Philosophical Representation: Studies in in Attitudinal Instrumentalism 9781032307428, 9781032307435, 9781003306443

Table of contents :
Cover
Half Title
Series
Title
Copyright
Contents
Preface
Acknowledgments
1 Philosophical Explanation
1.1 Realist vs. Instrumentalist Attitude
*1.2 Case Study 1: Frege on Number
1.3 Case Study 2: De Re Modality
1.4 Case Study 3: Indirect Reference
1.5 Semantic Descent
2 Justified Attitudinal Realism
2.1 Theoretical Identifications
2.2 Semantic Representations in Metaphysics
2.3 A Brief Aetiology
2.4 Philosophical Theoretical Representations
3 Attitudinal Instrumentalism in Semantics
3.1 Formal Semantic Evaluation
*3.2 Representing Truth
*3.3 Indirect Reference Again
4 Semantics and Ordinary Language
*4.1 Attitudinal Instrumentalism and Analysis
4.2 Performativity
5 Propositions and What Is Said
5.1 The Metaphysics of What Is Said
5.2 Attitudinal Instrumentalism and Propositions
*5.3 The Russell-Myhill Paradox
6 The Content Program
6.1 Significance and Content
6.2 Attitudinal Instrumentalism and Content
6.3 Attitudinal Instrumentalism and Metasemantics
6.4 Attitudinal Instrumentalism and RTM
7 Rules and Representation
7.1 Representing Behavior
7.2 Calculating
7.3 Inferring
7.4 Rules as Representations
Postscript
Bibliography
Index

Citation preview

Philosophical Representation

This book focuses on how we should treat philosophy’s theoretical representations. It argues in favor of an instrumentalist attitude towards pivotal cases of theoretical representation in philosophy that are commonly regarded under a realist attitude. Philosophy is awash with theoretical representations, which raises the question of how we should regard them. This book argues that representations in philosophy should not be regarded under a realist attitude by default as individually disclosing the nature of what they represent. Ori Simchen introduces the reader to the general theme of representations in philosophy and our attitudes towards them via case studies: numbers, modality, and belief. He offers a framework for deciding when a realist attitude towards a theoretical representation is warranted and concludes that the representations deployed in the case studies fail the proposed test. The next part of the book illustrates the attractiveness of attitudinal instrumentalism towards representations in semantics, in the philosophy of mind, and within the problematics of rule-following. Philosophical Representation will appeal to researchers and advanced students working in the philosophy of language, philosophy of mind, metaphysics, philosophical logic, and philosophical methodology. Ori Simchen is Professor of Philosophy at the University of British Columbia, Canada. He is the author of Semantics, Metasemantics, Aboutness (2017), and Necessary Intentionality: A Study in the Metaphysics of Aboutness (2012).

Routledge Studies in Contemporary Philosophy

Unconscious Networks Philosophy, Psychoanalysis, and Artificial Intelligence Luca M. Possati Updating the Interpretive Turn New Arguments in Hermeneutics Edited by Michiel Meijer Conservatism and Grace The Conservative Case for Religion by Establishment Sebastian Morello The Ethics of Interpretation From Charity as a Principle to Love as a Hermeneutic Imperative Pol Vandevelde The Nature and Practice of Trust Marc A. Cohen A Plea for Plausibility Toward a Comparative Decision Theory John R. Welch Living with the Dead On Death, the Dead, and Immortality J. Jeremy Wisnewski Free Will’s Value Criminal Justice, Pride, and Love John Lemos For more information about this series, please visit: www.routledge.com/ Routledge-Studies-in-Contemporary-Philosophy/book-series/SE0720

Philosophical Representation Studies in Attitudinal Instrumentalism

Ori Simchen

First published 2023 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 © 2023 Ori Simchen The right of Ori Simchen to be identified as author of this work 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. Library of Congress Cataloging-in-Publication Data A catalog record for this book has been requested ISBN: 978-1-032-30742-8 (hbk) ISBN: 978-1-032-30743-5 (pbk) ISBN: 978-1-003-30644-3 (ebk) DOI: 10.4324/9781003306443 Typeset in Bembo by Apex CoVantage, LLC

