Engaging Kripke with Wittgenstein (Routledge Studies in Twentieth-Century Philosophy) [1 ed.] 9781032139975, 9781032147321, 9781003240792, 1032139978

Table of contents :
Cover
Endorsements
Half Title
Series
Title
Copyright
Dedication
Contents
List of Abbreviations
List of Contributors
Introduction
1 On the Alleged Incompatibility Between Wittgenstein and Kripke
2 Real Names
3 Kripke’s Wittgenstein and Kripke’s Causal-Historical Picture of Reference
4 Modality: Wittgenstein’s Tractatus Versus Saul Kripke
5 Does It Make Sense to Say That the Standard Meter Is One Meter Long?
6 Who Is Afraid of Truth Gaps? Wittgenstein and Kripke on the Standard Meter
7 Kripke’s Standard Meter—A Religious Dream?
8 Overlooked Distinctions: The Mirage of Contingent A Priori
9 How Long Is the Standard Meter in Paris?
10 The Illusion of Intransitive Measurement: Diamond, Kripke and Wittgenstein on the Standard Meter
11 Kripke’s Transcendental Realist Fantasy and Wittgenstein’s Transcendental Idealism, After All
12 The Ancient Roots of Wittgenstein’s Liberatory Philosophy: How Revisiting the Ancients Can Illuminate the Difference Between Wittgenstein’s Philosophy of Freedom and Kripke’s Philosophy of Mere Anarchy
Index

Citation preview

“This volume re-shapes the conversation regarding the intricated connections between Wittgenstein’s and Kripke’s work. It is, without a doubt, a must-have for any scholar working in either the Analytical tradition or Wittgensteinian philosophy.” Juan J. Colomina-Almiñana, Louisiana State University, USA “At important points in his work, Kripke was in dialogue with the thought of Wittgenstein. The editors have assembled an impressive team of international Wittgenstein scholars with a deep knowledge of the analytic tradition to expand and explore this dialogue, re-examining the relationship between the work of two philosophers, providing fresh insights, and revealing tensions between Kripke’s interpretation of Wittgenstein on rule-following and his own views about meaning. The focus is on names, modality and the meter-rod, but the issues raised touch on some of the deepest questions in the philosophy of language: the connection between meaning and practice, the nature of the a priori, transcendental realism versus transcendental idealism, and the aims and methods of philosophy. This volume must be a starting point for all future discussions of these issues.” Marie McGinn, University of York, UK “Wittgenstein and Kripke are in certain important respects very similar and in others very different philosophers. This inspired volume explores these comparisons along multiple interesting dimensions.” Paul Boghossian, New York University, USA

Engaging Kripke with Wittgenstein

This volume draws connections between Wittgenstein’s philosophy and the work of Saul Kripke, especially his Naming and Necessity. Saul Kripke is regarded as one of the foremost representatives of contemporary analytic philosophy. His most important contributions include the strict distinction between metaphysical and epistemological questions, the introduction of the notions of contingent a priori truth and necessary a posteriori truth, and original accounts of names, descriptions, identity, necessity, and realism. The chapters in this book elucidate the relevant connections between Kripke’s work and Wittgenstein, specifically concerning the standard meter, contingent apriori, and rule-following. The contributions shed light on how Kripke’s philosophical outlook was influenced by Wittgenstein, and how mainstream analytic philosophy and Wittgensteinian philosophy can fruitfully engage with one another. Engaging Kripke with Wittgenstein will be of interest to philosophers working on Wittgenstein, Kripke, and the history of analytic philosophy. Martin Gustafsson is Professor of Philosophy at Åbo Akademi University, Finland. He is working mainly within the philosophy of language, philosophy of action, and the history of analytic philosophy. He has published papers on the philosophy of Elizabeth Anscombe, J. L. Austin, Stanley Cavell, Donald Davidson, Gottlob Frege, Ian Hacking, W. V. O. Quine, Gilbert Ryle, Ludwig Wittgenstein, and others. Oskari Kuusela is Associate Professor in philosophy at the University of East Anglia. His main philosophical interests relate to philosophical methodology, the history of analytic philosophy, and ethics. His monographs include The Struggle Against Dogmatism (2008) and Wittgenstein on Logic as the Method of Philosophy (2019). He is also the co-editor of several edited collections on Wittgenstein, including The Oxford Handbook of Wittgenstein (2011). Jakub Mácha has published on philosophy of language and classical German philosophy. He is the author of Wittgenstein on Internal and External Relations: Tracing All the Connections (2015) and The Philosophy of Exemplarity: Singularity, Particularity, and Self-Reference (2023). He co-edited several volumes: Wittgenstein and the Creativity of Language (2016), Wallace Stevens: Poetry, Philosophy, and Figurative Language (2018), and Wittgenstein and Hegel: Reevaluation of Difference (2019).

Routledge Studies in Twentieth-Century Philosophy

The Legacy of Nietzsche’s Philosophy of Laughter Bataille, Deleuze, and Rosset Lydia Amir Heidegger’s Ecological Turn Community and Practice for Future Generations Frank Schalow Lectures on a Philosophy Less Ordinary Language and Morality in J.L. Austin’s Philosophy Niklas Forsberg Heidegger and the Contradiction of Being An Analytic Interpretation of the Late Heidegger Filippo Casati Camus and Fanon on the Algerian Question An Ethics of Rebellion Pedro Tabensky Wittgenstein’s Philosophy in 1929 Florian Franken Figueiredo Henri Bergson and the Philosophy of Religion God, Freedom, and Duration Matyáš Moravec Engaging Kripke with Wittgenstein The Standard Meter, Contingent Apriori, and Beyond Edited by Martin Gustafsson, Oskari Kuusela, and Jakub Mácha For more information about this series, please visit: www.routledge.com/RoutledgeStudies-in-Twentieth-Century-Philosophy/book-series/SE0438

Engaging Kripke with Wittgenstein The Standard Meter, Contingent Apriori, and Beyond Edited by Martin Gustafsson, Oskari Kuusela, and Jakub Mácha

First published 2024 by Routledge 605 Third Avenue, New York, NY 10158 and by Routledge 4 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN Routledge is an imprint of the Taylor & Francis Group, an informa business © 2024 selection and editorial matter, Martin Gustafsson, Oskari Kuusela, and Jakub Mácha; individual chapters, the contributors The right of Martin Gustafsson, Oskari Kuusela, and Jakub Mácha to be identified as the authors of the editorial material, and of the authors for their individual chapters, has been asserted in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. ISBN: 978-1-032-13997-5 (hbk) ISBN: 978-1-032-14732-1 (pbk) ISBN: 978-1-003-24079-2 (ebk) DOI: 10.4324/9781003240792 Typeset in Sabon by Apex CoVantage, LLC

Dedicated to the memory of Saul Kripke

Contents

List of Abbreviations List of Contributors Introduction

xi xii 1

MARTIN GUSTAFSSON, OSKARI KUUSELA, AND JAKUB MÁCHA

  1 On the Alleged Incompatibility Between Wittgenstein and Kripke

9

PANU RAATIKAINEN

  2 Real Names

28

SEBASTIAN SUNDAY GRÈVE

  3 Kripke’s Wittgenstein and Kripke’s Causal-Historical Picture of Reference

60

ALEXANDER MILLER

  4 Modality: Wittgenstein’s Tractatus Versus Saul Kripke

82

SANFORD SHIEH

  5 Does It Make Sense to Say That the Standard Meter Is One Meter Long?

108

ALEXANDRE N. MACHADO

  6 Who Is Afraid of Truth Gaps? Wittgenstein and Kripke on the Standard Meter JAKUB MÁCHA

127

x  Contents   7 Kripke’s Standard Meter—A Religious Dream?

141

CHRISTIAN HELMUT WENZEL

  8 Overlooked Distinctions: The Mirage of Contingent A Priori

158

OSKARI KUUSELA

  9 How Long Is the Standard Meter in Paris?

178

CORA DIAMOND

10 The Illusion of Intransitive Measurement: Diamond, Kripke and Wittgenstein on the Standard Meter

213

MARTIN GUSTAFSSON

11 Kripke’s Transcendental Realist Fantasy and Wittgenstein’s Transcendental Idealism, After All

235

AVNER BAZ

12 The Ancient Roots of Wittgenstein’s Liberatory Philosophy: How Revisiting the Ancients Can Illuminate the Difference Between Wittgenstein’s Philosophy of Freedom and Kripke’s Philosophy of Mere Anarchy

269

RUPERT READ

Index295

Abbreviations

NN PI TLP WRPL

Saul Kripke, Naming and Necessity Ludwig Wittgenstein, Philosophical Investigations Ludwig Wittgenstein, Tractatus Logico-Philosophicus Saul Kripke, Wittgenstein on Rules and Private Language

Contributors

Avner Baz is Professor of Philosophy at Tufts University and the author of two seminal books about ordinary language philosophy and methodology in analytic philosophy in general (When Words Are Called For, 2012;  The Crisis of Method in Contemporary Analytic Philosophy, 2017). In these works, he argues against the viability of the so-called “method of cases” for the analysis of concepts like  knowledge,  truth,  or  causality, and he diagnoses a misconceived picture of language that he claims underlies standard philosophical practice today. Cora Diamond is University Professor and Kenan Professor of Philosophy Emerita at the University of Virginia. Diamond has published a collection of essays The Realistic Spirit: Wittgenstein, Philosophy, and the Mind (1991). She is the editor of Wittgenstein’s Lectures on the Foundations of Mathematics: Cambridge 1939 (1976). Her latest book is Reading Wittgenstein With Anscombe, Going on to Ethics (2019). Martin Gustafsson is Professor of Philosophy at Åbo Akademi University, Finland. He is working mainly within the philosophy of language, philosophy of action, and the history of analytic philosophy. He has published papers on the philosophy of Elizabeth Anscombe, J. L. Austin, Stanley Cavell, Donald Davidson, Gottlob Frege, Ian Hacking, W. V. O. Quine, Gilbert Ryle, Ludwig Wittgenstein, and others. Oskari Kuusela is Associate Professor in philosophy at the University of East Anglia. His main philosophical interests relate to philosophical methodology, the history of analytic philosophy, and ethics. His monographs include The Struggle Against Dogmatism (2008) and Wittgenstein on Logic as the Method of Philosophy (2019). He is also the co-editor of several edited collections on Wittgenstein, including The Oxford Handbook of Wittgenstein (2011). Jakub Mácha has published on philosophy of language and classical German philosophy. He is the author of Wittgenstein on Internal and

Contributors xiii External Relations: Tracing All the Connections (2015) and The Philosophy of Exemplarity: Singularity, Particularity, and Self-Reference (2023). He co-edited several volumes: Wittgenstein and the Creativity of Language (2016), Wallace Stevens: Poetry, Philosophy, and Figurative Language (2018), and Wittgenstein and Hegel: Reevaluation of Difference (2019). Alexandre N. Machado earned his Doctor of Philosophy (2004) from the Universidade Federal do Rio Grande do Sul, under the supervision of Prof. Dr. Paulo E. Faria. His dissertation is titled Lógica e Forma de Vida: Wittgenstein e a natureza da necessidade lógica e da filosofia, and in 2004, it has got from the Associação Nacional de Pós-Graduação em Filosofia the prize of best doctoral philosophy dissertation in Brazil. The prize was the publication of the dissertation as a book (Editora Unisinos). In 2000, he spent one year of a scholarship studying at the University of Oxford under the supervision of Prof. Dr. Gordon P. Baker. From 2005 to 2008, he was Professor at the Universidade Federal da Bahia. Since 2009, he has been an associated professor at the Universidade Federal do Paraná. He has published several papers on philosophy of language, philosophy of logic, skepticism, Wittgenstein, and Frege. Alexander Miller is Professor of Philosophy at the University of Otago, New Zealand, where he has been teaching since 2012. He is the author of Philosophy of Language (3rd edition, Routledge 2017) and Contemporary Metaethics: An Introduction (2013). He is also a co-editor (with Crispin Wright) of Rule-Following and Meaning (2002) and (with Bob Hale and Crispin Wright) of A Companion to the Philosophy of Language (2nd edition, 2017), and the editor of Language, Logic and Mathematics: Themes From the Philosophy of Crispin Wright (2020) Panu Raatikainen is a professor of philosophy at the Tampere University. He received his doctorate in theoretical philosophy from the University of Helsinki in 1998. Raatikainen has worked as Academy Research Fellow of the Academy of Finland and as Fellow at the Helsinki Collegium for Advanced Studies. He has also been a visiting research fellow at the Institute of Philosophy, School of Advanced Study, the University of London, and at the Graduate Center of the City University of New York (CUNY). He is presently Affiliated Research Scholar with the Saul Kripke Center (CUNY Graduate Center). Raatikainen is an author of numerous articles and book chapters. His research has dealt with the philosophy of language, the philosophy of mind, the philosophy of science, logic, the philosophy of mathematics, and the recent history of philosophy.

xiv  Contributors Rupert Read is Emeritus at the University of East Anglia in Norwich, UK. His academic work includes ecological and political philosophy (including critiques of Rawlsian liberalism and of “natural capital”, and work on the precautionary principle). He is also the author of several books, including Wittgenstein’s Liberatory Philosophy, published by Routledge in 2021. He now Directs the Climate Majority Project. Sanford Shieh is Professor of Philosophy at Wesleyan University. He works on the philosophy of logic and metaphysics through the philosophical history of the analytic tradition. He recently published Necessity Lost: Modality and Logic in Early Analytic Philosophy, vol. 1, and is working on vol. 2, Necessity Regained. Sebastian Sunday Grève is Assistant Professor at Peking University and a member of the Chinese Institute of Foreign Philosophy. He joined Peking University in 2019. Previously, he taught philosophy at the University of Oxford, where he gained his doctorate in 2018. He works broadly in philosophy, on both practical and theoretical issues. Christian Helmut Wenzel studied mathematics and philosophy: the PhD degree in algebraic geometry in 1990 in the USA and the PhD degree in Kant’s aesthetics in 1999 in Germany. He has been a visiting scholar at L’École Normale Supérieure, Harvard, Duke, Stanford, Oxford, and Goethe University of Frankfurt, and is currently Distinguished Professor at National Taiwan University. His fields of interests are Kant, Wittgenstein, aesthetics, phenomenology, philosophy of mind, and Chinese philosophy. He published two books on Kant’s aesthetics, with Walter de Gruyter in 2000 and with Blackwell in 2005, and articles in KantStudien, British Journal of Aesthetics, History of Philosophy Quarterly, Philosophy East and West, Journal of Chinese Philosophy, Logique et Analyse, Philosophical Investigations, Synthese, and in collections. He wrote reviews for Mind, Philosophy East and West, The Review of Metaphysics, Notre Dame Philosophical Reviews, European Journal of Philosophy, and British Journal of Aesthetics. His current focus is on the nature of mental representation and free will.

Introduction Martin Gustafsson, Oskari Kuusela, and Jakub Mácha

The aim of this volume is to deepen our understanding of the relationship between two of the most important thinkers in the tradition of analytic philosophy: Saul Kripke and Ludwig Wittgenstein. During the last five decades, Kripke was arguably the most influential analytic philosopher. His name is associated with ideas that set much of the agenda of contemporary analytic metaphysics, philosophy of language, and philosophy of logic: a strict distinction between metaphysical and epistemological questions, the introduction of the notions of contingent a priori truth and necessary a posteriori truth, the replacement of Fregean, Russellian and Searlean/ Strawsonian accounts of names with an account of names as rigid designators, the causal or historical-chain theory of reference, an externalist conception of meaning, and the employment of the notion of possible worlds as a way to elucidate the concept of necessity. Wittgenstein’s influence is well known; it reaches all the way back to the publication of his Tractatus Logico-Philosophicus in 1922, while his strongest postwar influence stems from what is known as his later philosophy, most prominently articulated in the Philosophical Investigations from 1953. Kripke and Wittgenstein are sometimes presented as polar opposites on the planet of analytic philosophy. On the one hand, Wittgensteininfluenced commentators have depicted Kripke as an extreme advocate of the “Augustinian” picture of language which Wittgenstein aims to undermine in the Investigations. On the other hand, Kripke-influenced thinkers have presented Wittgenstein’s philosophy as mired in a quasi-verificationist and meaning-is-use form of anti-metaphysics that belongs to the youthful past of analytic philosophy. However, a careful reading of both philosophers reveals a more complex picture. Many of Wittgenstein’s direct targets, including Frege, Russell, and the logical positivists, are Kripke’s targets too. It is also notable that in his criticism of these thinkers, Kripke sometimes makes use of examples taken from Wittgenstein, such as the Moses example in PI, §79. Moreover, as Panu Raatikainen argues in this volume, readings of Kripke as a devoted “Augustinian” are problematic, DOI: 10.4324/9781003240792-1

2  Martin Gustafsson, Oskari Kuusela, and Jakub Mácha if not outright wrong. Questions can also be raised about whether the Wittgensteinian critics have exaggerated Kripke’s commitment to extreme natural kind essentialism, and whether they have paid enough attention to Kripke’s emphasis on several occasions that he is not putting forward a full theory but a picture. Interestingly, the latter leaves more room for exceptions and reservations than a full philosophical theory would do, not altogether differently from Wittgensteinian clarificatory models or pictures (cf. PI, §§130–131). In accordance with these points, even if there is much disagreement between the contributors to this volume, they agree that the relation between Kripke and Wittgenstein is much more intricate and interesting than some black-and-white caricatures suggest, and that we need to explore this relation in depth in order to get clearer about what analytic philosophy is and should (aim to) be today. Kripke’s best known and most extensive engagement with Wittgenstein’s work is in his 1982 tour de force, Wittgenstein on Rules and Private Language. This book was the main impetus for the vast discussion on linguistic rules and normativity in the 1980s and 1990s, an important theme of which was also whether, and if so how, Kripke had misread Wittgenstein. Later on Kripke’s discussion of Wittgenstein on rule-following has had significant influence on analytic philosophy of language, quite independent of any concerns relating to Wittgenstein exegesis or work on the philosophy of language inspired by Wittgenstein. The emphasis of the present volume lies elsewhere, however. Although several contributors bring up the issue of rule-following, the book’s main focus is on themes explored by Kripke in Naming and Necessity and in his shorter articles on logic, metaphysics, and semantics. All of Kripke’s previously mentioned contributions to contemporary philosophy are discussed, and their relations to Wittgenstein’s thought are discussed in detail. In this vein, several chapters focus on Wittgenstein’s example of the Standard Meter in remark 50 of the Investigations with which Kripke takes issue in Naming and Necessity when introducing the notion of the contingent a priori that brings into question the traditional philosophical association of a prioricity and necessity. This is a point where Kripke explicitly disagrees with Wittgenstein who maintains that one cannot either ascribe or deny the Standard Meter the property of having the length of one meter insofar as it plays the logical role of a mode of representation rather than object of measurement. Evidently, the two philosophers use the Standard Meter example to make quite different points: Kripke a point about the difference between reference-fixing and giving meaning, and Wittgenstein a point regarding the idea of logically simple elements such as Russell and he himself postulated in the Tractatus. Several contributors to this volume tackle this cluster of problems in different ways, with some of them perceiving more agreement than disagreement between the two philosophers,

Introduction 3 while others aim to bring to light inherent differences and even incompatibilities between Wittgenstein and Kripke. Consensus has not been an aim of the volume. As already mentioned, the contributors differ much in their interpretations and evaluations of Kripke’s and Wittgenstein’s thought. Some argue that there are deep differences and incompatibilities between the two, and take a stand on who is right and who is wrong. Others adopt a more conciliatory approach, arguing that the differences between Wittgenstein and Kripke have been exaggerated. Genuinely novel perspectives and analyses are provided, resulting in a fuller picture of the Kripke–Wittgenstein relation than the one given by the extensive yet somewhat one-sided discussion of the issue of rulefollowing. As editors, we hope, before all, that the different interpretations and views offered will stimulate further discussion regarding the significance of Kripke and Wittgenstein for philosophy today.1 To briefly outline the contributions to this volume, Panu Raatikainen starts the volume with a discussion of the relationship between Wittgenstein’s and Kripke’s accounts of reference, ostensive definition, essentialism, the necessary a posteriori, and their attitudes towards philosophical theories. Raatikainen argues that the followers of both Kripke and Wittgenstein have exaggerated the differences between the two philosophers which are not nearly as great as they have seemed to many. Thus, for example, Kripke’s account of reference is not an instance of the “Augustinian” picture of meaning criticized by Wittgenstein or subject to Wittgenstein’s criticisms of naïve accounts of ostensive definition. Neither is Wittgenstein a semantic internalist, contrary to what some of his followers have suggested, and he seems to have no need to reject the notion of necessary a posteriori. As Raatikainen puts it, on several occasions, Kripke and Wittgenstein “pull to the same direction”. This is followed by Sebastian Sunday Grève, who, similarly detecting more agreement than disagreement, discusses Frege’s, Russell’s, Kripke’s, and Wittgenstein’s accounts of names, explaining how insights from the latter two philosophers help to resolve problems that arise for the former two. Here an important issue, emphasized by Kripke and Wittgenstein alike, is the independence of the referring function of names from descriptions, with Sunday Grève emphasizing that while Russell is committed to what is known as the description theory of names in the case of ordinary names (although not in the case of logically proper names), Frege is not. Sunday Grève’s overall conclusion is that there is much more accord between Kripke’s and Wittgenstein’s accounts of names than has been usually recognized, with both rejecting the description theory and recognizing the character of names as rigid designators (to put the point in Kripke’s terms). Indeed, Sunday Grève suggests that, despite Kripke’s reservations, rigid designation ought to be considered as a general criterion for being a name, although

4  Martin Gustafsson, Oskari Kuusela, and Jakub Mácha identifying which expressions really are names is complicated by the phenomenon of family-resemblance. He also maintains that Kripke’s historical chain account of the determination of reference is consistent with what Kripke and Wittgenstein say about rule-following in the broad sense that both reference-fixing and rule-following involve communal practices. The consistency of Kripke’s interpretation of rule-following with his account of the determination of reference is questioned by Alexander Miller, who discusses the relationship between Kripke’s account of referencefixing in Naming and Necessity and his skeptical argument in Wittgenstein on Rules and Private Language, according to which there are no matters of fact capable of determining reference. Despite certain suggestions to the contrary, according to Miller, an unresolved conflict remains between Kripke’s accounts of language in the two works, due to how his skeptical considerations regarding a dispositional account of rule-following apply to his own causal-historical picture of the determination of reference too. As Miller argues, the situation here is crucially different from a similar looking one in ethics where an apparent conflict between non-cognitivism in metaethics and cognitivism in normative ethics is resolvable. By contrast, the conflict between what Kripke says in the two works cannot be solved by limiting the skepticism about dispositional accounts to semantic meta-level and the causal-historical account to first-order semantics. Sanford Shieh’s chapter discusses certain similarities and differences between Wittgenstein’s early account of modality and its place in philosophy, and Kripke’s account of modality. Shieh argues that although Wittgenstein’s early work can be seen as bringing the concepts of necessity and possibility back into the heart of logic from their banishment by Frege and Russell, and something similar can be said of Kripke in response to Quine’s criticisms of Carnap, the views of the two philosophers differ with regard to the basis of the concern of philosophy and/or logic with modality. As Shieh explains by examining the development of Wittgenstein’s early philosophy and the problems to which he is responding, for Wittgenstein, the ground for judging the correctness of an account of logical possibility and necessity is being able to articulate a coherent account of propositions and of logic. For Kripke, by contrast, a correct account of modality is something that satisfies our intuitions about relevant matters. Shieh then further argues that Wittgenstein’s account enables him to avoid certain problems regarding the conflicts of intuitions that arise for Kripke. In his contribution, Alexandre N. Machado presents the main tenets of Kripke’s theory of contingent a priori which constitute the basis for Kripke’s disagreement with Wittgenstein, who denies that the Standard Meter can be either ascribed or denied the length of one meter. Machado stresses that Kripke’s theory is at odds with our normal practices of measuring, arguing that Wittgenstein’s claim is based on two premises. First, every object

Introduction 5 that has a length in the metric system is comparable to the Standard Meter. Second, it is not possible to compare the Standard Meter to itself. Machado then further argues that the Standard Meter must not be conceived as an abstract entity, as well as seeking to avert the objection that Wittgenstein’s argument is based on the confusion between metaphysical and epistemological questions. Machado concludes by addressing the objection that his interpretation is based on a substantial conception of nonsense criticized by the representatives of (what is known as) the resolute reading of Wittgenstein’s early work. Continuing the discussion on the Standard Meter, Jakub Mácha argues that Kripke’s apparent disagreement with Wittgenstein’s claims about the Standard Meter arises from two different ways of fixing reference. Kripke proposes that “meter” rigidly refers to the length that the Standard Meter has at time t0, whereby this length is an abstract object postulated by the theory of absolute space. Wittgenstein, in contrast, seems to presuppose that “meter” rigidly refers to the Standard Meter. Mácha points out that both ways of fixing reference have their mutual advantages and disadvantages. A difference between Wittgenstein and Kripke is that Wittgenstein’s way of fixing reference entails that statements attributing to the Standard Meter a definite length in meters are without truth-value, while for Kripke such attributions are contingently true or false. A  truth-value gap however reappears in Kripke’s modal theoretical framework in the context of which existential and modal claims about basic particulars are without truth-value. Mácha concludes that both Wittgenstein and Kripke cannot but allow for certain truth-value gaps which constitute instances of paracomplete reasoning. Christian Helmut Wenzel begins his contribution with a discussion of Kripke’s readings of Wittgenstein and Kant in Naming and Necessity, whereby he points out what he takes to be misunderstandings concerning the two authors. Next, Wenzel turns to Kripke’s example of the Standard Meter and the way he uses it to separate metaphysics from epistemology. Kripke claims, in opposition to what he takes to be the tradition since Kant, that there are contingent truths that can be known a priori, with necessity and the a priori thus coming apart. In response, Wenzel argues that Kripke’s own account seems to be consistent, provided one is willing to accept his interpretation of the “a priori”, although Wenzel also admits that there are hidden assumptions here and certain doubts remain. He concludes that Kripke’s interpretation of the notion of a priori is significantly different from what Kant meant by the term “a priori”. Further engaging with the example of the Standard Meter, Oskari Kuusela argues that Kripke’s introduction of the epistemological-metaphysical category of contingent a priori fails due to its reliance on an unrecognized wavering between different uses of the sentence “Stick S is one meter long

6  Martin Gustafsson, Oskari Kuusela, and Jakub Mácha at time t0”. While the sentence can be used either in the logical role of a contingent true/false proposition or that of an a priori statement, there seems to be no way of using it so that it performs both logical roles at once. In any case, no such cases seem to emerge from the examination of different interpretations of how Kripke might have intended the sentence to express something that is both contingent and a priori. Here Kripke’s failure to explicitly distinguish between the contingency of arbitrary stipulations that are not true/false and the contingency of contingent true/false propositions partly appears to add to the confusion. If Kuusela is right, the notion of contingent a priori is merely a metaphysical mirage arising from logical unclarity, even though it is certainly a philosophically enlightening case to contemplate. Kuusela concludes by proposing a different Wittgensteininspired account of the logical status or definitional sentences in terms of their non-temporal use that, he argues, does not suffer from the problems with Kripke’s account and which seems also able to resolve the problems raised for Kripke’s account by Keith Donnellan and Nathan Salmón. In her contribution “How Long Is the Standard Meter in Paris?”2 Cora Diamond connects Kripke’s Naming and Necessity discussion of the Standard Meter with his treatment of rule-following in  Wittgenstein on Rules and Private Language. Diamond makes the connection via a central thematic in Wittgenstein’s own writings and lectures, namely, his frequent analogies between describing, measuring, and rule-following. Diamond rejects verificationist interpretations of Wittgenstein’s Standard Meter paragraph (in particular, the interpretation she finds in Norman Malcolm’s attempted defense of Wittgenstein against Kripke). Instead, she argues that Kripke fails to recognize a difference Wittgenstein explores in his distinction between transitive and non-transitive uses of words—namely, the difference between a genuine comparison and a non-comparison represented as a comparison. According to Diamond’s Wittgenstein, to say of the Standard Meter in Paris that it is one meter long is analogous to trying to show how tall one is by putting one’s hand on one’s head. Developing this point in connection with Wittgenstein’s discussion of samples, calculations and proofs, Diamond identifies the connection between measures and rules which constitutes the link between Kripke’s two books. At the end of her paper, she explains how her account of Wittgenstein’s viewpoint can help us understand Putnam’s criticism of Kripke, and the contrast Putnam makes between appeal to sortal identity and appeal to the absolute notion of identity with which Kripke is working. Martin Gustafsson further explores the Standard Meter example by developing a diagnosis originally proposed by Cora Diamond (2001), namely, that Kripke’s treatment of the example involves a wavering between what Wittgenstein calls “transitive” and “intransitive” uses of words. Such wavering makes it appear as if a genuine comparison is being made even

Introduction 7 if it isn’t, as in the case where someone puts her hand on her head to prove that she knows how tall she is (cf. PI, §279). According to Gustafsson’s reading, Kripke’s insisting that the Standard Meter is one meter long involves a similar conflation. Gustafsson argues that such wavering makes it impossible for Kripke to adequately account for the most basic feature of measuring qua practice, namely, its being a matter of repeated comparisons. Gustafsson goes on by relating the disagreement between Kripke and Wittgenstein to the actual development, function and use of increasingly sophisticated and precise standards within the metric system, asking to what extent Wittgenstein’s viewpoint can avoid simpleminded forms of conventionalism and pragmatism and do justice to the notion of metrological progress. According to Gustafsson, it is one of the central lessons of Diamond’s reading of Wittgenstein that he can not only allow for such a notion of progress but help us see why a Kripkean approach fails in this regard. Avner Baz’s chapter is a response to what he describes as a dominance of transcendental realism in contemporary analytic philosophy. Starting from the disagreement between Kripke and Wittgenstein concerning the sense that it would (or would not) make to say of the Standard Meter that it is, or is not, one meter long, he seeks to make the case for a form of transcendental idealism, according to which our objective representations of the world—our true or false “cognitions”—have “transcendental” sense conditions. It therefore makes no sense to suppose that the world as reflected in those representations is given entirely independently from those conditions, contrary to what transcendental realists seem to assume. This much remains true, Baz argues, even after we follow Wittgenstein, and recognize, pace Kant, that our sense-making practices are varied, complex, and plastic, and that these practices and their sense-conditions evolve historically. This, Baz holds, calls us to replace thinking about what the sense-conditions of our sense-making practices must be with “looking and seeing” what, in some given case and some moment in time, those conditions, or some of them, are (cf. PI, §§66, 93, 578). In the final chapter, Rupert Read discusses Kripke from the point of view of his recent liberatory reading of Wittgenstein, comparing the views of Socrates, the Stoics, and the Ancient skeptics with Wittgenstein on the one hand, and with Kripke’s meaning skepticism in Wittgenstein on Rules and Private Language on the other hand. Read argues that, unlike the notion of freedom that Wittgenstein articulates, Kripke’s interpretation of Wittgenstein’s discussion of rule-following in terms of meaning skepticism implies a notion of freedom as mere unconstraintness or licentiousness which ultimately only amounts to a fantasy of freedom. In this connection the Ancient skeptics can be seen as an intellectual backdrop to the notion of liberatory philosophy that Read ascribes to Wittgenstein, and which,

8  Martin Gustafsson, Oskari Kuusela, and Jakub Mácha among other things, aims also to liberate us from the illusion of “ ‘total’ freedom” that Kripke’s meaning skepticism implies. Ultimately the notion of freedom Read finds in Kripke cannot even be expressed, and it amounts to nothing at all, according to him. Notes 1 It was not part of our original plan to produce a volume with only male contributors, besides the previously published essay by Cora Diamond. We regretfully admit defeat to circumstances in this regard. 2 Previously published in T. McCarthy and S. C. Stidd (eds.), Wittgenstein in America, 2001, and reprinted with permission from Oxford University Press.

References Diamond, Cora (2001/this volume) How Long Is the Standard Meter in Paris? In T. McCarthy and S. C. Stidd (eds.), Wittgenstein in America. Oxford University Press, 104–139. Wittgenstein, Ludwig (2009) Philosophical Investigations, the German text, with an English translation by G. E. M. Anscombe, P. M. S. Hacker, and J. Schulte, revised 4th edition by P. M. S. Hacker and Joachim Schulte. Blackwell.

1 On the Alleged Incompatibility Between Wittgenstein and Kripke Panu Raatikainen

1.1 Introduction The publication of both Wittgenstein’s PI and Kripke’s NN had a dramatic and long-lasting impact on the philosophical world. The philosophical outlook of these two influential and original thinkers is certainly rather dissimilar. Eager followers of both tend to emphasize their differences and see their views as fundamentally incompatible. In this chapter, I prefer to take a little more conciliatory attitude: it seems to me that their views sometimes cohere a bit more than is common to recognize. Without belittling the undeniable differences of these two unique philosophers, I would like to argue that there are, in addition, underneath the surface, interesting points of contact: more than once, Kripke and Wittgenstein arguably at least “pull to the same direction.” My focus in what follows is somewhat more on Kripke; in particular, I  want to settle some apparently popular misunderstandings concerning Kripke’s views relevant for the theme. These considerations also hopefully help make clearer what the genuine and substantial differences between Wittgenstein and Kripke then really are. Much ink has been spilled over Kripke’s reflections on rule-following in his WRPL, which were obviously inspired by Wittgenstein’s relevant considerations. However, I shall set that theme aside here. Instead, I shall focus on the certain somewhat less-scrutinized relations between the later Wittgenstein and the Kripke of NN. One may wonder, though, why there is no mention of Kripke’s significant ideas of, for example, causalhistorical chains of reference from NN in his discussion of meaning-skepticism in WRPL? They would seem at least prima facie relevant. Although NN was published a decade earlier than WRPL, one may speculate whether Kripke developed these ideas in the opposite order. Namely, in the Preface of NN, Kripke reported that most of the views of NN were formulated in about 1963–1964 (NN, p. 3). In the Preface of WRPL, Kripke said that he came to think about these themes in the way expounded in the book around 1962–1963 (WRPL, p. viii).1 Consequently, we know at least that DOI: 10.4324/9781003240792-2

10  Panu Raatikainen Kripke already knew Wittgenstein’s PI quite well when his new ideas that became to constitute NN started to emerge. We may perhaps also charitably assume that he understood the relevance and the force of various considerations by Wittgenstein even if he has not explicitly underwritten them in NN or elsewhere. It is quite well known that Kripke mentions Wittgenstein in a somewhat critical light at a couple of places in NN; namely, in the discussion of the standard meter (NN, pp. 54–57; cf. PI, §50) and Wittgenstein’s discussion of “Moses” (NN, pp. 31–33; cf. PI, §79). The case of the standard meter is convoluted, and there is already an ample literature on it. I shall also set it aside, as well as the whole theme of contingent a priori. The latter seems to me, though interesting, in the end less important than what I take to truly be the key conclusions of NN2 (even many otherwise loyal followers of Kripke apparently have varying degrees of doubt concerning them). I shall also be very brief with the “Moses” case: Kripke’s principal targets were Strawson (1959) and especially Searle (1958), who advocated the cluster theory variant of descriptivism as a general theory of reference. Although neither explicitly mentioned Wittgenstein, it is plausible to assume that their proposal was inspired by his remarks on “Moses” (PI, §79). Kripke noted the connection and cited Wittgenstein (NN, p. 31). It is unclear, though, whether Wittgenstein really intended to put forward any sort of general theory of names, and what exactly was his true aim here (see, e.g., Travis 1989; Schulte 2009; Bridges 2010). There are also less obvious gestures towards Wittgenstein in NN: for example, in the middle of discussion of the sentence “Socrates is called ‘Socrates’ ” and the threat of circularity, Kripke suddenly remarks: “See how high the seas of language can rise. And at the lowest points too” (NN, p. 73). This seems to echo Wittgenstein’s remark, “See how high the seas of language run here!” (PI, §194). 1.2  Kripke and the Augustinian Picture of Language Wittgenstein famously began PI with a quote from Augustine. Instantly after that (still in §1), Wittgenstein identified as his target “a particular picture of the essence of human language” which, put schematically, goes as follows: (A1) The individual words in language name objects. (A2) Sentences are combinations of such names. (A3) Every word has a meaning. (A4) This meaning is correlated with the word. (A5) The meaning of a word is the object for which the word stands.

Alleged Incompatibility Between Wittgenstein and Kripke 11 It is customary to call this conjunction of views “the Augustinian Picture of Language.”3 Wittgenstein then proposed that first, this one-sided focus on names suggests a highly misleading picture and overlooks vast variety of different kinds of uses of expressions and sentences, and second, that it gives a flawed account of even proper names. For example, he noted that if a person named “N.N.” dies, or the legendary sword called “Excalibur” gets destroyed, we would not thereby say that the meaning of “N.N.” died (PI, §40), or that the name “Excalibur” no longer has meaning (PI, §§39, 44). Wittgenstein instead concluded that for a large class of cases in which we employ the word “meaning” it can be defined thus: “the meaning of a word is its use in the language” (PI, §43). Wittgenstein also notably put forward critical considerations relating to ostensive definitions. For him, (A1)–(A2) and the idea that ostensive definitions constitute the foundation of language were intimately related. Kripke by contrast focused in NN visibly on proper names and their reference (and to some extent on natural kind terms, which he contended have “a greater kinship with proper names than is generally realized”; NN, p. 134). He was primarily interested in the following question: in virtue of what does a name stand for a particular object? Kripke also suggested that a new proper name is typically—though not necessarily—introduced to a language with the help of an ostension. Consequently, one can easily get the impression that there is a fundamental conflict of views between the two philosophers here. In other words, one may wonder whether Kripke was committed to “the Augustinian Picture,” thoroughly or at least partially. To begin with, it is quite evident that Kripke never even pretended to present an overarching theory4 of words and sentences, not to mention the essence of human language. His ambitions were much more modest, and his interests were far more local and specific. Therefore, he clearly was not for that part—that is, (A1)–(A2)—committed to “the Augustinian picture.” Nonetheless, did Kripke not advocate Millianism, that is, the Direct Reference Theory—the view that a proper name directly designates an object, only the object contributes to what is expressed (“the Russellian proposition”), and that the object is the meaning of the name? And if so, certainly he is vulnerable at least to Wittgenstein’s critique of the later parts of the “Augustinian picture”—of (A5) in particular? One must keep a sharp eye here. For example, one must be cautious with what exactly it is that Kripke agreed with Mill? Kripke did indeed say, in NN: My own view . . . regards Mill as more-or-less right about “singular” names. (NN, p. 127)

12  Panu Raatikainen The present view [Kripke’s own] .  .  . endorses Mill’s view of singular terms. (NN, p. 135) Kripke later stated that his own view is closer in various respects to Mill’s view than to the descriptivist tradition (see Kripke 1973/2013, p.  11; Kripke 1979, 125)—even that “a Millian line should be maintained as far as is feasible” (1979, p. 137; my emphasis). And Kripke did endorse the substitutivity of co-referential names in the contexts of alethic modalities (i.e., contexts involving the notions of necessity and possibility). Kripke certainly contended that proper names do not have “connotation” or “sense,” if the latter is interpreted in descriptivist lines. To this extent at least, he really did agree with Mill. However, contrary to what seems to be a very popular interpretation, Kripke never identified the meaning of a proper name with the object it denotes. The contrary assumption seems to be based on a problematic background assumption, a false dichotomy, that the meaning of a name must be either descriptive or the bearer (see Raatikainen 2020). Furthermore, in Kripke’s view, proper names do not denote their bearers directly, in some absolute sense of “directly.”5 Instead, the referential relation between the two may be constituted by a long historical chain of uses of the name by various language users. Moreover, contrary to what many seem to have assumed, Kripke never maintained that the chain is cast-iron once the expression is introduced: he allowed that the chain can sometimes break down6 and that the reference can even shift from one referent to another in specific circumstances.7 In the new 1980 introduction to NN, Kripke points out: My view that the English sentence “Hesperus is Phosphorus” could sometimes be used to raise an empirical issue while “Hesperus is Hesperus” could not shows that I do not treat the sentences as completely interchangeable. (NN, p. 20) Furthermore, it indicates, according to Kripke, that “the mode of fixing the reference is relevant to our epistemic attitude toward the sentences expressed” (NN, pp. 20–21). He then moves on to reflect how this relates to the question what “propositions” are expressed by these sentences, and in general, how to treat names in epistemic contexts. Kripke grants that these are “vexing questions,” and concludes: I have no “official doctrine” concerning them, and in fact I am unsure that the apparatus of “propositions” does not break down in this area. [footnote omitted] Hence, I sidestepped such questions; no firm doctrine regarding the point should be read into my words. (NN, p. 21)

Alleged Incompatibility Between Wittgenstein and Kripke 13 Kripke never presented any positive theory of meaning whatsoever—not even a theory restricted to proper names.8 In any case, it is a mistake to count Kripke as an unreserved advocate of the full-blown Direct Reference Theory. In particular, Kripke did not commit himself to (A3)–(A5), which Wittgenstein criticized. 1.3  Ostensive Definitions and Ostensive Teaching What then about ostension in Kripke and Wittgenstein’s critique? To begin with, the notion of ostensive definition which Wittgenstein was primarily pondering was a very strong notion cherished mainly by the logical positivists of the Vienna Circle in the 1930s (see Baker and Hacker 1986). According to that view, ostensive definitions were supposed to be the ultimate source of all meaning and provide the foundation of both language and knowledge as follows: every meaningful sentence was supposed to be reducible to elementary sentences, the latter in turn analyzable in terms of ostensive definitions of their primitive expressions, and in this way be all conclusively verifiable or falsifiable. Understanding the latter expressions was supposed to consist in the ability to apply them to given objects unfailingly—the capability to recognize an item as the same as the item to which the expression was applied in the occasion of ostensive definition. Ostensive definitions were expected to be immune to misinterpretation and the application of the defined expression infallible. Items so namable were assumed to be what is given by direct acquaintance and is actually directly observed, sense data or such, and themselves be the meanings of those expressions (ibid.). Kripke’s mundane view of the role of ostension in the occasion of “baptism” of ordinary names is evidently nothing like that. Kripke’s main target of criticism in NN, descriptivism, is instead closely related to the logical positivist version of “the Augustinian Picture” with their idea of ostensive definitions, both contentually and historically. Far from being committed to the latter, Kripke can be rather viewed as carrying out its critique further: his all-important arguments from ignorance and error against descriptivism at the same time effectively refute that picture too.9 Furthermore, Wittgenstein’s key point was in any case that one simply cannot construct an entire language from scratch (especially, without already having another language; cf. PI, §32), provide the foundation of language, simply by using ostensive definitions: [T]he ostensive definition explains the use—the meaning—of the word when the overall role of the word in language is clear. .  .  . One has already to know (or be able to do) something in order to be capable of asking a thing’s name. (PI, §30)

14  Panu Raatikainen We may say: only someone who already knows how to do something with it can significantly ask a name. (PI, §31) Such a project of providing the foundation of language is emphatically not what Kripke was aiming at. Therefore, he could have easily agreed with Wittgenstein here. He was simply noticing that the introduction of a new proper name often involves ostension. There can well already be a lot of language (or language-like thought) in place. In as much as it is also a part of the Augustinian picture that language users in general learn a word ostensively by learning which object it corresponds to,10 Kripke obviously did not advocate this view even in the case of proper names. He on the contrary criticized it in his own way: according to him, a name is very often learned from other language users in a situation in which the bearer of the name is absent; one does not even need to learn a way to recognize the object or a way to describe it uniquely. The practices of the linguistic community, which stretch back in time—the historical chains of communication and reference-borrowings—take care of reference, in Kripke’s picture. In it, language users participate in a general practice of reference-borrowing. One can perhaps even view it as a kind of “use” or “usage,” in a Wittgensteinian mood, if one wants. In summary, at least as far as the focus is on “the Augustinian picture” and ostensive definitions (or ostensive teaching), the alleged incompatibility of the views of Kripke and Wittgenstein are merely specious and simply not real. 1.4  Theories in Philosophy As well known, Wittgenstein rejected utterly the idea that legitimate philosophy could result theories or theses. According to Wittgenstein, “we may not advance any kind of theory. There must not be anything hypothetical in our considerations” (PI, §109). Philosophical problems are to be solved “through an insight into the workings of our language, and that in such a way that these workings are recognized—despite an urge to misunderstand them”—“not by coming up with new discoveries, but by assembling what we have long been familiar with” (ibid.). Accordingly, “If someone were to advance theses in philosophy, it would never be possible to debate them, because everyone would agree to them” (PI, §128). “Philosophy is a struggle against the bewitchment of our understanding by the resources of our language,” Wittgenstein aphoristically summarized his view (PI, §109). It appears to be a quite common interpretation that Kripke in contrast aimed to put forward a strong and generalizing philosophical theory of metaphysics and language and is therefore definitely in the opposite camp. Some sympathizers of Wittgenstein seem to consider Kripke’s NN as more

Alleged Incompatibility Between Wittgenstein and Kripke 15 or less the worst example in contemporary philosophy of the kind of philosophy Wittgenstein contested. Yet I would like to suggest that their distance may not be here as immense as it is usual to think. In fact, Kripke said even several times in NN that he is not presenting a theory;11 for example: Let me state then what the cluster concept theory of names is. (It really is a nice theory. The only defect I think it has is probably common to all philosophical theories. It’s wrong. You may suspect me of proposing another theory in its place; but I hope not, because I’m sure it’s wrong too if it is a theory.) (NN, p. 64) I think I said the other time that philosophical theories are in danger of being false, and so I wasn’t going to present an alternative theory. (NN, p. 93) At any rate more refinements need to be added to make this even begin to be a set of necessary and sufficient conditions. In that sense it’s not a theory, but is supposed to give a better picture of what is actually going on. (NN, p. 96) Kripke’s comments on the description theory of reference in the new 1980 introduction to NN are also interesting: he granted there the “power” of the once prevailing complex of ideas, that is, descriptivism, he then abandoned. Kripke wrote: “The natural and uniform manner by which these ideas appear to account for a variety of philosophical problems—their marvelous internal coherence—is adequate explanation for their long appeal” (NN, p. 5). And he then confessed of himself: “it took some time to get free of its seductive power” (ibid.; my emphasis). Such a talk of “seduction” is of course familiar from Wittgenstein. A larger part on NN is precisely simply attempts to get free from the seduction of that powerful philosophical theory, and not so much proposing one’s own general philosophical theory. Kripke’s discussion of the once popular thesis—Quine was an influential advocate—that whether a particular has a certain property contingently or necessarily depends on the way it is described12 appears likewise relevant here: Suppose that someone said, pointing to Nixon, “That’s the guy who might have lost.” Someone else says “Oh no, if you describe him as ‘Nixon,’ then he might have lost; but, of course, describing him as the winner, then it is not true that he might have lost.” Now which one is

16  Panu Raatikainen being the philosopher, here, the unintuitive man? It seems to me obviously to be the second. The second man has a philosophical theory. (NN, p. 41) That is, Kripke seemed to suggest that it is plain common sense that the pointed person, Nixon, might have lost, period; whereas the antithesis according to which this is not unequivocally true but depends critically on how the person is described complicates without need the simple issue— that the latter is a counterintuitive consequence of a substantial (and problematic) philosophical theory. Kripke apparently saw himself by contrast merely elaborating the obvious here. Does this not have a certain Wittgensteinian ring? Kripke also insinuated that the much-discussed problem of “transworld identification” is, in reality, largely a pseudo-problem (NN, p. 48 (fn. 15), p. 50) generated by “a totally misguided way of looking at things” (Kripke 1971, p. 11)—a flawed philosophical theory or picture of how one should consider “possible worlds.” The picture involves viewing commonplace counterfactual scenarios as if they were entire separate foreign countries or distant planets, which we then observe through some kind of telescope. Consequently, it is assumed that the worlds are and must be given purely qualitatively. We then allegedly have to somehow identify world by world, who in the given world is, say, Nixon, via purely qualitative properties.13 Kripke commented: “All of this talk seems to me to have taken the metaphor of possible worlds much too seriously in some way” (Kripke 1971, p. 11). His own no-nonsense alternative is the following: “on the contrary, we begin with the objects, which we have, and can identify, in the actual world. We can then ask whether certain things might have been true of the objects” (NN, p. 53). Kripke said that good deal of the literature on “transworld identification” is just intuitively bizarre (NN, p. 76). Again, at least I myself sense something Wittgensteinian in the tone of Kripke here. Undeniably Kripke did sketch, as an alternative to descriptivism, a new “picture” of how reference works: his notable picture of historical chains. According to it: “Through various sorts of talk the name is spread from link to link as if by a chain” (NN, p. 91). However, that was in fact little more than everyday knowledge of how names are often transmitted and how we typically acquire a name; not a Philosophical Theory (with capital “P” and “T”). It is an “oversimplified”14 model not completely unlike the simple language-games Wittgenstein described and definitely not even intended as an overarching theory of language. Kripke moreover expressed skepticism concerning the possibility of reductive analysis of important philosophical concepts such as reference: “philosophical analyses of some concept like reference, in completely different terms which make no mention of reference, are very apt to fail” (NN, p. 94). Accordingly, few have categorically

Alleged Incompatibility Between Wittgenstein and Kripke 17 denied what Kripke described there; even his opponents have most often either attempted to accommodate the phenomenon of reference-borrowing in their dissenting views, or simply ignored it and focused on other (real or alleged) aspects of Kripke’s ideas. Wittgenstein wrote: “Philosophy may in no way interfere with the actual use of language; it can in the end only describe it” (PI, §124). Isn’t this quite a bit what Kripke was doing here? Admittedly, especially in the third, last lecture of NN, Kripke allowed himself to be more speculative and contemplate some more tentative lines of thought—I am thinking of his reflections of the necessity of origin, for example. This may well have been “hypothetical” in the sense that Wittgenstein would not have accepted in philosophy. All in all, even if Kripke may well have had somewhat less radical attitude towards philosophical theses and theories than Wittgenstein, their differences in this respect should not be exaggerated either. 1.5  Some Wittgensteinian Opposition to Kripke Some self-proclaimed Wittgensteinians such as Hacker (1996), Hanfling (1984, 2000), Glock (2003, 2017) and Loomis (2017), for example, have quickly dismissed Kripke’s whole approach. Hacker, for example, writes: It is a leitmotif of Wittgenstein’s reflections on meaning that the meaning of an expression is given by what are accepted as correct explanations of meaning, which constitute rules for the use of the expressions explained. Rules for the use of expressions are not true or false, and are not answerable to reality for their correctness (an aspect of what he called “the arbitrariness of grammar” or “the autonomy of language”). (Hacker 1996, p. 250) In Hacker’s interpretation, Kripke and Putnam by contrast argued that “scientific discoveries about the inner constitution of the items” belonging to the extension of a natural kind term “may reveal its real meaning” (ibid.). Hacker concludes: “If this account were true, it would spell ruin for Wittgenstein’s philosophy. However, the scientific realist semantics is gravely flawed” (ibid., p. 251). As Loomis sees it, Kripke’s views stand at odds with Wittgenstein’s accounts of necessity and apriority from TLP onward. According to him: Wittgenstein’s accounts involved an identification of expressions of necessity with tautologies, or conventional rules of syntax or grammar, which were known a priori either through calculation, as in the Tractatus, or though stipulation. (Loomis 2017, p. 355)

18  Panu Raatikainen Loomis concludes that “Wittgenstein was thus committed to the very identifications [of necessity and apriority] that Kripke denied” (ibid.). Glock writes that the essentialism of Kripke and Putnam “creates a gap between nature and meaning, but it is subject to Wittgensteinian objections” (Glock 2017, p. 240). Hacker and Glock then refer to Dupré (1993) and Hanfling (1984, 2000); Loomis refers to Needham (2011). According to Hanfling, the Wittgensteinian philosophy of “what we say” is “about the meanings of words and these ‘lie open to view,’ given that the meaning of a word is displayed in its normal use.” The latter assumption is, he continues, contrary to the realist account of Kripke and Putnam, “which drives a wedge between meaning and use, so that according to it the meanings of our words can be hidden from us” (Hanfling 2000, pp. 237–238). Yet these critiques are disappointingly sketchy and undetailed, and often simply off the mark. For example, much of Hanfling’s critical assessment focuses on details (often in Putnam and not Kripke) that are tangential to the core issues, and/or is directed primarily against a very strong and generalizing theory, the ascription of which especially to Kripke is questionable. Hanfling also argues against the view that meaning never changes, which he attributes to Kripke and Putnam; yet definitely neither of them contended that. Glock for his part also suggests that transworld identification poses a serious challenge to Kripke. This, however, ignores Kripke’s frequent discussion of that alleged problem which, I think, quite successfully deflates it (see earlier). Besides that, these critics basically just defer the issue to certain philosophers of science. It is striking that they (apart from Hanfling; see later) virtually reduce Kripke’s multifaceted ideas on reference to extreme natural kind essentialism they ascribe to him. Kripke’s pivotal ideas of historical chains of communication and reference-borrowing, which often involve no natural kind terms at all, and their far-reaching philosophical consequences (see footnote 1), are not even properly mentioned. Unlike many others, Hanfling does mention historical chains (or rather “causal chains”) but then only muddies the water: the crucial conclusion of Kripke and Putnam is not, as Hanfling suggests (ibid., p. 239), that ignorant or erring language users do not understand “Cicero” or “Columbus,” for example, or are not competent with such names.15 On the contrary, their proposal is that even such language users are able to refer successfully owing to other language users and resulting historical chains. The central claim is only that what they believe and how they use the word individually may not be alone sufficient to determine the correct bearer of the name. One should recognize that Kripke’s most powerful arguments against descriptivism are not fundamentally based on essentialism and need not fundamentally involve natural kinds at all. They are rather grounded on the mundane observation that people are often, unlike descriptivism

Alleged Incompatibility Between Wittgenstein and Kripke 19 predicts, rather ignorant and have many false beliefs about various items they nevertheless talk about (“the arguments from ignorance and error”; see footnote 9). If descriptivism were correct, all such people would fail to use many relevant words successfully in referring. They either would not really understand any of those commonly used words, or would refer quite randomly on alternating items, and the result would be a sort of radical skepticism concerning reference. Although Wittgenstein never commented this exact issue, it seems to me that the latter conclusion would be strongly against the spirit of the later Wittgenstein’s thought. After all, he contended, early and late, that ordinary language is in order as it is. 1.6  Natural Kinds and Essential Properties As to natural kinds and their debated essential properties, instead of presenting what one might have expected—more or less Wittgensteinian arguments—these critics largely simply defer to certain standard critiques of essentialism by some philosophers of science (Dupré and Needham in particular). However, arguably such objections are in reality much less pertinent here than many philosophers seem to think.16 It is seemingly a widely shared impression that Kripke (together with Putnam (1975)) put forward a general theory according to which all natural kinds have absolute (interest-independent) and intrinsic microphysical essences—where an essence is understood as amounting to precise necessary and sufficient conditions, with entirely sharp boundaries (no indeterminacy), for belonging to the kind in question. And philosophers of science have not got tired in arguing that such a theory does not stand closer scrutiny. Nevertheless, its popularity notwithstanding, such an interpretation has very little basis in NN. We have already noted earlier that Kripke denied repeatedly that he intends to present any well-developed and generalizing theory. Moreover, critics often focus on certain peculiarities of Putnam’s particular view (in the early 1970s), and many uncritically assume that Kripke is automatically committed to all of them too. Yet Kripke in fact never subscribed many of those ideas, was explicitly critical towards some of them, and was overall much more cautious to make any generalizations. Moreover, Dupré’s critique focuses mainly on the complexities of biological kinds. Kripke in fact said very little about them; and pace critics, he did not contend that only intrinsic genetic properties matter (admittedly Putnam was less careful here). Philosophers of chemistry such as Needham in turn focus largely on certain intricacies of chemical compounds, and their critical observations do not automatically generalize to chemical elements. It should then be recognized that Kripke’s separation of necessity and a priori knowability does not depend on the prevalence of counterexamples; even

20  Panu Raatikainen few will do. Consequently, if at least some chemical elements support his critical arguments, that is quite enough. The story of oxygen, for example, seems to provide a rather convincing case (see Hendry 2010; Raatikainen 2021, 2024). And again, Kripke’s significant conclusion need not involve natural kinds and essential properties at all: an identity statement with two proper names, such as “Ricardo Klement is Adolf Eichmann,” which can be known to be true only a posteriori and still arguably expresses necessary truth, is sufficient. Wittgenstein undeniably raised doubts against the conviction that the sense (Fregean “Sinn”) of an expression must be determinate. Kripke, as well known, did not believe in senses at all, at least if they are interpreted along the descriptivist lines. However, Wittgenstein at the same time questioned the determinacy of the extensions of many words—and that the latter would possess sharp boundaries and precise necessary and sufficient conditions. And did not Kripke (with Putnam and others) contend that at least natural kinds do? Therefore, in as much as Kripke assumed that the extensions of natural kind terms, for example, are determinate and have strict necessary and sufficient conditions, Wittgenstein’s critique of determinacy is potentially relevant against him too. However, already in NN, Kripke conceded: “To the extent that the notion ‘same kind’ is vague, so is the original notion of gold. Ordinarily, the vagueness doesn’t matter in practice” (NN, p. 136). Later, Kripke has discussed, for example, the vernacular word “water” and whether the somewhat puzzling heavy water should have belonged to its extension or not. He concluded that the relation between natural language and scientific usage has a certain “degree of looseness” (Kripke 2023). The allowance of vagueness also entails that natural kinds may not have sharp sufficient conditions. This is compatible, though, with taking some properties, such as having the atomic number 79, or containing oxygen, as a property which is necessary for belonging to the kind. 1.7 Necessary A Posteriori and Externalism It is certainly true that in the austere framework of the early Wittgenstein’s TLP, there was definitely no place for the kind of separation of necessity and a priori and necessary truths which could only be known a posteriori that Kripke later suggested. With the later Wittgenstein, however, the situation might be a bit less straightforward. That is, Wittgenstein himself later demolished many cornerstones of TLP which were his original reasons for such a denial—and it is not entirely clear what exactly takes their place. Possibly the spontaneous reaction of Wittgenstein could still have been negative, but who knows. It seems that this kind of questions simply were not that central for him anymore.

Alleged Incompatibility Between Wittgenstein and Kripke 21 In any case, Wittgenstein’s background was very much in the extensional logic of Frege and Russell. Its influence is obvious in TLP. But although it is in a lesser role in his later philosophy, even with all his genius, he probably simply never clearly foresaw the raise of modal reasoning which crucially goes beyond extensional logic17—and especially the novel notion of possibility (and necessity) grounded on counterfactual scenarios, which was only for the first time clearly formulated by Kripke. Kripke rightly highlighted that reflections of counterfactual scenarios are a common part of our thinking in both everyday life and science. Kripke then basically observed that, in order to avoid making such counterfactual reasoning empty and futile, some things must be kept constant even in the varying counterfactual scenarios. On Kripke’s view, certain identities and other constancies across the scenarios can be built into the framework of counterfactual scenarios by stipulation: we reflect, for example, what could have happened to Nixon; that we are talking about Nixon is part of the framework, and the question of who is Nixon in a given scenario (“the problem of transworld identification”) never arises. Or, if we want to consider how gold would behave in various counterfactual (perhaps even counternomic) scenarios, we are talking about gold (the element with atomic number 79; give or take some tolerable degree of indeterminacy) and how it would behave—and not about a substance which merely looks and feels like gold: “ ‘Possible worlds’ are stipulated, not discovered by powerful telescopes” (NN, p. 44.). In contrast, it seems plausible that the kind of alleged necessity (which would go beyond “tautologies” or analytic a priori) Wittgenstein primarily had in mind and wanted to rule out was the purported class of deeply metaphysical synthetic a priori truths of the German idealist tradition, knowable by pure reason. The Kripkean a posteriori necessity which delimits counterfactual scenarios is so qualitatively different from the latter that it may be misleading to consider them as if they were only slight variants of one and the same notion. Is it even credible to assume that Wittgenstein had any reflected opinion concerning Kripke’s counterfactual possibilities? Although the label “externalism” is more obviously applicable to Putnam and Burge, for example, it is also quite common to count also Kripke as an advocate of meaning externalism—the view that the meaning of a referring expression may not always and exhaustively be determined by the (narrow) mental states of an individual language user. Their arguments, if sound at all, seem at the same time count against the sufficiency of individual’s actual use and dispositions to use the expression too. As we have seen, several Wittgenstenian philosophers see such externalist ideas both fundamentally incompatible with Wittgenstein’s views and severely flawed. They also more or less identify externalism with extreme natural kind microessentialism. However, in Kripke’s intuitively compelling picture,

22  Panu Raatikainen what determines the reference of an expression as used by an individual depends on historical chains and earlier users of the expression. It is thus often determined neither by the mental states nor by the behavior dispositions of the current individual language user. This already amounts to externalism and, to repeat, it depends in no way on any strong and general microessentialist theory of natural kinds, or whatever. For whatever it is worth, my own gut feeling has been for long that if only one reads the later Wittgenstein with an open mind, at least seeds of externalism can be seen here and there. For example, from §138 onwards in PI, Wittgenstein moved on to discuss understanding and the apparent fact that we sometimes grasp a meaning of a word in a flash. The latter may suggest that understanding is a specific kind of mental state—a mental image of some sort perhaps. Wittgenstein then put forward a series of considerations which undermine this way of interpreting “understanding.” Wittgenstein’s examples were often mathematical terms, which behave likely somewhat differently from mundane proper names and kind terms on which Kripke principally focused. And Wittgenstein concentrated on the use of a word, whereas Kripke’s attention was on the determination of the reference of a referring expression. Nevertheless, one can perhaps see at least certain analogies between Wittgenstein’s reflections and those of Kripke: Wittgenstein argued that the presence of a certain mental image in one’s mind is neither necessary nor sufficient for being able to use a word correctly and thus understanding a word. Kripke for his part contended that the presence of a certain description in one’s mind—associated with a word—is neither necessary nor sufficient for being able to successfully refer with the word. Wittgenstein wrote, for example: What is essential is to see that the same thing can come before our minds when we hear the word and the application still be different. Has it the same meaning both times? I think we shall say not. (PI, §140) Later in PI, once more focusing on mathematical expressions, but perhaps the moral is again more general, Wittgenstein was apparently arguing that others may very well know better than I whether I understand a sentence or an expression (see, e.g., PI, §§513–517; cf. Kenny 1973, p. 148). I am not alone in seeing certain externalist tendencies in the reflections of the later Wittgenstein. Rowlands (2003), for example, views Wittgenstein as at least a predecessor of the more contemporary meaning externalism. Child (2010) does not hesitate to count Wittgenstein quite straightforwardly as an externalist. Child points out that Wittgenstein even used occasionally thought experiments not completely different from Putnam’s famous Twin Earth science fiction: that is, Wittgenstein invited us to

Alleged Incompatibility Between Wittgenstein and Kripke 23 imagine that God creates somewhere an exact copy of England, but so that it has existed only two minutes. Wittgenstein then reflects whether people in the Twin England would really calculate (Wittgenstein 1978, VI-34). Child argues that properly interpreted, Wittgenstein’s key views are entirely compatible with contemporary semantic externalism. Sorgiovanni (2020) for his part develops a Wittgensteinian version of social externalism, based partly on Wittgenstein’s same considerations on understanding and mental images I briefly mentioned earlier.18 Most probably more examples could be found if only the literature were searched more extensively. Moreover, likely much more could be said about this theme. Indeed, I am inclined to think that this might turn out to be a fruitful line of research for the future Wittgenstein scholarship: to re-evaluate Wittgenstein’s work in relation to externalism. It may well prove that Wittgenstein’s thought in its entirety is less categorically internalist than some philosopher speaking on his behalf have insisted. 1.8  Concluding Remarks Wittgenstein and Kripke worked in different time periods and in very unlike philosophical environments. They reacted to rather dissimilar philosophical challenges. Differences in their views are therefore inevitable. It seems, though, that some over-enthusiastic admirers of them frequently exaggerate the incompatibility of their views. The degree of their disagreement should not be inflated either. They both criticized, for their own part and from different angles, a general picture of language which derived from Frege, Russell, Wittgenstein’s own early TLP and the logical positivists. Sometimes their contributions rather complement each other. In general, we should approach the works of these two great philosophers dispassionately and with an open mind. They both deserve to be studied and compared carefully—to be objects of quality scholarship as free as possible from dogmatic prejudice and bias. I have argued that, appearances notwithstanding, Kripke’s views on names and reference are not vulnerable to Wittgenstein’s critique of “the Augustinian Picture of Language” and of ostensive definitions, but that their views are here in fact quite compatible. Furthermore, arguably the attitudes of these two philosophers towards theories in philosophy are not as a matter of fact as dissimilar as many have quickly judged. I have contended that some Wittgensteinian critics oversimplify Kripke’s pregnant views and erroneously reduce them to extreme microessentialism concerning natural kinds. Although Kripke was certainly inclined towards the view that a natural kind may have some of its properties necessarily, he also allowed a certain degree of vagueness and looseness there and did not propose any overarching and strong essentialist theory. I have also underlined

24  Panu Raatikainen that in any case, most of his significant path-breaking ideas on meaning and reference do not in the least depend on such views on natural kinds. Finally, I have suggested that perhaps Wittgenstein was not as unequivocally a semantic internalist as some of his ardent followers have insisted. If I am on the right track, the views of Wittgenstein and Kripke may not have been that irreconcilably incompatible in this regard either. Notes 1 If Kripke really kept the ideas that became WRPL in his mind two decades without his later important ideas affecting them at all, this may perhaps tell something interesting about his mind. 2 In Raatikainen (2024), I suggest that those are (1) the arguments from ignorance and error against descriptivism (and related traditional views on meaning and reference) (cf. footnote 9); (2) the largely new idea of reference borrowing, and the resulting historical chain picture of reference; (3) the clear separation of the (possible) use of a description in the initial fixation of the reference of an expression from its meaning (in particular, even if a name is introduced with the help of a description, the name does not thereby necessarily become synonymous with the description); and (4) the conclusion that there are necessary truths which are knowable only a posteriori. 3 It is quite well recognized that Augustine does not really commit himself explicitly to all these ideas; the analyses of this discrepancy have varied; for an illuminating discussion, see Stern 2004. 4 More of the “theory” aspect in the next subsection. 5 As, for example, Russell’s “logical proper names” allegedly denoted sense data, objects of acquaintance, or such. 6 See Kripke’s discussion of “Santa Claus” (NN, p.  93) and “George Smith” (NN, pp. 95–97). 7 See NN, p. 163; Kripke 1973/2013, pp. 136–137; cf. Raatikainen 2024. 8 Devitt, a close ally of Kripke, has suggested from early on (Devitt 1974, 1981) that the Kripkean historical chain relevant for a name can play, at least in many respects, the role of the sense, or the meaning, of the name. Kripke himself has remained officially uncommitted, but he has at least mentioned the idea few times; see NN, 1972, p. 346, n. 22 (the note was omitted from the 1980 book version); and Kripke 1979, p. 248; see also Raatikainen 2020. 9 For a clear summary of those arguments, see Devitt and Sterelny 1999, pp. 54–57. Very briefly, Kripke argued that an average language user may often be both unable to recognize the bearer of the name and incapable to associate with the name any correct and sufficiently identifying description: they may be too ignorant (e.g., one only knows that Cicero was a famous Roman, or that Feynman is a physicist; NN, p.  81) and/or too erring (e.g., one believes that Einstein was the inventor of the atomic bomb, or that Columbus was the first European to discover America; NN, p. 85; Kripke’s vivid, purely fictional Gödel–Schmidt-story (NN, pp. 83–84) also entertainingly illustrates the error aspect). Similar arguments can be easily constructed for all sorts of referring expression. 10 This idea is not explicitly included in (A1)–(A5), but it clearly occurs in the quote from Augustine and is discussed by Wittgenstein under the label “ostensive teaching.” 11 See NN, pp. 64, 93, 96, 97, 139.

Alleged Incompatibility Between Wittgenstein and Kripke 25 12 Quine’s discussion involving the “mathematical cyclist” example in particularly well-known; see Quine 1960, pp. 199–200. 13 Kripke discussed the theme in this way at several passages thorough the first half of NN; see also Kripke 1971, pp. 10–13. 14 Kripke’s own characterization; see NN, p. 162. 15 Hanfling cites certain remarks by Putnam (1975), but I contend that he misinterprets it. Putnam’s real point is arguably that competence with a particular word requires participation to the historical chain of that word; a language user is not competent, for example, with a phonetically indistinguishable word of her Doppelgänger on Twin Earth—even if they share by definition exactly the same narrow mental states and skills. And in any case, this remark is more a grace note in Putnam’s work and not the main conclusion. 16 In the following paragraphs, I  draw from my recent papers, Raatikainen 2021 and especially Raatikainen 2024. In those papers, I argue in some detail that although the overall picture is certainly more complicated than the brief remarks of Kripke (and Putnam) may suggest, nevertheless the facts in the end support their central philosophical conclusions rather than undermine them. 17 As it happens, his former student and eventually a close friend and trustee, Georg Henrik von Wright, nevertheless played a role in it (see, e.g., von Wright 1951). 18 It would not be appropriate here to begin to repeat in detail what these scholars say; I refer the reader to their interesting works directly.

References Baker, G. P. and Hacker, P. M. S. (1986) Wittgenstein and the Vienna Circle: The Exaltation and Deposition of Ostensive Definition, in S. Shanker (ed.), Ludwig Wittgenstein—Critical Assessments, Vol. 1, 241–262. Revised in Hacker, P. M. S. (2001) Wittgenstein: Connections and Controversies. Clarendon Press, 242–267. Bridges, Jason (2010) Wittgenstein vs. Contextualism, in A. M. Ahmed (ed.), Wittgenstein’s Philosophical Investigations: A Critical Guide. Cambridge University Press, 109–128. Child, William (2010) Wittgenstein’s Externalism, in Daniel Whiting (ed.), The Later Wittgenstein on Language. Palgrave Macmillan, 63–80. Devitt, Michael (1974) Singular Terms, Journal of Philosophy 71, 183–205. Devitt, Michael (1981) Designation. Columbia University Press. Devitt, Michael and Sterelny, Kim (1999) Language and Reality, 2nd edition. Blackwell. Dupré, John (1993) The Disorder of Things: Metaphysical Foundations of the Disunity of Science. Harvard University Press. Glock, Hans-Johann (2003) Quine and Davidson on Language, Thought and Reality. Oxford University Press. Glock, Hans-Johann (2017) Philosophy and Philosophical Method, in H.-J. Glock and J. Hyman (eds.), A Companion to Wittgenstein. John Wiley & Sons, 231–251. Hacker, P. M. S. (1996) Wittgenstein’s Place in the Twentieth Century Analytic Philosophy. Blackwell. Hanfling, Oswald (1984) Scientific Realism and Ordinary Usage, Philosophical Investigations 7, 187–205.

26  Panu Raatikainen Hanfling, Oswald (2000) Philosophy and Ordinary Language. Routledge. Hendry, Robin F. (2010) The Elements and Conceptual Change, in H. Beebee and N. Sabbarton-Leary (eds.), The Semantics and Metaphysics of Natural Kinds. Routledge, 137–158. Kenny, Anthony (1973) Wittgenstein. Penguin Books. Kripke, Saul (1971) Identity and Necessity, in M. K. Munitz (ed.), Identity and Individuation. New York University Press, 135–164. Reprinted in Kripke, S. (2011) Philosophical Troubles: Collected Papers, Vol. 1. Oxford University Press, 1–26. (Page references are to the reprint). Kripke, S. (1972) Naming and Necessity, in D. Davidson & G. Harman (eds.), Semantics of Natural Language. Reidel, 253–355. Abbreviated as NN, 1972. Kripke, Saul (1973/2013) Reference and Existence: The John Locke Lectures. Oxford University Press. Kripke, Saul (1979) A Puzzle about Belief, in A. Margalit (ed.), Meaning and Use. Reidel, 239–283. Reprinted in Kripke, S. (2011) Philosophical Troubles: Collected Papers, Vol. 1. Oxford University Press, 125–161. (Page references are to the reprint). Kripke, S. (1980) Naming and Necessity. (Reprint of 1972, with an addenda and a new introduction.) Harvard University Press. Abbreviated as NN. Kripke, Saul (1982) Wittgenstein on Rules and Private Language. Harvard University Press. Kripke, Saul (2023) Naming and Necessity Revisited (forthcoming). Loomis, Eric (2017) Necessity and Apriority, in H.-J. Glock and J. Hyman (eds.), A Companion to Wittgenstein. John Wiley & Sons, 346–358. Needham, Paul (2011) Microessentialism: What Is the Argument?, Noûs 45, 1–21. Putnam, Hilary (1975) The Meaning of “Meaning”, in K. Gunderson (ed.), Language, Mind, and Knowledge. Minnesota Studies in the Philosophy of Science VII. University of Minnesota Press, 131–193. Reprinted in Putnam, H. (1975) Mind, Language and Reality: Philosophical Papers, Vol. 2. Cambridge University Press, 215–271. (Page references are to the reprint). Quine, Willard Van Orman (1960) Word and Object. MIT Press. Raatikainen, Panu (2020) Theories of Reference: What Was the Question? in A. Bianchi (ed.), Language and Reality From a Naturalistic Perspective: Themes From Michael Devitt. Springer, 69–103. Raatikainen, Panu (2021) Natural Kind Terms Again, European Journal for Philosophy of Science 11, article number: 19. Raatikainen, Panu (2024) Kripke and the Reference of Natural Kind Terms, in C. Besson et al. (eds.), Meaning, Modality, and Mind: Essays Commemorating the 50th Anniversary of “Naming and Necessity”. (forthcoming). Rowlands, Mark (2003) Externalism: Putting Mind and World Back Together Again. Acumen. Schulte, Joachim (2009) “Moses”: Wittgenstein on Names, in Hans-Johann Glock and John Hyman (eds.), Wittgenstein and Analytic Philosophy: Essays for P. M. S. Hacker. Oxford University Press, 63–82. Searle, John (1958) Proper Names, Mind 67, 166–173.

Alleged Incompatibility Between Wittgenstein and Kripke 27 Sorgiovanni, Ben (2020) Wittgensteinian Content-Externalism, European Journal of Philosophy 28, 110–125. Stern, David G. (2004) Wittgenstein’s Philosophical Investigations: An Introduction. Cambridge University Press. Strawson, P. F. (1959) Individuals. Routledge. Travis, Charles (1989) The Uses of Sense: Wittgenstein’s Philosophy of Language. Clarendon Press. von Wright, Georg Henrik (1951) An Essay in Modal Logic. North-Holland Publishing Co. Wittgenstein, Ludwig (1961) Tractatus Logico-Philosophicus, translated by D. F. Pears and B. F. McGuinness. Routledge & Kegan Paul. Wittgenstein, Ludwig (1978) Remarks on the Foundations of Mathematics, revised edition, edited by G. H. von Wright, R. Rhees, and G. E. M. Anscombe. Blackwell. Wittgenstein, Ludwig (2009) Philosophical Investigations, the German text, with an English translation by G. E. M. Anscombe, P. M. S. Hacker, and J. Schulte, revised 4th edition by P. M. S. Hacker and Joachim Schulte. Blackwell.

2 Real Names Sebastian Sunday Grève

In “A Puzzle about Belief,” Kripke begins the introduction of his own view of proper names by reminding the reader of John Stuart Mill’s: “According to Mill, a proper name is, so to speak, simply a name. It simply refers to its bearer, and has no other linguistic function” (1979/2011, p. 126). This passage expresses Kripke’s belief that his own view of proper names, like Mill’s, comes close to what names in general seem to be. This broader question, concerning names in general, will be discussed in detail towards the end of this chapter. But regarding proper names in particular—with which it is both customary and natural to begin any fundamental discussion of names in general—it is clear that Mill’s and Kripke’s respective accounts are basically identical. This comes out, for example, in the following passage from Mill’s A System of Logic (in which he uses, and effectively introduces, his distinction between connotation and denotation, which is similar to but not the same as Frege’s distinction between sense and reference): Proper names are not connotative: they denote the individuals who are called by them; but they do not indicate or imply any attributes as belonging to those individuals. .  .  . Proper names are attached to the objects themselves, and are not dependent on the continuance of any attribute of the object. (Mill 1843, p. 33) He gives “John” and “Dartmouth” as examples. Of the latter, he explains: A town may have been named “Dartmouth,” because it is situated at the mouth of the [river] Dart. But it is no part of the signification . . . of the word “Dartmouth,” to be situated at the mouth of the Dart. If sand should choke up the mouth of the river, or an earthquake change its course, and remove it to a distance from the town, the name of the town would not necessarily be changed. (Mill 1843, p. 33, quotation marks added) DOI: 10.4324/9781003240792-3

Real Names 29 Frege, Russell, and Wittgenstein (both early and late) all agreed with Mill’s and Kripke’s definition of proper names, or so I shall argue. To be sure, there exists plenty of significant disagreement between these towering figures, but none of it is to be located in the definition of proper names. 2.1  Frege Versus Russell In “The Philosophy of Logical Atomism,” Russell gives the following definition: Proper Names = words for particulars. Definition.

(Russell 1918, p. 523)

This is in agreement with Mill and Kripke.1 But Russell’s immediate qualification already shows the stark disagreement that nevertheless exists between him and them: “I  have put that down although, as far as common language goes, it is obviously false.” It is of course not “obviously false” at all. Instead, it is Russell’s atomistic conception of particulars (or, as Mill would say, individuals) that makes him think this. That conception of particulars, in turn, developed as a consequence of the combination of Russell’s theory of knowledge and his theory of descriptions. Specifically, there was on the one hand his distinction between knowledge by acquaintance and knowledge by description and, on the other, his analysis of (ordinary) proper names as definite descriptions (or, to be perfectly precise, descriptions that, if successful, will be uniquely identifying). On this basis, Russell came to believe that the only things that could be designated (or, as Mill would have said, denoted) by a sign such that no further logical analysis would be possible are those to which “I have a direct cognitive relation . . . i.e. when I am directly aware of the object itself” (1911, p.  209)—“such things as little patches of color or sounds, momentary things” (1918, p. 497)—and these “logical atoms,” as he also called them, were his “particulars.” Thus, Russell writes: The names that we commonly use, like “Socrates,” are really abbreviations for descriptions; not only that, but what they describe are not particulars but complicated systems . . . The only words one does use as names in the logical sense are words like “this” or “that.” (Russell 1918, p. 524) He gives the following example: We say “This is white.” If you agree that “This is white,” meaning the “this” that you see, you are using “this” as a proper name. . . . It is only

30  Sebastian Sunday Grève when you use “this” quite strictly, to stand for an actual object of sense, that it is really a proper name. (1918, p. 525) An important reason why Russell’s theory has seemed attractive to many people is its treatment of the problem of singular negative existential statements—a problem that Kripke, in advancing his alternative account, still struggled with until the end.2 Wittgenstein, in Philosophical Investigations (1953), gave a reconstruction of Russell’s reasoning that merits being quoted at length: For one is tempted to make an objection against what is ordinarily called a name. It can be put like this: a name ought really to designate a simple. And one might perhaps give the following reasons for this: the word “Nothung”, say, is a proper name in the ordinary sense. The sword Nothung consists of parts combined in a particular way. If they are combined differently, Nothung does not exist. But it is clear that the sentence “Nothung has a sharp blade” has a sense, whether Nothung is still whole or has already been shattered. But if “Nothung” is the name of an object, this object no longer exists when Nothung is shattered into pieces; and as no object would then correspond to the name, it would have no meaning. But then the sentence “Nothung has a sharp blade” would contain a word that had no meaning, and hence the sentence would be nonsense. But it does have a sense; so there must still be something corresponding to the words of which it consists. So the word “Nothung” must disappear when the sense is analysed and its place be taken by words which name simples. It will be reasonable to call these words the real names. (PI, §39)3 The ingenuity and analytical power of Russell’s description theory of names—according to which what are ordinarily considered to be names are really abbreviations for descriptions—is indisputable. But his idea that the word “this” is the only real name is in complete disagreement not only with Mill and Kripke but also with Frege and Wittgenstein.4 It should be noted, however, that early Wittgenstein had at one point developed a very similar account.5 Through the reception of his Tractatus LogicoPhilosophicus (1922), early Wittgenstein’s work may thus well have contributed to the fact that Russell’s description theory remained dominant in one version or another among Anglophone scholars until the 1960s.6 Frege went to the opposite extreme.7 He argued that, in addition to ordinary proper names, many more types of expression are correctly regarded as proper names. In fact, he argued that any meaningful expression that

Real Names 31 figures in a well-formed declarative (or assertoric) sentence is correctly regarded as a name, including definite descriptions (contrary to Russell) and even the sentences themselves. He writes for instance: “Every assertoric sentence concerned with the reference of its words is therefore to be regarded as a proper name, and its referent, if it has one, is either the True or the False” (1892a, p. 34). However, Frege emphasized that concept expressions were not to be regarded as proper names but, at most, as common names. Still, he consistently avoided calling concept expressions “names” of any sort, because he believed that doing so would obscure a fundamental difference between objects and concepts. Frege’s distinction between objects and concepts is the result of his function–argument analysis of language, which was key to the revolutionary development of a system of predicate logic in his 1879 Begriffsschrift (literally, “concept-script”). Frege analyzes a declarative sentence by removing one or more words from it. The incomplete expression that remains—for example, “. . . is green” or “. . . reads a paper on Frege”—is conceived as the analogue of a functional expression in mathematics. This is what he calls a “concept expression.” “Indeed, we may say,” Frege writes, “a concept is a function whose value is always a truth-value” (1891a, p. 15). As noted already, Frege calls all other expressions that may figure in a well-formed declarative sentence (including the sentence itself) “proper names.” The strictness of his corresponding distinction between objects and concepts, as well as the generality of this distinction, may be seen from the following pair of quotations: I call anything a proper name if it is a sign for an object. (Frege 1892b, p. 197) An object is anything that is not a function, so that an expression for it does not contain any empty place. (Frege 1891a, p. 18) So, Frege thinks that from a logical point of view we may divide what there is into objects and concepts. Persons and truth-values, for example, will be objects. It is still widely supposed that Frege subscribed to a description theory of proper names. But this is unfair to Frege. He certainly never explicitly subscribed to such a theory.8 But many people have thought that, even if Frege did not explicitly advance a description theory of proper names, his notion of sense commits him to one regardless. I will now show that Frege is in fact not committed to any description theory of proper names. My argument begins by rejecting the claim that his notion of sense entails that a name, if it is to function correctly, must be associated by a language user with a description.9

32  Sebastian Sunday Grève Frege introduces the notion of sense as a necessary complement to that of reference in order to explain the possible cognitive value of identity statements of the form “a = b.” One of his examples is the statement that the Morning Star and the Evening Star are identical, which was once— in ancient times—an important scientific discovery. Now Frege says that with nothing but the notion of reference available to us, according to which signs stand for (or designate, refer to) objects, the stated identity relation could only be explained either as one holding between mere signs or as one holding between objects that the signs may refer to. But then, as he goes on to point out, any true identity statement would be either trivial or arbitrary. For if it were explained as a relation holding between objects, then the cognitive value of “a = b,” if true, would be the same as that of “a  =  a” (and, hence, the statement would be trivial). Yet if the relation were explained as one holding between mere signs (regardless of what they may refer to), then the statement “a  =  b” would have to be either false or else a mere stipulation (i.e., arbitrary). Thus, Frege concludes that in order to explain the cognitive value of (nonstipulative) true identity statements of the form “a = b” one has to recognize that “the difference between the signs amounts to a difference in the mode of presentation of the thing designated” (1892a, p.  26). For this reason, Frege decides to also adopt, in addition to the notion of a sign’s reference, “what I should like to call the sense of the sign, wherein the mode of presentation is contained” (p. 26). Contrary to what illustrative examples such as “Morning Star = Evening Star” might suggest, however, Frege’s notion of sense does not reduce to any sort of description account of names. In order to demonstrate this, it should first be noted that, just like the distinction between concept and object, Frege applies the distinction between sense and reference quite generally (i.e., both to concept expressions and to everything he calls “proper names”).10 This is important in the present context, because certain theoretical commitments

Letter to Husserl, 24 May 1891b, my translation

Real Names 33 will be seen to follow. The diagram I am reproducing here, which Frege included in a letter to Husserl, is very useful in this connection. Elsewhere, Frege writes regarding the case of proper names: “Thus it is via a sense, and only via a sense, that a proper name is related to an object” (1997b, p.  135). I  said earlier that Frege’s distinction between sense and reference was similar to Mill’s distinction between connotation and denotation.11 Had I said they were the same, then what Frege says here would clearly have been inconsistent with Mill’s saying, as quoted earlier, “Proper names are not connotative” (Mill 1843, p. 33). However, what Mill’s distinction actually comes down to is the following position (again, as quoted earlier): “Proper names .  .  . are not dependent on the continuance of any attribute of the object” (p.  33). And with that Frege can agree. The following passage is apt to show this, but some interpretative work is required. In the course of explaining the criteria on the basis of which his theory distinguishes different propositions, Frege explains: Accordingly, with a proper name, it is a matter of the way that the object so designated is presented [i.e., a matter of the sense of the proper name]. This may happen in different ways [i.e., a proper name can have more than one sense], and to every such way there corresponds a special sense of a sentence containing the proper name. . . . So we must really stipulate that for every proper name there shall be just one associated manner of presentation of the object so designated [i.e., just one sense]. (Frege 1918, pp. 65–66, my insertions) What is most important here, for the present discussion, is the final sentence. But exactly what Frege is saying, and why, is not immediately obvious. Frege arrives at this conclusion following his consideration of two types of cases in the passage directly preceding the one quoted. The first type of case shows that the same proper name may be used to refer to the same object while being understood differently by different people and may thus, on Frege’s account, yield different propositions when used in the same context.12 The second type of case shows that, on Frege’s account, any two coreferential proper names will yield different propositions when used in the same context. Both of these principles result from two important features of Frege’s account of sense and propositions (Gedanken). First, Frege holds that senses are objective. Primarily, what this means is that they are shareable between competent language users; whatever else an individual may associate with an expression besides what belongs to its sense or reference, Frege calls “ideas” (Vorstellungen), which he takes to be subjective and not shareable. Second, Frege conceives of propositions as being composed of the senses of the constituent expressions of the whole expression (typically, sentences) whose sense the proposition is.

