A Historical and Systematic Perspective on A Priori Knowledge and Justification 3031068734, 9783031068737

Citation preview

Philosophical Studies Series

Ivette Fred-Rivera

A Historical and Systematic Perspective on A Priori Knowledge and Justification

Philosophical Studies Series Editor-in-Chief Mariarosaria Taddeo, Oxford Internet Institute University of Oxford Oxford, UK Advisory Editors Lynne Baker, Department of Philosophy University of Massachusetts Amherst, USA Stewart Cohen, Arizona State University Tempe, AZ, USA Radu Bogdan, Department of Philosophy Tulane University New Orleans, LA, USA Marian David, Karl-Franzens-Universität Graz, Austria John Fischer, University of California, Riverside Riverside, CA, USA Keith Lehrer, University Of Arizona Tucson, AZ, USA Denise Meyerson, Macquarie University Sydney, Australia Francois Recanati, Ecole Normale Supérieure Institut Jean Nicod Paris, France Mark Sainsbury, University of Texas at Austin Austin, TX, USA Barry Smith, State University of New York at Buffalo Buffalo, NY, USA Linda Zagzebski, Department of Philosophy University of Oklahoma Norman, OK, USA

Philosophical Studies Series aims to provide a forum for the best current research in contemporary philosophy broadly conceived, its methodologies, and applications. Since Wilfrid Sellars and Keith Lehrer founded the series in 1974, the book series has welcomed a wide variety of different approaches, and every effort is made to maintain this pluralism, not for its own sake, but in order to represent the many fruitful and illuminating ways of addressing philosophical questions and investigating related applications and disciplines. The book series is interested in classical topics of all branches of philosophy including, but not limited to: • • • • • • • •

Ethics Epistemology Logic Philosophy of language Philosophy of logic Philosophy of mind Philosophy of religion Philosophy of science

Special attention is paid to studies that focus on: • the interplay of empirical and philosophical viewpoints • the implications and consequences of conceptual phenomena for research as well as for society • philosophies of specific sciences, such as philosophy of biology, philosophy of chemistry, philosophy of computer science, philosophy of information, philosophy of neuroscience, philosophy of physics, or philosophy of technology; and • contributions to the formal (logical, set-theoretical, mathematical, information-­ theoretical, decision-theoretical, etc.) methodology of sciences. Likewise, the applications of conceptual and methodological investigations to applied sciences as well as social and technological phenomena are strongly encouraged. Philosophical Studies Series welcomes historically informed research, but privileges philosophical theories and the discussion of contemporary issues rather than purely scholarly investigations into the history of ideas or authors. Besides monographs, Philosophical Studies Series publishes thematically unified anthologies, selected papers from relevant conferences, and edited volumes with a well-defined topical focus inside the aim and scope of the book series. The contributions in the volumes are expected to be focused and structurally organized in accordance with the central theme(s), and are tied together by an editorial introduction. Volumes are completed by extensive bibliographies. The series discourages the submission of manuscripts that contain reprints of previous published material and/or manuscripts that are below 160 pages/88,000 words. For inquiries and submission of proposals authors can contact the editor-in-chief Mariarosaria Taddeo via: [email protected] More information about this series at https://link.springer.com/bookseries/6459

Ivette Fred-Rivera

A Historical and Systematic Perspective on A Priori Knowledge and Justification

Ivette Fred-Rivera Department of Humanities, Faculty of General Studies University of Puerto Rico at Río Piedras San Juan, Puerto Rico

ISSN 0921-8599     ISSN 2542-8349 (electronic) Philosophical Studies Series ISBN 978-3-031-06873-7    ISBN 978-3-031-06874-4 (eBook) https://doi.org/10.1007/978-3-031-06874-4 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

For Georgina and Juana

Preface

I would like to express my deep gratitude to Arnold Koslow for his very detailed and helpful comments. It was indeed Koslow who suggested me to work on a priori knowledge and on Hale. I would also express my great gratefulness to the memory of Robert S. Cohen and Marx Wartofsky. They were very supportive of my work. Their wisdom, sense of humor, and beauty of spirit were always very inspiring to me. I would like to express my deepest sense of gratitude and appreciation to the memory of Bob Hale and to Crispin Wright. Their kindness, generosity, and intellectual encouragement, I so much value. What has motivated me the most in finishing this book during this 2020 pandemic was the memory of the love, strength, and support I received from my mother: Georgina Rivera-Rodríguez. I also have an older recognition that goes back to my childhood: I want to thank, with all my heart, my great grandmother: Juana Rodríguez-­ Figueroa. The memory of her unconditional love, temperance, and thoughtfulness has been a constant source of inspiration and love. My greatest debt is to them. San Juan, Puerto Rico

Ivette Fred-Rivera

vii

General Introduction: The Problem of A Priori Knowledge

Two important tasks in the epistemology of a priori knowledge occupy me in this book. First, the most urgent: to provide an explicit characterization of the notion of “a priori knowledge” and related epistemological notions. This task is the most urgent since we have first to clarify what we are talking about before addressing important questions about a priori knowledge. Second, an equally important task though not as urgent as the first task since without the first, the second cannot be settled: I come up with a plausible notion of infallibility which is compatible with the fact that we are fallible knowers (in that compatibility resides precisely its plausibility) and offer an answer to the question whether infallibility, properly understood, has a place only in the realm of a priori knowledge – in other words, whether infallibility is an a priori matter. The notion of a priori knowledge, as it is discussed today, stems from the epistemology of Kant.1 Kant distinguished between two kinds of knowledge: a posteriori knowledge and a priori knowledge. A posteriori knowledge is knowledge whose justification must be based upon experience. (It is also called empirical knowledge.) A priori knowledge is knowledge whose justification need not rest on experience. (It is also referred to as knowledge justifiable independently of experience.)2 Now Kant recognized that some empirical knowledge is required in order to obtain even a priori knowledge, since, for him, all knowledge begins with experience. But once we have the experience required to learn the required concepts, experience does not play any further role. Mathematics and logic are considered paradigms of disciplines constituted by a priori knowledge. In addition, many sentences the content of which is neither purely logical nor purely mathematical are said to be known a priori: “ All bachelors are unmarried men,”, “All bodies are extended” and “Nothing is simultaneously red and green all over.”

 Kant, Immanuel. Critique of Pure Reason.  Translated by Norman Kemp Smith. New  York: St. Martin’s, 1956. 2  Ibid, Introduction, B2, pp. 42–43. 1

ix

x

General Introduction: The Problem of A Priori Knowledge

The notion of a priori knowledge is one of those notions that has been widely utilized by philosophers despite the fact that it is terribly vague. Before deciding if the notion of a priori knowledge is vacuous or not, important or not, coherent or not, let’s try to get clear about what the a priori amounts to. In order to clarify the notion of a priori knowledge, one has to explain what the “independence of experience” that is characteristic of it consists in; that is, one has to provide an illuminating account of the kind of independence of experience that is involved. It is a separate and subsequent issue whether some of our knowledge is indeed a priori. In this book, although I do in fact believe that a priori knowledge is possible, I shall give no argument for that. My concern will be rather, on the assumption that there is a priori knowledge, to say what it consists in: what marks it as a priori. In order to get clear about the property of being a priori we have to settle what “a priori” primarily applies to. I believe that an essential insight here is that the notion of an a priori justification is the primary notion that needs to be characterized in the epistemology of a priori knowledge. My basic proposal is that the distinction between a priori knowledge and empirical knowledge is grounded first and foremost in a distinction between ways in which we can obtain knowledge, and only secondarily in differences in the products. Furthermore, any adequate account of the way in which a priori knowledge is independent of experience has to allow room for a degree of dependence on experience: certain experiences may be necessary to equip ourselves with the concepts needed if we are to entertain a candidate for a priori knowledge in the first place – or indeed, in the case of inferential a priori knowledge, if we are to understand the premises for the inference in question.3 Let me indicate what kind of an account I am seeking. It is necessary for any account of a priori knowledge to be able to satisfy most (if not all) of the following adequacy conditions. In my view, the conditions for such an adequate account are: (1) It has to make sense. (2) It has to be an account that involves no notions which are problematic or, at least, the minimal number of notions which are so. (3) It has to be an account that is not narrowly circular, that is, the notions involved in the account can be related – of course, how could they be useful to characterize the notion in question if they had no connection with it at all – but should not be so close that the account can shed (some) light on the nature of a priori knowledge.

 Basic a priori knowledge is knowledge which is not obtained by any inference from other premises. For example, elementary arithmetical truths like “2 + 2 = 4” and trivially analytic truths like “All bachelors are unmarried men” are considered items of basic a priori knowledge. In contrast, inferential a priori knowledge is knowledge obtain by inference from premises already known a priori. For example, the conclusion of an argument constitutes inferential a priori knowledge given that the premises in the inference are already known a priori. 3

General Introduction: The Problem of A Priori Knowledge

xi

(4) The account should accommodate most, if not all, the truths we usually consider a priori, that is, it should get the extension of a priori truths right.4 (5) It has to be an account that explains the possibility of a priori knowledge, and, in so doing, respects its problematic nature. (6) The account ought to illuminate the issue of the certainty of a priori knowledge. If a priori knowledge is certain: where does the certainty come from? Why are these conditions of adequacy desirable? I don’t claim that they are exhaustive, but they certainly reflect the salient concerns in the philosophy of a priori knowledge. Furthermore, I do not intend to provide an answer to all of them in this book, but will address them in my account, as best as I possibly can. I will provide a detailed and comprehensive discussion about the problem of a priori knowledge from a historical as well as a systematic point of view. Usually philosophers opt one way or the other, but not both. Given that a priori knowledge is one of the basic problems of philosophy, it has numerous and important ramifications in different philosophical areas, and which I am unable to discuss in this book. I won’t be exhaustive here but rather will be concentrated only on views directly related to my approach. The book consists of three parts. The first part consists of three chapters followed by a conclusion. Chapter 1 discusses Kant’s views about a priori knowledge. Kant was the first philosopher who most systematically worked on the notion of a priori knowledge. His views will be examined in detail and some of the questions and responses we have inherited from his analysis of the notion. In particular, I find very helpful to try to answer the question whether Kant thought, or his view implies, that a priori knowledge involves (entails) some sort of infallibility. The most important questions of the first chapter are: (a) whether Kant succeeded in characterizing the notion of a priori knowledge, and, therefore, what he meant by the notion of “experience independence” distinctive of a priori knowledge; and (b) whether Kant considered a priori knowledge to involve some sort of infallibility. In the second chapter, I shall closely examine Quine’s criticisms of the notion of a priori knowledge. The relationship between his notions of a prioricity and analyticity will be examined, and how the attack on analyticity affects the possibility of a priori knowledge. There is ample justification to examine Quine’s position: for, first, his discussion of these matters has been enormously influential, and, second, it is a discussion which leaves its opponents – defenders of a prioricity – with interesting lines of investigation still open. I argue in this chapter for two main points: first that a priori knowledge does not have to be conceived as infallible (and so as requiring unrevisability as Quine requires a priori knowledge to do), and second that the scope of revision of items of a priori knowledge (i.e. of a priori warrants and a priori statements) might include empirical revision.

 It is understood that there is a certain looseness in this condition because of the disagreement among philosophers as to which are the a priori truths. 4

xii

General Introduction: The Problem of A Priori Knowledge

The focus of the third chapter is Putnam’s various views about the connection between a priori knowledge and the issue of revisability/unrevisability. In this chapter I shall elaborate on issues that, according to Putnam, Quine suggests. Also I discuss Putnam’s views in their own merit since they shed some light on important topics about a priori knowledge. In this chapter, I analyze very important papers of Putnam, explain how he changes his views on the topic, and evaluate them as a whole. Putnam’s position is very interesting because it is dialectical. He is in a middle position. He is very critical of the traditional notion of the a priori as entailing unrevisability. However, he also recognizes that there is at least one a priori truth, a weak formulation of the principle of non-contradiction (“Not every statement is both true and false”), taken as a principle which operates as a norm for any conceivable rationality. Part II is concerned with my work on Bob Hale. Hale’s work5 on a priori knowledge provides a very useful departing point in my project. He is the first philosopher who most carefully has scrutinized Philip Kitcher’s important challenges to a priori knowledge. However, Hale’s own important contributions to a priori knowledge – i.e., his criticisms of Kitcher and his own proposals  – have not been practically analyzed. His discussion bears directly on a number of important issues in connection with the notion. For instance, he offers proposals for the characterization of the notion, forcibly argues for the compatibility of a priori knowledge and revision, addresses the issue of the non-falsifiability of a priori statements, and – given the mere fact that we are fallible creatures prone to make mistakes everywhere  – he does remain neutral for any possibility of infallibility, properly conceived, in the a priori realm. Given that Hale’s work bears directly on the issues I am interested, it is quite relevant to discuss his work in detail. The third part consists of two chapters followed by a conclusion. In Chap. 9, I will offer more illuminating (explicit) characterizations of the notions of “a priori knowledge,” “warrant,” and “method”; will provide a glossary of terms; and will proceed to evaluate the suggestions analyzing whether the truths we usually regard as a priori come out as a priori on my account. In Chap. 10, I will try to make sense of the concept of infallibility among others. I shall argue that the properties “a prioricity” and “infallibility” are primarily properties of methods. I will elaborate on the thesis that infallibility is a matter of methods alone and then will address the important issue whether there are empirical methods which are infallible in my sense. In the concluding section, I shall recapitulate the most important theses of the chapter and book.

 Hale, Bob. Abstract Objects.  Oxford: Basil Blackwell Ltd, Chapter Six “Platonism and Knowledge II: Non-Empirical Knowledge”, pp. 123–48, 1987. 5

Acknowledgments

I would like to thank the original publisher for granting me permission to use all or part of the articles: “On Wright’s characterization of the A Priori,” Diálogos, 73, pp. 127–38, 1999; “Putnam’s views on a priori knowledge and revision,” Diálogos, 75, pp. 123–43, 2000; and “Philip Kitcher’s views on a priori knowledge,” Diálogos, 88, pp. 119–133, 2006.

xiii

Contents

Part I  Kant, Quine and Putnam on The A Priori 1

 Kant’s Views on A Priori Knowledge ����������������������������������������������������    3 1.1 Kant’s Main Concern in the Critique������������������������������������������������    4 1.2 Is There A Priori Knowledge? How Is A Priori Knowledge Possible? ������������������������������������������������������������������������������������������    8 1.3 What Does “A Priori” Mean? Does “A Priori” Mean “Precedence in Time”?������������������������������������������������������������������������������������������   10 1.4 Was Kant an Innatist? ����������������������������������������������������������������������   12 1.5 Necessity and Universality as the Criteria of A Priori Knowledge������   13 1.6 On Kant’s Conception of Necessity��������������������������������������������������   15 1.7 Is Kant’s Definition of A Prioricity a Purely Negative One? Did Kant Succeed in Characterizing Both A Priori Knowledge and the Class of A Priori Truths?������������������������������������������������������   18 1.8 Does A Priori Knowledge Involve Some Sort of Infallibility? ��������   20 1.8.1 Kant’s Views ������������������������������������������������������������������������   20 1.8.2 Kitcher’s and Friedman’s Views on Kant������������������������������   26 1.9 Conclusion����������������������������������������������������������������������������������������   30 References��������������������������������������������������������������������������������������������������   32

2

 Quine’s Views on A Priori Knowledge ��������������������������������������������������   35 2.1 The Problem of A Priori Knowledge������������������������������������������������   35 2.2 Quine’s Empiricist Attack on the Notion of A Priori Knowledge������   38 2.3 Does Quine Distinguish Between the Notions of A Prioricity and Analyticity?��������������������������������������������������������������������������������   40 2.3.1 Quine’s View of A Prioricity Before “Two Dogmas” ����������   42 2.4 How to Understand Revision of A Priori Statements? Can A Priori Statements Be Falsifiable by Experience? ������������������   45 2.5 Can Epistemological Holism Be Reconciled with the Belief in A Prioricity?����������������������������������������������������������������������������������   50

xv

xvi

Contents

2.6 Conclusion����������������������������������������������������������������������������������������   51 References��������������������������������������������������������������������������������������������������   51 3

 Putnam’s Views on A Priori Knowledge������������������������������������������������   55 3.1 Putnam in “‘Two Dogmas’ Revisited”����������������������������������������������   56 3.2 Putnam in “There Is At Least One A Priori Truth”��������������������������   57 3.3 Putnam in “Analyticity and Apriority”���������������������������������������������   59 3.4 Putnam in “Possibility and Necessity” ��������������������������������������������   61 3.5 Some Remarks on “‘Two Dogmas’ Revisited”��������������������������������   64 3.6 Some Remarks on “There Is At Least One A Priori Truth”��������������   65 3.7 Some Remarks on “Analyticity and Apriority”��������������������������������   67 3.8 Some Remarks on “Possibility and Necessity”��������������������������������   68 3.9 Conclusion����������������������������������������������������������������������������������������   69 Conclusion of Part I ����������������������������������������������������������������������������������   71 References��������������������������������������������������������������������������������������������������   73

Part II  Hale’s Views on A Priori Knowledge and Revision 4

 Hale’s General Epistemological Views Regarding A Priori Knowledge������������������������������������������������������������������������������������������������   77

5

 Kitcher’s Views on A Priori Knowledge������������������������������������������������   83 5.1 Kitcher’s Account of the Notion of A Priori Knowledge������������������   85 5.2 On Kitcher’s Thesis That A Priori Knowledge Is Incompatible with Revision������������������������������������������������������������������������������������   86 5.3 The Issue of Long Proofs or Calculations����������������������������������������   87 5.4 Knowledge Obtained by “Non-empirical Processes” ����������������������   88 5.5 Some Remarks on Kitcher’s Views��������������������������������������������������   89

6

 Hale’s Reactions to Kitcher’s Views ������������������������������������������������������   93 6.1 Hale’s Claim That A Priori Knowledge Is Compatible with Revision��������������������������������������������������������������������������������������������   93 6.2 The Issue of Long Proofs Again and the Role of Memory ��������������   96 6.3 Some Remarks on Hale’s Attack on Kitcher������������������������������������   98 6.4 Hale’s Remarks on Kant ������������������������������������������������������������������  100 6.5 Some Remarks on the Role of Memory in Our Acquisition of A Priori Knowledge����������������������������������������������������������������������  101

7

 “Pure” Hale and Related Issues��������������������������������������������������������������  103 7.1 Revision and Defeasibility of Items of A Priori Knowledge������������  103 7.1.1 Casullos’s Interpretation of Hale’s Views ����������������������������  106 7.2 Empirical Indefeasibility as a Hallmark of the A Priori ������������������  109 7.2.1 Some Remarks About Hale’s Views on the Defeasibility of Items of A Priori Knowledge��������������������������������������������  112 7.2.2 Field’s Default Propositions��������������������������������������������������  115

Contents

xvii

7.2.3 Kitcher on Field’s and Friedman’s Claim About the Empirical Indefeasibility of the A Priori������������������������������  119 7.2.4 Wright’s Entitlements, Warrants for Free ����������������������������  122 7.2.5 Roles of Experience in A Priori Knowledge������������������������  132 7.3 Hale’s Assertions on A Priori Knowledge����������������������������������������  141 7.4 Hale’s Preferred Notion of A Priori Knowledge in Abstract Objects������������������������������������������������������������������������������  143 8

 Critical Examination of Hale’s Views on A Priori Knowledge������������  147 8.1 A Difficulty Involved in Hale’s Proposal in Abstract Objects����������  147 8.1.1 Hale’s First Reaction to My Circularity Objection to (1) (and (11)) ������������������������������������������������������������������������������  148 8.1.2 Some Developments of (1) ��������������������������������������������������  149 8.1.3 Problems with (12) and (13)��������������������������������������������������  151 8.2 A Revised Account���������������������������������������������������������������������������  153 8.2.1 Some Remarks About (H)����������������������������������������������������  153 8.2.2 Problems with (H)����������������������������������������������������������������  158 8.3 Is It Coherent to Talk of Revision in Connection with A Priori Knowledge?��������������������������������������������������������������������������������������  160 8.3.1 Some Remarks on Revision and A Prioricity ����������������������  162 Conclusion of Part II����������������������������������������������������������������������������������  168 References��������������������������������������������������������������������������������������������������  170

Part III  A Prioricity and Infallibility 9

What Is the A Priori? ������������������������������������������������������������������������������  175 9.1 Wright’s Proposal������������������������������������������������������������������������������  175 9.2 Characterizations of the Notions of “A Priori Method”, “A Priori Warrant” and “A Priori Knowledge” ��������������������������������  176 9.3 What Is “Experience”?����������������������������������������������������������������������  180 9.4 Is the Sensory Deprivation Suggestion Any Good?��������������������������  183 9.5 On Basic A Priori Knowledge����������������������������������������������������������  185

10 A  Priori Knowledge and Infallibility������������������������������������������������������  187 10.1 Glossary������������������������������������������������������������������������������������������  187 10.2 Theses on Infallibility ��������������������������������������������������������������������  192 10.3 Some Clarifications������������������������������������������������������������������������  195 10.4 Helpful Lists������������������������������������������������������������������������������������  199 10.5 The Contingent A Priori������������������������������������������������������������������  199 10.6 Is Infallibility Exclusively a Property of Certain Methods? ����������  203 10.7 Which Methods Are Infallible?������������������������������������������������������  205

xviii

Contents

Conclusion��������������������������������������������������������������������������������������������������������  211 References ��������������������������������������������������������������������������������������������������������  219 Author Index����������������������������������������������������������������������������������������������������  225 Subject Index����������������������������������������������������������������������������������������������������  227

About the Author

Ivette Fred-Rivera  studied her Master’s degree in Philosophy at the University of Puerto Rico, Río Piedras. Her PhD is from the Philosophy Department of the City University of New York Graduate Center. She is a professor at the University of Puerto Rico, Río Piedras, since 1998. She has researched and lectured in Europe and India. Ivette is also a world traveler and a photographer, with a great passion for art and culture, especially from Asia. She has published on philosophy and art. She is editor (with Jessica Leech) of Being Necessary: Themes of Ontology and Modality from the Work of Bob Hale, Oxford University Press, 2018.

xix

Part I

Kant, Quine and Putnam on The A Priori

The first part consists of three chapters followed by a conclusion. Chapter one discusses Kant’s views about a priori knowledge. Kant was the first philosopher who most systematically worked on the notion of a priori knowledge. His views will be examined in detail and some of the questions and responses we have inherited from his analysis of the notion. In particular, I find very helpful to try to answer the question whether Kant thought, or his view implies, that a priori knowledge involves (entails) some sort of infallibility. In the second chapter I shall closely examine Quine’s criticisms of the notion of a priori knowledge. The relationship between his notions of a prioricity and analyticity will be examined, and how the attack on analyticity affects the possibility of a priori knowledge. There is ample justification to examine Quine’s position: for, first, his discussion of these matters has been enormously influential, and, second, it is a discussion which leaves its opponents - defenders of a prioricity - with interesting lines of investigation still open. The focus of the third chapter is Putnam’s various views about the connection between a priori knowledge and the issue of revisability/unrevisability. In this chapter I shall elaborate on issues that, according to Putnam, Quine suggests. Also I discuss Putnam’s views in their own merit since they shed some light on important topics about a priori knowledge. In this chapter, I analyze very important papers of Putnam, explain how he changes his views on the topic, and evaluate them as a whole.

Chapter 1

Kant’s Views on A Priori Knowledge

Abstract  The task of this chapter is to closely examine Kant’s views on a priori knowledge. His views will be examined in detail and some of the questions and responses we have inherited from his analysis of the notion. In particular, I find very helpful to try to answer the question whether Kant thought, or his view implies, that a priori knowledge involves (entails) some sort of infallibility. The most important questions of the first chapter are: (a) whether Kant succeeded in characterizing the notion of a priori knowledge, and, therefore, what did exactly he mean by the notion of “experience independence” distinctive of a priori knowledge; and (b) whether Kant considered a priori knowledge to involve some sort of infallibility. Keywords  A priori · Infallibility · Intuition · Synthetic a priori knowledge · Necessity Kant was the first philosopher who more systematically worked on a priori knowledge. Undoubtedly, Kant is also the philosopher who most profoundly has thought about the notion of a priori knowledge. The depth, the terminology, the breath of his reflections, the distance from us, are challenging to the contemporary reader. Such difficulty, though, should not impede us from studying, carefully, his work.1 I can’t discuss exhaustively Kant’s philosophy of a priori knowledge in this chapter. I will discuss his views that relate more directly to mine. He gave more than one use to the term “a priori” applying it to judgments, categories, intuitions, for example. Since my focus is on (propositional) a priori knowledge, I will concentrate on the issues strictly related to Kant’s application of the term “a priori” to judgments. My main approach to Kant will be more systematic rather than historical, or mainly historical, though I tried to respect the historical Kant. What I intend to do is  I consider that Michael Friedman, Charles Parsons and Jaakko Hintikka have helped, enormously, to bring Kant’s philosophy of the a priori to the contemporary debate.  We owe them this achievement.  1

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 I. Fred-Rivera, A Historical and Systematic Perspective on A Priori Knowledge and Justification, Philosophical Studies Series 151, https://doi.org/10.1007/978-3-031-06874-4_1

3

4

1  Kant’s Views on A Priori Knowledge

to suggest a viable reading of his views on a priori knowledge. A central question in our discussion is whether he considered a priori knowledge to involve some sort of infallibility. I begin with a brief introduction of what I take to be Kant’s main concern in the Critique of Pure Reason (henceforth, Critique),2 followed by eight sections. In the second section I consider the question whether there is a priori knowledge for Kant. In the third section I discuss what he meant by “independence of experience” in connection with a priori knowledge. Section four deals with the question whether Kant was an innatist. Section five is devoted to a close examination of his criteria of universality and necessity for a priori knowledge. The sixth section is concerned with the nature of necessity in Kant. The seventh section takes up the question whether his notion of a priori knowledge is a purely “negative” one, i.e., whether it is adequately characterized as non-empirical or non-a posteriori. In section eight I examine the important issue whether Kant considered a priori knowledge as involving a notion of infallibility. Section nine includes the concluding remarks.

1.1 Kant’s Main Concern in the Critique I want to make clear that I will only be giving the following overview in order to set the stage of my own discussion, and that I am aware that there are many aspects of the Kant’s aims in the Critique which I will not be discussing at all. It is quite possible that many readers of Kant would not agree with my characterization of Kant’s aims. What are then the fundamental aims I have in this chapter? To set out my reading of Kant, to briefly characterize his treatment of the related notions of the a priori, necessity, etc., and, most importantly, to clarify whether he thought that there was a notion of infallibility distinctively associated with a priori knowledge. Kant states that an important task of metaphysics is to explain the possibility of (our having) synthetic a priori knowledge. This raises the question of the Kantian distinction between a priori and a posteriori judgments, and the distinction between analytic and synthetic judgments.3 Analytic judgements are those in which the extraction of the concept of the predicate from the concept of the subject is governed by the principle of non-contradiction – the concept of their predicate is contained in the concept of their subject. Some of Kant’s examples of true analytic judgments (i.e. analytic truths) are “All bodies are extended”4 and “All triangles are three-sided

 I shall refer to the standard English translation by Kemp N.  Smith. All the Kantian passages quoted are from this translation. 3  Kant uses the term “judgment” and I will be using it in this chapter to facilitate my own discussion of Kant. Nonetheless, Kant’s term “judgment” can be interpreted as having the same sense as the term “proposition”. Propositions may be regarded as what are expressed by suitable declarative sentences and we shall also take them to be truth-bearers. 4  A7; B11, p. 48. 2

1.1  Kant’s Main Concern in the Critique

5

figures”. Synthetic judgements, for instance, “All bodies are heavy”5 and “All triangles have the three interior angles equal to two right angles” are those in which the extraction of the concept of their predicate from the concept of their subject is not only governed by the principle of non-contradiction. Kant does not think that the predicate concept can be ‘extracted’ from the subject concept in a synthetic judgment at all, i.e. he had no notion of another way of extracting the predicate concept, other than in accordance with the principle of non-contradiction. A correlated Kantian distinction is that between a priori and a posteriori judgments. A priori judgements are those which need not to appeal to experience in their support. An example of an a priori (analytic) judgment is: “A body is extended”. Two allegedly a priori (synthetic) judgements in natural science that Kant offers are: “In all changes of the material world the quantity of matter remains unchanged” and “In all communication of motion, action and reaction must always be equal”. These judgements are necessary. (We will see soon that “necessity” is a criterion of a priori judgements.) A posteriori judgements are those which must appeal to experience in their support. All analytic judgements are a priori. They involve no appeal to experience. This is true even when they depend upon the analysis of empirical concepts. Yet, not all synthetic judgements are known a posteriori. A crucial Kantian claim is that there are synthetic a priori judgements. According to Kant, synthetic a priori judgements are those which exhibit a necessary connection between concepts but cannot be derived by merely conducting an analysis of concepts. For Kant, an example of a synthetic a priori judgment – “a priori”, contrary to Hume – is the principle of causality, that “Every alteration must have a cause”, construed as a strictly universal and necessary judgment, though the concept of cause is not contained in the concept of the subject (i.e. in the concept of event). Also, the judgements of mathematics are examples of synthetic a priori judgements.6 Kant comments7 that Hume was very concerned with synthetic judgments which state the connection of an effect with its cause. Hume believed to have shown that such an a priori synthetic judgment is entirely impossible. For Kant, if we accept

 A7–A8; B11–B12. PP. 48–49.  For Kant, most mathematical judgements are synthetic a priori. There are synthetic a priori judgements in science also. 7  Kant’s words: 5 6

He [Hume] occupied himself exclusively with the synthetic proposition regarding the connection of an effect with its cause …. and he believed himself to have shown that such an a priori proposition is entirely impossible. If we accept his conclusions, then all that we call metaphysics is a mere delusion whereby we fancy ourselves to have rational insight into what, in actual fact, is borrowed solely from experience, and under the influence of custom has taken the illusory semblance of necessity. If he had envisaged our problem in all its universality, he would never have been guilty of this statement, so destructive of all pure philosophy. For he would then have recognised that, according to his own argument, pure mathematics, as certainly containing a priori synthetic propositions, would also not be possible; and from such an assertion his good sense would have saved him. (B19–B20; p. 55)

6

1  Kant’s Views on A Priori Knowledge

Hume’s conclusions, then all what we call metaphysics is illusory. We believe we are having rational insight, when what occurs is that we borrow solely from experience; and under the influence of habit we think that causality is necessary. If Hume had considered our problem in full generality, he would have recognized that, according to his view, pure mathematics, as certainly containing a priori synthetic judgments, would likewise be impossible. Kant believed that Hume would have rejected such a claim. Here Kant seems to be saying that necessity is an objective property of judgments, in contrast with the subjectivistic account of necessity that Hume gave.8 Kant thought that Hume failed to realize that mathematical judgements are synthetic a priori, so Hume did not realize either that traditional metaphysics could not be abandoned without affecting mathematics. Kant does not discuss the possibility that Hume would be willing to analyze mathematical necessity as founded on custom or habit too. In any case, such a possibility is considered much later in twentieth century philosophy. We ought to remember that, for Hume, mathematics occupies itself with ‘relations of ideas’, and would be analytic in Kant’s terminology. Kant argues that Hume’s empiricism cannot explain all of our knowledge. It may serve to explain our knowledge of both analytic and a posteriori truths, but it cannot account for our synthetic a priori knowledge, for instance, for our knowledge of the truth of some synthetic mathematical judgements.9 Knowledge of analytic truths is unproblematic because we are just making explicit in the concepts of their predicate what is already contained or thought – perhaps confusedly – in the concepts of their subject. Synthetic a posteriori truths are known by establishing that the predicate applies to an object we have picked out in the external world. In Kant’s view, synthetic a priori judgements constitute a real problem for empiricism. Hume only accounts for relations of ideas and matters of fact. For Hume, mathematical judgements are analytic, so they would present no problem. He would have to show only that the principles of physics are a posteriori. For Kant, since synthetic a priori judgements are informative, the concept of their predicate cannot be derived solely by analyzing the concept of their subject. And in virtue of their a priori character, the connection between the concept of their predicate and the concept of their subject cannot be justified by observing the external world. Analytic judgements are not the primary concern of the Critique. They do not extend our knowledge but only articulate it. The Critique is primarily concerned with (true) a priori synthetic judgements  – a priori synthetic truths  – since they extend our knowledge. The central questions of the Critique are: “How are a priori

 I shall discuss in section five the important issue of the nature of necessity in Kant, i.e., whether it was an absolute notion or one relative to our way of knowing. 9  Why synthetic a priori knowledge has to be a problem for empiricism? The empiricist could deny that there are synthetic a priori judgments. He could explain judgments of arithmetic and analysis, for example, as analytic (in some sense of analytic) and geometrical judgments as empirical. But the view that geometrical judgments are “empirical” is anachronistic for Hume as well as for Kant. The purported “empirical” status of geometry was brought up by the discovery of non-Euclidean geometries in the nineteenth century. 8

1.1  Kant’s Main Concern in the Critique

7

synthetic judgements possible?” and, more importantly: ‘How is it possible for us to acquire a priori knowledge of some synthetic a priori judgments?’10 A priori synthetic judgements occur in mathematics, physics, and metaphysics. Kant observes that these disciplines do not advance by the mere analysis of concepts. Kant considers the synthetic a priori judgements of each of these disciplines, and asks how they can be justified.11 Now my concern will not be the semantical distinction analytic-­ synthetic of judgments or the metaphysical distinction between necessary and contingent judgments but rather the epistemological distinction between a priori and a posteriori knowledge. The primary task in the epistemology of a priori knowledge is to characterize what is an a priori justification. To do that, we don’t need to recur to the semantic distintion between analytic and synthetic judgments. We can characterize the notion of an a priori justification without recurring to the notion of analyticity. Kant himself does not characterize the notion of a priori knowledge through the notion of analyticity. These are related notions but independent notions. The concept of a priori justification does not imply the concept of analyticity, and the concept of analyticity does not explain the possibility of a priori knowledge.12 Obviously, complete insulation from the notion of necessity is not possible, specially in the light of Kant’s characterization of all a priori truths as necessary truths (whether they are analytic or synthetic).

 Casullo considers that Kant has not explained the claim that the source of the synthetic a priori knowledge is different from, and more problematic than, the source of analytic a priori knowledge. In his view, knowledge of analytic propositions requires knowledge of the principle of contradiction and the content of concepts. Yet he never addresses the source of such knowledge. In the absence of such an account, there is no basis for assuming that the source of analytic a priori knowledge is different from the source of synthetic a priori knowledge, let alone that the latter is more epistemically problematic than the former. (A priori Justification, p. 214) I don’t think that it is correct to say that Kant took it for granted. Kant does not explain – explicitly – analytic knowledge because he considers it obvious. It comes from the analysis of concepts guided by the principle of non-contradiction. Analytic knowledge does not add anything new to our knowledge. The source of synthetic a priori knowledge is intuition (as Kant technically understands it). The whole Critique is dedicated to show and explain, particularly, the synthetic a priori nature of mathematical knowledge; different and problematic knowledge because it relies on reasoning and intuition, on visualization and construction of concepts in our minds, in imagination, and not merely on our apprehension of mathematical concepts. Synthetic a priori judgments add new information, they are ampliative. Kant gives examples to show the difference between analytic a priori knowledge and synthetic a priori knowledge. He has basis, provides reasons, in the examples provided in his explanations. Clearly, the subsequent discussion of these issues, that have lasted until today, shows the problematic nature of a priori knowledge, whether analytic or synthetic, as Casullo is fully aware of being himself a protagonist in such discussions. 11  According to Kant, the following three questions arise: (1) How is pure mathematics possible? (2) How is pure physics (or the pure part of physics possible)? (3) How is pure metaphysics possible? The success of mathematics and physics proves that they are possible. What demands explanation is how they are possible. In contrast, in the case of metaphysics we have to ask whether it is possible, and then inquire into how it is possible. (B xvii; p. 22) 12  See Casullo, Albert. A Priori Justification. Oxford: Oxford University Press, pp. 237–38, 2003. 10

8

1  Kant’s Views on A Priori Knowledge

1.2 Is There A Priori Knowledge? How Is A Priori Knowledge Possible? Kant had set himself the task of investigating the possibility of a priori knowledge – particularly synthetic a priori knowledge 13 – as the enterprise of investigating “how much we can hope to achieve by reason, when all the material and assistance of experience are taken away”.14 As he reiterates: “For the chief question is always simply this: what and how much can the understanding and reason know apart from all experience?”15 On the question how a priori knowledge is possible, Kant considers two ways of explaining how we possess synthetic a priori knowledge. Either our concepts must conform to objects, or objects (as known) must conform to our concepts. “Objects as known” is an extremely important qualification for Kant. If our concepts must conform to the objects, then we cannot explain how can we know anything a priori in regard to the latter. On the other hand, if the objects must conform to our concepts, the situation looks more promising.16 This point of view will facilitate the explanation of the possibility of our having a priori knowledge of objects prior to their being given.17

 Analytic judgements are a priori also, but they do not seem to be particularly problematic for Kant. The idea here seems to be that necessity can only be known through reason since experience cannot teach us what holds necessarily. But we can know necessities a posteriori by testimonial evidence for example. This possibility does not seem to have occurred to Kant. 14  Preface to first edition. A xiv, pp. 10–11. 15  Ibid, A xvii, p. 12. 16  Kant says: In the former case I am again in the same perplexity as to how I can know anything a priori in regard to objects. In the latter case the outlook is more hopeful. For experience is itself a species of knowledge which involves understanding; and understanding has rules which I must presuppose as being in me prior to objects being given to me, and therefore as being a priori. They find expression in a priori concepts to which all objects of experience necessarily conform, and with which they must agree. (Bxvii–Bxviii; pp. 22–23) 13

 Kant explains that he got this insight from the Copernican revolution. We must therefore make trial whether we may not have more success in the tasks of metaphysics, if we suppose that objects must conform to our knowledge. This will agree better with what is desired, namely, that it should be possible to have knowledge of objects a priori, determining something in regard to them prior to their being given. We should then be proceeding precisely on the lines of Copernicus’ primary hypothesis. (B xvii, p. 22) Kant claims that he will establish in the Critique, apodeictically not hypothetically, this change in point of view. (note a, Preface to the second edition, p. 25) To some extent, this contrast between apodeictic and hypothetical certainty will be useful for our discussion of the question whether for Kant a priori knowledge must involve some sort of infallibility. 17

1.2  Is There A Priori Knowledge? How Is A Priori Knowledge Possible?

9

Kant affirms that since we possess a priori knowledge, we must have a faculty or capacity of a priori knowledge.18 This doctrine was also held by the rationalists. They believed, as Kant did for a long time, that this faculty of a priori knowledge provided us with knowledge of things-in-themselves. (Although this is Kant’s notion – not a rationalist notion.) However, Kant claims that if we analyze what is involved in the possession of a priori knowledge, we shall realize that a priori knowledge must be derived from the nature of the mind, and not from the nature of things. According to Kant, it is only on the assumption that objects (as known) must conform to our concepts that we can explain the possibility of synthetic a priori knowledge: “… we can know a priori of things only what we ourselves put into them.”19 Kant’s position is that if things appeared to us just as they are in themselves, we could not know them independently of experience. We could only recognize that in so far as we have experienced them, they possessed certain characteristics, and we might go so far as to anticipate that they would continue to do so. Kant considered it impossible to have a priori knowledge of the universal and necessary character of things-in-themselves. We can have a priori knowledge through the categories, for instance, only if they are due to the nature of the mind; only if they are imposed by the mind on the objects known. We can have a priori knowledge of the universal and necessary characteristics of objects of experience, only in so far as they are objects of experience. Kant thought to have responded to the question whether there is a priori knowledge by assuming that we in fact possess a priori knowledge. As I understand it, the task at hand was to characterize a priori knowledge, and to explain how it is possible, given that we actually have it. Though Kant thought he assumed the existence of a priori knowledge, he in fact provided an argument for it: namely, the argument for the necessity of a priori knowledge. Roughly, the argument goes like this: Experience cannot teach us what is strictly universal and necessary. Experience can only teach us about generalizations of fact. Since we have knowledge of necessary truths, we must obtain it in another way. Only the faculty of reason is sufficient to provide us with knowledge of necessary truths. Since only the faculty of reason is sufficient to provide us with knowledge of necessary truths, and reason does not rely on experience to produce knowledge, then such knowledge must be a priori. The previous argument constitutes an argument for the existence of a priori knowledge only on the assumption that we in fact possess knowledge of necessary truths. In a derivative sense the existence of a priori knowledge is assumed too by the fact that Kant assumed we had knowledge of necessary truths and argued that such knowledge cannot possibly be derived from experience. However, Kant could  B4; p. 45; Preface to first edition, A xii; p. 9.  Ibid, Bvii–Bxxiii; pp. 22–25. But what this latter quote could mean? The phrase ‘what we put into the objects’ makes no sense. And if I say: ‘what we put in our concepts’, then this suggests that our a priori knowledge is after all knowledge of analytic judgments. 18 19

10

1  Kant’s Views on A Priori Knowledge

not conclude that we have synthetic a priori knowledge, even in assuming that we have knowledge a priori of necessary truths. As already said, Kant should not deny that we can obtain knowledge a posteriori of truths which can be knowable a priori.

1.3 What Does “A Priori” Mean? Does “A Priori” Mean “Precedence in Time”? In this section I discuss what Kant meant by “independence of experience” in connection with a priori knowledge. In the introduction to the Critique, Kant affirms: There can be no doubt that all our knowledge begins with experience … In the order of time, therefore, we have no knowledge antecedent to experience, and with experience all knowledge begins. (B1, p.41) But though all our knowledge begins with experience, it does not follow that it all arises out of experience. (ibid) … we should understand by a priori knowledge, not knowledge independent of this or that experience, but knowledge absolutely independent of all experience. (B3; p.43)20

Kant uses often words like “before” and “precedes” in connection with a priori knowledge.21 One may therefore suppose that he is speaking of temporal precedence. As H. J. Paton points out,22 there is, however, no consistency in such usage which is frequently applied to the empirical.  Some other passages are: Experience is, beyond all doubt, the first product to which our understanding gives rise, in working up the raw material of sensible impressions. Experience is therefore our first instruction, and in its progress is so inexhaustible in new information, that in the interconnected lives of all future generations there will never be any lack of new knowledge that can thus ingathered. Nevertheless, it is by no means the sole field to which our understanding is confined. (A1; pp. 41–2) For it may well be that even our empirical knowledge is made up of what we receive through impressions and of what our own faculty of knowledge (sensible impressions serving merely as the occasion) supplies from itself. If our faculty of knowledge makes such an addition, it may be that we are not in a position to distinguish it from the raw material, until with long practice of attention we have become skilled in separating it. (B2; p. 42) … whether there is any knowledge that is independent of experience and even of all impressions of the senses. Such knowledge is entitled a priori, and distinguished from the empirical, which has its sources a posteriori, that is, in experience. (B2; pp. 42–3) 20

 B 67; B 132; B 145.  Paton, H. J. Kant’s Metaphysic of Experience. London: George Allen & Unwin Ltd., 1936, first edition, vol. 1, p. 79. Paton explains: Intuition is said to precede thought. Knowledge is said to start with the senses, to proceed thence to understanding, and to end in reason. On the other hand, transcendental truth is said to 21 22

1.3  What Does “A Priori” Mean? Does “A Priori” Mean “Precedence in Time”?

11

It is important to observe that in certain cases the a priori does involve temporal precedence.23 Though the “a priori” does not involve essentially temporal precedence. All our knowledge begins with experience, and there is no knowledge that precedes experience in time. Yet, although ‘all of our knowledge begins with experience, some of our knowledge is neither derived nor in any sense dependent on experience’. Paton correctly observes that, for Kant, the a priori is what is logically, or objectively, prior.24 For example, time is objectively prior to every change; it is the formal condition of its very possibility. Even though, in a subjective sense  – that is, in actual consciousness – the idea of time is, like every other, given only through the stimulus of sense-perceptions.25 The same applies to the a priori intuition of space and to all other a priori concepts or categories. According to Kant, it is the future employment of the categories that is independent of experience. There is no doubt that their employment is always independent of experience, though we can make them clear to ourselves only after we have actually used them in experience.26 But once we have made them clear, we know that our employment of them thereafter must be independent of experience. I conclude that what Kant meant by “independence of experience” in connection with a priori knowledge is not to be understood as precedence in time but rather as what is independent of experience in terms of justification. Of course, it is precisely the notion of “experience independence” what is in need of clarification to be useful at all.

precede empirical and to make it possible, and original apperception is said to precede all particular experience. Where two things reciprocally condition one another, or form necessary parts of a wider whole, Kant seems to use these temporal expressions of either in relation to the other. (p. 79) 23

 Paton affirms: Thus of any individual circle we can say, before we have experienced it, that all the angles subtended by any arc of it will be equal. We might even make discoveries about a particular kind of geometrical figure, before we had found any example of that figure in the physical world. Furthermore, if space as known a priori is due to the nature of our mind, we can say that our mind has the form of space in it as a potentiality before experience begins. Such statements Kant certainly makes, and they are legitimate statements. Where his expressions can be interpreted in this way, it seems only fair so to interpret them.

It is possible that he was at times misled by these legitimate statements into confusing logical and temporal priority … What seems to me certain is that such confusion is no part of his essential doctrine, and would have been indignantly denied by him if the question had been put to him explicitly. (ibid, p. 79; my emphasis)  Paton, ibid., vol. I, p. 80.  Ibid. 26  See first Critique, A 196, B 241. 24 25

1  Kant’s Views on A Priori Knowledge

12

1.4 Was Kant an Innatist? Some interpreters of Kant, for example, Paton,27 have suggested that Kant was some sort of innatist. This interpretation is offered as a way of resolving the tension between two important claims of Kant, namely, “That all knowledge begins with experience”28 and “That a priori knowledge is knowledge absolutely independent of all experience”.29 Paton describes our possession of the categories along these lines: Pure concepts are said to lie already prepared in the human understanding, but they are developed on the occasion of experience. We can discover in experience the occasioning causes of their production. The impressions of the senses supply the first stimulus to bring experience into existence, an experience whose matter comes from sense, and whose form comes from pure intuition and thought. Without data even the elements of a priori cognitions would not be able to arise in thought. From these and many other passages we can say that on Kant’s view the a priori is at work in experience from the start – there is no experience without a form – and it is gradually made clear in consciousness by reflection. In that sense a priori knowledge is acquired and not innate. Kant is not concerned with the question of how experience develops – that is a matter of psychology – but with what is contained in experience (Prol §21a (IV 304)), or with the presuppositions and conditions of experience. He does not suggest that in infancy we begin by knowing space and time and the categories, and then proceed to construct a world of colours and sounds.30 Sense-impressions, space and time and the categories are at work in experience from the start, but it is only gradually that we disentangle them from one another.31

Here we face the question: how can Paton affirm that sense impressions, space and time, and the categories are at work in experience from the start and in the same breath that Kant did not suggest that in infancy we begin by knowing space and time and the categories? Perhaps, Paton wants to say that it is the capacity to have sense impressions and organize them in space and time that is innate. Paton thinks: “if space as known a priori is due to the nature of our mind, we can say that our mind has the form of space in it as a potentiality before experience begins.” (Paton, vol. 1, p.79) Kant seems to suggest this: The Critique admits absolutely no divinely implanted or innate representations … There must, however, be a ground in the subject which makes it possible for these representations to originate in this and no other manner … This ground is at least innate … (Allison, The Kant-Eberhard Controversy, pp. 135–6, AAVIII: 221–23; my emphasis)

The claim that we possess the categories from the start, that is, from the beginning of our life, is more controversial, and certainly, too strong an interpretation of Kant.  Paton, op. cit., p. 78.  Kant, B1, p. 41. 29  B 3; p. 43. 30  Paton, op.cit., vol. 1, p. 78; my emphasis. 31  Ibid, p. 318; my emphasis. 27 28

1.5  Necessity and Universality as the Criteria of A Priori Knowledge

13

But it is implied that the categories are all in the mind from the beginning, and this I take to mean that the categories are innate; only our knowledge of them is acquired. They are in our mind and later we get aware of them and know them. I reject an innatist interpretation of Kant, namely, any interpretation which states that some concepts or truths are in the mind from the beginning of our life. It seems to me that the suggestion that Kant is some sort of innatist is of no help whatever. For whether it is specific items of knowledge, or merely concepts, that are supposed to be innate, the thesis of innatism, far from resolving the tension itself is in tension with the first component of the problem, the claim that all knowledge begins with experience. The point is obvious that if whole items of knowledge are thought to be innate, then these cannot be said to “begin with experience”. But even if it is merely certain concepts that are thought to be innate, there will presumably still be a purely reflective route to certain items of a priori knowledge featuring just those concepts. And to be sure, this knowledge will not, in any relevant sense, begin with experience. Kant ought not to be considered an innatist. The tension can be resolved I argue as follows: A priori knowledge is independent of experience in the sense that no experience plays any evidential role in the acquisition of such knowledge. It is equally true, according to Kant, that all knowledge begins with experience in the sense that only a creature in possesion of experience and empirically acquired concepts can come to know anything, be it empirically, or a priori.

1.5 Necessity and Universality as the Criteria of A Priori Knowledge This section is devoted to a close examination of Kant’s criteria of universality and necessity for a priori knowledge. I insist, following Pap and Prichard, that they should not be treated as separate and do collapse together into the criterion of necessity. Contrary to Kant, I do not think that these criteria succeed in identifying the class of a priori truths. Kant recognizes at this point in the introduction,32 that the a priori has not yet been fully characterized and looks for a criterion to differentiate infallibly between a priori and empirical knowledge. He proceeds to display (strict) universality and necessity as the marks of a priori knowledge. First, Kant argues that experience can only provide knowledge in the sense that a thing in fact has a certain property, but it cannot go further in teaching us that it cannot be otherwise. If a proposition in being thought must be thought as necessary, then it is an a priori judgement. If it is not derived from an a priori judgement, then it is an absolutely a priori judgement. Second, Kant goes on arguing that experience cannot confer on its judgements true or strict universality. It only can confer comparative or assumed universality through induction. Comparative universality is what we can affirm a judgement has when, 32

 B 2–B 3; p. 43.

14

1  Kant’s Views on A Priori Knowledge

so far hitherto observed, there is no exception to it. If a judgement is thought with strict universality such that no exception from what is asserted is allowed as possible, it cannot be derived from experience. On the contrary, it is valid absolutely a priori. Kant distinguishes between comparative or empirical universality and strict universality. Empirical universality is only an arbitrary extension of a validity holding in most cases to one which holds in all, for instance, in the proposition, ‘all bodies are heavy’. When, on the other hand, strict universality is essential to a judgement, this indicates a special source of knowledge, namely, a faculty of a priori knowledge.33

Experience can provide only generalizations from facts. We can say by appeal to experience that “All ravens are black” (or “All bodies are heavy”) in so far as we have observed that ravens are black (or that bodies are heavy). But we cannot say that they must be black, or that there can be no exception to the general judgement. When we say, for example, “That all triangles have the interior angles equal to two right angles”, what we are affirming is a necessary and universal claim. The merely general admits of exceptions, but the strictly universal does not. The question may arise whether the universality of space and time involves also their necessity which is required, if we are to regard space and time as known a priori. For Kant, what is known a priori is also necessary. Something more than a matter of fact (or empirical) universality is demanded. Remember that change, for instance, is a universal property of everything we know; yet Kant considered it as derived from experience,34 and not deducible from the idea of time.35 It is not clear that Kant was right about this. Can there be time without change? As I already said, for Kant, necessity and strict universality are the sure criteria of a priori knowledge. Supposedly sometimes the contingency of judgements is something that can be shown more easily than their empirical delimitation, or, vice versa, their unlimited universality can be more convincingly proved than their necessity. Therefore, Kant recommends us to employ these criteria separately. Each of the two criteria, taken by itself, infallibly picks up only a priori items of knowledge.36 Arthur Pap holds that the two criteria of universality and necessity merge into one: the criterion of necessity.37 I think Pap is right. Kant was wrong in distinguishing between strict universality and necessity. What is “necessity” for Kant? If  Ibid.  B3. 35  B58. 36  B 4; p. 44. 37  Pap, Arthur. Semantics and Necessary Truth, pp. 22–23. Prichard also suggests that these are ultimately identical. (Kant’s Theory of Knowledge, p. 4, n. 3.) A quote from Pap: The two criteria coalesce in one, the criterion of necessity. What does universality mean? Kant does not mean that there are no universal empirical propositions that are true, i.e. that have no exceptions. What he intends to say is that we never know with certainty that such a proposition is true, that there always remains the possibility of its being false. A strictly universal proposition 33 34

1.6  On Kant’s Conception of Necessity

15

something can be thought as strictly universal, no exceptions to it are thought as possible, that means that it could not have been otherwise. Are these concepts extensionally equivalent while maintaining their conceptual difference, or is there a stronger equivalence? Another way to express the same point is that it does not seem to be possible to explain what “strict universality” means without appealing to the fact that no exceptions are thought as possible; and what could the latter mean other than saying that the judgement is necessary?

1.6 On Kant’s Conception of Necessity Kant affirms that truths are known a priori because they are necessary,38 for example, mathematical truths. On the issue of necessity, I think it would be helpful to distinguish between the following two questions: (1) in what, for Kant, does necessity consist? and, (2) what characteristics does Kant take to demarcate the class of necessary truths? The answer to the second question may well be that the necessary truths are just those which are both knowable a priori and which hold universally. I, for my part, cannot think of any propositions which are both general and a priori which – if one is at all sympathetic to the notion of necessity – one would not also want to regard it as holding of necessity. The usual candidates for contingent a priori truths – like “I am here” – all seem to be particular.39 But the converse thesis – that all necessities are a priori and general – runs counter to the Kripkean “metaphysical” necessities (or alleged necessities) of constitution or origin – truths like “Water is H2O”, “Kant is a human being”, etc. – are neither a priori nor general. The conjunction of a prioricity and generality may be a mark, however, of “conceptual” necessity.40 Regarding the question in what does necessity consist, Kemp Smith affirms that for Kant necessity is “absolute” necessity: A priori judgements claim absolute necessity. They allow of no possible exception. They are valid not only for us, but also for all conceivable beings … Empirical judgements, on which has no conceivable exceptions, which is another way of saying that it is necessary. (ibid, pp. 22–23)  B3.  Kripke, Saul. “Identity and Necessity” in Identity and Individuation. Edited by M. K. Munitz. New York: New York University Press, 1971. 40  As opposed to what? Absolute necessity? Conceptual necessity is opposed to metaphysical necessity. Conceptual necessity is concerned with necessary relations among concepts; metaphysical necessity, on the other hand, is concerned with how things are. Both are absolute: that is, they hold in all possible worlds. An example of a conceptual necessity is “All bachelors are married”; an example of a metaphysical necessity is “Water is H2O”. See Hale’s Necessary Beings: An Essay on Ontology, Modality and the Relations Between Them on this issue. We should be careful not to adjudicate to Kant a Leibnizian or Kripkean conception of truth in all possible worlds. 38 39

16

1  Kant’s Views on A Priori Knowledge the other hand, possess only a hypothetical certainty. We recognise that they may be overturned through some addition to our present experience, that they may not hold for beings on other planets or for beings with senses differently constituted. Whereas the opposite of a rational judgment is not even conceivable, the opposite of an empirical judgment is always possible. The one depends upon the inherent and inalienable nature of our thinking; the other is bound up with the contingent material of sense.41

But if a priori judgments depend upon the “inherent and inalienable nature of our thinking”, they cannot be absolutely necessary.42 This claim is at odds with the whole point of the passage. If it is true that they depend upon the “inherent and inalienable nature of our thinking”, then it is not possible to understand necessity here as absolute necessity, at least not with respect to synthetic a priori knowledge.43 Rather, it must be construed as necessity “relative to us”, that is, to creatures endowed with our own intellectual capacities.44 As to the question of the constitution of necessity, I think that Kant would answer it in different ways, depending on whether we are concerned with synthetic a priori or analytic truths. There is something actual about his conception of necessity  – namely, a category of necessity that pertains to the actual world, rather than to all possible worlds. So much is presumably implicit in any conception which allows synthetic a priori knowledge and, hence, necessary by virtue of their being correctly codifying certain structural features of spatial, or temporal, experience. Kant affirms: That which in its connection with the actual is determined in accordance with universal conditions of experience, is (that is, exists as) necessary.45 The proposition that nothing happens through blind chance (in mundo non datur casus) is therefore an a priori law of nature.46

I think that Kant did not rely on an absolute notion of necessity, but rather on a notion of necessity relative to our way of knowing in his characterization of synthetic a priori knowledge.47 This certainly applies to the necessity attached to (some) synthetic a priori knowledge, and there is a question as to whether Kant gave a  Smith, Kemp. A Commentary to Kant’s Critique of Pure Reason. New Jersey: Humanities Press, p. 28. 42  Kant uses the expression “absolutely necessary”. Any knowledge that professes to hold a priori lays claim to be regarded as absolutely necessary. (Axv; p. 11)

41

 More on this forthcoming.  See B 44–5, B 59 and B146. It seems that, for Kant, necessity is associated with legality, but we could ask if the legality in question is for us and the phenomenic world, or if it is absolute and independent of us. It is difficult to hold this last position. 45  Kant, ibid., p. 239; my emphasis. 46  Kant’s emphasis; ibid., p. 248. 47  Kitcher says: For Kant, something is necessary (and universal) if it is true of all those worlds of which we can have experience, constituted as we are. Unlike Leibniz, Kant does not operate with an absolute 43 44

1.6  On Kant’s Conception of Necessity

17

different account of necessity in so far as it pertains to analytic truth. I think Kant gave in fact a different analysis of necessity, depending upon whether we are concerned with analytic (a priori) truths or with (some) synthetic a priori truths. Kant says: True mathematical propositions owe their truth to the structure which our mental faculties impose on experience. Those propositions can be known through the acts of pure intuition, processes in which we disclose to ourselves that structure which informs experience. We have an explanation of how mathematics as a body of synthetic a priori knowledge is possible. (p. 232; my emphasis)

But then the Kantian view is untenable as a view of mathematical knowledge. In a nutshell: if what is necessary is what is due to the structure of the mind, then it cannot be absolutely necessary. This is a good reason to reject Kant’s view. This is basically Russell’s complaint against Kant’s view of necessity.48

notion of necessity. (“Kant and the Foundations of Mathematics”, Philosophical Review 84, 1975, p. 24) It is interesting to note that Philip Kitcher shares my view on Kant’s notion of necessity as relative to our way of knowing and, nonetheless, finds it useful to explain the notion in the language of possible worlds semantics. I propose to explicate Kant’s conception of necessity by appeal to the device of possible worlds. Bizarre as this approach may seem, it will, nonetheless, prove its worth in understanding Kant’s views on mathematics. Let us use the term ‘proposition’ to convey the sense in which Kant uses ‘judgment’ …. For Kant a possible world is a totality of possible appearances – that is, experiences which could be experiences for us, constituted as we are. (It is assumed that we all have the same constitution). We shall follow Kant in taking the concept of a possible experience to be primitive. Kant has a broad notion of necessity in that some propositions which are logically possible fail to hold in any Kantian possible world. (p. 24) I find this attempt very misleading. The notion of necessary truth in Kant and in possible world semantics is not the same. First, note that a possible world, in Kant’s sense, is not just any world free of contradiction  – as it is in possible worlds semantics  – but rather any possible world of appearances for us. Kitcher seems fully aware that the two notions are different, so it is surprising how he can claim also that the notion of “possible worlds” can be very useful in understanding Kant’s notion of necessity. (In a sense, I think Kant is right: how could we think of a possible world if it is not by thinking about it as we are constituted?) Then, necessary truth in Kant’s sense could be understood as truth in all possible worlds in which we can have experiences. Necessary truth is not to be understood as truth in all possible worlds since there are possible worlds in which we do not exist. Let’s clarify that a notion of necessity can be relative in the sense of being relative to our way of knowing as humans (relative to our species), and for that reason, it has to be considered as subjective. Because the notion of being relative does not have to mean that the necessity in question permits anything conceivable for each of us – what we subjectively consider it is the case – but rather than the notion of necessity is circumscribed to its relationship to knowers of our species, constituted as we are. 48  Russell, Bertrand. “How A Priori Knowledge is Possible” in The Problems of Philosophy. New York: Oxford University Press, 1973. Russell directs his objection to the notion of certainty associated with mathematics and logic, but his point applies as well to the notion of necessity. The main, fatal, objection to Kant’s view is that the thing to be accounted for is the certainty that the facts must always conform to logic and arithmetic. To say that logic and arithmetic are

18

1  Kant’s Views on A Priori Knowledge

To sum up, I think Kant wanted to say that for us experience – at least, the only conception of experience we can have – has to be structured in certain general ways, but that he did not consider us entitled to claim that any possible experience of any being has to be so structured.

1.7 Is Kant’s Definition of A Prioricity a Purely Negative One? Did Kant Succeed in Characterizing Both A Priori Knowledge and the Class of A Priori Truths? In this section I examine the question whether Kant’s notion of a priori knowledge is a purely “negative” one, i.e., whether it is adequately characterized as non-­ empirical or non-a posteriori. This issue is important because if Kant did not succeed in characterizing a priori knowledge positively enough, then that task remains. Hale observes49 that Kant’s “definition” of a priori knowledge is an entirely negative one, namely, knowledge that is non-empirical or knowledge that is not a posteriori. Paton affirms that this negative definition is supplemented by a positive criterion.50 Hale makes some interesting comments on Kant’s view that are worthy of mention, even briefly. For Hale, though Kant characterizes necessity and strict universality as positive marks of the a priori, his explanation of a priori knowledge is completely negative. According to Hale, Kant does not provide a general positive account of what makes a ground for belief non-empirical. It is rather assumed what empirical grounds for belief are, and non-empirical grounds are simply grounds for belief that are not empirical.51 Kant only affirms the general claim that they are to be characterized as those grounds which justify belief independently of experience. Hale explains that this point has been ignored, and it has been assumed that Kant distinguished between both sorts of grounds by a positive feature. Then, an easy step (not unavoidable though) is to conclude that this positive feature which makes a ground for belief a priori involves more exacting standards than those involved in the characterization of empirical grounds to be able to produce empirical knowledge. Hale observes that from the claim that a priori grounds have to comply with more exacting standards than empirical grounds, one may easily think that there is no a priori knowledge or much less than we previously thought.

contributed by us does not account for this. Our nature is as much a fact of the existing world as anything else, and there can be no certainty that it will remain constant. (p. 78)  Hale, Bob. Abstract Objects, pp. 125–26.  For Pap also: “Kant’s explicit definition of a priori knowledge is a negative one: ‘knowledge that is independent of experience and even of all sense-impressions.’” (op. cit., p. 22) 51  Hale, pp. 125–6. 49 50

1.7  Is Kant’s Definition of A Prioricity a Purely Negative One? Did Kant Succeed…

19

Hale concludes that it would be desirable to provide a positive characterization of what a priori knowledge amounts to. Hale is right about this. Contrary to what Hale claims, though, I think that Kant tries to give a positive characterization of the notion of a priori knowledge when he specifies universality and necessity as the main characteristics of a priori items of knowledge. Yet this characterization is of the class of necessary truths and not of the notion of an a priori justification. However, Hale’s charge raises the important question as to whether Kant succeeded or not: has Kant in fact given us a positive characterization of the notion of a priori knowledge, or are we left with a purely negative characterization of a priori knowledge as being non-empirical or non-a posteriori? Paton seems to suggest that Kant provided positive criteria for the determination of the class of a priori truths, and that this fact is tantamount to the claim that Kant succeeded in characterizing a priori truths. Contrary to Paton, I do not think Kant succeeds in characterizing accurately with his criteria the class of a priori truths. For Kant, all a priori truths are necessary. There is no place for contingent a priori truths. Nevertheless, I believe that Kant is correct in characterizing conceptual necessity as what is universal and known a priori. How are contingent a priori truths different from synthetic a priori ones? Contingent a priori truths are synthetic and not necessary, like “I am here”, in contrast with other synthetic a priori truths which are necessary like “Every alteration must have a cause”. What would Kant say about the judgment “I am here”? A quick answer would be to say that since that judgment is contingent, and only what is necessary is a priori for Kant, then it is not a priori. Yet I think this is a superficial answer. A more fair reading of Kant is to recognize that he simply did not have the necessary distinctions to settle this issue at his disposal. We just don’t know what he would have said about the statement “I am here”. For Hale, Kant did not succeed in giving an account of what makes a ground for knowledge “a priori”. I don’t want to commit myself to such a strong claim since it would involve a very careful reading of the first Critique. Perhaps Hale’s point is a weaker and correct one: we won’t find what we are looking for, namely, an explicit definition of the notion of a priori knowledge. Now from that modest point of view it does not follow that there is no possible (Kantian) account of a priori knowledge that we can reconstruct from his views. Actually what Hale is trying to do is to interpret the Kantian notion of “experience-independence”.52 Let me speculate a bit more before finishing with this topic. Hale’s view is that Kant was not explicit about what makes a ground for knowledge “a priori” and, consequently, that he does not clarify in any detail the “independence of experience in terms of justification” that he claims to be distinctive of a priori knowledge in contrast with empirical knowledge. What can partly explain Hale’s view on Kant is that Kant appears to have concentrated primarily on the properties that a priori

52

 P. 138.

20

1  Kant’s Views on A Priori Knowledge

judgments have. Kant offers his criteria to differentiate judgments a priori from the rest. They are supposed to be strictly universal and necessary. Moreover, a related point: I think that Kant was not clearly explicit about what is a non-empirical ground simply because Kant did not appear to accept grounds for belief as being more basic than the “judgments” we could possibly know by their means. In any case, this is a much later development. However, I believe that there is an ambiguity in Kant’s use of the term “judgment” which leaves open the possibility that he was referring to grounds too, and not to truths, or not only to truths or judgments expressing them.

1.8 Does A Priori Knowledge Involve Some Sort of Infallibility? I find very helpful to try to answer the question whether Kant thought, or his view implies, that a priori knowledge involves (entails) some sort of infallibility. If the answer to this question were affirmative, then another very interesting question arises: whether infallibility is a distinctive property of a priori knowledge. Unfortunately, Kant was not explicit about these questions, so I will mainly be trying to explore whether his views on a priori knowledge have any implicit bearing on these questions. On the other hand, in my view, for two contemporary and influential interpreters of Kant, namely, Philip Kitcher and Michael Friedman, the answer to these questions is affirmative for Kant. I found very helpful to study Kant carefully to see whether it is clear, or at least plausible, to hold a Kitcher-Friedman interpretation of Kant.

1.8.1 Kant’s Views Kant comments53 that in his investigation he will prescribe to himself the maxim of not permitting to hold mere opinions, and anything which resembles a hypothesis should be rejected. Any knowledge that is a priori must be, he says, absolutely necessary.54 It is extremely important in determining all pure a priori knowledge to avoid any kind of hypothesis or conjecture, since it is such a determination that must serve as a standard and, therefore, as a paradigm for all apodeictic certainty.55

 Preface to the first edition, A xv; p. 11.  Ibid. This proved to be a naive attitude towards Aristotelian logic as Frege in the Begriffschrift improved it. (English translation: Conceptual Notation, and Related Articles. Oxford: Clarendon Press, 1972.) 55  A xvi, p. 11. The notion of “apodeictic certainty” is left unexplained, what is the most unfortunate since it would have illuminated greatly our question. 53 54

1.8  Does A Priori Knowledge Involve Some Sort of Infallibility?

21

Kant also discusses the status of logic in his day, and observes that as a subject, it has not needed to retrace a single step since it had been invented by Aristotle.56 It has only removed certain needless subtleties to achieve more clarity or more elegance in its presentation, without affecting the certainty of the science. Furthermore, it is argued that logic has not advanced a single step. Logic appears to be “a closed and completed body of doctrine”.57 Kant compares the history of mathematics with that of logic. With the Greeks, mathematics had entered “the secure path of knowledge”. But it was not as easy for mathematics as it was for logic (in which reason is allegedly only concerned with itself) to construct itself that royal road. On the contrary, mathematics remained for a long time among the Egyptians, in the groping stage. The transformation of its methods must have been due to a revolution brought about by Euclid. He marked out the path upon which mathematics had to enter. In following such a path, “secure progress throughout all time and in endless expansion is infallibly secured.”58 Kant distinguishes between philosophical knowledge and mathematical knowledge even though both are obtained by the faculty of reason. The same faculty, reason, operating with different methods. This is a very important passage: Mathematics presents the most splendid example of the successful extension of pure reason, without the help of experience. Examples are contagious, especially as they quite naturally flatter a faculty which has been successful in one field, [leading it] to expect the same good fortune in other fields. Thus pure reason hopes to be able to extend its domain as successfully and securely in its transcendental as in its mathematical employment, especially when it resorts to the same method as has been of such obvious utility in mathematics. It is therefore highly important for us to know whether the method of attaining apodeictic certainty which is called mathematical is identical with the method by which we endeavour to obtain the same certainty in philosophy, and which in that field would have to be called dogmatic. Philosophical knowledge is the knowledge gained by reason from concepts; mathematical knowledge is the knowledge gained by reason from the construction of concepts. To construct a concept means to exhibit a priori the intuition which corresponds to the concept. For the construction of a concept we therefore need a non-empirical intuition. The latter must, as intuition, be a single object, and yet none the less, as the construction of a concept (a universal representation), it must in its representation express universal validity for all possible intuitions which fall under the same concept. Thus I construct a triangle by representing the object which corresponds to this concept either by imagination alone, in pure intuition, or in accordance therewith also on paper, in empirical intuition – in both cases completely a priori, without having borrowed the pattern from any experience. The single figure which we draw is empirical, and yet it serves to express the concept, without impairing its universality. For in this empirical intuition we consider only the act whereby we construct the concept, and abstract from the many determinations (for instance, the magnitude of the sides and of the angles), which are quite indifferent, as not altering the concept ‘triangle’. Thus philosophical knowledge considers the particular only in the universal, mathematical knowledge the universal in the particular, or even in the single instance, though still always a priori and by means of reason. Accordingly, just as this single object is determined by certain universal conditions of construction, so the object of the

 Preface to the second edition, B viii; p. 17.  Ibid. 58  B xi; p. 19. 56 57

22

1  Kant’s Views on A Priori Knowledge concept, to which the single object corresponds merely as its schema, must likewise be thought as universally determined.59

Philosophical knowledge is obtained through the reasoning of concepts; mathematical knowledge through reasoning by the construction of concepts. Kant asks himself whether the method to obtain apodeictic certainty in mathematics is the same as the method by which we attempt to obtain the same certainty in philosophical knowledge. He questions whether apodeictic certainty can also be acquired in philosophical knowledge. When we can acquire adodeictic certainty in one area, in applying certain methods, it is simply natural to ask ourselves if we can extend that success to other areas of knowledge. For Kant, in constructing a concept in mathematics, we are exhibiting, in an a priori manner, the intuition that corresponds to a concept. Kant distinguishes between nonempirical intuitions and empirical ones for the same concept. An intuition, nonempirical or empirical, must be a single object, a particular object, which is a construction of a concept, ‘it is a universal representation that must express the universal validity of the concept for all possible intuitions which fall under the same concept’. (p. 577) Kant illustrates these ideas with the example of a triangle. We have a concept of triangle. We can construct a figure of a triangle in our minds, in imagination alone, in pure intuition (nonempirical intuition), or we can draw also a triangle on paper, in empirical intuition. Both constructions are objects; both constructions are intuitions. It is important to realize that, for Kant, we can construct triangles, in pure intuition, in imagination, and in empirical intuition, both completely a priori. The triangle I draw is empirical but it expresses without damage the universality of the concept “triangle” because we abstract from accidental properties of the figure, like the magnitude of its sides and angles, and concentrate only on the essential properties of the concept of triangle, exhibited in the constructed figure. The universal validity of the concept of a triangle can be expressed a priori in pure imagination, in nonempirical intuition, as well as in empirical intuition. This is possible, in both cases, a priori, because the exhibited pattern has not been borrowed from any experience.60 Kant explains: Philosophy confines itself to universal concepts; mathematics can achieve nothing by concepts alone but hastens at once to intuition, in which it considers the concept in concreto, though not empirically, but only in an intuition which it presents a priori, that is, which it has constructed, and in which whatever follows from the universal conditions of the construction must be universally valid of the object of the concept thus constructed. (A 716; B 744) (p. 578)

As Friedman points out: Kant’s account must thus be defended against the commonly held position that universal truths cannot be derived from reasoning that depends on particular representations … This raises questions about how one can be sure that an intuition adequately displays the content

59 60

 A 713/B 741, pp. 576–77.  (A713/B741).