We create models to explain nature, but the models wind up gatecrashing nature and driving away the original inhabitants. David Mitchell, Ghostwritten

Contents

Preface Acknowledgments 1

Philosophical Explanation

1.1 *1.2 1.3 1.4 1.5 2

3

1

Realist vs. Instrumentalist Attitude 1 Case Study 1: Frege on Number 4 Case Study 2: De Re Modality 6 Case Study 3: Indirect Reference 10 Semantic Descent 13

Justified Attitudinal Realism

2.1 2.2 2.3 2.4

ix xix

17

Theoretical Identifications 17 Semantic Representations in Metaphysics 22 A Brief Aetiology 30 Philosophical Theoretical Representations 35

Attitudinal Instrumentalism in Semantics

39

3.1 Formal Semantic Evaluation 39 *3.2 Representing Truth 43 *3.3 Indirect Reference Again 51 4

Semantics and Ordinary Language

*4.1 Attitudinal Instrumentalism and Analysis 61 4.2 Performativity 72

61

viii Contents 5

Propositions and What Is Said

81

5.1 The Metaphysics of What Is Said 81 5.2 Attitudinal Instrumentalism and Propositions 85 *5.3 The Russell-Myhill Paradox 88 6

The Content Program

6.1 6.2 6.3 6.4 7

Significance and Content 93 Attitudinal Instrumentalism and Content 95 Attitudinal Instrumentalism and Metasemantics 98 Attitudinal Instrumentalism and RTM 101

Rules and Representation

7.1 7.2 7.3 7.4

93

109

Representing Behavior 109 Calculating 111 Inferring 113 Rules as Representations 120

Postscript Bibliography Index

126 128 133

Preface

Philosophy is notorious for asking questions at a very high level of generality, seemingly so far removed from our earthly daily trappings as to strike many as irrelevant at best. Philosophy’s childlike manner of posing difficulties out of the blue—What is time? How do I know I am not dreaming? How do I know you have a mind?—is often emphasized by its detractors over its origination in human affairs. This makes it an easy target for self-fashioned intellectual adults who see philosophy as old-fashioned and impertinent. But there are times when even those who are otherwise gripped by philosophy’s ethereal aspect cannot help but reflect on it as a human enterprise immersed in the flow of time. For reasons too complex to summarize, we are living in a time when lofty reflections as such, including philosophical ones, demand renewed attention and support. Pondering whether asking seemingly timeless questions is sustainable or whether it is just a waste of time is itself a familiar philosophical preoccupation. In what follows, I would like to make an extended case for philosophy’s aspirations and methods as continuous with those of our other theoretical endeavors. In Philosophical Investigations, Wittgenstein writes: And we may not advance any kind of theory. There must not be anything hypothetical in our considerations. We must do away with all explanation, and description alone must take its place. And this description gets its light, that is to say its purpose, from the philosophical problems. (2009: §109) Such words have spawned the famous—many would say infamous—antitheory legacy of Wittgenstein’s philosophical oeuvre. How to interpret them, on the other hand, is far from clear. It just isn’t obvious what remains of philosophy once we do away with all theories and explanations. Aren’t generalizations about philosophy, even a general claim to the effect that philosophical problems arise from “the bewitchment of our understanding by the resources of our language” (§109), theoretical contributions within