34  Sebastian Sunday Grève The first kind of case Frege considered is the possibility that two people may on occasion refer to the same object using the same proper name (say, “Smith”) in the same context without sharing any knowledge about the object except perhaps what they are both saying on the occasion (say, “Smith was at the meeting”).13 Seeing that it is thus possible, under certain combinations of knowledge and ignorance, that the same proper name may be successfully used in the same context by different people to designate the same object without those people understanding each other, because they understand the proper name differently, Frege infers that the one will “not associate the same proposition with the sentence” as the other. Given the sense-based compositionality of propositions, Frege knows this has implications for the correct understanding of the sense of a proper name. Specifically, he takes it to mean that in such a case different people associate different senses with the same proper name, while the referent is one and the same. Having made this observation about ordinary language, Frege quickly turns his attention to an ideal language instead—one that would be ideally suited to the goals of science—and concludes (as we saw earlier), “So we must really stipulate that for every proper name there shall be just one associated manner of presentation of the object so designated.” So, he says, for any given proper name, there must be only a singular sense that belongs to it. But, at this point, Frege abruptly breaks off his present line of investigation by saying, “It is often unimportant that this stipulation should be fulfilled, but not always” (1918, p. 66). He appends a very short paragraph on the sense of the first-person pronoun “I” and moves on to a lengthy discussion of objections to his account of propositions from idealism and skepticism. It is unfortunate that Frege did not seem interested in developing his conception of sense any further with regard to the senses of proper names, not least since it is not difficult to see that, if the sense of a proper name is to be singular (as he says), then it will further follow that the sense of a proper name must be unique. This is so, because sharing the same singular sense would entail identity: if one were to suppose that there were two proper names with the same singular sense, then there really would only be one proper name. Furthermore, there is one other essential feature of the sense of a proper name that will follow, as is shown by the second kind of case Frege considers. The second kind of case is the possibility that two people may on occasion refer to the same object using two different proper names in otherwise identical contexts without knowing the relevant identity (say, Morning Star  =  Evening Star) and without sharing any knowledge about the object except perhaps what they are both saying on the occasion (say, “The Morning Star is actually a planet” and “The Evening Star is actually a planet”).14 It takes only a little reflection to see that there is no limit

Real Names 35 to the possible combinations of knowledge and ignorance under which coreferential proper names may be successfully used in an otherwise identical context by different people without understanding each other. To consider another example, suppose that the names “Boo Boo Smith” and “Dr. Smith” refer to the same person. Then, two people may successfully refer to this person using either of these names in otherwise identical contexts, for example, one says “Boo Boo Smith was at the meeting” and the other says “Dr. Smith was at the meeting,” while sharing no particular knowledge about the designated person except perhaps what they are both saying on the occasion. In fact, it is possible that these two people hold no particular beliefs about the designated person other than perhaps that they are called “Boo Boo Smith” or “Dr. Smith,” respectively, and that this person was at the meeting; imagine, for instance, that all they had done was to look at a list of attendees, but the lists they looked at were different in that one contained the one name and one contained the other. In general, what this means is that, on Frege’s account of sense and reference, the successful reference of a proper name on a given occasion requires no particular knowledge, nor indeed any particular beliefs, regarding the referent on the part of the language user. However, this is enough to conclude that Frege’s conception of sense does not entail that a name, if it is to function correctly, must be associated by a language user with a description. Moreover, since Frege is not committed to any particular theory of how the reference of a proper name is fixed in a language, we can conclude that he is not committed to any description theory of proper names.15 To summarize, it follows from the second type of case Frege considers that, if the sense of a proper name is to be singular (or unique), then the sense of a proper name must also be (what might be called) minimal. “So we must really stipulate,” as Frege puts it, that the sense of a proper name be restricted to the particular type of sign by which competent language users produce the proper name on the syntactical level (where, for instance, “Smith,” “Smith,” and “Smith,” and varying intonations of /smɪθ/, will be productions of the same type of sign in writing and speech, respectively). Notice that a minimal sense will still be sufficient, and on Frege’s account necessary, to explain the possible cognitive value of identity statements of the form “a = b.”16 It may be objected against this interpretation of Frege’s theory that, for most of his career, he consistently wrote as if (ordinary) proper names in ordinary language typically had more than one sense.17 However, it would actually be easy (albeit unnecessary, in my opinion) to increase the apparent coherence in the development of Frege’s account of the sense and reference of a proper name—starting with his writings from around 1892, when “On Sense and Reference” was published, and spanning at least 26 years from then onwards—by transposing his ideal of minimal unique senses of

36  Sebastian Sunday Grève proper names into an account of proper names in ordinary language as not necessarily having a singular sense but, possibly, a plurality of senses with a core sense that is minimal and unique. On this kind of account, the overall sense of the proper name “Aristotle,” say, when used to designate the famous ancient Greek philosopher, might comprise, for instance, that he was a student of Plato or that he was a teacher of Alexander the Great, but at its core the sense of the proper name, that is, the mode of presentation of the thing designated, would just be the word “Aristotle.” Perhaps it will be thought that the conception of the sense of a proper name as being minimal and unique would prevent Frege from expanding the category of proper names to cover all of the many logically relevant expressions he wants it to cover. But this is not so. Naturally, the more complex the sign is, the more complex its minimal unique sense will tend to be. If we respect Frege’s principle of beginning the analysis of any given piece of discourse from an understanding of the composed whole, then there will be no reason to suppose that, for instance, the sense of a given assertion, such as “Aristotle was the student of Plato who taught Alexander,” should reduce to the syntactical level; on the contrary, the Fregean analysis would begin by recognizing the sense of the whole expression as being a proposition (Gedanke). Returning to Frege’s expansion of the category of proper names, it is informative to note some of his explanations in the letter to Husserl regarding an important difference between their respective theories: All I should like to say about it now is that there seems to be a difference of opinion between us on how a concept word (common name) is related to objects. The following schema should make my view clear: [Here Frege inserts his diagram, as shown earlier.] With a concept word it takes one more step to reach the object than with a proper name, and the last step may be missing—i.e., the concept may be empty—without the concept word’s ceasing to be scientifically useful. (Letter to Husserl, 24 May 1891b) In an unpublished draft from around the same time, Frege explicitly addresses the terminological issue: The word “common name” leads to the mistaken assumption that a common name is related to objects in essentially the same way as is a proper name, the difference being only that the latter names just one thing whilst the former is usually applicable to more than one. But this is false, and that is why I prefer “concept word” to “common name”. . . . A concept word must have a sense too and if it is to have a use in science, a reference; but this consists neither of one object nor of a plurality of objects: it is a concept. (1997b, p. 135)

Real Names 37 This last pair of quotations offers a clear view of Frege’s conception of all logically relevant linguistic expressions as names, complete with sense and reference, following the theoretical model of proper names. The only reason why Frege cannot regard all logically relevant expressions as proper names is that he defines the latter as words for “objects” and makes a fundamental distinction between concepts and objects; consequently, a concept name cannot be a proper name. Someone less concerned with such a strict distinction between concepts and objects might just as well take the Fregean conception to be that all logically relevant expressions are proper names, where the objects referred to by concept expressions are concepts. Either way, if we follow Frege in confining our focus to declarative uses of language, we can adequately express this part of his theory simply as the view that all words are names.18 As noted previously, Frege’s view in this respect is diametrically opposed to that of Russell. But Frege’s idea that all words are names will probably seem just as paradoxical as Russell’s idea that the only real name is the word “this.” Neither idea finds many supporters among contemporary scholars, yet there remain some valuable lessons left to be learned from both of these ideas. 2.2  Kripke and Wittgenstein The first eighty or so sections of Wittgenstein’s Investigations are a sustained theoretical discussion of names, running more or less uninterruptedly at least until (and including) Section  79. In particular, Wittgenstein begins—right from the start of Section 1—with a critique of the idea that all words are names. And he soon adds, beginning in Section  38, a critique of the idea that the only real name is the word “this.” Given what was said in this chapter so far, these are obviously critiques of Frege and Russell. But Wittgenstein barely hints at the fact that these two thinkers are indeed among the targets of his criticisms. There are many possible reasons why he should have proceeded in this way. One reason surely has to do with the fact that he deemed his own earlier self to deserve just as much criticism in this respect as Frege or Russell. Another reason is that his critique of these ideas is intended to operate at a deeper, or more general, level. Thus, he cites passages from Augustine and Plato, in Sections 1 and 46, respectively, in order to illustrate not only the venerable heritage of these ideas but also, more importantly, their deep rootedness in human thought about language in general. For example, the notorious quotation from Augustine with which he opens the text of the Investigations is primarily intended to help impress on the reader the intuitiveness of the more general idea that words stand for things. It is in this idea, Wittgenstein suggests, that we find the roots of those other ideas, namely that all words are names, as advocated by Frege, and that names really designate simples, as advocated by Russell and Wittgenstein’s earlier self.19 This chapter is not the place to explain Wittgenstein’s philosophical development. The

38  Sebastian Sunday Grève crucial difference, in the context of the present exposition, is that the later Wittgenstein—of the Investigations—agrees with Kripke (and Frege), as against Russell and his earlier self, that ordinary proper names deserve to be taken at face value. In “Russell’s Notion of Scope,” Kripke observes: In my book [Naming and Necessity (1980, henceforth cited as NN)] I actually stipulate that I simply take the concept of a name as given as it normally is intuitively used in ordinary language without proposing any further criterion. It is decidedly not my purpose to give a technical criterion for being a name. (See NN, p. 24.) A view, such as Russell’s ultimate view that ordinary names are not “really” names, is ruled out by definition . . . Nor do I take rigidity to be an alternative criterion for naming . . . On the contrary, I state that definite descriptions can be rigid too, though typically they are not. (Kripke 2005/11, p. 227, note 7)20 “Rigidity” is, of course, Kripke’s term for the modal characteristic of names that Mill (as I read him) expressed by saying, “Proper names . . . are not dependent on the continuance of any attribute of the object” (Mill 1843, p. 33). We shall return to the topic of rigidity and whether or not it constitutes a criterion for naming. For now, notice that Kripke’s explicit aim, as stated in the above quotation, is clearly in the spirit of the Investigations. Wittgenstein at one point expresses this spirit thus: “Philosophy must not interfere in any way with the actual use of language, so it can in the end only describe it” (PI, §124). Although Kripke and Wittgenstein thus, with their shared nonrevisionist intentions, avowedly reject both Frege’s idea that all words are names and Russell’s idea that the only real name is the word “this,” I believe it can be shown that they are at least weakly committed to a substantial synthesis of these ideas. Before an explanation can be given of what exactly this synthesis consists in, and what it entails, I shall have to address the reasons for which Kripke and Wittgenstein have usually, but in my view falsely, been portrayed as if they had advanced opposing accounts of the relevant issues. Here I shall have to limit myself to showing just the following two things. First, Wittgenstein’s later philosophy does not disagree with Kripke’s arguments in Naming and Necessity in the ways that Kripke himself sometimes claimed it did. On the contrary—and this will be my second point— Wittgenstein’s later philosophy contains all of the key ingredients that, if suitably refined and combined, may yield a version of Kripke’s main line of argument. Kripke sometimes claimed that Wittgenstein was a proponent of a modified description theory, also called a cluster theory.21 According to this kind of theory, in order for a name to do its referential work, language users must associate descriptions with it but only some of these descriptions need hold true of the referent.22 As his sole evidence, Kripke

Real Names 39 usually cites Section 79 of the Investigations. As far as I am aware, however, Kripke never offers any reason to believe that Wittgenstein endorses the relevant propositions that are under discussion in that section, and on the rare occasion that he quotes parts of the text—which, to my knowledge, he did only twice in his published writings—he omits large and significant chunks.23 Here is one significant part that Kripke always omits, including from his most extensive quotation of relevant material (compare NN, p. 31): According to Russell, we may say: the name “Moses” can be defined by means of various descriptions. For example, as “the man who led the Israelites through the wilderness”, “the man who lived at that time and place and was then called ‘Moses’ ”, “the man who as a child was taken out of the Nile by Pharaoh’s daughter”, and so on. And according as we accept one definition or another, the sentence “Moses did exist” acquires a different sense, and so does every other sentence about Moses. (PI, §79) But when placed in their context, these sentences clearly indicate that the ensuing discussion in the following paragraph, which Kripke quotes, is likely to be just a critical discussion of Russell’s theory: But if I make a statement about Moses, am I always ready to substitute some one of these descriptions for “Moses”? I  shall perhaps say: By “Moses” I mean the man who did what the Bible relates of Moses, or at any rate much of it. But how much? Have I decided how much must turn out to be false for me to give up my proposition as false? So is my use of the name “Moses” fixed and determined for all possible cases? (PI, §79) There really is nothing at all about this series of questions that would suggest that Wittgenstein is here endorsing a cluster theory of names. In fact, it would seem more plausible to interpret him here as rejecting the cluster theory, because he does not seem to believe there to be good answers available to the critical questions that he is asking, especially since he leaves them unanswered. The only other part of the text that Kripke quotes is the beginning of the section, which goes as follows: Consider this example: if one says “Moses did not exist”, this may mean various things. It may mean: the Israelites did not have a single leader when they came out of Egypt—or: their leader was not called Moses— or: there wasn’t anyone who accomplished all that the Bible relates of Moses—or: . . . (PI, §79)

40  Sebastian Sunday Grève In Wittgenstein’s text, this is then followed by “According to Russell [etc.]” as quoted above. It seems likely that Kripke mistook Wittgenstein here, at the beginning of the section, as implying a commitment to the description theory of names; specifically, that he mistook him as implying that the reason why someone’s saying “Moses did not exist” may mean various things was a function of various things that the name “Moses” may mean depending on the various descriptions that speakers may associate with the name. But this is an implausible reading. Instead of advocating or implicitly applying a description theory of names, Wittgenstein here simply notes that on an occasion where it would be natural for someone to say “Moses did not exist,” this may mean any of the various things he lists. It is this common-sense observation—which is made on a pragmatic, rather than a semantic, level—that Wittgenstein then uses to lead his reader on to a critical examination of Russell’s theory along the lines indicated earlier. Thus, in Section 79 of the Investigations Wittgenstein endorses neither Russell’s original nor any other version of the description theory of names. In fact, Wittgenstein explicitly agrees with the type of definition that Mill and Kripke gave. For example, in the course of discussing the idea that all words are names, at the beginning of the Investigations, Wittgenstein first notes: Of course, what confuses us is the uniform appearance of words when we hear them in speech, or see them written or in print. For their use is not that obvious. Especially when we are doing philosophy! (PI, §11) With regard to the possible application of that sort of idea, that is, that all words are names, he proceeds to give the following explanation (his example of “language (8)” being a variation of the builders’ language-game from Section 2): If we say, “Every word in the language designates something,” we have so far said nothing whatever; unless we explain exactly what distinction we wish to make. (It might be, of course, that we wanted to distinguish the words of language (8) from words “without meaning” such as occur in Lewis Carroll’s poems, or words like “Tra-la-la” in a song.) (PI, §13) Then he says: The word “designate” is perhaps most straightforwardly applied when the name is actually a mark on the object designated. Suppose that the tools A uses in building bear certain marks. When A shows his assistant such a mark, the assistant brings the tool that has that mark on it.

Real Names 41 In this way, and in more or less similar ways, a name designates a thing, and is given to a thing. When philosophizing, it will often prove useful to say to ourselves: naming something is rather like attaching a name tag to a thing. (PI, §15) It is unquestionable that Wittgenstein here endorses the view that names, as Mill puts it, “are attached to the objects themselves.” In Section  26, Wittgenstein expresses the view again, and more assertively: “To repeat— naming is something like attaching a name tag to a thing” (PI, §26).24 Of course, what precisely Wittgenstein thought this entails is a different question, which must now be addressed. It is useful, in this connection, to look to Wittgenstein’s discussion of rules and rule-following, especially insofar as its lessons apply to the question of what constitutes linguistic meaning and reference. This is closely related to the account Kripke outlines of how the reference of a term is, as he usually puts it, fixed. In particular, Wittgenstein’s rejection of an interpretation-based account of rule-following can easily be brought to bear on the description theory of names. In fact, Wittgenstein does just this in the only section of the Investigations that explicitly continues the discussion of the name “Moses” from Section 79 (which was quoted earlier): Suppose I  give this explanation: “I  take ‘Moses’ to mean the man, if there was such a man, who led the Israelites out of Egypt, whatever he was called then and whatever he may or may not have done besides.”— But similar doubts to those about the name “Moses” are possible about the words of this explanation (what are you calling “Egypt”, whom the “Israelites”, and so forth?). These questions would not even come to an end when we got down to words like “red”, “dark”, “sweet.” (PI, §87) In the context of his general discussion of rule-following (i.e., the discussion that proceeds explicitly in terms of rules), and perhaps most explicitly in Sections  201 and 202, Wittgenstein takes the infinite regress of possible interpretations as an important consideration in favor of his own practice-based account of what it is to follow a rule. It is with this type of consideration in mind that he notes, for example, “Explanations come to an end somewhere” (PI, §1) and “I  follow the rule blindly” (§219). Now, between the two “Moses” sections Wittgenstein compares rules to signposts: “A rule stands there like a signpost” (§85). Then, at the end of the second “Moses” section, from which I  have just quoted, he returns to this comparison and concludes: “The signpost is in order—if, under normal circumstances, it fulfils its purpose” (§87). Thus, with respect to the primary question of the section, Wittgenstein is saying that a proper

42  Sebastian Sunday Grève name, under normal circumstances, will just refer successfully to its referent, so that there will be no need for an explanation of its meaning. And, thus, looking back at the first of the two “Moses” sections (§79), where Wittgenstein first started questioning the requirement of the description theory that a language user associate descriptions with a name, Wittgenstein can now be seen to be positively rejecting this requirement. In this sense, Wittgenstein might perhaps also have said, in analogy to his saying that we follow rules blindly, that we use names blindly.25 In general, Wittgenstein’s account of rule-following perfectly accommodates Kripke’s account of how the reference of a term is fixed. Kripke’s own interpretation of Wittgenstein does so too. That is, Kripke’s account of Wittgenstein’s account of rule-following perfectly accommodates Kripke’s account of how the reference of a term is fixed.26 In Wittgenstein on Rules and Private Language (1982), Kripke suggests that Wittgenstein’s claim that rule-following is a practice should be understood in terms of communal practice. Specifically, he suggests that Wittgenstein’s claim should be understood as being that what constitutes a standard of correctness, on the sole basis of which something may be an instance of following a given rule, is that there exists a sufficient amount of agreement in this respect among the relevant community of rule-followers. Kripke had his doubts as to whether this claim about the nature of rule-following was true, and as to whether Wittgenstein was correctly interpreted in this way.27 I share these doubts. But for the present discussion, the two claims, the substantive one and the interpretive one, can be taken to be true enough. For with regard to our shared natural languages, it seems right to think that the relevant standards of correctness are indeed constituted in the form of communal practices. Kripke outlines his account of reference-fixing for proper names by way of what he takes to be a paradigmatic example: Someone, let’s say, a baby, is born; his parents call him by a certain name. They talk about him to their friends. Other people meet him. Through various sorts of talk the name is spread from link to link as if by a chain. A speaker who is on the far end of this chain, who has heard about, say Richard Feynman, in the market place or elsewhere, may be referring to Richard Feynman even though he can’t remember from whom he first heard of Feynman or from whom he ever heard of Feynman. . . . A chain of communication going back to Feynman himself has been established, by virtue of his [the speaker’s] membership in a community which passed the name on from link to link. (NN, p. 91) Fundamentally, the reference of a given term is fixed, Kripke thinks, “by the fact that the speaker is a member of a community of speakers who use

Real Names 43 the name” (NN, p. 106). On this basis, and given what was said earlier about Wittgenstein’s account of rules and about Kripke’s interpretation of it, I conclude that Kripke’s account of what constitutes the reference of a given proper name is but an instance of Wittgenstein’s account of what constitutes the standard of correctness of a given expression of a rule. The following qualification must be noted. Kripke’s interpretation of Wittgenstein’s account of rules and rule-following is a skeptical one, according to which past facts do not determine what it is to follow a rule correctly at any given moment or, for that matter, what it is to use a name correctly at any given moment. So all that really counts, on this understanding of the issue, is communal agreement with regard to a single particular instance of following a rule or using a name. However, in his account of referencefixing Kripke rigorously emphasized the historical element. He argued, to my mind persuasively, that the contemporary linguistic community may be entirely wrong about the referent of a given name—hence, it is possible that they do not hold one correct belief about the referent—and yet they may well be using the name successfully to refer to its referent. And the reason for this, Kripke thought, lies in a general principle that forms part of the sociohistorical nature of our natural languages, which is that “in communication and language learning, the relevant linguistic features are normally intended to be preserved without any explicit intentions having to be entered into” (Kripke 1986, p. 242). So this principle, Kripke thinks, is the precise reason why the reference of a given proper name may be preserved within a community in virtue of the name’s having been passed on by tradition from link to link, even if not a single member of the community associates with the name any correct description of its referent. But it is not obvious that this principle is consistent with Kripke’s interpretation of Wittgenstein (although, of course, there is not necessarily any independent reason to suppose that it cannot be accommodated by Wittgenstein’s account itself). The principle may seem inconsistent with Kripke’s interpretation, because, as explained earlier, this interpretation seems to exclude all historical considerations. There are two possible solutions to this exegetical issue. First, we can distinguish using a name correctly from using it successfully (i.e., so that reference is achieved). The former may possibly not depend on historical facts even if the latter does. But if we adopted this distinction alone as our solution, then there would not seem to be any connection between rule-following and reference-fixing, contrary to my claim that Kripke’s account of reference-fixing is an instance of Wittgenstein’s account of rulefollowing. Therefore, I  think we should also adopt the second solution to the issue, which is to argue that history is what naturally constitutes a practice. Although it is not necessary that the requisite agreement among the community of rule-followers, on Kripke’s interpretation, is constituted

44  Sebastian Sunday Grève historically, for all we know this happens to be the case for our natural languages. Kripke was no doubt aware of this naturally constitutive role of history with regard to rule-following that occurs as part of our natural languages. Moreover, he was no doubt also aware of the emphasis Wittgenstein placed on this point. Not only is it implicit in Wittgenstein’s notion of a practice, but also it is indeed central to his related notion of a form of life.28 For the same reason, Wittgenstein reminds us early on in the course of his discussion of names that “giving orders, asking questions, telling stories, having a chat, are as much a part of our natural history as walking, eating, drinking, playing” (PI, §25). I have argued that Frege, Russell, and Wittgenstein (both early and late) all agreed with Mill’s and Kripke’s definition of proper names. Each of them thought that what they themselves took to be real proper names— that is, ordinary proper names in the cases of Mill, Frege, later Wittgenstein, and Kripke and “atomic names” in the cases of Russell and early Wittgenstein—are not abbreviations of descriptions and do not require, in order to function correctly, that a language user associates any descriptions with them. But I have not yet offered direct support for the subordinate claim that these thinkers all agree with the second part of Mill’s definition. The second part of Mill’s definition is that proper names, as he puts it, “are not dependent on the continuance of any attribute of the object” (Mill 1843, p. 33). The case of this principle has its own complications, which cannot be discussed in full here. However, if we take “attribute” to mean nonessential property (where an essential property is one whose loss entails that the object will cease to exist), and we construe the rest of the statement as the sort of counterfactual claim that Kripke wishes to make (more on which in a moment), then all of our philosophers may well be in agreement with each other. Of course, what is essential in a given case will often be disputed. Perhaps this is the type of negligible disagreement that Kripke had with Wittgenstein concerning the standard meter, which is the only remaining point on which Kripke claimed they disagreed regarding these matters that I have not yet addressed. Kripke objected to Wittgenstein’s writing “There is one thing of which one can state neither that it is 1 metre long, nor that it is not 1 metre long, and that is the standard metre in Paris” (PI, §50). Kripke argues that this claim is false, insofar as the length of any macrophysical object might change, but the phrase “one meter” would continue to refer to the same length even if the standard meter in Paris suddenly shrank to half of its original length. By contrast, Wittgenstein here seems to be considering the meaning of the phrase “one meter” to be defined as being synonymous with that of the expression “the length of the standard meter in Paris,” so that the length referred to by the phrase “one meter” would change in accordance with any change in the length of the standard meter in Paris. He makes clear that this is what he is suggesting by giving

Real Names 45 an analogous example: “Suppose that samples of colour were preserved in Paris like the standard metre. So we explain that ‘sepia’ means the colour of the standard sepia which is kept there hermetically sealed” (PI, §50). I am not sure what Wittgenstein believed the full definition of the term “one meter” actually was at the time of his writing, and it might perhaps have been reasonable to think that the reference of this particular term, at least as officially defined between 1927 and 1960, was not completely fixed. I am sure, however—especially following what has been said in this chapter so far—that whatever Wittgenstein’s reasons were for expressing himself in the manner he did, his having expressed himself thus in no way shows that he would reject any part of Kripke’s theoretical account of proper names, including the idea of rigid designation. Rather, their disagreement would seem to concern no more than whether, at some time or other, the phrase “one meter” was a rigid designator or not (which, come to think of it, is indeed not as easy a question to answer as it might appear initially). 2.3  The Search for Real Names Having introduced the notion of rigid designation to the theory of names undoubtedly counts as one of Kripke’s most important contributions to this area of research. And it encapsulates his construal of the second part of Mill’s definition of proper names. Kripke defined a rigid designator as something that will designate the same object in every possible world where it exists (and nothing else in any possible world). Thus, Kripke construes Mill’s point that “proper names . . . are not dependent on the continuance of any attribute of the object” in terms of the claim that proper names will designate the same object in every possible world where that object exists. Earlier, I suggested we should understand Mill’s “attribute” to mean nonessential property, where an essential property is one whose loss would entail the object’s ceasing to exist. Kripke’s notion of rigid designation, together with that of a possible world that it employs, molds this suggestion into an account that is at once rigorous, precise, and intuitive.29 As Kripke writes: Of course we don’t require that the objects exist in all possible worlds. Certainly Nixon might not have existed if his parents had not gotten married, in the normal course of things. When we think of a property as essential to an object we usually mean that it is true of that object in any case where it would have existed. (NN, p. 48) Given the historical perspective developed in this chapter, there is good reason to think that Frege, Russell, and Wittgenstein can all agree with Kripke’s account of proper names as rigid designators, at least to the extent that it may hold for what each of them took to be real proper names. In

46  Sebastian Sunday Grève particular, I have argued that the later philosophy of Wittgenstein contains all of the key ingredients that, if suitably refined and combined, may yield a version of Kripke’s main line of argument. Not only does Wittgenstein’s account of rules and rule-following accommodate Kripke’s account of how the reference of a term is fixed and hence Kripke’s account of rigid designation, in fact Wittgenstein in the Investigations rejects the description theory of names (most explicitly, in his discussion of the name “Moses”) and endorses instead the type of definition that Mill and Kripke have given of ordinary proper names.30 This endorsement comes in the form of Wittgenstein’s conception of naming as being like attaching a name tag to a thing. Given this conception, we should not be surprised to find that Wittgenstein actually gives an accompanying account of reference-fixing, in terms of ostensive definition, that is identical with Kripke’s.31 For example, “One can ostensively define a person’s name, the name of a colour [ein Farbwort], the name of a material, a number-word, the name of a point of the compass [Himmelsrichtung], and so on” (PI, §28).32 What may be more surprising is Wittgenstein’s relatively liberal attitude towards expanding the category of proper names, which shines through here most clearly in his suggestion that it is not only a person’s name that can be ostensively defined. He goes on to elaborate this suggestion by arguing that, for instance, “the definition of the number two, ‘That is called “two” ’—pointing to two nuts—is perfectly exact” (§28). The reason this may be surprising is that any expansion of the category of proper names may seem to be inconsistent with Wittgenstein’s critique of the idea that all words are names. But Wittgenstein’s critique is not aimed at just any expansion of the category. Rather, it is specifically aimed at an expansion of the category that is unknowing or careless. He stresses two main reasons for caution. First, Wittgenstein convincingly argues that naming has a particular place in our natural languages as they are learned and used, but it is neither the foundation nor obviously the pinnacle of our linguistic activities when viewed in this way. He stresses that much already needs to be in place in a language before naming becomes so much as possible (see esp. PI, §§6, 27, and 30–32), and that, in the natural course of our lives with language, naming things is only a means to an end—“a preparation for the use of a word” (§26)—that is practically embedded within some larger linguistic activity, which is almost never of a scientific or philosophical nature. Second, he observes that “the relation between name and thing named” materially occurs in a variety of ways: Among many other things, this relation may also consist in the fact that hearing a name calls before our mind the picture of what is named; and sometimes in the name’s being written on the thing named or in its being uttered when the thing named is pointed at. (PI, §37)

Real Names 47 With these precautions in mind, however, Wittgenstein is happy to speak of “names of certain actions and properties” (PI, §1) as well as “names of sensations” (§244). The latter case is a good example. Wittgenstein famously asks the question “How do words refer to sensations?” and answers: Here is one possibility: words are connected with the primitive, natural, expressions of sensation and used in their place. A child has hurt himself and he cries; then adults talk to him and teach him exclamations and, later, sentences. They teach the child new pain-behaviour. . . . The verbal expression of pain replaces crying. (PI, §244) So, in Wittgenstein’s view, we can conceive of sensation words as names that refer to sensations, but we must not think that the relation between name and thing named will be exactly the same as in the case of a person’s name.33 The latter condition is important, because this kind of difference entails that an inquiry into the nature of the thing named will have to be different too. I said I  believe that although Kripke and Wittgenstein oppose Frege’s idea that all words are names and Russell’s idea that the only real name is the word “this,” they are at least weakly committed to a substantial synthesis of these ideas. The synthesis I  have in mind is the proposition that rigid designators are the real names. From this, as will be seen, it also follows that some words that were not previously thought to be names are in fact names. It may be objected that, as we have already seen, it was expressly not Kripke’s belief that rigidity constitutes a criterion for naming. But I think that in this instance he was wrong about what he believed or, at any rate, what he ought to have believed. For we also saw that he tended to believe—and this belief I think is correct—that his own view of proper names comes close to what names in general seem to be: for example, when he said that “a proper name is, so to speak, simply a name” (1979/2011, p. 126) and when he described his intention to “take the concept of a name as given as it normally is intuitively used in ordinary language” (2005/11, p. 227, note 7). I think this gets modern ordinary usage right. A similar tendency finds expression in Wittgenstein’s saying, “When philosophizing, it will often prove useful to say to ourselves: naming something is rather like attaching a name tag to a thing” (PI, §15). This shared attitude can further be seen in both authors’ practice of simply saying “name” rather than “proper name.” In Naming and Necessity, Kripke makes this quite explicit: “By a name here I will mean a proper name, i.e., the name of a person, a city, a country, etc.” (NN, p.  24). In Wittgenstein’s Investigations, the singular term “proper name” occurs only twice and the plural “proper names” does not occur at all, despite the extensive discussion of

48  Sebastian Sunday Grève names (and proper names) in the book. But if we believe that by “names” we normally mean proper names, that proper names are what names in general seem to be, and that proper names are rigid designators, then we will already have moved quite some way towards the idea that rigid designators are the real names. Below, I set out an argument that I believe speaks decisively in favor of this view, at least from the perspectives of Kripke and Wittgenstein. There has been a great deal of controversy over what other kinds of expression, apart from proper names, may designate their objects rigidly. But that proper names do so is very nearly as uncontroversial among experts as it is generally uncontroversial that water is H2O. In addition, Kripke (and he was not alone in this) argued that what he called natural kind terms, for example “cow,” “tiger,” “gold,” and “water,” are rigid designators too.34 If this is right, then obviously many other terms may turn out to be rigid, in particular perhaps other terms that are ordinarily called (or, at any rate, used to be called) “common names.” I am suggesting that this probably includes the terms “name” and “rigid designator.” We humans have discovered that something is water if, and only if, it is H2O. I  believe we may also have discovered that something is a name if, and only if, it is a rigid designator. Kripke convincingly showed that all proper names are rigid designators. I am claiming that this is so because in general a name just is a rigid designator. And I believe this is indeed what Kripke was getting at when he remarked: According to the view I advocate, then, terms for natural kinds are much closer to proper names than is ordinarily supposed. The old term “common name” is thus quite appropriate for predicates marking out species or natural kinds, such as “cow” or “tiger.” (NN, p. 127)35 The main reason Kripke gave for not taking a term’s rigidity as a criterion for naming is that “definite descriptions can be rigid too, though typically they are not” (2005/11, p. 227, note 7). But instead of taking the rigidity of a definite description as a reason against identifying names with rigid designators, we should just take it to show that some definite descriptions are names. So, for example, the definite description “the element with atomic number 79” and the definite description “the successor of 2” may just be alternative names for gold and the number 3, respectively. Similarly, if it is true that I am necessarily the organism that descended from the combination of the sperm and the egg from which I actually descended—such that whoever might have descended from a different sperm or egg would not have been me—then a definite description of the form “the organism that descended from sperm s and egg e” will be one of my names. On the

Real Names 49 other hand, there will be no genuinely empty names. If what appears to be a name does not actually refer to anything, then it cannot be a real name. And I think that Kripke was probably right to think that apparent names that occur in fictional discourse, such as “Sherlock Holmes,” are only pretended names, as he called them (and hence not real names).36 On the other hand, I  think that many of the things Wittgenstein in the Investigations called names—names of colors, numbers, sensations, actions, properties, etc.—can probably be shown to indeed be real names, but these are obviously difficult questions, and providing satisfactory answers to them will probably require the work of many generations of scholars to come.37 In one way, I am merely proposing to do what Frege, Russell, Wittgenstein, and Kripke all did too, or at least showed a clear tendency in that direction, namely, to use proper names as a paradigm for what names in general are. Building on Kripke, I have proposed that this should mean taking rigid designators to be the real names. And part of the importance of this view is that it will send one (philosophers and scientists alike) looking for real names. Notably, this type of inquiry has only a minimal metaphysical commitment in the form of a basic (and, I would say, healthy) sort of realism, paired with a critical, methodical awareness of the complex relationship between language and world. It actually has no particular commitment to any of the traditional metaphysical categories (“substance,” “natural kinds,” etc.).38 Rather, as in Frege, the primary reference of some names will be concepts (on some intuitive, nontechnical understanding of “concepts”).39 As far as I can see, this even allows for implementation in all sorts of antirealist frameworks. But how, it may finally be objected, could all this not be contradicting the very core of Wittgenstein’s later philosophy? The answer to this question is relatively simple. Wittgenstein was opposed to bad science, bad philosophy, and especially perhaps bad metaphysics. He was not opposed to good science, good philosophy, or good metaphysics.40 In his work, he was largely concerned to offer a critique of the sorts of inquiry that he thought were bad. This was a personal and professional project that he was deeply committed to. As a consequence, it can easily seem as if he had left practically no room for even so much as asking, meaningfully, about the nature of certain things.41 But this is really not the case.42 Still, some of Wittgenstein’s influential remarks about concepts having a family-resemblance type structure may yet appear to speak against the proposed view or, at any rate, against its general application. His best-known example of such a concept is that of a game, but he held that language and many other important concepts also belong in this category.43 Specifically, he argued that these concepts could not possibly be adequately explained on the basis of necessary and jointly sufficient conditions, because these concepts are constituted in a different kind of way.44 Even a mathematical

50  Sebastian Sunday Grève concept such as that of number, he argued, has in fact grown and developed in the manner of a family: Why do we call something a “number”? Well, perhaps because it has a—direct—affinity with several things that have hitherto been called “number”; and this can be said to give it an indirect affinity with other things that we also call “numbers”. And we extend [dehnen aus] our concept of number, as in spinning a thread we twist fibre on fibre. (PI, §67) Wittgenstein is eager, and right in my view, to point out that a concept’s being structured in this way does not mean that there is anything wrong with it: “The strength of the thread resides not in the fact that some one fibre runs through its whole length, but in the overlapping of many fibres” (PI, §67). Nonetheless, if a concept is so structured, it will be in an important way unstable (or, as Wittgenstein puts it, not “rigidly bounded”). For example, it is thus possible—and Wittgenstein thinks it is indeed the case—that we do not actually “use the word ‘number’ for a rigidly bounded concept” (PI, §68). Wittgenstein duly considers the possible objection that this kind of instability might be a mere function of our ignorance. “But this is not ignorance,” he quickly replies, “We don’t know the boundaries because none have been drawn” (§69). If Wittgenstein is right, then, in this kind of case, the word—for instance, the word “number,” “game,” or “language”—may not be a real name, because it may not designate the same concept in every possible world where it exists. To see more clearly why and how this follows, we must first introduce an important distinction that neither Kripke nor Wittgenstein seems to be making (at least not explicitly), which can be expressed in terms of, on the one hand, applying a concept and, on the other, extending it. Thus, I am not sure which of two possible points Wittgenstein is trying to make, or whether he is indeed aware that there are these two different points, when he states that this is not a case of ignorance. I suspect, however, it is no coincidence that his explicit talk of “rigid boundaries” (feste Grenzen) in fact indicates the correct distinction, since this distinction corresponds to the difference between a boundary that is precise and one that is rigid. Notably, a boundary that can move is not rigid, but it may yet be precise at any given moment. Imagine we froze time and collected all the linguistic data at this moment concerning every relevant speaker’s disposition to apply a given term to everything they know. Imagine, for example, that we did this on the basis of a comprehensive forced choice (yes or no) survey. If this is theoretically possible, and if it is true that concepts are constituted by the application that relevant speakers make of relevant terms—which, I  take it,

Real Names 51 Wittgenstein can accept—then family-resemblance concepts will in fact be both rigidly and precisely bounded at any given moment, although we will normally not have exact knowledge of where this boundary lies.45 This is to isolate the case of what we might call the total application of a concept at a moment. In reality, however, concepts are more or less dynamic, and they change over time depending on the use that speakers make of relevant terms regarding old and new cases. This is to take into consideration what we might call extending (developing) a concept.46 Now I will try to show that it is this, the question of extending a concept, that we should be primarily concerned with in the context of the present argument. The majority of speakers tend, not unreasonably, to know and care little about whether natural languages develop in a way that increases their repertoire of real names, while those who care face a difficult task. It should therefore not be surprising that, even if current linguistic usage is perfectly determinate (i.e., all concepts both rigidly and precisely bounded at any given moment), the community of speakers of a natural language considered as a whole will often be so ignorant and careless that they collectively apply and, over time, extend a concept so liberally that, in nearby possible worlds, the concept may quickly develop in radically different directions. It is as a consequence of this kind of instability of a concept that terms referring to it may not designate the same concept in every possible world where it exists and, so, may not be real names. Thus, Wittgenstein was right to say that in the case of family-resemblance concepts, we are not ignorant of rigid boundaries, because no such boundaries exist. And it is indeed plausible that many of our concepts are constituted by a family-resemblance type structure (and hence will not normally be concepts that are rigidly bounded).47 What Wittgenstein fails to mention is that usually the underlying fact that no rigid boundaries exist for a given concept is partly due to ignorance, including ignorance of our current linguistic usage. Thus, Wittgenstein’s idea that some concepts have a family-resemblance type structure shows that finding real names that are not proper names is no easy task, which requires among other things careful attention to the way relevant expressions are actually used in the language.48 It is helpful, in this connection, to consider the history of some relatively uncontroversial examples of real names that are not proper names (e.g., “cow,” “gold,” “water”). For it would certainly seem that had it not been for the joint efforts of a great many people, over a long period of time, these terms might well never have been found to be real names and, perhaps, would never have developed into real names in the first place. Kripke, it seems to me, was aware of this particular complication, but perhaps he failed to see the full extent of its practical significance. His possible genealogy of the term “gold” and his discussion of it are apt to demonstrate both these points. For example, what he describes as “the vagueness [of] the original

52  Sebastian Sunday Grève notion of gold” seems to be just what I have described as a concept’s instability, but I think he dismisses the problem too quickly by merely stating that “ordinarily, the vagueness doesn’t matter in practice” (NN, p. 136). Here is how he begins his discussion: If we imagine a hypothetical (admittedly somewhat artificial) baptism of the substance, we must imagine it picked out as by some such “definition” as, “Gold is the substance instantiated by the items over there, or at any rate, by almost all of them”. . . . The “almost all” qualification allows that some fool’s gold may be present in the sample. If the original sample has a small number of deviant items, they will be rejected as not really gold. If, on the other hand, the supposition that there is one uniform substance or kind in the initial sample proves more radically in error, reactions can vary: sometimes we may declare that there are two kinds of gold, sometimes we may drop the term “gold”. (These possibilities are not supposed to be exhaustive.) (NN, pp. 135–136) Kripke’s little genealogical story makes apparent that there may well have been a time in history when the use of a term such as “gold” was not rigidly bounded, hence a period during which the concept gold was a familyresemblance concept and the word “gold” not a real name. During such a period, as Kripke notes at the end of the quotation, the concept might have developed differently from the way it actually did. For example, the word “gold” might have come to be used to cover gold as well as fool’s gold, and so the word “gold” might never have become the real name it arguably is today. Moreover, as Kripke also notes, it is possible that “certain properties, believed to be at least roughly characteristic of the kind and believed to apply to the original sample, are used to place new items, outside the original sample, in the kind” (NN, p. 137) or that “the ‘original sample’ gets augmented by the discovery of new items” (pp. 138–139). Thus, in our alternative history of the word “gold,” the original sample might perhaps have been a mix of gold and pyrite, with the concept later being extended to also include the minerals chalcopyrite (CuFeS2) and mica. If chemistry had then (i.e., at a still later stage in our alternative history of the word “gold”) discovered the element with atomic number 79, then the theoretical identity statement “element with atomic number 79 = gold” would of course have been false, which shows that the use of the word “gold” would have developed in such a way as not to have been a term for the concept gold but, instead, some concept with a family-resemblance type structure, such as gold-or-pyrite-or-chalcopyrite-or-mica-or- .  .  . (while the concept gold might have come to be designated as “schmold” or “soft gold” instead). Kripke stresses that “scientific investigation generally discovers characteristics of gold which are far better than the original set” (NN, p. 138). This is right, but only on the condition that we interpret what is good (or

Real Names 53 “better”) as that which is conducive to something like a scientific understanding of the world and hence to the development of our words into real names. As we have just seen, even for a concept such as gold to have been so much as amenable to scientific investigation it was necessary for the concept to have had a particular kind of history, that is, a particular kind of tradition within which the words that are used to express it are passed from link to link in such a way that their use is developed as one that carries the potential of their being or becoming real names. In other words, it required a certain scientific spirit. Perhaps Kripke underestimated the influence of nonscientific and antiscientific tendencies in human societies, when he formulated the important principle, quoted earlier, that “the relevant linguistic features are normally intended to be preserved” (1986, p. 242).49 For better or worse, one broad consequence of the ubiquity of these tendencies in human cultural history is the widespread existence of the conceptual phenomenon that Wittgenstein described in terms of family resemblance. Wittgenstein’s idea thus marks the difficulty involved in the scientific and philosophical search for real names. But insofar as it contains a convincing account of why it has perhaps been particularly difficult to see how terms such as “love,” “knowledge,” “intelligence,” and “democracy” could possibly be or become real names, it should at the same time encourage anyone who cares to undertake this kind of task to believe that it is indeed achievable and that progress comes in many forms. Notes 1 Kripke explicitly acknowledges his agreement with Russell’s definition of proper names. See, for instance, his 1979/2011, p. 126, note 3, and 2013, p. 13. 2 See esp. Kripke 2013, pp. 144–160. 3 Translations of works by Frege and Wittgenstein have been amended where necessary, without further indication. The term “real name,” it should perhaps be noted, is the standard translation of Wittgenstein’s expression “eigentlicher Name,” which appears in both Tractatus Logico-Philosophicus (1922) and the Investigations. 4 Kripke offers a number of arguments against Russell’s idea that the word “this” is the only real name in his 2013 (pp. 19–28). 5 Wittgenstein had probably been familiar since before the First World War with Russell’s idea that the only real name is the word “this”; for early occurrences of the idea in Russell’s work, see esp. Russell 1911, p. 224, and 1984, pp. 39–40. See also note 19 below. 6 Searle 1958 and Strawson 1950 and 1959 show how dominant Russell’s description theory still was at the time; see also the discussion in Donnellan 1966 and Kripke 1977/2011. 7 J. L. Austin’s translation of Frege’s The Foundations of Arithmetic (1884), which was originally published in 1950, marks the beginning of the Frege revival. 8 Kripke acknowledges that Frege did not explicitly subscribe to a description theory of proper names. See, for example, his 1979/2011, p. 126, note 3. 9 My rejection of the claim that Frege’s notion of sense entails that a name, if it is to function correctly, must be associated by a language user with a description,

54  Sebastian Sunday Grève I believe, still contradicts Kripke’s mature view of Frege. See esp. his 2008/11, p. 280, and 2011c, p. 302, note 26. 10 Marshall 1953 and 1956 and Grossmann 1961 falsely suggested that Frege’s distinction between sense and reference was not intended to apply as generally as I have said it was. 11 In Naming and Necessity (1980), Kripke (in my view, falsely) implies that Frege’s and Mill’s distinctions are the same. See, for example, NN, p. 134. 12 Kripke sometimes took Frege’s first kind of case to imply a commitment on Frege’s part to a description theory of proper names; see for instance NN, p. 30 and his 1979/2011, pp. 126–127 (esp. p. 126, notes 2 and 3, and p. 127, note 4), and 2008/11, p. 278, note 72. I explain in the text why I believe this is wrong. 13 For the first kind of case he considers, Frege’s own example is the sentence “Dr. Gustav Lauben was wounded” as used by Herbert Garner and Leo Peter respectively. 14 For the second kind of case, Frege’s own example is the pair of sentences “Dr. Lauben was wounded” and “Gustav Lauben was wounded,” where the proper names “Dr. Lauben” and “Gustav Lauben” are coreferential. 15 Kripke claims at one point that Frege took the sense of a referring term to be the way its reference is “determined” or “fixed” (see NN, p. 59). Kripke provides no evidence for this claim. The only passage I can think of in which Frege may seem to be saying such a thing is one already cited in the text, which stems from an unpublished draft from the early 1890s. There Frege writes that “it is via a sense, and only via a sense, that a proper name is related to an object” (1997b, p. 135). But it would be wrong to interpret “related” here to mean determined or fixed. On the contrary, it is obvious from the context in which this sentence occurs that Frege is merely emphasizing the fact that on his theory every proper name has a sense. 16 The minimal sense of a given proper name such as “Smith” satisfies Kripke’s later notion of a sense that is immediately revelatory: “A sense is revelatory of its referent if one can figure out from the sense alone what the referent is. . . . A sense is immediately revelatory if no calculation is required to figure out its referent” (Kripke 2008/11, pp. 259, 261). Kripke uses the name “George W. Bush” as an example (on p. 260). 17 For the passage that has most commonly been taken (in my view, falsely) to show that according to Frege’s theory proper names in ordinary language typically have more than one sense, see his 1892a, pp. 27–28. 18 Arguably, the view that all words are names has a theoretical forerunner in Augustine’s De Magistro (which should not be confused with what has sometimes been called “the Augustinian picture of language” that is the target of Wittgenstein’s critique in the Investigations). For a recent discussion of Augustine’s theory, see Nawar 2021. 19 The idea that names really designate simples is expressed in the Tractatus in sentences 2.02 and 3.2–3.202. The conception of real names is then derived in the following series of remarks: 3.23, 3.32, 3.326, and 3.341–3.3411 (“The real name of an object is what all symbols that designate it have in common,” 3.3411). 20 For Kripke’s discussion of early Wittgenstein, see for instance Kripke, 2013, pp. 16–18. 21 In Naming and Necessity, Kripke does not actually ascribe the cluster theory to Wittgenstein (see also my note 25), but he does consistently do so in later publications. See, for example, 2011b, p. 53, note 3, and p. 57, and 2013, pp. 9–10 and 31.

Real Names 55 22 Two well-known expositions of the cluster theory of names are Searle 1958 and Strawson 1959, pp. 191–192. 23 The two places in which Kripke cites parts of Section 79 of the Investigations are NN, p. 31 and Kripke 2013, pp. 9–10. 24 Ruth Barcan Marcus used the same comparison, between naming and tagging, as Wittgenstein; see her 1961, esp. pp.  309–310. Kripke discusses Marcus’s tagging conception of proper names in NN, pp. 100–101 and his 1971/2011, pp. 6, 7, and 17 (note 13). 25 Kripke interprets Section 87 of the Investigations along the same lines as I do, but he never seems to infer that this makes it unlikely that Wittgenstein should have subscribed to a cluster-of-descriptions theory of proper names. See Kripke 1982, pp. 81–82. 26 To my knowledge, Kripke never explicitly connected his account of referencefixing and his account of Wittgenstein on rule-following. However, there is reason to believe that the geneses of these two elements of Kripke’s philosophy bear an interesting relation to each other. Judging by the prefaces to the respective books, it seems likely that each set of considerations influenced the other. In his book on Wittgenstein, Kripke says that it was in 1962 to 1963 that he “came to think about it in the way expounded here” (1982, p. viii), while in the case of Naming and Necessity Kripke says that “most of the views were formulated in about 1963–64” (NN, p. 3). 27 For Kripke’s doubts concerning the community view about rule-following and whether Wittgenstein is correctly interpreted along these lines, see esp. his 1982, p. 102, note 83 (pp. 102–104), and p. 112, note 87 (p. 146). 28 In the Investigations, Wittgenstein uses the term ‘form of life’ (Lebensform) only three times, in sections 19, 23, and 241. For detailed discussion of Wittgenstein’s special use of this term as a way to stress that an account of any part of human nature must attend to it as a historical phenomenon, see my ‘Artificial Forms of Life’ (unpublished manuscript). 29 For Kripke’s work on possible world semantics, see esp. his 1959, 1963a, and 1963b. See also NN, p. 48, note 15. 30 For a comparison of the notion of a possible world and Wittgenstein’s notion of a language-game, see my 2018 (esp. pp. 177–178). 31 For Wittgenstein’s account of reference-fixing that is identical with Kripke’s, see esp. PI, §§26–31. 32 Wittgenstein speaks not only of words for numbers and colors (German Zahlwörter and Farbwörter), respectively, but also of names of numbers (Zahlnamen, e.g., in PI, §28) and names of colors (Farbnamen, e.g., in PI, §51). 33 Kripke agrees with Wittgenstein that we can conceive of sensation words as names that refer to sensations (see, e.g., his well-known argument against the identity theory of mind, which begins “Let ‘A’ name a particular pain sensation,” NN, p. 146). However, in Wittgenstein’s Investigations there may thus seem to be an inconsistency between Section 244 (as quoted and interpreted in the text) and Section 293, because in the latter section one reads: “If we construe the grammar of the expression of sensation on the model of ‘object and name,’ the object drops out of consideration as irrelevant.” If, however, we understand “the model of ‘object and name’ ” here to be one that commits the error I have described in the text, then there will be no inconsistency. For a more detailed discussion of this issue, see my 2024. 34 Putnam was another prominent defender of the view that some natural kind terms are rigid designators. See Putnam 1973 and 1975. 35 Kripke also discusses natural kind terms in his 2013, pp. 45–46.

56  Sebastian Sunday Grève 36 For Kripke’s discussion of fictional discourse, see his 2013; for a brief statement of his account of pretended names, see p. 29. 37 Kripke noted that the theory of rigid designation may also apply to corresponding adjectives. His examples include the three pairs “heat”—“hot,” “sound”— “loud,” and “light”—“red.” See NN, p. 134. 38 If I  understand Kripke’s use of terms such as “substance,” “natural kinds,” etc. correctly, it will not commit him to strong metaphysical interpretations of them. 39 As mentioned at the end of the first section of this chapter, using a suitably general notion of object we (unlike Frege) can take it that the objects referred to by these names are concepts. Such a notion of object seems intuitive and unproblematic. And it avoids the concept horse paradox of Frege’s account (see Frege 1892b; for an excellent discussion of Frege’s solution, see Conant 2000). 40 Like other twentieth-century philosophers, Wittgenstein used the terms “metaphysics” and “metaphysical” in a more or less exclusively pejorative manner. I do not think we should follow him in this. 41 What Wittgenstein says about the possibility of metaphysics, including in the Investigations, can often seem rather conflicting. However, it must be clear that he was not opposed to asking what any given thing is, but only to particular ways of doing so. See also Glock 2019, pp. 189–191. 42 It may seem as if I am recommending to reform language, specifically our use of words such as “name” and “naming,” whereas Wittgenstein in the Investigations said that philosophy should leave the actual use of language as it is (see esp. PI, §124), and perhaps Kripke also shared this view. But I am not sure that I am recommending to reform language in proposing the view that rigid designators are the real names. In any case, my proposal need not be understood in this way, for one may as well take real names to be a species of names. 43 For Wittgenstein’s discussion of family-resemblance concepts, see esp. PI, §§65–67. 44 One might think that insofar as family resemblance may be a biological function it should at least be possible to discover the equivalent of a genetic code. I  suppose Wittgenstein’s metaphorical families are not necessarily biological families, but ones that may be extended by marriage as well as reproduction. 45 If my interpretation is correct, then Wittgenstein’s account of family-resemblance concepts will be in agreement with epistemicism about vagueness—the view that vagueness is a form of ignorance—as it has been expounded by Timothy Williamson. See esp. Williamson 1994, Ch. 7. 46 The distinction between the application of a concept and extending a concept is different from that between a concept’s extension and its intension. In particular, the total application of a concept at a moment is different from the concept’s extension, as it is not a mere set of objects but also includes a statistical component. And, as I go on to explain in the text, extending a concept is different from its intension, because the latter is itself among the things that may change as a consequence of extending a concept. 47 It is possible, albeit unlikely, that a concept develops purely in the way of a family and yet becomes rigidly bounded, because it is theoretically possible that the development of such a concept reaches a necessary limit, with all its subconcepts also being rigidly bounded. The concept number might perhaps be thought a possible candidate for such a development. 48 By explaining the difficulty of finding real names that are not proper names, Wittgenstein’s account of family-resemblance concepts provides a possible

Real Names 57 response to an objection that has often been advanced against accounts of rigid designation for terms other than proper names, according to which this kind of account leads to an overgeneralization of the category. For a brief survey of this literature, see LaPorte 2006/22, section 4. For some useful discussion, see also Salmon 2005. 49 Historically, religion has probably had the strongest anti-scientific influence in the world, but it seems that modern secular ideologies are steadily catching up.

References Conant, James (2000) Elucidation and Nonsense in Frege and Early Wittgenstein, in Alice Crary and Rupert Read (eds.), The New Wittgenstein. Routledge, 174–217. Donnellan, Keith S. (1966) Reference and Definite Descriptions, The Philosophical Review 75, 281–304. Frege, Gottlob (1879) Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Louis Nebert. Frege, Gottlob (1884) Die Grundlagen der Arithmetik: Eine logisch mathematische Untersuchung über den Begriff der Zahl. Wilhelm Koebner. Translated as The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number by J. L. Austin, 2nd, revised edition. Blackwell, 1953. Frege, Gottlob (1891a) Funktion und Begriff. Hermann Pohle. Cited after the translation “Function and Concept” in his 1997a, using original pagination numbers. Frege, Gottlob (1891b) Frege an Husserl 24.5.1891, in his Wissenschaftlicher Briefwechsel, edited by Gottfried Gabriel, Hans Hermes, Friedrich Kambartel, Christian Thiel, and Albert Veraart. Felix Meiner, 1976, 94–98. Cited after the translation “Letter to Husserl, 24.5.1891” in his 1997a. Frege, Gottlob (1892a) Über Sinn und Bedeutung, Zeitschrift für Philosophie und philosophische Kritik 100, 25–50. Cited after the translation “On Sinn and Bedeutung” in his 1997a, using original pagination numbers. Frege, Gottlob (1892b) Über Begriff und Gegenstand, Vierteljahrsschrift für wissenschaftliche Philosophie 16, 192–205. Cited after the translation “On Concept and Object” in his 1997a, using original pagination numbers. Frege, Gottlob (1918) Der Gedanke——eine logische Untersuchung, Beiträge zur Philosophie des deutschen Idealismus 1, 58–77. Cited after the translation “Thought” in his 1997a, using original pagination numbers. Frege, Gottlob (1997a) The Frege Reader, edited by Michael Beaney. Blackwell. Frege, Gottlob (1997b) [Ausführungen über Sinn und Bedeutung], in his Nachgelassene Schriften, edited by Hans Hermes, Friedrich Kambartel, and Friedrich Kaulbach. Felix Meiner, 1969, 128–136. Cited after the translation “Comments on Sinn and Bedeutung” in his 1997a, using original pagination numbers. Glock, Hans-Johann (2019) What is Meaning? A  Wittgensteinian Answer to an Un-Wittgensteinian Question, in James Conant and Sebastian Sunday (eds.), Wittgenstein on Philosophy, Objectivity, and Meaning. Cambridge University Press, 185–210. Grossmann, Reinhardt (1961) Frege’s Ontology, The Philosophical Review 70, 23–40.

58  Sebastian Sunday Grève Kripke, Saul (1959) A  Completeness Theorem in Modal Logic, The Journal of Symbolic Logic 24, 1–14. Kripke, Saul (1963a) Semantical Analysis of Modal Logic I: Normal Modal Propositional Calculi, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 9, 67–96. Kripke, Saul (1963b) Semantical Considerations on Modal Logic, Acta Philosophica Fennica 16, 83–94. Kripke, Saul (1971/2011) Identity and Necessity, in Milton K. Munitz (ed.), Identity and Individuation. New York University Press, 135–164. Cited after the reprint in his 2011a, 1–26. Kripke, Saul (1977/2011) Speaker’s Reference and Semantic Reference, Midwest Studies in Philosophy 2, 255–276. Cited after the reprint in his 2011a, 99–124. Kripke, Saul (1979/2011) A Puzzle about Belief, in Avishai Margalit (ed.), Meaning and Use. Reidel, 239–283. Cited after the reprint in his 2011a, 125–161. Kripke, Saul (1980) Naming and Necessity. Harvard University Press. Kripke, Saul (1982) Wittgenstein on Rules and Private Language. Harvard University Press. Kripke, Saul (1986) A Problem in the Theory of Reference: The Linguistic Division of Labor and the Social Character of Naming, in Philosophy and Culture (Proceedings of the 17th World Congress of Philosophy). Editions du Beffroi, Editions Montmorency, 241–247. Kripke, Saul (2005/11) Russell’s Notion of Scope, Mind 456, 1005–1037. Cited after the reprint in his 2011a, 225–253. Kripke, Saul (2008/11) Frege’s Theory of Sense and Reference: Some Exegetical Notes, Theoria 74, 181–218. Cited after the reprint in his 2011a, 254–291. Kripke, Saul (2011a) Philosophical Troubles. Oxford University Press. Kripke, Saul (2011b) Vacuous Names and Fictional Entities, in his 2011a, 52–74. Kripke, Saul (2011c) The First Person, in his 2011a, 292–321. Kripke, Saul (2013) Reference and Existence: The John Locke Lectures. Oxford University Press. LaPorte, Joseph (2006/22) Rigid Designators, in Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/archives/spr2022/ entries/rigid-designators/ Marcus, Ruth Barcan (1961) Modalities and Intensional Languages, Synthese 13, 303–322. Marshall, William (1953) Frege’s Theory of Functions and Objects, The Philosophical Review 62, 374–390. Marshall, William (1956) Sense and Reference: A Reply, The Philosophical Review 65, 342–361. Mill, John Stuart (1843). A System of Logic, Ratiocinative and Inductive: Being a Connected View of the Principles of Evidence, and the Methods of Scientific Investigation. Cambridge University Press. Nawar, Tamer (2021) Every Word is a Name: Autonymy and Quotation in Augustine, Mind 130, 595–616. Putnam, Hilary (1973) Meaning and Reference, The Journal of Philosophy 70, 699–711.

Real Names 59 Putnam, Hilary (1975) The Meaning of “Meaning”, in Keith Gunderson (ed.), Language, Mind, and Knowledge: Minnesota Studies in the Philosophy of Science 7. University of Minnesota Press, 131–193. Russell, Bertrand (1911) Knowledge by Acquaintance and Knowledge by Description, Proceedings of the Aristotelian Society 11, 108–128. Cited after the reprint in his Mysticism and Logic and Other Essays. Longmans, Green & Co, 1918, 209–232. Russell, Bertrand (1918) The Philosophy of Logical Atomism, The Monist 28, 495–527. Russell, Bertrand (1984) Theory of Knowledge: The 1913 Manuscript (The Collected Papers of Bertrand Russell, Vol. 7), edited by Elizabeth Ramsden Eames. Allen and Unwin. Salmon, Nathan (2005) Are General Terms Rigid? Linguistics and Philosophy 28, 117–134. Searle, John R. (1958) Proper Names, Mind 266, 166–173. Strawson, Peter F. (1950) On Referring, Mind 235, 320–344. Strawson, Peter F. (1959).  Individuals: An Essay in Descriptive Metaphysics. Methuen. Sunday Grève, Sebastian (2018) Logic and Philosophy of Logic in Wittgenstein, Australasian Journal of Philosophy 96, 168–182. Sunday Grève, Sebastian (2024) Insurmountable Privacy of Thought, in Herbert Hrachovec and Jakub Mácha (eds.), Platonism. De Gruyter. Sunday Grève, Sebastian (unpublished manuscript) Artificial Forms of Life. Williamson, Timothy (1994) Vagueness. Routledge. Wittgenstein, Ludwig (1922) Tractatus Logico-Philosophicus, revised edition, translated by D. F. Pears and B. F. McGuinness. Routledge & Kegan Paul, 1974. Wittgenstein, Ludwig (1953) Philosophical Investigations, 4th, revised edition, edited by P. M. S. Hacker and Joachim Schulte, translated by G. E. M. Anscombe, P. M. S. Hacker, and Joachim Schulte. Wiley-Blackwell, 2009.

3 Kripke’s Wittgenstein and Kripke’s Causal-Historical Picture of Reference Alexander Miller

Proper names are a confounded business. For example, suppose I  wanted to call this chair Jacob. What did I  really give the name to? The shape or the chair? . . . The possibility of giving names to things presupposes very complicated experiences. (Wittgenstein to Friedrich Waismann 25 December 1929, as recorded in Ludwig Wittgenstein and the Vienna Circle)1

3.1 Introduction Saul Kripke’s Naming and Necessity and Wittgenstein on Rules and Private Language have played a pivotal role in shaping both late 20th-century and contemporary philosophy of language and mind. In Lecture II of NN, Kripke outlines a “picture” of how the references of certain sorts of natural language expressions are determined: a picture, in other words, of the facts that determine reference. In Chapter 2 of WRPL, on the other hand, Kripke presents a number of arguments, suggested to him by a reading of the later Wittgenstein’s “rule-following considerations”, the conclusion of which is that there are no facts capable of determining reference. There thus appears to be a straightforward conflict between Kripke’s two famous texts. In this chapter I will be concerned with the nature of the relationship between them and with the question whether this appearance of conflict is genuine or not. I’ll proceed as follows. Section 3.2, I’ll give a brief reminder of the sceptical argument developed by Kripke in Chapter 2 of WRPL, followed in Section 3.3 by a very brief reminder of the causal-historical picture of reference outlined by Kripke in NN. In Sections 3.4 and 3.5, I’ll consider arguments by (respectively) Colin McGinn and Penelope Maddy, the intended upshot of which is that (something like) the causal-historical picture of reference in NN is capable of disabling the sceptical argument of WRPL. I’ll argue that McGinn and Maddy are both wrong, and that the causal-historical DOI: 10.4324/9781003240792-4

Kripke’s Wittgenstein and Kripke’s Causal-Historical Picture 61 picture of reference fails to neutralise Kripke’s Wittgenstein-inspired scepticism about the existence of facts capable of determining reference. And then, I’ll go on in Section 3.6 to argue that the underlying source of the conflict between Kripke’s two books is actually very direct: the causal picture of reference defended in NN and the dispositional theory of meaning attacked in WRPL are arguably instances of the same kind of naturalistic approach to the determination of meaning and reference. It seems that NN, in its espousal of a causal-historical picture of reference, and WRPL, in its scepticism about dispositional theories of meaning, respectively advocate and reject instances of the same general form of naturalism about meaning and reference. In Section 3.7, I’ll develop the idea that the appearance of contradiction here might be obviated by drawing on an analogy with a pair of positions in metaethics and normative ethics respectively. It is possible, without inconsistency, to hold an expressivist position in metaethics at the same time as a broadly utilitarian position in normative ethics (in which we reject at the metaethical level the idea that moral judgements express beliefs about utility while holding at the level of normative ethics that utility is the standard of right action). In similar fashion, we could perhaps view WRPL as advocating a kind of expressivism about semantic judgement at the meta-level (on which ascriptions of meaning do not express beliefs about speakers’ dispositions), while advocating a causal picture of reference at the level of first-order semantics (on which speakers’ dispositions provide standards for selecting the referents of linguistic expressions), so that there is in fact no contradiction between the positions defended in the two books. In Section 3.8, however, I’ll argue that promising as it sounds, although this manoeuvre may work in the ethical case, there are specific considerations which suggest that it is bound to fail in the case of meaning and reference. The conclusion of the chapter, then, is that ultimately there is indeed a direct conflict between the position defended in NN and the view suggested to Kripke by his reading of Wittgenstein in WRPL. 3.2  Kripke’s Wittgenstein’s Sceptical Argument In Chapter  2 of WRPL, Kripke’s Wittgenstein’s sceptic (hereafter “KW’s sceptic”) argues for a “sceptical paradox”: there are no facts in virtue of which ascriptions of meaning, such as “Jones means addition by ‘+’ ”, are true. Since the argument generalises, there are no facts in virtue of which any speaker attaches a determinate meaning to any of the expressions of his language. It is worth noting that although Kripke doesn’t highlight it himself, the sceptic’s argument exploits the idea that the meaning of an expression determines its reference: any fact which constitutes the meaning of the “+”-sign must determine that it refers to the addition function. Given this

62  Alexander Miller principle, the sceptic can argue that since there are no suitable facts capable of determining that “+” refers to the addition (as opposed—see later—to the quaddition) function, it follows that there are no suitable facts capable of conferring truth on an ascription of meaning to the “+”-sign.2 Suppose that Jones is asked to answer the query “68 + 57 =?”, a calculation that he has never before been asked to perform and a calculation in which both of the arguments (here 68, 57) are larger than any of the numbers in calculations he has performed previously. (We know that such an example and threshold exist given that Jones, a finite creature, has performed only finitely many computations in the past.) Jones confidently answers “125”. This answer seems to be correct in two ways: first, it is arithmetically correct, given that the number 125 is indeed the sum of the numbers 68 and 57; it is also metalinguistically correct, given that the “+” sign denotes the addition function (the function that gives the sum of two numbers presented to the function as arguments). KW’s sceptic argues that Jones’s confidence that “125” is the correct answer is not well placed: This sceptic questions Jones’s certainty about his answer, in . . . the “metalinguistic” sense. Perhaps, he suggests, as Jones used the term “plus” in the past, the answer he intended for “68 + 57” should have been “5”! Of course the sceptic’s suggestion is obviously insane. Jones’s initial response to such a suggestion might be that the challenger should go back to school and learn to add. Let the challenger, however, continue. After all, he says, if Jones is now so confident that, as he used the symbol “+”, his intention was that “68 + 57” should turn out to denote 125, this cannot be because he explicitly gave himself instructions that 125 is the result of performing the addition in this particular instance. By hypothesis, he did no such thing. But of course the idea is that, in this new instance, he should apply the very same function or rule that he applied so many times in the past. But who is to say what function this was? In the past he gave himself only a finite number of examples instantiating this function. All, we have supposed, involved numbers smaller than 57. So perhaps in the past he used “plus” and “+” to denote a function which we will call “quus” and symbolise by “⊕”. It is defined by x ⊕ y = x + y, if x, y < 57 = 5, otherwise. Who is to say that this is not the function Jones previously meant by “+”? (Adapted from WRPL, pp. 8–9) The challenge posed by KW’s sceptic is: find a fact about Jones which constitutes his meaning addition rather than quaddition by the “+” sign, which makes it the case that “+” as he uses it refers to the addition (and not the quaddition) function. Kripke (WRPL, pp. 11, 26) imposes two constraints

Kripke’s Wittgenstein and Kripke’s Causal-Historical Picture 63 on candidate responses to this challenge. First, any response must provide an account of the type of fact that makes it the case that Jones denotes addition (and not a quaddition-like function) by his use of “+”. Second, it must be possible to “read off” from this fact what constitutes correct and incorrect use of the “+” sign.3 In other words, it must show why Jones is justified in giving the answer “125” to the query “68 + 57=?” and why “125” is the answer Jones ought to give.4 In challenging us to find a suitable meaning-constituting—or reference-determining—fact KW’s sceptic allows us unlimited and omniscient access to facts of two types: (a) facts about the previous linguistic behaviour and behavioural dispositions of Jones and fellow members of his speech community; and (b) facts about Jones’s mental history and “inner life”. The sceptic considers and rejects a variety of possible meaning-constituting (reference-determining) facts. These include facts about: Jones’s previous behaviour (WRPL, pp. 7–15); general thoughts or instructions that Jones might have given himself (WRPL, pp. 15–17); how Jones is disposed to use the “+”-sign (WRPL, pp. 22–38); the relative simplicity of hypotheses about what Jones means or refers to by the “+”sign (WRPL, pp. 38–40); Jones’s qualitative, introspectible mental states (including mental images) (WRPL, pp. 41–51); sui generis and irreducible mental states of Jones’s that are “not to be assimilated to sensations or headaches or any ‘qualitative’ states” (WRPL, pp. 51–53); and Jones’s relation to objective, Fregean senses (WRPL, pp.  53–54). KW’s sceptic insists that in each case the proposed meaning-constituting (or reference-determining) fact violates one or both of the two constraints imposed on candidate responses. It seems, then, that facts about meaning—and determinate reference—have as Kripke puts it, “vanished into thin air” (WRPL, p. 22). For the purposes of our discussion in this chapter, the most important of the responses to KW’s sceptic to consider is the dispositionalist response. According to a simple form of the dispositional theory, Jones’s meaning addition by “+” is constituted by the fact that he is disposed to respond to queries of the form “x + y =?” by giving the sum of the numbers denoted by “x” and “y”. KW’s sceptic argues that this response fails to determine the addition function as the referent of “+” (WRPL, pp. 26–7). Jones’s dispositions to respond to arithmetical queries are finite: some numbers are simply so large that Jones’s brain lacks the computational wherewithal to process calculations involving them and indeed so large that Jones will be dead long before he is even able to grasp them. Define the skaddition function as follows: x ψ y = x +y, if x, y are small enough that Jones can grasp them and perform calculations involving them = 5, otherwise

64  Alexander Miller The dispositions that Jones actually possesses are consistent with “+” as he uses it referring to the skaddition function (and indeed an open-ended and potentially infinite set of functions with similar singularities), so they fail to determine the addition function as the referent of “+”. As Kripke observes (WRPL, pp. 27–32) the dispositionalist about meaning may try to respond to this objection by invoking ceteris paribus or ideal conditions for the manifestation of the relevant dispositions: for astronomically large numbers I’ll die before I  finish responding to arithmetical queries involving them, but if we include in the ideal conditions a proviso to the effect that I live long enough, we can say that I’m disposed to respond in ideal conditions with the sum (and not the skum) of the relevant numbers. So according to this more sophisticated form of dispositionalism, Jones’s meaning addition by “+” is constituted by the fact that he is disposed in ideal conditions to respond to queries of the form “x + y =?” with the sum of the relevant numbers. Kripke argues that this move fails as a defence of dispositionalism. The dispositionalist aspires to give a reductive account of meaning: the meaningconstituting dispositions—and the attendant ideal conditions—are to be specified in wholly non-semantic and non-intentional terms. How plausible is it that this can be done? The obtaining of the ideal conditions has to guarantee that Jones does not respond with something other than the sum of the relevant numbers. But note that if Jones means subtraction by “+”, he’ll respond with “11” and not “125”. And if he means multiplication by “+” he’ll respond with “3876”. Indeed, the set of functions f such that if Jones meant f by “+” he would respond with something other than the sum has an infinite number of members. So the obtaining of the ideal conditions has to guarantee that none of these eventualities obtains. How could a set of conditions specified in entirely non-semantic and non-intentional terms guarantee that an open ended and potentially infinite set of alternative meaning hypotheses (in which Jones means one of these other functions) fails to obtain? Even if we include provisos guaranteeing that Jones lives long enough and has sufficient cognitive capacity to carry out the calculation, and so on, without an explicitly semantic proviso to the effect that Jones means addition by “+”, we’ll fail to guarantee that Jones will in the ideal conditions respond with the sum. And we can’t include such an explicitly semantic proviso without rendering the account circular in a way that stymies its reductionist aspirations.5 The reductive dispositionalist view thus fails to satisfy the first of the two constraints on answers to KW’s sceptic: it fails to determine addition (as opposed to some quaddition-like alternative) as the function denoted by “+”.6 If reductive dispositionalism and the other sorts of response all fail to provide a plausible answer to the sceptic, it seems that we can find no fact capable of making in true that a speaker means something by the expressions

Kripke’s Wittgenstein and Kripke’s Causal-Historical Picture 65 of his language.7 This threatens to spiral into the “insane and intolerable” (WRPL, p. 60) conclusion that “all language is meaningless” (WRPL, p. 71). Kripke describes this conclusion as “incredible and self-defeating” (ibid.), and KW tries to avoid it by developing a “sceptical solution” in which Jones can with perfect propriety be described as, for example, meaning addition by “+” even given the conclusion that there is no fact capable of making this so (WRPL, p. 69). We’ll return later to the sceptical solution in Section 3.7. Our immediate concern, in the next section, is with the causal-historical picture of reference outlined by Kripke in NN. 3.3  The Causal-Historical Picture In Lectures I and II of NN, Kripke launches a full-frontal attack on what he calls the Frege–Russell view of names. According to the Frege–Russell view a name has the reference it does because it is synonymous with, or an abbreviation of, a definite description. Kripke’s famous modal argument suggests that the synonymy relation postulated by the Frege–Russell view implies that many clearly contingently true sentences have to be regarded— implausibly—as necessary truths. On Kripke’s alternative picture, names are what he calls rigid designators: unlike definite descriptions they refer to the same individual no matter what counterfactual situation is under discussion. Moreover, in general we cannot even view definite descriptions as fixing the reference of these rigid designators: it is in general neither necessary nor sufficient for a use of a name to refer to a given individual that the user of the name associates it with a definite description uniquely satisfied by that individual. As an alternative to the Frege–Russell view, Kripke proposes what has come to be known as the “causal-historical”8 picture: Someone, let’s say, a baby, is born; his parents call him by a certain name. They talk about him to their friends. Other people meet him. Through various sorts of talk the name is spread from link to link as if by a chain. A speaker who is on the far end of this chain, who has heard about, say, Richard Feynman, in the market place or elsewhere, may be referring to Richard Feynman even though he can’t remember from whom he first heard of Feynman or from whom he ever heard of Feynman. He knows that Feynman is a famous physicist. A certain passage of communication reaching ultimately to the man himself does reach the speaker. He then is referring to Feynman even though he can’t identify him uniquely .  .  . a chain of communication going back to Feynman himself has been established, by virtue of his membership in a community which passed the name on from link to link. (NN, p. 91)

66  Alexander Miller At the origin of the chain, the relevant object or individual will be christened with the name in a baptismal ceremony. This may be via ostension, but it may also be via the use of a description. This does not constitute a concession to the Frege–Russell view, since, as John Burgess nicely explains “this description need not remain permanently associated with the name” (Burgess 2006, p. 172). Having been baptised, the object or individual “continues to be denoted by that name even if the description used and every other circumstance of the baptism is forgotten or misremembered” (ibid.). In order to avoid fairly obvious counterexamples, moreover, for speakers at various points in the chain “the new user should intend to use the name for the same object the old user was using it for” (ibid.). As Kripke himself puts it: An initial “baptism” takes place. Here the object may be named by ostension, or the reference of the name may be fixed by a description. When the name is “passed from link to link” the receiver of the name must, I think, intend when he learns it to use it with the same reference as the man from whom he heard it. (NN, p. 96) In Lecture III of NN, Kripke suggests that a similar picture be adopted for natural kind terms. As Burgess summarises the view: Using a description, perhaps involving demonstratives and requiring supplementation by ostension, that is true of them or at least that the baptist thinks is true of them, a natural kind or individual may be picked out and given a “common name”. This common name or natural kind term thereafter passes from speaker to speaker, with the original description being perhaps very soon completely forgotten. (2006, p. 181) For example, if the baptist uses the description “the shiny, yellow, malleable metal in front of me” to fix the reference of “gold”, the kind term will refer to the stuff with atomic number 79, and this reference will be passed along the causal-historical chain to future users of the term. There have been some attempts in the literature to use the causalhistorical picture of reference to respond to KW’s sceptic’s argument. I’ll consider two such attempts, those developed by Colin McGinn (1984) and Penelope Maddy (1984). In the next two sections, I’ll argue that neither of these is successful. 3.4 McGinn Colin McGinn (1984, pp. 164–166) considers whether we might reply to KW by picking up on the suggestion in NN that a name n correctly applies

Kripke’s Wittgenstein and Kripke’s Causal-Historical Picture 67 to an object o if and only if o lies at the origin of the causal chain leading up to applications of n to o, and the parallel suggestion for natural kind terms, that, for example, “gold” applies to an object if and only if that object is of the same kind as the original sample which initiated the causal chain leading up to uses of “gold”.9 How might these suggestions secure determinate reference for, for example, “Kripke” and “tiger” in the face of KW’s sceptic’s challenge? Before answering this question it’s worth noting McGinn’s comment that Kripke fails to consider the causal theory of reference as a potential solution to the sceptical argument in WRPL because in the latter “he tends to formulate his sceptical problem in terms of the notion of meaning and not that of reference” (1984, p. 166). In fact, McGinn is mistaken about this, since as we saw in Section 3.2, there is no such separation in the sceptical argument. The sceptic assumes that meaning determines reference, so that whatever constitutes the fact that an expression has the meaning that it has must determine its reference. Why, then, might we think that the relevant causal facts are incapable of securing the fact that the name “Kripke” refers to Kripke and the fact that “tiger” refers to tigers? Consider an application of the name “Kripke” to Hilary Putnam at some future time t*, and consider the sceptical suggestion that this application is correct, because by “Kripke” we actually mean Kripnam, where x = Kripnam iff (a) it is time t prior to t* and x = Kripke or (b) it is time t later than or equal to t* and x = Putnam All of the causal facts about the use of “Kripke” prior to t* are consistent with the name referring to Kripke and with the name referring to Kripnam, so they fail to determine the reference of the name. Likewise, consider an application of “tiger” to an aardvark at time t* and consider the sceptical suggestion that this application is correct because by “tiger” we actually mean tigvark, where x is a tigvark iff (a) it is time t prior to t* and x is a tiger or (b) it is time t later than or equal to t* and x is an aardvark Again, KW’s sceptic will argue that all of the causal facts up to t* are consistent with the alternative hypothesis, so that ultimately they fail to determine the class of tigers as the things to which “tiger” is correctly applicable. McGinn thinks that the causal theorist has a ready answer to these sceptical suggestions: [T]he non-standard extension Kripnam for “Kripke” . . . will not qualify for the simple reason that Putnam is causally isolated from my present use of “Kripke” (or we can suppose as much): the sceptical hypothesis was that “Kripke” correctly applies to Putnam after some future time t*, but the causal theory can exclude this possibility by observing that it is Kripke who lies at the origin of the causal chain leading up to my

68  Alexander Miller present use of “Kripke”—I need have had no causal contact with Putnam at all, still less the kind of causal contact that determines reference. (1984, p. 165) Likewise: [M]y current use of “tiger” has a sample of tigers at its causal origin and not any aardvarks so that the sceptic is defeated if he claims that “tiger” might correctly apply to aardvarks after some future time t*. (1984, pp. 165–166) Neither of McGinn’s suggestions convincingly overturns the sceptical argument, however: the sceptic can reply that it is irrelevant that Putnam isn’t the causal origin of uses of “Kripke” since it is nonetheless true that Kripnam is at their causal origin. After all, given the sceptic’s definition, the object at the causal origin of uses of the name is indeed Kripnam. Likewise, the objects at the causal origin of uses of “tiger” are, given the sceptic’s definition, tigvarks. How, then, can the causal theorist respond to the sceptical challenge? It seems that the causal theorist would need to cite some fact along the following lines: were I presented with Putnam at some time at t* or beyond I would not apply the name “Kripke” to him and were I presented with an aardvark at some time at or beyond t* I would not apply “tiger” to it. In other words, I’m not disposed to apply the name “Kripke” to Putnam at time t* or beyond, and I’m not disposed to apply “tiger” to aardvarks at time t* or beyond. Clearly, we are now back again relying on something like a dispositional theory, hence back again facing the problem afflicting dispositional theories rehearsed in Section 3.2.10 Thus, McGinn’s attempt to deploy the causal theory of reference against KW’s sceptical argument fails to overturn it.11 3.5 Maddy Penelope Maddy (1984) concentrates on the case of a natural kind term like “gold”. She notes that the causal theorist tells a story according to which my current use of “gold” is linked by a historical chain of reference-preserving links that stretches back to an initial event in which the word is introduced in a baptism. As Maddy notes (1984, pp. 475–476, n. 7), it could be argued that indeterminacy afflicts the historical chain, but like Maddy, we’ll put this worry to one side and focus on the initial baptismal act: The baptist picks out samples of the metal in question. He points at these, pronounces “gold!”, and from that moment, the word refers to

Kripke’s Wittgenstein and Kripke’s Causal-Historical Picture 69 whatever is like this, that is, to all members of the natural kind containing the samples. (1984, p. 464) Maddy correctly notes that the sceptic can question whether the baptismal act secures referential determinacy: If the extension of the term “gold” is to contain everything “like this”, the referent of “this” must be determinate. Wittgenstein12 argues that it is not. The baptist points towards the sample, but who is to say whether he is pointing at the metal, or at its shape, or at its colour?” (ibid.)13 She argues, however, that the indeterminacy which threatens here can be closed down via an appeal to “neurological speculation” (p.  465) and a focus on “a more structured perceptual connection” (p. 464) between the baptist’s perceptual states and features of his environment. I’ll outline a slightly simplified version of Maddy’s argument. The reason that the baptist’s ostensive act picks out the kind of metal (gold) exemplified by the sample rather than its shape (say, square) or colour (say, yellow) is that the baptist is perceiving the kind of metal exemplified by the sample rather than its shape or colour. How so? Maddy’s idea turns on the thought that the perceptual state is underpinned by a kind of neural structure (Maddy calls these “cell assemblies”) and that the content of the perceptual state is determined by facts about how the neural structure in question is correlated causally with features of the environment. The perceptual state caused by the sample of gold is underpinned by neural structure ψ (say). Square cardboard cut outs don’t produce ψ, and neither do yellow flowers. However, gold triangles do cause ψ, as do gold bracelets. This set of complex causal facts makes it the case that in the initial baptismal event the baptist was perceptually responding to the nature of the sample qua metal, rather than to its shape or colour. Since the nature of the sample qua metal consists in its having atomic number 79, it is this that the baptist picks out when he pronounces “gold” in the initial baptismal ceremony. We can see, then, that for Maddy the determinate reference of “gold”, as it is used in the baptismal ceremony, is derivative on the content of the perceptual state that the baptist occupies when performing the baptism, and the content of the perceptual state is determined by facts about how it is causally correlated with features of the environment. This means, however, that Maddy’s strategy faces problems very similar to those (described in Section 3.2) that beset the reductive dispositionalist account of meaning. Contentful perceptual states can represent things as they are but they can also misrepresent them: I  can have a perceptual experience with the

70  Alexander Miller content that such and such is gold when in fact the item causing me to have the experience is not in fact gold, and in the presence of a piece of gold I can fail to have an experience with that content. Thus, we cannot simply identify the content of a perceptual experience with the features of objects that cause me to have it, on pain of ascribing a disjunctive content that it doesn’t possess and that would render it impossible for the perceptual experience to be a misrepresentation. It would seem that the content of the experience would need to be regarded as determined, if at all, by a certain select subset of the causal correlations it is capable of entering into. Characterising this select subset in non-semantic and non-intentional terms is—for all that Maddy has said—of a piece with the problem faced by the reductive dispositionalist in characterising a suitable set of ideal conditions in terms that do not take the notion of content for granted. So, the causal theorist faces some severe problems in determining the reference of “this” in the “like this” of the baptismal ceremony, in other words, in determining the relevant feature of the sample that is the focus of the baptist’s act. There are further shortcomings in Maddy’s story. Put to one side the problem outlined in the previous paragraph, that of determining the reference of “this” in the baptist’s “like this”. As Maddy notes: The next problem naturally concerns the “like”. The extension of the term is to consist of whatever is like those samples. What determines this? (1984, p. 469) Recall from the preceding page the idea that the perceptual state caused by samples of gold is underpinned by neural structure ψ. Given that whatever else stimulates the neural structure ψ will be in some respect similar to the sample: The temptation is to say that this similarity is the “like” in “like this”, that the extension of the term “gold” consists of whatever stimulates [ψ]. (ibid.) Tempting as it is, Maddy notes that this suggestion faces some serious problems. Since some pieces of gold (those too small or too far away, for instance) will fail to stimulate ψ while some pieces of Iron Pyrites will, we again face the problem of narrowing down the extension of “gold” by regarding it as containing a subset of those things that stimulate ψ and also some of the things that don’t stimulate ψ. And Maddy makes it clear that she thinks no progress is to be made by invoking ceteris paribus conditions, given the success of Kripke’s argument (against reductive dispositionalism)

Kripke’s Wittgenstein and Kripke’s Causal-Historical Picture 71 that it will not be possible to characterise these conditions in non-semantic and non-intentional terms (1984, pp. 476–477, n. 20).14 Maddy argues, however, that there is no need for the causal theorist to go down the route of seeking to identify suitable ceteris paribus conditions: The interpretation of the word “like” in “like this” was by no means left up for grabs; the whole idea is that by isolating a sample, the baptist fixes the reference of the term to members of its natural kind. It isn’t up to the baptist to determine what belongs in the same kind as the sample; the world determines that. (1984, p. 470) Maddy argues that it is an objective, mind-independent and languageindependent fact that the piece of gold in front of me and the piece of gold in a far distant part of the universe have the atomic number that they do, and that their doing so accounts for the phenomenal properties that regulate our use of “gold”. And she notes that Wittgenstein can object that “the world is not pre-packaged into natural kinds independently of our linguistic activity” (1984, p. 471), but this is to open a substantial can of worms so that “the debate [between the causal theorist and Wittgenstein] is once more at a standoff” (ibid.). It seems to me, however, that the appeal to objective, mind-independent and language-independent natural kinds will not help with the problem about determinacy. In response to the question “What makes it the case that the item in front of me and the item on Neptune belong to the extension of ‘gold’?”, the observation that they belong to the same kind will help only if it has been determined that the word “gold” refers to that kind. And this, as yet, has not been established. That is to say, Wittgenstein can concede that the world itself determines that the two samples belong to the same kind, but what he needn’t concede is that the world itself determines that the word “gold” refers to that kind. Thus, Maddy’s play with the notion of objective scientific kinds presupposes that the determinate reference of “gold” has been fixed—and we are still to be given an account of how that is so. It seems, then, that Maddy confuses two distinct claims: (i) For any natural kind that the baptist’s sample belongs to, the world itself determines whether any other given object belongs to it and (ii) The world itself determines what natural kind the expression “gold” refers to. And as yet, we have no plausible story from Maddy as to how the causal theory of reference can deliver (ii).

72  Alexander Miller Maddy’s attempt to use the causal theory of reference to neutralise KW’s sceptic’s argument, like McGinn’s, thus falls prey to the arguments developed by Kripke in Chapter 2 of WRPL.15 3.6  Dispositional Theories and the Causal-Historical Picture If the causal-historical picture of reference adumbrated in NN provided resources to undermine the claim in WRPL that there is no “straight” solution to KW’s sceptic’s challenge, that would constitute a clear source of tension between the two texts. The arguments of the previous two sections suggest that this is not the case. But this does not mean that there is no such tension. Indeed, although more work would need to be done to drive the point home, prima facie at least it appears that KW’s sceptic’s argument against reductive dispositionalism undermines the “causal-historical” picture of reference sketched in NN. I will now suggest further that NN’s picture of reference and WRPL’s stance on reductive dispositionalism are straightforwardly incompatible. To see the incompatibility, note Paul Boghossian’s observation that “[I]n all essential respects, a causal theory of meaning is simply a species of a dispositional theory of meaning” (1989, p. 164). Boghossian continues: The root form of a causal/informational theory is given by the following basic formula: O means (property) P by predicate S iff (it is a counterfactual supporting generalization that) O is disposed to apply S to P. (ibid.) Although it is perhaps not immediately obvious, the causal-historical picture outlined in Section 3.3 fits this rubric. In the first instance, the view would be along the following lines in the case of a natural-kind term like “tiger”: (a) Speaker O refers to kind K by “tiger” iff K is the kind exemplified by the sample which lies at the origin of the causal chain leading up to O’s current use of “tiger”. We saw in Section 3.4 that in order to secure determinacy in the face of the sceptic’s tigvark suggestion, (a) would require supplementation by something along the lines of: (b) “Tiger”, as used by speaker O, correctly applies to x iff O is disposed to apply “tiger” to x.