1.8  Does A Priori Knowledge Involve Some Sort of Infallibility?

23

of a concept, the relation between pure and empirical intuition, and, in particular, which of the intuitively displayed features can safely be ignored. (Friedman 2010, 2012)

These are important questions. Kant, simply, states that we can successfully do all these tasks in mathematics. Kant adds: ‘Philosophy sees the particular in the universal; mathematics, the universal in the particular’. How philosophy can consider the particular in the universal? Is conceptual analysis enough? It appears that it is through conceptual analysis plus the ability, perhaps, of imaginining in pure intuition a particular example, an exemplary image in the mind of the corresponding concept, a pure intuition of a concept, if we are to interpret what he says about philosophy seeing the particular in the universal; in mathematics, he explains, is the other way around, seeing the universal in the particular, from the particular instances of the concept, from the particular intuitions, pure or empirical, we have to see the universal applicability of the concept, its universal truth. How do I get the mathematical concepts? How mathematics can be more secure and successful in extending the use of the faculty of reason than philosophy if, in order to be able to construct a concept, we have first to have, and fully understand, the concept? Is that a task of philosophy? If so, then mathematics would be dependent on the success of philosophy, contrary to what Kant is saying in B 741. His answer is that we invent mathematical concepts. It does seem that the tasks of getting the concepts and constructing from them correspond to mathematics. Kant comments on geometrical knowledge that the task of the geometer is: to bring out what was necessarily implied in the concepts that he had himself formed a priori, and had put into the figure in the construction by which he presented it to himself. If he is to know anything with a priori certainty he must not ascribe to the figure anything save what necessarily follows from what he himself set into it in accordance with his concept.61

Two comments are in order here. Firstly, this passage is ambiguous. On one interpretation, Kant says that the geometer must be only concerned with what necessarily follows from the geometrical concepts in her construction of figures which exhibit these consequences. Some things follow necessarily from what is conceptually thought about the figure. On another interpretation, he seems to be leaving the matter ultimately to the knower who formed herself a priori the concept. If this is so, then there is room for error. Secondly, we can infer that there is another sense of “a priori” in Kant. This sense of “a priori” is a constructive one: what we can construct in our minds obeying what necessarily follows from the concepts, that we have likewise constructed to ourselves. The claim that the notion of a prioricity entails infallibility does not fit with the passage B 756. it is also true that no concept given a priori, such as substance, cause, right, equity, etc., can, strictly speaking, be defined. For I can never be certain that the clear representation of a given concept, which as given may still be confused, has been completely effected, unless I know that it is adequate to its object. But since the concept of it may, as given, include many

61

 B xii; p. 19.

24

1  Kant’s Views on A Priori Knowledge obscure representations, which we overlook in our analysis, although we are constantly making use of them in our application of the concept, the completeness of the analysis of my concept is always in doubt, and a multiplicity of suitable examples suffices only to make the completeness probable, never to make it apodeictically certain. Instead of the term, definition, I prefer to use the term, exposition, as being a more guarded term, which the critic can accept as being up to a certain point valid, though still entertaining doubts as to the completeness of the analysis. Since, then, neither empirical concepts nor concepts given a priori allow of definition, the only remaining kind of concepts, upon which this mental operation can be tried, are arbitrarily invented concepts. A concept which I have invented I can always define; for since it is not given to me either by the nature of understanding or by experience, but is such that I have myself deliberately made it to be, I must know what I have intended to think in using it. I cannot, however, say that I have thereby defined a true object.62

Kant’s view of definition is very strict. No concept given a priori such as cause, substance, etc., admits of a proper definition. We can never be certain that the clear representation of a given concept is complete. A representation of a given concept may still be confused. This contrasts with Kant’s maxim of avoiding any opinion or hypothesis in regard to a priori knowledge that we presented earlier.63 Kant distinguishes between the terms “definition” and “exposition”: what is exposited is that which is accepted, but its analysis may not be complete; one can doubt the completeness of the analysis. He concludes that neither empirical concepts nor a priori given concepts admit definition.64 The only candidates for a definition that remain are concepts which are arbitrarily invented by us. I must know what I have intended to think in using the concept. However, to say that the defined concept applies to an object is a separate matter. For if the concept depends on empirical conditions, this arbitrary concept of mine does not assure me of the existence of, or the possibility of, an object to which to apply the concept. I do not even know from it whether it has an object at all.65 Thus, the only concepts that allow of definition are those ‘which contain an arbitrary synthesis that admits of a priori construction’.66 According to Kant, mathematics is the only science that embodies definitions. Mathematical definitions can never be in error (wrong). “For since the concept is first given through the definition, it includes nothing except precisely what the definition intends should be understood by it.”67 But in the passage B 756, it is completely ignored that we could pick up the wrong definitions. We may have to alter them or choose others. This is important. Moreover, can’t we have what seems to be a valid proof in logic and mathematics, and then later discover a conterexample, and a flaw in the “proof”? The putative proof appeals only to a priori considerations.  A 728 – B 756; A 729 – B 757; pp. 586–7.  A xv, p. 11. 64  A 729–B 757; p. 587. 65  Ibid. 66  Ibid. 67  A 731–B 759; p. 588. 62 63

1.8  Does A Priori Knowledge Involve Some Sort of Infallibility?

25

Kant talks about apodeictic certainty in connection with a priori knowledge. Apodeictic certainty is contrasted with hypothetical certainty. He claims that he shall establish in the Critique, apodeictically not hypothetically, the Copernican insight that objects must conform to our concepts.68 Also Kant affirms that the nature of all apodeictic certainty requires the principle of non-contradiction.69 If “apodeictic certainty” meant “(absolute) necessity”, then it can be argued that when Kant affirmed that a priori knowledge was apodeictically certain, he was not implying that it is infallible knowledge, namely, that knowledge a priori carry a special kind of sureness, but rather that a priori knowledge is knowledge of necessary truths. Kant seems to connect the issue of the necessity of a proposition, and our knowledge of such necessity, with the issue whether the proposition in question is true or false, and our knowledge of the specific truth-value of the proposition. Albert Casullo70 objects to Kant that he is conflating knowledge of the modal status of the proposition – knowing whether it is necessary or contingent – with knowledge of its specific truth-value – knowing whether it is true or false. The distinction between knowing the modal status of a proposition and knowing its truth-value is made by Casullo in response to Kripke’s cases of contingent a priori judgements and necessary a posteriori judgements.71

 Preface to the second edition, note a, p. 25.  A 10–B 14; p. 52. Nevertheless, it may be that for Kant “apodeictic certainty” meant “necessity”, and that it was not then an entirely epistemic concept. Kant identifies both concepts in the following passage: it [mathematical knowledge] carries with it throughly apodeictic certainty, i.e., absolute necessity, which therefore rests upon no empirical grounds. (Prolegomena, p.  32, translated by Paul Carus. Open Court Publishing Company, La Salle, Illinois; my emphasis.) 68 69

 See his ‘Kripke on the A priori and the Necessary’, reprinted in Moser’s anthology A priori Knowledge. Oxford: Oxford University Press, 1987. 71  Casullo argues: Let’s us grant the claim that mathematical propositions are necessary and consider the key claim that experience cannot provide knowledge of necessary propositions. The phrase ‘knowledge of necessary propositions’ masks a crucial distinction between knowledge of the general modal status of a proposition as opposed to knowledge of its truth-value. The basis of Kant’s contention that knowledge of necessity is a priori is the observation that ‘Experience teaches us that a thing is so and so but not that it cannot be otherwise’. This observation establishes at most that the general modal status of necessary propositions cannot be known on the basis of experience. It does not support the conclusion that the truth-value of a necessary proposition cannot be known on the basis of experience. For it allows that experience can provide knowledge that a thing is so and so. Hence, Kant’s observation fails to support his key claim that knowledge of mathematical propositions such as ‘7 + 5 = 12’ is a priori. For this is a claim about knowledge of the truthvalue of such propositions rather than a claim about knowledge of their general modal status. (ibid, p. 5; Casullo’s emphasis) When Casullo affirms that knowledge of the modal status of a proposition can only be known a priori, he is like Kant ignoring the fact that we can obtain this knowledge by testimony, therefore, by experience also. 70

26

1  Kant’s Views on A Priori Knowledge

But to connect is not necessarily to conflate. Where is the evidence for the latter? Casullo does not offer it. It seems to me that the separation of the issue of truth-­ value from that of necessity is not obviously in tune with Kant’s own thinking. Can we talk of “necessary” without referring to “necessarily true”? That is: for him the necessity arises through the way in which we must come to grasp a truth-value. So necessary-truth is a special sort of truth, not just a property tacked on independently to a truth. In fact, this is the primary support for the idea (which I share) that Kant’s notion of the synthetic a priori is given relative to capacities of human cognition – and not absolutely. I think that since Kant does not distinguish between the modal status and the truth-value of a proposition, that partly explains precisely why some authors, for instance, Casullo and Philip Kitcher, have attributed to Kant the view that a priori knowledge entails infallibility.

1.8.2 Kitcher’s and Friedman’s Views on Kant Kant’s notion of a priori knowledge has been taken by some authors, like Kitcher, for example, to entail infallibility. My support for this contention is the following passages of Kitcher: Kant’s picture presents the mind bringing both its own creations and the naive eye of the mind scanning these reactions and detecting their properties with absolute accuracy.72 in the Kantian case … the propositions which are alleged to be known a priori are taken to be necessary, so that the question of whether it would be possible to have an a priori warrant for a false belief does not arise.73

A consequence of Kitcher’s argument is that a priori warrants only warrant true beliefs. If that were not the case, it would show, for Kitcher, that a priori knowledge is not independent of experience, for example, the “experience” of finding a mistake in our warrant for a belief. (It is clear that the notion of experience involved is very broad). What better to guarantee that a priori warrants must always produce true beliefs than taking them as producing knowledge infallibly. Moreover, since Kitcher accepts the possibility of a priori knowledge of contingent propositions, he goes on constructing a notion of a priori justification that has to deliver knowledge infallibly independently of the modal status of the proposition in question. Kitcher refers to Kant: The mathematician ‘constructs his concepts in a priori intuition,’ and by doing so he is able to ‘combine the predicates of the object both a priori and immediately’ (A732, B760), thus obtaining starting points for proofs; then ‘through a chain of inferences guided throughout

 This passage appears originally in Kitcher’s paper, “Kant and the Foundations of Mathematics”, Philosophical Review 84, p. 50, 1975. 73  Kitcher, The Nature of Mathematical Knowledge, p. 24. 72

1.8  Does A Priori Knowledge Involve Some Sort of Infallibility?

27

by intuition, he arrives at a fully evident and universally valid solution to the problem’ (A717, B745). (“Kant and the foundations of mathematics”, p. 39)

This quote is based on different passages of Kant, and it is quite confusing. The last part of the quote based on the passages A717 and B745 can easily give the misleading impression that for Kant all inferential knowledge is evident, what would be an absurd consequence. The example of the geometrical construction in question is a simple one, so the deductions are short and not very complicated, so that is why Kant thinks that the deductions are evident. Friedman emphasizes74 the importance of symbolization in Kant’s philosophy, and how it serves to distinguish mathematical reasoning from other kinds of reasoning, for example, philosophical reasoning. this ‘symbolic concreteness’ of mathematical proof accounts for the difference between philosophical and mathematical certainty. Since philosophical argument is discursive or conceptual, ambiguities and equivocations in the meanings of general concepts are always possible. Mathematics, on the other hand, works with concrete or singular representations that allow us to be assured of the correctness of its substitutions and transformations ‘with the same confidence with which one is assured of what one sees before one’s eyes’. (291.29–30) As Kant puts it in the first Critique, the step by step application of the easy and secure rules of calculation ‘secures all inferences against error by setting each one before our eyes’ (A734/B762) (op.cit., p. 85)

Friedman explains how and why mathematics is not only synthetic, but also known a priori. The rigorous representation of mathematical concepts and propositions requires schemata: constructions in pure intuition. In the case of arithmetic we are given the general capacity for successively iterating any operation in time; in the case of geometry we are given in addition certain fixed, specifically spatial operations as input: the constructions underlying Euclid’s geometry. We can only think the propositions of mathematics by …. presupposing the required constructions, and it follows …. that the true propositions of mathematics are then necessarily true … The truth of the true propositions of mathematics follows from the mere possibility of thinking or representing them, and this is the precise sense in which we know them a priori.75

In an important note, Friedman asks himself the following question: What about the false propositions of mathematics? They too can only be adequately thought or represented by means of the constructions that guarantee the truth of the true propositions of mathematics; the conditions for adequately thinking and reasoning with any mathematical proposition thereby imply their impossibility. The situation is precisely analogous, in fact, to the status (for us) of a logical contradiction.76

The point seems to be that we can understand the false propositions of mathematics by thinking and representing the true ones, and then coming to the conclusion that their negations are impossible – mathematical truths are assumed to be necessary, so their negations are contradictions.  Friedman, Michael. Kant and the Exact Sciences. Harvard University Press, 1992, p. 85.  Friedman, p. 127. 76  Note 51, p. 127. 74 75

28

1  Kant’s Views on A Priori Knowledge

Now it is not clear that Friedman is saying only this. For example, we might use a geometrical figure to give a counterexample to a certain (false) mathematical claim. Also there are impossibilities that are not contradictions. In the mathematical case, even if we grant that Kant was so confident about the help of symbolization and the powers of our intellectual capabilities  – which he expressed in relation to mathematical definitions77 – we have to take into consideration the trivial fact that mathematical knowledge does not merely consist of definitions, but that it also necessarily involves inference in our acquisition of new mathematical knowledge. Kant speaks about geometrical axioms as being self-­ evident. But these again are only parts of mathematical knowledge. Some long proofs present a problem of unsurveyability, and that in relation to them, Kant’s optimistic views do not apply so easily, or not at all. So, what is Kant really saying? It is not straightforward because Kant simply assumed that all our a priori knowledge was of necessary truths; that necessity was an infallible criterion to distinguish a priori truths from empirical truths. But, are we infallible about recognizing the difference between this sort of necessity and physical necessity? It seems that Kant’s explanation of why certain truths are a priori is because they are necessary. However, this response is not much of an explanation until we define the intended kind of necessity. Friedman interprets Kant as maintaining that the faculty of pure intuition is powerful enough to give us knowledge of mathematical truths, being synthetic and a priori. Unfortunately, Friedman does not say anything about long proofs.78 Neither does Kant. Friedman affirms that pure intuition could not be understood according to a perceptual model as some interpreters of Kant have suggested as a way to explain Kant’s metaphor of “seeing with the mind’s eye”, since perception could not have the generality nor the precision that Kant assigns to pure intuition.79 But, then, Friedman is uncritical of Kant’s conception of pure intuition. Friedman does not consider that perhaps the faculty of intuition does not have the powers it is supposed

 Kant does not claim that logic has definitions, only mathematics.  Actually, there are some related remarks: when Kant himself uses ‘visual inspection’ and ‘eye of the mind’ metaphors, it is almost always in connection with inference and proof. Thus, in the passage from the Enquiry, Third Reflection, § 1 … Kant says that we can check the correctness of algebraic substitutions and transformations ‘with the same confidence with which one is assured of what one sees before one’s eyes. At A734/B762 we are told that the procedure of algebra “secures all inferences against error by setting each one before our eyes.” The intuition involved here is not a quasi-perceptual faculty by which we “read off” the properties of triangles from particular figures, but that involved in checking proofs step by step in ‘operating a calculus.’ (Friedman, op. cit., p. 92) The issue of long proofs is not arised. 79  Friedman concludes: It is then easy to see that pure intuition, conceived on this quasi-perceptual model could not possibly perform such a role. Our capacity for visualizing figures has neither the generality nor the precision to make the required distinctions. (op. cit., p. 90) It is interesting to observe that Friedman rejects a quasi-perceptual understanding of the operations of pure intuition because then pure intuition could not perform its operations absolutely accurately. 77 78

1.8  Does A Priori Knowledge Involve Some Sort of Infallibility?

29

to have in the first place. So, it is not clear how Friedman would reconcile his view on Kant with the fallibility of our ways of knowing even a priori knowledge. Friedman defends two senses of the a priori in Kant following Reichenbach: Reichenbach distinguishes [in The Theory of Relativity and A Priori Knowledge] two meanings of the Kantian a priori: necessary and unrevisable, fixed for all time, on the one hand, and ‘constitutive of the concept of the object of [scientific] knowledge’, on the other. Reichenbach argues, on this basis, that the great lesson of the theory of relativity is that the former meaning must be dropped while the latter must be retained … What we end up … is thus a relativized and dynamical conception of a priori mathematical-physical principles, which change and develop along with the development of the mathematical and physical sciences themselves, but which nevertheless retain the characteristically Kantian constitutive function of making the empirical natural knowledge thereby structured and framed by such principles first possible.80

Friedman adopts this distinction of Reichenbach in the construction of his own notion of a prioricity. Nonetheless, Friedman does not clarify the issue of our fallibility in connection to these two ways of understanding the Kantian a priori. As Kitcher suggests, it seems that the question of whether it would be possible to have an a priori warrant for a false belief does not arise for Kant.81 Perhaps Kant did not think such a question could arise. Did he not neglect the possibility of seemingly valid proofs or seemingly correct definitions? I think it is unfair of Kitcher to adjudicate to Kant the view that there is no possibility of an a priori warrant justifying a false belief by merely invoking Kant’s claim that all a priori knowledge is knowledge of necessary truths. We have to know how the justification for the necessary truth stands – it may not amount to knowledge. And if the warrant produces knowledge, it is because it is a good or sound warrant. The modal status of the truth known

80  Friedman, M. “Transcendental Philosophy and A Priori Knowledge” in New Essays on the Apriori. Edited by Paul Boghossian and Christopher Peacocke. Oxford: Oxford University Press, p. 370, 2000. 81  Kitcher states: … to generate knowledge independently of experience, a priori warrants must produce warranted true belief in counterfactual situations where experiences are different. This point does not emerge clearly in the Kantian case because the propositions that are alleged to be known a priori are taken to be necessary, so that the question of whether it would be possible to have an a priori warrant for a false belief does not arise. Plainly we could ensure that a priori warrants produce warranted true belief independently of experience by declaring that a priori warrants only warrant necessary truths. But this proposal is unnecessarily strong. Our goal is to construe a priori knowledge as knowledge which is independent of experience, and this can be achieved, without closing the case against the contingent a priori, by supposing that, in a counterfactual situation in which an a priori warrant produces belief that p, then p. On this account, a priori warrants are ultra-reliable; they never lead us astray. (Kitcher, op. cit., p. 24; my emphasis) Kitcher’s strategy to deal with the possibility of the contingent a priori is to move the modality (i.e. necessity) from the truth known to the warrant, such that a priori knowledge does not have to be knowledge of necessary truths, but at the same time a priori warrants necessarily produce true beliefs, they necessarily deliver truth. So, we can accept the possibility of a priori knowledge and still capture a certain necessity attached to a priori knowledge: the fact that a priori warrants necessarily deliver truth. But what Kitcher seems to forget is that truth is a necessary condition for any knowledge.

30

1  Kant’s Views on A Priori Knowledge

by its means is a separate matter. Kitcher accepts this. But Kitcher adjudicates his conception of a “warrant” to Kant. Unfortunately, Kant did not elaborate on the notion of an a priori justification. Since the notion of a priori justification is the crucial one to characterize in the epistemology of a priori knowledge, contrary to Kitcher and Friedman, it remains unclear if, for Kant, a priori knowledge implied some sort of infallibility.

1.9 Conclusion Kant exhibited a tremendous enthusiasm and trust in our intellectual faculties. This enthusiasm is shared by the thinkers of his time. In the Enlightenment, the powers of human reason were thought to be unlimited. He was a man of his time, though he was very critical of the traditional method of doing metaphysics – he sets limits to metaphysics in the first Critique. He assumes that since we have a priori knowledge that is necessary and universal, we have to possess a faculty or capacity that can explain our possession of knowledge of this sort. According to Friedman, given that his logic could not explain how we can have knowledge of an infinite number of objects, he sought to explain this knowledge by endowing much power to pure intuition and, in that way, accounting for the secure a priori knowledge we in fact possess. On the other hand, Kant accepts that new concepts can be introduced, for instance, in mathematics. Nevertheless, if new concepts are introduced by means of definitions, then no error is supposed to arise. Of course, our exercise of the faculties of reason and understanding can be faulty. That is one of the main points in the Critique: namely, to put limits to the faculty of reason since it naturally tends to complete or extend the causal chains, for instance, beyond the determinate or conditioned. The antinomies of reason result from the misapplication of the categories of the understanding – by the exercise of the faculty of reason  – beyond what is object of experience, or, the same thing, beyond the realm of appearance. The issue whether Kant’s notion of a priori knowledge entails that we have infallible access to a priori items of knowledge is very complex. Now it can be argued that, for Kant, our knowledge of the truth of some propositions is infallible. For instance: can we be wrong about the proposition that “Every alteration must have a cause” or about the trivially analytic ones? It may be that, for Kant, of at least some items of a priori knowledge, we are infallible. Kant intends to account for a necessity which we are supposed to know: that objects of experience necessarily conform to the mathematical laws of space and time. Does he also intend to account for our knowledge of this kind of necessity? At first sight, it would seem that this is not the case. Kant does not regard the human mind as transparent in itself, (see his discussion of transcendental reflection of concepts in the first Critique) or as more easily understood than the physical world.

1.9 Conclusion

31

Though, there is a sense in which Kant’s view is put forward to explain our knowledge of necessity, and not merely to explain the necessity we know. The status of space and time in experience is special, and it is because of this special status that Kant holds they must be attributed to the nature of the mind. No other explanation can account for the fact that our knowledge of space and time possesses apodeictic certainty and also applies universally to all objects of experience. Kant’s theory is not merely possible or probable. He claims that it is absolutely certain.82 Paton comments that “the fact that now there are different kinds of geometry and different kinds of space is not in itself fatal to Kant’s doctrine that our knowledge of space is a priori; for a priori knowledge may be acquired gradually and may at any stage be confused or ‘indistinct’”. I think that Kant was more optimistic about our acquisition of mathematical knowledge than he was of our knowledge a priori of the categories, contrary to what Paton seems to imply. Paton appears to be treating any kind of a priori knowledge on a par. It is clear that Kant accepted the possibility of having confused or indistinct concepts in our knowledge of the categories, but not so clear if this is so in mathematical knowledge. Actually, the opposite seems to be true. Now it is true that Kant recognizes that our knowledge of the categories may be confused or indistinct. But in doing this, he refers to our knowledge of their specific constitution. Our basic knowledge that the categories are necessary conditions for the possibility of our thinking an object of a possible experience is taken as absolutely indisputable. Nevertheless, in proving this he appeals to some obscure arguments in the Transcendental Deduction. Contrary to Kitcher and Friedman, I conclude that the issue of infallibility in connection with a priori knowledge is not a clear issue in Kant at all. As a matter of fact, this whole issue is very intricate and has helped me to disentangle some of the aspects of our question, for instance, the role the alleged necessity of the judgments known a priori has in connection with the possible infallibility we can have in our acquisition of a priori knowledge.83 Even more, Kant’s views do not entail that a priori knowledge entails some sort of infallibility. Kant knew about long proofs from Euclid. Kant would have accepted that we are liable to err when carrying out long proofs – which nevertheless contain axioms which would themselves be known a priori. Finally, a very important point is in order. Naturally, whether Kant did succeed or not in characterizing both the notion of a priori knowledge and the notion of “experience independence” distinctive of it, has a direct bearing on the attempt to answer whether Kant considered a priori knowledge to involve some sort of infallibility. It is difficult to get clear about the answer he would have given to this question given that he was not clear about the characterization of a priori knowledge in

 A 49–B 66; p. 86.  See chapter X, section 3, pp.  330–36, where I discuss some of the confusions involved in this area. 82 83

32

1  Kant’s Views on A Priori Knowledge

the first place. Kant does not even explicitly characterize what is the “independence of experience” characteristic of a priori knowledge. A more explicit characterization of a priori knowledge constitutes a necessary step in order to clarify its relationship with the notion of infallibility, properly conceived. One thing emerges very neatly from our discussion of Kant. Both the urgency for providing an explicit characterization of the notion of a priori knowledge as well as the importance of the question whether infallibility is a distinctive property of a priori knowledge remain. I address these extremely difficult questions in the last chapter.

References Bennett, J. 1966. Kant’s Analytic. Cambridge: Cambridge University Press. Boghossian, P. 1997. Analyticity. In Companion to the Philosophy of Language, ed. B. Hale and C. Wright. Oxford: Blackwell. Boghossian, P., and C. Peacocke. 2000. New Essays on the A Priori. Oxford: Oxford University Press. BonJour, L. 2005. In Defense of the A Priori. In Contemporary Debates in Epistemology, ed. M. Steup and E. Sosa, 98–105. Malden: Blackwell. Carnap, R. 1962. The Logical Foundations of Probability. Chicago: Chicago University Press. Casullo, A. 1977a. The Definition of A Priori Knowledge. Philosophical and Phenomenological Research 38: 220–224. ———. 1977b. Kripke on the “A Priori” and the Necessary. Analysis 37: 152–159. Reprinted in Moser. ———. 1988a. Necessity, Certainty and the “A Priori”. Canadian Journal of Philosophy 18: 43–66. ———. 1988b. Revisability, Reliabilism, and A Priori Knowledge. Philosophy and Phenomenological Research XLIX (2). ———. 2003. A Priori Justification. Oxford: Oxford University Press. ———. 2006. Knowledge, A Priori. In The Encyclopedia of Philosophy, ed. D.M. Borchert, vol. 5, 2nd ed., 79–86. Detroit: MacMillian Reference. ———. 2012. Essays on A Priori Knowledge and Justification. New York: Oxford University Press. Casullo, A., and J. Throw, eds. 2013. The A Priori in Philosophy. Oxford: Oxford University Press. Caygill, H. 1995. A Kant Dictionary. Cambridge: Blackwell. Chisholm, R.M. 1977. The Truths of Reason. In Theory of Knowledge, 2nd ed. Englewood Cliffs: Prentice-Hall. Reprinted in Moser. Coffa, J.A. 1991. The Semantic Tradition from Kant to Carnap: To the Vienna Circle. New York: Cambridge University Press. Craig, E.J. 1975. The Problem of Necessary Truth. In Meaning, Reference and Necessity, ed. Simon Blackburn. Cambridge: Cambridge University Press. Creath, R. 1990. Dear Carnap Dear Van: The Quine-Carnap Correspondence and Related Work. Berkeley: University of California Press. Dancy, J., and E. Sosa, eds. 1985. Introduction to Contemporary Epistemology. Oxford/New York: B. Blackwell. ———, eds. 1992. Companion to Epistemology. Oxford/Cambridge, MA: Blackwell. Edidin, A. 1984. “A Priori” Knowledge for Fallibilists. Philosophical Studies 46 (Spring 84): 189–198. Frege, G. 1952. On Sense and Reference. In Translations from the Philosophical Writings of Gottlob Frege, ed. M. Black and P. Geach, 56–78. Oxford: Basil Blackwell. Reprinted in Part in Benacerraf and Putnam. ———. 1953. The Foundations of Arithmetic. Oxford: Basil Blackwell. Friedman, M. 1992. Kant and the Exact Sciences. Cambridge, MA: Harvard University Press.

References

33

———. 2000a. Transcendental Philosophy and A Priori Knowledge: A Neo-Kantian Perspective. In Boghossian and Peacocke, 367–383. Oxford: Oxford University Press. ———. 2000b. Geometry, Construction and Intuition in Kant and His Successors. In Between Logic and Intuition: Essays in Honor of Charles Parsons, ed. G.  Scher and R.  Tieszen, 186–218. Cambridge: Cambridge University Press. ———. 2010. Synthetic History Reconsidered. Domski and Dickson 2010: 573–813. ———. 2012. Kant on Geometry and Spatial Intuition. Synthese 186: 231–255. Guyer, P., ed. 1992. The Cambridge Companion to Kant. Cambridge, MA: Cambridge University Press. ———., ed. 2006. The Cambridge Companion to Kant and Modern Philosophy. Cambridge: Cambridge University Press. Hale, B. 1987. Abstract Objects. Oxford: Basil Blackwell. ———. 2015. Necessary Beings: An Essay on Ontology, Modality and the Relations Between Them. Oxford: Oxford University Press, Reprint edition. Hale, B., and C. Wright, eds. 1999. Companion to the Philosophy of Language. Wiley-Blackwell. Hintikka, J. 1965. Kant’s ‘New Method of Thought’ and His Theories of Mathematics. Ajatus 27: 37–47. ———. 1967. Kant on the Mathematical Method. The Monist 51 (3): 352–375. [Reprinted in Posy 1992]. ———. 1969. On Kant’s Notion of Intuition (Anschauung). In The First Critique, ed. T. Penelhum and J.J. MacIntosh. Belmont: Wadsworth Publishing. ———. 1984. Kant’s Transcendental Method and His Theory of Mathematics. Topoi 3 (2): 99–108. [Reprinted in Posy 1992]. Jenkins, C.S.I. 2008. A Priori Knowledge: Debates and Developments. Philosophy Compass 3 (3): 436–450. Jenkins Ichikawa, J., and B.W. Jarvis. 2013. The Rules of Thought. Oxford: Oxford University Press. Kant, I. 1902. Prolegomena. Trans. Paul Carus. La Salle: Open Court Publishing Company. ———. 1956. Critique of Pure Reason. Trans. Norman Kemp Smith. New York: St. Martin’s. Kim, J., and E. Sosa, eds. 1995. A Companion to Metaphysics. Cambridge: Blackwell. Kitcher, Philip. 1975. Kant and the Foundations of Mathematics. Philosophical Review 84: 23–50. ———. 1980a. A Priori Knowledge. Philosophical Review 89: 3–23. ———. 1980b. Apriority and Necessity. Australasian Journal of Philosophy 58: 89–101. Reprinted in Moser. ———. 1981. How Kant Almost Wrote “Two Dogmas of Empiricism”. Philosophical Topics 12: 217–250. ———. 1983. The Nature of Mathematical Knowledge. Oxford: Oxford University Press. Kitcher, Patricia. 1984. Kant’s Transcendental Psychology. New York: Oxford University Press. Kitcher, Philip. 2000. A Priori Knowledge Revisited. In New Esssays on the Apriori, ed. P. Boghossian and C. Peacocke, 65–91. Oxford: Oxford University Press. Kripke, S. 1971. Identity and Necessity. In Identity and Individuation, ed. M.K. Munitz. New York: New York University Press. ———. 1980. Naming and Necessity. Cambridge, MA: Harvard University Press. ———. 1982. Wittgenstein on Rules and Private Languages. Cambridge, MA: Harvard University Press. Maddy, P. 1980. Perception and Mathematical Intuition. The Philosophical Review 89: 168–196. ———. 1990. Realism in Mathematics. Oxford: Oxford University Press. Mill, J.S. 1950a. Philosophy of Scientific Method. New York: Hafner Publishing. ———. 1950b. A System of Logic. Reprinted in Mill. Moser, P.K. 1987. A Priori Knowledge. Oxford: Oxford University Press. Pap, A. 1946. The A Priori in Physical Theory. New York: King’s Crown Press. ———. 1958. Semantics and Necessary Truth. New Haven: Yale University Press. Parsons, C. 1964. Infinity and Kant’s Conception of the ‘Possibility of Experience’. The Philosophical Review 73 (2): 182–197.

34

1  Kant’s Views on A Priori Knowledge

———. 1967. Foundations of Mathematics. In The Encyclopedia of Philosophy, ed. Paul Edwards, vol. 5–6, 188–212. New York: Macmillan. ———. 1969. Kant’s Philosophy of Arithmetic. In Philosophy, Science and Method: Essays in Honor of Ernest Nagel, ed. S.  Morgenbesser, P.  Suppes, and M.  White. New  York: St. Martin’s Press. ———. 1983. Mathematics in Philosophy: Selected Papers. Ithaca: Cornell University Press. ———. 1992. The Transcendental Aesthetic. In Guyer 1992, 62–100. ———. 2010. Two Studies in the Reception of Kant’s Philosophy of Arithmetic. In Domski and Dickson, 135–153. ———. 2012. From Kant to Husserl: Selected Essays. Cambridge: Harvard University Press. Paton, H.J. 1936. Kant’s Metaphysic of Experience. London: George Allen & Unwin Ltd. First Edition, vols. 1 & 2, 1936. Prichard, H.A. 1976. Kant’s Theory of Knowledge. New York: Garland Pub. Russell, B. 1973. The Problems of Philosophy. New York: Oxford University Press. Wilder, R. 1975. Evolution of Mathematical Concepts. New York: Wiley. Yablo, Stephen. 1993. Is Conceivability a Guide to Possibility? Philosophical and Phenomenological Research 53 (1): 1–42. Allison, Henry E. 1973. The Kant-Eberhard Controversy. Baltimore: John Hopkins University Press.

Chapter 2

Quine’s Views on A Priori Knowledge

Abstract  In this chapter I shall closely examine Quine’s criticisms of the notion of a prioricity. There is ample justification to examine Quine’s position: for, first, his discussion of these matters has been enormously influential, and, second, it is a discussion which leaves its opponents – defenders of a prioricity and analyticity – with interesting lines of investigation still open. I argue for two main points: first that a priori knowledge does not have to be conceived as infallible (and so as requiring unrevisability as Quine requires a priori knowledge to do), and second that the scope of revision of items of a priori knowledge (i.e. of a priori warrants and a priori statements) might include empirical revision. Keywords  A prioricity · Analyticity · Epistemological holism · Revision · Unrevisability I begin with an introduction presenting the problem of a priori knowledge in the context of Quine’s discussion, followed by five sections. In the second section I take up Quine’s attack on a priori knowledge. Section three addresses the question whether he does distinguish between the notions of a prioricity and analyticity in “Two Dogmas”. In the fourth section, I discuss how to understand “revision” in Quine. In section five I argue that epistemological holism and belief in a priori knowledge ought not to be incompatible. Section sixth consists of the conclusion.

2.1 The Problem of A Priori Knowledge The existence of a priori knowledge has always been a problem for empiricists. The problem arises from the incompatibility of the following two theses. I. The thesis of empiricism: that all knowledge is (ultimately) grounded on experience. II. The thesis that there is a priori knowledge, that is, knowledge which is independent of experience. Mathematics and logic are considered paradigms of disciplines © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 I. Fred-Rivera, A Historical and Systematic Perspective on A Priori Knowledge and Justification, Philosophical Studies Series 151, https://doi.org/10.1007/978-3-031-06874-4_2

35

36

2  Quine’s Views on A Priori Knowledge

constituted by a priori knowledge. In addition many sentences the content of which is neither purely logical nor purely mathematical are said to be known a priori: “All bachelors are unmarried men”, “All bodies are extended” and “Nothing is simultaneously red and green all over”. The conflict is that if these sentences are known independently of experience, then they constitute an exception to the thesis of empiricism – that all knowledge is ultimately grounded in experience – and thus could be seen to constitute a refutation of it. Another way to try to refute the thesis of empiricism is to maintain that there are truths which are not falsifiable by experience. For example, it seems impossible to come up with a set of observations which would constitute empirical disconfirmation of “2 + 2 = 4”. When there appears to be empirical discomfirmation of elementary arithmetical statements, for example, we tend to always either find that there is a mistake involved in our calculation, or are inclined to think that there is such a mistake though we have not yet found it. Some empiricists, those who deny the existence of a priori knowledge in general, have believed that mathematical knowledge is empirical, that it rests on sensory experience. An immediate example of such a view is Mill’s. For Mill, mathematical propositions are inductive generalizations based on an extremely large number of instances. He tries to explain the certainty of our knowledge of some mathematical truths by the fact that arithmetic, for instance, is widely applied to the physical world. The fact that the number of supporting instances is so large accounts for our believing these generalizations to be necessarily and universally true. There are well-known criticisms of Mill’s position, i.e., those made by Frege in the Foundations.1 It is worth noting that Mill makes an important distinction between real and merely verbal propositions. I think he would allow that the latter are in some sense known a priori, but deny that they embody real or substantial knowledge. John Skorupski in his book on Mill makes a good case that Frege’s criticisms of Mill are far less telling than they are commonly supposed to be.2 I take it that the best possible objection to Mill’s view is directed to the idea that mathematical propositions are in principle directly confutable by e.g. counter-arithmetical counting results.3

1  Frege, Gottlob. Foundations of Arithmetic. Translated by J.  L. Austin. Oxford: Basil Blackwell, 1953. 2  Skorupski, John. John Stuart Mill. London and New York: Routledge, 1989. 3  According to Michael Resnik, Mill does not allow empirical falsification of arithmetic. (Frege and the Philosophy of Mathematics. Ithaca, N.Y.: Cornell University Press, p. 152, 1980.) But I find this incoherent. For Mill, mathematical truths are inductive generalizations about physical objects. Therefore, their justification must be based on experience – it does not seem to be permissible their having an a priori justification. Now clearly when our justification of X can be based on experience, it does not follow that X can be falsified by experience. For an empirical statement P, P or not P can be justified by P, but “P or not P” cannot be falsified by experience. But it is one thing to say “X can be based on experience” and another “X must be based on experience if at all”. The latter is what I take Mill to be saying. How can’t mathematical statements (or logical statements) be falsifiable by experience when their justification must be based on experience being the former inductive generalizations about

2.1  The Problem of A Priori Knowledge

37

After Mill, some empiricists, the logical positivists,4 who accepted the existence of a priori knowledge – though they were out to undercut the notion – and considered mathematical and logical truths to be known a priori, tried to account for our certainty of mathematical truths by explaining them in terms of their being true by convention or true in virtue of the meanings of the terms involved (i.e. in terms of their being analytic). The logical positivists were, like Mill, empiricists, however, they rejected Mill’s view that mathematical propositions are inductive (empirical) generalizations. They argue for an even stronger conclusion: that mathematical propositions are not supported by sensory experience at all. The argument5 goes as follows: If a proposition is an empirical hypothesis, then it is at least theoretically disconfirmable by observations. This means that if a hypothesis is empirical, then it is possible to indicate what kind of empirical evidence would disconfirm it. There is no evidence (empirical or of any sort) that would disconfirm propositions of elementary arithmetic. Since there is no disconfirming evidence for mathematical propositions, then mathematical propositions are not empirical hypotheses of any sort. They are neither empirical generalizations nor empirically supported theoretical hypotheses. We don’t let anything count as a counterexample to mathematical laws. That is the way we use mathematical laws in general. The alleged special certainty we have and the necessity of mathematical truths results from our conventions to use language the way we do. Since mathematical truths are analytic, they lack factual content. They are interesting, very useful and a challenge for the intellect of fallible creatures like us. We are finite creatures with limited intellectual capacities who cannot apprehend at once long and complex truths. But for a being who is not limited in this way, mathematical truths would be trivial. According to the logical positivists, what traditionally has been conceived as a serious threat to empiricism, namely, the existence of a priori knowledge – knowledge which is a counterexample to the empiricist claim that all knowledge is ultimately grounded on experience  – in the end proves to be no threat at all. Now the challenge for the empiricists is to explain how such trivial truths can be at the same time so useful in their applications to empirical sciences. Even though Ayer himself posits this as a

physical objects? I don’t see how Mill can sustain both claims: (1) that “mathematical truths” are inductive generalizations about physical objects, and (2) that they cannot be falsifiable by experience. Mill has to allow for the possibility of empirical falsification of mathematical statements because they are allegedly inductive generalizations about physical objects that, when true, they are only contingently true, so they could be false, and when that is the case and we know it, then we are supposed to know that a posteriori. Another puzzling issue is to what extent “mathematical truths” are mathematical given that, on Mill’s view, they are about physical objects. 4  I am fully aware that there are more arguments in all positivism. What I intend here is to provide an overview to motivate my own discussion of Quine. 5  This is not the only argument logical positivists offer against a priori knowledge, but it is certainly one of the most important ones.

38

2  Quine’s Views on A Priori Knowledge

real problem to be addressed, he does not provide that explanation. Rather the explanation he gives is in terms of psychological novelty.6 Arguments against the logical positivist notion of mathematical truth and mathematical knowledge (and logical truth and logical knowledge) are well-known too, such as those of Quine, in “Truth by Convention”.7 Quine demonstrated that convention cannot explain the truth of logical laws. Since logical laws form an infinite class, they must be captured as instances of general principles. But as logic is required to accomplish the inference from general laws to these instances, conventionalism cannot offer a complete explanation of logical truth.8

2.2 Quine’s Empiricist Attack on the Notion of A Priori Knowledge In “Two Dogmas of Empiricism”, Quine begins by attributing two dogmas to modern empiricism: (a) a belief in the dichotomy between analytic and synthetic truths, and (b) a belief in a sort of reductionism, according to which every meaningful sentence is equivalent to some sentence the terms of which refer to immediate sensory experience. Quine criticizes9 the view that analytic truths are those which hold no matter what. In considering this conception of analyticity, Quine examines as well an influential positivist view of a prioricity as epistemic unrevisability. Quine questions the actual epistemological significance of such a prioricity on the basis of the following consideration: any statement can be held true come what may, if we make drastic enough adjustments elsewhere in the system of accepted statements. By the same token, the converse also holds: no statement is immune to revision.10 A basic

 Ayer, A. J. “The A priori”. Chapter 4 of Ayer’s Language, Truth and Logic, 2nd edition. London: Victor Gollanncz, Ltd., 1946. 7  Quine, W. V. O. “Truth by Convention” in The Ways of Paradox and Other Essays. Cambridge, MA: Harvard University Press, pp. 77–106, 1976. 8  Quine summarizes his argument of “Truth by Convention” in his other essay “Carnap and Logical Truth”: 6

Briefly the point is that the logical truths, being infinite in number, must be given by general conventions rather than singly; and logic is needed then to begin with, in the metatheory, in order to apply the general conventions to individual cases. (“Carnap and Logical Truth” in The Ways of Paradox, p. 108) 9  Quine writes: The verification theory of meaning, which has been conspicuous in the literature from Peirce onward, is that the meaning of a statement is the method of empirically confirming or infirming it. An analytic statement is that limiting case which is confirmed no matter what. (“Two Dogmas of Empiricism” in From a Logical Point Of View. Cambridge, Mass.: Harvard University Press, p. 37, 1980; my emphasis) 10  “Two Dogmas”, p. 43.

2.2  Quine’s Empiricist Attack on the Notion of A Priori Knowledge

39

outcome of Quine’s opposition to the two dogmas is that “our statements about the external reality face the tribunal of sense experience not individually but only as a corporate body”.11 The positivist verifiability criterion – according to which the meaning of a statement is identical with the method of verifying it – assumes that we can examine individual sentences for empirical content. It is precisely this aspect of empiricism that Quine rejects and refers to as the dogma of reductionism.12 The dogma of reductionism and the other dogma – that there is a clear distinction between analytic statements and synthetic statements – are closely connected. The dogma of reductionism supports the other in the sense that if talk of confirmation of a statement is significant, it would be also significant to talk about a limit case of statements which are true no matter what, that is, analytic statements. That is to say that the second dogma – the reductionist one – supports a particular interpretation of the first. If statements can be confirmed or disconfirmed individually, then it is possible to talk about a limiting case of a statement which is confirmed, in isolation, no matter what.13 According to Quine, in the face of a recalcitrant experience we can revise one or more of our beliefs. Quine would invoke a principle of conservatism to retain those statements that clash least with the rest of our body of beliefs. He has called this principle a “maxim of minimum mutilation”. The last alternative available to us in testing is to question the principles of logic and mathematics involved. Thus, for instance, the testing in which Newtonian physics was replaced by Einstein’s theory of relativity resulted in, among other things, the replacement of Euclidean geometry by a non-Euclidean variety.14 In somewhat the same experimental spirit it has been suggested that the logical principles used for quantum mechanics should be those, not of two-valued logic, but of a deviant logic.15 Now while this proposal has by no means met general support, its importance lies in the fact that it can be made, that is, in the face of negative findings an alternative, albeit not a very likely one, would be to revise the standard principles of logic.16

 “Two Dogmas”, p. 41.  Quine affirms: The dogma of reductionism survives in the supposition that each statement, taken in isolation from its fellows, can admit of confirmation or infirmation at all. (ibid) 13  The concept of analyticity is a semantical concept. What is interesting from our point of view is that the characterization in question is epistemological – what appears to be a ground for thinking that Quine did not distinguish between the notions of analyticity and a prioricity. More on this issue in the next section. 14  In the nineteenth century, non-Euclidean geometries were formulated as alternatives to the Euclidean paradigm. Mostly, the transition from Euclidean to non-Euclidean geometries was considered a change in language, while the underlying facts remain the same. This insight gave rise to conventionalist approaches in the sciences, for example, in the work of Helmholtz or Poincaré, which were later taken up by philosophers like Quine. 15  “Deviant Logics” in Philosophy of Logic. Englewood Cliffs, N.J.: Prentice Hall, pp. 85–6, 1970. 16  “The Ground of Logical Truth” in Philosophy of Logic, p. 100. 11 12

40

2  Quine’s Views on A Priori Knowledge

For Quine, revision is governed by two principles: simplicity and conservatism. We want to effect as simple and tidy a system as possible, and we want to preserve as much of our previous beliefs as possible. Note that these are global considerations dictating features of the overall system rather than any part of it. As a result there is much latitude in where to revise within the system; in fact any statement is open to revision, including the statements of logic and mathematics, and any statement may be retained come what may in the way of evidence, should we choose to retain it. In order to revise some beliefs, we may have to revise others because of their logical connections. Logical and mathematical beliefs are not different in kind from other beliefs but only in the degree of our reluctance to abandon them.

2.3 Does Quine Distinguish Between the Notions of A Prioricity and Analyticity? According to Putnam, one of the notions of analyticity that Quine reacts to (or rejects) is analyticity understood as epistemic unrevisability. This is allegedly one of the senses that the logical positivists had of the notion of analyticity: analytic statements are statements which are confirmed no matter what.17 Putnam also says that the interesting notion of analyticity is this one; and even though Quine talks about analyticity, what he had in mind was a prioricity. So, given that for Quine everything is revisable, there could be no such thing as an unrevisable a priori statement. Kitcher offers another interpretation to explain the conviction he shares with Putnam that the notion of a prioricity is the central notion under Quine’s attack. For Kitcher, the most important section of “Two Dogmas” is the last one, where Quine is challenging the claim that analytic truths are knowable a priori rather than simply the existence of analytic truths. Kitcher explains: Defenders of analyticity have often construed the main thrust of Quine’s most famous attack, ‘Two Dogmas of Empiricism’, as arguing that the concept of analyticity is undefinable in notions Quine takes to be unproblematic .... I locate Quine’s central point elsewhere. The importance of the article stems from its final section, a section which challenges not the existence of analytic truths but the claim that analytic truths are knowable a priori.18

I take it that, for Kitcher also, the main notion under attack in Quine is the notion of a priori knowledge. Kitcher refers to the following argument of Quine to support his conclusion: … it becomes folly to seek a boundary between synthetic statements, which hold contingently on experience, and analytic statements, which hold come what may. Any statement

 Another notion of analytic truths that the logical positivists had was the celebrated notion of “truths in virtue of meaning alone”. 18  Kitcher, Philip. The Nature of Mathematical Knowledge. New  York and Oxford: Oxford University Press, p. 80, 1983. 17

2.3  Does Quine Distinguish Between the Notions of A Prioricity and Analyticity?

41

can be held true come what may, if we make drastic enough adjustments elsewhere in the system ... Conversely, by the same token, no statement is immune to revision. Revision even of the logical law of the excluded middle has been proposed as a means of simplifying quantum mechanics; and what difference is there in principle between such a shift and the shift whereby Kepler superseded Ptolemy, or Einstein Newton, or Darwin Aristotle? (my emphasis)19

It is clear that in this passage Quine is characterizing the notion of analyticity he attacks in epistemological terms, what appears to be a basis for Kitcher’s claim – that the main notion under attack is epistemological – or Putnam’s claim that the interesting notion of analyticity Quine attacks is epistemic – i.e., analyticity understood as epistemic unrevisability. That is, it may seem that an analytic statement is epistemically unrevisable, or holds “come what may”. However, it cannot be overlooked that statements that hold come what may, may not even be true. According to the last quote, it seems that the status of “holding come what may” is up to us, at least, to some extent. The status of “holding come what may” is allegedly one which we as (fallible) knowers adjudicate to statements, and given our fallibility, we may hold statements come what may that are in fact false. If that is so, then this notion and the notion of epistemic unrevisability are not logically equivalent since the latter notion is supposed to be an objective one: statements themselves are expected to be unrevisable on their own independently of our judgment that that is so. So, it is a mistake of both Putnam and Kitcher to treat these two notions on a par. I think that this mistake is due to the fact that the passage of Quine is confusing; the above quote is confusing because the notion of “holding contingently on experience” appears to be an objective notion – by that I simply mean a notion which holds or not of statements independently of our judgments on the matter – and is contrasted with a notion which is not objective. Kitcher concludes that Quine connects analyticity to a prioricity through the notion of unrevisability. Kitcher expresses this contention in his own terminology. If we can know a priori that p then no experience could deprive us of our warrant to believe that p. Hence statements which express items of a priori knowledge are unrevisable, in the sense that it would never be rational to give them up. But 'no statement is immune from revision'. It follows that analytic statements, hailed by Quine's empiricist predecessors and contemporaries as a priori, cannot be a priori; or, if analyticity entails a priority, there are no analytic statements.20

Again, the argument is that if there are analytic statements, then they cannot be known a priori – since there cannot be any a priori (unrevisable) statement. But they have to be a priori, what else could they be? And if they would have to be a priori, then there can’t be any. That there are no analytic statements is a consequence of there being no a priori-unrevisable statements.

19 20

 “Two Dogmas” in From a Logical Point of View, p. 43.  Kitcher, Philip. The Nature of Mathematical Knowledge, p. 80.

42

2  Quine’s Views on A Priori Knowledge

2.3.1 Quine’s View of A Prioricity Before “Two Dogmas” It shall help us to discuss Quine’s view of a prioricity before “Two Dogmas”, in particular, in the Lecture “The A Priori” since in the latter Quine wrote explicitly about the relationship between the notions of a priori knowledge and analyticity. Quine affirms21 against Kant that studies in the foundations of mathematics show that there is no need to appeal to intuition and, consequently, that geometrical truths can be considered as true in virtue of the conventions of language, and, therefore, are analytic in nature. This latter consequence is of extreme philosophical importance because it does away with the category of the synthetic a priori. “The analytic and the a priori become coextensive.”22 In an interesting passage of the lecture “The A priori”, Quine even affirms that there are a priori truths, that a priori truths are those which are unrevisable, and that a priori truths are analytic. The more firmly accepted sentences we choose to modify last, if at all, in the course of the evolving and revamping our sciences in the face of new discoveries. And among these accepted sentences which we choose to give up last, if at all, there are those which we are not going to give up at all, so basic are they to our whole conceptual scheme. These, if any, are the sentences to which the epithet “a priori” would have to apply … it is convenient so to frame our definitions as to make all these sentences analytic, along with others, even, which were not quite so firmly accepted before being raised to the analytic status. (Correspondence, p. 65; my emphasis)

According to Quine, the view that the a priori is analytic is a syntactic decision, but that does not entail that is less important for that reason.23

 Quine says: But the development of foundational studies in mathematics during the past century has made it clear that none of mathematics, not even geometry, need rest on anything but linguistic conventions of a definitional kind. In this way it becomes possible to relegate geometry to the analytic realm, along with the rest of mathematics. This empties out the a priori synthetic. (Creath, Richard. Dear Carnap Dear Quine Correspondence. Berkeley, CA: University of California Press, Lecture I “The A Priori”, p. 48, 1990.) 21

 Ibid.  He writes: Kant’s recognition of a priori synthetic propositions, and the modern denial of such, are thus to be construed as statements of conventions as to linguistic procedure. The modern convention has the advantage of great theoretical economy; but the doctrine that the a priori is analytic remains only a syntactic decision. It is however no less important for that reason: as a syntactic decision it has the importance of enabling us to pursue foundations of mathematics and the logic of science without encountering extra-logical questions as to the source of the validity of our a priori judgments. The possibility of such a syntactic procedure has furthermore this important relevance to metaphysics: it shows that all metaphysical problems as to an a priori synthetic are gratuitous, and let in only by ill-advised syntactic procedures. Finally, the doctrine that the a priori is analytic gains in force by thus turning out to be a matter of syntactic convention; for the objection is thereby forestalled that our exclusion of the metaphysical difficulties of the a priori synthetic depends upon our adoption of a gratuitous metaphysical point of view in turn. (pp. 65–6; my emphasis) 22 23

2.3  Does Quine Distinguish Between the Notions of A Prioricity and Analyticity?

43

Though Quine embraces Carnap’s account of a priori truth as truth by convention in this lecture (actually, Lecture 1 is closely related to the latter work “Truth by Convention”), and later in “Truth by Convention“he rejects altogether this notion of truth, it seems plausible to me that in “Two Dogmas” Quine still holds that the analytic and the a priori are coextensive but, of course, this is only speculation since it could be an earlier view. Why is it important whether Quine distinguished or not between the notions of a prioricity and analyticity after all? I have tried to quell the anxiety of those who might question the relevance of Quine’s work to a discussion of a priori knowledge given that he talks mainly about analyticity and the word “a priori” occurs scarcely in his writings.24 An answer to this question is to hold that the two notions are coextensive so whatever Quine says about the notion of “analyticity” would hold true of “a priori knowledge” as well. I want to make two points concerning the reasonableness of attributing to the Quine of “Two Dogmas” the view that the notions of analyticity and a prioricity are coextensive. First of all, since my concern is merely to justify consideration of Quine’s “Two Dogmas” views in the course of a thesis on a prioricity, the coextensiveness thesis is not strictly necessary for my purpose – all I need is that in denying that any statements are analytic as traditionally conceived, Quine is also denying that those statements which traditionally would have been regarded as analytic can be known a priori – or at least can’t be known a priori in the way we traditionally have considered them to be known a priori, namely, by the exercise of conceptual analysis.25 When we adopt such a syntax, in which the a priori is confined to the analytic, every true proposition then falls into one of two classes: either it is a synthetic empirical proposition, belonging within one or another of the natural sciences, or it is an a priori analytic proposition, in which case it derives its validity from the conventional structure, or syntax, of the language itself –“syntax” being broadly enough construed to cover all linguistic conventions. (p. 66) 24  Charles Parsons affirms that Quine has attacked the notion of a priori knowledge. He [Quine] has carried out an elaborate criticism of the notion of a priori knowledge, particularly where it was explained by the analyticity of the propositions known a priori. (Parsons, Mathematics in Philosophy. Ithaca, New York: Cornell University Press, p. 177, 1983) Nonetheless Parsons does not say if he thinks that for Quine all a priori truths are analytic. What Parsons does say is that if one explained knowledge a priori of mathematical truths by appeal to analyticity, then Quine’s attack on analyticity would undermine such explanations. Parsons thinks that the a priori ought to be distinguished from the analytic as well as from the necessary. He affirms that it is possible to defend the a prioricity of mathematics independently of the analytic-synthetic distinction. I am persuaded by arguments against the analyticity of mathematics coming from Quine and from other sources, some going back to Kant. But just as the a priori needs to be distinguished from the necessary, so it needs to be distinguished from the analytic. The possibility is thus open of a defense of the a priori character of mathematics independent of the thesis that it is analytic and even of the analytic-synthetic distinction. I am inclined to think that such a defense is possible, but it is not offered in these essays or elsewhere in my writings. (ibid, p. 18) 25  I make the latter qualification since Quine does say that, if say, our dreams made better predictions than science, he’d go with dreams – would that be “a priori” knowledge? If so, he seems to be saying it is possible.

44

2  Quine’s Views on A Priori Knowledge

Now, the passages I quoted suggest that earlier at least he certainly would have taken the view that those statements which traditionally would have been regarded as analytic can’t be known a priori. But it is possible that he changed his mind and, for some reason, said nothing about that (and it is also possible that he did not change his mind and that is why he did not say anything about it either) in “Two Dogmas”. Second, however, I do not think I need to settle the matter in any case. It will be sufficient justification for my discussing Quine that an interesting question arises whether a defender of the thesis that some truths can be known a priori is in position to agree with what Quine says in “Two Dogmas”, or whether a prioricity must be a casualty of the line Quine takes in that paper if it is sustained. Quine’s own view of the relation between the two concepts is not really important to my purpose. In other words, I can be able to sidestep the whole question about Quine’s actual view of the relation between a prioricity and analyticity in “Two Dogmas” – to take on all the questions I want to consider about that paper without a commitment one way or the other. What Quine attacks in the last third of “Two Dogmas” are the ideas of non-­ empirical knowledge – knowledge insulated from the body of total empirical science; and the issue of unrevisability in connection with a priori knowledge. The first has to do with whether there are any grounds for belief which are available independently of the course assumed by empirical science. Quine denies that there is a priori knowledge in this sense.26 It is a weakness of Quine’s discussion that he persistently runs the issues of non-empirical knowledge and that of unrevisability in connection with a priori knowledge together. And the weakness is not to be disguised, as by Putnam, by pretending that there is some “interesting” sense of “analyticity“or “a prioricity” which somehow unites them. In my view, we should not simply identify the question whether there are grounds (perhaps grounds sufficient to support claims to knowledge) available independently of experience for holding certain beliefs with the question whether such, or any, beliefs are unrevisable. In denying that there are any analytic truths in the sense of truths which hold purely in virtue of meaning, Quine at least cuts himself off from the obvious line of explanation of a priori knowledge (the obvious line of answer to the question: what a priori knowledge consists in (how is it possible?)), namely that it is knowledge given to us by rational reflection on meaning. So, if he means to leave a priori knowledge in place, it is a good question how he would propose to answer this question. I actually doubt if he has ever separated analyticity from a prioricity. In any case, the suggestion, in the last third of “Two Dogmas”, that all statements are ultimately subject only to holistic pragmatic appraisal as part of total empirical science is surely inconsistent with acknowledgment of the possibility of a priori knowledge

 Also Quine denies the existence of a priori analytic truths because he is skeptical about the existence of meanings. Meanings would have to exist in order for there to be truths “true in virtue of meaning alone”. 26

2.4  How to Understand Revision of A Priori Statements? Can A Priori Statements....

45

as ordinarily conceived, namely, as knowledge obtained through conceptual analysis.27 Putnam, in my view, is quite wrong to equate analyticity, or a prioricity, with unrevisability. Of course, Quine looks better if you make the conflation. But if a priori knowledge can be substantial – if it involves some sort of real cognitive process – then it has to be a possibility that the process can misfire.28 So error has to be possible. So revision has to be possible. It is possible that we adopt certain axioms in good faith, finding them a priori plausible, and where a contradiction comes as a surprise. In that situation, we have, of course, to conclude that we were wrong to accept the axioms, even before we are clear about what revision to effect. Someone could argue that I am confusing “revisability of knowledge” with the “revisability of statements”. But I ought to press him hard to explain what he has in mind by “the revisability of statements”. Actually I do not think “revisability of knowledge” is particularly happy either. It is primarily “claims to know” that may be revisable or not, according as the basis for such claims may be overturned by new information. I do not think I am making any substantial confusion here, but the terminology really does need straightening out.29

2.4 How to Understand Revision of A Priori Statements? Can A Priori Statements Be Falsifiable by Experience? Quine urges that no statement is immune from revision. No sentence or set of sentences is in principle unrevisable for in an attempt to fit theory to observation any sentence or set of sentences may become a candidate for revision. Logic and mathematics, as any other purported a priori knowledge, are parts of our system of background assumptions and are in principle open to revision. In particular, logical truths are theoretical principles of the most fundamental sort which we are far more

 In considering “Two Dogmas”, Casullo concludes: The concept of a priori justification does not involve or entail the concept of analyticity, and the concept of analyticity does not explain how a priori knowledge is possible. Articulating the concept of a priori justification and explaining how a priori knowledge is possible require empirical investigation. (A Priori Justification, p. 238) To recognize an important role for empirical investigation in our acquisition of a priori knowledge is also a lesson that we have learnt from Quine, even if his epistemological holism is incoherent; and from Kitcher, for different reasons, since there is an epistemological interplay between science and mathematics. 28  Of course, there is knowledge a priori that is not substantial, for example, knowledge that “a = a.” My point is not that the statement “a = a” is revisable, because it cannot be revisable, but rather that my claim to know that a = a is revisable, even when it is not substantial knowledge. My warrant for knowing that “a = a” is defeasible, that is, it is possible that with an incrementation of my present information I will disregard my claim to know, for example, if I am very drunk and claim to know that “a = a” I am simply wrong in claiming that I know it. 29  I provide a glossary of the epistemological terms I use in chapter ten, section 10.1, pp. 187–92.  27

46

2  Quine’s Views on A Priori Knowledge

“reluctant to give up” in particular circumstances than our everyday beliefs or even fundamental theoretical principles in science. For Quine, it is conceivable that in response to some fundamental difficulty in science, a new theory could be formulated that proposes a modification of part of elementary logic or arithmetic.30 Dummett and Hale31 interpret Quine as an opponent of a priori knowledge who argues, not only that all knowledge is revisable, even knowledge of a logical truth, but that it can be revisable in response to experience. Quine offers as an example of this thesis applied to logical truths that the logical law of excluded middle may have to be abandoned in response to, for example, quantum mechanics.32 Both Dummett and Hale claim that a priori knowledge must not be revisable or falsifiable by empirical evidence. In other words, a priori knowledge has to be independent of experience in terms of both justification and revision. As Dummett and Hale affirm, Quine’s no-immunity thesis would not be as controversial if it did not suggest the need for revision, even of logic and mathematics, in response to empirical evidence. If Quine had claimed only that mathematical and logical statements are not immune from revision, without any specification of what sort of considerations call for a revision, he would not have pointed out the controversial possibility of having to adjust a logical law in order to accommodate quantum mechanics. It would have been enough to suggest the possibility of revising logic for logical or philosophical reasons. Quine needed a case in which the proposed revision appeared to be such a response. Quine accepts that the merits of the proposal to revise logic in response to quantum mechanics may be dubious, but that should not be a problem since what is really relevant is that these proposed revisions have been offered.33 In other words,

 Parsons points to the difficulty Quine faces to account for the obviousness of some logical and mathematical truths: The empiricist view, even in the subtle and complex form it takes in the work of Professor Quine, seems subject to the objection that it leaves unaccounted for precisely the obviousness of elementary mathematics (and perhaps also of logic). It seeks to meet the difficulties of early empiricist views of mathematics by assimilating mathematics to the theoretical part of science. But there are great differences … the existence of very general principles that are universally regarded as obvious, where on an empiricist view one would expect them to be bold hypotheses, about which a prudent scientist would maintain reserve, keeping in mind that experience might not bear them out … (“Mathematical Intuition”, p.  151, in Proceedings of the Aristotelian Society, NS 80, pp. 145–68, 1979–80; reprinted in Palle Yourgrau (ed.), Demonstratives. Oxford: Oxford University Press, pp. 195–214, 1990). Kant’s view explains this obviousness: how could we think otherwise arithmetic applied to the physical world if it is not by accepting that is part of our constitution to perceive the world? But this explanation has the cost of abandoning the objectivity of even elementary mathematics. 31  Dummett, “Is Logic Empirical?” in Truth and Other Enigmas. Cambridge, Massachusetts: Harvard University Press, p. 269, 1980; Hale, ibid., p. 146. 32  “Two Dogmas”, p. 43. 33  For Quine, The merits of the proposal may be dubious, but what is relevant just now is that such proposals have been made. Logic is in principle no less open to revision than quantum mechanics or the theory of relativity. (“The Ground of Logical Truth” in Philosophy of Logic, p. 100.) 30

2.4  How to Understand Revision of A Priori Statements? Can A Priori Statements…

47

Quine seems to be contented merely with the possibility of revising logical laws for empirical reasons, regardless of the significance of such a possibility. Nonetheless, it may seem that it ought to be crucial to Quine’s thesis that a proposal for such a revision is meritorious. This is justified by appealing to how implausible is to defend a weaker interpretation of the bare possibility of revision, meritorious or not. It has to be meritorious, even if hypothetically. Quine needs to produce a proposal, even if not ultimately acceptable, that would be substantial enough to permit us to consider the possibility of there being one should another proposal of that sort be made which we ought to accept. It seems clear that all Quine needs is to make a case that there could be good grounds for revision for empirical reasons, i.e., he does not need actually to produce such a good case. In “Two Dogmas” Quine does not defend the worth of revising logic for empirical reasons. It is Putnam who examines in “Is Logic Empirical?” another possible revision of logic for empirical reasons. In this occasion, it is not a revision of the law of excluded middle, but one that consists in abandoning the distributive law. This proposed revision of a logical law is offered also as a response to quantum mechanics.34 Dummett affirms that Quine himself has totally reversed his position in the chapter “Deviant Logics” in Philosophy of Logic. According to Dummett, Quine remarks that it is impossible for anyone to deny a law of classical logic. Because if someone fails to accept some formula as a formulation of a logical law, his failure would show conclusively he was not giving, to the logical constants appearing in the formula, the same meanings as those attached by the classical logician. Hence he had not denied anything held by the classical logician, but merely changed the subject matter. This is the celebrated “change of meaning” argument.35 For Dummett, Quine believes that there is a context in which an appeal to this argument is appropriate, and finds this significant when Quine has been critical about this argument on other occasions. Dummett explains: The conclusion of the argument is the very opposite of the thesis maintained in ‘Two Dogmas’: if it were correct, we could hold the laws of classical logic to be immune from revision in response to experience, and perhaps in response to philosophical criticism as well.36

This interpretation will be clearly in tension with Quine’s claim that no statement is immune from revision. First, let’s comment that Quine does not speak of “change of meaning” but rather of “change of doctrine”. Let’s see how Quine sees the matter. In the essay “Deviant Logics” Quine sets for himself the task of considering a substantial kind of deviation in logic. He explains that it is a substantial one because it does not merely consist of changing the procedures for obtaining the class of logical truths, but a change in that class itself. It is not either merely just a change in

 Dummett, “Is Logic Empirical?”, p. 270.  Ibid. 36  Ibid, pp. 270–71. 34 35

2  Quine’s Views on A Priori Knowledge

48

demarcating what to consider a logical truth and what not. The issue is rather to reject part of our logic as not true at all.37 Quine considers the possibility of rejecting the law of non-contradiction, consequently what would follow from the occasional acceptance of a sentence and its negation as being both true. A usual response to this situation is that a conjunction between a sentence and its negation would imply every sentence. So, the rejection of the law of non-contradiction commit us to consider every sentence as true and, consequently, to losing the distinction between what is true and what is false. A possible answer to this problem of indiscriminate deducibility is to make adjustments to prevent such a deducibility of all sentences from an inconsistent sentence. Quine responds that in this dispute neither party is right. Though each party considers that they are talking about negation, this is certainly not the situation. Quine observes that one ceases to regard the notation as negation as soon as one regards an inconsistent sentence as true, and deny that such a sentence would imply every other. Here, evidently, is the deviant logician predicament: when he tries to deny the doctrine he only changes the subject matter. (“Deviant Logics”, p. 81; my emphasis) … whoever denies the law of excluded middle changes the subject. This is not to say that he is wrong in so doing. In repudiating ‘p or ¬p’ he is indeed giving up classical negation, or perhaps alternation, or both; and he may have his reasons. (ibid, p. 83)

He then goes on arguing how difficult it would be to reject something so basic – the excluded middle principle. It is hard to face up the rejection of anything so basic. If anyone questions the meaningfulness of classical negation, we are tempted to say in defence that the negation of any given closed sentence is explained thus: it is true if and only if the given sentence is not true. This, we may feel, meets the charge of meaninglessness by providing meaning, and indeed a meaning that assures that any closed sentence or its negation is true. However, our defense here begs the question; let us give the dissident his due. In explaining the negation as true if and only if the given sentence is true, we use the same classical 'not' that the dissident is rejecting. (ibid, pp. 84–5)

Quine wants to claim that the principle of minimum mutilation should operate in the context of any revision, and not that the laws of logic are unrevisable, as Dummett thinks. But in any event let us not underestimate the price of a deviant logic. There is a serious loss of simplicity, especially when the logic is not even a many-valued truth-functional logic. And there is a loss, still more serious, on the score of familiarity. (ibid, p. 86)

This last quote fits the pragmatic view about revision of logic, but I have to say more about the change of doctrine argument. Quine’s endorsement of it is the basis for Dummett’s view that Quine has changed his position. I interpret the situation as follows. According to Quine’s view, it ought to be possible that pragmatic criteria – like the principle of minimum mutilation – also can be revised, if that is what is better. Pragmatic criteria could be different too. So, let’s imagine a situation where what fits better is to give up the principle of minimum mutilation and that we then try to revise 37

 “Deviant Logics” in Philosophy of Logic, pp. 80–1.

2.4  How to Understand Revision of A Priori Statements? Can A Priori Statements…

49

the principle of excluded middle. But when we try to revise, Quine observes that the attempts he considers that deny the excluded middle amount to changing the subject matter. So, we are not revising but changing the subject matter; we are talking about something else. But everything is revisable, so revision ought to be possible in any case. This is the paradox that seems to be involved in Quine’s reasoning and which lies behind Dummett’s view that Quine has changed his position. Nevertheless, it may be the case that Quine only thought that the attempts he considered in “Deviant Logics” all amount to changing the subject matter and not that all attempts amount to that. In other words, it may be possible to revise the law of excluded middle without changing the subject matter even though Quine only considered in that paper particular attempts that do change the subject matter; so the reasoning behind Dummett’s view is incorrect since it generalizes to all attempts – however, a question remains: what would a revision of a logical law that did not consist in changing the subject matter look like? It does not appear to be enough to say that it is possible; what we need is a clear idea of how a revision of a basic logical law like the law of excluded middle or the principle of non-contradiction that would not involve a change in the meanings of the logical constants which appear in them, and, therefore, a change in subject matter, would look like. Is this a real possibility or is it only imaginable as a possibility? There is another problem with Quine’s methodology. The situation is even worse in the case of the principle of non-contradiction since it is another example of a principle which governs any revision. This principle states that we have to revise previously accepted statements whenever we confront a situation where truth is assigned to statements which logically conflict with each other. But everything is revisable in principle, even the principle of non-contradiction ought to be revisable. However, this principle cannot be revised because any revision would have to be governed by it, and, therefore, presupposes its acceptance. But it should be revisable. Dummett and Hale think38 Quine posits revision of a priori statements for empirical reasons. Both are eager to reject this claim. But I do not see why. After all, what that would establish is that we did not know after all, a priori or otherwise. We ought to check our results with as many routes as possible to minimize error. I consider that it is simply a necessary condition of the applicability of ordinary arithmetic that things can seem, empirically, both to be as arithmetic requires (as, for example, when we count the boys in a classroom and get 5, and the girls and get 7, and then taken all together get 12) and to go against arithmetic (as when in the previous counting we get 13 as the result instead). If such things were not possible, arithmetic would be useless in empirical contexts. So, ordinary experience can seemingly comply with or go against arithmetic. To repeat: it is just what is necessary if arithmetic is to be applicable. Of course, this empirical evidence is almost always dominated by proofs which are a priori ways of knowing. A priori warrants are almost always considered as superior over empirical ones. But, it does not follow from this fact that there is no form of empirical warrant for and against arithmetical statements. Again, if arithmetic tells us to disregard certain experiences 38

 Dummett, “Is Logic Empirical”, p. 269 and Hale, ibid., p. 146.