x Preface philosophy? Stanley Cavell, the longtime admirer and expositor of the Investigations, emphatically agrees that metaphilosophy is just more philosophy: If I deny a distinction, it is the still fashionable distinction between philosophy and meta-philosophy. The remarks I make about philosophy (for example, about certain differences from other subjects) are, where accurate and useful, nothing more or less than philosophical remarks, on a par with remarks I make about acknowledgment or about mistakes or about metaphor. I would regard this fact—that philosophy is one of its own normal topics—as in turn defining for the subject, for what I wish philosophy to do. (1969: xviii) It would seem that generalizations about philosophy, which are also theoretical contributions within philosophy, are not to be discarded en masse, even by Wittgensteinian standards. This much is clear, however: philosophy is predominantly an explanatory enterprise. It advances theories. This is the uncontroversial backdrop to Wittgenstein’s programmatic call, expressed with one ‘may’ and three ‘must’s, for philosophy’s reorientation. But in the rush to replace philosophical explanation with “description alone”, the Wittgensteinian impulse can easily overlook central features of the subject qua human explanatory activity. My aim here is to attend to philosophical explanation as such. My approach appears to cohere with the Wittgensteinian injunction at a metalevel. My aim is not to offer any kind of metaphilosophical theory, a theory whose subject matter is philosophical theorizing, but rather to describe various philosophical theories in an effort to gain insight into philosophy as an explanatory activity. To paraphrase the passage from Wittgenstein, the metaphilosophical description gets its light, that is to say its purpose, from the philosophical theories. This is the methodology I aim to pursue in this book. I aim to explore such questions as these: Should theoretical representations in philosophy be taken in general to reveal the nature of what they represent? Or should they be taken in some other way? How are we to decide how to regard philosophy’s theoretical representations? If we conclude that some such representations should not be taken to reveal the underlying nature of what they represent, what value might they still have for the larger enterprise? The present inquiry should be of interest even to those who are otherwise hostile to the traditional aspirations of the subject. When all is said and done, philosophy’s explanatory endeavors are human endeavors and should therefore command the attention of anyone with a humanistic interest. On the other hand, to those who are comfortable with philosophy’s traditional aspirations, this book should be seen as an attempt to achieve self-understanding both on the side of producing philosophical theories and on the side of consuming them.

Preface xi

It is a platitude that philosophy is a broadly theoretical enterprise. Philosophers advance theories that are meant to contribute to our understanding of the world, including our place in it. But here is another platitude about philosophy: philosophical disagreements are particularly pernicious and difficult to resolve. To the uninitiated, they seem more akin to theological disputes than to theoretical ones. In this respect, philosophy is an outlier among other theoretical endeavors. What accounts for this special character? My overall conjecture is that philosophers tend to forget that philosophical reflection is a species of human explanatory activity, treating its products more like instances of divine revelation than like artifacts with clearly circumscribed explanatory roles. The impetus for this project is a simple observation of a contrast in how we regard individual theoretical representations in general within various explanatory settings. There is, on the one hand, what I’m going to call a realist attitude towards theoretical representations, which I will also sometimes refer to as attitudinal realism. This is the attitude we adopt when we regard theoretical representations as revealing the nature of whatever they represent. The appeal to the nature of things here isn’t meant to invoke some worked-out essentialist doctrine in metaphysics. The attitude I’m characterizing as realist need not be, and often isn’t, doctrinally informed. I take it that theoretical representations are commonly regarded as telling us what the things they represent individually really are, regardless of our more sophisticated opinions on such questions as whether essences are real or nominal. Examples of adopting a realist attitude in this sense are familiar from the popularization of natural science as the enterprise whose business is to tell us what portions of the natural world really are at bottom. Take the somewhat generic theoretical representation of gold within physical chemistry as a transition metal, an element occupying the middle block of the periodic table. Or take the more specific representation of gold as element Au with atomic number 79 (a favorite philosophical example). Or take the physical-chemical representation of water as hydrogen hydroxide (another favorite example). Or take the astrophysical representation of the sun as a sphere of hot plasma converting hydrogen into helium. In all such cases, the representation is entrusted with revealing the nature of whatever it represents on its own, so to speak. Representing gold as the element with atomic number 79 is itself meant to capture or encapsulate what the represented substance really is. Similarly, for the representation of gold as a transition metal, targeting more general features gold shares with other elements. To represent gold as a transition metal characterizes the nature of the substance, too, albeit incompletely. This talk of the representation “itself ”, revealing the nature of the represented is surely an idealization. Representing a substance as an atomic element with 79 protons in the atomic nucleus, or representing it more generally as a transition metal, clearly requires an extensive theoretical background. But it’s a useful idealization once a comparison is drawn between our