Kripke’s Wittgenstein and Kripke’s Causal-Historical Picture 73 And the same thing goes in the case of names of individuals. Initially we have: (c) Speaker O refers to individual o by “Kripke” iff the individual o lies at the origin of a suitable causal chain leading up to O’s current use of “Kripke”. Additionally, in order to secure determinacy of reference in the face of the sceptic’s Kripnam suggestion, a supplement along the following lines would be required: (d) “Kripke”, as used by speaker O, correctly applies to x iff (O is disposed to apply “Kripke” to x). Given this, the incompatibility of NN and WRPL is clear: in advocating a causal-historical picture of reference, NN is effectively advocating a form of dispositional theory of meaning, whereas the rejection of dispositional theories of meaning is the centrepiece of Chapter 2 of WRPL. To put it in the broadest terms, we can say that if (reductive) dispositional theories of meaning are a paradigm form of semantic naturalism, NN advocates that paradigm form of semantic naturalism while WRPL rejects it.16 3.7  A Possible Escape Route? In Chapter 2 of WRPL, the causal-dispositionalist view of meaning is repudiated, while, in NN, it is defended. One way in which we might try to obviate the appearance of contradiction here would be to return to the distinction we mentioned briefly at the end of Section 3.2, between straight and sceptical solutions to the argument of KW’s sceptic. The sceptical solution attempts to undercut the sceptical argument by denying that meaningconstituting facts are necessary for the propriety of our meaning-ascribing practices. One way of developing the sceptical solution involves viewing it as an expressivist/quasi-realist account of semantic judgement.17 On this way of looking at things, the claim that no straight solution is plausible would amount to the rejection of cognitivist views of semantic judgement on which they express beliefs about semantic states of affairs. To see how this might help dissolve the appearance of contradiction mentioned earlier, let’s think about a superficially similar scenario in the ethical domain, and in particular how it might be possible to be a metaethical expressivist about moral judgement while holding, for example, a utilitarian view in normative ethics. I’ll do this by taking Simon Blackburn’s quasi-realism about moral judgement as our stalking horse.18 In the first instance, Blackburn sees himself as giving an explanatory story about the nature of moral judgement. A  cognitivist explanation, for

74  Alexander Miller Blackburn, is an explanation that proceeds by attempting to identify distinctively moral states of affairs and then construing moral judgements as expressing beliefs that these states of affairs obtain. Cognitivism faces a crippling dilemma. Either we identify moral states of affairs with natural states of affairs or we construe them as non-natural and sui generis. If we take the former route, we face the challenge posed by Moore’s openquestion argument: moral judgements appear to have a normative aspect, and/or an internal link to motivation, not possessed by beliefs about naturalistic states of affairs. On the other hand, if we take the latter route and attempt to construe moral judgements as expressing beliefs about non-natural and sui generis states of affairs, the account succumbs to the sorts of metaphysical and epistemological challenges faced by Moore and the intuitionists.19 Blackburn’s way of avoiding this dilemma involves giving an explanation of moral judgement that does not help itself to the idea of a distinctively moral state of affairs. In mounting his alternative explanation, Blackburn adopts what might be called methodological non-cognitivism: in our explanation, we can avail ourselves of natural states of affairs, beliefs about natural states of affairs, and non-cognitive sentiments or attitudes directed at natural states of affairs—but not beliefs about distinctively moral states of affairs. We start out with the assumption, for example, that the judgement that X is wrong expresses the sentiment B!(X) and then attempt to construct a notion of moral truth: roughly, and as a first approximation, we could say that a moral judgement is true if it belongs to M*, the set of attitudes that would remain after all opportunities for improvement in attitudes, and dispositions to form them, have been taken (Blackburn 1984a, p. 198). This would allow us to view some moral judgements as genuinely true or false: and since we would have earned the right to do so on the basis of methodologically non-cognitivist materials, we would not have “sold out” to moral cognitivism in having done so. Blackburn’s quasi-realist doesn’t deny the existence of moral states of affairs (hence his realism), he simply refuses to take them for granted in the materials he deploys in his explanatory account (hence his quasi-realism).20 The multiple challenges faced by accounts of moral judgements along these lines are well known (see Chapter  4 of Miller (2013) for an overview), but what is important for our current concern is that it seems possible to adopt it while holding a position in normative ethics that initially appears to align with naturalistic cognitivism. A utilitarian view, on which the standard of right action is maximising utility (say), might appear to be committed to a metaethical cognitivist view on which the judgement that X is right expresses the belief that X maximises utility. But there is no necessary connection between utilitarianism and cognitivism: it is possible to embrace utilitarianism from an expressivist perspective. To see how, think of the disposition to express the attitude of approval (H!) to actions insofar

Kripke’s Wittgenstein and Kripke’s Causal-Historical Picture 75 as they have the characteristic of maximising utility. Call this disposition, D. We could embrace utilitarianism by taking up an attitude of approval towards this disposition itself: H!(D). And having done so, we can think about whether this attitude would belong to the set of attitudes M* that would remain after all opportunities for improvement in attitude, and dispositions to form them, have been taken. This latter exercise is essentially what we do when we engage in normative ethics, and if it turns out that H!(D) in fact is a member of M*, we can conclude that it is true that actions are right if and only if they maximise utility. But we will not have left ourselves open to the open-question argument, since our account involved no attempt to explain moral judgement by identifying moral rightness with maximising utility and using such an identity to characterise the content of moral beliefs. We can reject metaethical naturalistic cognitivism and the idea that moral judgements are to be explained in terms of naturalistic states of affairs while arguing for a utilitarian normative ethic.21 If we view the sceptical solution in Chapter  3 of WRPL as proposing a metasemantic expressivist account of semantic judgement, might it be possible to square this with acceptance of a causal-dispositional story at the level of first-order semantic theory?22 Just as facts about the utility of actions might form the basis for the selection of right action even though moral judgements are not to be construed as expressing beliefs about the utility or otherwise of actions, could causal/dispositional facts form the basis for selecting the referents of linguistic expressions even though judgements about meaning are not to be construed as expressing beliefs about causal/dispositional states of affairs? If so, NN could perhaps be regarded as engaging in the first of these—arguing that causal/dispositional facts are an appropriate basis on which to assign referents to linguistic expressions—while WRPL could be regarded as taking a stance on the second— arguing that meaning-ascribing judgements should not be construed as expressing beliefs about causal/dispositional states of affairs.23 Just as in normative ethics, we don’t simply aim to classify actions as right or wrong but attempt to delineate the general principles which govern this classificatory process, in philosophical semantics, we won’t just aim to assign referents to expressions but attempt to identify the general principles which govern this classificatory process24: so the idea would be that just as a metaethical expressivist can be a utilitarian in normative ethics, a purveyor of the sceptical solution might embrace a causal-historical/dispositional view in philosophical semantics.25 3.8  No Way Out The suggestion mooted in Section 3.7 strikes me as the best prospect for squaring the views of NN with the arguments developed in WRPL. In the

76  Alexander Miller end, however, the analogy between the moral case and the semantic case breaks down at a crucial point, undermining the idea that the two texts can be viewed as compatible. The problem concerns the resources available for use by the expressivist explanation in the two cases. Recall that in the moral case, the expressivist is allowed: non-cognitive sentiments and attitudes, natural states of affairs, and beliefs about the obtaining of natural states of affairs. Without helping himself to a notion of moral truth, the ethical quasi-realist seeks to construct a notion of moral truth out of the materials at his disposal by focusing on the notion of improvement in attitude and identifying the true moral judgements as those which express attitudes belonging to M*. As Blackburn summarises the proposal: [T]he root idea is that the virtue of truth is constructed from the virtues of method. (Blackburn 1984a, p. 237) The crucial reflection here is that, in any given case, a method is something that can be deployed in ways that are better or worse. In other words, the notion of a method presupposes the notion of a standard for assessing attempts to apply it. Or to put it another way, the notion of a method presupposes the notion of a rule which sorts items into different evaluative categories. Now the notion of a rule is of a piece with the notion of meaning: just as a rule sorts behavioural episodes into those which comply with it and those which don’t, the meaning of an expression does likewise with respect to uses of that expression. This is why Wittgenstein focuses on, precisely, rules and language in the passages which inspired WRPL, and indeed why the notions of rule and language feature in the book’s title. A consequence of this is that the expressivist about meaning, unlike the moral expressivist, is barred by his own methodology from taking for granted the notion of a standard and its attendant notions of compliance and non-compliance. The “root idea”, then, that allowed the moral expressivist to argue his way to a utilitarian position in normative ethics is simply not available to the quasi-realist about meaning. While utilitarianism might conceivably emerge in good standing from the metaethical expressivist’s construction of moral truth, the causal-historical/dispositional picture cannot emerge in similar fashion from KW’s sceptical solution. 3.9 Conclusion It seems, then, that the causal-historical picture adumbrated in NN presupposes a straight solution to KW’s sceptical challenge, while WRPL denies that a straight solution is possible. In conclusion, though, we should note that pointing out this apparent inconsistency does not necessarily amount

Kripke’s Wittgenstein and Kripke’s Causal-Historical Picture 77 to a criticism of Kripke: after all, he himself doesn’t explicitly endorse the arguments developed in WRPL. He writes that WRPL “should be thought of as expounding neither ‘Wittgenstein’s’ argument nor ‘Kripke’s’: rather Wittgenstein’s argument as it struck Kripke, as it presented a problem for him” (WRPL, p. 5). Even so, he clearly does find the arguments developed in WRPL to be challenging and important. The question of how they relate to the views outlined in NN is likewise an important and challenging matter for devotees of Kripke’s two classic texts.26 Notes 1 Wittgenstein (1979, p. 51). 2 Kripke puts it in terms of the denotation of the “+”-sign at the start of Chapter 2 (WRPL, pp. 7–8), but later puts it in terms of reference (WRPL, p. 54). 3 For our purposes here, giving a response to a query that includes the “+” sign counts as a use of that sign. 4 The nature and plausibility of this second, “normativity”, constraint is a controversial matter: for an overview of some of the relevant literature see Miller (2022) and Section 4 of Miller and Sultanescu (2022). 5 I take this to be the sort of worry Kripke is pointing to in his discussion of the more sophisticated form of dispositionalism (WRPL, pp. 27–32). For further elaboration, see Boghossian (1989, pp.  164–177). This sort of consideration still poses a problem for views on which facts about reductively characterised dispositions are held to metaphysically necessitate meaning facts. For example, Scott Soames (1997) claims that the Kripkean point (familiar from NN) “that many necessary consequences of propositions are not a priori consequences of them” (1997, p. 231) opens up space for the idea that some non-intentional fact about a speaker’s dispositions metaphysically necessitates the fact that he means addition by “+”. Soames concedes that Kripke gives reasons (concerning, broadly, the “normativity” of meaning (see note 4)) for thinking that the meaning fact cannot be an a priori consequence of the reductively characterised dispositional fact; but he argues that if we switch to thinking of the putative relationship between the two facts as one of non-a priori consequence Kripke has simply given us no reasons to doubt the plausibility of the view. He writes: [KW’s sceptic] has insisted that if I  meant anything in the past, then what I meant must be determined by nonintentional facts; and I have agreed, provided that the relation is one of necessary consequence. I grant that if I meant anything in the past, then what I meant must be a necessary consequence of nonintentional facts about me, my environment, my community, and so on. But it is not evident that there is a problem here, since none of the sceptic’s arguments show that such a relation fails to hold. Indeed, they scarcely even attempt to show this. (1997, p. 230) Contra this, note that in order for the fact that Jones is disposed to give the sum to metaphysically necessitate the fact that he means addition by “+”, the conditions in which the disposition would be manifested have to be specified in a way such that their holding metaphysically guarantees that Jones responds with the sum. So they have to metaphysically guarantee that he does not mean any of the

78  Alexander Miller functions in the open-ended and potentially infinite set of functions that yield something other than the sum of the relevant input numbers. How could a nonsemantically and non-intentionally characterised set of ideal conditions achieve that? Soames fails to show that there is any basis for confidence that this question can be answered in a way that favours the reductive dispositionalist. (An interesting question, which I  can’t go into here, is how the considerations broached in this note relate to Wittgenstein’s remarks in PI, §183.) 6 KW’s sceptic also argues that dispositionalism fails to satisfy the second constraint and the idea that meaning is normative (WRPL, pp. 23, 37). In addition to the works cited in footnote 4 here, see Sultanescu (2022) for a helpful discussion. 7 A response which attempts to answer the sceptic by providing a meaningconstituting fact is what Kripke calls a “straight solution” (WRPL, p. 69). 8 Kripke himself dislikes the “causal-historical” label (comments in a CUNY seminar attended by the author in February 2022) and would prefer simply “historical chain” (see also Burgess 2006, pp. 172–173) but the “causal” label has become entrenched in the literature (it is used, e.g. by Hattiangadi, Kusch, McGinn, and Maddy) so I’m hoping I’ll be forgiven for continuing to use it in this chapter. 9 In this context, McGinn construes the causal theory as providing a set of necessary and sufficient conditions for the correct application of a name or natural kind term (1984, p. 165), possibly going beyond Kripke’s reticence about suggesting necessary and sufficient conditions for reference (NN, p. 93). I’ll let this point pass as I’m going to argue that even if we construe the causal theory as offering necessary and sufficient conditions it fails as a straight response to KW’s sceptic (and if it is not offering necessary and sufficient conditions it’s hard to see how it could even be a candidate for offering a straight solution). That said, there are some very interesting residual questions in this vicinity: could it be that in rejecting the search for necessary and sufficient conditions for reference here, Kripke is actually signalling that the causal-historical view in NN is not a form of reductive dispositionalist “straight solution”, as in WRPL? This matter deserves a fuller discussion than I can attempt here. I will say, though, that I’m sceptical as to whether the reticence about necessary and sufficient conditions in NN signals a principled contrast like the contrast between straight and sceptical solutions in WRPL: whereas in WRPL there’s a relatively clear contrast between truthconditional accounts of meaning and assertibility-conditional accounts of meaning, there seems to be nothing comparable in NN to yield a point of contrast, in general terms, with accounts of a concept that eschew the search for necessary and sufficient conditions for its application. That said, I think that treating the attack on reductive dispositionalism in WRPL and the causal-historical view in NN as operating on different levels is the best chance for a rational reconstruction of Kripke’s views that would allow us to view the two texts as consistent: see sections 3.7 and 3.8 later for an attempt along these lines and an argument that it is bound to fail. The issue of Kripke’s “reticence” in NN would certainly bear further discussion. (I’m very grateful to Olivia Sultanescu for raising this issue.) 10 As we’ll see later, this is not at all surprising given that causal theories are in fact forms of dispositionalism. 11 It appears that McGinn requires something along the lines of David Lewis’s account on which certain sceptical possibilities for the referents and extensions of expressions can be ruled out on grounds of “unnaturalness” (Lewis 1983). This would be a major supplementation, requiring much work (and among other things a response to Kripke’s remarks about the candidate response to the sceptic which invokes the relative simplicity of meaning hypotheses (WRPL,

Kripke’s Wittgenstein and Kripke’s Causal-Historical Picture 79 pp. 38–40)). For some discussion and pointers to the relevant literature, see the postscript to Section 4 in Miller and Sultanescu (2022). 12 Maddy puts it in terms of “Wittgenstein”, but as she notes “My account of the rule-following problem derives from Kripke’s extremely helpful book” (1984, p. 475, n. 2). 13 This is what is known as the “qua problem” (Devitt and Sterelny 1993, Ch. 4): is he pointing at the sample qua metal, qua shape, or qua colour? 14 As noted earlier, Maddy fails to see that a problem of this sort is faced by her account of how the content of the baptist’s perceptual states is determined. In addition to the problem concerning how the extension of “gold” is determined, Maddy notes (1984, p. 477, n. 22) that there is the further problem of seeing how the normativity of meaning can be accommodated by the causal theorist. She is optimistic about the causal theorist’s prospects for dealing with this, but doesn’t go into detail in the paper under consideration. 15 In order to stop the gap in her account, Maddy could try appealing to the ideas of “reference magnetism” and natural properties suggested by the work of David Lewis (see note 11 above). Although some of the things Maddy says gesture in this direction (see esp. (1984, p.  472)), the suggestion requires a development and defence that she fails to provide. And as we noted earlier in response to the thought that McGinn might deploy a Lewisian story at this point, this is far from being a straightforward matter. For congenial critical discussions that also conclude that the causal theory of reference is unable to neutralise KW’s sceptic’s argument, see Hattiangadi (2007, pp. 141–144) and Kusch (2006, pp. 133–136). 16 It’s worth noting that as Boghossian points out (1989, p. 164) causal-informational theories are only one form a dispositional view can take. Conceptual role theories would be another form of the same general dispositional view. This shows that McGinn is wrong in his conjecture (1984, p. 166) that Kripke doesn’t consider causal theories of reference in WRPL because of his extensive focus on the mathematical example of the “+” sign (mathematical objects, being abstract, are generally regarded as causally inert). Contra McGinn, Kripke does consider causal theories of reference albeit indirectly via considering dispositional theories in general, and this doesn’t commit him to attributing causal powers to abstract objects such as numbers and functions, since expressions referring to these get dealt with by conceptual role theories, another type of dispositional view. 17 See Miller (2020) for a fuller elaboration (and also Miller (2010, 2015) for a critique of other, non-expressivist construals of the sceptical solution). 18 Blackburn (1984a, Chs. 5 and 6). 19 This is just an oversimplified thumbnail sketch to give the shape of Blackburn’s position. The issues are in fact much more complicated (e.g., “Cornell realists” will argue that moral properties are both natural and sui generis: see Chapter 7 of Miller (2013)). 20 As Blackburn puts it, we “distinguish where we start, as we attempt to give a theory of ethics, from where we end up” (1996, p. 91). This is why I called Blackburn a methodological non-cognitivist rather than a non-cognitivist simpliciter: his non-cognitivism, such as it is, concerns the materials he allows himself to start out with, not where he ends up (where he’ll happily embrace moral knowledge and moral truth). I’m grateful to Cameron Ogle for suggesting the “methodological non-cognitivism” label. For a paper that does nicely highlight this facet of Blackburn’s view, see McDowell (1987). (Of course, McDowell goes on to criticise Blackburn on other grounds, but these are not our concern here.)

80  Alexander Miller 21 Note that the methodological non-cognitivist starting point in effect imposes a “no circularity” constraint on what the quasi-realist can use in his explanatory story, but it does not follow from this that in the attempt to construct a notion of moral truth we have to start out from a point where all our moral judgements are collectively suspended. In that (justificatory) part of the project, we are “working from within”, and not “playing the fake game of trying to certify values without values” (Blackburn 1996, p.  89). (This is a point missed by McDowell in his otherwise exemplary (1987) exposition of Blackburn.) 22 Note that “metasemantic” here is to be distinguished from “metalinguistic” as used in the exposition of the sceptical scenario in §2 earlier. The expressivist position in semantics considered in the present section is a position in metasemantics in the same sense in which quasi-realism in the moral case is a position in metaethics. 23 Blackburn is perhaps advocating something along these lines in his paper on KW (1984b, p. 37). 24 So on the way of looking at things proposed here, practical ethics would correspond to what in the philosophy of language is called by Robert Stalnaker (2017, p.  903) “descriptive semantics”, normative ethics would correspond to Stalnaker’s “foundational semantics”, and metaethics would correspond to what I term “metasemantics”. (I’m unsure whether Stalnaker would follow me in distinguishing between foundational semantics and metasemantics in a way that parallels the distinction between normative ethics and metaethics.) 25 The fact that the causal-historical picture explicitly involves intentions to preserve reference without raising any question about what constitutes the fact that these intentions have the content that they do suggests that Kripke’s concerns in NN are of a different order from those in WRPL. (This is also suggested by his inclusion, among the facts that determine reference, of facts about what we think; see, e.g. Kripke, NN, p. 95.) The maneuver considered here would provide one way of capturing this difference: the causal-historical picture would be viewed as best systematizing our intuitive judgements about reference rather than providing a constitutive account of putatively reference-determining meaning facts. (Only the latter is governed by a no-circularity constraint, so the circularity objection to reductive dispositionalism outlined in Section 3 doesn’t rule out the proposed maneuver: the real circularity problem at this point in the story is the one outlined in the next section). 26 I’m grateful to the editors of this volume for helpful feedback, and also to Finn Butler, Grant Gillett, Ali Hossein Khani, John Shand, Olivia Sultanescu, and Seth Whittington.

References Blackburn, Simon (1984a) Spreading the Word: Groundings in the Philosophy of Language. Clarendon Press. Blackburn, Simon (1984b) The Individual Strikes Back, Synthese 58(3), 281–301. Reprinted in Miller and Wright (2002). Blackburn, Simon (1996) Securing the Nots: Moral Epistemology for the QuasiRealist, in W. Sinnott-Armstrong and M. Timmons (eds.), Moral Knowledge: New Readings in Moral Epistemology. Oxford University Press. Boghossian, Paul (1989) The Rule-Following Considerations, Mind 98(392), 507– 549. Reprinted in Miller and Wright (2002).

Kripke’s Wittgenstein and Kripke’s Causal-Historical Picture 81 Burgess, John (2006) Saul Kripke: Naming and Necessity, in John Shand (ed.), Central Works of Philosophy Volume 5 (The Twentieth Century: Quine and After). Acumen Publishing. Devitt, Michael and Sterelny, Kim (1993) Language and Reality: An Introduction to the Philosophy of Language. MIT Press. Hattiangadi, Anandi (2007) Oughts and Thoughts: Rule-Following and the Normativity of Content. Oxford University Press. Kripke, Saul (1981) Naming and Necessity. Blackwell. Kripke, Saul (1982) Wittgenstein on Rules and Private Language. Harvard University Press. Kusch, Martin (2006) A Sceptical Guide to Meaning and Rules. McGill-Queen’s University Press. Lewis, David (1983) New Work for a Theory of Universals, Australasian Journal of Philosophy 61, 343–377. Maddy, Penelope (1984) How the Causal Theorist Follows a Rule, Midwest Studies in Philosophy IX, 457–477. McDowell, John (1987) Projectivism and Truth in Ethics, reprinted in his Mind, Value and Reality. Harvard University Press, 1998. McGinn, Colin (1984) Wittgenstein on Meaning. Blackwell. Miller, Alexander (2010) Kripke’s Wittgenstein, Factualism and Meaning, in D. Whiting (ed.), The Later Wittgenstein on Language. Palgrave MacMillan. Miller, Alexander (2013) Contemporary Metaethics: An Introduction, expanded 2nd, revised edition. Polity Press. Miller, Alexander (2015) Rule Following, Error Theory and Eliminativism, International Journal of Philosophical Studies 23(3), 323–336. Miller, Alexander (2020) What Is the Sceptical Solution? Journal for the History of Analytical Philosophy 8(2). Miller, Alexander (2022) The Normativity of Meaning and Content, in P. Stalmaszczyk (ed.), The Cambridge Handbook of the Philosophy of Language. Cambridge University Press. Miller, Alexander and Sultanescu, Olivia (2022) Rule-Following and Intentionality, in Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy, Summer 2022 edition. https://plato.stanford.edu/archives/sum2022/entries/rule-following/. Miller, Alexander and Wright, Crispin (eds.) (2002) Rule-Following and Meaning. McGill-Queen’s University Press. Soames, Scott (1997) Skepticism About Meaning: Indeterminacy, Normativity, and the Rule-Following Paradox, Canadian Journal of Philosophy 27(supplement), 211–249. Stalnaker, Robert (2017) Reference and Necessity, in Bob Hale, Alexander Miller, and Crispin Wright (eds.), A Companion to the Philosophy of Language, expanded 2nd, revised edition. Wiley-Blackwell, 902–919. Sultanescu, Olivia (2022) Meaning, Rationality, and Guidance, Philosophical Quarterly 73(1), 227–247. https://doi.org/10.1093/pq/pqac004. Wittgenstein, Ludwig (1979) Ludwig Wittgenstein and the Vienna Circle: Conversations Recorded by Friedrich Waismann, edited by Brian McGuinness, translated by Joachim Schulte and Brian McGuinness. Basil Blackwell.

4 Modality Wittgenstein’s Tractatus Versus Saul Kripke Sanford Shieh

Progress, far from consisting in change, depends on retentiveness. . . . Those who cannot remember the past are condemned to repeat it. (George Santayana, The Life of Reason) Hegel remarked somewhere that all great world-historical facts and persons happen, so to speak, twice. He forgot to add: once as tragedy, the other as farce. (Karl Marx, Der achtzehnte Brumaire des Louis Bonaparte) Especially in the US, one finds undergraduate classes, taught by a team of lecturers, meant to “survey” the great works of the “Western canon.” In one such class Wittgenstein’s Tractatus was somehow raised to the canon, and a member of the team pressed into being its exponent. Members of the team discuss the lectures with small groups of students, and generally require the students to read not much more than those parts of the texts directly addressed in their lectures. But since our temporary champion of the Tractatus intended to distil his lecture from some rumors he had heard about the book in graduate school and in the scholarship of his specialization, when asked what the students should read, he replied, “Have them read all of it; it’s short.” A conscientious and observant member of the class, who carried out this lecturer’s assignment to the letter, would surely have noticed how often Wittgenstein speaks of possibility. Indeed, perhaps even someone casually flipping through the Tractatus for the first time at a bookshop might be so struck. Here is a very small sampling:1 2.15(2) This connection of the elements of a picture is called its structure, and the possibility of this structure its form of depiction. 3.11 We use the sense-perceptible sign (sound or written sign, etc.) of the proposition as a projection of a possible situation.

DOI: 10.4324/9781003240792-5

Modality 83 4.124 The obtaining of an internal property of a possible situation is not expressed by a proposition, but expresses itself in the proposition that represents it, by an internal property of the proposition. 5.473(2) A possible sign must also be able to designate. Everything that is possible in logic is also permitted. 6.33 We do not believe a priori in a law of conservation, but we do know a priori the possibility of a logical form. That student, who as it happens reads German, might also have noticed that in this Abhandlung qualified as Logisch, “every possibility” is said to be the “concern of logic,” and “all possibilities” are said to be “its facts” (2.0121). What is one to make of the presence of possibility, and of modalities in general, in the Tractatus? Among the first thinkers to have paid serious attention to the Tractatus are leading members of the Vienna Circle, Moritz Schlick (1930) and Rudolf Carnap (1930). They saw, in the remarks on the propositions of logic in this book, a conception of logic and mathematics that conjoins coherently with empiricism. These opponents of traditional metaphysics certainly would have no truck with traditional metaphysical views of modality, and so Carnap in particular, found in the Tractatus an explanation, or, as he would come to say, an explication, of the contrast between necessity and contingency as at bottom the contrast between logically and non-logically true propositions. This anti-metaphysical orientation is taken up, more recently, by resolute approaches to the Tractatus. The apparent appeal to modality is not even a reductive account of necessity and possibility to logical notions. Rather, it is an aspect of the book to be overcome, to be seen as nonsensical. Cora Diamond, for example, sees Wittgenstein as consistently opposing conceptions of “necessity imaged as fact,” as what is “the case,” albeit in all possible worlds (1988, p. 195). She takes Wittgenstein’s characterization of “[l]ogical necessity [a]s that of tautologies” to imply that “sentences about necessity . . . really are . . . entirely empty” (1988, p. 198). For another example, Warren Goldfarb argues that Wittgenstein intends the reader of the Tractatus to see that the metaphysical conception of “possible states of affairs” appearing in the 2’s lands in “incoherence,” and “implode[s]” (1997, pp. 66, 70). Against these anti-metaphysical readings of modality in the Tractatus stands an opposed tradition of seeing the Tractatus as resting on modal notions. Among the earliest anti-positivist interpreters of the Tractatus is Wolfgang Stegmüller, who claims that “the Tractatus is ‘saturated’ [‘durchtränkt’] with intensional concepts” (1966, p. 181). In particular, the notion of picturing relies on a “conceptual framework of a class of possible worlds”

84  Sanford Shieh (1966, p.  184). Similarly, G. H. von Wright holds that “[t]he notion of propositional significance in the Tractatus is itself a modal notion” (1982, p. 188). More recently, Raymond Bradley claims that the views of the Tractatus “are so clearly in accord with the views of contemporary theorists, such as Kripke, that we may, with charity, see them as sketchy anticipations of the latter” (1992, p. xvii). One of these anticipations is a “highly plausible intuition[]: that objects can occur in states of affairs other than those in which they actually occur” This “intuition[] is embodied in the particular view of possible worlds to which both Wittgenstein and Kripke subscribe.” Moreover, Bradley claims that for both Wittgenstein and Kripke, this intuition is plausible because [I]t is plausible to think or talk about objects as existing in states of affairs which are not actual, that is, to think counterfactually of them as being connected in merely possible states of affairs “as they do not have to be in reality”. (1992, p. 134)2 These modal readings of the Tractatus point to the questions on which I’ll focus in this chapter: • In what sense, if at all, is “propositional significance” in the Tractatus a modal notion? If it is, what are Wittgenstein’s reasons for taking it to be? • To what extent is the conception of modality operative in the Tractatus “so clearly in accord with” Kripke’s conception? I will pursue these questions through philosophical history. Philosophical history is not a mere recounting of positions. It’s not enough for me to identify the views of the Tractatus, and spell out how it contrasts with those of Kripke, or of other philosophers. My interest is in Wittgenstein’s and Kripke’s grounds for their views. A philosophically fruitful way of uncovering these grounds and their significance is to try to discover what philosophical issues they were confronting, and how the conceptions that they end up articulating may be seen as responding to these issues. The path to grasping these issues is the historical development of their philosophical views. In Section 4.1, I show how and why, in the Tractatus, Wittgenstein held that a primitive notion of possibility is intrinsic to what it is to be a proposition that represents the world truly or falsely. The grounds for this Tractarian position emerge from tracing Wittgenstein’s thinking starting with a rejection of Russell’s theories of judgment, through an attempt to formulate an alternative in the “Notes on Logic”3 and realization of problems with that attempt, to the resolution of these problems in the Tractatus. In

Modality 85 Section 4.2, I elaborate Kripke’s founding of the legitimacy of modality on non-theoretical intuitions about what might or might not be true of things. The nature of this justification is made clear by seeing it as an answer to Quine’s critique of the account of modality in Carnap’s project of displacing fruitless traditional metaphysical disputes, an answer which aims at re-legitimizing traditional modal metaphysics. These accounts show that one central difference between these conceptions of modality is that Wittgenstein’s justification of modality makes no use of non-theoretical intuitions about essential and contingent properties. In Section 4.2, I also show that conflicts among our modal intuitions together with Kripke’s attempt to adjudicate them undermine the claim that these intuitions furnish a non-circular justification of modality. Since Wittgenstein’s Tractarian justification of modality does not rely on intuitions, it is, prima facie, not vulnerable to this difficulty. All this may suggest that I fundamentally disagree with anti-metaphysical perspectives on Tractarian modality. This is not so. Possibility in the Tractatus is not depictable, but rather “shows forth.” There is no philosophical theory of modality, no theoretical representations of possibility. But that does not imply that what seems to be a theory of modality is mere nonsense. To understand the Tractatus on modality is not to grasp a range of thoughts, but to recognize fundamental logical features of thought and reality. 4.1 The Tractatus and Primitive Possibility The larger philosophical stakes underlying the place of modality in the Tractatus is the connection between logic and modality. Frege and Russell, central figures of early analytic philosophy, reject a venerable philosophical tradition of characterizing deductive validity in terms of necessity and possibility: the conclusion of a valid argument, as Aristotle (1964) puts it, follows “out of necessity” (Analytica Priora, pp.  24b18–20) from its premises. But, for Frege, “calling a statement necessary has no meaning for us” (1879, §4, 5; emphases in original). Russell is less diplomatic: “Modality ought to be banished from logic” (1905, p. 520). For them, deductive validity is not explained in terms of necessity and possibility. I cannot here give more than the briefest sketch of Frege’s and Russell’s grounds for their anti-modal views. For them, logic governs reasoning, which is composed of judgments. Judgments have objects, thoughts or propositions, the primary bearers of truth. But commitments central to their philosophies imply that there are no such things as necessary or possible truth distinct from plain truth. The significance of the Tractatus in relation to these stakes is that Wittgenstein brings modality back into the foundations of logic, by showing possibility as intrinsic to the nature of propositions or thoughts.

86  Sanford Shieh Wittgenstein’s grounds for this modal conception of proposition derive from his attempt to overcome the difficulties he discerned in one of Russell’s theories of judgment. I begin with a sketch of how Russell arrived at that theory. When Russell, together with Moore, turned against British absolute idealism, they came to hold that the “object of a belief” or a judgment (Moore 1901, p. 717) is a proposition, a non-linguistic and non-mental entity composed by relations relating entities. Propositions don’t represent, but rather contain what they’re about. A crucial part of this theory is that truth is not correspondence to reality, but rather an indefinable property of propositions. Similarly, falsehood is not the absence of correspondence with reality, but a primitive property of propositions. In addition, as Russell puts it, “a fact appears to be merely a true proposition” (1904, p. 523). Starting around 1906, Russell began to have doubts about the idea of propositions with a primitive property of falsity. The problem may be formulated thus, following Russell in taking Othello to be history rather than fiction. A false proposition like that expressed by (1) Desdemona loves Cassio consists of an entity in which the relation of love unites Desdemona to Cassio, with the unanalyzable property of falsehood. But if the relation of love unites Desdemona to Cassio doesn’t this mean that Desdemona loves Cassio? Doesn’t this amount to the existence of a fact or state of affairs consisting of Desdemona Cassio? But a fact is a true proposition. (For more on this problem, see Cartwright 1987, 2003; Sullivan and Johnston 2018.) By 1910, Russell concludes that there are no such things as MooreRussell propositions. What then is judgment? Russell’s answer is the multiple-relation theory of judgment (MRTJ). On the MRTJ, judgment or belief is a state consisting of a subject standing in the belief relation to the objects of her belief. The objects are not united. A judgment is true if the objects are indeed connected as the subject believes them to be. It is false if the objects are not so connected. This sidesteps the problem of false propositions since, when Othello has the false belief that Desdemona loves Cassio, there is no entity in the world consisting of Desdemona standing in the relation love to Cassio. Truth on the MRTJ is correspondence between beliefs and the existence of complexes or facts in the world. Russell is quite aware of a problem facing the MRTJ. (2) Othello believes that Desdemona loves Cassio (3) Othello believes that Cassio loves Desdemona ascribe distinct beliefs to Othello, since the belief of (2) is false while that of (3) is true.4 However, these beliefs involve the same three objects:

Modality 87 Desdemona, Cassio and love. If there is no more to the MRTJ than the view that belief relates a subject to the objects of her belief, how does it explain the difference between beliefs (2) and (3)? It is now standard in the secondary literature to call this the “direction problem.” Russell advanced two main answers to this difficulty. The second of these appears in a manuscript titled Theory of Knowledge (Russell 1984), on which Russell was working in the summer of 1913. In May 1913, Wittgenstein presented Russell with at least two criticisms, one of which is directed specifically at what Russell was writing at that time. Shortly after the second criticism, Russell abandoned this manuscript unfinished. This interaction between Russell and Wittgenstein is one of the great Rorschach blots of philosophical history, since we have no direct evidence of what exactly Wittgenstein’s criticisms were. My responses to this blot add up to the speculation that Wittgenstein’s criticisms led Russell to conclude that neither of his two main answers to the direction problem succeeds. Hence, it’s unclear that the MRTJ is a viable theory of judgment. Since logic for Russell governs correct inference among judgments, it is equally unclear that he has a viable philosophical account of logic. I will not here go into my speculations.5 Instead, I turn to Wittgenstein’s “Notes on Logic,” in which we find a theory of propositions intended to escape the criticisms he made of the MRTJ. Wittgenstein reinstates propositions as elements of judgment. Propositions are facts. A fact is an aspect of a collection or a composite. Facts have forms, something that they have in common with other facts. Any fact can be used to represent, or, in Wittgenstein’s terminology “symbolize,” any fact with the same form. So used, the representing fact is a proposition. The symbolization requires conventionally adopted or stipulated rules (for “convention,” see NL, S-15, 3–14; for stipulation, see “laying down,” ibid., 4–8). These rules fix: • What entities object in the representing fact stand for, the “meanings” of these entities (2–17, 3–15, 4–8). • What fact about these meanings are “of like sense” with the representing fact, that is, what fact about these meanings makes the representing fact true (4–8). • What fact about these meanings are “of opposite sense” with the representing fact, that is, makes the representing fact false (4–8). These rules specify how a propositional fact is compared with facts, or as Wittgenstein puts it, “A  proposition is a standard to which facts behave” (S-18; see also 4–8). Propositions are not only facts; they are facts together with rules of comparison. The fact that “that this inkpot is on this table,” to use Wittgenstein’s example in “Notes on Logic” (1–2), may be a proposition if it’s stipulated that the inkpot means Aristotle, the table means Plato, the fact

88  Sanford Shieh that Aristotle is younger than Plato makes the propositional fact true, and the fact that Aristotle is not younger than Plato makes the propositional fact false. This last example points to a critical ingredient of the theory of propositions in “Notes on Logic”: the notion of negative fact (NL, 1–7, 8; 3–1). What is stipulated to make the fact that the inkpot is on the table false is the negative fact that Aristotle is not younger than Plato. Recall that what felled Russell’s theory of propositions, and drove him to the MRTJ was the problem of false propositions. Thus, the “Notes on Logic” theory’s claim to have overcome the deficiencies of Russell’s conceptions of judgment depends on the coherence of the notion of negative fact. From the first of Wittgenstein’s wartime Notebooks,6 we see that he had by late 1914 come to realize that he did not have a coherent account of negative fact, and thus also no coherent accounts of falsity. This is what Wittgenstein called the “truth-problem (Wahrheits-Problem)” (NB, 24 September 1914). Together with a standard set of stipulated rules, a fact about the sentence (4) Catalina denounced Cicero is false if the negative fact that Lucius Sergius Catalina did not denounce Marcus Tullius Cicero obtains in the world. But, if (4) is false, it does not describe any aspect of the world. Doesn’t this mean that there is no fact that corresponds to (4)? Could we hold that a negative fact is just the absence of a fact? Then it is the absence of any fact that corresponds to (4) that makes it false? Well, then wouldn’t it also be the absence of any fact corresponding to the sentence Iago loves Cassio that makes this propositional fact false? The absence of a fact is not a feature of the world, not something obtaining in the world. Then it’s not clear how 1. the absence of any fact corresponding to “Catiline denounced Cicero” 2. the absence of any fact corresponding to “Iago loves Cassio” are different. But it seems these absences have to be different, because • absence 1 doesn’t make “Iago loves Cassio” false, • absence 2 doesn’t make “Catiline denounced Cicero” false. Wittgenstein’s truth-problem is a version of an ancient problem of falsity as posed, for example, by Plato (1985): how is it possible to “say, speak, or think that which is not . . . correctly . . .?” (Sophist, 238c).7

Modality 89 I want to highlight three moments in Wittgenstein’s struggles with the Truth-Problem. First, Wittgenstein begins his attack on this problem with his initial consideration of the idea that propositions may be taken to be pictures or models (NB, 29 September 1914). Second, he tries out the idea that picturing the non-existent requires that each fact in the world has a “logical structure” and a picture has “form,” something in the picture that is “identical with reality” (NB, 20 October 1914). The idea is that what, in the first instance, corresponds in the world to a proposition is a structure or form, the very same as the structure of the proposition. The truth or falsity of a proposition is then determined by whether there exists a fact with that structure. So now falsity does not require the existence of some negative fact having the special characteristic of not obtaining. Falsity is absence, but absences are individuated by logical structures. Third, Wittgenstein soon has doubts about the common form solution to the Truth-Problem: How can there be the form of p, if there is no fact of this form? And in that case, what does this form really consist in?! (NB, 29 October 1914) Perhaps this worry comes from Wittgenstein’s remaining allegiance to Russell’s ideas. For Russell form is what is common to a class of complexes, so there is no form if there are no complexes. If certain facts don’t exist, then their form don’t exist either, and so there would be no form to correspond to the false picture. But, just a few days later, Wittgenstein entertains a new idea. A proposition as a picture consists of names representing things and “connected . . . like a tableau vivant,” and “logical connection must of course be possible for the represented things” (NB, 4 November 1914; first emphasis mine). With the hindsight afforded by the Tractatus, we see Wittgenstein here on the verge of taking a possible connection, that is, a possible structure, rather than an existing structure, to be what corresponds to a picture. The wartime notebooks yield no decisive evidence that Wittgenstein took this step, although the Truth-Problem seems to fade from view in 1915–1916. What we do know is that two remarks absent from the Prototractatus (1971), together with an addition to a remark of the Prototractatus, are among the last items to make it into the Tractatus: 2.033 Form is the possibility of structure. (Emphasis mine) 2.15 That the elements of the picture stand to one another in a determinate way represents [stellt vor] things as so standing to one another. This connection of the elements of a picture is called its structure, and the possibility of this structure its form of depiction [Form der Abbildung]. (Emphasis mine)

90  Sanford Shieh 2.151 The form of depiction is the possibility that the things stand to one another as do the elements of the picture. (Emphasis mine) 2.033 and 2.151 are not in the Prototractatus. 2.15(1) is Prototractatus 2.151.2.15(2) incorporates an addition to the following remark of Prototractatus: 2.15101 This connection of the elements of a picture is called its form of depiction. Through these additions, Wittgenstein distinguishes crucially structure from form. He thus takes the step merely contemplated in the Notebooks, and now incorporates the notion of possibility. Thus, the final coming into being of the Tractatus involved the adoption of a structure/form distinction. The significance of this distinction is, among other things, a transformation of the meaning of a number of formulations from “Notes on Logic” and Notebooks: • • • •

Propositions are facts. Propositions are pictures of facts. A proposition pictures a fact by having a form that the fact also has. The truth and falsity of propositions result from a comparison of propositional facts with what they picture, namely, facts in the world.

In the Tractatus, the meanings of these formulations are inflected with modality, in virtue of the notion of form’s incorporation of a primitive conception of possibility. A key effect of this transformation is the notion of state-of-things (Sachverhalt): 2.031 In a state-of-things objects stand to one another in a determinate way. 2.032 The way in which objects hang together in a state-of-things is the structure of the state- of-things. In view of 2.033, we see that a state-of-things is the realization or the obtaining of a possibility. A state-of-things “obtains” (besteht) just in case a possibility of things standing to one another in a determinate way is realized. Picturing in the Tractatus is fundamentally modal. A  picture is a fact. According to 2.15(2), the “connection of the elements of a picture is called its structure.” So, the elements of a picture are in fact connected in the determinate way which is the structure of the picture. Again according to 2.15(2), the “form of depiction” is the possibility of this structure, the

Modality 91 possibility of the elements being connected in that determinate way. But, to repeat, the elements are actually connected. Hence the form of depiction, the possibility of connection, is realized by the obtaining state of pictorial elements. A picture is a realization of a form. Suppose that the possibility of structure realized by a picturing fact is also a possibility for the things correlated with pictorial elements to be connected in a state-of-things. Then the picturing fact can represent a possible obtaining of a state-of-things involving the objects correlated with the pictorial elements. A picture is true if the possibility it presents as obtaining is realized by the things whose representatives are the elements of the picture. The falsity of a picture consists of the non-realization by things of the possibility presented by that proposition.8 Distinct unrealized possibilities individuate distinct falsehoods. This allows reinstating negative facts: they are unrealized possibilities. We have almost overcome the Truth-Problem of propositions. The modal nature of picturing is, in the first place, the modal nature of thought, which, according to Tractatus 3, is logical picturing of facts. Propositions are a subset of logical pictures: those which have sense-perceptible expression. And so the nature of picturing blocks the Truth-Problem by incorporating modality into the nature of propositions. Modality gains its central place in the Tractatus in virtue of founding a coherent conception of falsity and truth of thought and proposition. Let’s recapitulate the role of the historical-philosophical investigation in establishing this conclusion. The proximate ground for the Tractarian conception is that it furnishes a coherent conception of falsity. To see how it does, one has to see that, and how, in Wittgenstein’s wartime notebooks, the falsity of propositions posed a philosophical problem. Fully to grasp that problem, however, requires one to realize that the notion of proposition about which the problem arises is articulated in Wittgenstein’s “Notes on Logic.” The philosophical significance of that notion of proposition for Wittgenstein, which also shows why he took a coherent account of falsity to be indispensable, lies in its being an attempt to resolve Russell’s difficulties in formulating a theory of judgment that could be part of a satisfactory conception of logic. This justification of modality does not rest on “intuitions” of the plausibility of thought and talk of objects existing in non-actual states of affairs, as Bradley claims in a passage cited earlier (1992, p.  134). Wittgenstein is not arguing that, because we find it intuitively plausible that there are such things as counterfactual circumstances or states of the world in which actual objects occur, these entities exist. The argument is, rather, that unless the presence or absence of states-of-things is realizations or otherwise of possibilities, there is no coherent conception of thought that is open to falsity as well as to truth.

92  Sanford Shieh The modal nature of propositions is not the whole story of how the Tractatus brought modality back into logic. In particular, one might wonder, what becomes of Aristotle’s idea of deductive validity as conclusions following “out of necessity” from premises? Any answer would have to make something of 5.131, where “the truth of one proposition following from the truth of others” is said to “express itself” through “internal” relations of “the form of these propositions.” But what I make of it is for another occasion.9 4.2  Kripke and the Second Return of Modality Wittgenstein in the Tractatus (along with C. I. Lewis in writings culminating in Symbolic Logic)10 brought modality back from its banishment by Frege and Russell. This was the first return of modality in the history of analytic philosophy. But not the only one. There was a second exile, at the hands of Quine. And a second return, effected most prominently, albeit not solely, by Kripke.11 To clarify the philosophical bases of Kripke’s justification of modality, I start with the impetus for Quine’s critique of quantification into modal contexts, Carnap’s account of modality in Philosophy and Logical Syntax and The Logical Syntax of Language. One of the aims of these works is to provide a way out of traditional metaphysical debates which are inconclusive and fruitless “because there was not even a common criterion for deciding the controvers[ies]” (Carnap 1963, p. 44). Carnap advocates a way of correlating “material mode” sentences which “seem to concern . . . objects, such as the structure of space and time, the relation between cause and effect, . . . the necessity, contingency, possibility or impossibility of conditions, and the like” with “formal mode” sentences which “concern linguistic forms” (1935, pp. 59–60). Focus on the formal mode points towards ways of specifying linguistic frameworks in which one could provide explicit and precise standards for evaluating claims. This enables replacement of perplexities and disputes over metaphysical questions about the real nature of objects by pragmatic questions about the relative advantages and disadvantages of various language systems. In the case of modality, Carnap proposes correlating impossibility, as a quality of states of affairs, with the syntactical property of being a contradictory sentence of a language system, and the necessity of a situation with the syntactical property of being an analytic sentence of that system. One philosophical perplexity that Carnap aims to dissolve by moving to these syntactic replacements of modal properties concerns what he takes to be Wittgenstein’s Tractarian notion of essential or internal property: in the material mode, a “property of an object c [such that] it is inconceivable that

Modality 93 c should not possess it (or: [] c necessarily possesses it)” (1937, p. 304).12 This “definition” leads to an antinomy: Being related to Charles is an essential property of [the father of Charles]. But being a landowner is not an essential property of the father of Charles. For, even if he is a landowner, it is conceivable that he might not be one. On the other hand, being a landowner is an essential property of the owner of this piece of land. . . . Now, however, it happens to be the father of Charles who is the owner of this piece of land. [Thus]it is both an essential and not an essential property of this man to be a landowner. (Carnap 1937, p. 304) Carnap proposes to dissolve this apparent contradiction by replacing the second-order property of being an essential property with the syntactical property of relative analyticity: a predicate is analytic relative to a sequence of “object designations” just in case the sentence resulting from filling the place-holders of the predicate with these terms is analytic. Applying this translation scheme to the problematic essential properties of the example, the contradiction disappears because “ ‘landowner’ is an analytic predicate in relation to the object-designation ‘the owner of this piece of land’, but it is not an analytic predicate in relation to the object-designation ‘the father of Charles’ ” (1937, p.  304). We now see that the puzzle engendered by the material mode definition of essential property “lies in the fact that it is referred to the one object instead of to the object-designations, which may be different even when the object is the same” (1937, p. 304). In this particular case, one might additionally think of the source of the trouble in another way. What is conceivable about an object, the example suggests, depends on how one thinks of or describes it, and these different ways are expressed by different “object-designations,” that is, different definite descriptions. So, to the extent that essence is fixed by (in)conceivability, we determine what is essential or not to some object by how we speak of it. Carnap thus proposes classifying properties such as being essential as “pseudo-object” or “quasi-syntactical”: they seem to be properties of extra-linguistic objects, but are applied as if they are properties of the language we use to mention these objects. Let’s call essential or necessary properties explicated in this way “Carnapian.” Many contemporary analytic philosophers are likely to have heard that Quine objected to quantifying into modal contexts. What precisely this means we see from Quine’s earliest presentations of his objection to modality. Existential generalization from a modal sentence like (5) 9 is necessarily greater than 7

94  Sanford Shieh that is, inferring (6) Something is necessarily greater than 7 from (5) is unwarranted. Quine in fact claims that (6) is “meaningless” (1943, p. 123). Quine’s principal reason for this conclusion is this: One and the same number x is uniquely determined by the condition:

(7) √x = x + x + x ≠ x and by the condition:



(8) There are exactly x planets,



but (7) has “x > 7” as a necessary consequence while (8) does not. Necessary greaterness than 7 makes no sense as applied to a number x; necessity attaches only to the connection between “x > 7” and the particular method (7), as opposed to (8), of specifying x (1953, p. 149).

Whether an object has the property of being necessarily greater than 7 depends on how that object is specified, that is, by what condition it is picked out. Hence, it is, in Carnap’s terms, a pseudo-object property, just like the property of being an essential property. Quine accepts Carnap’s explications of modality, considered as pseudoobject properties of states of affairs, in terms of metalinguistic predicates—analytic and contradictory—of sentences describing these states of affairs. Quine of course is skeptical about whether there is a defensible explication of analyticity. But modulo doubts about analyticity, and Quine never rejects this Carnapian explications of modality. His critique of modality relates to Carnap’s explication of necessary properties of objects in terms of relative analyticity. The claim that something has a necessary property is replaced by the (metalinguistic) claim that a sentence formed by putting a designation of the object in the placeholder of a predicate expressing the corresponding non-modal property is analytic. Different designations or specifications lead to different verdicts about the analyticity of the resulting sentences, and so different verdicts about whether the necessary property holds of the object. Suppose now we ask: is there an object that has this necessary property? There is no determinate answer. Reverting to Quine’s example, there is an object necessarily greater than 7, if we think of that object as uniquely determined by condition (7). But if we think of that object as uniquely determined by condition (8), it doesn’t have that modal property, so we can’t conclude that there is an object necessarily greater than 7. More generally, objectual quantificational generalizations over modal properties have no determinate

Modality 95 truth conditions. But then there is no meaningful explication of modal properties of objects. Now, it’s clear that, if we toss out the verdict determined by condition (7), or that determined by condition (8), then we would obtain determinate truthconditions for the existential quantification (6). This is what Quine means by “adopting an invidious attitude toward certain ways of uniquely specifying [the object], and favoring other ways” (1961, p. 155). But, Quine in effect asks, “What basis is there for rejecting some specifications and retaining others?” All these conditions are, after all, ex hypothesi satisfied by the object. It is at this point that Quine brings in “Aristotelian essentialism”: the favored specifications are those “somehow better revealing the ‘essence’ of the object” (1961, p. 155). If, say, satisfying condition (7) is an essential property of 9, but satisfying (8) is not, then any property whose possession by 9 follows from 9’s satisfying (7) is necessary to 9, but not so for properties consequent on 9’s satisfying (8). Clearly unless these essential properties are not determined by how objects are described or thought of, they would collapse into Carnapian essential properties, and so wouldn’t provide any answer to Quine’s criticism. Call essential or modal properties understood in this way “essentialist,” as opposed to “Carnapian.” But are there essentialist essential properties? Quine has argued that essentialism leads to contradictions, using a variation on Carnap’s example of the land-owning father of Charles (1960, p. 199). I will not go into this argument, since Ruth Marcus (1961, pp. 317–319) outlines persuasive grounds against its success. Marcus’s arguments, however, don’t overturn Quine’s critique of quantification into modal contexts. Even if the idea of essentialist essential properties implies no antinomies, it doesn’t follow that there are coherent and non-arbitrary standards, fixed independent of conditions satisfied by object, for ascriptions of such properties. Quine’s critique remains a challenge to essentialism. The challenge is taken up by Saul Kripke in “Naming and Necessity”: [I]t is very far from being true that this idea [that a property can meaningfully be held to be essential or accidental to an object independently of its description] is a notion which has no intuitive content, which means nothing to the ordinary man. Suppose that someone said, pointing to Nixon, “That’s the guy who might have lost”. Someone else says ‘Oh no, if you describe him as ‘‘Nixon’’, then he might have lost; but, of course, describing him as the winner, then it is not true that he might have lost’. Now which one is being the philosopher, here, the unintuitive man? It seems to me obviously to be the second. The second man has a philosophical theory. The first man would say, and with great conviction, “Well, of course, the winner of the election might have been someone else. The actual winner, had the course of the campaign been different, might have been the loser, and someone else the winner; or

96  Sanford Shieh there might have been no election at all. On the other hand, the term ‘Nixon’ is just a name of this man”. When you ask whether it is necessary or contingent that Nixon won the election, you are asking the intuitive question whether in some counterfactual situation, this man would in fact have lost the election. (NN, p. 265; emphases in original) Together with “Identity and Necessity” (Kripke 1971), this text completed the second return of modality to analytic philosophy. Kripke’s defense of essentialism here has two parts. First, he holds that names have no descriptive content. In contrast to ‘the winner of the election’, which describes its referent, ‘Nixon’ “is just the name of this man.” The ground for this lies in our intuitions. We accept, intuitively that, for example, “no one other than Nixon might have been Nixon” (NN, p.  270), while the winner of the election might not have been the winner. Thus, proper names such as ‘Nixon’ designate their actual referents with respect to any counterfactual circumstances we use this expression to describe (provided that the actual referent exists in those circumstances). Definite descriptions such as ‘the winner of the election’ refer to distinct entities in distinct counterfactual circumstances. This is of course the now familiar distinction instituted by Kripke between names as rigid designators and descriptions as non-rigid. A consequence of this distinction is that a name provides no materials for drawing analytic consequences from conditions satisfied by its bearer, that is, it doesn’t afford a basis for ascribing Carnapian modal properties to the bearer. However, and this is the second part of Kripke’s defense of essentialism, we nevertheless intuitively accept ascription of modal properties using names; for instance, the “ordinary man” accepts that Nixon might have lost the election. These intuitions indicate a pervasive prephilosophical agreement on ascriptions of essential and accidental properties to objects, independent of how they’re described. Kripke’s answer to Quine’s challenge to modality is like Grice and Strawson (1956)’s reply to Quine’s attack on the analytic/synthetic distinction. In the presence of systematic non-collusive agreement on ascriptions of essential and contingent properties to objects, there is no need to specify the principles underlying these claims in order to justify their use. The existence of such agreement represents, in effect, a “common criterion for deciding controversies” that Carnap sees as missing in traditional metaphysical disputes. Kripkean intuitionally based essentialism may therefore be understood as an attempt to justify traditional metaphysical theorizing about modality. It should now be clear that there is a fundamental difference between Kripke’s justification of modality and that of Wittgenstein in the Tractatus.

Modality 97 Modal intuitions, more precisely, pervasive agreement in modal intuitions, play a foundational role in the Kripkean justification. In contrast, as we’ve seen, intuitions of modality play no role in Wittgenstein’s argument that a primitive conception of possibility underlies a coherent conception of thought about the world open to falsity as well as truth. I turn now to doubts about the success of Kripke’s intuitionally grounded justification of modality. One of the most striking uses Kripke makes of his intuitively grounded essentialism is to argue “that certain statements of identity between names, though often known a posteriori, and maybe not knowable a priori, are in fact necessary, if true” (Kripke 1971, pp. 153–154). The argument begins by establishing the necessity of all identities expressed using only rigid designators. Let a and b be rigid designators. Our intuitions expressed using them then reveal essentialist modal properties of their referents. Intuitively, it’s not possible for a not to be a. So, being identical to a is a necessary property of a. Now suppose b is identical to a. Then b is just another name for a so every property that a has b also has. So, b is necessarily identical to a.13 It follows that even empirically established identity statements, such as Kripke’s best-known examples Hesperus is Phosphorus Heat is molecular motion express necessary truths, provided that they contain only rigid designators. I want to look at an objection to this conclusion which Kripke discusses explicitly. Some “people feel the other way” (Kripke 1971, p. 154) about the necessity of identity, and this feeling comes from a certain “idea” that they have: What is the idea people have? They say, “Look, Hesperus might not have been Phosphorus. Here a certain planet was seen in the morning, and it was seen in the evening; and it just turned out later on as a matter of empirical fact that they were one and the same planet. If things had turned out otherwise, they would have been two different planets, or two different heavenly bodies, so how can you say that such a statement is necessary?” (Kripke 1971, p. 155; emphases mine)14 Kripke here gives voice to an intuition that conflicts with the necessity of identity, and so with the essentialism on which it is based. Evidently he is committed to rejecting it. However, intuitions are the foundation of Kripke’s defense of essentialist modal properties. So, the question is, how

98  Sanford Shieh can he reject this particular intuition, call it the Hesperus intuition, without rejecting modal intuitions in general? Kripke’s strategy is this. When we say, (9) Hesperus might not have been Phosphorus, we are attempting to express an intuition of a genuine possibility of nonidentity, but not the possible non-identity of Hesperus and Phosphorus. We are, rather, either intuiting that an object similar to Phosphorus might not be identical with Hesperus, or that an object similar Hesperus might not be identical to Phosphorus. “Similar” here reflects two Kripkean ideas. It satisfies the same “description used to fix [the] reference” (Kripke 1971, p. 157) of “Phosphorus” or of “Hesperus.” It also means that those who fixed the reference of these terms are “in the same epistemological situation” with respect to the heavenly bodies picked out by the reference-fixing descriptions (Kripke 1971, p. 157, n. 15). This genuine intuition of contingency is mistakenly expressed as (9). It is correctly expressed as (10) The first object that appears in the evening sky might not have been identical to the last object that appears in the morning sky. Since (10) contains the reference-fixing descriptions of the names occurring in (9), it is easy to confuse the two, and use (9) instead of (10) to express what we are really, correctly intuiting. The crucial point is this. Faced with a purported modal intuition that conflicts with the necessity of identity, Kripke reconstrues the expression of that purported intuition, sentence (9). It seems that (9) expresses an intuition that an object, free of any descriptive way of thinking of it, has a modal property, the property of being possibly distinct from Phosphorus. But, in fact, Kripke claims, the intuition that “people” are really trying to express is that this object, thought of in the reference-fixing way given by a description, has the modal property of being possibly distinct from Phosphorus. The real intuition is not about an essentialist modal property, but a Carnapian modal property. But now, here’s another expression of an intuition of contingency: (11) Nixon might have lost the election Kripke of course takes to express the intuition that Nixon, independent of being described or thought about in any way, has the (essentialist) modal property of possibly losing the election. Call this the Nixon intuition. But if Kripke holds that (9), containing rigid designators, does not in fact express

Modality 99 an intuition about an essentialist modal property of a planet, why should one not hold that (11), also containing a rigid designator, does not in fact express an intuition about an essentialist modal property of a person? If is (9) reconstrued as (an attempt to) express a Carnapian modal property of a planet, why should we not equally reconstrue (11) as expressing a Carnapian modal property of Nixon, one that he has in virtue of being thought about in some way, say, as the 36th vice president of the USA? Why should the Hesperus intuition be explained away while the Nixon intuition is taken at face value? Prima facie, Kripke’s reason for favoring the Nixon intuition is that it’s the basis for essentialism. Prima facie, the reason for the invidious attitude to the Hesperus intuition is that it’s contrary to the necessity of identity. Why is this an adequate reason for not taking the Hesperus intuition at face value? As we have seen, Kripke’s argument for the necessity of identity depends on the premise that statements in which only rigid designators occur express intuitions about essentialist modal properties. Thus, the ground of necessity of identity is, in the end, nothing other than essentialism. Hence, the reason for discounting the Hesperus intuition is, ultimately, that it is contrary to essentialism. It follows that, prima facie, modal intuitions do not constitute grounds for justifying essentialism independent of essentialism. Kripke’s intuitionally grounded justification of essentialism is circular.15 The Hesperus intuition is not the only one that Kripke needs to reconstrue. Here is another much-discussed intuition of contingent identity. If a statue is made by shaping a lump of clay, then it seems to be nothing other than that lump of clay. If one were to mash up the statue, then the statue would ceases to exist. But the lump of clay remains a lump of clay. Hence, the statue is only contingently the same thing as the lump of clay.16 Another intuition goes against Kripke’s view that origin or constitution is essential to artifacts and organism. It seems perfectly coherent for a potential customer at a furniture shop to say to the salesperson, “If this table had been made wood of instead of plastic, I would buy it.”17 Is the customer not, prima facie, expressing the intuition that one and the same table might have had a different material constitution? It remains unclear that there is pervasive pre-philosophical and intuitive agreement on which properties are essential and which contingent to which entities. Ultimately, it seems that Kripke, as he puts it, “has a philosophical theory,” and it’s this theory, not modal intuitions, that grounds his reply to the Quinean challenge to modality. So, prima facie, Kripke hasn’t rehabilitated traditional metaphysics in face of Carnapian doubts, nor has he answered Quine’s challenge to the coherence of generalizations over modal properties. Since the Tractarian argument for primitive possibility does not rest on modal intuitions, it is not vulnerable to the troubles over conflicting intuitions we have now canvassed. This, of course, is not to claim that there are no problems with the Tractarian modal account of the nature of representation

100  Sanford Shieh of the world. But it shows that, in one respect, the Tractarian justification of modality is in less problematic shape than the Kripkean justification. 4.3  The Undepictability of Form It would be misleading to conclude simply that while the Tractatus offers a viable account of the role of modality in the philosophy of logic, it’s open to question whether “Naming and Necessity” successfully answers Quinean doubts about modality. Such a conclusion suggests that my account of modality in the Tractatus so far seems to be something like part of a philosophical theory of thought. Clearly this conflicts with the view, especially emphasized in the resolute approach to the book, that Wittgenstein presents no philosophical theories in it, because it is (mostly) mere nonsense. In this concluding section, I suggest that my reading is in fact consistent with one strand of resolution. I start with the idea that there is no depiction of logical form. Tractarian primitive possibilities are forms of depiction. Some pictures depict by spatial form. This means the depiction of possible spatial states-ofthings by realizations of possibilities of spatial configurations. As Wittgenstein puts it: 2.171 The picture can represent every reality whose form it has. A spatial picture anything spatial, a colored anything colored, etc.18 But possible spatial situations may be depicted, in speech, by temporal configurations of sounds. Such pictures nevertheless require some common possibility of structuring, logical form: 2.18 What any picture, of whatever form, must have in common with reality to be able to depict it at all—correctly or incorrectly—is logical form, that is, the form of reality. A picture that depicts by logical form is a logical picture, and thoughts are logical pictures. But forms of depiction are not depictable: 2.172 A picture cannot depict its form of depiction, however; it shows it forth [es weist sie auf]. To appreciate the significance of this undepictability, I dwell briefly on an account of what logical form is, and why there is no picturing of it, drawn from Sullivan (2001). In a spatial picture of spatial configurations, for example, that a wooden block is to the left of another may represent that a car is to the left of

Modality 101 another. That being to the left holds of the blocks, which is the picturing fact, represents that this very relation, being to the left holds of the cars depicted. How this spatial relation in this picture or model represents is “transparent” (Sullivan 2001, p.  107); one need not consult a key to grasp that its holding in the picture represents its holding in the situation depicted. One might say that, in a spatial picture, the relative spatial positions and relations of what is represented occur, as it were, in propria persona in that which represents. Similarly, the occurrence of a patch of green in a photograph, or a “naturalistic” painting represents, say, a lawn’s being green, even if not exactly the same shade of green.19 This contrasts with a patch of green on a computer screen’s display of a weather map, which does not represent, say, a city and its surroundings as all colored green. The occurrence of green in the photograph and the painting is transparent; it represents its own instantiation in what is depicted. One might object that the green patch represents the color of the lawn, not the greenness of a part of a canvas or a region of a photograph. But what color of the lawn? Green, of course, the color of that part of the depicting canvas or photograph. Here’s another example of representing in propria persona. In The Messenger, John Malkovich, as is said, “plays” Charles VII; that is, his presence and actions in the film represent the presence and actions of Charles VII. But, in Being John Malkovich, he plays himself; he figures in propria persona in what the film depicts. This, of course, is not to deny that Malkovich is Malkovich and not a picture of him. Who would think otherwise? It is obvious that picturing does not require pictorial elements to be representatives of themselves. A green patch could stand for rain; Malkovich could play Charles VII; one dot’s being to the left of another could represent one note to be played earlier than another. Conversely, the inscription “green” could stand for the color green; Tom Hanks could play Malkovich; some sounds occurring earlier than some others could stand for one car’s being to the left of another. These alternatives to propria persona representation “abstract” from “material identity” of pictorial element and depicted entity (Sullivan 2001, p. 109). But “abstracting from” some aspect of what is pictured is possible only if something else can take its place, can be its representative or proxy, in the picture. We can abstract from spatiality of what is pictured because, for example, temporal relations can stand in place of spatial relations in a non-spatial picture of a spatial configuration. Now, if there is some element of any picture that cannot be proxied, then that element must represent in the way that green in a photograph represents the lawn’s being green, or being left of in a model composed of blocks represents being left of holding of cars, or Malkovich taking to Catherine Keener represents himself talking to Maxine Lund. That element would

102  Sanford Shieh represent itself, occur in propria persona, in what is depicted. And if that aspect is logical form, then we have a line of thinking for the conclusion that every picture must have logical form. So, why must there be something in every picture that represents in this propria persona way, by occurring also in the depicted? Here’s an answer. One could abstract from the spatiality of depiction by using a non-spatial relation in place of a spatial relation, and non-spatial relata in place of spatial relata, but it’s hard to see how one could abstract away from some relation’s holding of the same number of relata to picture a spatial relation’s holding of that number of spatial relata. One might say that, for example, something standing in some relation to another thing is the most abstract, “non-material,” way in which a specific spatial fact, consisting of one block being left of another, is put together. This “way of being put together” is the limit of abstraction. Nothing can take its place, be its proxy, in a fact if that fact is to picture the fact that one car is left of another. And, of course, the maximally abstract “way” in which this depicted fact “is put together” is also that something stands in some relation to another. This maximally abstract way of being put together is logical form. But now, why is logical form not depictable? We canvassed in the preceding cases of propria persona picturing, where facts in which occur some relation or object depict facts about that very same relation or object. Logical form, on the conception just formulated, occurs in every depicting fact in the sense that it’s the maximally abstract “way” the depicting fact is “put together,” and occurs in every fact depicted by being also the same “way” in which the depicted “put together.” Why aren’t these cases of propria persona depiction? Why isn’t each picture, put together in a way that is its logical form, a depiction of the very same way of being put together, the very same logical form, of the fact it depicts? The answer to these questions lies in the Tractatus distinction between form and structure. The “way in which things are put together” in a fact, which in the foregoing account of logical form we had been identifying with form, is not in fact form, but rather structure. Form is the possibility of structure. The “way” in which pictorial elements are “put together,” are “connected,” is the structure of the depicting fact. In actually having this structure, the depicting fact realizes that possibility of being so connected which is its form. In realizing form, the pictorial fact is thereby capable of depicting things as connected, as “put together,” in the same “way,” into a structure that realizes that same possibility.20 But pictures can be false. The possibility realized by the picturing fact may in fact not be realized by those things. If a picture is false, then the things proxied are not connected, not “put together,” in the “same way” that their proxies are connected in the picturing fact. There always is a “determinate” (2.15) combination of

Modality 103 pictorial elements. But with falsity, there is no combination of things that corresponds to the picturing fact. Let me put the point in another way. A consequence of form’s not being structure is that, contrary to what Wittgenstein had considered in Notebooks, what is essential to picturing is not the correspondence of something in reality to something in a picturing fact. A  thought is a logical structure, but its representativeness does not lie in its corresponding to a situation with the same logical structure. The reason is that, while truth is correspondence of structure with structure, falsity is not. Reality, we see from 2.06, is the “obtaining and not-obtaining of states-ofthings.” In reality, there are only things and presence or absence of connections of things. So, form, that is, possibility, is not an aspect of reality. If logical form is that which makes all picturing possible, then it is neither in the picturing fact nor in the reality pictured. Logical form is distinct from any pictorial element or way in which pictorial elements are connected. The view of logical form we had been considering, as the limit of abstraction from parochial forms of depiction, misconceives form. On that view, logical form is supposed to be undepictable because there cannot be a pictorial element standing in its place. So, it is thought to be the structure that is in all picturing facts. But, on the interpretation I’ve been developing, logical form is neither pictorial element nor structure. That is why there is no depiction of logical form. To take logical form to be undepictable, and so unthinkable, is not, however, to take sentences apparently about possibility and necessity to be merely “entirely empty,” merely nonsense. There is no depiction of form, but a picture “shows forth” its form.21 Diamond has argued that Wittgenstein aims at bringing readers of the Tractatus to recognize the “selfdefeatingness” of some of its sentences, and thereby to “redirect[] our attention” to certain “logical features of the use of ordinary sentences” (Diamond 2002, pp. 270, 259). Logical form and forms of depiction are some of these features, so that the point of the apparent philosophical theory of modality is to bring us to a recognition of their showing forth. Notes 1 References to the Tractatus (Wittgenstein 1922) are by remark number only. My English translations very occasionally depart in small ways from the two standard ones, and I am much indebted to Michael Beaney for sharing with me a version of his forthcoming translation. The reader is advised to consult the original. 2 Some even more recent commentators who sees a significant role for modality in the Tractatus are Glock (2006), Ricketts (2014), Zalabardo (2015), and Floyd (2016, 2018).

104  Sanford Shieh 3 References to “Notes on Logic” (NL) are in the form x-y for manuscript x, remark y, except when x=S, in which case the reference is to remark y of Russell’s “Summary” at the beginning of “Notes.” 4 Mihaela Fistioc pointed out to me that, taking Othello factually, it’s not clear that belief state (3) is false. 5 They are recounted in Shieh (forthcoming(a), forthcoming(b)). 6 The Notebooks will be cited by date of entry. 7 See Narboux (2009) for an illuminating discussion of the relations between Plato’s discussion of not-being and falsity in the Sophist and Wittgenstein’s concerns leading to the Tractatus. 8 I ignore here a complication. According to 4.022, “a proposition shows how things are [wie es sich verhält],” but “how things are” may be that they realize a possible connection, or that they don’t realize that possible connection. Truth and falsity have different constitutions in these two cases. I discuss this complication in Shieh (2021b). 9 I tell the full story in Shieh (forthcoming(b)). 10 Apart from Symbolic Logic (1932), Lewis’s principal responses to Russell are in Lewis (1912, 1913, 1917, 1918). I discuss Lewis’s critique of Russell in Shieh (2017, 2021a). 11 I discuss this return in much greater detail in my (2013, Sections 4–13). 12 In the Tractatus, ‘essential’ is applied mostly to linguistic entities, but 2.011 speaks of what is ‘essential’ (wesentlich) to a thing (dem Ding). ‘Internal’ (intern) is often applied to relations, but see 4.123, inter alia, where it’s applied to a property (Eigenschaft) of a thing (Gegenstand). 4.123 is most likely what Carnap is alluding to. 13 The line of thinking presented here is an intuitive version of the derivation of thesis 2.31 in Barcan (1947, p. 15); see also Marcus (1961, pp. 308–309), who uses a notion of “tagging” objects with proper names, an early version of Kaplan (1989)’s notion of direct reference. See also Wiggins (1980, pp. 109– 110; 2001, 114–115) and Williamson (1996). 14 Kripke perhaps sees this “feeling” as what underlies Quine’s response to Marcus emphasizing “empirical” discoveries of identities between names as “tags” (1961, p. 327). 15 My account of Kripkean essentialism, and of the key role of reconstruals in its justification, is deeply influenced by Della Rocca (1996, 2002). My argument differs from Della Rocca (2002) in using Carnapian modal properties instead of anti-essentialist counterpart theories.   Häggqvist (2006)’s reply to this line of argument focuses on a different argument for the necessity of identity, apparently not requiring essentialism as a premise, but rather only the premise that ‘Hesperus’ and ‘Phosphorus’ are rigid designators. For, given this premise, the statement ‘Hesperus is Phosphorus’ describes, in every possible world in which the planet Venus exists, the selfidentity of Venus, and so is necessarily true. But rigid designation, as we’ve seen, is also grounded on modal intuitions. Hence Kripke still faces the question: why the invidious attitude towards the Hesperus intuition? 16 The original example is discussed in Gibbard (1975). 17 The example is derived from one in Levin (2007), who, however, appears to insist that what the customer says is in fact incoherent. 18 For discussion of spatial form see Ricketts (1996). 19 I’m grateful to the editors for pointing out that this qualification is required. 20 There’re complications here involving the “projective relation” of 3.12 and 3.13, but I set them aside.

Modality 105 21 Of course “shows forth” in 2.172 is a rendering of “aufweisen”. However, it is connected to the “showing” of ‘zeigen’ in 4.121: “A proposition shows [zeigt] the logical form of reality. It shows it forth [weist sie auf].” For an illuminating discussion of the notions of showing or showing forth in the Tractatus, see Narboux (2014).

References Aristotle (1964) Analytica Priora, edited by W. D. Ross. Clarendon Press. Barcan, Ruth C. (1947) The Identity of Individuals in a Strict Functional Calculus of Second Order, Journal of Symbolic Logic 12(1), 12–15. Bradley, Raymond D. (1992) The Nature of all Being: A Study of Wittgenstein’s Modal Atomism. Oxford University Press. Carnap, Rudolf (1930) Die alte und die neue Logik, Erkenntnis 1(1), 12–26. Carnap, Rudolf (1935) Philosophy and Logical Syntax. Kegan Paul, Trench, Trubner & Co. Carnap, Rudolf (1937) The Logical Syntax of Language, translated by Amethe Smeaton. Kegan Paul, Trench, Trubner & Co. Carnap, Rudolf (1963) Intellectual Autobiography, in P. A. Schilpp (ed.), The Philosophy of Rudolf Carnap, The Library of Living Philosophers XI, Open Court, 3–84. Cartwright, Richard (1987) Philosophical Essays. MIT Press. Cartwright, Richard (2003) Russell and Moore, 1898–1905, in Nicholas Griffin (ed.), The Cambridge Companion to Bertrand Russell. Cambridge University Press, 108–127. Della Rocca, Michael (1996) Essentialists and Essentialism, The Journal of Philosophy 93(4), 186–202. Della Rocca, Michael (2002) Essentialism versus Essentialism, in Tamar Szabó Gendler and John Hawthorne (eds.), Conceivability and Possibility. Clarendon Press, 223–252. Diamond, Cora (1988) Throwing Away the Ladder, in Cora Diamond, The Realistic Spirit: Wittgenstein, Philosophy, and the Mind. MIT Press, 179–204. Diamond, Cora (2002) Truth Before Tarski: After Sluga, After Ricketts, After Geach, After Goldfarb, Hylton, Floyd, and Van Heijenoort, in Erich H. Reck (ed.), From Frege to Wittgenstein: Perspectives on Early Analytic Philosophy. Oxford University Press, 252–279. Floyd, Juliet (2016) Chains of Life: Turing, Lebensform, and the Emergence of Wittgenstein’s Later Style, Nordic Wittgenstein Review 5(2), 7–89. Floyd, Juliet (2018) “Ultimate” Facts? Zalabardo on the Metaphysics of Truth, Australasian Philosophical Review 2(3), 299–314. Frege, Gottlob (1879) Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. L. Nebert. Gibbard, Allan (1975) Contingent Identity, Journal of Philosophical Logic 4(2), 187–221. Glock, Hans Johann (2006) Truth in the Tractatus, Synthese 148(2), 345–368. Goldfarb, Warren (1997) Metaphysics and Nonsense: On Cora Diamond’s The Realistic Spirit, Journal of Philosophical Research 22, 57–73. Grice, H. P. and Strawson, P. F. (1956) In Defense of a Dogma, The Philosophical Review LXV(2), 141–158.

106  Sanford Shieh Häggqvist, Sören (2006) Essentialism and Rigidity, The Philosophical Quarterly 56(223), 275–283. Kaplan, David (1989) Demonstratives: An Essay on the Semantics, Logic, Metaphysics, and Epistemology of Demonstratives and other Indexicals, in Joseph Almog, John Perry, and Howard Wettstein (eds.), Themes from Kaplan. Oxford University Press, 481–563. Kripke, Saul A. (1971) Identity and Necessity, in Milton Munitz (ed.), Identity and Individuation. NYU Press, 135–164. Kripke, Saul A. (1972) Naming and Necessity, in Donald Davidson and Gilbert Harman (eds.), Semantics of Natural Language, 2nd edition. Reidel, 253–355. Levin, Janet (2007) Can Modal Intuitions be Evidence for Essentialist Claims? Inquiry 50(3), 253–269. Lewis, C. I. (1912) Implication and the Algebra of Logic, Mind 21(84), 522–531. Lewis, C. I. (1913) A New Algebra of Implications and Some Consequences, The Journal of Philosophy, Psychology and Scientific Methods 10(16), 428–438. Lewis, C. I. (1917) The Issues Concerning Material Implication, The Journal of Philosophy, Psychology and Scientific Methods 14(13), 350–356. Lewis, C. I. (1918) A Survey of Symbolic Logic. University of California Press. Lewis, C. I. and Langford, C. H. (1932) Symbolic Logic. The Century Co. Marcus, Ruth Barcan (1961) Modalities and Intensional Languages, Synthese 13(4), 303–322. Moore, G. E. (1901) Truth and Falsity, in James M. Baldwin (ed.), Dictionary of Philosophy and Psychology, Vol. I. The Macmillan Company, 716–718. Narboux, Jean-Philippe (2009) Négation et totalité dans le Tractatus de Wittgenstein, in Christiane Chauviré (ed.), Lire le Tractatus de Wittgenstein. Vrin, 127–176. Narboux, Jean-Philippe (2014) Showing, the Medium Voice, and the Unity of the “Tractatus”, Philosophical Topics 42(2), 201–262. Plato (1985) Sophist, edited by John Burnet. In Platonis Opera, Vol. I. Clarendon Press. Quine, Willard V. (1943) Notes on Existence and Necessity, Journal of Philosophy 40, 113–126. Quine, Willard V. (1953) Reference and Modality, in From a Logical Point of View, 1st edition. Harper/Row, 139–159. Quine, Willard V. (1960) Word and Object. Technology Press of the Massachusetts Institute of Technology. Quine, Willard V. (1961) Reply to Professor Marcus, Synthese 13(4), 323–330. Ricketts, Thomas (1996) Pictures, Logic, and the Limits of Sense in Wittgenstein’s Tractatus, in Hans Sluga and David G. Stern (eds.), The Cambridge Companion to Wittgenstein. Cambridge University Press, 59–99. Ricketts, Thomas (2014) Analysis, Independence, Simplicity, and the General Sentence-Form, Philosophical Topics 42(2), 263–288. Russell, Bertrand (1904) Meinong’s Theory of Complexes and Assumptions (III), Mind 13(52), 509–524. Russell, Bertrand (1905) Necessity and Possibility, in Alasdair Urquhart and A. C. Lewis (eds.), Foundations of Logic, 1903–05, Collected Papers of Bertrand Russell, Vol. 4. Routledge, 407–420.

Modality 107 Russell, Bertrand (1984) Theory of Knowledge, in Elizabeth Ramsden Eames and Kenneth Blackwell (eds.), Theory of Knowledge: The 1913 Manuscript, Collected Papers of Bertrand Russell, Vol. 7. Allen & Unwin, 1–178. Schlick, Moritz (1930) Die Wende der Philosophie, Erkenntnis 1(1), 4–11. Shieh, Sanford (2013) Modality, in Michael Beaney (ed.), The Oxford Handbook of the History of Analytic Philosophy. Oxford University Press, 1043–1081. Shieh, Sanford (2017) Pragmatism, Apriority, and Modality: C. I. Lewis against Russell’s Material Implication, in Peter Olen and Carl Sachs (eds.), Pragmatism in Transition: Contemporary Perspectives on C. I. Lewis. Palgrave Macmillan, 103–145. Shieh, Sanford (2021a) Strict Implication and the Pragmatic A  Priori, in Quentin Kammer, Jean-Philippe Narboux, and Henri Wagner (eds.), C. I. Lewis: The A Priori and the Given. Routledge, 104–131. Shieh, Sanford (2021b) What could be the Great Debt to Frege? Or, Gottlobius ab paene omni naevo vindicatus, Disputatio. Philosophical Research Bulletin 10(18), 5–62. Shieh, Sanford (forthcoming(a)) Wittgenstein and Russell. Elements of the Philosophy of Ludwig Wittgenstein. Cambridge University Press. Shieh, Sanford (forthcoming(b)) Necessity Regained. Vol. 2 of Modality and Logic in Early Analytic Philosophy. Oxford University Press. Stegmüller, Wolfgang (1966) Eine modelltheoretische Präzisierung der Wittgensteinschen Bildtheorie, Notre Dame Journal of Formal Logic 7(2), 181–195. Sullivan, Peter M. (2001) A Version of the Picture Theory, in Wilhelm Vossenkuhl (ed.), Ludwig Wittgenstein: Tractatus Logico-Philosophicus. Akademie Verlag, 89–110. Sullivan, Peter M. and Johnston, Colin (2018) Judgments, Facts, and Propositions: Theories of Truth in Russell, Wittgenstein, and Ramsey, in Michael Glanzberg (ed.), The Oxford Handbook of Truth. Oxford University Press, 150–192. von Wright, Georg Henrik (1982) Modal Logic and the Tractatus, in Wittgenstein. Blackwell, 185–200. Wiggins, David (1980) Sameness and Substance. Harvard University Press. Wiggins, David (2001) Sameness and Substance Renewed. Cambridge University Press. Williamson, Timothy (1996) Knowing and Asserting, Philosophical Review 105(4), 489–523. Wittgenstein, Ludwig (1922) Tractatus Logico-Philosophicus, translated by F. P. Ramsey. Kegan Paul, Trench, Trubner & Co. Wittgenstein, Ludwig (1971) Prototractatus: An Early Version of Tractatus LogicoPhilosophicus. Cornell University Press. Wittgenstein, Ludwig (1979a) Notebooks, 1914–1916, 2nd edition, edited by G. H. von Wright and G. E. M. Anscombe, translated by G. E. M. Anscombe. Basil Blackwell, abbreviated as NB. Wittgenstein, Ludwig (1979b) Notes on Logic, in Notebooks, 1914–1916, 93–107, abbreviated as NL. Zalabardo, José L. (2015) Representation and Reality in Wittgenstein’s Tractatus. Oxford University Press.

5 Does It Make Sense to Say That the Standard Meter Is One Meter Long? Alexandre N. Machado

5.1 Introduction Consider the following imaginary dialogue between Wittgenstein and Kripke: Wittgenstein: I’d like to know how long this table is. Kripke: It is this long [putting one hand on one end of the table and the other hand on the other end].1 Wittgenstein: But that I can see! And even if I could not see, I know that if an object A is between other two, B and C, in such a way that there is no space between A and B and between A and C, the distance between the A’s end touching B and A’s end touching C is the same as the distance between B and C. What I don’t know is the length of this table according to some measurement system, like the metric one, or the British one. Kripke: Oh, I also know that. From now on I’ll call the length of this table ‘table’, and anything that is as long as this table will be one table long; if it is twice longer, it will be two tables long, and so on. Now I know that this table is one table long. Is this what you wanted to know? Wittgenstein: How many meters long is this table? Kripke: Well, I don’t know that. But I know how long this table is according to a measurement system, and that is what you wanted to know, isn’t it? To anyone who has never read Kripke’s Naming and Necessity, he would appear to be acting very weird in this dialogue. At least prima facie he would appear simply not to understand Wittgenstein’s questions. Someone who has read Kripke’s book might say that, although Kripke does understand Wittgenstein’s questions, he gives at most useless answers, even DOI: 10.4324/9781003240792-6

Does It Make Sense to Say That the Standard Meter  109 if they are true. If there is something Kripke doesn’t understand in this dialogue, the Kripkean might say, is at most that Wittgenstein wants a useful answer. This chapter can be seen as an attempt to show, among other things, that failing to see that Wittgenstein wanted useful answers is failing to understand his question. In the next section, I’ll outline what Kripke says in Naming and Necessity that somehow would justify the strange things he says and does in this imaginary dialogue. Someone might think that this dialogue does not present Kripke’s position in a charitable way. I hope that what I’m going to say in next section will undo this impression, as long as I’ll show that what Kripke says and does in this dialogue is completely in accordance with his theory of contingent a priori statements. I must stress that nothing of what follows is a general critique of the theory of contingent a priori statements. All I aim to show is that the example of contingent a priori statement Kripke offers when he criticizes Wittgenstein is not a good one. Therefore, to object that there are better examples is simply irrelevant to my point. And it is philosophically important to show that Kripke’s example is not good because Kripke’s mistakes are based on misunderstandings about the nature of our practices of measuring with standards, and because this kind of misunderstandings about our practices happens in other philosophical discussions, like in the one about how to analyze the statement ‘I am here’, for example. 5.2  Kripke and the Contingent A Priori Kripke wants to show that the concepts of a priori and necessity, as long as they are applied to statements, not only are different concepts but also are not coextensive. That is to say, he wants to show that there are necessary statements the truth-value of which can be known only a posteriori and that there are contingent statements the truth-value of which can be known a priori. A type of statement that, according to Kripke, provides examples of a contingent a priori statements is the one by means of which one attributes a property F to an object a that is taken to be the standard of F. Kripke thinks that when a is contingently F and the statement ‘Fa’ is made right after the baptism of the property F, the baptizer of this property can know a priori that this contingent fact is the case. It is by discussing the standard meter example that Kripke formulates his critique of Wittgenstein. The standard meter is a stick the length of which was, until not long ago, taken to be the standard of one meter.2 Let’s call this stick ‘S’, like Kripke does. That S is the standard of one meter entails that it is a necessary and sufficient condition for something x (an object or distance) to be one meter long that x is as long as S. But when S was chosen to be the standard meter, it might have

110  Alexandre N. Machado happened that it had not the length, say, C, it actually had. Therefore, S contingently had the length C at that moment. But it turns out that C is just one meter long. Therefore, S was contingently one meter long at that time. But the standard meter’s baptizer knows, after the baptism, without the need of any empirical investigation, that S is one meter long. Therefore, he knows that a priori. But if the statement ‘S is one meter long’ is contingent, then the baptizer knows a priori that this contingent statement is true. A natural reaction to Kripke’s argument is to say, like Norman Malcolm (1995) did, that if one meter is the length of S, then it is not possible for S not to be one meter long, for that would be possible only if S could not have the length it has, only if S could be different from itself.3 Kripke’s answer consists in showing that this objection is based on the false assumption that the statement ‘Meter is the length of S’, when said by the baptizer during the baptism, is a definition that determines the meaning of ‘meter’. Of course, if ‘meter’ was synonymous with ‘the length of S’, then to say that the length of S is not one meter would be synonymous with saying that the length of S is not the length of S. Kripke, however, claims that although the statement ‘Meter is the length of S’, when said by the baptizer, can be said to be a definition of ‘meter’, it is not a definition that determines the meaning of this term. What this definition does instead is to fix the reference of ‘meter’. At the instant t0, when the baptizer baptized it, S was contingently related to the length that was fixed as the reference of ‘meter’. The standard for one meter, therefore, is not simply the length of S, but it is its length at t0. Although the description ‘the length of S at t0’ serves to fix the reference of ‘meter’, it is not introduced in the baptism as synonymous with ‘meter’. In some other possible world, this description refers to other lengths different from the length the baptizer has fixed as the reference of ‘meter’. Therefore, in these other worlds, S’s length is not identical to the meter, but it is rather longer or shorter than the meter. That entails that in the description of these counterfactual situations, the word ‘meter’ has the reference the baptizer has fixed. And that is true about any counterfactual situation he describes using ‘meter’. That is to say, the word ‘meter’, according to Kripke, refers to the same thing in all possible worlds. This of course is not the denial that there is a possible world different from the actual one where the word ‘meter’ either is used to refer to another thing or has no reference. It only means that, whatever possible world that we, in the actual world, describe using the word ‘meter’, in all these descriptions this word refers to the same thing. Expressions having this feature are what Kripke calls rigid designators. The expression ‘the length of S’ in its turn, like most definite descriptions, is not a rigid designator, for in some counterfactual situations that we describe using this expression its reference is not the meter.