50

2  Quine’s Views on A Priori Knowledge

because they do not represent things as addition properly, for example, then it has to be true that those experiences, taken at face value, would disconfirm arithmetic. If arithmetic permits us to consider certain experiences as truthful, it will be because they comply with arithmetic. It is precisely the fact that arithmetical statements, which we know a priori, do possess empirical content in this way which makes the problem of the a priori so difficult. We seem to be able to know a lot about the world just by thinking about it. Of course, I am not saying that “unless we can make arithmetical errors, arithmetic is useless”. The point is rather that arithmetic would not be of any use to us in ordinary practical contexts unless it provided inferential shortcuts to conclusions which we could in principle corroborate independently by operational procedures. For example, if I have a squad of soldiers on parade, composed of ten ranks and three files, I can multiply to conclude that there are thirty soldiers in the squad. But that is a conclusion which could have been verified independently, by counting. Given that the applicability of arithmetic depends, in this way, upon the provision of such inferential shortcuts, it has to be possible for the results of the independent operational checks on its products – counting up all the soldiers – to seem to go contrary to it. That is the sense in which its possessing a kind of empirical content – thought that may not be the best way of putting the point – is essential to the applicability of arithmetic. Applicable mathematics tells us what to expect, given certain other findings. But in the general run of cases, that expectation may seem not be fulfilled. What is necessary for the characterization of a priori knowledge is not invulnerability of falsification or revisability for empirical reasons, but rather justifiability independently of experience. The crucial notion to characterize is the notion of “experience independence” allegedly characteristic of a priori knowledge. That does not mean, of course, that the issue of defeasibility/indefeasibility39 of a priori items of knowledge is not an important one, it is in fact a very important issue, but the point is that the two issues are separate.

2.5 Can Epistemological Holism Be Reconciled with the Belief in A Prioricity? Quine thinks of epistemological holism and belief in a priori knowledge as incompatible – or seems to do so in “Two Dogmas”. Holism challenges a priori knowledge because, as standardly interpreted, it implies that almost any belief whatever can be implicated in one’s grounds for almost any other belief, in such a way that grounds  In my view, the property of defeasibility applies firstly to warrants and, derivatively, to the beliefs they justify. A warrant (and its associated justified belief(s)) are defeasible when additional information cannot be ruled out which would either compromise our confidence that the warrant was correctly acquired – that the relevant method(s) were properly executed – or result in a total evidential picture in which the belief(s) in question are no longer justified. It is our essential fallibility – the fact that we are always capable of error – which ensures that defeasibility is so pervasive. 39

References

51

for belief may be open to defeat from the most unexpected sources. For example: my knowledge of a mathematical proposition may be based on what I take to be a proof of it; but my justification for believing that I have a proof may well be defeated if I get some kind of empirical evidence for my, perhaps temporary, unreliability on such matters – for instance, if I learn that a medication I am taking sometimes has a side effect of clouding a patient’s judgment. The grounds I have for that belief about the medication may again be potentially very diverse – perhaps I hear a discussion in a medical program on TV. This in turn will implicate collateral beliefs about the nature of the program – that it was a genuine studio discussion, for instance, rather than an excerpt in a drama  – and that it represented up-to-date, reliable medical opinion. And so on. From this we should draw the conclusion that if there is a priori knowledge, it cannot be indefeasibly certain in the sense that no conceivable further increment to our information could rationally undermine our certainty that the statement supposedly known a priori, was true. But, of course, that does the trick for Quine, that is, it undermines the possibility of a priori knowledge, only if we also accept that genuine a priori knowledge would have to have that kind of unattainable, indefeasible certainty. And for that claim Quine gives no grounds whatever.

2.6 Conclusion Quine urges that no statement is immune to revision. But a defender of a prioricity need not wish to resist the suggestion that logic, or other disciplines conceived to involve a priori statements, are revisable. There should be no interest in maintaining that we cannot be in error in judging a statement to have that status. Can we therefore give Quine the claim that any particular statement which we accept as a priori could, in certain circumstances, reasonably be discarded? To grant the claim need be to grant no more than that our assessment of any particular statement as a priori may always in principle turn out to have been mistaken. Quine has assumed, with the bulk of the philosophical tradition, that a prioricity involves indefeasible certainty. To claim that a statement is a priori, however, is only to make a claim about the way we know of its truth – there is no immediate reason why the claimant has to agree that, when statements are a priori, their truth must be known with special sureness.

References Azzouni, J. 1994. Metaphysical Myths, Mathematical Practice: The Ontology and Epistemology of the Exact Sciences. Cambridge: Cambridge University Press. ———. 2008. The Compulsion to Believe: Logical Inference and Normativity. PRO 25: 69–88. Benacerraf, P. 1973. Mathematical Truth. The Journal of Philosophy 70: 661–679. Reprinted in Benacerraf and Putnam.

52

2  Quine’s Views on A Priori Knowledge

Benacerraf, P., and H.  Putnam, eds. 1984. The Philosophy of Mathematics: Selected Essays. Englewood Cliffs: Prentice-Hall. Boghossian, P. 1997. Analyticity. In Companion to the Philosophy of Language, ed. B. Hale and C. Wright. Oxford: Blackwell. Boghossian, P., and C. Peacocke. 2000. New Essays on the A Priori. Oxford: Oxford University Press. Casullo, A. 2003. A Priori Justification. Oxford: Oxford University Press. ———. 2012. Essays on A Priori Knowledge and Justification. New York: Oxford University Press. Casullo, A., and J. Throw, eds. 2013. The A Priori in Philosophy. Oxford: Oxford University Press. Creath, R. 1990. Dear Carnap Dear Van: The Quine-Carnap Correspondence and Related Work. Berkeley, CA: University of California Press. Dummett, M. 1980a. “Is Logic Empirical” in Dummett. ———. 1980b. Truth and Other Enigmas. Cambridge, MA: Harvard University Press. Frege, G. 1953. Foundations of Arithmetic. Trans. J. L. Austin. Oxford: Basil Blackwell. Haack, S. 1974. Deviant Logic. London/New York: Cambridge University Press. Hale, B. 1987. Abstract Objects. Oxford: Basil Blackwell. Hale, B., and P. Clark, eds. 1996. Reading Putnam. Wiley-Blackwell. Hale, B., and C. Wright, eds. 1999. Companion to the Philosophy of Language. Wiley-Blackwell. Helmholtz, H. 1977a. On the Facts Underlying Geometry. In Herman Von Helmholtz: Epistemological Writings, ed. Robert S. Cohen and Yehuda Elkana, 39–58. Reidel. ———. 1977b. On the Origin and Significance of the Axioms of Geometry. In Herman Von Helmholtz: Epistemological Writings, ed. Robert S. Cohen and Yehuda Elkana. Reidel. Kant, I. 1956. Critique of Pure Reason. Trans. Norman Kemp Smith. New York: St. Martin’s. Kitcher, Philip. 1981. How Kant Almost Wrote ‘Two Dogmas of Empiricism’. Philosophical Topics 12: 217–250. ———. 1983. The Nature of Mathematical Knowledge. Oxford: Oxford University Press. Kripke, S. 1971. Identity and Necessity. In Identity and Individuation, ed. M.K. Munitz. New York: New York University Press. ———. 1980. Naming and Necessity. Cambridge, MA: Harvard University Press. Maddy, P. 1980. Perception and Mathematical Intuition. The Philosophical Review 89: 168–196. ———. 1990. Realism in Mathematics. Oxford: Oxford University Press. Mill, J.S. 1950. Philosophy of Scientific Method. New York: Hafner Publishing. Moser, P.K. 1987. A priori Knowledge. Oxford: Oxford University Press. Parsons, C. 1967. Foundations of Mathematics. In The Encyclopedia of Philosophy, ed. Paul Edwards, vol. 5-6, 188–212. New York: Macmillan. ———. 1983. Mathematics in Philosophy: Selected Papers. Ithaca, NY: Cornell University Press. Putnam, H. 1979. Analyticity and Apriority: Beyond Wittgenstein and Quine. In Midwest Studies in Philosophy, ed. P.  French, vol. 4, 423–441. Minneapolis: University of Minnesota Press. Reprinted in Moser. ———. 1983. ‘Two Dogmas’ Revisited. In Putnam, Realism and Reason, Philosophical Papers, vol. 3, 87–97. Cambridge: Cambridge University Press. Quine, W.V. 1960. Word and Object. Cambridge, MA: MIT Press. ———. 1961. Two Dogmas of Empiricism. In From a Logical Point of View, 20–46. Cambridge, MA: Harvard University Press. Reprinted in Moser. ———. 1966a. Carnap and Logical Truth. Synthese 12: 350–370. Reprinted in The Ways of Paradox. New York: Random House, pp. 100–25. ———. 1966b. Truth by Convention. In The Ways of Paradox, 70–99. New York: Random House. Reprinted in Benacerraf and Putnam, pp. 322–345. ———. 1970. Philosophy of Logic. Englewood Cliffs: Prentice Hall. Russell, B. 1973. The Problems of Philosophy. New York: Oxford University Press. Skorupski, J. 1986. Empiricism, Verification and the ‘A priori’. In Fact, Science and Morality, ed. G. Mac Donald and C. Wright, 143–162. Oxford: Blackwell. ———. 1989. John Stuart Mill. London/NY: Routledge. Williamson, T. 2002. Knowledge and Its Limits. Oxford: Oxford University Press.

References

53

———. 2007. The Philosophy of Philosophy. Malden, MA: Blackwell. ———. 2013. How Deep is the Distinction between A Priori and A Posteriori Knowledge. In The A Priori in Philosophy, ed. Casullo and Thurow, 291–312. Oxford University Press. Wittgenstein, L. 1956. Remarks on the Foundations of Mathematics. Trans. G. E. M. Anscombe. Oxford: Basil Blackwell. ———. 1968. Philosophical Investigations. Trans. G. E. M. Anscombe. Oxford: Basil Blackwell.

Chapter 3

Putnam’s Views on A Priori Knowledge

Abstract  The focus of this chapter is Putnam’s various views about the connection between the notion of a priori knowledge and the issue of revisability/unrevisability. Since he changes his view frequently I have found it useful to present his views in chronological order. Also following the chronological order of the articles permits us to deal with important topics on a priori knowledge. Putnam’s position is very interesting because it is dialectical. He is in a middle position. He is very critical of the traditional notion of the a priori as entailing unrevisability. However he also recognizes that there is at least one a priori truth, a weak formulation of the principle of non-contradiction (‘Not every statement is both true and false’), taken as a principle which operates as a norm for any conceivable rationality. Keywords  Analyticity · A prioricity · Revision · Unrevisability · Contextually a priori Putnam examines the notion of a priori knowledge in a series of important papers that I will analyze. The first four sections shall discuss the development of his views on a priori knowledge in the articles “‘Two Dogmas’ Revisited”, “There is at least one a priori truth”, “Analyticity and A prioricity: Beyond Wittgenstein and Quine” and “Possibility and Necessity”.1 The last four sections are devoted to a critical examination of his views in each of the articles. In the concluding section I evaluate his views as a whole.

 These four articles appear in Realism and Reason. Cambridge, Mass: Cambridge University Press, vol. 3, 1983. “Possibility and Necessity” appears first in this volume though it was the last published. 1

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 I. Fred-Rivera, A Historical and Systematic Perspective on A Priori Knowledge and Justification, Philosophical Studies Series 151, https://doi.org/10.1007/978-3-031-06874-4_3

55

56

3  Putnam’s Views on A Priori Knowledge

3.1 Putnam in “‘Two Dogmas’ Revisited” According to Putnam, Quine attacks several notions of analyticity. One notion of an analytic truth is that which is confirmed come what may or no matter what.2 Putnam thinks in this paper that Quine’s attack on this notion is correct.3 As Putnam observes, “on the face of it, then, the concept of a truth which is confirmed no matter what is not a concept of analyticity but a concept of a priority.” (p. 90) Nonetheless, both Quine and the positivists did take this to be a concept of analyticity. Putnam considers4 that Quine’s confusion does not invalidate his methodological argument against the notion of a prioricity. Putnam asks whether there are statements which always have the maximum degree of confirmation. If so, he continues, “these are simply truths which it is always rational to believe, nay, more, truths which it is never rational to even begin to doubt.”5 Quine’s methodological attack on this notion of a prioricity is based on the fact that the possibility of revision should be accepted even of logical laws.6 Putnam considers that the appropriate conclusion to draw from Quine’s remarks on revision is that some statements can only be overthrown by a rival theory, and not only by observational findings, and that there is not an absolutely unrevisable statement. (p. 94) For Putnam, statements which can only be overthrown by a rival theory are “contextually a priori”, that is, they enjoy a certain a prioricity before a new theory appears on the scene which questions them. Putnam introduces the notion of “contextual a prioricity” to account for the fact that some statements are so entrenched in our system of beliefs that only a rival theory, sometimes even only a revolutionary one, can overthrow them.7 Putnam explains: The obvious way to try to counter Quine’s oblique reference to the fact that scientific revolutions have overthrown propositions once thought to be a priori is to say that the seeming a priority of those propositions was ‘merely psychological’. But the stunning case is geometry. Unless one accepts the ridiculous claim that what seemed a priori was only the conditional statement that if Euclid’s axioms, then Euclid’s theorems (I think that this is what Quine calls ‘disinterpreting’ geometry in ‘Carnap and Logical Truth’), then one must admit that the key propositions of Euclidean geometry were interpreted propositions (‘about form and void’, as Quine says), and these interpreted propositions were methodologically immune from revision (prior to the invention of rival theory) as Boolean logic was prior to the proposal of the quantum logical interpretation of quantum mechanics. The correct

 “‘Two Dogmas’ Revisited”, p. 87.  Ibid. 4  Ibid, p. 92. 5  Ibid, p. 90. Putnam must mean something else by “maximum degree of confirmation”. Normally, the maximum of a degree of confirmation is 1. From this it does not follow that such statements are true. 6  Ibid. 7  PP. 95–6. 2 3

3.2  Putnam in “There Is At Least One A Priori Truth”

57

moral – the one Quine draws – is that some statements can be only be overthrown by rival theory; but that there is no such thing as an absolutely unrevisable statement. (pp. 93–4) there are statements in science which can only be overthrown by a new theory – sometimes by a revolutionary new theory – and not by observation alone. Such statements have a sort of ‘a priority’ prior to the invention of the new theory which challenges or replace them: they are contextually a priori. Giving up the idea that there are any absolutely a priori statements requires us to also give up the correlate idea (at least it was correlative for the empiricists) that a posteriori statements (and to the empiricists this meant all revisable statements and also meant all synthetic statements, all statements ‘about the world’) are always and at all times empirical’ in the sense that they have specifiable confirming experiences and specifiable disconfirming experiences. Euclidean geometry was always revisable in the sense that no justifiable canon of scientific inquiry forbade the construction of an alternative geometry but it was not always ‘empirical’ in the sense of having an alternative that good scientists could actually conceive. The special status of logical laws is similar, in my view; they are contextually a priori. (p. 95)

For Putnam, it is consistent to hold both that there are no a priori (unrevisable) truths and that there are analytic truths. It is alleged that the notion of analyticity in question is the one that Quine attacks: “a statement is analytic if it can be obtained from (or equivalently turned into) a truth of logic by substituting synonyms for synonyms.”8 Putnam explains that this definition is “linguistic” because the notion of synonymy belongs to the field of linguistics. According to Putnam, even a statement that really is analytic is not immune from revision, for even if a statement is a logical law, we are not forbidden by any methodological principle from revising it. We will just be making a mistake if we do. (p. 96) Putnam continues: even if we arrive at the correct geometry for space-time, still our geometry will not be unrevisable. It is just that we will – as a matter of fact – be making a mistake if we revise it. “‘Fallibilism’ does not become an incorrect doctrine when one reaches the truth in a scientific inquiry.” (p. 96) Analogously, “a really analytic statement is not a priori, because even when we happen to be right about logic, fallibilism still holds good. We never have an absolute guarantee that we are right, even when we are.” (p. 96) No truth is unrevisable.9

3.2 Putnam in “There Is At Least One A Priori Truth” What Putnam wants to argue in this paper is that there is at least one a priori truth in exactly the sense that Quine denied and he himself before: i.e., “at least one truth that it would never be rational to give up”.10 Putnam argued before that the laws of logic are revisable. For instance, quantum mechanics requires us to give up the distributive laws. It is alleged that nothing he will say in this occasion will contradict this position. Putnam explains that it is possible that not all the traditional laws of  P. 94.  P. 96. 10  P. 100. 8 9

58

3  Putnam’s Views on A Priori Knowledge

logic are a priori in the sense of unrevisable, but that only some of them are. It would be a mistake to try to understand the epistemology of all of logic and mathematics in terms of a single notion of a priori truth. (p. 100) Though he will revive the notion of a prioricity, he warns us that it does not mean that we should go back to the old confident way of using it, that is, to think that there are many more a priori truths than what there are really. Putnam says that it is not old fashioned a prioricity, but he has to mean by this, not that it is not the same concept or a quite similar concept, since it is quite similar, but rather that the use of the notion of a prioricity cannot be the old confident one. There are fewer a priori truths in the absolute traditional sense of the notion, but there are these truths. Putnam asks: is it possible that the minimal principle of contradiction, that is, “Not every statement is both true and false”, is then only a contextually a priori truth instead of an absolutely a priori truth?11 Quine explains part of the epistemic status of traditional a priori truths by what he calls their centrality. (p.  110) Putnam specifies: But we should be clear about what the centrality argument does not show. It does not show that a putative law of logic, for instance, the principle of contradiction, could not be overthrown by direct observation. Presumably I would give up the principle of contradiction if I ever had a sense datum which was both red and not red, for example. And the centrality argument sheds no light on how we know that this could never happen. (p. 110)

The point Putnam is making is that the centrality argument only can explain the special status of certain truths up to now; there is no explanation of this special status holding indefinitely. Another way of expressing the same point is that Quine’s centrality argument cannot explain the necessity of these truths, leaving in this way always open the possibility that even experiences, direct observations of the physical world, could falsify them. In a note,12 Putnam distinguishes between two kinds of revision: (a) when the revision consists of negating a statement that we took originally to be true, (b) when we revise some of the concepts of the statement in question. He thinks that revision in the first sense is not always possible, but that every statement is revisable in the second sense. Even the minimal principle of non-contradiction can suffer from a conceptual revision but it cannot be shown to be false. “Every statement is subject to revision; but not in every way.” (p. 111) A conceptual revision of the minimal principle of non-contradiction is proposed by mathematical intuitionists. They deny the applicability of the classical concepts of truth and falsity. In a further note,13 Putnam changes this view. Before he tried to argue for a ‘moderate Quinean’ view by claiming that ‘every statement is revisable but not in every  P. 101.  P. 110. 13  Putnam explains: 11 12

In the previous Note, I said we might give this up by giving up the classical notions of truth and falsity: for example by going over to intuitionist logic and metatheory. But surely if we

3.3  Putnam in “Analyticity and Apriority”

59

way’. Putnam affirms here that this move won’t work. Consider the statement: ‘Not every statement is both true and false.’ To give up that statement, the notions of truth and falsity would have to be understood in a non-classical sense.

3.3 Putnam in “Analyticity and Apriority” Putnam thinks that unlike “2  +  2  =  4”, which certainly seems a priori, there are mathematical facts that have a quasi empirical character. An example he gives of such a statement is: “Peano arithmetic is 10(20) consistent”. We can conceive of these quasi-empirical statements as their being false, whereas we doubt we can conceive of “2 + 2 + 4” being false. For Putnam, although all mathematical truths are metaphysically necessary, our knowledge of some mathematical truths is epistemically contingent. He explains: there may be no way in which we can know that certain abstract structure is consistent other than by seeing it instantiated either in mental images or in some physical representation.14

Let’s remember that Putnam thinks we need empirical statements obtaining not only when we know the truth of a mathematical statement by seeing it instantiated in physical figures, but also in the case of inferential mathematical knowledge, that is, when our knowledge of a mathematical statement consists of following a proof. He adds: If this point has not been very much appreciated in the past (although Descartes was clearly aware of this problem) it is because of the tendency to think that a fully rational, ‘ideally rational’, being should be mathematically omniscient: should be able to just know all mathematical truths without proof (perhaps surveying all the integers, all the real numbers, etc. in his head). This is just forgetting that we understand mathematical language through being able to recognize proofs (plus certain empirical applications like counting). (p. 125)

Putnam makes an important distinction between what is “epistemologically impossible” and what is “metaphysically impossible”. Yet there are still circumstances under which I would abandon my belief that Peano arithmetic is consistent: I would abandon that belief if I discovered a contradiction. Many philosophers will feel that this remark is ‘cheating’. They would say ‘But you could not discover a contradiction’. True, it is mathematically impossible (and even ­‘metaphysically impossible’ …) that there should be a contradiction in Peano arithmetic. But … it is not epistemically impossible. We can conceive of finding a contradiction in Peano arithmetic, and we can make sense of the question ‘What would you do if you came across a contradiction in Peano arithmetic?’ (‘Restrict squema’, would be my answer.)

did that we wouldn’t view it as giving up the concepts of truth and falsity themselves; rather we would view it as giving up an incorrect analysis of them. (p. 112) 14

 P. 124.

60

3  Putnam’s Views on A Priori Knowledge As a matter of fact, there are circumstances in which it would be rational to believe that Peano arithmetic was inconsistent even though it was not. Thus suppose I am caused to hallucinate by some marvelous process (say, by making me a ‘brain in a vat’ without my knowing it, and controlling all my sensory inputs superscientifically), and the content of the hallucination is that the whole logical community learns of a contradiction in Peano arithmetic … And this shows that even ‘Peano arithmetic is consistent’ is not a fully rational unrevisable statement. (p. 126; my emphasis)

Putnam appears to accept that all claims to knowledge are defeasible even when we claim to know an a priori truth in his sense. The explanation seems to be that one thing is our access to a priori truths – the epistemological situation we are in with respect to these truths – and quite another is the metaphysical status of these truths being metaphysically necessary or true in all possible worlds. This again seems to be a lesson Putnam puts forward as a consequence of Kripke’s having distinguished between the epistemological status and the metaphysical status of truths. Putnam is willing to accept that some basic arithmetical statements like “2 + 2 = 4” are a priori. The rest of arithmetical statements and, in general, mathematical and logical statements, are not considered a priori at all. Also the only logical law that he defends as a priori is a weak principle of non-contradiction. He is not even prepared to defend the a prioricity of the principle of non-contradiction. Then, we have an analogous situation in both mathematics and logic. In both disciplines, we find few a priori truths, and the majority of the truths in both fields are not a priori. That is why he does not defend the a prioricity either of logic or mathematics; and that the old-fashioned notion of a prioricity is not terribly important to philosophy. In an important passage below, Putnam talks about what he considers a “sane fallibilism”, and distinguishes it from a very strong and implausible fallibilism that he thinks is in clear tension with the existence of a priori truths in his sense. Of course, if fallibilism requires us to be sure that for every statement s we accept there is an epistemologically possible world in which it is rational to deny s, then fallibilism is identical with the rejection of a priori truth; but surely this is an unreasonable conception of fallibilism. If what fallibilism requires, on the other hand, is that we never be totally sure that s is true (even when s is a priori), or, even more weakly, that we never be totally sure that the reasons we give for holding s true are final and contain no element of error or conceptual vagueness or confusion (even when s is ‘Not every sentence is true’), then there is nothing in such a modest and sane fallibilism to prejudge the question we have been discussing. (“Analyticity and Apriority”, p. 136)

The question Putnam refers to here seems to be the possibility of knowledge of unrevisable statements, even when we don’t know for sure that we possess such knowledge. He accepts this sane fallibilism because he accepts that our knowledge claims are defeasible even when the statement involved is “Not every sentence is true” (this is a version of his weaker principle of non-contradiction: “Not every sentence is b oth true and false”).

3.4  Putnam in “Possibility and Necessity”

61

3.4 Putnam in “Possibility and Necessity” According to Putnam, Kripke15 is responsible for introducing a notion of necessity that completely reopens the issue of a priori knowledge. For those who interpret necessity epistemically, something is necessary if and only if it is knowable a priori. This is certainly Kant’s conception of necessary and a priori truths.16 Kripke tries to defend a non-epistemic notion of necessity: the notion of metaphysical necessity or truth in all possible worlds. Kripke’s notion is a way of responding to Quine’s criticisms of the traditional notion of necessity (as a prioricity).17 There are supposedly necessities that are not known a priori, so the Kantian doctrine that every necessary truth can be knowable a priori is allegedly false. For Putnam, Kripke’s emphasis on the notion of metaphysical necessity as a non-­ epistemic notion has been very illuminating for a phenomenon that occurs in the acquisition of our knowledge of pure mathematical truths. Sometimes our mathematical knowledge involves relying on empirical assumptions. Putnam offers the example of knowledge obtained via a very long proof and observes that some of the empirical assumptions involved are connected with memory, such as our memory of what has been shown in previous steps in order to know how the proof hangs together. On the other hand, Putnam affirms that this situation does not affect the metaphysical status of the truths known: they are metaphysically necessary, true in all possible worlds, even though our knowledge of them may involve empirical assumptions. That the metaphysical status of the truths known is not affected is taken as a consequence of Kripke’s having separated the epistemological distinction between a priori and a posteriori from the metaphysical one between necessity and contingency of the truths known.18 Traditionally, mathematics and logic are considered disciplines that yield a priori knowledge. Now there is a problem: quantum mechanics sees logic as logic of the physical world and as a non-classical logic. Normally, a non-classical logic means that negation is not classical (that is, not not P does not imply P). In Quantum Logics, negation is classical, but the law of distribution fails. So Quantum logic is non-classical in that sense. For Putnam, the discussion of quantum logic seems to posit serious difficulties to the traditional conception of logic (and mathematics too) as a priori. It is possible that even logic can turn out to be empirical and the notion of necessity may have to be scrapped.19 The notion of a prioricity that is at issue entails unrevisability: for Putnam, an item of a priori knowledge cannot be revisable.20 Since, for Quine, “no statement is

 Kripke, Saul. Naming and Necessity. Cambridge, MA: Harvard University Press, 1980.  Kant, first Critique. 17  Quine, “Two Dogmas”. 18  “Possibility and Necessity”, pp. 54–55. 19  Ibid, p. 47. 20  I am not aware whether this is Kripke’s notion of a prioricity too. 15 16

62

3  Putnam’s Views on A Priori Knowledge

immune to revision in the face of recalcitrant experience”,21 this destroys the claim that there can be a priori truths understood as unrevisable. Quine asks how would a revision of logic in response to quantum mechanical evidence be different from the revolution in which Copernicus replaced Ptolemy or Newton Einstein? The answer is that it would not. It is implied that logical laws and geometrical laws are empirical for this reason. They can both be open to revision, though logical laws are more protected in the sense that they would be revised only after revising or giving up other “laws” less entrenched in our system of beliefs. Putnam explains: … changing one’s geometry for the sake of simplifying physical theory, as we did when we adopted Einstein’s theory of general relativity, and changing our logic for the sake of simplifying physical theory, as proposed by Reichenbach (of course, Quine was not commenting on whether the proposal really would simplify physical theory to a worthwhile extent), are changes of the same kind. Neither is forbidden by scientific methodology. The laws of logic, on this perspective, are as empirical as the laws of geometry, only more abstract and better protected. Logic is the last thing we may revise, on Quine’s view, but it is not immune from revision. If Quine is right, ‘necessary truth’ is another famous subject that has no object.22

As things stand, I observe that the last sentence of the quote sits oddly next to the preceding discussion, in the light of which someone might wonder why the necessity of mathematical truths – conceived as not requiring their a prioricity – is supposed to be under threat. For Putnam, even if we have to concede to Quine the claim that some logical laws are empirical (or have empirical presuppositions), it does not follow that all logical laws are of this kind. One example of a logical law – which is not empirical – is the principle of non-contradiction. “The scope of the a priori is indeed shrinking; but the claim that every truth is empirical is still far from being an acceptable or even a coherent thesis.”23 Nevertheless, Putnam recognizes that the discussion about revising the laws of classical logic has a strong “a priori component”.24 He seems to accept that a revision of logic can be appropriate for logical or philosophical reasons when he offers the example of intuitionistic logic as a revision of classical logic. Furthermore, even if we did decide to accept quantum logic, we might be led to do so partly for a priori reasons.25 This suggests again, for Putnam, that the claim that “All truths are empirical” is not forced upon us from the fact that we may have to revise our logic for empirical reasons.  Quine, ibid., p. 43.  “Possibility and Necessity”, p. 51. 23  Ibid. 24  Ibid. 25  Dummett suggests a stronger view of the role of a priori reasons in his “Is Logic Empirical?”, pp. 288–89. According to Dummett, neither a mathematical discovery nor a discovery in quantum mechanics will settle the question whether classical logic ought to be replaced by quantum logic. That question is a philosophical one, and will have to be resolved by philosophical reasons, which are presumably a priori. 21 22

3.4  Putnam in “Possibility and Necessity”

63

Now, someone who feels that truth should be linked to verifiability (or at least to idealized verifiability), might well be led on a priori grounds to consider quantum logic once they realized that propositions might be ‘incompatible’ in the sense that the verification of one might in principle interfere with the verification of another. I don’t mean that this is the only way in which one can be led to consider or even accept quantum logic; and it is certainly empirical that there is such a relation of incompatibility in our world. But the possibility just envisaged illustrates the fact that even if we did decide to accept quantum logic, we might be led to do so partly for a priori reasons, a fact which suggests once again that ‘all truth is empirical’ is not the appropriate conclusion from the fact that we may have to revise our logic for empirical reasons. (p. 53)

As I understand it, the point seems to be that there might be falsifiability by experience for a priori statements, but because our acceptance of a consequent revision is partly guided by a priori reasons (or considerations), then the conclusion that all truth is empirical is false. Nonetheless, Putnam cannot still show that merely from the fact that our acceptance of a revision of logic is partly guided by a priori reasons, it follows that there are a priori statements (or even more, a priori truths). It is clear that “partly for a priori reasons” would not be enough to ensure non-empirical status. But what are “a priori reasons”? Are they just methodological principles governing any kind of investigation? According to Putnam, Quine himself has insisted on the difference between denying that there are a priori statements and denying that there is an a priori factor in scientific decision making. The point just made is one that Quine himself has long insisted on: denying that there are a priori statements is not the same as denying that there is an a priori factor in scientific decision making. Quine himself has suggested that ‘a priori’ and ‘a posteriori’ may be names of factors present in the acceptance of all statements, rather than the names of classes of statements. And the theory of these two factors would be nothing other than normative epistemology: the theory of what makes statements worthy of rational acceptance. (p. 53)

What is an a priori factor? Is this a priori factor “contextually a priori” or “absolutely a priori” in the sense of unrevisable? As I interpret Putnam, an a priori factor, being a component of a theory, is compounded by statements which have to be accepted for certain purposes of investigation as contextually a priori. What does “contextual” mean in this connection? I think that, for Putnam,26 a statement is contextual when its acceptance is needed in a certain context of investigation: its truth is accepted as a matter of the context in question. But what about being also a priori? Something can be left fixed for certain purposes, but this simply does not make it knowable a priori. Perhaps what Putnam means by “contextual a prioricity” is that these statements are held unrevisable for a specific period of time, not for all time, without committing himself to a particular way to know them a priori, i.e., to a particular way to characterize the sense in which they are known a priori.

26

 “‘Two Dogmas’ Revisited”, pp. 95–6.

64

3  Putnam’s Views on A Priori Knowledge

3.5 Some Remarks on “‘Two Dogmas’ Revisited” According to Putnam, giving up the idea that there are any absolutely a priori statements requires us to also give up the correlate idea that a posteriori statements are always and at all times ‘empirical’ in the sense that they have “specifiable confirming experiences and specifiable disconfirming experiences”.27 Let’s examine what this supposed implication entails. A Quinean thesis is: (A) There are no unrevisable statements. By parity of reasoning, (B) There are no synthetic statements. Synthetic statements are such that they are associated with other statements, and if these latter obtain, we must reject them. Since there are no synthetic statements, there are no statements that we must let go in certain circumstances. Another way of expressing the same point is as follows: (I) Everything is revisable. (II) Everything can be true come what may if we make the necessary adjustments, by parity of reason. For Quine, analytic statements and synthetic statements are empty classes. The following question arises: do these two statements, (I) and (II), have to go together? I don’t think so. What does Putnam think about this? It seems that for Putnam they have to go together. The problem with (II), as I see it, is that it entails that everything will go. This is too dangerous. Let’s illustrate the situation at the linguistic level, at the level of rules. There has to be some rules that state what is permissible. They are regulative principles, that could be revised, but they have a determinate meaning. I will make a couple of comments about Putnam’s claim that “No truth is unrevisable”. First, I think that it is important to note that the mere possibility of revision, for example, of an alternative logic, is not alone a threat to its alleged a prioricity. It has to be the possibility of a revision that we can take seriously. The proposed revision has to have some merit in order for us to take it seriously. Again we see that Putnam goes back and forth from the mere possibility of something (without consideration of how probable is, and therefore how rational is to accept such a possibility) to a possibility that really is meritorious of being taken seriously, without argument connecting the two possibilities. Second, a distinction should be drawn between a statement or set of statements being revisable for us because we simply are fallible creatures and cannot be completely certain when we know or not. In this sense, everything is revisable. But there is also a notion of revisability that relates objectively to the subject matter. This 27

 “‘Two Dogmas’ Revisited”, p. 95.

3.6  Some Remarks on “There Is At Least One A Priori Truth”

65

means that a correct geometry is (itself) unrevisable, and that is why it ought not to be revised; so if we revise it – even when we think it is rational to do so – we are making a mistake. After we have achieved all knowledge in a discipline, it seems that it cannot be revised any more (disregarding, of course, minor revisions for the purpose of more simplicity, clarity or elegance). So when one reaches truth in a discipline, the latter becomes objectively unrevisable, and only revisable for us as fallible creatures who cannot know for certain when we have achieved truth.

3.6 Some Remarks on “There Is At Least One A Priori Truth” Putnam asks: “how do we know that a direct observation might not in the future contradict the principle of contradiction?” (p. 110) The principle of non-­contradiction cannot be only contextually a priori but it is, for Putnam, an absolutely a priori (unrevisable) statement. Presumably, Putnam means that there could not be a direct observational falsification of the law (or I add a priori reasons to reject it) and that is why it is absolutely and not merely contextually a priori. If it were only contextually a priori – or “central” in Quine’s terminology – then the possibility of being falsified directly by experience cannot be ruled out. But since this principle cannot be falsified at all, it has to be absolutely a priori.28 The claim that a priori statements could be falsifiable directly by experience is a very strong claim. Quine himself does not make it. Quine does not say that all statements may be falsified directly by observation. Again we see that Putnam goes back and forth from the mere possibility of something (without consideration of how probable is, and therefore how rational is to accept such a possibility) to a possibility that really is meritorious of being taken seriously, without argument connecting the two possibilities. It is very important to understand that Quine is not claiming that, for example, mathematical statements can be falsifiable – individually – directly by experience, as in the case of strong revisions, where there is a change of truth-value, from truth to falsity, but rather that we can change the truth-value of even mathematical statements and logical ones given holistic considerations of our body of knowledge. For systematic reasons, it can turn out that some mathematical statements we took to be true, are taken as false, if this is a reasonable move for the preservation of our body of knowledge. It is like a decision in a way.

 Casullo questions Putnam’s proposal in “There is at least one a priori truth” because it is not explicit about whether our a priori justified beliefs in logical principles such as “Not every statement is both true or false” requires evidence, if so, what type of evidence would it be, if such evidence involves a vicious regress and the possibility of rejecting “Not every statement is both true or false” on the basis of a priori reasons. (A Priori Justification, pp. 82–85 and “A Priori Knowledge” in Essays on A Priori Knowledge and Justification, pp. 123–25.) 28

66

3  Putnam’s Views on A Priori Knowledge

I think that what is behind Putnam’s notion of a prioricity (as unrevisability), being such a strong notion, is his attempt to rescue part of the traditional conception of a priori knowledge as knowledge which cannot be falsifiable by experience (surprisingly, he thinks also that the notion of a prioricity cannot play the traditional role it had; we cannot go on using the old-fashioned notion of a prioricity). Since Putnam himself, like Quine, presents the case of a revision of logic allegedly for empirical reasons, not all logical truths come up as a priori according to his definition. Putnam does not reject the notion of contextual a prioricity when he adopts his stronger notion of a prioricity in “There is at least one a priori truth”. These two notions coexist in his philosophy. Putnam thinks that it is a mistake to believe that a single notion of a priori truth could explain all the epistemology of mathematics and logic. He says that some of the logical laws are revisable, and that is why they are only contextually a priori, and that some are not: they are absolutely unrevisable a priori truths. It seems also that he equates actual revision with empiricalness, and just the possibility of revision of these “truths” with the fact that they are merely contextually a priori. But the fact that there is actual revision does not imply either that there is empiricalness involved nor that these truths are only contextually a priori. Let me illustrate the revisions that Putnam29 talks about and why I think there is a problem with them. To simplify things, let’s say that “S” is a sentence and that we talk of revision in connection with sentences. A weak revision of “S” would involve that at time t1 we accept “S” is true. At another time, t2, we reject “S” is true. (Obviously, it could be just the other way around: we don’t accept at a previous time that “S” is true but at a later time we do accept it.) Why? Because we no longer accept something of that form; we no longer accept than “S” says that P. There is a change of beliefs about the constituents of the sentence. A strong revision of “S” consists of the following: at time t1 we accept “S” is true. At a later time t2 we reject “S” is true. Why? Because we continue to accept that “S” says that P, but we no longer accept P. But what about the case when we come to believe that our prior understanding of “S” was somewhat defective or confused? This case does not belong to any of the two cases of revisions that Putnam proposes. In this case, it is neither that we have changed the meanings of at least one constituent of “S” and believe something else, or that we believe the negation of “S” is true. This is a third case of revision, namely, when we reject the understanding of “S”: there is repudiation of understanding. Putnam appears to have this case of revision in mind but fails to recognize it as a separate case. Actually, the intuitionistic revision of logic is not a case of weak revision, as he understands it, but rather it is a revision of the third sort just described. Furthermore, the intuitionistic revision is proposed for the excluded middle, and not for the principle of non-contradiction.

29

 “There is at least one a priori truth”, p. 112.

3.7  Some Remarks on “Analyticity and Apriority”

67

I ask: does Putnam mean to imply that if one went over to intuitionistic logic, one could give up the weak law of non-contradiction? It is not clear that going intuitionistic makes this any easier at all in any case. Putnam explains that changing the meanings of the words – what I understand as a weak revision consisting of revising the meanings of the words – is a move that is only available for sentences and not for statements. He affirms that it is always possible to change the meanings of the words for sentences; and this is the reason why there are no unrevisable sentences. Then, I understand that, for Putnam, there could be unrevisable statements only if weak revision is never possible for them and if strong revision, i.e., accepting the negation of a statement we took originally to be true, is never rational for them. The reason Putnam offers for denying that statements can only be subjected to weak revision is not a good one. Weak revisions could be possible also for statements. It is just that in some cases, for Putnam, like with the minimum principle of non- contradiction, we would be making a mistake if we revise (change the meanings of the words). The situation is perfectly analogous to the case of weak revisions for sentences. Because sentences are always in principle revisable, strongly or weakly, for us, it does not follow that they are not always objectively revisable/ unrevisable.

3.7 Some Remarks on “Analyticity and Apriority” Putnam considers the status of ‘2 + 2 = 4’ to be quite different because our knowledge of it is immediate or basic. As a consequence, it may seem that, for Putnam, basic mathematical knowledge does not need the truth of any empirical statement. I don’t agree with Putnam – if that is what he is actually implying- in rejecting the need of the truth of empirical statements (or assumptions) in the case of non-­ inferential a priori knowledge. Basic empirical assumptions concerning the respectability of the knower’s state of mind, for example, would have to obtain in order for us to possess any knowledge. Of course, I am aware of what appears to be Putnam’s intuition that in the case of inferential knowledge obtained via long proofs, the necessary empirical assumptions are more numerous – i.e., there are more chances to make mistakes – given the difficulties involved than in the non-inferential a priori case. These presuppositions have to be taken into account in what he calls knowledge obtained by “epistemologically contingent grounds”. Actually, he seems to distinguish between ways in which a belief may be epistemologically contingent. But, again, I think that the matter is one of degree and not of absence of empirical presuppositions in the case of non-inferential a priori knowledge. Furthermore, something basic can be confused. Furthermore, once we distinguish between the roles that statements may have in justifications, we realize that the sort of empirical assumptions that Putnam has in mind in connection with inferential a priori knowledge do not play a justificatory

68

3  Putnam’s Views on A Priori Knowledge

role for a priori truths. They are rather assumptions that concern the respectability of the knower’s state of mind.

3.8 Some Remarks on “Possibility and Necessity” I understand that what Putnam calls “knowledge based on empirically contingent grounds” is knowledge based on empirical assumptions of some sort. I observe that two cases (at least) have to be distinguished here: (1) one thing is relying on empirical assumptions when, for example, we follow a long proof and we consider that our knowledge is a priori nonetheless; and (2) another is mathematical knowledge obtained by a computer proof. Putnam does not specify if he considers knowledge by computer proofs a priori, “partly a priori”, or a posteriori. To my understanding, it will be knowledge a posteriori at best. Furthermore, we must distinguish between roles empirical statements (or assumptions) can have, for example, in our acquisition of inferential mathematical knowledge: One of the roles is: (1) In justifying the conclusion of a proof in the reasoning: The proof of p, for the claim that p. A second role is: (2) The role they have in the reasoning for the conclusion that “I have a proof”: that is, the role they have for the claim “I have a proof that p”. In the first role, empirical assumptions function as collateral beliefs about the ability of the knower to follow a proof that p. They are presupposed in our inferential knowledge that p as background conditions and do not appear within the reasoning itself. That is why we can talk about this inferential knowledge that p being a priori despite relying on empirical assumptions. In contrast, in the second role, the same or related empirical assumptions appear within the reasoning -what is totally understandable since the claim known is not “p” itself, “p” mathematical- but rather “I have a proof that p”. My knowledge that “I have a proof that p” depends on the empirical assumption that I am intelligent enough to follow the proof, for example. My knowledge is probabilistic in that sense. The statement “I have a proof that p” is empirically defeasible; moreover, it is an empirical statement. I can abandon it if I discover that I made a mistake in carrying out the proof. There is a corresponding distinction between essential mistakes and incidental mistakes. The first are those that show that there can be no proof. The others are those which show that there is a mistake in the purported proof but do not show that there is no proof. There might be a proof, it is just that I carry out the reasoning incorrectly. At first glance, it seems that Putnam equates mere “revisability” with “empiricalness”, so whatever is revisable has to be empirical in character. This is quite questionable, and Hale30 is right in questioning this implication since revisability is not

30

 Hale, Abstract Objects, p. 143. Dummett makes the same point in “Is Logic Empirical?”.

3.9 Conclusion

69

per se incompatible with a prioricity.31 More is needed in order to obtain this conclusion. One should distinguish here between the sort of grounds for revisability on which one might hold that revisability does not carry empirical status with it – there is a difference between revising a statement because it is found to lead to a contradiction, say, and revising a statement because it conflicts with experimental or observational findings. On the issue of necessity, I consider Putnam’s interpretation of Kripke quite uncritical. Kripke is presumably presenting a necessity that is not a priori. Now neither Putnam nor Kripke say anything about whether general principles of the sort “If P, then necessarily P” are a priori or not. To clarify the issue whether the are necessities that can be known completely empirically, let’s examine the following argument: 1. If Water consists of H20, then it is necessary that it is. (Necessarily [Water = H20]). 2. Water is constituted of H20. (This is an empirical premise in Chemistry). 3. It is necessary that water consists of H2O. (1) is an instance of a general principle. Our acceptance of (1) involves the acceptance of a general principle like the following: (0) Stuffs have their constitution by necessity. What (0) expresses is that part of the concept of a substance is to be just that. This is a conceptual truth. So, the argument is not entirely empirical because it relies on a premise that is a priori. Now it is not entirely a priori either. The argument is “partly a priori”. Then, neither Putnam nor Kripke have shown that there is a necessity which is entirely empirical.

3.9 Conclusion Putnam’s position is very interesting because it is dialectical. He is in a middle position. He is very critical of the traditional notion of the a priori as entailing unrevisability. However he also recognizes that there is at least one a priori truth, a weak formulation of the principle of non-contradiction (‘Not every statement is both true and false’), taken as a principle which operates as a norm for any conceivable rationality. Putnam affirms that even though he recognizes the existence of at least one a priori truth, the notion of a prioricity is not terribly important to philosophy. For  A similar point is made by Casullo in A Priori Justification, pp. 116–17, and again in “Revisability, Reliabilism, and A Priori Knowledge” in Essays on A priori Knowledge and Justification, pp. 39–40. 31

70

3  Putnam’s Views on A Priori Knowledge

Putnam, the notion is not terribly important to philosophy because it can no longer play the traditional role it had. We don’t gain much by having a notion of a prioricity which entail unrevisability since there is few a priori knowledge. The majority of truths traditionally considered a priori are not included under his notion. Putnam ultimately thinks that the notion of a prioricity is important because of what indicates about rationality. In the end, Putnam thinks that a priori truths are unrevisable. What about the relative and absolute a priori distinction? This distinction is used by Putnam to clarify which truths are a priori in his strong sense of absolutely a priori or unrevisable, and those which are a priori but only in a weak sense, contextually a priori. Since he thinks there are very few a priori truths, let’s remember that he is not prepared to defend even the a prioricity of the full principle of contradiction, the notion of a prioricity is not terribly important to philosophy. The situation with the “a priori/a posteriori” distinction is analogous to the one with the “analytic/synthetic” distinction. There is such a distinction. Quine is wrong to deny this. But Quine is right in the sense that the distinction is a trivial one. We have another analogous situation in both mathematics and logic. In both disciplines, we find few a priori truths. The majority of the truths in both fields are not a priori. Then, what is the epistemic status that Putnam confers upon the vast majority of mathematical and logical truths? They are not (strongly) a priori in his sense. Are they quasi-empirical? Some of them are, like “Peano arithmetic is 10 (20) consistent” since they involve empirical presuppositions. Putnam thinks that our beliefs in the consistency of PA and on induction are not epistemologically contingent, or at least that they are not epistemologically contingent in the same way as “Peano 10 (20) is consistent”. Later he affirms that we could envisage epistemic circumstances under which we could reject the consistency of PA, though we would be mistaken since that is mathematically impossible. Perhaps, the majority of mathematical and logical truths are only contextually a priori (nothing quite clear indeed; the notion of contextual a prioricity is obscure). If so, then it is unsatisfactory to explain the fact that many mathematical and logical truths have been kept for millennia given that they are only contextually a priori. The problem with Putnam’s notion of a prioricity as entailing unrevisability is that it does not include the majority of what are usually considered a priori truths, in other words, it is too strong. And the problem with Putnam’s notion of a prioricity as “contextual a prioricity” is that it is too weak since this notion does not capture – let alone account for – the alleged special certainty that traditionally has been associated with mathematical and logical truths. Another problem with Putnam’s views is that he does not take the predicate “a priori” as primarily characterizing a particular way of knowing. He does not clarify the sense in which a priori truths are a priori, that is, because they are known in a particular way. So, his account does not illuminate the issue of the “independence of experience” characteristic of a priori knowledge but only concentrates on the supposed properties that a priori truths have: for instance, unrevisability allegedly. The mistake I am attributing to Putnam (and Quine) is that of supposing that in order for something  – a statement?, knowledge claim?, belief?, − to count as

Conclusion of Part I

71

analytic, or a priori, it has to be unrevisable. Let us take it that it is beliefs that are revisable or not. Then their thought is that in order for it to be possible to know a statement to be true a priori, there have to be grounds for believing it to be true such that, once we are apprised of those grounds, no possible improvement in our state of information could destroy the warrant which they confer. In the basic case it is statements – declarative sentences – which are analytic or not (true in virtue of meaning or not); ways of knowing, or justifying, which are a priori or not; and beliefs (“claims to know” being a particular kind of beliefs) which are revisable or not. Since these three concepts apply to different kinds of thing, there is no question of anyone’s clearheadedly “equating” them. At first glance, it seems that Putnam equates mere “revisability” with “empiricalness”, so whatever is revisable has to be empirical in character. This is quite questionable since revisability is not per se incompatible with a prioricity. One should distinguish here between the sort of grounds for revisability on which one might hold that revisability does not carry empirical status with it – there is a difference between revising a statement because it is found to lead to a contradiction, say, and revising a statement because it conflicts with experimental or observational findings. Revision is consistent with a prioricity. Revisions in mathematics, for instance, are conducted via rational reflections on mathematical concepts, for example, the concepts of number, set or the differentials in the beginning of analysis, and proofs. These are a priori ways of knowing. Finally, Putnam’s views do not take (not explicitly at least) the predicate “a priori” as primarily characterizing a particular way of knowing. Consequently, his views do not clarify the sense in which a priori truths are a priori, that is, because they are known in a particular way. So, Putnam’s account of the a priori does not illuminate the issue of the “independence of experience” characteristic of a priori knowledge. However, what is very useful about Putnam’s views on a prioricity is that they are sensitive to the issue of revisability/unrevisability in connection with a priori knowledge.

Conclusion of Part I Let’s remember that for Kitcher, it seems that the question of whether it would be possible to have an a priori warrant for a false belief does not arise for Kant. Perhaps Kant did not think such a question could arise. I think it is unfair of Kitcher to adjudicate to Kant the view that there is no possibility of an a priori warrant justifying a false belief by merely invoking Kant’s claim that all a priori knowledge is knowledge of necessary truths. We have to know how the justification for the necessary truth stands – it may not amount to knowledge. And if the warrant produces knowledge, it is because it is a good or sound warrant. The modal status of the truth known by its means is a separate matter. Unfortunately, Kant did not elaborate on the notion of an a priori justification. Since the notion of a priori justification is the crucial one to characterize in the

72

3  Putnam’s Views on A Priori Knowledge

epistemology of a priori knowledge, contrary to Kitcher and Friedman, it remains unclear if, for Kant, a priori knowledge implied some sort of infallibility. A more specific and related issue is whether Kant’s notion of a priori knowledge is a purely “negative” one, i.e., whether it is adequately characterized as non-­ empirical or non-a posteriori. This issue is important since if Kant did not succeed in characterizing explicitly and fully the notion of a priori knowledge, then that task remains. Since I think he failed, I propose my characterization in Chap. 9. One thing emerges very neatly from our discussion of Kant. The importance of the question whether infallibility is a distinctive property of a priori knowledge remains. I address this extremely difficult question and try to offer a resolution to it in the last chapter of this book. Quine urges that no statement is immune to revision. But a defender of a prioricity should not wish to resist the suggestion that logic, or other disciplines conceived to involve a priori statements, are revisable. There should be no interest in maintaining that we cannot be in error in judging a statement to have that status. Can we therefore give Quine the claim that any particular statement which we accept as a priori could, in certain circumstances, reasonably be discarded? To grant the claim need be to grant no more than that our assessment of any particular statement as a priori may always in principle turn out to have been mistaken. Quine has assumed, with the bulk of the philosophical tradition, that a prioricity involves indefeasible certainty. To claim that a statement is a priori, however, is only to make a claim about the way we know of its truth – there is no immediate reason why the claimant has to agree that, when statements are a priori, their truth must be known with special sureness. Putnam affirms that even though he recognizes the existence of at least one a priori truth, the notion of a prioricity is not terribly important to philosophy. For Putnam, the notion is not terribly important to philosophy because it can no longer play the traditional role it had. We don’t gain much by having a notion of a prioricity which entail unrevisability since there is few a priori knowledge. The majority of truths traditionally considered a priori are not included under his notion. Putnam ultimately thinks that the notion of a prioricity is important because of what indicates about rationality. In the end, Putnam thinks that a priori truths are unrevisable. What about the relative and absolute a priori distinction? This distinction is used by Putnam to clarify which truths are a priori in his strong sense of absolutely a priori or unrevisable, and those which are a priori but only in a weak sense, contextually a priori. Since he thinks there are very few a priori truths, let’s remember that he is not prepared to defend even the a prioricity of the full principle of contradiction, the notion of a prioricity is not terribly important to philosophy. The situation with the “a priori/a posteriori” distinction is analogous to the one with the “analytic/synthetic” distinction. There is such a distinction. Quine is wrong to deny this. But Quine is right in the sense that the distinction is a trivial one. Putnam’s thought is that in order to be possible to know a statement to be true a priori, there have to be grounds for believing it to be true such that, once we are apprised of those grounds, no possible improvement in our state of information could destroy the warrant which they confer.

References

73

Now, what is important about Putnam’s “final” view on a prioricity is that it is sensitive to the issue of unrevisability/infallibility in connection with a priori knowledge. I return to this issue in Chap. 8 and Part III of the book.

References Azzouni, J. 1994. Metaphysical Myths, Mathematical Practice: The Ontology and Epistemology of the Exact Sciences. Cambridge: Cambridge University Press. ———. 2008. The Compulsion to Believe: Logical Inference and Normativity. Protosociology 25: 69–88. Benacerraf, P., and H.  Putnam, eds. 1984. The Philosophy of Mathematics: Selected Essays. Englewood Cliffs: Prentice-Hall. Boghossian, P., and C. Peacocke. 2000. New Essays on the A Priori. Oxford: Oxford University Press. Casullo, A. 2003. A Priori Justification. Oxford: Oxford University Press. ———. 2012. Essays on A Priori Knowledge and Justification. New York: Oxford University Press. Casullo, A., and J. Throw, eds. 2013. The A Priori in Philosophy. Oxford: Oxford University Press. Coffa, J.A. 1991. The Semantic Tradition from Kant to Carnap: To the Vienna Circle. New York: Cambridge University Press. Creath, R. 1990. Dear Carnap Dear Van: The Quine-Carnap Correspondence and Related Work. Berkeley: University of California Press. Dummett, M. 1980a. Is Logic Empirical. In Dummett. ———. 1980b. Truth and Other Enigmas. Cambridge, MA: Harvard University Press. Field, H. 1989. Realism, Mathematics, and Modality. Oxford: Basil Blackwell. ———. 1996. The A Prioricity of Logic. Proceedings of the Aristotelian Society 96: 359–379. ———. 2000. A Priority as an Evaluative Notion. In Boghossian and Peacocke’s New Essays on the Apriori (2000), 117–149. Oxford: Oxford University Press. Frege, G. 1952. On Sense and Reference. In Translations from the Philosophical Writings of Gottlob Frege, ed. M. Black and P. Geach, 56–78. Oxford: Basil Blackwell. Reprinted in Part in Benacerraf and Putnam. ———. 1953. The Foundations of Arithmetic. Oxford: Basil Blackwell. Friedman, M. 1992. Kant and the Exact Sciences. Cambridge, MA: Harvard University Press. ———. 2000. Transcendental Philosophy and A Priori Knowledge: A Neo-Kantian Perspective. In Boghossian and Peacocke (2000), 367–383. Oxford: Oxford University Press. Gödel, K. 1984. What is Cantor’s Continuum Problem? In Benacerraf and Putnam. Goldman, A. 1967. A Causal Theory of Knowing. The Journal of Philosophy 64: 357–372. Grice, H.P. 1962. Some Remarks About the Senses. In Analytical Philosophy, ed. R.J.  Butler, 133–153. Oxford: Blackwell. Haack, S. 1974. Deviant Logic. London/New York: Cambridge University Press. Hale, B. 1987. Abstract Objects. Oxford: Basil Blackwell. Hale, B., and P. Clark, eds. 1996. Reading Putnam. Wiley-Blackwell. Hale, B., and A. Hoffmann, eds. 2010. Modality: Metaphysics, Logic and Epistemology. Oxford: Oxford University Press. Hale, B., and C. Wright, eds. 1999. Companion to the Philosophy of Language. Wiley-Blackwell. Kant, I. 1956. Critique of Pure Reason. Trans. Norman Kemp Smith. New York: St. Martin’s. Kitcher, Philip. 1975. Kant and the Foundations of Mathematics. Philosophical Review 84: 23–50. ———. 1980a. A Priori Knowledge. Philosophical Review 89: 3–23. ———. 1980b. Apriority and Necessity. Australasian Journal of Philosophy 58: 89–101. Reprinted in Moser. ———. 1981. How Kant Almost Wrote “Two Dogmas of Empiricism”. Philosophical Topics (12): 217–250.

74

3  Putnam’s Views on A Priori Knowledge

———. 1983. The Nature of Mathematical Knowledge. Oxford: Oxford University Press. ———. 2000. A Priori Knowledge Revisited. In Boghossian and Peacocke (2000), 65–91. Oxford: Oxford University Press. Kripke, S. 1971. Identity and Necessity. In Identity and Individuation, ed. M.K. Munitz. New York: New York University Press. ———. 1980. Naming and Necessity. Cambridge, MA: Harvard University Press. Pap, A. 1958. Semantics and Necessary Truth. New Haven: Yale University Press. Parsons, C. 1967. Foundations of Mathematics. In The Encyclopedia of Philosophy, ed. Paul Edwards, vol. 5–6, 188–212. New York: Macmillan. ———. 1983. Mathematics in Philosophy: Selected Papers. Ithaca: Cornell University Press. Putnam, H. 1975. Mathematics, Matter, and Method, Philosophical Papers. Vol. 1. Cambridge: Cambridge University Press. ———. 1976. Two Dogmas’ Revisited. In Contemporary Aspects of Philosophy, ed. Gilbert Ryle. London: Oriel Press. Reprinted in Putnam, Realism and Reason, Philosophical Papers, vol. 3, 87–97. Cambridge: Cambridge University Press, 1983. ———. 1978. There Is At Least One A Priori Truth. Erkenntnis (13): 153–170. Reprinted in Putnam, Realism and Reason, Philosophical Papers, vol. 3, 98–114. Cambridge: Cambridge University Press, 1983. ———. 1979. Analyticity and Apriority: Beyond Wittgenstein and Quine. In Studies in Metaphysics. Midwest Studies in Philosophy, ed. P.  French, T.  Uehling, and H.  Wettstein, vol. 4, 423–441. Minneapolis: University of Minnesota Press. Reprinted in Putnam, Realism and Reason, Philosophical Papers, vol. 3, pp.  115–138. Cambridge: Cambridge University Press, 1983. ———. 1983. Possibility and Necessity. In Realism and Reason, Philosophical Papers, vol. 3, 46–68. Cambridge: Cambridge University Press. Quine, W.V. 1960. Word and Object. Cambridge, MA: MIT Press. ———. 1961. Two Dogmas of Empiricism. In From a Logical Point of View, 20–46. Cambridge, MA: Harvard University Press. Reprinted in Moser. ———. 1966a. Carnap and Logical Truth. Synthese (12): 350–370. Reprinted in The Ways of Paradox, 100–25. New York: Random House. ———. 1966b. Truth by Convention. In The Ways of Paradox, 70–99. New York: Random House. Reprinted in Benacerraf and Putnam, 322–345. ———. 1970. Philosophy of Logic. Englewood Cliffs: Prentice Hall. Wilder, R. 1975. Evolution of Mathematical Concepts. New York: Wiley. Williamson, T. 2002. Knowledge and Its Limits. Oxford: Oxford University Press. ———. 2007. The Philosophy of Philosophy. Malden: Blackwell. ———. 2013. How Deep Is the Distinction Between A Priori and A Posteriori Knowledge. In The A Priori in Philosophy, ed. Casullo and Thurow, 291–312. Oxford University Press. Wittgenstein, L. 1956. Remarks on the Foundations of Mathematics. Trans. G.E.M. Anscombe. Oxford: Basil Blackwell. ———. 1968. Philosophical Investigations. Trans. G.E.M. Anscombe. Oxford: Basil Blackwell. Wright, C. 1980. Wittgenstein on the Foundations of Mathematics. Cambridge, MA: Harvard University Press. ———. 1983. Frege’s Conception of Numbers as Objects. Aberdeen: Aberdeen University Press. ———. 1984. Inventing Logical Necessity. In Language, Mind and Logic, ed. J.  Butterfield, 187–209. Cambridge: Cambridge University Press. ———. 1992. On Putnam’s Proof That We Are Not Brains in a Vat. Proc Aris Soc 92: 67–94. ———. 1993a. Scientific Realism and Observation Statements. International Journal of Philosophical Studies 1 (2): 231–254. ———. 1993b. Realism, Meaning and Truth. 2nd ed. Wiley-Blackwell. ———. 1994. Truth and Objectivity. Harvard: Harvard University Press. Reprint edition. Yablo, Stephen. 1993. Is Conceivability a Guide to Possibility? Philosophical and Phenomenological Research 53 (1): 1–42.

Part II

Hale’s Views on A Priori Knowledge and Revision 

This part is concerned with my work on Bob Hale. He is the first philosopher who most carefully has scrutinized Philip Kitcher’s important challenges to a priori knowledge. However, Hale’s own important contributions to a priori knowledge – i. e. his criticisms to Kitcher and his own proposals – have not been practically analyzed. His discussion bears directly on a number of important issues in connection with the notion. For instance, he offers proposals for the characterization of the notion, forcibly argues for the compatibility of a priori knowledge and revision, addresses the issue of the non-falsifiability of a priori statements, and – given the mere fact that we are fallible creatures prone to make mistakes everywhere  – he does remain neutral for any possibility of infallibility, properly conceived, in the a priori realm. Given that Hale’s work bears directly on the issues I am interested, it is quite relevant to discuss his work in detail. This part consists of five chapters followed by a conclusion. After an introductory chapter (Chap. 4) on Hale’s general views regarding a priori knowledge, I proceed to examine (in Chap. 5) Philip Kitcher’s views on a priori knowledge. Since Hale consider his work on a priori knowledge to be a response to Kitcher, it is useful to discuss Kitcher’s views. Hale was the first who more throughly reacted to Kitcher’s challenge to a priori knowledge. I begin to consider (in Chap. 6) Hale’s work on a priori knowledge which appear in his chapter “Platonism and Knowledge II: Non-Empirical Knowledge” of his book Abstract Objects. This chapter is concerned with Hale’s reactions to Kitcher. Chapter 7 deals with views that can be attributed to Hale independently of his response to Kitcher and that are published in the above-mentioned chapter: with what I call “Pure Hale”. I will be discussing in detail his view that empirical indefeasibility is a hallmark of the a priori. I will evaluate Casullo’s interpretation of Hale’s views. I will also examine new recent complications for the a priori related, to a greater or lesser extent, with this indefeasibility condition: Field’s “default propositions”, Wright’s “entitlements” or “warrants for free”, and Williamson’s challenge to the a priori in terms of experience allegedly playing a third role in a priori knowledge (justification) that is “neither purely enabling nor strictly evidential”. Then I proceed to evaluate Hale’s assertions on a priori knowledge, and identify a preferred one as a candidate for a definition of

76

 

the notion. In Chap. 8 I first focus on what I take to be Hale’s preferred notion of a priori knowledge in Abstract Objects, and show that this proposal does not work because of circularity. Later I examine more recent developments for a new characterization of a priori knowledge along Hale’s lines. I argue that there is an outstanding problem in connection with Hale’s new proposal for a priori statements as being those which are non-falsifiable by experience. That is, it is in too direct collision with Quine’s epistemological holism. The problem is that if Quine’s epistemological holism is right, Hale’s notion of a priori knowledge would be empty. In the end of this chapter I will closely examine whether it is coherent to talk of revision in connection with a priori knowledge  – as some authors have thought, including Hale – sorting out what has to be involved for such a coherence to be possible, and ending up with some remarks on the relationship between the notions of revision and a prioricity. As far as the issue of infallibility is concerned, Hale’s position in his chapter may seem to be that there is no room for infallibility in connection with a priori knowledge  – or knowledge in general  – given the undeniable fact that we are fallible creatures.

Chapter 4

Hale’s General Epistemological Views Regarding A Priori Knowledge

Abstract  In this chapter I introduce Hale’s general views regarding a priori knowledge. He is the first philosopher who most carefully has scrutinized Philip Kitcher’s important challenges to a priori knowledge. However, Hale’s own important contributions to a priori knowledge – i. e. his criticisms to Kitcher and his own proposals – have not been practically analyzed. His discussion bears directly on a number of important issues in connection with the notion. For instance, he offers proposals for the characterization of the notion, forcibly argues for the compatibility of a priori knowledge and revision, addresses the issue of the non-falsifiability of a priori statements, and – given the mere fact that we are fallible creatures prone to make mistakes everywhere – he does remain open or  neutral for any possibility of infallibility, properly conceived, in the a priori realm. Keywords  Causality · Platonism · Fallibility · Revisability · Warrant According to Hale, for any adequate general theory of knowledge to require some kind of causal condition is to require, roughly speaking, that for X to know that p, X’s belief that p must be causally connected with the fact that p in some adequate way.1 A good deal of the motivation for accepting a causal requirement as a necessary condition in an adequate general theory of knowledge arises from the perceived inadequacy of the standard account of knowledge in terms of “justified true belief”. The Gettier-type counterexamples have motivated the introduction of a causal constraint on knowledge as justified true belief to avoid having to classify as knowledge cases when one does merely possess a lucky guess. Hale distinguishes between weak and strong causal theories of knowledge.2 Hale observes that strong causal theories have difficulties for accommodating any sort of a priori knowledge. Strong causal theories are those which require that for knowledge that p, the true conferring fact that p itself must be appropriately causally related to the belief that p. On the  Ibid, p. 28.  P. 93.

1 2

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 I. Fred-Rivera, A Historical and Systematic Perspective on A Priori Knowledge and Justification, Philosophical Studies Series 151, https://doi.org/10.1007/978-3-031-06874-4_4

77

78

4  Hale’s General Epistemological Views Regarding A Priori Knowledge

other hand, weak causal theories like the one put forward by Philip Kitcher require only that for warranting belief that p, the belief should be caused by the grounds which warrant it. Note that now there is another causal relation: it is no longer required that the true conferring fact that p must cause the belief that p – and in doing so must warrant the belief that p – but rather than it is a necessary condition for knowledge that the ground for p shall be causally responsible for the belief that p and for warranting p as well. Hale comments on Kitcher’s causal proposal: What is further required ... is that the knower’s (true) belief shall be caused by the grounds which warrant it. This seems, if not unexceptionable, highly plausible.3 ... whilst he [Kitcher] may be said to be advocating a causal account of knowledge, it is only a weakly, and fairly uncontentiously, causal theory that is on offer. Certainly there is no suggestion here that for X to know that p, the fact that p must be suitably causally connected with X’s belief that p. The causal requirement is no more than that what grounds X’s belief that p shall be causally responsible for his belief, if he is to possess knowledge ... Just because the kind of causal theory Kitcher advocates does not require that, when X knows that p, the truth-conferring fact that p shall itself play a causal role, there is so far no special reason to expect his theory, in contrast with strong causal theories of the sort previously discussed, to confront any insuperable difficulty in accommodating knowledge a priori of necessary truths. But, for the same reason, it could pose no direct threat to platonism based upon the acausality of abstract objects, or states of affairs involving them. Kitcher’s endorsement of Benacerraf’s argument suggests a failure to appreciate the significance of this difference between the two types of causal account.4

That is, merely to require that for warranting belief that p, the belief should be caused by the grounds which warrant it, is quite plausible and that is compatible with the existence of a priori knowledge. As I understand it, this requirement is compatible with a priori knowledge since for a priori knowledge that p it is necessary that the ground is causally responsible for believing that p and, therefore, for knowing that p. Even in the case of inferential a priori knowledge, for example, rightly possessing a proof that p satisfies this weak causal requirement. How is it that rightly possessing a proof that p could cause belief that p? Because when one rightly possesses a proof for p then one justifiably could come to believe that p is true since it is the conclusion of a proof.5 Kitcher is not aware that this weak causal condition on knowledge is compatible with a priori knowledge. 6  P. 127.  Ibid. 5  It should be specified that the idea that Kitcher and Hale are defending here ought to be that the ground for knowledge has to have the ability to produce the belief in question. It would be implausible to require, on the other hand, that the belief was in fact produced by the ground. This would be too strong because we often can believe that p is true, for example, p being the conclusion of a proof, before following a proof that p. One can follow such a proof later on and know that p is true. As I understand it, the idea that Kitcher and Hale ought to be defending is rather that the ground for knowledge must have the ability to produce the belief, so if I have not thought that p before and then possess a justification for p then I can come to believe that p right then. 6  Kitcher endorses the Benacerraf epistemological challenge against the platonist understanding of mathematical knowledge as being about abstract objects. (The reference to Benacerraf is: 3 4

4  Hale’s General Epistemological Views Regarding A Priori Knowledge

79

Hale points out that the fact that a priori knowledge is compatible with a causal theory of knowledge  – since it can satisfy a weaker causal condition on knowledge  – is not enough to justify the claim that mathematical statements are about abstract objects. a strong causal theory is likely to have troubles making room for any kind of knowledge a priori, whether the truths so known are platonistically construed or not. This line of defense was wholly negative, however. And just for that reason, it is unlikely by itself to adequately relieve the general and widely felt anxiety that however natural the platonist’s semantics for statements of arithmetic, for example, may be, acceptance of the accompanying ontology leaves us in an epistemologically parlous state.7

The epistemological problem for the platonist is how to explain knowledge of abstract objects when there can be no causal route or contact with those objects. Hale asks: ‘what sort of positive account is available for the platonist?’8 The traditional answer is to appeal to a kind of knowledge that does not require causal contact with objects for warranting true belief. Our knowledge of logical and mathematical truths is non-empirical or a priori. Again, this merely constitutes a form of an answer – more elaboration is necessary. It is necessary to analyze the notion of non-empirical knowledge or knowledge a priori. Hale observes that since the notion of nonempirical knowledge is quite general, it is consistent with different explanations of how we acquire a priori knowledge. Hale thinks that inferential a priori knowledge is obtained by deductive reasoning from basic truths already known a priori. It is in relation to our apprehension of basic truths – truths not known inferentially – that there is most room for conflicting accounts. For instance, Gödel’s and Penelope Maddy’s views consider our a priori apprehension of basic truths to involve a sort of intuition, which is vaguely constructed following the model of sense perception. On the other hand, Hale considers it to be quite doubtful that the perceptual model can be successful in explaining our knowledge of basic a priori truths. Hale proposes the following alternative explanation of basic a priori knowledge: a priori knowledge is got “by recognition of conceptual connections”. Hale adds that such knowledge involves the exercise of “conceptual competence”.9 As a platonist, he is interested in making sure that ‘there ought to be no conflict between the view that mathematical statements describe properties and relations among mind-independent abstract objects, and the view that their truth is a matter internal to language, that is, their truth is owed to conceptual liaisons’. Hale assumes that this tension can be resolved.10 Benacerraf, Paul. “Mathematical Truth”, Journal of Philosophy, No. 70, pp. 661–79, 1973.) Broadly speaking, abstract objects are non-spatio, non-temporal entities which supposedly exist independently of the human mind and language. The Benacerraf epistemological challenge against the platonist consists in the need of explaining how it is that we can obtain knowledge of abstract objects given that we cannot have causal contact with these objects. 7  Hale, p. 123. The word “parlous” is an archaic form of “perilous”, and it is the word that Hale uses. 8  Ibid. 9  P. 124. 10  Ibid.