xii Preface attitude towards such cases and a different attitude we adopt towards other theoretical representations, what I am now calling an instrumentalist attitude, or attitudinal instrumentalism. An instrumentalist attitude towards a theoretical representation regards the representation as having a theoretical role within the larger explanatory context that does not include disclosing the nature of whatever is represented individually. This is how we regard the representation of gold as the standard for pre-20th-century monetary systems in economics, for example. It is also how we might regard the representation of gold as the skin of the god Ra within Egyptological explanation, the theoretical study of Ancient Egypt, or how we regard the representation of the meaning of a sentence as a set of indices or a function from indices to truth-values in truth-conditional semantics. The representation of gold as the standard for pre-20th-century monetary systems figures within a broad theoretical effort to reveal something important about the nature of the economy. But the representation is not entrusted with revealing something important about the nature of the represented substance. It isn’t the business of economic explanation to disclose the nature of substances. If someone were to suppose that being the gold standard captures the nature of gold, they would be badly mistaken about the kind of explanation at issue. And yet, the gold standard represents gold within economic explanation all the same. It might be supposed that adopting a realist attitude towards some representation R is simply to regard R as correctly ascribing properties to whatever R represents, whereas adopting an instrumentalist attitude towards R is simply to regard R as incorrectly ascribing properties to whatever R represents. This would be a mistake, however. The distinction between correctness and incorrectness in the ascription of properties is orthogonal to the contrast between realist and instrumentalist attitudes as conceived in this book. I may take an instrumentalist attitude towards the representation of the meaning of a sentence as a set of indices, in the sense that even though I regard the set as representing the meaning of the sentence for formal semantic purposes, I do not take the representation as itself disclosing what the meaning of the sentence really is. This is perfectly compatible with supposing that being true at those indices is a feature of the meaning in question for formal semantic purposes. From the other direction, one might adopt a realist attitude towards the representation of empty space as being filled with aether, in the sense that one regards being filled with aether as disclosing what empty space really is at bottom, even though being filled with aether is not (as it turns out) a feature of empty space. Realist and instrumentalist attitudes are just that—attitudes. They are attitudes we, experts and novices alike, naturally and intuitively adopt towards theoretical representations. Whether or not those representations correctly ascribe properties to whatever they represent is a separate issue. On the other hand—and this is worth repeating—regarding a theoretical representation as revealing (or not) the nature of whatever it represents is not presumed to be theoretically informed when it comes to the metaphysics

Preface xiii

of essence. We, experts and novices alike, adopt such attitudes towards the representations offered by theories in a way that is prior to such downstream doctrinal matters in metaphysics. The truth about essence has little bearing on whether or not those attitudes are, in fact, adopted by us. So we have these contrasting attitudes towards theoretical representations: a realist attitude and an instrumentalist attitude. It’s an idealized contrast but a useful one. Attending to it allows us to consider the question of aptness or warrant when it comes to theoretical representations deployed within philosophy itself. Are philosophy’s theoretical representations generally akin to representations of gold in the physical sciences? Or might they be more akin to social-scientific representations? The issue here falls under general philosophical methodology. Philosophy is awash with theoretical representations, and the question is how we should regard them. Should we, for example, regard set-theoretical representations of individual numbers within the foundations of mathematics as themselves revealing the nature of the numbers or not? Should we regard possible world representations of possibilities in the metaphysics of modality as themselves revealing the nature of possibilities or not? How are we to decide on such cases? The general approach of this book is to take common, untutored attitudes towards theoretical representations outside philosophy as measures for warrant when it comes to our attitudes towards theoretical representations in philosophy. There is a sizable philosophy of science literature on the role of theoretical representations within scientific explanation.1 I can’t do it justice or contribute meaningfully to this area of research on its own terms. For present purposes, I take for granted that an instrumentalist attitude towards the representation of gold as a monetary standard is warranted. Such a representation has no business telling us what gold really is. We can then compare such a case with the representation within the metaphysics of modality of Biden’s possible electoral loss in 2020 as Biden losing in another possible world and ask whether we should consider the possible world representation under an instrumentalist attitude as well. Or we can compare the modal metaphysical case to a case outside philosophy where a realist attitude towards a theoretical representation seems clearly warranted, such as the astrophysical representation of the sun as a sphere of hot plasma converting hydrogen into helium, and ask whether such warrant could plausibly extend to the possible world representation of Biden’s possible electoral loss. One higher-order attitude towards theoretical representations in philosophy is to regard them under a realist attitude by default. Call this default inclination to adopt a realist attitude towards theoretical representations in philosophy metaphilosophical realism. It is a higher-order attitude—an attitude towards attitudes towards theoretical representations in philosophy. Under metaphilosophical realism, a philosophical account ushering in a theoretical representation of X will invariably tell us what X is in the most demanding sense. The situation here is assumed to be not unlike the physical-chemical