Does It Make Sense to Say That the Standard Meter  111 As one can see, the a priori knowledge in question is based on the knowledge of a simple definition. But the statement one knows to be true, according to Kripke, is not analytic. It is rather a statement about a contingent fact instead. In other words: the statement has as its epistemic basis the knowledge of a definition, but such a definition is not what makes it true. Now it is easier to understand Kripke’s weird behavior in the dialogue in the preceding. He seems to be supposing the following theses: (1) Anyone can name any measure one can refer to. (2) Measures are abstract entities, which are in a contingent relation with the objects that have them. (3) We can only refer to a measure through the reference to objects that have them (we don’t have a Platonic eye). (4) Anyone who names a measure by means of the reference to a certain object that has this measure knows a priori that this object has this measure. One should notice that ‘measure’ in these theses refers to any measure: of length, of weight, of volume, of intensity, etc. If one accepts these theses, one should accept that one could know a priori the measure of anything one can refer to, just by thinking. One does not need to be in the presence of the object in order to know its measures. I have never been in Winston Churchill’s presence. But I can refer to him through his name. Thanks to that I can refer to his properties using his name in descriptions. For example, I can talk about Churchill’s height at the time he uttered the famous sentence ‘I have nothing to offer but blood, toil, tears, and sweat’. Now I define (fix the reference of) ‘winchill’ like this: Winchill = Winston Churchill’s height at the time he uttered the famous sentence ‘I have nothing to offer but blood, toil, tears, and sweat’. Now I know a priori that Churchill was one winchill tall at that moment. And in the same way, I can know a priori his weight and volume at that time, as well as the intensity he uttered that famous sentence, etc. At the end of the dialogue earlier, Kripke does nothing but applying these consequences of the theses (1)–(4) to the table’s case. Kripke has created a measurement standard, he has named the length of that particular table and, thus, he could know a priori its length according to this new standard, this new measurement system. 5.3  Comparison, Self-predication and Identity Wittgenstein does not agree that one can (meaningfully) say of an object that serves as a standard of a certain measure that it has this measure.

112  Alexandre N. Machado But that is not because that object has a different measure. According to Wittgenstein, one cannot (meaningfully) say of that object that it does not have this measure either. Wittgenstein says so in a famous section of the Philosophical Investigations, which is quoted by Kripke in an also famous passage of Naming and Necessity, and then he proceeds to criticize it. Wittgenstein says something very puzzling about this. He says: “There is one thing of which one can say neither that it is one meter long nor that it is not one meter long, and that is the standard meter in Paris. But this is, of course, not to ascribe any extraordinary property to it, but only to mark its peculiar role in the language game of measuring with a meter rule”. This seems to be a very “extraordinary property”, actually, for any stick to have. I think he must be wrong. If the stick is a stick, for example, 39’37 inches long . . ., why isn’t it one meter long? (NN, p. 54)4 And Kripke goes on saying that the statement ‘Meter is the length of S at t0’ only fixes the reference of ‘meter’ and does not determine its meaning. Kripke is right about one point: Wittgenstein’s claim is in fact puzzling, weird. And that’s why Nathan Salmon is right when he says that “Kripke has more plausibility on his side than Wittgenstein does” (Salmon 1988, p.  195). At a first sight, at least, Wittgenstein’s claim seems to be false indeed. If the standard meter is not (but neither fails to be) one meter long, what else could be it? But here, like elsewhere, Wittgenstein is trying to show differences, in despite of the similarities, being less important how the difference is described than perceiving it. At the end of this chapter, I’ll show that Wittgenstein’s point can be laid down in a, say, inverted way. The point now is that, although something might be counter-intuitive at the first sight, it can become obvious under reflection. The argument suggested by Kripke’s last quoted sentence is the following: (i) S is 39’37 inches long. (ii) 39’37 inches = 1 meter. (iii) Therefore, S is 1 meter long. But how do we know that these premises are true? How do we justify them?5 The premise (i) is justified when one measures S with a yardstick to find out that it is 39’37 inches long. The premise (ii), a conversion rule, is justified by inferring it from two propositions: the premise (i), and the proposition (iv) that S’s length is the standard of one meter. Therefore, the content of (ii) would be expressed more clearly in this way: 39’37 = the length that is the standard of one meter. But is (iv) the proposition that S is one meter long? If it was, then Kripke’s argument would be circular. But if

Does It Make Sense to Say That the Standard Meter  113 it isn’t, how could (iii) be the conclusion aimed at by Kripke? All one can validly conclude is that S has a length that is the standard of one meter, not that S has the same length of the standard, for this would entail that one can compare S to itself. When one says that a certain object is one meter long, one says something about a possible comparison between a certain object and the standard meter: that is, that the object is as long as the standard meter (or n times smaller or n times bigger). But how can one say that of the standard meter itself? In order to clarify this question, let me say something about what it means to say that S is the standard of one meter. The property of being a standard is not a natural property. To be a standard is to be used in a certain way in our linguistic practices. A standard is an object of comparison. Therefore, in general, something that cannot be compared to other objects cannot be a standard. There is a system of measurement with a standard of length only if there is an object (or a repeatable phenomenon), the length of which is the standard and if this object can be compared to others. And if the standard can be compared to the other objects, then the other objects can be compared to it. Therefore, an object has a measure in this system only if it can be compared to the standard.6 But if to be a standard of a measurement system is to be used in a certain way in our linguistic practices, then a standard is something that lasts in time, not something located at an instant of time. Thus, if S is the standard of one meter, then S’s length, whatever it is, at any time, is being taken to be the thing to which we should be able to compare to an object in order for this object to have a measure in the metric system. That’s why to say that S is 39’37 inches long is a reason to say that any object that is 39’37 inches long, if compared to S, will be as long as S and, because of that, it will be one meter long. But if the possibility of comparison to S is a necessary condition for anything to have a length in the metric system, then S should also satisfy this condition. But how can we compare S to S? What would this comparison consist in? We cannot put S alongside S in order to see if it is as long as S. That simply makes no sense. And if one cannot compare S to S, S cannot be the standard by means of which one tells what its size is. This possibility of comparison, according to Wittgenstein, is essential for an object to be a standard. But if this possibility is a necessary condition for anything to have a length in the metric system, and S cannot satisfy it, then S has no length in the metric system. In Kripke’s argument, S plays no role as the standard meter in order to reach the conclusion. Proposition (iv) does say that S’s length is the standard of one meter. But this saying does not imply that S is being used as a standard of the metric system in order to determine S’s length in this very system. In other words: S is not being used as a standard, what is indeed being used is only the information that it is a standard. Therefore, Kripke’s argument

114  Alexandre N. Machado does not show that we can say of the standard meter what we can say of any other object when we say that they are one meter long, that is, that they are as long as the standard meter. For this would imply that we could compare the standard meter to itself, what Wittgenstein claims to be impossible. Wittgenstein’s argument, as I  interpret him, could be formulated as follows: (1) For all x, if x has a length in the metric system, it is possible to compare x to S. (2) It is not possible to compare S to S. (3) Therefore, S has no length in the metric system. From now on, until Section 5.5, I’ll deal with objections to premise 2. Not all of these objections are Kripke’s. In Section 5.6, I’ll take into account an important objection to premise 1.7 One could object that one can compare the length of S at t1 to the length of S at t2. But how does this comparison would be made? We cannot put S at t1 alongside S at t2. Well, at t1 one can mark the length of S in a surface and later, at t2, one can compare S to these marks. But what if S does not fit the marks at t2? Does that mean that S would not be one meter long anymore? If it does, then does that mean that these marks, not S’s length, would be the standard of one meter? Therefore, although this diachronic comparison is indeed possible, it is no reason to say of the standard meter that it is or is not one meter long according to this standard. In his remarks on the standard meter, Kripke makes no reference to the practice of comparing objects to the standard meter. Commenting Wittgenstein’s ‘puzzling’ claim, he says that “[p]art of the problem which is bothering Wittgenstein is, of course, that this stick [S] serves as a standard of length and so we can’t attribute length to it”.8 However, Kripke seems to think that nothing incompatible with his arguments for his favorite example of contingent a priori could come from a reflection about how something can ‘serve as a standard’, especially because he thinks that the standard meter could be the length of S at t0. If t0 was any date in the 19th century, for instance, how could one compare any object to the length of S at t0? But here another objection could be made: somehow one can compare an object to itself in thought, without the need of putting it alongside itself. When one says that the standard meter is one meter long one compares it to itself in thought. This objection is reinforced by a certain understanding of the law of identity as the claim that every object is identical to itself. It is as if there was something like to compare an object to itself in order to see that all the properties it has . . . it has, as if the object fitted perfectly to itself. Well in fact, one can investigate to find out whether an identity statement of the form x = y is or is not true. When one does that, one investigates to

Does It Make Sense to Say That the Standard Meter  115 find out whether there is or there is not some property that an object a has and an object b hasn’t or vice versa. Sure, one can describe this investigation as the process of comparing a to b. And if in fact a and b are the same object, then this is the process of comparing an object to itself. However what one does here is to make a comparison in order to find out whether a is the same as b, not to find out whether (or that) a certain object has the property F that it has. In order to see that these are different cases, it is enough to see that the comparison to discover the identity, in this case, is the same as the one to discover the difference. The comparison is the same, whether a and b are or are not the same object. That is different, to repeat, from a putative comparison to find out whether a certain object has a property F that it has. This is what should be possible to do, if it was possible to compare a standard to itself. In other words: this is what should make sense if it was to make sense to talk about the comparison of a standard to itself. But this simply makes no sense. Nevertheless, it seems that the kind of comparison at stake here is the one involved not in the investigation about the truth-value of an identity statement with the form x = y, but the one involved in the investigation about the truth-value of an identity statement with the form x = x instead. It seems that when one perceives an object, one somehow also perceives identity, one perceives that the object holds a certain relation with itself, viz., that of being identical to itself. This seems to involve a comparison of the object to itself, for if it is not done by this means, how could one verify that this relation holds? It seems that one perceives that the object fits to itself, not only regarding its length but also regarding all its properties: all the properties it has. We seem to have an infallible paradigm of identity in the identity of a thing with itself. I feel like saying ‘. . . If you are seeing a thing you are seeing identity too.’ (PI, §215) But how does this putative comparison take place? When I perceive an object, all I  perceive is an object having certain properties, nothing else. When I imagine an object, all I imagine is an object having certain properties, nothing else. The putative comparison is a chimera. 5.4  Abstracta One could object that, by claiming that the standard meter is one meter long, Kripke is not assuming that one can compare S to itself. The standard meter according to Kripke, as we have seen, is the length of S at t0 and this is an abstract entity in a contingent relation with S at t0, which is rigidly

116  Alexandre N. Machado referred to by means of the word ‘meter’. Therefore, if there is any comparison involved here it is the comparison of S to this abstract entity. But how does this putative comparison take place? Given that we don’t have Platonic eye, how can one compare an object to this abstract entity?9 How can we perceive one of the terms of the comparison, the abstract entity? One could think that one perceives it while it is contingently related to S, while S contingently has this length. But if this explains how one can compare S to this length in order to see that S has it, it should explain how one can do the comparison in order to see that S does not have that length, given that it is a contingent fact that S has it. But how can one make such a comparison? If what one wants to do is to check whether S at t1 is as long as it was at t0, assuming that its length at t0 is the standard, what one needs is something one can compare S to at t1. But if that cannot be the length of S at t0 itself, but something that is as long as S at t0, then what one does after all is comparing concrete objects, not a concrete object to an abstract entity. What one does is to take another object, R, as the standard of S’s length at t0 and compare it to S at t1 in order to find out whether they have the same length. In such a case, the standard of one meter is R’s length, not S’s length at t0. One could object that the standard of S’s length at t0 is R’s length, because R’s length is the same as S’s length at t0. Thus, it seems that after all what one is doing is to compare S to this length by means of the comparison of S to other object. But what if R’s length at t1 was different from R’s length at t0? Usually we hope that what we take to be a standard of length will not change in length in time. However, the fact that it varies does not prevent it from being a standard, especially when there is nothing else available the size of which varies less. A standard of length is a standard even though it is mutable in length. Of course, our search for immutable standards of length shows that we in fact have an ideal for standards of length, an idea that governs our search for better standards of length, that is, the idea of something the size of which does not vary in time. But does that mean that we know something like that? Do we have an ideal because we know an ideal standard? Or else is it because we know our ordinary mutable standards and have good reasons to wish the immutability of the standards that we create the ideal of an immutable standard? We hope that R at t1 is as long as it was at t0 in order that we can verify whether S in t1 is as long as it was at t0. If we find out that R’s length has changed from t0 to t1, that must be because we compare R to another object T, and we hope that T’s length has not changed from t0 to t1, and that it is as long as R at t0, and so forth. At some point in this process, we simply take the length of some object during time as the standard of the length of other objects at certain instants in

Does It Make Sense to Say That the Standard Meter  117 time. We don’t take—because we cannot take—the length of an object at an instant of time as the standard of the length of other objects. Therefore, once more it seems that all we do is to compare concrete objects, not a concrete object to an abstract entity. Besides, even if the possibility of comparing an object’s lengths along time (by comparing this object to another one) allowed us to explain how we can compare a concrete object to an abstract entity, this kind of explanation is not available in the most important case at stake: the alleged attribution of one meter to the standard meter. In the last case, the alleged comparison should be between a concrete object at t—S at t—and an abstract entity at t—the abstract meter at t. How would that happen? There are additional difficulties for the postulation of an abstract entity in the scription of length. For instance: What is exactly the relation between S and the putative abstract meter? S allegedly is one meter long because a certain relation holds between it and the abstract meter. But is what this relation? Is S one meter long because it is as long as the abstract meter? But then why is the abstract meter one meter long? Is it because it is as long as the abstract meter? But if in order to be one meter long S must be in a certain relation to the length of another entity, why this is not so in the case of the abstract meter? That would generate an apparently vicious infinite regress (and here we would have a kind of third man argument).10 And if in order to be one meter long the abstract meter does not need to be in a certain relation to another entity’s length, why does S need to be so? Why S isn’t one meter long just because it is as long S?11 So the abstract entity ends up useless. There is another problem. Taken as an explanation of what it is for an object to have a determinate length, Kripke’s explanation so interpreted seems to be circular: S’s being one meter long is its being as long as the abstract meter and the abstract meter is one meter long. But then what is for the abstract meter to be one meter long? So, by postulation an abstract entity to explain the practice of measuring the length of objects we end up either in a vicious regress, or with the uselessness of this entity, or with a circularity. But maybe the earlier objection is attacking a straw man, as long as it assumes that, according to Kripke, the abstract meter has a certain length. It would not have a length, but it would be a length. A  length does not have a length as much as a geometric form does not have a geometric form. Triangularity, for example, is not triangular. But then what relation holds between S and the determinate length called meter? Well it is that of having that length. But what is to have that particular length in this case given that it is not be as long as another thing (whether abstract or concrete)? Of course, to say that it is to be as long as S at t0 is to take as explained what we are asking for explanation. What is for S to have the length it has at

118  Alexandre N. Machado t0, given that it is not to be as long as another thing (whether abstract or concrete)? It is useless to say that S is one meter long at t0 when the meter is S’s length at t0. The question now would be: what is for an abstract entity to be the length of another thing? 5.5 ‘S Is One Meter Long’ It is worth noticing if it still is not clear, that Wittgenstein does not want to deny that one can say of S that it is or is not one meter long. His point is: when one can say that, S is not being taken as the standard meter, and for that reason one is not saying of the standard meter that it is one meter long according to this standard. Some interpreters however give examples of situations in which it seems perfectly plausible to say of S, qua standard meter, that it is one meter long and that Wittgenstein has never meant to deny it. I’ll examine just one of these examples (see Gert 2002) that seems to be very convincing at first sight, to show that it is not useful for their purposes. Imagine that a thief wants to steal the standard meter, S, and that it is in a poorly lightened room in which there are other sticks that serve as standards of lengths in other measurement systems. To be sure that he will steal the right stick, he uses a meter rod to measure the sticks and find the one that is one meter long. Once he finds, it he says, ‘This stick is one meter long; it’s the standard meter,’ and he takes it. It seems that, in this situation, the thief says of the standard meter that it is one meter long. And he comes to know this by measuring the standard with a meter rod, like he could come to know the same thing about any other object. The thief knows that his meter rod should be as long as the object he wants to steal, because he knows that his meter rod was made to be as long as the object he wants to steal, for that is the standard of that length. However, the case here is analogous to the one in which one wants to know whether S’s length has changed from t0 to t1 by drawing marks on a surface at t0. The standard of S’s length at t1 are those marks, not S’s length at t0 itself. Analogously, the standard of one meter in the process of measuring S during the robbery is the thief’s meter rod, not S. To see this, suppose that, due to cold temperature, S has shrunk and has become shorter than the thief’s meter rod, and another stick, R, longer than S, has also shrunk and has become as long as the thief’s meter rod. The thief measures S and discard it. Then he measures R and says, ‘This stick is one meter long; it’s the standard meter,’ and he takes it. If during this process of measuring the sticks S was the standard meter, then it should have been used in this process either to measure objects or to calibrate meter rods. But it was not used in either way. S was taken as any object that can be measured by a meter rod.

Does It Make Sense to Say That the Standard Meter  119 In fact, the thief says falsely that R is the standard meter. The standard meter is S. But in order for the last statement to be true it is not necessary for S to be used as the standard meter. What is necessary is that S has a certain history, that is to say, that it has been the stick the length of which was taken, by convention, to be the standard of one meter. In this sense, ‘The standard meter is S’ could be true even if S was not as long as the meter rod used to check whether something is or is not one meter long, for being a standard, in this sense, does not entail to have a particular length. Therefore, although there is a sense in which one can say that during the robbery S was the standard meter, it does not follow from that that it was then used as the standard meter. So, in one sense, S was the standard meter; in another sense, it wasn’t. Only if in this other sense it was the standard meter that this would be a counter-example of the claim criticized by Kripke. Of course, other people might take S as the standard meter during the robbery. If that was the case then there would be two standards of one meter: the meter rod and S. But S, while being measured by the meter rod, is not the standard of this length. If it was and was not as long as the meter rod, then the meter rod should be discarded as a means to verify whether something is one meter long. That shows that Wittgenstein’s point is not that one cannot say of a standard of one meter that it is one meter long according to some standard of one meter, but that one cannot say of a standard of one meter that it is one meter long according to the standard this very object is. 5.6  Metaphysics Versus Epistemology One could object that the whole foregoing discussion was based in the confusion between metaphysical questions and epistemological questions. Wittgenstein’s argument would not be cogent, because the first premise would be false. One thing would be the metaphysical question about what it is for an object to be one meter long. Another very different thing would be the epistemological question about how one gets to know that something is one meter long. Being one meter long is to be as long as S. And, of course, S is as long as S. Therefore, of course, S is one meter long. There is, in fact, a difference between the way one knows that S is one meter long and the way one knows that other objects are one meter long. But in both cases, being one meter long is the same thing. One knows that S is one meter long because (a) one knows that a convention has settled that something is one meter long if it is as long as S and (b) one knows, without any comparison, but based only on the law of identity, that S is as long as S. The confusion on which the preceding discussion would be based would consist in thinking that a condition to know that objects different from S

120  Alexandre N. Machado are one meter long—comparing them to S—is a condition for anything to be one meter long, S included. However, all that we can know based solely on the law of identity is that S, at any instant in time t, is as long as S at t. But that is not the substantial knowledge that the standard of one meter is one meter long, unless the standard was the length of an object at a certain instant of time. But even if one could name the length of a certain object at a certain instant in time, that would not be enough for that length to be the standard of this length. In fact, as we have seen, it would not be possible for such a thing to be a standard of length. A standard is something that lasts in time. What the baptizer knows about S’s length at a certain instant of time is something he can know about any length of any object at any instant in time: for any object x, at any instant in time t, x at t is as long as x at t. And to know that is not to know the length of something according to a system of measurement containing a standard. A fortiori, it is not to know any object’s length according to the metric system. On the other hand, to have a determinate length in the metric system entails that statements with the form ‘x is n meters long’ have truth-value, whether the truth, or the falsity. But in order for statements with this form to have a truth-value, it is necessary that there is a standard of one meter, an object that lasts in time as the standard (or a regular and repeatable phenomenon that other things can be compared to). Therefore, the existence of a standard is not a merely epistemic requirement. It is not only a way of verifying whether the appropriate relationship between other objects and a certain abstract length holds. It is a condition for the rest of the objects’ having a length in this measurement system. Besides, if the standard is something that can be compared to the other objects, then the other objects can be compared to it. So, if an object cannot, in principle, not even indirectly, not even probabilistically (like sub-atomic particles), be compared to the standard meter (like S itself), it has no length in the metric system. That last affirmation is not based on a verificationist thesis according to which an object has a certain length only if one can know or verify what this length is. Instead it is simply a reminder of how our practice of measuring objects’ lengths with a standard works: standards of measurement are made to determine the measures of comparable objects (see note 6). But let’s suppose that the objector reformulates his objection by saying that to be one meter long is to be as long as S at any instant in time, no matter how long S is at any instant in time, so that one knows, based solely on the law of identity, that S, at any particular instant in time t, is as long as S at t. Therefore, one knows, without any comparison, that S, at any instant in time, is one meter long. The problem is that so reformulated, this objection entails that the statement ‘S is one meter long’ is a necessary one. There is no possible world W in which S, at any instant t, is not as

Does It Make Sense to Say That the Standard Meter  121 long as S at t (in W). And if S is the standard meter, then it is not possible for the standard meter not to be one meter long. Therefore, such an objection could not be Kripke’s. Nevertheless, whether it is Kripke’s or not, is it decisive? Does it show that it makes sense to say of the standard meter that it is one meter long? In order to answer this question, we should examine closer what is the sense of ‘S is one meter long’ according to this objection. In particular, what is the difference between saying that S is one meter long in this sense and saying that one accepts the convention of calling S’s length ‘meter’ and taking it as a standard of length? It seems that there is none. And if there is none, is that what one says of R, the stick that the thief wrongly believes to be the standard meter, when one says, based on a measurement, that it is one meter long? Is one saying that one accepts the convention of calling R’s length ‘meter’ and taking it as a standard of length? Of course not, for R’s length is not the standard meter, it is not the last court of appeal to decide whether something is one meter long or not. R has a length that is the same as the standard meter’s length. But while this last statement is a statement about the relation between the lengths of two objects, one of which is a standard, the statement ‘S is one meter long’, according to the last objection, seems to express a convention (it is a ‘grammatical’ statement in Wittgenstein’s sense). Therefore, although the statements ‘S is one meter long’ and ‘R is one meter long’ have the same syntactical structure, it seems that both say different things, and not only because their grammatical subject is different but also because the predicate does not mean the same thing in both cases. Thus, although it does makes sense to say of S, qua standard of one meter, that it is one meter long, in this sense one cannot say of any other object that it is one meter long, unless it is also a standard of one meter, which is quite possible. And this is Wittgenstein’s ‘puzzling’ claim, say, upside down: in the sense that one can say of the standard meter that it is one meter long, one cannot say that of any other object, unless it is also a standard of one meter. And that partially explains why Wittgenstein’s claim in Philosophical Investigations, §50, seems to be false. It is worth noting that although ‘S is one meter long’ is a grammatical statement when it has the sense just explained, it is not an analytic statement, if an analytic statement is one that is true in virtue of its sense, as if its truth maker and its sense were the same thing. To say that the statement of a convention is true is to accept this convention, as in general to say that a normative statement is true is to accept this norm. What may make to be weird saying this is a substantial conception of truth, like the correspondence theory of truth, for example. As I have said in note 1, in the end, my interpretation of Wittgenstein’s claim about the standard meter and my assessment of the debate is close to Malcolm’s. But I  think my argumentative path is different and better

122  Alexandre N. Machado than his, because he fails to show that the senses Kripke tries to ascribe to the parts of the statement ‘S is one meter long’ deprive this sentence of any sense. To sum up: when we say of an object that is not the standard meter that it is one meter long, we are describing a contingent relation between this object and the standard meter, that is, that the object is as long as the standard meter, but when we say of the standard meter that it is one meter long, we are accepting the convention according to which its length is the standard of one meter. So, in the second case, we are not stating a contingent fact that can be known a priori. 5.7  What Are the Nonsense Bearers? But it seems that this way of interpreting what Wittgenstein says in that particular text implies that I am attributing to him what the so-called resolute interpreters of the Tractatus, specially Cora Diamond (1991) and James Conant (1990), have called a ‘substantial’ conception of nonsense.12 According to the resolute readers, the traditional interpretation of the Tractatus and, therefore, of the relation between the Tractatus and the Philosophical Investigations, paradigmatically represented by P. M. S Hacker’s exegetical work (1997), implies that when the young Wittgenstein says that the Tractatus’ sentences are nonsensical, he is saying either that their sense is nonsensical or that that set of sentences cannot have sense. Analogously, when I say that, according to Wittgenstein, it makes no sense to say of the standard meter neither that is one meter long nor that it is not one meter long, then I am attributing to Wittgenstein either the thesis that the sense of ‘S is one meter long’ makes no sense, or the thesis that this sentence cannot have sense. After all, am I not saying that in the sense that we can say of other objects that they are one meter long it does not make sense to say that of the standard meter? Am I not saying that in a sense ‘S is one meter long’ makes no sense? Am I not saying that by ascribing certain senses to the parts of ‘S is one meter long’ the resulting sense is nonsensical? What I am indeed saying is that if we want the predicate ‘x is one meter long’ in ‘S is one meter long’ to have the same sense as it has in ‘This table is one meter log’, for instance, and if we want ‘S’ to be the name of the standard by means of which one says that any other object is or is not one meter long, then the result is a nonsensical sentence. In other words: if in order to ascribe sense to the sentence ‘S is one meter long’, we ascribe to ‘S’ and ‘x is one meter long’ the senses these expressions have, for example, in ‘S is not part of the British system of measurement’ and in ‘This table is one meter long’, respectively, then we end up ascribing no sense to that first sentence. The problem here is analogous to ascribing to ‘3’ and ‘x is green’ the senses

Does It Make Sense to Say That the Standard Meter  123 these expressions have in ‘3 + 3 = 6’ and ‘The grass is green’, respectively, in order to ascribe sense to the sentence ‘3 is green’. The result is what is traditionally called categorical mistake.13 The difference is that in the case of ‘S is one meter long’ we need a complex reflection to realize that. So, I am not saying that a certain sense we ascribe to the sentence does not make sense. I am saying that certain senses its parts have in other sentences and its syntax are no guarantee of its having sense.14 Am I  saying that, given the senses of its parts in other sentences and its syntax, the sentence ‘S is one meter long’ cannot have sense? That the answer here should be ‘no’ is something that should be clear when I said that one could say of S, qua standard meter, that it is one meter long, although the predicate ‘x is one meter long’ in this case has not the same sense as in ‘This table is one meter long’. There is no sentence that could not have sense, even those sentence that violates rules of English grammar, for these rules might change according to appropriate conventions. But even admitting that ‘S is one meter long’ not only can have but actually has sense, that is not the denial of what Wittgenstein says in Philosophical Investigations, §50, as I interpret it.15 Notes 1 This dialog occurred to me after I had a real dialog with a philosopher friend of mine in which I played roughly Kripke’s part. The dialog was meant to start a discussion about what Wittgenstein and Kripke say about the standard meter. 2 According to Salmon (1988, p. 193), the standard meter is not in Paris, but in a town near Paris. And the standard meter is not the length of the stick kept there, but the distance between two marks in that stick. However, I will pretend that the common story about the standard meter is true. 3 I think that Malcolm’s position in this debate is close to the truth in the following way. As I  intend to show, the statement ‘S is one meter long’ has no sense if we try to ascribe certain senses to its parts. The only sense one can find in it makes it a necessary statement. Malcolm’s mistake is that he does not have a good criticism of Kripke’s interpretation of that statement. He fails to show why Kipke’s attempt to make sense of that statement is not successful. Cora Diamond (2001) seeks to defend Wittgenstein’s position against Kripke’s criticism, although she thinks that Malcolm is wrong by thinking that “that we cannot drive apart, even in counterfactual situation, the length of S and the standard meter length. The argument rests on the false idea that we cannot describe the counterfactual situation in terms of our own meter length” (p.  118, p.  189 in this volume). However, I  agree with Doron Avital (2008, pp. 326–328) that to grant what Malcolm denies leaves her open to Kripke’s criticism, for it is, as I hope to show, to grant the most problematic thing in Kripke’s theory: that the standard meter is S’s length at a certain instant in time. 4 Just before this passage Kripke says: Above I  said that the Frege-Russell view that names are introduced by description could be taken either as a theory of the meaning of names (Frege

124  Alexandre N. Machado and Russell seemed to take it this way) or merely as a theory of their reference. Let me give an example, not involving what would usually be called a ‘proper name,’ to illustrate this. Suppose someone stipulates that 100 degrees centigrade is to be the temperature at which water boils at sea level. This isn’t completely precise because the pressure may vary at sea level. Of course, historically, a more precise definition was given later. But let’s suppose that this were the definition. Another sort of example in the literature is that one meter is to be the length of S where S is a certain stick or bar in Paris. 5 In Section  5.6, I  address the criticism according to which I  am confusing a metaphysical question with an epistemological one. Now I am just assessing the argument to see if it can justify the thesis that one can say of the standard meter that it is one meter long in the same sense that we say so of any other object. 6 Of course, one cannot compare the standard meter to objects that don’t exist anymore and have left no traces of their existence, for example. But that is not an impossibility in principle (like that of the standard meter, as I am about to argue). If the standard meter existed at the same time as that object in question, or if it had left some measurable traces (which seems to be perfectly possible), then that object could be compared to it. 7 Oskari Kuusela, in ‘The Mirage of Contingent A Priori,’ published in this volume, also argues both that Kripke’s inches argument is not enough to conclude that one can say of the standard meter that it one meter long in the same sense we can say that of other objects. His main point is that something cannot be an object of measurement and a standard of this measurement at the same time, that “[t]he logical roles of an object of representation and a means of representation are mutually exclusive” (p. 160). But here I seek to show what is intrinsically wrong with Kipke’s argument, independently of Kuusela’s/Wittgenstein’s point: it is either a circular argument, or an argument the conclusion of which is not the one aimed at by Kripke. 8 This is not entirely correct. Wittgenstein is saying that it makes no sense to attribute a certain length to the standard if it is the standard of that length, not that it makes no sense to attribute any length to the standard at all. But I think that Kripke knew that and that his lack of accuracy here is not due his missing this point. 9 Had we a Platonic eye, we could imagine or conceive a determinate length without imagining or conceiving any concrete object. But any determinate length one imagines or conceives is the length of concrete objects we imagine or conceive. 10 One might think that the infinite regress in question is not vicious as long as the series it starts is not incompatible with any logical law. Whoever, if in order to know the length of an object we must go through the whole series, then this knowledge is impossible. And it seems that the antecedent is true according to the theory under consideration. If one knows that A is one meter long, then one knows that it is as long as B, which one knows to be one meter long. But if one knows that B is one meter long, then one knows that it is as long as C, which one knows to be one meter long. And so forth ad infinitum. But one’s knowledge of an object’s length cannot be constituted by an infinite series of knowledges of the length of an infinite number of objects. 11 That would be the case only if, contrary to what says premise 1 of Wittgenstein’s argument, in order to an object be one meter long (or any other length in the metric system) it would not be necessary to be possible to compare it to the standard meter.

Does It Make Sense to Say That the Standard Meter  125 12 The importance of considering this objection is at the same time exegetical and philosophical, as long as the conception of substantial nonsense is in itself problematic. Thus, not only an interpretation of Wittgenstein’s work that attributes him this conception might face the accusation of not being charitable, but also the philosophical plausibility of the argument I’m trying to present would be under suspicion, if it depended on this notion. 13 For a detailed discussion about how to conciliate the idea of a categorical mistake with a non-substantial conception of nonsense, see my (2007, Ch. IV, §7). 14 Wittgenstein discusses this point in Philosophical Investigations, §351, by taking as an example the sentence ‘Just now it was 5 o’clock in the afternoon in the sun’. 15 I’d like to thank my friend Giovani Felice for invaluable critical comments to the first version of this paper. I also thank the students of the Post-Graduation Program of the Universidade Federal do Paraná who have attended a course of mine about this theme in the first semester of 2009 and contributed with detailed discussion. I thank those who contributed with invaluable comments and criticism at the following philosophical meetings where I read versions of this paper: XIII Colóquio Conesul de Filosofia das Ciências Formais, in 2009, at the Universidade Federal de Santa Maria, especially Oswaldo Chateaubriand, Marco Ruffino, André Porto, and Luiz Carlos Pereira; a seminar about this paper I gave at the Universidade Federal do Rio Grande do Sul, in November 2011, especially my friends Jônadas Techio, Eros de Carvalho, and Alfredo Storck; Workshop Wittgenstein: Linguagem, Pensamento e Normatividade, at the Universidade Federal do Rio Grande do Sul and PUCRS, in May  2012, especially Paulo E. Faria, Marcel Niquet, Juliano do Carmo, and Nythamar de Oliveira. I thank Paulo E. Faria again for recent comments and criticism to this last version of the paper. Last, but not the least, I thank the anonymous readers who contributed with invaluable comments.

References Avital, Doron (2008) The Standard Meter in Paris, Philosophical Investigations 31(4), 318–339. Conant, James (1990) Throwing Away the Top of the Ladder, The Yale Review 79(3), 328–364. Diamond, Cora (1991) Throwing away the Ladder: How to Read the Tractatus, in C. Diamond (ed.), The Realistic Spirit: Wittgenstein, Philosophy, and the Mind. The MIT Press, 179–204. Diamond, Cora (2001/this volume) How Long Is the Standard Meter in Paris? In T. McCarthy and S. C. Stidd (eds.), Wittgenstein in America. Oxford University Press, 104–139. Gert, Heather J. (2002) The Standard Meter by Any Name Is Still a Meter Long, Philosophy and Phenomenological Research 65(1), 50–68. Hacker, Peter M. S. (1997) Insight and Illusion: Themes in the Philosophy of Wittgenstein. Thoemmes Press. Kripke, Saul (1972) Naming and Necessity. Basil Blackwell. Machado, Alexandre N. (2007) Lógica e Forma de Vida: Wittgenstein e a Natureza da Necessidade Lógica e da Filosofia. Coleção Prêmio ANPOF. Unisinos.

126  Alexandre N. Machado Malcolm, Norman (1995) Kripke and the Standard Meter, in G. H. von Wright (ed.), Wittgensteinian Themes: Essays 1978–1989. Cornell University Press. Salmon, Nathan (1988) How to Measure the Standard Metre, Proceedings of the Aristotelian Society 88, 193–217. Wittgenstein, Ludwig (2009) Philosophical Investigations, 4th edition. Blackwell.

6 Who Is Afraid of Truth Gaps? Wittgenstein and Kripke on the Standard Meter Jakub Mácha

Both Wittgenstein and Kripke employ the Standard Meter case to illustrate certain insights. For Wittgenstein, the Standard Meter case is analogous to the claim that “being cannot be attributed to an element” (PI, §50). Kripke, meanwhile, invokes the Standard Meter to illustrate his key distinction between fixing reference and giving meaning. Wittgenstein writes in §50 of Philosophical Investigations: One would like to say, however, that being cannot be attributed to an element, for if it did not exist, one could not even name it, and so one could state nothing at all about it.—But let us consider an analogous case. There is one thing of which one can state neither that it is 1 metre long, nor that it is not 1 metre long, and that is the standard metre in Paris.—But this is, of course, not to ascribe any remarkable property to it, but only to mark its peculiar role in the game of measuring with a metre-rule. These two cases—attributing being to an element and attributing a length to the Standard Meter—are analogous. Both attributions propose a truthvalue gap, that is, the absence of truth-value for a certain proposition. If being or existence “consists in the obtaining and non-obtaining of connections between elements” (ibid.), then an element can be said neither to exist nor to not exist. The Standard Meter can be said neither to be one meter long nor not to be one meter long. Such truth gaps may appear puzzling.1 An element is a regular object. Why then can it not be said that it exists and even necessarily so? The Standard Meter is a regular stick. Why then can it not be said that it is one meter long? Kripke finds this truth-value gap puzzling. But this is not because he would find any truth-value gap misguided. He proposes a gappy solution to the liar paradox, for instance: the liar sentence lacks a truth-value (Kripke 1975). What Kripke finds puzzling is the particular truth gap involved in the Standard Meter case.

DOI: 10.4324/9781003240792-7

128  Jakub Mácha In this chapter, I attempt to reconstruct Kripke’s account of reference in a way that does not imply any such gap. I then reconstruct the account of reference that is implicit in Wittgenstein’s Philosophical Investigations. Seen in this light, Wittgenstein and Kripke advance different accounts of reference. I will argue that both accounts are admissible: each has its advantages and disadvantages, and I  am not claiming that Wittgenstein is right and Kripke wrong or vice versa. This approach allows us to discern significant differences in what must be presupposed in their respective accounts of reference. My main aim is to uncover these presuppositions (rather than to consider their plausibility). I focus primarily on the Standard Meter case. In Naming and Necessity, Kripke invokes the Standard Meter primarily in the context of his discussion of proper names in the first lecture. I would like to transpose the discussion into the context of natural kind terms, which feature in the third lecture. “Meter” and “being one meter long” are not proper names. Rather, “being one meter long” is a description of certain things, akin to Kripke’s other examples of natural kind terms, such as “water,” “gold,” and “heat.” 6.1  The Underlying Reality A tacit assumption in Naming and Necessity is the distinction between phenomenal appearance and underlying reality. Appearances include our shared world as well as a person’s private sensations and the objects in their visual field, which are open to their view. Meanwhile, the underlying reality behind the phenomenal world can be discovered and described by science (it is not the unknowable Kantian thing-in-itself). The underlying reality is described by physical theories. A physical theory accounting for the underlying reality may turn out to be wrong. The underlying reality is not a flat collection of elements or basic particulars, but is structured into what are called “natural kinds.” A physical theory also accounts for basic ontological categories such as substance and length. It would perhaps be more appropriate to call such a theory ontological. As we shall see in the final section of this chapter, Kripke maintains that the identity of particulars across possible worlds can be accounted for in terms of more “basic” particulars. Then, however, the basic (or most basic) particulars must be the same in every possible world. Hence, the same basic reality is presupposed in every possible world. The aim of physical theories is to give an account of the basic particulars that reality consists of. 6.2  Fixing Reference One of the key elements of Kripke’s account of naming is the act of fixing reference, sometimes also called the initial baptism. As I read Kripke’s

Who Is Afraid of Truth Gaps? 129 numerous descriptions of this act, it goes as follows: an object from the world of appearance is used to fix the object of reference in the underlying reality. Water is the substance instantiated by the items over there at time t0. The items over there, which make up the paradigmatic sample of water, belong to the world of appearance.2 Substance is a general category of the underlying reality—an ontological category. It can be shown that this particular substance is in fact H2O. The “items over there” do not need to be regular objects. They can be a subjective sensation, as when fixing the reference of “heat”: heat is that which is sensed by sensation S at time t0. Here, the reference is fixed by the cause of the sensation, which is, as we know, a motion of molecules. If this sort of reference-fixing is supposed to be at all determinate, a physical theory must be presupposed. This presupposition can be integrated into the definition: Given molecular theory, water is the substance instantiated by the items over there at time t0. Given the theory of basic elements and atomic numbers, gold is the element instantiated by the items over there at time t0. Physical theory provides a general account of the target domain to which the reference-fixing points.3 The definition can make this more explicit: Water is the specific molecule or combination of atomic elements that is instantiated by the items over there at time t0. Heat is the best explanation of sensation S within molecular theory at time t0. If one assumes another physical theory, the fixing of the reference would be completely different: Heat is the element among the four basic elements that causes sensation S at time t0. Within this Aristotelian theory, the reference of “heat” would be fixed to fire. In his discussion of ostensive definition, Wittgenstein argues that its “place in language, in grammar” must be given or presupposed prior to the definition (PI, §29). What these places in language are supposed to be is clear from Wittgenstein’s examples: number, color, length. These examples of grammatical places are, in fact, general categories that are accounted for by physical theories (except of course that number is a different category, but that need not concern us here).

130  Jakub Mácha Kripke claims that specifications of a reference linking a term to a physical theory (such as “water is H2O”) are necessary and a posteriori. The reference-fixer does not know in advance what the reference is called within the physical theory. However, if the physical theory is presupposed, the necessity in question is de dicto. It is necessary that water is H2O within molecular theory. Note, however, that molecular theory can turn out to be wrong (as a whole or in this specific case). The theory is not necessarily true. Within this theory, the items over there (at time t0) must necessarily be explained as H2O. In other words, H2O must necessarily appear as the items over there (at time t0). This leaves open the possibility that the items over there might in fact have been appearances of a different substance, for example, H2O2. What looks like water could in fact be hydrogen peroxide. This is, I think, the point of Kripke’s considerations about fool’s gold (i.e., something that looks like gold, but is not actually gold). What is decisive in the initial baptism is the outward appearance. Gold and fool’s gold have the same appearance. The act of fixing reference, that is, the initial baptism, works as follows: there is an appearance that fixes an object in the underlying reality. The name of this object within the underlying reality may be initially unknown, or the full account of it may be incomplete at the moment of baptism. But the object must be de dicto determined in the act of baptism (e.g., the substance instantiated by the items over there). How then can the object be fixed? What does fix the reference, that is, uniquely determine the object of reference? It is the initial sample (the items over there) as it appears together with the physical or ontological theory. The only empirical evidence that is needed is that of the original sample or, to be more precise, of the appearance of the original sample. No additional empirical evidence is needed to determine that the sample is in fact H2O. The sample together with molecular theory must be enough. This reasoning calls into question Kripke’s claim about the a posteriori character of “water is H2O.” Clearly, the baptizer4 may not know this in advance. However, this knowledge can be elicited by theoretical work within the physical theory. This is, of course, an empirical theory, but one that is presupposed in the act of baptism. We can say that the baptizer must already have an implicit knowledge of what the reference is called within the physical theory. Only with these reservations can claims such as “water is H2O” be taken as a posteriori. But how is the reference maintained over time? The answer is that the physical theory must do the job. It must be deduced within the theory that this specific appearance (of the paradigmatic sample) must necessarily be caused by this or that molecular structure. I think this can be done within physical theories such as molecular or atomic theory. We can define water,

Who Is Afraid of Truth Gaps? 131 gold, or heat in the way Kripke proposes. I shall argue in the next section that the Standard Meter case is less straightforward. 6.3  The Standard Meter So far, we have focused on fixing the reference of water, gold, and heat. What is the relevant physical or ontological theory in the meter case? The meter is the length of S at t0. Kripke is not explicit about what theory is presupposed. The reference is “an abstract thing . . . a unit of length” (NN, p. 55). The theory of the underlying reality must postulate such things and maintain that they are unchanging. A  theory that postulates unchanging length must be something like the theory of absolute space as proposed by Aristotle or Newton.5 Absolute space is, in fact, not a physical theory. It is a philosophical way of conceptualizing space. In contrast to molecular theory, the (theory of) absolute space does not provide any link between the underlying reality and its appearance. It is only an account of the underlying reality. If we followed Kripke’s stipulation that the meter is the length of S at time t0, we would not have anything concrete in our hands (or anything that can play a role of paradigmatic sample in our practices of measurement). Kripke’s proposal amounts to pointing at a certain length, which is an abstract entity. However, there is no fixing, because the theory of absolute space provides no link between this abstract length and its appearance. This space is called absolute precisely because it is independent of its appearances.6 The theory of underlying reality must include a connection between its elements and their appearances (or, alternatively, there must be an additional theory accounting for this connection between appearance and reality). The problem of Kripke’s account of the meter is that he does not provide any such account of what the corresponding appearance of this abstract length is after the act of baptizing, say at time t1.7 In other words, Kripke does not provide any account of how to maintain the reference to the abstract length over time (in contrast to his accounts of water, gold, or heat). Let us transpose Wittgenstein’s account of the meter into Kripke’s framework. If we want to retain the idea of reference—which may be questionable within Wittgenstein’s later philosophy8—then Wittgenstein must assume that “meter” rigidly refers to the paradigmatic sample S (the Standard Meter). The object of the reference belongs to the appearance; it is not an object from the underlying reality (be it an abstract object or a concrete one). In fact, assuming or postulating the underlying reality is not necessary. “Meter” is not a proper name, but rather a unit of length. The definition must assume that the notion of length is clear enough. The definition is: one meter is the length of S at any time, in any counterfactual situation.9 Kripke’s way of

132  Jakub Mácha defining the meter has the general category determined by the theory of the underlying reality. In Wittgenstein’s case, no such theory is presupposed, and hence the general category must be determined in some other way. Length is a general category that must be assumed. Wittgenstein points out a similar assumption in his discussion of ostensive definition. I would like to argue that he does not provide any convincing solution to this problem. At the end of the day he invokes “what may be called ‘characteristic experiences’ of pointing, say, to the shape” (PI, §35). In our case it would be pointing at the length. My point is that it is disputable that there is any characteristic experience of (pointing at) length. And even if there were such an experience this reasoning would nevertheless be unsatisfactory because nothing guarantees that there are distinctive experiences of this kind for any general or grammatical category. However, in the second part of the Investigations Wittgenstein provides another way of tackling this problem. Measuring with a meter ruler does not require any philosophical or scientific account of the category of length. Wittgenstein expresses this idea in the following remark: What “determining the length” means is not learned by learning what length and determining are; rather, the meaning of the word “length” is learnt by learning, among other things, what it is to determine length. (PI II, §338) I read this remark as saying that a method of measurement of length (i.e., “determining the length”) does not need to presuppose any prior account of what length is in general. Measuring with the meter stick is an instance of determining length. All we need here is some method of finding out whether an object is the same length as the Standard Meter. Then we can say that what “length” means is learned by discovering, among other things, what it is to compare the lengths of two objects. This method may be quite simple: place the meter stick next to the measured object and see whether they are aligned, that is, one blocks the view to the other and vice versa. This is a primitive social practice that can be refined. The point is that such a practice determines what length is—rather than one’s account of length determining the practice.10 Hence, the definition of meter as the length of S is rooted in such practice. To recap: as I reconstruct their views, Kripke proposes that “meter” rigidly refers to the length of S at t0—that is, to the length that S accidentally has at t0. This length is an abstract object postulated by the theory of absolute space. Wittgenstein, in contrast, seems to presuppose that “meter” rigidly refers to S (i.e., to the Standard Meter).11,12 The advantage of Kripke’s account is that the general category, that is, length, is determined by the theory that postulates the existence of the object of reference, which is

Who Is Afraid of Truth Gaps? 133 the theory of absolute space. The problem with Kripke’s account is that the theory of absolute space does not provide any explanation for how its objects are connected to its appearances (in contrast to Kripke’s other examples of fixing reference). The advantage of Wittgenstein’s account is that no (theory of) underlying reality must be presupposed. It seems that the chief problem with Wittgenstein’s way of approaching the issue in question is that it leaves us with the obviously counterintuitive truth-value gap we alluded to earlier. In the next section, we will consider how serious this problem is. 6.4  Truth-Value Gap How can Wittgenstein claim of the Standard Meter that one can say neither that it is one meter long nor that it is not one meter long? What Wittgenstein proposes is a truth-value gap, an instance of paracomplete reasoning.13 Within the preparatory language-game of fixing reference, only the Standard Meter is the meter. In other words, “meter” is the name of the paradigmatic rod. Wittgenstein’s paradoxical claim, however, pertains to the “game of measurement,” as he makes clear in §50. To say that the Standard Meter is one meter long (or that it is not) is not the result of any measurement. If this claim were taken as an empirical result, it would be breaking the general rule of grammar that empirical statements must not be confused with conceptual ones. This claim would be ungrammatical nonsense. And any negation of ungrammatical nonsense is ungrammatical too.14 According to Wittgenstein, the Standard Meter rod has no definite length in terms of measuring it in meters (i.e., within the game of measurement with this very rod). I  think one could advance a stronger claim: within this specific game of measurement, the Standard Meter is always the same length, by definition, that is, by virtue of being the standard. This is, in fact, only a restatement of the claim that “meter” is a rigid designator referring to the Standard Meter. This is not a metaphysical peculiarity of the Standard Meter rod. The Standard Meter is always the same length within the game of measurement, because we decided that all attributions of length will be considered against the Standard Meter. All attributions of length in meters are based on the measured object’s ratio to the Standard Meter. All change of this ratio will be interpreted as an extension or reduction of the measured object (and not the Standard Meter). This does not exclude the possibility that within another game of measurement, say with the Standard Foot, the Standard Meter rod could have a definite length (in feet) and that this length could vary (relative to the Standard Foot). Kripke finds this truth-value gap puzzling. His argument goes as follows. First, Stick S can be measured by the Standard Foot. The outcome

134  Jakub Mácha of this measurement can be that it is 3.44 feet long. Second, the length of one meter is equal to the length of 3.44 feet. From these two claims, it follows that stick S is one meter long. The first claim is an a posteriori result of measurement. The second claim is an a priori ratio between these two lengths within absolute space. Thus reconstructed, Kripke’s argument is valid. We can say of stick S that it is one meter long. And because the first premise is contingent, so is this conclusion. Kripke, however, presupposes his own way of fixing reference. His argument concerns the stick that was used for fixing the reference of “meter.” When, at a later point in time t1, this stick is measured using the Standard Foot, it is not the standard. (After quoting Wittgenstein’s remark about the Standard Meter, Kripke, in formulating his argument, refers to it as “the stick” or “stick S.”) This alone is enough to dismiss his critique of the truth-value gap proposed by Wittgenstein. However, we can find more reflections in Wittgenstein about what is going on when two standards are involved. First, Kripke attributes to Wittgenstein the claim that we cannot attribute length to the Standard Meter. However, Wittgenstein does not claim this. In fact, one standard or paradigm can be used to measure another one, as Kripke maintains. Then, however, the standard that is measured (e.g., the Standard Meter measured by the Standard Foot) ceases to be a standard. Wittgenstein writes in the Philosophical Grammar: “One sentence can never describe the paradigm in another, unless it ceases to be a paradigm” (1974, p. 346). If the Standard Meter is measured by the Standard Foot, the object of this measurement is the bare rod S as if it were a quite ordinary object, disregarding its role as the standard. What is problematic within Wittgenstein’s framework is the second premise of Kripke’s argument. Can we unproblematically assume that 1 meter = 3.44 feet? Well, if these two standards are really independent, their ratio cannot be an a priori truth. The Standard Meter can be measured by the Standard Foot and vice versa. The second premise is not a priori but an a posteriori result of a measurement. For Kripke, in contrast, this ratio involves two abstract lengths and two numbers, and thus it is a priori. We can imagine two units of length that are not mutually independent. Their dependence can be simply stipulated. One unit can be stipulated as a portion of another one, for example, 1 centimeter = 1/100 of a meter.15 Or two units can share the same paradigmatic rod: that is to say, their references were fixed using the same initial sample at the same time. One can use the Standard Meter rod to fix the length of one meter and, at the same time, to fix the length of one centimeter as 100th of the length of this same rod. Then, the claim that 1 m = 100 cm would be a priori. But this is not the case of 1 meter = 3.44 feet. These two units were defined using different paradigmatic rods (and at different times). However, if the references of “meter” and “foot” are fixed in Kripke’s way, that is, referring to abstract lengths in

Who Is Afraid of Truth Gaps? 135 absolute space, then they can be related to each other after all. Their objects of reference, that is, these abstract lengths, partly overlap. Then, the claim 1 m = 3.44 feet is a priori, and thus his argument can succeed.16 Hence, Kripke’s argument against Wittgenstein’s truth-value gap fails, because Kripke assumes that Wittgenstein is fixing reference in his (Kripke’s) way. This does not imply that reference cannot be fixed in either way. As we already know, both ways have their pros and cons. Another question is whether Kripke’s way of rendering the Standard Meter case supports the key distinction he draws between fixing reference and giving meaning. The answer is that it could do so if one makes clear what the domain of reference (the underlying reality) is, that is, if one provides an account of absolute space. And this would not be enough. We would also need to provide an explanation of how this absolute space appears to us. This is something that we can imagine, on a charitable reading, could be provided for Kripke’s other examples (gold, water, and heat).17 If we fix reference in Wittgenstein’s way (i.e., as a rigid designator referring to the rod S any time), the difference between fixing reference and giving meaning collapses. “Meter” refers rigidly to S and it means “the length of S.” This approach does not illustrate the distinction, though this does not imply that the distinction is wrong or inconceivable. 6.5  Primary Elements Before concluding, let us focus in more depth on the difference between appearance and reality. The underlying reality consists of basic elements that everything, including any appearance, is made up of. Any acceptable account of appearance must explain how it is composed of basic elements. This can be done in the cases of gold, water, or heat. But the theory of absolute space does not provide any such basic elements. The length of an object is not composed of abstract lengths. There is no basic or smallest length in absolute space.18 In this connection, it is worth recalling what Kripke says about the problem of “transworld identification.” A  few pages before his critique of Wittgenstein’s account of the Standard Meter, he makes the following remark: “We seek criteria of identity across possible worlds for certain particulars in terms of those for other, more ‘basic’, particulars” (NN, p.  50). And furthermore, in a similar vein: “The question of transworld identification makes some sense, in terms of asking about the identity of an object via questions about its component parts” (NN, p. 53).19 These basic particulars or component parts are postulated by the physical theory and so belong to the underlying reality. Modal and existential claims are made about appearances. The item over there, as it appears to us, is H2O or has the atomic number 78. The substance over there is H2O, but it might

136  Jakub Mácha be another substance or a mixture of substances. These attributions are about the item over there as it appears, and what is attributed is framed in terms of the underlying reality. Then, however, existential and modal claims about the basic elements must be without truth-value or ungrammatical. Consider the claim that H2O exists. It can only mean that there is an appearance whose underlying structure is H2O. But again, this is a claim about appearance. If one insisted that H2O does not exist within molecular theory, it could only mean that the expression H2O does not have any meaning within this theory, that is, it is ungrammatical. The upshot is that Kripke’s basic particulars are akin to the primary elements that Wittgenstein speaks about in §§46–50 of his Philosophical Investigations. These basic particulars are postulated by the ontological theory that must be presupposed in the act of fixing reference. (And since these particulars are postulated by a theory, they are closer to the color squares discussed in §48 than to metaphysical simples invoked in Socrates’s dream in the Theaetetus.) This discussion culminates in §50 where Wittgenstein asks: “What does it mean to say that we can attribute neither being nor non-being to the elements?” The answer is that “it makes no sense to speak of the being (non-being) of an element.” Wittgenstein argues that existential claims about primary elements are nonsensical. On that account, existential claims about Kripke’s basic particulars must be nonsensical too.20 The same holds true for modal claims, which are derived from existential ones. Primary elements/basic particulars are presupposed in any existential and modal talk. This means in Kripke’s framework that the underlying reality that provides an account of such basic particulars must be presupposed and is the same in every possible world. This remarkable feature of primary elements is, according to Wittgenstein, analogous to the Standard Meter case. Existential claims about primary elements are without truthvalue and so are claims attributing a specific length in meters to the Standard Meter. Hence, the Standard Meter must be, in some sense, a primary element. However, the Standard Meter has no prominent metaphysical feature (it is not among the basic building blocks of reality). As Wittgenstein makes clear, the Standard Meter has a “peculiar role in the game of measuring with a metre-rule” (§50). It is an instrument of the language by means of which we make statements about lengths of other objects. The Standard Meter is something presupposed in such statements. This is its peculiar property that it shares with primary elements. 6.6 Conclusion Many commentators have assumed their sides in this virtual debate between Wittgenstein and Kripke on what can be said about the Standard Meter. The narrative has been that either Wittgenstein or Kripke or

Who Is Afraid of Truth Gaps? 137 both must be wrong.21 Both advance claims that to an extent violate our common-sense way of speaking. Outside the philosophical context, nearly everybody would say that the Standard Meter is one meter long and that this is necessarily so. Kripke seems to be saying that Wittgenstein’s proposed truth-value gap is more puzzling (i.e., less intuitive) than saying that the Standard Meter is only accidentally one meter long. But intuition is not a decisive judge in philosophical debates. My aim has been to argue that their different accounts of the Standard Meter boil down to different ways of fixing reference. Wittgenstein and Kripke analyze the Standard Meter case utilizing different ways of fixing reference. In this particular case, they clearly differ. However, both are open to both ways of fixing reference. As I hope to have shown, both ways have their advantages and disadvantages, practical as well as philosophical. What drives Kripke’s way of fixing the reference of “meter” is a quite ordinary temptation to postulate absolute space behind the changing world of appearances. On his approach, lengths of objects are independent of the units in which they can be expressed. Wittgenstein’s account of the Standard Meter can be taken as a kind of resistance to this postulation of absolute space comprising abstract lengths. The ultimate consequence of this approach is the truth-value gap: we can say of the Standard Meter neither that it is one meter long nor that it is not. In the final section of this chapter, my goal was to show that even Kripke cannot avoid the truth-value gap. In his account of reference (and of modality in general), the theory of underlying reality (e.g., the theory of absolute space) must postulate basic particulars that are the same in every possible world. One can say of such basic particulars neither that they exist nor that they do not exist. The truth-value gap reappears. In broader outline, truth-value gaps are instances of paracomplete reasoning one ought not be afraid of.22 Notes 1 Not every truth-value gap is puzzling. Assertions involving a category mistake (e.g., “Caesar is a prime number”) can be taken to have no truth-value without this being cause for puzzlement. However, the cases discussed here (the Standard Meter, primary elements) are not instances of category mistakes. 2 This may not be quite clear from Kripke’s original formulation in Naming and Necessity. He put the point more clearly in subsequent writings. Consider the following report by Nathan Salmon: Kripke has suggested (in the Stanford lecture, and more recently in conversation) that his metre example can be bolstered through the use of a suitable description, perhaps “the length of the stick presented to me in the normal way by this visual perception”, used with introspective ostension to a particular veridical visual perception of S. (Salmon 1988, p. 203)

138  Jakub Mácha Kripke’s meter example is bolstered if we note that what matters is the appearance of the stick under normal circumstances. 3 It may seem strange to maintain that one cannot fix the reference of “water” as H2O before the invention of molecular theory. Of course, one can isolate and refer to a substance, without being aware that it is an element as defined by molecular theory—as Priestley did with oxygen before Lavoisier identified it within the framework of molecular theory. 4 I use the terms “baptizer” and “reference-fixer” interchangeably. They do not necessarily refer to a single person. 5 “Absolute space, in its own nature, without regard to anything external, remains always similar and immovable” (Newton, Principia I, p. 6). 6 Loomis expresses this independence in slightly different terms: “ ‘One meter’ designates a property that is identifiable independently of the particular thing that we select as the standard (it doesn’t matter here what kind of thing such a property is)” (1999, p. 298). 7 Kuusela, in this volume, argues that after the initial baptism, at time t1, we are not in the position to measure the length of stick S as it was at time t0. 8 My general approach in this essay is to extract from Wittgenstein’s writings an alternative account of reference that is comparable (and in some respects preferable) to that of Kripke. A different approach—advanced in Gustafsson’s chapter in this volume—would be to argue that Wittgenstein is rejecting the very idea that “meter” must refer to something. I maintain that Wittgenstein rejects the idea of reference to abstract objects such as lengths, numbers, or times, which leaves the idea of reference to regular objects (sticks, tables, persons, etc.) intact. 9 The addendum “any time, in any counterfactual situation” is only a way of saying that this designator is rigid, that is, holds in any possible world. The Standard Meter can, of course, be broken or dissolved in acid. We can probably exclude the worlds in which S does not exist and maintain that “meter” is a weakly rigid designator. 10 This point is addressed in Gustafsson’s chapter in this volume. 11 I think that Kripke would allow that the reference can be fixed in Wittgenstein’s way. That is to say, Kripke would allow that some properties can be defined by referring rigidly to a paradigmatic sample as it appears to us (and not to any underlying physical state or process). Kripke defines yellowness as follows: “Yellowness is picked out and rigidly designated as that external physical property of the object which we sense by means of the visual impression of yellowness” (NN, p. 128). Put this way, the definition is circular. But this need not trouble us here. What is important is that the object of reference is a manifest property of another object. This other object is the Standard Yellow. Given Kripke’s discussion of gold or water, the reference of “yellow” can be fixed by picking an object from some physical theory: e.g., yellow is light in the wavelength range of 570–580 nanometers. I think both ways of defining yellowness are admissible. My point is that Kripke defines color terms by reference to paradigmatic samples in the same way as Wittgenstein does (cf. his discussion of the Standard Sepia in PI, §50). 12 Loomis (1999, p.  304) formulates the same difference in terms of different standards: Here it is worth noting an interesting difference between Wittgenstein and Kripke concerning what exactly is functioning as the standard for “one meter”. For Kripke, it is the length of the bar. For Wittgenstein, it is the bar itself, not its length.

Who Is Afraid of Truth Gaps? 139 The expression “bar itself, not its length” may suggest that the length of the bar is not part of the standard. But Loomis means the bar, including its length, as an object of comparison: “Something is one meter long for Wittgenstein if it matches the endpoints of the bar, not if it matches the length of the bar” (ibid.). 13 See my book The Philosophy of Exemplarity (Mácha 2023) for a full paracomplete account of paradigms inspired by Wittgenstein’s remarks about the Standard Meter. 14 On this insight, see Jacquette (2010, p. 54). 15 Concerning the relationship between two units, Jacquette (2010, p. 61) distinguishes between a merely stipulative equivalence and an approximation (if the units are truly independent). 16 Curiously enough, in the Remarks on the Foundations of Mathematics, Wittgenstein would allow that an expression of ratio, e.g., 12 inches = 1 foot, is not an empirical proposition, but rather an expression of a rule: “No one will ordinarily see this last proposition [12 inches = 1 foot] as an empirical proposition. It is said to express a convention. But measuring would entirely lose its ordinary character if, for example, putting 12 bits each one inch long end to end didn’t ordinarily yield a length which can in its turn be preserved in a special way. . . . The proposition has the typical (but that doesn’t mean simple) role of a rule” (1978, VII, §§1–2). In an ordinary situation, the ratio between two units of measurement can be taken as a rule. Such a rule, however, does not entirely lose its empirical character, because “it can be used to make certain predictions” (ibid.). But what is the ordinary character of measuring? In ordinary situations (i.e., outside philosophical contexts) one can safely assume that units of length refer to abstract lengths. Then, however, Wittgenstein must allow that the references of unit terms (“meter,” “inch,” and “foot”) can be fixed in Kripke’s way. 17 Kripke’s distinction between the epistemological and the metaphysical domain (and between epistemic and metaphysical modality) can be seen as a variant of the traditional distinction between primary and secondary qualities. Primary qualities pertain to ontological reality and secondary qualities to the world of appearance. Examples of primary qualities are having the atomic number 78 or having the chemical structure H2O. The corresponding secondary qualities are having a yellowish color and being a transparent, colorless liquid. We could imagine other straightforward examples beyond those provided by Kripke. However, the Standard Meter example does not fit into this picture. Length (that is, extension) is a typical primary quality. As I read him, Kripke is committed to the distinction between apparent length (a secondary quality) and absolute length (primary quality)—and their accidental correspondence in the act of fixing the refence. This is where the analogy with primary and secondary qualities breaks down. If there is only one length, then the reference must be fixed in Wittgenstein’s way. 18 Wittgenstein expresses this idea in §47 of his Philosophical Investigations: “Is this length of 2 cm simple, or does it consist of two parts, each 1 cm long? But why not of one bit 3 cm long, and one bit 1 cm long measured in the opposite direction?” 19 Even if we grant that Kripke does not believe in transworld identification (personal communication), his account of basic particulars retains its validity. 20 What I want to say is that existential claims about Kripke’s basic particulars are without truth-value. Why, then, could we not ask whether, for example, phlogiston exists? Scientists can raise the question of whether phlogiston theory explains certain phenomena (e.g., combustion) better than molecular theory.

140  Jakub Mácha But once one of these theories is accepted, claims about the existence of the basic particulars postulated by the theory are without truth-value. 21 Cf. Salmon (1988, p.  195): “My answer is that Kripke and Wittgenstein are probably both wrong to some extent.” 22 I develop this idea of paracomplete reasoning in my recent book (Mácha 2023). A  logic is paracomplete if it gives up the law of excluded middle. Put informally, its domain is incomplete due to truth-value gaps that break with the law of excluded middle. My general idea is that paracomplete reasoning can be an alternative to paraconsistent reasoning, which must give up the law of noncontradiction.

References Jacquette, Dale (2010) Measure for Measure? Wittgenstein on Language-Game Criteria and the Paris Standard Metre Bar, in Arif Ahmed (ed.), Wittgenstein’s Philosophical Investigations: A  Critical Guide. Cambridge University Press, 49–65. Kripke, Saul (1975) Outline of a Theory of Truth, Journal of Philosophy 72(19), 690–716. Kripke, Saul (1980) Naming and Necessity. Basil Blackwell. Loomis, Eric (1999) Necessity, the A Priori, and the Standard Meter, Synthese 121, 291–307. Mácha, Jakub (2023) The Philosophy of Exemplarity. Singularity, Particularity, and Self-Reference. Routledge. Salmon, Nathan (1988) How to Measure the Standard Metre, Proceedings of the Aristotelian Society, New Series 88, 193–217. Wittgenstein, Ludwig (1974) Philosophical Grammar, edited by R. Rhees, translated by A. J. P. Kenny. Blackwell. Wittgenstein, Ludwig (1978) Remarks on the Foundations of Mathematics, revised edition, edited by G. H. von Wright, R. Rhees, and G. E. M. Anscombe. Blackwell. Wittgenstein, Ludwig (2009) Philosophical Investigations, the German text, with an English translation by G. E. M. Anscombe, P. M. S. Hacker, and J. Schulte, revised 4th edition by P. M. S. Hacker and Joachim Schulte. Blackwell.

7 Kripke’s Standard Meter—A Religious Dream? Christian Helmut Wenzel

7.1 Introduction Ever since Kripke gave his Lectures at Princeton in 1970, then published in Synthese in 1972 and as a book in 1980, his ideas of separating epistemology and metaphysics have drawn much attention. This is mainly due to the fact that these ideas include two novel and surprising claims, namely that there are truths that can be known a priori but are contingent, and that there are truths that are necessary but known only a posteriori. Traditionally, the a priori and necessity were understood as being intimately connected, and the same applies to the a posteriori and contingency. But Kripke argues that there are cases where they come apart. That was the big surprise. In his view, the a priori/a posteriori distinction belongs to epistemology, whereas the necessity/contingency distinction belongs to metaphysics. This already shows in his use of words. He does not say that something is a priori, but that it is known a priori to be true. In his view thereby arises the possibility of truths that are metaphysically necessary but not known a priori, and truths that are metaphysically contingent but need not be known a posteriori. Thus, the traditional links come apart, or at least seem to do so. The negation is not direct, that is, Kripke is not saying that there is something that is “necessary but not a priori.” Rather, the negation is indirect, one item being mediated through knowledge, saying that there is something that is “necessary but not known a priori.” But as I will show, traditionally the a priori is not limited to truths and what is known. Traditionally, there are things that are a priori elements of knowledge, such as time and space, that are not truths. Kripke’s idea of there being some kind of metaphysical necessity that is discovered empirically is I think the more interesting and difficult one. But here I concentrate on the other pair, aprioricity and contingency. I  concentrate on Kripke’s meterstick example, which I think is difficult enough but more manageable. Kripke’s example of the meter stick S and the claim that the sentence “S is one meter long” is contingently true but can be known a priori, has DOI: 10.4324/9781003240792-8

142  Christian Helmut Wenzel been discussed in several dozen articles over the last almost 50 years. The claim is sometimes rejected as not making sense and relying on ambiguity or equivocation.1 Contrary to such criticisms, I think that Kripke’s account does make sense and is consistent, at least provided one is willing to accept his way of seeing things. But I  will also show that in his comments on Wittgenstein and Kant, Kripke is sometimes not patient enough and does not sufficiently try to understand their views. This is apparent in the case of Wittgenstein and has been pointed out in several articles already. But it also applies in the case of Kant, and this has been less discussed. The notion of the a priori has a history, and Kant is one of the main figures in that history. Kripke talks of “the traditional characterizations” of the a priori (p. 34) and argues that these characterizations missed something or got something wrong. But I think that if one talks and argues like this, one should first try to get the characterizations right, and I think Kripke does not always do that, at least not in these lectures. Based on these considerations, my essay has three parts, first I give a presentation of Wittgenstein and Kripke, then of Kant and Kripke, and then of Kripke himself. Kripke will not fare well in the first two parts, but better in the third part. Regarding the third part, on the one hand, I think his own view is sound, although, or rather because, his receptions of Wittgenstein and Kant are wrong. On the other hand, I think that if we believe one should try to do justice to history when borrowing a term such as of the a priori, Kripke’s claims will appear very idiosyncratic and maybe even wrong. 7.2  Wittgenstein and Kripke The way Kripke takes up Wittgenstein has been much discussed in the literature. He quotes Wittgenstein from Section  50 of the Philosophical Investigations. There Wittgenstein writes: There is one thing of which one can say neither that it is one meter long nor that it is not one meter long, and that is the standard meter in Paris. But this is, of course, not to ascribe any extraordinary property to it, but only to mark its peculiar role in the language game of measuring with a meter rule. (NN, p. 54)2 Kripke comments: “this seems to be a very ‘extraordinary property,’ actually, for any stick to have. I think he must be wrong.” But clearly Kripke misunderstands Wittgenstein’s intentions in this passage. He does not see the language-game Wittgenstein has in mind.3 This game is intended as a primitive one, similar to the ones Wittgenstein has introduced in earlier

Kripke’s Standard Meter—A Religious Dream? 143 sections before Section 50. The standard meter is used to measure other objects, and that is where it ends. One could, of course, extend this game.4 One could make copies and then measure the standard meter against such copies. One could also merely imagine making such copies instead of actually making them and then realize by means of mere imagination that the standard meter will have to come out to be one meter long.5 It is natural for us to imagine such an extension, as it is also natural and useful to make copies. But it is not natural within the game itself the way Wittgenstein conceives of it. If we do imagine such an extension, we will indeed think, as Kripke says two pages later, that one knows “automatically, without further investigation” (p. 56) that the standard meter is one meter long. (Or at least that the person who actually makes the stipulation knows it automatically. I leave the problem of being in a privileged position out for now.) But all this is not part of the game Wittgenstein has in mind. The question of how long the standard meter is does not come up within that game. It is similar to the earlier languagegame involving slabs and beams of which Wittgenstein says: “Conceive this as a complete primitive language” (Section 2). The builder A calls out the names of the building blocks and the assistant B brings them according to their names, and that is all. This language has only four words. It is complete with these four words. In Section 8, Wittgenstein then considers an extension (eine Erweiterung) of this language. But this is then an extension, not the original game. Similarly, in Section 50, the game is supposed to be a primitive one and the question of “how long the standard meter is” does not come up. But then things are a little more complicated than that. Wittgenstein introduces the Platonic idea of “elements” in Section 46, which leads to Section  50. What Wittgenstein says about the standard meter should be seen in this more specific context developed from Section 46 on. Such Platonic elements are said to be “primary.” In German, Wittgenstein writes that they are “Urelemente,” and similarly in Section 50, he writes that the standard meter is “das Urmeter.” He quotes Plato saying that the elements have only names and there is no “explanation” for them (Anscombe translates “definition,” but the German “Erklärung” might be better translated as “explanation”). Everything else is complex and composed of these elements. Wittgenstein then embarks on lengthy discussions of what should count as elements and what as being composed. In Section 48, he explicitly applies the method of a primitive language-game to the passage from Plato: “Let us apply the method of Section 2 to the account in the Theaetetus.” The point in Plato is that one cannot even say of the elements that they exist or do not exist. For Wittgenstein, the point is that one cannot say of the standard meter that it is or that is not one meter long. When he introduces

144  Christian Helmut Wenzel his example, he says: “let us consider an analogous case.” The analogy is that one cannot say something of an element (about whether it exists or not) as one cannot say something of the standard meter (whether it is one meter long or not). For Wittgenstein, part of the idea of this language-game (or better just “game”) is that one cannot ask such a question. One can ask it only if one extends the game. In Section 50, Wittgenstein also introduces the example of a color sample, the “standard sepia” (Ur-Sepia), and he does this right after and parallel to the introduction of the standard-meter example. He says that the color sample is an “instrument” (ein Instrument) within a language-game. He says it is not “represented” but “a means of representation” (Mittel der Darstellung). By analogy, this applies also to the standard meter. It is an instrument for measuring and not measured itself, as the color sample is a means of representation and not represented itself. This is where the role of the instrument in the language-game ends. It is this context in Wittgenstein that Kripke has no patience to consider fully and carefully.6 If he did, I think he would not say, as he does, “I think he must be wrong” (p. 54). 7.3  Kant and Kripke The situation with Kant is more complicated and I  think more relevant. Wittgenstein talks of primitive language-games containing only a few words, but Kant offers a highly complex and abstract theory of transcendental philosophy and it is within this rich theory that he talks of the a priori. Being perfectly clear and explicit about the notion of the a priori in Kant’s transcendental philosophy is, I think, humanly impossible, including for Kant himself. The meaning of the word often depends on the context in which it is used. But I think I can offer enough material to show that Kripke misunderstands Kant, and to indicate that there are insights in Kant that Kripke might still want to use, or that would at least need more work to replace. Kripke applies the term “a priori” to our knowledge of statements and their truth, and he thinks that this is true for other philosophers as well. Thus, he says: “Philosophers have talked . . . [about] various categories of truth, which are called ‘a priori’, ‘analytic’, ‘necessary’ ” (my italics, p. 34). About the use of these terms at his own time, he says: “In contemporary discussions very few people, if any, distinguish between the concepts of statements being a priori and their being necessary” (my italics, p.  34). About Kant, he says: “First the notion of a prioricity is a concept of epistemology. I  guess the traditional characterization from Kant goes something like: a priori truths are those which can be known independently of any experience” (p. 34). Here, we should observe two things. First, Kripke

Kripke’s Standard Meter—A Religious Dream? 145 associates the a priori with statements and their truths and our knowing them. Second, he thinks this is also how Kant does it. But I think he is very much mistaken on the second point. Kant does not restrict the use of the a priori to statements and their truth, nor does he restrict it to knowledge. In fact, he has a very different conception of it, in one respect broader and in another more specific. Kant applies the term “a priori” not only to statements but also, and I think primarily, to “elements of cognition” such as time and space, the categories, and principles. (This might make one think of Plato’s “elements” that Wittgenstein refers to.) Time and space and the categories are a priori, because they are fundamental elements of cognition, that is, they “precede” cognition in the sense that they make cognition possible. For Kant, these elements are not merely known a priori, but they are a priori themselves. Even if we do not come to know them explicitly and do not make judgments about them expressing their a priori nature, they are a priori anyway. The point in Kant is that they make experience possible (giving rise to a positive characterization), not just that they are known independent of experience (a merely negative characterization). These elements play a constitutive role regarding cognition. Kant for instance says that the categorical imperative is a priori. People might not know it explicitly in its formulations, and some may even want to avoid recognizing it. But deep down we all know it anyway, Kant believes. It is not a statement but an imperative. Of course, Kant speaks of a priori cognitions (Erkenntnisse a priori) and these can sometimes be phrased in terms of statements, but more importantly, it is such elements of cognition that he says are a priori. Without them, we could not cognize anything or even so much as conceive of a statement. For Kant, time and space are a priori forms of intuitions, and they are also intuitions themselves. They are not concepts, but we have concepts of them. The categories are a priori concepts and when applied to time and space they produce schemata, which are something a priori again. Thus, for Kant, contrary to what Kripke says, first, the a priori is not a “concept of epistemology” in Krikpe’s sense, that is, it is not restricted to truths and statements; second, the a priori is not just about what is somehow “independent of experience” but also about what makes experience possible. Kant famously wants to reveal the conditions of the possibility of experience. It is this positive feature of the a priori in Kant that makes it applicable to various elements of cognition, such as time and space and the categories, and not just statements and their truth. This positive feature is lost in Kripke. Hence, when Kripke says: “I guess the traditional characterization from Kant goes something like: a priori truths are those which can be known independently of any experience” (p. 34), he is off the mark. The Kantian

146  Christian Helmut Wenzel project is to establish the basic structure of cognition. The question Kant asks is: How can a world appear to a cognizing being and be cognized and known to such a being? Kant thinks about the world as possible in the sense of being a possible object of cognition. The Copernican revolution consists in focusing on the cognizing subject. Instead of taking a mind-independent world as given and trying to derive features of experience and cognition from there, it begins with our experience and tries to derive conditions of the world that we can possibly experience and cognize. In that way, a priori features of the world as it appears to us and as we can cognize it are derived. For Kant, the categories turn out to be a priori conditions for our cognition, and time and space turn out to be “given” facts about appearance for us human beings. They are enabling conditions and this constitutes their a priori nature. For Kant, even reason is a “fact.” The original Latin meaning of “factum,” derived from the verb “facere” (to make), plays a role in this. We will see that this matters when it comes to Kripke’s explanation of why the stipulator can be said to know “a priori” that the standard meter is one meter long, even though Kripke might not be aware this. Thus, we have seen that Kant’s use of the term “a priori” is both broader and more specific than Kripke’s. Kant does not only apply it to statements. He uses it regarding the possibility of cognition in general and as such (überhaupt). Kripke’s offers novel and stimulating ideas of reference-fixing in contrast to a Fregean picture. But I think his accounts of epistemology and metaphysics are relatively thin in comparison with Kant, as I will show in the next section. 7.4  Kripke Himself So far, I have shown that Kripke does not do justice to Wittgenstein and Kant. But I  think, his own account of the contingent a priori, or more precisely of contingent truths that can be known a priori, is consistent and does make sense, at least if we accept his views and his understanding of contingency and the a priori. He writes: What then, is the epistemological status of the statement “Stick S is one meter long at t0”, for someone who has fixed the metric system by reference to stick S? It would seem that he knows it a priori. For he used stick S to fix the reference of the term “one meter”, then as a result of this kind of “definition” (which is not an abbreviative or synonymous definition), he knows automatically, without further investigation, that S is one meter long. On the other hand, even if S is used as the standard of a meter, the metaphysical status of “S is one meter long” will be that of a contingent statement, provided that “one meter” is regarded as a rigid

Kripke’s Standard Meter—A Religious Dream? 147 designator; under appropriate stresses and strains, heatings or coolings, S would have had a length other than one meter even at t0. (p. 56) On the one hand, the particular length of any stick is contingent. If heat had been applied to it, it would now be longer than it actually is. The stick happens to have the length it has. It is an accidental property. This is a common way of thinking and talking. It involves imagination and some counterfactual reasoning that we apply every day. When we make decisions, we often imagine the consequences, and after having made a choice, we sometimes think that we could have done otherwise. This kind of imagining how things are, could be, or could have been, is natural and applies also to matters that have nothing to do with free will, such as the weather conditions or when playing roulette. J. J. C. Smart gives an example of a plate that fell down and luckily did not break and of which we say that it easily could have broken. We imagine how things could turn out, or how they could have turned out. I see no problem in this and how Kripke makes use of it. Of course, free will (thinking that one could have done otherwise) is a big problem, and it is also not obvious which properties of objects should count as accidental and which properties as essential (whether the length of an object is an accidental or essential property). But coming up with a general theory about what is accidental and what essential, is another problem. Regarding the example of the meter stick, I think we can accept that the stick is contingently as long as it is, that is, one meter long. This relies of course on his idea of fixing a reference by means of a definition, or description, and I think we can accept this idea. On the other hand, Kripke says that the stipulator knows “automatically, without further investigation” that the stick is one meter long, and he understands this as knowing it “a priori.” Kripke thinks he is justified in using this term in this way, because it is in tune with what he earlier said about Kant: “I guess the traditional characterization from Kant goes something like: a priori truths are those which can be known independently of any experience” (p.  34). Indeed, the stipulator knows it without further investigation, and that means for Kripke that he knows it “independently of any experience.” But actually, the situation implies only that the stipulator knows it independent of any further experience, because he knows it “without further investigation.” It does not imply that he knows it “independently of any experience,” which is what would be required for Kant the way Kripke puts it. (Kant would speak of experience “in general” or “as such,” überhaupt.) Kripke seems not to notice this difference. The difference between “further” and “any” seems to escape him. Alternatively, we might say that Kripke is content with the “further” and tacitly changes

148  Christian Helmut Wenzel the meaning of “a priori.” This I  think is the case. But this changes the game dramatically, as will become obvious in what follows. As we have seen, for Kant, “a priori” means more than mere independence of this or that particular experience. Kant has a positive characterization as well. A more careful consideration of the word “any” would have led Kripke to see this. To get at the bottom of the matter, we must unpack what Kripke has in mind and what he says in other contexts. Later on, he says that the stipulator “can in some sense know [it] a priori” (p. 63). But in what sense exactly does the stipulator know it “automatically” and “in some sense” a priori? Kripke offers no further explanation. But I think, it is not difficult to do so, at least on first blush. We naturally have a concept of length, and it is in a sense a relative notion. Things have a length relative to other things. Even a single object has a length relative to its width. If we imagine that there was only one object in the world and it had no width but only length, our imagination would be challenged. But this is not how things in our world are. In our world, there are usually many physical objects around and they allow us to naturally speak of lengths. Thus, the scenario Kripke describes is commonsensical. Of course, to make a stipulation official and for practical use, there should be witnesses and we should make copies of the meter stick. We did both in the case of the standard meter. But one can also argue, as Doron Avital does, that length is something intrinsic, non-relative, a priori, or Platonic.7 If we think of the Kantian a priori elements of cognition, we can try to build a bridge from such a non-relative reading to the relative one: relying on these elements, introducing a standard length is a priori possible, as I will explain in more detail later. In his lectures, Kripke often talks of souls and baptism. The word “baptism” appears 17 times in the three lectures in Naming and Necessity. He also thinks of the reference-fixing of “one meter” as some kind of baptism (see footnote 42). There seems to be something religious and spiritual going on, even in the case of the meter stick. Kripke writes about the stipulator: “There is a certain length which he wants to mark out. He marks it out by an accidental property, namely that there is a stick of that length” (my italics, p. 55). That “certain length” seems almost like a soul, or something having a soul, something abstract and impalpable. At least it can be named.8 Once it has a name, we can refer to it, and we imagine that we have fixed the abstract meter and have some kind of handle on this “certain length” the stipulator wants to “mark out.” The length called “one meter” is like a soul in this context. A “certain length” is something rather abstract, without any substance and hard to grasp. It seems to be ephemeral and eternal at the same time. As Malcolm pointed out early on, the way Kripke introduces the example is indeed strange.9 It seems to get things the wrong way around. How can one have

Kripke’s Standard Meter—A Religious Dream? 149 a “certain” length in mind to start with? If one could really do that, the chance of a given stick accidentally having exactly this length would be zero, because there are infinitely many different lengths (even uncountably infinitely many, as the real numbers are uncountably many), and there are only finitely many physical objects around to pick up and use to do the reference-fixing. But we can also read the passage more generously and assume that the stipulator has somehow only roughly a “certain length,” or a Platonic idea, in mind. I suggest we do that. But why does the stipulator know “automatically, without further investigation” that S is one meter long once he has carried out the stipulation, so that we may say he knows it “a priori”? I think the idea here is that if one makes such a stipulation, one already assumes many things. Objects do have lengths and these lengths do not randomly change or fluctuate, neither over time nor if one moves the objects from one place to another. Otherwise, measuring the length of objects would hardly make any sense. When one chooses a stick as reference and standard, one imagines all objects surrounding it being instantaneously, or at least potentially, measured against it. (One might also imagine God paying attention and doing the instantaneous measurement for us, as God is invoked when a priest baptizes a child.) I think this is part of the idea of fixing the reference of “one meter.” Something like this is also what Kripke presupposes when he imagines another standard, namely an inch, and that the stick could be 39.37 inches long. Thus, there are tacit assumptions behind the “automatically” and the “a priori,” and if one does not want to rely on Kantian transcendental philosophy, other justifying arguments would be needed.10 Introducing copies or other standards and then measuring the standard meter against such objects and concluding that it is one meter long are not part of Wittgenstein’s game. The standard is called “Urmeter” and Plato’s elements are “Urelemente,” and as Plato’s elements can be named but not explained, so the standard can be introduced and used, but not measured. Measuring the standard meter against copies is not something what we would ordinarily do. But it is something we could do, and this is enough for Kripke. We could do all this, and by our tacit assumptions about lengths being stable over time and under spatial dislocation, we would “automatically, without further investigation” know that the stick is one meter long. All this is assumed when we introduce a standard for measurement. If we had doubts about this, we would not even get started and introduce a standard length. But we do not have such doubts, and we have in fact introduced standards of lengths. All this is common sense. That objects have lengths and that introducing standards is possible are something one might try to argue for by relying on Kant’s a priori elements of cognition, involving time and space and the categories, the interdependence of concepts and intuitions, and also consciousness. Imagining Kripke’s

150  Christian Helmut Wenzel scenario within the Kantian framework, the stipulator as cognizer and conscious being seeing the stick and having an “intuition” (Anschauung) of it plays a crucial role. One can try to show within the Kantian framework in what sense the stipulator is in a privileged position, and furthermore that we all can imagine being the stipulator, because the a priori elements of cognition are universal. They belong to all human beings. The conditions of experience are necessary for experience, and what can be derived from these conditions is necessarily true of objects of experience. In Kant, it follows that causality, substance, accidents, and many other categories are a priori and therefore applicable to objects of experience. Based on this, the stipulator knows “automatically” that the standard meter is one meter long. He knows it based on these enabling a priori conditions of cognition. Furthermore, he knows that S is “necessarily” one meter long, because it follows from these conditions. “Necessity” here is relative to these conditions.11 This is the way Kant links the a priori with necessity relative to experience in general (überhaupt). This would explain why the stipulator knows it “automatically.”12 (This kind of “necessity” is of course not the kind of modality Kripke has in mind when he says that S is contingently one meter long. We will come back to this.) But there is more going on. During the stipulation, one attends to the actual situation and does not imagine counterfactual scenarios. This is why baptism is a ritual performed with great care and attention to what one is doing and to what is going on. Priests and other institutional representatives concentrate on the actual situation when baptizing. In religious rituals, beside the priest, God is thought to be present as well. I believe this is in the background also in Kripke’s considerations and motivations. I cannot prove this point. I did not ask him about this. But I personally feel it in the text at many places, and it is a fact that he very early on learned Hebrew and that his father was a rabbi. I furthermore think that it is this religious background that adds very much to the value of his work. This also I am not going to try to prove in this chapter. But it led me to add “a religious dream” to the title of my essay. Besides these considerations about what is known “automatically,” there is another way of looking at things. One can also engage in counterfactual considerations in the way Kripke does. Then, one says that the standard meter like any physical object is only accidentally as long as it is, which in this case, after stipulation, means that it is only accidentally one meter long. There is nothing wrong with seeing things this way too, and Kant would have no problems with it. Again, after all, it is common sense. Simply put, Kripke puts a sentence such as “S is one meter long” into two different boxes, the epistemology box and the metaphysics box. In the former, it is known a priori (and necessary in Kant’s way of understanding “necessity” as I have explained earlier). In the latter, it is contingent (and

Kripke’s Standard Meter—A Religious Dream? 151 Kant would perfectly agree to this). In the former, one restricts attention to the actual world and tacitly relies on Kantian a priori elements of cognition (the way our world must be in order to be cognizable for beings like us). In the latter, one includes counterfactual considerations (contingencies in addition to the a priori conditions of how the world must be).13 In Wenzel (2004), I have argued that the statement about the length of S is contingent in one respect and a priori in another, and that the two are not compatible: It is obviously true that something could have happened to stick S before the time t0. . . . What is known a priori here is, I claim, something completely different: What is known a priori is the possibility of making such a stipulation. (p. 478) I still think that these are two very different aspects, but I do not see them as being incompatible any more. Kripke sees the statement in two different respects, and I now think this is acceptable. In 2004, I wrote: “It is after all not one and the same statement that is contingently true and known a priori.” I  now do not think so any more. We can be more generous. There is nothing wrong with seeing a statement in two different respects, or focusing on two very different aspects of it. But another point that I raised in 2004 and still think is true and problematic is that Kripke understands the a priori very differently from the way Kant understands it. Let me summarize what we have so far. I have shown that the “a priori” aspect regarding the statement “S is one meter long” can be seen as derived from the Kantian a priori elements of cognition, time and space, the categories, and consciousness, which make experience possible. It is these elements that make the stipulation possible and meaningful, and it is with respect to these elements that the stipulator knows it “automatically.” This part has nothing to do with the particular stick S and the particular length it has. Any stick would do. The “necessity” Kant would see applies to what can be derived from the a priori elements of cognition. In this sense of “necessity,” relative to these elements and the conditions of the possibility of experience, the stick that has been used for the stipulation is necessarily one meter long (because it is a priori possible to make copies, etc., and the elements are conditions of the possibility of experience). Alternatively, we can think of counterfactual scenarios and say that the stick has its length only accidentally. Then we say “S is one meter long” is accidentally true. This too makes sense. Doing both at the same time is a little confusing. This is because (a) the (Kripkean) a priori consideration requires restricting our attention to the actual world and reflecting about future possibilities (for instance, the making of copies and measuring the

152  Christian Helmut Wenzel stick against these copies) and reflecting about the a priori elements and conditions that go into our knowing something “automatically”; while (b) the contingency consideration requires imagining counterfactual past situations (that heat could have been applied to it). This combination of (a) and (b) makes Kripke’s example easily confusing. The two respects are very different from each other. They go into different directions, future and past; and they focus on different aspects or worlds, the actual and the counterfactual. But besides this demand on our imagination and understanding, there is nothing wrong with what Kripke wants. Kripke wants two different boxes, and I think he can have them, at least regarding this example and as far as we have scrutinized the two respects so far. The meter-stick example appears thus to be rather trivial. Knowing that S is one meter long “automatically” is simply not further argued for. As I have indicated, one could refer to Kant’s transcendental philosophy, his notions of time and space and the categories and consciousness as conditions of the possibility of experience, to argue for it. The other pair though, necessity and the a posteriori, receives much more attention in Kripke. When discussing it, he introduces ideas of physical necessity, something that could compare with Kant’s development of conditions of the possibility of experience that Kant uses to offer an a priori basis for physics. Discussing this would be more interesting and more complicated. But this is not the pair I am considering here. Kripke’s broader interest is to separate epistemology and metaphysics, and we may ask whether the meter-stick example is convincing in this respect and helpful in introducing the separation. Simply put, can he really have his two boxes? Let us look once more at the contingency and the aprioricity claim, one by one. Contingency and metaphysics: We say that the stick has its length only accidentally. Heat could have been applied to it and it then would be longer than it actually is, that is, longer than one meter. But one might wonder about this. If the world is deterministic, this will not be a possibility. Heat was not applied to it and it was impossible that it could have been applied to it, so a determinist might say. Hence our thinking that it could have happened might be merely due to our limited insight into the determining factors, and the idea of metaphysical contingency would then be in danger of being merely epistemological. In support of Kripke, we can reject such worries in the following way. We can use Smart’s example of a plate that was accidentally dropped while washing dishes. Luckily it did not break. We know from experience and from physics that the chances of breaking are high when such a plate is dropped from such a height and falls on such a floor. It did not break, but a slight variation of the initial conditions would have very likely led to its breaking to pieces. We know this from experience and from physics. Similarly, we know that slight changes in temperature

Kripke’s Standard Meter—A Religious Dream? 153 before the time of stipulation would have resulted in the stick being slightly longer. All this is true also in a deterministic world, even though these slight changes could not possibly have occurred. What we know and express in these conditional statements is about the world and how things really are (no matter whether determinism is true or not). If we are not skeptics about experience, physics, the existence of the external world, and such, then it is not merely an epistemological claim that the plate could have broken or that the stick could have been longer. It is then a common-sense claim about the world. This would save Kripke’s claim about contingency. But if we want also to justify the common-sense claim and understand metaphysics more fundamentally, we might have to turn to Kantian transcendental philosophy, which would undercut Kripke’s attempt to separate epistemology and metaphysics. The a priori and epistemology: Kripke says that the stipulator knows “automatically, without further investigation,” that stick S is one meter long. I have suggested that such “a priori” knowledge (as Kripke calls it) could be defended and substantiated by relying on Kant’s conception of the a priori. This conception is based on a priori elements such as time and space, the categories, and consciousness. The stipulator’s knowing automatically that the stick is one meter long is grounded in these elements. It can be justified with respect to these elements. But one might then object that this notion of the a priori is not only epistemological but also, at the same time, ontological and metaphysical, if we understand things in the Kantian way. The a priori elements of cognition make experience possible, but they are also the conditions of the objects of experience. They dictate how a world we can possibly experience must be. They are therefore conditions also for ontology and metaphysics, at least if we restrict our attention to worlds that we can possibly experience and do not consider any ontology or metaphysics of worlds that we cannot experience. Hence, if we go this Kantian way in defending Kripke, there is a danger of not having fully freed ourselves from Kantian metaphysics, as Kripke might want to. We would rely on the Copernican revolution, which would lead from epistemology to metaphysics, encompassing the latter. Hence there is a problem. I  do not see any indication that Kripke would go this Kantian way. He justifies, or would justify, the “automatically” and the “a priori” by relying on the necessities he believes physics has revealed. But this too would make epistemology rely on metaphysics. There is another way of defending Kripke’s claim that the stipulator knows “automatically” that stick S is one meter long, a way without Kant and more rooted in philosophy of language. When asking himself how long the stick is, the stipulator might reason as follows, inspired by Kripke: I used S to “mark out” a certain length, which I called “one meter.” I fixed that length “by an accidental property of that length” (p. 75). I stipulated

154  Christian Helmut Wenzel “that ‘one meter’ is to be a rigid designator of the length which is in fact the length of S at t0” (p. 56). Hence, “one meter” refers to a length that is “in fact the length of S at t0.” That length (referred to by “one meter”) is in fact identical to it (the length of S at t0). Hence, “the length of this stick is a meter” (p. 63), q. e. d. This way of arguing involves referring to a length in two different ways, rigidly by a name and non-rigidly by an accidental property of a stick. This is the way Kripke would want it, but this way of defending Kripke is subject to criticisms put forward by Malcolm and others about the idea of starting out with having a “certain length” in mind. One could again substantiate this idea by introducing Kantian considerations, but then one would fall back to introducing considerations implicit in the Copernican revolution that lead to metaphysics and do not leave epistemology separated from metaphysics. Hence, the problem seems not to easily go away, and seen in this respect, it is not perfectly clear that Kripke can have his two boxes. To offer a brief summary at the end. First, regarding the a priori, it seems to me that Kripke changes the meaning of the “a priori,” turning “independent of any experience” (in general, as such, überhaupt) to “independent of further experience” and leaving out the positive aspect (what is constitutive for experience). Second, regarding the concept of contingency, he relies on intuitive essence/accidence considerations paired with ostensive reference-fixing and causal theories of reference that he believes give him access to metaphysics independent of epistemology. It is this second point that I  find problematic. Scientists often believe that the natural sciences grasp reality as it is in itself, but like any theory, the scientific theories also reflect our interests and it is not clear that they grasp things as they are in themselves. The same applies to what we take substances and causes to be. The Kantian idea of the thing in itself and the problems it gives rise to do not easily go away.14 Notes 1 Dummett (1981) sees ambiguities (p. 123); Malcolm (1981) does not accept the contingency claim (pp. 21, 23–4); Loomis (1999) focuses on what the standard of one meter might be and concludes that the argument does not work; Wenzel (2003) argues that the meter cannot be referred to in the counterfactual world (p.  370)——but I  now realize that such reference is not necessary and that Kripke thinks of the statement from the point of view of the actual world; Wenzel (2004) argues that contingency and the a priori require two distinct aspects that are not compatible with each other (p. 477)——but I now think we may see them as being compatible; Stojanovic (2004) again sees equivocations; Chen (2011) argues that both of Kripke’s arguments, for contingency and for the a priori, do not work (pp. 126–127). 2 All quotes from Kripke are from Naming and Necessity.

