reliable process that produced a belief. My perceptual processes are reliable and typically involve experiences. I reasonably believe that there is a duck in the pond because I seem to see a duck in the pond. Given reliabilism, my belief is justified, most fundamentally because it was produced by a reliable process. Yet my experience was a mental state that was a crucial part of the process that produced my belief. It justifies my belief, albeit in a derivative way. It therefore counts as evidence.9 Perhaps beliefs and experiences are the only things that can be evidence. Perhaps not. It depends on whether there are other kinds of mental states or events with justifying power. If, in the absence of further considerations, anger at Max justifies believing that Max did something wrong, then anger can be evidence. And this is so regardless of whether anger is, strictly, a belief or an experience. Evidentialism gives evidence a starring role in its theory of reasonable belief. Reliabilism gives it a supporting role. Both, however, accommodate the idea that experience is often evidence. Indeed, almost every epistemological theory can make room for the idea that experience is at least sometimes evidence.10 It is not particularly controversial whether experiences can be evidence. We saw earlier that it’s controversial how fundamental evidence is to reasonable belief. In the rest of this chapter, we focus on a controversy concerning when experiences are evidence.

5  Are Experiences (of a Certain Sort) Always Evidence? 5.1  Experience Enthusiasm We’ve seen that experiences are sometimes evidence. Some epistemologists argue that every experience E is evidence for believing that one is having E. Suppose E has the content that the car is red. If these epistemologists are right, it doesn’t follow that E is evidence for believing its content, namely, that the car is red, but only evidence that one is having the experience that the car is red. Even those who are most enthusiastic about experience’s role in justifying beliefs deny that every experience is evidence for believing its content. When you vividly imagine being a millionaire, no one thinks that you thereby gained evidence that you are a millionaire. Experience enthusiasts hold that every experience with a certain phenomenal character makes it reasonable to believe its content.11 They tend to be connoisseurs of phenomenal character, drawing subtle (sham?) distinctions between the phenomenal character of various kinds of experience. They generally agree that imaginations have the wrong phenomenal character and that at least some (part of) perceptual experiences have the “right” phenomenal character. Beyond that, there’s more disagreement about which experiences have the right phenomenal character. The possibilities include seeming to remember, intuition about what’s possible or what’s morally right, and religious experience. 23

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For the purposes of this chapter, I  take no stand on what the best version of experience enthusiasm is or on what the “right” kind of phenomenal character is. Since there is wide agreement that visual experience (or some part thereof) generally has the “right” phenomenal character, I’ll present an argument that all instances of seeming to see—that is, all visual experiences—are evidence for their contents. You’ll need to consult the various theories to get more information about which phenomenal character in the experience is the “active ingredient”.

5.2  The Bad to Resist Belief Argument Consider some arbitrary instance of your seeming to see something: you seem to see that P.12 Also, suppose that you have no relevant counterevidence to P or any other consideration that bears on whether P is true. You have neither evidence that P is false nor evidence that your perceptual experiences are unreliable. As far as you know, no one disagrees with you about P and you haven’t ingested any hallucinogens, etc. The only potentially relevant consideration bearing on whether P is true is, apparently, that you seem to see that P. In this kind of situation, what doxastic attitude (i.e., belief, disbelief, withholding judgment) would it be reasonable for you to take toward P? Many philosophers—even those who ultimately reject experience enthusiasm (e.g., Siegel 2017: xiv–xvi)—find it intuitive that you should believe P. Perhaps the intuitive nature of this answer counts in its favor, as many experience enthusiasts will hold. Yet some experience enthusiasts are more ambitious. They try to milk an argument out of this intuition. You may not bother to believe everything your visual experience tells you. But if you form a doxastic attitude toward P in the relevant circumstances, it’s bad to resist believing P. At least, that’s the driving conviction of what I call the Bad to Resist Belief Argument.13 The argument begins with the idea that your experience makes certain things unreasonable to do. 1. If you seem to see that P in the absence of other relevant considerations, then your experience makes it unreasonable to disbelieve that P (or believe any proposition incompatible with P).   Sane individuals generally do not believe the opposite of what they seem to see, unless they have some special reason to do so. And we’ve stipulated that there are no special reasons—the experience is the only potentially relevant consideration you have bearing on whether P. Why would you disbelieve P when the only relevant consideration bearing on whether P is that you seem to see that it’s true?   Your experience also seems to make something else unreasonable: 2. If you seem to see that P in the absence of other relevant considerations, your experience makes it unreasonable to withhold judgment about P.   Suppose my laptop is lying broken on the floor. I wonder what caused my laptop to break. The only relevant information I have is that the laptop was sitting firmly on the counter, the laptop is covered with the same sticky goo that is all over my five-year-old’s fingers, and there are no other people or pets in the house. To withhold judgment about whether my five-year-old broke the computer seems ridiculous. To withhold judgment would be to ignore what’s “staring me in the face”. If you seem to clearly see that some specific thing is in front of you, it seems at least as ridiculous to withhold judgment

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about whether it’s really there. To do so would be to ignore what appears to be staring you in the face.   So far, we’ve seen that our experience makes it unreasonable to disbelieve or withhold judgment about P. If it’s not reasonable to disbelieve or withhold judgment about P, then it must be reasonable to believe it. Something’s gotta give, right? In other words, there is some reasonable stance that you can take toward P: 3. If you seem to see that P in the absence of other relevant considerations, your experience makes it reasonable to believe that P, disbelieve that P, or withhold judgment about P.   Since we’ve already eliminated the latter two options (reasonable to disbelieve or withhold judgment), we reach our conclusion: 4. Therefore, if you seem to see that P in the absence of other relevant considerations, then your experience makes it reasonable to believe that P. If we take “you” to be the general “you”, 4 applies to all of us no matter what we seem to see. It says that no matter what we seem to see, our seeming to see it makes it reasonable to believe it. In other words, it says that seeming to see that P is always evidence for P. You may wonder whether 4 always holds. For example, what if we seem to see a purple penguin perfectly performing a pirouette? We should probably disbelieve what we seem to see, but that’s because we have other relevant information: we know from background knowledge that such a thing is almost certain not to happen. Yet 4 still holds even in this outlandish case. Seeming to see the purple penguin perfectly performing a pirouette is still evidence that there is a purple penguin doing such a thing. In the absence of further considerations, it would be reasonable to believe that there is such a penguin precisely because of your experience. It’s just that we have other evidence that outweighs that experience and makes it, all things considered, unreasonable to believe that there is such a penguin.14 Let’s consider the structure of the argument more carefully. 1 and 2, taken together, are the claim that experience commits one to believing its content. For 1 and 2, taken together, tell us that the experience makes it unreasonable to disbelieve or withhold judgment about the experience’s content (or believe something incompatible with that content) in the absence of further information. The third premise rules out the possibility that an experience can have committing power without having justificatory power. Suppose that, in the absence of further considerations, an experience that P can commit one to believing P without making it reasonable to believe P. When that possibility occurs, it will be unreasonable to disbelieve or withhold judgment about P (or believe any incompatible proposition) without being reasonable to believe P. Such situations are called epistemic dilemmas, because there is no reasonable doxastic attitude that you can take toward P. You won’t be reasonable if you believe, disbelieve, or withhold judgment. Premise 3 rules out the possibility of epistemic dilemmas. It says that whenever you seem to see something, at least one of your options (believing, disbelieving, withholding judgment) will be reasonable. The first two premises establish that every experience (of a certain kind) commits one to believing its content. The third premise establishes that, if an experience has committing power, then it also has justificatory power. The argument, then, essentially reasons from the claim that experiences always have committing power to the conclusion that they always have justifying power.15

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5.3  The Weakest Part of the Argument The weakest part of the argument, in my view, is the third premise. It is still an open question whether something can commit you to having a belief without justifying that belief. It is an open question whether epistemic dilemmas are possible. Unjustified beliefs are a potential example of something that has committing power without having justificatory power. Unjustified beliefs don’t have justificatory power. They can’t make other beliefs reasonable. Garbage in, garbage out. If some televangelist irrationally believes that bad things happen only to bad people, he can’t reasonably infer that only bad people were killed by the tsunami. Nonetheless, unreasonable beliefs arguably have committing power. Consider reductio ad absurdum reasoning. Tim irrationally believes some philosophical theory T that you regard as ridiculous. You point out that T entails, say, that no one knows their own name. That is, you point out that Tim’s belief that T commits him to believing that no one knows their own name. Did you thereby show that it was reasonable for Tim to believe that no one knows their own name? Of course not. By showing that Tim was committed to something absurd, you were showing that he should give up his irrational belief that T. Arguably, what reductio reasoning shows us is that it is possible for something to have committing force (with respect to believing that no one knows their own name) without having justifying force in the same respect.16 The success of the previous argument for experience enthusiasm, then, depends on a successful argument that there are no epistemic dilemmas, or equivalently, that there is always one reasonable doxastic attitude to take toward a proposition.17 I should also note that, even if we can prove that there are no epistemic dilemmas, it may not follow that the previous argument succeeds. We would also need to show that the explanation for why there are no dilemmas is compatible with the claim that experience is always evidence. If we can show that there are no such dilemmas and that the explanation for their non-existence is so compatible, then the previous argument would provide a strong reason to be an experience enthusiast.

5.4  What About the Causal History of an Experience? Critics of experience enthusiasm will protest that the causal history of an experience makes a difference to whether it counts as evidence. Suppose Jill seems to see that Jack is angry at her, but it only seems that way because of her irrational pre-existing belief that Jack is angry. Critics of experience enthusiasm insist that Jill’s visual experience is not evidence—it lacks justificatory power—precisely because of its causal history (i.e., that it was caused by a prior irrational belief and, indeed, an irrational belief with the same content as the seeming).18 Experience enthusiasts often reply that they find the critic’s verdict about Jill’s experience counterintuitive.19 When we consider cases like the Jack and Jill case, why is there disagreement in what the enthusiasts and critics find (counter)intuitive? The Bad to Resist Belief Argument stresses the first person. It forces you to ask, “given the information I  would have available to me in such a situation, should I  believe, disbelieve, or withhold judgment?” The causal history objections to experience enthusiasm switch to the third person: they ask us to evaluate a situation in which we know something that the subject doesn’t, namely, that her experience has a bad causal history. The switch to the third person invites the worry that the experience enthusiasts and critics may be talking

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past one another. Experience enthusiasm’s plausibility depends on the assumption that reasonable belief, being tightly connected to the first-person perspective, may fall well short of knowledge.20 The critics suppose, in contrast, that things going well from the first-person perspective is not enough for reasonable belief and, therefore, they assume that there is a tighter connection between reasonable belief and knowledge. I will not decide the winner of this debate here. If the third premise is true, the Bad to Resist Belief Argument strongly supports the existence of a certain type of reasonableness: a type so tightly connected to the first-person perspective that the causal history of an experience makes no difference to whether that experience is evidence. However, if experience enthusiasts can’t successfully explain the importance of this alleged type of reasonableness in a way that fits well with their experience enthusiasm, then we may have to side with the critics after all.21

Conclusion Experiences are mental events with phenomenal character, and so there is something it’s consciously like to have them (§2). Evidence is, roughly, a mental state that exerts justificatory power, and paradigmatically, evidence also exerts committing power too. In the absence of further considerations, if you have paradigmatic evidence for P, then it is reasonable for you to believe P and unreasonable for you to disbelieve or withhold judgment about it (§§3–4). While there is disagreement about how fundamental evidence is for reasonable belief, almost every epistemological theory makes room for the idea that experience is at least sometimes evidence (§4). Experience enthusiasm is the view that experiences with certain kinds of phenomenal character are always evidence. Many people, including critics, find some version of experience enthusiasm intuitive. The Bad to Resist Belief Argument is intended to show that experience enthusiasm is true, but it is inconclusive. Consider a situation in which you have an experience that P (where the experience has the “right” phenomenal character) in the absence of further considerations. In such a situation, it is unreasonable to disbelieve P or withhold judgment about it. What isn’t clear is whether it follows that it’s reasonable to believe P. If it does, then experience enthusiasm is true (§5).22

Notes 1 Note that I said in the mind, not in the head. Phenomenal externalism is the view that phenomenal character does not supervene on a subject’s internal states. It may be determined, for example, by relations to external objects. As I understand phenomenal externalism, it denies that phenomenal character is in the head, but it doesn’t deny that phenomenal character is in the mind. 2 We can arrive at a more precise understanding of experience by relying on Bayne and Chalmers’s distinction between phenomenally conscious states and phenomenal states (2003: 28–29). Suppose there is something it’s like for you to believe that Paris is in France. We can allow that the belief is phenomenally conscious, i.e., we can allow that it exemplifies phenomenal character. Yet the belief is not itself the exemplification of this phenomenal character, and it is not itself individuated solely by its phenomenal character. Experiences are phenomenal states, i.e., they are the exemplification of phenomenal character and are individuated solely by their phenomenal character. 3 This claim is controversial (see, e.g., Travis 2004), despite its relative modesty. I’m not assuming that perceptual experiences are individuated by representational content or that the fundamental nature of experience is representational. Nor am I assuming that perceptual content is conceptual.

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Chris Tucker 4 Discussion in the Board Certified Epistemologists group helped improve this section. Thanks to those who participated! 5 Williamson (2000: ch. 9) holds that justified belief is not sufficient for evidence, and so he and I will disagree about which further beliefs are justified. Yet the disagreement is not driven by our differing accounts of evidence’s ontology (experience vs. proposition) but our claims about what normative statuses are sufficient for evidence (justified belief vs. knowledge). 6 I focus on process reliabilism because it is the bigger threat to whether experience is sometimes evidence. Indicator reliabilism holds, roughly, that a mental state justifies a belief whenever the mental state reliably indicates the truth of the belief. It is easy to see that experiences can have justificatory power on such a view. 7 See, e.g., Lyons (2009: 25, 30), Goldman and McGrath (2015: 36). 8 Alternative accounts of evidence’s ontology will hold that the evidence isn’t strictly the premise belief but rather its propositional content or the fact that makes the belief true. Yet these accounts will still demand some connection to the subject’s mental states or events. 9 Lyons (2009: 74–76) disagrees. Since he holds that all evidential justification is justification by transmission and that experiences can’t be justified (and so can’t transmit justification), he infers that experiences can’t be evidence. I reject his assumption that all evidential justification is justification by transmission. 10 Even Williamson-style knowledge-first epistemology can make room for the idea that experience is evidence or that certain kinds of experience that P make P part of one’s evidence. Suppose I know P on the basis of perception. My experiencing P might partly constitute my perceptual knowledge that P. And we might insist that knowing P suffices for having justification that P. Thus, my experience that P has the (derivative) power to make P justified and so counts as evidence. 11 I ignore the differences between enthusiasts, so that I can focus on an argument that is close to all their hearts. Enthusiasts include the proponents of phenomenal conservatism (Huemer, Tucker), as well as views that defend the evidential value of experience within a certain domain, such as perceptual dogmatism (Jim Pryor) or intellectual dogmatism (Bengson, Chudnoff). Some experience enthusiasts hold that all evidence ultimately boils down to experience, and so endorse the (misleadingly named) phenomenal conception of evidence, the thesis that a subject’s evidence supervenes on her non-factive mental states. 12 This argument is worded on the assumption that perceptual experiences have content. A plausible version of this argument can be presented without explicitly assuming that perceptual experiences have content; however, I worry that the intuitions that lead philosophers to deny that experiences have content tend to challenge the intuitions behind the Bad to Resist Belief Argument. 13 Bengson (2015: 738–740) endorses something like this argument. Huemer gives a superficially similar argument, which I discuss later in n. 15. 14 As good Bayesians, shouldn’t we always have some prior probability distribution for every possible circumstance that we might seem to see? If so, then there is never a case in which an experience will be the only relevant information, as my set-up supposes. In reply, it’s not clear to me that we should be good Bayesians when we explicate informal notions, such as “reasonable” or “unreasonable”. Nor is it clear that evidence, in the sense I’ve been discussing it here, is the same thing that goes by “evidence” in Bayesian theories. 15 Huemer (2006, 2013) defends an argument that is, in certain respects, similar to the one presented here, but Huemer’s reasoning is different. He assumes the Rational Explanation Thesis: if one experience is evidence and the other isn’t, then one must have a rational explanation for why one experience is evidence and the other isn’t (see premise 6 on 2013: 746). The issue here is metacoherence: if you rationally treat one experience as evidence and not the other, then you must now possess some rational explanation for why these experiences can be treated differently. To secure Huemer’s conclusion that a certain kind of experience is always evidence (or always has justifying power), Huemer must assume that having a rational explanation is necessary regardless of whether one actually reflects on which of one’s experiences are evidence. I reject the Rational Explanation Assumption, and it is incompatible with Huemer’s own “Happy Coincidences” solution to metacoherence puzzles. This solution claims, first, that you don’t need a meta-justification until you reflect on your first-level justification. It claims, second, that when you reflect an independent source may provide the needed meta-justification by a happy coincidence (2011, section 6). But if the need for the meta-justification (e.g., an explanation of why one experience is evidence and the other isn’t) doesn’t apply until you reflect, then the Rational Explanation Thesis is false.

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Experience as Evidence 16 If you endorse the first two premises of the Bad to Resist Belief Argument and the causal history objection mentioned in the next subsection, then you have an additional reason to think that something can have committing force without justifying force. 17 I’m focused on dilemmas internal to reasonableness/rationality. In contrast, Nick Hughes (forthcoming) defends the existence of epistemic dilemmas that involve the interaction of reasonableness and truth. The (non-)existence of such dilemmas is irrelevant to the success of the Bad to Resist Belief Argument. 18 See, e.g., Siegel 2012, 2017. 19 See, e.g., Chudnoff (forthcoming) and Huemer (2013). 20 Proponents of experience enthusiasm must reject, for example, the idea that “The property of being doxastically justified just is that property which turns true unGettiered belief into knowledge” (Goldberg 2012: 240). 21 It’s also worth mentioning that sometimes critics issue causal history objections to experience enthusiasm at their own peril. See my 2014. 22 Thanks to T. Ryan Byerly, HR Gentry, Clayton Littlejohn, and Declan Smithies for very helpful comments on earlier drafts.

References Bayne, Tim and David Chalmers. 2003. “What Is the Unity of Consciousness?” The Unity of Consciousness: Binding, Integration, and Dissociation. Alex Cleeremans (ed.). Oxford University Press. Bengson, John. 2015. “The Intellectual Given.” Mind 124: 707–760. Chudnoff, Eli. Forthcoming. “Experience and Epistemic Structure: Can Cognitive Penetration Result in Epistemic Downgrade?” Inference and Consciousness. Anders Nes and Timothy Chan (eds.). Routledge. Conee, Earl and Richard Feldman. 2008. “Evidence.” Epistemology: New Essays. Quentin Smith (ed.). Oxford University Press, 83–104. Goldberg, Sanford. 2012. “A  Novel (and Surprising) Argument Against Justification Internalism.” Analysis 72: 239–243. Goldman, Alvin and Matthew McGrath. 2015. Epistemology: A Contemporary Introduction. Oxford University Press. Huemer, Michael. 2006. “Phenomenal Conservatism and the Internalist Intuition.” American Philosophical Quarterly 43: 147–158. ———. 2011. “The Puzzle of Metacoherence.” Philosophy and Phenomenological Research 82: 1–21. ———. 2013. “Phenomenal Conservatism Über Alles.” Seemings and Justification. Chris Tucker (ed.). Oxford University Press, 328–350. Hughes, Nick. Forthcoming. “Dilemmic Epistemology.” Synthese. Early view available here: https:// doi.org/10.1007/s11229-017-1639-x Lyons, Jack. 2009. Perception and Basic Beliefs: Zombies, Modules, and the Problem of the External World. Oxford University Press. Siegel, Susanna. 2012. “Cognitive Penetrability and Perceptual Justification.” Noûs 46 (2): 201–222. ———. 2017. The Rationality of Perception. Oxford University Press. Travis, Charles. 2004. “The Silence of the Senses.” Mind 113: 57–94. Tucker, Chris. 2011. “Phenomenal Conservatism and Evidentialism in Religious Epistemology.” Evidence and Religious Belief. VanArragon, Raymond and Kelly James Clark (eds.). Oxford University Press, 52–73. ———. 2014. “If Dogmatists Have a Problem with Cognitive Penetration, You Do too.” Dialectica 68: 35–62. Williamson, Timothy. 2000. Knowledge and Its Limits. Oxford University Press.

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2 E = K, BUT WHAT ABOUT R? Timothy Williamson

1  Educated Common Sense and Formal Theory Holocaust deniers lack evidence that the Holocaust never took place. Even on what evidence they have, their claim is not very probable. Such observations should be commonplace. They tell against subjective theories of evidence, on which your evidence consists of your internal mental states, or your perceptual and intellectual seemings, or what you are certain of, or what you take for granted, or something like that. For Holocaust denial may do very well by all such subjective standards, if the denier is sufficiently consistent and blinkered. Instead, most of the relevant evidence is publicly available. There are better ways of deciding what happened in history than by introspection. Thinkers with no capacity at all to recognize the difference between good and bad evidence in various areas are in no position to start theorizing philosophically about evidence: they have too little to test their theories against. Fortunately, many people do have such a capacity. We may call it educated common sense. But we should not expect to get far in theorizing about evidence by educated common sense alone. For it often relies on heuristics, quick and dirty ways of thinking, reliable enough for ordinary purposes but capable of sometimes leading us astray.1 Here is an example. We routinely speak and think in terms of weighing the evidence, assessing the balance of the evidence, and so on. Sometimes the evidence for a hypothesis outweighs the evidence against, sometimes it is the other way round, and sometimes the evidence is evenly balanced. Thus we unreflectively use the metaphor of a pair of scales to structure our thinking about evidence. It is often helpful to do so. The metaphor has structural consequences. In particular, it implies that putting together two pieces of evidence for a hypothesis yields even stronger evidence for that hypothesis. But that is a fallacy, as probability theory soon shows. For even if the probability of a hypothesis h on evidence e1 is very high, as is the probability of h on evidence e2, the probability of h on the conjoined evidence e1 & e2 may still be very low. For instance, suppose that a number N has been chosen at random from the integers 1, 2, 3, . . ., 100; each value for N is equally likely. We receive evidence about N from a completely reliable device. Let h be the hypothesis that N is odd, and e1 the proposition that N is one of 1, 3, 5, . . ., 49, 50 (so N is either 50 or both odd DOI: 10.4324/9781315672687-4 30

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and less than 50). Then the probability of h conditional on e1 is 25/26, so e1 makes excellent evidence for h. Similarly, let e2 be the proposition that N is one of 50, 51, 53, 55, . . ., 99 (so N is either 50 or both odd and over 50). Then the probability of h conditional on e2 is also 25/26, so e2 too makes excellent evidence for h. But the conjoined evidence e1 & e2 entails that N is 50, which is inconsistent with h. Thus the probability of h conditional on e1 & e2 is 0, so the conjunction is decisive evidence against h. In such cases, the metaphor of weighing the evidence leads us wildly astray. Of course, in a toy model like this, we can easily see what is going wrong and correct accordingly. But in more realistic cases, where the evidence is richer, more complicated, and messier in its bearings, we are in more danger of committing the fallacy unawares.2 Thus we should be wary of relying on educated common sense in laying down structural constraints on evidential relations. Here is another example. Common sense feels strongly that nothing can be evidence for itself: that would be circular! Now consider a standard definition of the evidence-for relation in a probabilistic framework: e is evidence for h just in case the probability of h conditional on e exceeds the unconditional probability of h; in other words, e raises the probability of h. To be more precise, we need to say what probability distribution is relevant, and what makes e evidence at all, but for now we can bracket those issues. In the special case when e has probability 1, the probability of h conditional on e is just the unconditional probability of h, so e is not evidence for h. Thus if e is evidence for anything, e has probability less than 1. But the probability of e conditional on itself is trivially 1. Thus, by the definition, if e is evidence for some hypothesis, e is evidence for itself.3 Consequently, the standard probabilistic definition of evidence-for clashes with common sense. If we side with common sense, we lose the systematic advantages of the probabilistic approach, for which common sense has no comparably powerful and precise substitute to offer. Indeed, common sense has a long track record of obstructing progress in the development of fruitful theoretical frameworks by digging in its heels against pseudoanomalies in logic and basic mathematics, which are really just limiting cases of a simple general rule. Common sense did not want 0 to be a number; it did not want a contradiction to entail everything; it did not want an axiom to have a one-line proof consisting of just the axiom itself. In each case, common sense was blinded by superficial differences to underlying similarities. The limiting case of evidence as evidence for itself is another such case where formal theory is a better guide.4 The way to defeat a theory of evidence is not by appeals to educated common sense but by producing a better theory of evidence. It may be better partly because it can explain more of what we pre-theoretically know about evidence. It may also be better partly because it is formally simpler and stronger. In particular, an apt challenge to any theory of evidence is to show how it integrates with a probabilistic framework. That is not to make the inappropriately Procrustean demand that all serious thinking about evidence should be done in probabilistic terms. The point is just that much (though far from all) of our most rigorous, sophisticated, and subtle thinking about evidence is already done in such terms, so a theory of evidence which fails to engage properly with that framework is off the pace. But there is no question of reducing the theory of evidence to the mathematics of probability theory: what constitutes evidence is a question of epistemology, not of mathematics. In short, the appropriate methodology for theorizing on this topic, as on so many others, is abductive. One aspect of this methodology is that a theory of evidence can regiment

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the term ‘evidence’ as it sees fit, as long as it remains in contact with the general topic. For theoretical purposes, we want our key theoretical terms to cut the subject matter at its natural joints, wherever they are, and locating them is a task for the theory itself. We should not expect ‘evidence’ as a theoretical term to trace every nook and cranny of the word as ordinarily used in English. The rest of this chapter concerns one specific theory of evidence, proposed in Knowledge and Its Limits (Williamson 2000) as doing justice to the demands of both formal theory and educated common sense. The present aim is not to compare it explicitly with its rivals (discussed in other chapters of this book) but to explain the resources it brings to such comparisons. The next section summarizes the theory and some considerations in its favour, mainly in their original form. Sections 3 and 4 develop the account in response to some salient challenges.

2 E = K The job description for evidence includes three general tasks. First, evidence rules out some hypotheses by being inconsistent with them. Second, in inference to the best explanation (closely related to abduction), evidence is what the best hypothesis best explains. Third, in probabilistic confirmation, evidence is what the probability of the hypothesis is conditional on. All three tasks require evidence to be propositional, true or false in various circumstances. What is inconsistent with a hypothesis is propositional: its truth-condition is disjoint from the theory’s. What a hypothesis explains is propositional: the hypothesis explains why or how its truth-condition obtains. What the probability of a hypothesis is conditional on is propositional: the probability of h conditional on e is normally defined as the probability of the conjunction of h and e divided by the probability of e, where both h and e are treated as ‘events’ in the probability space, which are in effect truth-conditions. Of course, the term ‘evidence’ is often applied more widely: for example, to material evidence in a court of law, and by some philosophers to mental states. But when it comes to the three tasks of evidence just described, what does the work is not the non-propositional evidence itself but some proposition about it. Thus for theoretical purposes it is more perspicuous to restrict the term ‘evidence’ to the propositional. Presented with an account of what constitutes evidence, one should ask: which propositions does it propose as evidence? Unfortunately, many accounts fudge this elementary question. For example, philosophers who speak of ‘intuitions as evidence’ often leave it unclear whether the proposition supposed to be in one’s evidence is the proposition one intuits or the proposition that one intuits it. To serve the three tasks, what is needed is not just a proposition but a true proposition. That a hypothesis h is inconsistent with the evidence rules out h only by entailing that h is false; but if the evidence were false, it would be inconsistent with some true hypotheses. Inference to the best explanation and probabilistic confirmation would also be more problematic if the evidence to be explained or conditionalized on were false. Of course, in applying the principle that all evidence is true, one must be careful to distinguish the proposition h (or e) from the proposition h* (or e*) that h (or e) holds approximately, otherwise one can easily generate fallacious ‘counterexamples’. Clearly, the question is not just what evidence is ‘out there’, but what evidence a given agent has—which true propositions they have access to in the relevant epistemic sense. The 32

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salient form of access is simply knowledge. Thus your total evidence is just the totality of truths you know. This is the equation E = K. Since you know p only if p is true, this immediately explains why evidence has to be true. If you do not know p, p is not available to serve as part of your evidence (though it may seem to be). Conversely, if you do know p, p is available to serve as part of your evidence. Although someone might be tempted to restrict your evidence to truths you know in some special, supposedly basic way—for instance, by sense perception, or by introspection—the case of evidence for the Holocaust already suggests that no such restriction is faithful to the actual role of evidence in our cognitive lives. The publicly available evidence for the Holocaust consists of all sorts of historical facts. Such an account of evidence is easy to integrate with a probabilistic framework. The probability of a hypothesis h on your evidence is simply the probability of h conditional on the conjunction of all the truths you know. Unlike views which allow false evidence, this view does not have to deal with the possibility of inconsistent evidence, probabilities conditional on which are ill-defined, for truths are always mutually consistent. That all evidence is true does not mean that evidence supports only true hypotheses. Of course, the evidence for a false hypothesis cannot be logically conclusive, since only truths follow deductively from truths. But a falsehood can still be highly probable on someone’s evidence, for the conditional probability of a falsehood on a truth can be high. For example, when someone is skilfully framed for a crime she did not commit, the false hypothesis that she is guilty is highly probable on true evidence as to where fingerprints were found, what witnesses said, and so on. True evidence can be misleading. One salient consequence of E = K is that we are often in no position to know whether a given proposition belongs to our evidence, for we are often in no position to know whether we know something. For example, someone sees a mule cleverly painted to look like a zebra in the zoo; he falsely believes that he saw a zebra; indeed, he falsely believes that he knows that he saw a zebra, and that the proposition that he saw a zebra is part of his evidence; for all he knows, the proposition that he saw a zebra is part of his evidence. Thus sometimes a proposition is not part of one’s evidence, even though one is in no position to know that it is not part of one’s evidence (negative introspection fails for evidence). More subtly, it can be argued, sometimes a proposition is part of one’s evidence, even though one is in no position to know that it is part of one’s evidence (positive introspection fails for evidence). In these ways, it is not transparent to one’s evidence what one’s evidence includes.5 The risk of error is not the only reason for the non-transparency of evidence. Consider an animal with perceptual evidence (that is, knowledge) streaming in through various sense modalities. Virtually none of that evidence is of the form ‘my evidence does not include p’. If it happens to include some evidence incompatible with p, a clever animal may be able to deduce ‘my evidence does not include p’ (because evidence is always true), but if p is independent of all its actual evidence, how is it to recognize that? Even if it somehow manages to make its evidence satisfy positive introspection, and to derive all the logical consequences of combined elements of its evidence, negative introspection may still fail. For none of the propositions obtained in those ways need entail anything special about p. The animal would need a further capacity to survey all its evidence and register the absence of p. That might be an extremely demanding cognitive task, especially if the evidence from different sense modalities comes in different formats (verbal, visual, olfactory, . . .) and its entailments are hard to compute. Even if it has some capacity to survey its evidence, it will not be instantaneous—certainly it is not in the human case. The animal may have to wait for a 33

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signal that p has been found. If no signal comes within, say, five minutes, the animal may give up and assume ‘my evidence does not include p’ (human memory sometimes works like that). But while the animal is waiting for a signal, for all it knows the signal will still come, and so its evidence does not yet include ‘my evidence does not include p’, even if in fact its evidence does not include p. At that time negative introspection fails for the animal’s evidence. Should we dismiss such creatures as irrational? In doing so, we risk dismissing ourselves as irrational. Of course, humans are irrational to some extent, but epistemology becomes uninteresting if we idealize away from too many of the limitations inherent in real-life knowledge. The non-transparency of evidence can easily look problematic. For if you are in no position to know what your evidence includes, you may well be in no position to know how probable a proposition is on your evidence, and so be in no position to be guided by your evidence on how to treat that proposition. But guidance on how to treat propositions is just what we want evidence for. Thus the result might be used as an objection to E = K. However, non-transparency is an objection to E = K only if some other approach does better. But, arguably, other approaches to evidence end up facing the same problem. For example, suppose that one’s evidence consists of those truths one currently introspects. It is often hard to know just which truths one currently introspects. Inner life is an unclear, fleeting, elusive affair—at least in my case (perhaps the reader is luckier). I find it on the whole much easier to assess what I observe of my external physical environment than what I introspect of my own internal mental world. Going internalist does not solve the problem of non-transparency. Of course, to say that non-transparency is everyone’s problem is not yet to solve it. How can we live with non-transparent evidence? The next section gets to grips with that challenge.

3  What Is R? Since the problem of non-transparency was introduced with reference to sceptical scenarios, let us consider them further. A sceptical scenario is usually characterized as a bad case by contrast with a corresponding good case. For example, in the good case, the thinker sees ‘there is blood on the knife’ in the normal way, and thereby knows and believes ‘there is blood on the knife’. In the bad case, there is no bloodied knife, but a demon causes the thinker to have a visual experience as of seeing ‘there is blood on the knife’; the total experience is perfectly indiscriminable ‘from the inside’ from the total experience in the good case; she believes falsely ‘there is blood on the knife’, without seeing or knowing that there is. Internalists typically insist that the thinker has exactly the same evidence in the good and bad cases and conclude that the belief ‘there is blood on the knife’ has exactly the same level of justification in the two cases. Given E = K instead, the evidence is not exactly the same in the two cases. In the good case, the thinker’s evidence includes the proposition ‘there is blood on the knife’, since she knows that there is. In the bad case, by contrast, the thinker’s evidence does not include the proposition ‘there is blood on the knife’, since she does not know that there is. Thus there is scope to deny that the belief ‘there is blood on the knife’ has exactly the same level of justification in the two cases. Thomas Kelly (2016) uses this example to raise a problem for E = K. He begins by distinguishing two different ‘intuitions’: 34

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The first intuition is that a thinker in the bad case has exactly the same evidence as a thinker in the good case. Perhaps abandoning this intuition is not much of a cost (if it is any cost at all). A different intuition is the following: when a thinker in the bad case takes his experiences at face value and forms beliefs about the external world in the usual manner, those beliefs are not simply unreasonable, in the way that they would be if, for example, the thinker adopted those same beliefs on a whim, or in the absence of any reason to do so at all. Abandoning this intuition would seem to be a much heavier price to pay. Kelly goes on to argue that the second intuition is hard to reconcile with E = K in the example, since in the bad case the thinker may know nothing to give significant support to the proposition ‘there is blood on the knife’. He considers true fallback propositions such as ‘it appears that there is blood on the knife’ and ‘my experience is as of there being blood on the knife’, but he points out that, on some plausible views, in normal cases of perception, a thinker who does not suspect that something is amiss will not even consider such fallback propositions, but will simply go straight ahead and form beliefs about the external world, such as ‘there is blood on the knife’. Presumably, if she does not even consider the fallback propositions, she does not come to believe them either. But then, since knowledge entails belief, she does not know the fallback truths. Therefore, given E = K, they do not belong to her evidence. Thus E = K threatens to eliminate any evidence for the proposition ‘there is blood on the knife’. But, as Kelly says, ‘Intuitively, this belief is at the very least better justified than it would be in the absence of the relevant visual experience’. Even if some beliefs can be justified without evidence, the false belief ‘there is blood on the knife’ is hardly a good candidate for that status. One might try to respond to Kelly by being more liberal in ascribing knowledge, arguing that in some relevant sense the thinker does implicitly know ‘it appears that there is blood on the knife’ or ‘my experience is as of there being blood on the knife’, even though all she explicitly formulates is ‘there is blood on the knife’. But a young child might be able to think simple thoughts about the external world such as ‘there is blood on the knife’ while still lacking the semantic sophistication to think meta-cognitive thoughts such as ‘it appears that there is blood on the knife’ or ‘my experience is as of there being blood on the knife’: to ascribe implicit knowledge with the latter contents to the child is quite a stretch. So let us just concede to Kelly that the thinker does not know any of the relevant fallback truths; thus by E = K she lacks evidence for her belief ‘there is blood on the knife’. What then? When formulating the key intuition in the quoted passage, Kelly describes the thinker’s beliefs as ‘not simply unreasonable’. Like the distinction between rationality and irrationality, the distinction between reasonableness and unreasonableness can be understood in two contrasting ways. We can focus either on the proposition thought or on the agent thinking it. If we focus on the proposition, we naturally wonder what evidence there is for it. If instead we focus on the agent, we naturally wonder what cognitive dispositions they are exercising. Of course, the two questions are not completely independent of each other. To a first approximation: good cognitive dispositions typically generate knowledge, or at least beliefs well supported by the thinker’s evidence; bad cognitive dispositions typically generate beliefs poorly or not at all supported by the thinker’s evidence, and so not knowledge. Nevertheless, the two questions are far from equivalent. In the bad case where there appears to be blood on the knife, nothing is wrong with the thinker’s cognitive dispositions; the relevant ones are just those involved in acquiring ordinary visual knowledge. However, the thinker is exercising those good cognitive dispositions in unfavourable circumstances, where they unluckily generate beliefs unsupported by his evidence. There is also a converse 35

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phenomenon, which Maria Lasonen-Aarnio (2010) calls ‘unreasonable knowledge’: sometimes, the thinker exercises bad cognitive dispositions in favourable circumstances, where they luckily generate knowledge (see also Lasonen-Aarnio 202X, 2021).6 In the bad case, our positive assessment of the thinker’s cognitive dispositions naturally leaches into our assessment of the belief they generate: it has good origins. But we should not confuse that positive feature of the belief with a quite different positive feature which it lacks: support from the thinker’s evidence. Thus proponents of E = K can meet Kelly’s challenge to explain why the thinker’s beliefs in the bad case ‘are not simply unreasonable, in the way that they would be if, for example, the thinker adopted those same beliefs on a whim, or in the absence of any reason to do so at all’. For beliefs adopted ‘on a whim, or in the absence of any reason to do so at all’ are paradigms of beliefs with bad origins, generated by cognitive dispositions which typically generate beliefs not supported by the thinker’s evidence. The mistake is to assume that the difference in reasonableness must be specifically a difference in evidential support, rather than in the quality of the underlying cognitive dispositions. That is why this section is entitled ‘What is R?’; ‘R’ stands for ‘reasonableness’ (or, to similar effect, ‘rationality’). For completeness, we can also briefly consider the epistemic status of the thinker’s belief ‘there is blood on the knife’ in the good case, where by hypothesis it constitutes perceptual knowledge, and so perceptual evidence, given E = K. As the case has been developed, that knowledge does not rest on evidence such as ‘it appears that there is blood on the knife’ or ‘my experience is as of there being blood on the knife’: those fallback propositions are no more believed and no more known in the good case than they are in the bad case. Given the richness of vision, the thinker’s visual knowledge in the good case is presumably not exhausted by the single proposition ‘there is blood on the knife’, but that does not mean that her visual knowledge ‘there is blood on the knife’ is somehow based on other visual evidence of a radically different kind. Given E = K, the knowledge ‘there is blood on the knife’ is not strictly unsupported by evidence, because it is itself evidence, and so trivially has probability 1 given the thinker’s evidence, but that is not a (feeble) attempt to understand knowledge in terms of evidential relations. Rather, the point is that there is a limit to how much heavy lifting we should expect evidential relations to do in epistemology: yet again, knowledge comes first. This treatment of good and bad cases makes essential use of norms on cognitive dispositions. Such norms require further consideration.

4  Anti-agnostic Norms The cognitive dispositions at issue in Section 3 were dispositions to acquire knowledge or belief. As a first approximation, the dispositions were qualified as ‘good’ or ‘bad’ according to the quality of the cognitive states they were dispositions to generate—specifically, the evidential status of the beliefs, with knowledge as the best status. That may suggest that norms on dispositions to believe are derivative from norms on belief. However, there is more to it than that. On one natural understanding, a norm on belief is broadly functional in nature: beliefs which violate it are defective. This approach has the advantage of applying straightforwardly to the beliefs of unsophisticated cognizers such as young children and non-human animals. After all, such creatures act on their knowledge of their external environment, and on their beliefs about it; they are just as vulnerable as adult humans to many sceptical 36

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scenarios. Now, for a norm of non-defectiveness on belief to be violated, there must first be a belief: without a belief, there is nothing to be defective. Analogously: for the norm of promise-keeping to be violated, a promise must first have been made: without a promise, there is nothing to be broken. One can comply with the norm of promise-keeping simply by not making any promises. Similarly, one can in principle comply with a norm of nondefective belief simply by not having any beliefs. Indeed, that is what extreme sceptics recommend. If one has no beliefs, one has no beliefs with a defective evidential status. If the only norm in play is one banning defective belief, by far the simplest way of complying with it would be to avoid believing altogether. By that standard, Kelly’s thinker’s belief ‘there is blood on the knife’ is unjustified in the good case as well as the bad one, since even in the former it constitutes an unnecessary risk of defectiveness. Of course, to avoid believing altogether is psychologically impossible for normal humans, and for other animals which naturally form beliefs. But a determined sceptic could probably avoid forming a particular belief, such as ‘there is blood on the knife’. Thus believing becomes a frailty of our lower nature. That line of thought concedes far too much to scepticism. Suspension of all belief is not an ideal. It is pathological even on the functional approach with which we started. Agnosticism is dysfunctional. Animals need knowledge of their environment on which to act. For both predators and prey, it is a matter of life and death. Since animals need knowledge of their environment, they need a cognitive system to produce that knowledge, and plenty of it. The system has to be open to knowing. The inevitable downside of such a system is that it will be open to believing falsely in unfavourable circumstances, of which sceptical scenarios are just an extreme case. Your cognitive system would be defective if it did not dispose you to believe ‘there is blood on the knife’ in the bad case. What the argument of Section 3 really requires is a norm of non-defectiveness on whole cognitive systems, not just a norm of non-defectiveness on individual beliefs.7 A good cognitive system is positively disposed to gather knowledge, not just negatively disposed to gather only knowledge. There is a trade-off between the two dispositions: too high a threshold means gathering too little knowledge, too low a threshold means gathering too much non-knowledge. A good system finds an appropriate mean between the two extremes. Given E = K, to gather knowledge is to gather evidence. Thus a good cognitive system is positively disposed to gather evidence. This point helps with cases in the literature of agents who manifest unconscious bias in evidence-gathering: they behave in ways which make them unlikely to acquire evidence that would challenge their prejudices. Their decisionmaking may be reasonable given their evidence, but their evidence constitutes a severely biased sample (see Miracchi 2019; Lasonen-Aarnio 2021). In an extreme case, all the agent’s beliefs constitute knowledge. For example, in a job search, he may pay much more attention to the CVs of candidates with the desired race and gender profile than to the CVs of other candidates, with the result that he acquires much more knowledge about the former candidates than the latter. Naturally, some of the knowledge may tell in favour of the candidate, some may tell against. But in a large field, with many well-qualified candidates, probably some candidate with the desired profile will have a good enough CV for his evidence about them to be more favourable than his much sparser evidence about any of the candidates without the desired profile. The agent may even come to know that his evidence favours that candidate with the desired profile more than it favours any other candidate, and accordingly decide to vote for that candidate. 37

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That process does not have to involve any belief which falls short of knowledge—though of course it is likely to. A norm of non-defectiveness on individual beliefs will not pick up what has gone wrong in such a process. A  norm of evidence-gathering will help. The agent was insufficiently open to acquiring knowledge from the CVs of candidates without the desired profile. Given E = K, the agent was insufficiently open to acquiring evidence from those CVs. ‘Openness’ here is not a merely passive quality; it involves a disposition to seek knowledge. Sometimes the seeking is as easy as just reading the page in front of you; sometimes, of course, it is much harder, and involves long and arduous searching. However, a norm of knowledge-gathering must be constrained by feasibility. One cannot search simultaneously for knowledge relevant to all the questions one is capable of asking. One must have priorities, and those priorities will often be practical rather than epistemic. In the job search case, the priority was high because an important decision was at stake. A secretary with no role in the decision-making, idly leafing through the CVs with the same levels of attention as the decision-maker, does not count as equally negligent, because their priorities are different, for practical rather than epistemic reasons. Even the decision-maker may not count as negligent until the moment of decision. For, having looked through the CVs and recognized that his present evidence favoured one of the candidates, he could have decided that it was time to read through all the CVs carefully. Instead, he simply formed the intention to vote for that candidate. That was negligent, because it was based on inadequate evidence-gathering, but its inadequacy was as a basis for an important practical decision. If he also formed the belief ‘this is the best candidate’, then that belief did not constitute knowledge and was based on epistemically inadequate evidence, but he could have jumped to the intention without forming the belief. Thus we cannot expect a norm of knowledge-gathering to do all the normative work in such cases, without reference to practical considerations. Still, we should not go to the opposite extreme either and expect to absorb the epistemic into the practical. Cognitive systems have considerable autonomy, in part for good practical reasons. One often does not know in advance what knowledge is going to come in handy. When our cognitive systems are working properly, knowledge streams into us during waking hours. Animals are naturally curious: knowledge is comparatively cheap to acquire and store, and too little of it is usually worse than too much. Knowledge-seeking is not confined to scholars: the nosey and the prying enjoy it too. Not all evidence-gathering takes the dignified or pompous form associated with the phrase ‘intellectual virtue’. A nondefective cognitive system is constantly on the look-out for cheap knowledge: what requires cultivation is the taste for expensive knowledge. The normative role of evidence is best understood within a framework of functional norms on cognitive systems. The equation of evidence and knowledge integrates smoothly with such a framework, which also naturally hosts a crucial distinction between evidential and dispositional forms of rationality.

Notes 1 Williamson 2020a makes a more detailed case that heuristics play a significant role in generating various philosophical problems, in particular concerning the semantics of conditionals. The term ‘heuristic’ is intended to recall both the heuristics and biases programme in psychology (going back to works such as Kahneman, Slovic, and Tversky 1982) and the partly contrasting tradition of work on adaptive rationality (see, e.g., Gigerenzer, Hertwig, and Pachur 2011), though the exact connections are left open.

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E = K, but What About R? 2 The problem is not restricted to our thinking about evidence. We apply the same metaphor in our thinking about reasons: ‘weighing reasons’, ‘the balance of reasons’, etc. Unfortunately, the literature on reasons is less used to applying probability theory as a corrective. 3 If e has probability 0, probabilities conditional on e are usually taken to be undefined, but then e is not evidence for anything. 4 Resistance to evidence being evidence for itself is central to the critique in Brown (2018) of the account of evidence defended in this chapter and in Williamson (2000). 5 The case in Williamson (2000) for the non-transparency of evidence is further developed in Williamson (2014, 2019, 2020b). For some recent dissent, see Salow (2018). 6 For more discussion of this contrast, see Williamson (2017, 202X, 202Y). 7 For more discussion of norms on cognitive systems, see Williamson (202Y).

References Brown, Jessica. 2018: Fallibilism: Evidence and Knowledge. Oxford: Oxford University Press. Gigerenzer, Gerd, Hertwig, Ralph, and Pachur, Thorsten (eds.). 2011: Heuristics: The Foundations of Adaptive Behavior. New York: Oxford University Press. Kahneman, Daniel, Slovic, Paul, and Tversky, Amos (eds.). 1982: Judgment Under Uncertainty: Heuristics and Biases. Cambridge: Cambridge University Press. Kelly, Thomas. 2016: ‘Evidence’, in Edward Zalta (ed.), The Stanford Encyclopedia of Philosophy (Winter Edition) . Lasonen-Aarnio, Maria. 2010: ‘Unreasonable knowledge’, Philosophical Perspectives, 24: 1–21. Lasonen-Aarnio, Maria. 2021: ‘Dispositional evaluations and defeat’, forthcoming in Jessica Brown and Mona Simion (eds.), Reasons, Justification and Defeat. Oxford: Oxford University Press. Lasonen-Aarnio, Maria. 202X: ‘Virtuous failure and victims of deceit’, forthcoming in Julien Dutant and Fabian Dorsch (eds.), The New Evil Demon. Oxford: Oxford University Press. Miracchi, Lia. 2019: ‘When evidence isn’t enough: Suspension, evidentialism, and knowledge-first virtue epistemology’, Episteme, 16: 413–437. Salow, Bernhard. 2018: ‘The externalist’s guide to fishing for compliments’, Mind, 127: 691–728. Williamson, Timothy. 2000: Knowledge and Its Limits. Oxford: Oxford University Press. Williamson, Timothy. 2014: ‘Very improbable knowing’, Erkenntnis, 79: 971–999. Williamson, Timothy. 2017: ‘Ambiguous rationality’, Episteme, 14: 263–274. Williamson, Timothy. 2019: ‘Evidence of evidence in epistemic logic’, in Mattias Skipper and Asbjørn Steglich-Petersen (eds.), Higher-Order Evidence: New Essays, 265–297. Oxford: Oxford University Press. Williamson, Timothy. 2020a: Suppose and Tell: The Semantics and Heuristics of Conditionals. Oxford: Oxford University Press. Williamson, Timothy. 2020b: ‘The KK principle and rotational symmetry’, Analytic Philosophy, 62, forthcoming. Williamson, Timothy. 202X: ‘Justifications, excuses, and sceptical scenarios’, forthcoming in Julien Dutant and Fabian Dorsch (eds.), The New Evil Demon. Oxford: Oxford University Press. Williamson, Timothy. 202Y: ‘Epistemic ambivalence’, forthcoming in Nicholas Hughes (ed.), Epistemic Dilemmas. Oxford: Oxford University Press.

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3 EPISTEMOLOGICAL DISJUNCTIVISM AND EVIDENCE Duncan Pritchard

Introductory Remarks Disjunctivist views about the content of perceptual experience have been defended for some time, often as part of a broadly naïve realist account of perception. Very roughly, such views hold that there is no common metaphysical component of both ordinary veridical experience (the ‘good case’), and corresponding indistinguishable experiences involving hallucination, such as when one is brain-in-a-vat (BIV) being ‘fed’ one’s experiences by supercomputers (the ‘bad case’).1 Rather, such experiences are on this view different in kind, in that the content of the former experience is at least partly determined by it being a veridical perception in a way that the content of the latter experience cannot be determined. (Of course, there is a negative epistemological property that is in common to both experiences, which is that they are indistinguishable, but the point is that this property doesn’t pick out a significant metaphysical property). Call disjunctivism of this kind metaphysical disjunctivism. Given that the content of one’s experiences can have a bearing on the evidential or rational support that is available for one’s perceptual beliefs, then there is a direct connection between metaphysical disjunctivism and the epistemic support one’s perceptual beliefs enjoy. In particular, we should not conclude that just because a pairing of good/bad case experiences are indistinguishable to the agent concerned that the epistemic support offered by the experience in the good case can be no better than the epistemic support offered by the experience in the bad case. Instead, if metaphysical disjunctivism is true, then it may well be that the epistemic support one’s experiences generate in the good case is significantly better than the epistemic support generated by the indistinguishable experiences had in the corresponding bad case.2 In what follows, we will focus our attention not on metaphysical disjunctivism, but rather on its sister position, epistemological disjunctivism. The core difference between the two is that whereas metaphysical disjunctivism offers a metaphysical position from which one might be able to extract some surprising epistemological consequences, epistemological disjunctivism offers an epistemological position that delivers those surprising epistemological consequences directly. With the two proposals differentiated, we can then ask what the DOI: 10.4324/9781315672687-5 40

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logical relationships are between metaphysical and epistemological disjunctivism. Does the former entail the latter? Does the latter entail the former? Or is the relationship between the two views less a matter of logical entailment and more one of dialectical affiliation? For example, one might plausibly contend that it is hard to make sense of the philosophical motivation for epistemological disjunctivism without a prior commitment to metaphysical disjunctivism. In any case, these further questions are largely orthogonal to the purposes of this piece. On the one hand, if metaphysical disjunctivism doesn’t have interesting epistemological consequences, then its bearing on evidence won’t be of concern to us. On the other hand, if epistemological disjunctivism is true, then it has ramifications for the nature of evidence regardless of whether this position entails (or otherwise leads to) metaphysical disjunctivism. It follows that our proper concern here is directly with the evidential ramifications of epistemological disjunctivism.

Epistemological Disjunctivism There is a standard version of epistemological disjunctivism in the contemporary epistemological literature. It is derived from earlier work by John McDowell (e.g., 1995), but the main presentation of the view is due to myself.3 According to this proposal, in epistemically paradigm cases of perceptual knowledge, one’s knowledge is supported by rational support that is both factive and reflectively accessible. In particular, in such cases one’s reflectively accessible rational support for knowing that p is that one sees that p, where seeing that p entails p (and hence is factive). We can see why the position is an epistemological form of disjunctivism by seeing how it plays out in a pairing of experiences in a good case (i.e., a scenario where the conditions are epistemically paradigmatic) and a corresponding indistinguishable bad case (e.g., a radical sceptical scenario, such as the BIV case). One might naturally suppose that since one is unable to distinguish between the experiences had in the good and the bad case, then the rational support enjoyed by one’s beliefs in the good case can be no better than the rational support enjoyed by one’s belief in the bad case.4 After all, for all one can tell, one might be in the bad case, so how is one to have rational support for one’s beliefs that would be unavailable in the bad case? Epistemological disjunctivism runs directly counter to this thought, however, since it maintains that there is rational support reflectively available to the subject that is unavailable to the subject’s counterpart in the bad case. After all, since the subject is radically deceived in the bad case, she can hardly be in a position to see that p, not least because p is almost certainly false, but even if it does happen to be true, the subject in our bad case is not going to stand in the robust epistemic relationship to p of seeing that p.5 At best, the rational support reflectively available to the subject in the bad case is going to be that of seeming to see that p, which is obviously a non-factive rational standing.6 The upshot is that rather than one’s rational support in the good case being no better than it is in the corresponding bad case, it can instead be significantly superior. Moreover, proponents of epistemological disjunctivism maintain that there is no common rational core to the rational standing of the subject’s belief in the good and bad cases, as if one could simply understand the rational standing in the good case as being the rational standing available in the bad case supplemented by some additional rational support. Rather, the difference in rational support is one of kind. Seeing that p cannot be decomposed into, say, merely seeming to see that p plus some other additional rational support. The difference 41

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between the two rational standings is thus one of kind and not merely of degree. We thus have the disjunctive aspect of epistemological disjunctivism: either one is in the good case and enjoys factive rational support, or one is in the bad case and enjoys, at best, non-factive rational support (with there being no significant common core of rational support which applies to both cases).7 There are a few things to note about our characterization of epistemological disjunctivism. First, in common with metaphysical disjunctivism, the thesis is primarily about perception. That said, the view might well be extendable to other sources of knowledge—such as memory, testimony, and so on—though we will not be exploring these possibilities here.8 Second, this is a thesis only about epistemically paradigm cases of perceptual knowledge, and not a thesis about perceptual knowledge in general.9 Third, epistemological disjunctivism is explicitly cast in terms of rational support rather than evidence. This last point requires further discussion, given the evidential focus of this piece. Can we straightforwardly translate claims about reasons into claims about evidence? I think many in contemporary epistemology would regard such a replacement as largely harmless. Aren’t one’s reasons one’s evidence? That is, if my reason for believing that my car has been stolen is that the policewoman testified to this effect, then isn’t such testimony also the evidence I have for believing that my car is stolen? Moreover, doesn’t one’s evidence have to be available to one in order for it to count as one’s evidence? If so, then isn’t it as available to one as one’s reasons are? For example, the policewoman’s testimony is only your evidence because you are aware of it; had you not been, then it wouldn’t be your evidence at all. But, insofar as you are aware of it, then it can also function as your reasons for believing the target proposition. For what it is worth, my own view on these matters is that reasons and evidence play such different roles in our epistemic economy that replacements of this kind are usually far from harmless. But it will take us too far afield to explore these issues here.10 Accordingly, I will follow the mainstream and straightforwardly translate the rational support in play in epistemological disjunctivism into evidential terms. We thus get the view that in epistemologically paradigm cases of perceptual knowledge one’s belief in the target proposition is supported by reflectively accessible factive evidence.11 We also get a corresponding account of what is disjunctive about epistemological disjunctivism, so characterized. Either one is in the good case, and hence enjoys reflectively accessible factive evidence (provided by one seeing that p), or one is in the corresponding indistinguishable bad case and only enjoys, at best, reflectively accessible non-factive evidence (e.g., provided by one seeming to see that p). Moreover, there is no significant common core to the evidential standing in the good case and the corresponding evidential standing in the bad case, such that one cannot decompose the factive evidential standing in the good case into the non-factive evidential standing in the bad case supplemented by additional evidence. Rather, the evidential difference in play here is one of kind rather than degree.

Classical and Non-classical Forms of Epistemic Internalism One can best appreciate the radical nature of epistemological disjunctivism by seeing how it constitutes a non-classical form of epistemic internalism. Classical forms of epistemic internalism tend to endorse the following three theses (here expressed, given our current concerns, in terms of evidence rather than reasons or some other epistemic standing):

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Accessibilism S’s internalist epistemic support for believing that φ is constituted solely by facts that S can know by reflection alone.12 Mentalism S’s internalist epistemic support for believing that φ is constituted solely by S’s mental states.13 The New Evil Genius (NEG) S’s internalist epistemic support for believing that φ is constituted solely by properties that S has in common with her recently envatted physical duplicate.14 There are debates amongst epistemic internalists regarding which of these theses holds the ‘whip hand’ when it comes to determining the nature of epistemic internalism, but one can easily see why a commitment to all three theses would tend to go together.15 Plausibly, after all, the reason why one’s mental states play the role in determining the evidential standing of one’s beliefs that mentalism describes is that one has the kind of reflective access to one’s mental states that is at issue in accessibilism. Conversely, one could argue, in line with accessibilism, that we are interested in that which is reflectively accessible when it comes to evidential standing precisely because that relation picks out one’s mental states and they are key to determining evidential standing, in line with accessibilism. Moreover, the path from accessiblism and mentalism to (NEG) is also fairly straightforward. If evidential support is to be understood in terms of one’s reflectively accessible mental states, as accessibilism and mentalism maintain, then it is hard to see how the evidential support one’s beliefs enjoys in the good case can be any better than the evidential support enjoyed by one’s beliefs in the corresponding bad case. After all, the experiences in play in these two scenarios are ex hypothesi indistinguishable to the subject concerned, and so presumably there cannot be evidence that is reflectively accessible to the subject in the good case that is not also reflectively accessible to one’s counterpart in the bad case. Classical forms of epistemic externalism, in contrast, reject all three theses. Take process reliabilism, for example.16 According to this proposal, it is the reliability of one’s beliefforming processes that determine epistemic standing, and hence would be relevant to determining the strength of one’s evidence. Such a proposal would not satisfy any of the three conditions for classical epistemic internalism just set out. It would not satisfy accessibilism, since whether or not a process is reliable is not something that will usually be reflectively accessible to the subject. It would not satisfy mentalism, since the evidential support one’s beliefs enjoys is determined by the reliability of the processes in play and does not have anything essentially to do with one’s mental states. And it would not satisfy NEG, because one’s beliefs in the good case, where the belief-forming processes in play will tend to be highly reliable, will enjoy stronger levels of evidential support than the beliefs of one’s counterpart in the bad case, where few, if any, of the belief-forming processes in play will be reliable. Classical epistemic internalism thus accepts all three of these theses, while classical epistemic externalism rejects all three. Epistemological disjunctivism is a non-classical form of

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epistemic internalism in that it accepts at least one and rejects at least one of these classical epistemic internalist theses. In particular, whereas epistemological disjunctivism explicitly endorses accessibilism, and is compatible with mentalism, it rejects NEG. Before explaining why this is the case, there is an important caveat we need to add here. Recall that epistemological disjunctivism is only a thesis about perceptual knowledge in epistemically paradigm conditions. As such, when one says that the view endorses, for example, accessibilism, this is to be understood only in terms of what the view is committed to with regard to epistemically paradigm cases of perceptual knowledge. In particular, there is nothing to prevent a proponent of epistemological disjunctivism from being an epistemic externalist about knowledge in general (and thus also about evidence, specifically).17 With this caveat in play, we can easily see why epistemological disjunctivism is committed to accessibilism, since it holds that one’s factive evidential support in the good case should be reflectively accessible. Moreover, we can also see the consistency with mentalism, so long as we allow that seeing that p is a mental state. Note, however, that this move is much more controversial, since proponents of mentalism usually assume a conception of mental states that involves only narrow content, and hence which would exclude factive mental states like seeing that p.18 Still, we can at least say this much: that epistemological disjunctivism is compatible with mentalism to the extent that we do not add this further restriction regarding types of mental state that qualify. What epistemological disjunctivism is committed to denying is precisely NEG. This is because, as seen earlier, it is a fundamental commitment of the proposal that one’s evidential support in the good case is factive, and hence clearly superior to the evidential support available to one’s counterpart in the bad case, which is at most non-factive.19 Epistemological disjunctivism thus constitutes a non-classical form of epistemic internalism, in that while it endorses at least one core epistemic internalist thesis, it also rejects at least one core epistemic internalist thesis.20

The Viability of Epistemological Disjunctivism One of the big questions facing epistemological disjunctivism is whether it is a viable position. Indeed, until relatively recently it was a view that was not explicitly considered by mainstream epistemologists since it was held to be completely untenable. Part of the reason for this is the supposed inherent plausibility of NEG, a claim that even epistemic externalists will usually grant is constitutive of epistemic internalism.21 In particular, epistemological disjunctivism seems to be trying to do something that is simply impossible, which is to fuse core elements of epistemic internalism and epistemic externalism. On the one hand, epistemological disjunctivism is meant to capture epistemic internalist insights by demanding that one’s evidential support is reflectively accessible. But, on the other hand, the view also tries to capture epistemic externalist insights by arguing that such reflectively accessible evidential support can nonetheless have worldly import, in virtue of being factive. According to traditional ways of understanding the epistemic externalism/internalism distinction, such an intermediate position is not credible—either the evidential support is reflectively accessible, in which case it can’t have worldly import (much less be factive), or the evidential support is factive, in which case it can’t be reflectively accessible. The way that proponents of epistemological disjunctivism have gone about demonstrating the viability of this proposal is via a three-stage process. First, to show that our everyday epistemic practices are shot-through with appeals to factive evidence. Second, to 44

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demonstrate that epistemological disjunctivism is a view that we would want to endorse were it available.22 Finally, third, to argue to the effect that the reasons offered for rejecting epistemological disjunctivism are unsound, where this can be shown without appealing to anything independently controversial (much less anything that would already commit one to epistemological disjunctivism). Note that this is an essentially negative way of defending the view. That is, it is shown that the arguments against epistemological disjunctivism are dubious and hence, since it is part of our everyday epistemic practices and an otherwise attractive position to hold, that we should endorse it.23 Let’s take these three stages in turn. That our everyday epistemic practices naturally involve appeal to factive evidence ought to be relatively unproblematic. Suppose I am on the phone to my boss, who expresses scepticism that a colleague is in work today (perhaps because she tends to skip work whenever the boss is away). I might well naturally respond to such scepticism by saying that I know that she’s in work because I can see that she’s here— she’s right in front of me. Indeed, in the circumstances it would be very odd if I backed up my claim to know by appealing to something that fell short of this factive evidence, such as by saying that it merely seems to me as if she in front of me right now. The more qualified latter claim would only be appropriate in very special kinds of conditions—such as when one has been offered grounds for thinking that what one sees is not to be relied upon (e.g., an hallucinogenic has been slipped into one’s coffee)—and would make no sense at all in conditions which one takes to be epistemically paradigm. Of course, even the opponent of epistemological disjunctivism can accept this point about our everyday epistemic practices. But they will contend that we shouldn’t take such practices at face value. Second, the claim that epistemological disjunctivism is an attractive position, if true. Again, I take this to be relatively uncontroversial, in that even opponents of epistemological disjunctivism will likely grant this claim (in that they will focus instead on whether the position is true, rather than whether it is attractive). Part of the attraction of the view resides in the fact already noted that it offers a way of accommodating both epistemic externalist and internalist insights. Classical epistemic internalism seems to cut off evidential standing from worldly import, in that, in line with NEG, the best kind of evidential standing that our beliefs can enjoy is nonetheless entirely compatible with massive error in our beliefs (i.e., of a kind that would hold in a radical sceptical bad case, such as a BIV scenario). In contrast, classical epistemic externalism ensures that the evidential standing of our beliefs can have genuine worldly import, but does so by making such evidence opaque to us, in that it is no longer by its nature reflectively accessible. Epistemological disjunctivism steers a midway course between both views by ensuring that our reflectively accessible evidence can have worldly import (indeed, worldly import of the strongest kind, in virtue of being factive). Moreover, if we can make sense of such a position, then it has the potential to offer new ways of approaching age-old epistemological problems. Consider, for example, the problem of radical scepticism, which has bedevilled philosophy for millennia (or at least centuries, if we confine our attention to the specifically Cartesian variety of this problem). Radical sceptical arguments essentially trade on the fact that the evidential support our beliefs enjoy, even in the very best cases, can be no better than that enjoyed by the beliefs held by our counterparts who are subject to radical sceptical scenarios, such as the BIV scenario. With this claim in place, it becomes relatively easy for proponents of radical scepticism to leverage their radical sceptical conclusions. And yet epistemological disjunctivism, if true, offers a way of cutting off this sceptical line of argument at the source, via its rejection of NEG.24 45

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The case for epistemological disjunctivism thus ultimately turns on whether it can block the arguments against its viability. It would take us too far afield to consider all of the objections one can put to epistemological disjunctivism, so let me instead focus on what I take to be the most serious objection.25 All parties to this debate, including epistemological disjunctivists, will grant that good and bad cases are, ex hypothesi, indistinguishable to the subject concerned. And yet, if epistemological disjunctivism is true, then there is something reflectively accessible to the subject in the good case—viz., the factive reason—that is unavailable to the subject in the bad case. Given that this is so, why can’t the subject in the good case reflectively access the factive reason and on this basis come to know that she is in the good case rather than the bad case? The problem is that, if this is so, then it seems that the subject in the good case can come to know that she is in the good case rather than the bad case, and hence can in a sense distinguish between good and bad cases, something which, ex hypothesi, she is meant to be unable to do. Call this the distinguishability problem for epistemological disjunctivism. The way epistemological disjunctivists respond to this problem is by arguing that there can be ways of knowing the difference which aren’t thereby ways of telling the difference, where the latter involves a specific discriminative capacity. Moreover, they contend that this is a distinction that all epistemologists should accept, and hence that it is dialectically available to the epistemological disjunctivist (i.e., it is not a thesis that in any way already presupposes a commitment to epistemological disjunctivism). Set aside epistemological disjunctivism for a moment and consider a case where a subject comes to know, via perception, that there is a zebra in the enclosure before her at the zoo. In normal circumstances, the kind of perceptual abilities needed to identify a zebra as such are fairly limited. In particular, one would not need to possess the rather special perceptual ability to discriminate between zebras and cleverly disguised mules. Now imagine that someone raises the possibility that the creature might be a cleverly disguised mule. Note that they are not offering evidence in support of this alternative scenario, but merely raising it as an alternative scenario. Given that one cannot discriminate between zebras and cleverly disguised mules, does one still know that the creature before one is a zebra? Well, if this is still known, it is not in virtue of one’s perceptual abilities alone, since they are, by stipulation, entirely silent about this possibility. But notice that this is not the only epistemic support that one has available in this case. In particular, at least as far as most mature subjects go, there will be a wealth of background evidence that one can bring to bear which collectively excludes this error-possibility, such as what one knows about wellrun zoos, the plausibility of such a deception, the likelihood that such a deception would be spotted before long, the costs involved in undertaking such a deception, and so on.26 With this background evidence suitably marshalled, one is in an evidential position to enable one to know that the creature before one is a zebra rather than a cleverly disguised mule even though one cannot perceptually discriminate between zebras and cleverly disguised mules.27 The point is that with this distinction in play, the epistemological disjunctivist can appeal to this distinction to explain why one might be able to know that one is in the good case rather than the bad case. Just as in the scenario we have described, the error-possibility at issue is not evidentially motivated, but merely raised as a possibility. Moreover, with epistemological disjunctivism in play the subject has available to her a distinctive form of evidential support that is factive. Putting these two points together, the subject in the good case has a reflective route available to her where she can rationally conclude that she is in the good case rather than the bad case. But this is entirely compatible with the undeniable 46

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fact that one lacks a discriminative faculty that enables one to distinguish between good and bad cases.

Concluding Remarks Of course, merely showing how epistemological disjunctivism might deal with a core objection that it faces is not the same as offering a full defence of the view. But at least it demonstrates that epistemological disjunctivism has resources available to meet objections (and recall also that the objection just considered is claimed to be the most difficult one facing the view). We have, then, at least a prima facie case for the viability of the position. Given the points made earlier about the way in which such a position seems rooted in our everyday epistemic practices, and the attraction of such a position if it were true, this makes the view very worthy of our further consideration, particularly given that it occupies such a distinctive and unorthodox position in the normal taxonomy of epistemological proposals.28

Notes 1 Note that for convenience I have immediately opted for an illustrative instance of the bad case that involves a radical sceptical scenario. Bad cases needn’t be so radical, however—a localised hallucination, for example, where one’s perception is disturbed only in some specific respect, could also count as a bad case. 2 For some of the key defences of metaphysical disjunctivism, see Hinton (1967a, 1967b, 1973), Snowdon (1980–1, 1990–1), and Martin (2002, 2004, 2006). For an excellent survey of the range of metaphysical disjunctivist positions on offer in the literature, see Soteriou (2014). See also Pritchard and Ranalli (2017) for a survey of disjunctivist views as they bear on the problem of radical scepticism. 3 See especially Prichard (2012). See also Neta and Pritchard (2007), Pritchard (2007, 2008, 2011a, 2011b, 2015a, 2018a, 2018b). For two recent symposia on Pritchard (2012), see: Littlejohn (2015), Pritchard (2015b, 2015c), Schönbaumsfeld (2015), Zalabardo (2015), Goldberg (2016), Littlejohn (2016), Neta (2016), and Pritchard (2016a, 2016b). See also Williamson’s (2000a, 2000b) knowledge-first account, which has some parallels with epistemological disjunctivism, but which is also sufficiently dissimilar that it is best to keep apart from the view (e.g., in that it is explicitly cast as a form of epistemic externalism rather than epistemic internalism). I briefly discuss this proposal at several junctures later—see endnotes 11, 19, and 20. See also Pritchard (2011b). 4 Note that we are here setting aside the possibility that there might be independent rational support that could be brought to bear which enables one to rationally conclude that one is in the good case rather than the bad case, such as abductive reasons. See Vogel (1990) for a sophisticated defence of such a proposal. See Pritchard (2015a, part 1) for a general critique of this sort of proposal, particularly as it might function in the context of a radical sceptical bad case. 5 Indeed, on standard views of seeing that p—see Dretske (1969), Williamson (2000a, ch. 1), and Cassam (2007), for instance—seeing that p actual entails knowing that p. But even on proposals that reject this entailment thesis—e.g., Pritchard (2011a, 2012, part 1)—it is still maintained that seeing that p is a robustly epistemic notion in that it necessarily puts one in an objectively good position to know that p. For further critical discussion of the putative entailment between seeing that p and knowing that p, see Turri (2010). 6 It’s actually far from clear what the epistemological disjunctivist should say about the subject’s rational standing in the bad case. See Pritchard (forthcoming) for discussion of this point. 7 The point about there being no significant common core of rational support which applies to both cases is to accommodate the point noted earlier with regard to metaphysical disjunctivism, which is that there is undeniably a negative epistemological property that is common to both cases—i.e., that the cases are indistinguishable to the subject.

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Duncan Pritchard 8 McDowell (1994, 1995) certainly seems amenable to this approach, even going so far as to suggest that it might work for inductive knowledge (which is arguably the least plausible domain to introduce epistemological disjunctivism). 9 See Pritchard (2011a, 2012, part 1) for an account of what makes a scenario epistemically paradigm. 10 Part of the issue here is that I think we in any case need a more nuanced conception of rational support, something which a straightforward translation between reasons and evidence will obscure. See Pritchard (forthcoming) for more on this point. 11 Interestingly, Williamson’s (2000a, 2000b) knowledge-first account—which as noted earlier (see endnote 3) has some similarities to epistemological disjunctivism—is directly expressed in terms of evidence rather than reasons. 12 For two key defences of accessibilism, see Chisholm (1977) and BonJour (1985, ch. 2). 13 The locus classicus when it comes to defences of mentalism is Conee and Feldman (2004). 14 For two key defences of the new evil genius intuition, see Lehrer and Cohen (1983) and Cohen (1984). See also the excellent survey article of work on this topic by Littlejohn (2009). 15 Much of the debate is concerned with the relative merits of accessibilism or mentalism as the overarching account of epistemic internalism. See, for example, Conee and Feldman (2004). 16 Such a position is, of course, most closely associated with Goldman’s (1976, 1979, 1986, 1988) work. 17 Indeed, that is in fact my own position. See Pritchard (2019, 2023). 18 See, for example, Conee and Feldman (2004). 19 This is yet another juncture on which epistemological disjunctivism diverges from Williamson’s (2000a, 2000b) knowledge-first account—which as noted earlier (see endnote 3) bears some noteworthy similarities—in that the latter always treats evidence as factive (since it has probability 1), whereas epistemological disjunctivism is not committed to this claim. 20 Interestingly, Williamson’s (2000a, 2000b) knowledge-first approach, which as noted earlier (see endnote 3) bears some similarities to epistemological disjunctivism, is in fact a non-classical form epistemic externalism. This is because, unlike process reliabilism, it is at least consistent with one core epistemic internalist thesis, that of mentalism (at least on a liberal construal of this thesis). See Pritchard (2011b) for discussion of this point. 21 That is, standard forms of epistemic externalism often treat the intuitions behind NEG as something that needs to be accommodated by their own proposals. Consider, for example, how Goldman (1986, 1988) modifies his process reliabilism in order to account for why there might be a sense in which a subject’s epistemic position is no better than that enjoyed by her envatted counterpart. 22 As I rather provocatively put the point in Pritchard (2012, 1), epistemological disjunctivism is the ‘holy grail’ of epistemology. 23 See Pritchard (2012) for just such a negative defence of epistemological disjunctivism along this three-stage line. See also McDowell (1995) for a similarly negative defence of the view, though as I explain in Pritchard (2012, part 3), McDowell’s defence is allied to a broader philosophical quietism. 24 For more details regarding how epistemological disjunctivism might be marshalled against radical scepticism, see Pritchard (2007, 2008, 2012). Note, however, that in more recent work I have argued that epistemological disjunctivism fares much better as an anti-sceptical strategy when it is paired with the kind of hinge epistemology outlined by Wittgenstein (1969). See, e.g., Pritchard (2015a, 2018a, 2018b). 25 For a fuller list of objections against epistemological disjunctivism, and the development of counterarguments, see Pritchard (2012, passim). 26 If such background evidence is lacking, then I think we should allow that the mere raising of this error-possibility could defeat knowledge. After all, if one really has no evidential basis for preferring the zebra scenario over the competing cleverly disguised mule scenario, then it is hard to see how one can have a sufficient evidential basis for knowing the former. 27 See Pritchard (2010) for a more detailed defence of this claim and why it undermines various kinds of epistemological revisionism, such as certain arguments against the closure principle, epistemic contrastivism, epistemic contextualism, and so on. 28 Thanks to Giada Fratantonio, John Greco, Ram Neta, and Michael Williams for some useful discussions about epistemological disjunctivism and evidence/reasons.