80

4  Hale’s General Epistemological Views Regarding A Priori Knowledge

Hale is not explicit about how it is that basic a priori knowledge can be acquired by “recognition of conceptual liaisons” and involves “conceptual competence”. It seems to me that Hale’s proposal is to understand knowledge a priori of basic truths via the notion of analyticity, vaguely constructed as “truth in virtue of meaning alone”. However, Hale does not offer an account of the notion of analyticity, at least not in the chapter with which we are concerned. What about basic truths which are synthetic a priori? This question is not addressed either.  According to Hale, the view that some of our knowledge is a priori is quite plausible, for instance, our knowledge of logic and mathematics. And that view is independent of any prior ontological interpretation of logical and mathematical truths. That is why he neither provides an argument for the a prioricity of mathematical and logical knowledge nor for the existence of a priori knowledge in general. The view that some of our knowledge is a priori, and specifically that our logical and mathematical knowledge is typically of that character, is perhaps sufficiently plausible for positive supporting argument to be unnecessary, and none will be attempted here.11

Nonetheless, Hale recognizes that the appeal to the plausibility of our mathematical and logical knowledge as being a priori does not by itself constitute a decisive consideration against the causal theorist of knowledge. It is worth reminding ourselves that the conception of our knowledge of logic and mathematics ... as a priori has considerable initial plausibility, quite independently of any prior attachment to any platonistic interpretation of say, number theory. It is just because that is so, as Wright has argued, that the apparent incapacity of causal accounts of knowledge to accommodate any kind of knowledge a priori affords an independent reason to suspect their claim to embarrass the platonist. But it is, as he grants, well short, of being decisive.12

In short, even if one accepts that it is plausible that some of our knowledge is a priori, this alone is not enough to justify the platonist reading of these truths. The reason is this: if the a prioricity of mathematical and logical knowledge is independent of the ontological construction of their truths, then a defense of the former does not constitute a defense of platonism. However, that the a prioricity of mathematical and logical knowledge is independent of the ontological construction of their truths is very embarrassing for strong causal theories. Strong causal theories are in a difficult position if they cannot accommodate a large area of knowledge. And, if they cannot accommodate a large area of knowledge, they cease to be exhaustive epistemological theories, that is, theories which account for all our knowledge; and this is a good reason to reject them (at least as paradigmatic theories of knowledge). I shall not be concerned with Hale’s ontological commitments but will concentrate rather on his epistemology of a priori knowledge. It is possible to clarify the epistemology of a priori knowledge without doing ontology, or at least without depending heavily on a particular ontological position like platonism, let’s say. The epistemological points I want to make ought to stand on their own and not be subjected to the fate of any particular ontological theory. However, if it is not possible 11 12

 P. 125.  P. 124–5.

4  Hale’s General Epistemological Views Regarding A Priori Knowledge

81

to isolate completely epistemology and ontology, it seems that to try to do so constitutes a desideratum. Hale himself appears to do the same when he recognizes that the view that there is a priori knowledge is quite plausible independently of platonism. Of course, there is an initial attraction of platonists for a priori knowledge. Since a priori means of knowing do not require the satisfaction of a strong causal condition for knowledge, they make it possible how to explain our knowledge of mathematical objects, conceived as abstract objects. Since we won’t need the satisfaction of a strong causal condition, it is not necessary to have contact with abstract objects in order to acquire knowledge about them. Hale, as a platonist, is interested in responding to the epistemological challenge of how to explain our knowledge of abstract objects when we cannot have causal relations with them. Moreover, I recognize that there is a connection between the epistemological and the ontological issues. For part of what makes a statement a priori or knowable a priori is what the statement is about. Again, the idea is that what a statement is about has an important role in explaining  how a priori knowledge is possible. Since I won’t be discussing ontological issues in the book, I won’t be addressing this interesting issue here either. Furthermore, I will follow Hale in assuming the existence of a priori knowledge, as Kant did, so I won’t be giving an argument for the existence of a priori knowledge either. On the assumption that there is a priori knowledge – for the purpose of clarifying the notion – then the task at hand is to say what it consists in: what makes it a priori? In order to clarify the notion of a priori knowledge, one has to explain, and be explicit about, the “independence of experience” that characterizes a priori knowledge in contrast to empirical knowledge. We can accomplish that without recurring to ontological discussions or at least to keep them to a minimum.

Chapter 5

Kitcher’s Views on A Priori Knowledge

Abstract  Hale’s defense of the notion of a priori knowledge takes the form of a response to Philip Kitcher. He is the first philosopher who most carefully has scrutinized Philip Kitcher’s important challenges to a priori knowledge. For Hale, since what can be said about a priori knowledge could as well constitute a response to Kitcher’s views, it is relevant to discuss them. Kitcher is a (weak) causal theorist who constructs a notion of a priori knowledge on which mathematical knowledge is not a priori. Keywords  A priori warrant · A priori knowledge · Mathematical knowledge · Non-empirical process · Unrevisability Hale’s defense of the notion of a priori knowledge takes the form of a response to Philip Kitcher.1 For Hale, since what can be said about a priori knowledge could as well constitute a response to Kitcher’s views, it is relevant to discuss them.2 Hale affirms: But it is clear that defense [of the notion of a priori knowledge] is much needed, not only because scepticism about the applicability of the notion of a priori knowledge has not always, or even typically, been motivated by adherence to a specifically causal view of knowledge, but also because at least one writer [Kitcher] has developed a notion of knowledge a priori within a framework of a broadly causal epistemology whilst arguing that our mathematical knowledge cannot be of that ilk.3

Let me clarify that I will only be briefly discussing the views of Kitcher that Hale reacts to. So I won’t be discussing Kitcher’s views in any detail but only as much as  Kitcher’s book. The Nature of Mathematical Knowledge.  Analogously, I think that what can be said about a priori knowledge could as well constitute a response to Hale’s views; that is why I discuss his views in detail in this part of this book. Hale is my interlocutor. This is a very useful way to organize a historical and systematic discussion of the important issues concerning a priori knowledge. 3  Hale, p. 125. 1 2

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 I. Fred-Rivera, A Historical and Systematic Perspective on A Priori Knowledge and Justification, Philosophical Studies Series 151, https://doi.org/10.1007/978-3-031-06874-4_5

83

84

5  Kitcher’s Views on A Priori Knowledge

it is relevant for my subsequent discussion of Hale.4 I will be depending heavily on Hale’s presentation of Kitcher’s views for this reason. Kitcher is a (weak) causal theorist who constructs a notion of a priori knowledge on which mathematical knowledge is not a priori. Now let me briefly explain the tradition from where Kitcher is coming from. Traditionally, mathematical knowledge has been considered one of the paradigmatic instances – besides logical knowledge which is also considered a priori – of knowledge for its exactitude and the special certainty it confers. Mathematics had been considered “the queen of disciplines” since it is in its domains where our search for certainty was supposed to finally be stopped and be fully realized. As I understand it, mathematics enjoys such a privileged status because of its methods for acquiring mathematical knowledge.5 Mathematical methods had been considered to be a priori. Since mathematical knowledge is usually obtained by a priori routes, and it was considered a paradigm of knowledge, it followed that a priori methods were better routes for knowledge than empirical ones. Furthermore, it was assumed that a priori routes were not only better routes for knowledge than the empirical ones, but also that they always were secure (infallible) routes for knowledge. (Note that the last step of the argument is not forced upon us, that is, that a priori routes are infallible does not follow from any of the previous premises.) Kitcher’s position is very interesting because it is an example of such a conception of an a priori infallible route (though he does not distinguish between methods and warrants as ways of acquiring a priori knowledge) while denying that mathematical knowledge is a priori.6

 Kitcher, in his essay “A Priori Revisited” in New Essays on the A priori (Boghossian and Peacocke, Oxford University Press, 2000), presents some changes on his views about a priori knowledge from his book The Nature of Mathematical Knowledge. Hale does not react to those. I will be discussing them in Sect. 7.2.3. 5  I consider that, nonetheless, the best available explanation of the certainty of a priori mathematical knowledge is because of its methods. As we will explain in chapter ten, some a priori methods are infallible; and mathematical methods (most of them) are infallible. But things have to be sorted out very carefully, for instance, the sense of infallibility involved, in order to rescue the truth of this assertion. 6  Kitcher’s book constitutes an attack on the thesis that mathematical knowledge is a priori. The distinction between “methods” and “warrants” is very important. I will be explaining this distinction very carefully in the glossary I provide in chapter ten. But for now let me briefly say that a method is a cognitive routine which can be performed correctly or incorrectly on the occasion, and we get warranted belief (or not) as a result. A warrant is a particular implementation of a method. For example, “constructing proofs” is a method; the particular proof I construct is my warrant for its conclusion. As we will see in chapters nine and ten the notion of infallibility applies primarily to methods, and only derivately to warrants. 4

5.1  Kitcher’s Account of the Notion of A Priori Knowledge

85

5.1 Kitcher’s Account of the Notion of A Priori Knowledge For Kitcher, as well as for many other epistemologists, an adequate general account of knowledge has to put some constraint upon how a state of true belief must be produced if it is to amount to knowledge. Kitcher’s proposal is that a suitable constraint has to be concerned with the psychological processes which produce beliefs. Since his proposed constraint is on psychological processes, he calls his view “psychologistic”. An example of a belief-producing psychological process is the process of “following a proof”.7 Kitcher’s general analysis of the concept of knowledge is: (1) X knows that p if and only if X believes that p and X’s belief that p was produced by a process which is a warrant for it. (p. 17)

Kitcher specifies that (1) is just the starting point for a general characterization of the concept of knowledge.8 Kitcher introduces the term “warrant” to refer to those processes which produce belief “in the right way”. The notion of what it is for a process to warrant a belief is deliberately vague to leave open which of the various psychologistic accounts is preferable. The notion of “warrant” or “justification” makes possible a distinction between different ways we acquire knowledge, i.e., a priori or a posteriori. Kitcher’s analysis of the notion of a priori knowledge is: (2) X knows a priori that p if and only if X knows that p and X’s belief that p was produced by a process which is an a priori warrant for it. (3) α is an a priori warrant for X’s belief that p if and only if α is a process such that, given any life e, sufficient for X for p, (a) some process of the same type could produce in X a belief that p; (b) if a process of the same type were to produce in X a belief that p, then it would warrant X in believing that p; (c) if a process of the same type were to produce in X a belief that p, then p. (p. 24)

How do we get the a priori from this characterization? The a priori is attached to the warrant. Given that X has the necessary concepts to entertain p, an a priori warrant for X for p: could produce belief that p, warrant p, and, given that the warrant produced belief that p, then p is true. ‘If someone knows a priori that p then she could

 Kitcher, pp. 42–3.  But how can the right hand side of (1) be logically equivalent to its left hand side? In the left hand side of (1), truth is implied since knowledge entails truth. In the right hand side, there is no talk of truth. It appears then that in order for the right hand side to be logically equivalent to the left hand side, a warrant has to imply the truth of p. However, if a warrant implies the truth of p then it has to be an infallible warrant. And if so, then the concept of an infallible warrant won’t be distinctive of the concept of a priori knowledge, as Kitcher maintains. (We will discuss this shortly.) Kitcher is trying to provide here a general analysis of the concept of knowledge. I think this problem may be explained by the fact that (1) is allegedly only providing a starting point in this analysis. Unfortunately, Kitcher does not elaborate on (1) in his book. 7 8

86

5  Kitcher’s Views on A Priori Knowledge

know that p whatever sufficiently rich experience she had had (sufficiently rich experience to entertain the proposition to be known).’9 Again, given that a subject is equipped with the necessary concepts to entertain a belief to be known, p, a process of the type in question would, were it to produce the belief that p, produce a warranted and true belief. Any belief produced by an a priori warrant is knowledge. It is assumed that the knowers in question are humans and that their intellectual capacities remain fixed across all these possible lives.10 Kitcher’s general problem becomes: how can there be warrants that always produce knowledge? Kitcher tries to show that there can be no a priori mathematical knowledge. For Kitcher, a priori grounds for belief must be such that it could not be rational to regard them as insufficient to justify belief under any experiential context. Mathematical grounds allegedly do not satisfy that condition on a priori grounds.

5.2 On Kitcher’s Thesis That A Priori Knowledge Is Incompatible with Revision For Kitcher, a priori beliefs must be unrevisable because they are produced by a priori warrants. A priori warrants only produce and warrant true beliefs.11 Mathematical beliefs cannot be warranted by a priori warrants because some of the mathematical beliefs we take ourselves to be justified in believing are false and their justifications faulty. Kitcher claims that routes to mathematical knowledge can always be upset by unkind experience,12 they can lead us astray, so they cannot be a priori for that reason. Kitcher’s point is twofold: routes to mathematical knowledge are not infallible, so they are not a priori; and they can be upset by unkind experience making things even worse for the defender of mathematical routes as being a priori. Experiences which cast doubt on the accuracy of the book (by appearing to expose errors in many ‘theorems’, let us say), and in which eminent mathematicians denied the conclusion, would interfere with the ability of the process to warrant the belief. If I check through the proof in a book, thinking I see how the inferences go, and if the proof is very complex, then, under the circumstances in which there is weighty evidence against both book and theorem, it would be unreasonably arrogant and stubborn of me to form the belief.13

Kitcher understands the term “experience” as the knower’s total sensory experience; and “independent of experience” is understood counterfactually: knowledge that could have been obtained by a process of the same type that actually produced it, no matter what the course of the subject’s sensory experience is, provided it was  P. 24.  PP. 26–7. 11  P. 24. 12  Unkind evidence is evidence against a warrant or the belief it warrants. 13  P. 43; my emphasis. 9

10

5.3  The Issue of Long Proofs or Calculations

87

sufficient to allow him to acquire the relevant concepts required to grasp the proposition in question. Kitcher claims that the “processes which apriorists take to generate our mathematical beliefs would be unable to warrant those beliefs against the background of a suitably recalcitrant experience”.14 Kitcher explains: If apriorists are to escape this criticism on the grounds that the analysis of a priori is too strong, then they must allow that it is not necessary for an a priori warrant to belong to a type of process members of which could warrant the belief in question given any sufficient experience. To make this concession is to abandon the fundamental idea that a priori knowledge is knowledge which is independent of experience. The apriorist will be saying that one can know a priori that p in a particular way, even though, given appropriate experiences, one would not be able to know that p in the same way. But if alternative experiences could undermine one’s knowledge then there are features of one’s current experience which are relevant to the knowledge, namely, those features whose absence would change the current experience into subversive experience ... To reject condition (3b) ... would be to strip apriorism of its distinctive claim.15

Kitcher argues that if apriorists try to respond to his criticism alleging that his analysis of a prioricity is too strong, then they have to accept that it is not necessary for an a priori warrant to belong to a type of process which could warrant belief provided there are sufficient experiences for the acquisition of the conceptual repertoire needed for a priori knowledge. For Kitcher, if the apriorist makes this concession, he will be abandoning the crucial claim that a priori knowledge is independent of experience. A priori knowledge would be dependent on experience. The apriorist will find himself in the following awkward position: that one can know a priori that p in a particular way, even though, given unkind experiences, one would not be able to know that p in the same way. Now if there were alternative experiences that could undermine one’s a priori knowledge that p, then there are features of one’s actual experience which are relevant to the a priori knowledge, that is, those features whose absence would change the current experience into subversive experience. If the apriorist rejects condition (b) – that is, if a process of the same type were to produce in X a belief that p, then it would warrant X in believing that p – of Kitcher’s analysis, he would be stripping a priori knowledge of its distinctive character.

5.3 The Issue of Long Proofs or Calculations Kitcher discusses whether long proofs can be a priori in his sense. He argues that long proofs cannot generate a priori knowledge of their results.16 Kitcher relies at this point on Descartes’ view17 that long proofs are problematic sources of ­knowledge  PP. 88–9.  Ibid; my emphasis. 16  PP. 40–3. 17  Descartes, Rene. Rule VII, Philosophical Writings. Edited by E. S. Haldane and G. R. T. Ross. Cambridge University Press, vol. 1, p. 19, 1967. I won’t discuss whether Kitcher’s interpretation 14 15

88

5  Kitcher’s Views on A Priori Knowledge

since we cannot apprehend them all at once. According to Kitcher, Descartes’ proposal is to go over the proof several times until we are able to apprehend it as a whole, all at once, and do not have then to rely upon the memory of having justified its earlier steps. Obviously, there is going to be a limit, an upper bound, to what we can achieve by this method. Then, what happens with our knowledge of truths that exceed this upper bound? Kitcher’s response is that there can’t be any a priori knowledge obtained via long proofs and that there are no rules of inference that preserve a prioricity. That is, there are no rules of inference such that if we start with premises supposedly known a priori, we are assured of ending up with statements known a priori. For Kitcher, the situation is even worse: our a priori knowledge of the premises, our starting points in the proofs, would be lost. The reason is the following: since we cannot apprehend the proof all at once, there is a switch of grounds from an a priori warrant in the beginning for the knowledge of the premises to knowledge based upon the memory of having followed such a warrant. Knowledge based upon memory can provide a reliable warrant, but not an a priori warrant. Kitcher concludes that there could be no rules of inference that could preserve a prioricity since, if there were any, we could construct proofs of arbitrary length whose results, if their premises where known a priori, would be known a priori as well.

5.4 Knowledge Obtained by “Non-empirical Processes” Kitcher clearly allows that mathematical knowledge can be obtained by non-­ empirical processes. But he thinks that it is important to realize that though these processes are considered non-empirical they are not to be considered a priori warrants. These processes fail to come up to his standards for being a priori warrants. One of the non-empirical processes that Kitcher considers was proposed by Gödel.18 Gödel’s proposal was that mathematical knowledge can be generated by a sort of non-sensory apprehension  – Gödel calls it “mathematical intuition”  – directed on the platonistically conceived abstract subject matter of mathematics. Kitcher asks: Why might someone who believed that we had such a faculty be led to think that the knowledge which it generated was a priori? Because mathematical intuition is a non-empirical process. Anyone who confuses non-empirical processes which actually warrant belief with a priori warrants will read Gödel as upholding a priorism. Other examples of non-empirical processes which engender belief are following proofs or computations. Kitcher does not explain what he means by a “nonempirical process”. Nonetheless, he seems to be committed to the following theses:

of Descartes’s view is correct. 18  Gödel, Kurt. “What is Cantor’s Continuum Problem”. Reprinted in Benacerraf and Putnam (eds.). The Philosophy of Mathematics. Englewood Cliffs: Prentice Hall, pp. 470–485, 1984.

5.5  Some Remarks on Kitcher’s Views

89

A. Certain belief-producing processes (for example, following proofs) are non-­empirical processes. They may be significantly contrasted with empirical processes which engender belief mainly because they can somehow (to be explained) be available independently of experience. B. Some of these nonempirical belief-producing processes can generate knowledge (produce true warranted belief). C. Some mathematical knowledge is generated by such nonempirical processes.

For Kitcher, while the absence of certainty is compatible with knowledge, it rules out a priori knowledge. Kitcher rejects Kripke’s claim that a priori knowledge does not necessarily involve being certain.19 The notion of “certainty” in question is left unexplained. Kitcher argues that the process of following a proof may give us knowledge – nonempirical – of its conclusion, but not a priori knowledge, because we can conceive empirical circumstances in which it would be irrational to cling to the proof. In such a situation, our having followed the proof would not be enough for knowledge. How can I distinguish between empirical and nonempirical processes? In order for the process of “following a proof” to be an a priori warrant, it must always produce knowledge. 

5.5 Some Remarks on Kitcher’s Views Before proceeding to discuss Hale’s criticisms of Kitcher’s views, I will be identifying Kitcher’s most vulnerable points in this section. What does Kitcher mean by “belief” when he affirms that unkind experiences “would interfere with the ability of the process to warrant the belief”? Is it the psychological state of believing or the objective belief, the proposition believed? This is important when we try to figure out what unkind experiences are interfering with. On the one hand, there is the psychological reading of the term “belief”. According to this reading, Kitcher’s point is a simple one: if there is strong empirical evidence against a warrant for p then one should not believe p (the proposition). Suppose I think have followed a long and complicated proof that p. I find out later on that mathematicians think the purported proof is flawed. Given that I am not a mathematician, I should not believe p. Then since one should not believe the belief, one cannot know the belief (the proposition). It is a necessary condition for knowledge that we believe the belief. It is in this qualified sense, that a priori knowledge is not completely independent of experience, and in that Kitcher is right.

 Kitcher, p.  43. The reference to Kripke is: Kripke, Saul. Naming and Necessity. Cambridge, Mass: Harvard University Press, 1980, p. 39.  Kripke affirms: Something can be known, or at least rationally believed, a priori, without being quite certain. You’ve read a proof in the math book; and, though you think it’s correct, maybe you’ve made a mistake. You often do make mistakes of this kind. You’ve have made a computation, perhaps with an error. (ibid) 19

90

5  Kitcher’s Views on A Priori Knowledge

However this reading would be a weaker interpretation of Kitcher’s position. Since to believe the proposition involved is a necessary condition for knowledge of any sort, it does not involve the distinctive character of a priori knowledge. And Kitcher proposes an account of the latter, so he ought to take into consideration the distinctiveness of a priori knowledge. What I mean is that since any knowledge is dependent on experience in this way, if there is a priori knowledge, as Kitcher thinks there is, its characteristic “independence of experience” has to be accounted for in a way which respects such experience dependence. Moreover, if experience always has this disturbing role – I should specify that what experience can always primarily disturb is our psychological act of believing and indirectly the proposition believed – even when it is misleading experience,20 that ought to show to Kitcher that there cannot be independence of experience and, therefore, there can be no a priori knowledge. But Kitcher insists that there is a priori knowledge. Actually I think that Kitcher goes back and forth between the conception of revision as always possible even when it is the wrong thing to do, as in the case of revision, for example, being called for by misleading experience, and revision as the right thing to do on the occasion. But actual knowledge in general is only compatible with revision for the wrong reason and incompatible with revision for the right reason (more below). On the other hand, Kitcher seems to be talking about the proposition believed as well as the psychological act of believing. Thus, another explanation of “the belief” in the phrase “would interfere with the ability of the process to warrant the belief” is that it is the proposition believed, so that, according to Kitcher, a priori warrants must be “ultra reliable”, that is, they must always, in all counterfactual situations in which they are invoked, produce true beliefs (not only beliefs but always beliefs that are true). According to this interpretation, for Kitcher, it is not possible to separate the issue whether a belief has been acquired by an a priori warrant, and that belief’s being knowledge. A priori warrants are “ultra-reliable” because they always infallibly produce knowledge by their means. (Note that I use the terms “ultra-reliable” and “infallible” interchangeably for that reason.) Someone could ask: how “infallible” is involved in (3c)? Remember, “(3c) if a process of the same type were to produce in X a belief that p, then p.”21 Of course, the term “infallible” does not appear in (3c). It is involved in the sense that, for Kitcher, it is a necessary condition for processes to be a priori that they will always end producing true justified beliefs. That is, an a priori process is such that it produces justified belief and it is always the case that that justified belief is true. Isn’t such a process infallible given that a priori knowledge is true justified belief a  Kitcher is reacting to this passage of Kripke. Neither Kripke nor Kitcher. explain what they have in mind when they talk about the notion of certainty. Kitcher’s assertion that the absence of certainty is compatible with knowledge, but not with a priori knowledge is problematic. Knowledge is only compatible with probability of 1. Feelings of sureness is another matter. Kitcher particularly stresses the role of misleading experience on p. 84 of his book. 21  Kitcher, p. 24. 20

5.5  Some Remarks on Kitcher’s Views

91

priori? Note that condition (3c) is derivable from (3b). (3b) imposes a condition on warrants to be a priori, namely, that under no experiential background in which they are available, can we regard them as insufficient to justify belief that p. A priori warrants always warrant belief. A corresponding distinction can be drawn between the ability of the process to warrant belief, the proposition to be known, and the ability of the process to sustain my act of believing. The first is an epistemological matter; the second a matter of psychology. Kitcher’s thought is that not only experience but even misleading experience can affect my ability to believe the proposition (the belief), so a priori knowledge cannot be independent of experience. In this sense, even misleading experience is always capable of interfering with my a priori knowledge, given that to believe (the psychological state of believing) is a necessary condition for knowledge. The underlying assumption in Kitcher’s argument is that if a priori warrants were not ultra-reliable, then “experience” could undermine a priori knowledge, and that would show that the latter is not independent of experience and, therefore, by definition, not a priori at all. It is interesting to note that what Kitcher would have needed is that some a priori warrants must be ultra reliable in order to have a priori knowledge in the first place. It is also assumed that only experience could undermine alleged “a priori” warrants. Kitcher does not consider the epistemic possibility of a priori grounds being undermined by a priori reasons. He does not allow for that possibility because he thinks that a priori warrants cannot be undermined in any way. I think that since Kitcher constructs the term “experience” very broadly, even if he could accept that there could be a priori reasons that could undermine an a priori warrant or its result, he would still characterize this case as the experience of having a priori reasons to reject an a priori warrant or its result, what would show that they were not a priori after all. Kitcher explains that the aforementioned experiences, like those which put into question the accuracy of proofs by appearing to show errors in many of the theorems, “would interfere with the ability of the process to warrant belief”. I propose that a distinction should be drawn here. We want to distinguish between (a) a warrant that is good from (b) a warrant we believe to be good. A warrant, if it is a good one, has to warrant the belief. That is why it is a good warrant. (A warrant warrants belief that p if it gives us a pretty good reason to believe that p.) In the case when our warrant is the possession of a proof that p, that the proof that p warrants p is not a matter of degree; it is an absolute yes or no; it does or it does not warrant p, contrary to what the phrase “would interfere with the ability of the process to warrant belief” appears to convey (my emphasis). A separate matter is our believing that a warrant is a good one. To think that we have a proof, for example, is a matter which admits of degree. We can be more or less confident in believing that our warrant is sound. On the other hand, to think rightly that we have followed a proof that p is surely not a matter of degree. Kitcher is obviously right in the sense that we have to believe the proposition in order to be able to know it. Also, our belief that p would involve the accompanying belief that our warrant for it is a good one; otherwise we won’t count ourselves as being justified in believing the proposition in question, let alone knowing it.

92

5  Kitcher’s Views on A Priori Knowledge

It is wrong to think that we have to be very confident about this second-order belief – i.e. the belief that the warrant is good – in order to be justified in believing that p, and in order to know a priori that p, if one knows that p. (Note that the belief that a warrant is good is also accompanied by other collateral beliefs like that I have understood the reasoning in its entirety.) The matter is one of degree here since our necessary belief that the warrant is good, our having confidence in the warrant, admits degrees. Although we ought to attach to the warrant some appropriate degree of confidence (sureness) in order to be able to take ourselves as in possession of pretty good reasons which justify our believing a proposition. But, again, this is independent from the fact that does not admit of degrees: namely, that the warrant is good or not as a matter of fact. As already said, Kitcher is right in claiming that empirical considerations can undermine a priori knowledge in the sense that they can undermine our ability to believe that a warrant is sound and, consequently, our ability to believe the proposition which it (presumably) justifies. However, we still can believe, or even know, a proposition without being sure that our warrant for it is good. Kitcher ignores the fact that a warrant could be good, regardless of our thinking that it is; a warrant could be objectively an a priori warrant in his (strong) sense even if we don’t know it. I believe that the reason why Kitcher ignores this fact is because he simply cannot accept it. He understands the notion of a warrant – of any sort – “psychologistically”. In the case of an priori warrant, since the a priori warrant is a mental process, like following a proof, and not the proof itself, we have to believe that the warrant is a good one in order for the warrant always to produce belief, that is, to make us believe the belief that p. Now we have seen that we don’t have to be totally confident about the second-order belief that our warrant is sound in order for the warrant always to make us believe the belief that p. But, I think that Kitcher’s most vulnerable point is: How can there be belief-­ producing processes which remain available, warranting, and truth-guaranteeing under such a wide range of experiences a subject can have?

Chapter 6

Hale’s Reactions to Kitcher’s Views

Abstract  In this chapter I will be discussing only the views of Hale which constitute a direct response to Kitcher. In contrast with Kitcher, for Hale, a priori knowledge as well as a priori beliefs do not have to be absolutely unrevisable. It is perfectly reasonable that we can reject mathematical beliefs we thought were true or reasonably justified because subsequent evidence shows or appears to show that they are false or that our grounds for them are not as sound as we previously thought. Given that a priori knowledge is not conceived as requiring absolute unrevisability of a priori beliefs and a priori warrants, as Kitcher does, then a pressing issue becomes what scope of revision is consistent with a reasonable construction of a priori knowledge. Keywords  Fallible · Revision · Proof · Following a proof · Memory

6.1 Hale’s Claim That A Priori Knowledge Is Compatible with Revision In contrast with Kitcher, for Hale, a priori knowledge as well as a priori beliefs do not have to be absolutely unrevisable. It is perfectly reasonable that we can reject mathematical beliefs we thought were true or reasonably justified because subsequent evidence shows or appears to show that they are false or that our grounds for them are not as sound as we previously thought. Consequently, a priori warrants do not have to be infallible  – i.e. they do not have always to produce true justified beliefs or (a priori) knowledge – in order to be a priori. Hale explains: any defense of the claim that we can have knowledge a priori …. must accommodate the fact that we are liable to error in such matters, not merely in the fairly unexciting sense that an individual may, through inattention, make slips in computation or be taken in by a fallacious proof, but in the more momentous sense that the mathematical community as a whole may find itself obliged to revise confidently held mathematical beliefs, where the demonstration that revision is called for does not merely consist in the exposure of routine error which prior training equipped it, in principle, to avoid, but itself advances mathematical

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 I. Fred-Rivera, A Historical and Systematic Perspective on A Priori Knowledge and Justification, Philosophical Studies Series 151, https://doi.org/10.1007/978-3-031-06874-4_6

93

94

6  Hale’s Reactions to Kitcher’s Views knowledge. Traditionally, the conception of logic and mathematics as bodies of truths known a priori went hand in hand with the belief that here at least the ideal of certainty might be realized. This particular liaison can be, as has been, challenged. Kripke (1980, p. 39), in particular, plausibly claims that acquisition of knowledge by following a proof is consistent with absence of certainty that the proof contains no error.1

Hale is saying that any defense of the notion of a priori knowledge has to come to terms with the fact that we are fallible creatures. We may not only make mistakes due to lack of attention or enough concentration, but may make mistakes in a more significant way. That is, revision can be called for which does not merely consist of exposure of routine error but itself advances mathematical knowledge. For instance, mathematicians may have to revise beliefs they held to be true because new evidence appears that shows that they were wrong. Then, as Hale points out, the following question arises: If … knowledge a priori is not to be understood as requiring absolute unrevisability, a pressing question concerns just what scope of revision is consistent with a reasonable construal of what such knowledge amounts to. The central task here is … to get clear about what should, and what need not, be built into the notion of experience independence in terms of which, at least since Kant, knowledge a priori is customarily characterized.2

That is, given that a priori knowledge is not conceived as requiring absolute unrevisability 3 of a priori beliefs and a priori warrants, as Kitcher does, then a pressing issue becomes what scope of revision is consistent with a reasonable construction of a priori knowledge. As already said, Hale questions Kitcher’s assumption that warrants must always in all counterfactual situations produce knowledge in order to be a priori. Hale asks: ‘Why do we have to assume that a priori warrants always, in all counterfactual situations in which they are available, must produce true beliefs?’ 4 Hale explains that there is a confusion at this point. It is undeniable that, for X to know a priori that p, it must be true that p. Likewise, p must be true, if X is to know a posteriori that p. It is obvious that from the satisfaction of this necessary condition for knowledge of any sort – that what is known is true – it does not follow that in the case of a priori knowledge, the satisfaction of this condition – that p is true – must  Hale, p. 125; my emphasis. The reference Hale makes in this passage is to Kripke’s Naming and Necessity, p. 39. 2  Hale, p. 125. 3  Hale does not explain what he means by “absolute unrevisability” (or “absolute indefeasibility”). Hale uses the notions of “absolute unrevisability” and “absolute indefeasibility” interchangeably. As I understand it, absolute unrevisability (indefeasibility) is presumably a property of warrants and the beliefs which they warrant. A warrant and the belief that it warrants are absolutely unrevisable when they cannot be revised (or defeated) either by empirical reasons or by a priori reasons. That is, they cannot be revised at all. Hale thinks that the notion of a priori knowledge does not require for a priori warrants and a priori statements that they have to be absolutely unrevisable (or absolutely indefeasible). As we will discuss in chapter seven, Hale argues that the notion of a priori knowledge is compatible with revisions of a priori warrants and a priori statements, but only when such revisions are called for by a priori reasons. 4  Hale, p. 129. 1

6.1  Hale’s Claim That A Priori Knowledge Is Compatible with Revision

95

be guaranteed by the fact that X has a priori grounds to believe that p. Kitcher’s condition (c) demands that a priori warrants are infallible in order to ensure that a priori knowledge is truth-entailing. This condition is gratuitous because truth is already entailed simply by “X knows that p”. According to Hale, the above-mentioned conflation is precisely the mistake Kitcher makes regarding a priori warrants. But why assume that a priori warrants must produce true beliefs? On the face of it, there is simply a confusion at this point. Obviously, for X to know a priori that p, it must be true that p (just as it must be true that p, if X is to know a posteriori that p). It clearly does not follow that the satisfaction of this condition, in the case of a priori knowledge, must be ensured by the fact that X has a priori grounds to believe that p. It seems that, by conflating the truth-entailing character of knowledge (of any sort) with the conditions on the way in which a belief is held required for it to qualify as knowledge a priori, Kitcher gratuitously inflates the concept of knowledge that is independent of experience into that of infallible knowledge.5

Hale thinks that Kitcher conflates the truth-entailing character of knowledge (of any sort) with the distinctive character of a priori warrants. For Kitcher, a priori warrants are infallible, that is, by their means we always will end up having knowledge, i.e. true justified beliefs. But I do not regard this as Hale’s major objection to Kitcher. Hale goes out of his way to point out that Kitcher’s real reason for insisting on the infallibility of a priori warrants lies in his reasons for insisting on (3b), as Kitcher understands it. As Hale points out, in order for Kitcher’s argument to establish that reasonable uncertainty 6 is compatible with knowledge, but not with a priori knowledge, a proof followed has to be sound. Otherwise, one’s having followed a “proof” (a sequence of formulas) is not enough to give us knowledge, even though one may be deceived into believing it does. … none of the envisaged unkind variants upon my kind, actual experience can be ones in which I am confronted with decisive grounds for thinking the proof flawed or its conclusion false. That is, Kitcher must rely, as he seems to realize, upon the possibility of unkind variants of my actual experience in which I am presented with non-conclusive, indirect evidence which casts a doubt upon the proof or its conclusion, but which is, in fact, misleading. 7

It follows that the unkind experiences against the proof or its result do not conclusively show that the proof is flawed or that its result is false. Hale explains that Kitcher has to be thinking of experiences which misleadingly make us doubt a sound proof or its conclusion.

 Hale, p.129; my emphasis.  Kitcher talks about reasonable uncertainty being compatible with knowledge but not with knowledge a priori. In Chap. 5, note 20, p. 90, I explained why this assertion is problematic. 7  Hale, p.136. 5 6

96

6  Hale’s Reactions to Kitcher’s Views

6.2 The Issue of Long Proofs Again and the Role of Memory Hale comments that Kitcher is right in not being satisfied with Descartes’ remedy, but observes that Kitcher is uncritical about it, and even seems to accept it. The problem with Descartes’ solution, as Hale describes it, is that it suggests that grounds for belief that p can only function as such when they are present to the knower’s mind. The contention is that, for example, a proof that p can be one’s grounds for believing that p only when one is actually reviewing or focused on the proof that p. According to Kitcher, Descartes proposes to substitute for the actual following of the inferential steps one’s memory of having followed the inferential steps. Hale objects that this proposal cannot solve the problem of the inability to have a long proof all present to the mind. We will have the same difficulty all over again: there would be as many memories as inferential steps, so we will have the same difficulty of not having enough room for memories in our heads. 8 Nonetheless, Hale warns us that he does not deny the real importance of memory in our acquisition of a priori knowledge.

 Hale reacts to Kitcher as follows:

8

Clearly something has gone badly wrong here ... First, while Kitcher is rightly dissatisfied with (what he takes to be) Descartes’ remedy, he seems uncritically to accept, and indeed to endorse, the bizarre suggestion that grounds to believe that p can only function as such while they are ‘present to the mind’ – that a proof that p from certain other propositions X can only be a man’s grounds for belief that p while his attention is actually focused upon a deduction of p from those premisses, together with his grounds for accepting them. But it is just false that, when you enquire after his grounds for his belief that p, and I reply that he believes that p because it follows from X, which he also believes, I am claiming that he is, right now, contemplating a deduction of p from X, along with his grounds for accepting them. I should be quite unabashed to learn that, at the time of my report, our man was sound asleep, or engrossed in a game of chess. It is true that I may, more cautiously, report that he believes that p because he believes that it follows from X. But the point is thus hedging my report is not to make allowance for the near certainty that he is not currently reviewing any deduction of that conclusion from those premisses, but simply to avoid endorsing the claim that p does follow from X. And it is also true that my report may be mistaken because, he has, in the meantime, changed his grounds – but the possibility that is in question here is that he has, for example, come to think that the premisses X are insufficient grounds to believe that p , and now, if he still holds that belief at all, would appeal to other grounds; it is not that, no longer having any deduction of p from X in his current mental view, he has perforce shifted to believing that p on the strength of his memory of having once derived it. Further, if it really were needful to have all before the mind, it would in any case be no solution to substitute memories for attention to the inferential steps themselves and the grounds on which their premisses are accepted – for in that case, the kind of memories required would be acts of current recall, and we should have just as much difficulty finding room in our heads for enough of them as we allegedly do in accommodating the inferential sequence itself. If, on the other hand, remembering in the dispositional sense, which does not require on the spot reviewing of the contents of our memory, is enough, then the problem supposedly alleviated by invoking memory has been misdescribed in the first place.” (pp. 139–40)

6.2  The Issue of Long Proofs Again and the Role of Memory

97

None of this should be taken as denying the real importance of memory in the present context. If our man is asked why he believes that p, it will normally be by a straightforward exercise of memory that he comes up with his answer. And should it prove that he has now totally forgotten the grounds upon which he believes that p, and can come up with no others, we should conclude that his continued belief is merely a groundless habit – though it is worth noting that it is commonly no easy matter to establish that someone has indeed totally forgotten; if having been temporarily quite enable to recall his reasons for believing that p, he subsequently manages, without undue prompting, to come up with some, which he claims, with apparent sincerity, to have recovered rather than invented afresh, we should be unlikely to insist that, during the period within which he was unable to reproduce them his belief that p was groundless. And there is no question that our capacity to follow and understand any but the simplest proofs is dependent upon (short-term) memory – understanding a proof of any complexity is largely a matter of grasping how it hangs together, and we are not in a position to accomplish that unless we can remember the bits that fits into the structure we must discern, if we are to understand the proof. But none of these familiar facts has any tendency to support the peculiar claim that when a man believes that p on the grounds (as we should normally say) that it follows from certain propositions X, which he also has grounds to believe (though not ones he is currently reviewing), properly and strictly speaking, his grounds for belief are provided, not by the proof of p from X (which he could reproduce, if called upon to do so) but by his memory of having constructed or followed such a proof.9

Hale is thinking in this connection of the worry that requiring actual surveyability may be inappropriate since most of the time we only remember that we followed a proof. Rarely can we remember the proof in any detail. So, actual surveyability as a condition for a priori knowledge does not seem to be what is going on in mathematical practice. Hale does not deny the importance of memory in our acquisition of a priori knowledge. We have to understand the proof in order to know a priori its result, and that largely depends on our memory of its earlier steps; we have to understand how the proof hangs together. The point Hale is making is that our grounds for belief that p, in the case of inferential knowledge a priori that p, is the proof that p, and not our memory of having followed a proof for p. Hale specifies that one should be able to reproduce the proof, if called upon to do so, in order to be entitled to claim to know a priori that p. When such a recall (or reproduction) takes place it is not that a change of grounds – from memory of having followed the proof (an empirical warrant) to actually following the proof – has taken place but rather than all along my grounds for p were the proof for p. Hale correctly explains that length of proofs alone may not be particularly problematic but length combined with complicated structure. My claim … that sheer length raises no special problem, and that, while long proofs may, when very complicated in structure, be epistemologically problematic, it would be an error to suppose that their unsurveyability disqualifies them as routes to a priori knowledge, but leaves us able to acquire empirical knowledge by their means-applies equally, I think, to big calculations.10

 Hale, p.140; my emphasis.  Hale, p. 260.

9

10

98

6  Hale’s Reactions to Kitcher’s Views

If long proofs and calculations are problematic for acquiring knowledge a priori of their results, they will be equally problematic as sources of empirical knowledge. 11 For knowledge, what is required is the same in both cases (a priori and a posteriori): that (long) proofs or calculations are in fact sound, so their results are correct (true). This is against Kitcher who holds, according to Hale, that while long proofs and calculations cannot be sources of a priori knowledge of their results, they are fine to produce empirical knowledge. 12 Hale’s point is that if following a proof (long or otherwise), for example, produces knowledge, despite unkind experiential background, it must be a real proof. So why isn’t this knowledge a priori?

6.3 Some Remarks on Hale’s Attack on Kitcher Note that an important view that Hale shares with Kitcher is that the notion of “a priori warrant” is the basic notion to be characterized in the epistemology of a priori knowledge. 13 The intuition is that in order to distinguish between a priori

 The complicated scenarios arising from the relationship between informal proofs (sketches) and formal proofs, and its implications to our mathematical knowledge, are analyzed by Azzouni in his paper “The Compulsion to Believe: Logical Inference and Normativity”. I take it that Azzouni’s work developes Kitcher’s socio-historical conception of mathematical knowledge. 12  Kitcher, p. 43. 13  Hale, p. 138. Actually, Kitcher’s position regarding the thesis that the notion of “a priori warrant” is the basic notion to characterize is not straightforward in the following passage: 11

“A priori” is an epistemological predicate. What is primarily a priori is an item of knowledge. Of course, we can introduce a derivative use of “a priori” as a predicate of propositions: a priori propositions are those which we could know a priori. In many contemporary discussions, it is common to define the notion of an a priori proposition outright, by taking the class of a priori propositions to consist of the truths of logic and mathematics (for example). But when philosophers allege that truths of logic and mathematics are a priori, they do not intend merely to recapitulate the definition of a priori propositions. Their aim is to advance a thesis about the epistemological status of logic and mathematics. (Kitcher, ibid, p.21) What does Kitcher have in mind by saying that what is primarily a priori is an “item of knowledge”? Given that he goes on saying that there is a derivative use of a priori which applies to propositions, I take it that an “item of knowledge” refers to “warrant”. This is consistent with both the fact that for him a priori warrants always produce knowledge and that the notion of a priori warrant is the basic one. Then Kitcher goes on affirming that: My present aim is to distinguish a priori knowledge from a posteriori knowledge. We have discovered that the distinction requires us to consider the ways in which what is known is known. Hence I propose to reformulate the problem: let us say that X knows a priori that p just in case X has a true belief that p and that belief that p was produced by a process which is an a priori warrant for it. Now the crucial question is that of an a priori warrant, and our task becomes that of specifying the conditions which distinguish a priori warrants from other warrants.” (Kitcher, p.23; my emphasis)

6.3  Some Remarks on Hale’s Attack on Kitcher

99

knowledge and empirical knowledge we have to distinguish between the ways in which we obtain knowledge. For Hale, given that a priori knowledge does not require absolute unrevisability of a priori beliefs and a priori warrants, then a pressing issue for Hale becomes how much revision is consistent with a priori knowledge. Let me observe briefly that the claim that revision is consistent with a priori knowledge is incoherent as it stands. Contrary to Hale, Kitcher is right about the incompatibility of a priori knowledge with revision. However Kitcher arrives at this true conclusion by the wrong reasoning, and that is partly why I think Hale thought Kitcher was wrong about the incompatibility in question. According to Kitcher, a priori knowledge cannot be compatible with revision. By contrast, Kitcher thinks that empirical knowledge is so compatible. But this is a serious confusion, again, because knowledge of any sort is incompatible with revision. Revision is compatible with justification and belief (not with knowledge and truth). Only warrants and beliefs are revisable. I will be fully addressing this confusion in chapter ten and will try to resolve it since it is a pervasive problem which creates all sorts of misunderstandings. For now I will just say that the candidates for revision are beliefs, in particular, claims to knowledge (i.e. they are of the form: “I know that p”), and justifications (warrants). We change our minds about beliefs and the warrants which justify them. We can change our minds about what is in fact true. We may erroneously revise our beliefs and its warrants. In a weak sense, knowledge is compatible with revision since we can change our minds about what is in fact true and we are fully justified in believing. In another strong (normative) sense, knowledge is incompatible with revision because if we mistakenly revise, we cease to know since we cease to believe to be justified. Two cases are to be distinguished: (1) when revision is the right thing to do; and (2) when we mistakenly think that revision is the right thing to do. When we have knowledge then revision in the second sense is the only thing possible and then we end up not knowing or ceasing to know. But then Kitcher is wrong to think that the negation of (1) is only true in the case of a priori knowledge. In other words, when we have actual knowledge, then (rightly) revising is not possible in any case. As we will see, for Hale, the grounds for p should be the proof itself. But Kitcher is right that our grounds for believing a proposition p, or knowing p, in the case of inferential a priori knowledge (in Kitcher’s view: in the case of inferential “nonempirical” (“a priori”) knowledge) that p should be the process of following a proof. A proof becomes a warrant by its being appreciated. And we can only appreciate a proof by following it. What is wrong is to think like Kitcher that the experience independence of a priori knowledge cannot leave room for the experience dependence necessary for the truth that we have followed a proof that p. For Kitcher, since we can make mistakes in following proofs (or in constructing them), then

In the last quote it is clear that Kitcher considers the notion of an a priori warrant to be the crucial one to characterize.

100

6  Hale’s Reactions to Kitcher’s Views

“following a proof” cannot be an a priori ground for believing that p. However, if the process of “following a proof”, I should say, a sequence of formulas, is sufficient for knowledge, (remember that Kitcher considers the process of “following a proof” a non-empirical process which sometimes can engender knowledge) the sequence has to be a proof-token. Then, why “following a proof” cannot be an a priori ground for believing that p if when we know by their means it is implied that we did not make a mistake in following the proof?

6.4 Hale’s Remarks on Kant Confronted with the alleged compatibility between knowledge and revision, Hale proceeds to consider Kant’s view of a priori knowledge. Hale makes some interesting comments on Kant’s view that are worthy of mention, even briefly. Hale explains that Kant intended to characterize a priori knowledge as independent of experience in terms of justification or grounds, in contrast with knowledge based on causal relations. For Hale, though Kant characterizes necessity and strict universality as positive marks of the a priori, his explanation of a priori knowledge is completely negative. According to Hale, Kant does not provide a general positive account of what makes a ground for belief non-empirical. It is rather assumed what empirical grounds for belief are, and non-empirical grounds are simply grounds for belief that are not empirical. 14 Kant only affirms the general claim that they are to be characterized as those grounds which justify belief independently of experience. Hale explains that this point has been ignored, and it has been assumed that Kant distinguished between both sorts of grounds by a positive feature. Then, an easy step (not unavoidable though) is to conclude that this positive feature which makes a ground for belief a priori involves more exacting standards than those involved in the characterization of empirical grounds to be able to produce empirical knowledge. Hale observes that from the claim that a priori grounds have to comply with more exacting standards than empirical grounds, one may easily think that there is no a priori knowledge or much less than we previously thought.  Hale explains: It seems to me too that, while Kant, after giving that characterization (1963, B1–5), goes on to offer necessity and (strict) universality as positive marks of apriority, his official explanation is wholly negative. He offers, that is, no general positive account of what makes a ground for belief non-empirical – it is, rather, taken as understood what empirical grounds for belief are like, and non-empirical grounds are simply grounds for belief that are not of that sort. It is easy to overlook this point, and to suppose, in consequence, that non-empirical grounds must be distinguished from empirical ones by some positive feature. It is then a short, though not inevitable, step to the conclusion that to be a priori, knowledge must comply with more exacting standards than have to be met by ordinary empirical knowledge. And it can then readily seem that we have either no such knowledge at all, or vastly less of it than we thought. (p. 125–6) 14

6.5  Some Remarks on the Role of Memory in Our Acquisition of A Priori Knowledge

101

Then, for Hale, Kant did not succeed in giving an account of what makes a ground for knowledge “a priori”. I don’t want to commit myself to such a strong claim since it would involve a very careful reading of the first Critique. Perhaps Hale’s point is a weaker and correct one: we won’t find what we are looking for, namely, an explicit definition of the notion of a priori knowledge. Now from that modest point of view it does not follow that there is no possible (Kantian) account of a priori knowledge that we can reconstruct from his views. Actually what Hale is trying to do is to interpret the Kantian notion of “experience-independence”. 15 Let me speculate a bit more before finishing with this topic. Hale’s view is that Kant was not explicit about what makes a ground for knowledge “a priori” and, consequently, that he does not clarify in any detail the “independence of experience in terms of justification” that he claims to be distinctive of a priori knowledge in contrast with empirical knowledge. What can partly explain Hale’s view on Kant is that Kant appears to have concentrated primarily on the properties that a priori judgments have. Kant offers his criteria to differentiate judgments a priori from the rest. They are supposed to be strictly universal and necessary. Moreover, a related point: I think that Kant was not clearly explicit about what is a non-empirical ground simply because Kant did not appear to accept grounds for belief as being more basic than the “judgments” we could possibly know by their means. In any case, this is a much later development. However, I believe that there is an ambiguity in Kant’s use of the term “judgment” which leaves open the possibility that he was referring to grounds too, and not to truths, or not only to truths or judgments expressing them.

6.5 Some Remarks on the Role of Memory in Our Acquisition of A Priori Knowledge Hale does not want to deny that one hardly remembers a proof in any detail, specially so when the proof is long or complicated in structure. However, Hale would say that if one is not able to reproduce the proof, one’s continued belief that p, or knowledge that p, would be at best a posteriori: remembering that one followed a proof that p. Note that knowledge based on memory is to be considered a posteriori regardless of the nature of the memory in question. That is, there is no qualification whether it is a memory of knowledge a priori we had before – which is the only possible case which raises the question whether it ought arguably to be considered a priori – or whether it is a memory about either knowledge a posteriori of truths knowable a priori or knowledge a posteriori of a posteriori truths. However, Hale appeals in the above last quote only to what we normally say. I find it quite plausible to say that I know that p, when I am not currently reviewing my a priori knowledge that p – the proof – by my memory of having constructed or 15

 P. 138.

102

6  Hale’s Reactions to Kitcher’s Views

followed such a proof. I don’t understand why Hale is so worried about a switch of grounds  – from memory of having followed the proof (an empirical warrant) to actually following the proof – since such a switch does not interfere with the a priori knowledge that we can have of the same truths. A possible answer which sheds some light on the role of memory in this connection – and that I think is available to Hale – is to appeal to the following distinction: what is actually known a priori (by us) and what is knowable a priori (by us). When I follow a proof of a mathematical statement, following the proof is my ground for belief that p, and I know a priori that p. A statement is knowable a priori (for us) when there is an a priori warrant for it (a proof, for example) that we can possess, apprehend, and then know the statement a priori. When I only can remember that I followed a proof that p, I know a posteriori that p, since memory only can provide at best an a posteriori warrant. But it does not follow simply from that either that p is not knowable a priori (for us), or even worse, that p is a posteriori.

Chapter 7

“Pure” Hale and Related Issues

Abstract  In this chapter I will isolate the views that can be attributed to Hale independently of his reactions to Kitcher, what I call “pure Hale”. I will then be discussing in detail his view that empirical indefeasibility is a hallmark of the a priori. I will also examine new recent complications for the a priori related, to a greater or lesser extent, with this indefeasibility condition: Field’s “default propositions”, Wright’s “entitlements” or “warrants for free”, and Williamson’s challenge to the a priori in terms of experience allegedly playing a third role in a priori knowledge (justification) that is “neither purely enabling nor strictly evidential”. I conclude by analyzing Hale’s various assertions on a priori knowledge and identify one as a preferred candidate for a definition of a priori knowledge. Keywords  Empirical indefeasibility · Revision · Experience · Evidence · Preconditions for knowledge

7.1 Revision and Defeasibility of Items of A Priori Knowledge Hale explains that when someone’s ground for a belief he holds is defeasible, there is always the possibility that considerations may be presented which question the ability of the supposed grounds to be enough to warrant his belief.1 One then has to establish whether the evidence defeats the grounds in question.

 Hale talks about “justifications”, “grounds” and “warrants” for beliefs. I take it that these terms have the same reference for Hale. He certainly does not distinguish between them in the chapter. Actually he identifies “a priori grounds for belief” and “a priori warrants” in his chapter, p. 128. 1

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 I. Fred-Rivera, A Historical and Systematic Perspective on A Priori Knowledge and Justification, Philosophical Studies Series 151, https://doi.org/10.1007/978-3-031-06874-4_7

103

104

7  “Pure” Hale and Related Issues

Whenever a man’s justification for some belief he holds is defeasible, considerations may be adduced which cast doubt upon the capacity of his presumed grounds actually to warrant his belief. Such considerations constitute a prima facie defeat; further investigation may reveal that the doubt to which they give rise is well-founded, or that it is not.2

Hale proposes to distinguish between two senses in which our grounds for a belief may be defeasible or undermined by subsequent evidence. we may distinguish between two senses in which grounds for a belief may be said to be undermined by new evidence. In one sense, a man’s grounds for his belief that p are undermined by the citation of new evidence in the light of which, pending a more through investigation, it would be unreasonable for him to continue to repose in those grounds the degree of confidence with which he formerly entertained them. But his grounds may, quite differently, be undermined by adducing further considerations which actually show either that they are not in fact grounds for his belief that p at all, or that they are not as good as he supposed them to be, and are, perhaps, insufficient to warrant his belief. The experiences to which Kitcher appeals can indeed ‘interfere with the ability of the process [i.e. of following the proof] to warrant belief’, if that means that can undermine our grounds in the first, weaker sense. But they do not undermine our grounds in the second sense.3

That is, there are two senses in which a warrant for believing that p can be defeasible. A warrant is weakly defeasible if new evidence appears to show that the warrant is not in good standing. New evidence weakly undermines one’s warrant for believing that p when it calls for a careful examination and in the meantime suggest that it is unreasonable to have in the warrant the same degree of confidence which one formerly had of it. A warrant is strongly defeasible when it has been established that it is not good. A warrant can be undermined by adducing additional considerations which in fact show either that the presumed warrant does not ground one’s belief that p at all, or that it is not as good as one previously thought, and is, possibly, not sufficient to justify one’s belief. According to Hale, the experiences that Kitcher appeals to can undermine a priori warrants only in the first, weaker sense. If my sole ground for believing that p (p being some mathematical proposition) is that I have read what I take to be a proof that p in a math book, and then someone produces (a posteriori) evidence against the reliability of the book, I ought – so far – to give up my claim to know that p, at least until I have checked that the proof is fine. According to Hale, when I suspend my claim to know that p, I do just that, that is, I don’t back off into a claim to still know that p, but only a posteriori. (Of course, if I had not followed the approved proof at all, but merely heard that Hardy, for example, say, that it is knowable a priori that p, and I accept this on the basis of my belief that Hardy did not make mistakes, then my knowledge is at most a posteriori in the first place.) Nevertheless, the envisaged unkind experiences of my kind actual experiences do not necessarily undermine our grounds for belief in the second sense. For instance, if following a proof against kind background experience yields knowledge, the proof must be sound.

 Hale, p. 137.  Ibid.

2 3

7.1  Revision and Defeasibility of Items of A Priori Knowledge

105

If considerations of the envisaged unkind experiential background are relevant, we have to assume to be following the same proof. This shows that the unkind experiences Kitcher considers could not show that the proof is unsound. Hale explains: As we have seen, if following the proof against kindly background experience is to yield knowledge, the proof must be good, and if consideration of the envisaged unkind experiential background is to be relevant, we must suppose the same proof to be followed. Consequently, nothing in the unkind setting could show that the proof is flawed. Indeed, however ‘weighty’ we envisage the indirect evidence against the theorem or its proof as being, it has to be allowed that a sufficiently painstaking examination will reveal the doubt it raises to be unfounded. It is, then, perfectly possible for us to have grounds for belief that p, but to think that those grounds less than adequate, when in fact they are. In the presence of sufficiently weighty indirect reasons to doubt their adequacy, such doubt may be quite rational. In the kind of case with which we are concerned, where our grounds are provided by what purports to be a proof, any indirect reason to doubt its soundness will, of course, be a reason to doubt that it affords grounds for belief at all – a flawed proof is useless, and while it may be possible to repair the defect, or adapt it to establish a restricted version of the conclusion, we may ignore these possibilities here, since they make for no essential difference.4

To recapitulate: Considerations can be presented which reduce the confidence we have in a warrant or its result. These are perfectly compatible with our in fact knowing the proposition, and with the fact that the warrant is a good one. Knowledge is consistent with a certain degree of unsureness and it is only possible with a reasonable degree of sureness (confidence) that our warrant for believing that p is in good standing. This is the weak sense of defeasibility. The strong sense of defeasibility is when the considerations adduced show that we were in fact wrong, that the proof is not sound, or that the result is not true. According to Hale, a priori grounds are indefeasible by experience in this strong sense. Experience cannot show that an a priori warrant is unsound or that an a priori statement is false, though it can have an “incidental” role in our knowledge of these two things. Hale explains: Any satisfactory elucidation of the notion of experience-independence should respect the foregoing distinction [between the two senses in which grounds are defeasible]. Kitcher’s condition (3b) may be read as requiring that a priori grounds should not depend for their cogency upon specific features of the experiential setting in which they are invoked. So read, the condition is at least plausibly necessary for knowledge a priori. The crucial distinction is, however, obliterated, if it is read, rather, as requiring that there can be no experiential setting in which it would be rational to doubt them.5

Hale concludes that a satisfactory clarification of the notion of experience-­ independence ought to take into account these two senses of defeasibility of warrants (grounds). Also, he continues, an elucidation of the notion of a priori knowledge does not have to exclude the possibility that we can conceive an experiential background in which it would be rational to doubt the adequacy of a priori grounds to warrant belief. That it is always an epistemic possibility that a “proof” is unsound  Ibid.  Ibid.

4 5

106

7  “Pure” Hale and Related Issues

does not destroy its capacity (the capacity of the proof) to provide a priori grounds for accepting its conclusion.

7.1.1 Casullos’s Interpretation of Hale’s Views Casullo thinks that he is restating Hale’s views as follows: (H) If α is an a priori process and produces in X a belief that p, then there are no possible experiential settings in which α produces in X the belief that p and X’s grounds are undermined by genuine defeaters.6

(H) is talking about belief, not knowledge. It is important to realize that Casullo’s (H) is not Hale’s view. It is Kitcher who thinks that a priori grounds have to be indefeasible. Hale considers that a priori grounds are indefeasible by experience, not that they are indefeasible in general. What is an experiential setting in (H)? What are the a priori grounds for Casullo? The proof? Or the process of following a proof? He moves back and forth from talking about a proof to talking about the process of following a proof. Casullo affirms: The crux of Hale’s argument is that if S knows that p on the basis of following a proof from premises known a priori, then experientially justified genuine defeaters for S’s justification are not possible. (ibid, p. 74)

What is the problem here? If S knows a priori that p at t then there can’t be a genuine defeat. Casullo continues: Hale’s argument … conflates the requirements of knowledge with those of justification. The argument involves two claims: (1) if the process of following a proof yields knowledge of its conclusion, then the proof must be sound, and (2) all experientially justified undermining defeaters for beliefs justified by the process of following a sound proof must be apparent. But in order to show that a belief based on the process of following a proof satisfies (H), Hale must establish that (1*) If the process of following a proof yields justification of its conclusion, then the proof must be sound. (ibid; Casullo’s emphasis)

Note that (1) is trivially true. (2) should add “if knowledge that p is involved” or simply “given (1)”, even if it sounds repetitive. These claims should to be understood together, not separately. If a process of following a sound proof yields knowledge, then it yields justification. If (2) holds given (1), then (2) seems to be saying just that. On the other hand, Casullo analizes them, separately. In claim (1) Casullo talks about knowledge: “(1) if the process of following a proof yields knowledge of its conclusion, then the proof must be sound”; in claim (2) he switches to justification which is a weaker notion: “(2) all experientially justified undermining defeaters for beliefs justified by the process of following a sound proof must be  Casullo, A Priori Justification. Oxford: Oxford University Press (2003) p. 73, 2003.

6

7.1  Revision and Defeasibility of Items of A Priori Knowledge

107

apparent”. Then he concludes: “(1*) If the process of following a proof yields justification of its conclusion, then the proof must be sound.” (p. 74) This is confusing. Casullo talks about knowledge a priori in (1) and about justification a priori in (2). He thinks that Hale is forced to reject (1*) – which talks about justification, not knowledge – because he does not require that a priori warrants are indefeasible. Note that (H) talks about a priori justified belief, not about a priori knowledge. Of course, Hale won’t accept either (H) or (1*) because these are not his views. Hale says that “if the process of following a proof yields knowledge, then the proof must be sound”, and this is obviously true. Casullo explains: For if the process of following a flawed proof yields justification of its conclusion and S believes that p on the basis of following such proof, then there are genuine experiential defeaters for S’s justified belief that p. The testimony of eminent mathematicians that p is false or that the proof is flawed provide examples. (ibid, p. 74)

Hale won’t deny these obvious truths. For the eminent mathematicians, the evidence that the purported proof is not a proof is by a priori reasons, insisted Hale. Casullo continues: his contention that a priori justification is not … infallible is incompatible with the claim that beliefs based on the process of following a proof satisfy (H). (ibid, p. 74)

Again, neither (H) nor (1*) are Hale’s views, they are incorrect formulations of Casullo, so there is no incompatibility in Hale. Casullo confuses the proof, which, by definition, is sound with the process of following a proof. There is no flawed proof but rather no proof; the process of following a proof is always defeasible (by experience or by non experiential evidence). Hale’s view is that the a priori grounds, the purported proofs, are indefeasible by experience. It should be even stronger. Proofs themselves are indefeasible. If not, they won’t be proofs. When they are not proofs, the errors are demonstrated by a priori reasons. Actually, I think it is the other way around. It is Casullo, in misrepresenting Hale, who confuses knowledge with justification. Hale’s goal is to replace Kitcher’s condition (b) on a priori justification with a weaker condition that does not have the consequence that beliefs justified by the process of following a proof are not a priori because of the possibility of experiential defeating evidence. The condition Hale proposes accomplishes this goal, however, only if genuine experiential defeaters for beliefs justified by the process of following a proof are not possible. Genuine experiential defeaters for beliefs justified by the process of following a proof are not possible only if only sound proofs justify their conclusions a priori. The view that only sound proofs justify their conclusions a priori is incompatible with the view that a priori justification is weakly c-fallible. Since Hale is committed to the view that a priori justification is weakly c-fallible, he fails to provide a condition on a priori justification that avoids the consequence that beliefs justified by the process of following a proof are not justified a priori. The source of the problem is his failure to appreciate fully the implications of weak c- fallibility. (pp. 74–75) 7

 Casullo distinguishes between two senses of infallibility and calls them: Cartesian infallibility (or c-infallibility) and Peircian infallibility (p-infallibility). 7

108

7  “Pure” Hale and Related Issues

Casullo explains that if the process of following a flawed proof yields justification of its conclusion, and S believes that p on the basis of following such “proof”, then there are genuine experiential defeaters for S’s justified belief that p. The testimony of eminent mathematicians that p is false or that “proof” is flawed. Hale does not deny this. What Hale says is that, for the (eminent) mathematicians, the evidence that the purported proof is not a proof is a priori. In the last passage quoted, Casullo switchs of talk about a proof, to the process of following a proof; a flawed proof, and the process of following a flawed proof. We should keep all these cases clearly separated. Hale talks about infallibility in connection to Kitcker’s views not with his views. Hale talks about beliefs, justified beliefs; other times he talks about knowledge. I understand that Casullo conflates talk of justification and knowledge in Hale because Hale talks about both, and we have to be very careful when he talks about knowledge and when he talks about justification. Also, Casullo, like myself, does not defend the indefeasibility of a priori warrants by empirical evidence, so Casullo

S’s belief that p is strongly c-infallibly justified by source A if and only if S’s belief that p is justified by source A and it is not logically possible that S’s belief that p is justified by source A and p is false. S’s belief that p is weakly c-infallibly justified by source A if and only if S’s belief that p is justified by source A and it is not the case that p is false. There are other senses of c-infallibility. All entail some connection between justification and truth. (A Priori Justification, p. 57) S’s belief that p is strongly p-infallibly justified by source A if and only if S’s belief that p is justified by source A and indefeasible by any evidence. S’s belief that p is weakly p-infallibly justified by source A if and only if S’s belief that p is justified by source A and indefeasible by any experiential evidence. There are other senses of p-infallibility. All entail some connection between justification and defeasibility. (ibid) These notions are applied to belief by a source A, unspecified. Casullo has two corresponding notions of fallibility. S’s belief that p is strongly c-fallibly justified by source A if and only if S’s belief that p is justified by source A and p is false; S’s belief that p is weakly c-fallibly justified by source A if and only if S’s belief that p is justified by source A and it is possible that S’s belief that p is justified by source A and p is false. (p. 62) These notions are applied to belief justified by a source, not specified. Casullo analyzes the logical relations between these notions. He explains that he engaged in the articulation of the logical relations among the different notions of fallibility in order to avoid committing the mistakes he attributes to other philosophers, one of those, Hale. (p. 69) (He also criticizes Donna Summerfield’s account of a priori justification, but I won’t enter into that.) Casullo argues that Hale defends a notion of a priori justification that is incompatible with the claim that such justification is weakly c-fallible. (p. 72) But these distinctions are made by Casullo, not Hale. Hale does not talk about infallibility in his views. Only mentions infallibility when criticizing Kitcher. Hale does not define either the concept of fallibility. Casullo mentions “source” and does not specify what source he has in mind. In his examples, it is clear that what he means by “source” is “warrant”. Studying his examples, I see that Casullo does not distinguish between warrants and methods. He applies his notions of infallibility and fallibility to beliefs and warrants, not to methods as I do in the last part of the book.

7.2  Empirical Indefeasibility as a Hallmark of the A Priori

109

thinks he is unveiling Hale’s views to argue against his empirical indefeasibility condition for the a priori. More on this condition below.

7.2 Empirical Indefeasibility as a Hallmark of the A Priori Hale endorses a conception of the a priori as that which is not only justifiable independently of experience, but also that which can only be shown unsound or false independently of experience as well. That is, the candidates for a priori knowledge only admit of either a priori justification or revision by a priori reasons. Empirical indefeasibility is one of the hallmarks of the a priori.8 Hale does not claim merely that whenever an a priori statement appears to be conflicting with empirical evidence, or it is apparently falsified by empirical evidence, we always will find the corresponding revision by a priori reasoning – analogously as when we can know a posteriori, truths that can be known a priori – but rather that empirical disconfirmation is not possible for a priori statements and that empirical evidence can have only an incidental role in the defeat of a priori warrants. In an important note, Hale takes up the issues whether a priori warrants could be defeasible by empirical evidence and a priori statements could be in principle falsifiable by experience. Suppose some very large and difficult calculation has been performed, with a certain definite result. We may well have, independently of our calculation, weighty empirical evidence that the result ought to lie within certain limits. Unfortunately, it does not. We may thus, it seems, have empirical evidence that our calculation contains some mistake, even if, owing to its size and complexity, it is difficult to locate one, and our best efforts to do so have (so far, anyway) failed to disclose any errors. Does this possibility impugn the claims of calculation to be a potential source of a priori knowledge? A first, and obvious, point to note is that our result, obtained via the big calculation, will, in the kind of case envisaged, be based upon some assignment of particular values to certain empirical, e.g. physical, variables. The significance of this point is twofold. First, since our knowledge or belief in the correctness of those initial value assignments will be at best empirically grounded, there can be no question, in any case, of our having knowledge a priori of the result of the calculation (e.g. that a certain physical variable has this or that particular value).9

Let me explain. The example is: A long and complex calculation has been performed and its result disagrees with the one we expected according to independent weighty empirical evidence. Because of the complexity of the calculation, we have  Field argues in his essay “Apriority as an Evaluative Notion” (in Boghossian and Peacocke (2000)) that empirical indefeasibility is the most interesting characteristic of the notion of apriority – as he calls it (p. 117–119). Field thinks that “apriority” is an evaluative notion, beliefs justified a priori, for example, basic logical truths or rules, function as pre-conditions for the assessment of our belief systems, our evidential systems are not correct or incorrect, but good or bad for forming and revising beliefs. On the other hand, Hale is a Platonist who tries to defend a notion of a priori knowledge divorced from his metaphysical views. More on Field in the next section. 9  Hale, pp. 260–1. 8

7  “Pure” Hale and Related Issues

110

not been able to locate specifically the mistake in the calculation. The issue Hale wants to illustrate with this example is whether it provides us with empirical reasons to think that this particular calculation is faulty. We possess empirical evidence against its result, and, therefore, empirical (indirect) evidence against the warrant itself. More generally, Hale wants to know whether this example provides empirical evidence against the claim that calculation is a potential source of a priori knowledge. The result of the calculation – “that a certain physical variable has this or that particular value” – is not known a priori. The reason is that our knowledge of those initial value assignments is at best grounded empirically. Second, the discrepancy between our result and our empirically grounded belief about the range within which it must lie does not point selectively to a mistake in the calculation – we might, so far, pin the blame on our assignment of initial values.10

Because we don’t know where the mistake is in the calculation, we can say that it could be that the original assignment of the physical variables were mistaken, for example, that the measurements were done incorrectly. To get a more threatening looking case, we may suppose that we have, additionally, very strong empirical grounds to believe that our initial values for the physical variables are correct.11

Let us now suppose that the initial assignments of the physical variables are correct. It follows that the mistake is in the calculation itself. Now whilst there can be no question of our having a priori knowledge of the result as such, it does seem that our calculation should support a claim to such knowledge of a certain conditional statement, to the effect that if our initial value assignments, together with the relevant component general statements of the covering physical theory, are correct, then the value of some further physical variable(s) is such and such.12

Hale insists that the result of the calculation is obviously not known a priori given that the original value assignments of the physical variables are correct and at best grounded empirically. On the other hand, the calculation should support a priori knowledge of the following conditional: “If our initial value assignments, together with the relevant component general statements of the covering physical theory, are correct, then the value of some further physical variable(s) is such and such.”13 And the claim may now be that we have, in the situation envisaged, good empirical evidence against a statement which we supposedly know a priori.14

The statement that we supposedly know a priori is the above-mentioned conditional. Now if we look at the conditional, its antecedent is known to be true a posteriori (for, by hypothesis, the original value assignments were determined empirically

 P. 261.  Ibid. 12  Ibid. 13  Ibid. 14  Ibid. 10 11

7.2  Empirical Indefeasibility as a Hallmark of the A Priori

111

together with the covering physical theory), and the consequent is, in the case envisaged, the result of the calculation. If the result of the calculation is considered false by empirical considerations, then the conditional would be considered likewise false too. That is why Hale affirms that this example, after having made the appropriate clarifications, would appear to constitute empirical evidence against a statement supposedly known a priori. Hale observes: But now... it is important to ask ourselves just how essential it is to the case just sketched that our grounds for belief that our big calculation contains some undetected mistake are empirical. Suppose instead that we have carried through some very large and complex purely mathematical calculation, of the correctness of which it is, for obvious reasons, difficult to be fully confident. Suppose further that there is a standard method of obtaining approximate results for the kind of problem in question, and that this method is much simpler than the method employed in our big calculation to get a precise result. Applying this approximation technique, we find that the result of our big calculation is seriously out of line. Since we are prepared to repose greater confidence in the simpler and more straightforward technique, we have now good a priori grounds to believe that the big calculation contains some disclosed error. Does this situation differ materially from that envisaged previously? I submit that it does not, and that the possibility that we should be led by empirical considerations to think that a calculation contains a mistake raises no relevant issue that it is not already raised by the possibility of our having a priori grounds to think that the result of the calculation must have been done incorrectly. The essential points are these. First, if, in either case, the big calculation does indeed contain a mistake, it is no contingent fact that that is so, regardless of whether the considerations which lead us to think so are empirical or a priori.15

Again, Hale’s point is: there can be empirical grounds for suspecting that a mathematical statement is false (or that the warrant we use to “prove” it is unsound). Hale wants to claim that empirical grounds point to an error detectable a priori. In the case of an empirical generalization like All swans are white

empirical evidence against it constitutes a direct disconfirmation of the empirical generalization. For example: There is a swan which is not white. (A counterexample of a generalization implies (logically) the negation of the generalization. If A implies not B, then the truth of A disconfirms B.) Hale’s point is that empirical evidence is sufficient to falsify empirical statements. Empirical evidence is not sufficient to falsify a priori statements. We need the a priori evidence that our original a priori statement is false. For Hale, since empirical evidence against an a priori statement is incidental, empirical evidence cannot falsify an a priori statement. According to Hale, that empirical evidence cannot falsify an a priori statement is obviously true but not because the statement in question is in fact true since in that case the a priori evidence against it would be incorrect, but rather than given that it is in fact false, still empirical evidence could not falsify an a priori false statement.