Kripke’s Standard Meter—A Religious Dream? 155 3 Malcolm (1981) writes: In that situation, in that ‘language game,’ there is not such a thing as measuring the Urmeter. . . . If that is so, and if Kripke thinks Wittgenstein is wrong about that, then Kripke is the one who is wrong. (p. 20) I agree. Pollock (2004) argues at length that “Wittgenstein is right” (p. 156) and says of Kripke and Nathan Salmon that they “simply do not understand the concept of measurement” (ibid.). I think this goes too far. They cannot be so ignorant. That Pollock’s criticism of Kripke lacks sensitivity to context, has been shown by Dolev (2007). Thus, we see, as Kripke is not patient enough with Wittgenstein, so are many readers of Kripke in turn (including myself in former times, as I will explain later). 4 Anscombe translates “language-game of measuring,” while the German only says “Spiel des Messens” and not “Sprachspiel.” But I believe this does in the end not matter, especially in the light of what I say about Sections 46 and 48 later. 5 But notice that Kripke sees the stick as being contingently one meter long. Heat could have been applied to it. Hence the modality expressed in the “have to” must be a different one from the one he is after. 6 For a detailed account of how Wittgenstein used his quotes from Plato, see Kienzler (2013), who writes that “he had no interest in scholarly details, and he felt free to use the text according to his own needs and intentions” (p. 31). I think something similar can be said about Kripke regarding Wittgenstein, at least as far as his quote from Section 50 is concerned. 7 Avital (2008). 8 Wittgenstein quotes Plato in Section  46, before he introduces the meter-stick example in Section 50. Wittgenstein does not pay much attention to Plato, nor does Kripke pay much attention to Wittgenstein. But ironically, the problem in Plato that we might not be able to explain the elements but only be able to name them, as well as Plato’s concern with the soul, seems to reappear in Kripke. 9 Malcolm (1981): “What, according to him, is ‘the reference’ that is fixed for this phrase? It is not any physical stick or rod. It is ‘an abstract thing.’ .  .  . Kripke’s phrase ‘a certain length,’ is curious. What length?” (pp. 20–21). 10 I have pointed this out in Wenzel (2003): “What would be a priori about P [the statement that S is one meter long] in Kant’s eyes is, I  think, the knowledge that there is a certain order and continuity in the world, especially that lengths do not change chaotically, that the concept of length therefore makes sense, and that we can set up a standard of length” (p. 370); and similarly in Wenzel (2004): “What is known a priori is the possibility of making such a stipulation” (p. 478). 11 Isidora Stojanovic (2004) argues that “a priori” and “necessity” must be understood as being relative to circumstances, and if they are so relativized to the same circumstances in the standard-meter example, she argues Kripke’s example will not work. I think she has a point in saying that the notions are relative, but then again I think she is not patient enough in her reading of Kripke. For instance, I think Kripke does relativize contingency, but not to the past as she thinks Kripke does, but in the present to other possible worlds. 12 This gives support to Kripke’s account of the a priori in the meter-stick example. The worries Jeshion (2000) raises about de-re beliefs via stipulation are more basic. But I believe Kantian considerations might be of help there, too.

156  Christian Helmut Wenzel 13 Bo Chen (2011) for instance does not accept this. First, about Kripke’s idea that, quoting Kripke, “one designator (‘one meter’) is rigid and the other designator (‘the length of S at t0’) is not” (p. 56), he says: “We have to say that this is wrong” (p.  126). But I  don’t think it is wrong, and I  do not find his arguments convincing. He writes much of definiens and definiendum and sees them as either both rigid or both not rigid. I think we can easily follow Kripke’s intuitions and allow for the two boxes. Second, about Kripke’s claim regarding the a priori, Chen quotes Kripke: “I shall consistently use the term ‘a priori’ in the text so as to make statements whose truth follows from a reference-fixing ‘definition’ a priori,” and says “This is also confused for us” (p. 127). But it is not confusing. Again, we can follow Kripke’s intuitions, and we can see that the truth “follows” if we rely on Kantian elements of cognition as I have explained earlier. 14 I wish to thank Paisley Livingston, Jakub Mácha, and an anonymous referee for their corrections, questions, and comments.

References Avital, Doron (2008) The Standard Meter in Paris, Philosophical Investigations 31(4). Chen, Bo (2011) Proper Names, Contingency A Priori and Necessity A Posteriori, History and Philosophy of Logic 32(2), 119–138. Dolev, Yuval (2007) Mission Impossible and Wittgenstein’s Standard Meter, Philosophical Investigations 30(2), 127–137. Dummett, Michael (1981) Note on an Attempted Refutation of Frege, in Michael Dummett (ed.), Frege: Philosophy of Language, 2nd edition. Harvard University Press, 110–151. Jeshion, Robin (2000) Ways of Taking a Meter, Philosophical Studies 99, 297–318. Kienzler, Wolfgang (2013) Wittgenstein Reads Plato, in Luigi Perissinotto and Begoña Ramón Cámara (eds.), Wittgenstein and Plato: Connections, Comparisons and Contrasts. Palgrave Macmillan, 25–47. Kripke, Saul (1980) Naming and Necessity. Harvard University Press. Loomis, Eric (1999) Necessity, the A  Priori, and the Standard Meter, Synthese 121(3), 291–307. Malcolm, Norman (1981) Kripke and the Standard Meter, Philosophical Investigations 4, 19–24. Nagel, Thomas (2000) The Psychological Nexus, in Paul Boghossian and Christopher Peacocke (eds.), New Essays on the A  Priori. Oxford University Press, 434–471. Perissinotto, Luigi and Cámara, Begoña Ramón (eds.) (2013) Wittgenstein and Plato: Connections, Comparisons and Contrasts. Palgrave Macmillan. Pollock, W. G. (2004) Wittgenstein on the Standard Meter, Philosophical Investigations 27(2), 148–157. Stojanovic, Isidora (2004) The Contingent A  Priori: Much Ado About Nothing, Croatian Journal of Philosophy 4(2), 291–300. Wendel, Hans-Jürgen (1991) Apriorische Einsicht und metaphysische Notwendigkeit. Kripkes Kant-Kritik, Kant-Studien 82(1), 63–80.

Kripke’s Standard Meter—A Religious Dream? 157 Wenzel, Christian Helmut (2003) Knowledge, Belief, and the A Priori, Knowledge and Belief. Papers of the 26th International Wittgenstein Symposium 11, 369–370. Wenzel, Christian Helmut (2004) Kripke’s Contingent A  Priori: The MeterStick Example, in Dieter Hüning, Karin Michel, and Andreas Thomas (eds.), Aufklärung durch Kritik. Festschrift für Manfred Baum zum 65. Geburtstag. Duncker & Humblot, 477–480.

8 Overlooked Distinctions The Mirage of Contingent A Priori Oskari Kuusela

8.1 Wittgenstein and Kripke on the Standard Meter: Some Relevant Distinctions Ludwig Wittgenstein’s remark on the standard meter, made famous by Saul Kripke, occurs in the Philosophical Investigations in the context of a discussion of the view, held by Russell and Wittgenstein himself earlier, according to which the meaningfulness of names depends on their having a reference. As Wittgenstein explains, this view seems to require the postulation of logically simple objects as the referent of names in order to ensure that they have a reference and consequently meaning. Such logically simple, not further analyzable, objects might then be regarded as constituting the indestructible elements of reality, or a substance whose existence must be assumed in order for true/false representation to be possible.1 Kripke quotes only two sentences from this rather long remark, where Wittgenstein speaks of role of the standard meter in the language-game of measuring, presenting the meter as playing a role analogous to that of the postulated indestructible elements. As Kripke omits any reference to this analogy, and quotes Wittgenstein out of context in a way apt to obscure Wittgenstein’s point, it is worth quoting the remark in full. (I have enclosed within stars the sentences quoted by Kripke.) What does it mean to say that we can attribute neither being nor nonbeing to the elements?—One might say: if everything that we call “being” and “non-being” consist in the obtaining and non-obtaining of connections between elements, it makes no sense to speak of the being (non-being) of an element; just as it makes no sense to speak of the destruction of an element, if everything that we call “destruction” lies in the separation of elements. One would, however, like to say: being cannot be attributed to an element, for if it did not exist, one could not even name it, and so one could state nothing at all about it. But let us consider an analogous case. *There DOI: 10.4324/9781003240792-9

Overlooked Distinctions 159 is one thing of which one can state neither that it is one meter long, nor that it is not one meter long, and that is the standard meter in Paris. But this is, of course, not to ascribe any extraordinary property to it, but only to mark its peculiar role in the game of measuring with a meter-rule.* Suppose that samples of color were preserved in Paris like the standard meter. So we explain that “sepia” means the color of the standard sepia which is kept there hermetically sealed. Then, it will make no sense to state of this sample either that it is of this color or that it is not. We can put it like this: this sample is an instrument of the language, by means of which we make colour statements. In this game, it is not something that is represented, but is a means of representation. And the same applies to an element in language-game (48) when we give it a name by uttering the word “R”—in doing so, we have given that object a role in our language-game; it is now a means of representation. And to say “If it did not exist, it could have no name” is to say as much and as little as: if this thing did not exist, we could not use it in our language-game. What looks as if it had to exist is part of the language. It is a paradigm in our game; something with which comparisons are made. And this may be an important observation, but it is none the less an observation about our language-game—our mode of representation. (PI, §50) Kripke comments on the two sentences he quotes: This seems to be a very “extraordinary property”, actually, for any stick to have. I think he must be wrong. If the stick is a stick, for example, 39.37 inches long (I assume we have some different standard for inches), why isn’t it one meter long? Anyway, let’s suppose that he is wrong and that the stick is one meter long. Part of the problem which is bothering Wittgenstein is, of course, that this stick serves as a standard of length and so we can’t attribute length to it. Be this as it may (well, it may not be) is the statement “stick S is one meter long”, a necessary truth? (NN, p. 54) In his penultimate sentence, Kripke seems to put his finger on the crucial point. However, he does not stop to discuss it, but goes on to ask whether the standard meter is necessarily one meter long, and whether this means that it is something known a priori. Although Kripke’s concerns are obviously not exegetical, his failure to engage with Wittgenstein’s point is problematic, as I  will argue. What Wittgenstein says about the meter has significant consequences for the considerations on the basis of which Kripke introduces the notion of contingent a priori, that is, a property that has the epistemological status of being knowable without recourse to

160  Oskari Kuusela experience or “without further investigation” (NN, p. 56) and at the same time the metaphysical status of contingency.2 In order to bring to view certain distinctions relevant for discussing Kripke’s introduction of the notion of contingent a priori, let us examine Wittgenstein’s remark more closely. Why can one not assert or deny, according to him, that the length of the Parisian standard meter is one meter? A key issue is this: insofar as the standard meter plays the logical role of a standard of measure, thus functioning as a means of representation, it cannot simultaneously play the role of an object of measurement or representation. Although we can say of the stick as the object of measurement or representation that it has or does not have such and such a length, herewith making a true/false contingent statement about its length, we cannot say this about the stick when it is playing the logical role of a standard of measurement (of one meter).3 This obviously does not mean that the standard could not be taken as an object of measurement. It is certainly possible to measure the length of the standard meter, as we do when calibrating measuring instruments. However, when a stick that has been historically used as the standard of measurement is taken as an object of measurement, it does not play the logical role of a standard of measurement. When taken as the object of measurement the stick assumes the role of the object of measurement, that is, an object of representation. Statements about its length in this sense are therefore not statements about the stick qua a standard of measurement, and their possibility does not show the possibility ascribing a length to the stick qua standard of measurement. The preceding point is illustrated by the impossibility of measuring a measuring tape with itself. In precisely this sense, whenever the standard meter plays the logical role of a standard of measure, it cannot at the same time play the role of an object of measurement. The logical roles of an object of representation and a means of representation are mutually exclusive, as the impossible feat of using a measuring tape to measure itself illustrates.4 Thus, we reach the same point again: it is impossible to ascribe the property of the length of one meter to the standard meter or deny that it has this property, that is, to assert truly/falsely that it has or has not such and such a length, qua a standard of measurement. This possibility is excluded by the role of the stick in the language-game as the standard of measurement. This explains why Wittgenstein denies that we would be dealing with an extraordinary property of the meter stick instead of merely talking about its role in the language-game of measuring. Should someone attempt to employ the stick simultaneously as a standard and an object of measurement, this would not count as measuring, and there is no result from such a pretend measurement that would either affirm or deny that the stick has a particular length. Contrary to Kripke’s suspicions, it is therefore not some extraordinary property that stops us from ascribing a length to them qua standards of measure. It is just that this is not how measuring or the language-game of measuring works. The standard of meter or a

Overlooked Distinctions 161 measuring tape seemingly used to measure itself is not used to measure anything. Indeed, if it could be used to measure itself, this would be an extraordinary kind of measurement. It would be one that always gives the same result, regardless of any expansion or contraction of the stick. Evidently, such “measurements” are crucially different from real measurements made, for example, to calibrate measuring tools, and there’s little reason to call such pretend measurements “measuring”. It may be helpful to note that it would be problematic to object to the preceding by saying something like the following: Of course we can affirm that the standard of meter is one meter long! If we cannot affirm this, then, absurdly, it seems we do not know what standard of measurement we are employing, i.e. the meter. But if we can affirm that we are using the meter, then surely we must know what the length of the stick is! How could we affirm something we do not know?! This can be responded to as follows. Undoubtedly, one can affirm what system or standard of measurement one is or has been using, and relatedly it is of course possible to say of the standard meter qua standard that it is the standard for one meter as opposed to some other unit of measurement. Crucially, however, such an affirmation of what system of measurement one is using does not constitute an ascription of the property of the length of one meter to the standard in the sense of a true/false contingent statement about an object of measurement. What is affirmed is the use of a certain means of representation, not the length of the stick with the help of which this means of representation is specified qua an object of representation. Accordingly, the affirmation does not constitute a substantial knowledge claim about the length of the stick, unlike a contingent true/false statement about the length of an object of measurement would do. (I distinguish at the end of this section between two notions of contingency that Kripke does not explicitly distinguish.) The affirmation is simply a statement concerning the use of a particular standard of measure, that is, that one will do measurements in the metric system. The point I wish to make is the following. I can affirm what standard of measure I am using by saying, “This is one meter long”. Imagine, for example, that I am holding the meter stick in my hand and showing it to you. If we assume that I have just defined the length of one meter with reference to this stick, the statement that affirms what standard I am using can be described as a priori in the sense that it does not require any “further investigation”, that is, finding out what the length of the stick is by measuring it (cf. quote from NN, p. 56 in Section 8.2; I will discuss different ways of construing Kripke’s claim there). As explained earlier, however, when I  use these words to affirm which standard I  am using, I am not using the words as an assertion about the length of the stick in the sense of a contingent true/false length-ascription. It is, of course, possible to use the very same words to make an assertion about the length

162  Oskari Kuusela of the measuring stick. For example, if you doubt that the stick has been tampered with, I could use a measuring tape to measure it and confirm that the stick still is one meter long, stating “This is one meter long”. Evidently, however, the stick figures here as the object of measurement, and the latter statement is not a priori. This assertion is not a statement about the stick qua standard whose length I already know, but it ascribes a length to it qua an object of measurement. Importantly, the sentence “This is one meter long” can be used in more than one way, that is, (1) to make a true/ false assertion about the length of an object, (2) to define how long one meter is (cf. the example “This is one unit long” in Section 8.3), or (3) to affirm what standard of measurement one is using. (There might still be further uses; I do not wish to claim that this list is exhaustive.) What is not possible, however, is to use the words in these different ways at once, as if defining or affirming the length of the stick qua standard of measurement and simultaneously making a contingent knowledge claim about its length qua object of measurement. But there is no extraordinary metaphysical property that prevents this. It is just that no sense has been given to such a statement. One might just as well think that using the word “bank” simultaneously in different senses puts one in a position to speak about monetary institutions that have the extraordinary metaphysical property of only existing on river edges. (Here metaphysics starts to resemble magic, as if extraordinary uses of words could bring about, or give us access to, extraordinary facts.) To complete this initial clarification of relevant notions before discussing Kripke on the contingent a priori, it is also important to observe the following. In his discussion, Kripke seems to rely not only on different unacknowledged uses of relevant sentences but also on an ambiguity of the term “contingent”. It is one thing to say of an object of measurement that it is contingent what its length is. Contingency in this sense is a matter of the truth/falsity of contingent statements. It is contingently true that a certain stick has a particular length, and corresponding to this, statements about its length are contingently true/or false. But it is important to keep contingency in this sense, that is, the contingency of empirical statements, distinct from the contingency in the sense of the arbitrariness of definitions. Someone could have picked up a different stick to mark the length of one meter, and it is contingent in this sense how long “one meter” was defined to be. The contingency of this definition, however, is not a matter of the contingency of the truth/falsity of empirical statements. Had someone defined “one meter” differently from how it was actually defined, this would not amount to making a false statement, and neither does defining the meter as it was actually defined make true the definitional statement “This is one meter long”. Thus, the contingency of empirical truths is logically different from the contingency of definitions. The arbitrariness of a definition is not

Overlooked Distinctions 163 a matter of it stating a contingent truth about what it concerns. (I will say more about this distinction in Sections 8.3 and 8.4.) 8.2  Overlooked Distinctions: Kripke’s Mistake Let us now turn to Kripke’s question whether (what seems like) a statement about the length of the standard meter, “Stick S is one meter long at time t0”, employed to define the standard of one meter, constitutes a necessary truth, or more broadly what the metaphysical, epistemological or logical status of this statement is. Kripke is, of course, right that a stick with a different length could have been adopted as the standard for one meter. There is no necessity that any particular length should be adopted as the standard for meter but (leaving aside questions of practicality) the choice is arbitrary. As Kripke tells us, one way in which a standard different from the actual historical one could have come to be adopted is that the stick would have been heated, whereby its length would have differed from that of the stick that was actually defined as the standard. In Naming and Necessity, Kripke describes the situation as follows from the point of view of the person stating the definition of “one meter” with the intention to determine the reference of “one meter” and to rigidly designate the length of the meter. There is a certain length that he wants to mark out. He marks it out by an accidental property, namely that there is a stick of that length. Someone else might mark out the same reference by another accidental property. (NN, p. 55) Insofar as ascribing the status of a necessary truth to the definition would require that “one meter” could only be defined as a particular length that corresponds to 39.37 inches, the definition evidently does not state a necessary truth. According to Kripke, defining the standard meter or determining the reference of “one meter” by means of the sentence “Stick S is one meter long at time t0” constitutes a contingent a priori statement (see next quote).5 Or in any case, taking into account certain questions of interpretation to be discussed shortly, he maintains that this sentence can express a contingent a priori truth after the definition has been given. His argument in support of this claim seems to be that, since the statement does not state a necessary truth (stick S could have been of a different length), it must have the metaphysical status of a contingent truth.6 At the same time, he also maintains that its truth can be known a priori. In this way, Kripke then seeks to drive a wedge between the notions of necessity and a prioricity, in opposition

164  Oskari Kuusela to the philosophical tradition that has assumed that what can be known a priori is necessary in the sense of being independent from the contingencies of the world of experience. Kripke writes about the status of the statement in question: What then, is the epistemological status of the statement “Stick S is one meter long at t0”, for someone who has fixed the metric system by reference to stick S? It would seem that he knows it a priori. For if he used stick S to fix the reference of the term “one meter”, then as a result of this kind of “definition” (which is not an abbreviative or synonymous definition), he knows automatically, without further investigation, that S is one meter long. (NN, p. 56; cf. p. 63) This quote raises questions about how important it is for Kripke’s introduction of the contingent a priori that he envisages the person in the example to possess a priori knowledge of the length of the stick after he has defined the meter. Before considering this, however, let me connect Kripke’s claim with what I said in Section 8.1. I hope that this has made it possible to see the problem with construing the statement “Stick S is one meter long at time t0”, at time t0 when the definition is given, as a statement that is both a priori and states a contingent truth. This assumes that it would be possible to use “Stick S is one meter long at time t0” simultaneously as (1) a definition, that is, a stipulation by means of which the length of “one meter” is defined or the reference of “meter” fixed, and the truth of which can be known a priori, that is, independent of any empirical investigation or any “further investigation” (NN, pp. 54, 56; for Kripke on the notion of a priori, see also pp. 34–35, 158–160), and (2) as a contingently true statement about the length of the meter stick. As explained, however, this is not possible, because the logical roles of a standard of measurement and an object of measurement are mutually exclusive. Although a sentence such as “Stick S is one meter long at time t0” can be alternately used in the logical role of definition of “one meter” and to make a statement about the length of a stick qua an object of measurement, it cannot perform both roles at once. This it cannot do any more than a measuring tape can be used simultaneously as the means of measurement and the object of measurement to measure itself. Moreover, as noted at the end of Section 8.1, neither does the arbitrariness of the definition of “one meter” mean that the definitional statement states a contingent truth in the sense in which “Stick S is one meter long at time t0” states such a truth when employed to make a statement about the length of stick S qua an object of measurement. If construed as a claim about what the person knows at the moment of giving the definition, Kripke’s introduction of the notion of contingent a

Overlooked Distinctions 165 priori therefore seems to rely on an unnoticed or unacknowledged attempt to use of the sentence “Stick S is one meter long at time t0” simultaneously in two mutually exclusive logical roles or an unnoticed or unacknowledged wavering between the different uses of the sentence. On the one hand, the use of the sentence as a definition to fix the reference of “one meter” makes it look like the sentence would state something that is true a priori. (As Kripke says the stipulation seems to put us in a position to know something independent of any “further investigation”, and in this sense independently experience.) On the other hand, he also imagines the sentence as being used to make a true/false statement about the length of stick S, whereby it seems to state something contingently true about it. This creates the impression that the sentence would be doing both jobs at once, stating something true a priori and stating something contingent. But as explained in Section 8.1, this is confused; it involves a failure to keep track of different possible uses of the sentence. If so, it is likewise confused to conclude that there should be such an epistemological-metaphysical property as being contingent and knowable a priori, and that the sentence “Stick S is one meter long at time t0” provides an example of the ascription of such a property to stick S. Employed in the two roles at once, as Kripke tries to do, the sentence does not speak of anything, just as using “bank” simultaneously in its different senses (whatever that would mean) does not put one in a position to speak about special kind of monetary institutions that only exist on river edges. Neither can the contingency of the truth of the definitional statement be explained in terms of its arbitrariness. Insofar as “Stick S is one meter long at time t0” plays the role of a definition, it does not state a contingent truth about the length of stick S. Had “one meter” been defined as a different length, the sentence would not have stated something false. But perhaps, Kripke’s case for contingent a priori ought not to be understood in the preceding terms, and it is essential to his claim that the person in the example would be in possession of a priori knowledge only after the definition has been given. If so, he would not be claiming that the stipulative definition itself constitutes an instance of a priori knowledge. Although there certainly seems to be something very odd about the view that the person knows more or knows something different immediately after he has given the definition that he does not know at the moment of giving it—how is he in a different epistemological position after the definition?—let us put this to the side, and consider whether this way of construing Kripke’s case would help his case. So, at t1, one minute after defining the length of one meter, the person who defined the length of one meter turns to the stick used in the definition and says “Stick S is (was) one meter long at time t0”. Can this be understood as an instance of contingent a priori knowledge? Given that the length of one meter was defined with the help of the stick at time t0, we can

166  Oskari Kuusela certainly say of the stick qua standard that its length was one meter at t0. It was stipulated to be just that, and of course it is possible to know how long it was stipulated to be independent of recourse to experience or “without further investigation” (excluding problems like a serious amnesia). So, the statement, or what the person knows who defined the meter, qualifies as a priori in Kripke’s sense. This, however, is not a contingent true/false statement of length about the stick qua an object of measurement. Stick S was not measured at t0, and neither are we in position at t1 to measure its length at t0. Rather, this a priori statement corresponds to the case of affirming what standard of measurement is in question, that is, that the stick was defined as the standard for one meter, not some other length. (Indeed, if we could not know this “without any further investigation” it is hard to see how measuring would be possible at all. We cannot constantly be double checking our units of measurement by measuring them, but this generates a paradox: we are now imagined to somehow both have and not have a unit of measurement at our disposal.) That the sentence “Stick S is one meter long at time t0”, functions here as an affirmation of the standard stands out clearly, if we compare it with a knowledge claim concerning the event of the definition of the meter. That the stick was defined to be one meter long is an instance of contingent knowledge regarding a past event based on experience. This could not be known a priori, but only a posteriori. Knowledge that such and such an event took place is a standard example of a posteriori knowledge. And once again: the arbitrariness of the definition does not mean that affirming what standard of measurement one uses constitutes a statement of a contingent truth about the length of stick S. Now, we can of course infer from the stick having been stipulated to be one meter long at t0 that, had it been measured at t0 its length would have been one meter (assuming contrafactually that we would have had this unit of measurement, i.e., “one meter” at our disposal already at t0 when it was first defined). Again, however, this will not give Kripke what he is looking for, that is, an instance of knowledge that is both contingent and a priori. What we now have is a counterfactual statement about the past. The stick was not measured at t0, but if it had been, it would have come out as one meter, because that is how long it was stipulated to be. Indeed, there are an infinite number of true counterfactual statements that can be inferred from the stipulative definition of the stick as one meter long. For example, had we laid another two-meter-long stick next to the standard of meter, the other stick would have been double the length of stick S. But the possibility of inferring such counterfactual statements does not show that the person who defined one meter at t0 has at t1 a priori knowledge of how long the stick was at t0 which qualifies also as knowledge expressible in terms of a contingent true/false statement about the length of the stick. If we infer from the definition of the length of one meter that the stick used to

Overlooked Distinctions 167 define it was one meter long qua contingent true/false statement about the length of the stick, this is a trivial consequence of the definition. From the definition of the length of one meter at t0 by means of stick S, one can infer a statement about its length at t0. What is inferred is a statement of length regarding stick S qua a contingent statement about the length of the stick that at t1 that can be expressed by the sentence “Stick S was one meter long at time t0”. But when used to express a statement about the length of stick S in this sense, the sentence is no longer playing the role of the definition of the meter of which we could say that it is a priori. What we have now is a contingent statement of length inferred from the definition of “one meter” in terms of stick S. Once again, the statement therefore does not qualify as both a priori and contingent, but this appearance arises from unnoticed wavering between the different uses of the sentence in question. That the statement inferred from the definition is merely a usual kind of contingent statement is indicated by how English grammar requires one to formulate it in the past tense. (By contrast, it would be very complicated to state the definition of the meter at t1 with reference to the length of stick S at t0. This would require knowledge of how the physical conditions at t0 and t1 might affect its length, and the definition could not simply be stated by means of Kripke’s definitional sentence. Naturally, to speak of relevant physical conditions we would also have to assume relevant standards of measurement.) It is easy, and perhaps tempting, to imagine something like the following. Having defined the reference of “one meter” with the help of stick S one checks its length in one’s mind, and finds that the length of the stick qua contingent length of a physical stick corresponds to the length of one meter as an abstract object that constitutes the reference of “one meter”. Can this be understood as an instance of contingent a priori knowledge in Kripke’s sense? One can certainly have such an image in one’s mind “without further investigation”, and given the contingency of how long “one meter” was defined to be, it might now seem that here we finally have something that is both a priori and contingent. But again a closer examination of the case reveals that this is not so. First, as noted, the definitional statement itself does not state a contingent truth about the length of stick S, but it is merely arbitrary like stipulative definitions in general. Second, when comparing stick S in one’s mind to the reference of “one meter”, one is essentially imagining a measurement. This is just what measuring length is. It is a matter of comparing the length of an object with a standard of measurement to establish what the length of the object is. Thus, this case corresponds to the one where we measure the stick that was historically used to define the length of one meter by using the unit of measurement to establish the length of the stick that was originally used to define it. Here, the stick therefore figures as an object of (an imagined) measurement. Accordingly, the statement about the length of the stick is a usual kind of

168  Oskari Kuusela contingent statement about the result of measurement—except here no real measurement takes place. An imagined measurement is not a real measurement. (Measuring a stick in one’s mind is counts just as much as a measuring as building a house in one’s mind counts as building a house.) Although this case might suggest that here one is establishing the length of the stick independent of actually investigating its length, and thus a priori, this is not the case. To imagine that one established the length of an object is not to establish its length but to imagine one established its length. It therefore seems that, however we construe Kripke’s example, it does not come out right in the sense of providing an example of contingent a priori knowledge. The point could be put like this: similarly to how the bending of light waves can create a false impression of the physical presence of an object by projecting its image onto where the object is not, so Kripke’s way of bending the uses of the sentence “Stick S is one meter long at time t0” creates the false impression of the discovery of the category of contingent a priori truth. Due to how the impression of this discovery arises from a failure to distinguish between two logically exclusive uses of the sentence in question, however, Kripke’s introduction of contingent a priori has no more validity than the attempt to use the word “bank” in two different ways at once, in order to speak of monetary institutions that can only exist on river banks. This is what Kripke’s introduction of the property of contingent a priori in effect seems to boil down to: the conclusion that there is such a property is a mirage created by overlooked distinctions in the use of “Stick S is one meter long at time t0”. Perhaps it is worth emphasizing that it is no part of my argument to try to beat Kripke with the stick of ordinary language, that is, to tell him that language can only be used in such and such ways and that he has broken certain rules of language use. (Relatedly, my reference to language-games involves no claim about anyone having to conform to any particular rules of language use.) Kripke, or anyone else on his behalf, is free to introduce a use for his definitional sentence that makes it possible for it to perform the double-function Kripke envisages, as long as this is not done circularly, merely in order to uphold his claim about there being contingent a priori properties or truths. Such an explanation cannot give the sentence a comprehensible use any more than the circular definition “Saul uses ‘Moses’ to refer to whatever Ludwig uses it to refer to, and Ludwig uses ‘Moses’ to refer to whatever Saul uses it to refer to” can be used to define “Moses” (cf. NN, pp. 68–70, pp. 89–90). Both cases involve a failure to specify any use for the expression in question. My criticism, in other words, is that Kripke has not specified a use for “Stick S is one meter long at time t0” in the capacity of a contingent a priori statement, while I have neither the authority nor any wish to limit his freedom to give such a specification. Admittedly, it is difficult to see what a Kripkean use for the sentence could

Overlooked Distinctions 169 be, given its similarity with the case of the oxymoronic auto measuring tape. Nevertheless, I  am methodologically committed to not letting this prejudice me against attempts to give a use to Kripke’s sentence as a contingent a priori statement. Thus, my challenge to Kripke could be presented in the form of a question: how is the sentence to “Stick S is one meter long at time t0” used when it is allegedly used to state something that is both a priori and contingent? As observed in note 6, Kripke seems to assume that we can infer from the fact that his exemplary sentence does not express a necessary truth that it expresses a contingent truth (NN, p. 56). Arguably, however, the status of the sentence as not expressing a necessary truth does not suffice to settle its status as expressing a contingent truth, pace Kripke. His inference from the definitional sentence not expressing a necessary truth to its expressing a contingent truth is not sound but involves the false premise that these are the only options, besides running together contingency in the sense of the contingency of empirical true/false sentences and the arbitrariness of definitions. Let us now turn to this issue. 8.3  Definitions and Truth Rather than simply assuming that the sentence “Stick S is one meter long at time t0” states something true, a better question for Kripke to ask first would have been “whether the definition states a truth to begin with”. As I explain in this section, Kripke’s assumption cannot be taken for granted, and it seems that rejecting this assumption can help one to see more clearly what is going on in cases such as the definition of the meter that Kripke employs to introduce the notion of contingent a priori. Consider a case analogous to the definition of the meter. I define a unit of measurement called “unit” by picking up a pen and saying: “This is one unit long”. Just as Kripke describes the definition of the meter, I could have picked up something else, for example a shorter pencil, and defined its length as one unit. A natural way to describe the situation is to say that this definition, that is, the statement of a rule by means of which I establish what counts as one unit long, constitutes an arbitrary stipulation (and with this Kripke agrees 1981, pp. 54, 56; cf. Kuusela 2008, pp. 113–116, for the distinction between statements of a rule and true/false factual statements). But does this stipulation state a truth? As I have argued, it is not a true/false assertion about the length of any object. Indeed, the possibility of such a true/false assertion presupposes that “unit” has already been defined as a standard of measurement or a mode of representing lengths, but in the hypothetical situation we are considering “unit” is first being defined as a standard of measurement. True/false assertions in terms of “unit” are therefore ex hypothesi not yet possible in this situation, only

170  Oskari Kuusela after the definition has been given with reference to some object. It is also important that had I  picked up the pencil instead of the pen, or a third object, I would not have stated anything false or made a mistake in defining “unit”. One might be tempted to regard this exclusion of the falsity as implying that the definitional statement is true. But then defining “unit” with reference to anything whatsoever will count as saying something true. How very easy this makes the attainment of truth in comparison to empirical and mathematical truths can be regarded as a reason to think that the stipulation is best not regarded as a knowledge claim and that it does not state anything either true or false. An objection concerning the notion of knowledge in the case of the contingent a priori was made to Kripke by Keith Donnellan: If a truth is a contingent one then it is made true, so to speak, by some actual state of affairs in the world that, at least in the sorts of examples we are interested in, exists independently of our language and our linguistic conventions. How can we become aware of such a truth, come to know the existence of such a state of affairs, merely by performing an act of linguistic stipulation? (Donnellan 1977/2012, pp. 149–150) If the definition of the meter constitutes a true knowledge claim concerning a contingent fact in the world, this seems a suspiciously easy way to acquire knowledge. Moreover, as Donnellan points out, there is a difference between knowing what something is called, for example, that a certain measuring stick in Paris is called “the meter”, and de re knowledge regarding that object, for instance, its length in the sense of whether it’s closer to one yard than one foot, or shorter or longer than oneself (Donnellan 1977/2012, pp. 164–166, 170–171; I have changed the example). Kripke too expresses reservations regarding the notion of knowledge that appears to correspond to Donnellan’s point, admitting that such cases might give a reason to try to reformulate the traditional thesis about a prioricity and necessity, although he says he does not know what such a reformulation would be. [M]erely by fixing a system of measurement has [someone] thereby learned some (contingent) information about the word, some new fact he did not know before? It seems plausible that in some sense he did not, even though it is undeniably a contingent fact that S is one meter long. (NN, p. 63, footnote 26; my square brackets; the point about the possibility of reformulating the traditional thesis follows immediately after this quote)

Overlooked Distinctions 171 Problematically, Kripke seems here to pass over unnoticed the distinction between contingency in the sense of arbitrariness of definitions and the contingency of true/false empirical statements. Relatedly, Kripke has emphasized that his example of the definition of the reference of “one meter” is to be imagined as given in the presence of the stick. In such a case, the reference-fixer or whoever witnesses fixing the reference of “one meter” would seem to acquire knowledge, or whether the length of the meter stick is closer to the length of a yard or an inch (assuming they possess the latter concepts) or how this length relates to their own height. But now the knowledge in question no longer seems a priori. The knowledge in question seems a posteriori, since it depends on experience of how long the stick appears to be. (Nathan Salmon makes this point, as well as reporting on Kripke’s confirmation that he did have in mind a situation where the reference is fixed in presence of the meter stick; Salmon 1988, p. 200, note 9.) These considerations also reveal that cases presented by Kripke as examples of contingent a priori knowledge are not uniform. Even if a determination of reference, when given in presence of the object referred to (or in the presence of a standard, such as the meter), might provide knowledge of the object, this does not seem so in other cases. This is exemplified by Kripke’s example of fixing the reference of “Neptune” without witnessing the object, and which Donnellan discusses as part of his critical argument. In short, when a reference of “Neptune” is determined on the basis of the description “Planet that causes perturbations in the orbit of Uranus”, this does not seem to provide any knowledge regarding Neptune in the sense of information regarding a particular heavenly body. Rather, here some yet unknown object is postulated as the reference of “Neptune” without any knowledge of the nature of this object. For all we know on the basis of the presumed contingent a priori statement used to determine the reference of “Neptune”, the reference could be a gigantic statue of Aristotle with his dog orbiting in space.7 How might one respond to these problems regarding knowledge of contingent a priori? In contrast to Kripke, one could adopt the view that by stating my definition of “unit” I have not stated anything that is either true or false. Although “This is one unit long” can be used to make a true/false empirical statement about the length of an object, when this object is taken as the object of measurement and “unit” used as the standard of measurement, this is not how “This is one unit long” is used when employed to define “unit”. Statements of a rule in general might then be said to lack truth value in the following sense: they do not describe anything independently given which they would represent truly or falsely, for example, the length of a stick. As said, none of my alternative definitions of “unit” is true or false about anything in reality; neither the pen nor the pencil or

172  Oskari Kuusela any third object is the true length of “unit”, but its length is whatever I stipulate it to be. Relatedly, to elucidate the point, when a description of a game such as chess is given in terms of statements of a rule, those statements describe a possible game. The rules are not a true/false description of chess as an abstract object, and such a description of a possible game in terms of its rules is independent of whether anyone ever played or will play the game. (This independence is illustrated by the possibility that I could now invent a game and describe it in terms of rules, without the game ever being played.) Of course, one can then make further use of a description of a game in terms of rules to make empirical statements about actual games that people play, used to play, or perhaps fail to play. But this is to make a further use of the description in terms rules. As Wittgenstein points out, the notion of description is ambiguous between true/false descriptions regarding something independently given, such as a house or a tree, and descriptions in the sense of design, as when designing a game, calculus or physical objects, such as furniture, a house or an engine (MS 113, p. 27v from 1932/TS 211, p. 576/TS 213, p. 245r cf. MS 115, p. 59; see Kuusela 2008, pp. 114–116, for a quote and discussion).8 As Wittgenstein also emphasizes, adding a definition, such as my definition of “unit”, to a proposition does not (and ought not) affect the sense or truth-conditions of the proposition. For example, “Wittgenstein was 1.68 meters tall, and meter = the length of the Parisian standard meter” says the same as “Wittgenstein was 1.68 meters tall”. Both sentences are true in exactly the same circumstances, assuming “meter” means what it means. (The former sentence says no more than the latter just as consulting a dictionary does not add anything to the content of a sentence, even if it may help a person to understand the content of the sentence or the proposition it expresses.) A statement of a rule in this sense is then an instrument of language that puts one in a position to make true/false statements, but is not itself a true/false statement, which makes definitions incapable of affecting the sense or truth-conditions of sentences to which it is added (MS 113, pp. 22v–23r/TS 212, pp. 570–571). This point is also made in Investigations §50, where Wittgenstein comments, immediately after his statement on the standard meter, on his example of a standard sample of sepia, imagined to be employed as a color-standard like the Parisian standard meter is used as a standard for length: “This sample is an instrument of the language, by means of which we make colour statements”. Similarly, the sentence “Stick S is one meter long at time t0” when used to define the meter (to fix a reference of “one meter” or to stipulate how long a meter is) can be regarded as a statement of a rule that is itself neither true nor false, pace Kripke. Rather, the sentence puts one in a position to make true/false statements about lengths in terms of meters. In this sense, it is

Overlooked Distinctions 173 an instrument of language by means of which we make statements about length, but not itself a true/false statement about the length of anything, including the stick used to define “one meter”.9 8.4 Definitions and the Non-temporal Use of Statements of a Rule I conclude with a Wittgensteinian proposal regarding what seems a better way to understand the logical role of definitions, such as that of the meter, than the account offered in Naming and Necessity. Wittgenstein distinguishes statements of what he calls “grammatical rules”, including any definitions used to introduce terms, from true/false statements by characterizing the use of grammatical rules as non-temporal. (Similarly, he understands the use of mathematical and geometrical sentences as nontemporal.) (See MS 113, p. 29v/TS 212, p. 716/TS 213, p. 246r; MS 117, pp. 24, 37–8; MS 117, p. 25/MS 118, p. 18r; TS 221, pp. 156–7; MS 138, p. 8a; MS 164, p. 4.) Non-temporal use means that such sentences are not used to make statements about anything in time and space, either about particular cases or about something general, as opposed to empirical statements about particular cases and generalizations over them. That such statements do not concern anything in time and space then explains the sense in which they are exceptionless or universal. For example, “black is dark” in the capacity of a grammatical rule or grammatical statement does not concern any particular cases of blackness (or the uses of relevant word in English). It simply states the rule that whatever is black counts as dark. The case of the meter can be understood similarly. When defined with the help of a standard such as the Parisian meter stick, “one meter” is not used to refer to anything in reality, including the meter stick itself or the length of a meter construed as an abstract object. Rather, through this definition, the Parisian stick is adopted as the standard for “one meter”, whereby the stick now constitutes a mode of representing the length of one meter. Consequently, anything with this length will count as one meter long, universally and without exceptions, while the definition itself does not constitute a statement about the length of anything qua statement about the length of an object. Herewith the possibility of confusions, such as Kripke’s with regard to the contingent a priori, as I described it in the preceding, is excluded. The Wittgensteinian account thus excludes the possibility of confusedly envisaging the definition as a statement of length that can be known a priori but which nevertheless at the same time constitutes a contingent knowledge claim about the length of the Parisian stick. To be sure, another length could have been adopted as a standard for the meter. But the definition itself, understood as a grammatical rule, is silent

174  Oskari Kuusela about that. It does not state a contingent truth about the length of any stick chosen to be the standard of meter, but its function is to make possible measurements of length by means of the standard of meter. The definition determines a mode of representation, but it is not itself a statement that makes use of this mode of representation, in contrast to the measuring tape imagined to be used to measure itself.10 Relatedly, to refer back to what Wittgenstein says about simple objects in Investigations §50, there is now no need to assume that the definition of the meter somehow manages to establish a reference to a certain length across all possible worlds, like Tractarian names for simple objects, a reference which must be maintained on Kripke’s account of names in order to secure that propositions about lengths in metric terms do not change their truth-conditions. Rather than securing a rigid reference to an abstract object which we now need to add to our ontology, the definition is used to set up a linguistic instrument and to determine a mode of representation. Here, it might help to appreciate the broader significance of the Wittgensteinian account for discussions in metaphysics to recall his proposal that statements about essential features are to be understood as grammatical statements in the preceding sense. When a statement is made, such as “black is dark”, this is not a true/false statement regarding darkness that designates it as peculiar property universally connected with blackness, with not only the actuality but also the possibility of exceptions excluded. On a traditional understanding, according to which metaphysical statements state something true, a host of questions will arise at this point regarding our knowledge of such peculiarly exceptionless facts and the justification of statements concerning them. By contrast, relevant problems receive an immediate deflationary answer on the Wittgensteinian account. “Black is dark” is not an extraordinary, necessarily true knowledge claim. It is not a knowledge claim at all, but it expresses a rule according to which whatever is black is dark, and nothing black will not count as not being dark, given the way we have fixed the use of relevant expressions. Importantly, however, this does not mean that so-called metaphysical necessities are simply fixed by our linguistic rules or conventions in the style of Carnap’s conventionalism (Carnap 1956/1988). It is only that such exceptionless necessities, whatever their source might be, are expressed by means of grammatical statements. As Wittgenstein remarks in the Investigations: “Essence is expressed in grammar” (PI, §371; see Kuusela 2008, ch. 5; Kuusela 2019, Ch. 4 for discussion). On this account, identity and exceptionless necessity are the business of grammar, not the target of true statements about reality. Notes 1 As Wittgenstein points out, this kind of view can be found in Plato’s Theaetetus, and “Both Russell’s ‘individuals’ and my ‘objects’ (Tractatus

Overlooked Distinctions 175 Logico-philosophicus) were likewise such primary elements” (PI, §46; cf. §§38–39, 45). These postulated entities are notably different from the objects of everyday experience, and in this sense extraordinary, which, however, is essential for their being able to play the logical role of the ultimate terminus of reference. As Wittgenstein outlines, this logical role excludes the possibility of any descriptions or propositions regarding the postulated objects, including propositions concerning their existence. Instead, descriptions/propositions can only concern the relations between the postulated kind of objects (their combinations). 2 I will come back Kripke’s notion of a priori in Section 8.2. 3 It is also important that statements about the length of the meter in metric terms already assume the notion of the meter. I will come back to this in Section 8.3. 4 A linguistic instrument that might seem not to conform to this principle of mutual exclusion is examples. An example is a case employed to represent other cases, whereby the possibility of representation is based on the exemplary case sharing properties with the cases it represents. Here the means of representation, the exemplary case, is an instance of what it represents. However, since examples are not used to only represent themselves, but are meant to have generality, that is, to represent other cases not just themselves, it is not really the case that examples would not respect the distinction between means and objects of representation. In order to function as an example it seems that an exemplary case needs to be numerically distinct from what it represents, even if it would be otherwise identical with the cases it represents. But however this may be, the function of examples is not relevant for my critical argument concerning Kripke, since measuring is not a matter of using the standard of measurement as an example. The function of the Parisian standard meter is neither to be an example of measuring sticks in general nor is it an example of the length of a meter in the sense that things with a similar length count as one meter long. Rather, things with exactly this length count as meter long. Moreover, the standard also applies to things with a very different length, their lengths being represented as multiples or fractions of the meter. The latter is not part of the use of examples. 5 According to Kripke, this will not count as a determination of the meaning of “one meter” insofar as “one meter” is not synonymous with “the length of S at t0” (NN, p. 56). This point can be left to the side as having no bearing on my argument. 6 I return in Section 8.3 to the question whether the definition should be taken to express a truth at all. This means that there is also a question about the soundness of Kripke’s inference which seems to assume that if the truth expressed by the definitional statement is not necessary, then it must be contingent. Arguments involving the premise that so and so are the only options are of course notoriously tricky, almost as if designed to invite challenges in terms of other possibilities. (It might seem that the same applies to my argument about the different possible uses of the sentence about meter, but see qualifications at the end of this section.) 7 In certain respects this is as Kripke would like it to be. Any description regarding a rigidly designated referent might turn out to be false, and this is why Russell’s account of complex names (as opposed to logically proper names) is problematic, as Kripke argues (NN, pp. 48–49, 53, 57, 83–84). Nevertheless, a problem about the notion of knowledge does arise, i.e. whether relevant kinds of reference-determining descriptions constitute knowledge, and whether this knowledge is a priori or a posteriori. In the case of this example it is possible

176  Oskari Kuusela to stipulate that whatever, including a statue of Aristotle with his dog, might cause perturbations in the orbit or Uranus must be another object orbiting the sun, i.e. a planet. This, however, does not address the problem of whether what is at stake is knowledge about reality, but deciding to call anything affecting the orbit of Uranus “a planet” is a further stipulation. 8 Rudolf Carnap, possibly under Wittgenstein’s influence, is similarly clear in The Logical Syntax of Language that syntactical sentences in a metalanguage ought not to be understood as descriptive in the sense of true/false descriptions about something independently given, comparing syntactical sentences to descriptions of geometrical figures. Syntax in this sense is contrasted with what Carnap calls “descriptive syntax” which consists of empirical statements regarding the rules of particular actually existing languages (Carnap 1937/1967, pp. 6–7, 15, 53, 168). Of course, this similarity does not mean that Wittgenstein’s and Carnap’s views would be similar in other respects. I  will note an important difference relating to Carnap’s conventionalism at the end of this section. 9 Kripke gets a clear bill on whether the truth-conditions of “Wittgenstein was 1.68 meters tall” and “Wittgenstein was 1.68 meters tall and meter = the length of stick S at time t0” are the same. Although he emphasizes that the reference of “one meter” could have been determined differently from how it actually was determined, this does not affect the truth-conditions of “Wittgenstein was 1.68 meters tall and meter = the length of stick S at time t0” after the reference of “meter” has been determined rigidly across possible worlds. 10 In terms of Cora Diamond (2019), the definition is an instance of preparatory or propadeutic use of language as opposed to engaged uses, such as stating the results of measurement. Although the examples discussed by her in 2019 relate mostly to ethics, this terminology is readily applicable in the context of both theoretical and practical philosophy. Diamond discusses the standard meter in Diamond 2001 (reprinted in this volume).

References Carnap, Rudolf (1967) The Logical Syntax of Language. Routledge & Kegan Paul. (Originally published in 1937, shorter German version in 1934.) Carnap, Rudolf (1988) Empiricism, Semantics, and Ontology, in Meaning and Necessity: A  Study in Semantics and Modal Logic. The University of Chicago Press, 205–221. (Originally published in 1956.) Diamond, Cora (2001/this volume) How Long Is the Standard Meter in Paris? In T. McCarthy and S. C. Stidd (eds.), Wittgenstein in America. Oxford University Press, 104–139. Diamond, Cora (2019) Reading Wittgenstein With Elizabeth Anscombe, Going on to Ethics. Harvard University Press. Donnellan, Keith (2012) The Contingent A  Priori and Rigid Designators, in K. Donnellan, J. Almog, and P. Leonardi (eds.), Essays on Reference, Language and Mind. Oxford University Press, 147–178. (Originally published in 1977.) Kripke, Saul (1980) Naming and Necessity. Blackwell. Kuusela, Oskari (2008) The Struggle Against Dogmatism: Wittgenstein and the Concept of Philosophy. Harvard University Press.

Overlooked Distinctions 177 Kuusela, Oskari (2019) Wittgenstein on Logic as the Method of Philosophy: Reexamining the Roots and Development of Analytic Philosophy. Oxford University Press. Salmon, Nathan (1987–88) How to Measure the Standard Metre, Proceedings of the Aristotelian Society 88, 193–217. Wittgenstein, Ludwig (2000) Wittgenstein’s Nachlass: The Bergen Electronic Edition. Oxford University Press. Quotations by manuscript or typescript number following von Wright’s catalogue, abbreviated as MS/TS. Wittgenstein, Ludwig (2009) Philosophical Investigations. Wiley.

9 How Long Is the Standard Meter in Paris? Cora Diamond

In his lectures on “Naming and Necessity,” Saul Kripke raises questions about §50 of Philosophical Investigations, a long and complex section. He picks out and criticizes this pair of sentences: There is one thing of which one can say neither that it is one metre long, nor that it is not one metre long, and that is the standard metre in Paris.—But this is, of course, not to ascribe any extraordinary property to it, but only to mark its peculiar role in the language-game of measuring with a metre-rule. (PI, §50) I shall look at the relation between Kripke’s reading and criticism of that pair of sentences and his reading of Wittgenstein on rules. I  want to put Kripke-on-Wittgenstein-on-rules into a wider context of Kripke-in-disagreement-with-Wittgenstein. 9.1  Kripke on Wittgenstein and the Standard Meter In this section I summarize what Kripke has to say about Wittgenstein on the standard meter. Kripke first rejects Wittgenstein’s statement that one isn’t ascribing some extraordinary property to the standard meter in Paris, if one says that it can’t be said of it that it is one meter long or that it is not one meter long. Kripke disagrees; he says that that would indeed be a very extraordinary property, and that Wittgenstein must be wrong (NN, p. 274). If we measure the meter rod with a footrule, and it comes out 39.37 inches, then why isn’t it a meter long? He then uses the example of the length of the meter rod in developing his own ideas: he wants to explain why he denies that the statement that the rod is one meter long is a necessary truth. In order to explain why he denies this, he first describes how we can allow for the fact that the length of the rod varies. We could, he says, make a more precise DOI: 10.4324/9781003240792-10

How Long Is the Standard Meter in Paris? 179 definition of the meter length by specifying that a meter is the length of stick S at some particular time t0 (ibid.). Here we might note that this now supposedly more precise definition shows how far Kripke’s approach is from Wittgenstein’s. Wittgenstein is thinking of a language-game in which there is comparison of various objects with the meter rod in Paris; the reader knows what it is like to compare a measuring rod with something else, and that knowledge is needed if we are to see the point of Wittgenstein’s remark. If, however, we suggest, as Kripke does, that how long something is is determined, not by comparison with the rod in Paris, but by comparison with the length which it had at some particular time, it is now much less clear what language-game is being played. How am I to compare some object I now want to measure with the length the rod in Paris had five years ago? My point is not that there is no way to answer that question; there are certainly ways, involving the use of whatever theories, in which we could make such comparisons. The point is rather that, from Wittgenstein’s perspective, talk of a length used as a standard (a length, that is, with which we make comparisons) hangs in the air unless there is some context, either one that actually exists or one that we can imagine, in which we can see what is to count as making comparisons with the standard length. Kripke’s supposedly more precise definition of one meter is actually a definition which assumes that a standard length can be defined completely in advance and independently of our engaging in some activity of carrying out comparisons of lengths. (As Kripke sees the case, our activities of determining the length of things are not relevant to what it is we are referring to by “one meter,” hence needn’t be mentioned in discussing how reference is fixed. Nor is use in a languagegame relevant to what it is to refer to something, on Kripke’s view; there is an implicit reliance on what is here an unexamined idea of reference. These comments of mine involve a refusal to go along with Kripke’s way of separating what he thinks of as epistemological issues from metaphysical ones, including the metaphysics of reference, and so it could be argued that they beg questions against him; but my point here is merely that we are, without comment by Kripke, shifted into a mode of discussion which takes a particular conception of the issues for granted.) Kripke’s move towards a more precise definition should be seen as exemplifying what Stanley Cavell has called (in writing about Kripke on rules) “philosophy’s drastic desire to underestimate or to evade the ordinary” (1990, p. 68).1 Not that there need be anything un-ordinary about fixing a standard of length more precisely; what, in particular, indicates the philosophical move away from the ordinary is the willingness simply to ignore the connection between having a standard of length and having a way of telling how long things are (the willingness to ignore the connection with criteria which ‘articulate the ordinary’— see the quotation from Cavell in note 1).2

180  Cora Diamond Anyway, Kripke now has a more precise definition: a meter is the length of stick S at t0. Is it then, he asks, a necessary truth that S is one meter long at t0? No, he says, because the person giving the definition may have as his intention the fixing of reference of the term “one meter.” The person wants to refer to a certain length, which he picks out by an accidental property of stick S, the property of having that length at t0. It is easy to see that the stick did not have to have that property; it might have been heated at t0, and if it had it would have been longer: it would not in those conditions have had the length it had in the actual conditions. That S was that long at t0 is certainly not necessary. So, if we pick out a particular length by saying that it is the length that S had at t0, and if we say that a meter is by definition that length, then (this is Kripke’s argument) it is not a necessary truth that S is a meter long, because it is not necessary that it had, at t0, that length, the length we are referring to henceforward as “one meter” (NN, p. 274). (Here is another way of making Kripke’s point. Suppose that S had been heated at t0, and that we had defined the length one meter as the length that it had then. The result would be that we would have had a somewhat greater length as our standard meter. So although we would still have said that the length of S at t0 was the standard meter length, the length meant (referred to) by “one meter” would be a different and greater length. Case 1. S is 39.37 inches long at t0. We define “one meter” as its length at t0. Case 2. S is 40 inches long at t0. We define “one meter” as its length at t0. If we define “one meter” by the length S has in the Case 1 scenario at t0, then it is not a necessary truth that it has that length, since, in the Case 2 scenario, it has a different length.) Kripke goes on (NN, p. 275) to use the example to explain how he wants to distinguish between a priori statements and necessary ones. This is tied for him to the distinction between the epistemological status of a statement and its metaphysical status. If I fix the reference of the term “one meter” via the length which S has at t0, then I  can know the truth of “S is one meter long at t0” a priori, “without further investigation,” that is, without measuring it. But, as we have seen, S might perfectly well have had some other length at t0; it might not have had that length which we defined as the meter length. So it is not necessary that S have been one meter long at t0, any more than it is necessary that S have been 39.37 inches long at t0. Of no length is it necessary that S have been that long at t0. There are connections between defining a standard of length (something that is a measure of length) and having rules determining how length is measured. It would be possible to examine the relation between Kripke on the standard meter and Kripke on Wittgenstein on rules by starting with

How Long Is the Standard Meter in Paris? 181 the implications of Kripke’s treatment of the standard meter for the question what it is for something to be a measure, and how that does or doesn’t involve rules. But I take an alternative route; and I shall not reach until Part 9.7 Kripke’s treatment of rules and of Wittgenstein on rules. 9.2 Wittgenstein on the Length of the Standard Meter: Context and Connections One thing that may strike us, reading Kripke on Wittgenstein on the standard meter, is the contrast with his treatment of Wittgenstein on rules. Whatever one thinks of his interpretation of Wittgenstein on rules, Kripke clearly spent much time thinking about it and discussing it; whereas in the case of Wittgenstein on the meter rod, he appears to have taken Wittgenstein’s view to be not worth pondering—it is simply something Wittgenstein got wrong; it is useful merely as an example, and there is no suggestion that Kripke spent any time thinking about what was going on in the passage which he quotes and criticizes.3 In fact a great deal is going on in that passage. It is part of Wittgenstein’s extended discussion of philosophical ideas about names: names of simple elements, such that what is the case is the combination of such elements. So language describes what is the case by compounds of the simple names. What the names supposedly name is things, then, that cannot be said either to be or not to be. Wittgenstein’s argument in this extended passage is that that conception, which he utilized in the Tractatus, is the result of misunderstanding the role of samples in our language-game. The passage has connections with other important ideas in Wittgenstein’s early and later work. At its heart is the analogy between describing something and measuring; and the use of measurement analogies runs through Wittgenstein’s thought from the Tractatus onward.4 In the English translation of the passage, another connection emerges, between measures and rules. The Latin word regula, which gives us “rule,” has a group of earlier concrete meanings: a ruler for drawing lines, a footrule for measuring; in Latin and Italian also a pattern, a model, a sample or example. So the notion of a measure, the tool for measuring, the sample meter, connects with a whole group of central ideas in Wittgenstein’s philosophy. In lectures Wittgenstein made explicit connections between the use of rules and the use of measuring rods;5 I will get back to these in Part 9.6. The topics of PI, §50 had been important for Wittgenstein from the early 1930s onward. An earlier discussion in which connections with Kripke’s ideas can be seen is in Philosophical Remarks (Wittgenstein 1975, p. 72), in a passage immediately after the passage quoted in note 4, where the application of a yardstick to an object is treated as an analogy for the application of language to the world. He says there that what he once called

182  Cora Diamond “objects,” simples, were simply what could be referred to without any risk of their possible non-existence. With that conception in view, he asks: What if someone said to me “I expect three knocks on the door” and I replied “How do you know that there is: three knocks?”—Wouldn’t that be just like the question “How do you know there is: six feet?” after someone has said “I believe A is 6 feet tall”?6 Here we see the idea that, if we can speak truly or falsely of A’s being 6 feet tall, there must be the length to which we refer, the length which coincides with A’s height or fails to do so. An object which is actually used as a measure can exist or not exist, and so it may seem as if, in measuring, we are comparing the measured object with the actual measuring rod only as a way of comparing with a length. The actual rod, we may think, has a particular length, and it is that length which is the real measure.7 Immediately after the sentences in §50 which Kripke criticizes, Wittgenstein makes a further comparison, between having a standard meter in Paris, and having a standard in Paris fixing the color sepia. “Sepia” will mean the color of the hermetically sealed sample in Paris; and Wittgenstein says that it will make no sense to say of the sample that it has that color or that it hasn’t. Kripke would presumably also take Wittgenstein to be wrong about this. He might express disagreement by saying that the sample in Paris has a particular color. It is a plain contingent fact about that piece of dyed cloth (or whatever it is) that it has that particular color. So, if that color is now to be called sepia, then surely it is a contingent fact that the sample itself is sepia. A crucial part of the argument that I have put into Kripke’s mouth is the claim that the sample has a particular color;8 and that sort of claim gets a great deal of attention from Wittgenstein in the 1930s, especially in Part II of the Brown Book. I have included in an Appendix to this section some material from the Brown Book discussion of sentences in which we say that something has a particular such-and-such.9 Wittgenstein draws attention there to a contrast between two uses such sentences can have, which I shall illustrate here by a pair of examples, not Wittgenstein’s. “This rod has a particular length, namely 39.37 inches.” “This rod has a particular length,” said, for example, when one is concentrating on the thing’s length, and not going on to specify the length or to compare it in length with anything else. The first sentence goes on from “This rod has a particular length,” to specify the length, to describe the rod by relating it to something else; and

How Long Is the Standard Meter in Paris? 183 Wittgenstein calls that sort of use of such sentences the transitive use. The contrast is with saying such things as “This rod has a particular length” while attending to the thing’s own length, without any further specification or comparison. That use of “has a particular such-and-such” Wittgenstein calls intransitive. In this second case, though, we may seem to ourselves to be comparing the length of the rod with a prototype, but, if we were to point to anything to explain what length we meant when we said it had a particular length, we would point to the rod itself. Wittgenstein is concerned with the potentiality for philosophical confusion in the latter sort of case; the potentiality for confusion when we treat the concentrating-your-attention use of “It has a particular such-and-such” as a special reflexive case of the transitive use. (See, for example, his discussion, quoted in the Appendix below, of contemplating a drawing of a face, and saying of it: “It has a particular expression,” thinking of the expression as something distinct from the face, as though having got hold of the expression that the face has were getting hold of the prototype to which the drawn face corresponds.) The issues with which he is concerned in these Brown Book discussions can be traced back into the Tractatus, where he discusses the nonsense-sentence “Socrates is identical” (TLP, 5.473, 5.4733). He doesn’t say why he chooses that example of nonsense; the example is meant to bear on the philosophical confusion of treating selfidentity as a property things have. The word “identical” has two uses parallel to the two uses of expressions like “has a particular such-and-such.” Identification of a thing can be expressed in a sentence of the form “A is identical with B,” where two different expressions replace “A” and “B,” and we could call these identity statements transitive. We can, however, also concentrate our attention on a thing, and we might then want to say that it is identical with something, namely itself, and this is one source of the idea of self-identity as a property everything has. That idea is treated in the Tractatus as a kind of delusion; the implied diagnosis of the delusion is parallel to the diagnosis given in the Brown Book of cases in which we take ourselves to be making a kind of comparison between a thing and something about it which we explain by pointing to the thing itself, that is, in which an ‘intransitive’ use is taken to be a reflexive case of the transitive use. (The connection between the Brown Book discussion and the Tractatus view of identity surfaces in PI, §216.) There is a further important connection in the Brown Book between the cases discussed there and misunderstandings about names and reference, in particular with the idea that we can concentrate on something and give it a name, without at the same time committing ourselves in any way about the use of the name. I return to these issues in Part 9.5; I have wanted here only to bring out that Wittgenstein’s remarks about the standard meter are tied to a range of subjects which are central for his thought.

184  Cora Diamond Appendix to Part 9.2

From Brown Book (Wittgenstein 1969, p. 158): The troubles which we have been turning over since §7 were all closely connected with the use of the word “particular”. We have been inclined to say that seeing familiar objects we have a particular feeling, that the word “red” came in a particular way when we recognized the colour as red, that we had a particular experience when we acted voluntarily. Now the use of the word “particular” is apt to produce a kind of delusion and roughly speaking this delusion is produced by the double usage of this word. On the one hand, we may say, it is used preliminary to a specification, description, comparison; on the other hand, as what one might describe as an emphasis. The first usage I shall call the transitive one, the second the intransitive one. The contrast Wittgenstein means comes out sharply, he says, if we consider “peculiar” instead, of “particular”; and he explains the contrast with examples that are not connected to philosophical problems. Thus an example of the ‘transitive’ use of “peculiar” would be “This soap has a peculiar smell—the smell of ground-ivy leaves”; an example of the ‘intransitive’ use would be “This soap has a quite peculiar smell.” In this second case, “peculiar” is not used to introduce a comparison but more or less like “striking” or “out of the ordinary.” The first paragraph in what follows is a condensed version of an example meant to lead into the discussion of how intransitive uses of “particular” are connected with philosophical problems. (The last three-quarters of the paragraph are directly quoted, as are the following two paragraphs. All the material is from Wittgenstein 1969, pp. 160–1.)10 If I say “I have noticed that A comes into the room in a particular way,” I might, if asked, specify the way: “He always sticks his head into the room before coming in.” [That would be an example of the ‘transitive use’ of “a particular way.”] But suppose I have been observing A as he sits smoking; I want to draw him like this. I am contemplating, studying, his attitude; and as I contemplate it, I might be inclined to say and repeat to myself “He has a particular way of sitting.” But the answer to the question “What way?” would be “Well, this way,” and perhaps one would give it by drawing the characteristic outlines of his attitude. On the other hand, my phrase “He has a particular way . . .,” might just have to be translated into “I’m contemplating his attitude.” Putting it in this form we have, as it were, straightened out the proposition; whereas in its first form its meaning seems to describe a loop, that is to

How Long Is the Standard Meter in Paris? 185 say, the word “particular” here seems to be used transitively and, more particularly, reflexively, i.e., we are regarding its use as a special case of the transitive use. We are inclined to answer the question “What way do you mean?” by “This way,” instead of answering: “I didn’t refer to any particular feature; I was just contemplating his position.” My expression made it appear as though I was pointing out something about his way of sitting . . . whereas what makes me use the word “particular” here is that by my attitude towards the phenomenon I  am laying an emphasis on it: I am concentrating on it, or retracing it in my mind, or drawing it, etc. Now this is a characteristic situation to find ourselves in when thinking about philosophical problems. There are many troubles which arise in this way, that a word has a transitive and an intransitive use, and that we regard the latter as a particular case of the former, explaining the word when it is used intransitively by a reflexive construction. Thus we say, “By ‘kilogram’ 1 mean the weight of one litre of water,” “By ‘A’ I mean ‘B’,” where B is an explanation of A. But there is also the intransitive use: “I  said that I  was sick of it and meant it.” Here again, meaning what you said could be called “retracing it,” “laying an emphasis on it.” But using the word “meaning” in this sentence makes it appear that it must have sense to ask “What did you mean?” and to answer “By what I  said I  meant what I  said,” treating the case of “I mean what I say” as a special case of “By saying ‘A’ I mean ‘B’ ”. . . Suppose to the question “What’s a kilogram?” I answered, “It is what a litre of water weighs,” and someone asked, “Well, what does a litre of water weigh?” Wittgenstein goes on (1969, §16, p. 162) to discuss the case of a face-drawing, of which we might want to say, as we take in the expression, that “It has a particular expression,” but if we were to point to anything to explain what expression we meant, it would be to the drawing itself. “We are . . . under an optical delusion which by some sort of reflection makes us think that there are two objects where there is only one . . . [T]he phrase ‘getting hold of the expression of this face’ suggests that we are getting hold of a thing which is in the face and different from it.” In §15, in connection with the inclination to say that the word “red” came in a particular way when one answered the question “What color is the book there?” by saying “Red,” Wittgenstein speaks about the feeling that one could give this way in which the word comes a name, if it hasn’t already got one. In the kind of case with which he is concerned, we feel as though we could give a name to the thing on which we are focusing when we say “He has a particular way of sitting,” or “The word comes in a

186  Cora Diamond particular way,” “without at the same time committing ourselves about its use, and in fact without any intention to use it at all” (ibid., p. 159). 9.3  Malcolm on Kripke on Wittgenstein and the Standard Meter Norman Malcolm has criticized Kripke’s remarks about Wittgenstein and the standard meter.11 Although he treats Kripke with respect, nothing in Malcolm resonates with Kripke’s views, and the result, I think, is that his treatment is unhelpful. But it may be illuminating to see why it doesn’t work. Malcolm begins by explicating Wittgenstein’s remark about the standard meter in Paris not being sayably either a meter long or not a meter long. He fills in a possible background to the establishing of the meter standard; then he says that what Wittgenstein meant by the remark about the standard meter is that one cannot say that the standard meter has been determined by measurement to be one meter long (Malcolm 1995, p. 58). Well, for sure this is not what Kripke takes Wittgenstein to mean, since Kripke’s argument against Wittgenstein essentially depends only on the rod’s having a definite length. We refer to that length by the expression “one meter,” and the rod can be known to be one meter long without measurement, without investigation. (Kripke does refer to the possibility of measuring the meter rod in inches. But his point there is not that we need to measure the rod to determine that it is one meter long. It is rather that, given that we clearly can measure the rod in inches, and that we have previously established a conversion of 39.37 inches to the meter, why can we not say of a rod which is 39.37 inches long that it is one meter long?) Kripke is not denying what Malcolm puts into Wittgenstein’s mouth, that the length of the meter rod is not established by measurement. Malcolm’s reading of Wittgenstein makes the passage much more verificationist in character than it is; but Kripke is correct in not reading the Wittgenstein passage in a verificationist way. In fact, Wittgenstein’s remarks engage much more closely with Kripke’s conception than they would on a verificationist reading. Kripke’s conception of the meter rod as being one meter long depends upon there being lengths, including the length which we refer to by the term “one meter,” which, on his view, can be known a priori to be the length of the rod at t0. Kripke’s idea, if we put it into Wittgenstein’s language, is that the ‘yardstick of language’ laid up against the world gives a fit between the expression “one meter” (taken with the referential relation to a definite length, established for it) and the meter rod, a fit which is not determined by any empirical measurement. Such a conception of the ‘yardstick of language’ takes the capacity of the yardstick to measure to lie in the referential relations of its terms to such non-empirical objects as lengths. Kripke’s idea that the rod has some definite length, a length to which we refer through the rod’s having it, but which is only accidentally exemplified

How Long Is the Standard Meter in Paris? 187 by this rod, has complex connections to the ideas with which Wittgenstein is concerned in the passages quoted from Philosophical Investigations and Philosophical Remarks. After Malcolm explains Wittgenstein’s remarks about the meter rod, he turns to direct criticism of Kripke’s idea that the definition of the meter length as the length of the rod in Paris fixes the reference of the expression “one meter,” makes it refer to a certain length, the length which Kripke says it is not necessary that the rod in Paris has. If the people fixing the meter standard had had in mind some particular length before they decided to use the particular rod which they fixed on as a standard, and if they chose that particular rod because it had the particular length which they already had in mind, then, Malcolm says, it would make sense to say that these people establishing the standard wanted to mark out a certain length and picked a rod accordingly.12 But if they did not already have in mind any particular length, and, as we can imagine, simply picked out at random a stick S from a heap of sticks of different lengths, and stipulated that one meter was by definition the length of S, then it cannot be said that the definers wanted to mark out a certain length. Whatever length S had, that would be established as one meter; and, that being so, Malcolm concludes, there is nothing contingent about S being one meter long. The only contingency around would be the contingency of the use of S as opposed to some other stick (Malcolm 1995, pp. 59–60). Malcolm rejects Kripke’s claim that, in defining the meter length, we are fixing the reference of the expression “one meter.” He finds this way of talking obscure, but would have no serious objection to it if, by fixing the reference of “one meter” were meant only fixing it that “one meter” is to mean the length of S; what he rejects is the idea that, by the definition, the words “one meter” come to have as their reference an object, a certain length, a length which S contingently has. He has two objections to that idea. First, he objects to talking of “one meter” as referring to or naming or designating an object (ibid., p.  63).13 The second and more worked-out objection is that, if we were to go along with Kripke in this way of talking, the ‘object’ referred to by “one meter” would simply be whatever S’s length is. The object has no identity independent of whatever S’s length is. If S’s length had been different, the standard length, one meter, would be that length. We then still have a coincidence between the length one meter and the length of S. There is no counterfactual situation in which the length one meter and the length of S come apart, since the identity of the length referred to depends on the length of S (ibid., pp.  63–4).14 And Malcolm then returns to the idea that the only way to drive apart and treat as contingent the relation between the meter length and the length of S is by taking for granted a case in which the standard-setters have some specific length in mind before they pick on S to use as the standard.