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References BonJour, L. (1985). The Structure of Empirical Knowledge, Cambridge, MA: Harvard University Press. Cassam, Q. (2007). ‘Ways of Knowing’, Proceedings of the Aristotelian Society 107, 339–58. Chisholm, R. M. (1977). Theory of Knowledge (2nd edn.), Englewood Cliffs, NJ: Prentice-Hall. Cohen, S. (1984). ‘Justification and Truth’, Philosophical Studies 46, 279–95. Conee, E., & Feldman, R. (2004). Evidentialism: Essays in Epistemology, Oxford: Oxford University Press. Dretske, F. (1969). Seeing and Knowing, London: Routledge & Kegan Paul. Goldberg, S. (2016). ‘Comments on Pritchard’s Epistemological Disjunctivism’, Journal of Philosophical Research 41, 183–91. Goldman, A. (1976). ‘Discrimination and Perceptual Knowledge’, Journal of Philosophy 73, 771–91. ———. (1979). ‘What Is Justified Belief?’, Justification and Knowledge, (ed.) G. Pappas, 1–23, Dordrecht: Reidel. ———. (1986). Epistemology and Cognition, Cambridge, MA: Harvard University Press. ———. (1988). ‘Strong and Weak Justification’, Philosophical Perspectives 2: Epistemology, (ed.) J. Tomberlin, 51–69, Atascadero, CA: Ridgeview. Hinton, J. M. (1967a). ‘Experiences’, Philosophical Quarterly 17, 1–13. ———. (1967b). ‘Visual Experiences’, Mind 76, 217–27. ———. (1973). Experiences: An Inquiry into Some Ambiguities, Oxford: Clarendon Press. Lehrer, K., & Cohen, S. (1983). ‘Justification, Truth, and Coherence’, Synthese 55, 191–207. Littlejohn, C. (2009). ‘The New Evil Demon Problem’, Internet Encyclopaedia of Philosophy, (eds.) B. Dowden & J. Fieser, www.iep.utm.edu/evil-new/. ———. (2015). ‘Knowledge and Awareness’, Analysis 75, 596–603. ———. (2016). ‘Pritchard’s Reasons’, Journal of Philosophical Research 41, 201–19. Martin, M. G. F. (2002). ‘The Transparency of Experience’, Mind and Language 17, 376–425. ———. (2004). ‘The Limits of Self-Awareness’, Philosophical Studies 120, 37–89. ———. (2006). ‘On Being Alienated’, Perceptual Experience, (ed.) T. S. Gendler & J. Hawthorne, 354–410, Oxford: Oxford University Press. McDowell, J. (1994). ‘Knowledge by Hearsay’, Knowing from Words: Western and Indian Philosophical Analysis of Understanding and Testimony, (eds.) B. K. Matilal & A. Chakrabarti, 195–224, Dordrecht: Kluwer. ———. (1995). ‘Knowledge and the Internal’, Philosophy and Phenomenological Research 55, 877–93. Neta, R. (2016). ‘How Holy Is the Disjunctivist Grail?’, Journal of Philosophical Research 41, 193–200. Neta, R., & Pritchard, D. H. (2007). ‘McDowell and the New Evil Genius’, Philosophy and Phenomenological Research 74, 381–96. Pritchard, D. H. (2007). ‘How to Be a Neo-Moorean’, Internalism and Externalism in Semantics and Epistemology, (ed.) S. Goldberg, 68–99, Oxford: Oxford University Press. ———. (2008). ‘McDowellian Neo-Mooreanism’, Disjunctivism: Perception, Action, Knowledge, (eds.) A. Haddock & F. Macpherson, 283–310, Oxford: Oxford University Press. ———. (2010). ‘Relevant Alternatives, Perceptual Knowledge, and Discrimination’, Noûs 44, 245–68. ———. (2011a). ‘Epistemological Disjunctivism and the Basis Problem’, Philosophical Issues 21, 434–55. ———. (2011b). ‘Evidentialism, Internalism, Disjunctivism’, Evidentialism and Its Discontents, (ed.) T. Dougherty, 362–92, Oxford: Oxford University Press. ———. (2012). Epistemological Disjunctivism, Oxford: Oxford University Press. ———. (2015a). Epistemic Angst: Radical Skepticism and the Groundlessness of Our Believing, Princeton, NJ: Princeton University Press. ———. (2015b). ‘Précis of Epistemological Disjunctivism’, Analysis 75, 589–95. ———. (2015c). ‘Responses to My Critics’, Analysis 75, 627–37. ———. (2016a). ‘Précis of Epistemological Disjunctivism’, Journal of Philosophical Research 41, 175–81. ———. (2016b). ‘Responses to My Critics’, Journal of Philosophical Research 41, 221–38.

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Duncan Pritchard ———. (2018a). ‘Epistemic Angst’, Philosophy and Phenomenological Research 96, 70–90. ———. (2018b). ‘Epistemological Disjunctivism and the Biscopic Treatment of Radical Scepticism’, The Factive Turn in Epistemology, (ed.) V. Mitova, 15–31, Cambridge: Cambridge University Press. ———. (2019). ‘Epistemological Disjunctivism and Anti-Luck Virtue Epistemology’, New Issues in Epistemological Disjunctivism, (eds.) C. Doyle, J. Milburn & D. H. Pritchard, 41–58, London: Routledge. ———. (2023). ‘Moderate Knowledge Externalism’, Externalism About Knowledge, (ed.) L. R. G. Oliveira, 131–49, Oxford: Oxford University Press. ———. (Forthcoming). ‘Shadowlands’, The New Evil Demon: New Essays on Knowledge, Justification and Rationality, (eds.) F. Dorsch & J. Dutant, Oxford: Oxford University Press. Pritchard, D. H., & Ranalli, C. (2017). ‘Scepticism and Disjunctivism’, Skepticism: From Antiquity to the Present, (eds.) D. Machuca & B. Reed, 652–67, London: Bloomsbury. Schönbaumsfeld, G. (2015). ‘Epistemological Disjunctivism, by Duncan Pritchard’, Analysis 75, 604–15. Snowdon, P. (1980–1). ‘Perception, Vision and Causation’, Proceedings of the Aristotelian Society (new series) 81, 175–92. ———. (1990–1). ‘The Objects of Perceptual Experience’, Proceedings of the Aristotelian Society (suppl. vol.) 64, 121–50. Soteriou, M. (2014). ‘The Disjunctive Theory of Perception’, Stanford Encyclopaedia of Philosophy, (ed.) E. Zalta, http://plato.stanford.edu/entries/perception-disjunctive/. Turri, J. (2010). ‘Does Perceiving Entail Knowing?’, Theoria 76, 197–206. Vogel, J. (1990). ‘Cartesian Skepticism and Inference to the Best Explanation’, Journal of Philosophy 87, 658–66. Williamson, T. (2000a). Knowledge and Its Limits, Oxford: Oxford University Press. ———. (2000b). ‘Scepticism and Evidence’, Philosophy and Phenomenological Research 60, 613–28. Wittgenstein, L. (1969). On Certainty, (eds.) G. E. M. Anscombe & G. H. von Wright, (tr.) D. Paul & G. E. M. Anscombe, Oxford: Blackwell. Zalabardo, J. (2015). ‘Epistemic Disjunctivism and the Evidential Problem’, Analysis 75, 615–27.

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4 EVIDENTIAL INTERNALISM AND EVIDENTIAL EXTERNALISM Giada Fratantonio

1 Introduction1 Evidential Internalism (henceforth Internalism) is the thesis that one’s evidence supervenes on one’s non-factive mental states (roughly put, those mental states that do not necessarily entail anything about the external environment). Evidential Externalism (henceforth Externalism) denies Internalism and allows for external factors to determine what evidence one has.2 Traditionally, epistemologists have been Internalists. For instance, empiricists of the twentieth century like Ayer and Russell embraced an account of evidence that we can call the “phenomenological conception of evidence”.3 On this view, evidence is reducible to sense data the subject can be immediately conscious of (Cf. Russel, 1912; Ayer, 1936). However, the view is also widely held amongst contemporary epistemologists (Cf. BonJour, 1999; Wedgwood, 2002).4 Audi, for instance, writes: “evidence is . . . ultimately internal. It centrally involves my sensory states, memory impressions, inferences, and the like” (2001, p. 47). Recently, however, there has been a new trend in the literature, and Externalism has gained more popularity amongst epistemologists (see McDowell, 1995; Williamson, 2000; Littlejohn, 2012; Mitova, 2014; Schellenberg, 2016). To see how Internalism differs from Externalism in some important respect, consider Gary and Barry. Gary and Barry are “internal twins”, namely, they share all non-factive mental states: they both have an experience as of two bananas in a bowl, and they both believe that there are two bananas in a bowl. However, Gary and Barry differ in some very important way: Although Gary is now and then mistaken about some matter of fact, Barry is a radically deceived brain in a vat, as deceived as can be given that he has the same nonfactive mental states as Gary. Gary is in the good case; Barry is in the bad case. (Silins, 2005, p. 375) We can ask: do Gary and Barry have the same evidence? The Internalist will answer yes, while the Externalist will answer no. For while Internalists claim that whatever evidence

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one has is fixed by one’s non-factive mental states, according to the Externalists, instead, features of the external environment may be relevant in determining what evidence one has. In this chapter, I overview some of the main arguments and motivations behind Evidential Internalism and Evidential Externalism (Sections 2 and 3, respectively). I conclude by making some general observations on the advantage Externalism enjoys (Section 4). However, first, I want to make some clarificatory remarks on the nature of this distinction and how it remains relatively silent on important epistemological issues. To begin with, note that Internalism and Externalism are rather silent on what evidence is. Both views are compatible with psychologism, the thesis that evidence consists of mental states, as well as with propositionalism, the view that evidence consists of propositions.5 Furthermore, although it might be tempting to identify Externalist propositionalism with the thesis that evidence is factive, namely, the thesis that evidence is constituted by only true propositions, this would be a mistake.6 Consider the thesis that one’s evidence is all and only true propositions about how things appear to one. This is not an Externalist view because it entails that Gary and Barry have the same evidence. For, given that they share all non-factive mental states, things will appear exactly the same to both Gary and Barry. So, for instance, the proposition that there seems to be two bananas in the bowl (and all true propositions about how things seem) will be part of both Gary’s and Barry’s evidence. On this view, how things actually are in one’s external environment won’t matter for determining what evidence one has. Committing to factivity of evidence is thus not sufficient for being an Externalist. But subscribing to the idea that evidence is factive is not even necessary for being an Externalist. One can defend a theory on which one’s evidence is constituted by all and only the propositions one is justified in believing, while saying that justification depends on the reliability of one’s belief-forming process.7 On this view, Gary might have some false propositions amongst his evidence, but his total evidence would still be different from Barry’s. Only Gary, in a paradigmatic good case, is justified in believing that there are two bananas in the bowl, and hence, Gary’s evidence will include at least one item of evidence that Barry lacks: the proposition that there are two bananas in the bowl (Fratantonio & McGlynn, 2018, p. 84). Furthermore, to be an Externalist, one doesn’t even need to commit to the thesis that evidence entails the proposition it is evidence for. Consider Williamson’s thesis on which one’s evidence is all and only the propositions one knows (henceforth E=K) (Williamson, 2000, Ch. 9). Although it is a consequence of E=K that any proposition one knows is trivially entailed by one’s total evidence, it is compatible with E=K that one has evidence e for a proposition p (e.g., because e increases the probability of p) without one’s total evidence entailing p. Nevertheless, E=K is a paradigmatic Externalist theory: it predicts that Gary and Barry have different evidence despite sharing the same non-factive mental states. For only Gary, who’s in the paradigmatic good case, knows that there are two bananas in the bowl. The Evidential Internalism–Externalist distinction is also orthogonal to the debate concerning the nature of knowledge and epistemic justification. Both views are in principle compatible with Evidentialism about epistemic justification, i.e., the thesis that justification supervenes on evidence,8 as well as non-evidentialist views, such as the reliabilist view discussed earlier.9 In fact, both views are silent on whether there is any evidentialist requirement on knowledge at all. Nevertheless, as Silins has pointed out, the fact that Evidential Externalism doesn’t entail more traditional versions of externalism about epistemic justification, such as Reliabilism, can be seen as a benefit of the view (Silins, 2005). For it avoids some of the problems Reliabilists notoriously face, such as the generality problem. Roughly 52

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put, the problem of defining which type of process is the relevant type of reliable process that matters for assessing the justificatory status of a belief. For the rest of this chapter, I will thus assume Evidentialism about epistemic justification.

2  Evidential Internalism Now that we have a better idea of what Evidential Internalism and Externalism are, what they entail, and what they are silent on, we can ask: why should we favour one account over the other? In this section, I overview the main motivations and arguments for Internalism (and against Externalism). I will consider some reasons to favour Externalism in Section 3.

2.1  Rationality Internalism An important reason why epistemologists have traditionally been attracted to Evidential Internalism is that it seems to be entailed by a very intuitive picture of rationality. On this picture, rationality requires one to believe in accordance to the evidence one has. Crucially, this seems possible only if evidence is “unproblematically given to the subject” (Kelly, 2008, p. 943). But if one can believe in the light of one’s evidence only if evidence is the kind of thing one can have unproblematic access to, then one’s evidence cannot depend on circumstances “beyond our ken” (Cohen, 1984, p. 282): Evidential Internalism must be true. One way to respond for the Externalist would be to bite the bullet here and say that, contrary to appearances, we often don’t know what our evidence is and what rationality requires (Williamson, 2000, pp. 179–181). Alternatively, she could revise the relation between evidence and rationality in a way that explains how being rational is compatible with failing to know what evidence one has (e.g., because of some non-culpable mistake). For example, the externalist might say that one can be fully rational in believing that p iff one shouldn’t have expected to have any undefeated evidence against believing that p (Littlejohn, 2011, p. 496). On this view, rationality has to do with doing the best one can, which requires believing accordingly to what one takes one’s evidence to be. A discussion of what rationality requires would lead us too far afield. However, for the purpose of this chapter, it’s enough to conclude this brief section by saying that a leading line of reasoning behind Evidential Internalism, one that underpins the main arguments for Internalism that I will address in the next sections, runs schematically as follows: rationality requires believing in accordance to one’s evidence; one can believe in accordance to one’s evidence only if one can have unproblematic access to it. Crucially, if Evidential Externalism is true, then one cannot have unproblematic access to one’s evidence. Therefore, Evidential Internalism must be true.

2.2  The New Evil Demon Problem A core argument for Internalism is the New Evil Demon (NED) problem.10 Consider again Gary (in the good case) and his internal twin Barry (in the bad case). As seen in the previous section, Internalism predicts that Gary and Barry have the same evidence. That is, Internalism entails the following thesis: SAMENESS of EVIDENCE: if A and B are internal twins, then they have the same evidence. 53

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However, if Externalism is true, then Gary and Barry have different evidence. Further, assume an evidentialist theory of justification on which the justification one has is a function of one’s evidence. Then, it seems to follow that Garry and Barry aren’t equally justified in believing that there is a banana in the bowl. Crucially, this clashes with the intuition that Gary and Barry are equally justified in believing as they do. Call this the Equal Justification Thesis. If we take Equal Justification at face value, then the Internalist is right: evidence supervenes on one’s non-factive mental states. For if Gary and Barry have the same evidence, then their evidence has to be fixed by something they share, and it seems that the only things Gary and Barry share are their non-factive mental states. The classic externalist response here is to appeal to the “excuse manoeuvre”. On this line of response, the Externalist will be happy to say that Barry is blameless in believing as he does and to grant him an excuse, while insisting that Barry and Gary have nevertheless different evidence and justification (Cf. Littlejohn, forthcoming; Williamson, forthcoming; Pritchard, 2012, pp. 42–43). By doing so, the Externalist can explain why we tend to sympathise with Barry despite being systematically deceived, and she can do so without having to embrace Evidential Internalism. Two main worries have been raised for the excuse manoeuvre. First, as Gerken (2011) has argued, in order to avoid the charge of ad hocery, those who appeal to the excuse manoeuvre must provide an account of when exactly one deserves the status of blamelessly or excusably believing something.11 One way to explain this is, following Williamson, to appeal to some form of normative pluralism. Williamson has argued that justification is a matter of believing in accordance with the primary knowledge norm of belief, on which you should believe that p only if you know that p. On the other hand, according to his view, someone like Barry might nevertheless be complying with some derivative secondary norm, and that’s enough for deserving an excuse (Williamson, forthcoming). But even if the externalist can explain when exactly one deserves an excuse, one might worry that granting Barry an excuse for (wrongly) believing as he does, doesn’t seem to be enough. For Barry seems more than merely excusable. Intuitively, he’s doing epistemically well (Cf. Simion et al., 2016). However, it still seems possible to vindicate this intuition within an Externalist framework. For instance, according to Lasonen-Aarnio, Barry is more than merely excusable: in believing that there are two bananas in the bowl he is manifesting a good epistemic disposition, one that, in relevant counterfactual cases would be conducive to epistemic successes, e.g., true belief, belief that is proportionated to the evidence, and knowledge (Lasonen -Aarn io, 2021).12,13 A lot has been written on the NED problem.14 For our purposes, the following remark about the dialectic is enough. I believe the Internalist is right in saying that there is a sense in which Barry is doing well epistemically. However, while the Internalist takes equal justification as a datum that a theory of evidence should accommodate, I suspect the Externalist will have a few qualms about accepting the claim that Barry is doing just as epistemically well as Gary. For if in the overall epistemic evaluation of Barry and Gary we consider how much evidence and justification they have, then, the Externalist will insist, Gary is overall epistemically better off than Barry.

2.3  The Distinguishability Problem The next argument for Sameness of Evidence I consider is what I call, borrowing Pritchard’s terminology (2012, pp. 91–100), the Distinguishability problem. Similarly to the NED, the 54

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Distinguishability problem considers a subject in a paradigmatic good case and her radically deceived internal twin, such as Gary and Barry.15 However, contrary to the NED, the Distinguishability problem does not question whether and how the Externalist can explain the intuition that Barry is just as equally justified as Gary. Instead, it puts pressure on the following fact: Externalism entails that one’s evidence differs depending on whether one is in the good or in the bad case. But then, assuming that one can know what evidence one has and what evidence one would have were one in the good or bad case, one can figure out whether one is in the good or in the bad case. Although the Externalist might be happy to say that in the good case one can know that one is in the good case (and not in the bad case),16 she probably wouldn’t welcome the conclusion that one can figure out in the bad case that one is in the bad case (and not in the good case). After all, “part of the badness of the bad case is that one cannot know how bad one’s case is” (Williamson, 2000, p. 171). This argument allegedly represents a reductio ad absurdum of Externalism: Gary in the good case and Barry in the bad case must have the same evidence. The most traditional Externalist response to this argument is to reject its main assumption. In his Knowledge and Its Limits, Williamson has notoriously argued that having a proposition p as part of one’s evidence is not a luminous condition. That is, whatever evidence one has, one isn’t always in the position to know what evidence one has (Williamson, 2000, p. 951).17 Whether there are good reasons to embrace something in the neighbourhood of a luminosity claim is something I will go back to in Section 2.4. For now, however, it’s enough to notice that, as things stand, the Distinguishability problem seems to rest on a false premise.

2.4  The Armchair Access Problem The last argument against Externalism I  consider is Silins’s Armchair Access problem (Silins, 2005, pp. 379–384). Contrary to the previous arguments, this Access problem isn’t centred on the Sameness of Evidence thesis. Instead, it aims to show that Externalism is in tension with the following plausible thesis about what we can know “from the armchair”: “Armchair Access: it is sometimes the case that: one’s evidence includes a proposition e and one knows from the armchair alone that one’s evidence includes e” (Silins, 2005, p. 381). To understand this problem, the following two points are worth making. First, on the most charitable interpretation of Silins’s words, armchair knowledge of a proposition is compatible with having had enabling experiences, namely, experiences necessary to understand the concepts involved in the target proposition in the first place (2005, pp. 380–381). Second, note that Armchair Access is meant to be a weak claim, one that is compatible with Williamson’s anti-luminosity argument and something Externalists should thus be willing to embrace. Crucially, Silins argues, when we combine Externalism with Armchair Access, we reach the absurd conclusion that one can know from the armchair contingent propositions about the external environment. Consider again E=K. Take e to be any contingent proposition about the external environment. Assuming E=K and the factivity of knowledge, if e is part of my evidence, then e is true. But if I  can have armchair knowledge that my evidence includes e (Armchair Access), then, assuming further that I can know that E=K is true from the armchair, it follows that I can know from the armchair alone that e is true. But this seems absurd: contingent propositions about the environment are the kinds of things we cannot know from the armchair alone!18 55

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One option for the Externalist would be to reject Armchair Access altogether. After all, the Externalist might say, what motivates Armchair Access is a highly internalistic conception of rationality, and yet, as we have seen in Section 2.1, this is not uncontroversial (Cf. (Littlejohn, 2011, p. 490). However, I’m not sure this move will help the externalist to resist the Access problem. For all the Access problem needs to get going is only that we are sometimes in a position to know from the armchair what our evidence is. This seems plausible regardless of what we think rationality requires. How can the externalist accept that it is indeed sometimes possible to know our evidence from the armchair while resisting the seemingly absurd conclusion that we can know things from the armchair about the external environment? I believe there are two compatible and mutually supportive strategies the externalist can embrace (Fratantonio, 2018). On the one hand, the externalist can put pressure on the scope of Armchair Access by arguing that Armchair Access is indeed plausible only when restricted to non-environmentally sensitive propositions (e.g., logical and mathematical truths). The Externalist will thus reject a crucial premise of Silins’s argument: we cannot have armchair knowledge that our evidence includes e (where e is a contingent proposition about the external environment). Although Silins, who anticipates this move, takes this restriction to be ad hoc, it’s not clear to me why so. The reason why Armchair Access looks so plausible is that it merely states that we sometimes have armchair knowledge of what our evidence is. Given the notion of armchair knowledge Silins has in mind, it is unclear why it would be ad hoc to say that we can have armchair knowledge of some (but not all) of our (propositional) evidence (Fratantonio & McGlynn, 2018, pp. 86–87); Fratantonio, 2018, pp. 532–534). On the other hand, the Externalist can put pressure on the nature of armchair knowledge underpinning Armchair Access. For the conclusion that we can have armchair knowledge of propositions about the external environment sounds absurd only insofar we are assuming that “armchair knowledge” is knowledge based on merely enabling experience. However, there are good reasons to think that experience is not merely playing an enabling role in these cases of “armchair knowledge” of our evidence e, in which e is a contingent proposition about the environment. More precisely, as I have argued in Fratantonio (2018), these cases of armchair knowledge often seem to require one to conduct an inquiry on one’s epistemic status, where this inquiry involves the employment of imaginative capacities that highly resemble the ones we apply when evaluating counterfactuals and when assessing error-possibilities. Crucially, if Williamson is right in saying that our imaginative capacities rest on experience that plays a role that is more than merely enabling and less than strictly evidential (Williamson, 2013), then it’s plausible to think that experience plays this quasi-evidential role in cases in which we come to know “from the armchair” that e is part of our evidence (where e is a contingent proposition about the environment). If this is correct, then the fact that we can have armchair knowledge of our evidence e doesn’t sound so absurd anymore, even when e is a contingent proposition about the external environment.19

3  Evidential Externalism In the previous section, I considered some of the most prominent arguments for Internalism. Crucially, none of them seem to provide us with strong motivations for restricting evidence to non-factive mental states. The remainder of the chapter considers some motivations behind Externalism. 56

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3.1  Radical Scepticism A first reason why Internalism looks troublesome is that it seems to play a crucial role in a form of sceptical argument. Let’s consider again Gary, in a paradigmatic good case, and his recently envatted internal twin Barry. If Internalism is true, then, given Gary and Barry have the same non-factive mental states, they also have the same evidence. But, if they have the same evidence, and Barry doesn’t have any knowledge of how things are in the external environment, then how can Gary have knowledge on the basis of such impoverished evidence? The internalist will say that, given in Gary’s scenario the truth condition is also met, there’s a trivial and straightforward reason why Gary (but not Barry) knows, for instance, that he has hands. Furthermore, the internalist might say that Gary’s evidence, such as his seeming that he has hands, confers Gary’s (defeasible) justification for believing that he has hands.20 Crucially, things are not as easy for the internalist as they might look like. For instance, according to White, it’s plausible to say that if my evidence supports a proposition p and I thereby gain justification for p, then I should also raise my confidence in the truth of p. And yet, White argues: when it appears to me that something is a hand, my confidence that it is not a fakehand should decrease. For since this is just what a fake-hand would look like, the degree to which I suspect it is a fake hand should increase. (White, 2006, p. 531) On the one hand, Internalism restricts evidence to facts concerning one’s non-factive mental states, e.g., one’s sensory experiences. On the other hand, the sceptical hypothesis that one is a handless brain in a vat fed perfectly veridical experiences as of having hands entails that in the bad case one has the exact same sensory experiences one would have in the good case. So, unless one has antecedent and independent justification for believing that one is not a brain in a vat, then, if Internalism is true, one’s evidence in the good case doesn’t seem adequate to confer justification or knowledge. A promising internalist rejoinder is the so-called Explanationist response (Cf. Vogel, 1990; Conee & Feldman, 2008; McCain, 2014). The Explanationist will grant that Gary’s sense experiences by themselves are inadequate to underwrite justification (or knowledge). After all, the sceptical hypothesis entails that Gary has the sensory experiences that he has. However, the hypothesis that Gary in fact has hands best explains his evidence, namely, why he has the experience as of having two hands. More precisely, according to the Explanationist, our common-sense judgment about the existence of the world best explains the coherence, regularity, and continuity of our sense experiences, and this inference to the best explanation is enough to underwrite our justification for believing that there is an external world and that the sceptical hypothesis is false. Appealing to inference to the best explanation (IBE) in the context of scepticism has raised some worries. A first worry concerns the justificatory status of IBE itself. For instance, Fumerton (1992) has argued that the Explanationist assumes that our sensory experiences can be explained by a cause. Crucially, this presumption is unjustified, for it needs “a prior solution to scepticism about the physical world and we will be precluded from using [IBE] in order to get that solution” (p. 163).21 However, even if we put aside concerns about the justificatory status of IBE, the Explanationist response might still encounter problems. Susanna Rinard, for instance, has recently argued that our common-sense beliefs might actually not 57

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be the best explanation of the continuity of our sensory experience (Rinard, 2018). For example, an idealist theory could offer a simpler explanation of our sensory experiences given that it postulates fewer entities. But even if we grant that our common-sense beliefs best explain the continuity of our sensory experience, appealing to IBE doesn’t seem to be enough to provide us with justification for believing the falsity of the sceptical hypothesis. Roughly put, Rinard’s argument hinges on the idea that if, given what one knows, there are more ways in which p can be true than not-p, then one has more justification to believe p than not-p.22 If this is right, then, given that one knows that there are more ways in which our experience can be non-veridical than veridical (just think of the varieties of sceptical hypothesis that have been developed in the literature!), it seems that one is more justified in believing the sceptical hypothesis than the hypothesis that one’s experience is veridical. Whether these considerations are sufficient for rejecting the Explanationist response or not, the moral of the story is that the Internalist surely has a lot of work to do to resist this sceptical challenge. By contrast, the Externalist seems to be immediately better positioned, for she can easily say that Gary has better or more evidence than Barry. For instance, E=K predicts that given that Gary (but not Barry) knows that he has hands, his evidence entails that the sceptical hypothesis is false. Interestingly, Silins has recently questioned this advantage that Externalism seems to have. By focusing on Barry in the bad case, Silins plausibly points out that most epistemologists— externalists included—would deny that Barry is justified in believing that he’s in the bad case (as Section 2.3 shows).23 Furthermore, Silins claims, the Externalist will also deny that Barry is justified in believing that he’s not in the bad case (as discussed in Section 2.2). However, it’s plausible that if one lacks justification for believing that p, and one lacks justification for believing that not-p, then one has justification for suspending judgment on whether p is the case. If this principle is true, then the Externalist has to say that Barry in the bad case is justified in suspending judgment on whether he’s a brain in a vat or not. Crucially, Silins argues, this is highly implausible: Suppose that Barry did suspend the judgment in the proposition that [p], despite the fact that there seems to be that [p], and despite the fact that no defeating evidence is available to him. I take it to be very implausible that Barry would be justified in suspending judgment in the matter. (Silins, 2005, p. 392) I don’t think this constitutes a real threat to the Externalist. In particular, the Externalist can account for the intuition that it would indeed be weird if Barry did in fact suspend judgment on whether p is the case: given what Barry wrongly takes his evidence to be, we would expect him to believe that he’s not a brain in a vat. While appealing to something similar to the excuse manoeuvre discussed in Section 2.2, the Externalist will, however, insist that we shouldn’t conflate claims about what’s reasonable for Barry to believe given his limited knowledge about his own epistemic situation, with claims about what he has justification to believe (Fratantonio & McGlynn, 2018, pp. 99–100).

3.2  Publicity of Evidence Another reason one might think Externalism is a promising view is that, contrary to Internalism, it can account for the intuition that evidence is supposed to be a neutral arbiter, 58

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i.e., a public item everyone can appeal to. By taking one’s evidence to supervene on one’s non-factive mental states, Internalism doesn’t seem to capture this “publicity of evidence” intuition (Kelly, 2008, p. 949). Perhaps the Internalist can appeal to some form of pluralism about evidence. Conee and Feldman (2008), for instance, distinguish between scientific evidence, evidence that is publicly available and a reliable indicator of some state of affairs, and justifying evidence, evidence that confers one with epistemic justification. On this pluralist account, although scientific evidence can be useful for acquiring justifying evidence, the two notions are distinct. For example, one can have scientific evidence for p without grasping the connection between such evidence and p, thereby failing to have justifying evidence (2008, pp. 84–86). Conee and Feldman can thus vindicate this “publicity of evidence” intuition within the scientific and legal context, while insisting that justifying evidence (evidence we consider when evaluating people’s beliefs) is a matter of having something one can cite as basis for believing something, and this supposedly leads towards a picture of (justifying) evidence that is restricted to the content of one’s mind. But one might ask: why should we opt for pluralism when, by allowing evidence to extend beyond the mind, Externalism can offer a unified account of justifying and scientific evidence? Crucially, things might not be so easy for some paradigmatic Externalist views, e.g., E=K. For if the Internalist has to motivate why we should restrict evidence to nonfactive mental states, likewise the Externalist has to explain the plausibility of restricting evidence to known propositions only. Joyce, for instance, has argued that requiring all evidence to be knowledge sets the bar too high, for it clashes with our understanding of evidence as something that is context-sensitive and that comes in degrees (Joyce, 2004, pp. 297–298). And even if we adopt a more liberal externalist view, one that restricts evidence to true propositions only, externalism still seems at odds with our common-sense usage of “evidence” as what we appeal to in order to make sense of someone’s beliefs and actions. To put it in Joyce’s words: “Often when we speak of a person’s evidence [w] e try to give a rationalising explanation (or critique) of some things she believes, usually by citing other things she believes. Here the standard of truth is inappropriate” (Joyce, 2004, p. 296). The externalist could object that providing a rationalising explanation of a person’s beliefs merely requires accounting for what she (sometimes mistakenly) takes her evidence to be, but Joyce thinks this response is problematic. Imagine a juror who reaches the verdict that the defendant is innocent on the basis of false testimony that the defendant was asleep at the time of the murder. If Externalism is true, then we will speak falsely when saying—as we ordinarily do—that the juror had evidence for her verdict, thereby committing to an error-theory of the rational explanations we would ordinarily offer of the juror’s verdict. According to Joyce, rather than saying that the juror is mistaken about the evidence she has, we should say that the juror has been provided with misleading or false evidence (2004, p. 302). However, it’s not clear that the Externalist is committed to an error-theory here. The Externalist can say that the juror had misleading (yet not false) evidence for her verdict, namely, that the testifier said that the defendant was asleep (McGlynn, 2014, p. 74).24 Furthermore, while Joyce’s objections target some radical Externalist view, it’s not clear whether they would apply to all versions of Externalism. After all, as seen in Section 1, some versions of Externalism might even allow for one’s total evidence to contain some falsehoods. Ultimately, I  believe that arguing that Externalism is problematic because it doesn’t vindicate our intuitions about the notion of evidence is not a very promising strategy. 59

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If anything, Turri’s recent empirical studies suggest the opposite: the empirical data he’s recently presented indicates that our common-sense usage of “evidence” is largely truthsensitive. Interestingly, experiments asking the research participants to assess the justificatory status of someone’s belief have delivered similar results (Turri, 2018). That is, both our folk conception of evidence and our ordinary way of evaluating beliefs seems to be largely truth-sensitive, thereby questioning the plausibility of Conee and Feldman’s distinction between scientific and justificatory evidence.25

4 Conclusion In this chapter, I have discussed the debate between Evidential Internalism and Evidential Externalism. Note that this does not represent an exhaustive list of arguments against/for each view.26 The aim of this chapter was more modest, namely, to provide an overview of some of the main arguments that help to shed light on the motivations underlying these views. Let me thus conclude by clarifying what these motivations are. On the one hand, what is driving most Internalist arguments is the idea that evidence has to be the kind of thing we can have unproblematic access to. This, in turn, seems to be motivated by the following two claims: i) rationality requires one to respect one’s evidence; ii) respecting one’s evidence is possible only if one has access to it. On the other hand, by allowing evidence to extend beyond the mind, Externalism vindicates our folk notion of evidence, one on which evidence is a public item that can be shared by many, and the neutral arbiter that reliably indicates the truth of some proposition. However, while it seems that Externalism can somehow accommodate some of the previously mentioned Internalist intuitions, it’s difficult to see how Internalism can make sense of the “publicity of evidence” while insisting that one’s evidence supervenes on one’s non-factive mental states. Furthermore, while Internalism threatens to lead to scepticism, the Externalist has a straightforward solution to the sceptical problem: by rejecting Sameness of Evidence, she can easily say that one has better or more evidence in the good case than one’s internal twin in the bad case. At least for these reasons, I believe Externalism is a better option.

Notes 1 I am grateful to Natalie Alana Ashton, Liz Jackson, Maria Lasonen-Aarnio, and Greta Turnbull for comments on an early draft of this paper. 2 This way of framing the distinction is due to Silins (2005). 3 This way of labelling the view is due to Williamson (2000). 4 While defending a version of Internalism, Conee and Feldman don’t explicitly restrict evidence to non-factive mental states (Conee & Feldman, 2004, p. 57). However, they seem to be sympathetic to something similar to Evidential Internalism. 5 Although psychologism is usually associated with Internalism, Mitova (2014) is an example of Externalism that embraces psychologism. 6 Note that contrary to how the term is traditionally used, Pritchard (2012) talks about “factive” evidence as referring to the thesis that evidence entails the proposition it is evidence for. As I will show shortly, Evidential Externalism doesn’t entail this notion of factivity either. 7 For a classic defence of Reliabilism, see Goldman (1979, 1986). 8 The locus classicus for Evidentialism is Conee and Feldman (2004). 9 See Littlejohn (2018) for a view that rejects Evidentialism about justification while endorsing E=K. 10 Lehrer and Cohen (1983) and Cohen (1984) originally raised this argument against Reliabilism about epistemic justification.

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Evidential Internalism and Evidential Externalism 11 Note that Gerken raises this objection to the excuse manoeuvre as originally made in the context of the knowledge norm of action. Cf. Williamson (2000, ch. 5) and Hawthorne and Stanley (2008). See Brown (2018, ch. 4) for recent arguments against this knowledge-based account of justification and the excuse manoeuvre. 12 See also Lasonen- Aarnio ( forthcoming). 13 There is also a straightforward way in which the Externalist can grant Barry a positive epistemic standing: she can say that Barry has some evidence, e.g., evidence about how things look like. 14 See Littlejohn (2009) for a useful overview. 15 Note that Pritchard’s Distinguishability problem concerns a case of local scepticism. 16 As I will discuss in Section 3.1, this is a promising implication of Externalism. 17 For criticisms of Williamson’s argument, see Steup (2009) and Williamson’s reply in Williamson (2009). See also Amia Srinivasan for a further defence of anti-luminosity (Srinivasan, 2015). 18 This argument mirrors the more notorious McKinsey paradox (McKinsey, 1991). 19 Note that this strategy might not be available to Externalist views that embrace a strong accessibility requirement. For instance, see Fratantonio (2021) for arguments showing that the Access problem represents a real threat to Pritchard’s externalist Epistemological Disjunctivism (Pritchard, 2012). 20 Something along these lines is notoriously embraced by so-called dogmatists and phenomenal conservatists, e.g., Pryor (2000) and Huemer (2001). 21 See McCain (2017) for a response. 22 This is a simplification of Rinard’s own principle. Furthermore, note that Rinard formulates this principle in terms of the degree of credence one should have (Rinard, 2018, pp. 208–214). However, assuming our degree of confidence should match our degree of justification, this justificationbased principle is also plausible. 23 Magidor (2018) is an exception. 24 Cf. Leite (2013). 25 See also Littlejohn (2011) for linguistic evidence for Externalism. 26 For another relevant argument for Externalism, see Littlejohn (2012, pp.  91–92). For another interesting argument against Externalism, see Silins (2005). See Fratantonio and McGlynn (2018) for a response.

References Audi, R., 2001. An internalist theory of normative grounds. Philosophical Topics, 19(1–2), pp. 19–46. Ayer, A. J., 1936. Language Truth and Logic. London: Camelot Press. BonJour, L., 1999. Foundationalism and the external world. Philosophical Perspectives, 13, pp. 229–249. Brown, J., 2018. Fallibilism: Evidence and Knowledge. Oxford: Oxford University Press. Cohen, S., 1984. Justification and truth. Philosophical Studies, 46(3), pp. 279–295. Conee, E. & Feldman, R., 2004. Evidentialism. Oxford: Oxford University Press. Conee, E.  & Feldman, R., 2008. Evidence. In: Q. Smith, ed. Epistemology: New Essays. Oxford: Oxford University Press. Fratantonio, G., 2018. Armchair access and imagination. Dialectica, 72(4), pp. 525–547. Fratantonio, G., 2021. Reflective access, closure, and epistemological disjunctivism. Episteme, 18(4), pp. 555–575. Fratantonio, G. & McGlynn, A., 2018. Reassessing the case against evidential externalism. In: The Factive Turn in Epistemology. Cambridge: Cambridge University Press. Fumerton, R., 1992. Skpeticism and inference to the best explanation. Philosophical Issue. 2, pp. 149–169. Gerken, M., 2011. Warrant and action. Synthese, 178(3), pp. 529–547. Goldman, A., 1979. What is justified belief? In: Justification and Knowledge. Boston: D. Reidel, pp. 1–25. Goldman, A., 1986. Epistemology and Cognition. Cambridge: Harvard University Press. Hawthorne, J.  & Stanley, J., 2008. Knowledge and action. Journal of Philosophy, 10(105), pp. 571–590. Huemer, M., 2001. Skepticism and the Veil of Perception. Lanham: Rowman & Littlefield.

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Giada Fratantonio Joyce, J., 2004. Williamson on evidence and knowledge. Philosophical Books, 45(4), pp. 296–305. Kelly, T., 2008. Evidence: Fundamental concept and the phenomenal conception. Philosophy Compass, 3(5), pp. 933–955. Lasonen-Aarnio, M., forthcoming. Virtous failure and victim of deceit. In: J. D. F. Dutant, ed. The New Evil Demon. Oxford: Oxford University Press. Lasonen-Aarnio, M., 2021. Dispositional evaluations. In: J. Brown & M. Simion, eds. Reasons, Justification, and Defeat. Oxford: Oxford University Press, pp. 91–115. Lehrer, K. & Cohen, S., 1983. Justification, truth, and coherence. Synthese, 55(2), pp. 191–207. Leite, A., 2013. But that’s not evidence; it’s not even true! The Philosophical Quarterly, 63(250), pp. 81–104. Littlejohn, C., 2009. The New Evil Demon Problem [Online]. Available at: www.iwp.utm.edu/ evil-new Littlejohn, C., 2011. Evidence and armchair access. Synthese, 179, pp. 479–500. Littlejohn, C., 2012. Justification and the Truth Connection. Cambridge: Cambridge University Press. Littlejohn, C., 2018. Evidence and its limits. In: C. McHugh, J. Way & D. Whiting, eds. Normativity: Epistemic and Practical. Oxford: Oxford University Press, pp. 116–136. Littlejohn, C., forthcoming. A plea for epistemic excuses. In: J. Dutant & D. Dohrn, eds. The NEw Evil Demon. Oxford: Oxford University Press. Magidor, O., 2018. How both you and the brain in a vat can know whether or not you are envatted. Aristotleian Society Supplementary Volume, 92(1), pp. 151–181. McCain, K., 2014. Evidentialism and Epistemic Justification. New York: Routledge Studies in Contemporary Philosophy. McCain, K., 2017. In defence of the explanationist response to skepticism. International Journal for the Study of Skepticism, pp. 1–13. McDowell, J., 1995. Knowledge and the internal. Philosophy and Phenomenological Research, 55(4), pp. 877–893. McGlynn, A., 2014. Knowledge First? Basingstoke: Palgrave. McKinsey, M., 1991. Anti-individualism and privileged access. Analysis, 51(1), pp. 9–16. Mitova, V., 2014. Truthy psychologism. Philosophical Studies, 172(4), pp. 1105–1126. Pritchard, D., 2012. Epistemological Disjunctivism. Oxford: Oxford University Press. Pryor, J., 2000. The skeptic and the dogmatist. Nous, 34(4), pp. 517–549. Rinard, S., 2018. External world skepticism and inference to the best explanation. In: K. McCain & T. Poston, eds. Best Explanations: New Essays on the Inference to the Best Explanation. Oxford: Oxford University Press. Russel, B., 1912. The Problems of Philosophy. New York: H Holt. Schellenberg, S., 2016. Phenomenal evidence and factive evidence. Philosophical Studies, 173 (4), pp. 875–896. Silins, N., 2005. Deception and evidence. Philosophical Perspectives, 19(1), pp. 375–404. Simion, M., Kelp, C. & Ghijsen, H., 2016. Norms of belief. Philosophical Issue, 21(1), pp. 374–392. Srinivasan, A., 2015. Are we luminous? Philosophy and Phenomenological Research, XC(2), pp. 294–319. Steup, M., 2009. Are mental states luminous? In: P. Greenough & D. Pritchard, eds. Williamson on Knowledge. Oxford: Oxford University Press. Turri, J., 2018. The non-factive turn in epistemology: Some hypothesis. In: V. Mitova, ed. The Factive Turn in Epistemology. Cambridge: Cambridge University Press. Vogel, J., 1990. Cartesian skepticism and inference to the best explanation. Journal of Philosophy, 87(11), pp. 658–666. Wedgwood, R., 2002. Internalism explained. Philosophy and Phenomenological Research, 65(2), pp. 349–369. White, R., 2006. Problems for dogmatism. Philosophical Studies, 131(3), pp. 525–557. Williamson, T., 2000. Knowledge and Its Limits. Oxford: Oxford University Press. Williamson, T., 2009. Replies to critics. In: P. Greenough & D. Pritchard, eds. Williamson on Knowledge. Oxford: Oxford University Press. Williamson, T., 2013. How deep is the distinction between a priori and a posteriori. In: A. Casullo & J. C. Thurow, eds. The A Priori in Philosophy. Oxford: Oxford University Press. Williamson, T., forthcoming. Justification, excuses and sceptical scenario. In: J. Dutant & D. Dohrn, eds. The New Evil Demon. Oxford: Oxford University Press.

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5 THE EVIDENTIAL SUPPORT RELATION OF EVIDENTIALISM T. Ryan Byerly

Evidentialist theories of epistemic justification define epistemic justification at least partially in terms of what a person’s evidence supports, claiming that a person is justified in believing a claim just in case her evidence supports that claim. This evidential support relation—the relation that obtains when a person’s evidence “supports” a claim in the sense required by evidentialist views—is the topic of this essay. The question that animates the essay is, “Just when does a person’s evidence support a claim?” I begin in Section  1 by contextualizing the project of answering this question within the broader project of explicating the details of evidentialism. This contextualization will allow me to narrow the focus of the essay while also highlighting the potentially broader significance of its topic. I then turn in Sections 2–4 to offer a critical introduction to three different approaches to answering the question: explanationist approaches, probabilistic approaches, and psychologistic approaches.

1  The Support Relation in the Context of Evidentialist Theory An excellent place to begin one’s inquiry into the evidential support relation is with Earl Conee and Richard Feldman’s essay “Evidence” (2008). They begin this essay by offering a “bare statement” of a full evidentialist theory of epistemic justification that appeals explicitly to the relation of evidential support. Its central affirmations are: (T1) An agent S is justified in believing a claim p at a time t iff S’s evidence at t supports p. (T2) An agent S is justified in disbelieving a claim p at a time t iff S’s evidence at t supports ~p. (T3) An agent S is justified in suspending judgment with respect to p at a time t iff S’s ­evidence at t is counterbalanced with respect to p. While T3 doesn’t clearly invoke the evidential support relation in the way T1 and T2 do, it may be that it does so implicitly, insofar as the relation of evidential counterbalancing can be explained in terms of the relation of evidential support.

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This statement of evidentialism may be regarded as a partial explication of Conee and Feldman’s earlier statement of evidentialism in their classic paper “Evidentialism” (1985): (EJ) A doxastic attitude D toward a proposition p is epistemically justified for a person S at a time t iff having D toward p fits the evidence S has at t. T1–T3 partially explicate EJ by identifying when the attitude types of belief, disbelief, and suspension of judgment fit the evidence a person has regarding p. EJ itself provides an account of propositional justification. It can also be utilized to provide an account of doxastic justification through the addition of a requirement regarding proper basing. While T1–T3 partially explicate EJ, they do not by themselves provide a full evidentialist theory of epistemic justification, even when supplemented with a suitable proposal regarding the relationship between propositional and doxastic justification. This is because key concepts within T1–T3 are left crucially undetermined. As Conee and Feldman put it, Among the things needed to develop the theory more fully are accounts of what evidence is, what it is for a person to have something as evidence, when a body of evidence supports a proposition, and what the basing relation is. (2008: 84) This essay is concerned with accounts of the third item in the list—i.e., accounts of when the evidence a person has supports a proposition. The animating question is, “Just when does a person’s evidence ‘support’ a proposition p in the sense of ‘support’ relevant for T1– T3?” It is important to note at the outset that this sense of “support” may differ from other senses of “support.” For example, some epistemologists who reject T1–T3 may nonetheless appeal to a notion of evidential support as part of their alternative theory of epistemic justification; this sense would conflict with the sense that is the focus here, though there may also be overlap. Likewise, we might think that there is a sense of support that may not be essentially epistemic in which any proposition that entails another proposition thereby supports that other; but, as we will see, such a sense of support differs from that in view here, even if there is overlap between the two. The focus here is on accounts of the evidential support relation referenced by the language of “support” in T1–T3. While accounts of this evidential support relation would most immediately illuminate evidentialist theories of epistemic justification, they may inform epistemological theorizing regarding other topics as well. For instance, if knowledge or understanding require justification, and justification is at least partially explicable in terms of this evidential support relation, then knowledge and understanding are partially explicable in terms of it as well. Likewise, if some or all intellectual virtues are at least in part a matter of how a person behaves when her evidence does or does not support some claim in the relevant sense, then some or all intellectual virtues are partially explicable in terms of this evidential support relation. Examination of alternative approaches to accounting for this relation of evidential support is therefore clearly motivated for those committed to evidentialist theories of epistemic justification, and it may also yield benefits further afield in epistemological theorizing. Here I  will focus on three approaches to accounting for this relation that prominently employ either explanatory, probabilistic, or psychological concepts. 64

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2  Explanationist Approaches I’ll begin by considering approaches to accounting for the evidential support relation of evidentialism with which Conee and Feldman themselves express most sympathy— explanationist approaches. As a point of departure, a simple formulation of explanationism inspired by Conee and Feldman’s text (2008: 97–8) is as follows: (EXP) A subject S’s evidence E supports a proposition p at a time t iff p is part of the best explanation available to S at t for why S has E. EXP, combined with T1–T3, makes the epistemic justification of propositions for a subject a matter of the explanatory relationship between these propositions and the subject’s evidence. In this respect, it is reminiscent of views defended by Harman (1986), Lycan (1988), and Moser (1989). More recently, similar explanationist approaches to epistemic justification have been defended by McCain (2014a) and Poston (2014). Numerous objections have been raised to EXP and similar accounts of evidential support in recent scholarship.1 In this section, I concentrate on a sample of these objections that in my view motivate modification or abandonment of explanationist theories, beginning with objections to their necessity condition. In Section 4, I discuss an objection relevant to evaluating the concept of availability employed in these views. For now, I simply note that this concept is typically defined so as to require the subject S to have some kind of psychological orientation toward the explanatory relationship between p and E. An early objection to explanationist views argued against their necessity condition on the grounds that it failed to adequately capture the role of entailment relations in accounting for evidential support. For example, Lehrer (1974) argues that he could be justified in believing that a mouse is five feet from an owl on the basis of his knowledge that the mouse is three feet from a four-foot-high flagpole on which the owl is perched, together with his knowledge of the Pythagorean theorem. Yet, the fact that the mouse is five feet from the owl needn’t be part of the best explanation for why Lehrer has the evidence he does in the example regarding the distance between the mouse and the pole and the height of the pole. One approach to accounting for such cases, advocated for some time by Kevin McCain (2014a, 2014b), is to add a disjunct regarding entailment relations to the right-hand side of EXP as follows: (EXP+ENT) A subject S’s evidence E supports a proposition p at a time t iff either (i) p is part of the best explanation B available to S at t for why S has E or (ii) p is available to S as an entailment of B. However, Byerly and Martin (2015) argue that EXP+ENT cannot accommodate certain cases where a subject’s evidence supports a proposition by making it merely highly probable. For example, a golfer who has witnessed most but not all of his putts in similar circumstances go in may thereby have evidence supporting the claim that his current putt will go in. This needn’t be because his current putt’s going in explains why he has the evidence he currently does, nor because its going in is entailed by the best available explanation of his evidence. 65

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McCain (2015) appears prepared to grant that EXP+ENT is unable to adequately account for such examples. In its place, he has advocated a different refinement of EXP that he argues can account both for cases in which entailment relations seems to contribute to evidential support and for cases in which probabilistic relations seem to. This newer refinement, which results in a view of epistemic justification quite similar to Poston’s and Harman’s, exclusively utilizes explanatory relations: (EXP+EXP) A subject S’s evidence E supports a proposition p at a time t iff either (i) p is part of the best explanation B available to S at t for why S has E or (ii) p is available to S as an explanatory consequence of B. EXP+EXP accounts for the golf case because part of the best available explanation for the golfer’s evidence is that the ball he has just putted is rolling toward a cup in some circumstances C, and most balls rolling toward a cup in circumstances C go in; yet these propositions together explanatorily predict that the ball just putted will go in. They would explain its going in better than they would explain its not going in. Byerly and Martin (2016) argue against EXP+EXP, however, on the grounds that it cannot account for Lehrer’s case and for parallel cases involving probabilistic relations without countenancing symmetric explanations. For example, they ask us to consider a case in which a subject has and as part of the best available explanation for her evidence, suggesting that in such a case her evidence would support . The explanationist should not attempt to account for this case by claiming that is an explanatory consequence of the other two propositions. For the consistent application of this strategy will lead the explanationist to embrace symmetric explanations, which seems a significant theoretical cost. To see this, simply alter the case so that the subject has and as part of the best available explanation of her evidence instead. Consistent application of the proposed strategy would require claiming here that is an explanatory consequence of the other two propositions. But this will imply that the number of Cage films in 2006 partially explains the number of drownings, and the number of drownings partially explains the number of Cage films, thereby committing the explanationist to symmetric explanations. In McCain’s (2017) recent discussion of this objection, he appears to be sympathetic with applying the strategy proposed here, but offers no comments about how this strategy can be applied consistently without embracing symmetric explanations. Objections have also been raised against the sufficiency condition of EXP and similar principles. For starters, one might be worried by the problem of the bad lot. If p is part of the best explanation B available to S for why S has E, yet B is nonetheless a bad explanation, it would appear S is not justified in believing p, contrary to all of the versions of explanationist evidentialism we have thus far considered. Of course, a simple fix to these views may suffice: just require that in addition to being the best explanation, B is also a sufficiently good explanation (cf. McCain 2015: 339, n.19).

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Byerly and Martin (2015) argue that this fix is not enough. For there can be cases in which S has available an explanation B for her evidence that is both the best available and a good explanation, yet S shouldn’t believe B because S also has reason to think that evidence she has not yet investigated may favor an alternative explanation. For example, a detective may have identified a suspect mid-way through her inquiry who is a good suspect and the best currently available, and yet have reason to think that the real perpetrator may emerge only after investigating further evidence, as similar occurrences have not been uncommon in the past. As the exchange between McCain (2015, 2017) and Byerly and Martin (2016) illuminates, explanationists may differ with regard to their weighting of explanatory virtues, yielding different results regarding whether the subjects in such cases are justified. Yet, there may remain a further question raised by these cases about the relationship between explanationism and pragmatic encroachment, since it may appear that the stakes involved in the detective case make a difference for our epistemic evaluation of the detective. There seem to be two options worth exploring for explanationists regarding this question. They might claim that practical interests make no difference to epistemic justification as they are conceiving of it. But then a challenge is to identify more carefully the theoretical role played by justification. Plausibly they could not identify epistemic justification with epistemic obligation, as Conee and Feldman (1985: 19; cf. Feldman 2000) have wanted to, since it seems too strong to conclude that the detective should believe the suspect committed the crime, and this is partially because of the stakes of the inquiry. On the other hand, explanationists might argue that part of what it takes for an explanation to be sufficiently good is determined by practical interests. Such a version of explanationism may make an interesting addition to the literature, even if it runs counter to most contemporary evidentialists’ resistance to pragmatic encroachment. A final objection to the sufficiency of explantionism targets clause (ii) of EXP+EXP. Appley and Stoutenburg (2017) argue that, given the fact that not all explanatory relations are entailment relations, propositions justified by clause (ii) can have lower epistemic probability than propositions justified by clause (i). But, they argue, this creates a dilemma for the explanationist. Either the minimal degree of goodness in the explanations referenced in clause (i) is just above the threshold for justification, or it is more than just above that threshold. If it is just above the threshold, then there will be propositions that clause (ii) judges justified that fall below the threshold. If it is more than just above the threshold, then clause (i) will fail to count as justified propositions that are just above the threshold. I propose, however, that the explanationist can split the horns of the dilemma by requiring that the minimal degree of goodness for the explanations referenced in clause (i) is just above the threshold for justification, and that propositions justified by clause (ii) are sufficiently well explained by an explanation referenced in clause (i) that is sufficiently good that the resulting epistemic probability of the relevant propositions has a minimal level of being just above the threshold for justification. This solution does require a modification of the versions of explanationism thus far discussed. This brief review reveals that explanationist approaches to evidential support have proven resilient in the face of objections, even if this resilience requires modification to how explanationism is formulated. Perhaps the most threatening objection is the objection from Byerly and Martin, which aims to show that explanatory relations cannot do all of the supporting work that entailment and probabilistic relations appear to do, since the former cannot be symmetric while the latter can.

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3  Probabilistic Approaches Given the vulnerability of explanationist approaches in certain cases where evidential support appears to involve probabilistic rather than explanatory relations, we might consider approaches to accounting for the evidential support relation in terms of probabilistic relations. Such approaches would make evidence’s support of a proposition a function of the probability of that proposition given that evidence. Accounts of this type could be formulated as follows: (PR) A subject S’s evidence E supports a proposition p at a time t iff Pr(p│E) > n & F. Different probabilistic accounts of evidential support may differ regarding their interpretation of the kind of probability in view—i.e., their interpretation of “Pr.” They may also differ with respect to the threshold value of n. And they may differ with respect to what else is required for E to support p beyond having a value greater than n for Pr(p│E)—i.e., they may differ regarding the conjunct F. I will discuss two proposals of this kind here, each inspired by influential work in the epistemology of inductive inference. Each of the proposals I  will discuss was originally intended at most to account for inferential justification—justification for a proposition p that derives from the justification of other propositions. To yield a complete account of epistemic justification, these proposals must either be combined with the claim that there is no non-inferential justification, or they must be extended to account for non-inferential justification in addition to inferential justification. Here I  will concentrate on the latter possibility. The first probabilistic account I will call a “Carnapian” account after the philosopher Rudolf Carnap (1962). One of the hallmarks of Carnap’s approach to inductive logic and inferential justification was to interpret “Pr” as an objective—indeed, a priori—relation between E and p. The aim of his logical theory of probability was to account for the probability, in this sense, of any proposition p given any proposition q. Such an account would straightforwardly yield an account of the confirmation that any proposition provides to any other. It could also be employed to account for properties of epistemological significance: the epistemic status of a proposition p for a person S would be a function of the objective probability of p on S’s evidence. As suggested, Carnap’s theory was only intended to account for the confirmation that one proposition provides to another, and by extension the justification that one proposition provides to another. As such, it seems most suited to account only for inferential justification. However, we might imagine an extension of Carnap’s basic approach intended to account for non-inferential justification as well. For sake of simplicity, we can grant (as Conee and Feldman [2008] affirm) that non-inferential justification derives from a subject’s experiences. We then simply need a way to represent a subject’s experiences as part of E within PR. A simple suggestion would be to represent any subject S’s experience e with the proposition that S is having experience e. We could then further stipulate that E includes only propositions that are supported or that represent S’s experiences. With these modifications, Carnap’s approach can yield a thoroughly probabilistic approach to accounting for evidential support. One objection to this kind of Carnapian view is voiced by Conee and Feldman in their consideration of views that make evidential support a matter of an objective probabilistic 68

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relation between a subject’s evidence and a proposition. They write, “Where this probabilistic relation is beyond the person’s understanding, the person may not be justified to any degree in believing a proposition made probable by the evidence” (2008: 95). Whether a priori or not, it may be that the value of Pr(p│E) is beyond a person’s understanding; and if so, then the fact that it is above n will not imply that her evidence supports p. In embracing this objection, Conee and Feldman may be motivated by sympathy with a key motivating idea of internalism about justification—that a proposition cannot be justified for a subject if from that subject’s own perspective it would come as a surprise that p is true (BonJour 1985). Carnap in fact has a reply to this subject’s perspective objection. For, in his view, the crucial element of F is a bridge principle connecting Pr(p│E) to properties of epistemological significance. According to Carnap (1962: 201), the fact that Pr(p│E) = n will only justify S in having a degree of belief of n in p if S also knows E (and nothing else) and knows that Pr(p│E) = n. Thus, it is not his view that a person’s evidence supports just any proposition that it makes sufficiently probable. Of course, the precise bridge principle proposed by Carnap will not do if we want PR to yield a complete account of evidential support. For this principle references the subject’s knowledge of the value of Pr(p│E), which will presumably require that the subject has support for thinking that Pr(p│E) has this value. To yield a complete account of evidential support without succumbing to the subject’s perspective objection, the Carnapian will need to identify a relation between a subject and the fact that Pr(p│E) > n, which will render p expectable to the subject without requiring unanalyzed facts regarding what the subject’s evidence supports. One approach would be for Carnapians to model their approach to identifying a suitable relation on explanationist proposals regarding availability. For example, rather than proposing that S must be disposed to have a seeming that p is an explanatory consequence of E (cf. McCain 2014b), the Carnapian might propose that S must be disposed to have a seeming that Pr(p│E) > n. I will return to this topic later in discussing psychologistic accounts of support. A different, and more forceful objection to Carnapian views is simply that there is no such thing as Pr(p│E) as the Carnapian conceives of it. In particular, there is no objective probabilistic relation such that for any propositions p and q, there is a value n such that necessarily Pr(p│q) = n. There is no objective probabilistic relation such that, for example, it is necessarily true that the probability that there is a red ball given that John is having an experience as of a red ball equals n. Most philosophers have given up on Carnapian approaches to confirmation in light of this difficulty (Crupi 2015: 3.2), though these approaches do continue to be explored by some (e.g., Maher 2010). A second probabilistic approach embraces an interpretation of “Pr” likely to yield less skepticism regarding the existence of the relevant probabilistic relations. I  will call this approach “Bayesianism” because it borrows salient elements from Bayesian approaches to formal epistemology. However, it should be clear that I am here attempting to bridge between Bayesian approaches as they are typically presented and the topic of this essay, which is typically not addressed by these views (cf. Hajek and Lin 2017, who advocate such bridge work). The Bayesian view I have in mind here interprets “Pr” as the subject’s own probability function. So, in requiring that Pr(p│E) > n, PR is interpreted as requiring that S’s own probability for p given E is greater than n. While there is controversy regarding exactly what such subjective probabilities are supposed to be, it is a common view that they are basic features of the subject (see Eriksson and Hájek 2007). We might, for 69

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example, think of Pr(p│E) as a measure of how strongly disposed S is to affirm p given that S has E. Because on this view Pr(p│E) is already a kind of bridge connecting the subject to the relationship between E and p, it may be that no bridge principle analogous to Carnap’s is needed to escape the subject’s perspective objection. If not, we may ask what will be included in F instead? It will differ from one Bayesian to another, but a common minimal requirement for rationality proposed by Bayesians is that the subject’s probability assignments obey the Kolmogorov axioms and a conditionalization principle, such as Jeffrey’s (2004) principle of conditionalization. F, then, may imply that so long as S’s probability assignments obey these and perhaps some further requirements, S’s evidence E supports p iff Pr(p│E) > n. Just as with the Carnapian view, if we wish for this Bayesian view to accommodate both inferential and non-inferential justification, we may stipulate that any subject S’s experience e may be represented within E as the proposition that S is having experience e, and we may stipulate that E includes only propositions that are supported or which represent S’s experiences. Two objections to Bayesianism so described are worth discussing for our purposes. On the one hand, even the minimal requirements of most Bayesian views—that agents’ probability assignments obey the Kolmogorov axioms and a principle of conditionalization—are regularly violated by people (Kahneman et al. 1982). Yet, it would seem that even for such people, it is not the case that their evidence supports nothing. The difficulty is to see how a Bayesian view could be developed that could account for what such people’s evidence supports without sacrificing the impressive results of Bayesianism, which appear to depend upon these minimal stipulations. A second objection pushes in the opposite direction, charging the Bayesian approach with being too permissive regarding what is required of a subject’s prior probability assignments in order for her evidence to support a proposition. Even so-called Objective Bayesian views, which require further constraints on rationality beyond those identified earlier, remain very permissive regarding prior probability assignments. As Weisberg (2011) has noted, for example, the most popular Objective Bayesian constraints still permit one subject to assign a prior probability of 99/100 to a fair coin’s landing heads and another subject to assign 1/100. One form this latter objection can take that is of special interest in the present context is when advocates of an alternative approach to evidential support argue that their approach can solve this problem of the priors. This charge has recently been made by defenders of explanationism (e.g., Poston 2014). For example, while the Objective Bayesian may be quite permissive regarding what is required of a subject S’s prior probability assignments to Pr (there is a red object│S is having an experience as of a red object), the explanationist would plausibly require a probability assignment greater than n for a typical subject. So might an advocate of an approach to evidential support that employs intellectual virtues. Of course, one direction that could be taken in response to this kind of objection would be to combine Bayesianism with an alternative view, where the role of the latter is especially to account of non-inferential justification. However, this manoeuvre may not satisfy critics if they think their account of evidential support not only solves the problem of the priors, but also accounts for inferential justification just as well as Bayesianism. This has been precisely the position of some recent defenders of explanationism (e.g., Poston 2014), and we might imagine a similar contention being made by advocates of an account of evidential support appealing to intellectual virtues. 70

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4  Psychologistic Accounts Both explanationist and probabilistic accounts surveyed thus far have required that for a subject S’s evidence E to support p, S must “grasp the connection” (in a non-factive sense) between E and p, as Conee and Feldman (2008: 85) put it. This requirement, we’ve seen, can be motivated by the subject’s perspective objection. “Grasping the connection” here consists in a psychological state of the subject, such as her being disposed to have a seeming that p explains E, or a seeming that E makes p probable. While these requirements are only part of the story of support according to the accounts surveyed thus far, we might consider whether an account of support could be defended that was defined exhaustively in terms of such psychological states. One persistent objection to accounts of support that incorporate these kinds of psychological requirements is that they overintellectualize support. Bayesian critics of explanationism, for example, have argued that in cases where S’s evidence E makes probable p because p explains E, and S appropriately grasps that E makes p probable, it makes no further contribution to the epistemic status of p if S also grasps that p explains E (see Roche and Sober 2013; McCain and Poston 2017). A similar objection could perhaps be pressed in the opposite direction if, in such a case, the subject appropriately grasped that p explained E but not that E made p sufficiently probable. Opting for a more liberal view, one might propose that S’s evidence E supports p just in case S has (or is disposed to have) a seeming that E is appropriately probabilistically related to p or that E is appropriately explanatorily related to p (cf. Conee and Feldman 2008: 96). Yet at least three objections afflict such a proposal. First, it is unclear what normative motivation there would be for requiring the content of the grasping psychological state to include probabilistic or explanatory relations between E and p when no such probabilistic or explanatory relations are required between E and p for E to support p. Second, the charge of overintellectualism still retains force. For, plausibly, such a view requires that for any subject to be justified in believing a claim, she must be sophisticated enough to distinguish between her evidential states and what they represent and to be capable of conceptualizing probabilistic or explanatory relations between the two—both no mean feat. Third, there is some reason for skepticism regarding the existence of the particular kind of psychological state—seemings—required by this proposal (see, e.g., Byerly 2012). Jonathan Kvanvig (2014) has recently defended a view that incorporates a significant psychologistic element of the relevant kind but that avoids these three charges. For Kvanvig, psychological states regarding the evidential connection between E and p are only to be expected among the reflective and make a difference for evidential support only for the reflective. Kvanvig’s basic idea is that, upon reflection, a person can give himself rules for how to evaluate the support that evidence provides to propositions. Kvanvig then embraces a Kantian account of why following such self-generated rules could make a difference for epistemic normativity, when the rules meet certain requirements. Kvanvig’s account, then, is motivated by a more general account of normativity, avoids overintellectualizing support, and avoids commitment to the existence of seemings. It should be noted, however, that Kvanvig’s account is not a thoroughly psychologistic account. For while his account of justification for the reflective incorporates a grasping psychological state, his account of justification for the unreflective does not. Instead, it appeals to Chisholm-like epistemic principles stating what particular items of evidence support. One concern with this approach, voiced by Conee and Feldman (2008: 97), is that it fails to 71

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provide a unifying story about why it is that particular items of evidence support what they support. Another concern is that, by not incorporating a psychologistic element of the kind in view in this section, the account remains vulnerable to the subject’s perspective objection in the case of the unreflective. A recent attempt to construct a thoroughly psychologistic account of evidential support that is motivated by normative theory, avoids overintellectualizing support, and does not require seeming states is Byerly’s (2014) dispositionalist evidentialism. Like other views surveyed here, it employs dispositions to avoid the subject’s perspective objection. But unlike the dispositions identified in these other views, Byerly’s dispositions do not require capacities to distinguish between evidence and what it supports, or capacities to conceptualize probabilistic or explanatory relations. Like Kvanvig and others, Byerly distinguishes between different subtypes of a relevant epistemic property—here, justification—reflecting different levels of agentic involvement. One type of justification specifies requirements for fulfilling one’s role as a believer (which requires less agentic involvement), while the other specifies requirements for fulfilling this role with excellence (which requires more). Viewing each type of justification as valuable is motivated by a broader Aristotelian conception of normativity. For Byerly, S’s evidence E supports p, and so provides the first sort of justification for p, just when S is disposed in light of E to believe p. S’s evidence provides justification of the second sort for p just when S is disposed to believe p by virtue of a virtuous disposition. If we think of a subject’s disposition to believe p in light of E as analogous to a subject’s probability for p given E, then Byerly’s view shares much in common with the Bayesian views discussed earlier. Indeed, like these views, Byerly’s is quite permissive regarding one type of justification—even more permissive than these Bayesian views, since it doesn’t require the subject’s dispositions to obey the Kolmogorov axioms, for example. Yet Byerly also recognizes a more demanding type of justification, which he attempts to account for by proposing a synthesis of evidentialism and virtue epistemology, as others have (e.g., Baehr 2011; Cloos 2015). One challenge for this type of synthesis of evidentialism and virtue epistemology is to specify the relationship between intellectual virtue and explanatory and probabilistic reasoning. Advocates of these syntheses should want to contend that cogent explanatory and probabilistic reasoning is reflective of intellectual virtue. In this way, their accounts can explain the presence of justification in the golf case or the Cage films/drowning case. Yet they should also want to contend that cogent explanatory or probabilistic reasoning is not all there is to intellectual virtue. Doing so may help with the detective case and others like it and is essential for differentiating these syntheses from rival explanationist and probabilistic accounts of support. Whether these contentions can be defended in detail is yet to be seen.

Note 1 This even includes a set of objections from Conee (2020) himself. It is only because of a bit of unfortunate timing that these objections are not considered in this chapter.

References Appley, Bryan and Gregory Stoutenburg. 2017. “Two New Objections to Explanationism.” Synthese 194, 8: 3069–84.

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The Evidential Support Relation of Evidentialism Baehr, Jason. 2011. The Inquiring Mind: On Intellectual Virtues and Virtue Epistemology. Oxford University Press. BonJour, Laurence. 1985. The Structure of Empirical Knowledge. Harvard University Press. Byerly, T. Ryan. 2012. “It Seems Like There aren’t Any Seemings.” Philosophia 40, 4: 771–82. Byerly, T. Ryan. 2014. “A  Dispositional Internalist Evidentialist Virtue Epistemology.” Logos  & Episteme 5, 4: 399–424. Byerly, T. Ryan and Kraig Martin. 2015. “Problems for Explanationism on Both Sides.” Erkenntnis 80, 4: 773–91. Byerly, T. Ryan and Kraig Martin. 2016. “Explanationism, Super-Explanationism, Ecclectic Explanationism: Persistent Problems on Both Sides.” Logos & Episteme 7, 2: 201–13. Carnap, Rudolf. 1962. Logical Foundations of Probability. University of Chicago Press. Cloos, Christopher. 2015. “Responsibilist Evidentialism.” Philosophical Studies 172, 11: 2999–3016. Conee, Earl. 2020. “Evidential Support and Best Explanations.” Philosophical Issues 30, 1: 71–85. Conee, Earl and Richard Feldman. 1985. “Evidentialism.” Philosophical Studies 48, 1: 15–34. Conee, Earl and Richard Feldman. 2008. “Evidence.” In Epistemology: New Essays, ed. Quentin Smith, 83–104. Oxford University Press. Crupi, Vincenzo. 2015. “Confirmation.” In Stanford Encyclopedia of Philosophy, ed. Edward Zalta. Available at https://plato.stanford.edu/entries/confirmation/ Eriksson, Lina and Alan Hájek. 2007. “What Are Degrees of Belief?” Studia Logica 86, 2: 185–215. Feldman, Richard. 2000. “The Ethics of Belief.” Philosophy and Phenomenological Research 60, 3: 667–95. Hájek, Alan and Hanti Lin. 2017. “A Tale of Two Epistemologies?” Res Philosophica 94, 2: 207–32. Harman, Gilbert. 1986. Thought. Princeton University Press. Jeffrey, Richard. 2004. Subjective Probability: The Real Thing. Cambridge University Press. Kahneman, Daniel, Paul Slovic and Amos Tversky, eds. 1982. Judgment Under Uncertainty: Heuristics and Biases. Cambridge University Press. Kvanvig, Jonathan. 2014. Rationality and Reflection: How to Think About What to Think. Oxford University Press. Lehrer, Keith. 1974. Knowledge. Clarendon Press. Lycan, William. 1988. Judgment and Justification. Cambridge University Press. Maher, Patrick. 2010. “Explication of Inductive Probability.” Journal of Philosophical Logic 39, 6: 593–616. McCain, Kevin. 2014a. Evidentialism and Epistemic Justification. Routledge. McCain, Kevin. 2014b. “Evidentialism, Explanationism, and Beliefs About the Future.” Erkenntnis 79, 1: 99–109. McCain, Kevin. 2015. “Explanationism: Defended on All Sides.” Logos & Episteme 6, 3: 333–49. McCain, Kevin. 2017. “Undaunted Explanationism.” Logos & Episteme 8, 1: 117–27. McCain, Kevin and Ted Poston. 2017. “The Evidential Impact of Explanatory Considerations.” In Best Explanations: New Essays on Inference to the Best Explanation, 121–31. Oxford University Press. Moser, Paul. 1989. Knowledge and Evidence. Cambridge University Press. Poston, Ted. 2014. Reason and Explanation: A  Defense of Explanatory Coherentism. Palgrave Macmillan. Roche, William and Elliot Sober. 2013. “Explanatoriness is Evidentially Irrelevant, or Inference to the Best Explanation Meets Bayesian Confirmation Theory.” Analysis 73, 4: 659–68. Weisberg, Jonathan. 2011. “Varieties of Bayesianism.” In Handbook of the History of Logic, Volume 10, eds. Dov Gabbay, Stephan Hartmann, and John Woods, 477–552. North Holland.

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6 HOW CAN “EVIDENCE” BE NORMATIVE? Ralph Wedgwood

The term “evidence” plays a central role in contemporary Anglophone epistemology.1 In particular, it is widely assumed that “evidence” plays an important role in determining what one is justified in believing. It also seems extremely plausible that “justification” is a normative concept. As I shall argue here, however, some compelling assumptions about normativity make it quite doubtful whether the word “evidence”—in anything like the meaning that it has in everyday English—can play the central epistemological role that is usually ascribed to it. In raising these doubts about whether “evidence” can play a central epistemological role, I am not denying that we could in principle stipulate a technical sense for the term “evidence”, which would allow it to play such a central role. However, as I shall argue, this is a perilous course. The word “evidence” also has a meaning in everyday English; and the meaning that “evidence” has in everyday English strongly encourages assumptions that fundamentally conflict with its playing this sort of central role. Finally, I shall propose a hypothesis about the meaning that “evidence” has in ordinary English. According to this proposal, it is not a term that belongs to the kind of epistemology that gives an account of what it is for an individual’s beliefs to count as justified. Instead, it is a term that belongs to a kind of dialectical or social epistemology—the theory of what it is to show to an audience that something is the case.

1  The Normativity of Justification The questions that we shall focus on here concern the relationship between “evidence” and “justification”. So, I shall start by saying something about why “justification” seems to be a normative concept and what I take this to imply. Clearly, the word “justified” has a wide range of uses in everyday language. In many contexts, it could be true to say that an act is “morally justified” or that it is “legally justified”. In these contexts, there is something in some sense good or right about the acts that count as justified. So, in these contexts, the term “justified” seems to express a normative or evaluative concept. It seems undeniable that the term has a closely related meaning when we describe attitudes as “justified”—as when we talk of “justified fears” or “justified DOI: 10.4324/9781315672687-8 74

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admiration”. When we talk about “justified belief”, we are simply picking out another example of such a justified attitude. In fact, justification seems to be like a value, in the broadest sense of the term. Justification clearly comes in degrees—one act or one attitude can be more justified than another— and these degrees of justification provide a ranking of the alternative possible attitudes that a believer might have, ranking some of these attitudes as more justified than others. The role of this ranking seems to be to guide the believer’s reasoning towards the attitudes that count as more justified and away from those that are less justified. This seems to be the central role of evaluative concepts, to rank alternatives in an essentially reasoning-guiding way.2 In this way, the term “justified” is a gradable term. Of course, we also use the term “justified” in a non-comparative way, when we say that an act or belief is “justified” simpliciter or without qualification. In saying this, we normally seem to be saying that the act or belief is completely or fully justified—although we often seem to use this notion of a “fully justified” belief or act in a loose or imprecise way so that we often regard it as acceptable to call an act or a belief “justified” even if it is not quite as fully justified as it is possible for an act or a belief to be.3 There also seems to be senses of “ought” that are closely related to every such notion of what is “fully justified”. In such senses of “ought”, the statement that an attitude is unjustified seems to imply that, in a corresponding sense, the agent ought not to have the attitude. Similarly, when an act or an attitude is justified, there is sufficient reason for that act or attitude; and when an act or attitude is unjustified, there is decisive reason against that act or attitude. In these ways, then, the notion of a “justified belief” seems clearly to be a normative concept. The items that can be described as justified or unjustified include both (a) beliefs or doxastic attitudes towards individual propositions and (b) whole belief-systems—where your current belief-system consists of all of the doxastic attitudes that you now have. To keep things simple, in this chapter I shall focus on the justification of whole belief-systems, rather than on the justification of doxastic attitudes towards individual propositions. To fix ideas, I shall also assume a kind of holism about the relationship (if any) that evidence has to the justification of belief-systems. If “evidence” does indeed play a central role in the justification of belief, then the degree to which a believer is justified in having a given belief-system at a time t is determined, or at least constrained, by the total evidence that the believer has at t. Specifically, “justification” seems to be a distinctively agential normative concept: we use it to focus on the situation of an agent or a believer at a time and to evaluate the different possible belief-systems that are available to the believer at that time—ranking some of these belief-systems as fully justified and some of them as less justified than others. To say that a belief-system is “available” to a believer at a time is, roughly, to say that the believer has an opportunity to exercise her capacities at the time in such a way that she has the beliefsystem in question. Contrasting to what is “available” to the agent at the time, there are the facts that it is not available to the agent to change at that time—though any way of availing herself of the opportunities that she has for exercising her capacities at that time. These facts are “fixed” and “beyond the control” of the relevant agent at the relevant time. They constitute the parameters within which the agent can exercise her capacities, by having some belief-system or other. As I shall put it, these facts are simply “given” to the believer at the time.4 75

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In general, this kind of distinction, between the acts or attitudes that are “available” to an agent at a time and the facts about the agent’s situation that are simply “given” to the agent at that time, is a central feature of our use of every agential normative concept. This is just as much the case in our normative evaluation of beliefs as in our normative evaluation of acts. In this chapter, I am going to make a fundamental assumption about such normative evaluations. Specifically, this is the assumption that it is precisely the facts that are “given” to an agent at a time that determine which acts or beliefs are justified for the agent at the time. This assumption is familiar in ethics. When assessing what acts are permissible for an agent in a given situation, we distinguish between the facts about the agent’s situation that are given to her and out of her control, and the various courses of action that are available to her in that situation. The facts about what acts are permissible for the agent, and which are not permissible, are determined by the facts about her situation that are out of her control. This implies that what the agent ought to do cannot depend on what she actually does—it is determined purely by facts that are out of her control (while what she actually does is within her control). If this were not the case, then we could not know what the agent ought to do without knowing what she is going to do. But if the agent already knows what she is going to do, what point could there be in her inquiring into what she ought to do? It would also be hard to rule out strange “Catch-22” situations, in which there are only two available alternatives, A and B, but if one does A, one ought to do B and not A, whereas if one does B, one ought to do A and not B.5 I propose that this principle also applies to the justification of beliefs. The considerations that support the principle in the case of acts seem clearly to carry over to the case of beliefs (and other attitudes as well). In general, then, the beliefs that the believer is justified in having cannot depend on the beliefs that the believer actually has. In general, the degrees of justification of the belief-systems that are available to the believer do not depend on what she actually believes. Instead, they are determined purely by what is “given” to the believer— that is, by facts that are in the relevant way out of the believer’s control. This principle turns out to have fundamental implications for the role of “evidence” in epistemology.