15

 Ibid.

112

7  “Pure” Hale and Related Issues

7.2.1 Some Remarks About Hale’s Views on the Defeasibility of Items of A Priori Knowledge For Hale, the case where we have strong empirical evidence against the result of a calculation as well as a priori evidence against the same result is analogous, for example, to the more simple case when we have the experience of receiving a Russellian letter as well as finding the contradiction ourselves. The experience of receiving the letter is incidental. The problem is with what the letter contains, that is, the contradiction. Hale is claiming what can be called “the autonomy of the a priori”: that is, if there is a mistake involved in a route to a priori knowledge and if we are able to locate it, then we could do so by a priori considerations alone. But the view that our possessing a posteriori considerations for thinking that there is a mistake in the calculation, for example, is incidental is correct only if we always have at hand both kinds of considerations (a priori and a posteriori). I find this implausible. There is no guarantee that we are going to be always in that epistemological privileged position. Of course, when we have a priori evidence, the a posteriori evidence may be incidental or not necessary; on the other hand, when we yet don’t have a priori evidence then the a posteriori evidence is very important, though it may not be necessary in the qualified sense that if we possess a priori evidence at some point later on then we won’t need the a posteriori evidence. Returning to the simple case of the experience of receiving a Russellian letter, I don’t see the analogy between this experience and the experience of having strong empirical evidence against the result of a calculation. One thing is the experience of receiving the letter and this experience only containing what really posits the difficulty: the contradiction. The letter is not the ground for questioning the calculation or its result. The letter only contains (provides) the ground, the contradiction, which is what really poses the difficulty and constitutes the ground (a priori) for questioning the calculation or its result. In this case, the incidentality of the experience of receiving the letter is quite uncontroversial. We could just as well know of the contradiction by reading it in a book or by finding the contradiction ourselves, if we are in a position to accomplish that. But the interesting case is when empirical considerations can defeat directly – raise relevant issues concerning the defeasibility of – a priori grounds or its results. That is, it is quite another matter when there is empirical evidence against a calculation or its result – as Hale’s example seems to suggest  – that itself constitutes a ground, and may not merely contain (provide) a ground – as in the example of the experience of receiving a Russellian letter. Hale says in the last quote: the possibility that we should be led by empirical considerations to think that a calculation contains a mistake raises no relevant issue that is not already raised by the possibility of our having a priori grounds to think that the result of the calculation must have been done incorrectly. (p. 261)

Hale’s point is that if we are able to gather a priori evidence against a calculation, empirical evidence would be incidental: that is, it would not point to any

7.2  Empirical Indefeasibility as a Hallmark of the A Priori

113

distinctive problem with the calculation besides the one a priori considerations alone point out. The following quote may convey the thought that given that a mistake in a calculation is a matter of necessity, if one is to know that there is a mistake in the calculation, then one is to know it a priori. ... if, in either case, the big calculation does indeed contain a mistake, it is no contingent fact that that is so, regardless of whether the considerations which lead us to think so are empirical or a priori.16

At first sight, this implication can appear problematic because the notions of necessity and a prioricity are not coextensive,17 or at least not necessarily so in all cases. We are talking of mathematics in this context. Hale, of course, is aware of the latter. He is not claiming that the notions of a prioricity and necessity are coextensive. What I think he is implying is that provided that the notions are not coextensive, it does not follow that the possibility that some necessities can only be known a priori cannot arise – as, allegedly, some necessities can only be known a posteriori (like the identity statement “Hesperus is Phosphorus”). Then, another reading of that remark is possible: Hale is insisting here again on the same point that the a priori evidence is necessary. Hale seems to admit that there could be both a priori and a posteriori undermining, but that the a priori undermining has priority (he says it is “paradigmatic” (“essential”)). I take it that, for Hale, this situation would be entirely analogous to the case of having both an a posteriori justification and an a priori justification for the same (a priori) statement. But that may be too much to admit. And, if Hale does admit this, then why should only the a priori undermining “count” as it were? The following question arises: How can the incidentality of empirical evidence against an a priori statement, something Hale accepts, guarantee that such empirical evidence cannot falsify the a priori statement in question? I think that Hale would appeal at this point to his distinction between weak defeasibility and strong defeasibility. Empirical evidence can only weakly undermine items of a priori knowledge. That is, new empirical evidence can undermine one’s a priori grounds for belief that p when it calls for a careful examination and in the meantime suggest that it is unreasonable to have in those grounds the same degree of confidence which we formerly had in them. But the point clearly remains: if we accept a priori and a posteriori undermining, why is one superior over the other? This is worrisome since the empirical evidence is pointing to a problem, perhaps that the statement in question is false, so it should be taken seriously.18

 Ibid; my emphasis.  Kripke’s Naming and Necessity. Hale endorses this distinction. 18  For a detailed discussion of the relationship between a priori evidence and a posteriori evidence for the same a priori knowable truths, see Casullo’s A Priori Justification, pp. 45–46, where he distinguishes what he calls “undermining evidence” and “overdetermination of evidence”. 16 17

114

7  “Pure” Hale and Related Issues

If Hale says that empirical considerations do not raise any further relevant issue that a priori considerations do raise, how can he say that a priori statements are indefeasible by experience? His two claims that a priori statements are not falsifiable by experience and that empirical considerations can raise the same relevant considerations – but no more – than a priori considerations in the defeat of warrant or a falsification of its result which we supposedly knew a priori, seem to be incompatible. The second seems to imply that a priori statements can be falsified by experience. For Hale, empirical evidence is not necessary. I already have explained why this assertion is problematic. Nonetheless, empirical evidence does not seem to be sufficient to obtain knowledge of truths knowable a priori. Note that this assertion does not contradict the possibility of a posteriori knowledge of such truths since a posteriori knowledge of truths knowable a priori appears to be only possible given that there is a priori knowledge of these truths which a posteriori knowledge must be based upon. This is surely true in the case of knowledge a posteriori based on testimony of a priori evidence. Such a posteriori knowledge is only possible if there is something to testify about, in the case in question, if there is a priori knowledge to refer to. In a qualified sense then knowledge based on testimony is sufficient for knowledge but only because it depends upon the knowledge a priori obtained already. Testimonial (empirical) evidence of a priori evidence is contrasted with empirical evidence in general. Empirical evidence in good standing is sufficient for knowledge of an empirical statement. Hale’s discussion points to another very interesting question: what is the relationship between an a priori justification and an a posteriori justification for the same proposition or truth? Is one stronger than the other? In the case of testimony we have seen that the a priori evidence is stronger, not because necessarily it is more certain than the other, but rather because it is a necessary condition for the possibility of such a posteriori knowledge. Note that the converse is not the case. It seems that a consequence of Hale’s view is that the only way we can have knowledge a posteriori of truths that are knowable a priori is by testimony of a priori evidence. That is, it seems that testimony is the only a posteriori way to know truths knowable a priori. Let me conclude this section by observing that the fact that a truth can be known in both ways, a posteriori and a priori, does not make such truth a posteriori. It is interesting to note that we do not call truths that can be known in both ways “mixed truths” but rather continue to considering them “a priori”. A possible explanation for the latter is: A priori warrants are more secure than a posteriori warrants, so that we ought always to prefer the a priori warrant for a truth over an a posteriori warrant for the same truth; and for this reason, the truth is “a priori”. I don’t think this explanation is needed. The justification needed, in my view, for considering “mixed truths”, nonetheless, “a priori truths” does not have to depend upon the claim that a priori warrants are more secure than a posteriori warrants. (They may well be; that is a separate issue.) Rather it depends upon two alternative claims: (1) that the notion of (a priori) warrant is more basic than the notions of (a priori) belief and truth; and, more importantly, that (2) a priori warrants only warrant a priori statements (and truths, at best).

7.2  Empirical Indefeasibility as a Hallmark of the A Priori

115

Note that (1) and (2) are compatible with the following interpretation of the phrase “more secure” in the statement “A priori warrants are more secure than empirical ones for the same beliefs (or truths)”. It is possible to understand the phrase “more secured” here as expressing merely the fact that those a posteriori warrants like testimony, for example, have to depend for their reliability upon the reliability of the a priori warrants which they refer to. For example, I can be told about a mathematician’s proof and know its theorem only if there is such a proof. This is a very interesting topic indeed and it has to do with what can sensibly be said about the relationship between a priori warrants and a posteriori warrants for the same beliefs, in particular, with the issue of the strength of such warrants which I think ought to be considered as the main criterion for determining their relationships.

7.2.2 Field’s Default Propositions In this section, I want to discuss some important recent developments related to the condition of the indefeasibility by empirical evidence for the a priori that Hale proposes on his account. Field defends19 two senses for a priori propositions: “a weakly a priori proposition as one that can be reasonably believed without empirical evidence; an empirically indefeasible proposition as one that admits no empirical evidence against it; and an a priori proposition as one that is both weakly a priori and empirically indefeasible.” Field offers20 a corresponding characterization for methodologies or rules for forming and revising beliefs: “a methodology or rule [is] weakly a priori iff it can be reasonably employed without empirical evidence; empirically indefeasible if no empirical evidence could undermine the reasonableness of its employment; and a priori if it meets both conditions. Again, I think that the most interesting component of apriority is empirical indefeasibility.” Here Field talks about propositions and methodology or rule as being a priori. He does not call this methodology or rule a priori warrants. Field does not require that an a priori proposition or rule can be reasonably believed only by someone who has a nonempirical justification. He considers the possibility of propositions and rules that can be reasonably believed without any justification. He calls such propositions and rules “default reasonable.” (ibid, p. 119). Hale and Field coincide in requiring empirical indefeasibility for the a priori. The difference is how they justify a priori statements: Hale, in terms of a priori warrants, Field in terms of a priori propositions and rules being preconditions for performing certain cognitive tasks, at least, he wants to leave room for those. Field does not

19 20

 Field, 2001, p 117.  Ibid, p. 119.

116

7  “Pure” Hale and Related Issues

characterize positively the a priori in general. Hale does not talk either about preconditions nor about default propositions as being a priori. It seems to follow that all default reasonable propositions and rules are, trivially, weakly a priori, and a priori if and only if they are empirically indefeasible. For Field, “there is no obvious reason why propositions such as ‘People usually tell the truth’ shouldn’t count as default reasonable, and it would be odd to count such propositions as a priori.”21 The empirical indefeasibility condition is necessary to block this undesirable result since “People usually tell the truth” is defeasible by empirical evidence. “People usually tell the truth” is a sort of generalization. It can be accepted by default because we have gathered enough evidence for a long time that this is how people, usually, act. Our confidence grows with time. If we have no reason to suspect that people – someone – are lying to us, we take for granted that they are telling us the truth. We don’t have to call up justification or evidence, every time we decide to trust someone. This is an empirical issue. The statement is empirically defeasible. It is a default empirical proposition. We can decide to trust people that we recently met, given them the benefit of the doubt, and maintain or retire that initial trust according to their behavior. This attitude towards others depends on character: how trusting or not one is. When things go wrong, when we are cheated or disappointed by trusting, it is rational to abandon that trust. I trust my vision because I have very good eyesight and am very perceptive. I trust my memory because I can learn things by heart. So I trust my eyes and my memory. One trusts or takes for granted the presuppositions in question because they have worked in the past. Field’s example “People usually tell the truth” is not a priori, it is trivially weakly a priori, for him, I will say, until we ask if it satisfies the empirical indefeasibility condition and realized that, since it doesn’t, it is a default a posteriori empirical proposition. He adds empirical indefeasibility to distinguish between default a priori propositions and default empirical propositions like “People usually tell the truth”. Field is not that clear, not fully explicit because he seems to put in the same boat our default belief in Modus Ponens and our default trust in people. But these are very different cases, we should not be deceived by their similarities since their differences are more important. Why is this sentence accepted without evidence or justification? The statement “People usually tell the truth” can be proved empirically. That, on the occasion, I decide not to, but simply accept it as true, taking it for granted, does not imply that, if I’m in a more demanding mood, I can prove it. Another thing is Modus Ponens, can I prove it? Field is very aware of the difficult (impossibility it seems) of proving Modus Ponens. One thing is not to be able to go further in our search of justification, like for Modus Ponens, and another to decide not to go further in our investigation, the information we have is enough, to reasonably belief the proposition “People usually tell the truth”. We have a choice in the second but not in the first case.

21

 Ibid, p. 120.

7.2  Empirical Indefeasibility as a Hallmark of the A Priori

117

Casullo (2003) argues against the empirical indefeasibility condition on a priori justification – something I do too – on the grounds that it rules out the possibility of propositions that are justified both a priori and empirically. I don’t think this condition rules out both justifications, but it, certainly, complicate the explanations to be given. It is not true that empirical indefeasibility per se does not allow a posteriori knowledge of truths that can be known a priori. Field, like Hale, accepts that some a priori propositions can be known (justified) in both ways, a priori and a posteriori. For Field, “complex and unobvious logical truths can admit empirical justification without diminishing their claims to a priori status.”22 When we are taking about empirical evidence against an empirical justification for an a priori proposition, there is no problem. Another thing is to have empirical evidence against an a priori warrant; and quite another thing is to admit empirical defeat against an a priori proposition. Does Casullo accept empirical defeat of a priori warrants as well as empirical defeat of a priori propositions? Field distinguishes between empirical justification and empirical evidence: The best way to deal with this argument is to distinguish between empirical justification and empirical evidence: evidence involves something like ideal justification, ideal in that limitations of computational capacity are ignored … If an observation doesn’t raise the ideal credibility of the claim, it shouldn’t count as evidence for it. Similarly, an observation must lower the ideal credibility of a claim to count as evidence against it … while the non-ideal credibility of, say, a complex logical truth can certainly be lowered by empirical evidence that well-respected mathematicians didn’t accept it, ideal credibility can’t be lowered in this way; for that reason, the evidence about the opinions of logicians really isn’t evidence against the logical truth.23

For Field, a priori truths can admit empirical justification, but not empirical evidence. Field allows that there are propositions or rules that one can justifiably or reasonably believed in the absence of any evidence or justification. The reason seems to be that they are so basic, that nothing else can serve as evidence or justification for them, without circularity. I consider that once they are accepted by default, we can appeal later on to a successful practice that legitimates its use. If they are axioms, for example, or basic a priori rules of inference, we can be successful in our ability to get valid results from them. Note that this is invoking empirical evidence and it is the picture that Kitcher defends: Field doesn’t make what seems to me a rather obvious point, namely that confidence in the progressiveness of inquiry ought to incline us to think that our evidential system is a good one. As we reflect on the history of science, it does appear that we’ve learned a lot about the world and we’ve learned a lot about how to learn about the world, and, while admitting our fallibility on all counts, we ought to endorse the view that we have a good evidential system. Field does, however, offer a related, forward-looking, point, noting that the possibility of a future system that would be superior to ours doesn’t undermine the claim that our system is a good one. An important part of his case here is that evidential systems aren’t correct or

 Ibid, p. 118.  Ibid, p. 118. Hale makes a similar point: if my evidence for not accepting a logical truth is that eminent mathematicians reject it, then my evidence is empirical. Another thing is that logicians have a priori reasons to reject a purported logical truth. 22 23

118

7  “Pure” Hale and Related Issues incorrect, so that we can’t insist that the apriority of logic turns on whether our belief in classical logic is licensed by the right evidential system.24

As Casullo rightly argues, Field’s notion is not clear enough to explain the relationship between evidence, justification, credibility, revision and knowledge: Field’s proposal faces a number of questions. First, it entails that there is no evidence, empirical or nonempirical, for or against any logical truth. Hence, the concept of evidence can play no role in distinguishing between epistemically acceptable and epistemically unacceptable acquisition or revision of beliefs regarding logical truths. In effect, it tells us little about the actual, as opposed to the ideal, epistemology of logic. Second, since a person who believes a complex and unobvious logical truth, in the face of empirical observations that well-respected logicians do not accept it, is not justified in believing it and does not know it, the relationship between the concepts of evidence, ideal justification, and ideal credibility – as opposed to the concepts of justification and nonideal credibility – and the concept of knowledge remains unclear.25

For Casullo: Whatever one thinks of the plausibility or implausibility of classifying propositions such as “I am not now dreaming” or “People generally tell the truth” as a priori, the traditional conception of a priori knowledge does not have this consequence. The traditional conception is positive: it requires that a priori justified beliefs have a particular type of justification rather than that they lack a particular type of justification. The traditional conception maintains: (APJ) S’s belief that p is a priori justified (reasonable) if and only if the justification (reasonableness) of S’s belief that p derives from some nonexperiential source.” (ibid, p. 324)

Casullo is right that the a priori requires a particular kind of justification, rather than no justification, and that the a priori has to be positively characterized. Field has not given such a characterization. The question is whether Casullo succeeded in his characterization of the a priori. Casullo’s formulations of a priori knowledge and a priori justification are: I (Casullo 2003) defend the following … articulation of the traditional concept: (APK) S knows a priori that p if and only if S’s belief that p is justified a priori and the other conditions on knowledge are satisfied; and. (APJ) S’s belief that p is justified a priori if and only if S’s justification for the belief that p does not depend on experience.26

I don’t think that Casullo succeeded. His characterization is similar to Hale’s, so, it suffers from a similar difficulty: it is not positive enough.27

 Kitcher, “A Priori Knowledge Revisited” in New Essays on the A Priori. Paul Boghossian and Cristopher Peacocke (eds.) Oxford: Clarendon Press, p. 86, 2000. 25  Casullo, “Articulating the A Priori-A Posteriori Distinction” in Essays on A Priori Knowledge and Justification. Oxford: Oxford University Press, p. 320, 2012. 26  Casullo, A Priori Justification. Oxford: Oxford University Press, 2003. 27  I will discuss this issue in Chap. 8, Sect. 8.1. 24

7.2  Empirical Indefeasibility as a Hallmark of the A Priori

119

7.2.3 Kitcher on Field’s and Friedman’s Claim About the Empirical Indefeasibility of the A Priori Kitcher has a detailed discussion of the views of Field and Friedman, who also defend the indefeasibility of the a priori by empirical evidence, alleging reasons other than Hale’s. It is important to discuss them here in order to compare his views in “A Priori Knowledge Revisited” with his previous views in his book The Nature of Mathematical Knowledge. As a preamble, Kitcher states: It seems to me that the discussions of the past decades have made clear how intricate and complex the classical notion of the a priori is, and that neither the Strong conception nor the Weak conception (nor anything else) can provide a coherent explication. In the end, it doesn’t matter much whether we declare that mathematics isn’t a priori (cleaving to the Strong conception) or whether we argue that mathematics is a priori (on the basis of the Weak conception). The important point is to understand the tradition-dependence of our mathematical knowledge and the complex mix of theoretical reasoning and empirical evidence that has figured in the historical process on which current mathematical knowledge is based.28

Kitcher compares Field and Friedman’s views: Both Hartry Field and Michael Friedman have offered defenses of the apriority of types of propositions traditionally favored with this status, defenses that seem to take into account many of the points I’ve been urging. Field is concerned with the apriority (or “aprioricity“ as he calls it) of classical logic. Friedman wants to argue for the apriority of mathematics. In both instances, the defense takes the same form, in that beliefs in the pertinent propositions are supposed to be needed for people to perform certain kinds of cognitive tasks – engage in any assessment of evidence (Field), or formulate and assess the kinds of theories that we take to represent the pinnacle of our empirical knowledge (Friedman). I think this represents a confusion … between apriority and a quite different idea, the notion of a propositional precondition, and that the confusion makes the Weak conception seem more attractive than it actually is.29

It is an open question whether this is the sole role of the a priori that they have given  – Field and Friedman don’t offer an illuminating characterization of the a priori. It is the only role that Kitcher comments here. The connection between a prioricity and propositional preconditions for knowledge has become important, especially, on the issue of Field’s default propositions and rules and Wright’s ‘entitlements” or “warrants for free”, which I will discuss in the next section. Kitcher is right in pointing out that there is a confusion here between a priori statements and a priori warrants and purportedly a priori preconditions for knowledge. Kitcher explains in a very important passage:

 Kitcher, “A Priori Knowledge Revisited” in New Essays on the A Priori, pp. 84–85). Kitcher is referring to the strong conception of the a priori as what is “necessary and unrevisable, fixed for all time”; and the weak conception as what is “constitutive of the object of [scientific] knowledge”. 29  Kitcher, “A Priori Knowledge Revisited”, p. 85. 28

120

7  “Pure” Hale and Related Issues

Although Field is much less friendly to apriorism than Friedman, there’s a striking convergence in their recent strategies. In a penetrating recent discussion of philosophical naturalism, Friedman follows Reichenbach in distinguishing two notions of the a priori: “necessary and unrevisable, fixed for all time, on the one hand, “constitutive of the object of [scientific] knowledge”, on the other.” The real hero of the story is Carnap, who “brought this new, relativized and dynamical conception of the a priori to its most precise expression”. According to Carnap, our formulations of hypotheses and our assessment of them presuppose a mathematico-­logico-linguistic framework, and, within any such framework, the mathematical principles play a constitutive role, so that they cannot be questioned while we remain with the framework. Of course, as Carnap took pains to point out, we can change frameworks, inscribing a different set of principles in our practice of formulating and testing empirical hypotheses. In changes of framework, however, we appeal not only to empirical evidence but also to specifically mathematical and even philosophical considerations. Instead of the holistic vision of evidence familiar from Quine, Friedman offers an alternative ... the picture of a dynamical system of beliefs, concepts, and principles that can be analyzed, for present purposes, into three main components: an evolving system of empirical natural scientific concepts and principles, an evolving system of mathematical concepts and principles which frame those of empirical science and make their rigorous formulation and precise experimental testing possible, and an evolving system of philosophical concepts and principles which serve, especially in periods of conceptual revolution, as a source of suggestions and guidance in choosing one scientific framework rather than another. All of these systems are in continual dynamical evolution, and it is indeed the case that no concept or principle is forever immune to revision. Yet we can nonetheless clearly distinguish the radically different functions, levels, and roles of the differing component systems. In particular, although the three component systems are certainly in perpetual interaction, they nonetheless evolve according to their own characteristic dynamics. (Friedman, ‘Naturalism’, p. 13) There is much here with which I agree. What puzzles me most is why this should be thought of as any kind of rehabilitation of apriority … mathematicians try to devise ways of responding to unanswered questions, they develop generalizations of methods and concepts that have previously been introduced, they attempt to find rigorous replacements for forms of reasoning that appear to yield correct conclusions but do not accord with prevailing standards  – and, in doing all this, they propose definitions and axioms that systematize previous mathematics. The ultimate roots of their practice lie in experience, and, from time to time, connections with the empirical sciences are reforged, and particular parts of mathematics are inspired by the needs of particular lines of investigation into natural (or social) phenomena. Hence, there is genuine co-evolution between mathematics and science … The knowledge of contemporary mathematicians may be proximally produced by their reflections on what they have absorbed from the past, reflections that do not depend on any specific sensory input, but it is ultimately dependent on the collective experiences of the tradition in which they stand.30

Kitcher is puzzled the most about why all this Carnap-Reichenbach conception should be considered as a revival of a prioricity. Why not? Because he still thinks that this will contradict the availability of a priori warrants independently of tradition, independently of experience, and defended by the traditional a priorist. Is that so?  Kitcher, ibid., pp. 88–89. The complete reference to Friedman is: “Philosophical Naturalism” in Proceedings and Addresses of the American Philosophical Association 71, No. 2), pp. 5–21, 1997. The Friedman’s passage quoted by Kitcher is on p. 13. 30

7.2  Empirical Indefeasibility as a Hallmark of the A Priori

121

Kitcher is right about stressing – again – the dependence on the corpus of knowledge in our acquisition of mathematical knowledge. The question is how this corpus relates to a priori warrants. This corpus functions as a given background. Now the background is huge: mathematical knowledge, mathematical tradition. Kitcher, himself, affirms that, in carrying out these processes, there is no dependence on any particular empirical input in the execution of a specific warrant. That may be enough for a warrant to count as a priori. Kitcher continues: If this is Friedman’s picture, then he and I are in fundamental accord. We can even agree to call mathematical knowledge “relatively a priori“, or, as I would prefer, “proximally a priori”, so long as we are clear that this Weak conception diverges from traditional ideas about a priori mathematical knowledge. For the tradition sees the dynamic of the mathematical subsystem in very different terms. Mathematicians are supposed to have ways of warranting their beliefs that stand outside the historical process, that are independent of tradition … Field’s efforts to secure the apriority of logic seem to me to be an ingenious last-ditch attempt to bind the relativized notion of apriority (the Carnap-Reichenbach, “constitutive”, conception) to the more traditional notion, by arguing that the framework-­constituting principles are immune to empirical evidence. I’ve argued that those efforts fail. The proximal a priori is the best one can hope for. (ibid, p. 90)

Kitcher is correct that Field is wrong in requiring empirical indefeasibility for the a priori. Let’s remember that Kitcher in his book The Nature of Mathematical Knowledge required that a priori warrants have to be ultra reliable, indefeasible in general, in order to be absolutely independent of experience. Now, in this paper, he is more open to the defeasibility of a priori warrants (‘the proximal a priori”), and stresses that his main problem with the traditional conception of the a priori is its belief in warrants available independently of tradition; the dependence on tradition counts as empirical. Kitcher considers that Field uses the notion of propositional precondition to defend the tradition independence of our logical knowledge; and Friedman to maintain traditional theses about a prioricity while accepting the relative tradition dependent character of the a priori. (pp. 90–91) Kitcher’s views have to be qualified, though. I don’t see why Kitcher is so worried about accommodating “the lore of our ancestors”. There is no need to deny the dependence on tradition, the dependence on the knowledge of previous mathematicians, on the testimony of teachers, in our acquisition of a priori mathematical knowledge. Kitcher is quite right about all these dependencies. The question is why does he think that a prioricity is in conflict with tradition dependence. It may be a historical issue, in the sense that this dependency has not been fully recognized, but not a conceptual conflict. Again Kitcher’s words: “The most fundamental feature of my attack on apriority is my attempt to debunk tradition-independence.” (p.  90) All the abovementioned types of mathematical knowledge that Kitcher discusses in the above quoted passage are a posteriori because they depend on testimony which can yield a posteriori knowledge of mathematical truths. The point is rather than given all this a posteriori knowledge as background, in the case of inferential knowledge that p, I can myself follow a proof that p, I can myself construct the proof for the truth of p. If I can do that then I know a priori that p as well. If I don’t follow a proof that p, then I don’t know a priori that p in the case

122

7  “Pure” Hale and Related Issues

of inferential knowledge that p. When it is the first time that we know that p by a new discovered proof that p, then my knowledge is a priori to begin with. This a priori knowledge will be available later on for dissemination by testimony, which is a posteriori knowledge that p. Kitcher seems to be confused himself between knowledge a priori and preconditions for knowledge, ignoring that some a priori truths can be known a priori and a posteriori. His historicism about mathematical knowledge can be understood as a (huge) propositional precondition. All the issues that he correctly emphasizes  – about the importance of the tradition in which we are immersed – work as background conditions for the acquisition of a priori knowledge. They are not part of the a priori warrant itself, they are background conditions that make possible for the subject to be in a position to know. I see no problem with tradition dependence in this way. I think that Hale won’t see one either. In general, apriorists defend a priori knowledge (justification) acknowledging the importance of the corpus of mathematical and logical knowledge. Kitcher concludes: I recommend declaring a truce on the apriorism/empiricism debate on the grounds that logic, mathematics and … whole chunks of other disciplines count as a priori in the Weak sense. That truce should be coupled with a clear understanding of the places in which the Weak conception departs from classical lore about apriority, agreement on the tradition-­ dependence of our logical and mathematical knowledge, and a resolve to explore the complex ways in which experience has figured in the genesis of our current logical and mathematical knowledge. (p. 91)

I agree with Kitcher about these three important tasks for the a prioricist, that is: (1) “a clear understanding of the places in which the Weak conception departs from classical lore about apriority”, (2) “agreement on the tradition-­dependence of our logical and mathematical knowledge”, and (3) “a resolve to explore the complex ways in which experience has figured in the genesis of our current logical and mathematical knowledge”. Indeed, I have learnt so many important lessons about a priori knowledge from Kitcher (as well as from  Hale, as this book evidentiates); Kitcher, who has been such a critical philosopher of the notion, though he has weakened some of the points he made earlier against a priori knowledge (justification) in his book.

7.2.4 Wright’s Entitlements, Warrants for Free Wright has a related notion to Field’s, entitlement: The attempt to justify P would involve further presuppositions in turn of no more secure a prior standing...and so on without limit; … 31

 Wright, “On Epistemic Entitlement: Warrant for Nothing (and Foundations for Free)?” in Proceedings of the Aristotelian Society, supp., 78, pp. 191–192, 2004. 31

7.2  Empirical Indefeasibility as a Hallmark of the A Priori

123

Wright explains the rationale for the entitlement as follows: wherever we need to carry through a type of project, or anyway cannot lose and may gain by doing so, and where we cannot satisfy ourselves that the presuppositions of a successful execution are met except at the cost of making further presuppositions whose status is no more secure, we should – are rationally entitled to – just go ahead and trust that the former are met.32

The entitlement is not an entitlement to believe the presuppositions in question but to accept or trust them, where acceptance is a more general propositional attitude than belief that includes belief and trust as subcases. Entitlement is a species of warrant that does not require evidence. Note that this is an attitude that does not entail that the presupposition or entitlement in question is a priori. At this point it is an open question whether the entitlement is a priori or a posteriori. It seems that if no evidence is put forward for the acceptance of the entitlement, then the issue is not evidential, and if it is not evidential, then it is neither a priori nor a posteriori. Wright talks about “cornerstones” as connected to cognitive projects, being noncognitive themselves. Wright calls “a proposition a cornerstone for a given region of thought just in case it would follow from a lack of warrant for it that one could not rationally claim warrant for any belief in the region.”33 They are very basic beliefs and are a subset of the entitlements. I understand that not all the entitlements are cornerstones. Examples of cornerstones propositions are: “There is an external world”, “I’m not a brain in a vat”, and “The history of humankind is a long one”. Warrants for free are nonevidential warrants to accept, rather than to belief, entitlements and cornerstone propositions. It seems to me that acceptance of entitlements does not have to exclude that we can gather evidence later on, in some cases, reasons to accept the entitlements, as we test their success in practical contexts, that could become (indirect) justifications or evidence for them; or is it rather that we should not treat those as evidence for entitlements? I don’t think so. If we accept subsequent evidence for them, they may cease to be entitlements. Being fallibilists, we should accept that entitlements are not fixed for all time but can be changed over time. Actually, in the case of cornerstones, what appears to be the case is they are overwhelmingly corroborated to begin with. Calling this corroboration evidence or not is a separate issue. What is the difference between believing that p and accepting that p? It does seem to be the same thing, practically speaking. Epistemologically speaking, in believing that p, there is evidence involved; in accepting that p, there is no evidence for p. This is an important difference. Wright moves the discussion to entitlements, beyond evidence, belief and truth, basic concepts of epistemology. Since the notion of belief does not entail truth  – we can be justified in having false beliefs  – the notion of belief is problematic. Wright makes the most of the problematic nature of the concept of belief with his notion of entitlement while, at the same time, he is trying to respond to the sceptic. 32 33

 Ibid, p. 192.  Wright, Crispin. “On Epistemic Entitlement”, pp. 167–68.

124

7  “Pure” Hale and Related Issues

What entitlement has to do with the a priori? Where is the connection between the two notions? Wright considers the possibility that “what we have, at the level of the most basic laws of logic, is not knowledge, properly so regarded, at all but something beneath the scope of cognitive enquiry, – a kind of rational trust, susceptible [neither] to corroboration nor rebuttal by any cognitive achievement.”34 Wright says “not just trust but rational trust”. What does it mean “a kind of rational trust, susceptible [neither] to corroboration nor rebuttal by any cognitive achievement”? Does it mean that we can’t reject entitlements if future evidence contradicts them? Why can’t these entitlements be corroborated, even if indirectly, by our successful applications of them, nor rejected later on by our possible failures? May we distinguish between different types of entitlements, some revisable, some not? For example, Wittgenstein talks of a similar solid ground in On Certainty, but a revisable one. Revisability should not be excluded in our acceptance of entitlements, given our fallibility, we can change our minds about them to respond to change in the world, and change in our cognitive projects. Wright distinguishes35 between entitlements: strategic entitlements, entitlements of cognitive project, entitlements of rational deliberation, and entitlements of substance. I am focusing on entitlements of cognitive project here. The issue of their revisability should be clear. Casullo compares Field’s views with Wright’s: Wright’s account differs from the account of … Field in a crucial respect. The entitlement that we have to basic logical principles is not an entitlement to believe that they are valid; it is an entitlement to trust or accept that they are valid. Entitlement is a species of positive epistemic status that does not underwrite either justified belief or knowledge. Wright’s account, however, has two important features in common with the account of Field. First … Field allow that there are propositions and rules that one can justifiably or reasonably believe in the absence of any evidence or justification. Wright allows that there are propositions and rules that one is rationally entitled to accept without any evidence or justification. Second … Field maintain that such propositions and rules have a priori status. Wright maintains that, on his account, the epistemological status of basic logical principles is a priori, although he does not explicitly address whether other entitlements to cognitive project are a priori.36

I agree with Casullo’s assessment of Wright. Also Wright is correct in not considering that all entitlements are a priori. It depends on the cognitive project and its associated presuppositions. If we are trusting our perception, and if we apply the a priori/a posteriori distinction to entitlements, then the entitlements about perception would be a posteriori. But then we are talking about “nonevidential a posteriori entitlement”. I will add to Casullo’s assessment that for Field such propositions and rules have a priori status, that Field admits: My definition classifies default reasonable propositions and rules as, trivially, weakly a priori; so that they are a priori if and only if they are empirically indefeasible. If one were

 Wright, “Intuition, Entitlement and the Epistemology of Logical Laws”, 2004, p. 174.  Wright, “On Epistemic Entitlement: Warrant for Nothing (and Foundations for Free)” in Proceedings of the Aristotelian Society, Supplementary Volumes, Vol. 78, pp. 178–203, 2004. 36  Casullo, “Articulating the A Priori–A Posteriori Distinction”, pp. 322–323. He analyzes Harman’s views also (that’s why the plural sense of verbs used), but I focus only on what he says about Field. 34 35

7.2  Empirical Indefeasibility as a Hallmark of the A Priori

125

to hold that a priori justification is required for reasonable belief in an a priori proposition and for reasonable employment of an a priori rule, then default reasonable propositions and rules could never count as a priori. That would be the most undesirable: surely among the most plausible examples of default reasonable a priori propositions and rules are simple logical truths like ‘If snow is white then snow is white’, and basic deductive rules like modus ponens and ‘and’-elimination. It would be odd to exclude these from the ranks of the priori merely because of their being default reasonable. (Field, “Apriority as an Evaluative Notion”, p. 119)

What about the analytic ones? It is interesting that Field does not say that some of these basic truths and rules are analytic, so justified by our understanding of their meanings, and not simply accepted by default. Field’s example “People usually tell the truth” is a default empirical proposition, not a weakly a priori proposition, as Casullo affirms: “For Field, all default reasonable propositions are weakly a priori.” (ibid, p. 323) Field, explicitly, explains this: If our concept of apriority were simply weak apriority we would have the opposite problem: default reasonable propositions would automatically count as a priori. But there is no obvious reason why propositions such as ‘People usually tell the truth’ should not count as default reasonable, and it would be odd to count such propositions as a priori. Empirical indefeasibility seems to be the obvious way to distinguish those default reasonable propositions that are a priori and those that aren’t. (“Apriority as as Evaluative Notion”, p. 120).

For Field, “People usually tell the truth” can be accepted by default. He refers to it as simply default reasonable and not as trivially weakly a priori. Field adds: There is another possibility worth considering: I have argued against saying that a priori propositions and rules are those that require non-empirical justification to be reasonably believed, but why not say that they are those that admit nonempirical justification? The answer is that this too might exclude simple logical truths, or rules like modus ponens and ‘and’-elimination. (For the only obvious way to try to give ‘a priori justifications’ for them is to appeal to the truth-table for ‘and’. But as has often been pointed out, ‘justification’ of ‘and’-elimination by the truth-table for ‘and’ requires the use of ‘and’-elimination (or some equivalent principle) at the meta-level: one must pass from ‘“A” and “B” are both true’ to ‘“A” is true’. If this counts as a justification it is a circular one, and it is not obvious that ‘circular justification’ makes sense. (‘Apriority as as Evaluative Notion”, p. 120).

Is there anything that can prove Modus Ponens, noncircularly? That’s Field’s point. The beliefs we accept as entitlements seem to be needed for the execution of cognitive projects, and beliefs that can’t be justified because nothing has the force of validating them, we cannot justify them because they are irrational but rather because justification for them does not exist without recurring to a vicious circle that presupposes them, or without recurring to further beliefs which are less secured than them. One thing is Modus Ponens, another the evidence we can gather for its validity; another more is “I believe that Modus Ponens is valid”, which is an empirical statement. I share Field’s concern about circularity. But because a characterization of a priori propositions and rules may exclude some very basic logical truths or rules as being justifiable, it does not follow that we should characterize all a priori truths as accepted by default all across the board; these are special cases; the rest can be characterized as a priori, epistemically, instead of safeguarding these few special

126

7  “Pure” Hale and Related Issues

(crucial) cases by converting all a priori propositions and a priori rules into default (a priori) propositions. Casullo affirms also that there is no explanation of the relationship of entitlements and a prioricity. This is not knowledge or justification. It is an attitude of acceptance, of good faith. But the issue is that default or entitlement attitudes may be the explanation for accepting something so basic to epistemology as the basic laws of logic. That’s what Field and Wright have in mind. For Casullo, Field and Wright maintain that a propositional attitude (belief or acceptance) can have a positive epistemic status (justified, reasonable, or entitled) in the absence of any evidence or justification. In doing so, there seems to be a distinction between epistemic (positive role) and evidential role, so that an entitlement can have a positive epistemic role (such that its characterization does not involve negatives) without having an evidential (positive) role in a cognitive project. Casullo says about Wright’s entitlements: Wright maintains that he is offering an account of the epistemological status of basic logical principles on which they are a priori. Although he is not explicit on the issue, his claim that his account has the consequence that basic logical principles are a priori appears to presuppose an analogue of (APJN): (APEN) S’s acceptance that p is a priori entitled if and only if the entitlement of S’s acceptance that p does not originate in empirical evidence.

If this is correct, then it follows that, on Wright’s account, all entitlements of cognitive project are a priori, including one’s acceptance that one’s cognitive faculties are properly functioning and that one’s environmental circumstances are suitable for their successful application.37 This characterization (APEN) does not explain what is a priori evidence but merely says that it is evidence for a belief that does not depend on empirical evidence. The old problem: without a clear characterization of the notion of a priori justification, we are just restating the obscurities that Williamson talks about, which convey, the uneasiness we have had with the notion, associated mainly with platitudes that say nothing, are empty at this point. It is even worse now because we are moving the discussion of the a priori beyond or beneath or away from the concepts of belief, truth, and knowledge. Furthermore, I advert, in general, in the discussions also the conflation of various concepts – like warrant, belief, acceptance, reasons to believe, claims to knowledge  – without clarifying them, i. e., without specifying what things have these properties, but merely mentioning or enumerating them. If what is the a priori – the basic concept – is not clear enough, it can easily be seen how unclear are all these other dependent concepts.38

 Casullo, ibid., p. 323. The reference is to: “(APJN) S’s belief that p is a priori justified (reasonable) if and only if the justification (reasonableness) of S’s belief that p does not depend on empirical evidence.” 38  I’m not going to provide explanations of all these concepts. I’m going to explain only the ones that are related directly to my project in Chap. 10. 37

7.2  Empirical Indefeasibility as a Hallmark of the A Priori

127

For Casullo, if this is a correct consequence, then, on Wright’s account, all entitlements of cognitive project are a priori, including one’s acceptance that one’s cognitive faculties are properly functioning and that one’s environmental circumstances are suitable for their successful operation. Again, if the entitlement does not originate in evidence, then it is trivially true that it does not originate in a priori evidence or empirical evidence. But trusting our cognitive faculties does not come out as a priori, automatically, because our trust can depend on empirical evidence, like that I am alert and fully understand the questions. Our trust may not be a mere entitlement. It depends on the case. Thus, it does not follow that, on Wright’s account, all entitlements of cognitive project are a priori, contrary to what Casullo says. This is an incorrect reading of Casullo. It depends on the cognitive project. Note that (APEN) is a formulation of Casullo, not Wright’s. Casullo explains: Wright does not explicitly discuss the application of the a priori–a posteriori distinction at the level of entitlements, or the apparent consequence that the conjunction of his account with (APEN) yields the result that all entitlements of cognitive project are a priori. Field, however, is aware that the conjunction of his account with (APJN) yields the result that all default reasonable propositions are a priori and wishes to resist it. Hence, he adds to (APJN) an empirical indefeasibility condition. (ibid, p. 323) The a priori–a posteriori distinction becomes a distinction that, at its most fundamental level, is between two sources of warrant: experiential and nonexperiential. Where warrant is for free and does not derive from any source, the distinction does not apply since the basis for the distinction is absent. (ibid, p. 325)

I agree with Casullo that if a warrant is for free, then it is neither a priori nor a posteriori. The distinction between a priori and a posteriori does not apply to warrants for free. Note that the problem does not go away for apriorists by asserting that entitlements (warrants for free) are not a priori. The issue is that some entitlements are necessary for the acquisition of a priori knowledge. They should be understood as preconditions. The a priori has to be positively characterized, instead of adding more negatives to the notion. Wright explains: To take it that one has acquired a justification for a particular proposition by the appropriate exercise of certain appropriate cognitive capacities – perception, introspection, memory, or intellection, for instance  – always involves various kinds of presupposition. These ­presuppositions will include the proper functioning of the relevant cognitive capacities, the suitability of the occasion and circumstances for their effective function, and indeed the integrity of the very concepts involved in the formulation of the issue in question. (“On Epistemic Entitlement”, p. 189) That is not to deny that, if one chose, one could investigate (at least some of) the presuppositions involved in a particular case. I might go and have my eyesight checked, for example. But the point is that in proceeding to such an investigation, one would then be forced to make further presuppositions of the same general kinds (for instance, that my eyes are functioning properly now, when I read the oculist’s report, perhaps with my new glasses on.) Wherever I get in position to claim justification for a proposition, I do so courtesy of specific presuppositions – about my own powers, and the prevailing circumstances, and my understanding of the issues involved – for which I will have no specific, earned evidence.

128

7  “Pure” Hale and Related Issues

This is a necessary truth. I may, in any particular case, set about gathering such evidence in turn – and that investigation may go badly, defeating the presuppositions that I originally made. But whether it does or doesn’t go badly, it will have its own so far unfounded19 presuppositions. Again: whenever cognitive achievement takes place, it does so in a context of specific presuppositions which are not themselves an expression of any cognitive achievement to date. (“On Epistemic Entitlement”, p. 189)

Casullo thinks: We are now faced with a dilemma. The traditional conception of the a priori, in conjunction with the family of views articulated in this section, entails that some knowledge (justified belief) is neither a priori nor a posteriori. Yet it is part of the traditional story regarding the a priori that all knowledge (justified belief) is either a priori or a posteriori. That story is premised on the assumption that all justification originates either in evidence or in some cognitive state or process of the believer. (ibid, p. 324)

Then Casullo concludes: The superior resolution is to endorse the traditional conception of a priori knowledge and embrace the consequence that some knowledge (justification) is neither a priori nor a posteriori.39

I don’t understand this. What is justification? What is evidence? Casullo formulates a priori knowledge in terms of justification and evidence. Can there be any knowledge or justification without evidence? These two passages are contradictory: when Casullo affirms that the distinction does not apply to entitlements, and when he says that some knowledge (justification) is neither a priori nor a posteriori: entitlements. I consider that all knowledge and justification is a priori or a posteriori, as the traditional conception of the distinction states. Justification and knowledge require evidence. Entitlement does not. It is another category, as its proponents clearly state that. Entitlement is not justification; it does not constitute knowledge. We should not apply the (traditional) distinction to entitlements, not because some knowledge (justification) is neither a priori nor a posteriori, as Casullo considers to be the “superior” resolution, but rather because entitlements are neither justification nor knowledge. Note that excluding entitlements as a priori candidates does not preclude them from relating to a priori truths. They can be preconditions for a priori knowledge. In any case, it is the task of entitlement theorists to expand the notion of the a priori to include some entitlements or default propositions as a priori; and to explain their relations.  Entitlements can have an epistemic role without having an evidential role in our knowledge of the truth of a proposition; epistemic in the sense of being preconditions for knowledge, like the necessary experiences for concept acquisition, epistemic in the sense of allowing cognitive (epistemic) projects to be carried out, in both cases, without being evidence or part of the ground we have for the truth of a proposition. “I am alert enough” is not part of my justification for a mathematical

 Casullo, A. “Articulating the A Priori-A posteriori Distinction” in Essays on A Priori Knowledge and Justification. Oxford: Oxford University Press, p. 326, 2012. 39

7.2  Empirical Indefeasibility as a Hallmark of the A Priori

129

truth. I see also a distinction between different types of presuppositions or entitlements: ones that are just taken for granted to facilitate things, to not complicate matters, unnecessarily, for example, I may be able to register all the relevant experiences I had in learning a concept, but take that learning process for granted to move on; other presuppositions that have to be taken for granted, that we have no choice but to take them for granted, like Modus Ponens or the existence of the external world because they are crucial for cognitive projects and are unprovable. It remains open at this point whether the a priori can be applied to entitlements, and what sorts of conditions have to be specified. Lisa Warenski, on the other hand, applies aprioricity to entitlements: It seems that a no non circular justification to very basic deductive and inductive principles can be given. There is a prima facie problem for claims about their apriority: a principle cannot be a priori justified if it cannot be justified at all. Some philosophers have argued that although we may not have a justification for our basic inference rules, we are entitled to employ them – or at least we are epistemically blameless in doing so. If our acceptance of these rules is epistemically responsible independently of empirical evidence (and the rules are empirically indefeasible), the basis of our acceptance of them should count as a priori even if it is not what we might regard as full-fledged justification.40

But the a priori has to be characterized first! She accepts these entitlements as a priori, and partly justified, even if not fully justified. Warenski seems to have in mind degrees of justification and associated reasonableness in our beliefs. Again, Casullo’s “superior resolution” can be avoided. Wright, “On Epistemic Entitlement” explains: to be entitled to trust in the soundness of a basic inferential apparatus – to anticipate a discussion of the status of fundamental rules of inference on which I have not here embarked – is to be entitled to regard its correct deployment as serving the generation of proofs and hence, since what is proved is known, to be entitled to claim knowledge of the products of reasoning in accordance with it. In general, the effect of conceding that we have mere entitlements for cornerstones is not uniformly to supplant evidential cognitive achievements – knowledge and justified belief – with mere entitlements right across the board but to qualify our claims to higher order cognitive achievement.41

Wright recognizes that he has not explained the status of fundamental rules of inference in the passage quoted.42 Note that Wright is interested in clarifying the status of our second order beliefs, our claims to knowledge such as “I know that P”, and “I trust the soundness of Modus Ponens”. The entitlements are not supposed to substitute ‘evidential cognitive achievements, belief and knowledge, with mere entitlements across the board’. We have to be aware when we are dealing with evidence and when we are dealing with entitlement. They are presuppositions for knowledge.

  Warenski, Lisa. “Naturalism, Fallibilism and the A Priori”, Philosophical Studies, 142, p. 408, 2009. 41  Wright, “On Entitlement”, p. 208. 42  He tries to do that in another paper “Intuition, Entitlement and the Epistemology of Logical Laws”. Dialectica 58, No. 1, pp. 155–75, 2004a. 40

130

7  “Pure” Hale and Related Issues

We are basing our epistemic notions of justification, belief and knowledge on something nonepistemic: on warrants for free, less grounded, less secured. This is very uncomfortable, to say the least. We don’t have to be a Cartesian foundationalist in order to recognize that we cannot have a solid cognitive project if its base is merely taken for granted. Or is it only part of the base that has to be taken for granted? Wright says that, at this basic level, this is all we can hope for. It could be even worse for what he calls “the problem of leaching”: once we admit mere entitled acceptances into the role of cornerstones, we are bound to risk “leaching”, as it were – an upwards seepage of mere entitlement into areas of belief which we prize as genuinely knowledgeable or justified. (“On Epistemic Entitlement”, p. 178) The general picture is that the cornerstones which sceptical doubt assails are to be held in place as things one may warrantedly trust without evidence. Thus at the foundation of all our cognitive procedures lie things we merely implicitly trust and take for granted, even though their being entitlements ensures that it is not irrational to do so. But in that case, what prevents this ‘merely taken for granted’ character from leaching upwards from the foundations, as it were like rising damp, to contaminate the products of genuine cognitive investigation? (“On Epistemic Entitlement”, p. 207)

Given that I justifiably believe that P on the basis of presupposition C, which is taken for granted, what can stop me in moving upwards and say that my belief that P itself can be taken for granted, my justification for P can be taken for granted, and so on, such that the epistemic notions of belief, justification and knowledge can be contaminated by the notion of entitlement. All would be entitlement. This is a serious problem. It is a very important task for the entitlement theorist to resolve it. Wright distinguishes between our belief that P and our belief that we have reliable evidence for P, and thinks the risk we run in trusting a related presupposition C is inherited by the latter belief, not the first. What necessarily inherits the risk we run in trusting C without evidence is not our belief that P – for we may in fact have reliable evidence for P – but our belief that we have reliable evidence for it. To be sure, to claim to know P is indeed to promise that it is safe to accept P. However, that promise is not automatically worthless, or inappropriate, if the claim to know is not itself knowledgeable. (“On Epistemic Entitlement”, p. 209)

In an important passage, Wright explains: If the full extent of the epistemic credentials of the proposition that there is an external material world is that it is something in which one may rationally place trust, then that is also the full extent of the epistemic credentials of the proposition that sense experience provides a quotidian sort of knowledge about an external material world. So our claim to perceptual knowledge is going to be a ‘mere’ entitlement even if – if we do indeed have it – the knowledge itself is, naturally, something more. And so for putatively knowledge-­ acquisitive methods in general. If, for example, as I have argued elsewhere … our belief in the validity of our most basic rules of inference is likewise only a matter of (mere) entitlement, then while such rules may indeed be at the service of extending our knowledge – when relevant premises are known – we will at best be entitled to claim to know that they

7.2  Empirical Indefeasibility as a Hallmark of the A Priori

131

are so, rather than knowing that we know, and hence would have no second-order knowledge of the conclusions to which they lead in any particular case.43

The proposition “There is an external material world” is a better example than Field’s “People usually tell the truth” to compare with the default character of Modus Ponens. Wright is talking about entitlements with respect to second order knowledge (belief), not with respect to the basic truths, the axioms, or basic rules of inference themselves, or our knowledge of their consequences, but rather with respect to “our belief in the validity of our most basic rules of inference”, our knowledge that we know them, our claims to knowledge. The knower does not have to know that he knows in order to know. Someone can apply the rules which he is entitled to, even if he does not entertain these second order thoughts about their validity. Wright is fully aware of the worrisome nature of entitlements and is fully explicit about it: And I have not further encroached at all on the major question of the demarcation of entitlement: even if some notion of warranted but unevidenced acceptance does have an ineliminable part to play in any feasible methodology of enquiry and belief management, the question remains, how big a part, and what are its limits? The point has not gone away that it is not in general, or even usually, consistent with responsible belief management to accept things without evidence or relevant cognitive achievement. What are the principles that determine when one may do so and when one ought not? How do we distinguish the genuine entitlements from the prejudices, mere assumptions, and idées fixes? No less important than trying to delimit by what principles we may be rationally entitled to certain trustings is the project of determining when we are not, that is, when absence of evidence does indeed defeat rational acceptance. This is, of course, an absolutely crucial issue. It presents, in my judgement, perhaps the most major challenge remaining to the theorist of entitlement.44

The crucial challenge is to determine when we are not entitled to accept certain trustings, ‘when absence of evidence does indeed defeat rational acceptance.’ My focus in this book is on the notion of a priori knowledge and a priori justification, and my account leaves open the question whether there are entitlements which are a priori. It is the task of entitlement theorists to come up with a notion of aprioricity such that some entitlements or default propositions come out as a priori, and that resolves the leaching problem. I will say a couple of things, though. If there are a priori entitlements then it seems that they should be (some at least) understood as preconditions for knowledge, things we take for granted to pursue cognitive projects. Certainly, these would be the entitlements I would be interested in considering. The entitlements are supposed to be rational, it is not that anything goes, it is not a free for all situation, but rather to accept what is needed and convenient to carry out a cognitive project, which in turn, if successful, will give us more confidence that

 Wright, C. “On Epistemic Entitlement II: Welfare State Epistemology” in Scepticism and Perceptual Justification. Edited by Dylan Dodd and Elia Zardini. Oxford: Oxford University Press, p. 229, 2014. 44  Ibid, p. 245. 43

132

7  “Pure” Hale and Related Issues

we were right in trusting the cornerstones in the first place. Cornerstones have overwhelming corroboration. We can have indirect evidence for entitlements when we are successful in carrying out the cognitive projects they allow. What is important for me is to emphasize that, given our fallibility, these entitlements can be revised, can be abandoned, can be substituted, in principle, in the light of future evidence, future cognitive projects, a priori or empirical. Those that cannot be revised, if there are any, have to be clearly specified. Let’s not accept these entitlements  – background assumptions – automatically, as fixed for all time, going backwards in our understanding of the notion of a priori knowledge as involving some sort of special sureness, but rather accept that we can’t prove everything, need to proceed with what we have evidence for, and ought to accept some things without (full) evidence, at a particular time. This background of entitlements is revisable too. I take it that this is the core lesson of Wittgenstein’s On Certainty.45

7.2.5 Roles of Experience in A Priori Knowledge The traditional understanding of the a priori/a posteriori distinction accepts that experience can play two quite different roles in knowledge and justification: one evidential, the other enabling. In a very insightful paper, Miles and Wright46 clearly explain these roles of experience: Experience plays an evidential role when it provides the agent with her evidence for a certain judgement; it plays a merely enabling role when it is required only for the acquisition of the concepts drawn on in an understanding of the proposition that she is otherwise warranted in judging true. Since the justification of any proposition draws on an understanding of the concepts configured in it, and since concept-acquisition is an empirical process, defenders of the a priori are therefore normally willing to grant that justification a priori is not justification which is “independent of experience” in its enabling role. Their thought is rather that, in such justification, experience plays no evidential role.

These authors are responding to Williamson who poses47 a problem to the notion of a priori / a posteriori knowledge related to these two roles. For Williamson, the distinction between a priori and a posteriori knowledge is handy enough for a rough initial description of epistemic phenomena; it is out of place in a deeper theoretical analysis, because it obscures more significant epistemic patterns.48

 Wittgenstein, Ludwig. On Certainty. Oxford: Basil Blackwell, 1969.  Melis, Giacomo and Crispin Wright. “Oxonian Scepticism about the A Priori” in Beyond Sense? New Essays on the Significance, Grounds, and Extent of the A Priori. Edited by Dylan Dodd and Elia Zardini. Oxford: Oxford University Press, Forthcoming, p. 6. 47  Williamson, Timothy. “How Deep is the Distinction between A Priori and A Posteriori Knowledge” in The A Priori in Philosophy. Edited by A. Casullo and J. Thurow. Oxford: Oxford University Press, pp. 291–312, 2013. 48  Ibid, p. 169. 45 46

7.2  Empirical Indefeasibility as a Hallmark of the A Priori

133

If we don’t get clear about what is the a priori, then Williamson is right in saying that the distinction, being obscure itself, obscures epistemological issues. He does not clarify the notion of a priori knowledge because he is not sympathetic with the notion; he attacks it, exploiting its vulnerability. That’s why I am interested first in clarifying what is the a priori before deciding if it is vacuous, important, significant or not. Williamson considers49 what he takes to be a clear case of a priori knowledge and a clear case of a posteriori knowledge: (1) All crimson things are red and (2) All recent volumes of Who’s Who are red. Cases of knowledge of (1) are clearly a priori because by definition crimson is a specific type of red, whereas cases of knowledge of (2) are clearly a posteriori because it takes direct or indirect experience of recent volumes of the British work of reference Who’s Who to determine their color. Williamson explains50 about Norman, a subject knower: Suppose that Norman acquires the words ‘crimson’ and ‘red’ independently of each other, by ostensive means. He learns ‘crimson’ by being shown examples to which it applies and samples to which it does not apply, and told which are which. He learns ‘red’ in a parallel but causally independent way. He is not taught any rule like (Crimson), connecting ‘crimson’ and ‘red’. Through practice and feedback, he becomes very skilful in judging by eye whether something is crimson, and whether something is red. Now Norman is asked whether (Crimson) holds. He has not previously considered any such question. Nevertheless, he can quite easily come to know (Crimson), without looking at any crimson things to check whether they are red, or even remembering any crimson things to check whether they are red, or making any other new exercise of perception or memory of particular coloured things. Rather, he assents to (Crimson) after brief reflection on the colours crimson and red, along something like the following lines. First, Norman uses his skill in making visual judgments with ‘crimson’ to visually imagine a sample of crimson. Then he uses his skill in making visual judgments with ‘red’ to judge, within the imaginative supposition, “It is red”. This involves a general human capacity to transpose ‘online’ cognitive skills originally developed in perception into corresponding “offline” cognitive skills subsequently applied in imagination. That capacity is essential to much of our thinking, for instance when we reflectively assess conditionals in making contingency plans (See Williamson 2007: 137–78). No episodic memories of prior experiences, for example of crimson things, play any role. As a result of the process Norman accepts (Crimson). Since his performance was sufficiently skilful, background conditions were normal, and so on, he thereby comes to know (Crimson). Naturally, that broad-brush description neglects many issues. For instance, what prevents Norman from imagining a peripheral shade of crimson? If one shade of crimson is red, it does not follow that all are. The relevant cognitive skills must be taken to include sensitivity to such matters. If normal speakers associate colour terms with central prototypes, as many psychologists believe, their use in the imaginative exercise may enhance its reliability. The proximity in colour space of prototypical crimson to prototypical red is one indicator, but does not suffice by itself, since it does not discriminate between “All crimson things are red” (true) and “All red things are crimson” (false). Various cognitive mechanisms can be postulated to do the job. We need not fill in the details, since for present pur-

 Ibid, p. 295.  Melis and Wright quote entirely this very important passage of Williamson and I will follow them. 49 50

134

7  “Pure” Hale and Related Issues

poses what matters is the overall picture. So far, we may accept it as a sketch of the cognitive processes underlying Norman’s a priori knowledge of (Crimson). Now compare the case of (Who’s Who). Norman is as already described. He learns the complex phrase “recent volumes of Who’s Who” by learning “recent”, “volume”, “Who’ s Who” and so on. He is not taught any rule like (Who’s Who), connecting “recent volume of Who’ s Who” and “red”. Through practice and feedback he becomes very skilful in judging by eye whether something is a recent volume of Who’ s Who (by reading the title), and whether something is red. Now Norman is asked whether (Who’s Who) holds. He has not previously considered any such question. Nevertheless, he can quite easily come to know (Who’s Who), without looking at any recent volumes of Who’ s Who to check whether they are red, or even remembering any recent volumes of Who’ s Who to check whether they are red, or any other new exercise of perception or memory. Rather he assents to (Who’s Who) after brief reflection along something like the following lines. First Norman uses his skill in making visual judgments with “recent volume of Who’ s Who” to visually imagine a recent volume of Who’ s Who. Then he uses his skill in making visual judgments with “red” to judge, within the imaginative supposition, “It is red”. This involves the same general human capacity as before to transpose “online” cognitive skills originally developed in perception into corresponding “offline” cognitive skills subsequently applied in imagination. No episodic memories of prior experiences, for example of recent volumes of Who’s Who, play any role. As a result of the process Norman accepts (Who’s Who). Since his performance was sufficiently skilful, background conditions were normal, and so on, he thereby comes to know (Who’s Who). As before, the broad-brush description neglects many issues. For instance, what prevents Norman from imagining an untypical recent volume of Who’ s Who? If one recent volume of Who’ s Who is red, it does not follow that all are. The relevant cognitive skills must be taken to include sensitivity to such matters. As before, Norman must use his visual recognitional capacities offline in ways that respect untypical as well as typical cases. We may accept that as a sketch of cognitive processes underlying Norman’s a posteriori knowledge of (Who’s Who). 51

Williamson concludes: The problem is obvious. The cognitive processes underlying Norman’s clearly a priori knowledge of (1) and his clearly a posteriori knowledge of (2) are almost exactly similar. If so, how can there be a deep epistemological difference between them? But if there is none, the a priori  – a posteriori distinction is epistemologically shallow. (Williamson, ibid., pp. 296–97)

Jenkins and Kasaki observe: The similarities that Williamson notes concern primarily the cognitive processes or methods via which Norman comes to knowledge. So an alternative moral of Williamson’s discussion is not that there is something wrong with the a priori, but that a description of a subject’s cognitive processes or methods will not always suffice to enable one to identify the subject’s grounds or reasons.52

Note that Williamson’s examples are schematic though they are intended to pose a serious challenge to the distinction between a priori / a posteriori knowledge. If there is a superficial description of the cognitive processes involved in his examples,

 Williamson, ibid., pp. 295–96.  Jenkins, C. S. I., and Masashi Kasaki. “The Traditional Conception of the a Priori.” Synthese 192, no. 9, p. 2734, 2015, authors’ emphasis. 51 52

7.2  Empirical Indefeasibility as a Hallmark of the A Priori

135

then we only can see that there is a superficial difference between the two Norman cases. Let’s say “S knows that p”, and experience plays a role that is “neither purely enabling nor strictly evidential”, as Williamson says. What does it mean “not purely enabling”? Let’s say that an enabling role of experience enables the subject knower to acquire the necessary concepts and skills to know a proposition. Experience is supposed to be playing a role that is not purely doing that. What does it mean “strictly evidential”? Let’s say that a strictly evidential role for the truth that p is being part of the justification for the truth that p, and not simply being part of the background assumptions which are not part of the justification for p, but only allow the justification to be accomplished. So experience is supposed to not being playing a strictly evidential role. Is it playing a role that is evidential but not just evidential?, another additional role than evidential?, a mixed role?; or is it a role that is not enough to count as evidential? I think that empirical evidence converts any evidence in which it occurs as a proper part into empirical evidence, a mixed evidence of a priori and a posteriori components is considered empirical, a posteriori, not a priori. If experience is not enough to count as evidential, then it won’t be part of the justification for any knowledge (belief) that p. It won’t count as evidence (or part of the evidence) for p. Or is experience playing a role that is both enabling and evidential and that is why its role is not purely enabling nor strictly evidential? All this is obscure. The problem is that Williamson’s characterization of his examples is not clear enough. I agree with Casullo in saying: Williamson (296) acknowledges that he has offered only a “broad-brush description” that “neglects many issues.” Nevertheless, he (296) also contends that “we may accept it as a sketch of the cognitive processes” underlying both Norman’s knowledge of (1) and Norman’s knowledge of (2). Williamson, however, offers no evidence in support of that claim. It appears to be based entirely on his reflections from the armchair regarding how he acquires such beliefs. Such armchair reflection, however, does not constitute compelling evidence for a claim in cognitive psychology. At best, such reflection might yield insightful hypotheses about the underlying cognitive processes involved in coming to accept propositions such as (1) and (2). The hypotheses, however, cannot be confirmed on the basis of anecdotal evidence from the armchair. Empirical investigation is necessary.53

There is a question in contemporary epistemology about the relationship between the concept of justification and the concept of evidence. I consider that justification is more than evidence. We have evidence, we have to understand it, we have to apply it, possession of evidence is not enough, evidence is necessary but not sufficient, it is what we do with the evidence what counts as justification, so skills play a part, it could be the same skill learnt in experience, and applied to different contexts, contents, different types of propositions; so the a priori, being an epistemological

 Casullo, Albert. “A Defense of the Significance of the A Priori – A Posteriori Distinction” in D. Dodd and E. Zardini. Beyond Sense? New Essays on the Significance, Grounds and Extent of the A Priori.  The A Priori: Its Significance, Grounds, and Extend. Oxford” Oxford University Press, forthcoming, p. 13. 53

136

7  “Pure” Hale and Related Issues

notion, is not divorced, entirely, from the content of the propositions we know by their means; what is first needed is a strictly epistemological characterization of a priori justification (knowledge) that leaves open the modal and semantic status of the propositions known (justified). An a priori justification is independent of empirical evidence. A priori justification depends on experience in an enabling way, not in an evidential way. An a priori justification has different elements: ones related to experience, others independently of experience. It is enough to be a priori if experience does not play an evidential role in an a priori justification. The experience involved is taken as a background, not as part of the justification. Taking this background for granted is common to knowledge in general, either a priori or a posteriori. Clearly, when we are taking about empirical knowledge, empirical evidence, or empirical background assumptions, are not problematic. A priori knowledge (justification) can depend epistemically on experience. What is important is that it does not depend evidentially on experience. “Epistemic” and “evidential” roles are not the same. “Epistemic” is a broader concept than “evidential”. Casullo thinks: If we replace Williamson’s articulation of the concept of a priori knowledge with the traditional conception, it follows straightforwardly, that if S knows (justifiably believes) that p only if S can skillfully apply the concepts in p and S’s skillful application of those concepts depends constitutively on S’s past experience, then S knows (justifiably believes) a posteriori that p.

Casullo concludes: Therefore, both Norman’s knowledge of (1) and Norman’s knowledge of (2) are a posteriori. Our bottom-up understanding of the terms ‘experience’ and ‘evidence’ poses no obstacle to drawing this conclusion. Moreover, the conclusion should not be surprising or controversial. If Williamson is correct in maintaining that the cognitive processes underlying Norman’s knowledge of (1) and Norman’s knowledge of (2) are almost exactly similar and that both depend epistemically on experience, then both are known a posteriori. (ibid, p. 32)

But why skillfully applying a concept in imagination learned in past experience has to be considered a posteriori? I take it that Jenkins and Kasaki have a similar point: To make something in the vicinity of Williamson’s argument work, an extra premise would be needed to the effect that similarity of process entails … similarity of epistemic grounds or reasons. But this substantive claim stands in need of comparably substantive argument. (op. cit., p. 12)

Exactly. Similarity of cognitive processes does not entail similarity of cognitive outcomes. This substantive claim cannot be taken for granted but argued for. I disagree with Casullo. I think that, if Norman knows, then Norman’s knowledge of (1) is a priori and Norman’s knowledge of (2) is a posteriori. Recall that Williamson himself presents (1) as a clear example of a priori knowledge and (2) as a clear example of a posteriori knowledge, posing the challenge of distinguishing, clearly, between the two cases, given that they seem alike. What is needed is to explain the difference. Casullo, simply, takes it that they are the same.

7.2  Empirical Indefeasibility as a Hallmark of the A Priori

137

Applying the same skills in (1) and (2), assuming that they are the same, doesn’t mean, automatically, that the knowledge is a posteriori in both (in general, assuming that we are applying the same skills doesn’t mean, automatically, that the knowledge is of the same kind). Casullo, correctly, gestures at a distinction between epistemic roles and evidential roles in knowledge (justification), but he, incorrectly, does not apply this distinction to Norman’s knowledge of (1) and Norman’s knowledge of (2); and this application allows for (1) to be known a priori – since experience can play an epistemic role, in the sense that it has provided the experiences for learning the necessary concepts and skills to apply them, in our acquisition of a priori knowledge, but not the evidential role like being the proof or part of the proof, in the case of inferential a priori knowledge, or in our apprehension of a basic truth by reasoning alone – and (2) to be known a posteriori since experience plays an evidential role. Jenkins and Kasaki explain the difference between “epistemic” and “evidential” roles of experience: However, unless it is assumed that all there is to any epistemic role is evidential, it does not follow from the claim that experience plays an epistemic role that it plays an evidential one. One of us, in Jenkins (2008a), has argued for this point by noting that there is a gap between two negative conceptions of the a priori: (i) a priori knowledge as epistemically independent of experience, and (ii) a priori knowledge as evidentially independent of experience. The gap exists because (according to Jenkins) experience may be epistemically relevant for grounding certain concepts examination of which can lead to knowledge, but this concept grounding relation is different from the relation of evidential support (which is for a proposition or belief rather than a concept). (ibid, p. 2741; author’s emphasis) What is crucial for our purposes is that there is no apparent threat here to classifying the resultant knowledge as a priori in a deep and significant way. Since the role played by experience, while epistemic, is not that of justifying p, we are still at liberty to describe the justification for p as an a priori one, and this classification is as deep and significant as it ever was. (p. 2743; authors’s emphasis)

Melis and Wright54 proceed to embark in a very detailed analysis of Williamson’s examples. They reconstruct Williamson’s examples, create more needed examples along the lines of Williamson in order to make his argument more explicit and clear, they analyze the assumptions and consequences involved in the examples, and evaluate the strength of Williamson’s arguments. As Melis and Wright explain, it can’t be memory or recollection in Norman’s knowledge of Crimson what is involved because, by hypothesis, it is the first time that he is thinking and knowing it. No memory to recall. What we recall is the concept and the skill of applying it, both enabling roles. The only epistemically relevant features involved in Williamson’s description of the two Norman cases are the perceptual experiences necessary to develop Norman’s capacity to make reliable visual judgments with the expressions ‘red’, ‘crimson’ and ‘recent volumes of Who’s Who’.

54

 Melis and Wright, ibid.