188  Cora Diamond The argument by Malcolm that there is no way to drive apart the length one meter and the length of S is a bad argument in the first place, and also makes it impossible for Malcolm to see clearly what understanding of the situation grips Kripke. In Part 9.4, I show what is the matter with Malcolm’s argument. 9.4  How Long Might the Standard Meter Have Been? Let us imagine that we do not yet measure things against any standard measure, but that we have a practice of comparison of lengths. We can say of A and B that A is longer than B, or shorter, or the same length. We can also imagine comparisons of length which we do not actually carry out. I might draw a picture of a comparison, perhaps of the height of two children, a comparison which I have not made but might go on to make. Or I might draw a picture of a comparison which I could have made but didn’t, say a comparison of the height of Susan as she was two years ago with Robert as he was two years ago. My picture shows what it would have looked like if I had compared them. I can also draw a picture of a comparison between Susan’s height now and Susan’s height as I imagine it will be in two years’ time. I cannot actually put the Susans alongside each other, as they are in the picture, but I can draw them alongside each other. “You will be half a head taller,” I tell Susan as I show her the picture. I can also compare in imagination Susan’s height as it is with Susan’s height as it would have been if she had taken more vitamins. I can draw this comparison too; see Figure 9.1. She would have been taller if she had taken those vitamins. So it is contingent that she is the height she is; this says no more than we have already said.15 Suppose that we had agreed a year ago: whatever height Susan is a year from now, we shall define that as one meter. So we can add to our

Figure 9.1 

How Long Is the Standard Meter in Paris? 189 picture of Susan-compared-to-what-she-would-have-been-if-she-had-taken-her-vitamins an indication that Susan as she is defines our meter. But we can also go on and add more. In Figure 9.2 the present meter is drawn in and so also is what we would have called a meter if Susan had taken her vitamins and grown taller over the past year. We have drawn a situation in which, although Susan’s height is what is called a meter in that situation, her height is greater than what we have in fact fixed on as a meter. This is meant to show what is wrong with Malcolm’s argument that we cannot drive apart, even in a counterfactual situation, the length of S and the standard meter length. That argument rests on the false idea that we cannot describe the counterfactual situation in terms of our own meter length. The important point in the Susan example is that we can use Susan as she is and make a comparison between her and Susan as she would have been. We are not adding anything problematic if we go on to call her a measuring rod and if we measure with that measuring rod, in imagination, Susan as she would have been. Even if we imagine her to have been used also in that counterfactual situation as a measuring rod, we can still compare in imagination Susan as she is with Susan as she would have been, the measuring rod we have, compared in imagination with the measuring rod we would have had.16 Malcolm rules out that kind of comparison, because he doesn’t allow us to say that, if S had been heated at t0, it would have been longer than one meter in length. It is, on his view, necessarily one meter in length; and this “necessarily” is the ruling out of the kind of comparison I have drawn. Malcolm is not simply trying to make the point that whatever length S is, or whatever height Susan is, we shall call that one meter. That it is not meant to be simply that point comes out in his remark that we cannot identify the object, the meter length, except via whatever length S has. But that is exactly what we can do in imagination; and here I am

Figure 9.2 

190  Cora Diamond following Wittgenstein’s advice to connect our use of “we can imagine it” with “we can draw it.” (See e.g. Blue Book, Wittgenstein 1969, p. 4.) Malcolm’s argument interferes with Kripke’s doing something quite legitimate; it thus stops us from reaching the point at which he does something genuinely problematic. 9.5  Comparing the Meter Rod With Itself I have argued that there is nothing wrong with the last picture, in which we compare Susan’s height in the counterfactual situation with Susan’s height as it is. But now suppose we think along these lines. In the counterfactual situation, we have Susan as she would have been if she had taken her vitamins measured by our own standard of one meter: Susan as she is. In the actual situation, Susan herself could equally, we think, be compared with the length that we have fixed on as our measure: and so we get the next picture, Figure  9.3. Here we are thinking of the difference between the counterfactual situation, on the right in Figure 9.3, and our actual situation, on the left, in terms of the different results we get in the two situations using Susan’s actual height as our standard length. She has a certain height. The difference between the two situations is then that, using that height as our standard Susan-meter, she is (and could a priori be known to be) one standard Susan-meter in height in the actual case, while she is considerably taller than one meter in the counterfactual case. The picture we now have might not lead into any philosophical confusion: it might be merely a picturesque way of representing what the previous two pictures represent, namely that Susan (like other people) would have been bigger had she taken her vitamins. But the representation of Susan’s actual situation could be misleading. It is an example of the kind

Figure 9.3 

How Long Is the Standard Meter in Paris? 191 of representation Wittgenstein speaks of as ‘reflexive’. We are considering Susan’s height, but not, in this picture, considering it in comparison with anything else; but we nevertheless regard this case as a special case of a comparison. We are not comparing her height with that of another child, or with what her height will be, or with what it might have been; we are, as it were, reading her height off her, and seeing her as fitting it: she is just that height. We compare her with her height; they fit exactly. In PI, §279 Wittgenstein says: “Imagine someone saying ‘I do know how tall I am!’ and showing it by laying his hand on top of his head!” The case is not changed if the person who says this also says that his height defines a new unit of length, the W, and that he is exactly one W tall. This match between him and the length one W is not the result of a comparison made within some practice of comparing the heights of people with that of other people and with other things. Kripke’s idea of the a priori knowability of the statement that stick S is one meter long at t0 is parallel to the a priori knowability of the boy’s being one W tall, and that case is like the absurd case of laying one’s hand on top of one’s head to give one’s height. We have arrived by a roundabout route at something not very far from the point Malcolm made right at the beginning of his discussion. Malcolm says that Wittgenstein’s claim that the meter rod cannot be said to be one meter long or not one meter long means that it has no length determined by measurement. And the point we have reached is that there is a difference between using Susan’s height in real and imagined comparisons with other things, and saying of Susan that she has ‘some definite height’, thinking of her as compared with, and matching exactly, the height which we have read off her, that ‘definite height’. This is a non-comparison represented as a comparison. “How tall is Susan?” is here answered by laying a hand on top of her head. There needn’t, however, be anything wrong with representing a non-comparison as a special case of a comparison; if it does lead to some philosophical problem it will be particularly important not to try to get rid of the problem by simply ruling out such representations. Here I am criticizing Malcolm for failing to follow Wittgenstein’s methodological precept that one has to untie a philosophical knot by philosophy which is as complicated as the knot it is trying to undo. (What I have tried to do is to show the ‘disguised nonsense’ of Kripke’s remarks about the a priori knowability of the length of stick S at t0 by connecting those remarks with the patent nonsense of the boy’s idea that he can show you how tall he is by laying his hand on his head; see PI, §§464 and 524. Kripke’s remarks are in fact somewhat more hedged than the boy’s: in the first place he says only that there is a sense in which we can speak of the a priori knowability of the rod’s being one meter long, and in the second place he denies that a claim to know that the rod is one meter long is a claim to have got hold of a piece of contingent information, even though on his own view it is

192  Cora Diamond contingent that the rod is one meter long at t0; see NN, pp. 275, 346–7. I do not think that these hedgings affect the issues here.) The argument I have given does not imply that there is any kind of problem in describing a case in which the meter rod has changed its length.17 We can easily imagine a situation in which we wake up one morning and find that the rod that we have been using as a standard appears to have become longer or shorter. Even if we had defined “one meter” as the length of that rod, we might now say that the rod was not a meter long, and so in the imagined case we have separated the length of the rod from the length ‘one meter’. We can indeed make comparisons between the length of any rod, including our standard, and the length of the same rod as we remember it to have been the day before; making the rod into our standard hardly precludes such comparisons. Or, again, we can use our knowledge of natural laws to infer that, the temperature having changed by so much, the rod we were using as our standard has expanded to such-and-such degree; or our evidence may let us determine that it has not changed. The account which I have given of confusions that may be reflected in talk of a rod’s having a particular length doesn’t imply that our treatment of our standards of measurement cannot take seriously possible changes in the length of the standard itself. We may or may not need to control carefully for such changes, depending on the purposes for which we measure. (There is, however, nothing in principle the matter with having a standard that varies somewhat in length, or with having in circulation many standards, of somewhat various lengths; indeed, things were somewhat like that when the human foot was used as a measure, and what was roughly as long as a man’s foot could be called a foot long. The purposes for which measuring is used may not make it worth bothering with to have some way of settling apparent discrepancies.) When we control for changes in the length of the standard, we make use of physical laws which provide us with conditions in which such-and-such physical properties of such-and-such objects are constant; and such constancies may be used directly to define a standard of measurement, instead of being used simply to enable us to fix conditions in which some standard object itself will remain unchanged. The physical laws, together with other natural laws, give us reproducible procedures the results of which will always be the same (unless, of course, they are not, because, e.g., we have failed to control something we thought we were controlling). We can express the relevant constancies by saying such things as “There is a certain length, which is the wave length of so-and-so, under such-and-such conditions,” but the expression “a certain length,” if used in expressing a constancy or functional relation which is taken as the basis of our system of measurements, is thereby being given a reflexive, not a transitive, use. Physics gives us constancies; whether our descriptions of these use “a

How Long Is the Standard Meter in Paris? 193 particular length,” “a particular weight,” or related sorts of phrase in a transitive or in a reflexive way isn’t for physics to say. Our ways of thinking about physical constancies may, though, make it natural for us ro read an intransitive use as if it were a special case of a transitive use. On the case of standards defined directly through physical constancies, see Wittgenstein’s remarks on the definition of the kilogram, quoted in the Appendix to Part 9.2 above. When Wittgenstein asks us to imagine the question “Well, what does a liter of water weigh?” as a response to “A kilogram is the weight of a liter of water,” he means to draw to our attention that, if one were to say that a liter of water in such-and-such conditions always has a particular weight, the statement would be grammatically unlike “There is a particular weight that all the tomatoes from this plant have when they are ripe.” “Particular” in the latter case is transitive; but the question how much a liter of water weighs brings out that, in the sort of context Wittgenstein was considering, “There is a particular weight that a liter of water always has” contains an intransitive use of “particular.” The point here is not that there is some kind of rule that you can’t say that what a liter of water weighs is a kilogram; it is rather to make clear what you are doing if you do say that. The possibilities for philosophical confusion are at least as great in the case of theory-based definitions of standard units of measurement as they are in that of definitions using a standard object like the rod in Paris. More would need to be said about these matters if my topic were measurement, but it is the relation between Kripke’s views and Wittgenstein’s, and Kripke himself focuses on the kind of case in which a single standard object like the meter rod is used to fix the unit of length. It should, however, be clear that the issue of the different ways of using “particular” does not arise simply because of the kind of case that Kripke himself discusses. I began my criticism of Malcolm in Part 9.4 by imagining a practice of comparing the height of people with each other and with other things. In the background here is our actual practice, in which we learn such things as that one mustn’t stand on tiptoe when being compared in height with someone else, in which we learn that a ruler placed flat on the head of someone to compare that person’s height with that of someone else must go parallel to the floor, in which we put the two people back to back, and so on. In the example I  used, we gradually detach our idea of measuring height from that background of practice; we reach a point at which we think of Susan simply as ‘having a certain height’, and we begin to think of this as a matter of her fitting that height which we have read off her. This picture can lead into philosophical confusion through its seeming to illustrate a kind of measurement which is totally independent of the whole business of actually putting objects alongside each other, reading properly off instruments, and so on. It can begin to seem as if what we are doing if we do use Susan as a measuring rod is really comparing other

194  Cora Diamond objects, not with Susan (who is after all pretty continuously changing in height, and who sometimes stands up tall and sometimes slouches), but with that length which she herself fitted at the time we fixed our standard. And when we consider, not the Susan-meter, but the meter defined in terms of the wavelength of the light given off by krypton in certain conditions, or some other such physical constancy, the idea of the unit of measurement as detachable from our actual modes of comparison of objects to each other may be far more compelling. This issue of detachment from the languagegame is important; before returning to it I shall consider further Wittgenstein’s use of the idea of keeping something in Paris. 9.6  Wittgenstein and the Archives in Paris In the section of Philosophical Investigations in which he mentions the standard meter rod in Paris, Wittgenstein also imagines a case in which we keep standard color-swatches, like the standard sepia, in Paris too. This idea of ‘keeping a standard in the archives in Paris’ he gives a further extended use in his lectures on the foundations of mathematics. What we will keep in the archives in Paris will be whatever exactly turns out to be necessary for us to use in some language-game if some range of comparisons is to be made in that game. Thus, let us say that people reporting on colors are uncertain quite how close a match to the sample in Paris is necessary if they are to describe something as sepia. It might then be useful for them to have also a group of sepia-like shades kept in the archive with the standard sepia; these shades are sorted into sepia and non-sepia, so the shadesamples, with their labels, make plain how far from the standard sepia a color can be and still be called sepia. (Compare Quine on the use of ‘foils’ in comparisons: things “that deviate just barely too much to be counted” as belonging to the kind in question.)18 But a language-game with colorreports and requests for objects of a certain color and so on might in fact be played without a degree-of-match guide. When Wittgenstein explains his ideas about ‘keeping something in the archives’ in his lectures, he notes that, if we settle on a particular rod as a standard of length and put it into the archives, we might still be unclear how to make comparisons with the rod, and so we might want to deposit in the archives also a description or picture of the method of use of the standard rod. The picture might be of one or two examples of uses of the rod. That might be all we needed in order to go on with the language-game. The notion of ‘depositing something in the archives’, depositing it among the samples or paradigms with which comparison is made, is important for Wittgenstein’s philosophy of mathematics, for his treatment of the character of mathematics (and its relation to logic), and in particular for his treatment of calculation and of proof. A calculation is something we could

How Long Is the Standard Meter in Paris? 195 lay down in the archive of measurements as a standard of comparison, something by which we can describe what actually happens in an experiment; a proof also is described by Wittgenstein as something that can be laid down among the paradigms of language, the samples used in making comparisons.19 In Lectures on the Foundations of Mathematics, Wittgenstein’s extended discussion of the idea of the archives (1976, pp. 105–6) focuses on the establishing of rules of multiplication. He develops an analogy between such rules and standards of measurement like the meter rod. We could, he suggests, take a calculation, say the multiplication of 465 by 159, and put that in the archives in Paris. This is to be the standard for multiplication: “Do it like this.” Turing raised an objection to Wittgenstein’s idea: the trouble, he said, is that you cannot put all multiplications into the archive but only a finite number of them. So what if I do a multiplication not in the archive? Wittgenstein emphasized in his reply that the number of multiplications being infinite is entirely irrelevant to the way things in the archive establish what we are to do. Suppose there were people who only ever multiplied up to three-digit numbers, and whose entire set of multiplications, up to 999 times 999, were in the archives. There might nevertheless be some problem for them how this table was to be applied in particular cases. Having all the multiplications in the archives might for them not be enough to enable them to go on. Conversely, having only one or two might be perfectly enough. In our own case, we might simply put into the archives the multiplication table or a single sample multiplication—and that might be enough, “if everyone knew from it how to multiply in other cases.” So an important part of Wittgenstein’s reply to Turing is that what we need to have in the archives is whatever in our practice can be used as a standard without trouble. A  single example can be the standard we need for an unlimitedly large number of multiplications. Wittgenstein conceives of the archives in Paris as a storehouse of instruments used in various language-games. Just as a meter rod made of platinum and iridium and kept near Paris was in 1939 an instrument used in measurement, so multiplication tables are instruments used in a great variety of linguistic activities. These are instruments with which comparison is made, which we are trained to use; we do pick up the training and use them as standards, without trouble, in a vast number of cases. So, for example, if people with appropriate training can tell how to construct their own one-meter samples if they are given a statement defining the meter in terms of such-and-such physical constancy, and if people who use the samples thus constructed get on fine and don’t run into discrepancies, we might put a statement of the definition and a physics textbook into the archives, just as we might have in the archives a multiplication table.20

196  Cora Diamond Let us now go back to Kripke and to the move he makes early in his discussion of the standard meter, shifting from its definition via the length of S to its definition via the length of S at a particular time. 9.7  Kripke, Measures, and Rules As I mentioned in Part 9.1, Kripke’s discussion of the more precise definition of the meter, in terms of the length of a stick at a particular time, abstracts entirely from the actual use of the newly defined meter length in measuring things. It is plain that, if this new definition is to be applied in actual measurements, we shall use the stick in question plus some formula for calculating its difference from the length it was at t0. This matter isn’t in view at all in Kripke’s discussion as something relevant to the definition being a definition of length. Kripke’s idea is that, in virtue of the definition, we have fixed on a particular length, which is therefore in definite relations to the lengths of whatever objects we might wish to measure. How we actually go about discovering the relation between the fixed-on length and actual objects is not relevant to our having fixed on the length, not relevant to our being able to refer to it. (Kripke’s argument about reference is tied to his conception of the separability of metaphysics and epistemology, to which I shall return.) The length of the rod is intrinsically, in being a particular length, already a measure, already capable of being compared with measurable objects, including stick S at t0. So now we are back with the case we were considering in Part 9.5, the meter rod compared with itself. When we think of the case in which the rod is not actually being compared with anything else as a special reflexive case of a comparison, when we think of it as compared with the length which we read off it, we are taking it that the capacity of that length to be a measure is independent of any actual activity of measuring things using sticks or whatnot. The idea of our having reached a particular length with our words “one meter” is the idea of what we have named as having internal to it the possibility of use as measure. What it is for a thing to be or not to be that length is fixed by the length itself. (Malcolm was indeed objecting to this conception when he insisted that the length one meter has no identity distinct from that of the length of the stick S at t0, but I hope to have shown that his argument fails as an argument and doesn’t reach to the source of the problem.) What gives strength to the idea that the essential thing in measuring is the comparison with a definite length, conceived as ‘fitting’ the stick used in measuring, is that the stick itself is just a piece of wood or metal; we might say of it, Wittgenstein notes, that in itself it is dead; it cannot say that the body measured is of such-and-such length (PI, §430). The stick appears as a mere means through which we reach something that is intrinsically a measure. And so, in our philosophical view of the workings of the language of measurement,

How Long Is the Standard Meter in Paris? 197 what appears central is establishing the referential connection to the ‘definite length’; the actual practice of using words and sticks of wood or metal rods in measuring things disappears from view. Wittgenstein’s idea that we might want to say that the stick can’t say that the body to be measured is of such-and-such length connects most directly not with Kripke on the meter rod, but with Kripke on rules. When Kripke discusses Wittgenstein on rules, he considers the example of doing the sum 68 + 57, which he imagines to be a sum which he was not explicitly taught, and which he has not done in his past arithmetical practice. The problem here, the problem to which Wittgenstein draws our attention, is, Kripke thinks, that in such a case there is nothing that tells him that the answer he should give to “How much is 68 + 57?” is 125 not 5.21 This account of the problem shows that, as he is conceiving the situation, any table which he has used, any examples which he has worked over, are, as it were, dead and inert. They are silent; they don’t tell him that 125 agrees with them, and that 5 is inconsistent with them. The Wittgensteinian paradox, as Kripke explains it, is essentially an elaboration of this ‘inertness’ of our examples and rule formulations (written, spoken, or in our minds). They can be interpreted in various ways; they cannot themselves tell us how to go on when we are confronted with 68 + 57·22 They are (that is) like the meter rod, when it appears a mere dead piece of wood or metal, incapable itself of saying that a body is of such-and-such a length. When we consider the metal rod or piece of wood in abstraction from the context of the language-game, its only role appears to be that of allowing us to reach via our linguistic intentions its length, the particular length which it has, which is what will enable us to measure. And here we should think of Wittgenstein’s description of the idea that, when a rule is communicated to another person by examples, the fundamental thing which is communicated is something beyond what is actually presented to the other person; any explanation given via examples or tables merely uses the examples or tables to enable the other person to reach the something else which is essential (PI, §§209–10; Wittgenstein 1978, pp. 320–2). Wittgenstein’s image of the archives is meant to bring out that, although indeed no piece of wood or metal, no mathematical table or set of examples, looked at apart from practice, is as it were a live measure, we are as a matter of fact able to use pieces of wood or metal as standards of comparison, as measures; similarly, we can be shown examples of multiplication or addition and go on to compare with them, and to treat departures from them as adding wrong. There is such a thing as adding wrong, within the context in which we have no problems distinguishing what is in accord with the examples we have started from, or what is in accord with the tables, from what is inconsistent with those examples or with the tables. The metaphor of placing those sample calculations in the archives

198  Cora Diamond represents the fact that among us, in our practice, these do to fix what is correct arithmetic and what is incorrect, just as the platinum-iridium bar does (or did until i960) to fix measurement. In 1960 we needed something else for some highly specialized purposes. The archives represent the fact that what instruments we need in a linguistic activity depends on all sorts of things in the circumstances of those engaging in the activity. The things in the archives are then our live measures; they are there precisely because they are what we need; we don’t need something beyond them to tell us what is in agreement with them and what is inconsistent with them. If in a particular case we did, we would put it into the archives. The archives, then, provide a means of representing a fundamental idea in Wittgenstein’s later thought: that of ‘rotating’ our philosophical examination, rotating it around the fixed point of our real need (PI, §108). We need, for example, to carry out multiplications and to distinguish doing them right from doing them wrong. What standard can we use? What standard will, in our use of it, tell us “Do it so!” Kripke works with the idea that we need something that is not silent, that will tell us what to do; and he is right, we do. But we need then to be able to turn our attention to the instruments of language that do tell us what to do, in the sense in which the multiplication table which the child copies and memorizes tells the child what to do when she is asked to do a multiplication which perhaps she has never done before. Several reviewers of Kripke’s book mention his failure to see an important feature of Wittgenstein’s argument. When Wittgenstein speaks about the ‘paradox’ that nothing appears to fix what is in accord with a rule, he treats the appearance of paradox as the result of our own philosophical misunderstandings. Warren Goldfarb puts the point this way: the ‘paradoxmonger’ is presented by Wittgenstein as someone who “has assumed some notion of accord with a rule, but has divested it of the ways we go about taking things to be in accord or not.” That’s what makes it possible for the paradox to appear.23 I have been arguing that a related kind of characterization applies also to Kripke on the standard meter. If we ignore the fact that the standard meter, the metal rod in Paris, is there in the archives because it is for us a useful instrument of language, an instrument of comparison, it may seem merely a stick by which we become able to denote a particular length, where that length is a measure both of the meter rod and of anything else we might wish to measure. That idea parallels closely Kripke’s understanding of what following an arithmetical rule would be like if there were no Wittgensteinian paradox, what he thinks it does seem to us it is like, before we see the paradox. Just as the stick S supposedly puts us into a position to denote a particular length by the words “one meter,” our practice with examples of addition-sums we think puts us into a position to denote by

How Long Is the Standard Meter in Paris? 199 a word or symbol, say the plus sign, an arithmetical function. That function by its nature can stand as ‘measure’ of whatever I may go on to do in adding. If, when I  am confronted with “68 + 57” I  say “125,” what I say, ‘measured’ by the function which I denote by the plus sign, is correct. The parallel between Kripke’s understanding of measurement and his understanding of rules includes this further point: the standard meter in Paris, stick S, is itself thought of as compared with the length one meter: measured by that length, the stick (through which we came to be able to refer to the length) is one meter long; and similarly the original set of examples of addition sums, through which we came to be able to refer to the addition function, can be thought of as compared with the function. It provides the standard for judging them, as for judging any other putative addition; measured by it, they are correct additions.24 The Wittgensteinian paradox then fits into this Kripkean scheme as essentially an interference with our capacity, the capacity we think we have, to connect with the function. The paradox makes clear that anything I attempt to use as a means to connect with some particular arithmetical function connects as well with an infinite number of other functions. The addition examples I  use thus get me nowhere. If we step out of the Kripkean understanding and look at the situation as Wittgenstein does, the diagnosis will be that Kripke has given to the arithmetical examples the role which we give to the metal rod when we consider it abstracted from connection with our actual practice of measuring, and find it to be ‘dead’. The fundamental question, in Kripke’s account of his own central example, is whether by the word “plus” he has meant the plus function. He had, supposedly, always thought he had meant plus by the word “plus,” but the Wittgensteinian argument is then supposed to show that that is doubtful. But now what is this that he is supposed to have thought, before the paradox? We can here raise a question whether the sentence giving what he is supposed to have thought, “By the word ‘plus’ I meant the plus function,” is what it looks as if it may be, namely a ‘reflexive’ use of a kind of sentence which has an unproblematic ‘transitive’ use. Sentences of the form “By ‘A’ I meant B,” where the expression replacing “A” is different from that replacing “B,” would be transitive uses of the kind of sentence in question. (See the Appendix to Part 9.2, above, for Wittgenstein’s discussion of sentences of the form “By such-and-such I meant so-and-so.”) One can frequently clear up an ambiguity in what one said by giving a different expression and saying that that is what one meant. We have seen that, in other cases of intransitive uses of sentences which have both transitive and intransitive uses, it is possible to slide into philosophical confusion by treating the intransitive cases as special reflexive cases of the transitive use. Or, at any rate, this is what Wittgenstein tried to show. We saw such a movement in connection with the case of the meter length. We moved there

200  Cora Diamond from cases in which we can say of a thing that it has a particular length, 1.3 meters, say, by comparing it with the rod in the archives, to the idea that the rod in the archives has a particular length; and we think of it as in a sense measurable by that length, its length. We read its length off it, and it and that length match. I tried earlier to show how the movement to the reflexive use is aided by thinking of the counterfactual case, in which we have a different instrument of measurement, alongside our actual case: the counterfactual Susan-measure and the actual Susan both thought of as measured by Susan’s actual height. The same kind of movement to a reflexive use is involved in reaching Kripke’s understanding of our supposed pre-paradox belief. Here too the movement to a reflexive use is aided by thinking of counterfactual cases. By the word “plus” we might indeed have meant something different from what we do mean, say minus; this counterfactual may help us move towards thinking of the statement that by “plus” I mean plus as both not necessary and as nevertheless a priori knowable. In the case of the word “plus,” we have in the archives, we may suppose, some examples of additions, as, in the measurement case, we had a metal rod. The arithmetic examples are sample uses of expressions of the form “a plus b,” as the rod was the sample for “one meter.” In the reflexive treatment of the meter rod, we think of ourselves as denoting by “one meter” the length we have read off the measuring instrument itself; the instrument is, contingently it seems, that long. In the reflexive treatment of meaning, we take the function which we have read off the examples, we denote it by “plus,” and we see the examples and the function as matching, as wouldn’t be the case if we compare the function with examples we might have used to fix a different meaning for the word “plus.” Wittgenstein’s slogan “Don’t look for the meaning, look for the use” has various applications. One of them is in connection with the wish to make a reflexive use of the word “meaning.” I might have meant something else; I do mean what I mean; at least I think I do before I hear from Kripke about Wittgenstein’s paradox. As Kripke conceives the situation before we hear about the paradox, if we take ourselves to mean something by the word “plus,” the important thing for us will be the connection with that which we mean, the particular function; the examples and training and practice with the word in a sense fall away except as the means through which the connection is established. So anything that seems to show that such a connection is not established is seen as profoundly paradoxical. On this view of what it is to mean something by one’s words, any genuine ‘straight’ solution to the paradox would involve showing that, contrary to the kind of consideration adduced by the paradox-monger, we are able to establish a connection between our words or symbols and a particular function; we are able to denote a function, are able to mean plus by “plus.” This is why Kripke thinks that, had Wittgenstein stated his views straightforwardly,

How Long Is the Standard Meter in Paris? 201 it would have been clear that he was committed to a “sceptical denial of our ordinary assertions” about what we mean (WRLP, pp. 69–70). (Here I should want to emphasize the point that the conditions for a ‘straight’ solution to the supposed paradox are given through a reflexive use of language. Kripke’s description of what Wittgenstein allegedly shows us that there isn’t is also given through a reflexive use of language. There is no fact of my, or anyone’s, having meant plus by “plus.”) For there to be a fact of our meaning addition by “plus” is for there to be a connection between our words and something capable of a normative or ‘measuring’ role, independently of any activity of ours. And that is entirely parallel to what Kripke himself takes for granted is available in his own treatment of the measuring rod and its length. In much contemporary philosophy of language, ‘reflexive’ examples are treated as if they were not themselves possible indications of philosophical fishiness. By “Schnee,” we say, the Germans mean snow, by “snow” we mean snow. A transitive use is put first to make our intransitive use appear like a special case of the transitive use. Or we have: “Schnee ist weiss” is true-in-German if and only if snow is white, and “Snow is white” is true-in-English if and only if snow is white. My argument in this part of the paper has been that we should bethink ourselves of the similarity between saying “I  know what the sentence ‘Snow is white’ means, it means that snow is white” and saying “I know how tall I am, this tall!” while laying one’s hand on one’s head. The emphasis on “this tall” doesn’t make the words and gesture give one’s knowledge of one’s height; mental concentration on white snow (or anything else) doesn’t make the words “It means that snow is white” state something about meaning that one knows. My height can be used to give you someone else’s height, an English sentence to give you the meaning of a German one, or of another English sentence, but repeating a sentence and taking its quotes off is putting your hand on your own head. 9.8  Kripke, Winch, and Wittgenstein’s Deviousness This section is about Kripke’s claim that Wittgenstein is not straightforward; if he were, it would be clear, Kripke argues, that he is committed to the impossibility of genuinely true attributions of meaning (WRPL, pp.  69–78). Kripke’s claim that Wittgenstein is really denying what we usually believe depends on the distinction between, on the one hand, what we are entitled to assert (entitled in some language-game to call true) and, on the other, what is true because it asserts that such-and-such fact obtains, and that fact does obtain. According to Kripke, Wittgenstein denies that the fact that would make our attributions of meaning true ever does obtain, but holds that we are nevertheless entitled in our language-games to make

202  Cora Diamond such attributions and indeed to speak of them as true (WRLP, pp. 70–8, 86). In his criticism of Kripke on this matter, Peter Winch asks what we are to understand by a genuine fact, if not what is stated by a statement we take to be true. He says that Kripke gives no alternative acceptable explanation of what the genuine fact that supposedly isn’t there would be.25 My aim in this section is to show how Winch’s objection would appear, from Kripke’s point of view, to share the kind of deviousness that he sees in Wittgenstein’s own approach. And so I must first show what sort of answer Kripke could take to be available to Winch’s question as to what the genuine fact is supposed to be. I approach the issues here by turning again to the analogy with the case of the meter rod in Paris, thought of by Kripke as having a certain length, which we denote by the words “one meter,” and which can be thought of as a measure of the rod itself at t0. The analogy is then with the idea of the word “plus” as denoting, we think, a certain function, a function which stands as measure of any additions we may perform, including any examples which are in the archive. In both cases, what is taken to be the genuine ‘measure’ is conceived as something intrinsically capable of use as standard, independently of any proceedings in a language-game, and indeed as capable also of indicating what ways of playing any languagegames of ours would be improvements on what we have been doing. There is a further point. If the arithmetical function, addition, is conceived in this way as measure of actual calculations, then the truth of statements about whether someone had intended to add, or had meant addition by the use of some sign, is itself properly tested or ‘measured’ by whether there was an intentional connection with the addition function. If the function is the measure of our additions, then the truth test, or ‘measure’, of the statement that someone meant addition is that there is intentional connection with that function. Winch’s question as to what we are to understand as a genuine fact, if not what is stated by a statement which we take to be true, is then apparently answerable from Kripke’s point of view: a statement about someone’s meaning addition might be assertible in a language-game, but what it states is understandable via the notion of the addition function as itself a nonarbitrary measure of additions, and as something which may or may not be what the person had specifically intended as measure. (Compare the case of measuring with the meter rod. On a Kripkean account of measuring, the intention to measure the length in meters of something is the intention to make a comparison with a certain length; hence there is no intention to measure unless the intention reaches to the particular length; hence any language-game of describing people as measuring either takes seriously the need to establish a connection with some definite length or ignores that need and simply sets up assertion conditions for ascription of measurement

How Long Is the Standard Meter in Paris? 203 of length. Thus the activity I described in Part 9.5, in which “a foot long” has a use but does not refer to any one definite length, might be said to have mere assertion conditions for something’s being a foot long, for, on this view, there is no fact of the matter of a thing’s being a foot long, since no definite length is referred to by “one foot.”) Kripke’s conception of what it is for us to have a non-arbitrary standard against which to compare our additions is connected quite directly with precisely that distinction between assertion conditions and truth conditions that Winch questioned. If the samples and sticks and tables and formulae which we keep in the archives are conceived to be, not in themselves standards, but means by which we hope to be able to denote genuine standards, then Wittgenstein’s approach will indeed appear to leave room for ascriptions of meaning to be assertible even when they are not true. Winch does indeed make clear that Kripke’s distinction between assertion conditions and truth conditions is inseparable from Kripke’s underlying philosophical views; my point here is that it has a direct connection with the ‘reflexive’ understanding of measurement which we see in Kripke’s discussion of the standard meter.26 (This issue of ‘reflexive’ use comes up briefly in Winch’s discussion of Wittgenstein on the word “fit” (Winch 1987, p. 59).) The reflexive conception of measurement, of standards, goes with a conception of what it is for the mind to be in contact with a genuine standard or measure: such contact cannot be seen in our familiar dealings with sticks and swatches and multiplication tables. And so any argument like Winch’s, which insists that there is no access to truth conditions apart from an understanding of what counts as establishing when the truth conditions are satisfied, will appear to share Wittgenstein’s deviousness: for it asks us to look precisely at the ways in which people’s dealings with sticks and swatches and multiplication tables are used in determining what we can say they mean. 9.9  My Deviousness; and Connections with Putnam In Part 9.4, I took Kripke’s side against Malcolm, on whether the standard meter in Paris might have been longer than one meter. But my treatment of that question contains what Kripke might well take to be a kind of Wittgensteinian deviousness. In this final section I explain why; and I show some connections with Hilary Putnam on Kripke27 and with Kripke on identity. I have not used the expression “rigid designator” in discussing Kripke’s views on the standard meter, although Kripke himself was actually arguing that the expression “one meter” is a rigid designator of a certain length. In his discussion of Kripke’s ideas, Putnam points out that what Kripke describes in terms of rigid designators can be explained in terms of the ways in which a cluster of natural laws typically enables us to determine the reference of terms which we use in describing hypothetical situations.

204  Cora Diamond So, when we consider the hypothetical situation of the meter rod having been heated before the determination of the length one meter, we describe that situation as one in which the meter length defined within the hypothetical situation is greater in length than one meter; and our account, using our measure of one meter, rests on a cluster of laws. In the case of our hypothetically having heated the rod at t0 prior to defining “one meter” as the length of the rod at t0, we could, for example, use our laws to give a value for gravitational acceleration, measured in the hypothetical meter units, a value derived via our knowledge of how the rod would expand if heated one degree Centigrade, say. Putnam’s discussion is meant to enable us to separate Kripke’s notion of a rigid designator from the metaphysics to which it is attached in Kripke’s thought; and Putnam’s metaphysically purified notion relies on the very un-Kripkean idea of sortal identity. I too have been implicitly appealing to that same notion. When I described the counterfactual case in which Susan had taken her vitamins, I simply took it that Susan would still be Susan if she had taken those vitamins and grown taller. Kripke would hold that there is a justification for that: namely, the identity of Susan is independent of how much she grows. And that is not, for him, a matter of our criteria for identifying someone as the same human being, which is what I  was implicitly relying on. Let us consider here another sort of counterfactual. Take, for example, the idea that, if the being who is now Susan had in an earlier life committed some act of violence, she would have been reborn as a rat, and not as the human being that she is. Kripke’s view about this counterfactual might be that in no possible world is something a rat which in our world is Susan. There is no such counterfactual situation; and, further, the fact that there isn’t does not merely reflect our criteria or our concepts. Identity is identity; the identity of the being we call Susan is independent of our recognition of it as a human being, and independent of how we establish identity. Even if we actually only had a word for sortal identity, we could, on Kripke’s view introduce a word “schmidentity” for that relation which every object has only to itself.28 The schmidentity of the thing then determines whether a name attached to it on some one occasion refers on some other occasion or in some hypothetical circumstances to the same thing. The schmidentity of a thing depends on its nature, and is as independent of the criteria we use to establish sameness as any length is of the ways in which we actually establish how long something is. Although earlier I expressed agreement with Kripke in allowing the kind of case, represented in Figure 9.2, which Malcolm rejects, Kripke would find my implicit reliance there on our concept of a human being a kind of Wittgensteinian deviousness, a kind of evasiveness, evasion of the distinction between on the one hand how we establish reference and on the

How Long Is the Standard Meter in Paris? 205 other what it is we are referring to, and what its nature is, what can be the same as it. For, as I meant it, the notion of a human being was itself something in the archives, something alive in our thought and practices, our recognitions, our narratives, our imaginative treatments of what might happen or might have happened to a person. In PI, §377, Wittgenstein says “Perhaps a logician will think: The same is the same—how identity is established is a psychological question.” The ‘logician’ referred to there insists on the distinction which is central for Kripke, between identity itself and how it is investigated and established. For the logician of §377, Wittgensteinian deviousness would be a matter of identifying psychological questions with logical ones. For Kripke, the deviousness would lie in identifying epistemological questions with metaphysical ones, in treating questions from one domain of philosophy as if they lay in another. Kripke explains this division into domains in “Identity and Necessity,”29 but it is in view in “Naming and Necessity”; similar divisions of philosophy into its ‘domains’, and criticisms of philosophers who seem not to appreciate the boundaries, appear frequently in contemporary philosophy (although the emphasis is sometimes on the distinction between the domain of the theory of meaning and that of epistemology). The problem with the division into domains is that it looks as if it could be seen from somewhere above the level of philosophical dispute or discussion, as if philosophical disputes and discussions went on (at any rate when philosophers weren’t confused about the borders of the domains) within the various domains discernible from above, each with its own subject matter, the essence of things over here, and our knowledge of them, our access to them, over there. The apparent unquestionableness of this division into domains means that it is not seen as itself philosophical. The obviousness and near-inevitability that the division may have reflects, from a different point of view, what Cavell spoke of, in the passage I  quoted in Part 9.1, as philosophy’s drastic desire ro underestimate or to evade the ordinary; for the division supposes ideas of mind and meaning (ideas of the reach of mind to what it means) purified from the exchanges, the recognitions and failures, the doubts and certainties, of ordinary life.30 In the remarks of Cavell’s from which my quotation came, he described Kripke as underestimating or evading Wittgenstein’s preoccupation with the ordinary, with philosophy’s desire to underestimate or evade it. Wittgenstein’s attempt to turn attention to the ordinary, to alter the philosophical will to evade it, is an attempt to let us see the significance of the shapings of thought within our lives (the shapings we give to thought), which he speaks of as grammar. The uses to which he puts the notion of grammar can, that is, be seen as responses to the modes of thought, the evasions of the ordinary, that are expressed in the division of philosophy into domains. He says that essence is expressed by grammar, and that what kind of object something is, grammar says (PI, from

206  Cora Diamond §§371, 373). He isn’t saying there: “We cannot get hold of what we mean, and think about its essence, when we separate it from the ways in which we share words, share modes of thought and action.” That way of putting the point about essence and grammar suggests some clear idea of something that we cannot do. The aim of his philosophizing isn’t to make us see that there is something we can’t do (which is what Kripke takes him to be trying to do), but to change our understanding of what we had taken ourselves to be in search of. (A fundamental analogy for the understanding aimed at by philosophy, as Wittgenstein conceives it, is the understanding we achieve through a classic impossibility proof like that of the trisection of the angle, as Wittgenstein conceives that. See Juliet Floyd’s discussions of the latter case and of the analogy with the understanding aimed at by philosophy.)31 Putnam’s criticisms of Kripke, and the particular issue which he picks out, namely the contrast between appeal to sortal identity and appeal to an absolute notion of identity, lead us into the centre of the disagreement between Wittgenstein and Kripke. I have portrayed that disagreement as concerned with our conception of philosophy itself, its aims and methods. But, as the Putnam criticism brings out, there is a particular concept which plays a special role in the disagreement.32 Right at the centre of Kripke’s thinking is his idea of identity as a relation everything has to itself, and his idea of the law of identity, a law of logic, which he takes to be a substantial law, a law with content and with metaphysical implications. The notion of identity had for Wittgenstein too a special significance. He was convinced early in his life that the law of identity could only by a kind of illusion be taken to be a substantial law, a law with content and with metaphysical implications; he was convinced too that the idea of identity as a relation is confused.33 The special significance that identity has for Wittgenstein in his later thought emerges in his placing of two remarks about identity in the middle of his treatment of rules in Philosophical Investigations; the connection between the topic of rules and that of identity lies in the idea of a rule as providing a standard with which we can make a comparison, something which enables us to see what it is to go on in the same way. The remarks on identity at PI, §§215–16 immediately follow Wittgenstein’s discussion of following the rule always to write the same number: “2, 2, 2, 2, . . .” They also connect the treatment of identity (and thereby also the treatment of rules) with the discussion (in The Brown Book) of transitive and intransitive uses of words. The connection with The Brown Book comes out in PI, §216: “A thing is identical with itself.”—There is no finer example of a useless proposition, which yet is connected with a certain play of the imagination. It is as if in imagination we put a thing into its own shape and saw that it fitted.

How Long Is the Standard Meter in Paris? 207 We might also say: “Every thing fits into itself.” Or again: “Every thing fits into its own shape.” At the same time we look at a thing and imagine that there was a blank left for it, and that now it fits into it exactly . . . “Every coloured patch fits exactly into its surrounding” is a rather specialized form of the law of identity. When Wittgenstein speaks of the law of identity as connected with a certain ‘play of the imagination’, what he has in mind is the same kind of movement of thought described in the passages from the Brown Book that I  have discussed.34 The left-hand part of Figure  9.3 (in Part 9.5 above), where we take Susan to ‘fit’ the length we have read off her, illustrates the sort of imaginative movement Wittgenstein meant. (The idea to which Wittgenstein gives voice in PI, §215, that if you are seeing a thing you are seeing identity, is parallel to the idea—not Kripke’s idea but a closely related idea of Nathan Salmon’s—that if you are observing a thing, you are observing its length, you are in a cognitive relation to a particular length: just by looking at the object and its length, you can know of the length that the object has that length.35 There a play of the imagination becomes philosophical theory.) Identity, Wittgenstein said in 1913, is the very devil, and “immensely important.” He added that it hangs—like everything else—directly together with the most fundamental questions, especially with the questions concerning the occurrence of the SAME argument in different places of a function. Well, it certainly is a devil, one of the devils, a devil which is certainly with us still. And it still hangs together with the most fundamental questions, including questions concerning the occurrence of the same argument in different places of a function. (For when contemporary philosophers try to explain it, they appeal to the idea of a relation which holds between a thing and itself, taking for granted the practices in which we use ordinarylanguage variables like “a thing” and “itself.”) I cannot here go into the issue of Kripke and Wittgenstein on identity; I  have wanted in this final section only to show how the issue of Wittgensteinian deviousness can lead us first to questions about the division of philosophy into ‘domains’ and further to the issue of identity and its significance for Kripke and Wittgenstein.36 Notes This paper is dedicated to the memory of Peter Winch, and I would like to use his own words of appreciation for Wittgenstein to express my appreciation for him: my attitude to Peter’s work “has always been one of gratitude for the help it has given me in seeing what are the important questions, and what kinds of questions they are.”

208  Cora Diamond 1 The sentence from which the quoted phrase comes is: “I will simply say, starting out, that Kripke s account, in drastically underestimating, or evading Wittgenstein’s preoccupation with the ordinary (hence with ‘our criteria,’ which articulate the ordinary), evades Wittgenstein’s preoccupation with philosophy’s drastic desire to underestimate or to evade the ordinary.” 2 For Wittgenstein on some of the issues in this paragraph, see PI, p. 225; also, Remarks on the Philosophy of Psychology (Wittgenstein 1980, vol. 1, §§632 and 1109). 3 I have quoted Kripke’s remark that Wittgenstein simply got things wrong in §50; and it is clear that Kripke reads both the sentences about the standard meter, quoted earlier, to express Wittgenstein’s own view; that is, Kripke does not take either or both of them to be spoken by an ‘interlocutor’, whose views Wittgenstein would take to be subject to criticism. Heather Gert interprets PI, §50 so that it is not Wittgenstein’s own view that the standard meter cannot be said to be either one meter long or not one meter long. See her (2002). In what follows I focus on what Wittgenstein took to be the role of the meter rod in measuring; what ways of speaking of that role may show confusion will emerge in the discussion. 4 For an important passage from the years between the Tractatus and the Investigations, see Philosophical Remarks (Wittgenstein 1975, p. 72), in which the application of language to reality is metaphorically expressed as the application of a yardstick to what is measured by it: Wittgenstein speaks of the application of the yardstick of language. 5 Wittgenstein (1976, pp. 104–106; cf. also, other references to putting a calculation into the archives in Paris, pp. 112, 114). 6 The published English translation uses the plural verb “exist” with “three knocks” and with “six feet.” To say that six feet exist is to say that there are six feet, but the question with which Wittgenstein is concerned is not whether there are six feet, but whether there is the length six feet. In the German version of the question, what is asked is whether six foot exists, a form like that in which we speak of a six-foot length. I am grateful to James Conant for help with the translation here. 7 I am grateful to Thomas Ricketts for critical discussion of the issue of how Kripke’s views are related to those with which Wittgenstein is concerned in PI, §50. 8 Although I have put these words into Kripke’s mouth, they run very close to his use of “a certain length” in connection with the standard meter. 9 In the parallel material in Wittgenstein (1970), Wittgenstein uses the words “besonder” and “bestimmt” virtually interchangeably, e.g. in speaking of the idea that the name of a color comes in a particular way, on pp. 231–232. 10 I have corrected what appears to be the wrong placing of one pair of quotation marks in the third paragraph. 11 Malcolm (1995). Page number references are given in the text. 12 The case of the previously fixed-on length is somewhat closer to the original 1799 proceedings than is the case, central for Wittgenstein, Kripke, and Malcolm, in which no previously fixed-on length is used in picking a rod to keep as a standard. The latter sort of case does approximate to the situation after the discovery that the length fixed on in 1799 had been miscalculated, and before the redefinition of the meter in 1960 using atomic theory. During Wittgenstein’s life, the meter was not in fact defined by the length of a rod but by the distance between two scratches on a metal bar in Sèvres.

How Long Is the Standard Meter in Paris? 209 13 It should be noted that this use of length expressions as designating objects can unobjectionably go with talking about lengths in this sort of way: “The length five yards is greater than the length four meters.” This kind of non-temporal talk about lengths is alluded to by Wittgenstein in connection with comparable talk of colors. In addition to reporting on the colors of bodies, we can state the relationship of colors, as for example “Blue is darker than white.” Wittgenstein says that that is a different language-game (1984, p. 34). Malcolm’s remarks, unlike Wittgenstein’s, do suggest that non-temporal talk of the relation of lengths to each other or of colors to each other is inherently suspect. See also Wittgenstein’s earlier treatment of this kind of case, which is closer to Malcolm’s, in Wittgenstein’s Remarks on the Foundations of Mathematics (1978, Part I, §105). 14 Here Malcolm is rejecting the idea of “one meter” as what Kripke calls a rigid designator. My discussion of the dispute between Kripke and Malcolm does not depend on the introduction of that term. I return to questions about the metaphysical implications of the term in Part 9.9; my argument there reinforces my claim in Part 9.4 that Malcolm rejects too much of Kripke’s account. 15 The claim about contingency could be spelled out with scope indicators; I should say that that makes it no clearer than by using pictures. 16 Compare Kripke’s discussion (NN, p. 288) of the use of the distance between King Henry’s fingertip and his nose to define the yard length. As Kripke notes, if certain accidents had befallen the king, the distance between his fingertip and his nose would have been rather shorter than one yard. 17 The discussion of this case, and of the issues in the next paragraph, owes much to questions asked by Gary Ebbs and Gary Hatfield. 18 Quine (1977, p. 159). 19 See Wittgenstein (1976, pp.  104–14), and Wittgenstein (1978, Part I, §§32, 164; much of the rest of Part I is relevant). 20 I have heard it argued that the difference between the definition of the meter using a stick and the case of a definition using atomic theory is that in one case what we are comparing with when we measure things is a stick and in the other case we are genuinely comparing with a length, the length to which we have access through the theory-based definition. In the latter case, or so it is argued, reference to a certain length is not introduced merely through a philosophical gloss. A  full discussion of this argument would be beyond the scope of this essay; but here I  want only to note that the discussion might involve drawing attention to the multiplicity of kinds of linguistic instruments that we may put into the archives, including not only sticks and multiplication tables, but statements like “A meter is by definition so-and-so many times the length of such-and-such under such-and-so conditions.” The ideas we have of referential connections to a thing (to ‘a length’) abstract from the uses to which we are in fact able to put the instruments in the archives; and some of the discussion here would parallel points made in Part 9.7, in connection with Kripke’s account of the definition of the meter in terms of the length of a stick at a particular time, which also abstracts from the application of the standard. 21 See WRPL, esp. pp. 21–22. 22 As Kripke’s discussion on p. 52 makes clear, the issue as he sees it (and as he understands Wittgenstein’s view of it) is not the finitude of the number of cases of addition; for even if I had given myself explicit instructions about the case of 68 + 57, there would remain a question as to what those instructions tell me to do now, now that I actually have to do the sum. And even if I played myself

210  Cora Diamond a little tape-recording of the instructions I  earlier gave myself, the argument would be that the instructions don’t say what it is to follow them. It becomes clear at this point that the complaint that nothing tells me what answer to give to “How much is 68 + 57?” is, in a sense, mis-stated. For the complaint is rather that whatever tells me what answer to give (and many things, like a taperecording, might tell me) doesn’t really tell me what answer to give. I have lost any hold I had on what I mean by “telling me what answer to give”; and it now appears very obscure what I mean by saying that the earlier addition sums I did, or the explicit formulations of a rulé, do not tell me what to do now. I have no idea what it is that they don’t do. 23 Goldfarb (1985, p. 488). 24 The parallel between the two cases is closer still. The definition of the standard meter, as Kripke understands it, connects “one meter” with a certain length, but it could equally be thought of, given his treatment, as connecting “one meter” with a particular function from any measurable item and time to a number, a function the value of which for S at t0 is knowable a priori to be 1. Just as the addition function is (or is thought to be, prior to our grasp of the Wittgensteinian paradox) the standard for our additions, so the meter-length function is the standard for our actual measurings (unless we think that here too the Wittgensteinian paradox interferes). Cf. Zettel (Wittgenstein 1981, §141) for some discussion of how the specification of a single standard length can be taken to fix a system of measurement in various ways. 25 Winch (1987, p. 62). 26 I should perhaps make clear that I don’t intend any general claims about the possibility of a distinction between assertion conditions and truth conditions. 27 Putnam (1990). 28 Kripke introduces the relation schmidentity in response to a different objection. See NN, p. 310, also p. 350 n. 50. For Kripke’s views, I am also indebted to Putnam’s discussion, referring to Kripke’s Cornell Lectures on “Time and Necessity”; see Putnam (1990, pp. 64–67). 29 Kripke (1977, see esp. pp. 84–85). 30 Thus, in the case of the metaphysics of identity, the move away from the ordinary is at one stage in Kripke’s argument mediated through the introduction of the new term “schmidentity” for that relation everything has to itself. Here the question “What do I know of what it is to mean a relation?” is implicitly answered by turning right away from whatever I do with relations in ordinary life, whatever I know of them there. The general method Kripke there appeals to, in response to an account of the ways our concepts actually do work, is that of describing a hypothetical language, the operation of which is detached from ordinary life. 31 Floyd (1995, 2000). 32 Putnam’s criticisms imply that another particular concept also has a special role in the disagreement, that of reference. And indeed the differences between Kripke and Wittgenstein on reference, on what it is for our thought or our words to reach this or that, a length, a function, or whatever it may be, run through the various issues discussed in my essay. 33 See White (1977–1978, pp. 157–174), for a discussion of the Tractatus treatment of identity. See also Dreben and Floyd (1991). 34 See also §19 of Part II of the Brown Book, Wittgenstein (1969). 35 See Salmon (1987–1988, p. 205).

How Long Is the Standard Meter in Paris? 211 36 I am very grateful to have had the chance to present this paper at the Conference on Wittgenstein in America at the University of Illinois in Urbana-Champaign in 1995, and also for discussion of the paper at the University of Pennsylvania, the University of Bergen, and Vanderbilt University. I want to thank also James Conant, Thomas Ricketts, Gary Ebbs, Gary Hatfield, and Thomas Maier for comments and questions.

References Cavell, Stanley (1990) The Argument of the Ordinary, in Conditions Handsome and Unhandsome. University of Chicago Press. Dreben, Burton and Floyd, Juliet (1991) Tautology: How Not to Use a Word, Synthese 87, 23–49. Floyd, Juliet (1995) On Saying What You Really Want to Say: Wittgenstein, Gödel, and the Trisection of the Angle, in J. Hintikka (ed.), From Dedekind to Gödel: The Foundations of Mathematics in the Early Twentieth Century. Kluwer. Floyd, Juliet (2000) Wittgenstein, Mathematics and Philosophy, in Alice Crary and Rupert Read (eds.), The New Wittgenstein. Routledge. Gert, Heather J. (2002) The Standard Meter by Any Name Is Still a Meter Long, Philosophy and Phenomenological Research 65(1), 50–68. Goldfarb, Warren (1985) Kripke on Wittgenstein on Rules, Journal of Philosophy 82, 471–488. Kripke, Saul (1971/1977) Identity and Necessity, in S. P. Schwartz (ed.), Naming, Necessity, and Natural Kinds. Cornell University Press. Kripke, Saul (1972) Naming and Necessity, in D. Davidson and G. Harman (eds.), Semantics of Natural Language. Reidel. Kripke, Saul (1982) Wittgenstein on Rules and Private Language. Harvard University Press. Malcolm, Norman (1995) Kripke and the Standard Meter, in G. H. von Wright (ed.), Wittgensteinian Themes: Essays 1978–1989. Cornell University Press. Putnam, Hilary (1990) Is Water Necessarily H2O?, in Realism with a Human Face. Harvard University Press. Quine, Willard Van Orman (1969/1977) Natural Kinds, in Stephen P. Schwartz (ed.), Naming, Necessity, and Natural Kinds. Cornell University Press. Salmon, Nathan (1987–1988) How to Measure the Standard Metre, Proceedings of the Aristotelian Society 88, 193–217. White, Roger (1977–1978) Wittgenstein on Identity, Proceedings of the Aristotelian Society 78, 157–174. Winch, Peter (1987) Facts and Superfacts, in Trying to Make Sense. Blackwell. Wittgenstein, Ludwig (1922) Tractatus Logico-Philosophicus, translated from German by Frank P. Ramsey and Charles Kay Ogden. Harcourt, Brace  & Company, Inc. Wittgenstein, Ludwig (1958) Philosophical Investigations. Blackwell. Wittgenstein, Ludwig (1969) The Blue and Brown Books. Blackwell.

212  Cora Diamond Wittgenstein, Ludwig (1970) Eine Philosophische Betrachtung, in Rush Rhees (ed.), Schriften, vol. 5. Suhrkamp. Wittgenstein, Ludwig (1975) Philosophical Remarks. Blackwell. Wittgenstein, Ludwig (1976) Wittgenstein’s Lectures on the Foundations of Mathematics, Cambridge, 1939, ed. by Cora Diamond. Cornell University Press. Wittgenstein, Ludwig (1978) Remarks on the Foundations of Mathematics. Blackwell. Wittgenstein, Ludwig (1980) Remarks on the Philosophy of Psychology. Blackwell. Wittgenstein, Ludwig (1981) Zettel. Blackwell. Wittgenstein, Ludwig (1984) Remarks on Colour. Blackwell.

10 The Illusion of Intransitive Measurement Diamond, Kripke and Wittgenstein on the Standard Meter Martin Gustafsson 1. Any sensible reader of Kripke and Wittgenstein will realize that their discussions of the standard meter are extremely simplified. Clearly, their aim is not to do full justice to the actual development, function, and use of standards within the metric system, but to make distinct and uncluttered philosophical points. And yet, someone who moves on from studying the Philosophical Investigations and Naming and Necessity to learning about the incredibly intricate real-life institution of standardized metric measurement may have difficulties brushing aside the worry that Kripke’s and Wittgenstein’s simplifications are oversimplifications. With regard to Kripke, the sort of reference-fixing procedure he imagines seems to play no role whatsoever in the invention, calibration, refinement and application of measurement standards. And even if his account has a social-historical dimension of sorts, as it involves the idea of the referring expression’s being passed from link to link in a causal chain of dissemination throughout the community of speakers, this account seems both too sketchy and too dilute even to begin capturing the actual richness of real-life measurement and calibration practices. Wittgenstein, on the other hand, often acknowledges the central role of social practices and would certainly admit that in real life, standardized measurement is a much more complicated business than what his stylized sketch in PI, §50 suggests. However, it is not so easy to understand how he can accommodate an idea which seems central to standardized systems of measurement, namely, the idea that measurement methods can be genuinely improved in a sense that goes beyond merely pragmatic concerns or simpleminded forms of conventionalism (Riordan 2015, p.  39; for a distinction between simpleminded conventionalism and more careful varieties, see Riordan 2019. I will return to and briefly clarify this issue in Section 9). In recent times, the striving towards such improvement has led metrologists to abandon definitions of units in terms of artifacts in favor of definitions in terms of natural

DOI: 10.4324/9781003240792-11

214  Martin Gustafsson constants (such as the speed of light in the meter case and, most recently, Planck’s constant in the kilogram case). There seems to be something like genuine metrological progress going on here—but can Wittgenstein’s conception of practice really allow for any such notion? In this chapter, I shall argue that Kripke’s account is indeed vulnerable to the sort of worries sketched earlier. Thinking through the consequences of the most basic feature of measuring qua practice—namely, its being a matter of repeated comparisons—makes it clear that his notion of how the reference of “one meter” is fixed involves deep confusions and has no substantive connection with the real-life phenomenon of measurement. I also will show that Wittgenstein is in fact of great help when it comes to pinpointing Kripke’s misconceptions. However, the profound significance of Wittgenstein’s discussion is hard to grasp. In my view, no commentator has done a better job at bringing out that significance than Cora Diamond, in her paper “How Long Is the Standard Meter in Paris?” (this volume/2001; henceforth, HLSM). My discussion therefore engages closely with Diamond’s paper, and I aim to clarify what I take to be the central lessons to be learned from her reading. I am eventually led to confront the worry about Wittgenstein sketched earlier: How can he make sense of metrological progress? It may seem as if Diamond’s interpretation leaves no room for such progress. However, I shall argue that the depth of Diamond’s interpretation shows itself precisely in the fact that it allows us to make sense of such a notion, but without invoking the illusory sort of reference-fixing on which Kripke’s account is built. Since my primary interlocutors are Kripke, Wittgenstein, and Diamond, I will for the most part allow myself to discuss the standard meter and its use in almost as simplified terms as they do. Like them, I will often write as if the standard meter were a rod used among ordinary people to measure ordinary things. And I will ignore many other aspects of the actual development and use of the standardized metric system; for example, I will treat the standard meter as if it were an end standard rather than a line standard.1 Towards the end of this chapter, I will discuss certain aspects of the relation between the simplified scenarios and the actual development and use of the metric system. Even if my discussion there will be rather sketchy, I hope it will somewhat mitigate the frustration that may understandably be felt by readers who are knowledgeable about standardized metric measurement and its history. 2. Central to Diamond’s reading of Wittgenstein’s standard meter example are some passages from The Brown Book (Wittgenstein 1969), in which he makes a distinction between transitive and intransitive uses of words. Transitive uses involve genuine comparisons, as when I say, for example, “This wine has a peculiar taste—the taste of overripe lingonberries”. By contrast, if I just say “This wine has a peculiar taste”, without invoking

The Illusion of Intransitive Measurement 215 any comparison—when I use words such as “peculiar” or “particular” as a way of just emphasizing the peculiarity of the taste, calling attention to its being striking or out of the ordinary—then what we have is an intransitive use. Wittgenstein warns against constructions that make it appear as if what we have before us is a special case of a transitive use, when it is in effect intransitive—cases in which it may seem as if a genuine comparison is being made, even if it isn’t. One example of this is when someone puts his hand on his head to indicate that he knows how tall he is, as Wittgenstein asks us to imagine in PI, §279. According to Diamond’s Wittgenstein, another example of this would be to say: The standard meter in Paris has a certain length—namely, exactly one meter. So, according to Diamond, Wittgenstein’s point in PI, §50 is not that one is somehow forbidden to say, “The standard meter in Paris is one meter long”, or that this combination of words is necessarily unintelligible. Instead, she argues, his point is that saying so may be both a symptom and a cause of confusion, since it makes it seem as if some sort of genuine comparison between the standard meter and something else—the “length itself”, the “meter itself”, so to speak—is being made. And then it will seem a mystery what this strange act of comparison amounts to. This happens when it is conceived as a comparison which makes use of an entity quite different from those real, physical standards we normally employ when we make measurements of length—the length itself, as it were, an entity which is not handled in measuring but still somehow functions as the final and unassailable arbiter of how long things are, including the standard meter itself. There is a strong temptation to think that our measurements of length must be ultimately backed up by the existence of such an unassailable standard—for it seems that those ordinary, physical standards that we use cannot determine their application all on their own. Even the standard meter, taken all by itself, is a mere metal rod, whose precise length may vary over time and which can be “laid against reality” in all sorts of ways. This metal rod thus seems dead, inert, unless we somehow connect its function with the length it has, and it is this length that constitutes what we call “one meter”. In Naming and Necessity, Kripke does not bring up and does not even seem to recognize the possibility of the sort of puzzlement Diamond identifies. On the contrary, he takes it to be evidently unproblematic to say that the standard meter is exactly one meter long. However, in Kripke’s book on Wittgenstein on meaning and rules (Kripke 1982), this sort of puzzlement is absolutely central. He does not seem to notice the parallel between the two cases, and one of Diamond’s overall aims in her paper is to clarify the connection that Kripke overlooks. In the case of rule-following and meaning, what figures as standards are the rules and examples we actually formulate

216  Martin Gustafsson and make use of when we develop a series of numbers, use words, and so on—and Kripke puzzles over how those rules and examples can have such a “determining” or “normative” force if there isn’t some more unassailable standard which settles how those formulations and examples are to be understood. Taken all by themselves, they seem possible to interpret and apply in all sorts of different ways, and there appears to be nothing about those formulations and examples that allows us to distinguish between applications that are in accord with the rule or the meaning and applications that are not (nothing that determines that “plus” means plus rather than quus, say). On the other hand, Kripke argues, the idea of some meaning “behind” those practices that could serve as the unassailable standard for how they should be used is quite mysterious. According to Diamond, a similar puzzle should worry Kripke about the length he thinks we pick out when we say that the standard meter is one meter long. This length should seem as mysterious to him as those meanings he questions in his book on rule-following. Here, Diamond may seem to be misconstruing Kripke’s position right from the start. After all, in his discussion of the standard meter stick (and in Naming and Necessity generally), Kripke emphasizes that he is concerned with reference rather than with meaning, and with metaphysics rather than with epistemology. Moreover, he does not say, at least not explicitly, that the length of the standard meter constitutes the final and unassailable arbiter of how long things are. Presumably he would react against this characterization by insisting that his points about reference are metaphysical, and the question of what is used as the standard in actual measurements of length is an epistemological issue. So, Diamond’s objection may seem misplaced and question-begging—perhaps as an unwitting manifestation of precisely such Wittgensteinian and/or verificationist modes of thinking that Kripke meant to reject. However, as I will now proceed to show, Diamond’s point about transitive versus intransitive use is of critical significance, and her parallel with the rule-following discussion far from misplaced. 3. At the beginning of her paper, Diamond notes that Kripke would not be entirely satisfied with a definition according to which one meter is defined simply as the length of the standard meter rod. After all, the standard meter rod is a material stick that may expand or shrink due to variations in temperature and so on. So, Kripke argues, a more precise definition would be to specify that one meter is the length of the stick at some particular time t0. Diamond comments: [T]his now supposedly more precise definition shows how far Kripke’s approach is from Wittgenstein’s. Wittgenstein is thinking of a languagegame in which there is comparison of various objects with the meter rod

The Illusion of Intransitive Measurement 217 in Paris; the reader knows what it is like to compare a measuring rod with something else, and that knowledge is needed if we are to see the point of Wittgenstein’s remark. If, however, we suggest, as Kripke does, that how long something is is determined, not by comparison with the rod in Paris, but by comparison with the length which it had at some particular time, it is now much less clear what language-game is being played. How am I to compare some object I now want to measure with the length the rod in Paris had five years ago? (HLSM, p. 105, p. 179 in this volume) Diamond goes on by saying that she does not deny that there are ways of answering that question, ways “involving the use of whatever theories” we may need to calculate how temperature and other circumstances may have affected the standard meter rod at t0 (HLSM, p. 105, p. 179 in this volume). Her point is just that as long as no such ways of comparison are specified, talk of a length with which we make comparisons “hangs in the air”: Kripke’s supposedly more precise definition of one meter is actually a definition which assumes that a standard length can be defined completely in advance and independently of our engaging in some activity of carrying out comparisons of length. (HLSM, p. 105, p. 179 in this volume) What, then, is really the matter with this Kripkean assumption? Why, exactly, couldn’t we define a standard length in advance and independent of our activity of making comparisons of length? Indeed, isn’t it obvious that we can define one meter in such a way, by simply stipulating that it is the length that the standard meter stick has at a certain time t0? After all, it seems that there must be such a thing as “the length that the standard meter stick has at t0”, and that our definition manages to pick out that length and determine that the expression “one meter” refers to it. Certainly, it remains unclear how that length could function as a measure in practice—but one might feel that this is an epistemological red herring that in no way undermines the fact that the reference of “one meter” has been precisely determined by the suggested definition. Again, Kripke insists on a sharp distinction between using the standard meter stick at t0 to fix the referent of the expression “one meter”, and using it to define the meaning of the same expression. According to Kripke, “the ‘definition’ properly interpreted does not say that the phrase ‘one meter’ is to be synonymous . . . with the phrase ‘the length of S at t0’ ” (NN, 56; original emphases). Rather, to give this definition is to stipulate that “ ‘one meter’ is to be a rigid designator of the length which is in fact the length of

218  Martin Gustafsson S at t0” (ibid). After all, Kripke argues, it is not excluded by definition that S might have had a quite different length at t0, so a synonymy claim would be mistaken. Consequently, when Diamond ascribes to Kripke the view that “a standard length can be defined completely in advance and independent of our engaging in some activity of carrying out comparisons of length”, he would presumably want to clarify this by pointing out that by “defining a standard length” he only means fixing the referent of the phrase “one meter”. Indeed, it would seem that what Kripke wants to do is precisely to detach reference from activities of comparison so radically that it becomes completely accidental that we use a standard meter to fix the reference. From Kripke’s point of view, we could in principle have used some very volatile and short-lived object to the same effect—a line drawn in the sand erased by sea waves just a couple of seconds after we have used it to fix the reference of “one meter”. It is indeed crucial to Kripke’s view that the procedure of fixing the referent is in this sense instantaneous. More precisely, if fixing the reference involved repeated comparisons of length, there would be no guarantee against indeterminacy due to a change in the object we employ to do the fixing. A metal rod may shrink or expand, and if we allowed for such variation no determinate length would get fixed. Hence, the “precision” introduced by adding a reference to a point in time t0 is crucial for Kripke. From his viewpoint, the idea that the reference of “one meter” depends on our engaging in some activity of carrying out comparisons of length—an activity that involves the repeated application of ordinary, tangible standards— in confused, since it makes the reference indeterminate in a way that, from a metaphysical point of view, must be intolerable. It is true that Kripke thinks the temporally extended dissemination of the referring expression throughout the community of speakers is significant for the common use of the word “meter”, but that dissemination, as he conceives it, is primarily a matter of reference-borrowing—the transferring of an already fixed reference from one speaker to another. Certainly, Kripke’s picture does not preclude that reference changes over time due to new occasions of baptism, but the idea that reference is tied to the repeated applications of ordinary measurement standards is foreign to his whole outlook.2 At this point, someone with Wittgensteinian sensibilities may start suspecting that such detachment of reference from measurement practices means that Kripke’s notion of what it is to fix the reference runs into problems similar to the ones Wittgenstein pin-points in his discussion of private ostension. To be sure, Kripke does not think of reference-fixing as a private procedure. However, what is crucial here is not the private/public distinction, but the idea that the procedure is non-iterative in the sense just described. As Kripke conceives it, the procedure could not involve the

The Illusion of Intransitive Measurement 219 repeated application of a standard, since such dependence would undermine the sort of determinacy that is needed for the reference to be metaphysically fixed. (With this Kripkean conception also comes the sense that such dependence would be viciously circular, since the reference must supposedly first be fixed in order for there to be a genuinely applicable standard at all. More on circularity in Section 5.) The problem with this conception is that the non-iterative character of the procedure excludes the very possibility of comparison, the very possibility of measurement if you like; and thus it becomes totally unclear what it means to say that a determinate length has been fixed as the referent of “one meter”. For the notion of a length, as we know it, belongs within our temporally extended practices of measurement, of making comparisons—it is a transitive rather than intransitive notion. By contrast, Kripke’s conception of momentary reference-fixing makes his notion of length intransitive—at the same time as its appearance of sense is entirely parasitic on our ordinary, transitive talk of the lengths of things. Or, so I shall argue. 4. As Kripke imagines things, we fix the reference of “one meter” when we say that one meter is the length of the standard meter at t0. We pick out that length, and stipulate that it is what “one meter” refers to. Diamond’s criticism invokes the charge that Kripke treats this length as the final and unassailable arbiter of how long things are (in the metric system). Isn’t this charge misplaced, since it ascribes to Kripke the idea that the length plays a sort of epistemological role, a role as arbiter? Whereas his point is purely metaphysical? Let us think about this in a little more concrete detail. At t0, the referencefixing procedure takes place. From thereby on, “one meter” supposedly refers to the length thus picked out—the exact length that the standard meter rod had at t0. Now, let’s assume that at a later point, t1, the standard meter rod is used to measure some object—a flagpole, say. The flagpole is precisely five times longer than the rod—so we conclude that the pole is 5 meters long. Now, Kripke’s distinction between epistemology and metaphysics is not meant to prevent him from saying that this result may be mistaken, since the meter rod may have shrunk or expanded since t0. If the rod has shrunk, the flagpole is in fact shorter than five meters, since the reference of “one meter” was fixed at t0, when the rod was slightly longer. So, according to Kripke, what ultimately decides how many meters long the flagpole is, is indeed how long the pole is in relation to the length picked out at t0. Kripke will of course acknowledge that this length is not something that is or can actually be used to measure the length of anything—but this should not hide from view that he does envisage a sort of comparison between the length picked out at t0 and the flagpole, albeit one that cannot be carried out “in practice”. He might of course insist that the length picked out at t0 constitutes the final arbiter only in a “metaphysical” sense and

220  Martin Gustafsson that the imagined and practically impossible comparison involves no measurement in the “epistemological” sense of the word. However, it is far from clear that we should be satisfied with this notion of “non-epistemological” arbiter, involved in a purely “metaphysical” comparison. Thus, suppose that in order to clarify this notion, we draw a time-line where t0 and t1 are marked, and then draw the standard meter stick at t0 and beside it the picked-out length (which is exactly as long as the stick), and then, at t1, the standard meter stick—now slightly shorter than the stick at t0—lying beside the flagpole. Such a picture may seem to make the situation clear by showing the possibility that the flagpole would in fact not be fully five meters long despite the standard meter stick’s telling us so. However, such a picture is precisely not an adequate representation of how iteration over time matters to the issue at hand. Indeed, the relevance of time is in effect made invisible here, since when we have the time line exhibited spatially before our eyes, t0 and t1 are contemporaneously present to us. And then, of course, there is such a thing as comparing “the length of S at t0” with the flagpole. However, this comparison will be a perfectly ordinary, “epistemological” and practically viable comparison—namely, a comparison between a drawn line on a piece of paper and the drawn flagpole. And that is precisely the sort of comparison we did not want to illustrate. This suggests that there is a sort of wavering involved in Kripke’s idea that, at t0, we pick out a determinate length which thereafter constitutes the reference of “one meter” even if this length is never and cannot even in principle be used as an object of comparison. On the one hand, Kripke needs to say that the length (in meters) of an object which is measured at a later point—a flagpole, say—is ultimately, “metaphysically”, determined by reference to the length we picked out at t0. After all, that length constitutes the reference of “one meter” and must therefore be what one meter is. On the other hand, Kripke needs to say that a direct comparison between the length we pick out at t0 and other objects is impossible, even in principle. For anything that is actually used as an object of comparison in reallife measurement is itself vulnerable to alteration. Indeed, as soon as we try to clarify the idea of a “direct” comparison between the length itself and some other object (such as a flagpole)—for example, by drawing the sort of picture suggested earlier—the idea collapses. We must now use a perfectly ordinary object of comparison (a line drawn on a piece of paper) to make sense of the way in which the elusive length can constitute the unit of measurement. The “length itself” slips through our fingers, since we make inconsistent demands on it. We want it to constitute the ultimate measure, but we think it can have this function only by not being a measure at all. This is a difficult point, and I will spend the rest of this chapter clarifying it and spelling out some of its consequences. One might say: Kripke needs the length picked out at t0 to be both connected and disconnected from the

The Illusion of Intransitive Measurement 221 actual practice of measurement. Hence, his distinction between the metaphysical and the epistemological levels: he wants the length to be metaphysically connected to the practice, but epistemologically disconnected from it. In what follows, I will put pressure on this idea in a recognizably Wittgensteinian fashion. I will imagine various ways in which one may try to establish connections between Kripke’s definition of “one meter” and practices of measurement, and I  will think through in some detail what those proposed connections would amount to. My aim is to reach a point at which it becomes entirely clear that the underlying structure of Kripke’s confusion is that of a confused attempt to conceive the transitive character of measurement in intransitive terms. 5. As I mentioned, Diamond points out that a connection can be made between the reference-fixing definition suggested by Kripke and real-life practices of measuring. Again, Kripke’s definition is this: (D) One meter is the length of the standard meter stick S at t0. What, then, would it be to connect this definition to actual measurements, actual comparisons, assuming that t0 was, say, a point in time five years ago? As Diamond notes, one possibility is that we consult certain theories about how variations in temperature and other conditions make metal rods such as S shrink and expand. In order to make use of these theories, we would of course need to know what the temperature and those other relevant conditions were like at t0. So, let’s assume that all those data were once registered, so that we have or can assemble a list of them. If so, we can simply use our theories with these data as input, make the required calculations, and then go on to use our results to make comparisons with the standard length, thus defined—no problem, at least not in principle, it seems. So, let’s imagine a practice where each application of the standard meter rod is preceded by careful measurement of relevant conditions: temperature, humidity perhaps, maybe air pressure, and so on. Let’s also imagine that we have a list that specifies the values of those same parameters at t0. And we have theories by means of which we can use these data to calculate whether, and if so how much, the standard meter has shrunk or expanded since t0. This would seem like a practice that, so to speak, encapsulates definition (D). Of course, this practice would be quite cumbersome and therefore impractical when it comes to everyday, humdrum occasions of measurement. But we can imagine that on such everyday occasions, people are allowed to simplify things and use the meter stick as it is currently available, without checking the temperature and so on. Perhaps only scientists and engineers involved in very precise construction tasks would actually bother about adjusting their results in the light of how such conditions

222  Martin Gustafsson vary. Importantly, however, the participants in the practice would themselves conceive the everyday, simplified procedure as rough and imprecise, and tell their children that what is really referred to by “one meter” is defined along the lines of (D). If so, it may well be argued that this practice as a whole still encapsulates the definition, even if most uses of the meter rod are not strictly speaking in line with it. However, there is still a problem with the idea that the definition (D) is “connected” with this practice, in the relevant sense if the word. And this problem will lay bare a deep difficulty with Kripke’s whole viewpoint. So, let’s look at it in some detail. To begin with, it would seem that if the practice, the measuring procedure, is as I have described it, then what really matters about the time-specification t0 in definition (D) is not that it is that particular point in time, but that at that point in time the relevant conditions—temperature and so on—were such-and-such. The fact that those conditions were present precisely at t0, rather than at t1 or at t2 say, doesn’t enter into the relevant calculations. Once it is known what the conditions were at t0—once these people have a list where those conditions are specified—there is a sense in which the reference to t0 becomes superfluous. In fact, if the practice is as I have described it, it seems rather to encapsulate a definition in which the values of the relevant parameters are just listed without any reference to time: (D*) One meter is the length that the stick S has at temperature T, humidity H, air pressure P. Of course, it is true that, as I  imagined the practice, the original reason why precisely these values of the relevant parameters were listed was that they were the values that these parameters had at t0. However, that would seem like a merely historical explanation of why these values occur on the list. It doesn’t seem to affect the practice. Indeed, we can imagine that people eventually forget about the reason why precisely these values were once chosen to appear on the list—and that would not seem to change the practice as I have described it. The reference to t0 seems inessential to what these people refer to by “one meter”. So, what would a practice look like in which the reference to t0 is really essential? Well, then we would have to imagine that any list that specifies what the temperature, humidity, and so on, were at t0, is treated as provisional and revisable by the participants in the practice. We can imagine that there is a committee in this society assigned with the special task of doing further research about what the exact conditions at t0 were, and if evidence turns up which gives reason to change the list currently in use, the committee issues a verdict that the list be changed—and everyone follows suit. So, old measuring results are revised according to the novel findings, and

The Illusion of Intransitive Measurement 223 when new measurements are made the values of the new list are treated as determining the standard used. If this is what the practice looks like, it seems that we can say that a definition such as (D*) is only a revisable and preliminary guide as it were, and that the fundamental definition of “one meter” is still given by (D). The reference to t0 no longer seems superfluous. But why would one have a practice of this sort? Even if there are many different reasons for which it might be important to measure how long things are, it is difficult to come up with one that would motivate such an obsession with a specific point in time as that which fixes the standard used. Of course, one may imagine other reasons why the practice has such a shape. Perhaps t0 occurred on the day at which the country of these people gained its independence, and this independence was celebrated by the introduction of various standard measures. So, the fact that these people let their measuring practice depend on the decrees of the research committee is an expression of how highly they value the independence of their country. That would be a somewhat weird custom, but human customs are sometimes weird, and this would hardly be the weirdest custom one has heard of. So, it might seem that here we have a practice in relation to which Kripke’s definition (D) does not “hang in the air”, but where the cog really is connected with the mechanism. However, it is obvious that the imagined practice has little to do with Kripke’s own motivation for proposing definition (D). Expressing patriotic pride is certainly not the point of definition (D) as Kripke conceives it! In fact, it seems clear that in the practice just described, there is an important sense in which definition (D) still doesn’t connect with the relevant part of the mechanism—I mean, the mechanism that constitutes the actual measuring practice. To see this, imagine that the patriotic pride of this people fades away, that they stop taking the committee seriously and instead see it as laughable remnant of a narrow-mindedly nationalist past, and that they therefore stop adjusting the standard meter according to the committee’s pronouncements. Instead they simply settle on a definition such as (D*), without caring about whether the conditions it states correspond to the conditions actually present on Independence Day. Despite these changes, it would seem that their measuring practice has not changed in any respect that has to do with its being a practice of measuring length. And it would have lost nothing in terms of precision. When it comes to building bridges, making clothes, doing science, and so on, it will be just as useful as before. Indeed, it will probably run much smoother, now that the standard is held constant rather than being adjusted in accordance with new findings of the research committee. So, this attempt to connect definition (D) with a practice of measuring wasn’t successful after all: all it did was to add an arbitrary embellishment to a measuring practice, an embellishment that has nothing to do with what we can recognize as the measuring of length. Whereas Kripke clearly

224  Martin Gustafsson wants a definition such as (D) to be central to what length is. But what would this mean? This may seem like a strange question. However, remember that definition (D), as it stands, in splendid isolation, is in an important sense inapplicable. For if all we know about the defined length is that it is the length that the stick S had at time t0, then we have not yet determined any usable object of comparison. We have not yet identified a measure that can be used now, and that can be used repeatedly. This is what I take to be Diamond’s point, when she says that “Kripke’s supposedly more precise definition of one meter is actually a definition which assumes that a standard length can be defined completely in advance and independent of our engaging in some activity of carrying out comparisons of length”. What my discussion so far has shown, I hope, is that it is not so easy to explain how such a definition can ever be connected with an activity of carrying out comparisons of length in such a way that it is really central to the “mechanism” of measuring. Let me try to clarify further what I take the problem to be. Again, in order to carry out comparisons of length—in order to measure length—we need an object of comparison, a standard, that can be used now and repeatedly. Hence, to connect definition (D) with an activity of measuring, it would appear that we need somehow to implement the definition in terms of such a currently and repeatedly applicable standard. “The length of stick S at t0” is precisely not such a standard. A practice where we use the standard meter rod just as it is available, without checking for how it shrinks or expands due to changes in temperature and so on, employs a repeatedly applicable standard—namely, the meter rod itself. A practice where we do check for how the rod shrinks or expands due to changes in temperature and so on also employs such a standard—namely, the meter rod taken together with something like definition (D*) and relevant parts of physical theory. But the definition (D), as it stands, provides us with no such repeatedly applicable standard. Kripke says that a virtue of definition (D) is precision. The standard meter stick might shrink and expand, and therefore it can determine a precise length only if we stop the flow of time and define one meter in terms of the stick’s length at a particular moment. But then, wouldn’t a definition such as (D*) be just as precise? Well, yes, but notice that the procedure of applying (D*) would also involve many sources of possible imprecision: just think of all the concrete measurements of temperature, humidity, air pressure, and so on that we would have to make, and think of how the instruments used in those measurements might fail to exhibit the sort of constancy Kripke takes to be required for full precision. Of course, we may try to check their constancy in turn, but such checks for constancy will involve further measurements with instruments that in their turn will be liable to variation of the sort Kripke wants to exclude—and among these

The Illusion of Intransitive Measurement 225 measurements will certainly be measurements of length. So there will be a sort of holistic circularity that seems vicious from a Kripkean point of view: there won’t be the immediate, unassailable, and absolutely elementary sort of precision that seems to characterize definition (D). So, I think it’s clear that (D*), precise as it might seem, would not satisfy Kripke. What I’m getting at here is that nothing which can be used repeatedly as a standard of measurement would satisfy Kripke’s demand. For it is precisely the possibility of repeated use that as such makes possible the sort of variation that Kripke conceives as an intolerable “imprecision”. The length of stick S at time t0 is a precisely defined length, according to Kripke, exactly because it is inapplicable as an object of comparison. But on the other hand, he thinks of this length as a perfect object of comparison, if it were applicable as such, so to speak. That length would unequivocally determine the length of any object with which it was compared, were it only possible to employ in such comparisons. However, since it cannot be thus employed, we—creatures helplessly seized by the flow of time—must make use of imperfect replicas of this length when we make our measurements, and thus these measurements are bound to offer mere approximations to what we really refer to when we talk about length. Here we can see very clearly the pertinence of Diamond’s diagnosis of Kripke as wavering between transitive and intransitive uses. On the one hand, he wants to think of the length of the standard meter at time t0 as an object of comparison of a sort—for the very claim that it is “perfectly precise” in comparison with the material standard meter rod itself, or with any other standard of measurement that we may actually employ from one time to another, in itself purports to involve a comparison. (Kripke’s insisting that reference is not a matter of meaning or epistemology does nothing to undermine this point.) On the other hand, the precise determination that he thinks characterizes this length requires that the length cannot function as an object of comparison—for it is precisely its being withdrawn from the possibility of repeated application that gives it its supposed preciseness. 6. Kripke (and I’m still talking about the Kripke of Naming and Necessity, not the meaning-skeptical Kripkenstein) takes it to be evident that we can refer to the length of the standard meter stick S at t0 when we use the expression “one meter”. Now, I  don’t think we should try to reject this assumption by invoking some theory of reference according to which the word “reference” doesn’t really mean what Kripke takes it to mean. Rather, what we should do is just note that Kripke’s notion of reference involves inconsistent requirements, manifested in his wavering between intransitive and transitive uses. On the one hand, he thinks the reference of “one meter” can be determinate only if it is inapplicable as an object of comparison; on the other hand, to say that the definition (D) “fixes the reference” of the expression “one meter” surely presupposes that we can

226  Martin Gustafsson somehow present it as the original in comparison with which our actual instruments of measurement are mere replicas (of whose fidelity we can never be entirely certain). But now, what about the Kripkensteinian meaning-skeptic? Well, he of course doubts the existence of such pure, original objects of comparison— objects of comparison that are somehow withdrawn from the temporally extended, repeated use of material instruments and signs, but which nonetheless function as the ultimate standards for such uses. However, what makes him a skeptic is that he holds on to the conviction that if there is anything like determinate objects of comparison, they must have this strange character—at the same time as he fails to make clear sense of what such objects would be. Thus, he still wavers between transitive and intransitive uses, even if he vaguely recognizes that the object of comparison that he would like to identify slips through his fingers. He still expects the intransitive use to be transitive, and therefore feels that his ability to make sense of it as such constitutes a sort of failure. On the skeptic’s own understanding, this failure may be unavoidable, since no coherent sense can be made of the envisaged object of comparison. But the skeptic still feels that such an object is missing, and so he feels that the hopelessness of finding such an object makes the situation truly desperate and tragic. 7. What is it, then, to give up this expectation—to really see through the incoherent demand for a radically unusable standard which, precisely in virtue of its inapplicability, is supposed to constitute the reference of our terms? Diamond says that once this expectation is given up, we will see that “[t]here is . . . nothing in principle the matter with having a standard that varies somewhat in length, or with having in circulation many different standards, of somewhat various length” (HSML, p. 121, p. 192 in this volume). This way of talking may raise the worry I gestured at in the beginning of this chapter, namely, that Diamond’s Wittgenstein throws the baby out with the bathwater and embraces a simplemindedly conventionalist or pragmatist conception of what makes a measuring standard adequate. If there is nothing “in principle” the matter with having a standard that varies somewhat in length, or with having in circulation many different standards of somewhat various length, then how can we account for the idea of genuine metrological progress, where imprecise and unstable standards are replaced by more precise and stable ones? Isn’t the consequence of what Diamond is saying that there is no more objective criterion of metrological success than that a given system of measurement satisfies the practical needs of a specific community? Let me end this chapter by saying something about how this worry should be addressed. My strategy will be to first describe a practice of the sort Diamond is talking about, with standards that vary in length. My aim is to clarify the exact sense in which “there is nothing in principle the matter” with such a practice. I shall argue that the “in principle” that

The Illusion of Intransitive Measurement 227 Diamond has in mind is the “in principle” of the Kripkean skeptic, not of the working metrologist. In fact, I will argue that it is Kripke who cannot make sense of the aims of metrology, whereas those aims are perfectly compatible with Diamond’s point. 8. When I  was a kid, we often played marbles. The game was played with marbles and tin soldiers: the soldiers (which were of course modeled on the army of the glorious Swedish superpower of the 17th century) were used as targets, and the child who hit the soldier with a marble so that it fell to the ground became the happy owner of the soldier—whereas the child who was the previous owner of the soldier instead got all the marbles that had missed the soldier before it got hit. In Swedish toy stores at the time, you could buy material for tin soldier production: molds and tin. So, it was a forgiving game: if you had a bad day and lost many marbles and soldiers, you could cast new soldiers at home and come back next day as a rich man. An important part of the game was to measure out the distance from which the marbles were to be thrown. Here the rules were quite meticulous. Distance was measured in “steps”. One step was simply one foot, and it was considered very important that each step was taken so that the heel of the one foot touched the toes of the other. The complaint was often made that this rule wasn’t properly followed by the person who did the measuring. The distance varied with the kind of soldier that was being targeted. For an ordinary foot soldier, the distance was 12 steps. For a horseman, it was 25 steps. For an artillery piece, a cannon, in was 50 steps. Then certain tin soldiers were considered “rare”—they were soldiers for which molds were no longer easily available, soldiers that might have belonged to one’s parents’ collection, for example. In such cases, one of the older children assumed the role of an antiquities expert and made a supposedly informed judgment about what distance would be proper—for a “rare” foot soldier the distance might have been as much as 30 or 40 steps. Another funny aspect of the practice was that if a soldier was painted, the distance was increased. However, the increase had nothing to do with how beautifully the painting was made. The only thing that mattered was the number of colors used—one step was added for each color. If you used 20 colors to paint a foot soldier so that it looked like a speckled harlequin, the target distance became 32 steps. However, despite all these fairly meticulous rules, there was one thing that we never considered, as far as I remember—and that was the variation in foot size between the participants. No one person was responsible for measuring the distance from which the marbles were to be thrown. On one occasion, perhaps I did it; on the next, perhaps Johanna did it; and then Eric did it the third time; and so on. Now, the participants were children between, say, 9 and 13  years, so the size of their feet must have varied

228  Martin Gustafsson considerably. But I  can’t remember a single occasion on which this was brought up as an issue that needed to be addressed. Of course, if someone had shown up, say, in huge clown shoes and aspired to measure the distance, we would probably not have tolerated it. But the fact that the feet of 13-year-old Eliza were a couple of inches longer than the feet of 9-year-old Karl was simply ignored: Eliza could do the measuring and so could Karl, and no one complained about the difference. By contrast, if Karl had failed to put his heel in contact his toes while doing the measuring, there would have been loud complaints. So, that’s the practice. Many things can be said about it. One possible complaint would be that it is imprecise. One way to make it more precise would have been to decide that only Eliza was allowed to do the measuring. Alternatively, we could have constructed a stick, a “standard step stick”, by which the measuring was to be done. It may also be objected that the practice was unfair, in an elementary sense of fairness that would be readily available to any kid of that age. After all, if I set up one of my foot soldiers and 13-year-old Eliza did the measuring, I gained considerable advantage over Paula who set up one of her foot soldiers when 9-year-old Karl did the measuring. It may even be argued that the practice was inconsistent. Thus, suppose Paula’s foot soldier was painted in two colors, so Karl measured out a 14 steps distance; whereas my foot soldier was not painted, so Eliza measured out 12 steps, but due to the difference in foot size between Karl and Eliza, they ended up at the same point. However, 14 feet is not the same as 12 feet, right? It may also be argued that it was irrational of us to complain so much when someone did not put heel and toes in contact when he or she did the measuring, whereas we didn’t care at all about variations in foot size. So, it seems arguable that the practice yielded inconsistencies, and thus that what we meant by “step” was quite indeterminate. All these complaints make perfectly good sense. On the other hand, one may of course also argue that they are misdirected. Thus, the suggested ways of increasing the precision of the measuring technique would have had tangible disadvantages. If Eliza would have been the only one allowed to do the measuring, we could not have played on days when she was ill. If we had used a standard step stick, and the stick was lost, we couldn’t have played either (and kids constantly lose things—whereas their feet tend to keep attached to their legs). With regard to fairness, perhaps it should simply be admitted that the practice was unfair. On the other hand, maybe fairness just wasn’t so central to us: we played marbles and had fun, and the fairness of the game was good enough. With regard to the alleged inconsistency, we simply tolerated it, and the practice still worked to our satisfaction. But of course, we might also have become unsatisfied, and changed the practice in some of the ways just sketched. It may also have happened that

The Illusion of Intransitive Measurement 229 the practice developed in such ways that increased precision and fairness became more urgent. Perhaps the stakes got higher—large sums of money, say—and if so, we might well have wanted to change the measuring technique. And of course, there are many things for which the technique would not have worked, such as building houses and bridges. So, to say that “there is nothing in principle the matter with having a standard that varies somewhat in length, or with having in circulation many different standards, of somewhat various length”, is not to say that there is nothing the matter with having such a standard or set of standards. Rather, the point is that a criticism of a practice makes sense only as it involves some concrete suggestion for how to improve the practice, in light of a shared understanding of what the point of such an improvement would be. Such improvement may well involve replacing the old standard with a new one, but the crucial point is that the improved standard will have to be as applicable as the old one. By contrast, the skeptic’s complaint about a measuring practice offers no alternative standard that can be used as a genuine object of comparison. All it offers is an incomparable ghost of such a standard, whose seemingly absolute “precision” is only a matter of its inapplicability. 9. It is precisely at this point, however, that one might start worrying that the sort of view I find in Diamond’s Wittgenstein, and which I am myself proposing, amounts to a simple-minded sort of pragmatism, or perhaps “language-game relativism”. For I might seem to be suggesting that a criticism of a practice makes sense only as it involves some concrete suggestion for how to improve the practice in light of a shared understanding of what is the practical point or points of the practice. And several interrelated worries can be raised with regard to such a view. To begin with, if measuring by steps in the marble game that I have just described is a “practice” in the relevant sense, then surely practices are not isolated patterns of behavior but connected with other things we do in life. After all, measuring in steps in the described fashion was one form of length measurement that we kids knew, but we also knew how to measure with yardsticks, tapes, and so forth, as we did at carpentry and needlework lessons in school, for example. And what is important is that we recognized all those forms of measurement precisely as ways of measuring length. Thus, we were capable of comparing these methods with regard to precision and ranking measurement by yardsticks as more precise than measurement by steps. Importantly, this is because we also had available to us a primitive notion of what it is to differ in length—what it is for one thing to be longer than another—such that noting such a difference does not require any one particular standard of measurement, but simply amounts to putting two things side by side and seeing which one is longer. Consequently, a statement such

230  Martin Gustafsson as the following would have made perfectly good sense to us, and would indeed have been recognized by us as true: Measuring distance by steps, as we do it when we play marbles, is a relatively crude measuring procedure. Our feet differ in length, and hence the method gives different results in different cases. However, given the specific points of this game, the method still works great. More precise and consistent methods would be too cumbersome, and hence less well suited to our purposes. This means that we ourselves could separate quite sharply the following two questions: (1) What method is practically suitable, given the specific purposes of the marble game? And (2) How precise and consistent is this method? One might call the second question “theoretical”, since it raises the issues of precision and consistency without treating them as simply relative to some specific practical purposes, such as those of the marble game. This theoretical question is not a question raised “from sideways on”, to use John McDowell’s famous phrase. It is one that makes perfectly good sense to us, the marble players, “from within” our lives with language. Now, one might try to argue that a separation between these two questions is possible only because the marble game is such a very special and delimited practice. The idea, then, would be that a more pervasive, community-wide practice of measurement would not leave room for any similar distinction. But now, consider such a more pervasive practice. We can imagine a community in which people use a standard meter stick just as it is available, without considering whether it shrinks or expands over time. They just don’t care about checking whether the standard meter stick is stable or not. If anyone asks what they mean (or refer to) by “one meter”, they point to the stick, and that’s that. Let us also assume that, as it turns out, they don’t have to check the stability of the stick: it so happens that the stick they use is stable enough for their practice to work well, given their needs. They successfully build boats, houses, and bridges; they make nice clothes and so on. And they never notice any inconsistencies in their measuring results. In this case, would it even make sense for them to raise the issues of precision and consistency? Yes, it would. For it isn’t as if the phenomena of shrinking, expanding, roughness, and precision, as these people know them, are exclusively tied to what is determined by reference to the meter stick. They will have seen children and carrots and tree branches grow; they will have experienced the shrinking of clothes and icicles; and they will have seen sticks (the oars and masts of their boats, say) becoming shorter by being gradually worn down at the edges. Thus it would make perfectly good sense for these people to raise questions about the stability and precision of the standard meter stick, even if they in fact do not raise such questions, and even if

The Illusion of Intransitive Measurement 231 there is no already identified and specific practical need for it. At some point, some precocious geek within this society may well come up with the idea of starting a research project meant to investigate the stability and precision of the standard meter stick. This project might be seen as impractically “theoretical” and nerdy by her peers, but it will not be unintelligible to them. Of course, the need for such a research project might also arise due to new practical needs of the society—needs that require higher levels of precision and consistency, such as the need to build better weaponry in defense against pirate attacks, or a need for more precise navigation instruments to explore new waters. Or, the project might have started out as a purely “theoretical” one, and only later prove to be of practical significance as its results makes possible previously unheard-of scientific and technical developments. Or, most likely, there will be a very complicated interaction between the theoretical development of precise and stable standards, other scientific developments, and technological inventions. Indeed, such a development is not only thinkable but also rather similar what has actually taken place in our own society (Quinn 2011, Kershaw 2012). Now, it is important to see that there is no problem with accommodating such a development within the Wittgenstein-Diamond sort of conception that I  have been clarifying in this chapter. The essential point here is that the possibility of “theoretical” questions about the precision and stability of established standards of measurement in no way undermines the central insight of that conception, namely, the transitive character of measurement. Consider what the research project of the precocious geek in my imagined community would actually look like. Presumably, she would construct a number of replicas of the standard meter stick and use them as check-points; she might investigate the stability of these sticks by subjecting them to variations in temperature, atmospheric pressure, humidity, and so on and so forth. She might also simply inspect the standard meter carefully (e.g., with a magnifying glass) to see if it has been slightly worn down at the edges. At a later stage, she might come up with more advanced scientific techniques for investigating the stability of the stick, and she might eventually suggest that the stick be replaced by some more stable and precise standard. The crucial thing is that her procedures will be transitive through and through; at no point will she introduce or rely on some mere ghost of a standard whose seemingly absolute “precision” is only a matter of its inapplicability (since there just is no such thing as “relying on” such an inapplicable standard). However, the worries about the Diamond–Wittgenstein conception might still not be completely alleviated. For doesn’t the Kripkean notion of length still serve as a kind of ideal governing the search for increased precision and stability? Indeed, isn’t it even arguable that recent developments in metrology, in which artifact standards such as the Parisian standard

232  Martin Gustafsson meter and the International prototype kilogram have been replaced by definitions in terms of natural constants, confirms a sort of Kripkean intuition: the length (or kilogram) itself is distinct from the methods of measurement we employ when we decide how long things are, or what their weight is? Consider the following passage from the International Bureau of Weights and Measures, describing the value of defining the measures of the International system of units (SI) in terms of natural constants: The use of seven defining constants is the simplest and most fundamental way to define the SI. . . . In this way no distinction is made between base units and derived units; all units are simply described as SI units. This also effectively decouples the definition and practical realization of the units. While the definitions may remain unchanged over a long period of time, the practical realizations can be established by many different experiments, including totally new experiments not yet devised. This allows for more rigorous intercomparisons of the practical realizations and a lower uncertainty, as the technologies evolve. (BIPM 2013, pp. 9–10) At first sight, this may sound vaguely supportive of a Kripkean view. In fact, however, the units defined in terms of natural constants are very different from the non-epistemological and rigidly designated length that Kripke has in mind. The function of the defined units is still clearly and unwaveringly transitive, and thus, the “decoupling” that the BIPM is talking about in the just quoted passage is not at all the principled (and ultimately inconsistent) sort of decoupling that Kripke’s conception involves. Consider the 2019 definition of the meter: The meter is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299,792,458 when expressed in the unit m⋅s−1, where the second is defined in terms of the caesium frequency ΔνCs. The precision and stability of this definition are not gotten for free, as in a Kripkean procedure of reference-fixing. Nor is it achieved merely by arbitrary stipulation, as a simple-minded conventionalist may suggest. It is a hard-won scientific achievement, and the definition is a working component of the web of scientific theory and experiment. Thus, even if it is true that the definition “may remain unchanged over a long period of time” and that its “practical realizations can be established by many different experiments, including totally new experiments not yet devised”, its role and significance cannot be understood in isolation from practices of measurement. Certainly, the definition’s practical realizations and the ways in which we calibrate measuring rods and other instruments in relation

The Illusion of Intransitive Measurement 233 to it may vary and get revised over time, but this does not mean that the definition is independent of the existence of any such practical realizations and calibration procedures. If there were no practical realizations of the definition—if we had no idea whatsoever about how to go about using and calibrating instruments so that they “practically realize” the definition— the definition would not be recognizable as a definition of any unit of measurement, and thus not as a definition of length. Perhaps any established method of measurement and calibration can be replaced, but not all at once; the calibration, development, and replacement of methods will be gradual and will therefore rely on the use of other established methods, and also on experimental results and theoretical hypotheses. Even if the definition refers to natural constants rather than artifacts, the holistic character of measurement won’t go away; the metrologist is as much a sailor on Neurath’s raft as any other working scientist.3 This is not to deny that defining measures in terms of natural constants achieves a central goal of metrology, a goal that might be characterized by saying that length, thus defined, gains a sort of theoretical stability and precision which it cannot be credited with as long as it is defined in terms of an artifact which ties it down to some already devised practical realization. Perhaps this is even a reasonable way of making sense of the idea that defining length in terms of natural constants makes it an objective measure (as intriguingly argued in Riordan 2015). I will not enter any further into this discussion, but only point out that such stability, precision, and objectivity would be altogether different from the alleged stability, precision and objectivity of the length that Kripke takes himself to have identified simply by pointing at a metal rod at a certain point in time. The stability, precision, and objectivity achieved by working metrologists are what Kripke would call “epistemological” notions, and that is why they make sense. By contrast, the significance of Kripke’s metaphysical notions evaporate as soon as we think clearly about what measurement is. Notes 1 The French meter of the Archives, created at the end of the 18th century, was an end standard: the meter was defined as the distance between its ends. The standard meter used in Wittgenstein’s and Kripke’s times, created in 1889, was a line standard: the meter was defined as the distance between two lines engraved on its surface near its ends (Quinn 2011, p. 5). 2 In his thoughtful contribution to this volume, Panu Raatikainen proposes a more conciliatory reading, according to which Kripke’s conception can be understood as in line with Wittgenstein’s: The practices of the linguistic community, which stretch back in time—the historical chains of communication and reference-borrowings—take care of reference, in Kripke’s picture. In it, language users participate in a general

234  Martin Gustafsson practice of reference-borrowing. One can perhaps even view it as a kind of ‘use’ or ‘usage’, in a Wittgensteinian mood, if one wants. (Raatikainen, p. 14) As should be clear, I disagree with this reading. As I understand Wittgenstein, what is central to his conception of use or usage is not reference-borrowing in Kripke’s sense, but repetition (in the meter case, the repeated application of a measurement standard). Indeed, Wittgenstein would presumably regard the Kripkean notion of reference-borrowing as deeply misleading, as it obscures that notion of repeated use—of doing “the same thing”, again and again—which Wittgenstein sees as the key to clarity in this area. Thanks also to Arif Ahmed and Jakub Mácha for pressing me on this point. 3 My argument in this paragraph is sketchy, and can only be fully substantiated by careful investigations of actual cases. Deeply intriguing examples of such studies can be found in Hasok Chang’s works (e.g., Chang 1995, 2004). I cannot here enter a discussion to what extent my account is compatible with Chang’s conception of metrological progress via epistemic iteration, but my sense is that they are compatible.