2  Two Views of the Normative Significance of “Evidence” In this section, I shall contrast two different views that epistemologists have held about the normative significance of “evidence”. The first of these views of how “evidence” is related to justification is “evidentialism”. According to the classic formulation of Earl Conee and Richard Feldman (2004, 83), evidentialism is the doctrine that “the epistemic justification of a belief is determined by the quality of the believer’s evidence for the belief”. As Conee and Feldman (2004, 101) make clear, this principle entails a supervenience claim. For any two worlds w1 and w2, if the believer has exactly the same total evidence in both worlds, then for every possible belief-system that the believer could have towards the relevant set of propositions, the believer has exactly the same degree of justification for that belief-system in both of these worlds. If there is any difference between these two worlds with respect to the degree of justification that the believer has for a belief-system in those worlds, the believer must have different evidence in those worlds. 76

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However, as I interpret Conee and Feldman’s formulation, evidentialism is stronger than this supervenience claim. This is because it seems to be part of their formulation that evidentialism implies that the degree to which each of the available belief-systems is justified for the believer at the time not only supervenes on, but is also explained by, the evidence that the believer has at that time. Of course, this kind of evidentialism would be trivially true if all that was meant by the phrase “the evidence that the believer has at t” was “whatever explains the degrees to which the believer is justified in having each of available belief-systems at t”. If evidentialism is to be a non-trivial truth, it must employ some other sense of the term “evidence”. The second view about the relationship between “evidence” and justification is weaker than full-blown evidentialism. According to this weaker view, evidence does not fully determine the degree to which we are justified in having each available belief-system; instead, it imposes constraints on which available belief-systems can be fully justified. Perhaps the clearest example of this weaker view of the normative significance of “evidence” is provided by so-called subjective Bayesianism.6 It is important to see that most subjective Bayesians are not “evidentialists” in Conee and Feldman’s sense. One of the key elements of all Bayesian approaches to epistemology is the idea of a probability function. To keep things simple, I shall focus only on versions of Bayesianism according to which, for every believer and every time during that believer’s mental life, there is a unique probability function that corresponds to the belief-system that the believer is fully justified in having at that time. In general, on this view, the degree to which each of the available alternative belief-systems is justified for the believer at this time corresponds to the degree to which the belief-system approximates to this probability function. According to subjective Bayesians, the “evidence” that the believer has at time t consists of a body of propositions. This evidence imposes a constraint on which belief-system is fully justified for the believer at t. In particular, all the evidence-propositions have probability 1, and so all belief-systems that the believer is perfectly justified in having must involve the highest level of credence in these propositions. In this way, evidence imposes a constraint on fully justified belief-systems: fully justified belief-systems must respect the evidence in this way. However, when it comes to the other propositions that the believer has attitudes towards, subjective Bayesians do not accept that the levels of credence in those other propositions that are fully justified for the believer at the time are determined purely by the evidence that the believer has at that time. Most subjective Bayesians think that the prior credences that the believer had before this time are also part of what determines which belief-systems are justified for the believer at this time. More precisely, these Bayesians hold that there is a probability function P0(•) that in some way corresponds to the prior credences that the believer had at the earlier time t0; and the new probability function P1(•) that corresponds to the beliefsystem that the believer is fully justified in having now is P0(•|e), the result of conditionalizing that old probability function P0(•) on e, the conjunction of all the evidence that the believer has acquired since t0. So, according to these Bayesians, the truth about the belief-systems that are fully justified for you now does not supervene on the evidence that you now have. Another believer could have exactly the same evidence as you have, but—thanks to the other believer’s having different prior credences—the belief-systems that are fully justified for the other believer now could be quite different from those that are fully justified for you now. 77

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The only Bayesians who count as “evidentialists”, in the sense in which I am using the term here, are those who think that nothing other than the believer’s evidence makes any difference to how justified each of the available belief-systems is for the believer at the time. Some of these Bayesian evidentialists may take the maximally permissive view that any system of credences is fully justified, so long as it is probabilistically coherent and assigns credence 1 to every proposition that is part of the evidence. On this maximally permissive view, a system of beliefs and credences can be fully justified even if does not correspond to the result of conditionalizing any probability function that corresponds to the believer’s prior credences on the believer’s evidence.7 Other evidentialists might opt for so-called objective Bayesianism. According to objective Bayesianism, there is a special privileged Ur-prior probability function that all believers should ideally start out from before they acquire any evidence at all. In various different ways, this idea of a special privileged “logical probability” or “evidential probability” has been explored by J. M. Keynes, Rudolf Carnap, and Timothy Williamson.8 Typically, these objective Bayesians also appeal to conditionalization. However, they do not appeal to the idea of conditionalizing a probability that corresponds to the believer’s prior credences. Instead, they appeal to the idea of conditionalizing this special privileged Ur-prior probability function. In their view, the probability function that corresponds to the belief-systems that are fully justified for the believer at the time is the result of conditionalizing this special Ur-prior on the total evidence that the believer has at that time. However, the very idea of a special privileged Ur-prior probability function of this sort is intensely controversial among Bayesian epistemologists.9 For this reason, most Bayesians who are unhappy with the maximally permissive view say that the degrees to which the available belief-systems are justified for the believer now are determined in part by the believer’s past credences, and not just by the believer’s evidence. In this way, as we have seen, these subjective Bayesians are committed to rejecting evidentialism. We thus have two views of the normative significance of “evidence”: the strong evidentialist view that evidence determines the full truth about how justified the available beliefsystems are, and the weaker view that evidence constrains what belief-systems are justified. But this has not yet explained what the term “evidence” means in the context of epistemological theories that give “evidence” to either of these two kinds of normative significance. In what follows, I shall explore three interpretations of the term “evidence”. First, in the next two sections (Sections 3 and 4), I shall look at two technical senses that the term “evidence” could express in these contexts. In principle, there is no objection to stipulating that we are using any term with either of these technical senses. Moreover, each of these two technical senses of the term clearly allows the term to play one of the two normative roles that I have just described. As I shall show, however, neither of these technical senses for the term can be easily reconciled with all the linguistic intuitions that arise from our grasp of the everyday meaning of “evidence”. As a result, philosophers who use the term in this technical sense are easily led by these linguistic intuitions to endorse some highly questionable conclusions about justified belief. Then, in Section 5, I shall examine the everyday meaning of the word “evidence”. As I shall argue, it is even more problematic to combine this everyday meaning of the word “evidence” with either of the two views of the normative significance of “evidence” that I have canvassed earlier. Finally, in Section 6, I shall offer an alternative account of the word “evidence” in everyday English. “Evidence” in everyday English, I suggest, is fundamentally a dialectical and not an epistemological term. Roughly, “evidence” is what we can use in a 78

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given context to prove or to show that something is the case to a certain audience. If this is the correct interpretation of the word “evidence” in English, it will only invite confusion to make the term central to an account of the justification of an individual believer’s beliefs.

3  Evidence as What Is “Given” In the previous section, I  canvassed two views about the normative significance of “evidence”. In this section, I consider one technical sense in which the word “evidence” might be used, within the context of the theories that incorporate those views. Specifically, one meaning that the word “evidence” could express is the notion of what is, in the sense that I introduced in Section 1, “given” to the believer. This notion of what is “given” to the believer has clear normative significance. As we have seen, what is “given” to the believer at the time is precisely what determines which belief-systems are justified for the believer at the time. So, if we use the word “evidence” simply to stand for what is “given” in this sense, the strong evidentialist view of the normative significance of “evidence” is defensible: the “evidence” that you now have not only constrains which belief-systems are now justified for you but determines the full truth about which belief-systems are justified for you now. In saying that it is what is now “given” to you that determines the degrees to which the available belief-systems are justified for you now, I intend to remain neutral about which are the relevant facts that are “given”. That is, I intend to remain neutral about which of the facts that are out of the believer’s control at the relevant time that determine these available belief-systems’ degrees of justification. The relevant facts that are “given” might include external facts about the believer’s environment; or they might be restricted to internal facts about the believer’s mental states. In this way, the view that the facts about justification are determined by the “given” is compatible with both internalist and externalist views of justification. However, as we have already seen in Section 1, the facts that are now “given” to you cannot include any facts about the beliefs and credences that you now have. The beliefs and credences that you now have are within your control at the time. Thus, the facts about what beliefs and credences the believer has at this time do not themselves form part of the “given”. It is precisely these beliefs and credences that are assessed as more or less justified, on the basis of their relation to the “given”. One view of the relevant facts that are “given” to a believer at a time is the view that is held by most subjective Bayesians. On this view, the “given” includes facts of the following two kinds: 1. First, it includes facts about the sensory perceptions and similar non-doxastic states that the believer has at the time—that is, the mental states that impinge exogenously on the believer’s belief-system from outside. Since these mental states do not arise from any exercise of our reasoning capacities, and are incapable of being revised through reasoning, it seems plausible that they are in the relevant sense “out of the believer’s control”.10 2. Secondly, the “given” also includes some facts about the believer’s past mental life— which are no longer within the believer’s power to change through the way in which she uses her reasoning capacities at that time. Moreover, on this subjective Bayesian view, some facts about the believer’s past can be part of the “given” even if the believer is no longer aware of these facts. 79

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At the very least, it should be an open question whether this subjective Bayesian view of the “given” is correct. So—if the meaning of the word “evidence” is a way of referring to what is “given”—it should also be an open question whether one’s “evidence” includes facts of these two kinds. However, our linguistic intuitions about the word “evidence” make it hard for us to use the word to express this notion of the “given”. It is an open question whether what is now “given” in this sense includes facts about the past—such as facts about the prior credences that one had before now—even if one is no longer aware of these facts. But, given our intuitions about the everyday meaning of “evidence”, it seems bizarre to say that the attitudes that one had in the past are part of one’s current “evidence” if one is no longer aware of what these attitudes were. In general, it seems irresistible to suppose that the “evidence” that one possesses now is determined by some mental states that one has now. But two believers could have the same mental states now even if they had different attitudes in the immediate past. It seems, then, that these two believers have the same evidence now, even though they differ with respect to what is “given to them”. A clear illustration of this feature of the meaning of the word “evidence” is provided by the arguments that David Christensen (1994) and Abelard Podgorski (2016) deploy against the “conservative” view that we are normally rationally entitled to continue to hold the beliefs that we held in the past, so long as we lack any positive reason to doubt those beliefs. According to Christensen (1994, 69), this kind of epistemological conservatism implies that “an agent is in some measure justified in maintaining a belief simply in virtue of the fact that the agent has that belief”. He accepts that in certain cases, “the fact that one believes a proposition can help provide evidence that the proposition is true”. However, he thinks that this is clearly not true in general: there are cases in which the fact that one believed a certain proposition p in the past is not part of the evidence either for or against believing p now— even if in these cases it is psychologically quite possible for one to exhibit a kind of doxastic inertia and simply continue having the kind of doxastic attitude that one had in the past.11 Picking up on Christensen’s reflections, Podgorski (2016, 354) assumes that this kind of epistemological conservatism implies that the “mere fact that one already believes p can positively affect whether p is worth believing in a non-evidential way.” In this way, Podgorski assumes that the fact that one believed p in the immediate past does not in itself count as part of the evidence that can “positively affect” the rationality of continuing to believe p. As I claimed earlier, it is at least an open question whether facts about your past credences form part of what is now “given” to you. But our linguistic intuitions about the word “evidence” strongly encourage us to deny that these facts can be part of your current evidence. Thus, it seems that we should not use the word “evidence” to refer to what is given. Some other sense for the term “evidence” must be found, if it is to have the kind of normative significance that it is typically assumed to have.

4  Evidence as What Is “Evident” An alternative interpretation of “evidence” is as what is evident. As I shall use the term, it makes sense to make statements of the form “It is evident that p”; so I shall assume that (as I am using the term here) everything that is “evident” is a proposition. We do not need to worry here about what exactly makes a proposition “evident” in this sense; my arguments will be compatible with many different accounts of this. What we 80

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need is that the assumption that propositions that are “evident” in this sense are—more precisely—maximally evident. So, it is plausible that, if p is in this sense “evident” to you now, then every belief-system that counts as fully justified for you now must involve being maximally confident of p now. In this way, this sense of “evidence” clearly supports the weaker of the two views of the normative significance of “evidence” that I outlined in Section 2: in this sense, the “evidence” that you now have constrains the belief-systems that are fully justified for you now—in the sense that that every such fully justified belief-system must respect this evidence, by involving an attitude of maximum confidence towards all propositions that form part of this evidence. Within a probabilistic framework, for every believer and every time within that believer’s mental life, there is a probability function that in some way corresponds to the beliefsystem that is fully justified for the believer at this time. So, if a probabilistic framework of this sort also uses the word “evidence”, in the sense that we are focusing on in this section, then whenever a proposition p is part of your current evidence, p has probability 1 (according to the probability function that corresponds to the belief-system that is fully justified for you now). In short, every proposition that is part of the believer’s evidence has probability 1. One philosopher who seems to work with this conception of evidence is Timothy Williamson. Famously, Williamson (2000, Chapter 9) defends “E = K”, the principle that your present evidence consists of all and only those propositions that you now know. Moreover, he also adopts a version of the strong evidentialist view that the evidence that you now have determines which belief-systems are justified for you now. Specifically, Williamson (2000, Chapter 10) postulates a special privileged Ur-prior probability function P(•), and proposes that the “evidential probability” that any proposition q has for you now is P(q|E), the result of conditionalizing this special privileged function on E, the conjunction of the total evidence that you now have. This guarantees that every proposition that you know has evidential probability 1 for you now. Since he seems to accept that fully rational believers proportion their belief in every proposition p to p’s evidential probability, it follows that every fully rational believer has maximum confidence in every proposition that they know. In that sense, Williamson’s conception of evidence seems in line with the idea that evidence is what is “evident”. On the face of it, however, it seems extremely implausible to say that every proposition that I know is “evident” in this sense. For example, I know that Dushanbe is the capital of Tajikistan. But it would surely not be fully justified for me to be just as confident of this proposition as of the proposition that 1 + 1 = 2. The only fully justified attitudes for me to have towards these two propositions involve my being less confident that Dushanbe is the capital of Tajikistan than that 1 + 1 = 2. So, it would not be fully justified for me to be maximally confident that Dushanbe is the capital of Tajikistan—even though this is a proposition that I know. Suppose, then, that propositions such as that Dushanbe is the capital of Tajikistan are for this reason not included in my current evidence. Then my current evidence will have to include many fewer propositions than all propositions that I currently know. This in turn casts doubt on the strong evidentialist view that the evidence is enough by itself to determine the full truth about what belief-systems are justified for me now. For my purposes, however, I need not assume that those who use the term “evidence” in this second technical sense must adopt this strong evidentialist view. I shall assume only that they accept the weaker of the two views of the normative significance of evidence that 81

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I canvassed in Section 2—the view that the evidence that you now have constrains which belief-systems are fully justified for you now. Nonetheless, as I shall now argue, there is a problem with combining this weaker evidentialist view with the sense of “evidence” that we are focusing on in this section. The problem is that, given the everyday meaning of the word “evidence”, it seems extremely plausible to assume that acquiring evidence is a perfectly ordinary and familiar cognitive event—not just an event of a kind that happens all the time, but also an event that we are often aware of when it occurs. In short, the acquisition of evidence is an ordinary kind of learning event. Given this assumption, considerations of theoretical simplicity and economy encourage the further conclusion that all learning events take the form of the acquisition of evidence. If we assume that many ordinary learning events take the form of the acquisition of evidence, the best way to give a unified account of learning would be to accept that all learning consists in the acquisition of evidence. However, given this second technical sense of the term “evidence’ ” this further conclusion has an extremely controversial implication. Specifically, it implies that all learning is learning with certainty: this is because on this view, all learning takes the form of acquiring evidence, and “evidence” is effectively defined to consist of propositions that have probability 1. Many formal epistemologists accept the implication that all learning is learning with certainty.12 However, it is well known that this implication is highly controversial. Richard Jeffrey (1983, 165) famously argued that not all learning is learning with certainty. Jeffrey’s memorable example involves the experience of examining a piece of cloth by candlelight. Consider the propositions that the piece of cloth is green, and that the piece of cloth is blue. Jeffrey suggests that in this case, the experience may change the probabilities of these propositions without giving either of these propositions probability 1. Instead, Jeffrey proposed a different conception of learning, which is now generally known as “Jeffrey conditionalization”. On this conception, learning events are events that impinge on what is justified for the believer from outside; that is, these learning events impinge exogenously on the probability function that corresponds to the belief-system that is fully justified for the relevant believer at the relevant time. But these learning events need not require that any propositions should have their probability raised all the way to 1. The only general correct account of these learning events is that they impose new constraints on the probability function: certain propositions have their probability changed by this learning event, and so-called Jeffrey conditionalization identifies a plausible way to retain as much as possible of the old probability function while shifting to a new probability function that meets these constraints. In this way, Jeffrey’s account represents a radical shift away from any appeal to “evidence”, in the sense that we are concerned with in this section. On Jeffrey’s account, learning events need not involve anything’s becoming certain or evident. In that sense, they need not involve acquiring any “evidence” at all. On reflection, the suggestion that all learning is learning with certainty seems extremely dubious. Indeed, it is even doubtful whether we ever learn anything with maximum ­certainty—or, if we do, whether it is more than an utterly peripheral and marginal phenomenon. Thus, in the sense that we have been exploring in this section, it is doubtful whether the acquisition of “evidence” is more than an utterly marginal phenomenon. The fact that the everyday sense of “evidence” so strongly encourages the dubious assumption that it is a central and non-marginal phenomenon is a weighty reason not to use the word “evidence” in this sense. 82

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5  The Everyday Sense of “Evidence” The problems with these technical senses of “evidence” may suggest to some philosophers that it would be better to fall back on the sense that the word “evidence” has in everyday English. In this section, I shall argue that this approach faces even more severe problems than the approaches that we have considered so far. Strictly, in everyday English, much of our “evidence” might consist of physical objects— for example, a handwritten letter, or a line of footprints in the snow. I shall follow most epistemologists in allowing myself to regiment everyday English to the extent of restricting the evidence to propositions—including true propositions, which I shall assume to correspond in some way to facts.13 On this regimentation of everyday English, we shall say that the evidence does not strictly include the bloody knife itself, but the true proposition that the knife was covered in blood, and so on. Apart from this regimentation, however, I shall aim in this section to use the word “evidence” with the meaning that it has in everyday English. Some philosophers, following Williamson (2000), accept the thesis that, in everyday English, the “evidence” that you now have must consist of certain propositions that you now know. On this thesis about the meaning of “evidence”, both the facts that constitute your “evidence” and the facts that constitute your possession of that evidence fail to include many of the facts that, on a view like subjective Bayesianism, count as “given” to you. For example, facts about your nondoxastic states, such as your sensory experiences and episodic memories, and facts about your past beliefs, do not belong to your “evidence” unless you know these facts; but there seem to be many facts of this sort that you do not actually know. As we have seen, Williamson (2000) also accepts the strong evidentialist view that the degrees to which each of the available belief-systems counts as justified is wholly determined by your evidence. Thus, he is committed to denying that any of these facts—such as facts about one’s non-doxastic states and one’s past beliefs—play any role in determining what one is justified in believing unless one knows these facts. This raises an obvious concern about Williamson’s view: what one knows is simply too impoverished a basis to determine the full truth about the beliefs and credences that one is justified in having. It seems clearly possible for there to be two believers who know exactly the same set of propositions, and yet differ with respect to the levels of credence that are justified for them. This could be because these two believers have sufficiently different prior credences, or because their sensory experiences are sufficiently different so that they justify slightly different levels of credence in certain propositions (without making any difference to which propositions are known). In general, combining evidentialism with the thesis that all evidence-propositions must be known seems to overestimate the centrality of knowledge in our mental lives. Even if states of knowledge are an important and central part of our mental lives, rational thinking also involves a large number of other mental states and mental events. It is doubtful whether the rational significance of these other mental phenomena can be captured by the rational significance of knowledge alone. In this section, however, I shall not rely on Williamson’s strong thesis about the meaning of “evidence”—the thesis that your possession of all of the evidence that you now have is constituted by your knowledge of certain truths. Instead, I shall rely on a weaker assumption about the everyday meaning of “evidence”—specifically, the assumption that your possession of at least some of the evidence that you now have is constituted by your having certain beliefs. 83

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Many philosophers reject Williamson’s strong thesis. For example, Schroeder (2021, Chapter 5) insists that your possession of some of the evidence that you now have is not constituted by your knowledge of any proposition, but simply by your having an appropriate perceptual experience. But even Schroeder (2021, Chapter 4) assumes that your possession of some of the evidence that you now have is constituted by your having certain beliefs. Specifically, according to Schroeder, the kind of belief that constitutes your possession of this evidence is the kind of belief that can be called “full” or “outright” belief; this is the kind of belief that involves simply taking the proposition in question for granted—as some philosophers would say, simply treating it as true (rather than merely as probable) for all normal purposes.14 In the following section, I shall propose a general account of the meaning of the word “evidence” in English. This general account will explain why this assumption is true—that is, it will explain why it is true to say, in the relevant contexts, that your possession of at least some of the evidence that you now have is constituted by your having certain beliefs. In this section, however, I  shall just rely on the intrinsic plausibility of this assumption. Given that it is so widely endorsed by philosophers, relying on this assumption should not be too controversial here. However, as I shall now argue, there are still two serious problems with combining this assumption about “evidence” with either of the views about the normative significance of evidence that we canvased in Section  2. According to this assumption, the facts that constitute the believer’s possession of evidence include certain beliefs that the believer has at that time. The first problem is simply that, on this assumption, the facts that constitute the believer’s possession of evidence include facts about some of the very attitudes whose justification is in question. In general, as I argued in Section 1, the beliefs that you now have are not part of what is now “given to you”: they are part of what is assessed as justified or unjustified, on the basis of the facts that are now given to you. This is true of all of your current beliefs: all of your current beliefs are justified or unjustified to some degree, in a way that is determined by the relevant facts that are given to you. Thus, if your possession of some of the evidence that you now have is constituted by some of the beliefs that you now have, then to claim that it is your “evidence” that determines or constrains what belief-systems are justified for you is to invert the real order of explanation. On this interpretation of “evidence”, at least some of the facts that constitute your possession of “evidence” are not part of what is given—which is what really determines and explains constraints on what is justified—but are facts about the doxastic attitudes whose justification is in question. In other words, the fact that your total present evidence is E is not one of the facts that is “given”. Rather, the fact that E is your total present evidence is, in part, a fact about the beliefs that you now hold; and all such beliefs can be evaluated as more or less justified. Thus, it is just not the sort of fact that can explain the constraints on what we are justified in believing: it is precisely a fact about the doxastic attitudes that count as justified only if they meet those constraints. In addition, there is also a second problem: any view that gives “evidence” a special normative role is in effect a form of foundationalism. It seems undeniable that not every proposition that you have a doxastic attitude towards counts as part of your evidence. In particular, propositions in which you have a credence that is lower than 0.5 surely do not count as part of your evidence.15 So, given the everyday sense of “evidence”, your possession of the “evidence” that you now have is constituted by some but not all of your current 84

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doxastic attitudes. Thus, we are committed to an invidious distinction between two classes of doxastic attitudes: 1. There are “superior” doxastic attitudes that constitute your possession of evidence. 2. There are “inferior” doxastic attitudes that do not constitute your possession of evidence. On both of the two views about the normative significance of evidence that we are discussing here, your evidence is at least one of the sources of the justification that you have for beliefs. So, according to both of these views, whenever every belief-system that is fully justified for you involves a certain attitude towards a certain proposition p, we may say that that attitude towards p is “supported” by this evidence. Thus, the invidious distinction between the “superior” beliefs that constitute your possession of evidence and the “inferior” beliefs that do not constitute your possession of evidence corresponds to an equally invidious distinction between two kinds of evidential “support”. The “superior” beliefs are “supported” by the evidence in a trivial way—simply because they are beliefs of the appropriate sort in propositions that themselves form part of the evidence. By contrast, the “inferior” beliefs are supported by the evidence in some more indirect way—for example, perhaps because they can be inferred from this evidence by means of an appropriate inference. It is clear that this two-tier view is a form of foundationalism: on this view, the “superior” beliefs that constitute your possession of evidence have a kind of basic or nonderivative justification, while the “inferior” beliefs that do not constitute your possession of evidence have a derivative kind of justification—a kind of “inferential justification” or the like. This sort of foundationalism should surely be viewed as controversial. Even if it is not obviously mistaken, we should consider whether an alternative account of justification may be true. For example, according to one such alternative account, all of our beliefs are justified in fundamentally the same way: specifically, every doxastic attitude is justified, not as a particular attitude towards a particular proposition, but as a member of the entire beliefsystem of which it is a part; and the whole belief-system is justified both (a) by its internal coherence and (b) by its fitting in the right way with the facts about what is “given” to the believer at the time (such as facts about the sensory experiences and episodic memories that the believer has at that time, and about the prior credences that she had in the past before that time). If this alternative account is correct, foundationalism is mistaken in drawing an invidious distinction between two tiers of beliefs or doxastic attitudes—with the superior tier having a kind of primary justification and the inferior tier depending for its justification on having the right kind of support from the superior tier. As we have seen in this section, both views of the normative significance of evidence, when combined with the meaning that “evidence” has in everyday English, seem committed to this sort of foundationalism. But this sort of foundationalism should surely be regarded as highly controversial. Thus, the idea that “evidence”, in anything like the everyday meaning of the word, has normative significance in either of these two ways should be viewed as equally controversial. We should not allow ourselves to make use of the term “evidence” until we have assured ourselves that this controversial sort of foundationalism is true.

6  The Language of “Evidence” Here is a hypothesis about what has misled the epistemologists who rely so heavily on the term “evidence”. They have made a mistake about the meaning that the term has in 85

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everyday English. The central use of this term in everyday English, I propose, is rather different from the way in which it is used in these philosophical discussions. In fact, very few languages actually have a word whose meaning corresponds to that of the English word “evidence”. Neither the French word évidence nor the German word Evidenz means “evidence”; rather, they both refer to the property of being evident. I suggest that the best interpretation of the term “evident” in English is that it is a context-sensitive term, meaning something similar to terms like “clear” and “obvious”. Thus, for a proposition to count as “evident” in a given context is, roughly, for it to be open or available to be easily known by all the relevant participants in that context. While few languages have a word that corresponds to the English word “evidence”, every language known to me has words that correspond to “evident” or “clear” or “obvious”. Similarly, every language known to me also has a verb that means to show or demonstrate that something is the case. To “show” to an audience that some proposition p is the case is to make p evident or clear to that audience—that is, to make p open or available to be easily known by that audience. Although the term “evidence” originally meant what évidence means in French—namely, the property of being evident—this sense became obsolete at some point in the 19th century.16 Instead, as early as medieval times, the English word “evidence” was used to refer to documents, testimonies, or pieces of information that support an answer to some disputed question in law or theology or the like. In contemporary English, it seems that the primary meaning of “evidence” refers to what makes it evident that something is the case. Many philosophers have recognized that this is the core meaning of “evidence”. As Thomas Kelly (2016) puts it, “a central function of evidence is to make evident that which would not be so in its absence.”17 However, what these philosophers have missed is that, in its primary sense in everyday English, “evidence” refers to what makes something “evident”, not in the individualistic sense of being clear or obvious to an individual believer, but in a social and public sense. In general, in this primary sense, “evidence” is whatever can be used to show or to prove that something is the case to an audience.18 Thus, this primary sense of the term is not fundamentally epistemological, but dialectical—it is concerned not with the interior process of forming, revising, or maintaining beliefs but with the interpersonal process of showing that something is the case to an audience. Admittedly, in philosophical English, the term “evidence” has come to be used for rational grounds for belief. For example, it seems to have this sense when Thomas Reid (1785, 271) says: “We give the name of evidence to whatever is a ground of belief.” This use of the term seems to have come about through modelling the interior process of belief formation on the external dialectical process of showing that something is the case to an audience.19 Although this sense of “evidence” as “rational grounds for belief” exists, it seems to me that, in ordinary English, the term is still most commonly used in its dialectical sense. These are contexts in which there is a collective discussion about what is the case—such as in police investigations, legal proceedings, or scientific or scholarly debates. In these contexts, there is a question on which the participants in the conversation are trying to reach a collective answer, and certain other propositions are treated as belonging in the “common ground”—that is, as truths that all participants in the conversation are in a position to have common knowledge of. Some of these propositions in the “common ground” are of interest because they can be used to evaluate answers to the question that is under consideration; 86

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it is these propositions that are called “evidence”. The goal in any such dialectical context is to achieve a rational consensus about the question under consideration, and to do so by means of relying on the propositions that are treated in the context as “evidence”. If this is how the term is most commonly used in ordinary English, it seems that for a proposition to count as part of the “evidence” in a given context, the proposition must belong to the “common ground” in that context. It follows that what counts as “evidence” in the context of one conversation may not count as evidence in the context of another. When you are speaking to one audience, you may treat the fact that the earth is not flat as part of the evidence; in another context, when speaking to another audience, you could not treat the fact that the earth is not flat as part of the evidence, but rather as something that has to be shown on the basis of other evidence.20 If this account of the meaning of the word “evidence” is on the right lines, it can explain why it seems plausible, at first glance, to make “evidence” central to the epistemology of rational belief. Rational forming a belief can seem in important respects like an interiorized version of this sort of dialectical process of showing or proving something to an audience. Since we typically rely on evidence when we show something to be the case to an audience, it may seem undeniable that, in just the same way, we typically rely on evidence in rationally forming beliefs. This account can also explain why, when the word “evidence” comes to be used in epistemology in this way, the everyday meaning of the word makes it virtually irresistible to accept the assumption that I relied on in the previous section—that your possession of at least some of your evidence that you now have is constituted by some of your beliefs. In the dialectical sense, evidence must belong to the “common ground”; and so, in this sense, evidence typically consists of facts about the publicly observable world. But how can such publicly observable facts be part of the “common ground” within an interiorized process of showing something to be the case to oneself? By far the easiest way of making sense of how such a publicly observable fact can be part of one’s interior “common ground” is if one believes it. On closer inspection, however, it is clear that there are some profound differences between (a) rational believing and (b) the dialectical process of showing something to an audience. What we show to an audience is almost always a single proposition (or at most a small set of propositions). Moreover, in showing something to an audience, we typically rely not just on the evidence that we explicitly draw attention to but also on a vast host of implicit shared background beliefs and presuppositions—where most of these shared background beliefs and presuppositions count, at least normally, as knowledge. It would be obviously impossible simultaneously to show everything that one knows to any audience. By contrast, the notion of rational or justified belief that we are focusing on here is quite different. It is a broader notion that can apply to all of the beliefs that one holds at a given time, including those that are far from the forefront of one’s mind, and form part of the body of background beliefs on which we implicitly rely in performing conscious tasks like showing something to be the case. It is this broader notion that is central to the epistemological study of what it is for an individual’s beliefs to count as justified. This is not to say that the dialectical phenomenon of using “evidence” to “show” something to an audience is philosophically unimportant. On the contrary, it is a crucial aspect of social life. Indeed, one of the main ways in which we—as a whole community—can get to know scientific or historical truths or the like is by having these truths shown, on the basis of evidence, to appropriate groups within our community. This notion of social 87

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knowing is crucial, and clearly deserving of philosophical exploration.21 However, most of the epistemologists who appeal to “evidence” are not studying this notion of social knowing; instead, they are studying what it is for individuals’ beliefs to count as justified. If I am right, the notion of “evidence” really belongs in theories of social knowing, and not in theories of what it is for an individual’s beliefs to count as justified.

7 Conclusion As I have argued, the role that the evidentialists have ascribed to the “evidence” that you now have—the role of determining the degree to which each of the available belief-systems is justified for you now—is really played by something else. This role is played by what I have called “the given”. However, given the meaning of the word “evidence” in everyday English, your possession of some of the “evidence” that you now have is constituted by your current beliefs; but, as I have argued, facts about your current beliefs cannot be part of the “given”. In general, “evidence” is a dangerous term to use in epistemology. Because its primary everyday meaning is dialectical rather than epistemological, it gives rise to linguistic intuitions that are liable to lead epistemologists astray. In giving a theory of what it is for an individual’s beliefs to count as justified, we are better off without it.

Notes   1 Even Schroeder (2021), who insists that the reasons that determine whether or not it is rational to believe a proposition p do not all consist of evidence either for or against p, gives a prominent role to “evidence” and assumes that evidence for p always counts as a reason in favour of believing p.   2 For this way of thinking of evaluative concepts, see Wedgwood (2017).   3 For an illuminating defence of this view of “justified” as a so-called absolute gradable term, see Siscoe (2021).   4 This terminology may be found distasteful by followers of Wilfrid Sellars (1956), such as McDowell (1996). But I am not using the term “given” here in the same sense as is used in Sellars’s criticisms of the “myth of the given”. In the terminology of McDowell (1996, 31), what is “given” to the believer at a time t would be described as what the believer is “passively saddled with” at t.   5 In ethics, this is known as the principle of “normative invariance”. For discussions of this principle, see Carlson (1995, 101–102) and Bykvist (2007). For an early statement of this principle, see Prichard (2002, 99), who wrote in 1932: “the existence of an obligation cannot possibly depend on actual performance of the action.”   6 For a classic presentation of subjective Bayesianism, see Jeffrey (2004).   7 For an example of such a permissive view, see Van Fraassen (1984).   8 For different versions of the idea of probability as a “logical” notion, see Keynes (1921) and Carnap (1950). For an objective notion of “evidential probability”, see Williamson (2000).   9 Subjective Bayesians have been sceptical of this idea of a special privileged Ur-prior ever since Ramsey’s (1931) famous criticism of Keynes (1921). 10 For an illuminating explanation of the significance of the distinction between the mental states that are fixed in “central cognition” and those that consist in the operation of “modular” cognitive capacities, see Wilson (2022). 11 See Christensen (1994, 74f.). 12 For example, Williamson (2000) assumes that all learning involves the acquisition of knowledge, and every known proposition has probability 1. Similarly, Titelbaum (2012) is content to “model” all cases of learning as consisting in certain sentences coming to be “certain”. 13 For this point, see Williamson (2000, 194). 14 For this sort of view of “outright belief”, see Wedgwood (2012).

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How Can “Evidence” be Normative? 15 Schroeder (2021, Chapter 4) argues that even unjustified beliefs and beliefs in false propositions can constitute your possession of evidence, but even he does not argue that propositions in which you have a credence that is lower than 0.5 can be part of your evidence. 16 When Hume (1748, 10.4) says that “A wise man proportions his belief to the evidence”, I am inclined to read him as using the term “evidence” in the now obsolete sense of the proposition’s degree of evidentness—though unfortunately this is not the place to show that this is the right reading of this passage. 17 For this idea that evidence is what makes something evident, see also Rysiew (2011). 18 See the entry for “evidence” in the two most recent editions of the Oxford English Dictionary (1989, 2021). 19 This is the earliest clear occurrence of “evidence” in this sense that I have found. In my judgment, it is far from obvious that any of the earlier occurrences given in either of the two most recent editions of the Oxford English Dictionary (1989, 2021) must be interpreted as referring to the internal process of belief formation, as opposed to the dialectical process of showing something to be the case to an audience. 20 In some of my earlier work (Wedgwood 2020), I argued the correct theory of the meaning of the word “knowledge” is contextualist. If each proposition that counts as “evidence” in a context must be part of the “common ground”, in the sense that it must be true in the context to say that all participants are in a position to have “common knowledge” of that proposition, then “evidence” will inherit the context-sensitivity of “knowledge”: the correct theory of the meaning of “evidence” will also be contextualist. 21 For example, Bird (2022) defends a view of science as aiming at a kind of “social knowing”, in which supporting scientific theories on the basis of “evidence” plays a central role. I believe that everything that I say here is compatible with the central claims of Bird’s conception of science.

References Bird, Alexander (2022). Knowing Science (Oxford: Oxford University Press). Bykvist, Krister (2007). “Violations of Normative Invariance: Some Thoughts on Shifty Oughts”, Theoria 73 (2): 98–120. Carlson, Eric (1995). Consequentialism Reconsidered (Dordrecht: Kluwer). Carnap, Rudolf (1950). Logical Foundations of Probability (Chicago: University of Chicago Press). Christensen, David (1994). “Conservatism in Epistemology”, Noûs 28 (1): 69–89. Conee, Earl, and Feldman, Richard (2004). Evidentialism: Essays in Epistemology (Oxford: Oxford University Press). Hume, David (1748). An Enquiry Concerning Human Understanding (London). Jeffrey, Richard C. (1983). The Logic of Decision, Second edition (Chicago: University of Chicago Press). ——— (2004). Subjective Probability: The Real Thing (Cambridge: Cambridge University Press). Kelly, Thomas (2016). “Evidence”, in The Stanford Encyclopedia of Philosophy, ed. Edward N. Zalta . Keynes, J. M. (1921). A Treatise on Probability (London: Macmillan). McDowell, John (1996). Mind and World, with a New Introduction (Cambridge, MA: Harvard University Press). Oxford English Dictionary (1989). s.v. “evidence, n.”, second edition. Oxford English Dictionary (2021). s.v. “evidence, n.”. Podgorski, Abelard (2016). “Dynamic Conservatism”, Ergo 3 (13): 349–376. Prichard, H. A. (2002). Moral Writings, ed. Jim MacAdam (Oxford: Oxford University Press). Ramsey, F. P. (1931). “Truth and Probability”, in The Foundations of Mathematics and Other Logical Essays, ed. R. B. Braithwaite (London: Routledge and Kegan Paul). Reid, Thomas (1785). Essays on the Intellectual Powers of Man (Edinburgh: John Bell). Rysiew, Patrick (2011). “Making It Evident: Evidence and Evidentness, Justification, and Belief”, in Evidentialism and Its Discontents, ed. Trent Dougherty (Oxford: Oxford University Press): 207–225.

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Ralph Wedgwood Schroeder, Mark (2021). Reasons First (Oxford: Oxford University Press). Sellars, Wilfrid S. (1956). “Empiricism and the Philosophy of Mind”, Minnesota Studies in the Philosophy of Science 1: 253–329. Siscoe, R. W. (2021). “Belief, Rational and Justified”, Mind 130 (517): 59–83. Titelbaum, Michael G. (2012).  Quitting Certainties: A  Bayesian Framework Modeling Degrees of Belief (Oxford: Oxford University Press). van Fraassen, Bas (1984) “Belief and the Will”, Journal of Philosophy 81 (5): 235–256. Wedgwood, Ralph (2012). “Outright Belief”, Dialectica, 66 (3), Special Issue: Outright Belief and Degrees of Belief, ed. Philip Ebert and Martin Smith: 309–329. ——— (2017). The Value of Rationality (Oxford: Oxford University Press). ——— (2020). “The Internalist Virtue Theory of Knowledge”, Synthese 197: 5357–5378. Williamson, Timothy (2000). Knowledge and Its Limits (Oxford: Oxford University Press). Wilson, Jesse (2023). Cognitive Boundaries for Rational Coherence Requirements, PhD dissertation (Los Angeles: University of Southern California).

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PART 2

Evidence and Probability

7 VARIETIES OF MEASURES OF EVIDENTIAL SUPPORT* Peter Brössel

1 Introduction It is nowadays standard to explicate evidential or confirmational support within Bayesian epistemology. As Strevens (2008: 5) puts it: The popularity of the Bayesian approach is due to its flexibility, its apparently effortless handling of various technical problems, the existence of various a priori arguments for its validity, and its injection of subjective and contextual elements into the process of confirmation in just the places where critics of earlier approaches had come to think that subjectivity and sensitivity to context were necessary. Bayesian epistemology presupposes that rational reasoning in general and notions of evidential or confirmational support, in particular, are best captured in terms of probabilities. Bayesian epistemology distinguishes two qualitative conceptions of support. Both are simple, formally precise, and fruitful in various contexts: evidence E absolutely supports a hypothesis H relative to some probability function Pr if and only if the conditional probability of the hypothesis given the evidence exceeds the probability of the negation of the hypothesis given the evidence, i.e., if Pr(H|E) > Pr(¬H|E). Evidence E incrementally supports a hypothesis H relative to some probability function Pr if and only if the conditional probability of the hypothesis given the evidence exceeds the initial probability of the hypothesis, i.e., if Pr(H|E) > Pr(H). The primary debates in Bayesian epistemology concerning evidential or confirmational support measures focus on how to quantify degrees of support and how to interpret the underlying probabilities. Relevant to these debates is the intuitive distinction between “the potential further support” of some hypothesis H that might be gotten from finding E and the “actualized support” that H already receives from E. Intuitively, if one already is certain of evidence E, then E eventually provides actualized support to H. That means for Christensen (1999) that “our current confidence in E makes rational our current confidence in H”. In other words, the agent’s rational degree of belief in H depends not only on the non-evidential comparative plausibility considerations concerning H but also on the actualized support of H provided by the evidence E. In contrast, if one already knows 93

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that E and one updated one’s credences based on this information, E will not be able to provide any further support to H. Thus, the potential further support that might be gotten from finding out that E is minimal, although the actualized evidential support is perhaps substantial. Consequently, actualized support is traditionally often connected with degrees of confirmation, and one focuses on it when one holds the evidence fixed and compares different hypotheses concerning their belief-worthiness in the light of one’s evidence. If one is interested in quantifying the potential further support that might be gotten from the evidence, one holds the hypothesis fixed and compares different pieces of evidence concerning the impact they would have upon one’s degree of belief in that hypothesis if one would find them to be true. Therefore, potential further support is more strongly associated with the notion of evidential support. The paper is structured as follows. Section 2 introduces the most prominent measures of evidential or confirmational support. Section 3 focuses on the problem of measure sensitivity, i.e., the problem that the choice of measure affects a great many arguments in Bayesian epistemology. Section  4 focuses on the interpretation of probability used to capture support. Section 5 sums up the state-of-the-art and provides an outlook on possible future debates surrounding Bayesian theories of support.

2  Measures of Support Building on the previous qualitative notion of absolute support, philosophers proposed the following quantitative notion of absolute support: evidence E absolutely supports a hypothesis H to some degree r relative to some probability function Pr if and only if Pr(H|E) = r. In contrast, the literature contains a plethora of suggestions on how to measure the degree of incremental support (see Earman 1992, Ch. 5; Fitelson 2001). Concerning the quantitative notion of incremental support, Bayesians hold that the following requirement follows analytically from its qualitative foundation: Requirement 1 (Demarcation) A function c(·, ·) is a measure of (incremental) support relative to probability function Pr only if there is some (marker or neutral value) r ∈ R so that: For all hypotheses H and evidence E if 1 > Pr(H|E) > 0 and Pr(E) > 0, then ì > r, ï c ( H , E ) í = r, ï î< r,

Pr ( H | E ) > Pr ( H ) Pr ( H | E ) > Pr ( H )

Pr ( H | E ) > Pr ( H )

Among the most prominent Bayesian support measures in the spirit of this requirement are: (Carnap 1962) (Carnap 1962)

d ( H , E ) = Pr ( H | E ) - Pr ( H ) if Pr ( E ) > 0 r ( H , E ) = Pr ( H Ç E ) - Pr ( H ) if Pr ( E )

(Christensen 1999, Joyce 1999) S ( H , E ) = Pr ( H | E ) - Pr ( H ØE ) if 1 > Pr ( E ) > 0 94

Varieties of Measures of Evidential Support

ì ï d ( H, E ) ï1 - Pr ( H ) if Pr ( H | E ) ³ Pr ( H ) > 0 ïï (Crupi, Tentori, and Gonzalez 2007) Z ( H , E ) = í d ( H , E ) if Pr ( H | E ) < Pr ( H ) ï ï1 - Pr ( ØH ) ï1 if Pr ( H ) = 0 ïî ì é Pr ( E | H ) ù ï ú ï log ê ï ëê Pr ( E | ØH ) ûú (Fitelson 2001, Good 1960) l ( H, E ) = í ï¥ ï-¥ ï î

if Pr ( E | H ) > 0 and Pr ( E | ØH ) > 0 if Pr ( E ) > 0 and Pr ( E | ØH ) = 0 iff Pr ( E ) = 0 or Pr ( E | H ) = 0

ì Pr ( E | H ) - Pr ( E | H ) ï ï Pr ( E | H ) + Pr ( E | ØH ) ï ï ï (Kemeny and Oppenheim 1952) F ( H , E ) = í1 ï ï ï-1 ï îï

if Pr ( E | H ) > 0 and Pr ( E | ØH ) > 0

if Pr ( E ) > 0 and Pr ( ØH ) = 0

if Pr ( E ) = 0 or Pr ( H ) = 0

ì é Pr ( H | E ) ù ï log ê ú if Pr ( H | E ) > 0 (Milne 1996) r ( H , E ) = í ëê Pr ( H ) úû ï if Pr ( H | E ) = 0 î-¥ (Mortimer 1988) (Nozick 1981)

M ( H , E ) = Pr ( E | H ) - Pr ( E ) if Pr ( H ) > 0 N ( H , E ) = Pr ( E | H ) - Pr ( E | ØH ) if 1 > Pr ( H ) > 0

This plurality of measures is considered a challenge for Bayesian epistemologists: we need to determine which of these measures is the right or most suitable measure of support. On the one hand, many Bayesian epistemologists lean explicitly or implicitly toward a monistic position regarding the formal measures of support (Christensen 1999; Eells and Fitelson 2002; Fitelson 2001; Milne 1996; Vassend 2019). The thought is that for whatever purpose we want to use support measures, ideally, they should not give different verdicts concerning how strongly the evidence supports a hypothesis. On the other hand, the choice of measure “affects a great many arguments surrounding Bayesian confirmation theory (and inductive logic, generally)” (Eells and Fitelson 2002, 129), and there is no measure that satisfies all desiderata. In the following section, this problem takes center stage. 95

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3  The (Strengthened) Problem of Measures Sensitivity The strengthened problem of measure sensitivity (Brössel 2013) is that there are central arguments in Bayesian epistemology, but their validity is sensitive to the choice of measure of support. In particular, each argument relies on a different desideratum, but no confirmation measure validates all of them.

3.1  The Problem of Irrelevant Conjunction Critics of Bayesian confirmation theory pointed out that the qualitative notion of incremental support validates the following counterintuitive result: if E supports H, and I is irrelevant to H, E, and H ∩ E, then E also supports the irrelevant conjunction H ∩ I. Earman (1992) suggested that Bayesians could argue that examples like this are unproblematic as long as the quantitative notion of support ensures that the irrelevant conjunction H ∩ I is less supported than the relevant conjunct H. The following requirement, suggested by Hawthorne and Fitelson (2004), ensures that the irrelevant conjunction H ∩ I is less supported: Requirement 2 (Irrelevant Conjunction) If c is an adequate support measure, Pr(H|E) > Pr(H), Pr(E|H ∩I)  =  Pr(E|H), and Pr(I|H) ≠ 1, then: c(H, E) > c(H ∩ I, E). Support measures d, r, S, Z, l, F, and N satisfy Requirement 2. r and M do not satisfy it.

3.2  The Raven Paradox The well-known paradox of the ravens (Hempel 1945) consists of the following inconsistent intuitions: Raven Paradox 1 (i) a non-black non-raven (e.g., a white shoe) does not support the hypothesis “All Ravens are black.” (ii) A  non-black non-raven supports the hypotheses “All non-black things are non-ravens.” (iii) Logically equivalent hypotheses are equally supported by a given piece of evidence (equivalence condition). The standard Bayesian solution of the raven paradox is similar to the solution suggested for the problem of irrelevant conjunctions. In particular, contra intuition (i), Bayesians can admit that the observation of a non-black non-raven can support the hypothesis “All Ravens are black”, as long as it does so to a smaller degree than the observation of black ravens. Horwich (1982) relies on the following requirement to ensure that the raven hypothesis is less supported. Requirement 3 (The Raven Paradox) If c is an adequate support measure and Pr(H|E1) > Pr(H|E2) then: c(H|E1) > c(H|E2). Support measures d, Z, l, F, and r satisfy Requirement 3. r, S, M, and N do not satisfy it. 96

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3.3  Inductive Support as an Extension of Deductive Support In his Logical Foundations of Probability, Carnap aimed at providing a probabilistic notion of support that can be considered as an extension of deductive logic. According to Fitelson (2006) and Crupi et al. (2007), any argument to that effect should retain the idea that there is no better inductive support for some hypothesis than a deductive argument; and there is no worse support than an argument with premises that imply the falsity of the conclusion. As a consequence, these authors suggest the following requirement: Requirement 4 (Logicality) If c is an adequate support measure, then (i) if E implies H, then c(H, E) = max, and (ii) if E implies ¬H, then c(H, E) = min. (Fitelson 2006) Confirmation measures Z, l, and F satisfy Requirement 4. d, r, S, r, M, and N do not satisfy it.

3.4  Inductive Support and Belief-Worthiness It is generally acknowledged that Popper is one of the founding fathers of modern confirmation theory.1 Popper is very explicit in his work (Popper 1954, 1955, 1956) about what he takes to be the intended purpose of theories of confirmational support. Popper writes that: the degree of confirmation is supposed to have an influence upon the question of whether we should accept, or choose, a certain hypothesis H, if only tentatively. ... But Pr(H|E) cannot help here. Science does not aim, primarily, at high probabilities. It aims at a high informative content, well backed by experience. But a hypothesis may be very probable simply because it tells us nothing, or very little. A high degree of probability is therefore not an indication of ‘goodness’—it may be merely a symptom of low informative content. (Popper 1954, 146; emphasis in original, notation adapted) For serving this purpose, various philosophers argued that measures of support need to satisfy at least the following two requirements: Requirement 5 (Finality) If c is an adequate support measure, and Pr(H|E1) > Pr(H|E2), then c(H, E1) > c(H, E2). Requirement 6 (Reverse Finality)2 If c is an adequate support measure, Pr(H1) < Pr(H2) and Pr(H1|E) = Pr(H2|E), then c(H1, E) > c(H2, E). Finality and Reverse Finality capture Popper’s idea that scientists prefer hypotheses that are informative (and, thus, a priori improbable) but well-backed by the evidence (and, thus, a posteriori probable). In addition, the requirements are well-backed by intuition and could be said to follow analytically from the very idea of measuring incremental support. If one piece of evidence increases the probability of the hypothesis more than another piece of evidence, then the former provides more incremental support to that very hypothesis than 97

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the latter piece of evidence. Similarly, if two hypotheses are equally probable in the light of the evidence, but had different initial probabilities, then the hypothesis with the lower initial probability received more incremental support. Support measures d and r satisfy Requirements 5 & 6. r, S, Z, l, F, M, and N do not satisfy them.

3.5  Intermediate Summary The strengthened problem of measure sensitivity consists of six requirements relevant to Bayesian measures of incremental support and the fact that there is no single measure that satisfies all of them. Since these requirements all play an important role within crucial arguments of Bayesian epistemology, solving the problem might involve diminishing the fruitfulness of the Bayesian approach to understanding incremental support. Alternatively, we might give up monism. In particular, the previous considerations suggest using two different measures of support, one that focuses on confirmational support in the sense of belief-worthiness of hypotheses as desired by Popper, e.g., Carnap’s (1962) distance measure, and one that measures evidential support and satisfies Carnap’s logicality requirement, e.g., Crupi et al.’s (2007) normalized distance measure.

4  Support and Interpretations of Probability A Bayesian theory of evidential or confirmational support must also specify how probabilities should be interpreted. This chapter focuses on epistemic interpretations of probability, i.e., interpretations that take probabilities to describe or prescribe epistemic states. It will not consider interpretations such as the propensity or objective chance interpretation.

4.1  Degree of Belief Interpretation The standard interpretation of probabilities within Bayesian epistemology interprets them as degrees of belief. Accordingly, if the probability Pr(H|E) of hypothesis H given E equals r this is to be understood as the degree of partial belief in the Hypothe H given the information that B is r. The literature distinguishes between subjective and objective degree of belief interpretations. Subjective Bayesians hold that, in principle, each probability function can be interpreted as an agent’s degree of belief function, and different agents are permitted to choose different probability functions. They still would be equally rational. Objective Bayesians hold that there are stronger norms of rational degrees of belief than just obeying the probability calculus. They suggest that given the evidence available to an agent, there is just one objectively determined degree of belief function that all rational agents with the same evidence should have (Williamson 2011) or are justified to have (Maher 2004). Thus, to some extent, there is no difference in interpretation between subjective and objective Bayesianism but only a disagreement about how many and which probability functions can be interpreted as rational degree of belief functions. Furthermore, there is room for more moderate subjective positions between the radical subjectivist’s and the radical objectivist’s positions. In some contexts, it is problematic to interpret probabilities as representing the actual degree of belief of actual agents. For almost all sets of hypotheses, an interpretation of this kind would be descriptively inadequate because it is false that the actual degrees of belief of real-world agents obey the probability calculus (see Tversky and Kahnemann 1983). 98

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Alternatively, it is sometimes argued that probability must be given an interpretation as actual degree of belief of suitably ideal(ized) agents. However, Williamson (2000, ch. 10) argues that the probabilities relevant for understanding support cannot be coherently interpreted as actual degrees of belief of ideal(ized) agents. Williamson’s argument runs (very, very) roughly as follows (for a detailed exposition and criticism of Williamson’s argument see Eder 2019): ideal(ized) agents would never actually adopt a degree of belief function according to which the degree of belief in the proposition that there are ideal agents is low. However, for understanding support, probabilities must be admissible that assign a low proposition in that proposition. After all, our evidence supports that real-world agents are not ideal(ized) agents. Hence, if Williamson is right, degree of belief interpretations are unsuitable for understanding support. In the context of understanding incremental support, Glymour (1980) recognizes that the degree of belief interpretation is very problematic. As already said, evidence E incrementally supports hypothesis H given probability measure Pr just in case Pr(H|E) > Pr(H). If the evidence E is assigned probability 1, E cannot be probabilistically relevant for hypothesis H. Consequently, evidence E cannot support or counter-support any hypothesis H. The conditional probability of the hypothesis on the evidence equals the prior probability of the hypothesis if the probability of the evidence equals 1 (Pr(E) = 1). Now, evidence may be assigned probability 1 for one of two reasons. On the one hand, the evidence may receive probability 1 because it is trivial in the sense that it is highly unspecific, uninformative, or even tautologous. On the other hand, evidence may receive probability 1 because it is old, in the sense that for the agent, this proposition has been established with absolute certainty. However, this is highly problematic since it renders non-trivial evidence that is known to be certainly true probabilistic irrelevant to any hypothesis. As Glymour (1980) notes, the preexisting evidence of the 5600 arc advance seconds per century of Mercury’s perihelion seems to constitute a historical counterexample to such a theory of support. That Mercury’s perihelion has an arc advance of approximately 5600 seconds per century was first established in 1859. However, around 1916 the evidence of the 5600 arc advance seconds per century of Mercury’s perihelion was “old” evidence. But it was also considered persuasive evidence for Einstein’s general theory of relativity (because it can account for all 5600 arc advance seconds in contrast to Newtonian Mechanics, which can account for all but 43 arc advance seconds). That the standard Bayesian conception of confirmation renders old evidence confirmationally irrelevant is called the Problem of Old Evidence, and it is perhaps the most notorious and residual problem of Bayesian confirmation theory. However, as argued by Brössel (2012) and Brössel and Huber (2015), it is not so problematic when one acknowledges the distinction between actualized support and potential further support. If we want to measure the potential further support provided by the evidence, then the Problem of Old Evidence is a feature. Old evidence cannot provide any potential further support. The degree of belief interpretation of probability is suitable for measuring potential further support. Nevertheless, the Bayesian literature is swamped with articles that attempt to solve the Problem of Old Evidence while upholding the hypothesis that the interpretation of the relevant probabilities underlying actualized support takes its starting point in the agent’s subjective degrees of belief. One suggestion is to solve the Problem of Old Evidence by introducing the idea of learning logical or, more generally, evidential relations between evidence and hypothesis into the Bayesian framework (Garber 1983; Jeffrey 1983; Niiniluoto 1983). Others suggested counterfactually reassigning the probabilistic degrees of belief of the hypotheses and the old evidence (Howson and Urbach 1993). Finally, it has been 99

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suggested that the agent’s degrees of belief in the evidence are never actually one (Rosenkrantz 1983; Christensen 1999). However, none of these suggestions are widely considered to be satisfactory. Recent proposals in the spirit of the previous approaches (Hartmann and Fitelson 2015; Sprenger 2015) might change that. A closer investigation of these proposals will tell whether we can consider the Problem of Old Evidence (re)solved in the counterfactual subjective degree of belief interpretation framework.

4.2  Evidential Support Interpretation The second interpretation to be considered in detail is called the “evidential support” interpretation of probability or, more briefly, “evidential probability” (the latter term is borrowed from Williamson 2000). According to this interpretation, probability reflects evidence. The probability Pr(H|E) of some hypothesis H given evidence E is interpreted as the evidential probability of H in the light of evidence E. Proponents of this interpretation relate evidential probabilities to degrees of belief in the following way. Suppose the agent’s available evidence is E. In this case, the evidential probability of some hypothesis H in the light of this evidence (Prev(H|E)) equals the degree of belief that that agent should have in H (PrBel(H)). Again, one can distinguish between subjective and objective evidential probabilities. According to the subjective reading, probabilities reflect what is evidence in view of the agent. The probability function that is interpreted as evidential probabilities is distinguished from the degrees of belief of an agent by its role in the agent’s epistemic housekeeping. Suppose the agent’s available evidence is E. In that case, the agent uses the evidential probability of some hypothesis H in the light of this evidence (Prev(H|E)) to calculate her degree of belief in that hypothesis (PrBel(H)). Hence, according to the subjective interpretation, evidential probabilities represent what Levi (1980, 79) calls an agent’s “confirmation commitments”. According to the objective reading, these confirmation commitments in Levi’s sense are objective. That means the evidential probability is determined exclusively by the hypothesis in question and the evidence (and possibly the background knowledge and the world); the subjective mental state of the agent per se is irrelevant. To some extent, the objective evidential interpretation is similar to the logical interpretation of probability that has been advocated by Carnap (1962), Jeffreys (1939), and Keynes (1921). According to it, if the probability PrLogical(H|E) of some hypothesis H given E equals r, r is conceived of as the degree to which E partially entails H. Proponents of this interpretation hold that these logical probabilities should guide reasoning and, thus, capture normative reasoning commitments. They believe that the logical syntax of the hypothesis involved determines how one should reason. Contemporary proponents of the evidential probability interpretation often deny that logical syntax alone determines the probabilities that should guide our reasoning. Proponents of objective evidential probabilities must first point out the one probability function that adequately reflects evidence. This includes explaining how one can acquire knowledge about what evidential probability is assigned to a certain hypothesis given the available evidence. Second, they have to explain why the selected probability function should guide the reasoning of all rational agents. Proponents of the evidential probability interpretation of probability include, among others, Hawthorne (2005), Joyce (2005),3 Williamson (2000) (for the objective interpretation), Lange (1999), and Levi (1980) (for the subjective interpretation).

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Most proponents of evidential interpretation suggest them explicitly to capture the actualized support that a hypothesis receives from the available evidence. In particular, Hawthorne (2005), Brössel (2012), and Brössel and Eder (2014) suggest that an adequate account of rational reasoning should include both kinds of probabilities: probabilistic degrees of belief with respect to which we define potential further support and probabilistic evidential probabilities for capturing actualized support. To sum up, there are two central interpretations of probability for capturing degrees of support. It argued that both interpretations are relevant. Degree of belief interpretations are essential for capturing the notion of the potential further support provided by new pieces of evidence; evidential interpretations are relevant for capturing the actualized support a body of available evidence provides to one’s hypotheses.

5  Summary and Outlook This chapter introduced two of the central challenges of Bayesian epistemology concerning measures of support. The first challenge consists of the plurality of Bayesian support measures and the problem of measure sensitivity. The latter problem consists of a variety of desiderata for which there is no Bayesian support measure that satisfies them. Since these requirements all play an important role within crucial arguments of Bayesian epistemology, selecting one such measure might diminish the fruitfulness of the Bayesian notions of incremental support. The alternative this chapter suggests is to give monism concerning measures of support. To meet this challenge, this chapter suggested using two different measures of support, one that captures support in the sense of actualized support and focuses on the hypotheses’ belief-worthiness, and one that measures potential further support and focuses on the evidence’s potential to change the probability of the hypothesis in question. The second challenge concerns the two main interpretations of probability relevant for understanding support: the degree of belief interpretation and the evidential probability interpretation. Again the chapter advocated for pluralism. Since the evidential probability interpretation captures subjective or objective reasoning commitments, it is crucial for capturing the actualized support that some hypothesis receives. Probabilities interpreted in terms of degrees of belief should be used to explicate the potential further support that might be gotten from finding the evidence.

Notes * I am thankful especially to Vincenzo Crupi, Anna-Maria Asunta Eder, Branden Fitelson, and Jan Sprenger. These are the persons from whom I learned the most about Bayesian confirmation theory and with whom I  discussed the topic most controversially. Their comments and teachings have influenced all of my work in this area. Research on this chapter has been generously supported by an Emmy Noether Grant from the German Research Council (DFG), reference number BR 5210/1-1. 1 According to Popper (1955) and his contemporaries (e.g., Bar-Hillel 1955) Popper was the first to use the term “degree of confirmation” (more specifically its German counterpart “Grad der Bewährung”) in 1935 in the first edition of his Logic of Discovery. 2 One reasonable objection against this requirement is that one favors to believe the more informative hypothesis of two equally probable hypotheses only if they are sufficiently probable. Suppose, for example, both hypotheses are already falsified by the evidence. Thus, the probability of both hypotheses is 0. However, if both hypotheses are falsified a rational scientist would not necessarily

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Peter Brössel prefer one over the other just because it is logically stronger. Accordingly, the previous requirement on measures of support can be weakened as follows:   Requirement 7 (Weakened Reverse Finality) There is some r ∈ (0, 1] such that if c is an adequate support measure, Pr(H1) < Pr(H2), and Pr(H1|E) = Pr(H2|E) ≥ r, then c(H1, E) > c(H2, E).   Weakened Reverse Finality requires that if two hypotheses have the same risk of being false (where the risk is smaller than 1 − r for some r ∈ (0, 1]), the more informative hypothesis is more supported. This requirement is considerably weaker than similar requirements, which can be found in the works of Hempel (1960), Levi (1961, 1967, 1980), Hintikka and Pietarinen (1966), and Huber (2008). Additionally, almost all measures satisfy this desideratum. In particular, the support measures d and r proposed by Carnap (1962), the S measure of Christensen (1999) and Joyce (1999), and the r measure of Milne (1996) satisfy this requirement. Ditto for the measures M of Mortimer (1988) and N of Nozick (1981). The only support measures that do not satisfy weakened reverse finality are the Z measure of Crupi et al. (2007), the l measure advocated by Fitelson (2001), and Good (1960), and the measures F of factual support suggested by Kemeny and Oppenheim (1952). 3 Joyce (2005) assumes that sets of probability functions reflect evidence.

References Bar-Hillel, Y. (1955). Comments on ‘Degree of Confirmation’ by Professor K. R. Popper. The British Journal for the Philosophy of Science 6, 155–157. BrÖssel, P. (2012). Rethinking Bayesian Confirmation Theory. PhD. Dissertation, University of Konstanz (Philosophy). Brossel, P. (2013). The Problem of Measure Sensitivity Redux. Philosophy of Science 80, 378–397. BrÖssel, P., Eder, A. M. A. (2014). How to Resolve Doxastic Disagreement. Synthese 191 (11), 2359–2381. BrÖssel, P., Huber, F. (2015). Bayesian Confirmation: A Means with No End. British Journal for the Philosophy of Science 66, 737–749. Carnap, R. (1962). The Logical Foundations of Probability (2nd edition). Chicago: University of Chicago Press. Christensen, D. (1999). Measuring Confirmation. Journal of Philosophy 96, 437–461. Crupi, V., Tentori, K., Gonzaleze, M. (2007). On Bayesian Measures of Evidential Support: Theoretical and Empirical Issues. Philosophy of Science 74, 229–252. Earman, J. (1992). Bayes or Bust? A Critical Examination of Bayesian Confirmation Theory. Cambridge: MIT Press. Eder, A. M. A. 2019. Evidential Probabilities and Credences. British Journal for the Philosophy of Science. Online first. URL: https://doi.org/10.1093/bjps/axz043. Eells, E., Fitelson, B. (2002). Symmetries and Asymmetries in Evidential Support. Philosophical Studies 107, 129–142. Fitelson, B. (2001). Studies in Bayesian Confirmation Theory. PhD. Dissertation, University of Wisconsin-Madison (Philosophy). Fitelson, B. (2006). Logical Foundations of Evidential Support. Philosophy of Science 73, 500–512. Garber, D. (1983). Old Evidence and Logical Omniscience in Bayesian Confirmation Theory. In J. Earman (ed.), Testing Scientific Theories. Minnesota Studies in the Philosophy of Science 10. Minneapolis: University of Minnesota Press, 99–131. Glymour, C. (1980). Theory and Evidence. Princeton: Princeton University Press. Good, I. J. (1960). Weight of Evidence, Corroboration, Explanatory Power, Information and the Utility of Experiments. Journal of the Royal Statistical Society. Series B (Methodological) 22, 319–331. Hartman, S., Fitelson, B. (2015). A New Gerber-Style Solution to the Problem of Old Evidence. Philosophy of Science 82 (4), 712–717. Hawthorne, J. (2005). Degree-of-Belief and Degree-of-Support: Why Bayesians Need Both Notions. Mind 114, 277–320. Hawthorne, J., Fitelson, B. (2004). Re-Solving Irrelevant Conjunction with Probabilistic Independence. Philosophy of Science 71, 505–514.

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Varieties of Measures of Evidential Support Hempel, C. G. (1945). Studies in the Logic of Confirmation (I). Mind 54, 1–26. Hempel, C. G. (1960). Inductive Inconsistencies. Synthese 12, 439–469. Hintikka, J., Pietarinen, J. (1966). Semantic Information and Inductive Logic. In J. Hintikka, P. Suppes (eds.), Aspects of Inductive Logic. Amsterdam: North-Holland Publishing Company, 96–112. Horwich, P. (1982). Probability and Evidence. Cambridge: Cambridge University Press. Howson, C., Urbach, P. (1993). Scientific Reasoning: The Bayesian Approach (2nd edition). La Salle: Open Court. Huber, F. (2008). Assessing Theories, Bayes Style. Synthese 161, 89–118. Jeffrey, R. (1983). The Logic of Decision (2nd edition). Chicago: The University of Chicago Press. Jeffreys, H. (1939). Theory of Probability. Reprinted in: Oxford Classics in the Physical Sciences Series. Oxford: Oxford University Press, 1998. Joyce, J. (1999). Foundations of Causal Decision Theory. Cambridge: Cambridge University Press. Joyce, J. (2005). How Probabilities Reflect Evidence. Philosophical Perspectives 19, 153–178. Kemeny, J., Oppenheim, P. (1952). Degree of Factual Support. Philosophy of Science 19, 307–324. Keynes, J. (1921). A Treatise on Probability. London: Macmillan. Lange, M. (1999). Calibration and Epistemological Role of Bayesian Conditionalization. The Journal of Philosophy 96, 294–324. Levi, I. (1961). Decision Theory and Confirmation. The Journal of Philosophy 58, 614–625. Levi, I. (1967). Gambling with Truth. New York: A. A. Knopf. Levi, I. (1980). The Enterprise of Knowledge. Cambridge: MIT Press. Maher, P. (2004). Probability Captures the Logic of Scientific Confirmation. In C. Hitchcock (ed.), Contemporary Debates in the Philosophy of Science. Oxford: Blackwell, 69–93. Milne, P. (1996). log[p(h/eb)/p(h/b)] Is the One True Measure of Confirmation. Philosophy of Science 63, 21–26. Mortimer, H. (1988). The Logic of Induction. Paramus, NJ: Prentice Hall. Niiniluoto, I. (1983). Novel Facts and Bayesianism. The British Journal for the Philosophy of Science 34, 375–379. Nozick, R. (1981). Philosophical Explanations. Oxford: Clarenden. Popper, K. (1954). Degree of Confirmation. The British Journal for the Philosophy of Science 5, 143–149. Popper, K. (1955). ‘Content’ and ‘Degree of Confirmation’: A  Reply to Dr. Bar-Hillel. The British Journal for the Philosophy of Science 6, 157–163. Popper, K. (1956). Adequacy and Consistency: A Second Reply to Dr. Bar-Hillel. The British Journal for the Philosophy of Science 7, 249–256. Rosenkrantz, R. (1983). Why Glymour Is a Bayesian. In J. Earman (ed.), Testing Scientific Theories. Minnesota Studies in the Philosophy of Science 10. Minneapolis: University of Minnesota Press, 69–97. Sprenger, J. (2015). A  Novel Solution to the Problem of Old Evidence. Philosophy of Science 82: 383–401. Strevens, M. (2008). Notes on Bayesian Confirmation Theory. URL: www.nyu.edu/classes/strevens/ BCT/BCT.pdf, retrieved September 9th, 2011. Tversky, A., Kahneman, D. (1983). Extension Versus Intuitive Reasoning: The Conjunction Fallacy in Probability Judgment. Psychological Review 90, 293–315. Vassend, O. (2019). Confirmation and the Ordinal Equivalence Thesis. Synthese 196 (3), 1079–1095. Williamson, T. (2000). Knowledge and Its Limits. Oxford: Oxford University Press. Williamson, J. (2011). An Objective Bayesian Account of Confirmation. In D. Dieks, W. Gonzalo, T. Uebel, S. Hartmann, and M. Weber (Eds.), Explanation, Prediction, and Confirmation. Springer. pp. 53–81.

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8 POSITIVE RELEVANCE Peter Achinstein

The Positive Relevance Definition of Evidence According to a widely held definition, some information e is evidence that a hypothesis h is true if and only if it increases the probability of the hypothesis. In symbols, (1) e is evidence that h if and only if p(h/e) > p(h). In (1), p(h/e) is the (“posterior”) probability of h, given e, and p(h) is the (“prior”) probability of h without the assumption of e. Often one starts with some “background” information b that is being assumed, to which new information e is being added. The question then is whether, given b, e is evidence that h. For this kind of case, champions of positive relevance write: (2) e is evidence that h, given b, if and only if p(h/e&b) > p(h/b). (1) and (2) are called positive relevance definitions of evidence, where information is “relevant” for a hypothesis if it changes the latter’s probability, and it is “positively relevant” if it increases it. The fact that I just bought 80% of the tickets in a fair lottery, one ticket of which will win, is evidence that I will win, since the probability that I will win has jumped from 0, before I bought any tickets, to 0.8 afterwards. The fact that I just sneezed is not evidence that I will win the lottery, since that fact does not change the probability that I will win. Positive relevance (hereafter PR) definitions (1) and (2) are proposed by some philosophers and scientists who have subjective views about probability, as well as by some who have objective ones. A standard subjectivist position is that the probability of a hypothesis is a measure of one’s subjective degree of belief in that hypothesis, so long as one’s total set of degrees of belief in various propositions obeys the mathematical axioms of probability. Assuming that the latter condition (“probabilistic coherence”) is satisfied by a person X, e is X’s evidence for hypothesis h if and only if X’s conditional probability for h is greater than X’s prior probability for h. DOI: 10.4324/9781315672687-11 104

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By contrast with subjectivists, objectivists say that probability should be understood as being independent of the beliefs of any persons. Some in this camp hold that probability claims are a priori. The truth or falsity of a probabilistic claim of the form “the probability of h is (some number) r” is determined by a set of linguistic rules added to the usual axioms of mathematical probability (see Carnap 1952). Other objectivists say that probability claims of this form are, for the most part, empirical (see Salmon 2017; Achinstein 2001). Despite differences about the meaning of probability, PR theorists agree that (1) and (2) are true. They regard these as the gold standard among definitions. Because definitions (1) and (2) are expressed entirely in terms of probability, they are often referred to as representing a “Bayesian” approach to evidence.

Four Objections to Positive Relevance There are objections to the positive relevance definitions that PR enthusiasts need to consider in order to defend their position successfully. Here are four. Objection 1: These definitions do not provide sufficient conditions for evidence, because there are cases that satisfy them that are clearly not evidence. For example, let e be the information that I bought 1% of the tickets in this fair lottery, while you bought the other 99%; and let h be the hypothesis that I will win the lottery. My probability of winning once I have bought the tickets increases from what it was before I bought any ticket. But surely e is not evidence that I will win; it is evidence that you will. Or suppose that I have just entered an elevator. This increases the probability that I will be in an elevator accident, but surely it is not evidence that I will be. More generally, if the probability of h, given e, is low, e cannot be evidence that h, even if it increases its probability. Objection 2: The PR definitions do not supply a necessary condition for evidence, because there are cases in which e is evidence that h even though e does not raise the probability of h, indeed in which e even lowers the probability of h. Here is an example of the latter sort: Let e1 be the information that at 10 A.M., Paul, who has symptoms S, takes medicine M to relieve S. Let e2 be the information that at 10:15 A.M. Paul takes medicine M’ to relieve S. Let background information b be that M is 95% effective in relieving S within 2 hours, M’ is 90% effective in relieving S within 1 and ¾ hours but has fewer side effects; when taken within 20 minutes of taking M, M’ completely blocks the causal efficacy of M without affecting any of its own. Let h be the hypothesis that Paul’s symptoms will be relieved by noon. It seems reasonable to claim that, given e1 and b, information e2 is evidence that h, since M’ is 90% effective in relieving S, and its efficacy is not blocked by having taken M. But this violates the positive relevance idea, since e2 lowers the probability of h from 95% to 90%. This shows that something can be evidence for a hypothesis without raising its probability. Indeed it can be evidence even if it lowers its probability! Objection 3: The fact that a respected scientific authority in the field appropriate for h believes that h is true raises the probability that h is true. But it is not evidence that h is true. In the late 17th and early 18th centuries, the “incomparable Mr. Newton” believed that all bodies attract all other bodies with a force that varies directly according to the product of the masses of the bodies and inversely as the square of their distance. The fact that he believed that this law of gravity is true might have raised the probability of

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its truth very considerably, but it was not evidence for the law. Otherwise Newton could have cited it rather than the observed motions of the planets and their satellites, which would have been perhaps more convincing, at least to the uninitiated. Objection 4: The positive relevance definitions appeal to mathematical probabilities, which are best understood when applied a priori to games of chance, or empirically, to large populations, but not to hypotheses, unless the latter are about games of chance or large populations. In games of chance, at least those in which equiprobable outcomes are well-defined, the ratio of favorable outcomes to the total possible outcomes can be computed and the probability determined. With large populations involving items with or without a property P, the observed relative frequency of P in the population can be empirically determined and this number used to fix the limit of the relative frequency, i.e., the probability, of that property in the general population. But with theories the matter is different. How is one to determine either the prior or the posterior probability of string theory, for example? This is not a case in which we can say: “Well, there are two equiprobable outcomes: either it is true or it isn’t, so the probability that it is true is ½.” Nor is it the case that we can place string theory in a group of similar theories that have been tested and determine the “success rate” of these theories. (Reichenbach [1949] once proposed this idea.) The problem, then, for positive relevance defenders is how to determine the probability of a hypothesis, and therefore how to determine whether e increases that probability, and so is evidence.