138

7  “Pure” Hale and Related Issues

So, Williamson is offering an example where, so he claims, the very same type of cognitive process provides justification, and indeed knowledge, for both (Crimson), that all crimson things are red, and (Who’s Who), that all recent volumes of Who’s Who are red. If he is right, he has shown, at the least, that there is no important cognitive difference between one way of knowing the usually regarded a priori proposition, (Crimson), and one way of knowing the usually regarded a posteriori proposition, (Who’s Who). But of course there is an asymmetry in the traditional understanding of the notions. While an a posteriori proposition, traditionally regarded, is one which can only be known by, broadly speaking, empirical means, an a priori proposition, while it can be known a priori, may also be knowable a posteriori. So before Williamson’s example, even if we find no problem with his description of it, can put any kind of pressure on the distinction, it needs to be argued that Norman’s cognitive processes as described are not properly regarded as constituting an a posteriori mode of knowledge-acquisition. (ibid, p. 8)

We need to understand this intermediate role of experience involved in these examples, considering that there are a priori truths that can be known a priori and a posteriori. Williamson has to show that Norman’s cognitive processes are not cases of knowledge a posteriori. The second point Williamson wishes to use the example to make is that the traditional distinction between the evidential and the enabling role of experience in cognition misses an important third way in which experience can be involved in justification. This third way is tied to the knowledge-productive use of imagination in the kind of “offline” application of skills acquired through perception that Norman is meant to illustrate. (ibid, pp. 8–9)

The online application of the skills is acquired through perception; the offline application of the skills is produced in imagination. It is needed that: the parallel between Norman’s cognition in the two cases be given in sufficient detail to make it plausible not merely that he has done much the same thing but that in both cases he has done something by which he is properly convinced, and which – if nothing else goes wrong – could properly constitute the acquisition of knowledge. (ibid, p. 14) Williamson’s contention, then, is that the traditional distinction between cognitive processes in which experience plays an evidential role and cognitive processes in which it plays a merely enabling role is too crude – that there are significant cognitive processes, culminating in knowledge, in which the role of experience is more than enabling but less than evidential. (ibid, p. 9)

There is a discussion about this intermediate role of experience, some like Jenkins, accept it as such and try to explain it, others like Ichikawa think that this intermediate role can be accommodated as enabling role. I think that it does not matter one way or the other, whether we say that there is an intermediate role for experience or that we complicate the notion of enabling to include these cases and maintain the dual contrast between enabling and evidential in a priori knowledge. I will do the latter like Ichikawa. In my view, we don’t need a third intermediate role of experience but only complicating (enriching) the enabling role. In a very interesting passage, Miles and Wright connect this issue with the category of synthetic a priori, reviving this issue. Perhaps Williamson has reminded us, in short, of something characteristic about the methods of cognition that are relevant to the traditional synthetic a priori. In that case, it will

7.2  Empirical Indefeasibility as a Hallmark of the A Priori

139

simply have been a mistake – traceable perhaps to the legacy of positivism and the empiricists – to think of the a priori as exhausted by methods of cognition that demand only conceptual reflection or acquaintance with meanings. (ibid, p. 10)

Actually Jenkins and Kasaki also have some similar thoughts that Miles and Wright consider. Indeed, Kant’s approach to the distinction between the a priori and the posteriori may be capable of incorporating rather complex views about the involvement of the imagination, of the kind Williamson’s discussion brings to light. (op. cit., p. 2737)

I have entered into the roles of imagination in my Kant chapter. Jenkins and Kasaki, rightly, warn us to be careful in our understanding of these issues in Kant. Some caution is necessary here, as Kant’s usage of the term ‘imagination‘is diverse. He sometimes uses it in a relatively familiar way to refer to a faculty for imagining or conceiving possible objects. But he also sometimes uses the word ‘imagination’ in a technical way that has specific epistemological implications. Kant introduces imagination in his technical sense when addressing an important epistemological question: ‘How is the subsumption of [intuitions] under [pure concepts], the application of the category to appearances, possible?’ (A 137–8 / B176–7). For Kant, intuition or per ception is limited to sensory features of a singular object, but concepts are commonly applied to multiple different intuitions or perceptions. Imagination in the technical sense is a faculty which synthesizes different intuitions or perceptions so that they can be subsumed under the same concepts. In fact, according to Kant two distinct kinds of synthesis are performed by the imagination: (a) binding fleeting and transient perceptions as perceptions of the same object of a given kind, and (b) binding them as perceptions of objects of the same kind. (ibid, p. 2737)

Jenkins and Kasaki compare Williamson with Kant. Williamson seems to endorse (at least certain relevant aspects of) the traditional view, in that the content of Norman’s relevant experience (of red samples, crimson samples and copies of Who’s Who) is treated as singular and non-modal. If not, it is unclear why imagination would be appealed to at all in accounting for Norman’s knowledge of general propositions like (1) and (2). Imagination for Williamson, as for Kant, justifies the subject in moving beyond the limited contents of experience to something more general. (p. 2738) For the purposes of this paper, the most significant difference between Williamson and Kant is that upon noticing that the offline application of empirically honed skills in what he calls ‘imagination’ occurs in clear cases of both a priori and a posteriori knowledge, Williamson concludes that the a priori/a posteriori distinction is superficial and unimportant to epistemology. Whereas Kant, upon noticing a structurally similar point about the role of what he calls ‘imagination’ in both kinds of knowledge, sets about finding ways to navigate the epistemological complexity. One need not agree with the details of how Kant proceeds in this regard to find his kind of approach to the complexity more philosophically satisfying than Williamson’s. (p. 2740)

I completely agree with this important conclusion of Jenkins and Kasaki. Miles and Wright continue with their elaboration: In particular, if appeal to the reflective imagination is to count as conferring a priori knowledge only in cases where no episode-unspecific recollection is involved of what items are like which instantiate the concepts that the imagination makes play with, how many of basic arithmetical, geometrical, and a host of other types of claim are going to survive as knowable a priori? (op. cit., p. 13–14)

140

7  “Pure” Hale and Related Issues

If there is no need for specific memory, no particular experience is involved, it can count as a priori; or if there is a specific episodic memory involved, how essential is its occurrence? The point is to understand the generality in the example, the abstractness of the concept in a priori understanding. That’s Kant’s point and what Miles and Wright appear to be saying. I don’t think that conceding this much will reduce considerably the extension of the a priori. Miles and Wright articulate the processes involved in Norman’s grasps of the concepts of crimson and red. It is crucial to his purposes that Norman fully grasps the concepts of crimson and red, and yet prior to the episode in his imagination, that it have [has] been an open question to him whether all crimson things are red. The question is how, merely by imagining what is as a matter of fact a stereotypical shade of crimson, he somehow succeeds in closing the question off. What is it about the process that mandates his conviction? Why, now that for the first time he considers the question, and having visualised what is as a matter of fact a stereotypical shade of crimson, is Norman rightly inclined to discount the possibility that there might be other shades of crimson that are not red? How does the imaginative exercise make it plausible to him that there are no such shades? (ibid, p. 15)

Furthermore, Miles and Wright ask an important question: ‘What stops Norman making the incorrect, converse generalization that “All red things are crimson?’55 They point out that Williamson has not given enough detail of the cognitive processes involved in his examples Crimson and Who’s Who to discriminate between “All crimson things are red” (true) and the converse “All red things are crimson” (false), such that he has not made the case for the analogy between Crimson and Who’s Who. We had better suppose, therefore, that Norman has had no such feedback. He has merely become adept, by practice, in applying “crimson” to crimson things and “red” to red things. But how in that case, merely by visualising a typical case of crimson and, as it were, observing its redness, can Norman reach a rational conviction that all crimson things are red? Something epistemologically essential is clearly missing here: suppose the question had been, conversely, whether all red things are crimson, and that Norman had done exactly the same in response – imagined a shade of red that, as it might well be, was crimson; crimson is a pretty typical shade of red after all. What stops him making the incorrect, converse generalisation? That would not be a rational conviction. But Williamson has said nothing, in his account of Norman’s cognitive processing, to account for the difference. (p.15)

Miles and Wright conclude: None of that is true of the imaginative episode that convinces Norman of (Who’s Who). Even if we grant that Norman’s phenomenological routine is essentially the same for both (Square) [All squares are diamonds] and (Who’s Who), the reliability of the connection between what he does and the belief that he forms seems to have a quite different status in the two kinds of case: a difference which we can loosely summarize by saying that, in the (Who’s Who) case, any correlation between the process and the truth of the product is indeed wholly external – exactly as it is represented as being by Williamson’s evolutionary speculations – whereas in the case of (Square) it is not. That of course is exactly the difference we would expect if we were to regard what Norman does in the case of (Square) as a kind of informal proof of that proposition, and what he does in the case of (Who’s Who) as 55

 Ibid, p. 16.

7.3  Hale’s Assertions on A Priori Knowledge

141

a merely experimental operation. It’s natural to conjecture, therefore, that the real difference of importance marked by the a priori/a posteriori distinction as drawn bottom-up is to be located at this point. There may well be methods of corroboration that one can execute in the mind’s eye, as it were, whose products are, by bottom-up standards, ordinary a posteriori propositions. But their connection with the truth of those products will be external, and open to experimental corroboration. Not so with the relationship between a proof, even a “baby” proof, constituted by a simple informal routine in the imagination, and the truth of what is proved. In his notes posthumously published as the Remarks on the Foundations of Mathematics, Wittgenstein repeatedly returns to the question, what is the difference between a proof and an experiment? And his answer, roughly, is that the difference resides in the attitude we take to the relevant process. A majority, perhaps, will not much care for that answer, but the importance of the question for epistemology generally can hardly be doubted. It is an insight of Williamson’s discussion that some processes executed “in the head” can, in the right circumstances, provide experimental corroboration of ordinary empirical propositions concerning external matters. But that reflection does nothing to call into question the substance of the contrast between proving a proposition and experimentally confirming it. Perhaps a reminder is timely that it is that contrast that the traditional terminology of a priori and a posteriori methods of acquiring knowledge gestures at. (p. 21).

Let me explain. Cognitive processes can be similar applied to different things. Even if we accept that Norman’s phenomenological processes are essentially the same for Square and Who’s Who, the reliability of the belief he forms seems to be quite different in both cases. In Who’s Who, any correlation between the cognitive process and the truth of the product is totally external to the process. Whereas in the case of Square, it is not the case. In the case of a proof, even a “baby” proof, the relationship between the cognitive processes and its outcomes is a matter wholly internal to the process which does not require empirical corroboration. The authors are applying the distinction between proof and experiment that Wittgenstein discusses in his Remarks on the Foundations of Mathematics. Precisely, Melis and Wright’s application of Wittgenstein’s distinction between proof and experiment allows them to explain why experience does not play an evidential role in Crimson and Square while playing an evidential role in Who’s Who; particularly, why knowledge of Crimson is a priori and knowledge of Who’s Who is a posteriori.

7.3 Hale’s Assertions on A Priori Knowledge Let’s return to the issue of characterizing what is the a priori. Hale makes some assertions about a priori knowledge. It is important to get clear about what he means by them, i.e. what their status is. One of Hale’s assertions is the following: It would, obviously, be too much to require, for X’s knowledge that p to be a priori , that X could have known that p (or, better, could have come to know that p in the way he did), whatever his experiential background . We should certainly allow that experiences of certain kinds may be needed for X to acquire the relevant concepts requisite to entertaining the thought that p at all, but would not wish that to put the truth that p beyond X’s a priori ken. So, however precisely experience independence is to be cashed, it should be construed lib-

142

7  “Pure” Hale and Related Issues

erally enough for a priori knowers that p to have experiences sufficient for acquisition of the requisite conceptual repertoire. This may involve more than just the concepts explicitly involved in the thought that p; knowledge a priori that p may ... involve coming to appreciate that p by deducing it from other propositions known a priori -we need to allow X experiences sufficient for acquisition of concepts involved in his premisses, in cases of mediate knowledge a priori.56

The idea is that we have to allow room for certain experiences that may be necessary to equip ourselves with the necessary concepts to be able to entertain the thought that p in the first place. The experiences in question may also involve, in the case of inferential a priori knowledge that p, those that may be necessary for the acquisition of the concepts that appear in the premises. That is, experiences that may be necessary for concept acquisition have to be accommodated in an adequate notion of a priori knowledge. Another assertion Hale makes is: The obvious way to distinguish knowledge a priori that p from (undifferentiated) knowledge that p , where it is knowable a priori that p , is to require that the a priori knower’s justification for his belief that p should be independent of (all) experience save that which is needed for concept acquisition. We need the idea, that is, of a priori grounds for belief, or, ... of an a priori warrant.57

First, Hale is not providing a definition of a priori knowledge here, but rather a general principle that allegedly any definition of a priori knowledge should satisfy. Hale does not put this principle forward as a definition because he holds that a definition should specify positively what is going to define (i.e. its definiendum). For Hale, this principle is not a definition because it does nothing to elucidate the form of “independence of experience” characteristic of a priori knowledge. Another different matter is how to implement this principle. Second, Hale, following other writers like Kitcher, for example, takes the concept of an “a priori warrant” to be the basic concept in the epistemology of a priori knowledge. Hale agrees with Kitcher in requiring for the notion of “independence of experience”: The constraint imposed by condition (3b), of Kitcher’s analysis seems simply to be that a priori grounds should not depend for their cogency upon any specific features of the experiential background, and that seems reasonable enough.58 a priori grounds should not depend for their cogency upon specific features of the experiential setting in which they are invoked. So read, the condition is at least plausibly necessary for knowledge a priori that p.59

I take it that these assertions are consequences of the general requirement Hale imposes on any definition or elucidation of a priori knowledge which makes the

 Hale, ibid., pp. 127–8.  P. 128. 58  P. 134; my emphasis. 59  PP. 137–8. 56 57

7.4  Hale’s Preferred Notion of A Priori Knowledge in Abstract Objects

143

latter independent of experience, except in the sense of being dependent on those experiences which are necessary for the acquisition of the conceptual repertoire needed for a priori knowledge.

7.4 Hale’s Preferred Notion of A Priori Knowledge in Abstract Objects Hale makes another assertion – which I call (1) – that I understand as his preferred assertion about a priori knowledge. Hale agreed, in private conversation,60 that (1) would be the claim to work on if a satisfactory definition of a priori knowledge is to be elicited from the suggestions offered in his book. (1) For knowledge that p to be a priori, our justification for belief that p must not require the truth of any empirical statement.61

It is quite clear that (1) states at most a necessary condition for a priori knowledge. Condition (1) could be fulfilled without it’s being true that p, so it can’t possibly be sufficient as it stands. (1) could have been converted into a purported definition in the following way: (11) X knows a priori that p if and only if X knows that p and X’s justification for belief that p must not require the truth of any empirical statement.

Certainly the most obvious way to turn (1) into a sufficient condition also would be to augment it along the lines of (11). But, as we will see in chapter five, section one, there are problems with (1) and (11). Before I go into those, I shall make some remarks. (1) is intended to respect the distinction between two senses of defeasibility Hale spoke about. Hale says that the requirement formulated in the text (i.e. (1)) “accords with” Bennett’s suggestion. Hale expresses Bennett’s notion of an a priori statement, “judgment” in Bennett’s terminology (I suppose following Kant), as follows: A priori judgments are those which aren’t open to falsification by experience.62

Hale explains: Certainly it [Hale’s conception of a priori knowledge] accords with the suggestion ... that a priori judgments are those which aren’t open to falsification by experience – clearly, if our

 In private conversation, Hale explains that his main task in his chapter “Non-Empirical Knowledge” was the issue of revisability in connection with a priori knowledge and to respond to Kitcher who thinks that both are incompatible. Hale did not intend to provide a definition of a priori knowledge in his book. Rather his major task was to rebut Kitcher. 61  Hale, p. 138. 62  Hale, note 9, p.  259. For the suggestion, see Bennett, Jonathan. Kant’s Analytic. Cambridge: Cambridge University Press, p. 9, 1966. 60

144

7  “Pure” Hale and Related Issues

grounds to believe that p don’t require the truth of any empirical statement, the proposition that p itself must not have empirical consequences.63

Hale does not mean that as a matter of fact it is not going to be falsified. Clearly what is important (according to his proposal) is that the statement that p should not be open to empirical falsification at all. It will not be enough if it merely happens not to get falsified. Is there anything special meant here beyond “falsifiable”? There is a distinction between “open to falsification” and “falsifiable”. What is not open to falsification is, perhaps, a maxim (a moral rule). We don’t let anything to count against them. They are not open to falsification simply because they are not candidates for truth in the first place.64

 Hale, note 9, p. 259; my emphasis. It is not clear whether (1) and Bennett’s suggestion are logically equivalent. The problem is that Hale does not explain in his book what he means by “empirical consequences”. I think that what he means is that if a statement is a priori then it is not possible to derive from it any empirical statement by deduction. That is, from a priori statements alone one cannot derive any empirical statement. Empirical consequences seem to be empirical consequences obtained by deduction. According to this interpretation of the notion of “empirical consequence”, Bennett’s suggestion is rather a consequence of (1). My reason for this belief is the following: Hale thinks that if our grounds for believing that p don’t require the truth of any empirical statement, the proposition that p itself must not have empirical consequences. And if p does not have empirical consequences, it is not going to be falsified by experience. The consequent of the last conditional is Bennett’s suggestion. Let’s try the other direction: If a statement is not falsifiable by experience then it does not have empirical consequences. The problem is that this implication holds only if we accept at this stage that an a priori statement is characterized as not being falsifiable by experience. So we are begging the question. Let’s ignore this problem and assume that we can obtain this first conditional. Now another problem arises when we try to derive the second conditional: If a statement p does not have empirical consequences then our grounds for believing that p don’t require the truth of any empirical statement. The problem is that from a statement having no empirical (deductive) consequences nothing follows about its justification. That is, it does not follow that its justification does not require the truth of any empirical statement. Of course, the latter may characterize its a priori justification. (In any case, that is what Hale thought in the book.) However, even if an a priori justification for p could be characterized as one which does not require the truth of any empirical statement, it is left open at this point the possibility that our justification for p is as a matter of fact a posteriori given that we can obtain knowledge a posteriori of truths knowable a priori. So, if my interpretation of Hale’s notion of “empirical consequence” is correct, it follows that (1) and Bennett’s proposal are not logical equivalent. 64  It can be argued that moral principles don’t show the difference. They are not open to falsification, and they are not falsifiable. Of course, Hale is thinking only of statements which have truthvalues, but there is no harm in allowing the others if one wants the restriction to statements that have truth-value is important for (1) and (11). Otherwise one would know a priori that one ought not impose pain unnecessarily (moral rule). But even here, there are people who think those statements have a truth-value. 63

7.4  Hale’s Preferred Notion of A Priori Knowledge in Abstract Objects

145

Do “open to falsification” and “falsifiable” mean the same for Hale? Of course, they do not, but it is very possible that he didn’t take into consideration the difference in the book. Hale did not explicitly make any such distinction between “open to falsification” and “falsifiable“. He agrees (in private conversation) that one could and should make a distinction between statements which are not open to falsification of any kind because they are not candidates for truth at all (such as perhaps moral rules, or laws of the land (in contrast with putative laws of nature)) and statements which are. When Hale proposes that statements known a priori should not be open to empirical falsification, he is not saying that they should not be open to falsification at all. On the contrary, Hale meant to allow precisely for the possibility of their being shown to be false (and so falsified) by a priori considerations (just as Frege’s basic law V is shown to be false by the deduction of Russell’s paradox from it). Bennett affirms: ‘A priori’ and ‘a posteriori’ are among Kant’s hardest worked technical terms. His use of them is complex and many-layered, but all we need at this stage is the division of judgments into a priori and a posteriori on the basis of what risk a judgment runs of being falsified by experience. ‘Necessity and strict universality’, says Kant, ‘are ... sure criteria of a priori knowledge’. The context clearly implies that necessity and universality are entailed by apriority as well as entailing it. Thus, if the judgment that all Fs are G is a priori, then experience cannot render it false by yielding even a single F which is not G. If it is a posteriori, then it could be falsified by experience.65

In this quote we can see that Bennett does not use the term “open to falsification” at all. Bennett is talking in this passage about statements which are known (or knowable) a priori, and for a statement to be known a priori, it has to be true, and if it has to be true, then certainly it is a candidate for truth. Furthermore, given Kant’s view that the notions of a prioricity and necessity are coextensive, then a priori statements are necessarily true, and if so, certainly they are candidates for truth. Given Hale’s clarification of the understanding and acceptance of the distinction between “open to falsification“and “falsifiable“, then Hale was simply a bit informal in the passage quoted before and then Bennett and Hale’s proposals are both referring to the notion of “non-falsifiability by experience” rather than to the notion of “not open to falsification”. Let me now make a remark about their proposal so understood. It is a point of clarification. It might be argued (incorrectly) that Bennett and Hale’s claim that “a priori judgments are those which are not falsifiable by experience” is false.66 Consider the following statements: “A master criminal leaves no evidence of his crime” and “Bill Clinton is a master criminal”. The first is plausibly a priori – and indeed analytic – since a master criminal – a really accomplished criminal – has to  Bennett, ibid.; my emphasis. The reference to Kant is the first Critique, B 4.  Both Hale and Bennett refer to a priori judgments here. I talk about statements and propositions. Hale talks about judgments, statements and propositions in the same short passage, see note 9 p. 259. I assume that all these terms refer to the same thing. 65 66

146

7  “Pure” Hale and Related Issues

be good enough to ensure that he escapes detection. It follows that if the second is true, it will be undetectably true – since there won’t be any traces of Clinton’s criminality. So if the first is a priori, then the second, if true, will be unknowable. But I see no case for saying that the first is unknowable. So, the second is not falsifiable (or verifiable) by anything, and it is not an a priori statement. It cannot be an a priori statement because it is not knowable in the first place. Now this criticism is incorrect. Surely Hale (at least) meant only that if p is an a priori statement it is not falsifiable etc., i.e. he offered a necessary condition. The argument above assumes that non-falsifiability by experience is a sufficient condition for them, i.e., that non-falsifiability by experience is a necessary and sufficient condition for being an a priori statement. But non-falsifiability cannot be a sufficient condition for being an a priori statement because it has to be knowable too. For Hale, non-falsifiability by experience plus knowability of statements does imply their being a priori.

Chapter 8

Critical Examination of Hale’s Views on A Priori Knowledge

Abstract  In this chapter I will critically examine Hale’s proposals to characterize the notion of “a priori knowledge”. The chapter consists of three main sections followed by a conclusion. Only the first part of Sect. 8.1 is dedicated to Hale’s published work in contrast with the rest of the chapter. In section two I shall be dealing with the most recent developments where Hale (in seminars) proposes a new candidate, (H), for a definition of a priori knowledge. In section three I will closely examine whether it is coherent to talk of revision in connection with a priori knowledge – as Hale and other philosophers have thought – ending up with some remarks on the relationship between the notions of revision and a prioricity. In the concluding section I recapitulate the most important theses of this part of the book. Keywords  Empirical indefeasibility · Revision · Experience · Evidence · Preconditions for knowledge

8.1 A Difficulty Involved in Hale’s Proposal in Abstract Objects The suggestion I want to consider in this section is prefigured in the following claim of Hale’s: (1) “For knowledge that p to be a priori, our justification for belief that p must not require the truth of any empirical statement.”

Again, we can straightforwardly convert (1) into a purported definition in the following way:

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 I. Fred-Rivera, A Historical and Systematic Perspective on A Priori Knowledge and Justification, Philosophical Studies Series 151, https://doi.org/10.1007/978-3-031-06874-4_8

147

148

8  Critical Examination of Hale’s Views on A Priori Knowledge

(11) X knows a priori that p if and only if X knows that p and X’s justification for her belief that p must not require the truth of any empirical statement.1

Is this acceptable? Clearly, some qualification is going to be needed. What is it for a justification not to require the truth of any empirical statement? Consider the case of a purely mathematical or logical proof that P. (I assume that P is the conclusion of some proof). Here there will be, to be sure, no role for any empirical statement as a premise. But my justification for believing P, when so proved, will still require the truth of empirical statements like “I have followed a proof that P”, “I am competent to follow proofs of this kind”, and so on. Without justification for the truth of empirical statements of this sort, I should simply have no justification for the proved proposition, even in the face of the most straightforward and rigorous proof.2 This is one of various problems with (1) and (11), but I shall begin with perhaps a more immediate difficulty. The principal problem with this kind of proposal is circularity: we can’t yet be presumed to know what an empirical statement is, if our business is to explain what an a priori statement is – it is no good giving an account of a prioricity which simply makes an unreconstructed use of the idea of a statement’s being empirical.3 Of course the characterization can still be correct (though I shall raise doubts about that too) – the circularity problem has to do with whether or not it is explanatory. Does Bennett’s version escape the circularity criticism? We will see shortly.

8.1.1 Hale’s First Reaction to My Circularity Objection to (1) (and (11)) In private conversation as a reaction to my circularity objection, Hale proposed to give up the attempt to provide a definition of a priori knowledge. He suggested that we have instead to look at the concept in application. When we try to define, we try to provide necessary and sufficient conditions that do not appeal to notions which  I am following closely Hale’s original formulation of an a priori justification (warrant) in his book in constructing the right hand side of (11). Now we can express the same thing by inserting “does” instead of “must” resulting in: 1

X knows a priori that p if and only if X knows that p and X’s justification for her belief that p does not require the truth of any empirical statement. No modality is needed on the right-hand side of (11). What the right-hand side of (11) is saying is just that X’s justification is independent of experience only if the justification does not require the truth of any empirical statement. There is no point in the “must”. 2  I will elaborate on the distinction between a justification for p and a justification for my belief that p in pp. 258–59. 3  I recognize that, in general, it is possible to know what an a priori statement is (an a priori statement being a nonempirical statement) given that we have a clear characterization of what an empirical statement is. But at this point of the discussion of Hale, we cannot know what an a priori statement is in this manner since we don’t yet know what an empirical statement is.

8.1  A Difficulty Involved in Hale’s Proposal in Abstract Objects

149

are close enough to the term to be defined. For example, the notions of analyticity and synonymy are too close. One ought not to appeal to each other in trying to define these notions. According to Hale, the situation with the notion of a prioricity is analogous to the situation with the notion of analyticity. For Hale, being definable is not a condition for making sense. That a notion is not definable does not mean that it is not explainable. Furthermore, being explainable, providing an explanation, does not amount to providing a definition. It is possible that an explanation of the notion would crucially consist of providing examples and comments on the examples. Hale also suggests that the task is to get somebody to understand what it is for a statement to be subject to empirical revision or a priori revision. The suggestion is to explain the notion of a priori knowledge in terms of the kind of revision to which it is vulnerable, instead of defining the way we positively know a priori. We need an explanation of how there can be a priori knowledge. It may not matter that the a priori cannot be defined, but only explained. Now the task at hand is to characterize the notion of an a priori warrant in a way that is less circular – it may be that we can only reason in circles – or to get a bigger circle in order to shed more light into the concept of an a priori warrant. The task is to try not get the circle so quickly, as Hale does, such that we don’t remain without clarification of the concept of an a priori warrant. To this task I shall return in the next chapter. But, for now, let me discuss Hale’s more recent proposals to rebut my circularity objection.

8.1.2 Some Developments of (1) The worry about circularity in connection with any appeal to the idea of an empirical statement in a purported account of the a priori, is simply that it is not clear how to understand the empirical except as the complement of the a priori. If “empirical proposition” were to mean, roughly, “proposition not knowable a priori”, we would have a very small circle indeed. That suggests that we might improve matters by saying a little more about what qualifies a statement as empirical. The following modification of (1) (and (11) respectively) can be suggested to avoid the charge of circularity. First: (12) For knowledge that P to be a priori, our justification for belief that P must not require the truth of any statement Q such that Q is falsifiable by experience. Second: (1 ) X knows a priori that P if and only if X knows that P and X’s justification for belief that P must not require the truth of any statement Q such that Q is falsifiable by experience. 3

That is, the proposal is to substitute “statement falsifiable by experience” (or “experientially falsifiable statement”) for “empirical statement” in (1) (and (11)).

150

8  Critical Examination of Hale’s Views on A Priori Knowledge

This follows exactly the path suggested by my comment earlier on Bennett’s version. Are these new proposals an advance? (12) avoids circularity because it implicitly explains what an empirical statement is without appealing to the notion of an a priori statement, characterizing the empirical as what is disconfirmable by experience. This avoids circularity because the bargain was not supposedly to explain what experience is (that was taken for granted), but rather what “independence of experience” is. (12) (and (13)) may be vague – they don’t say what “experience” is – but at least they do not involve a vicious circle. We cannot define everything. Sooner or later we must rest upon something undefined. Can we develop this further? For instance, might (12) be simplified to: (2) X knows a priori that P only if the proposition that P cannot be falsifiable by experience. One concern with this is that we do not wish to exclude the possibility of a posteriori knowledge of propositions known a priori. (2) might seem to risk violation of this constraint. I suspect that this was what Hale probably had in mind4 when he did not offer (2) straight away. But it is incorrect to think that (2) excludes knowledge a posteriori of truths knowable a priori. Let me explain. Assume (2) is correct, and that the categories of knowledge a priori and knowledge a posteriori are exhaustive. Then it might seem that the following principle would hold for knowledge a posteriori that p: (3) X knows a posteriori that P only if the proposition that P is falsifiable by experience. From (2) and (3), it would indeed follow that if it is knowable a priori that p, then it is not knowable a posteriori that P. (3) clearly precludes knowledge a posteriori that P when P is a proposition knowable a priori. Now, it is not clear that one has to accept (3) just because one accepts (2). But, first of all, what would be wrong with just accepting (3)? (3) affirms that a posteriori knowledge is only knowledge of propositions that can be falsified by experience. Then, a priori propositions cannot be known a posteriori. Since it is presumably desirable to leave room for knowledge a posteriori of propositions that can also be known a priori – we don’t want to exclude knowledge of a priori propositions based upon testimony, for example – we have to reject (3). It is clear at any rate that (3) does not follow from (2). The logical form of (2) is: If P then not Q, while that of (3) is: If R then Q. (12) would be paralleled by the following characterization of a posteriori knowledge: (31) X knows a posteriori that P only if X’s justification for P requires the truth of some experientially falsifiable statements.

 P. 138.

4

8.1  A Difficulty Involved in Hale’s Proposal in Abstract Objects

151

(Note that the consequent of (31) is the contradictory of the consequent of (12)). (31) would, in any case, avoid the undesirable exclusion of the possibility of a posteriori knowledge of truths knowable a priori.

8.1.3 Problems with (12) and (13) First of all, the notion of “require” in the formulations (12) and (13) is unclear. What does it mean for a justification to require the truth of a statement? What should “require” mean in the formulation? Let’s distinguish two cases: (A) A justification for P requires the truth of Q just in case the justification proceeds by inference to P from a set of premises which include Q. The evident problem with this is that not all our a priori knowledge is inferential. So no constraint is imposed by (12), so interpreted, on non-inferential a priori knowledge; equivalently, no distinction is yet made from non-inferential empirical knowledge. To see this, suppose we interpret (13) along the same lines. And let’s take a non-inferential belief: say, “I am sitting comfortably” or “I am holding a pen in my hand.” Clearly the proposal is too broad. Any non-inferentially known proposition would count as known a priori because – being non-inferential – it does not require the truth of any other empirical statement other than the truth of itself, of course. Any proposition based non-inferentially on my memory, or on my sensory states, would qualify. So, (12), so interpreted, could not provide the basis for a biconditional account (it cannot be transformed into (13)). It only would provide for a necessary condition for a priori knowledge: X knows a priori that P only if X’s justification for belief that P is not given by inference from any statement Q such that Q is falsifiable by experience.

What is the problem with leaving matters there? It is that if we only offer a necessary condition for a priori knowledge, we leave it open what it would take for there to be any instance of knowledge of this kind. Obviously, the matter is not left entirely open since the necessary condition means that something won’t count as a priori knowledge if it does not satisfy the necessary condition. I said that I intended to offer no argument that there is such knowledge. But it certainly is on our agenda to try to explain what such an argument would have to accomplish. This demands that we offer a sufficient condition for knowledge to count as a priori. Another possible interpretation of the term “require” in the formulations is: (B) That I have justification for P is inferred from Q as a premise (possibly among others). If “requires” is interpreted more liberally – if the requirements of a justification of P are not just any premises which that justification utilizes but include certain collateral beliefs – for instance, in one’s own competence – on which justification for P may depend, then (12) is surely too demanding a condition to impose on a priori

152

8  Critical Examination of Hale’s Views on A Priori Knowledge

knowledge. For instance, Q might be a statement of the collateral conditions5 that have to obtain in order for me to be justified in accepting P; say, “I am not dreaming”, “I am paying proper attention”, and so on. Any account incorporating (12) with “requires” interpreted along these lines will be too strong. It will demand that there are no collateral conditions on a priori knowledge. This would be an unreasonable requirement. Even a priori warrants call for the satisfaction of conditions concerning the appropriate cognitive functioning of the knower. There is a possible objection to this second reading of the term “require”. That is: I don’t need to claim that “I am justified in accepting P”. The answer is that the preconditions obtain even if one does not state that they are. Moreover, given that these preconditions can always be expressed in the form of statements, then the point vanishes. It is the concern which has emerged about non-inferential a priori knowledge that motivates introduction of the simplification (2) above.6 It is important to realize that in (2), “Q” is gone. So this formulation promises to help avoid the problem of non-inferential beliefs coming out as a priori. For this reason (2) cannot just be a simplification of (12). Could we build the account we need on (2)? No: (2) cannot provide for a suitable biconditional because the result would be to conflate knowledge a priori with a posteriori knowledge of truths that can also be known a priori. Let me explain: (2) X knows a priori that P only if the proposition that P is not falsifiable by experience. (21) X knows a priori that P iff X knows that P and P is not falsifiable by experience. The right hand side of (21) is satisfiable by X’s a posteriori knowledge of truths known a priori by X; and it will then be equivalent to her a priori knowledge that P, for example. (2) does not have that consequence if it is understood only as a necessary condition.

 Collateral conditions are background empirical conditions that have to obtain in order for a subject to be justified in believing a proposition. I have called them also “preconditions”. They do not belong to the justification for p, that is, they don’t function as premises in an argument for p. Rather they are outside the argument, so to speak, functioning as background empirical assumptions (or conditions) for my being able to respond to the argument by believing that p. Since these background assumptions do play a role in my believing that p, they can be part of the explanation of why I failed to know that p. That is, background conditions expressed in the form of statements can be called for explaining why I didn’t manage to know that p, if that were the case. 6  Remember that (12) does not put any constraint for non-inferential a priori knowledge. So any non-inferential belief comes out as being knowable a priori since any non-inferential belief does not require the truth of any empirical statement (apart from the truth of itself). (2) adds the condition for knowledge a priori that p, that p itself cannot be falsifiable by experience. (2) rules out basic empirical knowledge coming out as a priori since p itself would be falsifiable by experience, so it would not satisfy (2). 5

8.2  A Revised Account

153

8.2 A Revised Account In response to the difficulty that (12) fails to distinguish between non-inferential knowledge a priori and non-inferential knowledge a posteriori Hale has suggested (in private conversation) the following proposal: (H) X knows a priori that P iff X knows that P and neither X’s justification for believing that P nor P itself implies (entails) the truth of any experientially falsifiable Q. This is designed to handle both problems emphasized in our discussion so far. First it leaves room for the possibility of a posteriori knowledge of truths which are also knowable a priori. For while (H) imposes a necessary and sufficient condition on an a priori justification for believing that P, it does not say anything about the range of the a posteriori. Second, (H) distinguishes between non-inferential a priori knowledge and non-inferential a posteriori knowledge since the definition does put a distinctive constraint on non-inferential knowledge that is a priori: viz. P itself cannot imply (entail) the truth of any experientially falsifiable Q. When Q is P, since P implies itself, P also cannot be falsifiable by experience. In contrast, in the case of non-inferential a posteriori knowledge that R, say “I am sitting comfortably”, since R implies itself and R is an empirical statement, R is falsifiable by experience. Since R is falsifiable by experience then it won’t satisfy the condition that R does not imply (entail) the truth of any experientially falsifiable proposition. So, non-­ inferential knowledge of R won’t count as non-inferential a priori knowledge.

8.2.1 Some Remarks About (H) When one knows a priori that p, and one’s knowledge that p is inferential, then one knows that p because one has a sound proof that p. When one doesn’t know that p, something has happened. For instance, (1) the purported proof is unsound. (1) would be an a priori reason to reject the alleged proof. (2) the proof is sound, but we don’t understand it. (2) is a partly empirical reason: one may be not intelligent enough; and a partly a priori reason: the proof is too difficult. (3) regardless of the soundness of the proof, there is unkind evidence and one doesn’t believe that p. So, one doesn’t know that p. In (3) one entirely drops belief that p. (3) is different from the case when one has unkind empirical evidence but still manages to believe that p. It is just that one is not

154

8  Critical Examination of Hale’s Views on A Priori Knowledge

very sure about it. If one manages to believe that p and the alleged proof is in fact sound, then one knows that p, even when one is not sure that one knows that p. Then, when one knows a priori that p, the empirical evidence concerning the prevailing circumstances, like one’s state of mind, is assumed. For example, when I know (a priori or otherwise) it is assumed that I am not too drunk. But that does not mean that it does not come into play in this context. It has a role, and since that role is assumed, it is taken for granted, one doesn’t state the prevailing empirical circumstances in the form of empirical statements to which one’s a priori knowledge in fact is dependent upon. That is precisely why it is not incoherent to appeal to these empirical reasons or considerations when things go wrong; they can be part of the explanation why things went wrong. That is, when I don’t know that p, it can be due to a priori reasons or empirical ones, or both, as examples (2) and (3) suggest. The empirical prevailing circumstances that were taken for granted when I thought I knew a priori that p would be clearly stated and tested since they could have a role in explaining why I did not succeed in knowing (a priori) that p. Is the justification for p the same as the justification for our belief that p? I don’t think so. I want to distinguish between the conditions for the existence of a justification and the conditions for rightly taking a justification to justify her in believing that p. For example, conditions for the existence of a justification, let’s say, a calculation which justified some arithmetical proposition entirely concern what is permitted by the rules of arithmetic, and thus involve no element of contingency. But rightly thinking oneself justified by what is in fact a correct calculation may well involve empirical presuppositions about oneself and the prevailing circumstances (that one is not confused, or too drunk, and so on.) Accordingly, I distinguish between the role assumptions can have in connection with our a priori knowledge: (1) In justifying the conclusion of a proof in the reasoning itself (2) In justifying my belief that I have a proof. Of course, the statement “I have a proof” is an empirical statement, and depends for its truth on empirical assumptions, for example, that I did not make any mistake in carrying out the proof. My knowledge is empirically defeasible. Let me illustrate. The statement “I am not good at proofs” can undermine my warrant (my purported proof) for p, but not undermine a proof for p. If I am not good at proofs, and I in fact made a mistake in carrying out a proof, my warrant is not a token of a proof. So, my warrant is defeated by the experience of having made the mistake, even if I don’t realize it. Of course, a proof is not defeasible at all. It is actually indefeasible: since a real proof is a sound argument, it is not possible to defeat it in any way. Likewise truths cannot be falsified. What is always defeasible are the ways we come to believe truths (or propositions). At this point, I propose to distinguish between two senses in which empirical evidence can defeat items of a priori knowledge. It is one thing to have empirical evidence against an a priori warrant. It is another thing to have empirical evidence against an a priori statement. That is, one sense is when empirical evidence shows that an a priori warrant for a statement is not good. Another is when empirical

8.2  A Revised Account

155

evidence shows that an a priori statement is false. It seems that it is more plausible that an a priori warrant can be undermined by experience than an a priori statement can be undermined by experience. Again, the fact that I am not good at proofs can undermine my purported proof. Someone could ask: But how can we know that a statement is false if it is not by showing that we did not have a real warrant for it? Through the warrant, we can know the truth or falsity of the statement. The answer is that even though we can only know that we don’t know a statement by learning that we failed to have a good warrant for it, that we failed to have a good warrant is not sufficient to show that the proposition itself is false. There may be another warrant that we still don’t possess. Naturally, Hale could simply restrict the non-falsifiability by experience requirement to a priori statements. That is perfectly in order since in any case the properties of falsifiability /non-falsifiability can only be meaningfully applied to statements, and not to warrants (rather defeasibility is a property of warrants). But it is implicit in Hale’s view also that a priori warrants are themselves indefeasible by experience, though he admits at other times that empirical evidence can be incidental in our knowledge of their defeat. In my view, making the appropriate clarifications, Hale’s position is compatible with (1) accepting the defeasibility of a priori warrants by experience and (2) the non-falsifiability by experience of a priori statements. But then, the first cannot imply the negation of the second: that is, when an a priori warrant is defeated by experience, it does not follow that the statement it justified has been falsified; there may be another (better) a priori warrant for the same statement. (Though if there is an a priori warrant for its denial, and we possess it, then it seems that the original statement has been defeated by experience when the original a priori warrant is defeated by experience. But we only say that the original a priori statement has been falsified when we find the a priori warrant for its denial.) The real difficulty is that the requirement of non-falsifiability by experience of a priori statements may be too strong. There seems to be a tension between the claim that a priori statements are indefeasible by experience and the possibility of having a posteriori knowledge of some a priori statements. It appears that Hale’s view would be more plausible if in the case of a priori knowledge, knowledge as well as refutation (defeat of warrants; falsification of statements) were an entirely a priori matter. But things get complicated because that does not seem to be the case. We have presumably a posteriori knowledge of truths that can also be known a priori. How can we reconcile Hale’s claim that a priori statements are nonfalsifiable by experience when we can have a posteriori knowledge of some of the statements that are knowable a priori too? Again, I think that Hale would say that in the case of alleged a posteriori knowledge of truths known a priori, the empirical considerations could only defeat the warrant (empirical), but not the proposition. I consider that falsifiability seems too narrow a concept. Hale and Field are wrong in insisting on falsifiability. For instance, in the sciences, very rarely general statements are actually falsified. I propose to focus on revisability instead, where revisability is more general than falsifiability. One might have reasons to revise certain statements, even if they are not falsified in a strict sense, for example for pragmatic reasons such as simplicity.

156

8  Critical Examination of Hale’s Views on A Priori Knowledge

Nevertheless, if Quinean confirmation holism is true, then there can be collateral empirical evidence against an a priori warrant or an a priori statement, for example, against the Parallel Postulate.7 For Quine, since any statement can be revisable by experience, and it is his view that a priori statements are not supposed to be revisable by experience (even more, they are not supposed to be revisable; they are supposed to be true “come what may”) it follows that there can’t be any. In contrast, for Hale, an a priori statement may not be true at all. According to Hale, in order for a statement to be a priori: (1) it has to be justifiable by an priori warrant; or (2) it has to be revisable only by a priori reasons. It seems that I need an example of an a priori proposition with the following logical form: A universal proposition: For every x, if F(x) then G(x), where F and G are empirical predicates. How can there be empirical undermining of a universal a priori proposition, all F’s are G, where F and G are empirical predicates? I take it that by an “a priori proposition”, it’s here meant a proposition for which there is some – perhaps defeasible – a priori warrant. The answer is the following: Such a proposition can be indirectly undermined if it participates in a theory which is running into difficulties – making false predictions, though not necessarily ones which involve either of the concepts, F and G – and when the best way of modifying the theory so as to restore its success is to junk that particular generalization. This of course is the kind of possibility that Quine always has in mind. But also I don’t see in general why there shouldn’t be the possibility of direct disconfirmation: the Euclidean Postulate of Parallels, for example, is equivalent to the thesis that the interior angles of a triangle always have the sum of 180 degrees. So the counter-evidence might just take the form of our measuring up lots of triangles and finding that their interior angles tend not to so sum up. Of course there will still be the possibility of saying that what we are measuring are not really triangles – that their sides are not really straight, for example. But they might perfectly well seem to be straight by whatever operational criteria we had. If we say, “still, they are not really straight”, then we make a move that is always possible to make if we want (perhaps irrationally, or dogmatically) to protect a hypothesis against disconfirming evidence. One can always deny that one is dealing with genuine F’s if some of them seem not to be G, and fall back on the fallibility of one’s methods for determining whether or not something is F in order to protect that denial. Likewise, simple arithmetical generalizations – say, whenever there are exactly seven F’s and exactly five G’s, then there are twelve F-or-G’s – might be disconfirmed by counting. One counts the F’s and get seven, one counts the G’s and get

 Roughly speaking, confirmation holism, as I understand it, is the thesis that knowledge is a system of interconnected beliefs such that changes in beliefs in one area of knowledge can have repercussions in other areas. Confirmation holism per se is not a problem, at face value at least. We have to distinguish between confirmation holism and Quinean holism. Confirmation holism is compatible with the view that the a priori is revisable only by a priori reasons. In contrast, Quinean holism is not so compatible. Quine does not specify what sort of revisions statements are vulnerable to. The reference here is Quine’s “Two Dogmas”. 7

8.2  A Revised Account

157

five, one counts the F-or-G’s, and get thirteen! Again, one can protect the original hypothesis by saying that there must have been a miscount, or that the number of things being counted must have changed somewhere along the line, etc. But, again, these are moves that can always be made if one wants to protect a hypothesis against disconfirmation. Nothing special about the a priori case here. In general, I see no problem about how a hypothesis which can be warranted a priori might be empirically disconfirmed. The point is not that there is no sense to be made of the idea but, rather, that we don’t in general allow empirical disconfirmation of such propositions. The difficulty is not in the very idea of a collision between what the a priori warrant suggests and what the empirical data suggest. It is rather that in general we regard the a priori warrants as dominant. But is there any reason why we always have to do so, specially if we are concerned with cases where there is no rigorous explicit proof and the a priori warrant is rather a matter of appeals to what we think we can conceive, and the like? Quine urges that no statement is immune to revision. But a defender of a prioricity need not wish to resist the suggestion that logic, or other disciplines conceived to involve a priori statements, are revisable. There should be no interest in maintaining that we cannot be in error in judging a statement to have that status. Can we therefore give Quine the claim that any particular statement which we accept as a priori could, in certain circumstances, reasonably be discarded? To grant the claim need be to grant no more than that our assessment of any particular statement as a priori may always in principle turn out to have been mistaken. I say “there should be no interest in maintaining that we cannot be in error in judging a statement to have that status”. What is the status exactly? Suppose we have an apparent a priori warrant for a particular statement, the Euclidean Parallel Postulate, for instance, which then runs into trouble in the context of empirical theory. Now certainly, a defender of the a priori should not have any interest in maintaining that our recognition of a priori warrants is infallible. And it may be that, in the kind of situation described, when we look again more carefully at the warrant, we find it contains mistakes or oversights. It is important to point out that a defender of the a priori who really wants to leave her position consistent with everything Quine says must do more than accept the fallibility of the epistemology of the a priori: she must allow, in addition, that a claim can be genuinely warranted a priori and yet still defeated by experience. Then there may have been nothing wrong with an a priori warrant except that the statement it warranted was a statement that was destined to be overturned in the light of wider, broadly empirical considerations. That is the same as saying that a priori warrants can be inconclusive, so that commitment is not just to admitting the fallibility of our appreciation of the a priori, but also to admitting that some a priori warrants provide less than conclusive grounds for what they warrant. The latter is not implausible when the a priori warrant is based on the mixture of imaginative and visualizational considerations which probably motivated defenders of the Euclidean Parallels Postulate. But it is less plausible in other cases, and I would presumably have to exclude examples of warrants acquired by infallible methods in the sense I discuss in Part Three. So if Quine’s thesis is that absolutely

158

8  Critical Examination of Hale’s Views on A Priori Knowledge

any statement may be revised without any implication that an original warrant for it was flawed in its own right, it is tantamount to the contention that there are no infallible a priori methods. It does mean that the account I will offer in Part Three cannot be fully consistent with the view I am ascribing to Quine as long as some a priori methods are infallible.8 Though Hale’s notion of a priori knowledge is compatible with revision, it does not admit revision of a priori statements by empirical reasons. It is interesting to note that Hale affirms that given that a priori routes are not infallible, agreement in results diminishes the chances of making mistakes.9 But Hale resists the following idea: that if we made a mistake, better to know it, in whatever way possible, by an a priori or an a posteriori route, it should not matter. In my view, there is no need to compromise to a view of a particular kind of defeasibility of a priori warrants and a priori statements. I shall expand on this issue in the next section.

8.2.2 Problems with (H) I shall outline no less than three difficulties with this proposal. Two are due to remediable shortcomings of formulation, but one seems deeper-reaching. (1) (H) does not say anything about how we might come by non-inferential a priori knowledge. Hale does not say that all justification is inferential. (H) allows for non-inferential a priori knowledge but it does not say anything illuminating about it. (Though, of course, this is a problem for everyone and not specific to Hale’s proposal.) (2) (H) talks about a priori known propositions. It would be desirable to include a priori knowable propositions also. This is desirable because we want to single out a class of truths with a certain feature. The distinction that interests us is not between truths that happen to be already known a priori and those known a posteriori. Rather we need a distinction that does not rely on what we contingently happen to know but draws on a feature that necessarily belongs to this class of truths. The matter is easily resolved. It is a basic logical point that when one puts a condition for something to be something, for example: Q iff … ,

 It is very implausible to suppose that the simplest items of (what we regard as) logical and mathematical knowledge might rationally be dumped in the light of holistic empirical considerations. What about the law of non-contradiction, for instance? Surely any rational empirical methodology, even that of sections five and six of “Two Dogmas”, must presuppose certain logical principles and put them in a position of privilege. And surely some principles like modus ponens, non-contradiction, etc., will always be so privileged. It seems a satisfying epistemology of logic should explain this. 9  Hale, note 12, p. 262. 8

8.2  A Revised Account

159

we can infer from it the following statement: It is possible that Q iff it is possible that ...

Thus from (H) we can obtain the following as a simple logical consequence: (H*) P is knowable a priori iff P itself implies (entails) the truth of no experientially falsifiable Q and it is possible for a thinker X to know that P on the basis of a justification which requires the truth of no experientially falsifiable Q.

Note that (H) and (H*) do not presuppose that there are known a priori truths, or that there is a priori knowledge. (H) and (H*) only put a condition for knowledge to be priori; it may not even be satisfied by any instance of knowledge. Let me stress again that a definition of a priori knowledge merely states the necessary and sufficient conditions for knowledge to be a priori. It does not follow from such a definition that there actually can be a priori knowledge but only that if there is any instance of knowledge that satisfies the conditions stated on the definition, it would count as a priori. When I have insisted that the conditions for a priori knowledge have to be sufficient as well as necessary what I have intended to convey is that we need to come up with conditions which, if satisfied, are able to determine whether instances of knowledge are a priori. The present project is to work towards an explanation of what it would take for there to be a priori knowledge; but the possibility is still open that, when we have such a characterization, we shall see that it applies to nothing. (3) Perhaps the notion of a priori knowledge can be circumscribed by (H) and (H*), but it may be empty. The problem is that if a holistic view is right, then there won’t be any instance of a priori knowledge that could satisfy Hale’s proposals. The reason is that there won’t be any statement that is not in principle revisable by experience. It is a consequence of Hale’s account that an interest in a priori knowledge is incompatible with Quinean holism. Hale endorses10 the traditional conception of the a priori as what is not only independent of experience in terms of justification, but also what can only be revised, i.e. shown unsound or false, independently of experience as well. A serious consequence of Hale’s definition of a priori knowledge is that is incompatible with Quinean holism. If Quine’s epistemological holism is right, Hale’s notion of a priori knowledge would be empty. And that would be problematic because those who are interested in the possibility of having a priori knowledge would have difficulties in accepting any attempted definition of a priori knowledge which cannot render as knowable a priori, or perhaps more immediately important cannot render them as known a priori, the truths we would like to regard as such. Much of the motivation for a search of a definition, or an elucidation, of the concept of a priori knowledge is to get clear about how we can explain our knowledge of many propositions, like mathematical and logical propositions, without looking at the world. Thus, given that it is an open question whether we are going to have empirical evidence against an priori statement, better to be more cautious and do not hold a 10

 Note 9, p. 259, and p. 148.

160

8  Critical Examination of Hale’s Views on A Priori Knowledge

position like Hale’s which is incompatible with Quine from the start. Now if it is to follow from our best characterization of a priori knowledge that there can be no such thing, it ought at any rate not to follow so immediately or quickly!11

8.3 Is It Coherent to Talk of Revision in Connection with A Priori Knowledge? There is an important distinction to be drawn between “a prioricity” and “a priori knowledge”. Actually, I find that this basic distinction has been overlooked in the literature, or at least, has not been made explicit. I myself came up with it in my attempt to make sense of the idea that it is possible to talk of revision in connection with a priori knowledge, or what I take to be an equivalent claim in the literature, that of not requiring unrevisable belief in connection with a priori knowledge (or the same thing that a priori knowledge does not require unrevisability).12 This simple way of talking is indeed quite misleading, and I find that proposing the distinction between “a prioricity” and “a priori knowledge” resolves the tension which many have overlooked. For example, Paul K. Moser affirms13 that one of the necessary conditions for an instance of knowledge of a proposition’s truth to be a priori (what he calls “minimal” a priori knowledge) is that the evidence (a priori) in question “makes the proposition in question more likely to be true than its denial.” (my emphasis; p. 2) Moser also affirms that a priori knowledge does not require epistemically unrevisable belief. A justified belief is epistemically irrevisable, let us say, if and only if it would not be epistemically rational to give up that belief under any circumstances, including circumstances where the world is radically different. It is epistemically rational to hold such a belief come what may. Clearly, minimal a priori knowledge does not require epistemic irrevisability, since such knowledge is compatible with the fact that one’s a priori justifying evidence  Although the tension between Quine’s holistic empiricism and a Hale-type account of the a priori only has the consequence too “immediately or quickly” that there is no a priori knowledge if one takes it to be both immediate and quick that Quine is right. Let me clarify that I don’t want to present the motive for looking for something different to Hale as being to avoid a conflict with Quine that is bound to involve defeat for the a priori. Rather, I present the general motive as being to find an account of the a priori which would show that Quine was wrong to dismiss it – if indeed he does (hard to say, since he persistently confuses the a priori with the analytic) – on the grounds that he actually has, even if those grounds are right, i.e., even if Quinean holism is right. 12  Hale, ibid., pp. 125, 143, 148; another example is Moser in A priori Knowledge; introduction, pp. 2–3. 13  Moser, ibid., pp. 2–3. For Moser, the concept of minimal a priori knowledge consists of an instance of knowledge of a proposition’s truth such that the evidence does not rely on sensory experience and that the evidence makes the proposition more likely to be true than its denial. The concept of minimal a priori knowledge, on his view, does not require unrevisable belief, innate knowledge, or self-evidence. That is why the concept is supposed to be minimal: it consists of only the two conditions specified. 11

8.3  Is It Coherent to Talk of Revision in Connection with A Priori Knowledge?

161

might be altered (e.g. expanded) in such a way that what was justified a priori in the original evidence is no longer justified in the altered evidence. Thus, even if all our justified beliefs are epistemically revisable, we may still have minimal a priori knowledge. (My emphasis; ibid, p. 3)

But this is incoherent as it stands. Knowledge entails truth. When I know p at a particular time, the belief that p is unrevisable at that time, since it is true, if not I could not know it. If it were true that all beliefs are epistemically revisable then there won’t be any instance of knowledge: neither a priori nor a posteriori knowledge. Why? Because there won’t be any true beliefs. Actually, Hale and Moser are not alone. Albert Casullo14 starts talking about justified beliefs a priori as being not necessarily unrevisable, but later on collapses into talking about knowledge a priori as being revisable. Hale,15 on the other hand, is less cautious. Hale talks mainly of knowledge a priori as being revisable. Kitcher16 talks about the notion of a priori knowledge and the notion of apriority, but he then seems to identify them. Their positions seem incoherent, that is why it is useful to try to make the position more clear to avoid that impression. The notion of “a prioricity” only refers to “justified belief in an a priori manner” (in short: “justified belief a priori”) where the “a priori manner” has been characterized properly. A prioricity is concerned primarily with the notion of an a priori warrant. The notion of an a priori warrant is only concerned with justification independent of experience. Therefore, the notion of a prioricity does not entail that the belief we acquire by an a priori warrant is true and, consequently, that it does constitute knowledge. Talk of revision makes sense in connection with the notion of a prioricity (i.e. in connection with warrants and the beliefs they form). It is indeed incoherent to talk about revision if we are talking about knowledge. It is a truism that knowledge is not mistaken. Knowledge and truth are inextricably linked in a way in which belief and truth are not. Since if we know p, either a priori or a posteriori, “p” must be true, and, therefore, if true, unrevisable. Talk about revision on the other hand in relation to a prioricity makes sense because to have an a priori warrant for belief that p amounts to having a pretty good reason to believe that p. That does not amount necessarily to knowledge – it is not enough. Warrants are defeasible, and, therefore, revisable. I have found it useful to make the distinction between “a prioricity” (i.e. justified belief a priori“) and “a priori knowledge“ for the following reasons: first, to make it coherent how philosophers defend the possibility of revision in connection with a priori knowledge. Second, because truth is not what is distinctive of a priori knowledge  – since it shares this property with any sort of knowledge  – but rather the alleged independence of experience that gets attached to the a priori warrant. The

  Casullo Albert. “Revisability, Reliabilism, and A priori Knowledge”, Philosophy and Phenomenological Research, Vol. XLIX, No. 2, December 1988. 15  Hale, ibid., p.125, p.143 and p.148. 16  Kitcher, ibid., p. 17. 14

162

8  Critical Examination of Hale’s Views on A Priori Knowledge

distinction between “a prioricity“ and “a priori knowledge” makes it possible to talk about revision in connection with the former and the possibility of infallibility in connection to the latter. It makes it explicit and coherent that a priori knowledge does not have to be infallible by merely being a priori since the a priori is primarily concerned with a way of acquiring a belief and it is not per se knowledge. However, there is an important sense in which knowledge and revision relate. We have to ask ourselves the following question: Can someone know that p and move into a situation where it is rational to give up p?; here “rationally” to be taken as “justifiably”. Revision is a change of mind, of opinion. It is possible that one may change one’s mind to what is in fact true. It is possible that there is rational pressure put on someone that is defective and that one gives up belief that p. Another important question is whether there is a kind of justification where revision as a matter of fact is the wrong thing to do: that is, where revision is in principle always possible but where the new evidence is always defective. There is an important notion of de facto indefeasibility which applies to warrants. A warrant is de facto indefeasible at t (and later times) if all further evidence against it is in fact misleading evidence. First, we cannot know that a warrant has this property at t, or any subsequent time, because we won’t be able to have the relevant evidence at our disposal. Second, we cannot know that a warrant has this property at t and later times because there is no guarantee that we can know about all future evidence against the warrant, provided that we are in a position to gather it all, that it is actually misleading evidence. A priori and a posteriori warrants can be de facto indefeasible. The property of de facto indefeasibility is not the same as the property of infallibility. The first is a weaker notion than the latter. When a warrant is necessarily, not simply de facto, indefeasible, then it is (indirectly) infallible in the sense of being the result of the correct prosecution of an infallible method. Knowledge requires that its successful warrants – those which produce knowledge on the occasion – are de facto indefeasible. Because if I know (in particular if I knew) then it is not possible to show correctly by any subsequent evidence that I am (was) wrong. Of course, that is not to deny that there is always the possibility of defeating evidence but the point is that in the case of a warrant which is de facto indefeasible this new defeating evidence will always be misleading evidence. Though there is no second level guarantee (a priori or otherwise) that warrants are de facto indefeasible. We simply cannot know that. It is always a possibility that we made a mistake in carrying out a warrant.

8.3.1 Some Remarks on Revision and A Prioricity I am attracted to the following view: Let’s for the sake of argument suppose that the analytic / synthetic distinction can be maintained. The analytic / synthetic distinction among statements is one between contents or subject matter; the

8.3  Is It Coherent to Talk of Revision in Connection with A Priori Knowledge?

163

epistemological distinction between a priori/empirical warrants is one between ways of acquiring beliefs. The possibility I am proposing is the following: A priori warrants only warrant (confirm or disconfirm) analytic statements (or some synthetic). A posteriori warrants can confirm or disconfirm any statement.

This view takes the a priori seriously because if we have a sound a priori warrant, then what we know can only be an a priori statement. An a priori statement is a statement knowable a priori. One can know an a priori statement a posteriori. A posteriori statements are only knowable a posteriori. Hale thinks that Edidin tries to defend a similar view – that a posteriori warrants can disconfirm a priori statements – distinguishing between defeating and confirming evidence.17 If Hale’s argument against Edidin in the book is any good, then that will be Hale’s objection against this view. Hale’s argument against Edidin’s view is: If, at some particular time, a state can be affected by conditions of a certain kind, then it can be at most a contingent fact that it is not affected by conditions of that kind at any other time during the period through which it obtains, including earlier times. And the point applies to the kind of state with which we are concerned here, i.e. states of (justified) belief. However I came to believe that p in the first place, if it is true that I can now lose my justification for it by coming to have subversive empirical evidence, then I could have lost my justification in that way at any earlier point. At least, that is so unless it is, in a very strong sense, impossible that such evidence should have been available then; and there is no good reason to suppose that that is ever, much less always the case. (Hale, p. 133; my emphasis)

But the experiences that Hale was thinking of could not have been in any relevant sense unavailable at the particular time t, when S (subject) was justified a priori in believing that p. They were what I call “Kitcher’s experiences”. These are for example that S may have misread a proof, that S may be too drunk, etc. These experiences are obviously always available. So, if I am still justified in believing that p independently of experience, for example, it is because these experiences did not defeat the claim that I am justified in believing that p. But there could be other experiences unavailable at time t that if I were aware of them could undermine my claim to be justified in believing a priori that p; and these experiences even though they are in principle able to defeat my claim to possess a priori knowledge, were in a relevant

 Edidin, Aaron. “A priori” Knowledge for Fallibilists. Philosophical Studies, Vol. 46, pp. 194–96, Spring 84. Hale discusses Edidin’s view in the following passage: 17

someone’s belief will be b-independent [backward-independent] of empirical evidence if such evidence plays no part in producing or sustaining it, and that the notion of a priority is best understood in terms of this kind of independence from empirical evidence, rather than in terms of f-independence [forward-independence], which is best taken as distinctive of the notion of (empirical) incorrigibility. Of crucial importance is the claim that b-independence does not entail f-independence. The thought is that I can know a priori that p, in virtue of having a justified true belief that p which is b-independent of empirical evidence, even though subsequent available evidence of that kind could undermine this belief, i.e. it isn’t f-independent of empirical evidence. (Hale, p. 131)

164

8  Critical Examination of Hale’s Views on A Priori Knowledge

sense unavailable at the time t when I thought I was justified in believing a priori that p, so they could not defeat that claim, simply because I could not have had that empirical evidence at time t. Hale thinks that if my argument is sound, then his argument against Edidin is unsound. Hale thinks that the relativity to time is fatal to Edidin’s view. The thought is [Edidin’s] that I can know a priori that p, in virtue of having a justified true belief that p which is b-independent of empirical evidence, even though subsequently available evidence of that kind could undermine this belief, i.e. it isn’t f-independent of empirical evidence. (Hale, p. 131)

Hale is right to complain about this position. Edidin’s view is incoherent. It implies that I can know a priori at an earlier time and then at a later time know that I was wrong about knowing a priori at an earlier time as subsequent empirical evidence may show. But if I knew then it is not possible to show by any kind of subsequent evidence that I was wrong. The situation is rather as follows: if at an earlier time t I thought that I knew a priori that p, and at a later time come to know, maybe by empirical evidence, that I was wrong, then I did not know p at t at all. This is my view, not Edidin’s. Hale’s second criticism (the charge of incoherence) does not apply to the view I am interested in. Hale is wrong in thinking that this (correct) criticism of Edidin’s view applies to my view. However, as I see it, Edidin’s position makes it clear that some clarification about how time and knowledge relate to each other is in order. When I know that p, I know that p at a particular time t. If at a later time I am unable to recall my justification in a decent manner, I don’t know that p anymore. I may remember to have known that p before but have forgotten about my justification for p. Analogously, when I know a priori that p, I know a priori that p at t. If at a later time I am unable to recall my a priori justification in a decent manner, I don’t know a priori that p anymore. In such a situation, I may remember to have known p before but have forgotten about its (a priori) justification. When my justification was a proof, and I don’t remember it at a future occasion then at that later time I don’t know a priori that p; if I still know that p, it is because I remember having followed a proof that p at an earlier time, but knowledge based on memory is a posteriori. If I don’t even remember to have followed a proof that p, then I don’t know that p at all at the later time. The question that naturally arises is: How does the fact that knowledge and time relate connect with revision? In the case when at a later time I am unable to recall my justification in a decent manner what has been revised is not the statement in question but the warrant which justifies it in the sense not that there was something wrong with the warrant but that one lost the warrant. In the case when I still know that p at a later time because I remember well to have followed a proof for p, for example, then there has been a switch of warrant, from an a priori warrant to an a posteriori one. Though it is true that in a sense if the justification or warrant for p has been switched over time, one can say that it has changed over time, and that is a revision also. Since I have lost my a priori warrant for p, I do not know a priori that p at a later time. When I don’t even remember having followed a proof that p before then I don’t know that p at all at a later time.

8.3  Is It Coherent to Talk of Revision in Connection with A Priori Knowledge?

165

The point is that one can know at some time and not know the same thing at another time. But the explanation of this situation is not the one Edidin offers. It may seem that it is incoherent to hold that one can know a proposition at a particular time, and not know the same at a subsequent time. But this is incorrect. There is a difference between the case when I knew at an earlier time and then at a later time where shown to be wrong (Edidin’s view) and the case when I knew at an earlier time a proposition and then at a later time I do not know the same proposition any more, not because I was shown to be wrong, but rather because I have lost the warrant for it during the lapse of time between the earlier time t and the later time t1. The second case is a simple consequence of the fact that our epistemic attitudes towards propositions can change with time, and there is nothing mysterious about that. I distinguish three basic kinds of defeat in connection with a priori warrants or beliefs: (a) There is something wrong with the purported proof. We reject the purported proof by a priori reasons. The reasoning is not reliable. It leads to contradictions. This defeat consists in finding mistakes. (b) Collateral defeating information: drunkenness, having a headache, etc. The reasoning may be fine but we are in no good condition epistemically to assimilate it. (c) We are perfectly competent in getting the warrant, justified in accepting p a priori, but the warrant can be defeated by empirical evidence not because there is something intrinsically wrong with the warrant but rather because counter empirical evidence is stronger. Again, an a priori warrant is complete, nothing is wrong with it, but its conclusion is swamped by bad empirical news. As I already said, defeasibility is a property of warrants. There are more specific cases to distinguish: 1. One learns that something is wrong with the warrant that one had. The method has not being properly executed. For example, you may have measured incorrectly because there was something wrong with the apparatus. 2. There appears new information that tells against the conclusion, but not mis-­ measurement is involved, for example. In this case the method is insufficient to guarantee the truth of the conclusion. 3. Additional information such that when one put together with the previous warrant, suspension of judgment occurs. An example of the third case is the following: P: Smoking causes cancer. Later we know: Q: Common cause for smoking and cancer. Then one doesn’t know which one is the cause of cancer. Suspension of judgment occurs as a result. Which of any of these apply to the a priori case? Certainly (1) applies. (2) is controversial. The Parallel Postulate constitutes an example. There are reasons to

166

8  Critical Examination of Hale’s Views on A Priori Knowledge

doubt the Parallel Postulate. There are collateral reasons to think not P. Case (3) may happen as well in the a priori case. There are different cases to distinguish when we are dealing with a defeasible warrant whose pedigree is fine. There is nothing wrong with its pedigree but nonetheless the warrant is not sufficient, it is inconclusive, as a way of establishing the proposition which it warrants. Two cases can be distinguish here: (I) This case is exemplified by Goldbach’s conjecture that every even number greater than 2 is the sum of two primes. We don’t have a proof, a conclusive confirmation, of this proposition. It can be envisaged that, for instance, a computer goes through all the integers and doesn’t find a counterexample. It works up to a very large number. Then there is good confirmatory evidence that the conjecture is true. This evidence is a posteriori since it relies on assumptions about the functioning of the computer. But let’s suppose that in principle, given sufficient time, one could gather the same evidence without sensory input. In this case, the a priori warrant is good because no counterexample has been found in a large number of cases studied. But the warrant is insufficient to conclusively warrant the conjecture. (II) Geometrical intuitions. The Parallel Postulate constitutes an example of this kind of case. The warrant (a priori) is fine but it is incompatible with a physical theory. (This is previous case (c) and (2)). A warrant can be a priori without being conclusive. In the geometrical case in particular, the a priori grounds that e.g. Kant must have thought he had for the Parallel Postulate fall short of conclusiveness. The crucial point is the apparent impossibility of imagining counter-examples – where imagining can mean something very concrete, for instance, drawing. There is prima facie space for empirical defeat of claims based on imagination just because the empirical world does not have to fall in line with our imaginings.18 We have to ask an important question: What kind of additions to these warrants may be possible? In the first case, the additional information to defeat the warrant involves finding a counterexample. That is, to defeat Goldbach’s conjecture, we need (ideally) to find a priori a counterexample. (Although if a computer finds a counterexample of Goldbach’s conjecture, then the evidence would be a posteriori since it involves empirical assumptions concerning the proper functioning of the computer. The computer finds the counterexample by the a priori method of computation. This case seems to be analogous to the case when we have a posteriori  Many of the arguments and theses in this book hinge to considerable extent on foundational discussions in the sciences. Notably, many prime candidates for a priori statements such as the Parallel Postulate are themselves heavily debated in the sciences and any philosophical assessment depends profoundly on the outcome of these scientific debates. My aim here is rather modest, not to give an account of these cases but rather suggest them as examples to test the tank insulation suggestion. 18

8.3  Is It Coherent to Talk of Revision in Connection with A Priori Knowledge?

167

evidence, for example, testimonial evidence, for a claim that is a priori.) In the second case, though, the additional information comes a posteriori. It can be argued that the Parallel Postulate is not a good example of an a priori statement being disconfirmed by experience since it is a priori true in uninterpreted geometry. But we ought not to forget now that we thought that Euclidean geometry was true of the physical world before non-Euclidean geometries appeared in the picture. Furthermore, we thought we knew that by a priori grounds. So the statement that we arguably thought knew a priori “Euclidean geometry is true of the physical world” has been revised by experience (i.e. the appearance of non-Euclidean geometries) in the sense that if it is true, it only can be shown to be true a posteriori. The Parallel Postulate originally was formulated without any specification about the lines in question, i.e., that the lines in question were only Euclidean lines. The formulation of the postulate had to be restricted. That is a revision as well. I therefore disagree with the suggestion that insofar as geometry is a priori, it has to be conceived as saying nothing about the physical world. In fact I think this is quite a general mistake that people make. It is crucial to recognize that much of pure mathematics – geometry is actually a special, and difficult case – expresses a priori knowledge of propositions whose application to the physical world involves no special interpretation of them. If one knows that seven times seven is forty-nine, one knows that if one has a square of soldiers on parade, with no gaps and with each row and each column seven women long, then one has forty-nine soldiers on parade in all. Arithmetic, as Frege stressed,19 is about all thinkable kinds of objects – so in particular, it is about physical objects. I also think there’s no hope for the idea that insofar as it is a priori, we should regard geometry as uninterpreted – if it’s uninterpreted, then it articulates no specific statements, a priori or otherwise. Also, a satisfactory account here has to explain why the Euclidean axioms were initially appealing – why everyone up to Kant thought they had to be true.20 If they had no interpretation, that’s utterly mysterious. The explanation has to concern facts about what people thought they could and couldn’t conceive. For example, it seems impossible to imagine a drawing in which we get simultaneously an impression of a pair of lines, each perfectly straight, and yet intersecting more than once. We can’t imagine this, and nor can we draw it. So a certain kind of appearance seems impossible – and that’s then treated as warranting the claim that counterexamples to the Parallels Postulate are not possible. Obviously this can only be a defeasible warrant, since the most that it can show is that space cannot appear locally non-Euclidean, not that it cannot be (globally) non-Euclidean. I think my example is good  – people thought they could know a priori that Euclidean geometry was true of the physical world, because they thought that the transition from “it seems impossible to imagine a setup which looks like a  Frege, G. The Foundations of Arithmetic. Oxford: Basil Blackwell, 1953.  The plausibility of the Kantian stance with respect to geometry depends to considerable extent on the feasibility of non-Euclidean geometries. Of course, Kant could not have known of these historical developments that came after his time. 19 20

168

8  Critical Examination of Hale’s Views on A Priori Knowledge

counterexample to the Parallel Postulate” to “the Parallel Postulate is true” was safe. But although not an unreasonable transition, absent further relevant information (like the astronomical observations that actually persuaded physicists to use non-­ Euclidean geometries) showed that it is certainly not a proof. Perhaps there’s a general point here: when propositions are warranted, a priori, on the basis of imaginings and conceivings, etc., there is a certain sense in which the warrant can’t penetrate deeper than the level of appearances – and the inference, from the premise that things cannot appear a certain way  – in some sense of “appear” – to the conclusion that they cannot be that way, is of course defeasible. To conclude: The claim that a priori beliefs can be revisable in light of empirical evidence is very controversial. It goes against almost the whole philosophical tradition on a priori knowledge. Even those who are sympathetic to the notion do not want to accept this possibility. Despite that, I believe that there are cases which tend to support the claim,21 though I am not committed to its truth. Even if it turns out that some a priori beliefs can be revisable in light of empirical evidence, that fact won’t show that the beliefs in question were not justified a priori.