xiv Preface representation of gold as atomic element Au, where being Au tells us what gold really is at bottom, what we’ve been speaking of all along in speaking of gold. As against metaphilosophical realism, we have a higher-order attitude we can now call metaphilosophical instrumentalism, which is the attitude I aim to promote in this book. The metaphilosophical instrumentalist will not treat a theoretical representation of X within some putative philosophical explanation, however successful, as revealing the nature of X by default. According to this stance, an instrumentalist attitude towards theoretical representations in philosophy may be warranted. We are not compelled to regard philosophy’s representations realistically. This higher-order attitude comes in different grades of strength. An extreme version denies that a realist attitude towards theoretical representations in philosophy is ever warranted. A more moderate version leaves room for the possibility of a warranted realist attitude towards some such representations. I have little to say in this book to decide among these alternatives.2 My main efforts are directed at promoting the general outlook and arguing against metaphilosophical realism. My target, metaphilosophical realism, is a prevalent higher-order attitude seldom articulated or discussed in its own right, let alone properly motivated. Evidence for its prevalence within various subfields of philosophy abounds. My alternative outlook is shaped by paying closer attention to cases where theoretical representations in philosophy are best viewed under an instrumentalist attitude. This can be illustrated with respect to first-order theories whose representations have been standardly viewed under a realist interpretation. Take Frege’s logicist program, for example, the topic of Section 1.2. Fregean logicism is a two-pronged effort to show that (i) mathematical truths are logical truths, and (ii) mathematical objects, notably natural numbers, are logical objects. Regarding (ii), Frege clearly thinks of his explicit definitions of the numbers as telling us what the numbers themselves really are at bottom, not unlike the way astrophysics tells us what the sun really is. Setting aside what became of this project in the wake of Russell’s discovery of his eponymous paradox, it is useful to consider Frege’s original theory through an instrumentalist lens. We know that representing the individual numbers in Frege’s way facilitates perspicuous second-order logical proofs of arithmetical claims, as per (i) An instrumentalist attitude towards such representations allows us to pry apart the two prongs of logicism. We can thus regard Fregean representations of the numbers as having explanatory utility other than revealing the nature of the numbers themselves, pace Frege. This particular lesson should be familiar to those who have been following the literature surrounding neo-logicism in the philosophy of mathematics. But in the present context, it can substantiate the sense of attitudinal instrumentalism as a viable option apart from this or that theoretical detail afforded by a first-order theory. Such examination will be undertaken throughout the book regarding various philosophical theories whose representations are best viewed as serving theoretical aims other than revealing the nature of