Positive Relevance Replies PR theorists tend to feel strongly about the correctness of their view. So let’s consider how they do or might reply. This will help to clarify the view and its implications. Reply to Objection 1: Some PR proponents (e.g., Carnap 1962 and Salmon 1975) reply that “evidence” in fact has two meanings, both to be understood in terms of probability. The first is the positive relevance meaning. The second is explicated in terms of high probability and is given by these definitions: (3) e is evidence that h if and only if p(h/e) > k, (4) e is evidence that h, given b, if and only if p(h/e&b) > k, where k represents some threshold for “high” probability. So, for example, if you object to saying that (e) my buying 1% of the tickets in the fair lottery is evidence that I will win, you are thinking of the “high probability” definitions (3) and (4), which e fails to satisfy. In the “high probability” sense, my buying 1% of the tickets is not evidence that I will win. But in the “positive relevance” sense it is evidence that I will win, since it increases the probability that I will win. Both senses of evidence are legitimate, and they should not be confused. Senses (1) and (2) capture the idea of making a hypothesis “firmer,” while senses (3) and (4) capture the idea of making a hypothesis “firm” (Carnap 1962, p. xviii). The fact that I am using the term in one sense cannot be criticized on the grounds that I am not using it in the other. (For other positive relevance replies, see Gimbel 2005, Kronz 1992, Maher 1996, and Roush 2005a.) Reply to Objection 2: Again, we appeal to the fact that evidence has two senses, the first given by (1) and (2), the second by (3) and (4). In the medicine counterexample, Paul’s taking medicine M’ is indeed evidence that his symptoms will be relieved, but it is so in the 106

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“high probability” sense, given by (3) and (4), not the positive relevance sense. His taking medicine M’ is evidence in this case because the probability is “high” even though it is lower than it was before, and so is not evidence in the sense of positive relevance. Reply to Objection 3: The fact that Newton believed that the law of gravity is true is evidence that the law is true, in both the positive relevance and the high probability sense. In the high probability sense, the fact that Newton believed this did something epistemic that we want evidence to do, viz. it gave those from the late 17th to the late 19th centuries a good reason for believing the law. And, in the positive relevance sense, it increased the strength of the reason for believing the law. The kind of evidence the objector has in mind in raising this objection should perhaps be called “scientific” evidence. It includes facts that Newton cited about the motions of the planets and their satellites, not facts about Newton’s beliefs. But “authoritative” evidence is still evidence in an important epistemic sense, just not evidence of a sort that scientists may want on an occasion in which they are seeking evidence pertaining to physical facts about the world. Reply to Objection 4: The positive relevance and high probability definitions do not require that a system of rules be supplied for assigning numerical probabilities, either prior or posterior, to hypotheses to determine whether some e is evidence for the hypothesis. They speak only about “increasing” the probability, and “high” probability, neither of which requires assigning specific numbers. In the same way we can say that the temperature of something has increased and that its temperature is high, or that the size of something has increased and that the size is large, without assigning, or even knowing how to assign, specific numerical temperatures or sizes. When Newton endorses his law of gravity, because of his genius we can say that the probability of the law of gravity has increased, and is even high, without assigning specific numbers to prior and posterior probabilities. (See Carnap 1952, 1962 for an attempt to provide a general system that does assign specific probabilities to hypotheses.)

The High Probability Definitions (3) and (4) Rejected. The Need for an Explanatory Connection A response noted to some of the previous objections to positive relevance is to invoke a second sense of “evidence” according to which high probability is sufficient. But this won’t do. The probability that (h) the great pianist Sir Andras Schiff will not become pregnant is extraordinarily high. It is so, even if (e) he plays Bach every morning. But contrary to (3), despite the fact that p(h/e) is very high, e is not evidence that h. Saying otherwise would be a bad joke! Why is that? What is missing? What is missing, the objector will say, is some “connection” between e and h. The fact that he plays Bach every morning has nothing to do with his not becoming pregnant. What is the missing “connection”? Perhaps we can find it by revisiting the medicine example introduced in Objection 2. That example also satisfies high probability: given e1 and b, it is highly probable that (h) Paul’s symptoms will be relieved by noon, given that (e2) he has taken M’ at 10:15, since (b) M’ is 90% effective, and when taken within 20 minutes of taking M, which Paul did (e1), M’ destroys the efficacy of M without affecting any of its own. Now, in this case, given e1 and the background information, it is very probable not only that Paul’s symptoms will be relieved by noon but, most important, that Paul’s symptoms will be relieved by noon because he has taken medicine M’. This “explanatory connection” 107

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between evidence and hypothesis is missing in the Bach example. Even though it is probable that Andras Schiff will not become pregnant, given that he plays Bach every morning, it is not probable that he will not become pregnant because he plays Bach every morning. There is probably no “explanatory connection” between putative evidence and hypothesis in this case. Let us say that there is an explanatory connection between h and e if e correctly explains why h is true, or h correctly explains why e is true, or something correctly explains why both h and e are true. (For an account of “correct explanation” to support this idea, see Achinstein 2001.) And let us replace the “high probability” conditions for evidence (3) and (4) with the following: (5) e is evidence that h only if p(E(h,e)/e) > k (6) e is evidence that h, given b, only if p(E(h,e)/e&b) > k, where E(h,e) means that there is an explanatory connection between h and e (which is not to be construed as a logical or semantical relation between h and e—otherwise the probabilities in (5) and (6) would be 1 or 0.) Conditions (5) and (6), as stated earlier, provide necessary conditions for evidence. If satisfied they will satisfy (3) and (4), if the latter are construed as necessary conditions, since if p(E(h,e)/e) > k, then p(h/e) > k (see Achinstein 2001). But, as the Bach example shows, the reverse is not the case. In that example, p(h/e) > k holds, but p(E(h,e)/e) > k does not. So if conditions (5) and (6) are required for evidence, we avoid the treacherous Bach example, admit the welcome medicine example, and explain the important difference between the two. On this conception, for e to be evidence that h what is required is not just that h be probable, given e, but that, given e, it be probable that there is an explanatory connection between the two. (5) and (6) are proposed as necessary conditions for a high probability concept of evidence. To make them sufficient we might add that e is true and that e doesn’t entail h. To cite an example, the fact that John’s blood was at the scene of the crime can’t be evidence that he committed the murder, if there was no blood or if it wasn’t John’s. And the fact that John’s blood was at the scene of the crime can’t be evidence that John’s blood was at the scene of the crime or that there was a crime. Logical or semantical entailment is too “close” to count as evidence. The positive relevance theorist who invokes a high probability concept of evidence, in addition to the positive relevance concept, may reply as follows: “Okay, I will accept your enhanced ‘explanatory’ idea built into the high probability concepts (5) and (6), but I still insist on the idea that there is another concept of evidence, given by increase in probability.” Perhaps that idea should be enhanced by incorporating an explanatory condition, as follows: (7) e is evidence that h if and only if p(E(h,e)/e) > p(E(h,e)) (8) e is evidence that h, given b, if and only if p(E(h,e)/e&b) > p(E(h,e)/b). Or perhaps we should forget about explanatory enhancement altogether and just accept the simple original positive relevance definitions (1) and (2). We need to pay more attention to positive relevance, i.e., to increase in probability, whether what is increased is the probability of h or the probability of E(h,e). 108

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Critical Response to Positive Relevance. A New Concept of Evidence What exactly does positive relevance give you? PR theorists say that evidence that is positively relevant for a hypothesis makes it “firmer” (Carnap 1962), or makes it “rational to be more confident in” (Maher 1996). Is this true? In general, in speaking of an x that is a stuff (e.g., water), or a state (e.g., pain, or in the present case, confidence or firmness), if there is more x present in one circumstance than another, then there is at least some x present in some degree in the former, even if there is none in the latter. If there is more water now than before, then there is some water now. If a hypothesis (or the explanatory connection between the hypothesis and the evidence) is firmer now than it was before, then it has at least some firmness now. Otherwise what is the difference between the two states? Now, insofar as concepts such as firmness and confidence depend on probability, as PR theorists claim, they are “threshold” concepts. Whether or not this varies from one person to another, a hypothesis must reach some threshold degree of probability for it to be at all firm or for one to be at all confident that it is true. (By analogy, “hirsute” is a threshold concept with respect to hair, as is “wealth” with respect to money.) Not just any amount or increase will do. Some just don’t reach the threshold. When I buy one ticket in a 10,000 ticket lottery, that increases the probability that I will win, but not enough to give me any confidence at all that I will win. A PR theorist may concede this point and say that what is important is increase in probability, even if that probability has to increase to a value beyond the threshold. But the medicine example shows that this is not so. In that case there is evidence (giving a 90% probability) that decreases the probability. If the PR theorist admits positive relevance is not a necessary condition for evidence because of such cases, and also that it is not a sufficient condition because of the threshold problem, what’s left? What is really important about evidence? What does it give you? Two advantages will be noted, one in the present section and one in the next. Let’s start with the basic idea that scientists, at least, want good reasons for believing what they do; otherwise they would simply be speculating, or believing on faith. If evidence provides such reasons it is obviously desirable. And, as we saw, a piece of information can increase the probability of a hypothesis without giving any good reason to believe it. How good is a “good reason for belief”? To give this idea some bite, let us say at least that if e is a good reason for believing h, then it cannot be a good reason for believing a hypothesis incompatible with h. Tossing a fair coin once is a good reason to believe it will land heads or tails, but not a good reason to believe it will land heads. Now, if evidence is indeed a threshold concept with respect to probability, then what will be necessary is that the lowest bound of the threshold be ½. That is, e is evidence that h only if p(h/e) > ½. With even lower bounds, e could be evidence for, and hence a good reason to believe, incompatible hypotheses. We can admit that tossing a coin will increase the probability of its landing either heads or tails or on its edge without being committed to saying that it is a good reason to believe it will land heads (by contrast to one of the other incompatible ways), or that we have at least some confidence that it will, or that the hypothesis that it will has some firmness. Utilizing these ideas, we can then employ the earlier “explanatory connection” idea and provide a final definition of evidence, as follows: (9) e is evidence that h if and only if p(E(h,e)/e) > ½, and e is true and does not entail h. 109

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(A similar definition can be supplied for evidence relativized to background information.) As with the high probability definition (3), for e to be evidence that h it is required that p(h/e) be “high,” at least greater than ½, i.e., at least greater than that of any incompatible competitor. (This is the case since E(h/e) entails h. See Achinstein 2001.) However, it differs importantly from (3) because high probability of h, given e, is not sufficient for e to be evidence that h. What is missing from (3) but present in (9) is the idea of an “explanatory connection” between e and h. If we require, as (9) does, that, given e, there is a high probability of such a connection (at least greater than ½), then we capture two central ideas the defender of (9) wants to capture: (a) if there is evidence that h, there is a good reason for believing h, and (b) if e is that evidence, then e provides that good reason. (a), but not (b), is captured by the high probability definition (3). Both (a) and (b) are captured by (9). Finally, of course, (9) is incompatible with the positive relevance definitions (1) and (7). Indeed, a supporter of (9) wants to reject (1) and (7). Although (7), but not (1), introduces the idea of the “probability of an explanatory connection between e and h, given e,” unlike (1) and (7), (9) requires this probability to be high and not just larger than the prior probability of h or larger than the prior probability of an explanatory connection between e and h. To be sure, all three accounts are “probabilistic”: they relate evidence to probability, which other traditional accounts, such as hypothetico-deductivism, Hempel’s “satisfaction” theory (see Hempel 1965), and “inference to the best explanation” (see Harman 1964, Lipton 2004, and Whewell 1847) do not. But if you are going to argue that evidence and probability are related, the differences between the three probabilistic accounts become significant. Perhaps the most important difference is that (1) is fully Bayesian: it characterizes evidence entirely in terms of probability. (7) and (9) are not: they introduce the idea of an explanatory connection.

The Value of Evidence: A Package Deal Providing a good reason to believe a hypothesis has been claimed to be one important value of evidence, especially if the latter is construed in terms of (9). There is another. If we, or more particularly scientists, employ the concept of evidence given by (9), an interesting consequence will follow that might initially seem unwelcome: “Authoritative” evidence will not be evidence. The fact that Newton believes the law of gravity will not count as evidence that the law is true. It will not satisfy the “explanatory connection” requirement. It will not be true that the probability is high that the reason that bodies obey Newton’s law is that Newton believes they do, or that the probability is high that the reason that Newton believes that bodies obey his law is that they do, or that the probability is high that something explains both why Newton believes what he does and why bodies in fact satisfy his law. In the third case, even if we say that Newton believes what he does because of the observed motions of the planets and their satellites, it is not the case that these observed motions explain why bodies obey the law. (In fact, in a famous passage at the end of the Principia, Newton admits that he cannot explain why bodies obey the law, and he refuses to speculate.) Now, unlike the counterexample cited earlier in which Andras Schiff plays Bach and doesn’t become pregnant, the fact that the authorities believe something in their field of expertise is usually, or at least often, a good reason to believe it. Otherwise, why believe textbooks, doctors, or bridge designers? If we admit this, then we are conceding that not everything that makes it reasonable to believe a hypothesis is evidence for that hypothesis. 110

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Suppose, then, that the authorities all say that h is true. And suppose these authorities are so good (in terms of training and past performance) that the fact that they believe h is indeed a very good reason to believe h. On this basis, h can be assigned a very high probability. If the fact that the authorities believe h gives h a very high probability, and therefore gives a good reason for believing h, then even if this fact is not evidence for h, in the sense given by (9), why should anyone, but a few authorities concerned with h, search for evidence for h, or even consider what does, or would count as, evidence for h? Even if some evidence for h is discovered, it might confer upon h a probability less than would the fact that the authorities believe that h is true. So, what value does evidence, in the sense of (9), bring in addition to giving a good reason to believe a hypothesis? Why, if at all, is it superior to facts about what the authorities believe? The usual line is that evidence is important because, and perhaps only because, it provides a good reason for believing a hypothesis. Yes, that is one important value, but there is another. Evidence, in the sense of (9), enables one to understand the world better than does information about what the authorities believe. When Newton provides evidence for the law of gravity in the Principia by appeal to the specific motions of the planets and satellites, he enables us to discover, or realize that there probably are, explanatory connections between these motions and a universal inverse-square central force, viz. gravity. Newton’s simply believing that the law of gravity holds (authoritative “evidence”) does not tell us anything about these explanatory connections. Scientists and others want a good reason for believing a hypothesis under consideration. They also want to know explanatory connections between the hypothesis and other facts. If they can find evidence in the sense of (9), they get both. That is a good package.

References Achinstein, Peter (2001), The Book of Evidence (New York: Oxford University Press). Achinstein, Peter, ed. (2005), Scientific Evidence (Baltimore: The Johns Hopkins Press). Achinstein, Peter (2018), Speculation: Within and About Science (New York: Oxford University Press). Carnap, Rudolf (1952), The Continuum of Inductive Methods (Chicago: University of Chicago Press). Carnap, Rudolf (1962), Logical Foundations of Probability (Chicago: University of Chicago Press), 2nd ed. Earman, John (1992), Bayes or Bust (Cambridge, MA: MIT Press). Fitelson, Brandon (2006), “Logical Foundations of Evidential Support,” Philosophy of Science 73, 500–512. Gimbel, Steven (2005), “Restoring Ambiguity to Achinstein’s Account of Evidence,” in Achinstein, ed. (2005), 51–67. Glymour, Clark (1980), Theory and Evidence (Princeton: Princeton University Press). Harman, Gilbert (1964), “The Inference to the Best Explanation,” Philosophical Review 64, 529–533. Hempel, Carl G. (1965), Aspects of Scientific Explanation and Other Essays in the Philosophy of Science (New York: Basic Books). Kronz, Frederick M. (1992), “Carnap and Achinstein on Evidence,” Philosophical Studies 67, 151– 167 (My reply is in the same issue, pp. 169–175). Lipton, Peter (2004), Inference to the Best Explanation (London: Routledge), 2nd ed. Maher, Patrick (1996), “Subjective and Objective Confirmation,” Philosophy of Science 63, 149–174. Mayo, Deborah (1996), Error and the Growth of Experimental Knowledge (Chicago: University of Chicago Press). Mitova, Veli (2017), Believable Evidence (Cambridge: Cambridge University Press). Reichenbach, Hans (1949), The Theory of Probability (Berkeley: University of California Press), p. 174.

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Peter Achinstein Roush, Sherrilyn (2005a), “Positive Relevance Defended,” in Achinstein, ed. (2005), 85–91. I reply in the same volume, 91–93. Roush, Sherrilyn (2005b), Tracking Truth (Oxford: Oxford University Press). Salmon, Wesley (1975), “Confirmation and Relevance,” reprinted in Achinstein, ed., The Concept of Evidence (Oxford: Oxford University Press), 95–123. Salmon, Wesley (2017), The Foundations of Scientific Inference (Pittsburgh: University of Pittsburgh Press), Special Anniversary ed. Whewell, William (1847), The Philosophy of the Inductive Sciences (Reproduced in Johnson Reprint Corporation).

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9 THE PARADOXES OF CONFIRMATION Jan Sprenger

The paradoxes of confirmation are a group of generalizable examples that challenge the adequacy of specific formal accounts of when evidence confirms a theory. They show how these accounts classify intuitively spurious cases of confirmation as genuine evidential support, revealing problematic structural features of the involved confirmation criteria. In defending themselves against the paradoxes, confirmation theorists typically explain why our pre-theoretical intuitions about evidential support are mistaken, and they embrace the seemingly paradoxical conclusion (e.g., as Hempel did for the raven paradox). The paradoxes do not aim at accounts of confirmation that express whether hypothesis H is credible or acceptable in the light of observation E, such as Carnap’s (1950) account of confirmation as firmness. Instead, they aim at accounts that capture whether E provides relevant evidential support for H—for example, by being predicted by H, by providing an instance of H, or by increasing the firmness of our degree of belief in H. In other words, they apply to probabilistic accounts such as Bayesian confirmation theory, but also to accounts based on deductive relations in first-order logic, such as hypothetico-deductive confirmation and Hempel’s satisfaction criterion. The paradoxes of confirmation are a group of three examples: (1) the paradox of the ravens, also known as Hempel’s paradox; (2) Goodman’s new riddle of induction, also known as the “grue” paradox; and (3) the tacking paradoxes, or more specifically, the problem of irrelevant conjunctions and disjunctions. Not all of them affect each account of confirmation. The paradox of the ravens arises most forcefully for naïve theories of confirmation by instantial relevance, where observing a black raven confirms the hypothesis that all ravens are black. Adding plausible additional assumptions, it then follows that this hypothesis is also confirmed by observations such as a white shoe. Also, Goodman’s new riddle of induction aims in the first place at instance-based accounts of confirmation: a particular observation (e.g., a green emerald) confirms mutually incompatible hypotheses that make wildly divergent claims about the future (e.g., that emeralds examined in the future will be green, blue, red, etc.). Finally, the tacking paradoxes show that on a hypotheticodeductivist account, the confirmation relation is maintained when an irrelevant conjunct (e.g., “the moon consists of green cheese”) is tacked to the confirmed hypothesis. Table 9.1

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Jan Sprenger Table 9.1 An overview of the most prominent accounts of confirmation as evidential support and their relation to the three paradoxes of confirmation. Accounts of Evidential Support

Paradoxes of Confirmation

Naïve Instantial Relevance (Nicod) Refined Instantial Relevance (Hempel) Hypothetico-Deductive (H-D) Model Increase in Firmness (Bayes)

Paradox of the Ravens

New Riddle of Induction

Tacking Paradoxes

yes yes (no) yes

yes yes (no) yes

no no yes yes

gives an overview of which account of confirmation and evidential support is affected by which paradox of confirmation. Thus, a paradox of confirmation has to be discussed relative to a specific account. Our discussion will also reveal some surprising findings. While the Bayesian account of confirmation as increase in firmness is affected by all three paradoxes, we will see that it is also good at developing responses, due to the inherent flexibility of the probabilistic framework. The chapter is structured as follows. Section 1 discusses the paradox of the ravens by explaining its historical genesis and formal analysis. Section  2 does the same for Goodman’s new riddle of induction. Section 3 shows how the tacking paradoxes challenge H-D confirmation and how they are mitigated on a Bayesian account. Section 4 draws general morals and concludes.

1  The Paradox of the Ravens Natural laws, and hypotheses about natural kinds, are often formulated in the form of universal conditionals, such as “all planets move in elliptical orbits”, “all ravens are black” or “all tigers are predators”. According to a longstanding tradition in philosophy of science, such hypotheses are confirmed by their instances (Nicod 1925/61; Hempel 1945a, 1965b; Glymour 1980): the hypothesis “all F’s are G’s” is confirmed by the observation of an F that is also a G (Fa ∧ Ga). This suggests the following condition first mentioned by Jean Nicod: Nicod Condition (Confirmation by Instances) Universal conditionals such as H  =  ∀x: (Fx → Gx) are confirmed by their instances, that is, propositions such as E = Fa ∧ Ga. At the same time, formal theories of confirmation should respect some elementary logical principles. For example, if two hypotheses are logically equivalent, they should be equally confirmed or undermined by a given observation E. This brings us to the Equivalence Condition If observation E confirms (undermines) hypothesis H, then it also confirms (undermines) any hypothesis H’ that is logically equivalent to H. Hempel (1945a, 1945b) observed that combining the Equivalence and the Nicod conditions leads to paradoxical results. Take the hypothesis that no non-black object is a raven: H = ∀x: ¬Bx → ¬Rx. A white shoe is an instance of that hypothesis. Thus, by the Nicod Condition, observing a white shoe (E  =  ¬Ba ∧ ¬Ra) confirms H’. By the Equivalence 114

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Condition, H’ is equivalent to H = ∀x: Rx → Bx so that E’ also confirms the hypothesis that all ravens are black. But why should the observation of a white shoe matter for our attitude towards the color of ravens? Ravens Intuition Observations of a white shoe or other non-black non-ravens do not confirm the hypothesis that all ravens are black. Hence, we have three individually plausible, but incompatible claims—the Nicod Condition, the Equivalence Condition and the Ravens Intuition—at least one of which has to be discarded. Since this paradox of the ravens was first formulated by Carl G. Hempel in his essays “Studies in the Logic of Confirmation” (I+II, cited earlier and reprinted in Hempel 1965a), it is also known as Hempel’s paradox. Hempel suggests to give up the Ravens Intuition and to embrace the paradoxical conclusion. Assume that we observe a grey bird that resembles a raven. This observation puts the raven hypothesis at risk: the bird may be a non-black raven and falsify our hypothesis. However, by conducting a genetic analysis we learn that the bird is no raven, but a kind of crow. Here, it sounds correct to say that the results of the genetic analysis support the raven hypothesis—it was at risk of being falsified and has survived a test (=the genetic analysis, see also Popper 1959/2002). This way of telling the story explains why observations of the form ¬Ra ∧ ¬Ba can confirm the raven hypothesis H = ∀x: Rx → Bx. But why did we have a different intuition in the first place? Hempel thinks that this is due to an ambiguity in the way the paradox is set up. In the previous crow/raven case, we did not yet know whether the newly observed bird was a raven or a crow. Therefore its investigation has confirmatory potential. By contrast, in the white shoe example, we know that the object before us is no raven: “this has the consequence that the outcome of the . . . test becomes entirely irrelevant for the confirmation of the hypothesis and thus can yield no new evidence for us” (Hempel 1945a, 19). That is, the observation of a white shoe should better be described as the observation of a non-black object (E = ¬Ba) relative to the background knowledge that the object is not a raven (K = ¬Ra). The Nicod Condition is not satisfied for E’ relative to H’ and K’, and so the paradox vanishes. Hempel’s analysis explains in particular why “indoor ornithology” (e.g., looking for white shoes) does not yield evidential support for the raven hypothesis. The presence of relevant background knowledge can thus make a huge difference to the confirmation relation. According to Hempel, confirmation should therefore not be modelled as a two-place relation between hypothesis H and evidence E, but as a threeplace relation between H, E and background knowledge K. Following this line of thought, Hempel replaces the Nicod Condition by a more refined and formalized account of instantial relevance: Satisfaction Criterion (Hempel) A piece of evidence E directly Hempel-confirms a hypothesis H relative to background knowledge K if and only if E and K jointly entail the development of H to the domain of E. In other words, E ∧ K |= H|dom(E). The development of a hypothesis to a set of objects {a, b} is the set of predictions the hypothesis makes if restricted to these entities. Thus, the development of ∀x: Fx to the domain of E = Fa ∧ Fb ∧ Ga ∧ ¬Ha is Fa ∧ Fb. As Goodman (1955/83, 69) puts it: “a hypothesis is genuinely confirmed only by a statement [observation] that is an instance of it 115

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in the special sense of entailing not the hypothesis itself but its relativization or restriction to the class of entities mentioned by that statement.” Unfortunately, as pointed out by Fitelson and Hawthorne (2011), Hempel’s constructive proposal does not match his analysis of the paradox. Since the satisfaction criterion is monotonic with regard to background knowledge, the confirmation relation remains intact when background knowledge is added. In particular, when we do know beforehand that a is no raven and observe a to be non-black (E = ¬Ba, K = ¬Ra), it will still be the case that E ∧ K = ¬Ra ∧ ¬Ba |= (Ra → Ba) = H|dom(E). Thus, even when we know beforehand that E is irrelevant for K, H ends up being confirmed on Hempel’s account. While Hempel spots correctly that the paradoxical conclusion of the raven example can be embraced by relegating the paradoxical aspect to implicit background knowledge, his own theory of confirmation does not implement that insight. For the Bayesian account of confirmation as increase in firmness, things are more complicated. According to that theory, confirmation or evidential support corresponds to an increase in subjective probability or degree of belief (see also the chapter on positive relevance by Peter Achinstein): Confirmation as Increase in Firmness For hypothesis H, observation E and background knowledge K, E confirms/supports H relative to K if and only if E raises the probability of H conditional on K: p(H| E, K) > p(H|K), and vice versa for disconfirmation. The Bayesian account of confirmation as probability-raising tells us something more than Hempel’s original analysis: it enables us to spot that instantial relevance may be a bad guide to confirmation. Indeed, the probability of a universal conditional can also be lowered by observing its instances. I. J. Good (1967) proposed a simple example to this effect, reproduced in Table 9.2. We compare two scenarios, S1 and S2, where objects are either black ravens, non-black ravens, or something else (e.g., grey crows). Suppose that we can rule out any other scenario on the basis of our background knowledge. Then the hypothesis H = ∀x: (Rx → Bx) that all ravens are black is true in S1 and false in S2. Moreover, since there are more black ravens in S2 than in S1, observing a black raven raises the probability that S2 is the case: p(Ra Ù Ba | S) =

100 1, 000, 100

Table 9.2 I. J. Good’s (1967) counterexample to the Nicod Condition shows how observing an instance of an universal conditional (“all ravens are black”) can lower its probability. Distribution of Objects

Scenario 1 (S1)

Scenario 2 (S2)

Black ravens Non-black ravens Other objects

100 0 1,000,000

1,000 1 1,000,000

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p(H | ¬Ra ∧ ¬Ba). This means that Ra ∧ Ba confirms H to a higher degree than ¬Ba ∧ ¬Ra for all evidential support measures that depend only on the prior and posterior probability of H. This includes the most important measures in the literature (Crupi 2015; Sprenger and Hartmann 2019, ch. 1; see also the chapter on confirmation measures in this volume). Ultimately, Fitelson and Hawthorne’s result reveals why a black raven is more important evidence for the raven hypothesis than a white shoe. While Fitelson and Hawthorne arguably resolve the comparative version of the ravens paradox, many authors have been aiming at a stronger result, that is, to show that the observation of a white shoe (or in general, a non-black non-raven) provides almost zero confirmation for the hypothesis that all ravens are black (e.g., Horwich 1982; Earman 1992; Howson and Urbach 1993). Such arguments for resolving the quantitative version of the ravens paradox rest, however, on disputable assumptions such as p(Ba | H, K) ≈ p(Ba | ¬H, K), that is, the truth of the raven hypothesis barely affects the probability that a randomly sampled object is black (for discussion, see Vranas 2004). For these reasons, the Bayesian response to the paradox is best summarized by (1) rejecting the Nicodian intuition that instances always confirm universal generalizations and (2) showing that under typical circumstances, a black raven confirms the raven hypothesis more than a white shoe. More discussion of Bayesian and non-Bayesian approaches to the paradox of the ravens can be found in Maher 1999; Huber 2007; Sprenger 2010.

2  The New Riddle of Induction Goodman devised his “new riddle of induction” in the third chapter of “Fact, Fiction and Forecast” (Goodman 1955/83) as a challenge to Hempel’s (1945a, 1945b) account of confirmation, the satisfaction criterion. However, it can be framed as a general problem: only lawlike statements should be confirmed by their instances and formal theories of confirmation usually can’t tell lawlike from accidental generalizations. While there is considerable discussion about how Goodman’s paradox should be understood (e.g., Jackson 1975; Okasha 2007; Fitelson 2008), we adopt a confirmation-theoretic reading where the paradox shows how hypotheses with incompatible predictions are confirmed by the same evidence. 117

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The following presentation follows Sprenger (2016, 190–191) and Sprenger and Hartmann (2019, 53–54). Consider the following case of a standard inductive inference: Observation at t = t1: emerald e1 is green. Observation at t = t2: emerald e2 is green. . . . Observation at t = tn: emerald en is green. Conclusion: All emeralds are green. The conclusion follows the premise by enumerative induction (i.e., the straight rule of induction): the observation of the emeralds confirms the general hypothesis that all emeralds are green. The inference seems intuitively valid and Nicod’s and Hempel’s confirmation criteria agree. Goodman now declares an object to be grue either (1) if it is green and has been observed up to time tnow = tn, or (2) it is blue and is observed for the first time after tnow. Notably, no object is required to change colour to count as grue. Consider now the following inductive inference: Observation at t = t1: emerald e1 is grue. Observation at t = t2: emerald e2 is grue. . . . Observation at t = tn: emerald en is grue. Conclusion: All emeralds are grue. The inference that all emeralds are grue looks fishy, but formally, it is based on the very same rule (i.e., enumerative induction) as the previous inference that all emeralds are green. More specifically, the observation of a green emerald prior to tnow is an instance of the “green” as well as the “grue” hypothesis and thus Hempel-confirms both hypotheses. It is therefore not clear which inferences and expectations about the future are licensed by the observations. While Hempel’s paradox showed that confirmation by instances does not exclude evidence which we find intuitively irrelevant, Goodman’s paradox shows that the same observations confirm incompatible hypotheses and cast doubt of the ability of a purely syntactic account of confirmation to support rational expectations about the future. A natural reaction to the paradox is to deny the use of the predicate “grue” in inductive inferences due to their explicit use of temporal restrictions. Goodman (1955/83, 79–80) responds that such a move would be arbitrary: we can redefine the standard predicates “green” and “blue” in terms of “grue” and its conjugate predicate “bleen”: an object is green if (1) it is grue and observed prior to tnow or (2) it is bleen and observed after tnow. Any preference for the “natural” predicates and the “natural” inductive inference is a relative, not an absolute matter and conditional on the choice of a specific language. For purely syntactic accounts of confirmation such as Nicod’s Confirmation by instances and Hempel’s Satisfaction Criterion, it is therefore difficult to avoid the conclusion that observing green emeralds confirms the hypothesis that all emeralds are grue. 118

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Goodman suggests to drive a wedge between “green” and “grue” by restricting the confirmation relation to predicates with successful prediction history. Instead, one could also accept that evidence can confirm incompatible hypotheses. For example, Einstein’s work on the photoelectric effect confirmed the hypothesis that light is composed of discrete quanta (photons) rather than a continuous wave. Thereby Einstein’s discovery also confirmed different and mutually incompatible versions of quantum theory (e.g., relativistic and nonrelativistic versions). The Bayesian’s answer to Goodman’s paradox follows this latter line: she admits that both hypotheses are supported by the observed evidence but denies that they are supported equally. Evidential support typically depends on some function of prior and posterior probability, and the “green” hypothesis is for evident reasons more plausible than the “grue” hypothesis. Moreover, many measures of evidential support validate the Matthew effect (Festa 2012; Festa and Cevolani 2017): evidential support is, ceteris paribus, higher for hypotheses with high prior plausibility, favouring the “green” over the “grue” hypothesis. Fitelson (2008) offers a different Bayesian solution. The choice of priors, however, is external to Bayesian inference: they are motivated by theoretical principles, past observations and scientific judgment. The rules of Bayesian inference state how we should amalgamate prior degrees of belief with observed evidence, but they do not state which prior degrees of belief are reasonable. Thus, Goodman’s paradox highlights the need for inductive assumptions in inductive inference and shows that Bayesian Confirmation Theory is not an inductive perpetuum mobile (see also Norton 2019).

3  The Tacking Paradoxes So far, we have been silent on one of the principal and most venerable models of confirmation in science: the hypothetico-deductive (H-D) model. It is at the basis of a lot of scientific practice that sees a theory as confirmed if its predictions obtain. For example, the prediction that light would be bent by massive bodies like the sun, and Eddington’s verification of this prediction during the 1919 eclipse was widely seen as a strong confirmation of Einstein’s General Theory of Relativity. The idea that successful and risky predictions are essential to our assessment of a scientific hypothesis was also put forward famously by Karl R. Popper (1959/2002, 1963). Another intuition that supports this approach to confirmation is the prediction-accommodation asymmetry: we typically prefer hypotheses with a good predictive track record over those which have been fitted ad hoc to the data (Whewell 1847; Worrall 1989; Hitchcock and Sober 2004). The H-D model regards a hypothesis as confirmed if predictions have been derived deductively from the hypothesis, and the hypothesis was necessary to make these predictions: Hypothetico-Deductive (H-D) Confirmation Observation E H-D-confirms hypothesis H relative to background knowledge K if and only if 1. H ∧ K is consistent; 2. H ∧ K entails E (H ∧ K |= E); 3. K alone does not entail E. The H-D approach to confirmation avoids the paradox of the ravens because the raven hypothesis H = ∀x: Rx → Bx does not make any predictions about whether a particular 119

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object a is a black raven or a non-black non-raven. The only thing H entails is that a cannot be a non-black raven. We can also reconstruct Hempel’s analysis of the paradox: relative to the background knowledge K1 = Ra, the observation E1 = Ba H-D-confirms the raven hypothesis. So does the observation E2 = ¬Ra relative to background knowledge K2 = ¬Ba— for example, the genetic analysis of a grey bird whom we cannot classify by the eye as crow or raven. In other words, black ravens, grey crows and even white shoes can all confirm the raven hypothesis as long as the observation constitutes a genuine test of the hypothesis. So the paradox of the ravens is handled in a satisfactory way by the H-D account. Similarly, Goodman’s paradox does not arise because the H-D account embraces the conclusion that contradictory hypotheses can be confirmed by the same evidence. Remember that the paradoxical aspect of Goodman’s paradox emerged from the fact that hypotheses with incompatible predictions are confirmed by the evidence. This is, however, only worrying for “inductivist” or “projectivist” accounts of confirmation, such as instantial relevance and probability-raising. By contrast, the rationale behind H-D confirmation is in the first place to assess the past performance of hypotheses in experimental tests (see also Popper 1959/2002, ch. 10). A more serious challenge for the H-D account is given by the so-called tacking paradoxes. Suppose H denotes the General Theory of Relativity, E denotes Eddington’s observation during the 1919 solar eclipse that star light is bent by the sun, and X a nonsensical hypothesis such as “The moon consists of green cheese”. H is hypothetico-deductively confirmed by observation E relative to background knowledge K, and so is H ∧ X because this hypothesis also entails E, due to the monotonicity of logical entailment. Thus, the conjunction of General Theory of Relativity and the hypothesis that the moon consists of green cheese has been confirmed. This sounds completely absurd since confirmation is transmitted “for free” to the irrelevant, and in fact, nonsensical conjunct which has never been tested empirically. The scheme can be generalized easily to other examples. The bottom line is that if E H-D-confirms H, then E also H-D-confirms any H ∧ X that is consistent with H and K. When we tack an irrelevant conjunct to a confirmed hypothesis, H-D-confirmation is preserved. This is highly unsatisfactory. An analogous (though less discussed) problem for H-D confirmation is the confirmation of a hypothesis H by evidence that is logically weaker than the deductively implied prediction E, such as the disjunction of E with an irrelevant observation O, that is, E ∨ O. In both cases, it seems that H-D confirmation misses out on a satisfactory account of evidential relevance (Moretti 2006). There have been several solution proposals trying to endow H-D confirmation with an account of evidential relevance. Early proposals by Horwich (1982) and Grimes (1990) must be regarded as having failed (e.g., Gemes 1998). Two more promising accounts have been developed in later work. The first is the account of relevant conclusions by Gerhard Schurz (1991), based on the idea that any predicate that relevantly occurs in a logical inference must contribute to the inference and cannot be replaced arbitrarily by a different predicate salva veritate. This account classifies an entailment such as ∀x: Fx |= Fa ∨ Ga as irrelevant since the entailment would remain valid if G were replaced by any other predicate. An analogous definition can be given for irrelevant premises. The definition of H-D confirmation is then amended by the requirement that the entailment H ∧ K |= E contains neither irrelevant premises nor irrelevant conclusions. The second proposal is based on the concept of content parts. The basic idea, introduced by Ken Gemes (1993), is that an entailment H |= E is relevant if and only if every relevant 120

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model of E (i.e., a model that assigns truth values only to those atomic formulae that affect the truth value of E) can be extended to a relevant model of H. In such a case, we call E a content part of H and amend the second clause of H-D confirmation by demanding that E be a content part of H ∧ K. This modification takes care of the problem of tacking irrelevant disjuncts to E; for tacking irrelevant conjuncts to H, complementary solutions have been suggested by Gemes (1993) and Sprenger (2013). More discussion of H-D confirmation and possible fixes for the tacking paradoxes is found in Sprenger (2011). For an account of confirmation based on instantial relevance (Nicod, Hempel), the tacking paradoxes do not arise since these accounts do not validate what Hempel calls the Converse Consequence Condition (i.e., if E confirms H, it also confirms logically stronger hypotheses). The Bayesian, however, has to respond to the tacking paradoxes since confirmation as increase in firmness subsumes H-D confirmation as a special case. If H entails E conditional on background knowledge K, it will be the case that p(E|H, K) = 1. By assumption, then also p(E|K) < 1, since otherwise K would already have entailed E, contradicting the assumptions of H-D confirmation. Thus, p(E|H, K) > p(E|K) and by Bayes’s Theorem, we infer p(H|E, K) > p(H|K) and E confirms H relative to K. The Bayesian replies, as usual, that the problem can be mitigated from a comparative point of view: if E raises the probability of hypothesis H, and E is intuitively relevant for H, the degree of evidential support for H is higher than for the hypothesis H ∧ X where X denotes, as before, an irrelevant conjunct. Obviously, such a claim is sensitive to the used measure of evidential support (see the chapter by Peter Brössel in this volume). For example, for the ratio measure r(H, E, K) = p(H|E, K)/p(H|K) we can derive showing that the conjunction H ∧ X is supported to the same degree as the original hypothesis H. The other principal measures of evidential support, like the difference or the likelihood ratio measure, fare better in this respect: whenever p(E | H∧X ∧ K) = p(E | H ∧ K), they reach the conclusion that H ∧ X is confirmed less than H (Hawthorne and Fitelson 2004, revised Theorem 2). This result on the tacking paradoxes includes H-D confirmation as a special case since p(E | H∧X ∧ K) = p(E|H ∧ K) = 1 whenever H entails E. Bayesian Confirmation Theory acknowledges the tacking paradoxes, but demonstrates at the same time how they can be mitigated. r(H∧ X, E, K) = p(H∧X | E, K)/p(H ∧ X|K) = p(E | H∧X ∧ K)/p(E |K) = 1/p(E|K) = p(E|H, K)/p(E |K) = r(H, E, K)

4 Conclusion The paradoxes of confirmation show how the absence of a theory of evidential relevance challenges purely formal accounts of confirmation: a syntactic criterion detects evidential support, but the case looks spurious to our pre-theoretical intuitions. “All ravens are black” is confirmed by observing a white shoe, “all emeralds are grue” by observing a green emerald, and observations of the planetary motions confirm Kepler’s laws together with the hypothesis that the moon consists of green cheese. The paradoxes consist of two groups: Goodman’s and Hempel’s paradoxes are particularly problematic for accounts of confirmation based on instantial relevance (Nicod, Hempel), whereas the tacking paradoxes attack accounts based on the concept of successful prediction, such as the H-D account (see again Table 9.1). Immunization strategies have no easy life: while Hempel’s account of confirmation fails to conform with his own analysis of the raven paradox, the H-D account can block the tacking paradoxes only at the price of considerable technical complications. The 121

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Bayesian account of confirmation as increase in firmness is in general more permissive than those accounts (e.g., it includes H-D confirmation as a special case), so it has to respond to all three paradoxes. On the other hand, the Bayesian has an additional strategy at her disposal, unavailable to purely qualitative (“all-or-nothing”) accounts of confirmation: she admits that intuitively irrelevant evidence may raise the probability of the hypothesis, but that it does so to a lesser extent than the relevant contrast class (e.g., black raven/white shoe). This comparative resolution is applicable to all three paradoxes—but it falls short of showing that the degree of support provided in the problematic case is close to zero. It is much more demanding to provide such a quantitative resolution. While the best treatment of the paradoxes remains an open research question, the existing results show that the paradoxes do not trivialize confirmation theory and that the latter remains a fruitful branch of philosophy of science and formal epistemology.

Acknowledgements This chapter rewrites excerpts from Sprenger (2010), (2011) and the first chapter of Sprenger and Hartmann (2019) and merges them with novel material. I would like to thank Bengt Autzen and Peter Brössel for their valuable feedback, and the editors of this volume, Clayton Littlejohn and Maria Lasonen-Aarnio, for their invitation to contribute. Research on this article was supported through Starting Investigator Grant “Making Scientific Inferences More Objective” (grant No. 640638) by the European Research Council.

References Carnap, Rudolf (1950). Logical Foundations of Probability. Chicago: University of Chicago Press. Crupi, Vincenzo (2015). Confirmation. In Ed Zalta (ed.), The Stanford Encyclopedia of Philosophy. Retrieved from https://plato.stanford.edu/archives/sum2018/entries/confirmation/. Earman, John (1992). Bayes or Bust? A  Critical Examination of Bayesian Confirmation Theory. Cambridge, MA: MIT Press. Festa, Roberto (2012). “For Unto Every One That Hath Shall Be Given”: Matthew Properties for Incremental Confirmation. Synthese 184, 89–100. Festa, Roberto and Gustavo Cevolani (2017). Unfolding the Grammar of Bayesian Confirmation: Likelihood and Anti-Likelihood Principles. Philosophy of Science 84, 56–81. Fitelson, Branden (2008). Goodman’s “New Riddle”. Journal of Philosophical Logic 37, 613–643. Fitelson, Branden and James Hawthorne (2011). How Bayesian Confirmation Theory Handles the Paradox of the Ravens. In James H. Fetzer and Ellery Eells (eds.), The Place of Probability in Science, pp. 247–275. New York: Springer. Gemes, Ken (1993). Hypothetico-Deductivism, Content and the Natural Axiomatisation of Theories. Philosophy of Science 60, 477–487. Gemes, Ken (1998). Hypothetico-Deductivism: The Current State of Play; the Criterion of Empirical Significance: Endgame. Erkenntnis 49, 1–20. Glymour, Clark (1980). Theory and Evidence. Princeton, NJ: Princeton University Press. Good, I. J. (1967). The White Shoe Is a Red Herring. British Journal for the Philosophy of Science 17, 322. Goodman, Nelson (1955/83). Fact, Fiction and Forecast (4th ed.). Cambridge, MA: Harvard University Press. Grimes, Thomas R. (1990). Truth, Content, and the Hypothetico-Deductive Method. Philosophy of Science 57, 514–522. Hawthorne, James and Branden Fitelson (2004). Re-Solving Irrelevant Conjunction with Probabilistic Independence. Philosophy of Science 71, 505–514. Hempel, Carl G. (1945a). Studies in the Logic of Confirmation I. Mind 54, 1–26. Hempel, Carl G. (1945b). Studies in the Logic of Confirmation II. Mind 54, 97–121.

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The Paradoxes of Confirmation Hempel, Carl G. (1965a). Aspects of Scientific Explanation and Other Essays in the Philosophy of Science. New York: Free Press. Hempel, Carl G. (1965b). Science and Human Values. In Aspects of Scientific Explanation, pp. 81–96. New York: Free Press. Hitchcock, Christopher and Elliott Sober (2004). Prediction Versus Accommodation and the Risk of Overfitting. British Journal for the Philosophy of Science 55, 1–34. Horwich, Paul (1982). Probability and Evidence. Cambridge: Cambridge University Press. Howson, Colin and Peter Urbach (1993). Scientific Reasoning: The Bayesian Approach (2nd ed.). La Salle, IL: Open Court. Huber, Franz (2007). Confirmation and Induction. In J. Fieser and B. Dowden (eds.), Internet Encyclopedia of Philosophy. Retrieved from www.iep. utm.edu/conf-ind/ on April 27, 2020. Jackson, Frank (1975). Grue. Journal of Philosophy 72, 113–131. Maher, Patrick (1999). Inductive Logic and the Ravens Paradox. Philosophy of Science 66, 50–70. Moretti, Luca (2006). The Tacking by Disjunction Paradox: Bayesianism Versus Hypothetico-Deductivism. Erkenntnis 64, 115–138. Nicod, Jean (1925/61). Le problème logique de l’induction. Paris: Presses Universitaires de France. Originally published in 1925 (Paris: Alcan). Norton, John D. (2019). A Demonstration of the Incompleteness of Calculi of Inductive Inference. British Journal for the Philosophy of Science 70, 1119–1144. Okasha, Samir (2007). What Does Goodman’s ‘Grue’ Problem Really Show? Philosophical Papers 36, 483–502. Popper, Karl R. (1959/2002). The Logic of Scientific Discovery. London: Routledge. Reprint of the revised English 1959 edition. Originally published in German in 1934 as “Logik der Forschung”. Popper, Karl R. (1963). Conjectures and Refutations: The Growth of Scientific Knowledge. London: Routledge. Schurz, Gerhard (1991). Relevant Deduction. Erkenntnis 35, 391–437. Sprenger, Jan (2010). Hempel and the Paradoxes of Confirmation. In Dov Gabbay, Stephan Hartmann, and John Woods (eds.), Handbook of the History of Logic, Volume 10, pp.  235–263. Amsterdam: North-Holland. Sprenger, Jan (2011). Hypothetico-Deductive Confirmation. Philosophy Compass 6, 497–508. Sprenger, Jan (2013). A Synthesis of Hempelian and Hypothetico-Deductive Confirmation. Erkenntnis 78, 727–738. Sprenger, Jan (2016). Confirmation and Induction. In Paul W. Humphreys (ed.), Handbook of Philosophy of Probability, pp. 185–209. Oxford: Oxford University Press. Sprenger, Jan and Stephan Hartmann (2019). Bayesian Philosophy of Science. Oxford: Oxford University Press. Vranas, Peter B. M. (2004). Hempel’s Raven Paradox: A Lacuna in the Standard Bayesian Solution. British Journal for the Philosophy of Science 55, 545–560. Whewell, William (1847). Philosophy of the Inductive Sciences, Founded Upon Their History. London: Parker. Worrall, John (1989). Structural Realism: The Best of Both Worlds? Dialectica 43, 99–124.

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10 GOOD PREDICTIONS AND BAD ACCOMMODATIONS Eric Christian Barnes

The Very Idea of a Prediction Novel predictions, intuitively, are empirical consequences of theories that strike us as particularly impressive as evidence—such as the prediction made by a competent meteorologist of the future state of the weather.1 Making such predictions successfully (on a regular basis) is of course not easy—it presumably requires considerable expertise. It is much easier to start with some known data and simply build a theory that explains that data (a so-called accommodation of the data)—this may require no expertise at all, perhaps merely a facility with words. (“Of course it rained yesterday, the prevailing atmospheric conditions made it inevitable!”) Predictivism is the thesis that novel predictions carry more evidential weight than accommodations. Some maintain that novel predictions are those predictions that are not known by the theorist at the time the theory is formulated. This was Karl Popper’s point when he asserted that Confirmations should count only if they are the result of risky predictions; that is to say, if, unenlightened by the theory in question we should have expected an event which was incompatible with the theory—an event which would have refuted the theory. (1963: 36) Popper hereby embraced a temporal conception of novelty: what makes a prediction novel is the fact that it is not known to be true (better, is expected to prove false) at the time the theory is constructed. Only predictions that are novel in this sense should ‘count’ for Popper—evidence that is known at the time the theory is formulated is irrelevant to Popper’s assessment of the theory. While this conception of novelty has some intuitive appeal, it quickly appears dubious upon reflection. For on this approach it matters entirely at what time a particular empirical consequence comes to be known—but why should the support provided by some observed fact for a theory depend on such an apparently irrelevant point such as when it was discovered? DOI: 10.4324/9781315672687-13 124

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Zahar (1973) and Worrall (1978) argue that what is important about an empirical consequence of a theory is not whether it was known before the theory was constructed but whether the theorist ‘used’ an empirical result in constructing a theory by specifically building the theory to fit that result—and thereby ‘accommodating’ it—novel consequences are those the theory was not built to fit. Gardner (1982: 3) deemed this particular conception of novelty ‘use-novelty’—in subsequent literature it is widely referred to as the ‘heuristic conception of novelty’. If we were to accept the heuristic conception of novelty, we are well positioned to understand the appeal of the temporal conception: if evidence is temporally novel then it must have been heuristically novel (unknown evidence cannot be used to construct a theory). Temporal novelty guarantees heuristic novelty. ‘Strong predictivism’ claims that predictions are intrinsically superior to accommodated evidence—‘weak predictivism’ claims that predictions are merely symptomatic of some other virtue of a theory that carries intrinsic evidential weight. If one thinks that heuristic novelty is in and of itself a kind of epistemic virtue, while temporal predictivism is merely symptomatic of heuristic novelty, then one could be a strong predictivist with respect to the heuristic conception and a weak predictivist with respect to the temporal conception. But strong heuristic predictivism is itself a curious thesis. For one could also wonder why it matters whether some evidence was used in a theory’s construction. Isn’t confirmation just a logical relationship between evidence and theory? Traditionally, philosophers have posited a distinction between the context of discovery and the context of justification.2 According to this distinction, discovery—the process of generating a new theory— is entirely a psychological process that itself has no bearing on justification (the logical process of evaluating how strongly a theory was supported by evidence). The distinction between the two contexts makes the point that in assessing how well a theory is supported evidentially it doesn’t and shouldn’t matter how a theory was ‘discovered’ or constructed. Strong heuristic predictivism forces us to repudiate that distinction (cf. Leplin 1987). To construct a theory is to formulate the theory by a cognitive act of the imagination. It is indeed a mistake, in my view, to make such an act the focus of one’s account of novelty. A proper account of novelty should preserve the distinction between the contexts of discovery and that of justification, as I will now explain. Let us call any person who evaluates the probability of some theory T a ‘T-evaluator’. Now when a T-evaluator makes a judgment about the probability of T she may well do this by looking carefully at the totality of evidence that bears on T, at various extra-empirical criteria that are relevant to its assessment (such as simplicity or fruitfulness), and at how well T coheres with relevant background knowledge. But as I  argue elsewhere (Barnes 2008: ch. 2) it is also the case that scientists count as evidence the judgments of other scientists—those they take to be competent—about the probability of theories and related propositions. I refer to scientists who do this as ‘epistemic pluralists’. Now let us consider a competent scientist, Connie, who constructs a new theory T that entails some (currently unverified) empirical consequence N1 (so N1 is temporally, and thus heuristically, novel). Connie assures us that N1 will turn out true, and it does. A pluralist T-evaluator is impressed and is prepared to assign a high probability to T based on both the demonstrated truth of its consequence N but also the demonstrated expertise of Connie, T’s constructor. But at this point Connie explains that while she did construct T and did predict N, she does not endorse T—in fact she is certain that T is false. She claims that if T is tested again, this time for another novel (also very unlikely) consequence N2, 125

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T will be shown false. She is obviously sincere. It seems to me that while the demonstrated truth of N1 still constitutes evidence for T (after all, N is a consequence of T), T is ultimately not confirmed in this scenario. This is because Connie, who has demonstrated predictive skill by accurately predicting N1, did not endorse T (indeed, she renounced T) upon constructing it. Now we suppose that another competent scientist, Endora, appears and claims that Connie is mistaken. Endora endorses T and claims that it is probably true—and that N2 will be shown true when tested. Now suppose N2 is shown to be true. The truth of N2 could testify, for our T-evaluator, to the credibility of Endora rather than Connie— specifically to Endora’s possession of a truth-conducive basis for endorsing T—despite the fact that she did not construct T. The long tradition of spelling out novelty in terms of the notion of construction reflects, I suspect, an uncritical tendency to assume that any constructor of a theory also counts as an endorser of that theory. To endorse a theory is to affirm that theory as true (or approximately true, or perhaps just empirically adequate) in the presence of some evaluator(s). In my philosophical reconstruction of endorsement, to endorse a theory is to post (viz., publicly present to evaluators) a probability for that theory that is high enough to establish the endorser as a proponent of that theory. This probability need not be particularly high, merely high enough to warrant further pursuit of T. Precisely how high this must be is a context-sensitive matter that I discuss in detail elsewhere (Barnes 2008: 35). I claim that N (a known consequence of T) counts as a novel confirmation of T relative to agent X insofar as X posts an endorsement-level probability for T that is based on a body of evidence that does not include direct observational support of N.3 So X does not base her endorsement of T on any observations that support N directly. Confirmations that are novel in this sense I deem ‘endorsement-novel’. Predictivism now amounts to the claim that when true evidence N confirms T, endorsed by X, T is more strongly confirmed (for some evaluator) when N is endorsement-novel than when it is not. This conception of predictivism rightly ignores the process by which a theory was constructed and focuses on the acts of endorsement by scientists that are clearly relevant to the scientific community’s assessment of theories. But why should it matter whether that endorsement was based on some observational datum or other?

Pro-Prediction Predictivism Philosophers have offered many reasons for accepting predictivism—on one approach, predictivism is true not because there is anything wrong with accommodations, but because predictions have a special virtue that accommodations lack. I call this the ‘pro-prediction’ approach. I turn now to several pro-prediction theories, starting with my own.

Endorsement-Novelty and the Background Beliefs of the Predictor Consider the following story: You are a newspaper editor. One of your writers, Morley, is writing an investigative story about a well-known politician named Jacks. Now Morley assures you that he has a very reliable source who is very close to Jacks and who supplies Morley with detailed information about him. You are skeptical—there are many dubious sources about, and

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Morley’s track record with prior sources is far from stellar (though you know him to be scrupulously honest). But you concede that it is possible that his source is reliable. Morley tells you that his source S has given him various bits of information about Jacks’s private life—this provides you with two pieces of evidence: (a1) S claims that Jacks has a tendency to visit a gambling den known as the Lucky Gent, not returning until near dawn. (a2) S claims that occasionally Jacks wears a curious outfit that is solidly green from top to bottom. Now you and Morley are among the few living people aware that there is a secret society, known as the Bull and Scones, which holds its secret meetings at the Lucky Gent and occasionally requires its members to dress in solid colors (you and Morley are both former members and there is a strict code of secrecy about such rules). Morley, believing his sources to be reliable, thereby thinks it reasonably probable that Jacks is a member of the Bull and Scones—call this theory T (he thus ‘endorses’ T to this degree). You see little reason to believe this yourself, given your doubts about Morley’s sources. It is extremely improbable that Morley’s sources have any information about the Bull and Scones society. Thus you see no reason to endorse T. Now let me pause and ask you to consider whether your knowing a1 and a2 causes any change in your assessment of Morley’s source’s credibility. These two bits of information display what might strike you as a curious pattern, but this scarcely seems like a reason to trust the source. Now you both know that members of the Bull and Scones travel every summer to Larkhall, Scotland, for the annual international meeting of the B&S Society—so Morley boldly predicts that his source will confirm that Jacks will travel there next summer upon being asked. He then asks his source whether Jacks has any plans for summer travel (being careful not to mention anything about Scotland). The source reports that Jacks plans to travel to Larkhall, and he reports this to you (bear in mind that Morley is scrupulously honest, and that his source surely has no knowledge of the Bull and Scones policies). Now consider two questions: how good is your evidence at this point for the claim that Jacks is a member of Bull and Scones, and how good is your evidence that Morley’s source is reliable? My intuition is that you now have good evidence both that Jacks is a member of the Bull and Scones society and that Morley’s source is reliable—but there is an aura of strangeness about this since all the observational evidence you have has come from a source about which you were rightly dubious, and no new evidence directly confirming the reliability of the source has been procured. How can this be? The dynamics of evidential support in this story reflect the time-honored truth that confirmation is not simply a two-place relation between theory and evidence, but a three-place relation between theory, evidence and background belief. In this story Morley plays the role of a predictor and you the evaluator. We have: K = Morley’s source S is reliable. (Morley’s background belief) T = Jacks is a member of the Bull and Scones club. (Morley’s theory)

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A  =  S affirms that Jacks visits the Lucky Gent and occasionally dresses in solid colors. (Accommodated evidence) N = S will affirm that Jacks travels this summer to Larkhall, Scotland. (Morley’s prediction) At the beginning of the story, you (the editor) assign K a fairly low (but not microscopic) probability. Evidence A is procured, and while this does not change your estimate of K’s probability you notice that the conjunction of K and A make T reasonably probable. Morley, however, actually believes K, and thus endorses T on the basis of A (bearing in mind that ‘endorsement’ does not mean accepting T as true but only as ‘reasonably probable’). Noting that T entails N, he thereby predicts N, and it is confirmed. N is endorsement-novel for Morley because he did not base his endorsement of T on any direct observational evidence for N. The critical point here is that N, in following from a theory that itself is made ‘reasonably probable’ by K and A, has turned out to be a reasonably probable consequence of K. N, moreover, is extremely improbable if K is false. Thus N strongly confirms K. But now that K is strongly confirmed, T is strongly confirmed as well, because T is strongly confirmed by evidence that has itself been made evidentially potent by K. N has a special power to confirm T that A lacks—this is because N confirms the background belief of the N-predictor in a way that A does not. A merely combines with K to suggest that T is reasonably probable. The accommodation of A (which amounts to Morley’s endorsement of T on the basis of A) does not involve any fallacy on the part of the predictor/endorser, but simply lacks the virtue of confirming background beliefs. Thus this is a form of ‘pro-prediction predictivism’.4 My position is that the story could be rewritten so that any one of the three pieces of evidence (Lucky Gent visits, solid color dress, and Larkhall trip) could function as the prediction while the other two are accommodated, and the same predictivist result would be obtained. In Barnes (2008: especially ch. 3) I develop this account of predictivism in detail and apply it to the historical case of Mendeleev’s periodic law (PL). PL as initially presented by Mendeleev asserts a nomological relationship—expressed by a periodic function—between the atomic weight of each element5 and its various chemical and physical properties. PL is the theoretical basis for his famed Periodic Table of the Elements. The story of Mendeleev’s presentation of PL, and its assessment by the scientific community, is thought by many commentators to illustrate the truth of predictivism. He showed in his initial presentation of PL how it could accommodate the 60+ known elements. However, Mendeleev also made several bold predictions—these were that three gaps in the Periodic Table would be filled by the discovery of new elements and that certain heretofore accepted values of atomic weights would be revised to accord with their position in the Table. It was, according to various commentators, only after Mendeleev’s predictions were confirmed that PL began to receive serious attention from the scientific community, and in 1882 he received the prestigious Davy Medal from the Royal Society for his work on PL. This was after two of his predicted elements had been discovered and two of the atomic weight predictions had been fulfilled. Maher offers a predictivist interpretation of this episode when he writes that “The only plausible explanation [for Mendeleev’s winning the Davy Medal] is that scientists were impressed by the fact that these latter pieces of evidence were verified predictions rather than accommodated evidence” (1988: 275). My preferred explanation of this preference for prediction runs as follows: Mendeleev endorses PL on the basis of a body of accommodated evidence (the 60+ known elements). 128

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When he does this, he is relying on several background beliefs, because the accommodated evidence can only establish PL when conjoined with these background beliefs. Skepticism about PL at this point is to a significant extent reflective of skepticism throughout the scientific community about these background beliefs. Now Mendeleev predicts various bold consequences of his theory. When these consequences come to be fulfilled, this dramatically increased the scientific community’s confidence that Mendeleev’s background beliefs were true, and this in turn generated a higher confidence that PL was true (given that PL followed fairly clearly from these background beliefs and accommodated evidence). Thus predictivism holds true in this episode because of the special power that predictions have to confirm the background beliefs of the predictor. The role of Mendeleev’s background beliefs in his story is comparable to that of Morley’s source in the example provided earlier. My theory is an example of weak endorsement predictivism—whether evidence is endorsement novel is not intrinsically relevant as evidence, but such novelty tracks underlying facts about the confirmation of background belief. I now turn to consider other ‘proprediction predictivisms’.

Reliable Methods of Making Predictions Patrick Maher (1988) presented a seminal thought experiment that contained two scenarios. In the first scenario, a subject (the accommodator) is presented with E, which is the outcome of a sequence of 99 coin flips of a single fair coin. E forms an apparently random sequence of heads and tails. The accommodator is then instructed to tell us (the evaluators) the outcome of the first 100 flips—he responds by reciting E and then adding the prediction that the 100th toss will turn up heads—the conjunction of E and this last prediction is theory T. In the other scenario, another subject (the predictor) is asked to predict the outcome of 100 flips prior to witnessing any of them—the predictor affirms theory T. Thereafter the coin is flipped 99 times and E is established, thus vindicating the predictor’s first 99 predictions. The question is whether we (the evaluators) have reason to regard T as more strongly confirmed in one of the scenarios than in the other. There is, of course, a palpable intuition that T is better confirmed in the predictor’s scenario. Maher’s explanation of the predictivist intuition is that the success of the predictor gives us strong evidence that the predictor ‘has a reliable method of making predictions’, evidence that is wholly absent in the accommodator’s case. This is of course intuitively plausible, simply because the predictor has indeed an amazing track record of successful prediction that demands explanation. Maher applies this to the case of Mendeleev, maintaining that his successful predictions confirmed that his method of making predictions (which he described as “looking for properties in the pattern of the elements” [1988: 276]) was a reliable one. His accommodations did not provide this type of confirmation. Various commentators have objected that Maher’s coin flip example is not typical of actual scientific practice. Howson (1988: 384–5) observes that while the predictor presumably manages to make his successful predictions by deriving them from some theory, we (the evaluators) don’t even know what the theory says, nor are we shown the evidence (other than E) on which the theory is based. Such ‘hiddenness’ is not characteristic of actual science in which theories and evidence are openly presented and publicly assessed. Worrall (2014: 58) likewise notes that Maher’s approach places much emphasis on the predictor and accommodator themselves (i.e., whether they have a ‘method’ of some kind) rather 129

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than on the theories and evidence at stake—Worrall argues this is not the way actual science works. Maher’s account is a weak heuristic account—he takes the fact that E was not used in theory construction in the predictor’s scenario to be symptomatic of the fact that the predictor ‘has a reliable method of making predictions’, which turns out to be a reliable method of constructing theories (1993: 329) Thus, in my view, his account makes the mistake of taking facts about theory construction to be epistemically relevant to theory assessment (cf. Maher 1993). But more fundamentally, I  find Maher’s critical concept of a ‘reliable method of constructing theories’ to be simply obscure. It is hardly obvious that the process of theory construction is typically the result of what should be called the application of some method. Such a claim apparently implies that there is some algorithm for constructing good theories—and this seems quite dubious as a general claim. Creativity and serendipity are thought to play important roles in theory construction (e.g., Kantorovich 1993) and these seem to count against the claim that theory construction is method driven. And what does it mean in any case to say of some method of theory construction that it is ‘reliable’? Presumably such a method would be one that could be counted on to generate theories that are true, approximately true or at least empirically adequate—but what would such a method even look like?6 I offer as a more intuitive explanation of predictive success the attribution of truth to the background beliefs of the predictor. It is the truth of these background beliefs that empowers a scientist to use accommodated evidence as a basis for endorsing (rather than simply constructing) a true (or truthlike, or empirically adequate) theory—this is because confirmation is a three-way relation between background belief, evidence and theory. Predictive success, in providing evidence for the background beliefs of the predictor, thus provides special evidence that the predictor is ‘on the right track’ in a very straightforward way. I believe this makes for a more perspicuous and satisfying account of why and when predictivism is true.

Conditional and Unconditional Confirmation John Worrall was, along with Elie Zahar, an early proponent of strong heuristic novelty (cf. Worrall 1978). In his more recent work (e.g., 1989, 2002, 2014) he has made it clear that while his account is often presented as a heuristic account, it is “at root a logical theory of confirmation” (2005: 819) that takes use-novelty to be symptomatic of underlying logical features that establish strong confirmation of theory. It is thus another weak heuristic account. A scientific theory is naturally thought of as consisting of a core claim together with some more specific auxiliary claims. It is often the case that the core theory will leave unstipulated various ‘free parameters’—the auxiliary claims fix values for these parameters. The Copernican theory of astronomy, e.g., has as its core claim that the earth and planets revolve around the sun. This core claim, however, leaves as free parameters many more specific values, such as the specific masses of the bodies involved and the specific trajectories of the planets as they revolve; Copernican auxiliary claims would fix the value of such parameters. Worrall proposes to understand the confirmational difference between prediction and accommodation as follows: when evidence e is ‘used’ in the construction of a theory, it is typically used to establish the value of a free parameter in some core theory T. The 130

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result will be a specific version T’ of T. Importantly, when e is used in this way it will typically provide no confirmation for the core theory T. Rather, it will simply offer a ‘conditional confirmation’ of T’: assuming there is evidence for T, e provides evidence for T’. Predicted evidence, for Worrall, is thus evidence that is not used to fix free parameters, and this will typically be evidence that itself confirms the core theory T. Such evidence either follows immediately as a consequence of T (plus natural, independently established auxiliaries) or is a consequence of T’ that was not itself used to fix the free parameter in T’. Thus prediction, unlike accommodation, provides unconditional support for T’. Hence, weak heuristic predictivism holds true. One nice illustration of Worrall’s account is his example of “creation science” (2002 195–8), whose core theoretical claim is that (T) God created the universe in 4004 BCE essentially as it now is. T leaves open many free parameters that can be filled in depending on how the world now is. Creationists, Worrall explains, simply use whatever data happens to exist to fix these details. So insofar as there is a fossil record that appears to support Darwinian evolution, creationists can simply assert that when God created the world He created the fossil record as it is, perhaps to test our faith—this produces a specific version (T’) of creationism. The creationist might attempt to argue that T’ is as well supported by the fossil record as Darwinism (since T’ entails this record), but this would be based on a failure to realize the merely conditional nature of the support the fossil record provides to creationism. It provides absolutely no evidence for T, but only evidence for T’ on the assumption that there is independent evidence for T. Assuming no such evidence for T, the fossil record provides no evidence for T’. Worrall’s account of predictivism is surely plausible and illuminates something fundamental about why prediction matters. Worrall has, however, produced an account that unduly restricts the forms that predictivism can take. The role of accommodated evidence, on his account, is used simply to produce a specific version of a theory from a more general variant, while predicted evidence simply confirms the general variant. While I would not go so far as Mayo in claiming that the former inference is “not especially interesting” (2010: 162), I do think predictivism’s domain of applicability is broader than this. Worrall’s theory, in fact, strikes me as a special case of my own broader theory. What he would describe as the ‘core idea of a theory’ I would construe as a background belief that is one source of endorsement of a specific theory. For example, the core idea of Mendeleev’s PL is presumably the claim that “the domain of the elements forms some kind of systematic unity”—in Barnes (2008: 90) I identify this as one of the background beliefs that motivated Mendeleev’s endorsement of PL. Worrall would claim that Mendeleev’s predictions, unlike his accommodations, confirmed the core idea of the theory (cf. Scerri and Worrall 2001, and especially Worrall 2005: 823–6), but this could also be read as claiming that his predictions had the special virtue of confirming this background belief, in line with my own account.7 But in limiting the power of prediction to its ability to confirm theory cores, he misses the broader power of prediction to confirm a variety of other background beliefs, such as methodological beliefs (e.g., about how to compute atomic weights, cf. Worrall 2005) and broader beliefs about the reliability of theorizing in the relevant stage of the science in question (cf. Barnes 2008: 94–6, 102–4), and presumably others as well. Predictions do not simply confirm theory cores—they show in a general way that predictors are working with true background beliefs and thus count as competent endorsers. Predictive skill, once again, is evidence of competence. 131

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Anti-Accommodation Predictivism Another way of defending predictivism is to argue that the act of accommodating data systematically tends to generate poor theories—predictions by contrast possess no particular virtue but are simply immune to this problem. For example, Lipton proposed his ‘fudging explanation’ of predictivism by pointing out that the process of accommodation lends itself to the process of ‘fudging theories’, i.e., proposing theories that do not cohere with operative constraints on theory choice (1991: ch. 8). To illustrate, the phlogiston theory claimed that substances emitted phlogiston while burning. But anomalous data existed in that some substances actually gained weight through combustion. To accommodate this anomaly it was proposed that phlogiston had negative weight—but the latter hypothesis was obviously fudged because it violated an operative constraint on theory choice (it violated the widely held background belief that substances do not have negative weight as well as rendering mysterious the fact that many substances lost weight when burned) (Partington and McKie 1937–8: 33–8). Hitchcock and Sober (2004) offer a theory of predictivism that can be viewed as an antiaccommodationist theory. Assuming that data are ‘noisy’ (i.e., imbued with observational error) a good theory will tend not to fit the data perfectly. If a scientist constructs a theory that fits the data better than a good theory should, that scientist is guilty of ‘overfitting’ the data. If an evaluator knows that a theorist built her theory to fit noisy data, the evaluator will tend to worry that the theorist has overfit the data and thus constructed a flawed theory. However, if the evaluator knows the theorist built her theory without access to such data, or without using it in the process of theory construction, the evaluator need not worry that overfitting has occurred. Thus predictions are not vulnerable to the suspicion of overfitting while accommodations are.8,9

The Question for Weak Predictivism All the theories of predictivism that have been surveyed in this chapter have been weak theories insofar as they claim either that prediction is linked to some evidentially laudable feature of theories or that accommodation is linked to some discrediting feature—neither prediction nor accommodation is represented as having intrinsic epistemic significance. Other than my own account, they have also been heuristic theories that define prediction and accommodation in terms of whether evidence was used in the construction of theory. However, these other theories could be re-formulated to incorporate endorsement novelty (by, e.g., claiming that accommodation tends to produce endorsement of fudged theory, rather than its construction). I would heartily urge that re-formulation. However, weak predictivism suffers a basic ambiguity: does it simply affirm a correlation between prediction/accommodation and good/bad making features of theories, or does it imply that working scientists actually rely on such correlations in their assessment of theories? It is tempting to argue that however plausible the postulation of such correlations may be, working scientists ignore them, for their focus is quite properly on the details of the good/bad making features of the theories themselves. Insofar as they are fully informed of such details, facts about prediction and accommodation are rendered evidentially superfluous. I thus posit a distinction between two species of weak predictivism: ‘thin predictivism’ denies that evaluators assign any epistemic significance to the correlations, while ‘tempered

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predictivism’ affirms that evaluators actually rely on such correlations in assessing theories (Barnes 2008: 25–6). Tempered predictivism will tend to hold when evaluators recognize that their own grasp of the good/bad making features of theories is imperfect—facts about prediction/accommodation then become useful as guides to such features. Now there is more than one reason why an evaluator might judge that her grasp of such features is imperfect. One such reason is that the evaluator knows that there are evidential features to which the evaluator has no access. One extreme case of such an evaluator is the non-expert—the evaluator of a theory that is proposed in a discipline in which the evaluator is not trained at all. Under certain conditions, the non-expert can be a predictivist, both by acknowledging good predictions and bad accommodations (cf. Barnes 2008: 44–51). But even experts can be rightly convinced that there are evidential features of theories to which they have no access. These include interdisciplinary experts and ‘imperfect experts’ who realize that their own knowledge of the relevant features is less than perfect (Barnes 2008: 51–4). Even fully certified experts may concede that despite their erudition, there may nonetheless be features they have not fully grasped simply because the issues are complex and are easy to misunderstand—these I call ‘humble experts’ (Barnes 2008: 54–6; cf. also White 2003: 672–32 and Lipton’s distinction between ‘actual support’ and ‘assessed support’ [1991: 150f]). These too will tend toward tempered predictivism.

Notes 1 It should be noted that the term ‘prediction’ is sometimes used to refer to any empirical consequence of a theory. Here I use ‘prediction’ in the sense of ‘novel prediction’, i.e., to entail some form of novelty (cf. Popper 1963). 2 Reichenbach (1938) introduced the modern version of this distinction. 3 For example, I  have direct observational evidence that the moon is spherical by observing the moon’s shape, say, through a telescope. I  have observational evidence for this claim that is not direct if I have observational evidence (not including observations of any moon’s shape) that supports a theory that entails that all moons are spherical. I also have direct observational evidence that the moon will be spherical tomorrow because this follows straightforwardly as a generalization on past direct observation. 4 For a detailed Bayesian articulation of the relevant arguments, see Barnes (2008: 64–80). 5 Of course in later versions of the law the role of atomic weight was replaced with that of atomic number. 6 A somewhat similar theory is presented in White (2003), which argues that prediction confirms the claim that the predictor is ‘reliably aiming at the truth’. 7 The matter is complicated by the fact that it is unclear on my own account whether predictivism did hold in the case of this particular background belief (cf. Barnes 2008: 101–2). There are cases, such as this one, in which accommodated evidence may happen to confirm background belief. Worrall’s theory exhibits similar exceptions (as I argue in Barnes (2005: 806); cf. Worrall’s [2005: 820–1] reply). 8 However, Hitchcock and Sober also argue that successful predictions may provide positive evidence that the theory that generated such predictions was not itself a product of overfitting—thus it could be argued that their theory also has a pro-predictionist component (as well as an antiaccommodationist one). 9 As another example of anti-accommodationism, Lange (2001) argues that the process of accommodating data has a systematic tendency to produce theories that are ‘arbitrary conjunctions’—if a conjunction is arbitrary, then the confirmation of one of its conjuncts provides no evidence that its other conjuncts are true.

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References Barnes, Eric Christian, 2005, “On Mendeleev’s Predictions: Comment on Scerri and Worrall”, Studies in the History and Philosophy of Science, 36: 801–12. Barnes, Eric Christian, 2008, The Paradox of Predictivism, Cambridge University Press. Gardner, Michael, 1982, “Predicting Novel Facts”, British Journal for the Philosophy of Science, 33: 1–15. Hitchcock, Christopher and Sober, Elliott, 2004, “Prediction vs. Accommodation and the Risk of Overfitting”, British Journal for the Philosophy of Science, 55: 1–34. Howson, Colin, 1988, “Accommodation, Prediction and Bayesian Confirmation Theory”, PSA 1988, 2: 381–92. Kantorovich, Aharon, 1993, Scientific Discovery: Logic and Tinkering, SUNY Press. Lange, Marc, 2001, “The Apparent Superiority of Prediction to Accommodation: A Reply to Maher”, British Journal for the Philosophy of Science, 52: 575–88. Leplin, Jarrett, 1987, “The Bearing of Discovery on Justification”, Canadian Journal of Philosophy, 17: 805–14. Lipton, Peter, 1991, Inference to the Best Explanation, Routledge. Mayo, Deborah, 2010, “An Adhoc Save of the Theory of Adhocness?” in Mayo, D. and Spanos, A. (eds.), Error and Inference: Recent Exchanges on Experimental Reasoning, Reliability and the Objectivity and Rationality of Science, Cambridge University Press, pp. 155–69. Maher, Patrick, 1988, “Prediction, Accommodation, and the Logic of Discovery”, PSA 1988, 1: 273–85. Partington, J. R. and McKie, Douglas, 1937–38, “Historical Studies on the Phlogiston Theory”, Annals of Science, 2: 361–404, 4: 1–58, 337–71. Popper, Karl, 1963, Conjectures and Refutations: The Growth of Scientific Knowledge, Harper and Row. Reichenbach, Hans, 1938, Experiment and Prediction, University of Chicago Press. Scerri, E. and Worrall, J., 2001, “Prediction and the Periodic Table”, Studies in the History and Philosophy of Science, 32: 407–52. White, Roger, 2003, “The Epistemic Advantage of Prediction Over Accommodation”, Mind, 112, no. 448: 653–83. Worrall, John, 1978, “The Ways in Which the Methodology of Scientific Research Programmes Improves Upon Popper’s Methodology”, in Radnitzky, G. and Andersson, Gunnar (eds.), Progress and Rationality in Science, D. Reidel, pp. 45–70. Worrall, John, 1989, “Fresnel, Poisson and the White Spot: The Role of Successful Predictions in the Acceptance of Scientific Theories”, in Gooding, David, Pinch, Trevor and Schaffer, Simon (eds.), The Uses of Experiment: Studies in the Natural Sciences, Cambridge University Press, pp. 135–57. Worrall, John, 2002, “New Evidence for Old”, in Gardenfors, P., Wolenski, J. and Kijania-Placek, K. (eds.), In the Scope of Logic, Methodology and Philosophy of Science, Vol. 1, Kluwer Academic Publishers, pp. 191–209. Worrall, John, 2005, “Prediction and the Periodic Law: A Rejoinder to Barnes”, Studies in the History and Philosophy of Science, 36: 817–26. Worrall, John, 2014, “Prediction and Accommodation Revisited”, Studies in History and Philosophy of Science Part A, 45: 54–61. Zahar, Elie, 1973, “Why Did Einstein’s Programme Supercede Lorentz’s? (I)”, British Journal for the Philosophy of Science, 24: 95–123.