References BIPM (2013) Draft Chapters 1, 2 and 3 of the 9th SI Brochure. Bureau international des poids et measures. Chang, Hasok (1995) Circularity and Reliability in Measurement, Perspectives on Science 3, 153–172. Chang, Hasok (2004) Inventing Temperature: Measurement and Scientific Progress. Oxford University Press. Diamond, Cora (2001/this volume) How Long Is the Standard Meter in Paris? In T. McCarthy and S. C. Stidd (eds.), Wittgenstein in America. Oxford University Press, 104–139, abbreviated as HLSM. Kershaw, Michael (2012) The “Nec Plus Ultra” of Precision Measurement: Geodesy and the Forgotten Purpose of the Metre Convention, Studies in History and Philosophy of Science, Part A 43, 563–576. Kripke, Saul (1980) Naming and Necessity. Harvard University Press, abbreviated as NN. Kripke, Saul (1982) Wittgenstein on Rules and Private Language. Harvard University Press. Quinn, Terry (2011) From Artefacts to Atoms: The BIPM and the Search for Ultimate Measurement Standards. Oxford University Press. Raatikainen, Panu (this volume) On the Alleged Incompatibility Between Wittgenstein and Kripke, pp. 9–27. Riordan, Sally (2015) The Objectivity of Scientific Measures, Studies in History and Philosophy of Science 50, 38–47. Riordan, Sally (2019) And How Experiments Begin: The International Prototype Kilogram and the Planck Constant, in N. de Cortenay, O. Darrigol, and O. Schlaudt (eds.), The Reform of the International System of Units: Philosophical, Historical and Sociological Issues. Routledge. Wittgenstein, Ludwig (1969) The Blue and Brown Books. Blackwell. Wittgenstein, Ludwig (2009) Philosophical Investigations. Blackwell.

11 Kripke’s Transcendental Realist Fantasy and Wittgenstein’s Transcendental Idealism, After All Avner Baz 11.1 Introduction 11.1.1  Transcendental Realism and Transcendental Idealism

Call the world as captured, or reflected, in our truth-evaluable representations (judgments, beliefs, thoughts, assertions, etc.), when those are true (or otherwise successful qua representations), ‘the objective world’. Call ‘transcendental realism’ any view on which that world is ‘as it is in itself’— as it is, that is, wholly independently of its being perceived and made sense of by human perceivers and sense-makers. Put otherwise, transcendental realism is the view that our representations (when true) add nothing—no new content—to what was there anyway, independently of their formation and of the conditions under which they have whatever sense they have for us. Call ‘transcendental idealism’ an opposing view, on which we play an ineliminable role in the constitution of the objective world, and cannot perceive, nor know, nor indeed so much as make sense of (the idea of) that world as it is in itself. Transcendental idealism is ‘transcendental’ (rather than ‘empirical’) in the sense that in no way does it take the world as captured in our (true) representations to be somehow illusory, or unreal, or ‘only in our mind’.1 It is an idealism concerning not the reality or existence of the objective world, but its sense: it is in the sense the world makes to us—in general, but here specifically as the object of our representations—that we are inextricably implicated, on this form of idealism. And the realism in question is ‘transcendental’ (rather than ‘empirical’), in that it is a commitment to more than just the possibility of assessing our representations in terms of truth and falsity—which no transcendental idealist would deny. For the transcendental realist, our representations are true precisely to the extent that they reflect the world just as it is independently of our perceiving it, forming representations of it, and assessing those representations in terms of truth and falsity (and in other terms as well).

DOI: 10.4324/9781003240792-12

236  Avner Baz 11.1.2  An Important Clarification

I said that transcendental idealism is ‘an opposing view’ to transcendental realism; and that immediately calls for clarification. To begin with, I will try to show in what follows that transcendental realism cannot ultimately be made sense of, which means that ‘transcendental realism’ does not really refer to a view—not, at any rate, if a view needs to make sense. Transcendental realism, I will argue, ultimately amounts to no more than the stressing or italicizing of certain words—be they words such as ‘really’, ‘out there’, ‘independent of us’, and so on, or the words of some particular representation or set of representations—accompanied by a certain play of the imagination, a Wittgensteinian ‘picture’. But if so, then my ‘transcendental idealism’ had better not refer to the simple negation of (what I call) transcendental realism. For the (attempted) negation of nonsense is itself nonsense; and the (attempted) negation, or denial, of a non-view is not an expression of a view. We just do not know what it would be, or mean, for us not to be implicated—in a sense yet to be explicated—in our truthevaluable representations, and in our evaluations of those representations (and so on), and therefore in the world as reflected in those representations. Another way of putting what is essentially the same point is that we do not know what it would be, or mean, for our representations not to be conditioned, or situated. And if so, then ‘transcendental idealism’, as used in this chapter, does not really name a view either—not, at any rate, if a view needs to have a sensical negation. If transcendental realism ultimately boils down to an empty, illusory stressing or italicizing of certain words, as I will propose it does, then transcendental idealism is best understood as the recognition and acknowledgment of that emptiness or illusion. 11.1.3 Expansions

Though the undeniable father of transcendental idealism is Kant, and though I  am using some of Kant’s basic terminology, I  have deliberately presented transcendental idealism, in its disagreement with transcendental realism, in a way that allows for versions of it that move beyond Kant, and even break with him more or less significantly. For one thing, my characterization leaves open the possibility (and indeed, the reality) that even our most basic forms of representation historically evolve, together with their ‘transcendental’ conditions—by which I mean all that lies in the background of any given representation or set of representations and contributes to its having whatever sense it has for us. Moreover, as this last gloss on ‘(transcendental) conditions of sense’ indicates, I’m using that notion more liberally than Kant did. I do not take it that for any representation or set of representations there is, or could be, the complete and final list

Kripke’s Realist Fantasy and Wittgenstein’s Idealism 237 of the conditions of its sense. What matters for transcendental idealism as understood in this chapter is just that, for any representation or set of representations, there are conditions for its making whatever sense it makes to us; and while it is often easy enough to point out some of those conditions—for example, as we will see, the objective representation of the length of something in meters only makes sense when there is some agreed-upon standard for the unit of ‘one meter’, and a practice of employing that standard, which makes that standard and that practice, then and there, conditions of sense for that representation—it makes no sense to try to specify all of those conditions, if only because any such condition has its own background conditions of sense, and because all too often, a condition of sense only reveals itself as such when its absence results in the absence of (clear enough) sense. ‘Transcendental idealism’ as used in this chapter also allows for more or less significant differences among human sense-makers when it comes to what makes (what) sense to them, and how, and under what conditions. The debate concerning the possibility, or intelligibility, of alternative forms of sense-making, or ‘mindedness’—a debate that has considerably exercised readers of the later Wittgenstein2—is a red herring, as far as the argument of this chapter is concerned. Regardless of whether Kant was right in proposing that some basic forms of sense-making, together with their transcendental conditions, are universal, or necessary for (human) empirical cognition as such, I take it to be undeniable that we may, and do, differ from each other more or less significantly in what makes sense to us and how, and under what conditions. Some readers of the later Wittgenstein, and in particular Thomas Nagel, have taken that as evidence for transcendental realism and against transcendental idealism.3 But it isn’t. Neither the existence nor the intelligibility of different sense-making ‘perspectives’ undermines transcendental idealism, precisely so long as those are all perspectives. What we cannot make sense of, I will propose, is sense that is independent of sense-making, and sense-making that is not situated or conditioned. 11.1.4  The Current Dominance of Transcendental Realism

Even before we make any attempt to clarify what the transcendental idealist means in proposing that we ‘play an ineliminable role in the constitution of the objective world’ and are ‘implicated in it’, I  think it is fair to say that, despite the best efforts of transcendental idealists of various stripes, contemporary analytic philosophy is largely dominated by transcendental realism. Invocations of something called ‘the world’ are pervasive in virtually all fields of philosophical inquiry.4 In many of those invocations, ‘the world’ is supposed to refer more or less exclusively to the world as reflected

238  Avner Baz and understood in the natural sciences, or perhaps just in physics; in some others, the exclusive authority of the natural sciences with respect to the world is denied, and ‘the world’ is meant to refer to something broader, even much broader, than the world as reflected within those sciences (as in Gabriel 2015; and earlier in Nagel 1986). But in either case, what’s invoked (appealed to, theorized about, and so on) is taken, and regularly claimed, to be some particular way, or ways—precisely the way or ways that are, or could be, captured in our true representations of it; and it is further insisted that its being that way, or those ways, is wholly independent of our representing it as being that way, or those ways, and (therefore) independent of the conditions of our thus representing it. This transcendental realist insistence underwrites much of the work currently produced within mainstream analytic philosophy.5 I suppose many contemporary analytic philosophers would regard the current dominance of transcendental realism as an instance of philosophical progress. What should give them pause, however, is not just the fact that transcendental idealism originally articulated itself, in Kant, as a critical response to traditional forms of (what Kant identified as) transcendental realism, but even more so the fact that the return to dominance of transcendental realism, in the past half a century or so, has not been the outcome of any serious assessment of, or argumentation against, transcendental idealism. In contemporary analytic philosophy, the transcendental idealist perspective rarely comes into view; and when it does, it is typically dismissed offhand, with little or no argument, and without so much as a serious attempt to understand it. Thus, we see Ted Sider, for example, early on in his Writing the Book of The World, candidly proclaiming: A certain ‘knee-jerk realism’ is an unargued presupposition of this book. Knee-jerk realism is a vague picture rather than a precise thesis. According to the picture, the point of human inquiry—or a very large chunk of it anyway, a chunk that includes physics—is to conform itself to the world, rather than to make the world.6 The world is ‘out there’, and our job is to wrap our minds around it. This picture is perhaps my deepest philosophical conviction. I’ve never questioned it; giving it up would require a reboot too extreme to contemplate; and I have no idea how I’d try to convince someone who didn’t share it. (2011, p. 18) Later on, Sider says, ‘The knee-jerk realist thinks that the world is “out there”, waiting to be discovered rather than constructed’ (2011, p. 65) and that to give up on that realist picture would be to ‘concede far too much to those who view inquiry as being merely the investigation of our own minds’ (2011, p. 66).

Kripke’s Realist Fantasy and Wittgenstein’s Idealism 239 Or take Gideon Rosen, who opens a paper that aims to assess the prospects of an idealist position we could nowadays take seriously, by declaring that Kantian idealism, and German idealism more broadly, presuppose a ‘Subject’, or ‘Mind’, that is ‘not identical with anything we encounter in the natural world’ and which ‘somehow constitutes or conditions that world’, and then goes on to say that ‘we just can’t bring ourselves to believe in this Mind anymore’ (1994, p. 277), and that is because ‘a flexible and relatively undemanding naturalism functions for us as an unofficial axiom of philosophical common sense’, which means that ‘if we can believe in minds at all, they are the embodied minds of human beings and other animals’, and ‘it is just plain obvious that empirical, embodied minds do not actively constitute the bulk of the inanimate world’ (1994, p. 277). At this point, those who have found some version of transcendental idealism compelling would likely feel that the position has been distorted beyond recognition by its transcendental realist detractors, and could respond to such summary dismissals of it in any number of ways: they could point out that to say that we play a role in the constitution of the objective world, or that we make an ineliminable contribution to whatever sense it has for us qua objective, is not the same as saying that all we can ever hope to know or understand is our own mind, or that we (literally) make the world; they could argue that, properly understood, our ‘constitution’ or ‘construction’ of the objective world stands in no contrast with empirical ‘discovery’, but rather goes hand in hand with it, in just the way that laying a measuring tape against a table goes hand in hand with finding out, thereby, how long it is—in meters, for example, or in some other unit; they could argue, with phenomenologists such as Heidegger and Merleau-Ponty, that our being embodied and in-the-world not only means that the traditional dichotomy Sider presupposes between ‘mind’ and ‘world’ is unsustainable, but also, pace Rosen, stands in no conflict with the idea that we play a role in the constitution of the objective world—on something like the contrary, it’s precisely the fact that our objective representations are situated, that they have worldly-historical conditions, that renders the world as reflected in them not a world as it is in itself; they could point out the tendency on the part of transcendental realists to conflate transcendental idealism and empirical idealism, and to falsely charge transcendental idealists with proposing that the empirical world is somehow illusory, or might for all we know be illusory (see, for example, Gabriel 2015, p. 43); they could argue that the transcendental realist’s characteristic reification of properties and of facts is unsustainable, for we do not know how to identify or establish (the presence of) either properties or facts apart from our ways of identifying them and of establishing them (or their presence);7 they could argue, following Charles Travis, that our true or false empirical representations are ‘context-sensitive’ in their truth-conditions, and that it therefore makes no sense to suppose that the world as reflected in those representations is

240  Avner Baz the world as it is in itself (see, for example, Travis 1997); and of course, they could go back and rehearse the argument of the Critique of Pure Reason, or of some other transcendental idealist text they find compelling. 11.1.5  The Plan for This Chapter

I doubt that any of the aforementioned responses, even if further elaborated, would significantly move contemporary transcendental realists. Some of those responses would likely be seen as nitpicky or too tightly tied to the particular formulations of this or that transcendental realist. Other responses operate at such high level of abstraction that they are not likely to be found compelling by anyone who has already committed her or himself to transcendental realism. I therefore propose to try a different tack in this chapter. I propose to anchor the broad and abstract disagreement between transcendental realism and transcendental idealism in the seemingly narrower and more concrete disagreement between Kripke and Wittgenstein concerning the sense it would make to say of the standard meter rod in Paris—assuming that it does function there and then as the standard for ‘one meter’—that it is, or that it is not, one meter long. A  paper by Cora Diamond (2001; reprinted in this volume) on Kripke’s disagreement with Wittgenstein concerning the meter standard, and a more recent paper by Martin Gustafsson that further develops Diamond’s diagnosis of that disagreement (this volume), have encouraged me to think that a particular moment in that disagreement—namely, the moment in which Kripke attempts to improve upon Wittgenstein’s example by proposing that ‘we could make the definition [of “one meter”] more precise by stipulating that one meter is to be the length of S at a fixed time t0’ (NN, p. 54)—brings out especially clearly the transcendental realist picture that ultimately controls Kripke’s thinking, and allows us to see just how misleading and ultimately misguided that picture is. My plan is to draw out what I see as the transcendental idealist upshot of Diamond’s and Gustafsson’s critical engagement with Kripke, by connecting it with relevant moments in Kant’s Critique of Pure Reason. Like Diamond and Gustafsson, I will mostly focus on Kripke and his response to Wittgenstein within the context of Naming and Necessity, rather than on Wittgenstein exegesis. As far as the purposes of this chapter are concerned, suffice it to say that my reading of PI 50 is pretty much the reading that has come to be called (by its critics) ‘the standard (or received) reading’ (see Narboux 2017, p. 113; Gert 2002): I understand Wittgenstein to be proposing, in his own voice and assertively, that it would make no sense to say of the standard meter in Paris that it is, or is not, one meter long, in a context in which it served as the—by hypothesis, one and only—standard for ‘one meter’8; and I understand him to further be proposing, once again

Kripke’s Realist Fantasy and Wittgenstein’s Idealism 241 in his own voice and assertively, that this is due not to any special property of that particular metal rod, but simply to its playing, there and then, the role of the (one and only) standard for ‘one meter’. In this way, Wittgenstein at once continues, challenges, and transforms, Russell’s and his own earlier attempts to articulate what may be called ‘conditions of sense’9: all that lies at the background of, and contributes to, our words’ having whatever sense they have for us—on any given occasion of their employment, and more generally. He is proposing to replace an account based on ‘thinking’ (what those conditions must be, or be like), with an account based on ‘looking and seeing’ (what they, or some of them, actually are). Much has been written about Kripke’s disagreement with Wittgenstein concerning the meter standard. Much has also been written about whether there is some version of transcendental idealism—however, theoretically deflated and problematically expressible—to be drawn from Wittgenstein’s later work. Nothing, however, has been written, so far as I know, about the bearing of the first issue on the second. And that is rather surprising, given that Wittgenstein’s remark about the standard meter is part of a series of remarks that investigate, more or less directly and more or less explicitly, the idea that there are conditions of sense, and given that transcendental idealism—from Kant onward—may most generally be understood as the idea, or recognition, that our sense-making is conditioned. I’m going to propose that that much remains true even after we follow Wittgenstein, move beyond Kant, and replace ‘thinking’ about what the conditions of sense must be, with ‘looking and seeing’ what, in some particular case or range of cases—measuring and representing length in meters, for example—they are. Kripke, on the other hand, and especially the Kripke of Naming and Necessity, is surely one of the primary contributors to the current dominance in analytic philosophy of transcendental realism. On one popular story, Kripke has revived pre-Kantian metaphysics by freeing it from the epistemological shackles that Kant, and any number of philosophers following Kant, had placed on it.10 One problem with that popular story is that the liberation of pre-Kantian transcendental realist metaphysics in Naming and Necessity is inter-mixed with, or camouflaged by, Wittgensteinian-sounding, anti-theoretical, deflationist disclaimers (cf. NN, pp. 64 and 93): the causal-historical account of naming is offered as no more than a ‘better picture’ of how names relate to their referents (NN, pp. 93–94)— and a picture, moreover, which is supposed to do greater justice than its ‘descriptivist’ alternative to the way in which what names mean, or refer to, in the mouths of individual speakers, depends on what those names mean or refer to ‘in the community’ (NN, pp.  94–95); the assumption of referents for our words whose ‘nature’, or ‘essence’, or even identity, does not depend on our discursive practices, or indeed on anyone ever

242  Avner Baz actually referring to them in speech or otherwise, is presented as based on nothing more than ‘intuitions’ (NN, pp. 14 and 42), which are, moreover, Wittgensteinian-sounding intuitions about ‘what we would say’ (NN, pp. 77, 119–121, 132); and the invocation of ‘possible worlds’ is similarly said to be based on, and to be no more than an abstraction from, our modal and counterfactual talk (cf. NN, p. 19, fn. 18). On my reading of Kripke, he is pulled, in both Naming and Necessity and Wittgenstein on Rules and Private Language, by certain ideas he derives from Wittgenstein, however obscurely, concerning the problematic nature of philosophical theorizing, and concerning the essential publicness of language and the dependence of what an individual speaker may intelligibly say and mean with her words on how those words are used in her ‘community’, and at the same time is pulled in something like the opposite direction by a picture, which is on full display in his disagreement with Wittgenstein concerning the standard meter, on which our words have (mean, refer to, denote, designate, etc.) ‘meanings’, or ‘referents’, that are altogether independent of our discursive practices and which are supposed to somehow determine—all by themselves and independently of us—the correct ‘application’ of those words to the world in all (future) cases.11 And that—I mean, the tendency to imagine that the sense we may find in things, or attribute to things, has somehow already been there, and would have been there, independently of us and of our sense-making practices and their conditions—is, after all, the heart of transcendental realism. 11.2 Kripke, Wittgenstein, and the Transcendental Realist’s Predicament 11.2.1  Kripke’s ‘Unexamined Idea of Reference’

Responding to Kripke’s proposal that we could make the definition of ‘one meter’ more precise by specifying that ‘one meter’ refers to the length of the rod at t0, Cora Diamond writes: Here we might note that this now supposedly more precise definition shows how far Kripke’s approach is from Wittgenstein. Wittgenstein is thinking of a language-game in which there is comparison of various objects with the meter rod in Paris; the reader knows what it is like to compare a measuring rod with something else, and that knowledge is needed if we are to see the point of Wittgenstein’s remark. If, however, we suggest, as Kripke does, that how long something is determined, not by comparison with the rod in Paris, but by comparison with the length it had at some particular time, it is now much less clear what languagegame is being played. How am I to compare some object I now want to

Kripke’s Realist Fantasy and Wittgenstein’s Idealism 243 measure with the length the rod in Paris had five years ago? My point is not that there is no way to answer that question; there are certainly ways, involving the use of whatever theories, in which we could make such comparisons. The point is rather that, from Wittgenstein’s perspective, talk of a length used as a standard (a length, that is, with which we make comparisons) hangs in the air unless there is some context, whether one that actually exists or one that we can imagine, in which we can see what is to count as making comparisons with the standard length. Kripke’s supposedly more precise definition of one meter is actually a definition which assumes that a standard length can be defined completely in advance and independently of our engaging in some activity of carrying out comparisons of length.12 (As Kripke sees the case, our activities of determining the length of things are not relevant to what it is we are referring to by ‘one meter,’ hence needn’t be mentioned in discussing how reference is fixed. . . . [T]here is an implicit reliance on an unexamined idea of reference. (2001, p. 105, p. 179 in this volume; note added by AB) Let me flesh out some of the insights contained in this passage and work out what I take to be the transcendental idealist upshot of those insights. I start with Kripke’s ‘unexamined idea of reference’. On Kripke’s transcendental realist picture, there are lengths—countlessly many, but each perfectly determinate—such that each physical object has one, and only one, of those lengths as its length,13 and such that for each of those lengths and for any physical object, that object either is, or is not, that length, altogether independently of our practices of length measurement and the standards employed in those practices; so that all that is left for us to do is to ‘fix’ one of those lengths—whichever of them we pick out or happen to hit upon—as the referent of some name, and thereby to determine the correct application of that name to any object and in all situations, both actual and merely possible. In this respect, as Diamond points out, the certain length that is (supposedly) designated by ‘one meter’ is, for the Kripke of Naming and Necessity, like the arithmetical function designated by ‘plus’, for the Kripke of Wittgenstein on Rules and Private Language: both are supposed to determine the correct application of the designating term in all cases (Diamond 2001, p. 129, p. 199, fn. 24 in this volume).14 This Kripkean picture is presumably supposed to apply in the case of other physical properties as well (cf. NN, p. 56): it is by virtue of coming to refer to, or designate, a certain determinate color, or mass, or (difference in) temperature, or shape, and so on, that the correct application of terms such as ‘red’, ‘one Kilo’, ‘one degree Celsius’, ‘square’, and so on, is supposed to be determined. When contemporary analytic philosophers speak about determinate properties that are had (or not had) by things, or about determinate facts that

244  Avner Baz obtain (or fail to obtain), altogether independently of our practices of identifying properties and establishing facts, they are relying, and indeed must be relying, on some such picture, it seems to me. Altogether missing from that picture is judgment, and more specifically the role of judgment in determining the right way of carrying on with a word or, if you will, its correct application. Once we have fixed, or ‘marked out’ (NN, p. 55), ‘a certain length’ as the referent of ‘one meter’, by ‘stipulating that one meter is to be the length of S at a fixed time t0’ (NN, p. 54), ‘one meter’ becomes a ‘rigid designator’, Kripke says: it ‘designates rigidly a certain length in all possible worlds’ (NN, p.  55). But since, as already noted, the talk of ‘possible worlds’ is said by Kripke to be nothing more, nor less, than an elucidatory abstraction from our counterfactual talk, to say of ‘one meter’ that it is a ‘rigid designator’ is just to say that, when used by us, it refers to that length in any description we may give of any counterfactual situation—including, importantly, the counterfactual situation in which it, that length, had not been had by S at t0. Strikingly and tellingly, Kripke talks of the certain length designated by ‘one meter’ as if it were an ‘object’ (NN, p.  106), which got fixed as the referent of ‘one meter’ by one of its ‘accidental properties’ (NN, p. 75), or ‘contingent marks’ (NN, p. 106)—namely, its accidental property of being had by S at t0 (NN, p. 75; see also pp. 106–7); ‘just as in the case of the name of the man we may pick the man out by an accidental property of the man’ (NN, p. 75); and just as presumably we picked out the species that is the referent of ‘tiger’ by accidental properties such as the animal’s look (NN, p. 121). In all of these cases, the referent is supposed to have already been there—fully determinate, identifiable, and ready to be named—before it got fixed as the referent of some term; and once fixed as the referent, it is supposed to determine the correct application of the term in all future cases. Even more strikingly, an upshot of Kripke’s picture and his account of naming is not just the counterfactual that S might not have been one meter long at t0, but also the counterfactual conditional that had we actually used his ‘more precise definition’ to fix the referent of ‘one meter’, and had the standard(s) for ‘one-meter’ we relied on in practice been different in length from S at t0—due to some miscalculation or miscalibration along the way, for example, or to causal forces we were unaware of or neglected to take into account—then we all would have been wrong in each and every one of our representations of the lengths of things in meters, even if those representations had been working perfectly fine for us. Indeed, if we had used Kripke’s ‘more precise definition’ to fix the reference of ‘one meter’, then there would have been a real possibility that, by Kripke’s lights, we are, at present, systematically wrong in our representations of the lengths of things in meters; in just the way that, by his lights, we all would be misapplying

Kripke’s Realist Fantasy and Wittgenstein’s Idealism 245 a proper name if we relied on some uniquely satisfied description to fix its referent, but for one reason or another misidentified the unique satisfier of that description.15 This consequence of a possibility of massive and systematic error on the part of competent length-measurers and users of ‘meter’ seems to me to suggest that something has gone wrong in Kripke’s account, and that the picture underlying the account is to be suspected. 11.2.2  A Closer Look at Kripke’s ‘More Precise Definition’

To see more clearly where Kripke has gone wrong, consider what our lengthmeasuring practices would have had to involve, if his ‘more precise definition’ had been correct of our ‘meter’, so that in measuring the length of things in meters, we had actually been comparing them with S as it was at to. In the passage quoted earlier, Diamond says that we could certainly think of ‘ways, involving the use of whatever theories, in which we could make such comparisons’, but that ‘Kripke’s supposedly more precise definition of one meter . . . assumes that a standard length can be defined completely in advance and independently of our engaging in some activity of carrying out comparisons of length’ (2001, p. 105, p. 179 in this volume). I note, first, that whatever ways we might have used to make those comparisons, and whatever theories we might have relied on in making them, those ways and theories would have been part of the background against which representations of length in meters would have had their sense, and therefore would have contributed to what ‘meter’ as used by us would have meant.16 I also note that those ways of comparing objects with the meter standard as it was at to would have involved further measurements (of temperature, barometric pressure, and so on), and therefore would have involved reliance on further standards and instruments (and the theories or models behind the design and application of those standards and instruments, etc.).17 This underscores the transcendental idealist insight that our representations of the world—of the length of things in meters, for example—do not capture or reflect a world ‘as it is in itself’.18 This is made even clearer in Gustafsson’s paper. He invites us to try to think through what relying on Kripke’s ‘more precise definition’ might look like in practice: Let’s imagine a practice where each application of the standard meter rod is preceded by careful measurement of relevant conditions: temperature, humidity perhaps, maybe air pressure, and so on. Let’s also imagine that we have a list that specifies the values of those same parameters at t0. And we have theories by means of which we can use these data to calculate whether, and if so how much, the standard meter has shrunk or expanded since t0. (Gustafsson, p. 221 in this volume)

246  Avner Baz Gustafsson notes that such a practice would be ‘quite cumbersome, and therefore impractical when it comes to everyday, humdrum occasions of measurement’ (p. 221 in this volume). I  take it that the envisioned practice would be cumbersome, because, in order for measurements of length to abide by Kripke’s ‘more precise definition’, auxiliary measurements and calculations would similarly need to be made not only when measurement devices or local meter standards were calibrated directly by comparison with the metal rod in Paris but also every time those were applied, and every time other devices or standards calibrated by comparison with them were applied, and so on. Gustafsson therefore anticipates that, at least in most cases, people would forgo those careful measurements (of temperature, humidity, etc.) and calculations. And if so, and if we wanted to still think of them as beholden to Kripke’s ‘more precise definition’, we would need to imagine them as regarding their everyday practice as ‘rough and imprecise’, he suggests (p. 222 in this volume). And we would further need to imagine that in initiating their children into their practices of length measurement and representation, they would teach them that though it’s normally perfectly acceptable to apply ‘meter’ without doing all of those auxiliary measurements and calculations, and perhaps mostly unacceptable to waste time and resources doing them, what ‘meter’ really means is ‘the length of S at t0’. But if they always, or nearly always, forwent those measurements and calculations in practice, then it’s not clear what it would mean to say that ‘meter’, their ‘meter’, (really) meant the length of S at t0, and referred to that length. Kripke’s notion of ‘what a word means (refers to, designates)’ is a piece of technical jargon that makes no contact with the ordinary notion and relies for its apparent sense on Kripke’s unexamined idea, or picture, of reference.19 11.2.3  Kripke’s Account and Actual Practice: The Case of the Kilogram

It would be instructive to compare Kripke’s imaginary case, as developed by Gustafsson, with actual historical cases in which certain objects or operations that had formally been set up as standards for units of measurement were hardly ever used as such in actual practice. One such case is that of the kilogram, which was originally defined as the mass of one cubic decimeter of distilled water, when at the melting point of ice. Originally, it was thought that the introduction of this new, ‘natural’ standard would increase the universality, stability, and precision of mass measurements, relative to those that relied on ‘merely conventional’ metal artifacts as standards (Riordan 2015, p. 41). As Riordan reports, however, in practice, ‘mass measurements were never performed directly against water but against objects that had themselves been (perhaps via a long chain) calibrated against the Kilogramme des Archives [which was calibrated, when originally made, against one cubic decimeter of distilled, ice-cold water, AB]’ (2015, p. 42). ‘Evaporating, expanding with changes in temperature,

Kripke’s Realist Fantasy and Wittgenstein’s Idealism 247 sticking to some vessels and repelled by others, water was difficult to weigh’, Riordan explains, ‘[and the] Kilogramme des Archives, originally made to be the premier exemplar of the kilogram, was soon acting as its definition’ (2015, pp. 42–43). I suppose it would not have been incorrect to say during that time—and I myself remember being taught as a child—that one kilogram was the mass of a cubic decimeter of water (perhaps without even bothering to add ‘ice-cold and distilled’), though it’s important to note that saying that to someone not already familiar with the practice of measuring and representing masses in objective terms would hardly have been informative. But if we keep in mind, as we should, that the Kilogramme des Archives gradually changed its mass, however insignificantly, during the 100  years or so in which it served as the de facto standard of ‘one kilogram’20; and if we also wished to abide by Kripke’s account of naming; what should we say was the referent of ‘one kilogram’ during that time? Which certain mass was it naming, or rigidly designating? I suppose there are several ways one could answer that question on Kripke’s behalf. One could insist that so long as the official definition of ‘one kilogram’ was ‘the mass of one cubic decimeter of ice-cold, distilled water’, that mass was the referent of ‘one kilogram’, and what it rigidly designated or named. (That answer is based on the undoubtedly false empirical assumption, which would itself be based on a conceptual confusion, that the mass of ice-cold, distilled water is absolutely determinate, or determinable, and never varies.) One could alternatively answer that it was the Kilogramme des Archives—the object used as standard in practice—that determined the referent of ‘one kilogram’ during that time, and that the referent therefore kept changing as the mass of that standard was changing. (That answer highlights another false assumption, which is essential to Kripke’s account of naming and to the transcendental realist picture, and to which I will return later, that for every physical object, there is the set of perfectly determinate magnitudes it has [at some given moment], and which it may serve to specify, or identify, whereas in reality the specification or identification of a magnitude by means of some physical object is always tied to context-sensitive standards of precision.) And finally, one could answer that the question cannot be answered correctly, and precisely, because ‘one kilogram’ was defined imprecisely during that period, by means of an object—again, the Kilogramme des Archives—that was gradually changing its mass. Together, these three possible answers underscore the disconnect that Diamond emphasizes between Kripke’s presumed referents—the certain length that is supposed to be separable from its worldly standards and rigidly designated by ‘one meter’ (when ‘precisely’ defined), the certain mass rigidly designated by ‘one kilogram’, and so on—and the practices of measurement and representation of measurement in which ‘one meter’, ‘one kilogram’, and so on, are doing their work for us.

248  Avner Baz 11.2.4 Kripke’s Referent of ‘One Meter’ as a Wittgensteinian ‘Beetle in a Box’

To bring out that disconnect even more clearly and draw out its transcendental idealist significance, let us go back to our imaginary community of length measurers who abide by Kripke’s ‘more precise definition’ of ‘one meter’ and imagine that the measurements of temperature, barometric pressure, humidity, etc., were at least normally carried out, together with the calculations that allowed those people to adjust their results, in order to correct for changes in S’s current length relative to its length at t0. For that practice to be intelligible, we would need to assume that they found those adjustments to be called for, given their needs, interests, aims, and so on, and given S’s behavior under varying physical conditions and the degree and frequency of changes in those conditions. Here Gustafsson astutely notes that, in that case, ‘what really matters about the time specification t0 in [Kripke’s definition] is not that it is that particular point in time, but that at that point in time the relevant conditions—temperature and so on—were such-and-such’ (p. 222 in this volume). And if so, Gustafsson continues, ‘there is a sense in which the reference to t0 becomes superfluous’ (p. 222 in this volume): it could be dropped from Kripke’s ‘more precise definition’ and replaced with a specification of the temperature, humidity, etc., that, together with S, would be, or serve as, the standard in that imaginary community for measurements of length in meters. And then, it is worth noting, that imaginary community would become not significantly different, in practice, from ours.21 Only their peculiar attachment to t0 would remain a (possibly explainable) mystery. And now, I  wish to take Gustafsson’s diagnosis one step further and propose that it’s not just the reference to t0 that’s superfluous. It’s Kripke’s referent—the certain length supposedly designated rigidly by ‘one meter’— that’s superfluous: it makes (or would have made had it been real) no contact with our actual practices, and could be dropped out of consideration as irrelevant to those practices, and to our understanding of those practices. And what’s left, once it drops out of consideration, is all we’ve ever actually had, and all that we really need: our standards and instruments, our ways of calibrating them, the theories that inform their construction and application, our practices of measurement more broadly, our norms of integrity (scientific or otherwise), our context-dependent standards of precision, the needs and interests to which those practices and norms and standards answer, etc.—in short, all that belongs to the background conditions of any particular measurement of length or representation of length in meters (or any other unit) and contributes to the sense it has for us. These, as Wittgenstein suggests, are the ‘grey rags and dust’ in which the ‘mouse’ of meaning—here, the meaning of ‘meter’, and of utterances featuring ‘meter’—is to be found (PI, §52), and which philosophers have been

Kripke’s Realist Fantasy and Wittgenstein’s Idealism 249 reluctant to examine (PI, §52), believing, with Kripke, that meaning comes, and may only come, from something like Kripke’s referents. But, as we’ve begun to see, Kripke’s posited referents—at least when it comes to such referents as lengths, masses, and so on—are idle: if meaning did not already reside in the grey rags and dust of our everyday practices and their worldly conditions, then no Kripkean referent could endow them with meaning, or inject meaning into them. Which is unsurprising, given that those referents are, at best, abstractions based on those practices. 11.2.5  The Transcendental Idealist Upshot of the Argument Thus Far

And this, it seems to me, is what Wittgenstein is trying to get us to see in PI, §50 and the remarks leading up to (and from) it. As I read him, Wittgenstein is responding, by at once deflating and transforming, the philosophical pursuit of, or demand for, grounds or basic conditions of sense.22 That was the pursuit, or demand, that led to the postulation of Tractarian or Russellian simple objects, or elements, which supposedly can only be named and whose existence can be neither intelligibly asserted nor intelligibly denied (PI, §46). As he does elsewhere, Wittgenstein is inviting us to ‘look and see’ what we do, in fact and in practice, rely on in carrying on with our words, instead of ‘thinking’ what must be (the case) for sense to be possible (PI, §66).23 Whatever exactly Tractarian elements or simple objects were supposed to be, they were theoretical posits, not anything with which we are actually familiar; for, as Wittgenstein notes, ‘experience certainly does not show us these elements’ (PI, §59). In this respect, those posited elements are like Kripke’s referent of ‘one meter’ (or ‘red’, or ‘tiger’, or ‘heat’, etc.). The later Wittgenstein is trying to get us to see that those theoretical posits are ultimately theoretically idle, and only give us the illusion of having explained our sense-making practices, while in fact generating confusion. What we find, when we look and see, is that a metal rod may be a condition of sense: given a suitable worldly background, and employed as a standard for a unit of length measurement, that rod may be all that is needed—that is, all that we need, given the history of our practices of measurement, and our particular range of historically evolving capacities and sensitivities, needs and interests, and ways of looking at and seeing and responding to things—to secure the sense of our representations of length in terms of meters. And insofar as that rod is, there and then, our means of representation—insofar, that is, as it is part of what we there and then are relying on to secure the sense of our representation—it cannot, there and then, be the object of our representation (PI, §50). More generally, whatever, at any given point, belongs to the background against which some representation has whatever sense it has for us may not there and then

250  Avner Baz be the object of that very representation. Not on pain of violating some abstract metaphysical or logical prohibition against self-representation (cf. NN, p. 108, fn. 50), but simply due to the figure-background structure that is essential to all sense-making and sense perception. And though anything belonging to the background of some representation could always, in principle, become the object of some other representation, there would then be the worldly background of that representation, which would not there and then be represented. The human perceiver and sense-maker is always already in the world, taking her bearing from it, but that, as I’ve already noted, would only seem to undermine transcendental idealism to someone who assumed that the world in which we find ourselves, from which we take our bearing, and against the background of which we form our representations, is just the world as reflected in those representations. 11.2.6  Kripke’s Counter-Factual

Kripke points out that the rod in Paris, S, might have been longer or shorter at t0 than it actually was, if, for example, the temperature in the room had been different at that moment (NN, p.  55). And that is undeniable. He goes on to say, however, that if that had happened, S would not have been one meter long. And that, as Diamond argues, is where confusion looms. Not necessarily; not because there is no way to understand the italicized words that would render them sensical and innocuous; but rather because of how Kripke wishes to understand those words, or would like to be able to mean them. Suppose we asked Kripke, ‘What, in stating your counterfactual, do you mean by “one meter (long)”? How long was S at t0? How long would S not have been if it had been longer or shorter at t0?’.24 Kripke’s answer to that question, or anyway the answer he would have given had his ‘more precise’ definition been in force, goes something like, ‘Well, by “one meter” I  mean one meter—the certain length S happened to have at t0 (whenever that was), and which (let us suppose) is also known as “39.3700787 inches” ’. But the first part of that answer would be empty: one hardly clarifies what one means by some word or expression by repeating that word or expression italicized or with greater stress. And the second part takes us right back to the metal rod in Paris and its role as standard for our practice of measuring length in meters, together with all of the auxiliary measurements and calculations mentioned earlier, and the standards used for them, and the theories informing them, and so on; or it relies on our already knowing what ‘one inch’ means, and hence on our already being familiar with measurement of length in inches, relying as it necessarily does on whatever serves as a standard for ‘one inch’, and so on. Either way, we are led, once again, to nothing more, nor less, than our measuring practices

Kripke’s Realist Fantasy and Wittgenstein’s Idealism 251 and their worldly standards, instruments, and conditions; and we never come to, nor need ever come to, Kripke’s referent—the ‘certain length’ that S presumably happened to have at t0. 11.2.7  The Transcendental Realist Illusion

Here, it might be objected: Granted, Kripke’s posited referent plays no role in our practice of measuring length, and makes no contact with that practice. Kripke himself acknowledges as much, when he notes at one point that ‘one meter’ refers not to an (abstract) object but to a unit of measurement, and further notes that the ‘the notion of reference may be unclear’ in this case (NN, p. 55). And let us further agree that a unit of measurement is not really identifiable apart from the standards we use for it, and—unlike the imagined referent of Kripke’s ‘certain length’—is not something an object can intelligibly be said to have or not to have. That does seem to support Wittgenstein’s proposal that it would make no sense to say of the object we use as the standard for ‘one meter’ that it is, or is not, one meter long. Still, whichever unit we choose to use and whichever standard(s) we use for it—for example, S as the standard for ‘one meter’—that standard, or standards, would (each) have a certain, determinate length; just as any other physical object has its determinate length (or anyway, determinate spatial dimensions), altogether independently of us. And, moreover, there is going to be a determinate mathematical relation between the particular length of the standard and the particular length of each other object, again altogether independently of us.25 In short, we are free to choose our units and standards, but once we’ve done that, the things themselves and their properties—their length, their mass, their color, and so on—will dictate which of our representations of them will be true, and which will be false.26 And isn’t that, ultimately, all that the transcendental realist claims, or need claim? The answer is ‘No’. The transcendental realist—whether of the naturalist sort like Rosen or of the non-naturalist sort like Gabriel—wants to be able to talk, intelligibly, about things having, or not having, determinate properties, or about determinate facts that obtain or do not obtain, altogether independently of our (context-sensitive) criteria for something’s having, or not having, some particular property, or being, or not being, some determinate way, and altogether independently of human judgment. He wants to claim for things as they are in themselves the very properties we may attribute to them in our representations; and he wants to think of those things and properties as constituting, all by themselves, the very facts we may establish, state, insist on, dispute, and so on. And we have not yet been given any reason to suppose that that could intelligibly be done, or that we have any clear idea of what doing it might be.

252  Avner Baz For to say of things that they are some particular way, or that there is some particular way they are, is no more informative—no more succeeds in stating or otherwise specifying some determinate empirical fact or set of facts—than saying that things are the way they are; and to say of something that it has a certain length (weight, color, etc.), or that its length stands in certain mathematical relations to the lengths of other objects, is not (yet) to attribute to it any determinate physical property (beyond perhaps the ‘property’ of being a physical object, which is not a physical property on par with lengths, weights, colors, and so on).27 ‘That something is a magnitude (quantum) may be cognized from the thing itself, without any comparison with another’, Kant writes in ‘The Analytic of the sublime’ in the third Critique, ‘[b]ut how big (wie groß) it is always requires something else, which is also a magnitude, as its measure’ (2000, p.  5: 248, Kant’s emphasis). The objective determination of how long, for example, something is requires a comparison with something else; and the comparison is something we (need to) do: it is not something that things as they are in themselves may do just with each other.28 And we know, in general, how to determine and represent the length of something, by comparing it, directly or indirectly, with something else; we know, in general, how to find, or determine, how many times one thing goes, or would go, into another. But if we wanted to identify, or determine, the length of something, or how long it is, without relying on any such comparison, whether actually carried out or just imagined, with something else that serves, there and then, as a standard and means of representation, we’d be under what Wittgenstein calls in the Brown Book an ‘illusion’ (or ‘delusion’)29—the illusion, namely, of thinking that you could identify a thing’s length (color, mass, temperature, etc.), and thereby turn it into the potential bearer or referent of some name, just by focusing your attention on it, or drawing someone else’s attention to it, which, as Diamond, drawing on Wittgenstein, insightfully suggests, would be like putting one’s hand on one’s head and saying ‘I’m this tall’ (2001, p. 120, p. 191 in this volume). 11.2.8  The Transcendental Realist Illusion in Salmon

The illusion Wittgenstein and Diamond identify is on full display in Nathan Salmon’s ‘How to Measure the Standard Metre’. According to Salmon, lengths are ‘abstract entities’, and ‘[o]ne function that is filled by the institution of using a unit of length, such as the inch, is that it provides standard or canonical names for infinitely many otherwise unnamed abstract entities (the particular lengths)’ (1988, p. 204, emphasis altered). But the institution of a system of units, and standards for those units, and practices of employing those standards to calibrate our measuring instruments and of using those instruments to measure things, and so on, are not essential,

Kripke’s Realist Fantasy and Wittgenstein’s Idealism 253 according to Salmon, to the identity of those abstract entities, and to physical objects having them, or not having them, as their length. The meter rod S at t0, for example, is taken by Salmon to have one—some determinate one—of those abstract entities, as its length. In Kripke’s imagined scenario, we name that length ‘one meter’ and thereby define a unit of length measurement, but we could equally successfully and intelligibly have named it ‘Leonard’, Salmon says, even apart from any intention of ever using ‘Leonard’ (1988, p. 196).30 And then Salmon writes this: When one looks at an ordinary, middle-sized object, one typically sees not only the object; one typically also sees its length. To put it more cautiously, one typically thereby enters into a cognitive relation to the length itself, a relation that is analogous in several respects to ordinary visual perception, but that (because perceiving subjects may stand in the relation to abstract qualities like lengths) may not correspond exactly with the relation, standardly called ‘seeing’, between perceivers and the concrete objects they see. One also typically thereby sees (perhaps in some other extended sense) the fact that the object has that very length. Of course, merely perceiving an object will not always result in such empirical knowledge. Perhaps in order to see an object’s length one must be able to take in the object lengthwise, from end to end, in one fell swoop. Perhaps the visual presentation cannot be under circumstances that create optical illusions . . . Perhaps not. In any case, if the reference-fixer does indeed see S under the required circumstances, he can thereby know of its present length, Leonard, that S is presently exactly that long. No physical measurement is required beyond merely perceiving the object. (1988, p. 205, see also pp. 209–211)31 So, on Salmon’s account, whenever we look (lengthwise, etc.) at an object, any middle-sized object—a fork, for example—we typically see (or “see”)32 not just it but also, additionally, an abstract entity, its length; and we also see (or “see”) that that object has that length. And that by itself puts us in a position to fix that length as the referent of whichever name we please—‘Leonard’, for example—and to know that the object is exactly that (Leonard) long, ‘simply by looking at its length, without measurement’ (1988, p. 211).33 Even setting aside the rather obscure cognitive relation that is ‘analogous in several respects’ to ordinary visual perception but in which we are supposed to stand to abstract qualities when we perceive the objects that have those qualities, a problem with Salmon’s account is that it contains a claim about what typically happens when we look at middle-sized objects (as long as we see them lengthwise, etc.) that is supported by no evidence,

254  Avner Baz empirical or other, and false of our perceptual experience.34 As often happens in philosophy, Salmon thinks this is what happens (in perception), because rather than looking and seeing, he is guided by what he thinks must happen. Committing what phenomenologists and Gestalt psychologists have called ‘the experience error’ (cf. Merleau-Ponty 1996/2012, p. 5/5),35 he attributes to the world as perceived the sort of contents, and determinacy of content, that are characteristic of the world as thought about or understood objectively; and, adhering to transcendental realism, he takes the latter to be altogether independent of us and of our representations of it, and takes perception (at least under favorable conditions) to present us with it—that is, with physical objects and their objectively determinate properties, and with facts (countlessly many of them we must suppose) to the effect that those objects have those properties (and do not have countlessly many others). As an account of normal (‘typical’) human perception, this is hopeless. Apart from judgment, or objective determination—measurement, paradigmatically, or even just an eyeball estimate, made within a suitable context and against a suitable background—things do not present themselves to us in perception as having determinate objective magnitudes. Rather, they present themselves to us as having motor and affective significances (see Merleau-Ponty 1996/2012, pp.  210ff./216ff.)—significances for our phenomenal body, not for our Kantian ‘understanding’ (the faculty of objective, empirical concepts); and those significances are, moreover, context-dependent, shifting, and more or less indeterminate: the same fork, for example, may be seen as (too) long in some contexts, (too) short in other contexts, and lacking even that much length-determinacy in yet other contexts. As an expression of the transcendental realist fantasy of a world that articulates itself without any need for any intervention from us, Salmon’s proposed account is very useful, however. Salmon’s lengths, just like Kripke’s, are abstract entities—magnitudes, I  suppose, countlessly many but each perfectly determinate and discrete—that do not depend on our practices (methods, techniques) of measuring and determining length, and for the units and standards employed in those practices, for being the particular, determinate magnitudes they are, and for being had, or not had, by particular objects. And not only are those abstract entities something that no one has ever perceived (or for that matter “perceived”) but also that they are also theoretically idle: they play no role in our practices of length measurement; and positing them does nothing to explain or elucidate those practices. Objectively establishable magnitudes—thought or talked about in the abstract—are not abstract entities independent of our practices of measurement and underwriting those practices, but rather, precisely, abstractions based on those practices.

Kripke’s Realist Fantasy and Wittgenstein’s Idealism 255 The problem with Salmon’s proposed account is not the assumption that upon looking at a fork (taking it in lengthwise in one fell swoop, etc.) and ‘fixing its length as the referent of some name’, we should be able to reidentify that length, and tell, whenever we look at any middle-sized object, and even without any measurement or comparison, that the object has, or does not have, it as its length. Salmon seems not to assume that (1988, pp. 205–206). Nor do I take him to assume that upon fixing the length of an object we’re looking at as the referent of some name, we should—even apart from any practices (methods, techniques) of identifying and reidentifying (i.e., establishing the presence of) objectively determinate lengths—be able to actually use that name to represent objectively the lengths of indefinitely many other objects, on indefinitely many other occasions. Salmon’s problematic assumption, rather, is that even without assuming, or relying upon, any of that, we may still talk intelligibly of seeing (or “seeing”), and naming, some determinate length.36 Paraphrasing an earlier-quoted remark of Diamond’s, we could say that Salmon’s problematic assumption is that our activities of determining the length of things are not relevant to what it is we would be referring to by ‘Leonard’, and hence needn’t be mentioned in discussing how its reference would be fixed. More generally, his problematic assumption is that objectively determinate physical magnitudes are independent of our practices of determining them.37 11.2.9 Standards of Precision, the Inherent Indeterminacy of Measurement, and More Trouble for the Transcendental Realist

Here, I must note a complication that I’ve thus far ignored, and which further undermines the transcendental realist’s picture. I’ve been talking about (physical objects having) determinate objective magnitudes—lengths, for example. And the transcendental idealist upshot of my discussion thus far may be put by saying that determinate objective magnitudes are objectively determinable magnitudes, that the objective determination of magnitudes is a form of practice, and that that practice—like any other sense-making practice—has its background conditions. More specifically, I’ve argued that when it comes to physical magnitudes such as length or mass, their objective determination requires units, and standards for those units, and techniques for measuring objects against those standards. What I’ve set aside thus far is the fact that the determination of physical magnitudes is always subject to standards of precision, and that precision in measurement is always relative—there is no absolute precision, or precision such that there could be no greater; there is, at best, precision that is good enough for all present intents and purposes. This is what van Fraassen means when he writes that ‘a measurement outcome is not infinitely precise . . . [and] the real outcome is not a number but an interval’ (2008, p. 163).

256  Avner Baz There is an inherent indeterminacy to (the determination of) physical magnitudes—an indeterminacy that is due not to any epistemic or perceptual limitation on our part, or to in-principle-eliminable shortcomings of our measuring devices and procedures, but rather to the fact that those physical magnitudes depend on units for their determination, and the units depend on standards, and the standards are themselves worldly things— material, if you will. We use matter to mathematize matter. For our concepts of physical magnitudes not to be empty, they need to be ‘operationalized’, as Chang puts it (2007, pp. 202–203): there needs to be a ‘material realization of the definition [of the unit]’ (2007, p. 203). And that means that the definition by means of a standard does not fix a mathematically determinate magnitude as the referent of the unit term. Kripke’s ‘certain (length)’ only gives us the illusion that it does. To see what I mean, imagine that we do measure the meter standard S, in inches, and find that it is indeed 39.37 inches long, as Kripke says. Or let’s even imagine that we are capable of determining, by way of measurement, that it is 39.3701 inches long, or even that it is 39.3700787 inches long. However precise our measuring device and technique might be, there is going to be some very small number, ε—say, 10–8—such that there will be no empirically meaningful, real distinction between S being 39.3700787 inches long, and its being any other magnitude between 39.3700787+ε inches long and 39.3700787-ε inches long. In other words, there is going to be an ineliminable indeterminacy in (the determination of) S’s length in inches. And the same goes for any measurement, or determination, of a physical magnitude; and that’s even before we consider the added indeterminacy of the (determination of the) environmental conditions that must be taken into account when turning instrument indications into measurement outcomes.38 Now of course, so long as the indeterminacy is small enough for all present intents and purposes, it doesn’t, and shouldn’t, bother us. We now know, for example, that the masses of the official replicas of the International Prototype Kilogram have diverged from that of the Prototype itself, increasing, on average, by 50 µg, over 100 years (a change of 5 parts in 108) (Riordan 2015, p. 43). But ‘the instability has not been noticed by working scientists’ (Riordan 2015, p. 43); and, with the exception of ‘the most precise experimental measurements’, the recent transition to an electronically realized kilogram, which would allow for much greater precision—1 µg, or 1 in 109—will be ‘of no consequence’ for ‘almost all . . . scientific and technical users, and for everyday commerce in the marketplace’ (Mills et al. 2011, pp. 3908–3909). In other words, a determination of mass that has an indeterminacy of plus or minus 50 µg, is evidently determinate or precise enough for almost all scientific purposes, and certainly for all other purposes.

Kripke’s Realist Fantasy and Wittgenstein’s Idealism 257 For Kripke’s account of naming, however, that indeterminacy does pose a problem, it seems to me, just as it poses a problem for transcendental realists more generally, who wish to be able to speak intelligibly of objects having, or not having, determinate physical properties altogether independently of our determination of those properties. By Kripke’s own lights, ‘one meter’, if it had been defined as ‘the length of S at t0’, would not have referred to some particular, ‘certain’ length—39.3700787 inches, for example—any more than it would have referred to countlessly many other lengths within the range of 39.3700787+ε inches and 39.3700787-ε inches, for some small enough ε.39 And the same goes for Salmon’s ‘Leonard’. Mathematically speaking, there is not some one particular length that S at t0 may enable us to fix as the referent of ‘one meter’, but rather countlessly many such lengths, all within a certain range. Moreover, at least on the story Kripke wishes to tell, that indeterminacy would presumably ‘infect’ all determinations of length in meters that use S (at t0) as the standard for the unit of one meter; and it would be further multiplied by the inherent indeterminacy of those determinations. And similarly for all other physical magnitudes, regardless of how precise our methods of determining them may become. Mathematically, they are all inherently and ineliminably indeterminate. Let me emphasize once again that the indeterminacy I’m talking about is due not—that is, not wholly—to any limitation on our part, or on the part of our instruments of measurement. Rather, it is due to the fact that the determination of a physical magnitude always relies on a comparison with some worldly standard—however theoretically and technologically sophisticated the realization of that standard might be; and such a comparison is always, to some degree, mathematically indeterminate. Not even God could eliminate that indeterminacy in determining the physical magnitudes of physical objects.40 11.2.10  The Transcendental Realist’s Conundrum

Here, transcendental realists might protest that the indeterminacy I’ve been talking about, and which philosophers who have studied scientific measurement have underscored, characterizes only our (or even God’s) determination and representation of physical magnitudes, but not the magnitudes themselves. The determination of the length of S in inches, for example, involves a comparison, and might well be indeterminate, but S’s length itself, they would insist, is perfectly, absolutely determinate. What I have been missing, they would argue, is what Dolev refers to as ‘the non-relational character’ of physical magnitudes (2007, p. 134). ‘The non-relational character of lengths belongs to the length of S itself’, he writes, ‘[S] has a fixed length, which is not determined by how we measure it’ (2007, p. 134); and

258  Avner Baz that length is ‘a spatial interval’, a ‘magnitude’, which is one of S’s ‘properties’, and is ‘not determined by our choice of standard’ (2007, p. 135). And the same is supposed to go for any other physical object: ‘It is one thing for the Olympic stadium to be 100 metres long, and a different thing for it to be 100 times longer than . . . S’ (Dolev 2007, p. 136).41 This last quotation underscores the transcendental realists’ conundrum, which I’ve been trying to bring out. They wish to ascribe to things ‘as they are in themselves’ the magnitudes—and empirical, objective properties more generally—that we may intelligibly ascribe to them in our representations; and so they need to be able to identify those magnitudes, in a way that would allow for their objective reidentification. For an identification that does not allow for reidentification is no identification; and an identification of a magnitude that does not allow for its objective reidentification is no identification of a physical, objective magnitude. If they identify some magnitude in terms of any of our units of measurement, however, as we have just seen Dolev doing, they undercut their own effort to convince us that the magnitude—its identity as the particular magnitude it is, as well as its being had, or not had, by particular objects—is independent of our practices of measurement and representation of measurement outcomes, with their unit-standards and other worldly conditions, and with their inherent indeterminacy. For of course, the stadium, for example, is 100 meters long not ‘absolutely’—whatever that might mean—but within a certain acceptable and attainable range of precision. But how else might transcendental realists identify their ‘magnitudes in themselves’, which supposedly are had, or not had, by ‘things as they are in themselves’? Their only other option, it seems to me, would be to point to the object—S, for example, or the stadium—as it is now (or at some other moment in time, t0), and say, for example, ‘that length’, relying on the object itself, as it is at some moment in time, to fix, or determine, its length (at that moment). That move, however, lands us right back with the nonsensicality, the emptiness, of putting one’s hand on one’s head and saying ‘I’m this tall’. Either that, or we turn the object, officially or unofficially, into a standard of length measurement, a (new) means of representation, thereby undercutting our transcendental realist attempt to identify the length itself—as it is independently of its being had by this or any other object—and to escape the inherent indeterminacy of length determination (or any other determination of a physical magnitude). 11.3  Conclusion: The Transcendental Realist’s Predicament All this takes us back to Kant, and to his basic transcendental idealist insight that ‘the concept of magnitude in general can never be explained except by saying that it is that determination of a thing whereby we are enabled to

Kripke’s Realist Fantasy and Wittgenstein’s Idealism 259 think how many times a unit is posited in it’, and that ‘this how many times is based on successive repetition, and therefore on time and the synthesis of the homogeneous in time’ (1998, p. A242/B300, my emphasis; see also p. A142/ B182). Add to this that there are no units of measurement apart from material, or materially realized, standards for those units, and no standards apart from normative practices of measurement in which they serve as standards, and you get the gist of what I’ve been arguing. The empirical, objective concept of magnitude—the concept, that is, of determinate (enough), mathematically capturable magnitudes that may feature significantly in objectively establishable causal explanations—presupposes units of measurement, and therefore standards of measurement, and practices of measurement that unfold in time and in which those standards are employed. Remove the practices, standards, and units, and that concept becomes ‘empty’.42 The incoherence of transcendental realism is the incoherence of thinking that our concepts, thus emptied, may nonetheless intelligibly apply to things, and moreover apply to things all by themselves, so to speak, without our having to actually apply them and become responsible for their application. What Kant is trying to get us to see in the ‘Transcendental Dialectic’, and what I’ve tried to show with respect to Kripke’s disagreement with Wittgenstein, is that our empirical concepts are not fit for that sort of practice-free, backgroundfree, and judgment-free ‘application’. We really have no idea what it might have been for our concepts, or for anything, to be so fit. Kripke’s referent of ‘one meter’, just like the referent of Salmon’s ‘Leonard’ or of Dolev’s ‘S’s fixed length‘,43 was supposed to be, or underwrite, a self-applying concept—a ‘use-independent concept’, as van Fraassen (critically) puts it (2008, p. 235). It was supposed to pull off the trick of applying to things, truly or falsely, without our having to actually apply it. So while superfluous as far as our practices of length-measurement are concerned, and making no contact with them, that referent is absolutely essential to Kripke’s account of naming and necessity and to the transcendental realist picture that informs that account. Thought of as a certain, determinate length that has always been there, long before it got ‘fixed’, or ‘picked out’, as the referent of ‘one meter’, so that all we needed to do was just to name it, that referent (together with the referents of ‘one kilogram’, ‘green’, ‘square’, ’55 miles per hour’, and so on) is essential to the transcendental realist story, and to whatever sense it may have appeared to have. Without (the positing of) Kripke’s self-applying referent, the idea that every physical object has a determinate length altogether independently of our practices of determining length and the standards (and standards of precision) employed in those practices, and altogether independently of human judgment, is really the idea of each of those objects putting its figurative arms around itself and declaring ‘I am this long’, or, more generally, ‘I am this way’.

260  Avner Baz Transcendental realists thus find themselves in the following predicament. They wish to claim for something that they think of as the world as it is altogether independently of our representations of it and the conditions of their sense, and altogether independently of human judgment, what’s captured or reflected in our (true) representations of it. But the moment they attempt to spell out that claim—to say what, for example, is there, altogether independently of us, and what particular way(s) it is—they find themselves doing nothing more than offering some representation of the world, which, as such, relies for its sense on a suitable background of interrelated practices (of measurement, calibration, calculation, experimentation, and so on), on a whole range of ‘means of representation’ (standards, samples, paradigms, measuring devices, together with our ways of applying them, the theories informing their design and application, norms of precision, and so on) that are used in those practices, and on the historically evolving human needs, interests, and sensibilities that have grounded, and continue to ground, those practices. Relying as they inevitably do on representations of the world, they never succeed in reaching beyond those representations to the world as it is in itself, not even when they italicize those representations or stress them.44,45 Notes 1 A note about my use of quotation marks: in addition to using them when quoting someone (or myself earlier in the paper), or when introducing a more or less technical terminology (as I do in the opening paragraph), I will sometime use them, as I do here, to mark a commonly-used piece of philosophical jargon, and to register my sense that it makes no clear sense, or is otherwise philosophically problematic. 2 See Williams 1981; Lear 1982, 1984. 3 See Nagel 1986, pp. 90–109. As we’ll see later, Nagel’s realist objections to Kant, Wittgenstein, and Strawson, systematically trade on conflating the ‘empirical’ and ‘transcendental’ versions of ‘realism’ and ‘idealism’. For a nuanced and insightful response to Nagel, on behalf of Wittgenstein, see Cerbone 2011. 4 Metaphysicians see themselves as describing or otherwise theorizing about ‘the world’; philosophers writing about perception think about it as the way we come to know and respond to ‘the world’; moral realists and antirealists often characterize their debate in terms of whether moral values or properties are in ‘the world’; semantic theorizers commonly think about linguistic sense or meaning in terms of words referring to (or denoting), more or less directly, ‘(entities, or sets of entities, in) the world,’ or in terms of ‘truth in (some set of possible) worlds’; philosophers reflecting on their own philosophical method describe themselves as investigating ‘(items in) the world’; and so on. 5 Consider, for example, Daniel Stoljar’s Philosophical Progress: In Defense of a Reasonable Optimism (2017). The progress for which Stoljar argues is supposed to consist of philosophers discovering, or establishing ‘facts’—be they facts about such things as freedom, morality, or meaning, or about the constitution of facts about such things as freedom, morality, or meaning, or even about

Kripke’s Realist Fantasy and Wittgenstein’s Idealism 261 (instances of) philosophical progress—where the facts themselves are taken by Stoljar to be, somehow, independent of human judgment and of our practices of establishing, in different ways, in different contexts, and for different intents and purposes, what the facts are. 6 In insisting that we do not make the world, Sider seems to be meaning to evince disagreement with Nelson Goodman’s idea of ‘worldmaking’ (see Sider 2011, pp. 65–66). But it’s worth noting that Goodman’s position vis-à-vis the disagreement between transcendental realism and transcendental idealism, as understood in this chapter, is actually complex. Agreeing with the transcendental idealist that the world as reflected in our representations is not the world as it is in itself—that the attempt to represent a world as it is in itself is doomed to incoherence—Goodman calls upon us to satisfy ourselves with representations (‘descriptions’, ‘depictions’) of the world, and give up the realist fantasy of somehow stepping outside those representations to reach ‘the underlying world’ (1978, pp.  3–4), which is somehow ‘ready-made’, in the sense that it has just the content, and determinacy of content, that are characteristic of our representations of it (cf. 1978, p.  94). For Goodman, Sider’s realist ‘requirement’ that ‘the world . . . really be as physics says’ (Sider 2011, p. 66) is illusory, and bespeaks, at best, a play of the imagination that takes us no further than the world as represented in physics. What Goodman failed to recognize or adequately acknowledge, however, is that what he calls ‘world-making’ is itself a worldly affair. In other words, he failed to recognize or adequately acknowledge the world in which and against the background of which we form our representations and engage in representational practices more broadly (as well as other practices of sense-making)—a world that as such is precisely not an object of representation for us, and so, by Goodman’s lights, is not then and there ‘made’. As I note later, any element or aspect of that world could in principle become an object of representation; but then there would be the world in which and against the background of which we would be forming that representation, and our relation to it would not be that of representing it truly or falsely (or ‘depicting’ it). 7 Christopher Peacocke has also recently insisted on a clear-cut separation between ‘properties and relations on the one hand [and] concepts, notions, or modes of presentation on the other’ (2019, p. 17). 8 Narboux notes that the qualification—‘in a context in which it served as the— by hypothesis, one and only—standard for “one meter” ’—is not explicitly made by Wittgenstein in PI, §50 (2017, p.  149). I  think the qualification is tacitly made, for without it, what Wittgenstein says—be it in his own voice or in someone else’s—would be patently wrong, and unilluminating in the context of his re-examination of the issue of conditions of sense. 9 In taking that to be Wittgenstein’s central concern in PI, §50 and surrounding remarks, I’m agreeing with Narboux. We disagree in that I take Kripke’s ‘semantic externalism’, as manifested in Naming and Necessity, to be closer than Narboux takes it to be to the sort of position Wittgenstein is questioning and attempting to dissolve in these remarks. 10 That’s the gist of the story Scott Soames tells in Soames 2003. In a recent paper, Howard and Laskowski refer to Kripke’s account of naming and necessity in Naming and Necessity as ‘the Kripkean revolution’ (2021, p. 86). 11 I’m setting aside the skepticism of Wittgenstein on Rules and Private language, which is also strikingly set aside in Naming and Necessity, and which concerns the referential connection between words and possible meanings, but not the

262  Avner Baz identity of those meanings themselves, or what complying with them in our ‘application’ of words would require. 12 In criticizing Kripke for imagining, and encouraging others to imagine, that a standard for a unit of length could be defined completely in advance and independently of our practices of length measurement, Diamond is anticipating the attention that has more recently been paid by philosophers and historians of science to the actual, historically evolving practices of setting up standards of measurement and applying them. Summarizing a key anti-Kripkean lesson of those recent studies, Eran Tal writes: [U]nit definitions do not completely fix the reference of unit terms, unless ‘fixing’ is understood in a manner that is utterly divorced from practice. Instead, choices of unit definitions, as well as choices of realization for a given unit definition, are informed by intricate considerations from theory, technology, and data analysis. (2011, p. 1094) 13 I’m here ignoring the added complication that with many sorts of physical objects, the question ‘How long?’ either makes no sense (e.g., balls) or makes no clear, or obvious sense (e.g., cups, bushes, chairs). 14 Again, I’m setting aside the skepticism of Wittgenstein of Rules and Private Language, which, strikingly, Kripke too is setting aside, or more precisely disregarding, in Naming and Necessity (see Diamond 2001, p.  131, p.  200 in this volume). One remarkable feature of that skepticism—and one place where it completely loses contact with Wittgenstein—is that it focuses just on the relation between the designating term and what it designates, while taking the ‘meanings’ it could designate, and what each of them would require for the term designating it to be used or applied correctly, to be perfectly determinate, and to require no judgment. 15 Kripke might say that those would be cases in which the reference of a name has shifted (NN, p. 163). But if the reference of ‘one meter’ shifted with even the smallest fluctuations in length of whatever object(s) (or the currently used physical-mechanical ‘realization’) we use as the standard for ‘one meter’, then I’m not sure what would be left of the idea that ‘one meter’ is a ‘rigid designator’, and Wittgenstein would surely be right in proposing that it makes no sense to say that the standard for ‘one meter’ is, or is not, one meter long. The appeal to ‘reference shift’ would be an ad hoc solution to a difficulty that is due entirely to Kripke’s unexamined idea of reference. The difficulty dissolves once we realize that, at least in such cases as that of ‘one meter’, Kripke’s posited referents make no contact with our practice, and may ‘drop[] out of consideration as irrelevant’ (PI, §293). 16 In Tractarian terminology, they would have been part of the symbol that the sign ‘meter’ would have embodied (see Narboux 2017, p. 134). 17 Not to mention the fact that temperature, for one, as an objective physical magnitude, has been dependent—from the time it was first ‘operationalized’ in terms of pressure and volume, all the way to the current definition of the kelvin in terms of the Boltzmann constant and the Joule unit of work—on the realization of the meter for the realization of its units, and hence for its measurement. 18 As Thomas Kuhn puts a key lesson of the study of the history of science: the supposedly solid facts of observation . . . proved never to be mere facts, independent of existing belief and theory. Producing them required apparatus

Kripke’s Realist Fantasy and Wittgenstein’s Idealism 263 which itself depended on theory, often on the theory that the experiments were supposed to test. (1992, pp. 5–6; and see also van Fraassen 2008, p. 44) And if we further consider the transition in recent years to defining units of measurement such as the meter or the kilogram in terms of physical ‘constants’ such as the speed of light or the Planck constant, then one could plausibly argue that our units, and concepts, of even the most basic physical magnitudes have become even more theory-dependent than they were one or two centuries ago. To get a sense of how theoretically and technically complex the realization of the ‘one second’ unit has become, now that it is done by means of Cesium-133 clocks, see Tal 2011. For repeated emphases of the theory-ladenness of measurement, see Tal’s SEP entry on Measurement in Science). ‘Inferences from instrument indications to measurement outcomes,’ Tal writes, ‘are nontrivial and depend on a host of theoretical and statistical assumptions about the object being measured, the instrument, the environment and the calibration process’ (Tal 2020). 19 Ordinarily, a competent answer to the question ‘What do you mean (here) by “x”?,’ would take the form of a paraphrase, or some other form of elaboration and elucidation, that is meant to clarify—well enough for present intents and purposes—how the word, as used by that speaker on that occasion or set of occasions, is to be understood. Outside philosophy, the answer favored by philosophers—‘By “x” I mean x’—which is meant to effect a connection between the word and some extra-linguistic entity or type of entity, would ordinarily mean either that the speaker cannot think of a way to further clarify what she has meant by ‘x’, or that she feels her words have not been taken, or followed, seriously enough. 20 During the time that the Kilogramme des Archives served as the official standard, it had official replicas spread around the world for obvious practical reasons; and those replicas were periodically brought to Paris and measured against it. And it was found that the masses of the official replicas of diverged over time from that of the Prototype itself, increasing, on average, by 50 µg, over 100 years (a change of 5 parts in 108) (Riordan 2015, p. 43). 21 For of course, such specifications of standard environmental conditions for the ‘realization’ of unit-standards, and formulas for making adjustments when those conditions deviate from the standard, are integral to metrology (see Tal 2011, 2020; see also Chang 2007, p. 49). 22 Here I’m in full agreement with Narboux 2017. 23 Narboux writes that ‘the Tractatus argued for the requirement [my emphasis, AB] that “simple signs” (einfache Zeichen)—i.e. signs designating “protoelements” (Urelemente)—be possible’ (Narboux 2017, p. 6). 24 Norman Malcolm was right, I  think, to press Kripke on that (see Malcolm 1981, p. 21). 25 I again ignore the fact that, in the case of some types of objects, ‘How long?’ would normally make no sense, and, in the case of certain other types of objects, would only make sense in some contexts. 26 This anticipated line of response from the transcendental realist may be gleaned from Sider. He gives the example of the sentence, ‘My computer screen measures exactly 15 inches’ (2011, p.  55) and says that the sentence ‘is true, but would have been false if “inch” had meant a slightly different candidate length’ (2011, p.  55). He then goes on to insist, however, that while the ‘one inch’

264  Avner Baz unit is conventional, and therefore so is the sentence in question, ‘facts about measurable quantities like length . . . are as objective as can be’ (2011, p. 55), and adds, in a footnote, that there is ‘some length, I’, such that the sentence ‘the screen has length l’ is ‘nonconventional’ (2011, p. 55). Similar ideas are expressed by Dolev (2007, pp. 134–135). My next task is to expose this sort of transcendental realist move as resting on an illusory play of the imagination, and ultimately empty. Sider may choose, if he wishes, to name the length of his computer screen ‘l’, thereby turning the screen, in effect, into the standard for ‘l’. But it would then make no sense to say of the screen that it has, or does not have, l as its length, or that it is, or is not, I long. Unless of course Sider has some other way of defining or identifying ‘l’—in terms of inches, for example— in which case he would be relying on some other unit of measurement, and some other standard. 27 As Wittgenstein notes, ‘Every rod has a length’—as uttered by a philosopher taking himself to be asserting some general truth—expresses (at best) a grammatical proposition, not an empirical one (PI, §251). 28 This is a good place to note that though I’m arguing most directly against transcendental realist accounts of physical magnitudes such as Kripke’s that are, in current jargon, ‘absolutist’, the competing ‘comparativist’ accounts have tended to be equally transcendental realist and, for that reason, equally problematic from my perspective. From the perspective of our perceptual experience of magnitudes, both accounts are false: we perceive things neither as having objectively determinate absolute magnitudes nor as standing in objectively determinate magnitude-relations to other things. From the perspective of objective experience (Kant’s ‘Erfahrung’), there is some truth in the comparativist account—namely, that objectively determinate magnitudes are objectively determinable magnitudes, that the objective determination of magnitudes is done by measurement, and that measurement, as Riordan notes, ‘is always a matter of comparison’ (2015, p. 39; see also Pollock 2004, p. 153). So Dasgupta is surely right when he argues that absolute magnitudes—or, more precisely, the absoluteness of a magnitude—would be ‘undetectable by us’ (2013, pp. 137ff). The comparativist account faces significant challenges of its own, however (see Sider 2020, pp.  119–167), and seems to conflict, not just with our perceptual experience of magnitudes, but also with our understanding of objective magnitudes and their empirical significance. As Peacocke notes, when an avalanche flattens a forest, for example, and we explain that by appealing to its momentum, it would be hard to make sense of the comparativist idea that what really or fundamentally explains the flattening of the forest is that the avalanche stood in various mass- and speed-relations to other objects (2015, p. 361). But the idea that we must choose between absolutist and comparativist accounts of magnitude—and so recoil from the difficulties faced by the one only to find ourselves entangled with the difficulties faced by the other—would only seem forced on us if we assumed, as both the absolutist and the comparativist do, that objective magnitudes and magnitude-relations are transcendentally independent of our practices of measurement, and of our practices of empirical inquiry and theorizing more generally. 29 I discuss that ‘illusion’ or ‘delusion’, as presented in the Brown Book, in considerable detail in Baz 2020. 30 Very similar ideas may be found in Peacocke, who suggests that for any given physical object, and for any magnitude (of some particular type) it has, we could name that magnitude ‘M’ (cf. Peacocke 2015, pp. 363ff.).

Kripke’s Realist Fantasy and Wittgenstein’s Idealism 265 31 Salmon’s one significant disagreement with Kripke is that whereas Kripke proposes that whoever uses S at t0 to fix the reference of ‘one meter’ can know, and know a priori, that S is one meter long, Salmon proposes that in order to know that, the reference-fixer ‘must look at . . . S’s length’ (1988, p. 208), which he takes to further imply that the knowledge will not be a priori. So Salmon sees, correctly, that there is a problem with Kripke’s story of how the ‘certain length’ that ‘one meter’ supposedly names is to be identified in a way that would make it independent of S, but goes on to make the mistake of supposing that just looking at S (under ‘favorable’ conditions) suffices for that. That’s precisely the illusion, or delusion, that Wittgenstein is trying to bring out and diagnose in the second part of the Brown Book, by means of the distinction between the ‘transitive’ and the ‘intransitive’ use of ‘a quite particular/peculiar’. 32 “See” (or “perceive”) stands for the special ‘cognitive relation’ in which, according to Salmon, perceivers stand to the magnitudes of the physical objects they see (or otherwise perceive). 33 Later in the paper, however, Salmon says: In the sense of ‘measurement’ in which knowing how long something is requires measurement against the standard, merely looking at the standard’s length (under the appropriately favorable circumstances) counts as measuring the stick itself. (1988, p. 215) 34 Peacocke too has proposed, more recently, that we normally perceive objects as having ‘unit-free’ and practice-independent magnitudes that are nonetheless perfectly determinate objective magnitudes (2015, pp. 378–380). 35 References to the Phenomenology of Perception are given with the page number of the pre-2002 editions of the Colin Smith translation, followed (as in the present case) by the page number of the 2012 Donald Landes translation. 36 Compare Wittgenstein: ‘One may say: with the mere naming of a thing, nothing has yet been done. Nor has it a name except in a game’ (PI, §49). I wish Wittgenstein had not put the point in a way that might encourage the thought that while the attempted naming is empty apart from the language-games, or games, for which it is a preparation, there is in principle no problem about the identity of the it that is thus emptily being ‘named’. It is still clear, however, that the point Wittgenstein is trying to make is precisely the one Salmon misses, and in effect denies. 37 That transcendental realist assumption is belied—or more precisely shown to be confused and ultimately unintelligible—not only by the sorts of Wittgensteinian reminders mostly offered thus far, but also by the actual history of the scientific measurement of physical magnitudes. One central lesson of that history, as van Fraassen puts it, is that ‘[t]he questions What counts as a measurement of (some physical quantity) X? and What is (that physical quantity) X? cannot be answered independently of each other’ (2008, p. 116). And here is Hasok Chang’s summary of a central lesson he draws from his careful and penetrating study of the history of the scientific measurement of temperature (a history to which he aptly refers, in the title of his book, as ‘inventing temperature’): It is very tempting to think that the ultimate basis on which to judge the validity of an operationalization [of some concept of physical quantity, AB] should be whether measurements made on its basis yield values that correspond to the real values. But what are ‘the real values’? . . . An unoperationalized abstract concept does not correspond to anything definite in the realm of

266  Avner Baz physical operations, which is where values of physical quantities belong. . . . Once an operationalization is made, the abstract concept possesses values in concrete situations. But we need to keep in mind that those values are products of the operationalization in question, not independent standards against which we can judge the correctness of the operationalization itself. (2007, pp. 206–207, my emphasis) [W]e must keep firmly in mind that the existence of such ‘real values’ [i.e., the limits of convergence of ever more precise measurement procedures, AB] hinges on the success of the iterative procedure, and the successful operationalization is constitutive of ‘reality’. If we want to please ourselves by saying that we can approach true values by iterative operationalizations, we also have to remember that this truth is a destination that is only created by the approach itself. (2007, p. 217, my emphases) 38 On this, see Teller 2018, which questions the realist assumption that there is some one determinate ‘true’ physical quantity to which actual measurement results more or less approximate. In another paper, Teller similarly argues that ‘there can be no such thing as THE actual precision [of a measuring system, hence a measurement instrument]. Actual precision is an idealization’ (2013, p. 199). 39 Another way of bringing out Kripke’s confusion would be to note, as Pollock does, that, on the story Kripke wishes to tell, S at t0 would be the only object in the world, and ever, whose length in meters may be known, not just a priori, but with absolute precision (Pollock 2004, p.  151). Except that by now we have lost all contact with our ordinary and normal criteria for ‘(greater or lesser) precision’, and therefore with what we ordinarily and normally mean by ‘precision’. 40 Pollock’s talk of measurements as ‘merely approximations’ (Pollock 2004, p. 151) is therefore misleading, for there is, at the end of the day (and of all days), no absolutely determinate magnitude to which all measurements of that magnitude merely approximate. As van Fraassen puts it, the metaphysician who postulates measurement-independent physical magnitudes and imagines ‘some god-like vision or ontological telescope to compare their values with what our instruments show’ is ‘building castles in the air’ (2008, p. 138; see also p. 242). 41 Similar ideas may be found in Peacocke 2015. 42 In the ‘Transcendental Analytic’, where Kant famously talks about empty thoughts, and hence concepts, practice barely comes into view; and the conditions of sense—that is, of concepts that are not empty—are mostly just cashed out in terms of ‘intuitions’ (cf. pp. A50–1/B74–5). The ‘Transcendental Dialectic’, however, makes clear, if only tacitly, that the intelligible application of concepts is not aptly thought of as the synthetization by a lone thinker of sensibly given ‘intuitions’, but rather is a form of worldly, historically situated, shared practice. 43 Or Peacocke’s (2015) ‘M’. 44 Or insist, with Sider, that the world really is as physics says it is (2011, p. 66), which takes us no further than the world as represented in physics. 4 5 I am grateful to George Smith for an eye-opening crash course in the history and philosophy or scientific measurement. Thanks also to Martin Gustafsson for several very helpful conversations on the subject of this paper.