Conclusion of Part II It is important to realize that the circularity charge in (1) and (11) involves two aspects: (a) a vicious circle is involved; and (b) it is not very illuminating. Even if Hale succeeds with (H*) in avoiding the first aspect of the circularity, and his definition is correct, still the second aspect of the circularity remains. An a priori justification is characterized as simply lacking a certain feature. As far as the issue of infallibility is concerned, it appears that Hale in his chapter leaves no room for infallibility in connection with a priori knowledge  – or  Other philosophers who share this conviction are: Casullo (ibid) and Edidin (ibid). Burge (in “Content Preservation”, The Philosophical Review, Vol. 102, No. 4, October 1993), and Wright (in some of the Hale-Wright correspondence published in Hale’s book) believe that the notion of a priori justification ought to be characterized independently of the issue of defeasibility (by a priori reasons or otherwise) that the a priori may be vulnerable to. As I take it, Burge and Wright leave open the possibility that there could be counter-empirical evidence against a priori beliefs or a priori warrants. Burge thinks that the predicate “a priori” applies primarily to justifications and entitlements (ibid, p. 458). Burge affirms: although some a priori justifications ... may be invulnerable to empirical considerations, such invulnerability does not follow from the notion of a priority ... I think that some beliefs with genuine a priori justifications ... are vulnerable to empirical overthrow”. (p. 461) According to Wright, the crucial notion to characterize is the notion of “experience independence” rather than the notions of defeasibility and indefeasibility. The issue of defeasibility/indefeasibility of a priori knowledge is a separate matter. That does not mean, of course, that the issue of defeasibility is not an important one, it is in fact a very important and interesting issue, but Wright’s point is that the two issues are separate. 21

Conclusion of Part II

169

knowledge in general  – given the undeniable fact that we are fallible creatures. Nevertheless, I have to be cautious and refrain from attributing to Hale this position since he simply does not discuss the issue of infallibility at all. The reason why he doesn’t in the book may be the one just mentioned, but it is only a possibility among others. On the other hand, that reason may have just been entirely non-philosophical.22 I agree, given the qualifications that I have discussed in chapter eight, with Hale’s claim that the notion of a priori knowledge (more accurately, the notion of a prioricity (i.e. a priori justified belief)) ought to be consistent with the possibility of revision. We are fallible creatures and we can make mistakes. I agree also with Hale that a priori warrants do not have to be infallible. The mistake Kitcher made, and that Hale quite correctly diagnosed as due to conflating the truth entailing character of knowledge and the independence of experience characteristic of a priori knowledge, is to think that an a priori warrant has to be ultra-reliable (infallible) to be a priori. However, Hale does not consider the idea that some a priori warrants may prove to be infallible, what Kitcher called “ultra-reliable”. The immediate point about infallibility is, of course, not whether what is in fact an item of a priori knowledge can be mistaken – no-one supposes that – but whether the prosecution of the methodology of a priori knowledge can lead to mistaken beliefs. Put like this, the answer, of course, is yes – people can get muddled, make mistakes in inference, miscalculate, etc. Those who allow for infallibility like Kitcher cannot mean to deny this. So what is involved? The question is a substantial one. The idea is that a certain kind of prosecution of the methodology of a priori knowledge cannot steer us false – whereas in the empirical case there are no controls, no safeguards on method such that, if they are complied with, the results are guaranteed to be true. Of course, the substantial question is to say what this ideal prosecution consists in. In the next chapters I shall try to accomplish this task. To sum up, (i) I doubt if it is coherent to think of human beings as being infallible anywhere. If we have access to substantial truths about the world, whose obtaining is independent of human judgment about the matter, then, however hard it may be for us to understand how this might be, there has to be the bare possibility of misapprehension, or ignorance, of the states of affairs described by such truths. Another way of putting the point would be to suggest that fallibility is implicit in objectivity, though that needs unpacking. (ii) That, however, is consistent with the infallibility of certain methods – with the idea that, at least in certain areas, we have methods of knowledge acquisition at our disposal such that, if we implement these methods properly, we are assured of winding up with true opinions. Of course, this will not guarantee the truth of what we actually come to believe by prosecuting those methods, since we may be mistaken in thinking that we have done so properly. Ordinary arithmetical calculation is an example of such a method: if one calculates properly, the results one gets are correct. That is a necessary truth. But it does not follow that

 For instance, Hale could just have simply chosen not to discuss the issue for more mundane reasons (i.e. like lacking space and time on the occasion). 22

170

8  Critical Examination of Hale’s Views on A Priori Knowledge

carefully achieved arithmetical opinions are infallible, since one may be mistaken in thinking that one calculated properly. As far as a priori knowledge is concerned, then, the interesting questions are: (a) whether a priori truths generally are associated with methods which are infallible in the sense I just have outlined; and (b) whether it is possible to judge with a superior, though not indefeasible, degree of sureness that the appropriate methods have, in particular cases, been correctly executed. Perhaps Hale just goes past these questions because of his assumption that a priori knowledge has to be compatible with revision. (And Quine because of his dogmatic assumption that a priori knowledge has to be unrevisable.) As a consequence, Hale does not address the interesting and very difficult question whether a conceivable notion of infallibility has a place only in the realm of a priori knowledge – in other words, whether infallibility, properly understood, is an a priori matter. I shall be discussing this crucial question in chapter ten when I shall turn to the task of disambiguating the notion of “infallibility” – among others – as a necessary step to get some clarification about the matter. This is what emerges from my discussion of Hale: (1) the task at hand is to illuminate more the notion of a priori warrant; (2) the constraint of “experience independence” ought to be effective only after the acquisition of the conceptual repertoire necessary for a priori knowledge and the obtaining of certain other necessary experiences that underpin the reliability of the knower’s state of mind; (3) there is a distinction between defeasibility and infallibility,23 what Hale did not seem to be aware of; and (4) there is at least one outstanding problem with Hale’s definition (H*) which we must seek to remedy: it is in too direct collision with Quine’s epistemological holism.

References Bennett, J. 1966. Kant’s Analytic. Cambridge: Cambridge University Press. Boghossian, P. 1997. Analyticity. In Companion to the Philosophy of Language, ed. B. Hale and C. Wright. Oxford: Blackwell. Boghossian, P., and C. Peacocke. 2000. New Essays on the A Priori. Oxford: Oxford University Press. Carnap, R. 1962. The Logical Foundations of Probability. Chicago: Chicago University Press. Casullo, A. 1977a. The Definition of A priori Knowledge. Philosophical and Phenomenological Research 38: 220–224. ———. 1977b. Kripke on the ‘A priori’ and the Necessary. Analysis 37: 152–159. Reprinted in Moser. ———. 1988a. Necessity, Certainty and the ‘A Priori’. Canadian Journal of Philosophy 18: 43–66. ———. 1988b. Revisability, Reliabilism, and A priori Knowledge. Philosophy and Phenomenological Research XLIX (2) December 1988. ———. 2003. A Priori Justification. Oxford: Oxford University Press. ———. 2012. Essays on A Priori Knowledge and Justification. New York: Oxford University Press.

23

 I will fully explain this distinction in chapter ten.

References

171

———. forthcoming. A Defense of the Significance of the A Priori – A Posteriori Distinction. In The A Priori: Its Significance, Grounds, and Extend, ed. D. Dodd and E. Zardini. Oxford: Oxford University Press. Casullo, A., and J. Throw, eds. 2013. The A Priori in Philosophy. Oxford: Oxford University Press. Caygill, H. 1995. A Kant Dictionary. Cambridge: Blackwell. Chisholm, R.M. 1977. The Truths of Reason. In Theory of Knowledge, 2nd ed. Englewood Cliffs: Prentice-Hall. Reprinted in Moser. Coffa, J.A. 1991. The Semantic Tradition from Kant to Carnap: To the Vienna Circle. New York: Cambridge University Press. Craig, E.J. 1975. The Problem of Necessary Truth. In Meaning, Reference and Necessity, ed. Simon Blackburn. Cambridge: Cambridge University Press. Creath, R. 1990. Dear Carnap Dear Van: The Quine-Carnap Correspondence and Related Work. Berkeley, CA: University of California Press. Dancy, J., and E. Sosa, eds. 1985. Introduction to Contemporary Epistemology. Oxford/New York: B. Blackwell. ———, eds. 1992. Companion to Epistemology. Oxford/Cambridge, MA: Blackwell. Descartes, R. 1967. In Philosophical Writings, ed. E.S. Haldane and G.R.T. Ross, vol. 1. Cambridge University Press. ———. 1981. Descartes: Philosophical Letters. Trans. and A.  Kenny, ed. Minneapolis: Minneapolis University Press. Dummett, M. 1980a. “Is Logic Empirical” in Dummett. ———. 1980b. Truth and Other Enigmas. Cambridge, MA: Harvard University Press. Edidin, A. 1984. ‘A priori’ Knowledge for Fallibilists, Philosophical Studies. Spring 46: 189–198. Frege, G. 1952. On Sense and Reference. In Translations from the Philosophical Writings of Gottlob Frege, ed. M. Black and P. Geach, 56–78. Oxford: Basil Blackwell. Reprinted in part in Benacerraf and Putnam. ———. 1953. The Foundations of Arithmetic. Oxford: Basil Blackwell. Friedman, M. 1992. Kant and the Exact Sciences. Cambridge, MA: Harvard University Press. ———. 2000. Transcendental Philosophy and A Priori Knowledge: A Neo-Kantian Perspective. In Boghossian and Peacocke, 367–383. Oxford: Oxford University Press. ———. 2010. Synthetic History Reconsidered. In Discourse on a New Method: Reinvigorating the Marriage of History and Philosophy of Science, ed. Michael Friedman, Mary Domski, and Michael Dickson, 573–813. Chicago: Open Court. ———. 2012. Kant on Geometry and Spatial Intuition. Synthese 186: 231–255. Hale, B. 1987. Abstract Objects. Oxford: Basil Blackwell. ———. 2015. Necessary Beings: An Essay on Ontology, Modality and the Relations Between Them. Oxford: Oxford University Press, Reprint edition. Hale, B., and C. Wright, eds. 1999. Companion to the Philosophy of Language. Wiley-Blackwell. Jenkins, C.S.I. 2008. A Priori Knowledge: Debates and Developments. Philosophy Compass 3/3: 436–450. Jenkins Ichikawa, J., and B.W. Jarvis. 2013. The Rules of Thought. Oxford: Oxford University Press. Jenkins, C.S.I., and Masashi Kasaki. 2015. The Traditional Conception of the a Priori. Synthese 192 (9): 2725. Kant, I. 1902. Prolegomena. Trans. Paul Carus. La Salle: Open Court Publishing Company. ———. 1956. Critique of Pure Reason. Trans. Norman Kemp Smith. New York: St. Martin’s. Kim, J., and E. Sosa, eds. 1995. A Companion to Metaphysics. Cambridge: Blackwell. Kitcher, Philip. 1975. Kant and the Foundations of Mathematics. Philosophical Review 84: 23–50. ———. 1980a. A Priori Knowledge. Philosophical Review 89: 3–23. ———. 1980b. Apriority and Necessity. Australasian Journal of Philosophy 58: 89–101. Reprinted in Moser. ———. 1981. How Kant Almost Wrote ‘Two Dogmas of Empiricism’. Philosophical Topics 12: 217–250. ———. 1983. The Nature of Mathematical Knowledge. Oxford: Oxford University Press.

172

8  Critical Examination of Hale’s Views on A Priori Knowledge

———. 2000. A Priori Knowledge Revisited. In Boghossian and Peacocke, 65–91. Oxford: Oxford University Press. Kripke, S. 1971. Identity and Necessity. In Identity and Individuation, ed. M.K. Munitz. New York: New York University Press. ———. 1980. Naming and Necessity. Cambridge, MA: Harvard University Press. ———. 1982. Wittgenstein on Rules and Private Languages. Cambridge, MA: Harvard University Press. Maddy, P. 1990. Realism in Mathematics. Oxford: Oxford University Press. Melis, G., and C. Wright. Forthcoming. In Beyond Sense? New Essays on the Significance, Grounds, and Extent of the A Priori, ed. Dylan Dodd and Elia Zardini. Oxford: Oxford University Press. Mill, J.S. 1950a. Philosophy of Scientific Method. New York: Hafner Publishing. Mill, J. S. 1950b. A System of Logic. Reprinted in Mill. Moser, P.K. 1987. A Priori Knowledge. Oxford: Oxford University Press. Pap, A. 1946. The A Priori in Physical Theory. New York: King’s Crown Press. ———. 1958. Semantics and Necessary Truth. New Haven: Yale University Press. Parsons, C. 1967. Foundations of Mathematics. In The Encyclopedia of Philosophy, ed. Paul Edwards, vol. 5-6, 188–212. New York: Macmillan. ———. 1983. Mathematics in Philosophy: Selected Papers. Ithaca: Cornell University Press. Paton, H.J. 1936. Kant’s Metaphysic of Experience. Vol. 1 & 2. 1st ed. London: George Allen & Unwin Ltd. Russell, B. 1973. The Problems of Philosophy. New York: Oxford University Press. Warenski, Lisa. 2009. Naturalism, Fallibilism and the A Priori. Philosophical Studies 142: 403–426. Wilder, R. 1975. Evolution of Mathematical Concepts. New York: Wiley. Williamson, T. 2002. Knowledge and Its Limits. Oxford: Oxford University Press. ———. 2005. Armchair Philosophy, Metaphysical Modality and Counterfactual Thinking. Proceedings of the Aristotelian Society 105: 1–23. ———. 2007. The Philosophy of Philosophy. Malden: Blackwell. ———. 2013. How Deep is the Distinction between A Priori and A Posteriori Knowledge. In The A Priori in Philosophy, ed. A. Casullo and J. Thurow, 291–312. Oxford: Oxford University Press. Wittgenstein, L. 1956. Remarks on the Foundations of Mathematics. Trans. G. E. M. Anscombe. Oxford: Basil Blackwell. Wittgenstein, Ludwig. 1969. On Certainty. Oxford: Basil Blackwell. Wright, C. 2004a. Intuition, Entitlement and the Epistemology of Logical Laws. Dialectica 58 (1): 155–175. ———. 2004b. On Epistemic Entitlement: Warrant for Nothing (and Foundations for Free)? Proceedings of the Aristotelian Society 78 (supp): 167–212. Wright, Crispin, and Martin Davies. 2004. On Epistemic Entitlement. Proceedings of the Aristotelian Society 78 (2004): 167–245. ———. 2014. On Epistemic Warrant II: Welfare State Epistemology. In Scepticism and Perceptual Justification, ed. Dylan Dodd and Elia Zardini. Oxford: Oxford University Press. Yablo, Stephen. 1993. Is Conceivability a Guide to Possibility? Philosophical and Phenomenological Research 53 (1): 1–42.

Part III

A Prioricity and Infallibility

There are two tasks I intend to accomplish. First, to provide more illuminating characterizations of the notion of a priori knowledge and related notions. Second, to disambiguate the notion of infallibility, and to clarify its relationship with the concept of a priori knowledge. In respect to the first task, what I intend is to provide accounts of these notions that are illuminating even if they do not amount to proper definitions. The idea is to respect and get clear about some of the intuitions we have in relation to a priori knowledge. In relation to the second task, what I intend to accomplish is to make conceivable the (mere) possibility of infallibility. It is necessary to sort out what would have to be involved for such a possibility to be realizable. It is another matter to argue that the possibility has been realized. I don’t have a knock-down argument for the latter, although, of course, that is not to deny that making coherent the possibility of infallibility paves the way for settling the question whether the possibility has been realized (actualized). This part consists of two chapters followed by a conclusion. In Chap. 9 I attempt to elucidate the concepts of an “a priori method”, an “a priori warrant” and “a priori knowledge”, and then proceed to evaluate the suggestions. Chapter 10 will be wholly devoted to an analysis of the relationship between the notions of a priori knowledge and infallibility. In the concluding section I round out the most important issues in the book.

Chapter 9

What Is the A Priori?

Abstract  In this chapter, I attempt to elucidate the concepts of “a priori method”, “a priori warrant”, and “a priori knowledge”. I elucidate these concepts by what I call “the tank insulation argument”. We will need these characterizations in order to get clear about the relationship between a priori knowledge and a defensible notion of infallibility. I will proceed to evaluate the proposals analyzing whether the truths we usually regard as a priori come out as a priori on my account. Keywords  A priori method · A priori warrant · A priori knowledge · Sensory deprivation · Tank insulation I will offer more illuminating (explicit) characterizations of the notions of “a priori knowledge”, “warrant” and “method”. I think that my proposal constitutes an elaboration of what I take to be a suggestion which Crispin Wright made originally in his Frege’s Conception of Numbers as Objects.1 However, Wright had not developed the suggestion in any detail either in his Frege book or in any of his writings. So, the proposal stayed as a suggestion, very interesting, though hardly developed. Wright’s proposal is highly intuitive and simple and, at the same time, fully captures in my opinion the intuition that lies behind Kant’s idea that a priori knowledge is independent of experience.

9.1 Wright’s Proposal Wright first introduced what I call “the sensory insulation tank suggestion” in the context of an argument against the causal theory of knowledge, specifically, on how the latter has difficulties in accommodating any kind of a priori knowledge and, in  Wright, Crispin. Frege’s Conception of Numbers as Objects. Aberdeen University Press, pp. 95–6, 1983. 1

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 I. Fred-Rivera, A Historical and Systematic Perspective on A Priori Knowledge and Justification, Philosophical Studies Series 151, https://doi.org/10.1007/978-3-031-06874-4_9

175

176

9  What Is the A Priori?

particular, a priori knowledge of necessary truths. The causal theory of knowledge requires that the state of affairs which confers truth upon the statement to be known plays a crucial role. Thus, for the causal theorist, the problem is that a priori knowledge does not require the fulfillment of any such causal relation with the world. what is distinctive of any piece of knowledge a priori is precisely that it has no essential causal antecedent save a training in certain relevant concepts. A man can lie suspended in a tank of lukewarm water, blindfolded, ears plugged, etc. – in short, in a state of total sensory insulation – and arrive, if he can concentrate well enough, at the end of elementary, and perhaps some less elementary, arithmetical and geometrical truths which he has never thought before. How, when the events in his consciousness are in this way causally quite unrelated to his present physical environment, is it possible for him to be exposed to the necessary causal influences?2

Wright explains (in private conversation) that the idea is not that a priori knowledge is what will be available to a thinker independently of any causal interaction with the world. The point of the tank idea is one of temporary causal insulation. Something is knowable a priori just in case someone who went into a state of sensory insulation could, while so insulated, come to know something she has never previously thought about.

9.2 Characterizations of the Notions of “A Priori Method”, “A Priori Warrant” and “A Priori Knowledge” First of all, I want to clarify why I suddenly talk about methods when I have been talking about warrants. The reason is that the notion of “method” is crucial for our purposes. I will take the notion of “method” to be the primary bearer of the predicate “a priori”. In order to accomplish the task of getting clear about the relationship between a priori knowledge and the notion of infallibility, properly conceived, it is necessary to draw the a priori / a posteriori distinction primarily at the level of methods. This would parallel the situation with the predicate “infallible” since I shall argue that the interesting notion of infallibility in epistemology is the one that applies primarily at the level of methods. Methods are ways of getting a result. The methods we are interested in are cognitive methods. Fundamentally, the a priori is a cognitive method by means of which we get into a situation where we are warranted in believing a proposition. It can be argued that this notion of “method” is vague: For example, are looking, seeing, asking a knowledgeable friend methods? It is not clear to me why it should be necessary to characterize in absolutely general terms what a “method” is. The important thing is that the idea be clear enough in the context in hand – when our interest is in a priori methods. There are certain things which one could in principle do in the tank  – calculate, infer, visualize, try to construct a coherent fiction,

 Ibid, pp. 95–6; my emphasis.

2

9.2  Characterizations of the Notions of “A Priori Method”, “A Priori Warrant” and “A…

177

etc.  – and other things (including, incidentally, looking, seeing, asking a knowledgeable friend, etc.) which one could not. According to the proposal, the belief that a priori knowledge is possible is the belief that methods of the former kind can be a source of knowledge. This idea is not compromised by the unavoidable vagueness in the notion of “method”, taken in its most general sense. An priori warrant is the product of an implementation of an a priori method. The property “a priori” ought to be applied derivatively to propositions believed, and to knowledge acquired, by being warranted a priori. What are warrants? They are cognitive processes which give us reasons (presumably pretty good reasons if they are good) to hold beliefs. Warrants produce belief “in the right way”. “The right way” does not entail that a warrant has to be able always to produce true beliefs. Warrants which can warrant belief given favorable circumstances may be unable to justify belief given unfavorable circumstances. My definition of the concept of an “a priori method” is as follows: Given that X possesses the concepts necessary for entertaining p, (Fapm) μ is an a priori method for X’s belief that p if and only if it is a routine (1) that is cognitive and whose implementation by X produces in her a warrant for the belief that p; (2) that can be implemented by X in a state of sensory deprivation. In general, a cognitive method is a method that generates belief that p. A method is a general routine which we implement in particular occasions resulting in our being warranted or not for our belief that p. An a priori method is one that satisfies (2), that is, it does not need sensory activity to be implemented and provide a warrant for a belief. Empirical methods need sensory activity. My definition of the concept of an “a priori warrant” is as follows: Given that X possesses the concepts necessary for entertaining p, (Fapw) ø is an a priori warrant for X’s belief that p if and only if it is a process (1) that is the result of an implementation of a method, (2) that can produce in X the belief that p, (3) that warrants X in believing that p, (4) that can be accomplished by X in a state of sensory deprivation. The implementation of a method generates a warrant for believing that p. In (Fapw(3)), the notion of “warranting” does not entail the truth of p, therefore, knowing that p, but rather “warranting” entails that a warrant provides good reasons to believe that p. My definition of “a priori knowledge“is as follows: Given that X possesses the concepts necessary for entertaining p, (Fapk) X knows a priori that p if and only if X knows that p and X’s belief that p was acquired by an a priori warrant.

178

9  What Is the A Priori?

Let me clarify the proposal. The position is that we don’t have to have sensory information while we carry out an a priori method. Also, an a priori warrant can be accomplished with no sensory input, that is, in a state of sensory deprivation as well. Let’s illustrate these components with the example of calculation. The method consists in the rules of calculation. Warrants are particular calculations, the results of the applications of the method. Our response to the methods is always fallible. Another example: in cookery, the method is the recipe, the way of getting the meal. The implementation is the way I actually carry out the recipe which can be successful or not. The result is the meal that I generated. In the best case, I get a (delicious) meal. The uptake of the warrant is the meal. The best response to the situation is that one eats the meal. The response to it: I may eat it or I may not. In the epistemological case, if one really generated a warrant, then one ought to believe the result. In the cookery case, there is no such a pressure; one may not eat the meal. I would say that methods are like recipes, that the relevant processes (warrants) are like episodes of cooking according to recipe, and that beliefs are like the meals which result. A priori methods – if they are indeed ones that can be implemented in the tank – will in a sense be capable of purely mental implementation; so the process of implementing them will be a psychological routine, but that is not to say that the method itself, or the product, is psychological (in any derogatory sense). There is a distinction between having a warrant and actually forming the belief that it warrants. It is conceivable that there could be epistemological pressure not to form the belief. To form the belief which a warrant justifies is a matter of psychology. On the other hand, that we ought to form the belief in question given that we possess a good warrant for it is an epistemological matter. (Fapk) attempts to capture “the independence of experience” characteristic of a priori knowledge in terms of the possibility of an a priori warrant to be constructed in a state of sensory deprivation. Note that (Fapk) is compatible with the possibility of knowledge a posteriori of truths that are knowable a priori. This compatibility constitutes a desideratum for any characterization of a priori knowledge since we presumably possess such a posteriori knowledge. (Fapk) only puts a constraint on the a priori justification, namely, that it can be accomplished in a state of sensory deprivation, and leaves it completely open whether experience is capable of providing another sort of justification. (Fapk) talks about a priori known propositions. It would be desirable, it seems, to include also a priori knowable propositions. This is desirable because we want to single out a class of truths with a certain feature. (Fapk)* P is knowable a priori iff it is possible for a thinker X to know that P on the basis of a justification which can be accomplished in a state of sensory deprivation (namely, by an a priori warrant). The distinction that interests us is not only between truths that happen to be already known a priori and those known a posteriori. Rather we need a distinction that does not rely on what we contingently happen to know but draws on a feature that necessarily belongs to this class of truths.

9.2  Characterizations of the Notions of “A Priori Method”, “A Priori Warrant” and “A…

179

I am proposing an analysis of the notion of a priori knowledge similar to the one Wright has proposed, and that Kitcher also considered, but finally rejected.3 An important observation: By (Fapw), I can pick out a class of beliefs in terms of the way by which they have been justified. There are those justified by a priori routes which ought to be contrasted with those justified by a posteriori routes. It is crucial to realize that one can claim that the class of such a priori beliefs is non-­ empty while still, if one wishes, denying that there is any a priori knowledge.4 To sum up, the question “how is a priori knowledge possible?” can take the form: how can it be that any belief having been reached by an a priori warrant, can be true too? A warrant should aim to presumption of truth. Warranting is what a good warrant does: it enables us to take a proposition as true. An a priori warrant enables us to take a proposition as true just by thinking. But how can that be? That a belief is acquired by an a priori warrant does not entail that that belief is knowledge. For it  Kitcher affirms:

3

Why not define a priori knowledge outright as knowledge which is produced by processes which do not involve perceptual mechanisms? The answer is that ... knowledge which is produced by a process which does not involve perceptual mechanisms need not be independent of experience. For the process may fail to generate warranted belief against a backdrop of misleading experience. (Nor may it generate true belief in all relevant counterfactual situations.) So, for example, certain kinds of thought experiments may generate items of knowledge given a particular type of experience, but may not be able to sustain that knowledge against misleading experiences. (Kitcher, The Nature of Mathematical Knowledge, p. 31) Let us assume that warrants for items of primary modal knowledge do not involve the processing of perceptual information ... that primary modal knowledge is obtained by some clearly non-perceptual process such as abstract reflection or experimentation in imagination. It does not follow that primary modal knowledge is a priori ... a priori warrants have to be able to discharge their warranting function, no matter what background of disruptive experience we may have. But a fact that a process is non-perceptual does not rule out the possibility that the ability of that process to warrant belief might be undermined by radically different disruptive experiences. I can imagine experiences which would convince me that my own efforts at experimentation in imagination were an extremely unreliable guide to anything at all. Hence, the last step in the popular argument illegitimately conflates nonperceptual sources of knowledge with sources of a priori knowledge. (Ibid, p.  35; my emphasis) Kitcher rejected this analysis for one main reason. This analysis allegedly conflates “non-empirical processes” of belief formation – in short, nonempirical warrants – with a priori warrants. Kitcher considers a priori warrants as “ultra-reliable”, that is, that they have to able to produce knowledge automatically, so to speak, just by the mere fact of their being a priori. Non-empirical processes cannot be of that sort; they are supposedly unable to sustain their warranting function given unkind experiences. I am not going to react to Kitcher here in any detail since I already did that in chapters five and six. I just wanted to illustrate that Kitcher considered the analysis of a priori knowledge I am proposing here, and to briefly point out his reason for rejecting it. 4  If there are a priori warrants, then it follows that there are a priori beliefs, since warrants are warrants for beliefs. In other words, given that there are a priori warrants, the class of a priori beliefs is non-empty as a consequence. The point I am making is that this fact is consistent with there being no a priori knowledge at all.

180

9  What Is the A Priori?

does not entail that the belief is true. The problem of answering the question “how is a priori knowledge possible?” is a serious one for two reasons: (1) a priori justification does not entail truth, as it does not in my account, and; (2) it is in tension with something we are at least inclined to think is involved in other cases of knowledge, namely, a satisfaction of a strong causal condition. How can we know anything just by thinking? How can thinking justify conclusions about truth? Any adequate notion of a priori knowledge should fully respect its problematic nature. My proposal captures entirely the problematic nature of a priori knowledge. What I have intended to accomplish with the proposals I offer in this section is: first, to provide at least a “Carnapian explication” of the notion of a priori knowledge.5 I have found the notion of a “Carnapian explication“very helpful in this context. As I understand the notion, the idea is that we are supposed to get hold on an intuitive concept, modify and develop it, to make it more sharp. For instance, the notion of a general recursive function is such an explication of the intuitive concept of a mechanical effective procedure. The former constitutes no analysis of the latter. We get something that intuitively we had and then get a concept more sharp that still respects what we had before. We don’t get exactly what we had before but we can still recognize what we had previously in an intuitive level of the understanding of the concept. Second, if (Fapk) (and the others) do not amount to definitions, I hope they can at least explain some of the intuitions regarding a priori knowledge. I think that it may be the case that to clarify the crucial intuitions regarding a priori knowledge we don’t need to have a proper (explicit) definition of a priori knowledge, though, of course, that would be very desirable.

9.3 What Is “Experience”? In order to avoid circularity with (Fapk), I will try to elucidate what “experience” is. “What is experience?” Experience is what is delivered by our five cognitive sense-organs. Some questions naturally arise: What is a sense-organ? Why are there only five? Broadly speaking, a subject’s experience is the flow of her sensory encounters with the world. A subject’s sensory states are caused by stimuli external to the body. Another sense of experience is involved in those sensory states brought about by internal stimuli. Why are there only five senses? I won’t be addressing this important question in any detail here.6 My only concern with the issue is to make it clear that in order to  Carnap, R. The Logical Foundations of Probability. Chicago: Chicago University Press, chapter one, 1962. 6  For an insightful paper on why there has to be only five senses, see H. P. Grice’s paper “Some Remarks About The Senses” in Analytical Philosophy. Edited by R.  J. Butler. Oxford, UK: Blackwell, pp. 133–53, 1962. 5

9.3  What Is “Experience”?

181

establish whether a particular type of process is an a priori warrant, the existence of worlds in which subjects are endowed with additional senses or faculties is entirely irrelevant. My focus is on the question whether a particular type of process could be carried out in by a subject with senses and abilities we actually have, not on whether the processes we are interested in could be carried out by creatures whose capacities for acquiring knowledge are substantially different from ours, e.g., they are augmented or diminished in a significant way. To decide whether or not a particular item of knowledge that p is an item of a priori knowledge we consider whether the type of process which produced the belief that p is a process which would have been carried out by the subject, with the kind of cognitive structure it actually has, if no other experiences – apart from those necessary for concept acquisition – had been fed into it, and whether, under such conditions, such processes would warrant belief that p, and possibly would produce true belief that p, if the subject is to have a priori knowledge that p. Another question that immediately arises is: what does “sensory deprivation” mean? A first approximate answer is: not seeing, hearing, or smelling, etc., for a period of time. Of course, the notion of experience is more general than that of sensory experience. In any case the kind of “experiences” that are possible for one in the tank include many that would ground claims that are intuitively not a priori knowledge. For instance, claims about what one just dreamt, or how one is feeling, or whether one has a headache, etc. So I need to say something about why a reflection on these matters doesn’t constitute an “a priori method”. One suggestion: an item of knowledge only counts as a priori if it could be known by any suitably conceptually endowed subject in a state of temporary sensory deprivation. Is it possible to arrive at knowledge in a state of sensory deprivation? According to the apriorist, the answer is “yes”. (Though I think that the claim that it is possible to arrive at new information in a state of sensory deprivation may not be special for the “apriorist”, most people would think it is true.) Given that an a priori warrant is one that can be carried out in a state of sensory deprivation, the following consequences obtain: 1. that it is possible to have no sensory experiences at all,7 of course after those needed for acquisition of the conceptual repertoire for a priori knowledge, and still hold these justifications; 2. one could do them “in the dark”, provided one understands the questions.8  Note that sensory deprivation does not mean “no experiences” (one feels warm, cold, etc. – as I explained on the previous page). 8  Can one read a proof in the insulation tank? Reading a proof involves at least one sense: seeing, so one cannot read a proof in the tank. Is it a consequence then that our a priori knowledge would be restricted? I can read a proof outside the tank but not in the tank. What is then the status of the sensory insulation idea? This seems to me to be a worry only if it is supposed that whenever we acquire knowledge a priori by means which rely on physical external aids  – typically reading and writing marks on paper – it is an essential feature of the methods we use that there is this reliance. But that doesn’t seem to be so. It seems plausible to suppose that whenever we do in fact rely on pencil and paper, 7

182

9  What Is the A Priori?

Certain experiences are necessary for acquiring a priori knowledge, but they are only those needed to provide the relevant concepts. Nevertheless, we have to reconcile the need for another kind of experiences: the experiences needed to account for the reliability of the knower’s state. At this point, it is important to draw the following distinction between conditions for (a priori) processes: (a) what are the conditions that enable one to carry out an a priori process? Are there any sensory conditions? The apriorist answer is “no”. Let me explain. These conditions are those that make the process possible. An a priori warrant is one for which no sensory input is necessary for the subject to carry it out. The other set of conditions for (a priori) processes: (b) conditions whose obtaining are needed in order for the subject to be able to respond to the process by believing that p. What is at issue is: what conditions are necessary for the person who undertakes the process to actually accept p in the end? There is room for empirical considerations here. These are collateral beliefs about the background, conditions that make (possible) a certain response to the (a priori) process. This second set of conditions for processes have to be accommodated in a notion of a priori knowledge too. Another related distinction has to be made in connection to the role of statements in justifications. A statement plays a justificatory role in a justification for p iff it is playing a role in justifying the truth of p. A statement may play a justificatory role for q, related to p in the sense that it expresses a pre-condition for our knowing the truth of p. For example, when p is the conclusion of inferential a priori knowledge, then all of the premises in the proof are playing a justificatory role for the truth that p (in short: for p). However, q, let’s say, “I follow a proof that p” (which implies the truth of r: “I am alert enough at the moment I am following the proof that p”) is not playing a justificatory role for the truth that p (any more than r); rather it expresses a precondition for my being able to obtain inferential a priori knowledge that p. Actually, the statement “r’ is partly a more basic pre-condition since it involves “alertness” which is a precondition for the acquisition of any kind of knowledge.

we could in principle carry out the same process in our heads  – if we were lucid and focused enough. It is, for example, surely a contingent fact about human beings that we are not as good at mental arithmetic as we are at written arithmetic, and it certainly seems to be no essential feature of the methods of calculation that they be carried out on paper. Similarly, very good chess players can play without a board. And so on. In general, the point of the sensory insulation idea is just that it is a graphic way of ensuring that there is no empirical input in the course of implementing the relevant method.

9.4  Is the Sensory Deprivation Suggestion Any Good?

183

9.4 Is the Sensory Deprivation Suggestion Any Good? The test for a proposed definition of a priori knowledge rests in its ability to classify appropriately knowledge as a priori. To examine a catalogue of truths supposedly known or knowable a priori9 will help to know whether my account render them as a priori: 1. Analytic truths: Let’s say that analyticity is construed as “true in virtue of meaning alone”. Given that these truths can be known by reflecting on the concepts which figure in them, we can easily see that conceptual analysis is an activity that can be accomplished in a state of sensory deprivation. So, analytic truths trivially come out as a priori. An example of an analytic truth that we know a priori is “Triangles are three-­sided figures”. 2. Logical truths: Logic is a purely deductive science. Since one neither verifies logical laws nor obtains logical consequences by perceptual processes, it is possible to obtain logical knowledge in a state of sensory deprivation. But what if one has to rely on the syntax of an expression (i.e. it has the form of a conjunction, etc.?) That experience is part of the necessary experiences for the acquisition of the conceptual repertoire necessary to obtain a priori knowledge. 3. Mathematical truths: If logicism were correct, then the a prioricity of mathematics would follow from the a prioricity of logic only if a prioricity is preserved by logical inference. On the other hand, if mathematics has its distinctive subject matter, for instance, arithmetical statements speak of numbers conceived as abstract objects, then again mathematical knowledge would come out a priori. If mathematical grounds are concerned with entities which are causally inert, as abstract objects are, then a mathematical ground can produce knowledge without having to rely on anything outside the reach of a subject’s mind. For instance, to know that the arithmetical statements “The number 2 is the third number in the natural number series” and “The number 2 is an even number” are consistent is something that we can know with our eyes closed, ears plugged, etc.. Note that there is a difference between what we actually do and what we could use in the tank. Of course we are not going to actually get insulated in the tank to know, for example, that these statements are consistent. The point is rather that for the characterization of a priori truths we have the following: it could be done. Our basic proposal is that in order for a proposition to be actually known a priori, it is a necessary and sufficient condition that the method whereby we came to know it

 I don’t claim that the list is exhaustive. These truths are the ones I have found.

9

184

9  What Is the A Priori?

could have been used by a lucid subject in the tank, that is, by a lucid subject in a state of total sensory deprivation. If mathematics were reducible to logic and set theory, since logic is a priori, and sets are abstract objects, then mathematical knowledge comes out as a priori again, provided the required inferences preserve a prioricity.10 4. The cogito: It comes out as a priori.11 5. Universally empirical knowledge: Examples of propositions which allegedly constitute universally empirical knowledge are “There is an external world”, “There are physical objects”, “Some objects have shapes”, etc. It can be argued that such knowledge should be considered as a priori since it requires no particular kind of experience beyond that needed for the acquisition of the relevant concepts. The traditional conception of a priori knowledge is too vague, it is not articulated enough, to decide alleged cases of universally empirical knowledge.12 Universally empirical knowledge does not come out as a priori according to (Fapk) because some experiences are needed for that knowledge, for example, the experience of at least one physical object to know that there are physical objects. It may appear that the contrary is the case because of the fact that any particular experience of any physical object is enough for such knowledge, that is, any particular experience of a physical object would do, the particularity of the object is irrelevant. Nevertheless, we cannot forget what is crucial: that the experience in question is not only relevant, but also necessary for that knowledge, and that is what makes it a posteriori instead of a priori. Universally empirical knowledge does not count as a priori according to (Fapk) because beyond the specified experiences, no experiences at all, not particular or otherwise, are needed to obtain a priori knowledge.

 It appears to some philosophers like Kitcher, for example, that the assumption that logical inference preserves a prioricity is too big an assumption. What I want to say is that for those who are sympathetic to the view that mathematical knowledge is a priori, it is not so. And we are concerned with those who are sympathetic to this view. Even more, it would be bad news if according to an account of the a priori, logic turns out not to be a priori. Logic is an a priori discipline if anything is. In the next section I will try to account for our knowledge of mathematical axioms. 11  I discuss this case on pp. 202–203, Sect. 10.5 of Chap. 10. 12  Contemporarily, Kitcher (The Nature of Mathematical Knowledge, p.  31) has considered the problem of universally empirical knowledge coming out as a priori, but although his analysis points to the right direction, in my opinion, it is not sharp enough to explain why this knowledge is not a priori since he does not elaborate on the notion of the particularity of experiences, for example. 10

9.5  On Basic A Priori Knowledge

185

9.5 On Basic A Priori Knowledge How is it possible to acquire basic a priori knowledge? I shall be modest; I don’t have much new to say here. I will discuss some examples and examine what conclusions can be drawn from them. The picture I endorse is a simple one: given certain concepts that we can learn even empirically, we can have the ability to go from the concepts to the apprehension of truths concerning them just by thinking.13 Provided we have the necessary concepts, it can occur to us, if we concentrate and are intelligent enough, that some statements are true, or follow, from the combination of, or reflection on, these concepts. For example, having the concept of a triangle, I come to know that “If a figure is a triangle, then it must have three angles”, and this follows trivially from the definition of a triangle; or less trivially, if we were a Dedekind or Frege in a state of sensory deprivation, the Dedekind-Peano axioms could occur to us. First of all, do we just think about the (basic) proposition in question? Possible cases to study that can help us to answer this question are the axioms of arithmetic, the Parallel Postulate, as a negative case of study, stipulation, and definition. In stipulation and definition, however, not just thinking is involved, but also laying down some principles. The cases that interest me as examples of propositions which constitute basic a priori knowledge are those which have the following characteristics: (1) the concepts in the statements are already familiar prior to the understanding of the statement, (2) we still have not thought the statements in question. Then, we think the statements in question. What happens in our thinking them? We persuade ourselves that they are true just by thinking. We have to think of the recognition of truth in the light of understanding. For example, if I understand what it is to apply color terms correctly, then I can know that colored objects cannot be colored with two different colors in the same areas.14 We have geometrical intuitions. We refine them and get some principles. There are propositions that seem good to us in the light of the concepts we have. Sometimes a process involved in the study of geometrical figures is visualization.15 We check a property by visualization and obtain generalizations about cubes,

 Of course, this is not a theory; it is not controversial. Anyone who accepts that there is basic a priori knowledge will agree with this picture. But my intention is not to provide an original theory but rather try to illuminate what goes on in our acquisition of basic a priori knowledge by studying some examples to establish what general conclusions we can draw from them. 14  What is interesting about color-exclusion is that even appearances of colors will lead us to the same result; the appearance of looking red or green, for example. We reflect on those appearances. There is a process of reflection involved. Even if we don’t have the convention of how to use color terms, it is a fact (empirical) that things look in a certain way, that they don’ allow of being of different colors all over. 15  It can be argued that visualization need not be used. I won’t deny that. My point is that given that we use it, to say what goes on in that process. Note that I am not saying that visualization is an infallible method. But, surely, most people will agree that it can be a potential source of knowledge. That is why I consider it. 13

186

9  What Is the A Priori?

for example. The properties on which we generalize are not accidental properties due to the process of visualization, but they are essential properties of the figures. We have to distinguish between visualizing and making explicit presuppositions. In visualization, we execute processes we use to convince ourselves that certain statements are true. We use diagrams. When we make explicit the presuppositions we are not simply recasting what we did in visualizing, we are trying to be more rigorous about what we visualize. We try to improve what we could understand in an intuitive level. This simple picture I am suggesting may not be restricted to analytic truths. I leave open the possibility that there could be a priori knowledge of “synthetic” a priori truths. Here is what happens when we proceed to formalize our informal knowledge or intuitions. Given that we can obtain some statements which state all the relevant relations among the concepts, we compare the statements we get. This comparison establishes the level of “basicness” among the statements. The task of establishing the degree of basicness of a statement is a logical one. We choose the statements that have more deductive power, the ones that by themselves alone can imply the rest. That is, logic helps us to establish which statements (or combination of statements) ought to be our axioms by serving as a tool for testing which statements have more deductive power or have more deductive consequences and at the same time constitute the smallest set (or combination) to do that. This entire procedure of acquiring axioms can be accomplished a priori in my sense. With the examples of colors, geometry, and basic arithmetic, I have tried to answer the following question: how do I persuade myself that these propositions are true? I think that the role of imagination in a priori knowledge is important. It can be a source for acquiring knowledge. Though, certainly, it is not infallible. Philosophers have the tendency to concentrate on logic, axioms, rules of inferences, logical consequences, and seem to forget the importance of imagination and ways of knowing that should be taken into serious consideration at this basic level too.

Chapter 10

A Priori Knowledge and Infallibility

Abstract  This chapter is devoted to an analysis of the relationship between a priori knowledge – as partly characterized by the proposed analysis of the notions of an a priori warrant and an a priori method – and the notion of infallibility. A variety of predicates – “fallible”, “infallible”, “defeasible”, “indefeasible”, “revisable”, “unrevisable”, “a priori”, “empirical”, etc. – are jostling with each other to apply to a variety of different kinds of things: truths, methods, warrants, knowledge. One needs to straighten all this out and set things up quite carefully, so that the basic ideas I want to discuss – for instance, the question of the possible infallibility of a priori knowledge – can be clear enough to be discussible at all. In the concluding section I round out the most important issues in the book. Keywords  A priori knowledge · Fallibility · Infallibility · Methods · Warrants

10.1 Glossary It strikes me that there are a lot of terminological problems in this area. A variety of predicates – “fallible”, “infallible”, “defeasible”, “indefeasible”, “revisable”, “unrevisable”, “a priori”, “empirical”, etc. – are jostling with each other to apply to a variety of different kinds of things: truths, methods, warrants, knowledge. One needs to straighten all this out and set things up quite carefully, so that the basic ideas I want to discuss – for instance, the question of the possible infallibility of a priori knowledge – can be clear enough to be discussible at all. I would hope and expect that, when this is done, some of the confusions would be cleared up. I don’t intend to provide proper definitions for all the epistemological terms I discuss. To accomplish that task would take me far from my focus here – which is to get clear about the notion of a priori knowledge and the notion of infallibility, and how they relate to each other. However, I have been using these epistemological terms, and very often they are used in the literature without any adequate (explicit)

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 I. Fred-Rivera, A Historical and Systematic Perspective on A Priori Knowledge and Justification, Philosophical Studies Series 151, https://doi.org/10.1007/978-3-031-06874-4_10

187

188

10  A Priori Knowledge and Infallibility

explanation. What I will offer are clarifications of the ways I use these terms. I shall also offer some reasons why these terms ought to be used in this manner. I will be saying a lot more about some of the epistemological terms in this part of the book, so in this glossary I intend to give a basic guide for the reader to be able to follow the discussion. To provide the glossary at this point, though, involves having to avail myself of discussion that comes later on. As I see the matter, the primary task in clarifying these epistemological terms is to get clear about what their bearers are: what things have these properties. It is important to bear in mind what I mean in saying that these properties apply objectively to their bearers. One has to distinguish between the bearers having those properties objectively, and our thinking that they possess them (which may not be true at all). For example, if a method is infallible, it is objectively that way. It is so intrinsically and not due to our inability to find something wrong with it. Obviously, if there is nothing wrong with the method intrinsically, then there is no way that we can correctly improve it, though we can incorrectly think we are doing so. In respect to infallible methods, it is not possible that there are ways of improving the method to make it more reliable without showing that it is wrong; that is, no improvement is possible for infallible methods. In contrast, it is possible that there are ways of improving fallible methods without showing that they are wrong. (1) Method By a “method” I simply understand a general routine which we can perform correctly or incorrectly on particular occasions and wind up warranted (or not) in certain beliefs as a result. The connection between methods and beliefs is the following: methods are ways for generating beliefs. The methods that are interesting from my point of view are those methods which must generate in a person, rational, reasons for thinking that the belief acquired by X in carrying out the method is likely to be true. In this way, hypnosis can be excluded, for example. A person in knowing that I have been hypnotized, let’s say, is not likely to believe that the belief I acquire by the process of hypnosis is true at all, or if the belief turns out to be true, this rational person would not be likely to think that the belief was justified. Hypnosis gives no warrant, it only causes the belief in the subject. On the other hand, if I believe B by method M, a proof, let’s say, then someone else has reasons to believe I am right. It is methods that are primarily infallible or fallible. An example of an infallible method is calculation. An example of a fallible method is observation. (2) A Priori Method The predicate “a priori” ought likewise to be applied firstly to methods. A priori methods, I propose as a first approximation, are those which could in principle be implemented in a state of sensory deprivation. Empirical methods require sensory activity.

10.1 Glossary

189

(3) Being Warranted To be warranted is to be in a state of information which we reasonably take to justify certain beliefs. States of being warranted are the products (results) of the warrants we get by implementing methods. Talk about “warrants” can create the mistaken impression that they are objects of some sort. But warrants are not objects but processes. For example, when what is warranting is an act of perception, perception (perceiving) is a process. Likewise, one can be warranted by ones’ memory, perception, by testimony. One is inclined to think of a warrant as an object having a proof in mind. An important qualification is in order here: in the case of inferential a priori knowledge, a warrant is not really a proof, but rather rightly possessing a proof. There is a distinction between having a warrant and being rightly warranted. We may possess a proof without realizing that it is in fact a proof. We may not understand the proof, so we cannot gain knowledge by its means. For inferential knowledge a priori that p, certainly the possession of a proof is a necessary condition but it is not a sufficient one. I may not be even sure that I have a proof, I may not know at all that I possess a proof. The property of defeasibility applies primarily to warrants, and warrants are typically defeasible. That is, there will usually be no conclusive guarantee either that we have not made a mistake in getting a warrant, or – even if no mistake has occurred – that further information would not compromise the justification we currently have. (More about defeasibility below.) (4) Being Warranted A Priori Being warranted a priori is thus a state that can be reached in a state of sensory deprivation. On the face of it, such warrants may be as defeasible as any others, for the same reasons. (5) Infallibility It is trivially but necessarily true that when we know a proposition p, then we are not mistaken about p. This is the sense of Kitcher’s notion of infallibility as Hale understands it. The interesting notion of infallibility – the nontrivial one – is one that primarily applies to methods. The question to ask concerning a method is whether if I execute it correctly and then apprehend the belief I ought to form according to the result, there is any residual possibility of that belief’s being mistaken. A method is infallible if and only if when it is applied correctly we end up always with true beliefs. Methods are the only candidates, as I see it, which can make plausible talk of infallibility in an interesting sense despite the fact that we are always fallible. They are the only candidates which can put us in the special epistemological position where we cannot possibly get it wrong.

190

10  A Priori Knowledge and Infallibility

(6) A Priori Infallible Method An a priori infallible method is one that satisfies (2) and (5). It can be carried out in a state of sensory deprivation and is infallible in the second sense mentioned in (5). (7) Defeasibility This property applies firstly to warrants and, derivatively, to the beliefs they justify. A warrant (and its associated justified belief(s)) are defeasible when additional information cannot be ruled out which would either compromise our confidence that the warrant was correctly acquired – that the relevant method(s) were properly executed – or result in a total evidential picture in which the belief(s) in question are no longer justified. It is our essential fallibility – the fact that we are always capable of error – which ensures that defeasibility is so pervasive. (7*) De Facto Indefeasibility A warrant is de facto indefeasible at t and later times if all further evidence against it is in fact misleading evidence. First, we cannot know that a warrant has this property at t, or any subsequent time, because we won’t be able to have all the relevant evidence at our disposal. Second, we cannot know that a warrant has this property at t and later times because there is no guarantee that we can know about all future evidence against the warrant, provided that we are in a position to gather it all, that it is actually misleading evidence. Warrants can be de facto indefeasible at t and later times without our knowing that they are. Note that a posteriori and a priori warrants can be de facto indefeasible. Very importantly, de facto indefeasibility is not the same as infallibility. The notion of de facto indefeasibility is weaker than the notion of infallibility. When a warrant is necessarily, not simply de facto, indefeasible, then it is infallible (indirectly) in my sense, that is, it is the result of a correct implementation of an infallible method. Knowledge requires that its successful warrants – those which produce knowledge on the occasion – are de facto indefeasible. Because if I know (in particular if I knew) then it is not possible to show by any kind of subsequent evidence that I am (was) wrong. A warrant can be objectively de facto indefeasible (indefeasible as a matter of fact) or objectively necessarily indefeasible (i.e. the warrant is the correct implementation of an infallible method) without our knowing that is objectively indefeasible one way or the other. That is why even these warrants are defeasible in the sense just mentioned in (7). (8) Success of Methods There is an important distinction to be made between a method of discovery which is in a particular case successful, and a method which in principle could only be successful. As I take it, an infallible method ought to be understood as a method which in principle could only be successful.

10.1 Glossary

191

(9) Revisability The candidates for revision are beliefs, warrants, and claims to knowledge. In the literature, we find two kinds of revisions for the first: (I) Revision of Beliefs (a) strong revision When subsequent information reveals that the original belief was false. (b) weak revision When subsequent investigation makes it appropriate to reshape the concepts occurring in the proposition. There can be circumstances in which it would be rational to rethink our concepts or to change them by others which do not guarantee the truth of the original belief. I propose a corresponding distinction at the level of warrants: (II) Revisions of Warrants (a) strong revision When the warrant is found to be faulty and rejected completely for that reason. For example, in the case of an alleged proof containing a contradiction and there has been no way of resolving the contradiction. We reject the warrant completely. (b) weak revision This is the case when the warrant is faulty but repairable. We just have to repair the problem and can still hold the belief under the revised warrant. (III) Revision of “claims to knowledge” Claims to knowledge are of the form: “I know that p” and they are true iff I know that p, otherwise, they are false. My claim to know that p can be subverted in the following ways: (a) when p is subject to weak revision and I end claiming to know a (slightly perhaps) different belief, (b) when my claim to know p is false because p is false, (c) when I have to reject my claim to know that p because the warrant I had was not a good one. Another situation is when I still claim to know that p but I am justified in doing so by a new warrant which can be an improvement of the old one, if that was possible, or a completely new warrant for my belief that p. This is not a revision of the claim to know. The claim to know that p says something different from the claim that p. I can justify my denial that I know that p without for that reason justify the denial that p. Also not every ground for asserting p is a ground for my claim to know that p.

192

10  A Priori Knowledge and Infallibility

(10) Falsifiability This property is applied primarily to beliefs or propositions, and secondly, to our claims to know a belief that has been subsequently falsified, shown to be false. Falsifiability of beliefs is the same as strong revision of beliefs. It results in a complete rejection of the warrant which allegedly justified the belief. The claim that “I know that p” is falsified when p itself is falsified. (11) Certainty Describing necessary propositions as certain doesn’t seem to be correct, since – obviously – a proposition could be necessary without even being known (or, some would hold, without being knowable – Goldbach’s conjecture, for example). The best notion of certainty is a normative one: a proposition may be described as certain not because one happens to be immovably convinced of it but because that attitude is rightly regarded as fully justified. Note that if certainty is so characterized, then it is possible for a proposition justifiably to be regarded as necessary without its being certain – in special circumstances where the grounds for regarding it as necessary are not all that strong – and the same may go for a proposition which is grounded a priori. Where the notions – certain, necessary, a priori – all seem to come together is in the simplest examples of the a priori: fundamental laws of logic, for example, and the simplest elementary arithmetical equalities. To recapitulate, it was crucial to provide a glossary for two main reasons: First, in order for the reader to get clear about what I have in mind. Second, I have found it extremely important to come up with a notion of infallibility that is workable enough to make it plausible that there is some room for infallibility, properly understood, despite the fact that we are fallible creatures and prone to make mistakes everywhere. It is too easy to disregard the possibility of infallibility given our inescapable fallibility. But I considered that to be a mistake. To postulate infallibility does not have to mean denying our fallibility. So, the important question becomes: what are the reasons that could be offered to postulate infallibility? I think that to take infallibility as a property primarily of methods is a necessary condition to accomplish this task. It was Wright’s work which firstly led me to think about this position.1

10.2 Theses on Infallibility I shall proceed to distinguish two theses on infallibility, and to evaluate them. I will not be attributing the first thesis to any particular philosopher but rather will consider it on its own merit as a possibility in logical space. I won’t contend though that they exhaust all the possibilities. I just have found them interesting.  Wright, Crispin. Realism, Meaning and Truth. Basil Blackwell, second edition, 1987.

1

10.2  Theses on Infallibility

193

(1) What is primarily infallible are procedures by means of which items of knowledge can be acquired. This thesis of infallibility may be understood as requiring two things: that knowledge must be restricted to cases where we possess infallible ways of knowing as well as incorrigible propositions, that is, risk-free methods of generating knowledge and propositions which in no circumstances could be false. Does the latter requirement mean that we have to be concerned only with necessary truths? It should not since we presumably should leave room for a priori knowledge of contingent truths. This points to a distinction between senses of the phrase “cannot be false”. I distinguish the following: (I) “cannot be false” in the sense that the proposition in question is a necessary truth; (II) “cannot be false” in the sense that it may be a contingent truth and nevertheless cannot be false in the world where it is true as long as it is entertained by the subject, for example, the cogito and some simple beliefs about our mental states belong to this group (I call them “cogito propositions”); and: (III) “cannot be false” in the following sense: when the proposition is generated by the correct prosecution of an infallible method it has to be true  – infallible methods only generate true beliefs; the modal status of the proposition known being a separate issue altogether. Thesis (1) would allegedly exclude the method of observation since it is not a totally reliable method; it is not immune from mistakes. A possible view about risk-free procedures is that only procedures which are self-guaranteeing or self-justifying are accepted. The propositions supposedly known by these “methods” are self-evident truths, for example, the cogito. Another version of thesis (1): (2) It consists of understanding thesis (1) – i.e. that what is primarily infallible are procedures by means of which items of knowledge can be acquired – wholly in terms of identifying methods of knowing which in themselves eliminate the risk of error. That is, (2) does not involve an attempt to discover propositions which are supposedly infallible. Again, what is the difference between theses (1) and (2)? The second thesis is entirely concerned with methods which can be infallible. Wright suggests this interesting thesis of infallibility in his Realism, Meaning and Truth in the context of a discussion about the relationship between an arithmetical computation and its result. A … prima facie promising aspect of the relation between a feasible computation and any arithmetical statement which it verifies or falsifies is this: that if someone (i) comprehendingly carries out the computation correctly; and (ii) correctly apprehends the outcome; and

194

10  A Priori Knowledge and Infallibility

(iii) possesses a correct understanding of the statement in question, the opinion he forms concerning the truth-value of the statement is bound to be correct; there is no further scope for error.2

Theses (2) on infallibility has to be qualified though. At first sight, the fact that we are always fallible would appear to preclude the possibility of such methods: that is, given that we are always fallible, prone to make mistakes, how can we have infallible methods? First, we could have infallible methods in my sense without being aware of having them given our limited intellectual capacities. Second: Provided that there are infallible methods, their metaphysical status is irrelevant for the epistemological points I am making about them. The latter conditional will obtain irrespectively of: (a) whether we have infallible methods, (b) whether we create them or not, and (c) whether infallible methods exist independently of us, as abstract objects arguably do, and we are just discovering them. A clarification is in order at this point, and it has to do with something I have insisted upon and, that surprisingly enough, has been almost totally ignored in the literature. There is a distinction between the defeasibility of grounds (warrants) and the possible infallibility of methods, and the fact that given the former, the latter can only be conceivable in conditional form,3 and in relation primarily to methods instead of ourselves implementing such methods. Infallibility is conditional upon the satisfaction of the appropriate precautions, and lies in the impossibility of no further error or mistake. That is, infallibility entails that there must not be the possibility of further error. Obviously all warrants can be subject to defeat (are defeasible in principle) due to our fallibility. That is, all warrants are defeasible in the sense that it is always an epistemic possibility that we have made a mistake in carrying it out, or even if we did not and, as a matter of fact, the warrant cannot be defeated, we may think otherwise. But given that the methods have been applied correctly on the occasion, and we apprehend correctly the belief we ought to form by an infallible method, then no other logical possibility of error remains. Another distinction is at work: the distinction between (cognitive) methods and warrants. A (cognitive) method is a general routine we can perform correctly or incorrectly and, consequently, get warranted belief (or not) as a result. The methods can be intrinsically infallible, but our implementation of them – which results in our rightly possessing a warrant – is not infallible because we are not infallible. Given these qualifications, the second sense is the one I will develop, that is, that infallibility is a matter of certain methods of knowing which in themselves eliminate the possibility of (further) error as described above. The nature of the proposition known will not play a major role in my development of this thesis. (2) is consistent – more precisely, totally analogous at the level of methods, not of warrants directly – with my view, shared by other philosophers, that the notion of an a priori justification is the fundamental notion to characterize in the epistemology of a priori knowledge. I have extensively argued for this claim in this book, so I won’t repeat myself here.

 Wright, ibid., p. 115.  Again, Wright is aware of the crucial fact that a conditional is involved here.

2 3

10.3  Some Clarifications

195

As I already said, I intend to make conceivable the (mere) possibility of infallibility. The crucial question, the first task, becomes in my view how to explain that we as fallible knowers can be in a position where we cannot get it wrong, where we cannot be mistaken. Whether the possibility has been realized is to argue for another matter (a second task). I don’t have a knock-down argument for the latter, though, of course, that is not to deny that accomplishing the first task paves the way for settling the second question, that is, that the possibility has been realized (actualized). Briefly, an answer to the second question is that if we prosecute an infallible method correctly, and correctly apprehend the result, we are guaranteed both that we are not wrong and that we cannot possibly be wrong. One could argue that in the basic case, we are infallible when we possess a belief acquired by a self-justifying process. I am inclined to reject basic knowledge of this kind as infallible because something basic can be confused. Also we are not infallible about our own private states. It seems also plausible to suppose that physiological psychology could develop to the point that we would be rightly justified in preferring neural readings to the subject’s report when they conflicted. I am inclined to think that when there is room for ourselves conceivably being infallible about more substantial truths, it appears to me to be the case that there is a method involved, and it involves the correct execution of an infallible method. I believe that infallibility can be accounted for wholly in terms of the existence of infallible methods and the correct implementation of them, independently of the status (i.e. analytic or necessary) of the propositions to be known. At least, I find that that would be a desirable result to have. It would fit nicely with taking the term “infallible” as applying primary to methods, and conceivably and derivatively to ourselves carrying out such methods, and likewise, in any case, to propositions believed by their means. I don’t yet have an argument for this conviction, but will be testing below if it is correct.

10.3 Some Clarifications My goal in this section is to clarify the relationship between knowledge and infallibility by analyzing statements that we ordinarily accept about them. Some of them are truisms; others are loose ways of trying to convey the same thoughts that these truisms express. The problem is that some of these loose ways of speaking are harmful. They can create the wrong impression that knowledge, by its merely being so out, entails infallibility. The following are some clarifications of the concept of knowledge. (I) Necessarily if I know that p, then “p” is true.4  The kind of modal involved in these statements is conceptual. These statements express conceptual truths about the concept of knowledge. But it is not an issue for me to settle what kind of modal is involved. 4

196

10  A Priori Knowledge and Infallibility

It is a truism that knowledge entails the truth of what is known. (Usually we express the same thought as simply “If I know that p, then “p” is true”. Actually, we tend to ignore the modal operator in front of these statements.) (I1) Necessarily if I know that p then I am not wrong about p. It is a platitude that one doesn’t count as knowing unless one is right. Even more trivial is that: (I11) Necessarily if “p” is true then I am not mistaken in believing that “p” is true (if I believe that p at all). It is banal that if p is true then I am not mistaken in believing that p. These are trivial consequences. It is crucial to note that the modal operator in (I), (I1), and (I11) governs the whole statement. We usually intend in ordinary English to convey the previous platitudes as follows: (II) If I know that p, then I cannot be wrong (or mistaken) about p. With (II) we try to capture (I1): “Necessarily if I know that p I am not wrong about p” (loosely: “If I know that p, I am not wrong about p”) by (II) If I know that p, then I cannot be wrong about p. (I) and (I1) are satisfied by any sort of knowledge. It may appear to someone that (I) and (I1) imply that my knowledge that p is infallible. This would constitute a trivialization of the notion of infallibility. This is not the interesting notion of infallibility since it does not point out the problematic nature of infallibility but rather trivializes it conflating it with knowledge per se. This loose way involved in (II) by which it is usually meant (I1) is problematic. (II) involves an operator shift and it indeed constitutes a fallacy. We see how the statement “I cannot be wrong about p” can give the wrong impression in this context that because we know there is stronger guarantee that necessarily we know, and that we cannot be mistaken. Because I know that p it does not follow that I cannot be wrong about p since it is not necessary that I know that p. I may not have known that p; I may have not even thought about p, so I might not have been right or wrong about p. In contrast, the following statement is fine: (II2) If p and I believe that p then I am not mistaken in believing that p. (Logically expressed: Necessarily if p and I believe that p then I am not mistaken in believing that p.) There is an important qualification to make at this point: the statement “I cannot be wrong about p” conveys three more possible meanings (at least): (a) At any time I think that p is true, I can’t be wrong in thinking that p is true since p is a necessary truth, that is, it is always true. Why? Because any time I entertain p and believe it to be true I am right because p is always true. This case only involves knowing the truth-value of p and does not involve knowing why it is

10.3  Some Clarifications

197

true or the way it is shown to be true.5 For example, if p is true and can be proven, and I know it by testimony, I know that it is true, but I don’t know its proof, I don’t know the reasons why it is true. We may not even know the content of p but just that it is true or that it is necessarily true. (b) I can’t be wrong about the subject matter of p. That is, I will always “track the facts” so to speak – if p is true I will believe that p and if not p is true then I will believe not p instead.6 (c) This case does not involve – necessarily – simply thinking that p is true because I will always be right about that given that p is a necessary truth – this is case (a) above – but rather when my warrant for knowing that p is the result of the correct prosecution of an infallible method. That is, given that, on the occasion, the method was properly executed, and that I apprehended the belief I ought to form according to the right prosecution of the infallible method in question, then I cannot be mistaken about p. This sense of “I cannot be wrong” is the one I am interested since it involves the non-trivial notion of infallibility I have in mind. Infallibility is generated when we form the belief we ought to form. If the method is infallible, the belief that we ought to form on the basis of the correct implementation of the method cannot be false. Note that I am not saying that the belief we actually come to have on the basis of the method (even if infallible) cannot be false because there is a gap, there is a causal chain, from the end of the calculation, for example, to the apprehension of its result. It is possible that we apprehended the result incorrectly, misread the result, something happened, and then we ended up with another belief that the one we ought to form. The statement “I cannot be mistaken about p” involves not only that I am not mistaken about p (presently) as a matter of fact since, as already said, this is a consequence of my simply knowing that p at any time t, but also three more things: (A) that “I cannot be mistaken about p at t, at the present time I know that p” because I necessarily had to know that p at t when I know that p at t as the result of the correct prosecution of an infallible method; (B) that “I could not possibly have been mistaken about p” whenever in the past I have come to know that p in the same manner; and (C) that “I won’t possibly be mistaken about p” in any future time when I will be in the process of coming to know that p again in the same manner as well. These inclusions are obvious consequences of the grammatical fact that the English verb “can” is atemporal. In short: any time I implement correctly an infallible method and correctly apprehend the belief I ought to form by the method, I end up with knowledge.

 I use here Casullo’s distinction between knowing the truth value of a proposition and knowing its modal status. Though I rejected in Chap. 1 Casullo’s distinction applied to Kant, that does not mean that I rejected his distinction altogether. 6  I am not endorsing this since it seems an implausible epistemic position. I am only explaining the different meanings the statement “I cannot be wrong about p” can convey. 5

198

10  A Priori Knowledge and Infallibility

It is indeed a very strong notion of infallibility that I have in mind. I think that it ought to be so if one is to avoid conflating the possibility of infallibility with the possibility of knowledge. One has to be able to distinguish between three claims: (i) that “if I know then I’m not mistaken”, and the corresponding fact that if I know then the possibility of error is in fact excluded; (ii) the claim that “I know but I can be mistaken at different times” which entails that the possibility of error is not necessarily excluded; and (iii) the claim that “I know and I cannot be mistaken” which entails that the possibility of error is necessarily excluded. The sentence “I can be mistaken” in (ii) means that I can be mistaken about p at different times: for example, at previous times I could have been mistaken, and at future times I can be mistaken, and also in the present time I might not have known. To conclude, let me briefly evaluate the following statements: (1) If I know that p at t, then I am not mistaken about p at t. (1) is a loose way of expressing “Necessarily If I know that p at t, then I am not mistaken about p at t”. It consists of merely dropping the modal operator in front of the statement. Since it does ignore the modal operator, it does not create the wrong impression of infallibility. (It may be harmful for other reasons.) (2) If I know that p at t then I cannot be mistaken about p at t. (1) is not logically equivalent to (2). In (2) what we have done is to switch the modal operator inside. It constitutes a fallacy. It leads to confusion and danger since in switching the modal operator inside the statement it creates the wrong impression that knowledge entails infallibility. The following statements are fine: ( 3) If I don’t know that p at t then I am not right or wrong about p at t. (4) If I don’t know that p at t and thought I knew p at t then I am wrong about p at t and wrong about my knowing that p at t. (5) If I know that p at t then it is an open question whether I cannot be wrong about p at t or not. That is, it is left open whether I must have known that p at t or not; the method might be infallible. (6) If I know that p at t then it is an open question whether I could have been wrong about p when I was coming to know that p, that is, in the process of coming to know that p at t; the method might be fallible. I have to address two important issues: (1) whether all a priori methods are infallible methods, and, (2) whether some empirical methods are infallible methods or not. I shall shortly return to these questions after Sect. 10.4.

10.5  The Contingent A Priori

199

10.4 Helpful Lists It will be helpful to try to come up with lists in connection with a priori knowledge. One of them is a list of possible procedures or methods by means of which we could acquire knowledge infallibly:7 (1) self-guaranteeing or self-justifying procedures We saw already the problem with those. (2) Calculation When calculating in the abstract realm, it is an infallible procedure; otherwise it is “quasi-infallible”.8 (3) Counting. When counting in the abstract realm, it is an infallible procedure. Otherwise it is “quasi-infallible”. ( 4) Construction of proofs, where done correctly. (5) Some cases of introspection. (6) Measurement. List of possible truths or statements that we can know infallibly: (1) Necessary truths (2) Contingently true propositions but only a restricted range of factual statements can be accommodated, namely, propositions which describe immediate experiences. For example, the proposition “I am sitting comfortably.” (3) Cogito propositions – example of contingent a priori truths.