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11 BAYESIAN NORMS AND NON-IDEAL AGENTS Julia Staffel

Introduction Bayesian epistemology provides a popular and powerful framework for modeling rational norms on credences, including how rational agents should respond to evidence. The framework is built on the assumption that ideally rational agents have credences, or degrees of belief, that are representable by numbers that obey the axioms of probability. From there, further constraints are proposed regarding which credence assignments are rationally permissible and how rational agents’ credences should change upon learning new evidence. While the details are hotly disputed, all flavors of Bayesianism purport to give us norms of ideal rationality. This raises the question of how exactly these norms apply to you and me, since perfect compliance with those ideal norms is out of reach for human thinkers. A common response is that Bayesian norms are ideals that human reasoners are supposed to approximate—the closer they come to being ideally rational, the better. To make this claim plausible, we need to make it more precise. In what sense is it better to be closer to ideally rational, and what is an appropriate measure of such closeness? This article sketches some possible answers to these questions.

1  Evidence in Bayesian Epistemology Standard Bayesian accounts of rational norms pertaining to degrees of belief share at least two basic assumptions. The first assumption is that we can model people’s credences by representing them as precise numbers between zero and one. The second assumption—called probabilism—is that, if a person has ideally rational credences, they must be representable as conforming to the axioms of probability.1 Most proponents of Bayesianism think that there are some additional requirements of rationality that ensure that rational agents properly take their evidence into account. Merely being probabilistically coherent is an extremely weak requirement, in the sense that it can be satisfied by thinkers who respond to evidence in bizarre ways; for example, by doing counterinduction. Counterinduction is an updating policy that is the opposite of induction. For example, if doing induction involves increasing your confidence that all ravens are black every time you see a black raven, counterinduction

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involves decreasing your confidence that all ravens are black every time you see a black raven. Popular principles that further restrict which credences are rationally permissible include the Principle of Indifference, the Principal Principle, the Reflection Principle, Conditionalization, and Jeffrey Conditionalization.2 Proponents of the Uniqueness Principle think that all the rational requirements taken together specify a uniquely rational credence assignment for any body of evidence a subject might possess. I will briefly state a version of each of these principles and explain in what way it constrains how a rational agent can respond to evidence.

Conditionalization: When learning a new piece of evidence E with certainty (and nothing else), a thinker’s new credence in any statement A should become equal to their old conditional credence c(A|E).3 Conditionalization prescribes how a thinker should respond to evidence that is learned with certainty. But this arguably doesn’t cover all instances of learning because we sometimes become more confident in a claim without becoming entirely certain of it. For example, looking closely at a shirt in a department store might increase your confidence that it is navy blue rather than black, but you’re still not certain. Uncertain learning is covered by the following updating rule:

Jeffrey Conditionalization: Suppose {E1, . . ., En} is a set of mutually exclusive and jointly exhaustive statements, such that the agent’s experience will change their credences in {E1, . . ., En} from cold(Ei) to cnew(Ei). Then, their new credences should be as follows: For any A, cnew(A) = ∑icold(A|Ei)cnew(Ei). Hence, the agent’s new credence in any statement A is a weighted sum of their old conditional credences, with the weights being the agent’s new credences in {E1, . . ., En}. But even if we adopt both of these updating principles, agents have a lot of leeway with respect to how they respond to evidence, since neither one of these principles prescribes what conditional credences they should have. Having conditional credences that encode counterinductive updating policies is perfectly compatible with following (Jeffrey) conditionalization. The following principles add more stringent requirements:

Principle of Indifference: If there is a set of n symmetrical alternatives, and the agent has no reason to think that any of the alternatives are more likely than any others, they should assign a credence of 1/n to each alternative. The Principle of Indifference governs cases in which an agent either has no evidence favoring any element of a set of symmetrical alternatives or has evidence that doesn’t discriminate between them. The principle is controversial, however, because it is very 136

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difficult to explain what makes alternatives symmetrical. Sometimes, there are even multiple incompatible ways of identifying symmetrical alternatives, which lead to conflicting recommendations for which credences to adopt. In games of chance, it’s often easy to tell whether alternatives are symmetrical because they subsume comparable “packages” of alternative outcomes. For example, rolling an even number and rolling an odd number with a six-sided die would count as symmetrical (three similar ways of achieving each), whereas rolling a six and rolling an even number would not be. But now imagine a factory producing cubes whose side length is at most 1 inch. You are asked to assign a credence to the claim “the next cube produced will have a side length of at most half an inch.” Having no information about how many cubes of different sizes are produced, you try to apply the indifference principle, so you try to spread your credences evenly over different sizes the cube could be. The problem is: do you apply it to side length (which should give you the answer ½), or do you apply it to, say, cube volume (which should give you the answer 1/8)? Or perhaps side area (1/4)? None of these ways of identifying symmetrical alternatives seems to be more natural than the other, yet they give conflicting recommendations about what credence to assign (this example is due to Van Fraassen 1989). A further class of principles requires ideally rational agents to match their credence functions to probability functions that are more informed than their own. Two examples of such expert principles are the Reflection Principle and the Principal Principle. The Reflection Principle asks rational agents to align their current credences and their known future credences:

Reflection Principle: For any claim A, real number x ∈ [0,1], and times t1 and t2, where t1 comes before t2, rationality requires that

(

)

ct1 Aêct 2 ( A ) = = x. The Principal Principle asks rational agents to match their credences to the objective chances. Here is a recent formulation of the principle due to Pettigrew (2016), which he calls the Evidential Temporal Principle: Evidential Temporal Principle (ETP): If an agent has a credence function c and total evidence E, and Tch is the proposition that ch is the current chance function, then rationality requires that

(

)

(

c Ai êTch = ch Ai êE

)

for all propositions Ai in {A1,. . ., An}, and all possible chance functions ch such that Tch is in {A1,. . ., An} and c(Tch) > 0. If ch is one of the possible chance functions, then a rational agent’s current credence in some statement Ai, conditional on ch being the current chance function, must agree with ch’s probability for Ai, where ch is being updated on the thinker’s current total evidence. The strictest constraint on how rational agents should respond to learning new evidence, however, is captured in the aptly named Uniqueness Principle. In its strictest, interpersonal 137

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form, it says that for any particular body of evidence, there is only one rationally permissible credence function one can adopt.

Uniqueness Principle: For any body of evidence E, and set of statements {A1,. . ., An} there is exactly one credence distribution on {A1,. . ., An} that is rationally permissible for a thinker who possesses E. In this strict form, the principle does not allow that different thinkers with the same evidence could rationally disagree. A weaker form of the principle only assumes intrapersonal uniqueness, i.e., that there is a unique rationally permissible credence function for each agent, but not necessarily the same one for every agent. The Uniqueness Principle is best thought of as a kind of meta-principle, since it doesn’t itself say anything specific about how agents should respond to evidence. If it is correct, then this must be because of sufficiently specific first-order principles that make prescriptions about rational responses to evidence. Defenders of permissivism by contrast, claim that there is more than one set of permissible credences for an agent who possesses a given body of evidence. However, once an agent has chosen a set of priors from the permissible ones, even many permissivists think that the agent has to stick with their choice. Flip-flopping between different initially permissible credence functions is not allowed, since this can violate other requirements, such as conditionalization. Philosophers usually don’t specify which particular credence functions are permitted by a given body of evidence. However, arguably irrational updating policies such as counterinduction would presumably be ruled out by the Uniqueness Principle, as well as by various forms of moderate permissivism.4 Different proponents of the Bayesian framework disagree about which, if any, of these additional proposed requirements of rationality we should accept, and how we should argue for them. But regardless of which flavor of Bayesianism is chosen, the resulting frameworks share the following features: first, they characterize norms of ideal rationality that don’t take into consideration whether the relevant norms are feasible for human reasoners to comply with. Second, they make use of the theoretical stipulation of a prior credence function. This prior credence function, which models an agent’s degrees of confidence before receiving any evidence, does not correspond to a mental state we could ever find in a real human being. However, since the agent’s priors primarily encode their dispositions for responding to evidence by fixing their conditional credences, they are a very useful fiction. Third, the resulting frameworks are best understood as providing norms of propositional epistemic rationality, rather than doxastic rationality. A credence is propositionally rational for an agent when her evidence supports adopting that credence, regardless of whether she actually has that credence or will ever adopt it. (By contrast, a credence can only be evaluated for doxastic rationality when the agent actually has it.) Fourth, the resulting framework is best understood as being evaluative, i.e., it helps us evaluate whether an agent has credences that would be ideally propositionally rational for them to adopt. Agents don’t have to know the rules as set out in the language of the model, nor consciously follow them, in order to be rational. Being rational only requires being representable as following Bayesian rules, rather than carrying out one’s reasoning in terms of explicit numerical probabilities. Understood in this way, Bayesian rules of rationality are not intended to provide explicit guidance to agents in their reasoning. 138

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Standard Bayesian frameworks that spell out requirements of ideal epistemic rationality can only make very coarse-grained distinctions when evaluating agents: either the agent’s credences conform to the requirements, or they don’t. This raises an immediate worry: we have ample evidence, which I will describe in more detail in the next section, that humans can’t be perfect Bayesian agents. Hence, they are all irrational by the standards of any Bayesian framework. But then we may ask: in what sense do the Bayesian norms even meaningfully apply to non-ideal agents like you and me? A common reply is that human agents (or better, their cognitive systems, since this is not a matter of conscious agency for the most part) should approximate the Bayesian ideals. The closer a human thinker’s credences are to being ideally rational, the better. While this sounds nice, it’s also awfully vague. What does it mean to be closer to ideally rational? Why is being closer better? In the next section, I explain in more detail why human agents can’t be perfect Bayesian reasoners, and after that, I’ll sketch how these questions can be answered.

2  Applying Bayesian Norms to Non-Ideal Agents It is well known among psychologists and philosophers alike that human reasoners systematically violate Bayesian requirements of rationality. I  will first summarize some of the psychological findings and then explain some more systematic reasons why we should expect human thinkers to not be perfectly rational. One of the most famous results from psychology is the proneness of human reasoners to violate probabilism by making baserate fallacies. The base rate fallacy occurs when thinkers overestimate the probability of an outcome, because they don’t factor in the low base rate of a relevant condition. For example, people commonly don’t realize that a positive result on a very reliable medical test may not indicate a high probability that the person has a disease, if the disease is sufficiently rare. One hypothesis is that this results from a conflation of the confirmatory force of a piece of evidence with the posterior probability that is warranted in light of all of one’s evidence (e.g., Mastropasqua et al. 2010; Tentori et al. 2016). Another well-studied violation of probabilistic coherence often occurs when reasoners “unpack” coarse-grained into fine-grained options (e.g., “going on vacation” could be unpacked into going to various destinations). We often assign the coarse-grained option a different credence than the sum of the “unpacked” possibilities, which is incoherent (Sloman et  al. 2004; Brenner et  al. 2002; Rottenstreich and Tversky 2002; Tversky and Koehler 1994). Psychologists have also studied whether human thinkers update their credences in response to new evidence in the way conditionalization requires. People are often too conservative in their updates, i.e., they don’t change their credences as much as the evidence warrants (Edwards 1982; Slovic and Liechtenstein 1971). Also, people don’t have rigid or stable conditional credences, as required by the Bayesian framework (Zhao and Osherson 2010). People’s conditional credences also don’t align perfectly with their unconditional credences, as required by the standard definition of conditional probability (Zhao et al. 2009; see also Evans et al. 2015 for discussion and references). This is just a tiny sliver of the vast psychological literature on probabilistic reasoning, and there is a lively debate about how to interpret the results. In fact, the debate about whether humans are rational has been so intense that it has sometimes been labeled the rationality wars (see, e.g., Wallin 2013; Hahn 2014 for discussion). However, many psychologists seem to agree that human thinkers employ reasoning strategies that diverge from perfect Bayesian procedures, yet produce outputs that are practically useful, for they 139

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approximate Bayesian results closely enough in most circumstances. Identifying what these heuristics actually look like is one of the major research programs in psychology. Some have drawn more pessimistic conclusions—that humans are quite terrible at reasoning with uncertain information, and generally very irrational. But this is arguably too pessimistic—it neglects the fact that psychologists are far more interested in finding reasoning tasks we’re bad at than ones we’re good at. Tasks that seem relatively simple, yet elicit poor performance, are especially interesting to psychologists because they provide the best clues for what heuristics and shortcuts the human mind employs in simplifying probabilistic reasoning tasks. This can easily lead one to forget that we’re actually fairly good at a lot of everyday reasoning with uncertain information. It should also be noted that people can of course learn to avoid making common reasoning errors like the base rate fallacy; for example, by studying and applying the rules of probability theory, rather than relying on intuitive judgments. However, since we cannot constantly employ effortful and time-consuming explicit reasoning strategies, learning how to make probability calculations won’t turn anyone into a perfect Bayesian agent. The need for shortcuts and simplifications becomes apparent once we consider the complexity of Bayesian reasoning from a computational point of view. As shown by Cooper (1990), Bayesian reasoning is NP-hard, which is a very general, worst-case result about the complexity of Bayesian reasoning.5 This doesn’t mean that every instance of probabilistic reasoning is difficult, but when the probability of A depends on the values of many other variables, it can easily take a very long time for the result to be computed. The general difficulty of implementing a perfect Bayesian reasoning algorithm can provide an explanation for why the human mind uses simpler heuristics for solving probabilistic reasoning tasks (see also Staffel 2018 for further discussion, and Icard 2016 for an account of the sampling heuristic). There are further obstacles that arise from specific aspects of the Bayesian requirements. For example, if something is an a priori determinable truth, then the Bayesian framework states that the propositionally rational credence to assign to it is 1.6 But there are plenty of claims that we can understand and entertain but for which we have not yet been able to determine whether they are true or false. Some, such as Goldbach’s conjecture that every even number greater than two is the sum of two primes, has not been proved by anyone, whereas in other cases, I personally might have been unable to prove something (yet someone else might have already done so unbeknownst to me). In those cases, our computational limitations prevent us from forming the propositionally required credence in a way that is properly based on our evidence. Similar problems arise from the Bayesian requirement that one must never assign a lower credence to the entailments of a claim than to the claim itself. The difficulties just mentioned arise for any Bayesian framework that accepts the probabilistic coherence requirement and (Jeffrey) conditionalization. An additional problem presents itself for defenders of versions of the Uniqueness Principle. Arguments for the principle generally proceed on abstract theoretical grounds. They often purport to show that assuming a more permissive view has unpalatable consequences and conclude that there isn’t much or any leeway for which prior credences can rationally be adopted. But none of the defenders of uniqueness have even attempted to specify what this uniquely rational credence function might be, and they tend to be pessimistic about whether we could ever fully specify it.7 Hence, if human thinkers are unable to even determine which credence would be ideally rational, this makes it even harder to comply with the requirements of ideal rationality (and unknowable whether a thinker is perhaps even partially 140

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compliant or very close, at least for most empirical claims). Even for defenders of permissive views this can be a problem, if they claim that a rational thinker must stick with a prior credence function once they have chosen one. Priors are stipulations in our models that don’t correspond to an actual credal state a human being has at any point in their life. Hence, while we might have some plausible candidates for a credence function that could be a person’s prior credence function, based on their current imperfectly rational credence assignments, it doesn’t seem possible to single out a unique assignment of priors for them in a non–ad hoc way. Having reviewed some of the reasons why human thinkers can’t be perfectly rational, this leads us to the question in what way Bayesian requirements of rationality apply to thinkers like you and me. It is commonly claimed that the Bayesian norms are ideals that should be approximated. Somehow, a human thinker’s credences are supposed to be better the closer they are to complying with the ideal Bayesian norms. Unfortunately, this response is hardly ever spelled out further, although it is in dire need of clarification: what does it mean for a person’s credences to be closer to or farther away from being ideally rational? And in what sense is it better to be closer to being ideally rational? For all we know, rationality might be a “winner takes all” property, such that only complete compliance delivers any benefits. Fortunately, there is some recent literature on how these questions can be answered, as I will explain in the next section.

3  Approximating Ideals One important question that needs to be answered to explain in what sense Bayesian norms apply to non-ideal agents is what it means to be closer to or farther away from being ideally rational. A natural way to try to measure approximations to ideal rationality is by using distance measures. We can represent a credence assignment by an agent to a set of statements as a vector X = (x1, . . ., xn), where each component of the vector represents one of the thinker’s credences. We can then use distance measures between vectors to determine how far away this agent’s credences are from the closest credence assignment that meets all the requirements of rationality, which is also representable as a vector Y = (y1, . . ., yn). For example, take the incoherent credence function c1(It’s raining) = 0.4, c1(It’s not raining) = 0.3, representable as the vector v1 = (0.4, 0.3). What is the closest credence function that is coherent, and how far away from it is c1? To determine this, we first have to choose a distance measure. Suppose we choose the popular Euclidean distance measure: X -Y 2 =

n

å(x - y ) i=1

i

2

i

Applied to our example, we need to find the credences that minimize ((x - 0.4)2 + (y - 0.3)2 ). It turns out that the closest coherent credence function is c2(It’s raining) = 0.55, c2(It’s not raining) = 0.45, and the distance between c1 and c2 is about 0.212. But the problem is that this is not the only distance measure we could use. We could also use, for example, the absolute distance measure: X -Y 2 =

n

å(x - y ) i=1

i

2

i

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Applied to our example, we would then have to find the credences that minimize x - 0.4 + y - 0.3 . While c2 is one of the closest credence functions in terms of absolute distance, it is not the only one; there is more than one closest one (e.g., (0.7, 0.3) or (0.5, 0.5) are equally close in absolute distance). The distance in this case is 0.3. Hence, the two different measures in this case disagree on how far away c1 is from being ideally rational and whether there is one or many closest coherent credence functions. For another example, suppose that there are two tautologies, T1 and T2. Abby assigns a credence of 0.8 to T1 and a credence of 1 to T2. Bob assigns a credence of 0.9 to each tautology. Probabilistic coherence dictates that the propositionally rational credence to assign to each tautology is 1. Who is closer to being ideally rational, Abby or Bob? If we use the absolute distance measure, we get the result that they are equally close. But if we use the Euclidean measure, we get the result that Abby’s credences are farther from being ideally rational than Bob’s. This is because the Euclidean, but not the absolute distance measure, is sensitive to how incoherence is distributed through an agent’s credence function, with more evenly distributed incoherence being seen as less bad than more dramatic, locally concentrated incoherence. These are just two instances of a more general problem: there are many different distance measures we could use to measure the degree to which a person’s credences approximate the closest ideally rational credences, and these distance measures often disagree about orderings of credence functions according to their degrees of rationality (Staffel forthcoming, ch. 3). We can make progress on selecting appropriate distance measures by turning to the second question, which asks why it is better to be closer to ideally rational than farther away. Do these measures of proximity even track anything we care about? After all, it is not always true that merely being closer to an ideal is beneficial. For example, being second in line for your dream job rather than fifth brings you closer to an ideal in a certain sense. Yet, it doesn’t get you any more of the benefits that would come with having your dream job than the fifth-ranked person gets. It’s a winner-takes-all scenario. For ideal rationality to be worth approximating, it must not be a winner-takes-all case of this kind (De Bona and Staffel 2018; Staffel forthcoming). Value-based conceptions of ideal rationality are especially suitable for responding to this challenge. On such a view, there is some value that agents who comply with requirements of rationality are in the best position to attain. Take, for example, the accuracy-first view of rationality (e.g ., Pettigrew 2016). This view claims that the fundamental epistemic value is accuracy, i.e., having credences that are as close to the truth as possible. All requirements of epistemic rationality are justified by showing that agents who comply with them are better situated to have accurate credences than agents who violate them. But if being ideally rational guarantees optimal access to (epistemic) value, then this can potentially explain why it is good to approximate ideal rationality: because doing so might deliver increasing portions of the relevant value. Hence, if we want to explain why approximating ideal rationality is beneficial even if we can’t ever fully comply with all the requirements, we can look for arguments that fit the following pattern (Staffel forthcoming, ch. 5): First, we identify some value that justifies some requirement of rationality, in the sense that complying with the requirement best promotes this value and violating the requirement precludes optimal promotion of the value. Then we explain how this value can be attained to greater or lesser degrees. Next, we turn back to the first question about distance measures. We must select a distance measure such that approximating ideal rationality according to this measure delivers increasing amounts of the relevant value. If such a measure exists, we’ve arrived at a value-based explanation of 142

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why it is beneficial to approximate ideal rationality. (Both the distance measure and the method of quantifying amounts of value must of course be independently plausible, so as to avoid ad hocism.) Several ways of filling in this pattern have been explored in the literature. I will now briefly survey them and then point to possible further extensions and open questions. As I  already mentioned briefly, one popular value-based way of justifying requirements of ideal rationality is the accuracy-based approach. It justifies the most basic Bayesian norm, probabilism, via the following accuracy-dominance argument: suppose we measure how closely someone’s credences approximate the truth with a suitable measure of accuracy. Then, if a person’s credence assignment is incoherent, there is an alternative, probabilistically coherent credence assignment that is closer to the truth in every possible world, i.e., no matter what the truth is. By contrast, if a person has coherent credences, then there is no alternative credence assignment that is more accurate in every possibly world, i.e., a priori determinable to be more valuable (see, e.g., Joyce 1998, 2009; Pettigrew 2016). As shown by De Bona and Staffel (2017), we can use this argument for probabilism as a starting point to fill in the argument schema given earlier. Roughly, if a person has incoherent credences, they can improve their accuracy in every possible world if they move closer to coherence along the direct path toward the coherent credence function that is closest to them.8 We can use our earlier example of c1 to illustrate this result with a diagram. The three black dots in the diagram mark three different credence functions: the leftmost dot represents c1, the rightmost dot c2, and the middle dot represents c3, which assigns 0.45 credence to rain and 0.35 to no rain. The solid black diagonal line shows all the possible coherent credence functions one could assign. The two black arrows indicate how far away the credences in c1 are from the truth in each of the two possible worlds. It is easy to see that as we move toward c2 on the dashed line, the resulting credences are closer to truth

Figure 11.1  Illustration of Approximation Theorem

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regardless of whether it rains or not. The credence function c3, which lies on the dashed line, illustrates De Bona and Staffel’s theorem: approximating coherence on the direct path to the closest coherent credence function leads to improvements in accuracy, regardless of what the truth is. The accuracy argument is not the only popular argument for probabilistic coherence. Another popular argument is the Dutch book argument. It shows that coherent credences are better at guiding actions than incoherent credences. More specifically, if we assume that a person’s credences determine fair betting prices, we can show that incoherent, but not coherent, credences justify accepting combinations of bets that lead to a sure loss. For example, the credence function c1 justified selling a $1 on A for $0.40 and a $1 bet on ~A for $0.30. The seller gains $0.70 from the sale of the bets, but must pay out $1 for the winning bet, thus suffering a certain loss of $0.30. We can again build on this result to fill in the previous argument schema. As shown by De Bona and Finger (2015), if we standardize the types of bets we can use in devising a Dutch book, so that each credence can only be used for at most one bet with at most $1 stakes, then reducing one’s absolute distance from coherence lessens the Dutch book loss to which one is vulnerable. Moreover, as De Bona and Staffel (2018) show, the accuracy result and the Dutch book result are compatible in the sense that every reduction in incoherence that results in a guaranteed accuracy improvement also leads to a reduction in standardized Dutch book loss (but not vice versa). As Staffel (forthcoming, appendix to ch. 6) shows, we can also build on the accuracy arguments for the Indifference Principle and for the Principal Principle given by Pettigrew (2016) to explain why approximating the indifferent credences, or the credences prescribed by the Principal Principle, has accuracy benefits. Furthermore, the same general strategy can be used to measure how different ways of responding to newly learned evidence affect how closely a person’s credences approximate the ideally rational credences (Staffel forthcoming, ch. 7). One advantage of the accuracy-first program is that it justifies all requirements of rationality based on a single value: accuracy. However, a proponent of a value-based conception of rationality could also argue that different requirements of rationality are underwritten by different values, which may or may not be comparable, and can possibly come into conflict. Views of this type call for more complex ways of measuring approximations to rationality. Staffel (forthcoming, ch. 6) shows how different ways of measuring approximations to individual requirements of rationality and aggregating the result into a total score are appropriate for different multiple-value views of rationality. It is an open question which, if any, value-based conception of rationality is ultimately correct, which will then determine how we need to justify why it is good for human thinkers to approximate ideal rationality. It is furthermore an open question what we should say about non-value-based conceptions of rationality. If requirements of ideal epistemic rationality are not justified because they help us attain some kind of value, but in some other way, then the approximation argument schema presented in this section won’t apply. On those kinds of views, there must either be a different reason for why it is good to approximate ideal rationality, or they have to claim that it is not and argue for a winner-takes-all conception of rationality. Additionally, future research might also turn to investigating principles that prescribe how to respond to higher-order evidence. All the principles introduced in the first section pertain to how we should respond to first-order evidence. Yet, there is also a lively discussion about how to respond to evidence about one’s own reliability in responding to evidence. If there are value-based arguments for such principles, we can try to use 144

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the approximation argument schema to explain why the ideal responses to higher-order evidence are worth approximating. It must be emphasized that this way of extending the Bayesian framework to make it applicable to non-ideal thinkers does not affect the type of normative judgments the framework provides. I mentioned earlier that ideal Bayesian requirements are best understood as providing evaluative norms of propositional rationality. This is still true of the framework once we expand it to capture degrees of approximation to the ideal. The measures of degrees of rationality help us evaluate from a third personal perspective how rational or irrational a person’s credence assignment is. We can furthermore use it to explain why particular reasoning strategies might help human thinkers approximate Bayesian reasoning under certain conditions. However, the framework is not intended to provide guidance to human thinkers about how to be more rational. A theory that can serve such a guiding, ameliorative function would have to look very different from the view offered here in order to make it followable by human reasoners. However, the view offered here can serve as the yardstick by which we can measure whether particular ways of advising non-ideal reasoners for how to improve are in fact successful.

Conclusion In the first section of this paper, I introduced a variety of putative requirements of rationality that characterize how ideal Bayesian reasoners should assign credences under a variety of evidential conditions. Those requirements vary widely in what they permit as a rational response to particular evidential situations, and Bayesians of different stripes disagree about which of the requirements to endorse. Yet, all of the putative requirements are part of ideal theories of epistemic rationality, which cannot be fully complied with by human thinkers. In Section 2, I surveyed a variety of reasons why human thinkers can’t fully comply with ideal Bayesian requirements of rationality. The challenge for Bayesians is then to explain how far their ideal norms apply to non-ideal thinkers. The standard Bayesian framework has little to say about non-ideal agents, other than that their credences violate the requirements of ideal rationality. We can solve this problem by showing why the Bayesian requirements of ideal rationality are worth approximating by non-ideal thinkers. Building on value-based arguments for requirements of ideal rationality, we can demonstrate that approximating ideal rationality in particular ways is epistemically beneficial for non-ideal agents, even if they can’t ever be fully rational.

Notes 1 It’s important to emphasize that people’s credences need to be representable as precise numbers, rather than being precise numbers. Nobody thinks that people actually have numerical, precise probabilities in their minds (the exception being when people have explicit beliefs about precise probabilities). Rather, precise numbers are used to measure a quantity—degrees of belief—that has the right structure to be captured by the probability axioms. Bayesianism is non-committal about the nature of credences apart from that and is meant to be compatible with a range of positions on the question of whether credences are psychologically real. 2 A survey that discusses the principles, and arguments for them, in more detail, can be found in Hájek and Staffel (forthcoming), and also in Titelbaum (forthcoming). Interested readers may also start their inquiries into the details of these principles by consulting the following works: Kopec and Titelbaum (2016) on Uniqueness; Lewis (1980) and Pettigrew (2016) on the Principal Principle; Van Fraassen (1984) and Briggs (2009) for the Reflection Principle; Jaynes (2003) and White

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Julia Staffel (2009) on the Indifference Principle; Skyrms (1987) and Greaves and Wallace (2006) on Conditionalization; Jeffrey (1965) and Diaconis and Zabell (1982) on Jeffrey Conditionalization. 3 An agent’s conditional credence c(A|E) is standardly defined in terms of her unconditional credences as c(A&E)/C(E). Informally, c(A|E) represents the thinker’s credence in A, assuming that E is true. 4 One might wonder here which principle is responsible for ruling out counterinduction. Perhaps the Principal Principle, although it seems that counterinduction should be deemed irrational even when an agent doesn’t know the objective chances. It’s possible that the chances always tell against counterinduction, so even if the agent doesn’t know what the chances are, they might know enough to rule it out as an updating policy. 5 For a problem to be in the complexity class NP, it must be the case that it can be solved by a nondeterministic Turing machine in polynomial time. In other words, the maximum amount of time it takes a non-deterministic Turing machine to solve the problem is determined by a polynomial function of the size of the input. A task is called NP-hard if it is at least as hard as any NP problem, and possibly harder. Hence, Cooper’s result tells us that the general task of determining the probability of some claim A based on a body of information is at least as hard as any problem in the complexity class NP. However, it’s important to keep in mind that this is a worst-case result, and it doesn’t tell us anything about the difficulty of any particular reasoning task. 6 The view that the (ideally) propositionally rational credence for a priori determinable truths is 1 is quite central to the Bayesian framework but is not necessarily shared by epistemologists more generally. It is controversial whether an agent really possesses the relevant (a priori) evidence when they are completely incapable of seeing how to derive the claim in question. 7 The same problem arises for permissivists who want to argue that there is a small permissible range of credence functions. We might equally want to know what that small permissible range is. 8 More technically, we can state their result as follows:   Approximating Some Closest Coherent Credence Assignment Promotes Accuracy   If c’ is an incoherent credence assignment on {A1, . . . , An}, and c is some d-closest coherent credence assignment to c’ on {A1, . . . , An}, then c strongly ℑ-accuracy dominates c’. Moreover, for any λ in the interval (0,1], let c* be a credence assignment on {A1, . . . , An} such that c*(Ai)= λc(Ai) + (1−λ) c’(Ai). For any λ ∈ (0,1], c* strongly -accuracy dominates c’.   De Bona and Staffel prove that this result holds just in case  is a convex, additive inaccuracy measure based on a strictly proper scoring rule, and d is a divergence that is suitably related to . For example, if  is the popular Brier score, d is Euclidean distance or squared Euclidean distance. If  is the log score, d is the Kullback–Leibler divergence.

References Brenner, L.A., Koehler, D.J. and Rottenstreich, Y. 2002. Remarks on Support Theory: Recent Advances and Future Directions. In T. Gilovich, D. Griffin and D. Kahneman (eds), Heuristics and Biases: The Psychology of Intuitive Judgment. New York: Cambridge University Press. Briggs, R. A. 2009. Distorted Reflection. The Philosophical Review 118 (1): 59–85. Cooper, G. F. 1990. The Computational Complexity of Probabilistic Inference Using Bayesian Belief Networks. Artificial Intelligence 42 (2–3), 393–405. De Bona, G. 2016. Measuring Inconsistency in Probabilistic Knowledge Bases. Ph.D. Thesis, Institute of Mathematics and Statistics of the University of São Paulo. De Bona, G. and Finger, M. 2015. Measuring Inconsistency in Probabilistic Logic: Rationality Postulates and Dutch Book Interpretation. Artificial Intelligence 227, 140–164. De Bona, G. and Staffel, J. 2017. Graded Incoherence for Accuracy-Firsters. Philosophy of Science 84 (2), 189–213. De Bona, G. and Staffel, J. 2018. Why Be (Approximately) Coherent? Analysis 78 (3), 405–415. Diaconis, P. and Zabell, S. 1982. Updating Subjective Probability. Journal of the American Statistical Association 77 (380), 822–830. Edwards, W. 1982. Conservatism in Human Information Processing. In D. Kahnemann, P. Slovic and A. Tversky (eds), Judgment Under Uncertainty: Heuristics and Biases. Cambridge: Cambridge University Press, 359–369.

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Bayesian Norms and Non-Ideal Agents Evans, J.St.B.T., Thompson, V.A. and Over, D.E. 2015. Uncertain Deduction and Conditional Reasoning. Frontiers in Psychology 6, 398. Greaves, H. and Wallace, D. 2006. Justifying Conditionalization: Conditionalization Maximizes Expected Epistemic Utility. Mind 115 (459), 607–632. Hahn, U. 2014. The Bayesian Boom: Good Thing or Bad? Frontiers in Psychology 5, Article 765, 1–12. Icard, T. 2016. Subjective Probability as Sampling Propensity. Review of Philosophy and Psychology 7 (4), 863–903. Jaynes, E.T. 2003. Probability Theory: The Logic of Science. Cambridge: Cambridge University Press. Jeffrey, R. 1965. The Logic of Decision. Chicago: University of Chicago Press. Joyce, J.M. 1998. A Nonpragmatic Vindication of Probabilism. Philosophy of Science 65 (4), 575–603. Joyce, J.M. 2009. Accuracy and Coherence: Prospects for an Alethic Epistemology of Partial Belief. In F. Huber and C. Schmidt-Petri (eds), Degrees of Belief. Vol. 342 of Synthese Library. Berlin: Springer, 263–297. Kopec, M. and Titelbaum, M. 2016. The Uniqueness Thesis. Philosophy Compass 11 (4), 189–200. Hájek, A. and Staffel, J. forthcoming. Subjective Probability and Its Dynamics. In M. Knauff and W. Spohn (eds), Handbook of Rationality. Cambridge: MIT Press. Lewis, David. 1980. A Subjectivist’s Guide to Objective Chance. In R. C. Jeffrey (ed), Studies in Inductive Logic and Probability, Vol. II. Berkeley, CA: University of California Press, 83–132. Mastropasqua, T., Crupi, V. and Tentori, K. 2010. Broadening the Study of Inductive Reasoning: Confirmation Judgments with Uncertain Evidence. Memory & Cognition 38 (7), 941–950. Pettigrew, R. 2016. Accuracy and the Laws of Credence. Oxford: Oxford University Press. Rottenstreich, Y. and Tversky, A. 2002. Unpacking, Repacking, and Anchoring: Advances in Support Theory. In T. Gilovich, D. Grin and D. Kahneman (eds), Heuristics and Biases: The Psychology of Intuitive Judgment. New York: Cambridge University Press, 474–488. Skyrms, B. 1987. Dynamic Coherence and Probability Kinematics. Philosophy of Science 54 (1), 1–20. Sloman, S., Rottenstreich, Y., Wisniewski, E. and Hadjichristidis, C. 2004: Typical Versus Atypical Unpacking and Superadditive Probability Judgment. Journal of Experimental Psychology: Learning, Memory, and Cognition 30, 573–582. Slovic, P. and Liechtenstein, S. 1971. Comparison of Bayesian and Regression Approaches to the Study of Information Processing in Judgment. Organizational Behavior and Human Performance 6, 649–744. Staffel, J. 2015. Measuring the Overall Incoherence of Credence Functions. Synthese 192 (5), 1467–1493. Staffel, J. 2018. How Do Beliefs Simplify Reasoning? Noûs 53, online first. Staffel, J. forthcoming. Unsettled Thoughts: A  Theory of Degrees of Rationality. Oxford: Oxford University Press. Tentori, K., Chater, N. and Crupi, V. 2016. Judging the Probability of Hypotheses Versus the Impact of Evidence: Which Form of Inductive Inference Is More Accurate and Time-Consistent? Cognitive Science 40, 758–778. Titelbaum, M. forthcoming. Fundamentals of Bayesian Epistemology. Oxford: Oxford University Press. Tversky, A. and Koehler, D.J. 1994. Support Theory: A Nonextensional Representation of Subjective Probability. Psychological Review 101, 547–567. van Fraasen, B. 1984. Belief and the Will. Journal of Philosophy 81 (5), 235–256. van Fraassen, B. 1989. Laws and Symmetry. Oxford: Oxford University Press. Wallin, A. 2013. A Peace Treaty for the Rationality Wars? External Validity and Its Relation to Normative and Descriptive Theories of Rationality. Theory and Psychology 23 (4), 458–478. White, R. 2009. Evidential Symmetry and Mushy Credence. In T. Szabo Gendler and J. Hawthorne (eds), Oxford Studies in Epistemology, Vol. 3, 161–186. Oxford: Oxford University Press. Zhao, J. and Osherson, D. 2010. Updating Beliefs in Light of Uncertain Evidence: Descriptive Assessment of Jeffrey’s Rule. Thinking & Reasoning 16 (4), 288–307. Zhao, J., Shah, A. and Osherson, D. 2009. On the Provenance of Judgments of Conditional Probability. Cognition 113, 26–36.

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12 THE VALUE OF EVIDENCE Bernhard Salow

Evidence is valuable: more informed opinions are more accurate, more informed decisions more successful. Except, of course, when they’re not. Sometimes, additional evidence misleads: it suggests believing P when P is false, suggests φ-ing when φ-ing is disastrous. This needn’t be anyone’s fault; it could just be bad luck, as when a randomly selected sample just happens to be unrepresentative. So getting more evidence is not always objectively valuable. But maybe it is always subjectively valuable: maybe we should always think that, on balance, additional evidence would improve our opinions and decisions. Even this is false. As we’ll see, there are clear cases where we should think no such things. But a restricted version of this claim may hold: it’s intuitively attractive, and there is an appealing, if controversial, explanation for why it would be true. The issue has been widely explored in decision theory. That discussion usually takes place against Good’s (1967) proof that, in certain circumstances, the expected utility of gathering additional evidence before deciding always has higher expected utility than deciding in ignorance. The question then becomes whether similar results are available outside of Good’s “classical” setting, and whether it carries over from decisions to beliefs.1 My approach will be different. Instead of explaining Good’s proof, I  will present a (related) non-mathematical argument for the same claim. Hopefully, this will make the issues accessible to a wider audience. It may also help clarify further which philosophical assumptions underlie Good’s result, and which are extraneous packaging.2 §1 will refine the claim to avoid clear counterexamples. §2 will lay out the argument for the refined principles. §3 and §4 discuss controversial objections to two steps in the argument and show how they could generate counterexamples even to the refined principles. §5 concludes.

1 Qualifications It’s tempting to think that additional evidence is always subjectively valuable: that we should always think that, on balance, we would be better off—epistemically and/or DOI: 10.4324/9781315672687-15 148

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practically—gathering additional evidence than avoiding it. Unfortunately, there are clear counterexamples. The simplest ones arise from the fact that additional evidence is usually costly: if nothing else, it requires time, effort and attention to collect and evaluate, all of which could be spent elsewhere. So gathering additional evidence isn’t always worth it. One might respond that evidence is still valuable because having it would still be good—if only we could have it without collecting it. But that doesn’t solve the problem, since just having the evidence can also carry costs. The evidence might rationalize beliefs that are painful; more controversially, it might rationalize beliefs that are morally problematic, even when supported by the evidence.3 Or perhaps someone is out to punish those who know too much, depriving them of opportunities, including opportunities to learn other things. All of these can generate costs to having evidence; sometimes, the benefits won’t outweigh these costs. There is, however, an intuitive distinction between these “extraneous” effects, and those we consider when we’re tempted to think that, on balance, more evidence is always better. In the epistemic case, where the primary potential costs involve missing out on better ways of improving our beliefs, we might say “sure, getting the additional evidence might not leave my beliefs more accurate than they would have been, since without it they would have become more accurate in other ways—but it still leaves them more accurate than they are right now.” In the practical case, where the potential costs are more varied, one might say “sure, getting the evidence might not make things better—but it would still improve my decisions, so that if we focus only on how it affects what choices I make in the decisions I actually face, we see an improvement.”4 In what follows, I will appeal to this intuitive distinction, without making it precise.5 A second type of counterexample involves anticipated failures of rationality. I  might know that, in my belief-formation and decision-making, I can’t help but attach weight to certain evidence that is either excessive (e.g. to my general impression of someone’s collegiality when I meet them in the highly artificial environment of a job interview) or completely misplaced (e.g. the weight I  am apparently inclined to give to someone’s race or gender when evaluating the strength of their CV).6 Or I  might know that certain evidence (e.g. intricate details about the pros and cons of various mobile phones) tend to overwhelm me, leaving me unable to make up my mind about what to do or think. In those cases, I can reasonably think I’m better off (both practically and epistemically) shielding myself from the evidence. A subtler style of counterexamples involves loss of background information. I  don’t always have to think that other people’s situation would be improved by receiving additional evidence—I might know that the relevant evidence is unreliable or biased, and would mislead them even if they (being unaware of these problems) handled it rationally. This worry doesn’t usually apply in my own case: after all, if I know (or have reason to suspect) that some evidence is unreliable or biased, I will have to take that into account when I handle it—and so, if I know that I will be rational, I shouldn’t expect to be misled. But I might worry that I  will lose the background information between now and the time I  would receive the evidence; the analogue to the third-personal worry then makes sense and could rationalize thinking that the additional evidence would leave me worse off. The three issues raised so far can all generate examples where we should think that, on balance, the additional evidence will make things worse. Not so with our final one. Sometimes, evidence is useless: it doesn’t bear on any decisions I’ll ever have to make, or any question worth getting right.7 When we know for sure that some evidence will be useless, 149

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we shouldn’t think it will improve matters. But we shouldn’t think it will make things worse either. We’ve thus seen four reasons why one might sometimes think that gathering additional evidence won’t make things better. But it would be interesting if these were the only reasons. Let an ideal case be one where we know for sure that (i) we will handle the evidence with perfect rationality, (ii) we won’t lose relevant background information in the interim, and (iii) gathering the evidence incurs no extraneous costs; and where, furthermore, (iv) we leave open that the evidence is useful. Then the problems discussed here are still compatible with: Practical Value: In ideal cases, we should always think that, on balance, gathering additional evidence will lead to greater success in pursuing our goals. Epistemic Value: In ideal cases, we should always think that, on balance, gathering additional evidence will make our opinions more accurate.8 It would be interesting if one or both of these were defensible. This would be interesting even if ideal cases never occur; for it would show that there are certain reasons, those stemming from the “direct” effects of evidence on rational and informed belief-formation and decision-making, that always favour additional evidence.

2  The Argument There is an appealing line of argument supporting Practical and Epistemic Value. I’ll apply it to a specific case before showing how it generalizes. Suppose you’re considering buying a house. Before you decide, you can find out, without cost, whether the house contains asbestos. You leave open that the information is useful: if forced to decide without finding out, you’d take the risk and buy; but if you found out that it does contain asbestos, you would not. Should you find out? Obviously yes—but let’s look at the argument. The effect of finding out depends on what you find and thus, in this case, on whether the house contains asbestos. If it doesn’t contain asbestos, you’ll still buy, so the outcome is the same. If it does contain asbestos, you won’t buy when you otherwise would have done. Moreover, conditional on the house containing asbestos, you think (even now) that it’s better not to buy it. (This is independently plausible, and a consequence of the idea that (a) your future decision not to buy would be the rational result of discovering that the house contains asbestos and (b) the rational reaction to some new evidence E is to adopt the views you previously held on the condition that E is true.9) So from your current perspective, finding out either makes no difference, or else results in a decision that you already think is better, conditional on the circumstances that would lead you to make it. So finding out has no downside and may well have an upside—it’s a no-brainer.10 To generalize this reasoning, we need some terminology. You face a decision between some options (e.g. Buy and); Don’t Buy let’s use “O” to pick out the one you would choose if you were to decide without investigating further (Buy, in our example).11 If you want, you can gather some additional evidence before deciding; let E1 E2. . . be the various total things you might discover if you do (e.g. E1=Asbestos and E2=No asbestos).12 Each of those would lead you to choose a particular option, so let’s use “On” to pick out the option you would

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choose if you were to receive En (so, in our example, O1=Don’t Buy and O2=Buy). We can then break the argument into a series of steps: 1. For each n, you think On is at least as good as On, conditional on En being true; and for some n, you think On is better than O, conditional on En being true. 2. So, for each n, you think On is at least as good as O, conditional on En being the evidence you would get by investigating; and for some n, you think On is better than O, conditional on En being the evidence you would get by investigating. 3. So, you should think the complex action For each n: do On if En is the evidence you would get by investigating is better than O. 4. You know for sure that gathering the evidence is equivalent to performing this complex action and that deciding without investigating is equivalent to performing O. 5. So, you should think gathering the evidence is better than deciding without investigating. 4 is true by stipulation, and the inference from 4 to 5 seems good. 1 also looks highly plausible, in light of the thoughts that (a) your future decision is rational, (b) in ideal cases, the rational reaction to some new evidence E is to adopt the beliefs you previously held on the condition that E and (c) you consider the evidence to be useful so that, for some En, On is different from O. I will argue shortly that the moves from 1 to 2 and from 2 to 3 are more controversial. But they, too, have strong prima facie appeal. The move from 1 to 2 is supported by the natural thought that “E is true” and “En is the evidence that you would get by investigating” look, at first blush, to be equivalent. And the move from 2 to 3 is underwritten by the plausible Sure Things: if you think that A isn’t worse than B conditional on any of a finite number of mutually exclusive and jointly exhaustive hypotheses, and better conditional on at least one of these, then you should think that A is better overall.13 We can run a similar argument for Epistemic Value. We can even adapt the example. Suppose that, instead of wondering whether to buy the house, you’re wondering how much it will be worth in ten years. You’re fairly confident the house doesn’t contain asbestos and will hence be worth at least £353,000. Finding out for sure that it doesn’t contain asbestos would only confirm that, so wouldn’t change your belief that this is true; finding out that it does contain asbestos would: you’d then only be willing to say that it will be worth at least £351,000. But, conditional on the house containing asbestos, you’re already unsure that it will be worth at least £353,000—so, presumably, you’d regard this change as an improvement in accuracy. So you think that gathering the evidence will either change nothing or improve your accuracy; and so you should think that, on balance, it will be an improvement. Again, we can generalize. Let’s use “B” to label your current belief state, and “Bn” to label the belief state you would occupy upon discovering En. A  belief state could be an assignment of attitudes to a range of propositions or to a single one. This does not affect the structure of the argument, which goes as follows: 1e. For each n, you think Bn is at least as accurate as B, conditional on En being true; and for some n, you think Bn is more accurate than B, conditional on En being true.

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2e. So, for each n, you think Bn is at least as accurate as B, conditional on En being the evidence you would get by investigating; and for some n, you think Bn is more accurate than B, conditional on En being the evidence you would get by investigating. 3e. So you should think that the result of the complex action For each n: adopt Bn if En is the evidence you would get by investigating is more accurate than B. 4e. You know for sure that gathering the evidence is equivalent (in its consequences for the accuracy of your belief state) to performing this complex action. 5e. So, you should think that gathering the evidence will lead you to have more accurate beliefs. The steps are analogous to 1–4, and mostly plausible for the same reasons. The main exception is premise 1e. The thoughts motivating 1 from earlier get us that Bn just are the beliefs you currently have, conditional on En being true, and that, in at least one case, these are different from B. It’s a substantial further claim that these beliefs always rate themselves as at least as accurate as B, and as more accurate when they differ from B. This further claim, however, is well-motivated: it’s just the requirement that accuracy be measured in such a way that rational states are immodest, thinking themselves more accurate than any specific alternative—a requirement that is extensively discussed and defended in the literature on accuracy.14 So this difference does not render the epistemic argument substantially less plausible than the practical one. (Another difference between the practical and epistemic cases is that it’s rather unnatural to speak of “actions” in the latter. But such talk in 3e and 4e is ultimately just a useful fiction—for example, we nowhere assume that you can choose which belief state to adopt.) We now have arguments for both Practical and Epistemic Value. These arguments make assumptions: that some form of “conditionalization” is the rational way to revise your beliefs in ideal cases; that “En is true” and “En is the evidence you would get” are, for our purposes, equivalent claims; that Sure Things is true; that rational belief states are immodest. While plausible, these assumptions aren’t obviously more plausible than Practical and Epistemic Value themselves. For this reason, we should think of these arguments as attempting to explain (rather than establish or support) Practical and Epistemic Value. They articulate the intuitive idea that we should favour gathering the evidence because, no matter what evidence we get, gathering it will (in ideal cases) lead us to make decisions or adopt beliefs that we already regard as better, on the supposition that these are the decisions or beliefs which the evidence will encourage. Note, moreover, that this explanation—unlike Good’s own argument—builds in relatively little background theory. In particular, it seems equally intelligible irrespective of how one represents doxastic states (e.g. as full beliefs, sharp credences, imprecise credences) or what decision theory one favours (i.e. of how one thinks that beliefs about descriptive matters and evaluations of complete states of affairs determine which things one should “think are better” than which others). Admittedly, some structure is taken for granted—most notably that people have beliefs about which things are better than which others conditional on various hypotheses. But this seems a datum about our psychology, something any theory should accommodate. Of course, as we will see shortly, various decision-theoretic or doxastic frameworks might reject one of our premises, and Practical and Epistemic Value with them. But, importantly, they do not reject the terms within which the explanation is developed. We can thus

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pinpoint quite precisely where they think the explanation goes wrong, and thereby get some insight into how Practical and Epistemic Value might fail. To illustrate this point, I  will focus on two potential weaknesses: worries about Sure Things which challenge the transition from 2 to 3, and worries about the equivalence between En “is true” and “En is the evidence you would get by investigating” that challenge the transitions from 1 to 2.

3  First Objection: Against Sure Things The transition from 2 to 3 (and from 2e to 3e) relies on Sure Things; this is required for us to “put together” your various conditional opinions about what’s best (or most accurate) given the different hypotheses about what evidence you would get into a single, unconditional, opinion. But, while attractive, Sure Things is not uncontroversial. Here are two widely discussed reasons to think it might fail. Many people are risk-averse:15 they think better of a guaranteed £3,000 than a 4/5 shot at £4,000. But this effect reduces when the “safer” choice still isn’t particularly safe: many of the same people think better of a 1/5 shot at £4,000 than a 1/4 shot at £3,000. If this combination is rational, Sure Things is false. Consider a version of the safer choice, involving a lottery with 20 tickets and two possible assignments of prizes: a “riskier” one that assigns £4,000 to tickets 1–4 (thus offering a 4/20 = 1/5 shot at £4,000), and a “safer” one that assigns £3,000 to tickets 1–5 (thus offering a 5/20 = 1/4 shot at £3,000). Then we can divide the 20 tickets into two sets: tickets 6–20, which win nothing no matter what, and tickets 1–5, all of which win £3,000 with the safer choice and 4/5 of which win £4,000 with the riskier one. Obviously, the safer and the riskier choice are equally good when the ticket drawn will be in the first set; and, by hypothesis, the people in question think the safer choice is better on the condition that the ticket drawn will be in the second set. Nonetheless, these people think that the riskier choice is better overall, violating Sure Things. A related fact is that many people are ambiguity-averse:16 they think better of options with clearer odds. Consider, for example, an issue on which you have complex but reasonably balanced evidence; say, whether Federer or Nadal will win the next time they play. If you are ambiguity-averse, you’ll require more favourable odds to bet on either answer than you would to bet on the outcome of a fair coin toss, since it’s less clear how risky the tennis bet is. But then you violate Sure Things. For consider some odds you’d take on the coin toss, but not on the tennis match; and then consider the condition that either the coin lands heads and Federer wins, or the coin lands tails and Nadal wins. On that condition, you should think it quite unclear how likely the coin is to land heads: all the complex evidence suggesting Federer wins suggests that it will, and all the complex evidence suggesting Nadal wins suggests that it won’t. So, being ambiguity-averse, you should think that, on that condition, it is better not to bet on the coin. And, for the same reason, you should also think it better not to bet on the coin on the condition that either the coin lands heads and Nadal wins, or the coin lands tails and Federer wins. But those two conditions are mutually exclusive and jointly exhaustive. So Sure Things requires you to think unconditionally that it is better not to bet on the coin—which you don’t. It’s not hard to see that these counterexamples to Sure Things give rise to counterexamples to Practical Value. Take the case of risk-aversion. One ticket was drawn from 20; not knowing the outcome, you can choose between the assignment that assigns £4,000 to

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tickets 1–4, and the assignment that assigns £3,000 to tickets 1–5. You think it better to opt for the first. You are then offered the opportunity to discover whether the ticket drawn is one of tickets 6–20 or one of tickets 1–5. You know that to take this opportunity is, in effect, to opt for the £3,000: for if you discover that it is one of tickets 6–20, it doesn’t matter what you pick; and if you discover that it is one of tickets 1–5, your risk-aversion will kick in and lead you to choose the safe £3,000. Since you think it’s better not to opt for the £3,000, you thus think it’s better not to investigate. Similarly, in the case of ambiguity aversion, you know that you will refuse to bet on the coin after discovering which of either the coin lands heads and Federer wins, or the coin lands tails and Nadal wins and either the coin lands heads and Nadal wins, or the coin lands tails and Federer wins is true. But you think that this is a good bet to take, and so you should avoid discovering which of these is true.17 We can also try to adapt these examples to generate counterexamples to Epistemic Value, but this is trickier. Consider first the case involving ambiguity. Right now, you believe that the coin is 50% likely to land heads. And you can foresee that, once you discover which of the two disjunctions is true, you will regard it as much less clear how likely the coin is to land heads. Call this latter state “suspended probabilistic judgement”. If this is a particular alternative attitude to the coin landing heads, and Immodesty is true, then we can generate an epistemic reason to avoid the evidence. After all, you currently regard this claim as 50% likely; so, by Immodesty, you think regarding it as 50% likely is, on balance, more accurate than any alternative attitude you could take, including suspending probabilistic judgement. But you know that, if you were to gather the evidence, you would end up suspending probabilistic judgement. So you should think that gathering the evidence will reduce your accuracy. This argument, however, only goes through if “suspended probabilistic judgement” is a single, particular attitude; and some deny that it is, arguing that you should suspend probabilistic judgement in different ways depending on which of the disjunctions you discover.18 If there are different attitudes here, it’s not clear that we get a counterexample; for Immodesty only commits you to taking your own attitude to be more accurate than any particular alternative, not more accurate than a compound of different attitudes to be adopted in different situations. On the other hand, it also isn’t clear that we don’t get a counterexample; to determine whether we do, we’d need to develop a theory of these states of suspended probabilistic judgement, including a theory of how accurate they are when things turn out to be one way or the other. And it turns out that such a theory is difficult to obtain, especially if we want to respect constraints like Immodesty.19 On the face of it, it’s even less clear how to adapt the case involving risk-aversion. This is not because it’s hard to make sense of risk-aversion in the epistemic domain; ever since William James, it’s been a common refrain that believers must balance the benefits of forming true beliefs with the cost of forming false ones, and one can clearly be more or less risk-averse in how one does this. But there seems to be no obvious way to use this idea to develop an epistemic version of this case, at least not without appealing to additional (and controversial) ideas about how to “trade-off” the accuracy of beliefs with different contents. Even if we can’t directly adapt the counterexample, however, once we reject Sure Things for this reason, it stops being clear that there couldn’t be one—to settle the matter, we’d need to develop a theory of risk-aversion and its interaction with accuracy, and then use that theory to see if counterexamples can be generated or ruled out.20 154

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4  Second Objection: The Structure of Evidence Another crucial step in our arguments assumes that “En is true” and “En is the evidence you would get by investigating” are, for our purposes, equivalent claims—so that your evaluations conditional on one align with your evaluations conditional on the other. This assumption is quite natural in simple cases: given the set-up of the house-buying example, “the house contains asbestos” seems equivalent to “finding out whether the house contains asbestos would reveal that it contains asbestos” and “the house contains no asbestos” equivalent to “finding out whether the house contains asbestos would reveal that it contains no asbestos”, as required. There are, however, reasons for concern. The claims could, in principle, come apart in two ways: (i) En could be true without being the evidence you would get, or (ii) En could be the evidence you would get without being true. Which, if either, is actually possible depends on one’s theory of evidence.21 Let’s start with (ii). The main worry here is that investigating might add En to one’s evidence despite its falsity.22 Theories of evidence that allow this might include certain “dogmatist” or “reliabilist” views, on which having an experience with content p adds p to one’s evidence as long as one has no “defeaters” and/or experience is generally a reliable indicator of what the world is like.23 For such theories will allow that, sometimes, illusions will result in false propositions being added to one’s evidence. So something could be the evidence you would get from investigating without being true. Theories which allow this threaten not just the move from 1 to 2, but also Practical and Epistemic Value themselves. For suppose that there are cases where one can antecedently recognize that further investigating could add a false proposition to one’s evidence. Then it should be possible to adapt these cases to generate ones where one knows that a proposition will be added to one’s evidence whether it’s true or not. One could then anticipate that one will, in the future be more inclined to believe or act on the relevant proposition than one is at the moment: after all, it will then be entailed by one’s evidence, while one currently leaves open that it might be false. So there will be specific decisions or beliefs that one can anticipate one will adopt if one gathers the evidence, but not if one doesn’t. Since one currently thinks better of the decisions and beliefs one would adopt if one doesn’t gather the evidence, one thus has reason to avoid the evidence. Let’s work through a toy example. Suppose that the dogmatist/reliabilist view sketched earlier is true, and that you know you will be shown an object of a certain colour: red if the house doesn’t contain asbestos, white if it does. Presumably the dogmatist/reliabilist will want to say that, in a case like this, the content of your experience will become part of your evidence, even if you can’t antecedently rule out that there will be an illusion which makes a white object appear red—assuming that there is no positive reason to think that there will be such an illusion. Now suppose that, before deciding to look at the object, an oracle—whose reliability and trustworthiness is beyond doubt—tells you that it will certainly appear red. This does not, presumably, add to your evidence the proposition that it is red, or anything that entails it; after all, you’ve not had an experience of it being red and weren’t antecedently able to rule out that it would appear red without being red. Presumably the oracle’s testimony also doesn’t affect what evidence you get when you look at the object; it didn’t, after all, give you positive reason to think that the experience will be illusory. So you can work out that, when you look at the object (and find, as you knew you would, that it appears red), you will strengthen your epistemic position with respect to 155

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its being red: at that point, unlike now, your evidence will entail that it’s red. Presumably this makes a difference to what you’ll be willing to do or think: you’ll be willing to stake slightly more on the object being red (pay $Y for the house, when you’d currently pay at most $Y-100); and start believing claims non-conclusively supported by its being red (say, that the house will still be worth at least $X in ten years), which your current evidence falls just short of supporting enough to justify believing. So you know that looking at the object will definitely result in a particular set of beliefs (believing the house will still be worth $X in ten years) or a particular decision (paying $Y to buy the house), which are different from the one you currently think best (believing only the weaker claim that it will still be worth $X-100, paying at most $Y-100 to buy the house). Since—trivially, or by Immodesty—you think that the beliefs and decisions you currently think are best are better than any other particular alternative, this means that you should think it better, where both accuracy and decision-making are concerned, not to look at the object for yourself.24 So if (ii) can happen, the argument fails, and Practical and Epistemic Value are under severe pressure. Similar things are true if (i) can happen. Cases satisfying (i) are ones where some En can be true without being the evidence you would obtain by investigating. At first sight, it seems obvious that there are such cases. In an only slightly more complicated version of the house-buying scenario, there’s a third possibility: instead of revealing that the house does or does not contain asbestos, the investigation might come out inconclusive. Then it seems that The house contains asbestos is one of the En, but could be true without being what you’d discover: there is, after all, a possibility in which the house contains asbestos but the investigation is inconclusive. But this initial impression is mistaken. For remember that En is a total body of evidence. And if the investigation reveals that the house contains asbestos, the total evidence from the investigation plausibly includes not just the fact that the house contains asbestos but also the fact that the investigation yielded a result. The real En is thus The house contains asbestos and the investigation revealed this—and that claim is not true in the case imagined, in which the investigation is inconclusive. It thus isn’t obvious that there can be cases satisfying (i). But it also isn’t obvious that there can’t be. It all depends on the structure of total bodies of evidence. Let us say that a body of evidence E is self-identifying if for each p, if E does/doesn’t contain p, E entails that one’s total evidence after the investigation would/wouldn’t contain p. If bodies of evidence are self-identifying, they clearly can’t be true without being the evidence you would get. If they are not, they clearly can be. Are bodies of evidence self-identifying? On some accounts, they are. For example, if someone’s evidence consists of an exhaustive description of their phenomenal state (together, perhaps, with a clause saying that there is nothing more to their phenomenal state and/or a clause describing the true theory of evidence), it arguably is. On other accounts, they are not. It’s uncontroversial that we can fail to know something without knowing anything that entails that we don’t know it, e.g. because it is false for some completely unexpected reason. So if someone’s evidence is just everything they know, then bodies of evidence typically won’t be self-identifying.25 If bodies of evidence are not self-identifying, (i) won’t be true, and so our explanation of Practical and Epistemic Value will break down. Will there also be counterexamples to the claims themselves? Not necessarily, but probably. That is: there are conditions weaker than (i) which still guarantee the value of evidence (though they don’t lend themselves to the kind of simple, intuitive explanation (i) does);26 but many of the ideas which would lead 156

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one to reject (i) would also lead one to reject these weaker conditions, and thus do give rise to direct counterexamples. For example, consider again the view that one’s evidence is just one’s knowledge. On a standard, anti-sceptical picture, perception gives rise to knowledge when everything is going well, but won’t give rise to knowledge when it isn’t (e.g. when appearances don’t match reality). Moreover, when perception fails to produce knowledge, you cannot know that it failed. We can then modify the case given earlier, to get a counterexample to Practical and Epistemic Value, by introducing a second potential source of knowledge. Suppose that, in addition to looking at the relevant object, you will also get to touch it to determine its temperature. Things have been set up so that the object will be both red and warm if and only if the house contains no asbestos. Again, you have no prior reason to doubt either of your perceptual capacities, and an oracle who tells you that (i) the object will certainly appear both red and warm and (ii) it is certainly at least one of the two. Now it seems that, in this case, you don’t yet know that the object is red nor that it’s warm—after all, you have neither seen nor touched it. But you do know that you will discover either that it’s red, or that it’s warm, or both.27 And any of those is additional evidence that the house contains no asbestos: each one only rules out possibilities in which the house contains asbestos (and the object thus fails to either be red or warm).28 So you know that the future evidence—no matter what it is—will support staking strictly more on the house containing no asbestos, in both your actions and your beliefs, than you currently would; and so, by the same reasoning as earlier, you should now think that the future evidence is better avoided.29

5 Conclusion Is evidence always valuable? More precisely, is gathering additional evidence subjectively valuable in all ideal cases? Perhaps. There is an intuitively compelling explanation why it would be. Roughly, it’s that no matter what evidence we get, gathering it will lead us to make decisions or adopt beliefs that we already regard as better, conditional on these being the decisions or beliefs which the evidence will encourage. But, as we have seen, that explanation is not uncontroversial. It assumes that we can combine conditional evaluations into a single, unconditional, opinion in line with Sure Things—a controversial assumption in decision theory. And it assumes that the hypothesis that some body of evidence is true and that it is the evidence we’d get by investigating are interchangeable—a controversial assumption in epistemology. Moreover, if either of these assumptions fail, there are likely to be counterexamples to Practical and Epistemic Value (though, as we saw, this follows more immediately in some cases than in others). The question thus remains surprisingly—and excitingly—open.

Acknowledgments Thanks to Maria Lasonen-Aarnio, Catrin Campbell-Moore, Kevin Dorst, Matt Mandelkern, and Josh Thorpe for helpful comments on earlier versions of this chapter.

Notes 1 Good’s result is anticipated in Blackwell (1951), Savage (1954, chs. 6–7), and a note from Frank Ramsey, posthumously published as Ramsey (1990). Footnotes 8, 14, 15, 16, 17, and 21 give references for discussions building on Good.

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Bernhard Salow 2 Compare Ahmed and Salow (2019, §4), although their explanation is slightly different. 3 Basu (2019) argues that racist beliefs—e.g. that the Black diner at table  8 will probably tip poorly—can wrong, even if they are true, behaviourally inert, and supported by your statistical evidence. Some authors, however, (including Basu herself) argue that these moral costs also raise the evidential standards required for such beliefs to be rational. See e.g. Basu and Schroeder (2019) and—in some sense—Moss (2018) for defence, and Gardiner (2018) for criticism. If this is so, examples involving morally costly beliefs will often fall into the second class of counterexamples discussed later.   Is there a similar concern about the additional evidence rationalizing morally problematic actions? I’m not sure. One might, for example think that if the action is morally problematic even when one has the relevant evidence, it can’t really be rational. Or perhaps it is, on a more narrowly instrumental sense of “rational”; but then the person in question must not care that much about morality, and so it’s not clear this would tell against gathering the evidence. (I might worry that if I learn where the money is hidden, I will—rationally—steal it. But if my qualms are insufficient to make stealing irrational, why should they be sufficient to require me not to find out?)   More generally, it’s tempting to think that the problem arises in the case of belief because the values determining whether you should gather some evidence are different from those that determine what you should believe when you have. And it is also tempting to think that the values determining whether to gather evidence and that determine how to act on the basis of that evidence will usually be the same; so it wouldn’t be surprising if the problem doesn’t carry over. That said, the question clearly deserves further attention. 4 We could try replacing the question “would I be more successful with the additional evidence?” with the question “should I defer my decisions to a hypothetical version of myself who has the additional evidence?” Unfortunately, this doesn’t work, since I’d still find out what I end up doing, hence what my more informed self recommends, and hence (sometimes) what the relevant evidence is. So deferring might still incur the costs of knowing. 5 I doubt it can be made precise without begging important questions in decision theory. For example, causalists like Gibbard and Harper (1978) and evidentialists like Jeffrey (1965) might disagree about whether an action carries “costs” when it gives you evidence that an unfavourable scenario obtains without causally bringing this about. 6 See e.g. Kunda (1999) on the “interview illusion”, and the “CV studies” of Steinpreis et al. (1999), Bertrand and Mullainathan (2004), and Moss-Racusin et al. (2012). Compare Gendler’s (2011) worry that I might know about myself that, while I process e.g. statistical evidence about crime rates and race to form reasonable statistical beliefs, I’m disposed to then draw further unreasonable inferences from these—and that I might prefer not to have this information for that reason. 7 This assumes that not all questions are worth getting right, i.e. that not all true beliefs make us more accurate in the relevant sense. If they do, there can be no completely useless evidence in the epistemic case. 8 The literature has mostly focused on Practical Value; Oddie (1997) was the first to isolate (and defend) Epistemic Value. Buchak (2010) and Campbell-Moore and Salow (2020) discuss a related distinction between the claims that gathering additional evidence is always required by instrumental or epistemic rationality. 9 I assume throughout that evidence consists of propositions. Some deny this because they think evidence consists of e.g. mental states, but still allow that there are propositions (namely that you are in such-and-such a mental state) which play a central role in determining what that evidence supports—such theorists may be able to adapt the argument given here. Others insist that there are no such propositions, e.g. because evidence gives rise “directly” to a new assignment of probabilities to at least some propositions; as discussed in Graves (1989), theories like this need to add further constraints on how this can happen to vindicate Practical and Epistemic Value. 10 Let me comment on “think better”, “think more accurate” and the like. My use of these is, I think, perfectly ordinary; but making philosophical sense of it is tricky. It does not mean “think that it is objectively better”: you might think it better to insure your house against flood damage despite taking flood damage to be unlikely. Nor does it mean “think that it is subjectively better, in light of your current evidence”: for even conditional on the house in fact containing asbestos, you do not think that your current evidence, which doesn’t include this information, tells against buying it. A natural analysis is that to think something better/more accurate is to assign it higher expected

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The Value of Evidence utility/higher expected accuracy; those who reject credences, utilities or accuracy measures, or think that expected values aren’t central to subjective evaluations, will need some other way to make sense of it. 11 For simplicity, I assume that there is always an option you’d definitely choose. 12 I use “discover” as a technical term for “come to have as part of your evidence”. While the natural language term “discover” is factive, I don’t assume here that evidence only consists of truths. Nor do I here assume that, if an Ei is true, you are guaranteed to discover it by gathering additional evidence. §4 will discuss both these ideas. 13 To be plausible as a general principle, Sure Things should also require that which of the hypotheses obtains is independent of whether you choose A or B. How exactly to spell out the “suitable independence” is controversial; but which En is the evidence you would receive by investigating seems like it will be suitably independent of whether you investigate in nearly all situations. For discussion of Practical Value in cases where it might not be, see Adams and Rosenkrantz (1980) and Maher (1990). 14 Oddie (1997), Greaves and Wallace (2006), Joyce (2009), and Horowitz (2019) all defend Immodesty. For criticism, see Maher (2002), Gibbard (2008), and Myrvold (2012). Oddie’s (1997) argument for Epistemic Value explicitly invokes Immodesty; Myrvold (2012) shows how failures of Immodesty can generate counterexamples. 15 The example is due to Allais (1953), the empirical evidence to Kahneman and Tversky (1979: 266f). For discussion of the relevance of risk-aversion to Practical Value, see Buchak (2010) and the references therein. 16 See Ellsberg (1961). Ambiguity is usually thought to require doxastic states more complex than precise credences, e.g. sets of probability distributions representing imprecise credences. The potential relevance of moving to such a framework for Practical Value is noted by Good (1974), who attributes the point to Isaac Levi and Teddy Seidenfeld. See Bradley and Steele (2016) and the references therein for discussion. 17 A complication is that many decision theories dealing with ambiguity permit rather than require ambiguity-aversion. This means that knowing you will decide rationally about whether to take the second bet is not enough to know that you will refuse it. If you have the right kind of uncertainty about which permissible option you will choose, you may then still be permitted to gather the relevant evidence. If, moreover, people are rationally required to have this kind of uncertainty (something I’m sceptical of, but won’t argue against here), we can salvage a weakening of Practical Value: that, in ideal cases, we should always think that, on balance, gathering additional evidence won’t lead to less success in pursuing our goals. See Seidenfeld (2004), Bradley and Steele (2016), and Moss (2021) for discussion. 18 See e.g. Joyce (2010); Topey (2012) raises concerns about this response. 19 See Seidenfeld et  al. (2012), Schoenfield (2015), Mayo-Wilson and Wheeler (2016), Das and Berger (2020). 20 Campbell-Moore and Salow (2020) pursue this approach, on the basis of Buchak’s (2013) theory of risk-aversion; they argue that there will indeed be cases where it’s epistemically better not to have the additional evidence. 21 Geanakoplos (2021), Ahmed and Salow (2019), Dorst (2020), and Das (2023) all discuss how these issues arise in something closer to Good’s own framework; the problem is essentially that the set-up assumes that the Ei form a partition (a set of mutually exclusive and jointly exhaustive propositions), and that the person will discover whichever member of that partition is true. But these assumptions won’t hold in general, if the theories of evidence discussed here are correct. 22 Another worry comes from cases where Ei would be true if I were to investigate, but wouldn’t be true if I don’t. “En would be true if I were to investigate” and “En is true” bear on most hypotheses the same way, so this isn’t usually a problem. But there may be cases where it is—e.g. “I would investigate if I were to investigate” and “I investigate” seem to bear very differently on how curious (or epistemically responsible) a person I am. I can’t pursue these complications here; they may interact with the ones raised earlier in footnote 12. 23 Goldman (2009) suggests something like the reliabilist version of this view; Miller (2016) offers it as a way of understanding the “perceptual dogmatism” defended by Pryor (2000) and others. Miller’s preferred way of understanding that position is more complex; but it predicts counterexamples to both Practical and Epistemic Value for similar reasons.

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Bernhard Salow 24 The focus on particular is important here. Immodesty (or the logic of “think better than”) does not mean you should always think your current beliefs, or your currently favoured decision, are better than whichever one you will adopt in the future, since it is usually uncertain what the latter is. But in the previous case, you can be certain what beliefs or decisions you will adopt in the future; this is what generates the problem. 25 Lewis (1996) endorses something like the first theory; Williamson (2000, ch. 9) defends the identification of evidence with knowledge. A potential complication is that what matters is not whether bodies of evidence really are self-identifying but whether they are self-identifying in all the possibilities we leave open. Salow (2019) argues that this difference matters in related problems; I will ignore that complication here. 26 Necessary and sufficient conditions within a Bayesian framework are identified by Geanakoplos (2021); for epistemological discussion and defence, see Dorst (2020). Dorst et al. (2021) identify necessary and sufficient conditions in a more general setting. 27 One might deny this, insisting that one can discover by perception that the object is red (warm) only if one already knows that appearances won’t be misleading; in which case one can deduce that it is red (warm) before looking at (touching) it. But taking this line consistently undermines the anti-sceptical potential of equating evidence with knowledge; for, on this view, we can only receive evidence involving the external world if we already know that appearances are not misleading. 28 Here it is crucial that, when you don’t discover that the object is red (or that it’s warm), you also don’t discover that you didn’t discover this. Otherwise, your new knowledge (i.e. your new evidence) would allow you to rule out that you’re in possibilities where the object is red and warm and everything is working normally, so that you come to know both those things by interacting with it; but those are possibilities in which the house contains no asbestos, so it’s then no longer clear that the evidence overall supports there being no asbestos. 29 For more discussion of cases like this, see Salow (2018, §2.3) and Das (2023); Williamson (2000, §10.5) and (2019, §4) discusses related cases. Dorst (2020, Appendix A.1) argues that such cases should be deemed impossible even if bodies of evidence aren’t always self-identifying.

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The Value of Evidence Dorst, K. (2020) “Evidence: A Guide for the Uncertain” Philosophy and Phenomenological Research 100: 586–632. Dorst, K., Levinstein, B., Salow, B., Husic, B. and Fitelson, B. (2021) “Deference Done Better” Philosophical Perspectives 35: 99–150. Ellsberg, D. (1961) “Risk, Ambiguity, and the Savage Axioms” The Quarterly Journal of Economics 75: 643–669. Gardiner, G. (2018) “Evidentialism and Moral Encroachment” in K. McCain (ed) Believing in Accordance with the Evidence: New Essays on Evidentialism. Cham: Springer. Geanakoplos, J. (2021) “Game Theory Without Partitions, and Applications to Speculation and Consensus” The B.E. Journal of Theoretical Economics 21: 361–394. Gendler, T. (2011) “On the Epistemic Costs of Implicit Bias” Philosophical Studies 156: 33–63. Gibbard, A. (2008) “Rational Credence and the Value of Truth” in T. Szabo Gendler and J. Hawthorne (eds) Oxford Studies in Epistemology (vol. 2). Oxford: Oxford University Press. Gibbard, A. and Harper, W. (1978) “Counterfactuals and Two Kinds of Expected Utility” in C. Hooker, J. Leach and E. McClennan (eds) Foundations and Applications of Decision Theory (University of Western Ontario Series in Philosophy of Science, 13a). Dordrecht: D. Reidel. Goldman, A. (2009) “Williamson on Knowledge and Evidence” in P. Greenough and D. Pritchard (eds) Williamson on Knowledge. Oxford: Oxford University Press. Good, I. J. (1967) “On the Principle of Total Evidence” British Journal for the Philosophy of Science 17: 319–321. Good, I. J. (1974) “A Little Learning Can Be Dangerous” British Journal for the Philosophy of Science 25: 340–342. Graves, P. (1989) “The Total Evidence Principle for Probability Kinematics” Philosophy of Science 56: 317–324. Greaves, H. and Wallace, D. (2006) “Justifying Conditionalization: Conditionalization Maximizes Expected Epistemic Utility” Mind 115: 607–632. Horowitz, S. (2019) “Accuracy and Educated Guesses” in T. Szabo Gendler and J. Hawthorne (eds) Oxford Studies in Epistemology (vol. 6). Oxford: Oxford University Press. Jeffrey, R. (1965) The Logic of Decision. Chicago: University of Chicago Press. Joyce, J. (2009) “Accuracy and Coherence: Prospects for an Alethic Epistemology of Partial Beliefs” in F. Huber and C. Schmidt-Petri (eds) Degrees of Belief. Dordrecht: Springer. Joyce, J. (2010) “A Defence of Imprecise Probabilities in Inference and Decision Making” Philosophical Perspectives 24: 281–323. Kahneman, D. and Tversky, A. (1979) “Prospect Theory: An Analysis of Decision Under Risk” Econometrica 47: 263–291. Kunda, Z. (1999) Social Cognition: Making Sense of People. Cambridge, MA: MIT Press. Lewis, D. (1996) “Elusive Knowledge” Australasian Journal of Philosophy 74: 549–567. Maher, P. (1990) “Symptomatic Acts and the Value of Evidence in Causal Decision Theory” Philosophy of Science 57: 479–498. Maher, P. (2002) “Joyce’s Argument for Probabilism” Philosophy of Science 69: 73–81. Mayo-Wilson, C. and Wheeler, G. (2016) “Scoring Imprecise Credences: A  Mildly Immodest Proposal” Philosophy and Phenomenological Research 92: 55–78. Miller, B. (2016) “How to Be a Bayesian Dogmatist” Australasian Journal of Philosophy 94: 766–780. Moss, S. (2018) “Moral Encroachment” Proceedings of the Aristotelian Society 118: 177–205. Moss, S. (2021) “Global Constraints on Imprecise Credences: Solving Reflection Violations, Belief Inertia, and Other Puzzles” Philosophy and Phenomenological Research 103: 620–638. Moss-Racusin, C., Dovidio, J., Brescoll, V., Graham, M. and Handelsman, J. (2012) “Science Faculty’s Subtle Gender Biases Favor Male Students” PNAS 109 (41): 16395–16396. Myrvold, W. (2012) “Epistemic Values and the Value of Learning” Synthese 187: 547–568. Oddie, G. (1997) “Conditionalization, Cogency, and Cognitive Value” British Journal for the Philosophy of Science 48: 533–541. Pryor, J. (2000) “The Sceptic and the Dogmatist” Noûs 34: 517–549. Ramsey, F. (1990) “Weight or the Value of Knowledge” British Journal for the Philosophy of Science 41: 1–4. Salow, B. (2018) “The Externalist’s Guide to Fishing for Compliments” Mind 127: 691–728.