Kripke’s Realist Fantasy and Wittgenstein’s Idealism 267 References Baz, Avner (2020) Aspect Perception and Philosophical Difficulty, in The Significance of Aspect Perception. Springer, 53–70. Cerbone, David (2011) Wittgenstein and Idealism, in Marie McGinn and Oskari Kuusela (eds.), The Oxford Handbook of Wittgenstein. Oxford University Press, 311–332. Chang, Hasok (2007) Inventing Temperature. Oxford University Press. Dasgupta, Shamik (2013) Absolutism vs Comparativism about Quantity, Oxford Studies in Metaphysics 8, 105–150. Diamond, Cora (2001/this volume) How Long Is the Standard Meter in Paris? In T. McCarthy and S. C. Stidd (eds.), Wittgenstein in America. Oxford University Press, 104–139. Dolev, Yuval (2007) Mission Impossible and Wittgenstein’s Standard Metre, Philosophical Investigations 30(2), 127–137. Gabriel, Markus (2015) Why the World Does Not Exist. Polity. Gert, Heather (2002) The Standard Meter by Any Name is Still a Meter Long, Philosophy and Phenomenological Research 65(1), 50–68. Goodman, Nelson (1978) Ways of Worldmaking. Harvester Press. Gustafsson, Martin (this volume). Howard, Nathan Robert and Laskowski, N. G. (2021) The World Is Not Enough, Nous 55(1), 86–101. Kant, Immanuel (1998) Critique of Pure Reason, edited and translated by Paul Guyer and Allen Wood. Cambridge University Press. Kant, Immanuel (2000) Critique of the Power of Judgment, edited by Paul Guyer, translated by Paul Guyer and Eric Matthews. Cambridge University Press. Kripke, Saul (1980) Naming and Necessity. Basil Blackwell. Kuhn, Thomas (1992) The Trouble With the Historical Philosophy of Science. Department of the History of Science, Harvard University. Lear, Jonathan (1982) Leaving the World Alone, Journal of Philosophy 79, 382–402. Lear, Jonathan (1984) The Disappearing “We”, Part I, The Proceedings of the Aristotelian Society 58, 219–242. Malcolm, Norman (1981) Kripke and the Standard Meter, Philosophical Investigations 4(1), 19–24. Merleau-Ponty, Maurice (1996/2012) Phenomenology of Perception, Colin Smith (trans.)/Donald Landes (trans). Routledge. Mills, Ian M., Mohr, Peter J., Quinn, Terry J., Taylor, Barry N., and Williams, Edwin R. (2011) Adapting the International System of Units to the TwentyFirst Century, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, 3907–3924. http://dx.doi.org/10.1098/ rsta.2011.0180. Nagel, Thomas (1986) The View From Nowhere. Oxford University Press. Narboux, Jean-Philippe (2017) Simplicity and Rigidity: Reading PI §50 after Kripke, in Emmanuel Bermon and Jean-Philippe Narboux (eds.), Finding One’s

268  Avner Baz Way Through Wittgenstein’s Philosophical Investigations: New Essays on §§1–88. Springer. Peacocke, Christopher (2015) Magnitudes: Mataphysics, Explanation, and Perception, in Danièle Moyal-Sharock, Volker Munz, and Annalisa Coliva (eds.), Mind, Language and Action: Proceedings of the 36th International Wittgenstein Symposium. De Gruyter. Peacocke, Christopher (2019) The Primacy of Metaphysics. Oxford University Press. Pollock, W. J. (2004) Wittgenstein on the Standard Meter, Philosophical Investigations 27(2), 148–157. Riordan, Sally (2015) The Objectivity of Scientific Measures, Studies in the History and Philosophy of Science, Part A 50, 38–47. Rosen, Gideon (1994) Objectivity and Modern Idealism: What Is the Question? In John O’Leary-Hawthorne and Michaelis Michael (eds.), Philosophy in Mind. Kluwer Academic Publishers, 277–319. Salmon, Nathan (1988) How to Measure the Standard Metre, Proceedings of the Aristotelian Society 88, 193–217. Sider, Theodor (2011) Writing the Book of the World. Oxford University Press. Sider, Theodor (2020) The Tools of Metaphysics and the Metaphysics of Science. Oxford University Press. Stoljar, Daniel (2017) Philosophical Progress: In Defence of a Reasonable Optimism. Oxford University Press. Tal, Eran (2011) How Accurate Is the Standard Second? Philosophy of Science 78(5), 1082–1096. Tal, Eran (2020) Measurement in Science, in Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy, Fall 2020 edition. https://plato.stanford.edu/ archives/fall2020/entries/measurement-science/. Teller, Paul (2013) The Concept of Measurement-Precision, Synthese 190(2), 189–202. Teller, Paul (2018) Measurement Accuracy Realism, in Isabelle Peschard and Bas van Fraassen (eds.), The Experimental Side of Modeling. University of Minnesota Press. Travis, Charles (1997) Pragmatics, in Bob Hale and Crispin Wright (eds.), A Companion to the Philosophy of Language. Blackwell, 87–107. van Fraassen, Bas (2008) Scientific Representation: Paradoxes of Perspective. Oxford University Press. Williams, Bernard (1981) Moral Luck. Cambridge University Press. Wittgenstein, Ludwig (2009) Philosophical Investigations, the German text, with an English translation by G. E. M. Anscombe, P. M. S. Hacker, and J. Schulte, revised 4th edition by P. M. S. Hacker and Joachim Schulte. Blackwell.

12 The Ancient Roots of Wittgenstein’s Liberatory Philosophy How Revisiting the Ancients Can Illuminate the Difference Between Wittgenstein’s Philosophy of Freedom and Kripke’s Philosophy of Mere Anarchy Rupert Read 12.1 Introduction In my book Wittgenstein’s Liberatory Philosophy (Read 2021), I argue that the well-known “therapeutic” conception of philosophy, of which I  was previously a champion, would be better reframed as and sublated into a liberatory conception of philosophy. This sees philosophy as, in its essence, a project of freedom, of freeing self-and-other from heteronomous attachment to tacit dogmas that deform thought and more. Chapters 8 and 9 of my book were devoted to setting out why the conception of freedom found in Wittgenstein’s rule-following considerations as these struck Kripke is by contrast a mere fantasy of freedom. It is a picture of “total” unconstraint—a picture, as we might put it, of mere anarchy being loosed upon the world. For our world as it is inhabited, meant and understood would not be possible, if Kripke’s line of thinking in Wittgenstein on Rules and Private Language were sound. Kripke’s line of thinking has resemblances to the post-truth nonsense of contemporary libertarianism (Read and Uçan 2019; Read 2019; Read 2021, p. 269). Also to Humpty Dumpty (Pitcher 1965). Kripke’s Wittgenstein, the character Kripke constructs in his little book, refuses to allow there to be any constraint on what his words can mean. This is freedom as licentiousness. As Wittgenstein emphasizes repeatedly, you are indeed free to say whatever you want in the sense of uttering whatever words you want: but much of what you may want to say may then and nevertheless be devoid of content.

DOI: 10.4324/9781003240792-13

270  Rupert Read Kripke’s Wittgenstein is a case in point: “he” succeeds in saying nothing at all. His sayings turn out to lack any stability at all. They merely flicker. My argument in those chapters was that Kripke’s Wittgenstein seeks to offer a new kind of scepticism, more radical than that already hinted at in Descartes (Conant 1992; Read 2021, Ch. 8). Cartesian scepticism has an internal dynamic that pushes it in the direction that is floridly visible in Kripke’s Wittgenstein. This is a would-be scepticism as to rules themselves. But the seeking (for such a scepticism) cannot be made out into anything stable. Thinking of the matter in this way could prompt us to consider the possibility of a semi-temporal taxonomy of scepticisms (Read 1995a, part 1). That is, we might typologize scepticisms as more—or less—epistemic; as putting more—or less—into doubt, etc. In the present case, we can think of Kripke’s as an attempt to turn the standard epistemic envisaging of scepticism into something more radical: something constitutive (or even metaphysical). A  doubt as to whether there is any there there, anything constituting meaning. (And my suggestion in the present chapter is that we can gain further traction on what this would-be constitutive scepticism wants to be by looking much deeper back into the history of philosophy, at the ancient “therapeutic” scepticism of Pyrrhonism.) James Conant makes a proposal allied to mine. In “Varieties of scepticism” (2004), he suggests that we characterize Kripke’s Wittgenstein’s as a “Kantian” scepticism—one that exploits the possibility of thought that Kant seemingly gave us: of seeing the very categorial constitution of the world as being unmakeable, uncompulsory. This is not, of course, to ascribe such a scepticism to Kant; it is to name a would-be possibility in philosophy. Conant’s proposal underscores how we might think of Western philosophy as involving the progressive radicalization of the sceptical impulse. Where does ancient philosophy fit in this schema?1 It certainly does not seem to fit neatly as offering the possibility of a less radical form of scepticism than the Cartesian. For it could be extremely—indeed, unduly—bold in what it purported to put into doubt, as we shall note. But nor, as we shall also see, does it come close to yielding a “Kantian” scepticism like Kripke’s. Far from it. And, I shall suggest, this is, a good thing too. I offer here an overview of what I see as the deepening dialogical effort to understand self and other in Ancient Philosophy, due initially to Socrates and the Stoics. This can (I suggest) and should be seen as part of the intellectual backdrop to the project of liberatory philosophy that I locate earlier all in Wittgenstein’s work.2 First, I briefly examine the Socratic conception of philosophy in relation to Wittgenstein’s; and then the Stoic conception; and then (at greater length) the ancient Sceptics’. When we see the available ancient “roots” of Wittgensteinian’s liberatory philosophy, it helps

The Ancient Roots of Wittgenstein’s Liberatory Philosophy 271 us to see more clearly how Kripke’s famous way of apprehending Wittgenstein on rules is a case in point of the (critical target of the) very teaching that Wittgenstein sought to give, in the following sense: Wittgenstein’s philosophy precisely aims to free us from the kinds of illusions of “total” freedom that Kripke’s little book manifests, that is, the freedom to interpret “plus” as “quus” or any other function, and the freedom to generalize that freedom.3 That is the main thing that my work on Kripke’s Wittgenstein has added to Conant’s, across the decades: concreteness on the sense in which wouldbe “Kantian” scepticisms are nothing at all—mere delusions of sense. Kripke’s Wittgenstein would unloose mere anarchy upon our world—a “complete” freedom. But it can’t even be stated. There is no “it”. There is no there there. In a more fundamental and direct sense than Cartesian scepticisms, Kantian/Kripkean scepticisms’ only excuse is that in the end they do not even exist. As I say, I think all this can be appreciated in a clearer light against the backdrop of Wittgenstein’s inheritance from, or affinity with, the greats of ancient philosophy. For the intriguing thing that links Pyrrho with Kripkenstein is that both are philosophical “extremists”. Both offer scepticisms that are surely excessive, in the sense of putting into doubt more than is humanly feasible to doubt. But this could make it sound as though, if only we were stronger or more consistent, we would be able to follow through on their projects. Whereas actually my line of thinking is that there is no such thing as being able to follow through on their projects. Kripkenstein, so far from being Wittgenstein, I shall argue is the very object of his critique. A faux fantasy of freedom, freedom as mere licence; as opposed to real freedom from dogma. Which is what the Pyrrhonists4 were seeking, with some success, over two millennia ago.5 “Seeking” being, as we shall see, the key word. 12.2  Socrates as Wittgenstein’s Ancestor Wittgenstein is a philosopher who talks and listens, rather than simply sets out his thoughts in print.6 It is sometimes noted, correctly, that Socrates’s role as just such a necessarily dialogical “midwife” has important parallels to Wittgenstein’s somewhat-similar role. But I believe that not enough has been made of this parallel: that it has not been recognized how deep it runs. Take the following crucial passage, from the Theaetetus (a dialogue to which Wittgenstein explicitly refers prominently fairly early on in his Philosophical Investigations (1958)). I quote at length: Socrates:

Such are the mid-wives, whose task is a very important one but not so important as mine; for women do not bring into

272  Rupert Read the world  at one time real children, and at another time counterfeits which are with  difficulty distinguished from them; if they did, then the, discernment of the true and false birth would be the crowning achievement of the art of midwifery—you would think so? Theaetetus: Indeed I should. Socrates: Well, my art of midwifery is in most respects like  theirs; but differs, in that I attend men and not women; and look after their souls when they are in labour, and not after their bodies: and the triumph of my art is in thoroughly examining whether the thought which the mind of the young man brings forth is a false idol or a noble and true birth. And like the mid-wives, I am barren, and the reproach which is often made against me, that I ask questions of others and have not the wit to answer them myself, is very just—the reason is, that the god compels me  to be a midwife, but does not allow me to bring forth. And therefore I am not myself at all wise, nor have I anything to show which is the invention or birth of my own soul, but those who converse with me profit. . . . It is quite clear that they never learned anything from me; the many fine discoveries to which they cling are of their own making. But to me and the god they owe their delivery. . . . Dire are the pangs which my art is able to arouse and to allay in those who consort with me, just like the pangs of women in childbirth; night and day they are full of perplexity and travail which is even worse than that of the women. . . . Come then to me, who am a midwife’s son and myself a midwife. . . . And if I abstract and  expose your first-born, because I  discover upon inspection that the conception  which you have formed is a vain shadow, do not quarrel with me on that  account, as the manner of women is when their first children are taken from them. . . . (Theaetetus, 148e–151d, emphases added). I shall not analyse this famous passage in detail7; I trust its general thrust (and intelligence, and indeed beauty) is evident. Briefly, what particularly interests me in this passage is: (1) the point about “counterfeits”, which seems already a quite-deeply “liberatory” moment in Socrates’s practice (It might be seen as anticipating Wittgenstein’s concern with the imprisoning power of delusions

The Ancient Roots of Wittgenstein’s Liberatory Philosophy 273 that we too willingly go along with; also Kierkegaard’s cognate analogy about counterfeit money); (2) how the midwifery metaphor includes an element crucial to Wittgenstein’s account but usually not referred to/noted in Socrates’—namely, pain (the “pangs”, etc.); how philosophy necessarily involves pain,8 if we are to have real progress (Read 2014, 2016); (3) Socrates’s self-characterization as barren parallels Wittgenstein’s not offering theses; (4) The idea in this passage from Socrates/Plato that one often in some sense already knows everything relevant to a philosophical problem but somehow doesn’t have a clear view, or something like that: here is a clear anticipation of Wittgenstein. Socrates too seemed to think that all of the necessary material was there for his interlocutors, if only they could learn to see or appreciate it. Compare too Socrates’s thoroughgoingly ethical inflection of philosophy, and his oral centring of philosophy, as precedents for Wittgenstein.9 I note that these affinities exist—and I think that part of their importance is that they may help us to “place” Wittgenstein in the history of philosophy; in a very different way to that which Kripke may have seemed to have offered in WRPL. 12.3  The Stoics as Wittgenstein’s (Virtual) Ancestors Now consider Wittgenstein’s closeness in certain salient respects to Stoicism (about whose potential relation to Wittgenstein, surprisingly, virtually nothing at all has ever been written).10,11 Wittgenstein had, unfortunately, very little direct contact with the work of the Hellenistic schools.12 But his affinities with them are, I suspect, deeper even than his affinities with Socrates. By way of lightly indicating some of these affinities, let me draw on Martha Nussbaum’s stimulating and innovative account of The Therapy of Desire (2018 (1994)).13 It will be seen from this brief drawing how the Hellenistic philosophers at their best are close to the picture of Wittgenstein I have sketched so far. I focus here on Stoicism: • Seneca’s famous constructive critique/radicalization of the concept of a “liberal education” (Seneca 2013, letter 88) issues in the thought that, as Nussbaum puts it: The only study truly worthy of the name liberalis is philosophy: for that liberates the mind. It is good to have had the basic education embodied

274  Rupert Read in conventional liberal studies, but philosophy is the only study whose activity is itself an exercise in human freedom. (2018, p. 347) So: there is a Stoic precedent for a Wittgensteinian philosophy of liberation. • While Foucault’s great second and third volumes of the History of Sexuality (1985, 1986) give us a splendid sense of the “medical” (therapeutic) value of Hellenistic philosophy,14 they sometimes fall short of delivering a true sense of the liberatory quest of Stoicism; for one cannot shake off the nagging worry that Foucault has difficulty, at the end of the day, regarding freedom as other than another technique of the deployment of Power. In Nussbaum’s words: At the end [of a serious encounter with Stoicism], we have not the images of habituation and constraint so prominent in Foucault’s writings, but an image of incredible freedom and lightness, the freedom that comes of understanding that one’s own capabilities, and not social status or fortune, or rumour, or accident, are in charge of what is most important. The procedures of Stoic argument model a kingdom of free beings—the ancestor (in terms of both content and causal influence) of Kant’s kingdom of ends, a kingdom of beings who are bound to one another. (2018, p. 354) So possibly (through a chain involving Kant), the Stoics did come to influence Wittgenstein after all; for my presentation of Wittgenstein in my book is of a kind of heir of Kant, radically improving upon (by transcending) the individualism, hyper-rationalism and quasi-subjectivism of Kant, in the name of a truer image of freedom.15 This is one in which we are free in our very commons of the mind,16 of sensation and of being (Read 2021, Ch. 10), and freed from the baleful constraint of virtually all traditional philosophical ideology (Read 2021, Ch. 11). Liberatory philosophy is the realization, for the first time, of what intellectual autonomy as opposed to heteronomy could, actually, fully mean that was worth meaning. • An important aspect of this is that liberation has to be through “empowerment”, showing how to employ “tools” by example. Stoicism is an intriguing precedent here in its emphasis on the practical exercises needed to attain freedom, exercises that were typically “demonstrated” by the would-be teacher. • Philosophy, for the Hellenes, is then essentially an activity. It requires action of one/of us, not merely spectatorship or an account as if entirely

The Ancient Roots of Wittgenstein’s Liberatory Philosophy 275 disinterested. As Nussbaum puts it, drawing directly on the metaphor of therapy: Finding out how human beings are diseased and what they need is a prelude to, and inseparable from, trying to heal them and give them what they need. The connection is this close, first of all, because the conception of the philosopher’s task as a medical one makes compassion and love of humanity central features of it. (2018, p. 33; cf. p. 3) Without relying on a direct therapy metaphor, I  endeavour here (and in much more detail my book) to provide a concrete case of much the same, for Wittgenstein. Compassion, a kind of healing that integrates and frees: these are, as I see it (Read 2021, Ch. 10), integral to the actual practice of much of the Philosophical Investigations (1958). • As with what Wittgenstein drew from Freud, in virtue of which he described himself as Freud’s “disciple” (despite abominating Freud’s scientism), the Stoics tend to see the person’s own judgement as ultimately criterial for (philosophical) success (Nussbaum 2018, pp. 20–27). That is: a “Platonist” model of the good as existing wholly independent of human beings cannot be right.17 We can see from the “model” of medicine how,18 rather, philosophy must be responsive to the considered judgements of one’s interlocutor; so long as those judgements are rejective of our interpretations, our interpretations are not yet valid.19 The claim of reason in philosophy turns out to be the claim that we must genuinely convince others of what we say (including about what they say or think); we cannot impose our judgements upon them. To do so would be complicit in and creative of a radical heteronomy unfreedom. • Finally, the function of a philosopher, according to Epictetus (as expounded by Nussbaum), is “defined in terms of the development of powers of choice”. Nussbaum immediately continues, stating that “nothing is as forcefully and as repeatedly stressed in the writings of all major Stoic thinkers” (Nussbaum 2018, pp. 329–330). To give one more key example then of such a thinker, Seneca sees “the result of philosophical instruction [as] that that mind itself can bring itself before its own bar, autonomous . . . and free”.20 The freedom, the liberatory conception of philosophy that is here implicit, is powerful. I shall soon turn to see how it contrasts with the version of freedom that is central in Kripke’s Wittgenstein. Before I do however, and before turning in that context to ancient scepticism in relation to Wittgenstein, let’s take stock of what we have already seen and risk some grander thinking and seeing from it.

276  Rupert Read 12.4  Taking Stock What I have outlined so far has consequences. As I see him, Wittgenstein is a true philosopher. Not an academic, but a lover of/seeker after wisdom in the tradition of Socrates, and in that of the Stoics (and, at their best, the Epicureans, the Cynics, and the Pythagoreans and, as we shall see later, the Pyrhonnians).21 His work is ultimately about living lives worth living (and: such lives will not be simply solitary).  Like the Hellenistic philosophers, Wittgenstein’s is, I suggest in Wittgenstein’s Liberatory Philosophy (2021), a philosophy for life.22 That is why I  outline how one might link Wittgenstein back in spirit to Ancient philosophies of life. I  am suggesting that Wittgenstein stands broadly in the tradition of Socrates, Seneca, Epictetus (and indeed Sextus) et al.—more, in the end, than of (say) Russell and Moore, etc. If this is right, then Wittgenstein has been very largely traduced by academic philosophy, to date. Wittgenstein’s conception of philosophy, in terms of being a freeing philosophy of life, in terms of its ethical demands on the reader/practitioner, and also in terms of its posing of a deep alternative to scientism,23 is a kind of contemporary version of the kind of thinking that the two greatest Stoics whose writings we have much direct access to, Seneca and Epictetus, promote. (There are of course striking differences, too. Above all, I think that Wittgenstein would have found the thrilling but ultimately problematic placing of emotionality and embodiment outside the human essence that is typical of Stoicism to have been a rejection of humanity itself.24 As I read the Philosophical Investigations, Wittgenstein is indeed seeking to return us our animality, our humanity and our community, in a way that enables us [as the Stoics did] better to criticize what may be wrong with it. But NOT to other it from ourselves, not, as they sometimes did; not in effect to deny essential aspects of ourselves.) This manner of reading of Wittgenstein may well be unfamiliar; you may be familiar more with Wittgenstein as an alleged player of “languagegames”, and/or a Wittgenstein who is an analytic philosopher whose thinking is close to that of Carnap, etc. In stressing, as I do in my book, the liberatory aspects of Wittgenstein’s philosophy, including for instance Wittgenstein’s famous dictum that “Philosophy is really not a problem of the intellect, but of the will”, I offer a much less (as one might put it) “Carnapian” Wittgenstein (Witherspoon 2000; cf. Conant 2000). The Wittgenstein encountered in my work, is a philosopher with clear and real affinities with the kind of thinking and acting present in Stoicism. Real connections (i.e. connections of substance and of style [and the latter may be even more important than the former]) can then be drawn between Wittgenstein and many old schools of philosophy in Athens and

The Ancient Roots of Wittgenstein’s Liberatory Philosophy 277 Rome. Why? I have suggested that the reason is: because those were philosophies for life, directly intended to help, to free. Somewhat similarly, I suggest that Wittgenstein is an ethical thinker who seeks for one to be able to free oneself from pressing problems. Liberatory philosophy in fact seeks for us to be able to free ourselves, together.25 With this background and vision in place, let us turn directly to the question of how to relate Wittgenstein to the ancient sceptics. I will seek to do this by positioning Sextus Empiricus and Wittgenstein in relation to “Kripkenstein”. 12.5 The Ancient Sceptics as Wittgensteinian Avant La Lettre: And in Contrast to Kripkenstein On how one should relate Wittgenstein to the Ancient Sceptics, a key point for we resolute readers of Wittgenstein’s oeuvre (Crary and Read, 2000) is of course to connect in the right way the ladder image in Sextus Empiricus to that in the Tractatus Logico-Philosophicus (Wittgenstein 1922) (cf. Reid 1998; Stern 2004, Ch. 2). (I’ll seek to execute some of this connecting in the right way in the remainder of this chapter.) It’s somewhat hard to overstate the importance of this point: the founding prooftext of resolution, which is a key aspect of Wittgensteinian liberation as I  understand it, is Tractatus Logico-Philosophicus 6.54: My propositions are elucidatory in this way: he who understands me finally recognizes them as senseless, when he has climbed out through them, on them, over them. (He must so to speak throw away the ladder, after he has climbed up on it.) The ladder image is at the very heart of ancient scepticism, suggesting already an elective affinity.26 Here is the heart of the key passage from Sextus Empiricus, from Against Logicians: [II 480–481] . . . like as purgatives after driving the fluids out of the bodies expel themselves as well, so too the argument against proof, after abolishing every proof, can cancel itself also. And again, just as it is not impossible for the man who has ascended to a high place by a ladder to overturn the ladder with his foot after his ascent, so also it is not unlikely that the Sceptic after he has arrived at the demonstration of his thesis by means of the argument proving the nonexistence of proof, as it were by a step-ladder, should then abolish this very argument. (1935, p. 489)

278  Rupert Read We see clearly here how Sextus regards the (step-)ladder metaphor and the purgative metaphor is used for the same purpose: to indicate how it is not that by climbing the ladder we reach a privileged point form which we can magisterially survey but that we are able to understand that the ladder itself was an illusion of sense.27 The purgative metaphor is arguably less exposed to risk than the ladder metaphor and would have better served Wittgenstein to emphasize, because the beauty of the purgative metaphor is that it is clear to the hearer how the purgative is expelled along with what it purges, and what remains is only: us, in good health once more.28 There is in fact one striking way in which Wittgenstein in effect employs just such a metaphor. Consider this important methodological moment near the opening of his Lectures on the Foundations of Mathematics: I may occasionally produce new interpretations, not in order to suggest they are right, but in order to show that the old interpretations and the new are equally arbitrary. I will only invent a new interpretation to put side by side with the old one and say “Here, choose, take your pick.” I will only make gas to expel old gas. (Wittgenstein 1976, Lecture I, p. 14; emphases added) Sextus would have recognized directly the point of making gas only to expel old gas (and itself). Moreover, as we shall fairly soon see in some detail, he would have recognized the philosophical power of offering one’s own interpretive lens not for the sake of establishing its “correctness” but for the sake of putting into question the existing interpretation, thus facilitating freedom therefore, without emplacing (oneself/others in) a new captivity. But a reader might be misled here into thinking that the whole activity of interpreting therefore becomes a kind of endless game, a merry-go-round that gets one nowhere but that one cannot get off. In order to rebut such a vision of philosophy, which is more or less Kripkenstein’s, let me turn explicitly to how to differentiate the Wittgensteinian (more or less liberatory) vision of philosophy from the Kripkensteinian. The Introduction to The New Wittgenstein (2000) questioned the very idea of taking an external standpoint on our life with language, on meaning, on thought. The leading idea that drove this collection (see especially pp.  5–7 of the Introduction to the collection) was that there is no such thing as making sense of the external standpoint; that “it” is fatally unstable. It does not get as far as being actually entered into; it is a delusion of thought, a delusion of sense to which we are attracted, but whose (non-) sense we can overcome.29 This might be called Wittgenstein’s therapeutic neo-Pyrrhonism, because it is what really using but then really throwing

The Ancient Roots of Wittgenstein’s Liberatory Philosophy 279 away the ladder amounts to. Or it might, better still, be called Wittgenstein’s liberatory philosophy. For detailed discussion of how all this works with regard to the particular illusion that Kripke attempts to adumbrate in WRPL, see my paper “The unstatability of Kripkean scepticisms” (Read 1995b). There, I set out how: “In the “statement” of concept-scepticism [i.e. of the Kripkenstein position], nothing has actually been said. Concept-scepticism is not a candidate for truth or for falsity—it cannot even get as far as being false” (Read 2013, p. 109). The idea that our ideas or concepts are themselves “completely” wide open to any abnormal interpretation is only an idea of an idea, only an imagined idea. It is just the kind of thing that needs purging, or overcoming, in the terms of Sextus’ great metaphors (but in a manner that does not leave itself allegedly standing, but that leaves us not asserting theses of our own). Thus: Kripke(’s Wittgenstein) offers a thoroughly faux freedom. Not the genuine element of freedom, of agency . . . but merely a fantasy of being able to mean anything (everything: we can allegedly re-interpret any word to mean whatever we like; but actually nothing: for endless interpretation alone never amounts to the meaning of anything) by any word. (Read 2021, p. 276) This is also what Philosophical Investigations 198 and 201 mean: that mere interpretation does not even get one started. Thus in 201, after the statement of the rule-following paradox addressed in 198, we have “It can be seen that there is a misunderstanding here”—Kripke’s, basically— “from the mere fact that in the course of our argument we give one interpretation after another; as if each one contented us at least for a moment, until we thought of yet another standing behind it”. This is exactly what Kripke’s Wittgenstein does: offer a purportedly endless series of interpretations.30 Wittgenstein goes on, “What this shows is that there is a way of grasping a rule which is not an interpretation”. “Hence there is an inclination”—the very inclination that Kripkenstein is subject to—“to say: every action according to the rule is an interpretation. But we ought to restrict the term ‘interpretation’ to the substitution of one expression of the rule for another”.31 While in 198, we already had “any interpretation hangs in the air along with what it interprets and cannot give it any support. Interpretations by themselves do not determine meaning” (Emphasis added). You can go on interpreting until you are blue in the face; no action in the relevant sense has yet occurred. Kripke’s Wittgenstein, like Derrida at times (Stone 2000), makes it seem as if an endless regress of interpretations is all that we can

280  Rupert Read have. Kripke evokes a sense of having presented us with a novel “sceptical paradox” that does not dissolve itself away only by way of sticking within the free play of unapplied interpretations that is the very object of Wittgenstein’s critical scrutiny in Philosophical Investigations 198 and 201. And this is why the Kripkean gambit amounts to nothing at all. For, as Wittgenstein made clear throughout his work (and especially in his final years), doubts require grounds, and would-be doubts that are totalizing don’t get as far as doubting anything. Kripke’s line of reasoning is vulnerable to this line of reasoning in a stark and complete fashion: I do not understand how one can doubt whether one means plus (rather than, say, quus) by “plus” in the present on the grounds of doubts about whether “plus” meant plus in the past. For, if one’s present meanings are thrown into doubt, then the doubts that one raises (in the present) about the past are also thrown into—complete—doubt. One cannot meaningfully entertain that one meant quus by “plus” on past occasions unless one . . . presumes, now, the meanings of “plus” and “quus”. So I see no way in which present use can be undercut without undercutting the very undercutting of past use with which present use was supposed to be undercut. (Read 2021, p. 273) To generalize the point: broadly epistemic considerations are needed to even motivate constitutive doubts. This is the purport of the “How do I know?” questions that pepper the early pages of Kripke’s book. But such constitutive doubts would make it impossible to even frame precisely those broadly epistemic considerations. And without those broadly epistemic considerations, the whole game of doubt never gets started. Of course, at a crucial moment in his text, Kripke attempts to defend the possibility of there being a constitutive scepticism by invoking the very figure of the ladder, Wittgenstein’s own, after Sextus: When we initially presented the paradox, we perforce used language, taking present meanings for granted. Now we see . . . that this provisional concession was indeed fictive. There can be no fact as to what I mean by “plus”, or any other word at any time. The ladder must be finally kicked away. (WRPL, p. 21, emphasis added) But there remains a crucial difference between (early) Wittgenstein’s and Sextus’s employments of the ladder metaphor, on the one hand, and Kripke’s, on the other hand. This difference can be seen in the very peculiar (though, in a way, honest) phrasing of Kripke’s case here. The initial

The Ancient Roots of Wittgenstein’s Liberatory Philosophy 281 move in his conjuring trick here (Read 2012, Ch. 4): “When we initially presented the paradox, we perforce used language”. As if there might have been some alternative! The fantasy is once again then of there being some wholly external point of view to language, some way of thinking that does not have to get “bogged down” in linguistic expression.32 As if, if we could only occupy that perspective, then we could see things aright: and see directly that there can be no such thing as meaning anything by any word. But the very idea of such a perspective is, according to resolute readers,33 the very critical target of Wittgenstein’s entire career. At 6.54 of the Tractatus, Wittgenstein suggests that philosophical Sätze hover between being sense and nonsense and that one needs to see them as nonsense in order to complete any philosophical journey.34 Sextus seeks to undermine the making of philosophical arguments, by way of an argument. The beautiful thing about what Sextus does, by way of his purgative and ladder metaphors, is to show how this need not involve destructive self-contradiction. Because neither Wittgenstein nor Sextus fantasizes a perfect place from which one can be free of these, and free of thought altogether. On the contrary: they both operate from “within” thought and language only.35 This suggests a Wittgensteinian take on why Sextus thought it admissible to use “weak” arguments to justify his case, as well as “strong”: precisely because he is not dreaming of some external point of view on language and thought. Rather, he is engaged in a dialogical exercise with his interlocutor or reader: to seek to bring him to a place of sustainable tranquility (ataraxia). For this purpose, he suggests we use arguments that are just as strong as are needed, and no stronger. (For the risk of “weighty” arguments is that they can be too solidly convincing.) As Wittgenstein might have put it: the new argument and the old need to stand side by side, enabling the reader a space of freedom to choose between them, without a feeling of being compelled to valorize one over the other; for one is doing one’s interlocutor a disservice if one makes it seem as though the novel argument one is offering is non-arbitrary, or true or superior once and for all. Doing thus—employing arguments as strong only as are needed— minimizes the chance of being tempted to think that one has come up with an argument that should stick around permanently, something more than (what Wittgenstein would see as) a purpose-relative reminder. It minimizes the risk of walking backwards into the embrace of a new dogma. It is worth looking into this vexed matter a little deeper. Here is the key passage in which Sextus makes the “weak arguments are OK” move: [Outlines of Scepticism III 280–1] [280] Sceptics are philanthropic and wish to cure by argument, as far as they can, the conceit and rashness of the Dogmatists. Just as doctors for bodily afflictions have remedies

282  Rupert Read which differ in potency, and apply severe remedies to patients who are severely afflicted and milder remedies to those mildly afflicted, so Sceptics propound argument which differ in strength—[281] they employ weighty arguments, capable of vigorously rebutting the dogmatic affliction of conceit, against those who are distressed by a severe rashness, and they employ milder arguments against those who are afflicted by a conceit which is superficial and easily cured and which can be rebutted by a milder degree of plausibility. This is why those with a Sceptical impulse do not hesitate sometimes to propound arguments which are sometimes weighty in their plausibility, and sometimes apparently rather weak. They do this deliberately, since often a weaker argument is sufficient for them to achieve their purpose. (Sextus Empiricus 2000, p. 216) Book III 280–1 is the only place where Sextus explicitly talks of a “philanthropic” aim—a coinage strikingly evocative of key themes in Wittgenstein’s “metaphilosophy”—in the entirety of the Outlines of Scepticism (2000) and, in fact, of all his work. Partly because this passage is unusual in his work, when Sextus talks about the distinction between “weak” and “strong” arguments, there is a huge scholarly dispute over what he means. It is often assumed that Sextus is admitting that he deliberately uses logically fallacious or sophistic arguments (Bailey 2002; Thorsrud 2003; O’Keefe 2006; Perin 2010), and that it only matters what has “therapeutic” utility irrespective of whether arguments even make sense. Superficially, this might appear similar to later Wittgenstein, but of course it would not really be. For this would be a problem, and not fitting Wittgenstein’s actual approach, in at least two ways: 1) It would make Sextus akin to a trickster, someone who doesn’t mind using deception and conceptual sleight of hand. 2) Perhaps more importantly still, it seems to imply that Sextus would have some standard or objective criterion about what constitutes a weak versus a strong argument. In other words, despite doing as he pleases for therapeutic ends, he nonetheless “knows” what constitutes a sound argument and has various once-and-for-all/dogmatic views about why this is so. Machuca (2019) has offered a recent and particularly interesting treatment which is happier for Sextus in its outcome, and of direct salient interest to the present piece. Machuca does not think that the “strong” versus “weak” arguments distinction means that Sextus thinks it admissible to use bad arguments to trick “feeble-minded” patients. For Machuca, the Sceptic suspends judgement about whether his arguments are sound (cf. Sextus Empiricus 2000, I 35): “Sextus does not say that some arguments

The Ancient Roots of Wittgenstein’s Liberatory Philosophy 283 are weighty and others are weak in their persuasiveness, but only that they appear to be so” (Machuca 2019, p. 203). [I]n order for an argument to be therapeutically efficacious, i.e., to succeed in persuading a given dogmatic patient, it must be deemed to be epistemically persuasive by him. More precisely, the therapeutic argument must strike the patient as being as epistemically persuasive as the opposite argument he himself puts forward, since it is this state of equipollence that, to all appearances, will make it possible for him to suspend judgement. (Machuca 2019, p. 207, emphasis added) On Machuca’s suggestion, the extent to which a patient is “conceit-ed” means how strongly they appear to hold a dogmatic belief, specifically, the extent to which they are “hard to persuade” or “make rash judgements”. Less “conceit-ed” patients are more cautious about the extent to which they hold various beliefs, and are thus easier to persuade of the equipollence of a contrary belief/view. Therefore, there aren’t “objective views about his therapeutic arguments” in the way it has been claimed there are by many interpreters (Bailey 2002; Thorsrud 2003; O’Keefe 2006; Perin 2010). Rather, the designations of “strong” and “weak” treatments and their respective “highly” and “mildly” conceited patients made by the Sceptical doctor/therapist are entirely contextually driven, and pragmatically measurable. If we assume Machuca’s reading, there seems to be some connection with a later Bakerian conception of philosophical “therapy”,36 where the doctor/therapist is purely concerned with the arguments/views/beliefs of the “patient” and does not make/require theses or claims. This would be a partial anticipation by Sextus, in other words, of the key theme in later Wittgenstein, emphasized by Baker (and by myself (Read 2019)), of the centrality of the judgement of the person one is dialoguing with on whether or not they find the interpretation one offers of their views convincing. (This is above all what Wittgenstein took from certain moments in Freud with which he was impressed: the “patient” as criterial for dialogical philosophical success; recall our discussion of this in the section on Stoicism.) Wittgenstein’s way of proceeding would be a little less . . . judgemental than Sextus’s hereabouts, less inclined perhaps to the use of words like “conceit” in the first place. But the fundamental impulse would be the same. I take all this as supportive of my (tentative) take: that Sextus is able to use both “strong” and “weak” arguments because he is not dreaming of some “external” point of view on language and thought. However, if Machuca is right (and I suspect he is), this should be seen in the broader context of what he (Sextus) means by “strength” of argument.

284  Rupert Read On the one hand, it is not the case that (1) Sextus is (we might say) radically therapeutic and can use whatever argument is necessary because all rational argumentation has gone out of the window in light of his sceptical conclusions. On the other hand, it is also obviously not the case that (2) Sextus has in mind an a priori criterion of rationality which he continuously refers to. Machuca’s way of understanding “strength” gives us a way to overcome this dilemma. The reason this is important is that (1) would seemingly suggest that Sextus has, ironically, embraced an “anything goes” approach to rationality on the basis of an would-be Archimedean point— he is judging it as a whole as if from sideways on—and would precisely represent the “external” point of view on language and thought I  claim he does not endorse (a point of view akin to the “libertarian anarchy” of “Kripkenstein”, who makes a once and for all totalizing judgement of— that is, against—meaning), and likewise of the kind that a resolute reading of Wittgenstein is precisely and focally concerned to extricate us from the fantasy of. Similarly, an a priori condition of rationality—that is (2)— would also, obviously, presumably involve an “external” point of view of the like kind. 12.6  Towards Conclusion: Aligning Wittgenstein and Sextus To sum up, the idea of being free of the “stain” of conceptuality, of language, is a nonsensical one that is present in Kripke—and not in Wittgenstein or Pyrrhonism (except as a temptation). It is a dogmatic commitment to something we have been given no reason to believe makes any sense at all: an appreciation of something true of language, which can only be appreciated truly as if from outside language altogether. The beauty of Pyrrhonian scepticism as we find it expressed at the very outset of Sextus’ Outlines of Scepticism is in fact precisely this: that, just like resolute-liberatory Wittgensteinians, Sextus’ Pyrrhonism resists any dogmatism in philosophy. These are the very first sentences of his book: Book I 1.1–3 [1] When people are investigating any subject, the likely result is either a discovery, or a denial of discovery and a confession of inapprehensibility, or else a continuation of the investigation. [2] This, no doubt, is why in the case of philosophical investigations, too, some have said that they have discovered the truth, some have asserted that it cannot be apprehended, and others are still investigating. [3] Those who are called Dogmatists in the proper sense of the word think that they have discovered the truth—for example, the schools of

The Ancient Roots of Wittgenstein’s Liberatory Philosophy 285 Aristotle and Epicurus and the Stoics, and some others. The schools of Clitomachus and Carneades, and other Academics, have asserted that things cannot be apprehended. And the Sceptics are still investigating. He goes on: Book I 1.7 The Sceptical persuasion, then, is also called Investigative, from its activity in investigating and inquiring; Suspensive, from the feeling that comes about in the inquirer after the investigation; Aporetic, either (as some way) from the fact that it puzzles over and investigates everything, or else from its being at a loss whether to assent or deny; and Pyrrhonian, from the fact that Pyrrho appears to us to have attached himself to Scepticism more systematically and conspicuously than anyone before him. (Empiricus 2000, pp. 3–4, emphasis added) In this sense, ancient [Pyrrhonian] scepticism comes to seem in spirit quite close to Wittgenstein’s thinking—immeasurably closer, in the end, than Kripke’s. The key word here is “investigator”, zetetikos, meaning the Sceptic as searcher, one who is able and willing to seek—one who goes on seeking and engaging in the open-ended, charitable activity of . . . philosophical investigation.37 For the continuing-to-search, rather than making dogmatic claims, or asserting (dogmatically) that no claims can be (successfully) made, is exactly what, according to the resolute approach to Wittgenstein’s thinking, we do—we seek. We seek to make sense. Rather than acting as language-police ruling out once and for all certain forms of words as allegedly fated to be nonsense prior to any search for a context of use.38 If we are to characterize the difference between Wittgenstein’s philosophy, and that of the Pyrrhonian sceptic, then, roughly, it might be this: that Wittgenstein applies something akin to a subtle Pyrrhonism to philosophy (understood widely), rather than to life as a whole, as the classical Pyrrhonists, perhaps rather excessively, tended at times to do.39 The trick is to have a philosophy of life (which I have suggested Wittgenstein focally does: this is a central thrust of ascribing to him a liberatory, ethical philosophy) without one’s philosophy undermining ordinary life—which at times Pyrrho40 and certainly Kripke’s Wittgenstein (leaving aside his “sceptical solution” (as I suggest, we should: cf. Read 2021, p. 284)) would appear to do. But what is wholly common (to the ancient (“Pyrrhonian”) “sceptic” and to the resolute-liberatory Wittgenstein) is: we keep searching. We keep

286  Rupert Read searching for sense. Any judgement that some would-be claim is nonsense is forever provisional—a mere reluctant pragmatic context-relative giving up of that search. This even applies to the words of Kripke in his book on Wittgenstein. That was the meaning of my effort in “What ‘There can be no such thing as meaning anything by any word’ could possibly mean” (Read 2000b); I searched for a way of its not turning out that Kripke’s book was riven by a failure by him to mean anything that has any coherence by his words, and in a way I found one. I offered a charitable interpretation of that pivotal conclusion of Kripke’s argument, one according to which it offers a contextualist reminder about meaning . . . but one that actually points in the opposite direction to libertarian anarchy. A Wittgensteinian semantic contextualism, which could be found against the grain in Kripke’s words, precisely undermines and stands against what seem to be the would-be ideas of Kripke’s Wittgenstein. Finally, let me very briefly consider an objection. Can my resolute interpretation allow Wittgenstein to suspend judgement on whether the nonsense one encounters or calls out really is nonsense, as (as I noted earlier) a Pyrrhonist would? It might seem that I have to be saying that he means— resolutely—it is just nonsense, and irredeemable, and must not be rescued or kept alive. But the essence of the response to this objection is that, for “resolute” Wittgensteinians, a particular instance of nonsense is not established in advance by a theory (as in Carnap), let alone arrived at wholesale by way of a broader a fortiori argument involving all language/meaning (as in Kripke). Would it be right to say that Sextus suspends judgement on whether belief really is belief (dogma)? If his suspension of judgement is universal, then presumably we do have to say this. Anything less would be . . . irresolute. . . . But this obviously isn’t the same as saying he can’t recognize belief. Presumably we must think then that Sextus has a certain kind of belief in mind (or a certain way of relating to beliefs). In the same way, while Wittgenstein also lacks a once-and-for-all view about what nonsense consists in and how it is “composed” (as opposed to Carnap and Kripke in different ways), this cannot preclude recognizing nonsense if and when it actually is dis-covered. It is integral to being resolute that one does not shy away, when without alternative, from invoking the term “nonsense” and meaning it. That is exactly the origin of the term “resolute”, as in not “chickening out”. Sextus’ suspension of judgement concerning whether a belief really is a belief must be seen in the broader context of the sort of claims/ways of relating to claims that he considers a barrier to tranquillity.41 Wittgenstein’s refusal to identify once-and-for-all what constitutes meaningful and

The Ancient Roots of Wittgenstein’s Liberatory Philosophy 287 nonsensical discourse should be seen in broadly the same way. As I see it then, the way that Sextus would suspend judgement on whether a belief is a belief is not really very different to how Wittgenstein relates to questions of meaning and nonsense. So then we can make a very final summing up by saying that what is true in the objection that I am here considering is that for Wittgenstein nonsense is nonsense (What else could it be?!). But what distinguishes “resolutists” from traditional “Carnapian” Wittgensteinians (Witherspoon 2000) is precisely our using nonsense as a term of criticism provisionally, rather than absolutistically: our practicing charity to the extent it possible. We don’t condemn others as allegedly violating “logical syntax” (and thus saying things which, because of the way they have been constructed, are allegedly necessarily meaningless), any more than we follow Kripke’s Wittgenstein in as it were generalizing such condemnation (to all language, which would get evacuated of meaning by the rule-sceptic). To find another or oneself mired terminally in nonsense is a last resort, not a first resort! As Sextus would have it: we keep seeking. We search for meaning. And I hope by now it is fairly plain how placing Wittgenstein in relation to ancient thought, and perhaps especially in relation to ancient scepticism, may help us to better understand this quest for sense.42 This trying to make sense, which characterizes what we do. . . . And this might even be of broader cultural import, at a time of polarization, of deliberate projects of mutual would-be impenetrability, of deliberate misunderstanding.43,44 Notes 1 In “Varieties of scepticism” (2004), Conant makes an interesting and (as usual) insightful suggestion on this score; it is not worked out in detail, however, unlike the suggestion I offer here. Conant’s primary intention is to characterize Modern varieties of scepticism. 2 A fairly comprehensive base-level account of the connections between Socrates and Wittgenstein can be found in Thomas Wallgren’s Transformative Philosophy (2006, p. 78f). 3 This latter freedom is an essential move that Kripke moves; I mean, essential in the project of having a scepticism that is seemingly not answerable. It can be referred to as the “quusification” of indefinitely large stretches of language (Read 2021, p. 264f). This strategy is invoked by Kripke at pp. 15–16 of WRPL. 4 The attentive reader will pick up already that I  am making in this chapter a distinction between Pyrrho and the Pyrrhonists (Sextus Empiricus is the philosophy who I shall be mainly discussing later in the relevant section). 5 And, I shall argue, what his greatest extant follower, Sextus Empiricus, perhaps succeeded in finding. 6 For a lovely account of this in relation to the Stoics (to whom I turn shortly), see Nussbaum’s The Therapy of Desire (2018, pp. 345–346). The way in which the Stoics emphasize orality, self-teaching and the dialogicity of real teaching is

288  Rupert Read often profoundly “Wittgensteinian” avant la lettre (As of course, is Augustine’s profoundly oral tone (cf. Read 2021, Ch. 1)). 7 It is the topic of the soon-forthcoming thesis of UEA graduate student Jack Manzi, who does so. 8 Might the anti-private-language considerations be seen as showing how the pain of philosophy is not something restricted to individual philosophers, but is something we deeply share. Philosophers may, because of their deformation professionelle, be inclined to think that such pain is precisely a paradigm instance of something private. 9 This too Jack Manzi is developing as a key theme in his thesis; a full treatment of it in relation to the Theaetetus is on its way, in that. 10 At least: not “directly”. A partial exception is the useful reflections on Wittgenstein and Epictetus scattered throughout The Philosophy of Epictetus (Scaltsas and Mason 2010). Indirectly, one might talk of (for instance) Hadot’s work (1995). 11 I haven’t yet mentioned Epicureanism. There are clearly parallels between Epicurus and Wittgenstein: perhaps most strikingly, in their attitudes to death (I am thinking especially of Tractatus 6.431  & 6.4311, in connection with the Epicurean insistence that death is nothing to the dead). Also very strikingly, and most saliently for present purposes, in aspects of their metaphilosophy. Compare Epicurus’ justly-famous remark, “For just as medicine is useless if it does not remove sickness from the body, so philosophy is useless if it does not remove suffering from the soul” (2011, fragment 221) with Wittgenstein’s Philosophical Investigations §254–255 (1958). If I  had but space and time, Epicureanism too would be more fully included in this chapter on ancient roots of Wittgenstein’s liberatory philosophy. 12 Bouwsma alludes tantalisingly to a conversation in which the Stoics and Epicurus were discussed (1986); but it appears as if Wittgenstein lacked direct acquaintance with them, and, in reply to the mentions of them, tended to draw on other figures that he knew more of (e.g. Dostoevsky). 13 For a negative account of Nussbaum’s book, see Osborne (1996). I am much more sympathetic; I  think Nussbaum captures key aspects of what I  myself have found (and taught) in the Stoics, and, for this reason, as well as for reasons of space (I can’t here offer a serious interpreting of what Stoicism is), I shall tend to rely on her account here. 14 Foucault however of course brilliantly resisted medicalization; and he sees Ancient philosophy (and perhaps especially Plato) as doing the same. Compare these two remarks from The History of Sexuality Vol. 2: “From the expert doctor, the free man could expect more than the means for a cure in the strict sense of the term; he ought to receive a rational framework for the whole of his existence” and “[In] the Laws, Plato distinguishes between two kinds of doctors: those who are good for slaves (they are usually slaves themselves) and who confine themselves to giving prescriptions without offering any explanation; and those freeborn doctors who attend to free men” (Foucault 1985, p. 107). (For contrasting perspectives on whether or not Plato can be helpfully considered to be an ancient predecessor/anticipator of Wittgenstein, see Rowett (2013) for the positive, and Read (2013) for the negative). 15 N.B. My claim here is not limited to Kant’s explicit, well-known ethical philosophy, which of course features prominently “the kingdom of ends”. It includes the whole ambit of Kant’s picture of the realm of human autonomy, which

The Ancient Roots of Wittgenstein’s Liberatory Philosophy 289 inflects the whole project of the Critiques (a project that Wittgenstein knew well). 16 Here I  have in mind Annette Baier’s wonderful book, The Commons of the Mind (1997). 17 As Nussbaum does, I  think this a broadly-accurate interpretation of Plato’s ethical-philosophical thought, but obviously cannot prove that here. Thus my scare-quotes; it is enough for present purposes that such “Platonism”, as Platonism is commonly understood, finds a contrast in the Stoics and Wittgenstein. 18 Though great care is needed in the application of this “model”, which is strictly limited. Compare this pointedly anti-scientistic remark, from Wittgenstein’s Culture and Value, which strikingly includes medicine within its ambit: “People have sometimes said to me they cannot make any judgement about this or that because they have never learnt philosophy. This is irritating nonsense, it is being assumed that philosophy is some sort of science. And people speak of it as they might speak of medicine” (1984, p. 33, emphasis added). 19 Towards the end of the present chapter, I  come to reflect on how this point applies to my own uncompromising critique of Kripke here. 20 Nussbaum is drawing directly here upon Seneca’s On Anger (2017): To be precise, on 3.36.1–3 of that work. 21 And in Augustine (Read 2021, Ch. 1; Read 2017). 22 For more on the double-meaning I attribute to this phrase, cf. Philosophy for Life (Read 2007). Especially the Conclusion, wherein I lay out how a philosophy for life in the “ordinary” sense of that phrase must also be a philosophy for——i.e. on the side of——life. This, obviously, is a matter of no little potential importance, at a time when the “progress” of our uncultured civilisation is threatening life itself by fuelling incipient climate breakdown, aka civilizational breakdown (Read 2022). 23 The temptation to be bewitched was always in us and always will be. It is born of the desire for things to be simple and for abstracts to be concrete. It is prominent at points in Plato. It takes different forms through the ages. In my work, including here, I particularly stress the form it has perhaps most often taken in our age, and thus the tendency that we most of all perhaps then tend to need freeing from: scientism. 24 Similarly, visible in the quotation from the Thaetetus earlier is a problematic tendency on Socrates’s part to valorize the mind or the soul as opposed to the body. 25 And this is one reason why I sometimes see the connection between Wittgenstein and Stoicism as perhaps the deepest of all these connections—because arguably only the Stoics were really able to find a proper place for society, not only as an object of concern or antipathy for the philosopher but as the fundament of us all (cf. Read 2021, Ch. 10). 26 I am certainly not claiming that Wittgenstein imported his ladder directly from Sextus’s. Though he would of course have been aware of Schopenhauer’s and Mauthner’s (and probably also Kierkegaard’s) somewhat-similar ladder metaphors, and Mauthner’s is especially likely to have been the primary influence upon him. We should note that Mauthner, a key antecedent as well as foil for Wittgenstein in the Tractatus, was explicitly a kind of neo-Pyrhonnian; Gershon Weiler argues that it was from him that the Tractatus’ ladder metaphor came (1958). 27 The major Buddhist exegete and Madyamaka philosopher Candrakirti also uses the purgative metaphor (in another kind of ancient philosophy) making

290  Rupert Read the same/a related philosophical point). Although this is not strictly connected to questions of influence on Wittgenstein, it is interesting to note how the ladder metaphor is used in basically the same way by Sextus and Wittgenstein, and the purgative metaphor in basically the same way by Sextus and Candrakirti (Smith 2021). 28 As a result, one is less likely to stick to eggshells of a purgative than of a ladder. 29 The attentive reader will already pick up how my characterisation of the fantasy of an external point of view syncs with my characterisation of the fantasy that Kripkenstein is subject to. This point is implicit and then explicit in the following text, and returns finally in the close of this section: in my characterisation of how not to misread Sextus as falling into the same fantasy. 30 See n. 3, here, for the key reference. 31 For a more complete exegesis of 198–201 making clear Kripke’s misreading, and the fateful way he ignores the quotations I  am highlighting, see Read 2000a. 32 As noted earlier, this fantasy is the central object of critique in The New Wittgenstein (Crary and Read 2000). 33 As I explain in the Introduction of Wittgenstein’s Liberatory Philosophy (Read 2021, Section 0.3), a liberatory approach to philosophy is inter alia a resolute approach to philosophy (and to Wittgenstein). 34 For how such resolution need not involve destructive self-contradiction, see Conant and Dain 2011. 35 As is made very clear in the Preface to the Tractatus. It might be thought that the point I make supra his cannot be turned against Kripke, because, in Naming and Necessity (1972), he insists that our present language is the basis for any evaluation of modal claims. If there is any elevated point, it is the present language—in that work. But that is the answer to this concern; there is a contradiction between Kripke’s two books, on this central point. Or, more accurately: there is an internal contradiction within WRPL which results in its being incapable of being given a determinate reading (the very fate that it wished to impart to language as a whole.) In his book on Wittgenstein and rules, Kripke tries, as I’ve just explained, to undercut present language going forward, the “leading edge” of present language that is its unfolding via rules and norms (Read 2001). 36 And, incidentally, with Nagarjuna’s fourfold negation (Westerhoff 2009). 37 ζητέω (e.g. ζητοῦσιν, ζητήσεωσ, etc.) is a word we find throughout Sextus [ζητέω (zētéō) to seek, search after, look for, investigate]. 38 There is a prima facie tension between what I say here and [the second sentence of] PI, §500: “But a combination of words is being excluded from the language, withdrawn from circulation”. The tension is partly resolved by way of the first sentence of 500: “When a sentence is called senseless, it is not as it were its sense that is senseless.” The key contrast-class in 500 is between this irresolute conception and the resoluteness of taking seriously that nonsense is nonsense. 499 helps to clarify further however how a once and for all word-policing exclusion is not what Wittgenstein has in mind: To say “This combination of words makes no sense” excludes it from the sphere of language and thereby bounds the domain of language. But when one draws a boundary it may be for various kinds of reason. If I surround an area with a fence or a line or otherwise, the purpose may be to prevent someone from getting in or out; but it may also be part of a game and the

The Ancient Roots of Wittgenstein’s Liberatory Philosophy 291 players be supposed, say, to jump over the boundary; or it may shew where the property of one man ends and that of another begins; and so on. So if I draw a boundary line that is not yet to say what I am drawing it for. Transitional impossibility proofs in maths, innovative ways of talking about our brains, or some forms of avant-garde poetry, for instance, may reinstall an excluded combination of words. Just think of the way that “the square root of minus one” came to have a use. The absolute boundary—it being nonsense to speak of multiplying a number by itself and getting a negative number—was in a certain sense jumped over. 39 I am here assuming something like the “rustic” interpretation of classical Pyrrhonism favoured by my teacher Jonathan Barnes (1982). As to whether or not Sextus himself turns out to be such a Pyrrhonist: It all comes down to what kinds of beliefs/views we think Sextus suspends judgement upon. If my argument in the preceding, leaning on Machuca etc., is sound, then it will turn out that Sextus is not really a “classical Pyrrhonist”. 40 The classic example of Pyrrho undermining ordinary life is in Diogenes Laertius’ Lives of the Eminent Philosophers IX (2018, p. 62): He lived a life consistent with these doctrines, avoiding nothing, taking no precautions, facing everything as it came, whether wagons, cliffs, or dogs, and in general judging nothing by the evidence of his senses. But he was kept safe, as Antigonus of Carystus says, by the friends who accompanied him. However, it is also worth noting that this account is disputed, even in the same passage from Diogenes: Aenesidemus, however, says that though in his philosophy Pyrrho embraced the principle of suspension of judgement, he nevertheless exercised forethought in his daily life. He lived to be nearly ninety. 41 See Sextus Empiricus’s 2000, I: 8 in relation to ataraxia; here Sextus tells us that reaching tranquility is the ability of the Sceptic. 42 Though noting of course a crucial difference between Sextus and (a resolute) Wittgenstein, in how they present this quest: Sextus is engaged in a continuous search for the truth rather than meaning specifically. But even this difference may not turn out to be that deep. When we Wittgensteinians search for sense, we are absolutely not doing so in the spirit of overly-knowing post-moderns who surreptitiously think/“know” that there is no truth, only meaning and its absence. We do so rather in the spirit of seeing truth and meaning as alwaysalready intertwined, as per Philosophical Investigations, §§136–140. 43 For some further discussion, see the recent special issue of the Nordic Wittgenstein Review on “Post-Truth” (Read and Uçan 2019). While Cavell’s work is of course in the back of my mind here. 44 Big thanks to Catherine Rowett for help in trying to make sense of what the (ancient) authors I  have been writing on here say; and trying to make sense of my own efforts. Bigger thanks still to my former student Joshua Smith, for entirely invaluable, generous assistance in figuring out the nitty-gritty of the potential Wittgenstein-Sextus nexus (as well as for pointing me to details of the Wittgenstein-Sextus-Madyamaka nexus). Chunks of what I have written here I have drawn directly from both sides of my correspondence with Josh. Thanks also to Atus Mariqueo-Russell for editorial assistance. And thanks finally to the editors for penetrating comments on an earlier draft.

292  Rupert Read References Baier, Annette C. (1997) The Commons of the Mind. Open Court. Bailey, Alan (2002) Sextus Empiricus and Pyrrhonean Scepticism. Clarendon Press. Barnes, Jonathan (1982) The Beliefs of a Pyrrhonist, Proceedings of the Cambridge Philological Society, New Series 28, 1–29. Bouwsma, O. K. (1986) Wittgenstein: Conversations 1949–1951, edited by J. L. Craft and Ronald E. Hustwit. Hackett Publishing Company. Conant, James (1992) The Search for Logically Alien Thought: Descartes, Kant, Frege, and the Tractatus, Philosophical Topics, 20(1), 115–180. Conant, James (2000) Elucidation and Nonsense in Frege and Early Wittgenstein’s Tractatus, in Alice Crary and Rupert Read (eds.), The New Wittgenstein. Routledge, 174–217. Conant, James (2004) Varieties of Scepticism, in Denis McManus (ed.), Wittgenstein and Scepticism. Routledge, 97–136. Conant, James and Dain, Ed (2011) Throwing the Baby Out With the Ladder: A Reply to Roger White, in Rupert Read and Matthew A. Lavery (eds.), Beyond the Tractatus Wars: The New Wittgenstein Debate. Routledge, 66–83. Crary, Alice and Read, Rupert (eds.) (2000) The New Wittgenstein. Routledge. Empiricus, Sextus (1935) Against Logicians, translated from Ancient Greek by R. G. Bury. Loeb Classical Library. Empiricus, Sextus (2000) Outlines of Scepticism, edited by Julia Annas and Jonathan Barnes. Cambridge University Press. [Also known as Outlines of Pyrrhonism]. Epicurus (2011) Selected Fragments, translated from Ancient Greek by Peter SaintAndre. Monadnock Valley Press. https://monadnock.net/epicurus/fragments. html. Foucault, Michel (1985) The History of Sexuality Vol. 2. The Use of Pleasure. Vintage. Foucault, Michel (1986) The History of Sexuality Vol. 3. The Care of the Self. Vintage. Hadot, Pierre (1995) Philosophy as a Way of Life: Spiritual Exercises From Socrates to Foucault, edited by Arnold I. Davidson, translated from French by Michael Chase. Blackwell. Kripke, Saul A. (1972) Naming and Necessity. Blackwell. Kripke, Saul A. (1982) Wittgenstein on Rules and Private Language. Harvard University Press. Laertius, Diogenes (2018) Lives of the Eminent Philosophers, edited by James Miller, translated from Ancient Greek by Pamela Mensch. Oxford University Press. Machuca, Diego E. (2019) Pyrrhonian Argumentation: Therapy, Dialectic, and Inquiry, Apeiron 52(2), 199–221. Nussbaum, Martha C. (2018) The Therapy of Desire: Theory and Practice in Hellenistic Ethics. Princeton University Press. O’Keefe, Tim (2006) Socrates’ Therapeutic Use of Inconsistency in the Axiochus, Phronesis 51(4), 388–407.

The Ancient Roots of Wittgenstein’s Liberatory Philosophy 293 Osborne, Catherine (1996) Love’s Bitter Fruits: Martha C. Nussbaum the Therapy of Desire: Theory and Practice in Hellenistic Ethics, Philosophical Investigations 19(4), 318–328. Perin, Casey (2010) The Demands of Reason: An Essay on Pyrrhonian Scepticism. Oxford University Press. Pitcher, George (1965) Wittgenstein, Nonsense, and Lewis Carroll, The Massachusetts Review 6(3), 591–611. Plato (1973) Theaetetus, translated from Ancient Greek by John McDowell. Oxford University Press. Read, Rupert (1995a) Practices Without Foundations? Sceptical Readings of Wittgenstein and Goodman. PhD Thesis. Rutgers University. Read, Rupert (1995b) The Unstatability of Kripkean Scepticisms, Philosophical Papers 24(1), 67–75. Read, Rupert (2000a) Getting Rule-following Right: The Anticipation in “Philosophical Investigations” of Paras 201–202 by Paras 197–199. UEA Papers in Philosophy, New Series 11, 25–36. Read, Rupert (2000b) What “There Can Be No Such Thing as Meaning Anything by Any Word” Could Possibly Mean, in Alice Crary and Rupert Read (eds.), The New Wittgenstein. Routledge, 74–82. Read, Rupert (2001) Is There a Legitimate Way to Raise Doubts About the Immediate Future “From the Perspective Of” a Doubted Immediate Past? in W. Lüttersfeld, A. Roser, and R. Raatzsch (eds.), Wittgenstein Jahrbuch 2000. Peter Lang, 89–112. Read, Rupert (2007) Philosophy for Life. Continuum. Read, Rupert (2012) A Wittgensteinian Way With Paradoxes. Lexington Books. Read, Rupert (2013) On Philosophy’s (Lack of) Progress: From Plato to Wittgenstein (and Rawls), in Luigi Perissinotto and Begoña Ramón Cámara (eds.), Wittgenstein and Plato: Connections, Comparisons and Contrasts. Palgrave Macmillan, 249–280. Read, Rupert (2014) Wittgenstein and the Illusion of “Progress” (Royal Institute of Philosophy) [Online]. YouTube, 24 October. www.youtube.com/ watch?v=hEPcQ6sIOTY. Read, Rupert (2016) Wittgenstein and the Illusion of “Progress”: On Real Politics and Real Philosophy in a World of Technocracy, Royal Institute of Philosophy Supplement 78, 265–284. Read, Rupert (2017) The Augustinian Picture and Its Counter-Picture: PI 1 and PI 43 as Twins, in Emmanuel Bermon and Jean-Philippe Narboux (eds.), Finding One’s Way Through Wittgenstein’s Philosophical Investigations: New Essays on §§1–88. Springer. Read, Rupert (2019) What is New in Our Time? The Truth in “Post-Truth”: A  Response to Finlayson. Nordic Wittgenstein Review, special edition. PostTruth, 81–96. Read, Rupert (2021) Wittgenstein’s Liberatory Philosophy: Thinking through his Philosophical Investigations. Routledge. Read, Rupert (2022) Why Climate Breakdown Matters. Bloomsbury.

294  Rupert Read Read, Rupert and Uçan, Timur (eds.) (2019) Nordic Wittgenstein Review, special edition. Post-Truth. Reid, Lynette (1998) Wittgenstein’s Ladder: The Tractatus and Nonsense, Philosophical Investigations 21(2), 97–151. Rowett, Catherine (2013) Plato, Wittgenstein and the Definition of Games, in Luigi Perissinotto and Begoña Ramón Cámara (eds.), Wittgenstein and Plato: Connections, Comparisons and Contrasts. Palgrave Macmillan, 196–219. Scaltsas, Theodore and Mason, Andrew S. (2010) The Philosophy of Epictetus. Oxford University Press. Seneca (2013) Moral Letters to Lucilius, translated from Latin by Richard Gummere. Stoici Civitas Press. Seneca (2017) On Anger (De Ira), translated from Latin by Aubrey Stewart. Lazy Raven Publishing. Smith, Joshua William (2021) “Snakes and Ladders”——Therapy as Liberation in Nagarjuna and Wittgenstein’s Tractatus, Sophia 60(2), 411–430. Stern, David (2004) Wittgenstein’s Philosophical Investigations: An Introduction. Cambridge University Press. Stone, Martin (2000) Wittgenstein on Deconstruction, in Alice Crary and Rupert Read (eds.), The New Wittgenstein. Routledge, 83–117. Thorsrud, Herald (2003) Is the Examined Life Worth Living? A Pyrrhonian Alternative, Apeiron 36(3), 229–249. Wallgren, Thomas (2006) Transformative Philosophy: Socrates, Wittgenstein, and the Democratic Spirit of Philosophy. Lexington Books. Weiler, Gershon (1958) On Fritz Mauthner’s Critique of Language, Mind 67(265), 80–87. Westerhoff, Jan (2009) Nagarjuna’s Madhyamaka: A Philosophical Introduction. Oxford University Press. Witherspoon, Edward (2000) Conceptions of Nonsense in Carnap and Wittgenstein, in Alice Crary and Rupert Read (eds.), The New Wittgenstein. Routledge, 315–349. Wittgenstein, Ludwig (1922) Tractatus Logico-Philosophicus, translated from German by Frank P. Ramsey and Charles Kay Ogden. Harcourt, Brace & Company, Inc. Wittgenstein, Ludwig (1958) Philosophical Investigations, translated from German by G. E. M. Anscombe. Blackwell. Wittgenstein, Ludwig (1976) Wittgenstein’s Lectures on the Foundations of Mathematics, Cambridge 1939, edited by Cora Diamond. Cornell University Press. Wittgenstein, Ludwig (1984) Culture and Value, edited by G. H. von Wright, translated from German by Peter Winch. Blackwell.

Index

abstract 79, 101 – 103, 115 – 118, 131, 144, 148, 155, 197, 199, 209, 240, 242, 249 – 250, 253 – 254, 265, 272, 289; entity 5, 111, 115 – 118, 131, 252 – 254; length 120, 131 – 135, 137, 139, 253; meter 117, 148; object 5, 79, 131 – 132, 138, 167, 172 – 174, 251 accident, accidental 95 – 96, 132, 137, 139, 147 – 154, 163, 180, 186, 209, 218, 244, 274 addition 61 – 65, 77, 197 – 202, 209 – 210 Alexander the Great 36 analytic philosophy 1, 2, 7, 85, 92, 96, 237 – 238, 241 Anscombe, G. E. M. 143, 155 a posteriori 1, 3, 20 – 21, 24, 97, 109, 130, 134, 141, 152, 166, 171, 175 appearance 23, 40, 60 – 61, 73, 128 – 139, 146, 167, 198, 219, 283 a priori 5, 6, 17 – 21, 77, 83, 97, 109 – 111, 122, 134 – 135, 141 – 156, 158 – 173, 175, 180, 186, 190 – 191, 200, 210, 265 – 266, 284; contingent 1 – 6, 10, 109, 114, 146, 158 – 159, 162 – 173 arguments from ignorance and error 13, 19, 24 Aristotle 36, 85 – 88, 92, 95, 129, 131, 171, 176, 285

arithmetic 62 – 64, 197 – 202, 243 ataraxia 281, 291 Augustine 10, 24, 37, 54, 288 – 289 Augustinian picture of language 1, 3, 10 – 14, 23, 54, 89 Avital, D. 123, 148, 155 baptism 13, 52, 66 – 70, 109 – 110, 128, 130, 138, 148, 150, 218 basic particular see element, primary Blackburn, S. 73 – 76, 79 Boghossian, P. 72, 77, 79 Bradley, R. 84, 91 Burgess, J. 66, 78 Bush, G. W. 54 Carnap, R. 4, 83, 85, 92 – 99, 104, 174, 176, 276, 286 – 287 Carroll, L. 40 causality 18, 79, 150, 244, 259, 274; causal-historical account of reference 1, 4, 9, 60 – 80, 154, 213, 241 Cavell, S. 179, 205, 291 Chang, H. 243, 256, 262 Child, W. 22 – 23 Cicero, M. T. 18, 24, 88 Columbus, C. 18, 24 common sense 16, 40, 137, 149 – 150, 153, 239 comparison of length 179, 188, 196, 202, 217 – 218, 224 – 226, 242 – 246

296 Index Conant, J. 55, 122, 208, 270 – 271, 276, 287, 290 condition: assertion 202 – 203, 210; of sense 7, 236 – 237, 241, 249, 261, 266; transcendental 236 – 237; truth 78, 95, 172, 174, 176, 203, 210, 239 connotation 12, 28, 33 contingency 6, 83, 92, 98, 141, 146, 152 – 155, 159, 161 – 162, 165, 167, 169, 171, 187, 209; contingent a priori (see a priori, contingent); fact (see fact, contingent) contradiction 61, 73, 93, 95, 140, 281, 290 convention, conventionalism 7, 17, 87, 119, 121 – 123, 139, 170, 174, 176, 213, 226, 232, 246, 264, 274 Copernican revolution 146, 153 – 154 counterfactual case/scenario/situation 16, 21, 44, 65, 72, 84, 91, 96, 110, 123, 131, 138, 147, 150 – 152, 154, 166, 187 – 190, 200, 204, 242, 244, 250 cynicism 276 de dicto 130 definition: of one kilogram 193, 247; of one meter 45, 110, 132, 163 – 171, 174, 179, 187, 196, 208 – 210, 217, 221 – 224, 232, 242 – 245, 248; of proper names 29, 44 – 45; ostensive 3, 11, 13 – 14, 23, 46, 129, 132; see also baptism denotation 28, 33, 77 de re 155, 170 Descartes, R. 270 Diamond, C. 83, 103, 122 – 123, 176, 213 – 234, 240 – 247, 250, 252, 255, 262 direct reference 11, 13, 104 dispositional, dispositionalism 4, 61 – 64, 68 – 80

Dolev, Y. 155, 257 – 259, 264 Donnellan, K. 6, 53, 170 – 171 dream 136, 150, 281, 283 Dupré, J. 18, 19 Eichmann, A. 20 element, primary 5, 128, 135 – 140,  175 Epictetus 275 – 276, 288 Epicurus 285, 288 epistemology 5, 119, 141 – 146, 150 – 154, 196, 205, 216, 219, 225 essentialism, essence 2, 3, 10, 11, 18 – 23, 93 – 99, 104, 154, 174, 205 – 206, 241, 269 Evening Star see Morning Star experience 60, 69, 70, 132, 144 – 154, 159, 164 – 166, 171, 175, 184, 230, 249, 254, 264 expressivism 61, 73 – 76, 79 – 80 extension 17, 20, 21, 56, 67, 69 – 71, 78 – 79, 133, 139, 143; see also intension fact: contingent 109, 111, 116, 122, 170, 182; picturing 91, 101 – 103; positive and negative 88, 89, 91; propositional 87, 88, 90 family-resemblance 49, 51, 52, 56 Feynman, R. 24, 42, 65 fixing the reference 2, 4, 5, 12, 42, 46, 55, 65, 66, 87, 98, 110, 111, 127 – 139, 146 – 149, 154, 156, 164 – 165, 171 – 172, 180, 187, 192, 213 – 221, 232, 243 – 245, 256 – 258, 262, 265 Floyd, J. 103, 206, 210 Foucault, M. 274, 288 freedom 7, 8, 168, 260, 269, 271, 275 – 279, 281, 287 Frege, G. 1, 3, 4, 20 – 23, 28 – 38, 44 – 49, 53 – 55, 63 – 66, 85, 92, 123, 146 Freud, S. 275, 283

Index  297 Gabriel, M. 238 – 239, 251 Gert, H. 118, 208, 240 Glock, H.-J. 17, 18, 56, 103 God 23, 149 – 150, 257, 266, 272 Gödel, K. 24 gold 20, 21, 48, 51 – 53, 66 – 71, 79, 128 – 131, 135, 138 Goldfarb, W. 83, 198, 210 Goodman, N. 261 grammar 17, 55, 121, 123, 129, 132 – 133, 136, 167, 173 – 174, 193, 205 – 206, 264 Grice, H. P. 96 Hacker, P. 13, 17 – 18, 122 Hanfling, O. 17 – 18, 25 Hanks, T. 101 Hesperus 12, 97 – 99, 104 Husserl, E. 32 – 33, 36 hydrogen peroxide 130 idealism 21, 34, 86; transcendental (see transcendental, idealism and realism) identity 6, 20 – 21, 32 – 35, 52, 55, 75, 96 – 101, 104, 111, 114 – 115, 119 – 120, 128, 135, 174, 183, 187, 196, 203 – 207, 210, 241, 253, 258, 262, 265; see also transworld identification ideology 56, 274 imagination 143, 147 – 148, 152, 188 – 189, 206 – 207, 236, 261, 264, 266 infinite regress 41, 117, 124, 279 intension 56, 83; see also extension intuition, intuitionism 4, 74, 82 – 85, 91 – 99, 104, 137, 145, 149 – 150, 156, 232, 242, 266 Jacquette, D. 139 judgment 74 – 75, 80, 82 – 87, 145, 235, 244, 251, 254, 259 – 262, 275, 282 – 287, 291; moral 61, 73 – 76; semantic 61, 73, 75; theory of 84 – 88, 91

Kant, I. 5, 7, 128, 142 – 156, 236 – 242, 244, 248 – 249, 260, 264, 266, 270 – 271, 274, 288 Keener, C. 101 Kripkenstein 225 – 226, 271, 277 – 279, 284, 290 Kusch, M. 78 – 79 language-game 16, 40, 55, 133, 142 – 144, 155, 158 – 160, 178 – 181, 194 – 197, 201 – 202, 209, 217, 229, 242, 265 Lewis, C. I. 92, 104 Lewis, D. 78 – 79 logical form 83, 100, 102 – 103, 105 logical syntax 287 Loomis, E. 17 – 18, 138, 154 Lund, M. 101 Machuca, D. 282 – 284, 291 Maddy, P. 60, 66 – 72, 78 – 79 magnitude 247, 252 – 259, 262 – 266 Malcolm, N. 6, 110, 121, 123, 148, 154 – 155, 186 – 193, 196, 203 – 204, 208 – 209, 263 Malkovich, J. 101 Marx, K. 82 McDowell, J. 79 – 80, 230 McGinn, C. 60, 66 – 68, 72, 78 – 79 measurement: instrument 114, 160, 193, 195, 198, 200, 224, 226, 232 – 233, 245, 248, 251 – 252, 256 – 257, 262, 266; method of 132, 213, 232 – 233; object of 2, 124, 160 – 166, 171; practices of 131, 219, 221, 230, 232, 247 – 249, 254, 258 – 259, 264; standard of 111, 120, 160 – 171, 175, 192, 195, 213, 218, 225, 229, 231, 234, 259, 262; unit of 139, 161, 166 – 169, 193 – 194, 220, 233, 246, 251, 258 – 259, 263, 265 measuring rod see meter rod Merleau-Ponty, M. 239, 254 metaethics 4, 61, 73 – 76, 80

298 Index metaphysics 1 – 2, 5 – 6, 14, 21, 49, 55, 74, 77, 82 – 85, 93, 96, 99, 119, 124, 133, 136, 139, 141, 146, 150 – 154, 159, 162 – 165, 174, 179 – 180, 196, 204 – 206, 209 – 210, 216 – 221, 233, 241, 250, 260, 266, 270 metasemantics 75, 80 meter rod 118 – 119, 132 – 134, 141, 147 – 148, 152, 155, 160 – 161, 164, 171, 173, 178 – 179, 181, 186 – 187, 190 – 198, 200, 202, 204, 208, 216 – 217, 219, 220 – 222, 224 – 225, 230 – 231, 240, 242, 245, 253 meter stick see meter rod metric system 5, 7, 113 – 114, 120, 124, 146, 161, 164, 213 – 224, 219 Mill, J. S. 11 – 12, 28 – 29, 30, 33, 38, 40 – 41, 44 – 46, 54 modality 4, 82 – 85, 90 – 100, 103, 137, 139, 150, 155 model 16, 37, 55, 101, 181, 275 Moore, G. E. 74, 86, 276 moral cognitivism 4, 74 – 75, 79 Morning Star 32, 34 Moses 1, 10, 39 – 42, 46, 168 multiplication 64, 195, 197 – 198, 203 Nagel, T. 237, 260 name, naming 38, 41, 46 – 48, 56, 128, 187, 241, 244, 247, 255, 257, 259, 265; atomic 44; cluster theory of names 10, 15, 38 – 39; description theory of names 3, 15, 30 – 41, 35, 38, 40 – 42, 46, 54; Frege-Russell view of names 65 – 66, 123; proper 11 – 12, 14, 28 – 31, 33 – 37, 43, 47, 54, 124, 131, 245 Narboux, J.-P. 104, 261 – 263 naturalism 61, 73, 239 natural kind, natural kind term 2, 11, 17 – 24, 48 – 49, 66 – 69, 71 – 72, 78, 128 Needham, P. 18 – 19

Neurath, O. 233 Newton, I. 131 Nixon, R. 15 – 16, 21, 45, 95 – 96, 98 – 99 non-cognitivism 4, 74, 76, 79 – 80 nonsense 5, 30, 82, 85, 100, 103, 122, 125, 133, 183, 191, 236, 269, 281, 285 – 287, 289 – 291 normative ethics 4, 61, 73 – 76, 80 number 46, 50, 55 – 56 Nussbaum, M. 273 – 275, 287 – 289 object of comparison 113, 139, 220, 224 – 226, 229 ontology, ontological 128 – 131, 136, 139, 153, 174, 266 paracomplete logic, reasoning 5, 133, 137, 139 – 140 paradigmatic example, sample 42, 129 – 131, 133 – 134, 138; see also meter rod physics 152 – 153, 192 – 193, 195, 238, 261, 266 Plato 36 – 38, 87 – 88, 143, 155, 273, 288 – 289 Platonic, Platonism 143, 148 – 149, 275, 289 possibility of experience 145, 151 – 152 possible world 45, 50 – 51, 55, 104, 110, 120, 128, 136 – 138 practice 7, 14, 20, 41 – 44, 47, 114, 117, 120, 132, 188, 191, 193, 195, 197 – 200, 214, 221 – 224, 226 – 230, 234, 237, 245 – 251, 255, 259, 262, 265 – 266 precision 218, 223 – 225, 228 – 233, 246 – 248, 255 – 256, 258 – 260, 266 predication 48, 93 – 94,121 – 123; self- 111 primary element see element, primary proper name see name, proper property: accidental 147 – 148, 153 – 154, 163, 180, 244; essential 44 – 45, 93 – 95, 147; internal 83, 92; metaphysical

Index  299 162, 165; modal 94, 98 – 99; syntactical 92 – 93 Putnam, H. 6, 17 – 21, 25, 67 – 68, 203, 206 Pyrrho 270 – 271, 278, 284 – 287, 291 quaddition see addition, quus quasi-realism 73, 80 Quine, W. v. O. 15, 92 – 95, 194 quus 62, 216, 271, 280, 287 realism 49, 73 – 74, 80, 238; transcendental (see transcendental, idealism and realism) reality 17, 84 – 86, 89, 100, 103, 105, 128 – 137, 139, 154, 158, 171 – 176, 208, 215, 235, 266 reference-fixing see fixing the reference regress 41, 117, 124, 279 religion, religious 56, 141, 148, 150 resolute 5, 82 – 83, 100, 122, 277, 281, 284 – 286, 290 Ricketts, T. 208, 211 rigid designator 45, 48, 99, 110, 133, 135, 138, 154, 203 – 204, 209, 217, 244, 262 Riordan, S. 213, 246 – 247, 264 ritual 150 Rosen, G. 239, 251 rule 2, 6, 17, 43, 62, 76, 87 – 88, 112, 123, 133, 139, 168 – 169, 171 – 174, 176, 178 – 181, 189, 194, 195 – 199, 206, 210, 215 – 216, 227, 270 – 271, 290 rule-following 2, 4, 6 – 7, 9, 41 – 44, 46, 55, 60, 79, 215 – 216, 269, 279 Russell, B. 1 – 4, 21, 23 – 24, 29 – 31, 37 – 40, 44 – 45, 47, 49, 53, 65 – 66, 84 – 89, 91 – 92, 104, 123 – 124, 158, 174 – 175, 241, 276 Santayana, G. 82 sceptical solution 65, 73, 75 – 76, 79, 285

scepticism (skepticism) 4, 7 – 9, 16, 19, 34, 61, 261 – 262, 270, 275, 277, 279 – 280, 284 – 285, 287 Schlick, M. 83 schmidentity see identity Searle, J. 10 Seneca, L. A. 273, 275 – 276 sensation 47, 55, 129, 274 Sextus Empiricus 276 – 284, 286 – 287, 290 – 291 Sider, T. 238 – 239, 261, 263 – 264, 266 skaddition see addition Smart, J. J. C. 147, 152 Socrates 7, 10, 29, 183, 270 – 271, 273, 276, 287 sortal 6, 204, 206 space 92; absolute 5, 131 – 138, 141, 145 – 146, 149, 151 – 153, 171, 173 speed of light 232, 263 Stalnaker, R. 80 standard foot 133 – 134 standard meter (metre) 2, 4 – 7, 10, 44 – 45, 108 – 109, 112 – 115, 117 – 124, 127 – 128, 131 – 139, 141 – 144, 146, 148 – 150, 155, 158 – 161, 163, 172, 175 – 176, 178, 180 – 183, 186, 188 – 189, 196, 198 – 199, 203, 208, 210, 213 – 225, 230 – 231, 233, 240 – 242, 245, 252 standard sepia 45, 138, 144, 159, 172, 182, 194 state of affairs 90 – 91 state-of-things see state of affairs stipulation 17, 21, 32, 34, 87, 131, 143, 148 – 151, 153, 155, 164 – 165, 169 – 170, 176, 232 Stoicism 273 – 274, 276, 283, 288 – 289 straight solution 72 – 73, 76, 78, 200 – 201 Strawson, P. 10, 96, 260 structure 49 – 52, 69 – 70, 82, 89 – 92, 102 – 103, 121, 130, 135, 139, 146, 221, 250 substance 21, 49, 52, 128 – 130, 135 – 136, 138, 150, 154, 158 Sullivan, P. M. 100

300 Index therapy 275, 283 transcendental 7, 144, 149, 152, 266; idealism and realism 7, 235 – 243, 245, 247 – 252, 254 – 255, 257 – 261, 263 – 265 transworld identification/identity 16, 18, 21, 128, 135, 139; see also identity Travis, C. 239 truth 1, 62, 74, 79 – 80, 97, 103 – 104, 144 – 145, 156, 175, 264, 266, 279, 284, 291; contingent 85 – 86, 88 – 92, 162 – 170, 175, 202, 235; necessary 20, 159, 163, 169 – 170, 178, 180 truth-value 5, 31, 109, 115, 120, 127, 133 – 137, 139 Twin Earth 22, 25 unit, of length, of measurement 131, 134, 137, 139, 161 – 162,

166 – 167, 169, 171 – 172, 191, 193 – 194, 204, 213, 220, 232 – 233, 237, 239, 241 – 242, 246, 249, 251 – 259, 262 – 265; see also measurement universal 150, 173 – 174, 237, 246,  286 utilitarianism 74 – 76 vagueness 20, 23, 51 – 52, 56 van Fraassen, B. 255, 259, 265 – 266 Vienna Circle 13, 83 water, H2O 20, 48, 124, 128 – 131, 135 – 136, 138 – 139, 185, 193, 246 – 247 Winch, P. 201 – 203, 207 Wright, G. H. von 25, 84 yardstick see meter rod