10.5 The Contingent A Priori Traditionally, a priori knowledge was associated exclusively with knowledge of necessary truths. Kant offers in the first Critique9 necessity as a criterion for distinguishing what is knowable a priori. In recent times, it has been argued by Saul Kripke that the notions of necessity and a prioricity are not coextensive. Kripke argues that there are necessary truths which can only be known a posteriori10 and  These lists may not be complete. These items are the ones I have found. I am not going to argue for the fallibility/infallibility of all the methods I suggest in the first list. They are suggestions. 8  Briefly, a “quasi” infallible method is an infallible method such that the base to which it is to be applied is unstable, i.e. the objects to which an infallible method is applied do change. 9  B 2- B 3, p. 43; B 4, p. 44. 10  Kripke, Saul. “Identity and Necessity” in Identity and Individuation. Edited by M. K. Munitz. New York: New York University Press, 1971. 7

200

10  A Priori Knowledge and Infallibility

also contingent truths which can be known a priori.11 An example of a necessary truth which can only be known a posteriori is “Hesperus is Phosphorus”. Kripke argues that “Hesperus” and “Phosphorus” are rigid designators, that is, in any world in which they refer, they refer to what they refer in the actual world, namely, the planet Venus. The knowledge that these names refer to the same planet was a scientific discovery. An example of a contingent a priori truth is a truth by stipulation: “The standard meter in Paris is one meter long”. According to Kripke, for the person that fixes the metric system by reference to stick S at t, let’s say, a meter in Paris, the proposition that “The standard meter in Paris is one meter long” is known a priori. Regardless of whether these cases exist, a lesson we obtain from Kripke’s arguments is that it cannot be taken for granted that the notions of necessity and a prioricity are coextensive. Argument is needed to prove this thesis. The issue of the contingent a priori is very complex and I cannot discuss it here in any detail. My goal is modest and clarificatory: namely, to explore how the possibility of the contingent a priori may be reconciled with my account of a priori knowledge. Remember that I proposed to capture the experience-independence characteristic of a priori knowledge as that which is involved in a position where we can know even when we are in a state of total sensory deprivation. It can be argued that the tank insulation suggestion is not good here because it involves sensory deprivation, and this creates a very confused, hallucinatory state. Of course, I am not saying that in such a state there is no possibility of being wrong. But, that sensory deprivation actually leads to confusion and to hallucination seems to me entirely irrelevant – it’s just a contingency, and we can easily imagine things otherwise. It may be that only some contingent a priori statements come out as a priori according to my characterization. What is needed is to find a proposition with genuine clear content and see whether it is contingent and known a priori.12 Furthermore, it may be that even if there is such a class of a priori propositions, nothing of general interest arises from studying such a category. Nonetheless, I will discuss some questions I find interesting. I will discuss two kinds of candidates for contingent a priori propositions: (a) those supposedly obtained by stipulation and (b) the cogito propositions (propositions like “I think”, “I have some beliefs”, etc.) Some of the contingent a priori is concerned with stipulation. When we stipulate we lay down some principles. It is not enough just thinking. Such stipulation can be problematic. First, can we do it in the tank? It does not seem so in some cases. It can involve reference to the external world. In the insulation tank, can we achieve such

 Kripke, Saul. Naming and Necessity. Cambridge, MA: Harvard University Press, 1980.  Wittgenstein’s view in the Philosophical Investigations, for example, is that in the standard meter case there is no proposition involved. There is something non-propositional involved. What is involved is a way of institutionalizing a particular length. There is no proposition involved but rather fixing a length. (The reference here is: Wittgenstein, L. Philosophical Investigations. Translated by G. E. M. Anscombe. Oxford: Basil Blackwell, p. 25, 1968. 11 12

10.5  The Contingent A Priori

201

a reference?13 For example, one cannot measure physical objects in the tank. That requires contact with the objects. A suggestion is that we can access such reference in the tank perhaps by memory. If so, then I don’t only have to have knowledge of concepts prior to the immersion to the tank but also have to be able to recall certain experiences I had previously like when I measured the standard meter. The idea is that we can remember that we achieved such reference prior to the immersion to the tank. Again, the supposedly knowledge a priori of “The standard meter in Paris is one meter long”, for instance, is controversial because it involves reference to physical objects and it appears that we cannot achieve that in the tank. The suggestion is that we can achieve such a reference in the tank by memory. But this suggestion is problematic for two main reasons: first, if knowledge by stipulation requires stipulating the reference of a term to a physical object by pointing at the physical object then establishing such reference can only be done a posteriori. If we refer by a description rather than pointing at, we will have to remember in the tank not only concepts but, for example, that there is a meter in Paris that can be referred to as the standard meter. We have to know that that object in Paris can be the reference of a definite description. This knowledge is not going to be available in the tank. It is empirical knowledge. Then establishing such reference by a description can only be done a posteriori.14 In both cases the memory we would need to rehearse in the tank would be a memory of knowledge a posteriori that we obtained prior to the tank. But then how can that be a priori knowledge if it is a memory of knowledge a posteriori? Second, if we could refer to physical objects in the tank (I already explained why this is not possible but let’s assume it for the sake of argument) then we could rehearse the a priori knowledge in the tank, so why do we need memory? Each way we see that knowledge obtained by memory cannot be a priori since in some cases the original knowledge was obtained a posteriori; not only that, it appears also that knowledge by memory of knowledge a priori we acquired previously should be  It can appear that Wright’s proof of the external world by a priori reasoning and his tank insulation idea as characterizing a priori knowledge are inconsistent. In particular, if one can prove that the external world exist in the insulation tank then one can refer to physical objects in the tank. But to achieve such a reference is problematic. Wright explains (in private conversation) that what he offers in his paper “On Putnam’s Proof that We are not Brains in a Vat” is not so much an a priori proof of the external world as a defense – up to a point – of Putnam’s alleged proof that we are not brains-in-vats. (Wright’s paper appears in Proc Aris Soc, No. 92, pp. 67–94, 1992.) In any case Wright thinks it is wrong to suppose that there would have to be an inconsistency between the characterization of the a priori in terms of what can be known under conditions of sensory deprivation and the possibility of an a priori proof of the external world – the upshot, striking but not incoherent, would be merely that it was possible to know of the existence of an external world in conditions of sensory deprivation. In particular, Wright does not think it would follow that one could refer to physical objects while in the tank. This all connects with the worry which has vexed a lot of people recently, about whether semantic externalism, so-called, doesn’t have some very strange-looking a priori consequences. 14  There are ongoing efforts in metrology to redefine the basic physical units like Helmholtz’ and Poincaré’s discussions of metrology from a conventionalist perspective. See the bibliography of this chapter. 13

202

10  A Priori Knowledge and Infallibility

considered a posteriori, just like knowledge by testimony of knowledge a priori obtained by someone else. So, some of the “contingent a priori” does not come out as a priori according to my account. Nevertheless, stipulation is not an infallible method. It seems that talk about fallibility or infallibility in connection with stipulation does not even make sense, it seems incoherent at first sight; or if it were coherent, then one would have to say that stipulation is infallible by stipulation, which makes stipulation come out infallible trivially. The idea is that the concept and paradigm are very close and do not leave room for the skeptical worry whether something satisfies the paradigm. There is supposedly no space for this question since “meter” and its paradigm are so close to make this question insensible. But this ignores that stipulation is a fallible method. But if we have stipulated correctly, can we gain truth? Not necessarily so. We may have to change our stipulations because our needs change. So, the standard of correctness can change as well. Another possibility: what about the paradigm being slightly damaged? Something can have the standard meter length, but is the latter still one meter long? The paradigm is subject to contingencies, it can change. The feature of the (b) cases  – the cogito propositions  – is that the attempt to doubt the proposition verifies it; that is, the attempt to doubt the proposition necessarily brings about a situation where the proposition in question is true.15 With the cogito propositions, there is a process, maybe a method involved. There is a process involved, namely, thinking. But not a method as in the mathematical case, for example, with the following features: (1) suspension of judgment about the truth-value of a proposition, (2) carrying out the method and, consequently (3) then figuring out the truth-value of the proposition we started with. I call a method which has these features a method of assessment. It is obvious that if there is a method involved in our knowledge of cogito propositions, it is certainly not a method of assessment. With the cogito propositions we don’t suspend judgments about their truth-value, for instance. The cogito propositions come out true in the tank by certain form of intellectual routine. The routine is not a method in the sense that it is not a method of assessment. A precondition of the doubt is that I exist. As part of the doubt you have to have the very thought in question. Another example of a contingent a priori truth is: “I have some beliefs”. In the tank I can know this proposition. These are psychological contingencies. It

 What is the status which Descartes conferred to the cogito? It is not clear what metaphysical status the cogito had for Descartes. I doubt if Descartes cleanly confronted the distinction between necessary and contingent a priori. He thought his existence indubitable, (and that it could be shown to be so by the cogito), but he must also have recognized that he did not exist of necessity. In any case if the cogito is indeed cogent, we will see that the thought-routine which it involves is something that can be run in conditions of sensory deprivation, and so whatever is known as a result of it is something that can be known a priori – at least, according to my definition. Equally, it had better be something that isn’t necessarily true. 15

10.6  Is Infallibility Exclusively a Property of Certain Methods?

203

constitutes knowledge by introspection. As in the case of cogito propositions, it seems harmless that we can know these things in the tank. The reason is that they only involve understanding. There are some complications with the cogito that make us rethink whether we can be infallible about it. What am I saying by “I think, therefore, I am”? I may not know who I am. The point is that the cogito propositions may be susceptible to a more sophisticated doubt.

10.6 Is Infallibility Exclusively a Property of Certain Methods? It can be argued that since I am taking infallibility as primarily a property of methods, I should try to argue for infallibility as a matter of methods alone to justify my application, and should reject the view that sees infallibility as in a way connected with the nature of the proposition known also. Is this really a consequence of my view or can I just ignore the matter entirely? First, I don’t think that it is a consequence of my view. Talk of properties applying primarily to certain bearers does not preclude the possibility of intelligibly applying that same property to other bearers. It is the other way around: in clarifying the primary uses of a property, other derivative uses get clarified as well. However, I will not ignore the suggestion that infallibility is only a matter of (certain) methods. Actually, I will try to analyze what is involved with that idea in this chapter. To try to answer this issue, one would have to get clear about what is an internal relation,16 and whether the content and modal status of the proposition possibly known by an infallible method are irrelevant. I believe that infallibility can be accounted for wholly in terms of the existence of infallible methods and the correct implementation of them, independently of the status (i.e. analytic or necessary) of the propositions to be known. At least, I find that that would be a desirable result to have. It would fit nicely with taking the term “infallible” as applying primary to methods, and conceivably and derivatively to ourselves carrying such methods, and likewise, in any case, to propositions believed by their means. I don’t yet have an argument for this conviction, but I will test below if it is correct. The following question naturally arises: what is there in the method itself that makes it infallible (or fallible)? I want to try to answer that question as follows: that the correct answer is internal to the method (more below). If infallibility is a matter of methods alone regardless of the nature of the truths known by their means, then it would seem to follow that it is possible that methods which deliver a priori contingent truths can be infallible. If that were not the case, that is, if methods which deliver a priori contingent truths cannot be infallible, then: 16

 I will explain the notion of “internal relation” shortly.

204

10  A Priori Knowledge and Infallibility

how can we explain that methods which deliver a priori contingent truths cannot be infallible without appealing precisely to the fact that the proposition in question is contingent as part of such an explanation? In the case of stipulation, we already have seen that it is a fallible method. In the case of an a posteriori method like testimony, say, it is also a fallible method because when we testify to others we can make mistakes, for example, if we report the conversation or a result incorrectly. But can we still be mistaken if we report the conversation correctly? Yes, because the result we report is false; the authority made a mistake. Stipulation is not an infallible method; rather it is a fallible method to know some contingent a priori truths. Testimony is a fallible method even when it concerns knowledge of necessary truths. Observe that the process by which I arrive at the cogito, thinking, is not in general an infallible process. One may wonder whether in cases like these of contingent a priori beliefs, if infallibility were involved, then the process alone would not generate infallibility but rather only in conjunction with the nature of the proposition at issue. Or, alternatively, is it that the possibility of an outcome being internal to a process independent of the modal status of the proposition in question? It may seem that these cases provide an affirmative answer to the first question, and a negative response to the second. But this is a mistake. These cases cannot provide the answers to those questions. If one were inclined to think otherwise it is because one is ignoring the fact that with the cogito propositions, there is a process, maybe a method involved, but clearly not a method of assessment. With the cogito propositions we don’t suspend judgments about their truth-value. In these cases the belief is immediately generated. To sum up, one might think that the infallibility of methods does not depend on the modal status of the propositions known by their means having the cogito propositions in mind. But this suggestion totally ignores that the case of the cogito, and similar beliefs, cannot settle this question because there is no method of assessment involved in these cases. I am inclined to think that the idea of an outcome being internal to a process as generating infallibility is true in the more complicated cases. In these simple cases of knowledge of a priori contingent propositions, since there is no method of assessment involved, if infallibility were involved, it trivially cannot be explained by the fact that the outcome is internal to the process by which we executed the method of assessment. If there is a method involved in our knowing our own existence, it is not a method of assessment. But what about our knowledge of trivially analytic truths and elementary truths of mathematics and logic? We intuitively expect that in these basic cases there could be more room for infallibility, if at all possible. With proofs we can expect more room for error. But my view is precisely that infallibility takes place in demonstrative knowledge. So it does not capture this intuition. I think the issues here are complicated and connect with some of the things I said in Chap. 9 about the defeasibility of the kind of intuitions which motivate mathematical axioms. If I stick to the line that I have been taking, that is, that infallibility

10.7  Which Methods Are Infallible?

205

is always a property of methods, and that we are always fallible in our implementation of them, then I am committed to this stance against the objection. But it is surely right that in the case of very simple and primitive logical mathematical truths, it is specially hard to make sense of the idea that we could be mistaken. But consider: “making sense” of the possibility will mean trying to imagine, in some detail, concrete circumstances in which it would seem to us that the best thing to say was precisely that we had our basic arithmetic, or our basic logic, e.g., wrong in one or other respect. What more is to give the impression of infallibility here than our inability to do this to our satisfaction, together perhaps with an empirical confidence that no unforeseen circumstances are going to arise – of an unimagined kind – in which we have to admit that we do have basic logic or mathematics wrong? If that is all what is involved here, then it certainly does not seem to merit infallibility. Although it may show that we are never going to accept anything as calling the most basic logical and mathematical intuitions into question. In any case, infallibility (i.e. a conceptual guarantee against error) is one thing. It is another thing not being able to conceive a situation in which one’s fallibility was brought home to one (for example, getting concrete evidence that we made a mistake) together with being empirically certain that that is not going to happen.

10.7 Which Methods Are Infallible? Are any empirical methods properly regarded as infallible? If so, then infallibility is not distinctive of some a priori methods. Let me try to explain in some detail some of the issues here and the way I am thinking about them. How is it possible that methods can be infallible while warrants are always in principle defeasible? The distinction between infallibility and defeasibility is very important. The notions come apart and we have to see clearly that and why they do so. It seems we should say that warrants are always defeasible in principle even when acquired by the prosecution of an infallible method. For it is always an epistemic possibility that a method was not properly applied, however careful we were. But if an infallible method was properly executed and we formed the belief we ought to form on that basis, then the warrant, − the result of the execution of that method, − cannot be defeated as a matter of fact, (though we might erroneously come to think that it has been defeated as a matter of fact). Suppose I consult a truthful oracle. Here is where the distinction between methods which are sometimes successful and methods which are always (necessarily) successful play a crucial role. Infallible methods are those which can only be successful. “Consulting a truthful oracle” is not an infallible method because it is not a method which is always necessarily successful. (more below) Recall that a priori methods, whether infallible or not, are those which can be accomplished in a state of sensory deprivation, and that an infallible method is one such that, if it is done correctly, has a correct outcome. In mathematics, both conditions would seem to hold of necessity. At any rate, much mathematics could

206

10  A Priori Knowledge and Infallibility

presumably in principle be accomplished in a state of sensory deprivation – it would be hard (probably too hard for normal human beings, specially in the case of geometry) but not impossible. And mathematical methods seem necessarily infallible. For with mathematical methods – calculation is the simplest example, but the point is general – the outcome is internal to the method. There is no way the outcome of a correct calculation can vary, and only if it could vary could its correct execution lead to an erroneous outcome. The last remark has to be qualified though in a very important sense. First of all: why is it true? Consider a method which yields a root to an equation. There may be several. I respond that the crucial thing, when an outcome is internal to the method, is that a subjunctive conditional along the following lines is necessarily true: had that outcome (or any of a range of outcomes – like, for example, the case of the equation with multiple roots above) not been obtained, the method would not have been correctly applied. That gets rid of the truthful oracle. Because it is not true that had the oracle given a different answer, then necessarily we would not have asked the truthful oracle. For our question might have concerned a contingency, about which the facts might have been different. It can be argued that despite the fact that there is a method which yields a root to an equation, and that there may be several, that the root to be found is more specific, so it is not just a root among many, but a specific root among many. In this case there is only one correct answer. We are looking for a specific root. It all depends, I suppose, on the numbers involved: so if certain numbers are involved in an equation, then its root is unique. Analogously, for example: an algebraic law: “a + b = b + a” involves different identities depending on the numbers involved. But given that certain specific numbers are involved then there is only one possible correct identity. Here is another example. Many different conclusions are possible on the basis of a correct disjunction elimination step on a particular premise. What is characteristic of internal relations generally is, rather, that the obtaining of the relation is essential to the identity of the things related. Even a better example: any statement which may be validly inferred by the disjunction introduction rule from P, say, is such that it would not be the statement it is were it not so inferable. Likewise, if an equation has many roots, each of them will be such that it is an essential feature of them to be a root of that particular equation. Again, what is characteristic of internal relations in general is that the statement that expresses that the internal relation obtains is a necessary truth. But infallibility may not be distinctive of a priori methods. We have to explore the possibility that there could be empirical methods which are infallible. I will try to explain why people have thought otherwise (of infallibility as distinctive of a priori knowledge in any case). Are their reasons good ones? There seems to be a confusion between different things: (a) truth as a necessary condition for propositional knowledge of any kind, (b) necessary truth, as it is the outcome of the correct implementation of a method in the mathematical case, and

10.7  Which Methods Are Infallible?

207

(c) necessarily the outcome is true as in the correct implementation of infallible methods. If we implemented an infallible method correctly, then necessarily the belief we ought to form by the method is true.17 That does not mean that the belief is a necessary truth. The modal status of the belief is a separate question. On the other hand, taking infallibility as primarily applied to methods does not by itself exclude the possibility that the beliefs we can come to know by their means are all necessary truths. The point is that these are two separate issues, though connected in some other respects – as in the strong intuition that if we are dealing with an infallible method and by means of it arrive at a truth that is a necessary truth, then we have the feeling that the infallibility involved has been doubled or it is two-fold. There is a sense in which we feel have reached a double guarantee of infallibility. We have to distinguish three components in connection with fallibility and infallibility: (1) we (the subject knowers): who are always fallible (2) methods: could be infallible (3) warrants (what the methods deliver): could be objectively indefeasible but given (1) they are always defeasible. However, a salient point about infallibility, as we are understanding it, is that it is only possible in conditional form, as it were: if we execute the method correctly, then p, the result, will be true. Cannot this hold in empirical cases too? It does seem so. If I observe correctly that there is a table in front of me, then there has to be a table out there. How can I observe correctly and be wrong about what I observe? Well, what does it mean to observe “correctly”? Clearly, my organs can be functioning normally, and so in that sense I am observing correctly, but that does not ensure that I will get a correct answer. For I may fall victim to a sensory illusion, for instance, or otherwise misinterpret what I perceive. I can observe correctly – in the sense that my eyes are functioning properly, there is good light, etc. – but given that the table may be a fake one or the result of a visual illusion (like being a hologram), arrive erroneously at the belief that there is a table in front of me. It seems that in the case of the empirical method consisting of simple sensory observation, correctness of implementation – in the sense of proper sensory function, in suitable conditions – is not enough to guarantee the truth of a belief warranted thereby. The question of whether any empirical methods are infallible in the way that say, calculation is, is I think a very complicated one. Consider counting as a method for  Is “get to know that p” an infallible method? For if one knows that p, p has to be true. Why isn’t “getting to know that p” a method? One thing that might be said is that the concept of method has a certain generality: if a method is to be something whereby knowledge can be gained, then in general the characterization of a method should not prejudge the truth-value of any particular proposition which might be assessed by the method. Though I consider that “to get to know that p” is the goal of a method, not the method itself. Now, if in applying a method, one always get to know that p then the method is infallible. 17

208

10  A Priori Knowledge and Infallibility

determining the answer of an empirical question, say, the number of people in a room. We should reckon this method infallible just in case there is no way that it can be done right yet we can get the wrong answer. Put like that, isn’t such a method infallible? Can you count correctly yet get the wrong answer? The issue is tricky. We can count abstract entities as well as physical objects. In my view, counting, as applied to physical objects, is not a straightforwardly infallible method. There is no guarantee that in correctly counting physical objects, one gets a correct answer to a particular set question. Counting physical objects is merely a “quasi-infallible” method since, obviously, we can arrive at a wrong answer to the question, how many people are in a room, because the number of people being counted may have changed in the course of my counting. Now, consider a circle that is decreasing in radius as a function of time.  One can do pure mathematics in relation to objects conceived as changing, provided one is given a mathematical characterization of the change (for example of the rate of change, or its extent). Graphs, for example, are typically about such things. Mathematics can be applied to changing things, provided the changes allow of unchanging mathematical representation at some level. So a bit of care is needed in the formulation of the idea that mathematics has an unchanging subject matter. It might still seem that counting correctly, i.e. correctly following the rules of counting in relation to physical objects that do not move around or otherwise change, necessarily generates knowledge. But even that does not seem right. What if the objects being counted are fakes? In that case, then whether we get a correct result will depend on how we formulate it. In what does “the result” consist? Indeed: if what we had to be right about concerned only the number of objects, genuine or fake, then if the objects, whatever they are, don’t move around or change, and we count them correctly, then it seems we must be right about how many of them there are. But such an instruction to count “objects” would be hardly intelligible. Any intelligible such instruction will concern the F’s, for some specific sortal predicate F, like “table”. And if “the result” has to reflect the nature of the objects counted, in particular, be sensitive to whether they are real or fake F’s, then correct counting, as far as it goes, won’t guarantee being right about how many F’s there are even when the (apparent) F’s are stable and unchanging. Counting can be fallible too when in counting the numbers we rely on some sense-dependent means (for example, “How many chords did she just play?”) However counting would seem to be an infallible method when applied to abstract objects defined by their essential characteristics (“Find the number of primes between 12 and 42”), when there is, naturally, no question of fakery. In any case, it is clear that a distinction is called for between methods whose correct implementation is successful under certain conditions only and methods whose correct implementation is always successful; only the latter should count as infallible, period, and, consequently, counting, applied to physical objects, is not an infallible method. That invites the thought that we might elucidate a range of notions of “quasi” – (i.e. relative) infallibility by adding conditions to the antecedent of the

10.7  Which Methods Are Infallible?

209

“infallibility-conditional”18 – conditions such as, for the case of counting, that the objects to be counted should not change in the course of counting. Again, if a method is infallible provided, properly applied, it is guaranteed to lead to a correct result, then there may be a variety of notions of infallibility, depending on certain relativities in the guarantee in question: for instance, certain empirical methods may be infallible relative to the assumption that things do not change in relevant respects while the method is being applied. But there is an obvious risk of trivialization if we are allowed to be too free with such additions. In order to make an interesting issue of the question whether some empirical methods are quasi-infallible, it thus becomes crucial to get clear about which such additional conditions may usefully be contemplated. This is not an easy task and may not be even an attractive one to undertake. But the resulting taxonomy may still be important. One other major issue is worthy of mention. We noted that correct observation – in the sense of proper sensory function under normal conditions – cannot conclusively settle whether what one is seeing is a table or, say, a hologram. The content of the proposition, “There is a table there” exceeds anything that can be once and for all established by finite episodes of vision or indeed other forms of sensory episode. But that seems to be a function of the content of the concept, “table”. Might the situation be different if we considered instead a statement framed in terms of more purely observational concepts? Are there any concepts so intimately related to observation that they don’t allow for any analog of the shortfall between observation and the facts that apply in the example of the table? One range of candidates for such concepts are those of color, sound, and Lockean secondary qualities generally. However something can look red in all respects and not be red – there are phenomena like “red shift” in relation to distant stars, and illusions of color generated by background. But perhaps an interesting “infallibility conditional” can be generated for these concepts; perhaps we can circumscribe the range of ways in which appearances can mislead and then if none of these applies, observation will be infallible with respect to e.g. color. A thought is that no method can be absolutely infallible if its outcome is subject to extraneous causal influences. So it is tempting to conjecture that only where there is an internal relation between method, starting point, and outcome is infallibility possible, and hence that it is restricted to a priori knowledge if it exists at all. But this whole issue needs extended treatment. The immediate task is to explore what forms of relaxation/complication of the original simple condition expressed in the antecedent of infallibility conditionals – “If method M is correctly executed on the relevant occasion and the subject S forms the belief she ought to form according to the outcome, then that belief is true” – may be well-motivated on general grounds.  An infallibility-conditional expresses in its antecedent the conditions that have to obtain for infallibility to take place: in my view, for example, (1) that an infallible method was properly executed on the occasion and (2) that we formed the belief we ought to form according to the correct implementation of the method, for example. Then the belief generated is true and we end up with knowledge – the latter conjunction is expressed by the consequent of the infallibility-conditional. 18

210

10  A Priori Knowledge and Infallibility

But, why should infallibility require that no causality is involved in the process? – surely there is causality involved in anyone’s actually calculating, for example. What is true is that when the relation between bases, process, and outcome is internal, then there are no causal conditions such that, had they varied, the outcome could have been different although the basis and process were the same.

Conclusion

The issue of infallibility in connection with a priori knowledge is not a clear issue in Kant at all. As we have seen, this whole issue is very intricate and has helped me to disentangle some of the aspects of our question, for instance, the role the alleged necessity of the judgments known a priori has in connection with the possible infallibility we can have in our acquisition of a priori knowledge. In my view, Kant’s views do not entail that a priori knowledge entails some sort of infallibility. Kant knew about long proofs from Euclid. Kant would have accepted that we are liable to err when carrying out long proofs – which nevertheless contain axioms which would themselves be known a priori. Obviously, whether Kant did succeed or not in characterizing both the notion of a priori knowledge and the notion of “experience independence” distinctive of it, has a direct bearing on the attempt to answer whether Kant considered a priori knowledge to involve some sort of infallibility. It is difficult to get clear about the answer he would have given to this question given that he was not clear about the characterization of a priori knowledge in the first place. Kant does not even explicitly characterize what is the “independence of experience” characteristic of a priori knowledge. A more explicit characterization of a priori knowledge constitutes a necessary step in order to clarify its relationship with the notion of infallibility, properly conceived. Let’s recall that for Kitcher and Friedman, it seems that the question of whether it would be possible to have an a priori warrant for a false belief does not arise for Kant. Perhaps Kant did not think such a question could arise. I think it is unfair of Kitcher and Friedman to adjudicate to Kant the view that there is no possibility of an a priori warrant justifying a false belief by merely invoking Kant’s claim that all a priori knowledge is knowledge of necessary truths. We have to know how the justification for the necessary truth stands – it may not amount to knowledge. And if the warrant produces knowledge, it is because it is a good or sound warrant. The modal status of the truth known by its means is a separate © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 I. Fred-Rivera, A Historical and Systematic Perspective on A Priori Knowledge and Justification, Philosophical Studies Series 151, https://doi.org/10.1007/978-3-031-06874-4

211

212

Conclusion

matter. Unfortunately, Kant did not elaborate on the notion of an a priori justification. Since the notion of a priori justification is the crucial one to characterize in the epistemology of a priori knowledge, contrary to Kitcher and Friedman, it remains unclear if, for Kant, a priori knowledge implied some sort of infallibility. Since I think Kant did not succeed in characterizing, explicitly and fully, the notion of a priori knowledge, I proposed my characterization in the last chapter. The importance of the question whether infallibility is a distinctive property of a priori knowledge remained. I addressed this extremely difficult question and tried to offer a resolution to it in the last chapter of this book. One thing emerged very neatly from our discussion of Kant. Both the urgency for providing an explicit characterization of the notion of a priori knowledge as well as the importance of the question whether infallibility is a distinctive property of a priori knowledge remain. I addressed these difficult questions in the last chapter. Quine urges that no statement is immune from revision. No sentence or set of sentences is in principle unrevisable for in an attempt to fit theory to observation any sentence or set of sentences may become a candidate for revision. Logic and mathematics, as any other purported a priori knowledge, are parts of our system of background assumptions and are in principle open to revision. In particular, logical truths are theoretical principles of the most fundamental sort which we are far more “reluctant to give up” in particular circumstances than our everyday beliefs or even fundamental theoretical principles in science. For Quine, it is conceivable that in response to some fundamental difficulty in science, a new theory could be formulated that proposes a modification of part of elementary logic or arithmetic. Dummett and Hale interpret Quine as an opponent of a priori knowledge who argues, not only that all knowledge is revisable, even knowledge of a logical truth, but that it can be revisable in response to experience. Quine offers as an example of this thesis applied to logical truths that the logical law of excluded middle may have to be abandoned in response to, for example, quantum mechanics. Both Dummett and Hale claim that a priori knowledge must not be revisable or falsifiable by empirical evidence. In other words, a priori knowledge has to be independent of experience in terms of both justification and revision. I don’t agree with Dummett, Hale and Field in taking that the a priori ought to be characterized in terms of non-falsifiability by empirical evidence. Falsifiability seems too narrow a concept. At least as far as I am aware, in the sciences, very rarely general statements are actually falsified. I proposed to focus on revisability instead, where revisability is more general than falsifiability. One might have reasons to revise certain statements, even if they are not falsified in a strict sense, for example, for pragmatic reasons such as simplicity. A defender of a prioricity should not wish to resist the suggestion that logic, or other disciplines conceived to involve a priori statements, are revisable. There should be no interest in maintaining that we cannot be in error in judging a statement to have that status. Can we therefore give Quine the claim that any particular statement which we accept as a priori could, in certain circumstances, reasonably be discarded? To grant the claim need be to grant no more than that our assessment of any particular statement as a priori may always in principle turn out to have been

Conclusion

213

mistaken. Quine has assumed, with the bulk of the philosophical tradition, that a prioricity involves indefeasible certainty. To claim that a statement is a priori, however, is only to make a claim about the way we know of its truth  – there is no  immediate reason why the claimant has to agree that, when statements are a priori, their truth must be known with special sureness. The problem with Putnam’s notion of a prioricity as entailing unrevisability is that it does not include the majority of what are usually considered a priori truths, in other words, it is too strong. And the problem with Putnam’s notion of a prioricity as “contextual a prioricity” is that it is too weak since this notion does not capture – let alone account for – the alleged special certainty that traditionally has been associated with mathematical and logical truths. Putnam’s views do not take the predicate “a priori’ as primarily characterizing a particular way of knowing. He does not clarify the sense in which a priori truths are a priori, that is, because they are known in a particular way. So, his account does not illuminate the issue of the “independence of experience” characteristic of a priori knowledge but only concentrates on the supposed properties that a priori truths have: for instance, unrevisability allegedly. The mistake I attributed to Putnam (and Quine) is that of supposing that in order for something – a statement?, knowledge claim?, belief?, − to count as analytic, or a priori, it has to be unrevisable. Let us take it that it is beliefs that are revisable or not. Then their thought is that in order for it to be possible to know a statement to be true a priori, there have to be grounds for believing it to be true such that, once we are apprised of those grounds, no possible improvement in our state of information could destroy the warrant which they confer. In the basic case it is statements – declarative sentences – which are analytic or not (true in virtue of meaning or not); ways of knowing, or justifying, which are a priori or not; and beliefs (“claims to know” being a particular kind of beliefs) which are revisable or not. Since these three concepts apply to different kinds of thing, there is no question of anyone’s clearheadedly “equating” them. At first glance, it seems that Putnam equates mere “revisability”with “empiricalness”, so whatever is revisable has to be empirical in character. This is quite questionable since revisability is not per se incompatible with a prioricity. One should distinguish here between the sort of grounds for revisability on which one might hold that revisability does not carry empirical status with it – there is a difference between revising a statement because it is found to lead to a contradiction, say, and revising a statement because it conflicts with experimental or observational findings. Revision is consistent with a prioricity. Revisions in mathematics, for instance, are conducted via rational reflections on mathematical concepts, for example, the concepts of number, set or the differentials in the beginning of analysis, and proofs. These are a priori ways of knowing. Finally, Putnam’s views do not take (not explicitly at least) the predicate “a priori” as primarily characterizing a particular way of knowing. Consequently, his views do not clarify the sense in which a priori truths are a priori, that is, because they are known in a particular way. So, Putnam’s account of the a priori does not illuminate the issue of the “independence of experience” characteristic of a priori knowledge.

214

Conclusion

Putnam affirms that even though he recognizes the existence of at least one a priori truth, the notion of a prioricity is not terribly important to philosophy because it can no longer play the traditional role it had. We don’t gain much by having a notion of a prioricity which entails unrevisability since there is few a priori knowledge. The majority of truths traditionally considered a priori are not included under his notion. Putnam ultimately thinks that the notion of a prioricity is important because of what indicates about rationality. In the end, Putnam thinks that a priori truths are unrevisable. What about the relative and absolute a priori distinction? This distinction is used by Putnam to clarify which truths are a priori in his strong sense of absolutely a priori or unrevisable, and those which are a priori but only in a weak sense, contextually a priori. Since he thinks there are very few a priori truths, let’s remember that he is not prepared to defend even the a prioricity of the full principle of contradiction, the notion of a prioricity is not terribly important to philosophy. The situation with the “a priori/a posteriori” distinction is analogous to the one with the “analytic/synthetic” distinction. There is such a distinction. Quine is wrong to deny this. But Quine is right in the sense that the distinction is a trivial one. Now, what is important about Putnam’s “final” view on a prioricity is that it is sensitive to the issue of unrevisability/infallibility in connection with a priori knowledge. Let’s recall that the circularity charge I made in chapter eight against Hale’s proposal in his book Abstract Objects  involves two aspects: (1) a vicious circle is involved; and (2) it is not very illuminating. Even if a Hale-type account would succeed with (H) – (H) X knows a priori that p iff X knows that p and neither X’s justification for believing that p nor p itself implies (entails) the truth of any experientially falsifiable q – in avoiding the first aspect of the circularity, and his definition is correct, still the second aspect of the circularity remains, it is not very illuminating, not positive enough. In Hale’s view, an a priori justification is characterized as simply lacking a certain feature. That is why one of my tasks in the third part of this book has been to try to provide more illuminating suggestions than Hale’s about the notions of an a priori warrant and a priori knowledge among other related notions.  I tried to develop a view that is weaker than Hale’s since my view doesn’t put any constraint on the kind of defeating evidence against an a priori warrant or an a priori statement, and still respects the intuitions regarding a priori warrants and a priori knowledge. What is really relevant in my view for the characterization of an a priori warrant or an a priori statement is not immunity from revisability, or falsification, by empirical reasons, but rather justifiability independently of experience. I have attempted to capture the experience independence of a priori knowledge wholly in terms of the way the justification is carried out. Given that we don’t know if Hale’s view can be correct, I prefer to be scrupulous and maintain a weaker view that does not commit me to a position on the nature of defeating evidence against alleged candidates for a priori knowledge. Provided that it is an open question whether we are going to have empirical evidence against an a priori warrant or an a  priori statement, better to be more cautious.

Conclusion

215

Hale does not appear to have distinguished between warrants and methods or at least has not used the distinction at all. As a consequence, Hale does not address the interesting and very difficult question whether the notion of infallibility has a place only in the realm of a priori knowledge – in other words, whether infallibility is an a priori matter – or whether that is not the case. In general, there is a distinction between the defeasibility of warrants and the possible infallibility of methods. We have to distinguish between the infallibility of certain methods and our fallibility in carrying them out. In his book  Abstract Objects, Hale accepts the defeasibility of a priori warrants and, for that reason, may have thought that a priori routes for knowledge cannot be infallible. But Hale fails to distinguish between defeasibility and infallibility. It is obvious that we are fallible, but it does not follow that there are no infallible methods such that if we execute them properly can get infallible results. As far as the issue of infallibility is concerned, it appears that Hale in his chapter leaves no room for infallibility in connection with a priori knowledge – or knowledge in general – given the undeniable fact that we are fallible creatures. Nevertheless, I have to be cautious and refrain from attributing to Hale this position since he simply does not discuss the issue of infallibility at all. The reason why he doesn’t in the book may be the one just mentioned, but it is only a possibility among others. On the other hand, that reason may have just been entirely non-philosophical. I agree, given the qualifications that I have discussed in chapter eight, with Hale’s claim that the notion of a priori knowledge (more accurately, the notion of a prioricity (i.e. a priori justified belief)) ought to be consistent with the possibility of revision. We are fallible creatures and we can make mistakes. I agree also with Hale that a priori warrants do not have to be infallible. The mistake Kitcher made, and that Hale quite correctly diagnosed as due to conflating the truth entailing character of knowledge and the independence of experience characteristic of a priori knowledge, is to think that an a priori warrant has to be ultra-reliable (infallible) to be a priori. However, Hale does not consider the idea that some a priori warrants may prove to be infallible, what Kitcher called “ultra-reliable”. Actually, Kitcher’s work has stimulated my own view on infallible methods (not warrants). Kitcher and Hale do not talk about methods but warrants, so they don't compare or distinguish between them. The immediate point about infallibility is, of course, not whether what is in fact an item of a priori knowledge can be mistaken – no-one supposes that – but whether the prosecution of the methodology of a priori knowledge can lead to mistaken beliefs. Put like this, the answer, of course, is yes – people can get muddled, make mistakes in inference, miscalculate, etc. Those who allow for infallibility like Kitcher cannot mean to deny this. So what is involved? The question is a substantial one. The idea is that a certain kind of prosecution of the methodology of a priori knowledge cannot steer us false – whereas in the empirical case there are no controls, no safeguards on method such that, if they are complied with, the results are guaranteed to be true. Of course, the substantial question is to say what this ideal prosecution consists in. In the last chapter I tried to accomplish this task. To sum up, (i) I doubt if it is coherent to think of human beings as being infallible anywhere. If we have access to substantial truths about the world, whose obtaining

216

Conclusion

is independent of human judgment about the matter, then, however hard it may be for us to understand how this might be, there has to be the bare possibility of misapprehension, or ignorance, of the states of affairs described by such truths. Another way of putting the point would be to suggest that fallibility is implicit in objectivity, though that needs unpacking. (ii) That, however, is consistent with the infallibility of certain methods – with the idea that, at least in certain areas, we have methods of knowledge acquisition at our disposal such that, if we implement these methods properly, we are assured of winding up with true opinions. Of course, this will not guarantee the truth of what we actually come to believe by prosecuting those methods, since we may be mistaken in thinking that we have done so properly. Ordinary arithmetical calculation is an example of such a method: if one calculates properly, the results one gets are correct. That is a necessary truth. But it does not follow that carefully achieved arithmetical opinions are infallible, since one may be mistaken in thinking that one calculated properly. As far as a priori knowledge is concerned, then, the interesting questions are: (a) whether a priori truths generally are associated with methods which are infallible in the sense I just have outlined; and (b) whether it is possible to judge with a superior, though not indefeasible, degree of sureness that the appropriate methods have, in particular cases, been correctly executed. Perhaps Hale, along with many other philosophers) just go past these questions because of  their  assumption that a priori knowledge has to be compatible with revision. (And Quine because of his dogmatic assumption that a priori knowledge has to be unrevisable.) As a consequence, Hale does not address the interesting and very difficult question whether a conceivable notion of infallibility has a place only in the realm of a priori knowledge – in other words, whether infallibility, properly understood, is an a priori matter. I discussed this crucial question in chapter ten when I turned to the task of disambiguating the notion of “infallibility” – among others – as a necessary step to get some clarification about the matter. What emerged from my discussion of Hale is: (1) the task at hand is to illuminate more the notion of a priori warrant; (2) the constraint of “experience independence” ought to be effective only after the acquisition of the conceptual repertoire necessary for a priori knowledge and the obtaining of certain other necessary experiences that underpin the reliability of the knower’s state of mind; (3) there is a distinction between defeasibility and infallibility, what Hale did not seem to be aware of; and (4) there is at least one outstanding problem with Hale’s definition (H*) which we must seek to remedy: it is in too direct collision with Quine’s epistemological holism. The second main task I have tried to accomplish in this part of the book is to make sense of the concept of infallibility. The crucial issue in my judgement was to explain how given that we are fallible creatures we could nonetheless be in a position where we cannot get it wrong. I have tried to explain the coherence and possibility of such an epistemic position. I don’t have a knock-down argument for the claim that in some areas we have knowledge infallibly as a matter of fact. Though, of course, that is not to deny that making coherent the possibility of infallibility will pave the way for the resolution of the question whether we in fact have knowledge infallibly in certain areas. My

Conclusion

217

point is that I will be satisfied if I have adequately accomplished the task of explaining the coherence and possibility of the notion of infallibility I am attracted to. The question to ask concerning a method is whether if I execute it correctly and then apprehend the belief I ought to form according to the result, there is any residual possibility of that belief’s being mistaken. I argued that a method is infallible if and only if when it is applied correctly we end up always with true beliefs. To settle the issue whether some empirical methods are infallible it becomes crucial to get clear about what we are allowed to add as a condition in the infallibility-­ conditional such that there could be empirical methods which are infallible. This is not an easy task and may not be even an attractive one to undertake. As soon as we allow ourselves, for example, to “freeze” physical objects so that they don’t change as long as we apply any method to them, and to “assume” that they are real instead of illusory, then how are we going to stop adding more and more conditions? The danger I see with the maneuver of enriching the infallibility conditional in this manner is that it would result in infallibility coming out very cheap indeed. The notion of infallibility I have defended could be in danger of getting trivialized in this way, so infallibility in general would be again trivialized as a consequence. For reasons of space and time I can’t provide the full treatment this very interesting issue deserves in this book. But I will say a little more before finishing this topic. It can be argued that if the notion of infallibility runs the risk of trivialization, that would show that it’s not a deep issue. Is that so bad? It will be bad if as a consequence no sense of infallibility can be found. I don’t think that would be a consequence. Though what we could find out is that there is some relativity to infallibility. I consider that it won’t be so bad if we find that there are degrees of infallibility. That will involve finding more and various assumptions – according to the subject matter – such that depending on whether they have been satisfied the method will deliver infallibly knowledge. To conclude, it is clear that I have suggested the view that the interesting sense in which infallibility is conceivable as obtaining is in the realm of the a priori. I conclude that it does seem that no a posteriori method is absolutely infallible and, it is certainly the case, that not all a priori methods are infallible. However, a priori truths are generally known by the correct prosecution of infallible methods. That the interesting sense in which infallibility is conceivable as obtaining is in the realm of the a priori is, in general, what we traditionally have thought, and what we intuitively expected to occur, if at all. But it was crucial to lay down what underlines this basic intuition. And that is precisely what I hope to have accomplished in this book with a very important qualification. Infallibility is not infallibility any more: that is, we are not infallible about anything, some methods are.

References

Allison, H.E. 1973. The Kant-Eberhard Controversy. Baltimore: John Hopkins University Press. Ayer, A.J. 1946. Language, Truth and Logic. 2nd ed. London: Victor Gollanncz, Ltd. ———. 1956. The Problem of Knowledge. London: Macmillan. Azzouni, J. 1994. Metaphysical Myths, Mathematical Practice: The Ontology and Epistemology of the Exact Sciences. Cambridge: Cambridge University Press. ———. 2008. The Compulsion to Believe: Logical Inference and Normativity. Protosociology 25: 69–88. ———. 2012. Talking About Nothing. Oxford: Oxford University Press. ———. 2015. Semantic Perception. Oxford: Oxford University Press. ———. 2020. Attributing Knowledge: What It Means to Know Something. Oxford: Oxford University Press. Bealer, G. 1999. The A Priori. In The Blackwell Guide to Epistemology, ed. J. Greco and E. Sosa, 243–270. Malden: Blackwell. Benacerraf, P. 1973. Mathematical Truth. The Journal of Philosophy 70: 661–679. Reprinted in Benacerraf and Putnam. Benacerraf, P., and H.  Putnam, eds. 1984. The Philosophy of Mathematics: Selected Essays. Englewood Cliffs: Prentice-Hall. Bennett, J. 1966. Kant’s Analytic. Cambridge: Cambridge University Press. Boghossian, P. 1997. Analyticity. In Companion to the Philosophy of Language, ed. Bob Hale and Crispin Wright. Oxford: Blackwell. Boghossian, P., and C. Peacocke. 2000. New Essays on the A Priori. Oxford: Oxford University Press. BonJour, L. 2005. In Defense of the A Priori. In Contemporary Debates in Epistemology, ed. M. Steup and E. Sosa, 98–105. Malden: Blackwell. Burge, T. 1993. Content Preservation. The Philosophical Review 102 (4): 457–488. Burgess, J.P. 1990. Epistemology and Nominalism. In Physicalism in Mathematics, 1–15. Dordrecht: Kluver Academic Publishers. Carnap, R. 1962. The Logical Foundations of Probability. Chicago: Chicago University Press. Casullo, A. 1977a. The Definition of A Priori Knowledge. Philosophical and Phenomenological Research 38: 220–224. ———. 1977b. Kripke on the “A priori” and the Necessary. Analysis 37: 152–159. Reprinted in Moser. ———. 1988a. Necessity, Certainty and the “A Priori”. Canadian Journal of Philosophy 18: 43–66. ———. 1988b. Revisability, Reliabilism, and A priori Knowledge. Philosophy and Phenomenological Research XLIX (2). © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 I. Fred-Rivera, A Historical and Systematic Perspective on A Priori Knowledge and Justification, Philosophical Studies Series 151, https://doi.org/10.1007/978-3-031-06874-4

219

220

References

———. 2003. A Priori Justification. Oxford: Oxford University Press. ———. 2006. Knowledge, A Priori. In The Encyclopedia of Philosophy, ed. D.M. Borchert, vol. 5, 2nd ed., 79–86. Detroit: MacMillian Reference. ———. 2012. Essays on A Priori Knowledge and Justification. New York: Oxford University Press. Casullo, A., and J. Throw, eds. 2013. The A Priori in Philosophy. Oxford: Oxford University Press. Caygill, H. 1995. A Kant Dictionary. Cambridge: Blackwell. Chisholm, R.M. 1977. The Truths of Reason. In Theory of Knowledge, 2nd ed. Englewood Cliffs: Prentice-Hall. Reprinted in Moser. Coffa, J.A. 1991. The Semantic Tradition from Kant to Carnap: To the Vienna Circle. New York: Cambridge University Press. Craig, E.J. 1975. The Problem of Necessary Truth. In Meaning, Reference and Necessity, ed. Simon Blackburn. Cambridge: Cambridge University Press. Creath, R. 1990. Dear Carnap Dear Van: The Quine-Carnap Correspondence and Related Work. Berkeley: University of California Press. Dancy, J., and E. Sosa, eds. 1985. Introduction to Contemporary Epistemology. Oxford/New York: B. Blackwell. ———, eds. 1992. Companion to Epistemology. Oxford/Cambridge, MA: Blackwell. Descartes, R. 1967. Philosophical Writings. Vol. 1. Ed. E.S. Haldane and G.R.T. Ross. Cambridge University Press. ———. 1981. Descartes: Philosophical Letters. Trans. and ed. A.  Kenny. Minneapolis: Minneapolis University Press. Devitt, M. 2005. There is No A Priori. In Contemporary Debates in Epistemology, ed. M. Steup and E. Sosa, 105–115. Malden: Blackwell. Dummett, M. 1980a. Is Logic Empirical. In Dummett. ———. 1980b. Truth and Other Enigmas. Cambridge, MA: Harvard University Press. Edidin, A. 1984. “A Priori” Knowledge for Fallibilists. Philosophical Studies 46 (Spring 84): 189–198. Evans, G. 1985. Collected Papers. Oxford/New York: Clarendon Press/Oxford University Press. Field, H. 1989. Realism, Mathematics, and Modality. Oxford: Basil Blackwell. ———. 1996. The A Prioricity of Logic. Proceedings of the Aristotelian Society 96: 359–379. ———. 2000. A Priority as an Evaluative Notion. In Boghossian and Peacocke’s New Essays on the Apriori, 117–149. Oxford: Oxford University Press. Fred, I. 1999. On Wright’s Characterization of the A Priori. Diálogos 73: 127–138. ———. 2000. Putnam’s Views on A Priori Knowledge and Revision. Diálogos 75: 123–143. ———. 2006. Philip Kitcher’s Views on A Priori Knowledge. Diálogos 88: 119–133. Fred-Rivera, I., and J.  Leech, eds. 2018. Being Necessary: Themes on Ontology and Modality Fronm the Work of Bob Hale. Oxford: Oxford University Press. Frege, G. 1952. On Sense and Reference. In Translations from the Philosophical Writings of Gottlob Frege, ed. M. Black and P. Geach, 56–78. Oxford: Basil Blackwell. Reprinted in part in Benacerraf and Putnam. ———. 1953. The Foundations of Arithmetic. Oxford: Basil Blackwell. Friedman, M. 1992. Kant and the Exact Sciences. Cambridge, MA: Harvard University Press. ———. 2000. Transcendental Philosophy and A Priori Knowledge: A Neo-Kantian Perspective. In Boghossian and Peacocke (2000), 367–383. Oxford: Oxford University Press. ———. 2010. Synthetic History Reconsidered. In Discourse on a New Method: Reinvigorating the Marriage of History and Philosophy of Science, ed. Michael Friedman, Mary Domski, and Michael Dickson, 573–813. Chicago: Open Court. ———. 2012. Kant on Geometry and Spatial Intuition. Synthese 186: 231–255. Gödel, K. 1984. What Is Cantor’s Continuum Problem? In Benacerraf and Putnam. Goldman, A. 1967. A Causal Theory of Knowing. The Journal of Philosophy 64: 357–372. Grice, H.P. 1962. Some Remarks About the Senses. In Analytical Philosophy, ed. R.J.  Butler, 133–153. Oxford: Blackwell. Haack, S. 1974. Deviant Logic. London/New York: Cambridge University Press.

References

221

———. 1978. Philosophy of Logics. Cambridge/New York: Cambridge University Press. Hale, B. 1987. Abstract Objects. Oxford: Basil Blackwell. ———. 2015. Necessary Beings: An Essay on Ontology, Modality and the Relations Between Them. Oxford: Oxford University Press. Reprint edition. Hale, B., and P. Clark, eds. 1996. Reading Putnam. Wiley-Blackwell. Hale, B., and A. Hoffmann, eds. 2010. Modality: Metaphysics, Logic and Epistemology. Oxford: Oxford University Press. Hale, B., and C. Wright, eds. 1999. Companion to the Philosophy of Language. Wiley-Blackwell. ———. 2000. Implicit Definition and the A Priori. In Boghossian and Peacocke, 286–319. ———, eds. 2001. The Reason’s Proper Study: Essays Towards a Neo-Fregean Philosophy of Mathematics. Clarendon Press. Helmholtz, H. 1977a. On the Facts Underlying Geometry. In Herman Von Helmholtz: Epistemological Writings, ed. Robert S. Cohen and Yehuda Elkana, 39–58. Reidel. ———. 1977b. On the Origin and Significance of the Axioms of Geometry. In Herman Von Helmholtz: Epistemological Writings, ed. Robert S. Cohen and Yehuda Elkana. Reidel. Hempel, G.G. 1945. On the Nature of Mathematical Truth. The American Mathematical Monthly 52: 543–556. Reprinted in Benacerraf and Putnam. Jenkins, C.S.I. 2008. A Priori Knowledge: Debates and Developments. Philosophy Compass 3 (3): 436–450. Jenkins Ichikawa, J., and B.W. Jarvis. 2013. The Rules of Thought. Oxford: Oxford University Press. Kant, I. 1902. Prolegomena. Trans. Paul Carus. La Salle: Open Court Publishing Company. ———. 1956. Critique of Pure Reason. Trans. Norman Kemp Smith. New York: St. Martin’s. Kim, J., and E. Sosa, eds. 1995. A Companion to Metaphysics. Cambridge: Blackwell. Kitcher, Patricia. 1984. Kant’s Transcendental Psychology. New York: Oxford University Press. Kitcher, Philip. 1975. Kant and the Foundations of Mathematics. Philosophical Review 84: 23–50. ———. 1980a. A Priori Knowledge. Philosophical Review 89: 3–23. ———. 1980b. Apriority and Necessity. Australasian Journal of Philosophy 58: 89–101. Reprinted in Moser. ———. 1981. How Kant Almost Wrote “Two Dogmas of Empiricism”. Philosophical Topics 12: 217–250. ———. 1983. The Nature of Mathematical Knowledge. Oxford: Oxford University Press. ———. 2000. A Priori Knowledge Revisited. In Boghossian and Peacocke (2000), 65–91. Oxford: Oxford University Press. Kripke, S. 1971. Identity and Necessity. In Identity and Individuation, ed. M.K. Munitz. New York: New York University Press. ———. 1980. Naming and Necessity. Cambridge, MA: Harvard University Press. ———. 1982. Wittgenstein on Rules and Private Languages. Cambridge, MA: Harvard University Press. Lehrer, K. 1974. Knowledge. Oxford: Clarendon Press. Locke, J. 1959. Essay Concerning Human Understanding. Ed. A. C. Fraser. New York: Dover. Maddy, P. 1980. Perception and Mathematical Intuition. The Philosophical Review 89: 168–196. ———. 1990. Realism in Mathematics. Oxford: Oxford University Press. McDowell, J. 1989. Mathematical Platonism and Dummettian Anti-Realism. Dialectica 43 (1–2). Melis, G., and C. Wright. Forthcoming. Beyond Sense? New Essays on the Significance, Grounds, and Extent of the A Priori, ed. Dylan Dodd and Elia Zardini. Oxford: Oxford University Press. Mill, J.S. 1950a. Philosophy of Scientific Method. New York: Hafner Publishing. ———. 1950b. A System of Logic. Reprinted in Mill. Moore, G.E. 1959. Philosophical Papers. London/New York: Allen and Unwin/Humanities Press. ———. 1962. Some Main Problems of Philosophy. New York: Collier Books. Moser, P.K. 1987. A Priori Knowledge. Oxford: Oxford University Press. Pap, A. 1946. The A Priori in Physical Theory. New York: King’s Crown Press. ———. 1958. Semantics and Necessary Truth. New Haven: Yale University Press.

222

References

Parsons, C. 1967. Foundations of Mathematics. In The Encyclopedia of Philosophy, ed. Paul Edwards, vol. 5–6, 188–212. New York: Macmillan. ———. 1983. Mathematics in Philosophy: Selected Papers. Ithaca: Cornell University Press. Paton, H.J. 1936. Kant’s Metaphysic of Experience. Vol. 1 & 2. 1st ed. London: George Allen & Unwin Ltd. Peacocke, C. 1993. How Are A Priori Truths Possible? European Journal of Philosophy 1 (2): 175–199. ———. 2004. The Realm of Reason. Oxford: Oxford University Press. ———. 2005. The A Priori. In The Oxford Handbook of Contemporary Philosophy, Oxford Handbooks, ed. Frank Jackson and Michael Smith, 739–763. Oxford/New York: Oxford University Press. Plantinga, A. 1993. Warrant and Proper Function. New York: Oxford University Press. Poincaré, H. 1905. La science et l’hypothèse (Science and hypothesis). Paris: Flammarion. Prichard, H.A. 1976. Kant’s Theory of Knowledge. New York: Garland Pub. Putnam, H. 1975. Mathematics, Matter, and Method, Philosophical Papers. Vol. 1. Cambridge: Cambridge University Press. ———. 1976. 'Two Dogmas’ Revisited. In Contemporary Aspects of Philosophy, ed. Gilbert Ryle. London: Oriel Press. Reprinted in Putnam, Realism and Reason, Philosophical Papers. Vol. 3, 87–97. Cambridge: Cambridge University Press, 1983. ———. 1978. There Is At Least One A priori Truth. Erkenntnis 13: 153–170. Reprinted in Putnam, Realism and Reason, Philosophical Papers. Vol. 3, 98–114. Cambridge: Cambridge University Press, 1983. ———. 1979. Analyticity and Apriority: Beyond Wittgenstein and Quine. In Studies in Metaphysics. Midwest Studies in Philosophy, ed. P. French, T. Uehling, and H. Wettstein, vol. 4, 423–441. Minneapolis: University of Minnesota Press. Reprinted in Putnam, Realism and Reason, Philosophical Papers. Vol. 3, 115–138. Cambridge: Cambridge University Press, 1983. ———. 1983. Possibility and Necessity. In Realism and Reason, Philosophical Papers, vol. 3, 46–68. Cambridge: Cambridge University Press. Quine, W.V. 1960. Word and Object. Cambridge, MA: MIT Press. ———. 1961. Two Dogmas of Empiricism. In From a Logical Point of View, 20–46. Cambridge, MA: Harvard University Press. Reprinted in Moser. ———. 1966a. Carnap and Logical Truth. Synthese 12: 350–370. Reprinted in The Ways of Paradox, 100–25. New York: Random House. ———. 1966b. Truth by Convention. In The Ways of Paradox, 70–99. New York: Random House. Reprinted in Benacerraf and Putnam, 322–345. ———. 1970. Philosophy of Logic. Englewood Cliffs: Prentice Hall. Resnik, M. 1980. Frege and the Philosophy of Mathematics. Ithaca: Cornell University Press. Russell, B. 1973. The Problems of Philosophy. New York: Oxford University Press. Skorupski, J. 1986. Empiricism, Verification and the “A Priori”. In Fact, Science and Morality, ed. G. Mac Donald and C. Wright, 143–162. Oxford: Blackwell. ———. 1989. John Stuart Mill. London: Routledge. Steiner, M. 1975. Mathematical Knowledge. Ithaca: Cornell University Press. Stroud, B. 1965. Wittgenstein and Logical Necessity. The Philosophical Review LXXIV: 504–518. ———. 1984. The Significance of Philosophical Skepticism. Oxford: Oxford University Press. Wilder, R. 1975. Evolution of Mathematical Concepts. New York: Wiley. Williamson, T. 2002. Knowledge and Its Limits. Oxford: Oxford University Press. ———. 2005. Armchair Philosophy, Metaphysical Modality and Counterfactual Thinking. Proceedings of the Aristotelian Society 105: 1–23. ———. 2007. The Philosophy of Philosophy. Malden: Blackwell. ———. 2013. How Deep Is the Distinction Between A Priori and A Posteriori Knowledge. In The A Priori in Philosophy, ed. A. Casullo and J. Thurow, 291–312. Oxford University Press. Wittgenstein, L. 1956. Remarks on the Foundations of Mathematics. Trans. G.E.M. Anscombe. Oxford: Basil Blackwell.

References

223

———. 1968. Philosophical Investigations. Trans. G.E.M. Anscombe. Oxford: Basil Blackwell. ———. 1969. On Certainty. Oxford: Basil Blackwell. Wright, C. 1980. Wittgenstein on the Foundations of Mathematics. Cambridge, MA: Harvard University Press. ———. 1983. Frege’s Conception of Numbers as Objects. Aberdeen: Aberdeen University Press. ———. 1984. Inventing Logical Necessity. In Language, Mind and Logic, ed. J.  Butterfield, 187–209. Cambridge: Cambridge University Press. ———. 1992. On Putnam’s Proof that We Are Not Brains in a Vat. Proceedings of the Aristotelian Society 92: 67–94. ———. 1993a. Scientific Realism and Observation Statements. International Journal of Philosophical Studies 1 (2): 231–254. ———. 1993b. Realism, Meaning and Truth. 2nd ed. Wiley-Blackwell. ———. 1994. Truth and Objectivity. Harvard: Harvard University Press. Reprint edition. ———. 2004a. Intuition, Entitlement and the Epistemology of Logical Laws. Dialectica 58 (1): 155–175. ———. 2004b. On Epistemic Entitlement: Warrant for Nothing (and Foundations for Free)? Proceedings of the Aristotelian Society 78: 167–212. Wright, Crispin, and Martin Davies. 2004. On Epistemic Entitlement. Proceedings of the Aristotelian Society, Supplementary Volumes 78 (2004): 167–245. Yablo, Stephen. 1993. Is Conceivability a Guide to Possibility? Philosophical and Phenomenological Research 53 (1): 1–42.

Author Index

A Anscombe, G.E.M., 200 Aristotle, 21, 41 Austin, J.L., 36 Ayer, A.J., 37, 38 Azzouni, J., 98 B Benacerraf, P., 78, 79, 88 Bennett, J., 143–145, 148, 150 Blackwell, B., 36, 132, 167, 180, 192, 200 Boghossian, P., 29, 84, 109, 118 Burge, T., 168 Butler, R.J., 180 C Carnap, R., 38, 43, 56, 120, 180 Carus, P., 25 Casullo, A., 7, 25, 26, 45, 65, 69, 106–109, 113, 117, 118, 124–129, 132, 135–137, 161, 168, 197 Clinton, B., 145, 146 Copernicus, 8, 62 D Darwin, C., 41 Dedekind, R., 185 Descartes, R., 59, 87, 88, 96, 202 Dodd, D., 131, 132, 135 Dummett, M., 46–49, 62, 68, 212

E Edidin, A., 163–165, 168 Einstein, A., 39, 41, 62 Euclid, 21, 27, 31, 56, 211 F Field, H., 109, 115–122, 124–127, 131, 155, 212 Frege, G., 20, 36, 145, 167, 175, 185 Friedman, M., 3, 20, 22, 23, 26–31, 72, 119–122, 211, 212 G Gödel, K., 79, 88 Grice, H.P., 180 H Haldane, E.S., 87 Hale, B., vii, xii, 15, 18–20, 46, 49, 68, 77–81, 83, 84, 89, 93–170, 189, 212, 214–216 Helmholtz, H., 39, 201 Hintikka, J., 3 Hume, D., 5, 6 J Jenkins, C.S.I., 134, 136–139 Jenkins Ichikawa, J., 138

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 I. Fred-Rivera, A Historical and Systematic Perspective on A Priori Knowledge and Justification, Philosophical Studies Series 151, https://doi.org/10.1007/978-3-031-06874-4

225

226 K Kant, I., ix, xi, 3–32, 42, 43, 46, 61, 71, 72, 81, 94, 100–101, 139, 143, 145, 166, 167, 197, 199, 211, 212 Kasaki, M., 134–137, 139 Kepler, J., 41 Kitcher, P., xii, 16, 17, 20, 26, 29–31, 40, 41, 45, 71, 72, 78, 83–102, 104–108, 117–122, 142, 143, 161, 163, 169, 179, 184, 189, 212, 215 Kripke, S., 15, 25, 60, 61, 69, 89, 90, 94, 113, 199, 200 L Leibniz, G.W., 17 M Maddy, P., 79 Melis, G., 132, 133, 137, 141 Mill, J.S., 36, 37 Moser, P.K., 25, 160, 161 Munitz, M.K., 15, 199

Author Index Putnam, H., xii, 40, 41, 44, 45, 47, 55–73, 88, 201, 213, 214 Q Quine, W.V.O., xi, xii, 35–51, 56–58, 61–66, 70, 72, 120, 156–160, 170, 212–214, 216 R Reichenbach, H., 29, 62 Resnik, M., 36 Richard, C., 42 Ross, G.R.T., 88 Russell, B., 18, 145 S Skorupski, J., 36 Smith, N.K., ix, 4, 15, 16 Summerfield, D., 108 T Thurow, J., 132

N Newton, I., 41, 62 P Pap, A., 13, 14, 18 Parsons, C., 3, 43, 46 Paton, H.J., 10–12, 18, 19, 31 Peacocke, C., 29, 84, 109, 118 Peano, G., 59, 60, 70 Poincaré, H., 39, 201 Prichard, H.A., 13, 14 Ptolemy, 41, 62

W Warenski, L., 129 Williamson, T., 126, 132–141 Wittgenstein, L., 124, 132, 141, 200 Wright, C., 119, 122–133, 137–141, 168, 175, 176, 179, 192–194, 201 Z Zardini, E., 131, 132, 135

Subject Index

A Analyticity, 35, 38, 40–45, 55–57, 60, 67, 68 Analytic judgements, 4 Analytic statement, 57, 64 Analytic/synthetic distinction, 162 Analytic truths, 38, 40, 44, 183 An a priori factor, 63 A priori–a posteriori distinction, 127 A prioricity, 35, 212–215 A priori infallible method, 190 A priori intuition, 11, 27 A priori justification, 180 A priori knowledge, 83–92, 169, 177, 179, 182, 187, 199 Field’s default propositions, 115–118 Hale’s assertions, 141, 142 Hale’s preferred notion of, 143, 145, 146 Hale’s views abstract objects, 147 Casullos’s interpretation of, 106–108 circularity objection, 148, 149 defeasibility of items, 112, 113, 115 Kitcher on Field’s and Friedman’s claim, 119–122 revision and defeasibility, 103–106 revision and prioricity, 162–165, 167, 168 roles of experience, 132–135, 137–141 sensory deprivation analytic truths, 183 cogito, 184 logical truths, 183 mathematical truths, 183, 184 universally empirical knowledge, 184 talk of revision, 160–162

Wright’s entitlements, 122–131 A priori method, 176–181, 188, 205 A priori truth, 202 Apriority, 59 A priori warrant, 85–88, 90–95, 99 Aristotle, 21 Arithmetic, 36, 46, 49, 50, 59, 60, 182 Arithmetical statements, 36, 49, 60 Axioms, 45, 185, 186 B Basic a priori knowledge, x, 79, 80, 185–186 Basic truths, 79, 80 Belief, 89, 104, 107, 123, 178 C Carnapian explication, 180 Carnap-Reichenbach conception, 120 Causal theory of knowledge, 78–81 Certainty, 192 Circularity, 125, 168 Claims to knowledge, 191 Cogito propositions, 199, 202 Cognitive capacities, 127 Cognitive enquiry, 124 Cognitive mechanisms, 133 Cognitive method, 177, 194 Cognitive process, 134–136, 141, 177 Cognitive psychology, 135 Collateral beliefs, 182 Conceivability, 15, 195, 217 Concept acquisition, 181

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 I. Fred-Rivera, A Historical and Systematic Perspective on A Priori Knowledge and Justification, Philosophical Studies Series 151, https://doi.org/10.1007/978-3-031-06874-4

227

228 Conceptual competence, 79, 80 Conceptual repertoire, 87, 142, 143, 170, 181, 183, 216 Conclusive confirmation, 166 Conservatism, 39, 40 Construction of concepts, 7, 21, 22 Contemporary epistemology, 135 Contextual a prioricity, 56, 63, 66, 70 Contextually a priori, 56–58, 63, 65, 66, 70, 72 Contingent a priori, 19, 29, 199–204 Counting, 208 Critique, 101 D Declarative sentences, 213 Dedekind-Peano axioms, 185 Deductive and inductive principles, 129 De facto indefeasibility, 190 De facto indefeasible, 162 Default proposition, 115–119 Defeasibility, 105, 170, 190 Desideratum, 81 Deviant Logics, 47 E Empirical assumptions, 61, 67, 68 considerations, 112, 114 disconfirmation, 109 evidence, 111, 114, 168 hypothesis, 37 indefeasibility, 109, 117 intuition, 21–23 justification, 117 knowledge, 201 method, xii, 158, 177, 188, 198, 205–207, 209, 217 reasons, 154 statement, 150 warrant, 49, 97, 102, 163 universality, 14 Empiricism, 35–39 Entitlement, 127, 128 Epistemic role, 126, 129, 137 Epistemological complexity, 139 Epistemological holism, 35, 50, 216 Epistemologically impossible, 59 Epistemological theories, 80, 81 Evidential role, 13, 126, 129, 132, 135–138, 141

Subject Index Experience, 180 Experience independence, 211 F Fallibilism, 57, 60 Fallibility, 29, 41, 108, 157, 192 Fallible, 94 Falsifiability, 155, 212 Falsifiability of beliefs, 192 Falsifiable, 46, 145 Falsification, 144 Following a proof, 94, 98–100 Foundationalism, 130 G General recursive function, 180 Geometrical intuitions, 166, 185 Geometrical laws, 62 Geometry, 27, 42, 56, 57, 62, 167, 168 Glossary, 187–192 Goldbach’s conjecture, 166 H Hale, Bob a priori knowledge is compatible with revision, 93, 95 epistemological views on a priori knowledge, 77, 81 long proofs, 96, 98 memory, 96, 97, 101, 102 notion of a priori knowledge, 83 remarks on Kant’s view, 100, 101 I Imagination, 138, 139 Independence of experience, 81, 90 Independent of experience, 86 Infallibility, 4, 20, 23, 26, 30–32, 169, 170, 187, 189, 192, 195, 197, 203–206, 211, 215–217 Infallible, 90, 93, 95 Infallible methods, 188 Inferential knowledge, 121 Informal knowledge, 186 Innatist, 4, 12, 13 Internal stimuli, 180 Intuition, 3, 11, 12, 17, 21–23, 28–30, 79, 139, 175, 180, 186, 204

Subject Index Intuitionism, 58, 62, 66, 67 Issue of infallibility, 168 J Judgments, 101 Justification, 128, 211, 212, 214 Justified true belief, 77 K Kant, I. of a priori knowledge infallibility, 20 purely “negative” one, 18 critique, 4–7 definition and exposition, 24 geometrical knowledge, 23 independence of experience, 10 innatist, 12 Kitcher's and Friedman’s views on, 26, 30 mathematical definitions, 24 necessity, 13, 15 nonempirical intuitions and empirical ones, 22 philosophical knowledge and mathematical knowledge, 21, 22 possibility of a priori knowledge, 8, 10 universality, 13, 15 Kitcher, Philip a priori knowledge is incompatible with revision, 86 belief, 89, 90 following a proof, 100 infallible, 90 long proofs or calculations issue, 87 non-empirical processes, 88, 89 notion of a priori knowledge, 85 warrant belief, 91 Knowledge of propositions, 150 L Logical empiricism, 35, 37, 38, 122 Logical knowledge, 122 Logical laws, 56, 57, 60, 62, 66 Logical positivists, 37, 40 Logical truths, 183 Long proofs, 87, 88

229 M Mathematical intuition, 88 Mathematical knowledge, 83, 84, 86, 88, 89, 121, 122 Mathematical methods, 206 Mathematical propositions, 36, 37, 51 Mathematical truths, 15, 28, 36–38, 59, 61, 62 Mathematics, 208 Maxim of minimum mutilation, 39 Memory, 96, 97, 101–102, 134, 137 Memory of knowledge, 201 Mind, 189 Moderate Quinean’ view, 58 N Necessary a posteriori, 25 Necessity, 4, 6, 9, 13–17, 19, 25, 26, 28, 31, 58, 61, 62, 69 Non-contradiction, 58, 60, 62, 65–67, 69 Non-empirical intuition, 21, 22 Non-empirical justification, 115 Non-empirical knowledge, 79 Non-empirical processes, 88, 89 Non-Euclidean geometry, 167 Non-falsifiability, 155 Non-inferential empirical knowledge, 151 Non-inferential knowledge, 153 Non-inferential a priori knowledge, 158 Notion of infallibility, 170, 176, 187, 189, 196 Notion of prioricity, 161 Notion of “warranting”, 177 O Online’ cognitive skills, 133, 134 Open to falsification, 145 Ordinary arithmetical calculation, 169 P Parallel Postulate, 165, 166 Partly a priori, 68, 69 Perception, 134, 189 Philosophical considerations, 120 Philosophical knowledge, 21, 22 Physical variables, 110 Physiological psychology, 195 Platonism, 78, 80, 81 Possibility, 63–66 Posteriori, 57, 61, 63, 68, 70 Presumption of truth, 179

230 Presuppositions, 127 Proofs, 97, 98, 107 Psychological act of believing, 90 Psychology, 91 Pure intuition, 12, 17, 21–23, 28, 30 Putnam, H. analyticity and apriority, 59, 60 notion of a priori knowledge, 55 one a priori truth, 57, 65 possibility and necessity, 61, 63 synthetic statements, 64 on ‘two dogmas’ revisited, 64 Q Quantum logic, 56, 61–63 Quantum mechanics, 57 Quasi-empirical statements, 59 Quine, W.V. a prioricity and analyticity, 40 a prioricity before “Two Dogmas”, 42 epistemological holism, 50 no-immunity thesis, 46 on notion of a priori knowledge, 38, 40 revisable or falsifiable by empirical evidence, 46 revision of a priori statements, 45, 47, 48 Quinean confirmation, 156 R Recognition of conceptual liaisons, 80 Reductionism, 39 Revisability, 124, 191, 212–214 Revision, 58, 93, 94, 99, 100, 213 Revisions of Warrants, 191 S Sane fallibilism, 60 Sense impressions, 12 Sense of experience, 180 Sensory activity, 177 Sensory deprivation, 178, 181

Subject Index Simplicity, 40 Space, 12 Specific episodic memory, 140 Strict universality, 14, 15, 18 Sureness, 105 Synthetic a priori knowledge, 4, 6, 8–10, 16, 17 Synthetic judgements, 5–7 Synthetic statements, 64 T Testimony, 114, 204 Time, 12 Trivialization, 209 True beliefs, 177 Truth, 141, 168 Truth by Convention, 38, 43 Truthful oracle, 205 Truths or statements, 199 Two Dogmas of Empiricism, 38, 40 U Ultra-reliable, 90 Unfalsifiable by empirical evidence, 212 Universality, 13, 14 Unrevisability, 38, 40, 41, 44, 45, 61, 66, 69–71, 86 Unsureness, 105 V Visualization, 186 W Warrant, 104, 177, 178, 211, 213–216 Warrant belief, 87, 88, 91 Warranting, 179 Warrants for free, 123 Weak causal theories of knowledge, 78 Weak conception, 122 Wright, 175