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Bernhard Salow Salow, B. (2019) “Elusive Externalism” Mind 128: 397–427. Savage, J. L. (1954) The Foundations of Statistics. New York: Wiley. Schoenfield, M. (2015) “The Accuracy and Rationality of Imprecise Credences” Noûs 51: 667–685. Seidenfeld, T. (2004). “A Contrast Between Two Decision Rules for Use with Convex Sets of Probabilities: Gamma-Maximin versus E-Admissibility.” Synthese 140: 69–88. Seidenfeld, T., Schervish, M.J. and Kadane, J.B. (2012) “Forecasting with Imprecise Probabilities” International Journal of Approximate Reasoning 53: 1248–1261. Steinpreis, R., Anders, K. and Ritzke, D. (1999) “The Impact of Gender on the Review of the Curricula Vitae of Job Applicants and Tenure Candidates: A National Empirical Study” Sex Roles 41 (7–8): 509–528. Topey, B. (2012) “Coin Flips, Credences, and the Reflection Principle” Analysis 72: 478–488. Williamson, T. (2000) Knowledge and Its Limits. Oxford: Oxford University Press. Williamson, T. (2019) “Evidence of Evidence in Epistemic Logic” in M. Skipper and A. SteglichPetersen (eds) Higher-Order Evidence: New Essays. Oxford: Oxford University Press.

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13 SLEEPING BEAUTY’S EVIDENCE Jeffrey Sanford Russell

Here’s the familiar story of Sleeping Beauty (Elga 2000, 143): Some researchers are going to put you to sleep. During the two days that your sleep will last [Monday and Tuesday], they will briefly wake you up either once or twice, depending on the toss of a fair coin (Heads: once; Tails: twice). After each waking, they will put you back to sleep with a drug that makes you forget that waking. When you are first awakened, to what degree ought you believe that the outcome of the coin toss is Heads? I’ll start from the idea that the degree to which Beauty ought to believe the coin came up Heads is the same as the degree of belief which is supported by Beauty’s evidence. This hardly sounds innovative, but it encourages a little reorientation. Most of the literature on this puzzle focuses on update rules that relate Beauty’s beliefs on Sunday to her beliefs at later times. Thinking in these terms makes questions about propositions that are only sometimes true (or only sometimes entertainable) seem very important (see Titelbaum 2013 and references therein). If we focus instead on the import of the evidence Beauty has on Monday, and what this evidence supports, things get easier in some ways (compare the “time-slice” approach of Moss 2012; Hedden 2015). Here are some lessons I’ll discuss. First, part of Beauty’s evidence on Monday is that she is awake; we can argue straightforwardly that this evidence is relevant to the outcome of the coin flip, given other things she knows. Second, Beauty’s evidence can provide one-sided confirmation for Tails, without any possibility of confirmation for Heads. Third, Beauty might have additional evidence that screens off the evidence that she is awake from the coin flip; whether this is so depends on contentious issues about the nature of evidence, transparency, and defeat. I’ll use “you can tell that P” as a convenient shorthand for “you have evidence that entails P.”

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DOI: 10.4324/9781315672687-16

Jeffrey Sanford Russell

1  Relevant Evidence Let’s warm up with a variant story. You wake up disoriented, completely unsure where you are or what day it is. Of course you do notice: Woke. You woke up today. You find a stack of three index cards. (You can tell they are trustworthy.) You begin to read them, one by one. Day. It is either Monday or Tuesday. Coin. A fair coin has been flipped. At this point, the probabilities given your evidence look like Table 13.1. This much seems obvious, but it’s worth pausing to ask why. I don’t think it is because rationality requires that you satisfy some general indifference principle that applies in this case. Such principles face well-known difficulties (for example, van Fraassen 1989). Rather, I think Table 13.1 is correct because this is an artificial probability puzzle. We have conventions for filling in details in vignettes like these. If the story says a goat is behind one of three doors, we understand each door to be equally likely on your evidence (as specified so far in the story). We also understand which door it is to be independent of questions like which door you decide to open. Life doesn’t have to be this way. You could have inside information, or Monty Hall might look suspicious, or you might suspect that your choice is subliminally guided by a faint goatish smell. But those would be perverse interpretations of the story, as a puzzle. We might call these guiding conventions hermeneutic indifference principles. But it would be a mistake to conclude from the conventions of puzzle stories that we always are in situations where our background probabilities for arbitrary questions we don’t know much about are uniform and independent. When it comes to applying lessons from puzzles to real life cases, we will have to reconsider whether these assumptions are appropriate.1 We now turn to the third index card. Protocol. You do not wake up on Tuesday if the coin lands Tails. Equivalently:2 It is not the case that (the coin came up Heads and it’s Tuesday and you woke up today). The import of Protocol given your other evidence is easy to work out. It rules out the possibility Heads-and-Tuesday, while telling you nothing new about any of the other three cases. If we conditionalize Table 13.1 on Protocol, we get Table 13.2. So Woke, Day, Coin, and Protocol together support Heads to degree 1/3. This reasoning relied on the principle that we can work out what some evidence supports by breaking it up into pieces. Combined Evidence. For propositions E and H, let PE(H) be the degree of belief in H supported by evidence E. Then PE &E (H) = PE (H ∣ E2) 1 2 1 (as long as PE (E2) ≠ 0). 1

Table 13.1 Probabilities supported by Woke, Day, and Coin.

Heads Tails

Monday

Tuesday

1/4 1/4

1/4 1/4

164

Sleeping Beauty’s Evidence Table 13.2 Probabilities supported by Woke, Day, Coin, and Protocol.

Heads Tails

Monday

Tuesday

1/3 1/3

0 1/3

We first worked out the probabilities supported by the evidence without Protocol (Table 13.1), and then using Combined Evidence we can deduce the probabilities supported by all of the evidence together.3 Combined Evidence is not a diachronic principle. We imagined reading the index cards one by one, but this was just to help make certain conditional probabilities vivid. In particular, while our reasoning did involve conditionalizing one probability function to calculate another, it does not rely on the principle of (diachronic) conditionalization. That would be tendentious in this context (see Titelbaum 2013, sec. 4). Combined Evidence fits better with this alternative picture (compare “Synchronic Conditionalization” in Hedden 2015; see Meacham 2016 and references therein): Ur-Prior. There is a probability function P⊤—call it the ur-prior—such that, for any propositions H and E, PE(H) = P⊤(H ∣ E) (as long as P⊤(E) ≠ 0).

The idea is that the ur-prior encodes once and for all the relations of evidential support that different propositions bear to one another. Many have been skeptical that there is any such thing (for example, Ramsey [1926] 2010). I’m inclined to treat such worries not as showing that there is no ur-prior, but rather as suggesting that different probability functions might play the “ur-prior role” for different people, or at different times, or that it might be vague or otherwise hard to tell which probability function plays the ur-prior role. (Keynes [1921] and Carnap [1950] thought of the ur-prior as “logical” in some important sense, but that isn’t part of the Ur-Prior picture I am discussing.) Combined Evidence implies Ur-Prior, by considering the case of tautologous evidence ⊤.4 But it might be sensible to restrict Combined Evidence. Maybe it doesn’t make any sense to have only tautologous evidence—excluding even contingent evidence like I exist or I have some evidence. There are various restrictions of Combined Evidence to “reasonable” evidence propositions E1 and E2 that would suffice for the work we’re putting it to. So while it’s a natural fit, we don’t need to rely on the full-fledged Ur-Prior idea. Another thing to notice is that since all our reasoning was about evidence at one time, it doesn’t matter that your evidence has a special temporal profile. Maybe the evidence “I woke up today” is a “centered proposition” (as Elga took for granted), or maybe it is a proposition that is only sometimes true (see, for example, Sullivan 2014), or maybe that sentence expresses different propositions at different times and so corresponds to different evidence on different days (for example, Weatherson 2011). This makes no difference to our reasoning. Since we are only paying attention to what your evidence now supports, it could work any of these different ways equally well. Now back to Sleeping Beauty. Is her situation relevantly different from yours in the variant story? Upon waking on Monday, she has all of the evidence you have in the story: she 165

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can tell that she woke up today, that it is Monday or Tuesday, that a coin was to be flipped, and that she only wakes on Tuesday if the coin comes up Tails. So parallel reasoning tells us that this much of her evidence supports degree of belief one-third in Heads. It is true that she gained this evidence in a different way than you did—there were no index cards, and instead she was told Protocol on Sunday, rather than learning it after she woke on Monday. However she got it, though, Beauty’s evidence on Monday includes the conjunction of Woke, Day, Coin, and Protocol. Beauty also has some additional evidence that didn’t come into the variant story. She didn’t wake up entirely disoriented, and instead she knows she is involved in an experiment that could involve memory erasing. This might make a difference—I’ll consider one way it might matter in Section 2. So we haven’t settled the question in favor of the one-third answer. But we have gained some ground. Consider a standard objection to the Thirder: Between Sunday night and Monday morning, all she learns is ‘Today is Monday or Tuesday.’ Information about the passage of time doesn’t seem relevant to facts about coin flips, so Beauty’s credence in heads on Monday morning shouldn’t change from what it was on Sunday night—namely 1/2. (Titelbaum 2013, 1006; compare Lewis 2001) But this is not all she learns. She also learns that she woke up today; given the protocol, this information is relevant to Heads (compare Weintraub 2004).5 One way to make the relevance more vivid is to imagine a bystander with Beauty who also knows the experimental protocol, who is awake both days no matter what, but who also can’t tell whether it is Monday or Tuesday (for whatever reason—maybe they also get their memory erased Monday night; compare Stalnaker 2008, 63). When the bystander observes that Beauty wakes up, they thereby straightforwardly gain evidence against Heads. (Given Heads she might not have woken up then, whereas given Tails she certainly would.) But when Beauty wakes up, she also observes this, and thus gains access to the very same fact that the bystander does, with the same evidential import. There is an important difference between Beauty and the bystander. If Beauty had not woken up, the bystander would have gained this evidence instead—that Beauty didn’t wake up—and thereby gained evidence for Heads. But Beauty would not have gained this alternative evidence in that case. This brings us to a second standard objection to the Thirder. Beauty has an opportunity to gain evidence against Heads, but no opportunity to gain evidence for Heads. That conflicts with this principle: Confirmation Balances Out. If you could gain evidence against H, then you could gain evidence for H. This seems troubling. One way to press the point is to imagine Beauty thinking through the reasoning on Sunday evening: then she assigns Heads probability one-half, but she can anticipate that whatever happens, her probability for Heads upon waking on Monday will be one-third. This is an odd mismatch—a violation of the reflection principle. Why not just skip ahead and adopt credence one-third on Sunday? The reply is that Confirmation Balances Out is not generally true. Here’s a simpler case to illustrate this point. If I’m popular, I want to gain evidence for this. If I’m not, I’d rather 166

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remain ignorant. You know whether I’m popular. I can’t just ask you—then you might tell me I’m unpopular, which would make me sad. But I can put you up to this plan: if I’m popular, wake me up tonight; otherwise, let me sleep. If I find myself awake, I will have gained evidence for my popularity. But there is no danger of my finding myself asleep!6 (Alas, my happy epistemic state will be short-lived. If I ever wake up and remember that you didn’t wake me, evidence for my unpopularity will come home to roost. Eternal slumber is a high price to pay for permanent one-sided confirmation.) The basic asymmetry, at the heart of the Sleeping Beauty puzzle, is that when you’re awake, you normally can tell that you’re awake, but when you’re asleep, you normally can’t tell that you’re asleep. Indeed, if (like the bystander) Beauty could tell whenever she was asleep, things would not be very puzzling (compare the variants in Arntzenius 2003, sec. 4; Dorr 2002; Weintraub 2004). In that case, on Tuesday Beauty might get the evidence that she didn’t wake up, which would raise the probability of Heads to one (given the protocol). This possible confirmation would balance out the possible disconfirmation in the other three cases. But the fact that Beauty would sleep through her only shot at getting evidence that confirms Heads doesn’t mean she also loses her chance to get evidence that disconfirms Heads when she is awake on Monday. There is a theorem of the probability calculus in the vicinity of Confirmation Balances Out: Confirmation Theorem. If ℰ is a set of mutually exclusive and jointly exhaustive propositions (a partition), and some E ∈ ℰ disconfirms H (where E has positive probability), then some E ∈ ℰ confirms H.7 But the principle that Confirmation Balances Out only follows from the Confirmation Theorem if the set of propositions that you could have as evidence is a partition of the possibilities compatible with your current evidence. And this is not always so. (Compare the closely related discussion in Williamson 2002; Briggs 2009; Weatherson 2011.) In the simple “fishing for compliments” case, I  might get evidence that tells me I’m awake and popular; but while I might well be asleep and unpopular, in this case I won’t get any evidence that tells me so. So my possible bodies of evidence do not partition my possible predicaments. In the “good case” where I’m awake, my evidence rules out being asleep, while in the “bad case” where I’m asleep, I do not have evidence that rules out being awake. The Sleeping Beauty case is more complicated because it also involves losing track of time, but the essential feature is the same as the simple case: the propositions that might turn out to be Beauty’s total evidence do not partition her possible predicaments. In the “good cases” where she is awake (Monday & Heads, Tuesday & Heads, or Tuesday & Tails) she has evidence that rules out the “bad case” where she is asleep (Tuesday & Heads). But in that “bad case,” she will not have evidence that rules out being awake. The conditions of the Confirmation Theorem do not apply, and it is false that Confirmation Balances Out. The Confirmation Theorem tells us that if you can get evidence against Heads, then there is some alternative proposition that would count in favor of Heads—but it does not follow that this alternative proposition is also one that you might ever have an opportunity to learn.8 The usual challenge for the Thirder is to explain how any of Beauty’s evidence is relevant to the coin flip. Now the tables are turned. Beauty does have some evidence conditional on which the probability of Heads is 1/3. So defenders of non-Third answers face a challenge: 167

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what extra evidence besides Woke, Day, Coin, and Protocol might she have that shifts the probability away from 1/3 to something else?9

2  Wide Evidence According to one view, Evidence is Narrow: your evidence is entirely determined by features of your present qualitative phenomenal state—the way things appear to you. Thus your evidence is something you can share with (for example) a brain in a vat that is stimulated in just the right way. An alternative view says that Evidence is Wide. In a slogan, evidence ain’t in the head. (“Internalism” and “externalism” are common labels for these views.) In particular, your evidence includes facts about the world that you observe and remember: Observation is Evidence. If you observe that P, then it’s part of your evidence that P. Memory is Evidence. If you remember that P, then it’s part of your evidence that P. (The way I’ve characterized them, Evidence is Narrow and Evidence is Wide aren’t exhaustive alternatives: evidence might be wider than your phenomenal state, but not so wide as to include all that you observe or remember. But they are mutually exclusive because whether you observe that P is not determined by your present phenomenal state. I observe that I’m holding a pen, but my phenomenal duplicate in a vat does not observe that they are holding a pen, and instead merely seems to observe this.) One well-known wide evidence view is the “E=K” thesis: “knowledge, and only knowledge, constitutes evidence” (Williamson 2002, 185). What you know is not a matter of your present phenomenal state. But the thesis that Evidence is Wide can come apart from E=K. First, you may know things that aren’t evidence. For instance, it’s natural to think that knowledge you have inferred from observations shouldn’t be “double-counted” as evidence itself. Second, you may have evidence beyond what you know. Williamson (2002, ch. 1) argues that if you observe that P, or remember that P, then you know that P; but I’m not sure whether this is true. Sometimes seeing people don’t believe their eyes. Such a person might perfectly well observe that it’s raining, and thereby have as part of their evidence that it’s raining—but even so they don’t believe that it’s raining, and thus they don’t know it. If this can happen, and Observation is Evidence, then some evidence is not knowledge. (Similar remarks apply to memory.)10 So the wideness of evidence is not tied specifically to E=K. Wide evidence provides resources for a distinctive response to skepticism (see Williamson 2002, ch. 8). Norma has strong evidence that she is a university professor. For example, she observes that she teaches students, submits articles to journals, attends committee meetings, and so on. Skip is a phenomenal duplicate of Norma subject to a Truman Show–style hoax: her classroom is full of actors, the articles she writes don’t go to journals, and the committees whose meetings she attends are entirely fictitious. If Evidence is Wide, then Norma has evidence that Skip doesn’t, and the attitudes that are supported by Norma’s evidence are different from those supported by Skip’s. It’s compatible with Skip’s evidence that she has no students—indeed, she doesn’t! Skip can’t tell whether she has students; but Norma can tell that she has students, just by looking around her classroom. (Note that I’m assuming that the contents of observation and memory are themselves “wide,” or “thick,” in another sense. You sometimes observe that a student asked a question or remember that you defended your dissertation; you don’t merely observe or remember that beings who looked a certain way made certain noises.11) 168

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Let’s call this reply to the skeptic Asymmetric Dogmatism. Normal evidence (the good case) rules out being in a skeptical scenario (the bad case). But in a skeptical scenario, your evidence does not rule out either the good case or the bad case. Sleeping Beauty’s situation is also a kind of skeptical scenario. Let’s examine how these ideas apply. For a warm-up, think about when you woke up this morning. How did you know what day it was? In my case, I remembered that yesterday was Sunday (and that yesterday I did my usual Sunday things); I concluded that today was Monday. Of course, I could have been in alternative predicaments: covert agents from the Philosophical Defense Force could have drugged me to sleep through an entire day, or they could have wiped my memory of an entire day. My usual Monday-morning phenomenology did not by itself rule out these skeptical hypotheses. But this morning when I woke up I wasn’t in any of those devious scenarios. It was a normal case, not a skeptical one. If Evidence is Wide, then I had normal “good case” evidence, such as that yesterday was Sunday. (Again, I take it that the contents of memory are “thick”: what you remember isn’t just a slideshow of qualitative imagery. I remember that I broke my arm when I was six, that I worked on this draft last Friday—and I remember that yesterday was Sunday.) On Monday morning, Sleeping Beauty’s cognitive story so far is very much like mine. It was a perfectly normal night: she was briefed, she went to sleep, and she woke up. It is plausible that she remembers that she was briefed on the experiment yesterday. She had a good night’s sleep and woke up refreshed and ready for more epistemic science. It seems that all her cognitive processes are in perfectly good order to deliver her the evidence that yesterday was Sunday, and thus that today is Monday. If my evidence implies that today is Monday, then why wouldn’t Sleeping Beauty’s as well? Of course, sometimes you can’t tell what time it is. Waking up in the trunk of a car, you may have no idea how long you’ve slept, or how often you’ve woken (Elga 2004). If Beauty wakes on Tuesday, after a night of devious neurological tampering, she wakes with a mind full of temporal illusion, and thus plausibly with much less evidence than upon an ordinary waking. Does the mere threat of such tampering in the future suffice to undermine her memories on Monday? This is not clear. Tuesday wakings and Monday wakings are not symmetric. Tuesday is a skeptical scenario in relation to Beauty’s normal waking on Monday. If Evidence is Wide, it may well be that on Tuesday Beauty can’t tell what day it is, and on Monday she can—even if her experiences on the two days are qualitatively identical. If Evidence is Wide, the question of whether Beauty can tell what day it is on Monday is open. Some people will think that Beauty’s ordinary waking memories on Monday are defeated by other information she has about the experimental protocol (compare Elga 2004; Arntzenius 2003, 356). There are three ways this defeat could work. (1) Beauty does have evidence that entails that it is Monday, but she should not have the degrees of belief that her evidence supports. I set this option aside at the outset: what we are presently exploring are the attitudes that are supported by Sleeping Beauty’s evidence. (2) Beauty remembers that yesterday was Sunday, but it is not part of her evidence that yesterday was Sunday. This option conflicts with the thesis that Memory is Evidence, so I set it aside as well. The remaining option: (3) Beauty does not remember that yesterday is Sunday. Call this option Memory Defeat. She experiences an apparent memory that yesterday is Sunday—just as she will if she wakes on Tuesday—but unlike that case, this experience is perfectly veridical, and produced by the ordinary cognitive processes that produce genuine memories, without any “cognitive mishap.” Nonetheless, the view is that this is not enough to qualify it as 169

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a genuine memory. Cognitively, nothing unusual disrupted Beauty’s peaceful slumber on Sunday night. (Direct memory tampering only happens Monday night in this experiment, if at all.) Epistemically, though, it is as if someone had erased her memories and then replaced them with apparent memories that by accident had the very same content as the originals. It is tempting to look for a fourth option: Beauty remembers that yesterday was Sunday and does thereby have this as part of her evidence, but additionally she has further evidence which lowers the probability again. But that’s a non-starter. If some of Beauty’s evidence raises the probability that it is Monday all the way to one, then no further evidence can lower it again.12 One way to argue for this appeals again to the Combined Evidence principle. If PE1 (Monday) = 1, then for any further evidence E2 PE1&E2 = PE1 (Monday ∣ E2) = 1

(as long as PE1 (E2) ≠ 0). If Beauty’s memories (on their own) merely made it highly probable that it was Monday, then they could be defeated on their own terms by further probability-lowering evidence. But if Beauty’s memories have wide content that entails that it is Monday, this not an option. I don’t know whether Beauty can tell that it is Monday (on Monday), or whether her ability to tell what day it is (by memory or otherwise) is defeated. I find the defeat idea natural, but on reflection (reflection which is particularly influenced by Lasonen-Aarnio 2010, 2014), once we have granted that evidence is the sort of thing that might be asymmetric between Monday and Tuesday, I find it far from obvious whether it is in this case. (I suspect the answer might depend on details of Sleeping Beauty’s psychological story that are omitted or differ between alternative tellings.) If Sleeping Beauty can tell that it is Monday, then this straightforwardly gives us a striking answer to the question of what degree of belief in Heads is supported by her evidence on Monday. Starting from the evidence adduced in Section 1—Woke, Day, Coin, and Protocol, which supported one-third probabilities in Table 13.2—we add the further evidence Monday, applying the Combined Evidence principle. Thus this much of her Monday evidence supports the probabilities in Table 13.3, and degree of belief one-half in Heads. “Halfing” is a standard position. But we arrived at this number by a different route, and the overall position that emerges is quite different from more familiar Halfer views. First, Lewis (2001) argues for the Half answer, but he also agrees with the indifference reasoning from Elga (2000) that Monday-and-Tails and Tuesday-and-Tails should receive the same probability. So Lewis-halfers hold that Beauty’s probabilities should look like Table  13.4, instead. But if Beauty can tell that it’s Monday, then we should not accept indifference reasoning that says her evidence supports Monday-and-Tails and Tuesday-andTails to the same degree: for her evidence rules out Tuesday-and-Tails, but not Mondayand-Tails. (The indifference reasoning might be motivated by the thought that her evidence on Monday and her evidence on Tuesday are symmetric—but the line of reasoning we are Table 13.3 Probabilities supported by Woke, Day, Coin, Protocol, and Monday.

Heads Tails

Monday

Tuesday

1/2 1/2

0 0

170

Sleeping Beauty’s Evidence Table 13.4 Lewis-halfing.

Heads Tails

Monday

Tuesday

1/2 1/4

0 1/4

exploring rejects this thought.) This also leads Lewis to the peculiar view that if Beauty gains the evidence that it is Monday, she should raise her degree of belief in Heads to 2/3. Our reasoning does not take us there. Second, consider a standard argument for Halfing (compare Lewis 2001): (1) On Sunday, Beauty’s evidence supports credence one-half in Heads. (2) On Monday, Beauty’s credence in Heads should be the same as her credence on Sunday. Hawley (2013, 85) argues along these lines; he supports premise (2) with appeal to a principle he calls Inertia: If you should have degree of belief d that p at time t1, and between t1 and a later time t2, your cognitive faculties remain in order, and you neither gain nor lose relevant evidence, then you should also have degree of belief d that p at time t2. Hawley claims, furthermore, that between Sunday and Monday, Beauty neither gains nor loses evidence relevant to the coin flip. In particular, he argues (with many others) that when Beauty learns she woke up today, this is irrelevant to the coin flip. We have rejected this. Beauty’s evidence that she woke up today is relevant to the coin flip, given her further evidence Day, Coin, and Protocol. If one-third is not the right answer, it is because this isn’t all of Beauty’s relevant evidence (beyond that which she already had Sunday). In particular, if she also has the further evidence It’s Monday, then this further evidence screens off the relevance of her waking to Heads. Neither Woke nor Monday are independent of Heads given the rest of what Beauty knows—rather, they are exactly counterbalancing evidence. Third, while Hawley (2013) also argues for the conclusion that Beauty should have the “half-half-zero” probabilities in Table  13.3 (rather than the Lewis-halfer probabilities in Table  13.4), he recommends “the following optimistic policy: believe to degree 1 that it is Monday whenever awakened during the experiment” (p. 88). That is, Hawley recommends that Beauty should have the same probabilities if woken on Tuesday. The reasoning we have followed, though, starts from the idea that Beauty’s evidence on Monday is different from her evidence on Tuesday (even though her predicament is phenomenally the same). On Tuesday she can’t tell what day it is—so in this case the original Thirder reasoning remains untouched. The view we have arrived at (in contrast with Hawley’s) is that Beauty’s evidence depends on what day it is; on Monday her evidence supports Halfing, and on Tuesday it supports Thirding.13

3  Cosmological Evidence An account of the Sleeping Beauty puzzle according to which her evidence is asymmetric between Monday and Tuesday might seem a bit obtuse. You might think that the point of 171

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this puzzle is to explore how things go in cases where you can’t tell what time it is. So the details ought to be filled in however necessary to ensure that verdict. (If informing her of the experimental protocol does not suffice to defeat her ordinary evidence from memory, then more direct memory-destroying measures can be taken.) Lewis, for instance, stipulates that not only are the three possible wakings in the experiment “indistinguishable,” but also that “if she is awakened on Tuesday the memory erasure on Monday will make sure that her total evidence at the Tuesday awakening is exactly the same as at the Monday awakening” (2001, 171, my emphasis).14 Be that as it may, we also want to draw lessons from Sleeping Beauty for other cases where these details are not up for stipulation—perhaps because they are actual cases. Whether or not we count cases with asymmetric wide evidence as official Sleeping Beauty cases, if there are any cases like that, we do want to understand how things go for them. One important standard application of lessons from the Sleeping Beauty literature is in the epistemology of cosmology (see, for example, Bostrom 2002). According to some live cosmological hypotheses, the universe is vast—so vast that it is overwhelmingly probable that the chaotic motion of scattered atoms will coalesce into “Boltzmann brains” in the void. Moreover, this is likely to happen zillions of times, producing multitudes of Boltzmann brains with qualitative experiences just like those you are presently having. The worry is that Boltzmann brain hypotheses like these are analogous to Tails possibilities in the Sleeping Beauty—there are very many “wakings” rather than few—and so such hypotheses should receive outsized degree of belief. In that case, it seems that we should be highly confident in cosmological hypotheses according to which the universe is vast, and highly unconfident that we are the embodied creatures that we seem to be, rather than brains in the void. But—whether or not Sleeping Beauty has wide evidence about what day it is—if we have wide evidence about our own situations, this defuses the threat of Boltzmannian skepticism. Here is a hand; here is another. If these observations are part of my evidence, then my evidence is incompatible with being a Boltzmann brain. Thus, even if my own qualitative experience is strong evidence that I am in a vast universe full of brains in the void,15 the fact that I have hands tells me I am not such a brain in the void. This is counterbalancing evidence against such a cosmological hypothesis—leaving me right where I started on the question of the size of the universe. (If there are Boltzmann brains, they have no such evidence themselves—and so their cosmological credences should accordingly be very different from mine. But Boltzmann brains also haven’t really done any of the relevant science, or even read anything about it, so if evidence is wide then their credences should be very different from mine.)

4  Multifarious Evidence So far I have treated the idea of evidence as a fixed point; but I am sympathetic to the view that evidence is shifty. Your evidence is what you should take for granted, which supports beliefs to various degrees. But there may be no single thing that plays this role once and for all: it is natural to think that some facts may be taken for granted for some purposes, and others for others.16 We began by asking what degree of belief you ought to have; but the word “ought” is notoriously context-sensitive (see, for example, Kratzer [1981] 2002). Maybe even when we narrow attention to what you ought to believe in an “epistemic” sense, we still haven’t 172

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pinned down a single thing. If that’s right, then there may be no univocal question of what degree of belief Sleeping Beauty ought to have in Heads, and likewise no univocal question of what degree of belief her evidence supports, because there is no univocal question of what her evidence is.17 If that picture is right (and I think it might be) then one plan of attack is to clearly distinguish the different candidate kinds of “evidence,” and examine what attitude each of them supports, and then try to get clear on which notion of evidence is the relevant one for our particular purposes in a context. This goes both for the Sleeping Beauty puzzle and also for cosmological hypotheses.

Acknowledgment Thanks to Charity Anderson, Andrew Bacon, John Hawthorne, Alex Pruss, a seminar at the University of Southern California, and an audience at Baylor University for helpful discussion. Special thanks to Bernhard Salow for detailed comments.

Notes 1 Here are two reasons for belaboring this point.   This explanation for Table 1 does not depend on Elga’s “highly restricted principle of indifference,” that qualitatively indiscernible predicaments within a single possible world must receive equal probability (Elga 2000, 144).   Hermeneutic indifference principles can come into conflict. For example, if a story introduces a natural countable partition, the convention “assume uniformity” conflicts with the convention “assume coherence” (including countable additivity). I  take this to be what is going on in the variant in Ross (2010), which involves infinitely many days (see also Weatherson 2011). Ross argues that the case involves a “credal dilemma” where different epistemic norms are in conflict (supposing a principle like Elga’s). I conclude instead that different interpretive norms for the story conflict, and so it’s just not clear what the probabilities are in the story without more to go on. 2 I stipulate that the “if ” on the Protocol card is a material conditional. More on this in footnote 9. 3 Two background assumptions are baked into the notation. The first is that the relevant evidence consists of propositions. The second is that what is supported by some evidence propositions taken together is the same as what is supported by the conjunction of those propositions. 4 The converse almost holds; using the standard ratio definition of conditional probability, Ur-Prior implies Combined Evidence for cases where P⊤(E1) ≠ 0. 5 Elga (2000, 145) stipulatively uses the word “information” in a restricted sense: “an agent receives new information when she learns the truth of a proposition expressible by an eternal sentence of some appropriately rich language.” Titelbaum does not use the word in this restricted way—he allows here that there is such a thing as “information about the passage of time”—and neither do I. 6 This example is inspired by Salow (2018), who argues that such “intentionally biased inquiry” is impossible. Note that Salow rules out inquiry that involves forgetting—and he might argue (with Shakespeare’s Henry IV) that being asleep will “steep my senses in forgetfulness.” I don’t know about this, but the example illustrates the present point about imbalanced confirmation whether or not it is a true counterexample to Salow’s claim. (The firing squad from Leslie 1989 has a similar structure, though it is usually deployed for different purposes.) 7 Proof. Recall that P(H) is equal to a weighted average of the conditional probabilities P(H ∣ E) for E ∈ ℰ such that P(E) ≠ 0. So if one of these conditional probabilities is lower than P(H), some other conditional probability must be higher than P(H). 8 The complications of time require care. Since we are now explicitly comparing evidence at different times, we have to attend to the nature of temporary evidence. Suppose on Sunday Beauty has evidence it’s Sunday which is incompatible with her later evidence it’s Monday or Tuesday—so

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Jeffrey Sanford Russell this is a case of evidence loss. Then the evidence she might have on Monday does not partition the possibilities compatible with her Sunday evidence for the trivial reason that this evidence is incompatible with her Sunday evidence. This issue would equally arise even in perfectly ordinary cases when time passes. By itself, it need not utterly block the Confirmation Theorem: we can also consider confirmation with respect to intermediate hypothetical bodies of evidence. Consider the evidence that consists of Beauty’s Sunday evidence minus the evidence that it’s Sunday, and plus the evidence that it’s Monday or Tuesday—but without the additional evidence that Beauty is awake. Beauty never has just this evidence, but we can still consider abstractly what it would support. But with respect to this evidence, we still cannot apply the Confirmation Theorem, for the reason just discussed. 9 Bernhard Salow has suggested (in personal correspondence) that it is natural to interpret the protocol conditional (“You don’t wake up on Tuesday if the coin lands Heads”) as stronger than a mere material conditional. The additional modal information it conveys—something like “the protocol ensures that you don’t wake up on Tuesday when the coin lands heads”—might in principle be relevant to the coin flip. It is possible to construct a prior that includes various “protocol propositions” like this such that, without the protocol proposition as evidence, the probabilities of the four cells of the table are uniform, but adding the protocol proposition as evidence supports halfing. I can’t give this idea the attention it deserves here; my own judgment is that priors with this structure are not well-motivated, but this is an interesting route for the halfer to pursue. 10 Here’s an alternative diagnosis. Maybe sometimes you don’t see that P, but you can see that P. (Compare Williamson’s notion of what you’re in a position to know.) We might think your evidence doesn’t just include what you do see, but also what you can see. (We can similarly distinguish what you remember from what you can remember.) 11 Compare the “cognitive penetrability of experience” (Siegel 2012, inter alia)—though that discussion focuses on the content of “narrow” perceptual experience itself, rather than “wide” states like observation and memory. 12 The exception might be if she has further evidence with probability zero conditional on the fact that yesterday was Sunday. I set this complication aside. 13 Schwarz (2012, 237) also argues for this asymmetric policy, on different grounds. 14 This stipulation only makes sense given certain theories of the nature of temporary evidence. For example, it requires that when you can tell you’re awake on Monday, this is the same evidence that you have when you can tell you’re awake on Tuesday. 15 But I am not sure whether this part of the analogy holds up. Existing isn’t exactly like being awake, and I’m not sure what evidence we have which is analogous to “It’s either Monday or Tuesday.” 16 For example, Greco (2017) defends this picture. Analogous views about knowledge rather than evidence are very widely defended (for an overview, see Rysiew 2016). 17 I am also moved by the arguments from Srinivasan (2015) that there are no non-trivial norms (in particular, epistemic norms) which are followable in all circumstances. Then it might make sense to give different guiding advice about what one ought to believe, suitable for different circumstances or different purposes.

References Arntzenius, Frank. 2003. “Some Problems for Conditionalization and Reflection.” Journal of Philosophy 100 (7): 356–70. www.jstor.org/stable/3655783. Bostrom, Nick. 2002. Anthropic Bias: Observation Selection Effects in Science and Philosophy. Routledge. Briggs, R. A. 2009. “Distorted Reflection.” Philosophical Review 118 (1): 59–85. https://doi. org/10.1215/00318108-2008-029. Carnap, Rudolf. 1950. Logical Foundations of Probability. University of Chicago Press. Dorr, Cian. 2002. “Sleeping Beauty: In Defence of Elga.” Analysis 62 (4): 292–6. Elga, Adam. 2000. “Self-Locating Belief and the Sleeping Beauty Problem.” Analysis 60 (2): 143–7. https://doi.org/10.1093/analys/60.2.143. ———. 2004. “Defeating Dr. Evil with Self-Locating Belief.” Philosophy and Phenomenological Research 69 (2): 383–96. https://doi.org/10.1111/j.1933-1592.2004.tb00400.x.

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Sleeping Beauty’s Evidence Greco, Daniel. 2017. “Cognitive Mobile Homes.” Mind 126 (501): 93–121. https://doi.org/10.1093/ mind/fzv190. Hawley, Patrick. 2013. “Inertia, Optimism and Beauty.” Noûs 47 (1): 85–103. https://doi. org/10.1111/j.1468-0068.2010.00817.x. Hedden, Brian. 2015. “Time-Slice Rationality.” Mind 124 (494): 449–91. https://doi.org/10.1093/ mind/fzu181. Keynes, John Maynard. 1921. A Treatise on Probability. Dover Publications. Kratzer, Angelika. (1981) 2002. “The Notional Category of Modality.” In Formal Semantics: The Essential Readings, edited by Hans-Jürgen Eikmeyer and Hannes Rieser, 289–323. Blackwell. Lasonen-Aarnio, Maria. 2010. “Unreasonable Knowledge.” Philosophical Perspectives 24 (1): 1–21. https://doi.org/10.1111/j.1520-8583.2010.00183.x. ———. 2014. “Higher-Order Evidence and the Limits of Defeat.” Philosophy and Phenomenological Research 88 (2): 314–45. https://doi.org/10.1111/phpr.12090. Leslie, John. 1989. Universes. Routledge. Lewis, David. 2001. “Sleeping Beauty: Reply to Elga.” Analysis 61 (3): 171–6. Meacham, Christopher J. G. 2016. “Ur-Priors, Conditionalization, and Ur-Prior Conditionalization.” Ergo: An Open Access Journal of Philosophy 3. https://doi.org/10.3998/ergo.12405314.0003.017. Moss, Sarah. 2012. “Updating as Communication.” Philosophy and Phenomenological Research 85 (2): 225–48. https://doi.org/10.1111/j.1933-1592.2011.00572.x. Ramsey, F. P. (1926) 2010. “Truth and Probability.” In Philosophy of Probability: Contemporary Readings, edited by Antony Eagle, 52–94. Routledge. Ross, Jacob. 2010. “Sleeping Beauty, Countable Additivity, and Rational Dilemmas.” Philosophical Review 119 (4): 411–47. https://doi.org/10.1215/00318108-2010-010. Rysiew, Patrick. 2016. “Epistemic Contextualism.” In The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta, Winter. Metaphysics Research Lab, Stanford University. https://plato. stanford.edu/archives/win2016/entries/contextualism-epistemology/. Salow, Bernhard. 2018. “The ExternalistGuide to Fishing for Compliments.” Mind 127 (507): 691– 728. https://doi.org/10.1093/mind/fzw029. Schwarz, Wolfgang. 2012. “Changing Minds in a Changing World.” Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition 159 (2): 219–39. www.jstor.org/ stable/23262286. Siegel, Susanna. 2012. “Cognitive Penetrability and Perceptual Justification.” Noûs 46 (2). Srinivasan, Amia. 2015. “Normativity Without Cartesian Privilege.” Philosophical Issues 25 (1): 273–99. https://doi.org/10.1111/phis.12059. Stalnaker, Robert C. 2008. Our Knowledge of the Internal World. Oxford University Press. Sullivan, Meghan. 2014. “Change We Can Believe in (and Assert).” Noûs 48 (3): 474–95. https://doi. org/10.1111/j.1468-0068.2012.00874.x. Titelbaum, Michael G. 2013. “Ten Reasons to Care About the Sleeping Beauty Problem.” Philosophy Compass 8 (11): 1003–17. https://doi.org/10.1111/phc3.12080. van Fraassen, Bas C. 1989. Laws and Symmetry. Oxford University Press. Weatherson, Brian. 2011. “Stalnaker on Sleeping Beauty.” Philosophical Studies 155 (3): 445–56. Weintraub, Ruth. 2004. “Sleeping Beauty: A Simple Solution.” Analysis 64 (281): 8–10. https://doi. org/10.1111/j.0003-2638.2004.00453.x. Williamson, Timothy. 2002. Knowledge and Its Limits. Oxford University Press. https://doi.org/10.1 093/019925656X.001.0001.

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14 HIGHER-ORDER EVIDENCE Kevin Dorst

Higher-order evidence is evidence about evidence. But although that may seem clear enough, the term has been used to refer to (at least) two different things: 1. Evidence about whether various responses to your evidence are reliable. 2. Evidence about whether various responses to your evidence are rational. These types of evidence will often go together: since rational opinions are correlated with truth, evidence about rationality is usually evidence about reliability. But they can clearly come apart. Case 1: you pick up a textbook and start believing its claims—yet unbeknownst to you, it’s full of fabrications. Then your resulting opinions are (1) systematically unreliable but (2) perfectly rational. Case 2: an apparent crackpot emails you his magnum opus predicting the future, and you blithely believe his every word—yet, contrary to all your evidence, it turns out he can see the future. Then your resulting opinions are (1) systematically reliable but (2) completely irrational. Thus evidence that you’re in Case 1 is “higher-order evidence” that your opinions were unreliable but rational; evidence that you’re in Case 2 is “higher-order evidence” that your opinions were reliable but irrational. Upshot: it’s important to keep these two notions of “higher-order evidence” conceptually distinct. Some discussions have focused on (1),1 while others have focused on (2).2 This chapter will offer an opinionated summary of recent work on (2): how do rational people respond to evidence about what opinions are rationalized by their evidence? We’ll cover the basic questions that arise (§1), a fruitful set of methods for making progress on them (§2), a map of the current theoretical positions (§3), and a sketch of the relevance of these positions to other debates (§4).

1  The Questions The higher-order evidence literature is often motivated by a dilemma that takes (something like) the following form.3 Rationally using our evidence is hard, so we should often be unsure whether we’ve messed it up. As a result, we can receive evidence that we have messed it up—even if, in fact, we have not. For example, suppose you just completed a DOI: 10.4324/9781315672687-17 176

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math problem and you’re fairly confident in your answer of ‘427’—but you’re also sleepdeprived, and so are unsure if that confidence is rationally based on the evidence. Suppose that in fact it is, but then your TA (mistakenly) tells you that your answer is way off. This provides you with (misleading) higher-order evidence that your evidence didn’t rationalize confidence in ‘427’. More generally: (i) It’s possible to get misleading higher-order evidence: to have evidence that supports q, but then get evidence that makes it rational to believe that one’s evidence didn’t support q. This higher-order evidence seems like it could make it rational to believe “My evidence didn’t support ‘427’. ” Nevertheless, your original (so-called ‘first-order’) evidence is still there—for example, the parameters of the math problem. Thus it seems that your total evidence might still support the claim that ‘427’ is the right answer; after all, if it’s a math problem, the evidence seems to entail as much! Putting these pieces together, it seems you could have total evidence supporting “ ‘427’ is the right answer, but my evidence doesn’t support that.” More generally: (ii) From (i) it follows that it’s possible to have evidence that rationalizes believing “q but my evidence doesn’t support q”.4 Yet believing “ ‘427’ is the answer but my evidence doesn’t support that” seems like it would lead to clearly irrational behavior and beliefs—such as betting that your own evidence is misleading (Horowitz 2014). That supports: (iii) But the “epistemically akratic” state in (ii) can’t be rational. And thus we have a dilemma. The literature contains a multitude of responses. Rather than try to survey them, I’ll explain why the underlying issue—the plausibility of (i)—opens up a plethora of interesting questions in traditional, formal, and applied epistemology. The issue I have in mind arises within a single normative notion, rather than as a tension between differing normative notions. So pick your favorite: “what’s supported by the evidence”; “what you should think”; “what would be rational to think”; etc. I’ll use these interchangeably. The issue is: What is the import of higher-order uncertainty? First-order uncertainty is the kind much of epistemology focuses on: Will it rain tomorrow? Who will win the next presidential election? Do my colleagues think I smell? Etc. Higher-order uncertainty is uncertainty about what degree of uncertainty in these claims is rational: Should I be 50–50 or 60–40 that it’ll rain tomorrow? Should I be confident it’ll be a Democrat, or am I biased in my judgment? Should I wear more deodorant—or am I paranoid in my suspicions about my colleagues? Etc. Your evidence rationalizes higher-order uncertainty when it rationalizes being unsure what opinions your evidence rationalizes—or, more colloquially, when you should be unsure what you should think.5 How do we think precisely about higher-order uncertainty (and, thereby, higher-order evidence)? Higher-order uncertainty arises for a given normative notion when it fails to be introspective: when there is a rational (evidentially supported, etc.) failure to be certain of what is rational (evidentially supported, etc.). This can happen for any representation—outright belief, comparative confidence, mushy 177

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credence, etc.—but thus far the most fruitful way of modeling higher-order uncertainty has emerged within a framework that uses a unique (White 2005), precise (White 2009a) probability function P that encodes the rational degrees of belief. ‘P ’ is a definite description for “the rational credence function, whatever it is (given your evidence, now)”. So ‘P (q) = 0.6’ is true iff it’s rational to be 0.6 confident in q given your evidence. Likewise, ‘P (P (q) = 0.6) = 0.2’ is true iff it’s rational to be 0.2 confident that it’s rational to be 0.6 confident in q, and so on. Thus it’s rational to have higher-order uncertainty iff there is a proposition q and a threshold t such that you should be unsure whether you should be t-confident of q: 0 < P (P (q) = t) < 1.6 First question: can higher-order uncertainty be rational? If we say no, then we have adopted a Merging theory, collapsing all levels of uncertainty down to the first one. Our formal theory of higher-order uncertainty is simple: Access Internalism: If P (q) = t, then P (P (q) = t) = 1. If you should be t-confident of q, you should be certain that you should be. If this is our theory, our solution to the dilemma posed earlier is simply to deny (i): it turns out that it’s really not possible to receive misleading higher-order evidence after all. The main challenge for this approach is to explain why higher-order uncertainty is irrational and to build a philosophical theory that explains our apparently rational sensitivity to it—as when, for instance, we are sensitive to the disagreement of peers who share our evidence.7 Suppose instead we agree that higher-order uncertainty is sometimes rational—and therefore that Access Internalism is false. Then the pressing questions is: what kinds of higher-order uncertainty can be rational? The opposite extreme of Merging is a Splitting theory, which says that necessary connections between first and higher-order opinions are either minimal or nonexistent.8 Splitting theories deny (iii) in our previous dilemma, allowing that it can sometimes be rational to be epistemically akratic. More generally, they allow that each of the following can sometimes be rational (see §2): Living on the Edge: Having a given credence in q while being certain that the rational credence is no higher, and leaving open that it’s lower. (There are q and t, such that P (q) = t but P (P (q) ≤ t) = 1 and P (P (q) < t) > 0.)9 Unconfident Confidence: Having confidence in q without being confident that it’s rational to have confidence in q. (There are q and t such that P (q) ≥ t but P (P (q) ≥ t) < t.)10 Improbable Certainties: Being certain of q but having some credence that you shouldn’t be. (There are q and t ≥ 0 such that P (q) = 1 but P (P (q) < 1) > t.)11 Confidence Akrasia: Being confident of q but I shouldn’t be confident of q. (There are q and t such that P (q ∧ [P (q) < t]) ≥ t.)12 Effacing Evidence: Being sure that your evidence is misleading about q. (There are q, t: P (q ↔ [P (q) < t]) = 1 and P (¬q ↔ [P (q) > t]) = 1.)13 These “mismatches” between first- and higher-order opinions can lead to surprisingly counterintuitive effects. For instance, if you have Effacing Evidence, then receiving higher-order evidence that your evidence supports confidence in q (i.e., that P (q) > t) should lead you to lower your confidence in q.

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We might be inclined to deny that some of these are genuinely possible. If so, then we’ve moved from Splitting to Bridging: a theory that asserts that although higher-order uncertainty can be rational, there are still systematic connections between first- and higherorder opinions. Though intuitive, Bridging faces the challenge of drawing and defending a principled line that explains why some types of higher-order uncertainty can be rational, and others cannot. Much of what follows will focus on delineating the possible such lines. Summing up: the puzzle of higher-order evidence raises the question of which sorts of higher-order uncertainty can be rational. The more higher-order uncertainty that a theory allows, the weaker the connections it imposes between higher- and first-order evidence; the less higher-order uncertainty it allows, the stronger those connections. The role of a theory is to explain which types of higher-order uncertainty (hence higher-order evidence) are possible, and why. Next question: How can we decide between such theories?

2  The Methods The literature has used a mix of different methods, moving between (a) formulating and testing general principles, (b) examining simple cases, and (c) building toy formal models of those simple cases. The most fruitful approach involves using these methods in tandem: general principles are formulated to delineate and constrain our theory; cases are offered to stress test those principles; toy models are constructed to check the coherence of those cases and the tenability of those principles. It may be obvious why we need both (a) general principles and (b) cases—but why do we need (c) models? The relevant sense of “model” is a specific one familiar from logic—for example, possible-worlds models from modal logic. These are formal constructs that are used to interpret a (formal or informal) language, and thereby used to check whether claims in that language are consistent, true, etc. We need them because we often want to know whether various described situations are consistent with background principles, and yet it is often hard to tell. For example, is the situation in (1) consistent with the principle in (2)? (1) You are rational to be unsure whether the rational credence function is your own or is one that assigns a credence to q that is a bit higher or a bit lower. (2) You should always match your credence in a claim to your best estimate of the rational credence in that claim. (See the “Estimate-Enkrasia” principle in §3.) They certainly look consistent.14 After all, you might have a credence of 0.5 in q and be equally unsure whether the rational credence in q is 0.4, 0.5, or 0.6. Then your credence in q equals your best estimate of the rational credence in q. But this only checks one instance of (2), which is a universally quantified claim. And it turns out that if we try to draw a full model that makes both true, and we’ll find that we cannot—surprisingly, (1) and (2) are inconsistent, for (2) implies that higher-order uncertainty is irrational (Samet 2000; Dorst 2019b). Upshot: we can’t assess the plausibility of principles about higher-order uncertainty by simply trying out a few of their instances; we need to build models of them so that we can systematically check whether all their instances are satisfiable. What do such models look like? The conceptually simplest ones are probability frames (W, P), which consist of a set of worlds W and a function P from worlds w to probability

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distributions Pw over W.15 Let’s assume that only finitely many distinctions are relevant, so that W is finite and we can list all the worlds in some order w1, . . ., wn. Propositions are modeled as sets of worlds, with logical operations done via set theory: q is true at w iff w ∈ q; ¬q:= W − q; p ∧ q:= p ∩ q; p → q:= ¬p ∪ q; etc. The intended interpretation of P is that Pw is the rational credence function to have at w, so that ‘P ’ is a definite description—“the rational credence function, whatever it is”. Since W is finite, Pw can be thought of as simply an assignment of non-negative numbers to the wi that sum to 1, and for any proposition (set of worlds) q, Pw(q):= å xÎq Pw(x). P can then be used—in the way that is standard from modal logic—to define propositions about probabilities as sets of worlds in the frame. For example, for any q ⊆ W and number t, [P (q) = t]:= {w ∈ W |Pw(q) = t}.16 (Note: letting wRx hold iff Pw(x) > 0, a probability frame induces a standard Kripke frame (W, R), and [P (·) = 1] becomes a necessity operator with the standard Kripke semantics: [P (q) = 1] is true at w iff ∀x: wRx → x ∈ q.) Here’s a simple example. Suppose you’re presented with an argument for a hard-toassess claim—say, that a universal basic income is financially feasible. It’s natural to think that there may be an epistemic asymmetry when it comes to evaluating such an argument. In general, one can often tell good and bad arguments apart—good arguments generally seem good; bad arguments generally seem bad. But when it comes to the sorts of arguments you’re likely to come across in public discourse, there is a selection effect that distorts that tendency. Good arguments tend to be repeated because they are good; bad arguments tend to be repeated because they seem good. Thus amongst the arguments you’re liable to run into, good ones will tend to wear their goodness on their sleeves, whereas bad ones will tend not to wear their badness on their sleeves—instead, they’ll be masquerading as good ones (Dorst 2019c). Here’s a toy model of this epistemic asymmetry. There are two possibilities: the argument is either a good (g) or bad (b) argument. By the previous asymmetry, how confident you should be in these two possibilities depends on which possibility you’re in. If the argument is good, you should be (say) 80% confident that it’s good, while if the argument is bad, you should be only (say) 60% confident that it’s bad. This specifies a probability frame, which we can diagram as follows, drawing labeled arrows between worlds to indicate how much probability the origin world assigns to the target world:

Figure 14.1

Good/Bad Argument

In this toy model, if the argument is good (you’re at g), you should be 80% confident that the argument is good and 20% confident that it’s bad: Pg(g)  =  0.8 and Pg(b)  =  0.2. Meanwhile, if the argument’s bad (you’re at b), you should be 40% confident that it’s good and 60% confident that it’s bad: Pb(g)  =  0.4 and Pb(b)  =  0.6. Thus the proposition that you should be 80% confident it’s good is true only at g: [P (g) = 0.8] = {w|Pw(g) = 0.8} =  {g}. Meanwhile, the proposition that you should be 40% confident it’s good is true only at b: [P (g) = 0.4] = {w|Pw(g) = 0.4} = {b}. That means, in turn, that at g it’s rational for 180

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you to be 80% confident that it’s rational for you to be 80% confident that it’s good: Pg(P (g) = 0.8) = Pg({g}) = 0.8. Similarly, at b it’s rational for you to be 40% confident that it’s rational for you to be 80% confident that it’s good: Pb(P (g) = 0.8) = Pb({g}) = 0.4. Likewise: if the argument is good, it’s rational for you to be 20% confident that it’s rational for you to be 40% confident that it’s rational for you to be 80% confident that it’s good: Pg(P (P (g) = 0.8) = 0.4) = 0.2, since [P (P (g) = 0.8) = 0.4] = {b}. (Didn’t I tell you we need models?) In short, P is used to identify propositions about probabilities as sets of worlds in the frame, which in turn allows us to “unravel” higher-order claims of any complexity to be claims about what world you’re in. This is as it should be: the central insight of Hintikka and Kripke semantics is that what world you’re in determines what you know (what the rational credence function is; what is necessary; etc.); therefore, claims about the latter can be reduced to claims about the former (Hintikka 1962; Kripke 1963). We are simply embedding this standard modal-logic idea in a probabilistic framework.17 Although the mathematics may seem intimidating, it’s much simpler than it looks: all that’s needed is the basics of propositional modal logic and finite probability theory.18 A useful special case of probability frames are prior frames: probability frames in which the probability distributions at different worlds can each be recovered by conditioning a common prior distribution on different (propositional) pieces of evidence. Prior frames are natural for modeling situations in which you should be unsure what your evidence is (what you should condition on), but should be sure what various bodies of evidence support (what the rational prior is). Such frames can be represented with triples (W, E, π), where (W, E) is a standard (finite) Kripke frame in which E is a (serial19) binary relation between worlds. Let Ew be the set of accessible worlds from w, i.e., Ew:= {x ∈ W |wEx}. π is a regular20 “prior” probability distribution over W, and the probability functions at each world are recovered by conditioning the prior on the set of accessible worlds: Pw(·):= π(·|Ew). Prior frames are formally useful because it’s often possible to characterize probabilistic principles within prior frames making reference only to the characteristics of the binary relation E, without reference to π.21 Let’s look at another example. Legend has it that Tim Williamson—a well-known trickster—owns an unmarked clock that has a single hand that can be set to any one of the twelve hour-positions. Every day he sets the position randomly, so in the morning you should be equally confident that it’s pointing at each of the positions 1 through 12. If you walk past his office when the door’s open, you may be able to catch a quick glance at the clock. Suppose you do. Intuitively: you know that upon glancing at the clock, you should be able to tell roughly—but not exactly—where it’s pointing. Here’s one way to sharpen this description into a prior frame. You (initially) should be sure that: if it’s pointing at n, then upon glancing at it you should be sure that it’s pointing somewhere between n − 1 and n + 1. This generates the prior frame in Figure 14.2. The set of worlds is W = {1, 2, . . ., 12}. The accessibility relation E is encoded in the arrows, so, for example, E1 = {12, 1, 2}, E2 = {1, 2, 3}, etc. The prior π is encoded in the faded ‘1/12’ written next to each world. Since Pi(·) = π(·|Ei), it follows that at each world i you should be equally (1/3) confident that you’re at i − 1, i, and i + 1—for example, P2(1) = P2(2) = P2(3) = 1/3. This model leads to higher-order uncertainty: since what you should think depends on where the hand is pointing, and you should be unsure where it’s pointing, you should thereby be unsure what you should think. For example, at 2 you should be 1/3 confident in each of worlds 1, 2, and 3; meanwhile, at 3 you should assign credence 0 to being at 1. Therefore at 2 you should be unsure whether your confidence that you’re at world 1 should be 1/3 or 0: P2(P (1) = 1/3) > 0 and P2(P (1) = 0) > 0. 181

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Figure 14.2  The Unmarked Clock

This is a version of the case presented in Williamson (2014); see Salow (2018b); Ahmed and Salow (2018). It’s an intuitive-enough description, and an elegant toy model. So far, it illustrates two of our three methods: describing a simple scenario, and drawing up a toy formal model of it. But it also illustrates the need for the third method—motivating our theory with general principles—for if the model represents a genuine possibility, a variety of very surprising phenomena can be rational. First, the model allows Improbable Certainties.22 Let Early = {1, 2, 3} be the proposition that it’s pointing at 1, 2, or 3. Then at world 2 you should be certain it’s early, but everywhere else you should be unsure of this: [P (Early) = 1] is true at 2, and false everywhere else. Since at 2 you should be only 1/3 confident that you’re at 2, it follows that if it’s pointing at 2 then you should be sure that it’s early, yet be only 1/3 confident that you should be sure of this: [P (Early) = 1] ∧ [P (P (Early) = 1) ≤ 1/3] is true at 2. So you should think to yourself, “It’s early, but I probably shouldn’t be sure of that.” It follows that you should also think to yourself, “Supposing it’s not rational for me to be sure it’s early, it’s (still) definitely early”: P2(Early|P (Early) < 1) = 1.23 Second, the model allows Confidence-Akrasia. Let Odd = {1, 3, 5, 7, 9, 11} be the proposition that it’s pointing at an odd number. At 2 you should be 2/3 confident of Odd, since two of the three possibilities you should leave open are 1 and 3. But, for parallel reasons, at each of 1 and 3 you should be only 1/3 confident in Odd. Thus at 2 you should be 2/3 confident in the conjunction “the hand is pointing at an odd number, but I shouldn’t be (2/3) confident of that”: P2(Odd ∧ [P (Odd) < 2/3]) ≥ 2/3. Third, this model allows Effacing Evidence. Note that the reasoning from the previous paragraph applies at every world: at every Odd-world, [P (Odd) = 1/3] is true, and at every ¬Odd-world, [P (Odd) = 2/3] is true. Thus the biconditionals Odd ↔ [P (Odd) < 1/2] and ¬Odd ↔ [P (Odd) > 1/2] are true at all worlds. Since at each world you should be sure that you’re at one of the worlds, it follows that at each world you should be sure of these biconditionals: [P (Odd ↔ [P (Odd) < 1/2]) = 1] and [P (¬Odd ↔ [P (Odd) > 1/2]) = 1] are both true at all worlds. In other words, you should be certain that the rational credences are pointing in the wrong direction about Odd—certain, for instance, that credence 1/2 in Odd is more accurate than the rational credence in Odd, whatever it is (Horowitz 2014; Ahmed and Salow 2018; Salow 2018; Dorst 2020). Because of this, this clock model leads to radical failures of the Value of Evidence: the idea that you should always expect (free) evidence to help you make better decisions (Salow, 182

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this volume). For example, if you had to decide whether to bet at fair odds on Odd, against Odd, or abstain from betting either way, then you should be certain (both before and after glancing at the clock) that making the rational decision after glancing at the clock— whatever it is—will lead you to take the wrong bet and so lose money. Thus you should prefer to simply take no bet, rather than to look at the clock and take the option rationalized by your evidence (Ahmed and Salow 2018; Dorst 2020). At this point, you might start to think that something has gone wrong—we’ve ended up in a sort of paradox. Could it really be that in deciding whether to bet on whether the hand is pointing at an odd number, you should prefer not to look at the clock? If we want to avoid this result, we need to formulate general principles about the connection between first- and higher-order uncertainty that explain what’s gone wrong with our toy model.

3  The Answers Such principles can be thought of as (partial) theories of higher-order uncertainty, delineating what constraints must be met by a model for it to describe a genuine rational scenario. To defend such a principle, we need to do at least three things: 1. Explicitly formulate and motivate the principle. 2. Show that it is nontrivial, in the sense that it allows higher-order uncertainty. 3. Show that it is potent, in the sense that it rules out (some) paradoxical scenarios. As mentioned earlier, step 2 often leads to surprises—our first group of principles all (nonobviously) rule out higher-order uncertainty: Rational Reflection: P (q|P (q) = t) = t If you learn that the rational credence in q is t, adopt credence t in q.24 Estimate Enkrasia: P (q) = E[P (q)] Your credence in q should equal your best estimate of the rational credence in q.25 Stay Away from the Edge: If P (P (q) ≤ t) = 1 and P (P (q) < t) > 0, then P (q) < t You should not have a credence on the edge of the range of credences you think might be rational.26 No Intentionally Biased Inquiry: Rational inquiries are not biased in favor of any given proposition.27 These principles are all very natural; why do they turn out to be so strong? Focus on Reflection. When the rational credence function has higher-order uncertainty, it’s not certain what the rational credence function is. Thus learning about the rational credence function provides new information—and that information can change the rational credence function (Hall 1994; Elga 2013; Mahtani 2017; Dorst 2020). For example, consider our Good/Bad Argument model. There are two possibilities: the argument is good (g) or bad (b). If it’s good, you should be 0.8 confident it’s good; if it’s bad, you should be 0.4 confident it’s good. Thus conditional on the rational confidence being 0.8 that it’s good, how confident should you be that it’s good? In other words, what is P (g|P (g) = 0.8)? Well, you know that it’s good iff the rational credence that it’s good is 0.8. Therefore if you learn that the rational credence is 0.8, you should become certain that it’s good: P (g|P (g) = 0.8) = 1. The rational credence was 0.8 only because it didn’t know the 183

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rational credence was 0.8; so when that higher-order uncertainty is removed, the rational credence changes. Given this, Elga (2013) proposed a natural weakening of Rational Reflection. The idea is that when you learn about the rational credence function, you shouldn’t simply adopt its opinions—rather, you should adopt the opinions it would have were it to learn what you’ve learned. He first formulates Rational Reflection this way: Elga’s Reflection: P (q|P = π) = π(q)28 Upon learning what the rational credence function is, adopt its opinions. He notes that this principle straightforwardly crashes if the rational credence function has higher-order uncertainty, since P (P  =  π|P  =  π)  =  π(P  =  π) only if π(P  =  π)  =  1. In response, he proposes the natural refinement: New Reflection: P (q|P = π) = π(q|P = π) Upon learning what the rational credence function is, adopt the opinions it would have were it given that information. Letting P* be the credence function that would be rational, were you informed of what the rational credence function was (i.e. P*w (·):= Pw(·|P = Pw)), New Reflection is equivalent to the following: HiFi: P (q) = E[P*(q)] The rational credence in q equals the rational expectation of the credence that would be rational, were you informed of what the rational credence function was.29 New Reflection is a natural, well-motivated constraint, and it does not lead to higherorder triviality (see Pettigrew and Titelbaum 2014; Dorst 2020, 2019b). But it does face serious critiques. Some have argued that it is too strong (Lasonen -Aarnio 2015), while others have objected that it’s too weak (Pettigrew and Titelbaum 2014; Dorst 2020, 2019b). In particular, note that New Reflection is valid on our previous model of the Unmarked Clock30—thus New Reflection permits Improbable Certainties, Confidence-Akrasia, Effacing Evidence, and radical failures of the Value of Evidence. This observation suggests that New Reflection does not fully capture its own motivations. It says that when you learn exactly what the rational credence function is, you should adopt the credence it would adopt were it to learn what you learned. But there is a more general statement of that idea: if you learn anything, your credences should always be constrained by what you know about how the rational credence function would respond to what you learned. That doesn’t hold in our Unmarked Clock model. For example, suppose you’re at world 4. Then conditional on it being Early (i.e., {1, 2, 3}), you know the rational credence function leaves open that the hand is pointing at 2—and yet you should not leave open that it’s pointing at 2.31 Here’s a natural way to generalize New Reflection to avoid this. Letting Pr(q):= P (q|r) be the rational credence in q conditional on r (whatever it is): Reaction: If Pr(l ≤ Pr(q) ≤ h) = 1, then l ≤ Pr(q) ≤ h If you should be sure that the rational reaction to r is to adopt a credence in q in a given range, react to r by adopting a credence in that range.32 184

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Our model of the clock fails to validate Reaction (see footnote 31). So are we done? Can we say that what’s wrong with our model of the clock—and all the paradoxical results that ensue from it—is that it violates Reaction, which is the proper generalization of New Reflection? No. To say that, we’d need to show that our diagnosis (Reaction) won’t allow the same paradoxes to arise in other shapes. And we can’t show that because Reaction does allow them to re-arise. Example: two sycophants—Sybil and Phan—share evidence, but Sybil is confident that Phan is rational, while Phan is confident that Sybil is rational. Here’s a simple probability frame modeling their situation; s is the possibility where Sybil is rational, p is the possibility where Phan is: Reaction is valid on this frame, yet it allows Confidence Akrasia, Effacing Evidence, and radical failures of the Value of Evidence (Dorst 2020). Upshot: if we want to rule out these puzzles, we need something that forces a correlation between what the evidence supports and truth—Reaction (or New Reflection) is not enough. Dorst (2020) argues that the following is a natural candidate: Reliance: Pr(q|Pr(q) ≥ t) ≥ Pr(q) Learning that it’s rational to have confidence in q (given r) shouldn’t lead you to lower your confidence in q (given r). Reliance combined with Reaction is equivalent to the following: Trust: Pr(q|Pr(q) ≥ t) ≥ t Learning that it’s rational to have confidence in q (given r) should lead you to become confident of q (given r). Trust allows Living on the Edge and Unconfident Confidence, but rules out Improbable Certainties, Confidence Akrasia, and Effacing Evidence—and, within the class of prior frames, is equivalent to the Value of Evidence (Dorst 2020). One challenge for Trust is that it is too strong. Although it allows significant amounts of higher-order uncertainty (Dorst 2020), it rules out certain models of “double bad cases” that are naturally motivated by epistemic asymmetries in externalist epistemology (Williamson 2019; Das 2020b).33 A different challenge for Trust is that it’s too weak. Although it’s equivalent to the Value of Evidence within prior frames, that connection doesn’t hold in full generality: the Value of Evidence implies Trust, but it turns out the converse does not hold.34 Does that mean that Trust needs to be strengthened? Perhaps—but Ben Levinstein (2019) proves a result that partially alleviates this worry. The unrestricted Value of Evidence says that no matter what decision problem you face (betting, believing, etc.), you should expect the rational opinions to sanction decisions at least as good as your own. The Epistemic Value of Evidence says that no matter how you

Figure 14.3 Sycophants

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value accuracy, you should expect the rational credences to be at least as accurate as your own (Oddie 1997; Schoenfield 2016b). Levinstein shows, in effect, that Trust holds iff the epistemic value of evidence holds. Nevertheless, we may still want a stronger principle. One worth exploring further is a “graded” form of introspection that weakens Access Internalism: Graded Access: If P (q) ≥ t, then P (P (q) ≥ t) ≥ t If you should be confident of q, you should be confident that you should be. This is equivalent to the denial of Unconfident Confidence from §1, as well as to what Williamson (2019) calls “threshold-transfer” (compare Littlejohn 2019).35 Although Williamson (2019) shows that this principle leads to higher-order triviality within prior frames, it seems to allow significant higher-order uncertainty in the context of probability frames— note that it is valid on our Good/Bad Argument frame.36 Summing up: there are several natural “joints” to be explored on the scale between weak theories that allow maximal amounts of higher-order uncertainty (and therefore minimal connections between higher- and first-order evidence) and those that allow minimal amounts of higher-order uncertainty (and therefore maximal such connections). Figure 14.4 provides a map of these various positions and their known (⇒) or conjectured (?⇒)

Figure 14.4  Map of Principles

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entailment relations. Bolded principles are relatively unexplored as standalone constraints, and (arguably) deserve further investigation.

4  The Applications What can one do with these theories once they are developed? Most obviously, they offer replies to our initial dilemma. For instance, Value and Trust will say that (i) is true— sometimes we can get misleading higher-order evidence—but that Confidence Akrasia is irrational, meaning that (ii) does not follow. More generally, the amount of allowed higherorder uncertainty will have bearings on a variety of further debates: • Internalism vs. externalism, or the extent to which we have rational access to the requirements of rationality.37 • Whether and how you should defer to your (future) evidence.38 • Whether it’s possible to rationally, intentionally bias your inquiries.39 • Whether evidence of evidence is evidence.40 • Whether we should always prefer to gather and use free evidence.41 • How to respond to peers who share our evidence but disagree with us.42 Here I’ll focus on two further applications: ambiguous evidence and human (ir)rationality.

4.1  Ambiguous Evidence Sometimes we get ambiguous evidence (Elga 2010)—for example: a man on the street removes two tubes of toothpaste and a live jellyfish from a bag; how confident should you be that the next item will be a tube of toothpaste? There’s an ongoing debate about whether we should model the opinions of rational agents who face such evidence with precise probabilities, or sets of probability functions (Joyce 2010; White 2009a; Schoenfield 2012, 2017b; Konek forthcoming). But once we recognize the possibility of higher-order uncertainty, there’s another option: their evidence could rationalize precise credences along with higher-order uncertainty—there’s some precise credence you should have that it’ll be a tube of toothpaste, but you should be unsure what that rational credence is (Carr 2019b). Such higher-order uncertainty has strictly more structure than the set-theoretic representation, for in addition to the set of probability functions that you should leave open might be rational, it also includes various possible rational degrees of confidence over that set.43 Carr (2019b) makes a strong case for approach and develops the foundations. The next step is to put it to work. One promising avenue is decision theory. It’s notoriously difficult to find decision rules for sets-of-probabilities that behave well: many are subject to sure-loss arguments (Elga 2010; cf . Bradley and Steele 2014) or lead to violations of the Value of Evidence (Kadane et al. 2008; cf . Bradley and Steele 2016), for instance. The higher-order-uncertainty approach may help, due to its richer structure. For example, two standard sets-of-probabilities rules are “conservative” and “permissive”. The former says that an option is permissible iff it maximizes expected utility with respect to all probability functions in the set; the latter says: iff it maximizes expected utility with respect to some member of the set. In the higher-order uncertainty framework, the former is equivalent to saying that an option is permissible iff you should be certain that it maximizes 187

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expected utility; the latter is equivalent to saying: iff you should leave open that it maximizes expected utility.44 But in this framework, there are many other options. First, “maximize expected utility” remains an option, since you should have a precise credence function—you should just be unsure whether the one you have is rational. Thus the injunction “Choose an option o that maximizes expected utility, å t P (U (o) = t)· t” makes sense—although often you will rationally be unsure which option maximizes this quantity, since you will be unsure what P is. On this way of doing things, provably there are theories of higher-order uncertainty that validate (or fail to validate) the value of evidence (see Geanakoplos 1989; Dorst 2020; Das 2020b). Alternatively, since higher-order probabilities induce expectations of expectations, another rule you could follow is “maximize expected expected utility”, i.e., choose an option that maximizes the expectation of the expectation of utility.45 Interestingly, although uncertainty about expected utility usually leads to uncertainty about expected expected utility, you will usually be less uncertain about the latter—so that if we keep iterating expectations you will eventually be certain of the ordinal rankings of options.46 This implies, for instance, that decision rules of the form “iterate expectations until you are at least t-confident of some option that it maximizes (iterated) expected utility, and then do that” make sense and are worth exploring. Notably, all of these approaches coincide with “maximize expected utility” when P is higher-order certain, but come apart when it is not.

4.2  Human (Ir)rationality One of the motivations for studying higher-order uncertainty is that you and I often have it—we are often unsure whether we are thinking as we should. Thus as theories of rational higher-order uncertainty develop, one clear point of application is what they tell us about the (ir)rationality of human reasoners like us. For example, Brian Hedden (2018) shows that given minimal assumptions about higherorder uncertainty, hindsight bias—the tendency to think that events were more predictable after you learn that they occurred—is often rational. In particular, this follows from two claims: (1) higher-order uncertainty is often rational, and (2) Reliance—the claim that what the evidence supports is correlated with truth—usually holds. As another example, whenever higher-order uncertainty is rational it arguably follows that you can expect gathering more information to make it rational to raise your credence in some particular claim q.47 For example, suppose you’re about to be presented with an argument and you’re currently 50–50 on whether it’ll be a good or bad argument. Afterwards you’ll be in the scenario described by our Good/Bad Argument model in Figure 14.1. Then although your current rational credence is 50%, your current rational estimate for the future rational credence is 0.5(0.8) + 0.5(0.4) = 60%. In other words, you rationally expect that being presented with the argument should lead you to raise your credence that it’s a good argument. Interestingly, the Good/Bad Argument model validates the Value of Evidence—meaning it’s the sort of evidence you should prefer to receive. As such, it raises the possibility of a rational form of confirmation bias (Nickerson 1998): the tendency to gather evidence that you expect to confirm a given opinion. This means that the rationality of higher-order uncertainty may help refine our understanding of empirical work on confirmation bias (Dorst 2019c).

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5 Conclusion Every now and then, philosophers come across a subtle phenomenon—usually dreamt up in a toy case—that turns out to be everywhere once you look for it. Arguably, higher-order evidence is such a phenomenon. Our lives are full of both self-doubt and its attendant effects: we are constantly wondering whether we are thinking as we should, and this exerts significant rational pressure on how we think. Thus the roots and importance of higherorder evidence go deep. At the same time, the philosophical debate is young: many of the methods (§2), theoretical positions (§3), and applications (§4) are still being mapped. As such, higher-order evidence—and it’s correlate, higher-order uncertainty—represents an excitingly open topic that crisscrosses the boundaries of formal, traditional, and applied epistemology. Much remains to be done.48

Notes   1 E.g., Elga (2007); Christensen (2007c, 2010a); Lasonen- Aarnio (2010); Christensen (2016); Roush (2009, 2016, 2017); White (2009b); Schoenfield (2015, 2016a); Sliwa and Horowitz (2015); Isaacs (2019).   2 E.g., Williamson (2000, 2008, 2014, 2019); Briggs (2009); Christensen (2010b); Smithies (2012, 2015); Lasonen- Aarnio (2013, 2014, 2015, 2019); Greco (2014); Horowitz (2014, 2019); Pettigrew and Titelbaum (2014); Titelbaum (2015); Schoenfield (2016b, 2017a); Littlejohn (2018); Schultheis (2018); Salow (2018b, 2019); Skipper et  al. (2018); Carr (2019a, 2019b); Eder and Brössel (2019); Gallow (2019a, 2019b); Das (2020a, 2020b); Fraser (2020).   3 E.g., Greco (2014, 2019); Neta (2019); Littlejohn (2018); Worsnip (2018); Kappel (2019); Salow (2019); Skipper (2019b); Lasonen- Aarnio (2020).   4 See Worsnip (2018, 2019); Skipper (2019a); Lasonen- Aarnio (2020) for more on (ii).   5 Why have we moved from talk of higher-order evidence to higher-order uncertainty? Because you can get (nontrivial) evidence about X iff you can be uncertain about X. This falls out of a Bayesian picture of evidence but is also independently motivated: evidence is something that can change your mind—and if you can’t be uncertain about X, you can’t change your mind about X.   6 Don’t confuse P with your actual credences C: you can perfectly well be rational (P = C), know what your credences are (C(q) = t → C(C(q) = t) = 1), and be unsure whether those credences are rational (C(P = C) < 1); see Dorst (2019b).   7 Examples of Mergers: Smithies (2012, 2015, 2019); Greco (2014); Titelbaum (2015, 2019); Schoen-field (2017a); Salow (2018b, 2019); Tal (2018, 2020); Skipper (2020). See Williamson (2008); Lasonen- Aarnio (2013); Roush (2016); Dorst (2019b, 2020) for some of the challenges.   8 A standard Splitting position: the only connection is that if your evidence makes q certain, then   q is true. The probabilistic component of this is the “surely-factivity” axiom: P (q|P (q) = 1) = 1. See Williamson (2000, 2008, 2014, 2019); Lasonen- Aarnio (2013, 2015); Weatherson (2019).   9 Similar principles are discussed in Christensen (2007a, 2010b); Sliwa and Horowitz (2015); Schultheis (2018); Skipper et  al. (2018); Hawthorne and Isaacs (2020); Fraser (2020); Dorst (2021). 10 Equivalently, there are r and s such that P (P (r) > s) > s but P (r) ≤ s. (Let r = ¬q, s = 1 − t:   [P (q) ≥ t] ∧ [P (P (q) ≥ t) < t] iff [P (¬q) ≤ 1 − t] ∧ [P (P (q) < t) > 1 − t], iff [P (r) ≤ s] ∧ [P (P (r) > s) > s].) See (Dorst 2020, Fact 5.5); Littlejohn (2019); Littlejohn and Dutant (2019); Williamson (2019). 11 The phenomenon (with t ≥1) is discussed (with a focus on knowledge rather than rational certainty) in Williamson (2013, 2014); Cohen and Comesaña (2013); Goodman (2013). 12 This is effectively the denial of (iii) from our dilemma, though it involves akratic confidence (Horowitz 2014); variants involve akratic beliefs (Greco 2014) or estimates (Christensen 2010b; Salow 2019; Dorst 2019b). Note that the denial of Confidence Akrasia for all q and t is equivalent to the assertion of P ([P (q) ≥ t] → q) ≥ t, which is a material-conditional version of the “Trust” principle in §3.

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Kevin Dorst 3 See Horowitz (2014); Ahmed and Salow (2018); Salow (2018b); Dorst (2020). 1 14 And many seem to have presupposed that they are: (Christensen 2007b, 2010b; Pettigrew and Titelbaum 2014; Sliwa and Horowitz 2015; Roush 2016; Skipper et al. 2018; Gallow 2019a). 15 Dorst (2019b) gives an accessible introduction to these models; see also Gaifman (1988); Samet (2000); Dorst (2020); Levinstein (2019). Note: in the modal-logic jargon, these are “frames”, not “models”, because they do not include an interpretation function. As we’ll see, it’s not necessary. 16 As a formal language would get cumbersome here, we use a semi-formal one. ‘P ’ is a definite description for “the rational credence function, whatever it is”; ‘Pw ’ rigidly picks out the rational credence function associated with world w; for any q ⊆ W, ‘P (q)’ is a definite description for “the rational credence” in q, whatever it is; ‘Pw (q)’ rigidly picks out a particular number; and for any q ⊆ W and t ∈ [0, 1], ‘[P (q) = t]’ picks out the set of worlds w such that Pw (q) = t. 17 This basic move for studying higher-order uncertainty is common (Aumann 1976; G aifman 1988; Geanakoplos 1989; Samet 1999, 2000; Williamson 2000, 2008, 2014, 2019; Cresto 2012; Lasonen- Aarnio 2013, 2015; Lederman 2015; van Ditmarsch et  al. 2015; Campbell- Moore 2016; Salow 2018, 2019; Das 2020a, 2020b; Dorst 2020, 2019b; Levinstein 2019). Notably, probability frames are formally identical to what are known as Markov chains—though their intended interpretation is different. As such, an n-world probability frame can be represented with an n × n stochastic matrix in which the rows contain non-negative entries that sum to 1. Row i, column j of the matrix represents the probability that world i assigns to world j, i.e., Pw_i (wj). For instance, our Good/Bad Argument frame can be represented as: (0.8, 0.2; 0.4, 0.6). This representation is useful for bookkeeping and allows for the application (e.g., Samet 2000; Williamson 2008) of some general theorems (Bertsekas and Tsitsiklis 2008, ch. 7). 18 The first two chapters of Bertsekas and Tsitsiklis (2008)—a textbook freely available online— covers all the relevant material on probability; no prior mathematics needed. The other half is covered by the propositional-modal-logic portion of any standard textbook (e.g., Hughes et al. 1996; Sider 2010). 19 For all w ∈ W there is an x ∈ W such that wEx. 20 For all w ∈ W : π(w) > 0. 21 See Geanakoplos (1989); Williamson (2000, 2008, 2014, 2019); Lasonen- Aarnio (2015); Salow (2018b, 2019); Dorst (2020); Das (2020a, 2020b). 22 This, in fact, is why Williamson (2014) introduced it—though his focus was on knowledge. 23 This is a variant on what Dorst (2019a) calls “abominable conditionals”; it arises whenever there are Positive Access failures—cases in which P (q) = 1 but P (P (q) = 1) < 1. 24 Principles like this are discussed in Gaifman (1988); Samet (2000); Christensen (2007b, 2010b); Williamson (2008); Roush (2009, 2016); Elga (2013); Mahtani (2017); Gallow (2019a). See Samet (2000), Elga (2013), Williamson (2014), Gallow (2017), and Dorst (2020) for triviality results. 25 E here is the mathematical expectation with respect to P, i.e., E[P (q)] := ∑t P(P (q) = t) · t. Principles like this are discussed in Samet (2000); Christensen (2010b); Pettigrew and Titelbaum (2014); Sliwa and Horowitz (2015); Skipper et  al. (2018); Salow (2018b, 2019); Gallow (2019b). See Samet (2000) and Dorst (2019b) for triviality results. 26 Principles like this are discussed in Christensen (2010b); Titelbaum (2010); Salow (2018b); and Fraser (2020), and related ones are discussed in Schultheis (2018); Hawthorne and Isaacs (2020). See Dorst (2021) for the triviality result. 27 See Salow (2018b) for this principle and the triviality result; see also Titelbaum (2010); Das (2020b). The formulation of this principle (and hence the results) are contested—see Gallow (2019b). 28 Here ‘π’ is a rigid designator for a particular probability function. Elga’s Reflection is equivalent to Rational Reflection (Samet 2000), though things get more subtle when we have principles of the form P (q|Q(q) = t) = t and P (q|Q = π) = π(q), where Q ≠ P; see Gallow (2017). 29 See Dorst (2019b) for the equivalence to New Reflection, as well as Stalnaker (2019). 30 Since the probability function Pw associated with each world w is unique, New Reflection is satisfied at all worlds. 31 Early ⊆ [P (2|Early) ≥ ⅓], so P4(P(2|Early) ≥ ⅓ |Early) = 1, yet P4(2|Early) = P4(2|{3}) = 0. 32 Reaction entails New Reflection (let r = [P = π]), but not vice versa. Although it may look like Reaction follows from factivity (i.e., [P (q) = 1] → q), it doesn’t, for the antecedent of Reaction

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Higher-Order Evidence merely asserts that a conditional certainty (given r) holds: Pr(l ≤ Pr(q) ≤ h) = 1; not P (l ≤ Pr(q) ≤ h) = 1. 33 Using stochastic matrix notation (footnote 17), here’s an example of a frame that has the structure Williamson and Das discuss: (¼,¼,¼,¼; 0,½,0,½; 0,0,½,½; 0,0,0,1). See (Dorst 2020, Appendix A) for a reply to this case. Notably, Trust (and the Value of Evidence) do allow frames of this structure—they simply impose constraints on the probabilities. For example, they allow the following variant: (⅕,⅕,⅕,⅖; 0,½,0,½; 0,0,½,½; 0,0,0,1). 34 Contra Dorst’s (2020) Conjecture 7.3. Thanks to Branden Fitelson and Brooke Husic for help discovering this. 35 Threshold-transfer says that [P (P (q) ≥ t) ≥ t] → [P (q) ≥ t]. This is stronger than both Trust and the Value, which entail only a weakened version of the principle (Dorst 2020; Williamson 2019): [P (P (q) ≥ t) ≥ s] → [P (q) ≥ t·s]. 36 It is also valid on (½,¼,¼; ¼,½,¼; ¼,¼,½). What Williamson shows is that within prior frames, Graded Access comes very close to implying Negative Access (if P (q) < 1 then P (P (q) < 1) = 1). In prior frames this rules out higher-order uncertainty—but not so in probability frames. 37 See Williamson (2000, 2008, 2014, 2019); Mahtani (2008); Smithies (2012, 2015); Cohen and Comesan˜a (2013); Lasonen- Aarnio (2013, 2014, 2015, 2019); Schoenfield (2016b); Das and Salow (2018); Salow (2018b, 2019); Das (2020a); Gallow (2019b); Dorst (2019b); Carr (2019a); Weatherson (2019). 38 See Williamson (2008); Briggs (2009); Roush (2009, 2016); Christensen (2010b); Elga (2013); Pet-tigrew and Titelbaum (2014); Gallow (2017, 2019b); Schoenfield (2017a); Salow (2018b); Dorst (2020). 39 See Titelbaum (2010); Salow (2018b); Dorst (2019c); Gallow (2019b); Das (2020b). 40 See Eder and Brö (2019); Williamson (2019); Salow (2018a). 41 See Good (1967); Schoenfield (2016b); Ahmed and Salow (2018); Das (2020b); Dorst (2020); Levinstein (2019); Salow (this volume). 42 See Aumann (1976); Elga (2007); Christensen (2007c); Brössel and Eder (2014); Lederman (2015); Skipper et al. (2018); Dorst (2020). 43 Precisely, in addition to {π|P (P = π) > 0}, the rational credences P are also capture opinions about this set—e.g., P (P = π1) > P (P = π2). 44 Precisely, o1 is permissible iff (conservative:) P (∀o2: E[U (o1)] ≥ E[U (o2)]) = 1; or (permissive:) P (∀o2: E[U (o1)] ≥ E[U (o2)]) > 0. 45 For any random variable. Since in this framework P (X = x) varies across worlds, it follows that E[X] is itself a random variable that varies across worlds, and therefore that E[E[X]] is welldefined and potentially distinct from E[X] (Samet 2000; Williamson 2008). Thus “choose an option o that maximizes E[E[U (o)]]” makes sense. 46 Precisely: a consequence of the convergence theorems for Markov chains (e.g., Bertsekas and Tsitsiklis 2008, §7.3) is that in most finite probability frames, for any X, there’s a fixed point that the series E[X], E[E[X]], E[E[E[X]]] . . . will converge to at all worlds, meaning you rationally will become more and more confident of the values of these iterated expectations. 47 See Titelbaum (2010); Salow (2018b); Das (2020b). This has been contested by Gallow (2019b). 48 Thanks to Maria Lasonen-Aarnio, Bernhard Salow, and Mattias Skipper for helpful comments on earlier versions of this chapter.

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PART 3

The Social Epistemology of Evidence

15 EVIDENCE AND POWER Feminist Empiricist Approaches to Evidence Kristen Intemann

1 Introduction On September 27, 2018, Dr. Christine Blasey Ford testified before the U.S. Senate Judiciary Committee she was 100% certain that she was assaulted by then Supreme Court nominee Brett Kavanaugh and his friend Mark Judge when they were both in high school. She testified about several details of the assault, despite the fact that it had occurred many years previously. Judge Kavanaugh later testified he was 100% certain that he did not physically or sexually assault Dr. Ford or anyone. While a plurality of Americans (and a few senators) were uncertain who or what to believe, there was a significant gender gap in how the evidence was perceived. Polling in the days following the hearing found that among men, thirty-seven percent said they believed Ford, while thirty-nine percent believed Kavanaugh. Among women, fifty-two percent said they believed Ford, while only twenty-seven percent said they believed Kavanaugh (NPR/PBS 2018). This gender gap was also more pronounced than it was in response to the testimony of Anita Hill in 1991, when she made sexual harassment allegations against then Supreme Court nominee Clarence Thomas. In 1991, only twenty-six percent of women polled believed the testimony of Anita Hill, while fiftysix percent believed Judge Thomas, which was similar for men polled (Kolbert 1991). Of course, one difference was that both Anita Hill and Thomas Clarence were Black, while both Christine Blasey Ford and Brett Kavenaugh were white. While no doubt there are many complex political, social, and psychological factors that might account for the differences between the two cases, they raise important epistemological questions about whether the gender and/or race of both those offering evidence and those evaluating it makes a difference (or ought to make a difference). Can gender (and/or race) relations in society influence what we take as evidence for particular claims? Can gendered and/or racial stereotypes influence perceptions of whether testimony is “credible” or “reliable”? Can the social identity or circumstances of epistemic agents influence how much evidence is needed for believing a particular claim? And, perhaps most importantly, if social relations do make a difference to what we take to be evidence or credible testimony, what implications does this have for what constitutes good evidence? How should we structure epistemic communities or practices so as to minimize bias? While the significance of these issues may be apparent in the context of political or legal proceedings, the same questions 197

DOI: 10.4324/9781315672687-19

Kristen Intemann

can be asked in the context of other knowledge-producing practices, including science or medicine. Feminist epistemology is often characterized as a branch of social epistemology that examines the ways in which power dynamics and social relations influence the production of knowledge (Anderson 1995; Grasswick 2006).1 Feminist epistemologists maintain that gender (in combination with other, intersecting, social categories such as race, class, and sexual orientation) is one of the axes along which power is distributed in society and has a potential to influence what we know and how we know, including judgments about evidence. Feminist epistemologists seek to understand not only  how  our social relations of gender have shaped our evidentiary practices, but also whether and how these relations should play a role in responsible judgments about evidence and knowledge. The aim of this chapter is to understand the ways in which feminist epistemologists have found that social gender relations make a difference to evidentiary concepts and practices and can have implications for what counts as good evidence. While there are differences among feminist epistemologists, my focus will be on examining two feminist approaches to evidence that can be understood as varieties of feminist empiricism. Empiricism has been attractive to feminist scholars specifically because it provides resources to study knowledge practices themselves and involves a commitment to revise beliefs, including implicit assumptions, value judgments, stereotypes, and norms in light of new empirical evidence. I  will begin by providing an overview of some key tenets of feminist empiricist approaches to epistemology and evidence. Section  3 will then examine some of the specific ways in which gender, ethnicity, class, and other social attributes of epistemic inquirers may make a difference to evidentiary judgments. Section 4 will then explain and evaluate the normative prescriptions that two different feminist empiricist approaches give for how we should minimize bias in evidentiary judgments.

2  Central Tenets of Feminist Empiricist Views While there are differences among feminist empiricists (as will be discussed in Section 4) there are also commonly held tenets among them. The views that characterize such approaches are not all uniquely feminist. That is, some of these claims have also been made by non-feminist epistemologists. Nonetheless, they are broadly shared among who identify as feminist empiricists and are taken to be important to understanding how, exactly, feminist concerns enter into assessments of evidence. First, feminist empiricists take empirical evidence to be a central source of evidence for our beliefs. Feminist empiricists have held that empirical adequacy or success is a necessary and important constraint in evaluating claims, theories, and explanations (Longino 1990, 2002; Solomon 2001; Clough 2003; Borgerson 2011). At the same time, feminist empiricists have argued that experience and the evidence produced by our experiences is socially situated. Our beliefs and reasons are shaped by the kinds of experiences that we have, which are influenced and constrained by our material, social, and historical circumstances, including social forces related to membership in certain social categories (such as race, class, sex/gender, and sexual orientation). Some wondered why, for example, it took so long for Christine Blasey Ford to come forward with her allegations against Brett Kavanaugh. The timing seemed suspicious to conservatives, coming as it did after several previous FBI background checks and only right before Kavanaugh was being considered for a position

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on the highest court in the country. Yet individuals who have worked with, or have themselves been, victims of sexual violence argued that this was consistent with their experiences. It is not unusual for cases to go unreported (e.g., Read et al. 2007), and many only share the information several years after the incident, if at all (Adams-Curtis and Forbes 2004; Banyard et al. 2007). Victims are sometimes young when incidents occur, many are afraid that they will not be believed, some are concerned about reliving the trauma (particularly in ways that may be public), and many report feelings of guilt or responsibility associated with sexual assaults or violence (Goldblatt and Meintijes 1998; Ahrens 2006). Thus, those with relevant experiences were (correctly) less likely to view the timing of the accusation as evidence against its veracity. Insofar as social locations (such as gender, race, class) shape our experiences, they can also shape the evidence we have access to. Therefore, feminist empiricists believe that analyzing the ways in which social categories and relations can make differences to experience and evidentiary practices is epistemically important (Anderson 1995; Intemann 2010). Second, feminist empiricists take evidentiary judgments to be holistic. That is, taking something to be evidence for or against a particular claim or hypothesis depends on a variety of other background beliefs, some of which may be implicit (Longino 1990). Whether something is in fact evidence for or against a particular claim depends also on whether background assumptions are justified or count as good reasons according to some shared standards for evaluation. For example, Blasey Ford’s passing a polygraph test counts as evidence that Brett Kavanaugh committed sexual assault only in conjunction with a variety of other background assumptions, such as the assumption that polygraph tests are reliable indicators of honesty when properly administered, that the test was properly administered, and that there is no way that Blasey Ford could have been mistaken about her assailant or her own experiences. Background assumptions are what allow us to infer that some reasons or data constitute evidence for or against a claim. Of course, these background assumptions can themselves be justified or unjustified and can thus influence whether we err in what we take to be justified. As a consequence, a third important claim made by feminist empiricists is that the locus of justification is at the level of epistemic communities, rather than individuals (Nelson 1990; Code 1991, 2006). Individuals can only know (or have justified beliefs) insofar as those beliefs have underdone proper evidentiary scrutiny at the community level. This communalism is partly a consequence of the commitment to holism in two ways. If something can only be taken to be evidence for a claim in relation to other background beliefs, then background beliefs must themselves be open to criticism and justified. Yet, individual epistemic agents are not always aware of the implicit assumptions they make in taking something to be evidence for a claim (Longino 1990). Thus, it is only by being a member of a community that holds some shared standards of evaluation that potentially problematic background assumptions can be identified and challenged. Only evidential reasoning that withstands this process of critical scrutiny by a larger epistemic community can be justified (Longino 1990). Another reason that epistemic agents need to be a part of communities in order to know, is that experiences and access to evidence is necessarily partial and limited at the level of individuals. As explained earlier, if experience and evidence are socially situated, individuals occupying different social circumstances will have different experiences and access to different kinds of evidence. Pursuing and generating a fully body of relevant evidence requires not just drawing on one’s own experiences, but also receiving critical

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feedback on how we understand those experiences and interpret them as evidence. As Lynn Hankinson Nelson writes, What I  know depends inextricably on what we know, for some we. My claims to know are subject to community criteria, public notions of what constitutes evidence, so that, in an important sense, I can know only what we know, for some we. (Nelson 1990, 255) Consequently, the interrelations and interactions among epistemic agents and the implications these might have for how we collectively understand and interpret evidence are also epistemically important. A fourth claim endorsed by feminist empiricists is that value judgments (including social or political value judgments or those that many have called non-epistemic or noncognitive) may be among those background assumptions that influence our judgments about what we take to be evidence, how much evidence is needed, who has epistemic authority, or who is an expert (or what sorts of testimony are reliable). How exactly this occurs will be examined in Section 3. Nonetheless, feminist empiricists agree that there is the potential for value judgments to operate as background assumptions in our reasoning (in ways that may either be epistemically positive or negative). As Longino has argued, there is nothing that prevents value judgments from operating as background assumptions, even among conscientious epistemic agents. Moreover, some feminist empiricists have even argued that values themselves have empirical content and are a part of an interconnected system of beliefs that is subject to empirical constraint (Clough and Loges 2008; Solomon 2012). Finally, a fifth claim made by feminist empiricists is that epistemic communities can be organized in ways that either facilitate or thwart cognitive aims (such as minimizing bias, maximizing objectivity, and arriving at justified beliefs) and that power structures and social inequalities can also influence the ways in which communities are organized and epistemic practices. One central normative question for feminist empiricists, then, has been what practices might best produce evidence or knowledge that is more reliable, less biased or partial, or more justified? For feminist epistemologists, this generally involves a commitment to preventing or minimizing the negative influences of hierarchical power structures or social inequalities on our epistemic practices. Thus, feminist empiricist approaches to evidence examine how gender and other intersecting aspects of our social relations influence our experiences, judgments about what we take to be evidence, what in fact justifies evidentiary claims, and what evidentiary practices might best promote empirically adequate and less biased evidence (and ultimately knowledge). I will now provide an overview of some of the ways in which feminist empiricists have argued that social relationships, gendered stereotypes, and social values have in fact influenced evidentiary judgments.

3  Ways in Which Difference Can Make a Difference to Evidence There is significant empirical research that suggests that race, gender, class, and other social characteristics of inquirers can influence (sometimes subtly, sometimes not-so-subtly) our epistemic judgments about what we take to be evidence, the strength of that evidence, as well as how much evidence is needed to justify a particular claim. What follows is a 200

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non-exhaustive account of some of the ways that difference can make a difference in the production of knowledge.

Who Has Epistemic Authority? First, gender, as well as other intersecting categories such as race and class, have influenced who we take to be experts or as having epistemic authority. Historically, for example, women were stereotyped as “irrational” and less likely to be viewed as experts or deserving of epistemic authority. In the early 1950s, when Vera Rubin first hypothesized the existence of dark matter to explain observations that were at the time inconsistent with prevailing theories in astronomy, she was told by members of the audience at her American Astronomical Society talk that perhaps she should go home to her children and her paper was never published (Yount 2006, 126). While there might have been many factors that contributed to the dismissal of her work, it is plausible to think that some did not take her work seriously because she was a woman. Implicit biases have also been documented in mentoring, hiring and tenure decisions, citation practices, and grant evaluation (Moss-Bacusin et al. 2012). That is, it appears that men and women of color and white women have had the significance of their epistemic contributions undervalued, dismissed, or altogether ignored, on the basis of factors that are epistemically irrelevant. While stereotypes can influence judgments about who we recognize as having epistemic authority, social conditions can also prevent people from acquiring the means viewed as necessary for acquiring expertise or epistemic authority, such as education. For example, access to resources that facilitate interest and training in STEM disciplines is not equitably distributed among populations (De Welde and Larusen 2011). For example, in the U.S., one-third of K–12 schools are rural and one in five students attends a rural school, yet rural communities receive less funding for education that their urban counterparts, tend to have less access to technologies such as high-speed internet, and have a more difficult time recruiting and retaining qualified STEM teachers (Avery 2013). Many rural, poor, female, and indigenous STEM students also report a disconnect between academic STEM knowledge and their local knowledge practices, which they see as more relevant to the “real world” and things they care about (Avery and Kasam 2011). These factors make it more challenging for certain groups to pursue STEM education and careers. In addition, the culture of STEM disciplines in the academy often fail to be inclusive, even when there is no explicit discrimination with respect to epistemic authority. For example, the work demands of scientists may be incompatible with the demands of parenting and other kinds of domestic duties in some contexts (Morley and Lugg 2009; Mason et al. 2013). Certain groups may experience harassment, microaggressions, or a chilly climate that make participation in scientific communities undesirable even if one’s scientific work is not overtly discounted (Clark Blickenstaff 2005; De Welde and Laursen 2011; Wylie 2012). When certain groups are systematically denied access to epistemological communities or resources, one of the consequences is that certain kinds of experiences are systematically underrepresented within such communities in ways that cause problematic assumptions to go unchallenged, or certain alternative explanations be neglected. That is, it can result in bias at the level of epistemic communities, both in terms of what is taken to be evidence for particular claims, as well as what explanations are taken to be most plausible for the evidence. 201

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Judgments About Epistemic Credibility While social norms and implicit stereotypes can influence who is taken to have epistemic authority or relevant expertise, they can also play a role in who is taken to have epistemic credibility or trustworthiness. One might be viewed as being credible in light of their expertise, but not necessarily. One might grant that scientists working for tobacco companies have a certain degree of expertise as scientists, but we might think they are not credible or trustworthy sources insofar as they have significant economic or personal conflicts of interest. In epistemic inquiry, we often must rely on the testimony of others. In cases like those of Christine Blasey Ford, obviously testimony (and the credibility of such testimony) plays a central role in determining judgments made about what evidence exists for or against a particular claim (such as whether Brett Kavanaugh committed sexual assault, or whether he should be confirmed to the Supreme Court). Yet testimony also often plays an implicit role in most of our knowledge producing endeavors. Scientists, for example, must rely on the testimony of other scientists about past research and previous experimental results. An individual scientist often has neither the expertise nor the resources to test every single background assumption or auxiliary theory that she or he must rely on in building on past scientific knowledge. Chemists rely on the reports of other researchers to be able to duplicate results in creating certain chemical reactions or compounds. Biomedical researchers rely on the testimony of human subjects to identify and track potential side effects. Conservation biologists rely on the testimony of research assistants and other researchers to determine population levels of species. We rely on the testimony of scientists or other expert professionals to decide whether there is sufficient evidence to believe that a particular policy or course of action is justified. We rely on both the media and the testimony of candidates to decide whom to support in political elections. In short, testimony plays a significant role in deciding what to believe. Yet there is significant empirical evidence that gendered norms and stereotypes can influence judgments about whether one’s testimony is viewed as credible (see, for example, McKimmie et al. 2004; Schuller et al. 2005; ThomasHunt and Phillips 2004; Murray and Graham 2007; Dolan 2010). In the case of Blasey Ford, some seemed to believe her precisely because she conformed to certain gendered norms. She was “deferential,” “respectful,” “teary,” and “emotionally compelling.” Anita Hill, however, was not perceived the same way in 1991. Again, there may be many reasons for this, but she was not perceived as conforming to certain gendered and racial norms. She was perceived as “quiet,” “calm,” “cold,” and “emotionless ” (Jordan 1992). One reason fewer people found her credible may be because she did not conform to such implicit expectations about how a female victim of sexual assault should act. Similarly, women might have been more likely to believe that Blasey Ford was telling the truth because her experience resonated with their own experiences. In the case of Clarence Thomas, his assertion that he was the victim of a “hightech lynching,” may have resonated more with those who had experienced racism, or those who feared being perceived as racist for not believing him. The threat of stereotype bias, the risk of not being believed, or the likelihood of receiving other undesirable consequences as the result of giving testimony can also refer to what Kristie Dotson has referred to as “testimonial smothering” (Dotson 2011). Testimonial smothering, or the truncating or suppression of one’s own testimony can occur when one’s audience is unlikely to be willing or able to be receptive to or engage in uptake of the 202

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testimony (Dotson 2011, 244). Indeed, this seems to occur in many instances of violence and harassment, particularly in instances where there are unequal power dynamics. A consequence, however, is that some evidence (evidence that would have resulted from testimony) is suppressed or obscured.

Observation and Description of Evidence Gendered norms and stereotypes can also influence how we perceive and describe evidence. As many have argued, observation itself is theory laden and our perceptions of phenomena are also mediated by background assumptions and our conceptual categories (Duhem 1991; Hanson 1958; Kuhn 1977). Our background assumptions and conceptual categories can also be influenced by social value judgments and gender norms. Emily Martin (1991), for example, has shown that accounts of human reproduction often employed language that ascribed gendered stereotypes to the sperm and egg, characterizing the egg as passively floating through the fallopian tubes and subsequently “penetrated” by the sperm that actively “burrows” into the egg. In this case, implicit gendered stereotypes obscured perceptions of what was actually occurring. Subsequent research revealed that there is a complex chemical interaction between the surface of the egg and sperm (Martin 1991). Gendered stereotypes have also been reflected in observations of non-human animals. Early depictions of primates represented them as having many human-like qualities and social interactions (Schiebinger 2004). Primatologists relied on the assumption that females are coy and choosy of potential mates, neglecting the fact that female primates often had multiple sexual partners (Hrdy 2009). This was neglected, not because male primatologists in the field at the time were particularly bad observers, but rather because their expectations and unconscious background beliefs directed them toward observing certain things and away from observing others, influencing their perception of primate behavior. In archaeology, investigations into the evolution of human tool use reflect assumptions about, for example, what is a “tool.” Historically, many archaeologists focused on tools used in hunting and killing animals (tools generally associated with men). Male archaeologists did not take baskets or reeds used for foraging to be “tools.” Thus, early accounts of the evolution of tool use in humans focused solely on the activities traditionally assigned to males. Again, archaeologists in the field at the time simply did not “see” baskets as tools and thus did not take them to be relevant data (Wylie and Nelson 2007). These examples help to illustrate that background assumptions, including values, norms, and unconsciously held stereotypes form part of the lens with which we make observations. They can shape what we observe and determine the data that must be accounted for by a viable hypothesis. When such values are implicit and not critically evaluated, they can lead to accounts of phenomena that are partial or inaccurate. In this way, gendered norms and stereotypes can influence what we take to be evidence.

Standards of Evidence: How Much Evidence Is Needed? Evidentiary judgments include not only judgments about what the evidence is, but judgments about how much evidence is needed in order to accept beliefs as true or justified. As many have argued, how much evidence is needed can depend on the risk of being wrong 203

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(e.g., Douglas 2009). In criminal trials, we use a very high standard of evidence (guilt beyond a reasonable doubt) precisely because the consequences of error are so severe (limiting one’s liberty and life prospects for a significant amount of time). Accidentally convicting an innocent person is a risk that many find unacceptable, so there is a very high bar for evidence establishing guilt. In civil proceedings, the consequences of error are weighed differently. If someone is found liable in a civil case erroneously, they are likely to pay a significant fine. Yet, if someone is not found liable when they really were, a significant harm will be left without compensation. Thus, in civil proceedings, juries and judges use the standard that the evidence must make it more likely than not— a “preponderance” of the evidence—to show that someone is liable. Disagreements about the accusations against Brett Kavanaugh also may have resulted from disagreements about what standards of evidence were appropriate. Some believed that the burden was on Blasey Ford to show that he was guilty beyond a reasonable doubt. Senator Susan Collins of Maine stated that she thought the standard used in civil cases was more appropriate in this case. Yet a decision about promotion to the highest court in the land might not require the evidentiary demands used in either civil or criminal cases. Rather, one might think that the consequences of believing Blasey Ford, even if it turned out she was mistaken, were simply not that grave. Kavanaugh might miss out on a promotion, but he would continue to have a very powerful and respected position as a District Appeals Judge. Moreover, another highly qualified candidate could easily have been nominated. The consequences of not believing Ford if her claims were true, however, would promote a harasser to the Supreme Court and send a message to victims that they will not be believed. On this view, the claim just needed to be viewed as “credible,” which most agreed it was. How much evidence is needed depends on the risk of being wrong, which in turn depends on how bad the consequences would be. This is a value judgment. Moreover, in this case, it is a judgment that depends on ethical value judgments about how bad we think sexual harassment and sexual assault are, which might obviously reflect views about gender.

4  Feminist Empiricist Approaches to Minimizing Bias in Evidentiary Judgments As mentioned, feminist epistemology is concerned not only with identifying how gendered norms and relations influence evidentiary judgments, but also with the normative question of what ought to be done so as to ensure that this does not lead to problematic bias. Many of the previous examples show that social relations and stereotypes can influence evidentiary judgments in ways that lead to bias, limited evidence, or erroneous beliefs. So, the central question is: how can such negative epistemic consequences be minimized? Here I will focus on two approaches that most centrally differ in the way they claim epistemic communities ought to be structured in order to minimize bias in evidentiary judgments.

Critical Contextual Empiricism In response to the kinds of examples described earlier, Longino has developed and defended a view called critical contextual empiricism, or CCE (Longino 1990, 2002). CCE maintains that by structuring epistemic communities so that problematic assumptions are more likely to be identified and critically evaluated, the community as a whole can achieve a higher

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degree of objectivity. Knowledge is objective, on Longino’s view, insofar as the organization of an epistemic community satisfies the following four conditions (Longino 1990, 76): 1. there must be recognized avenues for the criticism of evidence, of methods, and of assumptions and reasoning; 2. there must exist shared standards that critics can invoke; 3. the community as a whole must be responsive to such criticism; 4. intellectual authority must be shared equally among qualified practitioners. There must be recognized avenues for criticism so that members of the community have the ability to point out problematic background assumptions or methods employed by other epistemic agents. At the same time, there must be some shared standards of evidence governing such criticisms so that critiques have meaning and force to other participants. Without some shared understanding about what constitutes good evidence, participants would merely talk past one another. Participants must also have equal intellectual authority, or the power to have their criticisms and research to be taken seriously. That is, participants with comparable expertise should not be dismissed on the basis of an irrelevant feature such as sex, race, or age. Moreover, members of the epistemic community must be responsive to criticism, particularly as it will appeal to the shared standards of evaluation that the community as a whole accepts. When epistemic communities are structured so as to meet these criteria, then any value-laden assumptions inappropriately influencing reasoning are more likely to be identified and critically evaluated (Longino 1990, 73–4, 80, 2002, 51). When values are different from one’s own, it is easier to see when they are influencing evidentiary reasoning. Thus, an epistemic community comprising individuals with diverse values will be more likely to identify and critically evaluate the ways that values, stereotypes, problematic assumptions, or limited experiences, negatively influence the reasoning individual epistemic agents. Yet, a potential limitation of CCE is that it does not expose the ways in which power structures and problematic norms operate to exclude certain people from participating in epistemic communities to begin with. While CCE requires that epistemic agents with appropriate expertise be granted equality of intellectual authority, they do not offer resources for identifying and address the barriers to participating in epistemic communities or having access to the resources necessary for achieving relevant expertise. It seems that what is needed, in order to address these concerns, is a commitment to ensuring that epistemic communities are appropriately socially diverse or comprise individuals who are more likely to capture a wide range of experiences and values that may be relevant to critically examining evidence. Of course, achieving such diversity requires identifying and correcting the ways that social, political, and economic forces informally discourage or prevent access to epistemic resources or epistemic credibility. Thus, epistemic communities must be committed to critically identifying and challenging such inequalities.

Standpoint Feminist Empiricism Standpoint feminist empiricism (SFE) calls for the achievement of a standpoint, or a critical examination of the ways in which cultural, social, political, and economic forces have excluded certain kinds of epistemic participation and allowed certain interests and values to

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be more dominant, so as to achieve more diverse and inclusive evidentiary practices (Harding 2015; Wylie 2011, 2012; Intemann 2010, 2017; Crasnow 2014). Achieving a standpoint requires epistemic communities to be critically aware of the social conditions under which scientific knowledge is produced (Harding 2004, 31). It involves identifying the ways in which members of marginalized groups have less access to epistemic resources, face additional social barriers to participation in epistemic communities, receive less uptake of their claims and insights, and are granted less epistemic authority or credibility (Wylie 2012, 66–67). Moreover, it involves a commitment to correct or minimize these socially and epistemically problematic conditions. Doing so is seen as necessary for increasing objectivity in evidentiary judgments. Thus, the achievement of a standpoint requires that participants share some moral and political values, particularly producing knowledge in ways that challenge, rather than reinforce, systems of oppression (Harding 1991, 126–127; Wylie 2011; Intemann 2017). SFE does not claim that members of oppressed or historically underrepresented groups have an automatic epistemic advantage or that such individuals will “know better.” Rather, it maintains that epistemic communities that work to achieve a continuing critical reflection about how social relations shape and limit knowledge, work to overcome negative influences of social structures, and are inclusive to diverse participants who may bring different experiences, values, and insights, are more likely to identify evidence that is more complete or less distorted and catch unjustified assumptions. In other words, SFE maintains that commitments to diversity and justice within epistemic communities is not only required by political or ethical considerations, but also has certain epistemic benefits. In particular, communities structured by such commitments will help to produce less biased and more reliable evidentiary judgments.

5 Conclusion Feminist epistemology, then, can be understood as a branch of social epistemology that examines how gendered norms, conditions, and stereotypes can influence evidentiary judgments and the production of knowledge. While there is more empirical work to be done to examine the full range of ways in which social relations can influence evidentiary practices and judgments, there is a significant body of work that shows this occurs in a variety of ways. Yet feminist epistemology is also concerned with drawing out the normative lessons from this empirical work, so as to develop accounts of evidence and justification that account for the roles that social relations and stereotypes play, while also aiming to minimize any negative or biasing influences of gender relations. FSE, in particular, offers important resources for continuing this work, as it requires us to think critically about the ways in which power constrains and limits what we know. While there is more work to do in understanding how these resources might be developed theoretically by feminist epistemologists and, practically, within epistemic communities, I hope to have made the case that this work is worthwhile.

Note 1 There are potentially examples of feminist epistemology that are not located within social epistemology (e.g., Antony 1995), but much of the literature within feminist epistemology characterizes itself in this way. For purposes of simplicity, I will focus on feminist social epistemology.

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16 EVIDENCE, RELATIVISM AND PROGRESS IN FEMINIST STANDPOINT THEORY1 Natalie Alana Ashton

1 Introduction Feminist standpoint theories suggest that people who are oppressed due to their race, gender and other social factors, can make, and have made, important progress in science. And whatsmore, they claim that this progress is possible specifically because of this oppression. In this chapter I will address two difficulties that arise when making sense of standpoint theories. The first difficulty is to identify a standard of progress that is compatible with one of standpoint theory’s central theses. The standpoint thesis says that justification is dependent on ‘socially situated’ perspectives, which suggests that the relevant standard of progress will be perspective-dependent too. However, standpoint theorists are usually understood to be making an absolute claim. The second difficulty relates to the role of evidence in standpoint theory’s second central thesis. This epistemic advantage thesis says that the standpoints of those who are socially oppressed can result in better, or more, justification than the perspectives of those who are socially privileged. On one interpretation the advantage simply boils down to having better access to evidence—being oppressed in various ways means having experiences that people who aren’s oppressed (in those ways, or at all) don’t have, and these experiences constitute and grant access to novel evidence. But it’s not immediately clear what the special contribution of oppressed people is on this view. On another interpretation, the advantage is an ability to redefine what counts as evidence. The special contribution of oppressed people is clearer on this picture, but as it goes beyond basically uncontroversial claims about evidence it risks drifting into essentialism. Elsewhere (forthcoming b) I have argued that there are various benefits to understanding epistemic perspectives as sets of Wittgensteinian ‘hinges’. In this chapter I will show that this feminist hinge epistemology provides a way to navigate the two previous interpretative decisions, clarifying the role of evidence and the notion of progress that feminist standpoint theorists require. Feminist standpoint theory works best when its standpoint thesis is taken to support a relativist understanding of progress, and when its epistemic advantage thesis is semi-evidential.

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2  Feminist Standpoint Theory Feminist standpoint theory is a branch of feminist epistemology which claims that social factors—such as a person’s race and gender—play a role in what and how they know, and that marginalised identities have something distinctive and useful to bring to the epistemic table. And they make these claims using the notions of ‘perspectives’, and ‘standpoints’. Perspectives are our epistemic points of view, which helps us interpret the world and decide which propositions are justified and which are not. They differ according to a person’s social ‘location’—their status as socially oppressed or socially privileged—and its accompanying experiences. If subjects who are socially oppressed critically reflect on these experiences of oppression, they can turn their perspective into a ‘standpoint’—an epistemically privileged perspective from which the nature of relevant social relations is visible.2 Subjects who are not oppressed don’t have these experiences, and as a result are less likely to achieve a standpoint and more likely to continue to have a distorted understanding of social relations. The view can be summed up by the following two theses: Standpoint thesis:3 justification depends on ‘socially situated’ perspectives.4 Epistemic advantage thesis:5 the perspectives of those who are socially oppressed can result in better (or more) justification (justified beliefs), than the perspectives of those who are socially privileged. The advantage thesis comes with a number of generally accepted caveats, which insulate it from claims that it is obviously implausible, or objectionable on feminist grounds. First, the epistemic advantage shouldn’t depend on essential categories. There needn’t be any properties which are essential to membership of the groups which have the epistemic advantage (Hartsock 1997; Smith 1997; Wylie 2003). As Fricker puts it, standpoints don’t depend on oppressed people (or even particular subsets of oppressed people, such as Latina women or gay men) being the same, only on their experiences being similar in certain ways (Fricker 1999: 201). Second, possessing epistemic advantage is neither a necessary nor a sufficient condition on membership of a particular group. Where it is present in oppressed people it is contingent on the fact that they live in a world containing oppression, and it is also possible for it to be developed by non-oppressed people (Medina 2013). Third, epistemic advantage is not automatic, but must be achieved through collaborative, critical reflection (Fricker 1999: 202; Medina 2013; Wylie 2003). Fourth, it needn’t be an advantage with regards to all objects of knowledge. Standpoint theorists are usually clear that the argument for advantage will need to be made on a domain-by-domain basis, and that it is easiest to find in domains of knowledge which involve social relations (e.g. Harding 1991: 46; Wylie 2003: 37; c.f. Fricker 1999: 203). Beyond these points of broad agreement there are different ways that each of these theses could be interpreted. In this chapter I’ll focus on two connected decisions that need to be made when interpreting standpoint theory. We need to decide what standpoint theorists mean when they say that some perspectives have ‘improved’ science—does this claim rest on a relativist or an absolutist understanding of progress? And we need to decide what role evidence plays in standpoint theories—is epistemic advantage a matter of having access to more evidence, or of being able to redefine our standards of evidence? I’ll discuss each of these decisions further in the following two sections. 210

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3 Progress The first difficulty that arises when trying to interpret standpoint theory is in identifying a notion of progress which is consistent with the view’s prior commitments. On the one hand standpoint theorists are committed to the standpoint thesis, which implies a perspective-dependent, or relativist, notion of progress. On the other, they seem to want to make absolutist, perspective-independent claims about the effects of feminist influences on scientific and epistemic investigations. This creates a tension, with the notion of progress at its centre.6 In Section 6 I’ll argue that feminist standpoint theorists should adopt a relativist notion of progress and give up on absolutist claims about scientific progress. But before that, I’ll explain the tension around the notion of progress in more detail, to make clear why I am taking this option, and the problems that I face in doing so. First, let’s see why the standpoint thesis leads to a relativist notion of progress. As I understand it, epistemic relativism is the satisfaction of the following three claims about justification, which I take from Kusch (2016a)7: Dependence: A belief has an epistemic status (as epistemically justified or unjustified) only relative to an epistemic system or practice. Plurality: There are, have been, or could be, more than one such epistemic system or practice. Non-neutrality: There is no neutral way of evaluating different systems and practices. (Kusch 2016a: 33–34) Recall that the standpoint thesis says that justification is dependent on socially situated perspectives. I take this to be an expression of Dependence, as perspectives are a kind of epistemic system. It clearly implies Plurality, as it makes reference to multiple perspectives (and the existence of multiple perspectives is an uncontroversial component of standpoint theory). Elsewhere (Ashton 2019a) I have argued that the standpoint thesis implies Non-neutrality, too. This is because any evaluation of different perspectives that we could offer needs to be justified, and the standpoint thesis tells us that justification is perspectivedependent. Accordingly, any evaluation of different perspectives that we could offer would also be justification-dependent, and so not neutral. A similar point holds for the concept of progress. Claims about progress necessarily involve evaluations of different standpoints—to say that progress is made by exchanging one perspective for another is to evaluate the second system as superior—so if the standpoint thesis entails a non-neutral, relativist understanding of the evaluations of perspectives, then it also entails a non-neutral, relativist understanding of progress. This is a point in favour of the relativist interpretation of standpoint theory, and makes clear what the difficulty is for those who attempt the absolutist interpretation. Anyone offering an absolutist interpretation of standpoint theory’s advantage claim needs to explain how this can be consistent with the situatedness of the standpoint thesis. I don’t think an absolute notion of progress can be reconciled with the situatedness of the standpoint thesis, and as this thesis is one of the most fundamental aspects of standpoint theory I don’t think it should be compromised on. Instead, I think we should choose an interpretation of progress which complements this thesis. However, there are difficulties with this option too, namely, that standpoint theorists often seem to endorse absolutist 211

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claims to the effect that feminist science just is better than traditional science, independent of any perspective. Here are three examples. First, standpoint theorists sometimes talk about feminist or other marginalised standpoints as being more accurate, or more correct, representations of the world than dominant perspectives. For example, Hartsock says that the perspectives of socially privileged people are “partial and perverse” [italics added]—in the sense of being factually misleading (Hartsock 1983: 287). This seems to imply that different standpoints are objectively closer to or further from some absolute measure of correctness than dominant perspectives. Second, standpoint theorists often deny that their views are relativist. The most extended denial of relativism by a standpoint theorist comes from Sandra Harding (1991, 1995), who argues that standpoint theory exhibits a “strong objectivity” (1991: ch. 6) which is decidedly not relativism.8 But even Medina, who advocates a “principle of equilibrium” when engaging with different perspectives, explicitly denies that his is “a relativistic principle that demand[s] giving equal weight to all perspectives” (Medina 2013: 195).9 Typically, standpoint theorists are very resistant to their accounts being interpreted as relativist. Finally, discussions of standpoint theory often appeal to real-life examples of scientific revisions to make their point. For example, Jennifer Saul’s (2003) discussion is based around Elizabeth Lloyd’s work on bias in investigations into the possible adaptive value of the female orgasm (1993). This case is striking precisely because the sexist assumptions and misconceptions Lloyd highlights appear, to an enlightened contemporary audience, so obviously false as to be ridiculous—and this effect is bolstered by Lloyd’s work now being accepted on independent, scientific grounds. The first decision to be made when interpreting standpoint theory isn’t easy—there are good reasons in favour of each side. In the next section I’ll discuss the second, related, decision that we face when interpreting standpoint theory.

4 Evidence The second decision we face when interpreting standpoint theory is to do with the role that evidence plays in the epistemic advantage thesis. The epistemic advantage thesis says that oppression can lead to better (or more) justification (or justified beliefs). There are two broad approaches to making sense of this claim, both of which give evidence a central role, but which come with different costs and benefits. One approach is to interpret the epistemic advantage as highlighting a difference in the evidence that different groups of people have access to (Ashton and McKenna 2018: 9–11). Aspects of Nancy Hartsock’s work seems to support this interpretation.10,11 Hartsock (1983) bases her standpoint theory on the “sexual division of labour” (Hartsock 1983: 292). She points out that men and women have traditionally played, and often still do play, different roles in society. Women are more likely to be responsible for cooking, cleaning and child-rearing than men, and their upbringing often reflects this expectation. She argues that this means they know more about—or have better access to evidence about—the ways that certain fundamental areas of society function, and so have an advantage when it comes to understanding social relations. On this interpretation the epistemic advantage is reasonably uncontroversial. Most people will agree that men and women (typically) occupy different societal roles and that differences in evidence make for differences in justification. This interpretation is even consistent with the classical, non-feminist conception of knowledge (Ashton and McKenna 2018: 11). 212

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But if this is all that epistemic advantage amounts to, we might question whether it is a particularly interesting thesis. A more controversial approach is to interpret the epistemic advantage thesis as a point about redefining our evidential standards, and so reconceptualising what we mean by evidence. Kim Wallen (1990, 2000) recounts how behavioural endocrinologists spent decades trying to understand how male rhesus monkeys ‘knew’ to initiate sex when female monkeys were ovulating, and only learned the truth—that it was in fact the female monkeys initiating sex—after an influx of female researchers entered the field. This wasn’t (just) because the female researchers had access to better evidence. The crucial initiating behaviour, of female monkeys slapping the ground in front of the males, had been recorded thirty years earlier. Instead these researchers helped reconceptualise what counts as evidence, because they lacked, or questioned, traditional assumptions about female sexual passivity, so that the recorded behaviours could now be treated as evidence (Ashton and McKenna 2018: 11–14). The second interpretation certainly makes for a more interesting thesis, but it also incurs some additional costs. First, on this interpretation the question of what standpoints comprise, and how they develop and change, is more pressing. The first interpretation of advantage is compatible with the ‘classical’, non-feminist conception of knowledge and so there’s nothing special to explain—on this view it’s sufficient to say that standpoints are sets of propositions which are updated upon encountering new evidence. But the second interpretation of advantage is more complicated. Standpoints aren’t just propositions which are updated in response to evidence. They also have an effect on conceptions of evidence, and so involve, or at least interact with, elements like values. The make-up and process of updating standpoints isn’t as clear on this interpretation, and so standpoint theorists who accept it will have more to explain. Second, proponents of this interpretation need to be careful not to run into essentialism, and not to imply that all oppressed people have an epistemic advantage automatically. These were some of the caveats, laid out in Section 2, that standpoint theorists generally agree to. If epistemic advantage is just a matter of access to evidence then no one has it without first having certain experiences. But if epistemic advantage is about the ability to redefine standards of evidence then matters are less clear. That’s not to say that this kind of account is guaranteed to run afoul of these caveats, just that we need more information before we can make a responsible evaluation. Before moving on, it’s important to note that the interpretative decisions outlined in this section and the last are connected. If the advantage of oppressed standpoints is only that they grant access to additional evidence, then there is no special reason (aside from maintaining consistency with the standpoint thesis) for the standpoint theorist to endorse a relative notion of progress. On this interpretation the scientists using dominant perspectives simply failed to account for evidence that they should have. They were straightforwardly mistaken, something which can be easily accounted for on the absolute understanding of progress. However, if the advantage of oppressed standpoints is that they redefine standards of evidence, then we might think there’s further reason to interpret progress as relative. On this account of advantage, the scientists weren’t straightforwardly mistaken, as their practices lived up to their standards. Our criticism of them comes from the fact that we now have, and judge them according to, different standards. This seems to count against the objective notion of progress and for the relativist notion. 213

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Having now discussed the two decisions that we face when interpreting standpoint theory, we can see that there are two possibilities open to standpoint theorists. One is to use an objective standard of progress and to base the epistemic advantage on access to evidence. This has the advantage of avoiding relativism but means endorsing a less interesting version of the epistemic advantage thesis and introduces a tension with the standpoint thesis. The other option is to endorse a relativist standard of progress and to argue for a more controversial interpretation of the epistemic advantage thesis based on redefining standards of evidence. On this option the epistemic advantage thesis is more interesting, and the standpoint thesis is taken seriously, but a cost is incurred in the form of endorsing a kind of relativism. In the remainder of this chapter I’ll take the second option, spelling out a version of feminist standpoint theory that incorporates a relativist notion of progress, a more interesting understanding of the epistemic advantage thesis, and stays faithful to the standpoint thesis.

5  Feminist Hinge Epistemology Feminist hinge epistemology (Ashton 2019b) is a version of standpoint theory that borrows from Wittgensteinian epistemology in order to define standpoints (and perspectives) as sets of ‘hinge commitments’. In this section I’ll briefly explain what hinge commitments are, and then outline how they can be deployed within standpoint theory. Hinge commitments (or just ‘hinges’) is the name given to a particular set of propositions, beliefs or other attitudes12 that were the focus of Wittgenstein’s last work, On Certainty. Wittgenstein identified these commitments as playing a special role in our epistemic inquiries—they cannot be epistemically evaluated (i.e. supported or doubted by reason or evidence) because they need to be taken as certain in order for any epistemic inquiry to go ahead: That is to say, the questions that we raise and our doubts depend on the fact that some propositions are exempt from doubt, are as it were like hinges on which those turn. That is to say, it belongs to the logic of our scientific investigations that certain things are in deed not doubted. But it isn’t that the situation is like this: We just can’t investigate everything, and for that reason we are forced to rest content with assumption. If I want the door to turn, the hinges must stay put. (OC 1969: §§341–343) The most frequently cited examples of hinges are very general commitments like ‘I am not being deceived by an evil demon’, as these are thought to be key to responding to radical scepticism. If propositions like this aren’t held fixed then epistemic inquiry (at least about the external world) can’t even get started, because any attempt to use evidence to support one’s claims can be undercut (e.g. Wright 2004a). In the same way that a door without hinges won’t turn, but just collapse, epistemic inquiry without hinge commitments falls apart. Thus sceptical challenges, which attempt to cast doubt upon the conditions of epistemic enquiry—rather than its contents—are illegitimate and can be reasonably ignored. However, Wittgenstein referenced a wide range of commitments that play the role of hinges, beyond just the anti-sceptical ones (see Kusch 2016a, 2016b; cf. Williams 1996; Coliva 2015), and so there is scope to use hinge epistemology to tackle issues other than 214

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radical scepticism. One such issue is the role that social factors play in epistemic justification, as embodied by the literature on feminist epistemology. I have argued (Ashton 2019b) that there are good reasons to defend a version of feminist standpoint theory on which standpoints are sets of hinge commitments. Much of mainstream hinge epistemology focuses on the legitimacy of holding hinge commitments fixed, but it has also been argued that they can be more flexible under certain circumstances. This flexibility is key to feminist hinge epistemology. The debate on the relationship between hinges and evidence is particularly relevant. Hinge epistemologists typically think that hinges are beyond evidential support. MoyalSharrock (2007: 75–80) points to passages in On Certainty which suggest that hinges are ‘foundational’—they offer justification and can count as evidence but cannot themselves be justified or supported with evidence: “To be sure there is justification; but justification comes to an end” (OC 192). Similarly, Pritchard emphasises the ‘groundlessness’ of hinges. He interprets Wittgenstein as saying (i) that hinges are maximally certain, (ii) that evidential support must be more certain than that which it supports, and so (iii) hinges cannot be evidentially supported (Pritchard 2016: 63–66). However he’s keen to emphasise that this isn’t due to a failing of our epistemic abilities, but is part of the very logic of justification; hinges aren’t just groundless, but ungroundable—denying them is impossible and incoherent (2016: 65). Crispin Wright and Martin Kusch think the relationship between hinges and evidence is more complicated than this. We might say that they see hinges as semi-evidential. Wright (2004b) agrees that very general, anti-sceptical hinges are non-evidential, because nothing could count as evidence for them before they themselves are assumed (2004b: 41). But he thinks that other hinges can be supported by evidence. He claims that there are norms-in-context, such as ‘I have two hands’, for which we have a lifetime of evidence (2004b: 36)—it’s just that this evidence isn’t often relevant. In ordinary situations, normsin-context function as hinges which are set aside from the processes of doubting and providing evidence. It is only in some situations (say, after a serious accident or operation) that they become “straightforwardly empirical” (Wright 2004b: 37) and can be supported by evidence. Kusch argues that some hinges (those about our having hands and others established through testimony, memory and simple deductive inference) have overwhelming evidential support, but that this support is unusual because it is inaccessible and “dialectically mute” (Kusch 2016b: 134). Similarly, mathematical propositions are immunized from further evaluation. The proposition 2 + 2 = 4 can be evidentially supported—for example, we could conduct an experiment with a balance and two pairs of equal weights—but most people’s belief in this proposition is not responsive to this kind of evidence. If we conducted the experiment with the weights and they failed to balance, we would not conclude that the proposition in question was false, but would instead check our equipment for damage (2016b: 134). The flexibility of this relationship between hinges and evidence leaves room to explain how even our most deeply held beliefs can be altered under the right circumstances. We saw in Section 4 that, along with an explanation of what exactly standpoints are, this is exactly what standpoint theorists need. So feminist hinge epistemology has the potential to solve some pressing questions for standpoint theorists. In the next section I’ll explain how feminist hinge epistemology assists with making the two interpretive decisions I’ve been discussing, but I’ll close this section with a brief statement of the view: 215

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Perspectives, and by extension standpoints, comprise hinge commitments. Some hinges will likely be common to all social groups, but others differ based on experiences relating to oppression. The epistemic advantage that oppressed people have amounts to a greater motivation (in the form of a desire to avoid the harms they experience as the result of racist and/ or sexist hinge commitments) to change from an ordinary context where all sets of hinges are legitimately held fixed, to one where noticing and evaluating certain harmful commitments is legitimate. In this evaluative context these hinges become responsive to evidence, and so it’s possible to carry out a process of reflective equilibrium on which existing norms and standards of evidence can be tested against one’s experiences and modified or replaced by new norms and standards of evidence.

6  Redefining Evidence & Relativist Progress In this section I’ll show how feminist hinge epistemology helps to secure the more interesting account of epistemic advantage and how it supports a palatable relativist notion of progress. Feminist hinge epistemology provides a way to support the second, more interesting understanding of epistemic advantage, and importantly it does so without falling afoul of the widely accepted caveats mentioned in Section 2. It does this by telling us what standpoints comprise and how they can develop and change. Namely, on this view, standpoints comprise semi-evidential hinge commitments, and they can be developed and changed by making adjustments to these commitments through a process of reflective equilibrium, following a shift from an everyday context to an evaluative one. In Epistemic Injustice (2007) Fricker discusses Susan Brownmiller’s (1999) account of the development of the term ‘sexual harassment’ as an example of hermeneutic injustice. I think it is also an example of evidential standards being revised. Before the concept of sexual harassment was available, those with privileged perspectives saw unwelcome sexual advances in the workplace as ‘harmless’ or ‘a bit of fun’, and certainly not as evidence of an unwelcoming or unsafe environment. Once women collectively reflected on their experiences of these behaviours as harmful and shifted to a context where socially accepted commitments like ‘women’s role is predominantly to please men’ could be articulated and challenged, they were able to carry out a process of reflective equilibrium, resulting in new evidential standards on which these behaviours are evidence of a problematic work environment.13 Importantly, nothing about this explanation contradicts the caveats on epistemic advantage. The ability to shift context isn’t an intrinsic or essential property of members of oppressed groups, it is something that they have contingently, due to experiencing oppression. And this advantage is not automatic: it is only achieved through a process of (typically collective) critical reflection. I said earlier that the two interpretative decisions we face when making sense of standpoint theory are connected. The more interesting understanding of epistemic advantage that I’ve just advocated gives us an additional reason to favour the relativist notion of progress over the absolutist one (on top of the reason I already identified, namely, of maintaining consistency with the standpoint thesis). Accordingly, I don’t think we should try to reconcile an absolutist interpretation of progress with this more interesting notion of evidence. Instead, I think the way to defend standpoint theory is to show that it can still secure everything standpoint theorists could want even with a relativist notion of progress. Feminist hinge epistemology can help here too. Given the motivations for preferring the absolute notion that I recounted in Section 3, we here need to (1) show that standpoint 216

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theorists using a relativist notion of progress are still able to say that some standpoints are better than others, and (2) explain why their scientific examples are so compelling, if it’s not that they are objectively justified.14 The key to a palatable relativist notion of progress is shared progress. Standpoint theorists (seem to) want a notion of progress that allows them to make claims such as ‘feminist science is better than its competitors’. They are, understandably, resistant to interpretations which would only permit them to make narrowly relativised claims such as ‘feminist science is better than its competitors according to a feminist perspective’. Claims like these have very little persuasive power, as there is no reason for someone outside of a feminist perspective to accept them. A shared notion of progress allows them to make relativised claims which nevertheless have persuasive power. It allows claims such as ‘feminist science is better than its competitors relative to the notion of progress that we [users of various specified perspectives] share’. Endorsing a shared notion of relativist progress therefore avoids the conflict between the interesting interpretation of the advantage thesis, without sacrificing the kinds of claims relevant to (1). This notion of shared progress sounds useful in the abstract, but do we have any reason to think that different standpoints and perspectives can or do share notions of progress in actuality? I think so, and feminist hinge epistemology can show why. In doing so it will achieve (2), by explaining how the scientific examples standpoint theorists use are so compelling, without appeal to absolute justification. The explanation goes like this. There is a theory of evidence, embedded within a perspective (or set of hinges), according to which certain phenomena (e.g. name calling, physical aggression) do count as evidence for a particular claim (e.g. an individual experienced mistreatment in the workplace), and other phenomena (e.g. flirtatious comments, requests for sexual favours) don’t. This theory of evidence, the assumptions that it is based on, and the conclusions and real-world consequences that it is taken to justify are harmful to members of marginalised groups. This motivates them to make a shift to an evaluative context in which some of the relevant commitments can be challenged. The process of reflective equilibrium I described earlier then takes place, and the outcome is a theory of evidence on which the phenomena (flirtatious comments and requests for sexual favours) do count as evidence for (workplace mistreatment). Once this theory of evidence has been articulated and the theories it justifies are available to members of privileged groups, its benefits can be seen even by those who weren’t motivated to make the context shift. The new theory of evidence makes available justifications for hypotheses which are simpler and have more predictive and explanatory power than the theories which were only justified by the old theory of evidence. This then gives socially privileged people the motivation to challenge the hinges of the dominant perspective, as well as a road map for doing so. This second group then conducts their own process of equilibrium, (at least partially) updates their assumptions and corresponding theory of evidence and agrees that the new theory of evidence and accompanying hinges is superior to the old one.

7 Conclusion I have discussed two difficulties that arise when interpreting standpoint theory and shown how feminist hinge epistemology supports an interpretation on which progress is understood as relative and epistemic advantage is based on redefining standards of evidence. Although this account is relativist it still allows standpoint theorists to make (relative) 217

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evaluations of standpoints and to explain why their scientific examples are so compelling, so it doesn’t have the costs often associated with relativism. And it has some important benefits too: it takes the standpoint thesis seriously, and it offers a way to support the more interesting advantage thesis without contravening the caveats standpoint theorists have laid out for themselves, meaning that it preserves the view’s internal consistency.

Notes 1 Research on this chapter was assisted by funding from the ERC Advanced Grant Project “The Emergence of Relativism” (Grant No. 339382). I’d like to thank Kathi Sodoma, Liam Kofi Bright, Giada Fratantonio, and Kristen Intemann for very helpful comments and discussion. 2 I think it’s tricky to make a clean distinction between perspectives and standpoints because I believe that perspectives are revised in a gradual manner, and that it doesn’t make sense to think of this process as completable. I use the term ‘standpoint’ when talking about perspectives that have been improved in some salient way, and ‘perspective’ at all other times. 3 Also called the situated knowledge thesis (Wylie 2003; Intemann 2010). 4 This is distinct from the situated knowledge thesis, mentioned earlier, which simply says that social factors have an effect on knowledge. 5 Also called the inversion thesis (Wylie 2003; Tanesini 2019). 6 This echoes debates on scientific progress between scientific realists (e.g. Worrall 1982; Psillos 1999) and anti-realists (e.g. Kuhn 1970), which I don’t have time to engage with here. 7 Kusch’s definition incorporates two further essential (and four non-essential) elements. All of these are important for understanding how relativism has been presented by different authors, but I have streamlined my definition for simplicity. In particular, I haven’t included Kusch’s ‘essential’ exclusiveness and notational confrontation, because I think these follow from pluralism: if these differences weren’t present then the multiple frameworks would collapse into one, and so pluralism would not be present either. C.f. Williams 2007 and Coliva 2015 who use similar triadic definitions of relativism. 8 That’s not to say that Harding necessarily endorses absolutism. I’ve argued (Ashton 2019a) that her strong objectivity is a form of relativism, and it’s been suggested to me (by Intemann and others) that Harding’s primary goal was only to avoid problematic relativism. Even so, her explicit denials of relativism make suggesting a relativist notion of progress more complicated. 9 I agree that Medina needn’t advocate an equal weight view, but argue that this is not the right standard for relativism. See (2019a). 10 Alessandra Tanesini has argued that Hartsock is better understood as characterising different “ways of experiencing” or different “cognitive styles”, and suggests the advantage of some standpoints over others could be defended with reference to epistemic virtues (Tanesini 1999: 143–144). Note that access to evidence is still crucial to this kind of account though, e.g. Medina’s (2013) account of epistemic advantage amounts to a disposition to develop epistemic virtues, but still attributes this disposition to differences in experiences. 11 See also Bright 2018: https://sootyempiric.blogspot.com/2018/06/empiricism-is-standpoint-epistemology. html 12 I use the neutral term ‘commitment’ because hinge epistemologists give different accounts of what hinges are. Whilst Wittgenstein refers to them as propositions (see earlier), Moyal Sharrock has argued that they are non-propositional beliefs (2004: ch. 2), and Pritchard that they are nonbeliefs (2016: 90–94). ‘Commitment’ seems to be a neutral term. 13 C.f. my example of changing standards of evidence in endocrinology (Ashton and McKenna 2018: 9). 14 I don’t have room in this chapter to also respond to the explicit denials of relativism I mentioned in Section 3, but see Ashton (2019a).

References Ashton, Natalie Alana. “Relativising Epistemic Advantage.” In Routledge Handbook of Philosophy of Relativism, edited by Martin Kusch. Routledge, 2019a.

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Evidence, Relativism and Progress Ashton, Natalie Alana. “The Case for a Feminist Hinge Epistemology.” Wittgenstein Studien 10, no. 1 (2019b):153–163. Ashton, Natalie Alana, and Robin McKenna. “Situating Feminist Epistemology.” Episteme (April 10, 2018): 1–20. https://doi.org/10.1017/epi.2018.11. Bright, Liam Kofi. “The Sooty Empiric: Empiricism Is a Standpoint Epistemology.” Accessed January 19, 2019. http://sootyempiric.blogspot.com/2018/06/empiricism-is-standpoint-epistemology.html. Brownmiller, Susan. In Our Time: Memoir of a Revolution. A  Delta Book. New York, NY: Dell Publishing, 1999. Coliva, A. Extended Rationality: A Hinge Epistemology. London: Palgrave Macmillan, 2015. Fricker, Miranda. “Epistemic Oppression and Epistemic Privilege.” Canadian Journal of Philosophy 29, no. sup1 (January 1999): 191–210. https://doi.org/10.1080/00455091.1999.10716836. Fricker, Miranda. Epistemic Injustice. Oxford: Oxford University Press, 2007. https://doi.org/10.1093/ acprof:oso/9780198237907.001.0001. Harding, Sandra. Whose Science? Whose Knowledge?: Thinking from Women’s Lives. Ithaca: Cornell University Press, 1991. Harding, Sandra. “ ‘Strong Objectivity’: A Response to the New Objectivity Question.” Synthese 104, no. 3 (1995): 331–349. Hartsock, N.C.M. “The Feminist Standpoint: Developing the Ground for a Specifically Feminist Historical Materialism.” In Discovering Reality. Synthese Library, vol. 161, edited by S. Harding and M. B. Hintikka. Dordrecht: Springer, 1983. https://doi-org.vu-nl.idm.oclc. org/10.1007/0-306-48017-4_15 Hartsock, Nancy C. M. “Comment on Hekman’s ‘Truth and Method: Feminist Standpoint Theory Revisited’: Truth or Justice?” Signs 22, no. 2 (1997): 367–374. Intemann, Kristen. “25 Years of Feminist Empiricism and Standpoint Theory: Where Are We Now?” Hypatia 25, no. 4 (2010): 778–796. Kuhn, Thomas S. The Structure of Scientific Revolutions, 2nd ed. Chicago, IL: Chicago University Press, 1970/1994. Kusch, Martin. “Wittgenstein’s On Certainty and Relativism.” In Analytic and Continental Philosophy Methods and Perspectives: Proceedings of the 37th International Wittgenstein Symposium, vol. 23. Berlin and Boston: De Gruyter, 2016a. https://doi.org/10.1515/9783110450651-003. Kusch, Martin. “Wittgenstein on Mathematics and Certainties.” International Journal for the Study of Skepticism 6, no. 2–3 (May 23, 2016b): 120–142. https://doi.org/10.1163/22105700-00603004. Lloyd, Elisabeth A. “Pre-Theoretical Assumptions in Evolutionary Explanations of Female Sexuality.” Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition 69, no. 2–3 (1993): 139–153. Medina, José. The Epistemology of Resistance: Gender and Racial Oppression, Epistemic Injustice, and the Social Imagination. Oxford: Oxford University Press, 2013. https://doi.org/10.1093/acpr of:oso/9780199929023.001.0001. Moyal-Sharrock, Danièle. Understanding Wittgenstein’s on Certainty. Basingstoke: Palgrave Macmillan, 2004. Pritchard, Duncan. Epistemic Angst: Radical Skepticism and the Groundlessness of Our Believing. Soochow University Lectures in Philosophy. Princeton: Princeton University Press, 2016. Psillos, Stathis. Scientific Realism: How Science Tracks Truth. London: Psychology Press, 1999. Saul, Jennifer Mather. Feminism: Issues & Arguments. Oxford: Oxford University Press, 2003. Smith, Dorothy E. “Comment on Hekman’s ‘Truth and Method: Feminist Standpoint Theory Revisited’.” Signs 22, no. 2 (1997): 392–398. Tanesini, Alessandra. An Introduction to Feminist Epistemologies. Introducing Philosophy 7. Malden, MA: Blackwell Publishers, 1999. Tanesini, Alessandra. 2019. “Standpoint Then and Now.” In The Routledge Handbook of Social Epistemology, edited by M. Fricker, P. J. Graham, D. Hendererson and N. J. L. L. Pedersen. London: Routledge. Wallen, K. 1990. “Desire and Ability: Hormones and the Regulation of Female Sexual Behavior.” Neuroscience and Biobehavioral Reviews 14, no. 2: 233–241. Wallen, K. 2000. “Risky Business: Social Context and Hormonal Modulation of Primate Sexual Desire.” In Reproduction in Context, edited by K. Wallen and J. Schneider, 289–323. Cambridge, MA: MIT Press.

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Natalie Alana Ashton Williams, Michael. Unnatural Doubts: Epistemological Realism and the Basis of Scepticism. Princeton Paperbacks. Princeton, NJ: Princeton University Press, 1996. Williams, Michael. “Why (Wittgensteinian) Contextualism Is Not Relativism.” Episteme 4, no. 1 (February 2007): 93–114. https://doi.org/10.3366/epi.2007.4.1.93. Wittgenstein, Ludwig, G. E. M Anscombe, and G. H. von Wright. On Certainty/Uber gewissheit/von Ludwig Wittgenstein/herausgegeben von G.E.M. Anscombe und G.H. von Wright. New York and London: Harper Torchbooks, 2001. Worrall, John. “Scientific Realism and Scientific Change.” The Philosophical Quarterly 32, no. 128 (July 1982): 201. https://doi.org/10.2307/2219324. Wright, Crispin. “On Epistemic Entitlement: Warrant for Nothing and Foundations for Free?” Aristotelian Society Supplementary Volume 78, no. 1 (July  1, 2004a): 167–212. https://doi. org/10.1111/j.0309-7013.2004.00121.x. Wright, Crispin. “Wittgensteinian Certainties.” In Wittgenstein and Scepticism, edited by Denis McManus. London: Routledge, 2004b. Wylie, Alison. 2003. “Why Standpoint Matters.” In Science and Other Cultures: Issues in Philosophies of Science and Technology, edited by Robert Figueroa and Sandra G. Harding, 26–48. ­London: Routledge.

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17 EPISTEMIC INJUSTICE IN COLLECTING AND APPRAISING EVIDENCE David Schraub and Joel Sati

Epistemic injustice refers to the distinctive wrongs that people suffer in their capacity as knowers (Fricker 2007). In this chapter, we argue that the process of evidence gathering— whether informal, as occurs in everyday deliberation and practice, or formal, as in the context of a judicial or prosecutorial investigation—implicates matters of epistemic injustice. Indeed, the former sort of evidentiary practice often forms the necessary foundation for the latter to occur. At the outset of a criminal inquiry, for example, who the police determine to be a person of interest and what detectives consider to be a lead will often dictate how a formal investigation will proceed or even whether it will be commenced at all. This chapter proceeds in three sections. The first section introduces Miranda Fricker’s (2007, 2012, 2013) conception of epistemic injustice, which considers the kinds of injustices people suffer in their capacity as knowers. Section 2 uses the example of “restoring trust” in the police to examine how particular epistemic concepts like “trust” and “community” channel and often stunt which sorts of claims are recognized as candidates for public investigation. In the third section, we apply these insights to the informal gathering of evidence in the policing context. We argue that choices in focus before formal legal processes commence can influence what information is considered as evidence, and in turn affect the outcome of more official legal proceedings (such as trials).

1  Evidence and Epistemic Injustice What we do with evidence is a social practice dictated by how it is we come to possess evidentiary information and what norms make certain pieces of information more compelling than others. Proper handling of evidence is often a matter of how we credit competing testimony, how we appraise different stories which seek to explain phenomena we observe, or, at an even more basic level, what bits of information make it onto our deliberative radar screen so that they can be considered at all. The practice of appraising evidence is one of listening and ignoring, crediting and dismissing, validating and rejecting. These practices, in turn, touch on important questions of justice—many of which are collected under the label “epistemic injustice.”

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Epistemic injustice refers to wrongs we do to someone when appraising or evaluating evidence they provide, which we argue includes injustices that occur in determining whether something counts as evidence in the first place.1 The term was coined by philosopher Miranda Fricker, who defined it succinctly as wronging someone in their “capacity as a knower” (Fricker 2007, 20), though under other names the problem and wrong of epistemic silencing has long been the subject of commentary in the Black feminist tradition (see Dotson 2011, 252 n.5, for a canvassing). Fricker explores the concept through two paradigmatic categories: testimonial injustice and hermeneutical injustice. For each, Fricker insists that the “central case” of epistemic injustice occurs when social identity prejudice— “prejudice for or against people owing to some feature of their social identity”—causes a given agent to be systematically, as opposed to idiosyncratically or locally, subjected to injustices, including epistemic injustices (Fricker 2007, 27–28, 156). A testimonial injustice occurs when we discount the testimony of a communicator (Fricker is indifferent to the mode of the communication, and certainly does not wish to limit the case to that of formal legal testimony) due to bias against the identity of the speaker. For example, many women find that their doctors consistently discredit their testimony regarding the amount of pain they experience—perhaps because they implicitly or explicitly assume women are weaker, more emotional, or more prone to complain (Hoffmann & Tarzian 2001; see Buchman, Ho & Goldberg 2017). A patient’s testimony regarding how his or her own body feels is an important piece of evidence for a doctor trying to determine the correct medical diagnosis and treatment. To be sure, it is not always overriding—a patient’s claim that they have only a minor cough but otherwise are healthy can be trumped by a medical scan showing they have early-stage lung cancer—but it is certainly relevant evidence, and in many cases the dominant evidence in establishing an initial diagnosis and course of action. Insofar as certain sorts of patients are not acknowledged by their interlocutors to possess valid knowledge germane to the conversation, they are disrespected as knowers and are victims of a testimonial injustice. A hermeneutical injustice is, according to Fricker, “the injustice of having some significant area of one’s social experience obscured from collective understanding owing to a structural identity prejudice in the collective hermeneutical resource” (Fricker 2007, 155). The classic example is the idea (or lack thereof) of “sexual harassment” prior to the term’s popularization in the late 1970s. A  significant social experience of many women was obstructed from broader public understanding. And the reason why was not (exactly) that women’s testimony on the subject was discredited, but that women (and men) lacked socially cohesive language available to them to describe and characterize the practice at all.2 Inside the category of hermeneutical injustice, Fricker also brings out the more systemic case of hermeneutical marginalization. If hermeneutical injustice applies at the case level—particular instances in which meaning-making for marginalized people is obscured—hermeneutical marginalization applies to a larger social situation. Fricker defines hermeneutical marginalization as occurring “when there is unequal hermeneutical participation with respect to some significant area(s) of social experience” (153–55). This distinction is an important one, for the concept of hermeneutical marginalization speaks to the general state of inequity in hermeneutical participation among groups. That is, when some have outsized influence in developing meaning and others do not have as much influence as their status qua human beings requires for them, the latter group is hermeneutically marginalized.

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A common example used to illustrate hermeneutical marginalization is the experience of sexual harassment prior to the popularization of the term. Fricker recounts the case of Carmita Wood, a staff member at Cornell University, whose male boss repeatedly made lewd gestures, brushed against her breasts, and cornered her and planted unwanted kisses on her mouth. The stress of these encounters was so great that she ultimately left her job. Yet, when asked by an unemployment claims investigator why she had quit, she found herself unable to find the language to explain the wrongs she had endured in a socially comprehensible fashion. Until “sexual harassment” emerged as an available and socially understood term, Fricker suggests, women experiencing such abuse were doubly-burdened—facing both the indignities of the harassment itself compounded by an inability to describe the experience in a manner intelligible to others (149–55). Hermeneutical marginalization thus captures a context in which people are systemically unable to render their experiences collectively legible. Furthermore, hermeneutical marginalization indicates how existing institutions that deal with the collection and adjudication of evidence do not recognize certain experiences as eligible for redress. Put differently, it becomes much harder to conceive of (much less mobilize against) an experience as a possible legal wrong if one is unable to categorize it as an experience, period. There is a vicious feedback loop: hermeneutical marginalization facilitates hermeneutical injustice, and hermeneutical injustice solidifies certain people’s position as hermeneutically marginalized, because their contributions are not seen as generating any meaningful evidentiary value. Hermeneutical marginalization describes the environment in which some subset of people is excluded from social generations of meaning, whereas hermeneutical injustice describes how marginalization negatively affects how those oppressed recount their experiences in a particular instance. Fricker herself links evidence and apportionment of epistemic credibility: a virtuous hearer “must match the level of credibility she attributes to her interlocutor to the evidence that he is offering the truth” (19). This suggests that credibility assessments have a perfectly legitimate distributional dimension—we do not and should not distribute it to everyone equally, and we are right to be incredulous toward persons whose claims are seemingly unbacked by evidence (see Coady 2017). From that we could fairly ask: if a person is adequately processing evidence and behaving in an epistemically responsible fashion, does a discussion of epistemic injustice add anything of use? We argue that it does. More specifically, we argue that an epistemic justice analysis of evidence allows us to examine the relationship between truth, reason, and justice in important areas of social deliberation (e.g., law, politics, and public debates), and what it means for something to be counted as evidence in light of this relationship. Rather than existing out in the world, notions that we take to be apolitical reflect the priors of those who have the power to define and operationalize them. Donald Nicolson argues that traditional epistemology of evidence overestimates “its ability to understand and improve the process of knowledge acquisition, and radically underestimat[es] the impact of perspective on knowledge and the degree of uncertainty inherent in knowledge claims” (2013, 21). Not only are epistemic concerns imbricated in relations of power, but the epistemologies of dominant groups retain their advantage because they come dressed in the language of objectivity. If notions like “reason” and “rationality” are politically loaded, reflecting value judgments made by those who control the levers of power, the epistemologies of the marginalized are seen as irrational and unsound (e.g., sexist views on the cognitive capacities of women, in

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which emotion and intuition is placed in diametric opposition to “reason” and “facts”). Moreover—as it relates to our argument—people who are hermeneutically marginalized are liable to suffer harm as a result of notions of evidence that neither includes them nor accounts for their experiences. While epistemic injustice always poses a risk to proper appraisal of the evidence— blocking certain claims and certain claimants from receiving the attention and consideration they deserve—it is particularly perilous in circumstances where it obstructs the willingness of parties to even initiate an investigation (including gathering and properly weighing evidence). These two classes of epistemic injustice—those that affect the incidence of investigation and those that affect the investigation itself—are connected to the extent that an institution that is liable to commit one is liable to commit the other. A commonly observed example occurs in the dismissal of claims of discrimination and oppression (ironically, including epistemic injustices). There is an entire body of rhetoric dedicated to the notion that members of social outgroups are especially uncredible in circumstances where they are contending that they are being marginalized, oppressed, or otherwise discriminated against (think statements of the “she’s just playing the [X] card” family) (see Schraub 2016; Bell 1992). In law, Sandra Sperino writes of “disbelief doctrines” where judges impose additional hurdles, unwarranted by statute or civil procedure rules, upon plaintiffs seeking to make discrimination claims (Sperino 2018; see Sperino & Thomas 2017; Schraub 2018). Here epistemic injustice can take on a dangerously self-insulating character: “prejudice yields the injustice, and simultaneously wards off complaints aimed at attacking the prejudice” (Schraub 2016, 286). The intuitively obvious example of this would be one of testimonial injustice—where a person’s declaration (that they’ve been wronged in a certain way, or that they have a suggestion that should be taken up) is not taken to be sufficient to look into the matter in circumstances where other claims and claimants are given due time. But there is an important hermeneutical dimension as well, where certain classes of claims are poorly suited to the sort of investigatory (evidence-gathering) processes which might provide conclusive validation (or rejection) of the assertion. The case of microaggressions, for example, typically involve incidents which at the individual level almost always have innocuous explanations and can easily be dismissed as, at worst, trivial annoyances. This can make them serve poorly as a locus for any sort of sustained investigation even if the hearer does not seem to harbor any testimonial biases. Implicit bias (and microaggressions often—though not always—are forms of implicit bias) is typically documented in the form of statistical disparities between how in- and outgroup members are treated. But these measurements offer no insight as to whether a specific case was an example even of implicit bias—indeed, they strongly suggest that some number of them are not products of bias. As Saba Fatima (2017) observes, this fact can easily create an internal sense of paranoia and second-guessing (Am I  being oversensitive? Did it really happen that way?) that will inevitably be exacerbated by the lack of any “smoking gun” evidence. In this way, whatever harms accrue directly through the microaggression can be compounded by the epistemic injustice of being functionally unable to validate through (individualized) evidence whether the sense of wrongedness is warranted. There is a one-two punch whereby one is both unable to translate one’s own experiences into socially validated phenomena and is undermined in one’s self-conception as a valid “knower” whose instincts regarding one’s own experiences reliably track the external world. 224

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2  The Hermeneutics of Community and Trust in the Police If weighing evidence correctly is largely a matter of interpretation and—perhaps more importantly—collection, then the decisions or structures which channel whose experiences or claims trigger investigatory action carry considerable weight. This can be seen in a very straightforward way in cases of testimonial injustice, where a person’s account of a given social phenomenon is not accorded due weight and thereby not treated as the sort of claim that demands response or further notice—in short, is not treated as (significant) evidence. Hermeneutical injustice and marginalization cases are more complex, but for that reason perhaps more interesting. Consider statements, frequently made after an episode of police violence, about the importance of “restoring trust in the community.” When politicians plead for a restoration of trust in the police, for example, they are generally referring to the importance of community members adopting a position of trust toward the police. Where there is a police presence, it is indisputably important that such trust exist. In cases where police officers legitimately need to use force, it is essential that community members trust that officers only use force in circumstances where it is necessary, that they use no more force than required for legitimate law enforcement ends, and so on. Likewise, it is important that the community trust that any complaints will be taken seriously and investigated thoroughly, that officers will accurately recount and report their conduct on the job, and that any review will be undertaken by impartial adjudicators. In many cases, where direct evidence (body cameras or neutral eyewitness testimony) is unavailable, the only evidence that exists regarding the legitimacy of police conduct is their own testimony. Epistemically speaking, then, it is essential to the proper functioning of a police department that trust exists between the department and the community that it serves. All of this is well and good. But there is an idea lurking under the surface of this discourse that hasn’t fully been excavated. The problem of community mistrust of police is presented as, in part, one of asymmetrical epistemic credibility: police are assumed to be worthy of great credence from the community, and if they don’t receive it, that is a sign that the relationship between the police and the community is diseased or malfunctioning— albeit whether it is a problem of police officers whose misconduct has stripped of their department of an entitlement to trust or a problem of community members whose hostility toward public servants lacks sufficient cause will often be sharply contested. Either way, however, trust is a resource that flows from community to police. But trust is a two-way street. And just as it seems essential that community members trust the police department in some fashion, so too should it be critical for the police (and, for that matter, the state whose laws the police are tasked to enforce) to trust the community. In broad strokes, this means believing that the community is not out to “get them,” is not an enemy or a hostile force, and is not generally a violent threat. In a more directly epistemic vein, it means trusting that community complaints about police misconduct are not rabblerousing, are not smokescreens by criminal actors seeking to evade justice, and are reflective of a genuine sentiment of maltreatment that demands consideration and potential redress. That trust, as a discursive category in relationships between police and community, is almost exclusively treated as something the latter gives (owes?) to the former, is demonstrative of how asymmetrical relations of power can largely dictate what sorts of claims are even taken as starting points for further consideration. When communities do not trust the police, the community regards that as a problem. But police not trusting communities 225

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doesn’t even register on that level—it is not recognized to be a problem at all, and hence reasoning and evidence-collection over the issue does not even begin. At the meta-level, this is itself illustrative of a sort of hermeneutical injustice—a type of experiential claim that seems to matter and should be very important (public servants carrying guns in my community don’t find me and mine to be trustworthy)—lacks the sort of publicly accessible language to enter into public debate at all. Relative to the concept of trust, hermeneutical injustice goes over and above articulating the mere lack of trust; it may be an inability to articulate the kind of lack of trust community members and law enforcement may have toward each other. And in practice, police not trusting community members leads to a host of epistemic injustices in everyday police-community interactions where ordinary, seemingly innocent civilian conduct (walking down the street, driving home from work, browsing at a store, entering a house) is recoded as presumptively dangerous, criminal, or threatening. Turn then to the notion of a community. The most obvious understanding of the relevant community in the policing context is one delineated by formal jurisdictional boundaries (e.g., the Montgomery County Police Department’s relevant community consists of the residents of Montgomery County). But community also might have a more complex, normatively laden meaning in this context. A properly functioning community vis-à-vis the police would be one that enjoys, on the whole, good relationships with the police—or perhaps more precisely, those who are owed good relationships with the police. Here, the community has an aspirational dimension, providing a standard by which police assess their conduct and by which community members hold police members accountable. In addition to being a community in the first, purely jurisdictional sense, community can refer to a target set of relations between its lay members and the police that ostensibly protect and serve them. A foundation to such a relationship would be in the reciprocal acknowledgment of due credibility by both police and community when hearing and assessing claims. But who qualifies as part of the community, so construed? Consider cases where the police are called on Black people who are taken to not belong in a particular place. On the part of the white caller, the dispatcher/police trust the caller. But when it comes to the Black subject in this scenario, police frequently act as if they are not part of the community. Indeed, one reason that police mistrust of the community may not be seen as a problem is because, in situations of police violence, the Black subjects of this violence are not taken to be members of the community. To the extent that wrongs may have been done in a particular instance, those wrongs are perceived as being enacted upon outsiders or strangers. And any mistrust that accrues among that population accordingly doesn’t matter—their perspective or testimony doesn’t even count as part of the evidence that goes into appraising whether the relationship between police and “community” is healthy (cf. Sati 2018). To not be a member of the community on this conception is to not have one’s capacity as a knower and a provider of evidence receive its due. Consider the case of the two Black men arrested and booked by Philadelphia police for being at a Starbucks without having purchased anything. On the one hand, it may seem that the police do not trust the people who are the targets of the calls; in this case, the targets are the Black gentlemen. On the other hand, it may be that police “trust” of the community is working just fine. That is, the police trust the community, but the notion of community with which they operate is a limited one, fractured along racial lines. The “community” consists of those who trust in the police and whom the police trust in turn; Black men at a Starbucks are not presumed to be part of that community. Thus, police mistrusting the Black gentlemen is not seen as marking a deviation from trusting members of the community; rather, police trust who they 226

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take to be community members’ word in enforcing the law against those who are taken not to belong in the community. Or alternatively, what we might be seeing is the police trusting the (suitably defined) community too much—a credibility excess wherein it is presumed that if a community member (again, suitably defined) calls the police there must be some serious wrongdoing that demands police intervention (see Medina 2010).3 Any way you slice it, the concept of community itself is here facilitating a state of hermeneutical marginalization. Certain classes of persons (Black men) are left unable to make their experiences intelligible or legible in the argot that governs what “counts” as a valid metric for assessing police efficacy or legitimacy. Other persons (white civilians and responding police officers) are in turn given excessive credence and weight in assessing whether police–community relations are functioning properly. Moving this notion of community along, the social context in which police are called on Black people implicate two questions: why do some communities (e.g., white people) feel entitled to a police force that serves and protects them, and to whom do police think themselves accountable? These questions are important because their answers determine where police begin their evidence collection, which in turn determines the outcome of a formal investigation. In this sense, informal evidence, or evidence that begets capital-E Evidence in an investigation, is as important a starting point as any for an examination of epistemic injustice.

3  The Failure to Gather Evidence as an Epistemic Injustice Particularly in cases of police misconduct, a common rejoinder at this point in the discussion is the plea to “wait for all the facts to emerge.” After all, in some of these cases it turns out that the use of force was justified, that the complaining civilian really was simply lying, or that the responding officers reacted reasonably given the information they had available. We agree. However, we observe that frequently the very point of contestation is the willingness of investigators to commit seriously and impartially to the project of gathering all the facts. More to the point, we stress that failure to do this represents a wrong even if, once the facts emerge, the allegation cannot be sustained. That is to say, one must disaggregate the harm that accrues from the failure to initiate a substantive investigation from the question of what that investigation—fairly undertaken—concludes. When a person with a reasonable prima facie claim is nonetheless not treated as a valid instigator of public investigation, they are wronged even if it turns out that their claim—had it been fully investigated—would not ultimately be sustained. As Laurence Tribe put it, “Both the right to be heard from, and the right to be told why, are analytically distinct from the right to secure a different outcome” (Tribe 1978, 503). The ability to reasonably contest wrongful treatment is important in a way that is conceptually different both from not being wronged in the first place, and from being ultimately vindicated in one’s case (see Fricker 2012, 301). Return again to the example posed by police violence against young persons of color. In, for example, the Trayvon Martin shooting, the public outrage that emerged over the case was not just because of the killing of a young Black man. It also stemmed in large part because the police—at least initially—did not even treat it as a candidate for an investigation (Lee 2013; Schraub 2020). They almost instantaneously credited George Zimmerman’s contention that he had acted in self-defense; it was only later, as public furor persisted, that they moved to arrest and prosecute him. In doing so, the Florida police made certain judgments regarding what sorts of claims would trigger them to even begin considering 227

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investigating a violent death as a potential crime—and the strong implication of the Martin case was that it did not, even on face, find the shooting death of a young Black man at the hands of a young white man to be worthy of greater attention. This sort of epistemic wrongdoing has heritage. Fricker provides a telling example around the police response to the murder of Stephen Lawrence, a young Black man, by a gang of white teenagers in the United Kingdom (the police investigation was so catastrophically mishandled that it yielded a famous inquiry, the MacPherson Report, which has become a touchstone anti-racism document). Fricker documents a series of epistemic wrongs the police perpetuated in the immediate aftermath of the killing, primarily directed at a key witness—Duwayne Brooks—a friend of Lawrence’s who had been present for the murder and had narrowly missed being attacked himself. The police arriving on scene did not treat him as one of the victims (even though he was clearly traumatized and scared); indeed, their operating assumption was that he and Lawrence had been part of a fight that had escalated into a murder. And even as a witness, he was largely ignored and overlooked, with the result that the perpetrators were able to escape in the crucial moments following the crime (Fricker 2012, 292). As the MacPherson Report put it: [T]he officers failed to concentrate upon Mr. Brooks and to follow up energetically the information which he gave them. Nobody suggested that he should be used in searches of the area, although he knew where the assailants had last been seen. Nobody appears properly to have tried to calm him, or to accept that what he said was true.  To that must be added the failure of Inspector Steven Groves, the only senior officer present before the ambulance came, to try to find out from Mr. Brooks what had happened. (quoted in ibid.) Notice how the wrong being articulated here stands separate from whether any evidence ultimately produced at trial is sufficient to convict someone beyond a reasonable doubt. Criminal conviction is a high bar, and it is baked into the foundation of the criminal justice system that some prosecutions (even of guilty parties) will ultimately yield acquittals. But the epistemic injustice here doesn’t directly relate to how the conversation concludes; rather, it connects to how it begins (or fails to begin properly at all). To be sure, the failure to vigorously investigate the killing at the outset can taint the ability to get reliable evidence later on (as the Lawrence case aptly demonstrates). Beyond that, it can reasonably cast doubt on the state’s genuine commitment to seeing justice done even once they have commenced the formal investigatory process. Thus, failure at the origins of investigation can, and often does, delegitimize subsequent proceedings. The outcome and the potential for epistemic injustices to poison informal evidence-gathering practices are one reason why we care about these informal practices to begin with. That said, when the police refused to treat Brooks as a witness who could help them solve a crime, or resisted investigating the killing of Trayvon Martin as a crime at all, they enacted a wrong against Brooks and the Martin family that is wholly distinct from whether the fruits of formal investigative labor would end up yielding a criminal conviction. The concept of epistemic injustice certainly has much to say about how formal decision-makers appraise evidence. But its unique contribution might be how it assigns moral weight to the more intermediary, investigative steps, those which come between more concrete substantive wrongs and final consideration and adjudication of what, if anything, can be done to redress them. 228

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This begins to circle the concept of epistemic injustice back to the particular personal and dignitary harms it can impose upon knowers whose experiential offerings are systematically obstructed from being taken into evidence. As Fricker writes, When you find yourself in a situation in which you seem to be the only one to feel the dissonance between received understanding and your own intimated sense of a given experience, it tends to knock your faith in your own ability to make sense of the world. (Fricker 2007, 44) Here too we begin to see problems such as “gaslighting” emerge as distinctive wrongs associated with the evidence-gathering (or perhaps more precisely, lack of evidence-gathering) process. Gaslighting, as Kate Abramson trenchantly observes, does not just present its victim as “wrong or mistaken.” Rather, it presents her as being in no condition to judge whether she is wrong or mistaken. The accusations are about the target’s basic rational competence—her ability to get facts right, to deliberate, her basic evaluative competencies and ability to react appropriately: her independent standing as a deliberator and moral agent. (Abramson 2014, 8) The person who is gaslighted is typically unable to get others to even begin the process of gathering and considering evidence, and in many cases will lose confidence in their own status as the sort of person who could generate reliable testimony. Discussing the institutional consequences of epistemic injustice in the informal evidencegathering stage should also come with some starting point for institutions to become epistemically virtuous. Fricker makes the empirical speculation that “it is very unlikely that courts, police teams .  .  . complaints boards .  .  . and so on would be capable of reliably delivering justice without embracing [justice’s] values and principles” (Fricker 2013, 1331). Treating hitherto marginalized communities as knowers and, as a consequence, reliable sources of information must become a central value of not only of a particular department or in a particular case, but of policing altogether. What would facilitate this goal? At the least, any reform effort must take aim at the distinctly epistemic problems that obstruct functioning, just relationships between evidencegatherers (often though not always state agents) and everyday citizens. A prescription that gets at a corrupt police culture would be to get rid of the “Blue Wall of Silence,” the internal pact that police officers have not to report indiscretion by other officers lest they suffer repercussions. The pact is an informal evidentiary practice insofar as it predates yet invariably influences what does or does not enter the formal record from the officer’s point of view. The National Institute of Ethics found that, in a survey of 3,714 officers, 79 percent of them believe that such a Blue Wall exists. About half of them do not think the presence of the Wall to be a problem (Trautman 2000). As recently as 2016, a San Francisco police official lamented that “It is bad enough that our officers are now being encouraged to be trained snitches on one another” (Wing 2016). Wing goes on to note that a police department that shows a commitment to discipline is seen to indicate capitulation to “cop-haters.” Such a label makes sense when these “cop-haters” are construed to exist outside of the community, expanding on the second notion of that term spelled out earlier. 229

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To sum up: epistemic injustice is an instructive concept in analyzing informal evidentiary practices, as well exemplified by cases of police misconduct. The decisions police make when pursuing leads and interviewing persons of interest, for example, have an effect on formal investigations and civilians. Accepting that epistemology is grounded in power relations does not commit us to a relativism in which anything goes. Instead, Nicolson argues, a skepticism, informed by power relations, is the best attitude to take toward what is considered to be the “truth” at any given point; we can expand on this to include a skepticism toward whether certain pieces of information coming from certain speakers carry evidentiary value. With this in mind, Fricker’s prescription that we become virtuous hearers gains new significance: can institutions be “virtuous hearers” in any intelligible sense? Though a good starting point, there is much more to be said on what virtuous appraisal of evidence entails. Nicolson contends that “Constant awareness that claims to truth can never be more than just claims discourages complacency and constantly invites the questions: under what conditions has this truth-claim been made, by whom[,] and whose interests is it likely to serve?” (Nicolson 2013, 43). Moving forward, we can further investigate who is able to ask these questions, the reach that these questions are able to garner, and whether asking and answering these questions can transform, in a more equitable direction, how we gather and how we appraise the evidence before us.

Notes 1 That is not all it is; there may be circumstances where one can commit an epistemic injustice in circumstances where the wronged party is not seeking to offer “evidence” in the strict sense. But such cases are beyond the scope of this chapter. 2 Of course, once that language is developed there might still remain significant testimonial injustices in how women who speak of sexual harassment in their lives are (dis)credited. 3 The business practice of calling the police on Black patrons who are imagined as criminal, vagrants, or threats exploits epistemic injustice along yet another dimension: many courts have declined to treat this action as even probative evidence of tangible racial discrimination because they discount Black testimony regarding how the threat of police intervention poses a serious hindrance to their ability to contract as equal customers. See Schraub (2018, 70–77) for discussion.

References Abramson, Kate. 2014. “Turning Up the Lights on Gaslighting.” Philosophical Perspectives 28.1: 1–30. Bell, Derrick. 1992. “The Rules of Racial Standing.” In Faces at the Bottom of the Well: The Permanence of Racism. New York: Basic: 109–126. Buchman, Daniel Z., Anita Ho  & Daniel S. Goldberg. 2017. “Investigating Trust, Expertise, and Epistemic Injustice in Chronic Pain.” Bioethical Inquiry 14: 31–42. Coady, David. 2017. “Epistemic Injustice as Distributive Injustice.” In Ian James Kidd, Jose Medina & Gaile Pohlhaus Jr. (eds.), The Routledge Handbook of Epistemic Injustice. London: Routledge: 61–68. Dotson, Kristie. 2011. “Tracking Epistemic Violence, Tracking Practices of Silencing.” Hypatia 26.2: 236–257. Fatima, Saba. 2017. “On the Edge of Knowing: Microaggression and Epistemic Uncertainty as a Woman of Color.” In Kirsti Cole & Holly Hassel (eds.), Surviving Sexism in Academia: Feminist Strategies for Leadership. London: Routledge: 147–157. Fricker, Miranda. 2007. Epistemic Injustice: Power and the Ethics of Knowing. Oxford: Oxford University Press.

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Epistemic Injustice in Collecting and Appraising Evidence ———. 2012. “Silence and Institutional Prejudice.” In Sharon L. Crasnow  & Anita M. Superson (eds.), Out from the Shadows: Analytical Feminist Contributions to Traditional Philosophy. Oxford: Oxford University Press: 287–304. ———. 2013. “Epistemic Justice as a Condition of Political Freedom?”  Synthese  190.7 (2013): 1317–1332. Hoffmann, Diane E. & Anita J. Tarzian. 2001. “The Girl Who Cried Pain: A Bias Against Women in the Treatment of Pain.” Journal of Law, Medicine & Ethics 29: 13–27. Lee, Cynthia. 2013. “Making Race Salient: Trayvon Martin and Implicit Bias in a Not Yet Post-Racial Society.” North Carolina Law Review 91: 101–57. Medina, Jose. 2010. “The Relevance of Credibility Excess in a Proportional View of Epistemic Injustice: Differential Epistemic Authority and the Social Imaginary.” Social Epistemology 25.1: 15–35. Nicolson, Donald. 2013. “Taking Epistemology Seriously: ‘Truth, Reason, and Justice’ Revisited.” The International Journal of Evidence and Proof 17: 1–46. Sati, Joel. 2018. “From Standoff to Foundations: On Black Lives Matter and All Lives Matter.” Social Epistemology Review and Reply Collective 7.9: 1–6. Schraub, David. 2016. “Playing with Cards: Discrimination Claims and the Charge of Bad Faith.” Social Theory and Practice 42.2: 285–303. ———. 2018. “Torgerson’s Twilight: The Anti-Discrimination Jurisprudence of Judge Diana E. Murphy.” Minnesota Law Review 103.1: 65–91. ———. 2020. “Deliberation and Dismissal.” University of Pennsylvania Journal of Constitutional Law 22.5: 1319–1387. Sperino, Sandra F. 2018. “Disbelief Doctrines.” Berkeley Journal of Employment and Labor Law 39.1: 231–252. Sperino, Sandra F. & Suja A. Thomas. 2017. Unequal: How America’s Courts Undermine Discrimination Law. Oxford: Oxford University Press. Trautman, David. 2000. “Police Code of Silence: Facts Revealed.” International Association of Chiefs of Police. www.aele.org/loscode2000.html. Tribe, Laurence. 1978. American Constitutional Law. New York: Foundation. Wing, Nick. 2016. “Police Union Official Calls Out ‘Snitch’ Cops, Shows Why Accountability Fails.” The Huffington Post, www.huffingtonpost.com/entry/san-francisco-police-snitch_us_57349f17e4 b060aa78197d54.

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18 PREJUDICED BELIEF Evidential Considerations Endre Begby

1 Introduction “Prejudice” is typically a term of disparagement. But what exactly is being disparaged? In everyday discourse, we sometimes speak as though certain belief-contents themselves are intrinsically prejudiced. But as epistemologists, we will presumably want to direct our normative attention toward the holders of these beliefs, and specifically, toward their grounds for holding them. In his seminal study on the topic, psychologist Gordon Allport offered as a definitional starting point the view that prejudice is a matter of “thinking ill of others without sufficient warrant” (Allport 1954: 6). As we shall see, many philosophers have followed him in defining prejudice in similar terms. What we mean to disparage when we call something a prejudice, then, would presumably be the agent’s epistemic justification for holding the belief. Perhaps everyday discourse can be pardoned under the assumption that there are certain beliefs about others—i.e., standard examples of prejudices such as “women are less intelligent than men” or “Muslims are terrorists”—that no one could ever be warranted in holding; so whenever someone does hold such a belief, we must assume that they do so by overgeneralizing from insufficient observations, by engaging in biased treatment of the evidence, etc. Accordingly, prejudiced belief would always be a manifestation of epistemic wrongdoing, of failing to abide by applicable canons of epistemic rationality. This chapter argues that this assessment is unduly optimistic. In particular, as we transition toward “non-ideal” forms of epistemological theorizing—emphasizing the particular and highly contingent cognitive and contextual constraints that ordinary agents are forced to operate under—we cannot make the case that some belief is epistemically irrational without carefully considering the agent’s epistemic situation. Accordingly, we cannot rule out a priori that the sorts of beliefs that we would typically classify as prejudicial might well, in particular instances, be amply supported by the totality of the evidence available to the agent. It seems advisable, then, to begin from a definition that leaves open what we should think about the epistemic standing of particular instances of prejudiced belief. I believe that a productive minimal understanding of prejudice, one that nonetheless makes sufficient DOI: 10.4324/9781315672687-22 232

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contact with more traditional views, will define prejudice as a negatively charged stereotype attaching to a particular social group and the members who comprise this group.1 Even on such a minimal understanding, prejudice must certainly be counted among the causes of a great many of our societies’ ills: poverty, violence, marginalization, maybe even war, are among the phenomena that can be caused and sustained by prejudice. Starting from such a definition, there are different, albeit complementary, perspectives that our inquiry into the epistemology of prejudice might take. On the one hand, one might consider the acquisition of prejudiced belief: how could anyone ever come into possession of a prejudiced belief if not by taking an epistemic wrong turn somewhere? On the other hand, one might focus on the maintenance of prejudiced belief: regardless of how one came into possession of these beliefs, there appears to be plenty of contrary evidence on offer in anyone’s normal course of experience; so, how could one remain prejudiced without violating canons of epistemic rationality? Both perspectives are regularly voiced in the literature (although the difference between them is rarely noted). For instance, Miranda Fricker writes that “[w]e must surely start with the presumption that, at least as regards explicit prejudice, we are epistemically culpable for allowing prejudice into our thinking” (Fricker 2016: 36, my emphasis). By contrast, other contributions draw our focus toward the blinkered and stunted cognitive outlook that results from the exigencies of trying to maintain prejudiced belief in light of the ample contrary evidence that surrounds one. In this vein, Quassim Cassam lists prejudice as an “intellectual vice” to be counted alongside “gullibility, dogmatism . . . closed-mindedness, and negligence” (Cassam 2016: 159; see also Zagzebski 1996: 152, for a similar perspective). Sometimes both notions appear side by side; here’s Fricker again, this time from her influential book Epistemic Injustice: “[t]he idea of a prejudice is . . . most naturally interpreted in an internalist vein as a judgement made or maintained without proper regard to the evidence” (Fricker 2007: 32–33, my emphasis). In what follows, I will attempt to make the case that in neither of these two dimensions— acquisition or maintenance—does prejudice necessarily correlate with culpable epistemic wrongdoing, or a warped and dysfunctional cognitive outlook.

2 Acquisition 2.1  Acquisition by Simple Induction The intuitive case against justified acquisition of prejudice is perhaps best seen if we think of it in terms of scenarios where subjects are presumed to start with no relevant information whatsoever, building their inductive generalizations from scratch. Johnny notices (correctly, let’s say) that the top students in his math class are all boys and infers that girls are comparatively less adept at math. If you were to ask him who he would turn to for help on a math puzzle, Jim or Jenn (neither of whom he knows), he would naturally respond “Jim.” It appears that Johnny holds a prejudice against girls, believing that they are less adept at math than boys.2 This prejudice shows itself in the way that he would treat arbitrary girls, even ones that he doesn’t know. But what has gone wrong, epistemically speaking, in this scenario? It is tempting to think that Johnny is guilty of what we might call “inductive overreach”: he just doesn’t have enough (or good enough) evidence to form the belief in question; moreover, whatever 233

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evidence he does have provides him with no warrant to believe anything about Jenn’s mathematical abilities in particular. The problem, then, of prejudice-in-acquisition, would be something like an innate tendency to “overgeneralize” on insufficient evidence. Consider, to this effect, Allport (1954: 7): A prejudiced person will almost certainly claim that he has sufficient warrant for his views. He will tell of bitter experiences he has had with refugees, Catholics, or Orientals. But, in most cases, it is evident that his facts are scanty and strained. He resorts to a selective sorting of his own few memories, mixes them up with hearsay, and overgeneralizes. No one can possibly know all refugees, Catholics, or Orientals. Hence any negative judgment of these groups as a whole is, strictly speaking, an instance of thinking ill without sufficient warrant. Surely, there is something to be said for this perspective. But it is doubtful that it can be the final word. For one, if we do approach it simply as an inductive problem, it is not immediately obvious that the evidence is insufficient. By comparison: Johnny notices (correctly, let’s say) that the tallest students in his class are all boys. He infers that boys generally grow taller than girls. If we were to ask him who is likely to be taller, Jim or Jenn (neither of whom he knows), he would naturally respond “Jim.” In structurally comparable inductive scenarios, then, we seem to have few qualms about generalizing from limited observational evidence in this way. But Allport might well have had a more radical view in mind: if any such generalization would lack warrant save in cases where one knows, independently, that every individual falling under the generalization possesses the property in question, this is just to say that no induction—in fact, no generalization at all—is ever epistemically permissible. But this is hard to accept. Generalization is the lifeblood of all empirical cognition, and it would be remarkable if there were any significant domain of application in which induction could be shown to be inherently epistemically unreliable. Is it specifically thinking ill of others that carries this restriction? Allport’s wording is unclear. But note, for instance, how we seem to have few reservations about similarly evidenced inductions in cases where the valence is positive rather than negative: Johnny has had several positive experiences with his neighborhood Catholics, noting their friendliness, generosity, and eagerness to help. Is he now epistemically misguided to think that these experiences constitute evidence that should incline him toward believing that he can rely on future encounters with neighborhood Catholics to provide a friendly smile and a helping hand?3 Now, all of this is, of course, compatible with the idea that induction provides only a relatively weak grounds for believing anything about future encounters. And so, one should be open to the possibility that not every person who falls into the stereotyped category displays the property in question or displays it to the same degree. But this doesn’t make prejudiced belief at all peculiar: rather, this requirement applies to the product of any inductive generalization. Even if we concede that someone is justified in holding a prejudiced belief, we should still require of them that they recognize the defeasibility of the underlying generalization and thereby display appropriate openness to new evidence. This points toward the question of how anyone could be justified in maintaining their prejudiced beliefs in light of such evidence. I will return to that question in Section 4, after first considering the possibility that we have in fact been quite wrong to think that induction from individual experience provides the most relevant framing for the epistemology of prejudice in the first place. 234

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2.2  Acquisition by Testimony The epistemology of prejudice is part of social epistemology, at least in the sense that the phenomenon we are concerned with arises in the context of social cognition, i.e., thinking about other people, and, in particular, thinking about them in terms of their group membership. Strikingly, many contributors to this discourse nonetheless persist in considering the question of the epistemic standing of prejudiced belief very much in terms of an individualistic conception of evidence. Quassim Cassam, for instance, invites us to consider the esteemed journalist Louis Heren, who believed that all politicians are “lying bastards.” This belief certainly seems to have the right shape for a prejudice. But whether it is a prejudice or not, argues Cassam (2016: 167–168), depends on the evidence that thinkers can call upon to support it. In Heren’s case, given his extensive experience in working with politicians, the belief is not a prejudice but rather an “empirically grounded heuristic.” Cassam doesn’t assert, but certainly seems to imply, that anyone who held the same belief but didn’t have a similar range of first-hand experience with politicians, would indeed be prejudiced. This emphasis on first-hand experience4 makes for a strikingly individualistic conception of the relevant evidence. This conception is psychologically implausible and stands in stark tension to the broader philosophical motivations for thinking of epistemology under a social guise in the first place. Psychologically, it is extremely implausible that we all arrive at our prejudiced beliefs individually, by drawing (perhaps overhastily) on the randomly scattered bits of evidence that are available to us. If that were the case, we would have a hard time explaining why so many prejudices are shared in any society. (The fact that they tend to be widely shared is presumably a reason why they are so damaging and systematic in their effects.) To adopt a phrase from Susanna Siegel (2017), prejudiced beliefs are often “culturally normal beliefs.” And in many cases at least, part of the reason why they are culturally normal is that they are disseminated and reinforced by explicit or implicit testimony. In such cases, the evidence that supports the prejudice (upon acquisition) isn’t individual observations of people’s performance in various scenarios, but the fact that someone—with suitable epistemic authority, let’s assume—told me that this is the case. Quite often, we can assume, their authority bears some sort of institutional or para-institutional imprint, such as teachers, parents, or other caregivers.5 Once we start thinking about prejudiced belief along these lines, we are looking at the question of epistemic justification in terms of a qualitatively different sort of evidence than we were previously. Now the question of justification is rather one about whether we could ever be in a position to justifiably accept such testimony. And it is hard to see how we couldn’t be. Our pervasive and justified dependence on others in forming our cognitive outlooks is well-documented (see, e.g., Hardwig 1985; Fricker 2006; Goldberg 2010). Social cognition is hardly an exception: we would be hopelessly inadept at navigating our social worlds if we were not generally epistemically entitled to take testimony on issues relating, say, to social facts, institutions, and norms. By way of example, imagine a precocious student, Johnny, who asks his teacher (c. 1860) what justifies English colonial rule over India. His teacher cites chapter-and-verse from Mill’s On Liberty: these Barbarians aren’t cognitively capable of self-rule, and that’s why it’s appropriate for England to assume guardianship over their political affairs. Our question now is simply, why couldn’t this constitute a sort of evidence that might contribute to Johnny’s justification for believing that people from the Indian subcontinent are intellectually inferior, even in the absence of extensive 235

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individual experience with them? After all, Johnny’s evidence for believing pretty much anything derives, at least in part, precisely from such testimony. There is a systematic problem in the offing here: if we want to condemn prejudice on epistemic grounds in either of these scenarios, we run the risk of ruling out sources of evidence or modes of epistemic reasoning that serve us eminently well in other domains and which no one would want to cast aspersions on in their broader application. In particular, the notion that epistemically responsible social cognition can only be based on individual experience cannot be sustained. Testimony is a pervasive source of learning, not least in the social domain. And unless we credit individuals with specific epistemic resources to discriminate among the good and the bad bits of the testimony that is offered to them, we have no grounds for saying that they are justified in taking the good bits only. In such scenarios, not taking the testimony on offer—the good and the bad—is essentially tantamount to a refusal to form one’s beliefs in the light of the totality of evidence at one’s disposal. But this is precisely an instance of epistemic irrationality, if anything is.

3 Maintenance I hope it will be granted, then, that individuals may justifiably come to acquire prejudiced beliefs, at least in certain kinds of evidential contexts. The justification might come either from evidence acquired through individual experience or from testimony. This concession moves our focus on to the next assumption that tends to structure philosophical discussion about prejudice, viz. that no one could maintain such beliefs for long without ignoring or discounting contrary evidence, and thereby displaying some form of epistemic irrationality. Allport proposes this sort of cognitive inflexibility as a test for distinguishing mere “error in prejudgment” from genuine prejudice. He writes (1954: 9): If a person is capable of rectifying his erroneous judgment in the light of new evidence he is not prejudiced.  Prejudgments become prejudices only if they are not reversible when exposed to new knowledge. A prejudice, unlike a simple misconception, is actively resistant to all evidence that would unseat it. On this perspective, the cognitive states that we have discussed so far may not even be prejudices, strictly speaking. A false “prejudgment” comes to constitute a prejudice only when the subject who holds it manifests a disposition to retain it even in the face of significant contrary evidence. An immediate problem with this sort of dispositional demarcation of prejudice lies in the supposition that prejudiced people, quite generally, do in fact have access to all the relevant evidence, and simply fail to make the appropriate use of it. But in lots of cases, the evidence in question, even supposing it exists, might be beyond their epistemic reach. They might, for instance, live in communities where such evidence is systematically suppressed.6 It seems we should want to know whether someone is prejudiced without having to settle how they would fare in evidential contexts significantly different from their own. Another problem, bitterly familiar in real-world contexts, is that widespread social prejudice will often create downstream effects that in turn “renders true” the prejudice, or at least appears to provide salient evidence in its favor.7 Consider a feedback loop between the widespread prejudice “women are less adept at math than men” and the apparent fact that relatively few of the top talents in math programs are women. Now there is plausibly a 236

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deeper structural explanation for why this evidence obtains. In a society where few women are given opportunity or encouragement to pursue mathematical education, it likely will be true that men are generally better at math than women, and all the extant evidence will favor this view. But the structural explanation doesn’t change the fact that it is evidence, and that individual subjects will be required to make epistemic use of it, as they will of any information available to them. But even setting these concerns aside, there is a deeper problem on the horizon. Allport argues that prejudiced belief is “actively resistant” to contrary evidence. And it probably is true that once a prejudiced belief is acquired, it will tend to exert a significant degree of influence over the interpretation of new evidence. But importantly, this effect is not unique to prejudice. Rather, prejudiced belief embodies an underlying form of generalization—one that we put to wide use in a number of different contexts—which appears quite generally to show a significant degree of rational resistance to new evidence. This effect is largely neglected by philosophers who emphasize the supposed contrast between the inflexible dogmatism of the “prejudiced mindset” with the flexible open-mindedness to new evidence that purportedly constitutes intellectual virtue. An example will help connect this idea with the argument of previous sections. Consider, Nomy Arpaly’s example of Solomon, “a boy who lives in a small, isolated farming community in a poor country” and who “believes that women are not half as competent as men when it comes to abstract thinking” (Arpaly 2003: 103). Solomon clearly harbors a false negative stereotype against women. Nonetheless, and as Arpaly concedes, this stereotype is not without evidential support. It appears that the stereotype is widely shared in his community, and we can assume that it has been repeatedly related to him by teachers and peers. Further, it may also be that women in his community have largely internalized the stereotype: as a result, Solomon may note that none of the women he has encountered have ever displayed the aptitude in question. Both testimonial and individually acquired evidence, then, appear to lend a significant degree of support to the stereotype. In light of this, Arpaly (2003: 104) and Fricker (2007: 33–34) agree that Solomon is not unreasonable in holding his belief about women at this point. As Arpaly puts it (ibid.), since Solomon has not been “exposed to striking counterevidence to it,” his belief is not “particularly or markedly irrational.” Following Allport, we may even be reluctant to call it a prejudice. To see how epistemic irrationality might enter into the picture, however, imagine that Solomon receives and accepts an entrance fellowship to a university. Solomon enrolls in a calculus class, where he regularly interacts with women who display the relevant aptitudes. He is now in possession of the kind of evidence that previously eluded him, namely, direct evidence of female intelligence. This new evidence, Fricker argues, rationally requires him to revise his beliefs about women. If he does not—if he persists in thinking that women are inferior to men in the realm of abstract thinking—then he is prejudiced, in Allport’s strict sense of the term. His stereotype will have transformed into a prejudice as a consequence of the changes to the evidential situation he is in. If he retains his previous belief even after being confronted with this new evidence, it can now only be because he harbors an irrational bias against female intelligence. Much is appealing about this view. Clearly, stereotypes are or embody generalizations of some kind. Qua generalizations, it is certainly reasonable to demand that they remain appropriately sensitive to new evidence. And here, as Arpaly and Fricker argue, is where 237

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Solomon’s epistemic failing lies: he culpably fails to update his belief about female intelligence in light of new evidence. But here it matters deeply what kind of generalization we are talking about. Things would be very straightforward indeed if, for instance, stereotypes were essentially universal generalizations. If so, Solomon would be in the situation of the field biologist who, after encountering his first black swan, refused to give up his belief that all swans are white. But it is extremely implausible that common instances of stereotype judgments ascribe a particular property to every member of some group or holds that every member displays the trait to exactly the same degree. For instance, if Solomon is appropriately sensitive to evidence, he will have long since recognized that men and women alike display a range of abilities in virtually every endeavor they might apply themselves to. Accordingly, a more plausible approach to the underlying generalization would rather account for stereotypes in terms more akin to typicality-judgments: it is typical of women that they are less intelligent than men; on average, women are less intelligent, and so forth. Once we take this approach, however, we must also allow that Solomon’s stereotype will embody a fair degree of flexibility in how it absorbs new evidence: for instance, Solomon might recognize that if both male and female intelligence displays some manner of normal distribution, then it is highly likely that some women are every bit as smart as some men. By contrast, if Solomon’s stereotype displayed the extreme rigidity of universal generalizations—for example, if he held that there is no woman who is half as smart as any man8—then he could maintain that stereotype only by culpably discounting evidence long before he enters the university. This suggests that a more appropriate model for thinking about stereotypes is in terms of so-called generic judgments.9 But as is widely recognized in the current literature, generic judgments display a peculiar kind of resilience in the face of apparently contradictory evidence.10 As Sarah-Jane Leslie (2008) points out, we hold that “ducks lay eggs” is true even after being reminded that only female ducks do. Likewise, we might maintain the belief that mosquitos spread the West Nile virus full well knowing that the vast majority of mosquitos don’t. Like any generalization, generic judgments are, of course, formed in the light of evidence and must remain sensitive to new evidence. But the manner in which they are sensitive to new evidence differs dramatically from universal generalizations. In particular, it would be futile to attempt to falsify generic judgments simply by pointing to instances—or even a large range of instances—which fail to display the trait in question. Generic judgments are stereotypes in the truest sense: they hold that it is salient, relevant, and typifying of a particular group that it displays a certain trait, without necessarily committing themselves to particular details about just how many members of this group display this trait, or to what extent they do. Accordingly, it is perfectly consistent with maintaining a negative stereotype against female intelligence that one recognizes that not all women are equally obtuse, and indeed that some are as smart as any man. With this in mind, let us return to the details of Solomon’s evidential situation after he enters the university. Solomon is already in possession of at least two bodies of evidence supporting his belief: first, testimonial evidence from teachers and peers; second, evidence from personal interactions with women in his community. The new evidence he acquires upon entering the university consists in encounters with women who display the relevant aptitude to a high degree. Now, if Solomon fully failed to recognize these women as providing evidence of the relevant kind in the first place, it would certainly reflect poorly on him as an epistemic agent. This neglect could only ever be the product of some kind of faulty epistemic mechanism, be it inattention or, more likely, implicit or explicit bias. But 238

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the point remains that Solomon could well recognize these particular women as highly intelligent yet still retain his stereotype against women at large. To see how, assume that Solomon reasons along the lines suggested earlier. Women are, on average, less intelligent than men. But much like some men are really quite dumb, some women are smarter than others. Indeed, some women may be just about as smart as any man. And calculus class is presumably where one might expect to encounter some of these women. Epistemically speaking, there need be nothing wrong with this line of reasoning: Solomon is perfectly within his rights to deploy it. What it shows is that far from contradicting his stereotype, the new evidence is in fact predicted by it (at least when combined with independently plausible background assumptions). Accordingly, the new evidence is consistent with his stereotype and does not, from the point of view of epistemic rationality, require a deep revision of it. Of course, none of this is to say that real-life Solomons are likely to deploy this sort of reasoning in managing their epistemic affairs, as opposed to culpably relying on various kinds of biases to discount new evidence. But it is to say that, given a plausible elaboration of the story, Solomon could well be epistemically justified in maintaining his negative stereotype against women even after he enters the university. While some degree of rational resistance to counterevidence is built into prejudiced beliefs, this resistance is not total, however. Certainly we can imagine some constellations of evidence that Solomon might be confronted with, which would require him to change his mind. But then we can ask, just how likely it is that someone like Solomon will encounter all that evidence, all the while not gaining any further evidence confirming his prejudice.11 If a real-life Solomon finds himself in a socio-epistemic environment that inculcates prejudiced beliefs through, say, its school curriculum, then it is likely that he is also in an environment in which contrary evidence is significantly suppressed. On reflection, we might still want to say that whenever there is prejudice, there is also bias. But “bias” here must mean something different. In particular, we can no longer presume the bias to be a feature of the cognitive outlook of individual epistemic subjects. Instead, bias can be effectively encoded into the evidence-base that otherwise rational epistemic subjects are forced to contend with, via the institutional and para-institutional structures that sustain prevalent social forces of exclusion.

4  Prejudice and Non-Ideal Epistemology Any serious philosophical engagement with prejudice must make significant concessions to what we might call “non-ideal epistemology.”12 Traditional epistemology has structured its inquiry according to a variety of different idealizations. One such idealization, which has not been particularly prominent in this chapter, is that of agents operating under no essential cognitive limitations. But of course, many cognitive limitations are intrinsic to the cognitive architecture of human beings. For instance, human beings have severely limited working memory. From one perspective, this is obviously non-ideal: even if we cannot conceive of a bounded cognitive system with unlimited working memory, it is nonetheless reasonable to assume, other things being equal, that a more capacious working memory is better. This is relevant because some of these limitations are plausibly implicated in the causal story of why human beings are forced to rely so much on stereotype generalizations in the first place. But on the other hand, having limited working memory isn’t intrinsically an imposition on our rationality anymore than, say, being unable to hear frequencies over 20 kHz is. And from the standpoint of non-ideal epistemology, we should rather ask, what are the optimal 239

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cognitive strategies that human beings can deploy, given that these are the limitations they are forced to operate with? Once this question is asked, however, we must be prepared for an answer that affirms that reliance on stereotype generalizations is indeed cognitively optimal, given our non-ideal starting point. I call this “endogenous non-ideality,” since it’s a form of non-ideality that arises from features of the cognitive system itself. However, there is another dimension of idealization that bears not on how we process our evidence, but on the character of the evidence we have access to in the first place. Some epistemologists start from an assumption of more or less perfect information, i.e., that epistemic subjects have access to all the information relevant to their inquiry. If they don’t make epistemic use of that information, it must be because they are lazy, blinkered, biased, etc. Any such assumption of perfect information is clearly implausible in light of our cognitive limitations. But even if we lift that idealization, we might still persist in thinking that there are no important biases built into the subset of information that they will have access to at any given time. But this is also implausible given what we know about how the flow of information is controlled and manipulated in human societies. Epistemic rationality requires us to form our beliefs in light of the information actually at our disposal. As I have argued in this chapter, this information is typically constrained in a variety of important ways. These constraints don’t merely manifest in random fluctuations in what evidence happens to be available at a particular time. In important ways, they can also bear the imprint of human agency and institutions.13 Call this “exogenous non-ideality,” since it is a form of non-ideality that is imposed on the subject by the epistemic context that she happens to find herself in. In many real-life settings, then, the information available to us will already itself bear the imprint of bias. Specifically, it may include evidence that supports, or even directly expresses, prejudiced content. This may be misleading evidence. But if we have no good reason to suspect that it is misleading evidence, it is nonetheless evidence that we are epistemically required to take into account.14 In such contexts, even a cognitive system scrupulously implementing a program of perfect epistemic rationality will arrive at perniciously false beliefs. Accordingly, we cannot make sweeping claims prohibiting certain beliefs merely on the basis on their content, without conducting a fine-grained study of the sort of informational context that epistemic agents are forced to operate within. Once that study is conducted, it may well turn out that many of the beliefs that we would like to dismiss as perniciously false are indeed perfectly epistemically justified.

Acknowledgments Many thanks to Thomas Kelly and Maria Lasonen-Aarnio for helpful comments on this chapter. Funding for this project is provided by SSHRC Insight Development Grant 430 2016 0460.

Notes 1 Many paradigmatic instances of prejudice will no doubt also be false. Should this be included in a working definition of prejudice? Since our focus is strictly on the question of whether prejudiced belief can be justified in light of evidence, we don’t need to settle this issue here. Even false beliefs can enjoy epistemic justification in the relevant sense. 2 Philosophers sometimes speak of prejudices as “outright beliefs.” However, there is no reason why we shouldn’t rather seek to model the underlying epistemic dynamics in terms of credences, since

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Prejudiced Belief even prejudiced people can have greater or lesser confidence in their beliefs, reflecting the relative strength of their evidence (as they see it). In different scenarios, then, Johnny can be loosely said to “believe” that girls are less adept at math than boys, even as his confidence in this generalization can vary quite considerably. 3 One might hold that induction-based stereotyping can violate moral norms even if it doesn’t violate epistemic norms (for discussion, see Blum 2004; Gendler 2011; Beeghly 2015). While this might provide some grounds for drawing a distinction between positive and negative stereotypes, it doesn’t obviously bear on the question of whether someone is epistemically irrational for committing even to morally prohibited negative stereotypes. The recent discourse on “moral encroachment” attempts to bridge this gap: moral and epistemic norms can interact in the sense that whenever someone stands to be harmed by my forming a belief about them, I must meet a higher bar of evidence or epistemic circumspection in order to be epistemically justified in holding this belief. (See, e.g., Bolinger 2018; Moss 2018; Basu 2019a, 2019b, as well as Gardiner 2018, for critical discussion.) But of course, there is nothing in this view that entails or even suggests that many ordinary instances of prejudiced belief couldn’t in fact meet this bar, wherever it is set. 4 See also Allport (1954: 7). 5 Drawing on Siegel (2017), one may also wonder whether children and adolescents may be able to draw inferences from established patterns of social interaction even without the support of explicit testimony. Such patterns provide plausible evidence about what “everybody knows” and should therefore, arguably, be granted some presumptive epistemic role in a properly social epistemology. See Begby (2018a) for some cursory remarks, and Begby (2021b, ch. 7), for a fuller account. 6 Or it might have been defeated through a move that I  elsewhere call “evidential preemption” (Begby 2021a), such as “the liberal media will tell you that p,” where it’s understood that what the liberal media tell you is not to be believed. 7 Cf. Intemann, this volume, Section 3. 8 This would be one way of construing Arpaly’s gloss of Solomon’s belief as “women are not half as intelligent as men” (Arpaly 2003: 103). 9 Cf. Begby 2013. 10 Leslie 2015, 2017. 11 Cf. Silva 2018. 12 See 2021b, ch. 3, for a full account. 13 For a simple example, consider the role of public institutions in setting the school curriculum. 14 See, e.g., Thomas Kelly (2009).

Works Cited Allport, Gordon. 1954. The Nature of Prejudice. 25th Anniversary edition. New York: Basic Books, 1979. Arpaly, Nomy. 2003. Unprincipled Virtue: An Inquiry into Moral Agency. Oxford University Press. Basu, Rima. 2019a. “What We Epistemically Owe to Each Other.” Philosophical Studies  176(4): 915–931. Basu, Rima. 2019b. “The (Wrongs) of Racist Beliefs.” Philosophical Studies 176(9): 2497–2515. Beeghly, Erin. 2015. “What Is a Stereotype? What Is Stereotyping?” Hypatia 30(4): 675–691. Begby, Endre. 2013. “The Epistemology of Prejudice.” Thought 2(2): 90–99. Begby, Endre. 2018a. “Straight Thinking in Warped Environments.” Analysis 78(3): 489–500. Begby, Endre. 2018b. “Doxastic Morality: A Moderately Skeptical Perspective.” Philosophical Topics 46(1): 155–172. Begby, Endre. 2021a. “Evidential Preemption.” Philosophy and Phenomenological Research 102(3): 515–530. Begby, Endre. 2021b. Prejudice: A Study in Non-Ideal Epistemology. Oxford University Press. Blum, Lawrence. 2004. “Stereotypes and Stereotyping: A  Moral Analysis.” Philosophical Papers 33(3): 251–289. Bolinger, Renee Jorgensen. 2018. “The Rational Impermissibility of Accepting (Some) Racial Generalizations.” Synthese 197(online first).

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Endre Begby Cassam, Quassim. 2016. “Vice Epistemology.” The Monist 99(2): 159–180. Fricker, Elizabeth. 2006. “Testimony and Epistemic Autonomy.” In J. Lackey and E. Sosa, eds., The Epistemology of Testimony. Oxford University Press. Fricker, Miranda. 2007. Epistemic Injustice: Power and the Ethics of Knowing. Oxford University Press. Fricker, Miranda. 2016. “Fault and No-Fault Responsibility for Implicit Prejudice: A Space for Epistemic ‘Agent-Regret’.” In Michael S. Brady and Miranda Fricker, eds., The Epistemic Lives of Groups: Essays in the Epistemology of Collectives. Oxford University Press. Gardiner, Georgi. 2018. “Evidentialism and Moral Encroachment.” In Kevin McCain, ed., Believing in Accordance with the Evidence: New Essays on Evidentialism. Dordrecht: Springer. Gendler, Tamar Szabó. 2011. “On the Epistemic Costs of Implicit Bias.” Philosophical Studies 156(1): 33–63. Goldberg, Sanford. 2010. Relying on Others: An Essay in Epistemology. Oxford: Oxford University Press. Hardwig, John. 1985. “Epistemic Dependence.” Journal of Philosophy 82(7): 335–349. Intemann, Kristin. Forthcoming. “Evidence and Power: Feminist Approaches to Evidence.” This volume. Kelly, Thomas. 2009. “Evidence: Fundamental Concepts and the Phenomenal Conception.” Philosophy Compass 3(5): 933–955. Leslie, Sarah-Jane. 2008. “Generics: Acquisition and Cognition.” Philosophical Review 117(1): 1–47. Leslie, Sarah-Jane. 2015. “Generic Generalizations.” In Stanford Encyclopedia of Philosophy. Stanford: Stanford University Press. Leslie, Sarah-Jane. 2017. “The Original Sin of Cognition: Fear, Prejudice, and Generalization.” Journal of Philosophy 114(8): 393–421. Moss, Sarah. 2018. “Moral Encroachment.” Proceedings of the Aristotelian Society 118(2): 177–205. Siegel, Susanna. 2017. The Rationality of Perception. Oxford: Oxford University Press. Silva, Paul. 2018. “A Bayesian Explanation of the Irrationality of Sexist and Racist Beliefs involving Generic Content.” Syntese 197(online first). Zagzebski, Linda T. 1996. Virtues of the Mind: An Inquiry into the Nature of Virtue and the Ethical Foundations of Knowledge. Cambridge: Cambridge University Press.

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19 EVIDENCE AND BIAS Nick Hughes

Evidentialism The core claim of evidentialism is that one ought to believe what one’s evidence supports: Evidentialism: One ought to believe what one’s evidence supports. Many epistemologists think this is so obviously true as to be almost platitudinous.1 However, as it stands it doesn’t tell us much. What is evidence? When is evidence your evidence? How strongly must it support a proposition for belief to be the correct attitude to adopt? What is the evidential support relation? How should we interpret the ‘ought’ in question? What is its logical form? To whom does evidentialism apply? What is its modal profile? Does it only apply to belief, or does it also apply to other doxastic attitudes? Which ones? A fully-fledged evidentialist theory must answer these questions and many more. Thus, evidentialism is schematic. It is compatible with a wide variety of answers, each of which will give us a different evidentialist theory. This may explain its appeal. Perhaps part of the reason evidentialism is so popular is that, with so many flavours on offer, most epistemologists have been able to find at least one to their taste. To see just how flexible evidentialism is, consider two contrasting forms it could take. According to an externalist view we’ll call exacting evidentialism, one’s evidence consists of all and only those propositions one knows to be true, and one may believe that p if and only if one’s evidence entails that p: Exacting evidentialism: One’s evidence consists of all and only those propositions one knows to be true. One may believe that p if and only if one’s evidence entails that p. Since no falsehood is known and no set of truths entail a falsehood, one consequence of exacting evidentialism is that one must never believe a falsehood. Many evidentialists will be unhappy with this consequence.2 Evidentialists usually think that you ought to be rational, and that rationality is a matter of believing in accordance with your evidence.3 Since it is sometimes rational to believe falsehoods, they will say that this form of evidentialism is too demanding. 243

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Consider instead, then, an evidentialism at the other end of the spectrum. According to an internalist view we’ll call easy-going evidentialism, one’s evidence consists of a subset of one’s non-factive mental states (one’s beliefs, phenomenal states, ‘intellectual seemings’, etc.), and one may believe that p if p is more probable on one’s evidence than not-p: Easy-going evidentialism: One’s evidence consists of a subset of one’s non-factive mental states. One may believe that p if p is more probable on one’s evidence than not-p. Easy-going evidentialism does not entail that one must never believe a falsehood. In fact, it is very undemanding indeed. Suppose you believe that the coin you are about to flip is biased 51% towards heads, and none of your other non-factive mental states conflicts with this belief. Easy-going evidentialism says that you may believe that the coin will land heads even before flipping it and seeing the result. Many evidentialists will be unhappy with this consequence. Intuitively, rationality requires you to suspend judgement on how the coin will land until you see the result. For this reason, they will say, easy-going evidentialism is not demanding enough. There is a vast gulf between these two forms evidentialism could take.4 Most epistemologists, whether they are internalists or externalists, would reject both and go for something in-between. But how should we narrow down the options? In this chapter, we’ll look at how empirical work on bias in cognitive and social psychology can help us to do so, and, ultimately, whether this work motivates rejecting evidentialism altogether. As we will see, the existence of biases has far-reaching implications for epistemology, though not for the reasons one might have expected.

Bias One often-touted virtue of evidentialism is that it provides a principle for belief-formation that we are, despite all our flaws, capable of following, whilst at the same time being suitably connected to the epistemic telos of truth.5 Is that right? Empirical work on bias gives us a reason to be sceptical about the first claim. Over the last fifty years, cognitive and social psychologists have repeatedly put to the test Aristotle’s definition of man as a rational animal. Many have viewed the results as a blow to our self-satisfied self-image. According to the dominant ‘irrationalist’ narrative, empirical work shows that we are prone to a range of irrational biases in reasoning and doxastic attitude formation.6 Since a comprehensive overview of this large body of research is impossible, we will focus here on a handful of biases that should be of special interest to epistemologists, and to evidentialists in particular.

Hindsight Bias First up: hindsight bias. This is a phenomenon whereby people who know the outcome of an event judge it to be more probable on the evidence available before the outcome than do people who are ignorant of the outcome. Neal Roese and Kathleen Vohs (2012) offer an example: A voter might believe that after accepting the Democratic nomination for president in August 2008, Barack Obama’s chances of winning the U.S. presidency was about 244

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60%. After Obama’s victory in November 2008, this same voter might look back, see the victory as more predictable than it was before the outcome was known, and conclude that Obama’s chances were at least 80% at the time of the convention. Hundreds of studies have confirmed that people exhibit hindsight bias.7 It affects judgements about topics as diverse as terrorist attacks, medical diagnoses, and accounting and auditing decisions.8 It has been documented in people from a variety of cultures and across age groups.9 It is widely regarded by psychologists as irrational.

Biased Assimilation Next: biased assimilation. As Charles Lord et al. (1979) describe it, this is a tendency people have to “accept confirming evidence at face value whilst subjecting disconfirming evidence to critical evaluation, with the result that they draw undue support for their initial positions”. An example: Scott Plous (1991) selected two groups of experimental participants. The first group strongly supported the use of nuclear energy, the second group strongly opposed it. Both groups were given the same literature on the risks and rewards of nuclear energy. Each group drew support for their pre-existing views from the literature—the pronuclear-energy group judged that on balance the arguments within the literature supported its use, the anti-nuclear-energy group drew the opposite conclusion. Like hindsight bias, biased assimilation is robustly documented and widely regarded by psychologists as irrational. Biased assimilation is often thought of as one part of a broader phenomenon known as ‘confirmation bias’.

Selective Exposure Raymond Nickerson describes confirmation bias as “the seeking or interpreting of evidence in ways that are partial to existing beliefs, expectations, or a hypothesis in hand” (1998: 175). The ‘interpreting’ part is biased assimilation. The remainder—the seeking—is known as ‘selective exposure’. The observation that we prefer to gather evidence that confirms our pre-existing beliefs and avoid evidence that disconfirms them is not new. In 1620 Francis Bacon wrote that “The human understanding when it has once adopted an opinion (either as being the received opinion or as being agreeable to itself) draws all things else to support and agree with it” (2008). A retro example: Sweeney and Gruber (1984) found that relative to Undecideds and supporters of George McGovern, Richard Nixon’s supporters reported less interest in, and paid less attention to, information related to the Watergate scandal. More recently, selective exposure has been invoked to explain the existence of online echo chambers.10 As with the other biases we have looked at it is empirically well-confirmed and widely regarded as irrational.

Implicit Bias Finally: implicit bias. This is a multifaceted concept. One aspect of it is a phenomenon whereby people’s judgements are unconsciously influenced by prejudices and stereotypes.11 For example, Jennifer Saul notes that “the same CV is considered much better when it has a typically white rather than typically black name, a typically Swedish rather than typically Arab name, a typically male rather than typically female name, and so on” (2013: 244). 245

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Unsurprisingly, given its obvious ethical and political implications, implicit bias is one of the most studied and discussed human biases. Once again, beliefs formed as a result of the influence of the bias are widely taken to be irrational.

Introspection These are just a handful of a large number of biases in reasoning and doxastic attitude formation that empirical work in cognitive and social psychology appears to have uncovered. Taken at face value, this work seems to show that we aren’t nearly as good at believing what our evidence supports as many philosophers have assumed. Bad news for the Aristotelian image of man. Worse still, empirical work also suggests that we are usually quite clueless about our biases. Not because we’re lazy, but because most biases operate at a subpersonal level we have little to no introspective access to their influence on us.12 As Timothy Wilson and Nancy Brekke put it, unlike bad food “[h]uman judgements—even very bad ones—do not smell” (1994: 121). You might think that you’re an exception: others might not be able to recognise their biases, but you have a good nose, and your beliefs aren’t off. This is predictable. Studies by Emily Pronin and colleagues suggest that whilst people are reasonably good at detecting bias in others, they are, by and large, blind to the influence of their own biases.13 They hypothesise that this asymmetry can be explained by what they call ‘introspection ­illusion’—the illusion that introspection is more reliable a method of gaining knowledge of one’s thoughts, feelings, motives, intentions, and other aspects of one’s mind than it actually is. Kristoffer Ahlstrom-Vij summarises the point nicely: Since the processes that give rise to bias tend to operate on a sub-personal level, outside the scope of our introspective gaze, our search [for them] tends to come up empty. From the fact that our search comes up empty, we then infer an absence of bias—despite the fact that such a search is more or less guaranteed to come up empty, given the inaccessibility of the relevant mechanisms. (2013: 280. Emphasis in original)14 The fact that the influence of many of our biases is introspectively undetectable makes debiasing difficult. Ahlstrom-Vij identifies two hurdles. First, since people don’t see themselves as biased, they are not motivated to engage in debiasing in the first place—if it ain’t broke, why fix it? Second, even when people can be persuaded to engage in debiasing efforts there is a risk of both undercorrection and overcorrection. Studies on debiasing have shown that we are prone to both errors.15 In general, the results of work on debiasing are disappointing. It is possible to reduce (if not eradicate) the influence of certain biases, but only with time and effort, and the results are usually only temporary. There is no silver bullet.

Optimism? According to the irrationalist narrative we are riddled with all manner of biases, and there is little we can do about it. It is not difficult to find implications for evidentialism within this story. For one thing, it is hard to see how it can be squared with internalism. Ultimately, I think this is correct. Indeed, I think that unconscious biases have profound implications for the formulation of evidentialism and may even require us to give it up altogether. But 246

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before we see just why this is, it will be useful to first look at how some psychologists and philosophers have pushed back against the irrationalist narrative. Not everyone agrees that the situation is as bleak as irrationalists portray it to be. One source of resistance points to the recent replication crisis in psychology. Many of the seminal studies which kick-started the irrationalist narrative have not been successfully replicated.16 This casts some doubt on the narrative. Another does not question the studies themselves, but rather their interpretation. According to one school of thought, most closely associated with Gerd Gigerenzer and the ABC research group, many of our so-called biases should not be thought of as irrational, but rather ‘ecologically rational’—rational for creatures like ourselves with limited time and computational powers, who cannot conform to the canons of ideal rationality.17 In effect, the proposal is that the cognitive rules we employ that give rise to biases are the best rules for us to employ, given our limitations. We would do worse at achieving our epistemic goals (truth, knowledge, etc.) were we to attempt to use more reliable rules.18 This line of thought should be of interest to those engaged in non-ideal epistemology. Finally, some epistemologists have questioned the philosophical assumptions made by irrationalists. In a recent article Brian Hedden (2019) has argued that, contrary to received wisdom, hindsight bias is often a perfectly rational response to one’s evidence, and not (just) because it is ecologically rational—Hedden maintains that hindsight bias need not even constitute a violation of ideal rationality. Simplifying greatly, he argues that knowledge of an outcome often provides one with a certain kind of higher-order evidence: in particular, it provides one with evidence about the evidence that was available before the outcome. Hedden argues that correctly responding to this higher-order evidence will often lead one to display hindsight bias, and that, as a result, this ‘bias’ need not be in breach of evidentialism’s imperative. In a similar vein, Thomas Kelly (2008) and Kevin Dorst (ms.) have used sophisticated theories of higher-order evidence to push back against the idea that confirmation bias is irrational. It is worth also noting that some evidentialists will be unbothered by selective exposure in the first place. Earl Conee and Richard Feldman (2004, 2011) maintain that even if a person’s evidence only favours believing that p because they avoided evidence against p, the resulting belief that p is still epistemically rational. This is because they regard norms of evidence-gathering as practical, rather than epistemic norms (Kelly agrees). Hence, they will deny that a propensity for selective exposure casts doubt on our ability to conform with evidentialism. Evidentialism, they will say, is a thesis about what you should believe given the evidence you actually have; not about what evidence you should have. Finally, Bernhard Salow (2017) has argued that it is impossible to intentionally, knowingly, seek out confirming evidence and avoid disconfirming evidence. However, this is compatible with the possibility of unintentionally, unwittingly, doing so, as Salow himself acknowledges.

Possibility None of Hedden, Kelly, or Dorst would claim that they have debunked the irrationalist narrative. They do not claim to have shown that every purported cognitive bias is, or could be, epistemically rational. Nor do they claim that the biases they discuss are necessarily rational; only that they can be under certain circumstances. Even if we accept Hedden’s arguments, it may be that our actual hindsight judgements do not normally fit with the evidence because we systematically overestimate the import of the higher-order evidence. 247

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Similarly, even if we accept Kelly and Dorst’s arguments it may be that our actual tendency to seek confirming evidence over disconfirming evidence is too pronounced, or that we give too little weight to disconfirming evidence and too much weight to confirming evidence, with the result that we violate the evidentialist imperative. Nevertheless, this work does at least call the irrationalist narrative into question. Arguably, it shows that psychologists have been philosophically naïve. When we also take into account the replication crisis and alternative ‘ecological’ interpretations of the data, perhaps the most reasonable stance to take towards the irrationalist narrative is to suspend judgement. Maybe it is correct, but the case has not yet been decisively made. Does this mean that reflection on cognitive biases cannot tell us anything about the formulation and prospects of evidentialism? Not necessarily. To see why, we need to consider its modal profile. Proponents of the view are not always clear on this, but there are good reasons to think that if evidentialism is true, it is necessarily true. Otherwise a lot of the literature would be hard to make sense of. It is difficult to see how modally remote worlds populated by envatted agents, evil epistemic demons, Boltzmann brains, philosophical zombies, infallible oracles, and the like could tell us anything about evidentialism were it merely contingently true: true for us in the actual world but not necessarily true for other agents in other worlds. These worlds, being modally remote, would simply be irrelevant. Yet, evidentialists do not treat them as irrelevant; they go to great lengths to accommodate them.19 This raises the question of what kind of necessity evidentialism is supposed to have. The obvious answer is: metaphysical. But whatever it is, the fact that it has at least enough modal strength to encompass these exotic worlds means that we need not wait for psychology to vindicate or debunk the irrationalist narrative to make use of it in shaping and assessing evidentialism. All we need is for the narrative to describe a possibility. And that it surely does. Whether or not we are actually prone to hindsight, confirmation, and implicit bias, we could have been, and these biases could have operated in a way that leads to violations of evidentialism. Moreover, their influence on us could have been introspectively inaccessible. With this in mind, consider a possible biased agent, Blixa. Let us stipulate that Blixa is unconsciously influenced by hindsight, confirmation, and implicit bias, with the result that he often unwittingly forms irrational beliefs that are not supported by his evidence—he goes beyond anything that ecological rationality or Hedden, Kelly, and Dorst’s, arguments would license. Blixa might be an actual person. But even if he is not, he is a possible person, and that suffices for our purposes. What does the possibility of someone like Blixa tell us about evidentialism?

Internalism Firstly, it tells us that access internalist versions of evidentialism are untenable. According to access internalists, one is always in a position to know which propositions it is rational for one to believe at any given time.20 Many of Blixa’s beliefs are irrational in virtue of their biased etiologies. But since the influence of these biases is unconscious, Blixa is not in a position to know that they are irrational. It follows that access internalism is false.21 Call this ‘the problem of inaccessibility’. The possibility of Blixa also causes trouble for other internalist evidentialisms. According to internalist ‘mentalism’, the rationality of a belief supervenes on one’s non-factive mental states.22 Plugging this idea into the evidentialist schema, we get the result that one’s 248

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evidence comprises entirely one’s non-factive mental states and that what one ought to believe is determined entirely by these states. It is not clear how this proposal can be reconciled with the idea that whether a belief is the result of bias can affect its rational standing. Reconciliation requires proponents of mentalism to show that hindsight, confirmation, and implicit bias can be adequately described solely in terms of non-factive mental states. It is far from obvious that this can be done. Psychologists working on bias do not take evidence to consist of non-factive mental states. Rather, they almost always (implicitly) take it to consist of worldly facts. So, any internalist re-description of the relevant biases will need to ‘internalise’ the evidence. The worry is that this process of internalisation will result in nonfactive mental states that are caused by bias counting as evidence. For example, internalists often take an agent’s evidence to consist in, inter alia, how things ‘seem’ or ‘appear’ to the agent. There is a risk of cases in which it seems or appears to the agent that p only because of the influence of bias. A study by B. Keith Payne (2001) found that participants primed with pictures of Black faces were more likely to incorrectly identify pictures of tools as guns than were participants primed with pictures of white faces. Payne hypothesises that this can be explained by the influence of implicit bias. Did it seem or appear to the participants primed with Black faces that the picture is of a gun? The natural answer is yes. If so, then this study illustrates the problem. Call it the ‘problem of laundered biases’.23 Internalist evidentialism faces another, related, problem (one that, as we will see, it shares with certain kinds of externalist evidentialism). Suppose that, unconsciously wanting to believe that people like him, Blixa engages in selective exposure: he gathers up all the evidence he can to support this belief and avoids acquiring counterevidence.24 Is it then rational for Blixa to believe that people like him? Arguably not. The resulting belief is tainted by the means by which the evidence for it was acquired. To avoid having to say that the belief is rational, evidentialists will need to complicate their view. In addition to the condition that one must believe what one’s evidence supports they will need to add a further condition: one must not selectively expose oneself to evidence.25 Insofar as the motivation for introducing this condition is ad hoc, this is a theoretical cost; the condition is, it seems, not introduced as a natural extension of the core evidentialist idea, but rather simply to patch up the theory against criticism. Call this the ‘problem of selective exposure’. As mentioned earlier, some evidentialists will insist that Blixa’s belief is rational, reasoning that the rationality of evidence-gathering is a practical rather than an epistemic matter. But there are reasons to be sceptical of this response. Later on, we will look at a theory of epistemic rationality (‘dispositionalism’) which suggests that it presents us with a false dichotomy.

Rationality Internalists might bite the bullet, of course. They might argue that the influence of unconscious biases has no effect on the rational standing of a belief: biased beliefs can nevertheless be rational beliefs. The claim would not be that such beliefs can be rational because they are ecologically rational (Gigerenzer’s line), nor because the alleged ‘biases’ are no such thing (Hedden, Kelly, and Dorst’s line). Rather, internalists might acknowledge that biased beliefs are epistemically suboptimal but maintain that since the influence of the relevant biases is unconscious it cannot make a difference to rationality, nor, ipso facto, to what one ought to believe. They might, for instance, insist that seemings and appearances with biased etiologies are evidence, and that beliefs based on them are rational in virtue of being supported by the evidence. 249

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As uncomfortable a position as this is to adopt, a certain kind of internalist may be drawn to it. Many philosophers see a tight connection between obligation, blame, and control. According to one broadly Kantian line of thought, at least as popular in ethics as it is in epistemology, if one is blameless for φ-ing, it cannot be that one ought to have done anything other than φ, and an outcome that is beyond one’s control, no matter how unfortunate, is not an outcome for which one can be blamed. It follows that it is always in one’s control to do as one ought to. Internalists who endorse this line of thought and maintain that one ought to be rational will infer that one cannot be blamelessly irrational, and that the rationality of a belief cannot depend on factors beyond one’s control. Since unconscious influences on belief are, in some fairly strong sense, outside of one’s control, these internalists will say that they cannot make a difference to rationality. And since they cannot make a difference to rationality, they cannot make a difference to what one ought to believe. The reasoning here is suspect in a number of ways. Here we will only look at its implausible consequences. Consider these passages from a short story by Vladimir Nabokov:26 What he really wanted to do was to tear a hole in his world and escape. ... “Referential mania,” Herman Brink had called it. In these very rare cases the patient imagines that everything happening around him is a veiled reference to his personality and existence. ... Phenomenal nature shadows him wherever he goes. Clouds in the staring sky transmit to one another, by means of slow signs, incredibly detailed information regarding him. His inmost thoughts are discussed at nightfall, in manual alphabet, by darkly gesticulating trees. Pebbles or stains or sun flecks form patterns representing in some awful way messages which he must intercept. Everything is a cipher and of everything he is the theme. Some of the spies are detached observers, such are glass surfaces and still pools; others, such as coats in store windows, are prejudiced witnesses, lynchers at heart; others again (running water, storms) are hysterical to the point of insanity, have a distorted opinion of him and grotesquely misinterpret his actions. He must be always on his guard and devote every minute and module of life to the decoding of the undulation of things.27 The correct response here is not blame, but pity. This is, in part, because the man has no control over his delusions—he is more a victim of them than he is their architect. Yet it is perfectly clear that he is profoundly irrational. There is more to rationality than mere blamelessness. So there is no motivation for rejecting the idea that unconscious biases can affect the rationality of belief on the grounds that such biases are beyond our control.

Externalism Internalist versions of evidentialism have a hard time accounting for the irrationality of biased beliefs. Do externalist versions fare better? At first glance at least some of them seem to. Consider, for instance, exacting evidentialism. A reminder, it says that: One’s evidence consists of all and only those propositions one knows to be true. One may believe that p iff one’s evidence entails that p. Exacting evidentialism does not by itself deliver the result that biased beliefs are irrational. This is because it is about the conditions under which one has justification to believe that p, 250

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not about the conditions under which a belief that p is justified. In other words, it is about propositional rather than doxastic justification. For all Exacting evidentialism says, one’s belief that p may be rational even though it is the result of bias, provided that one’s knowledge entails that p, even if one’s belief isn’t based on that entailing knowledge. However, proponents of exacting evidentialism will not accept this verdict. They will supplement the view with a theory of doxastic justification. An obvious supplement is the theory that one’s belief is justified just in case it is knowledge.28 And this view—the ‘knowledge norm of belief’—can easily explain why bias-infected beliefs are not rational: a biased etiology usually precludes a belief from being knowledge. At least one version of externalist evidentialism appears to be able to account for the irrationality of biased beliefs, then. Externalists should not be too sanguine, however. As we have already noted, most epistemologists will be unhappy with exacting evidentialism, the knowledge norm of belief, and similar truth-entailing views. If anything is consensus in epistemology, it is that false beliefs can be rational. If you mistakenly believe that the white table in front of you is red because, unbeknownst to you, it is illuminated by a red light source, then you are no less rational than your counterpart in the next room who is looking at a red table. If exacting evidentialism and the knowledge norm are taken to be claims about rationality, then, they will be roundly rejected. If they are divorced from rationality and merely taken to be claims about what one ought to believe, then most epistemologists will reject them on the grounds that one ought to be rational.29 This raises a question: is there a plausible externalist evidentialism that explains why biased beliefs are irrational whilst at the same time delivering the result that false beliefs can be rational? We should not assume a positive answer. It is incumbent on externalist evidentialists to show us that there is. Call this the ‘problem of false beliefs’. Finally, consider again one of the problems that internalist evidentialism faces: the problem of selective exposure. An evidentialism according to which one should only believe what one knows doesn’t face this problem, since a belief that is the product of selective exposure to the evidence will not usually be a knowledgeable belief. However, a less demanding externalist evidentialism will face the problem. Take, for example, a view according to which one’s evidence consists of one’s knowledge, and one may believe that p if and only if p is sufficiently probable on one’s evidence above some threshold n =