Preface xv

what they represent individually. Often the instrumentalist pitch will be familiar from the relevant philosophical literature, but it takes on a new significance within the larger methodological context of the book’s overall argument for metaphilosophical instrumentalism. The aim, once again, is to gain insight into philosophy as an explanatory activity by examining firstorder philosophical theories. This will be achieved by viewing those theories through an instrumentalist lens—hence the book’s subtitle, “Studies in Attitudinal Instrumentalism”. Metaphilosophical instrumentalism incurs a special explanatory burden. If certain theoretical representations do not themselves disclose the nature of whatever they represent, how can an entire theoretical system to which they belong succeed in its explanatory aims? The answer, in a nutshell, is that such a system can reveal something important about the nature of an overall subject matter without each of its “moving parts” revealing the nature of what it represents individually. Humdrum cases of such disparity between representational wholes and their parts are common. Think of a plastic model of a molecule, with rods representing chemical bonds connecting plastic spheres representing individual atoms. While the model as a whole can reveal an important structural aspect of whatever it represents, the individual plastic spheres and rods do not. Theoretical representations may reveal the nature of the represented collectively without doing so severally. Nature disclosure can occur at a macro-level for a system of theoretical representations without being achieved at the micro-level, one representation at a time. This is what I aim to make plausible regarding philosophical explanation quite generally. My plan is as follows. Chapter 1 introduces the reader to the general theme of theoretical representations in philosophy and our attitudes towards them via three case studies: numbers, modality, and belief. In each case, I highlight and discuss choice points between a realist and an instrumentalist attitude towards theoretical representations. Chapter 2 offers a framework for deciding when a realist attitude towards a theoretical representation is warranted and concludes that the representations deployed in the case studies examined in Chapter 1 fail the proposed test. It is further observed that those representations have a distinctly semantic origin despite being deployed outside semantics. For example, the semantic apparatus of truth at an index for a sentence φa representing the semantic significance of φa in the language of quantified modal logic ends up being deployed with minimal modifications to represent what it is for a to possibly φ within the metaphysics of modality. Observing this explanatory migration (so to speak) of the representation from the semantics of modal discourse to the metaphysics of modality solidifies the overall sense that the representation should be regarded under an instrumentalist attitude within the extra-semantic explanatory context. The latter context just isn’t the context for which the representation was initially devised. How likely is

xvi Preface it, then, that such a representation should reveal the nature of what it represents outside the original theoretical context? After discussing the matter as it plays out in recent discussions surrounding necessitism in the metaphysics of modality, I turn to examine the diachronic background of the common tendency to utilize theoretical representations from semantics within extrasemantic contexts. This also raises a separate question of which attitude we should adopt towards theoretical representations deployed within semantics proper. Chapter 3 discusses the latter issue and illustrates the attractiveness of attitudinal instrumentalism in several areas of semantic concern. Illustrating attitudinal instrumentalism in semantics as a live option opens up lines of inquiry into the utility of semantic theoretical representations in light of what we initially set out to explain. Chapter 4 considers an instrumentalist attitude towards theoretical representations in semantics as a neglected option for a more nuanced appreciation of the bearing of formal semantics on the phenomenology of meaning in natural language. The latter is often emphasized by the champions of ordinary language philosophy, notably Wittgenstein and Austin, and is often assumed, notably by Strawson, to evade the applicability of formal methods. But it can be shown that an instrumentalist attitude towards formal semantic representations is compatible with Wittgenstein’s critique of extant semantic doctrines due to Russell and Frege. Such an attitude is also especially useful in drawing a distinction in explanatory scope between semantics and Austinian speech act theory. Chapter 5 turns to the metaphysics of what is said and makes a case for an instrumentalist attitude towards structured propositions as representations of what is said. This additional case study also highlights the implications of paradox on theory construction by examining the notorious RussellMyhill paradox of propositions, which provides an extra boost for adopting an instrumentalist attitude towards structured propositions as theoretical representations of what is said. Chapter 6 looks at the content program in the philosophy of mind and language more generally through an instrumentalist lens. It discusses an under-appreciated legacy of the so-called new theory of reference: the easily overlooked point that contents can play certain theoretical roles within various explanatory settings that do not include revealing the nature of the semantic significance they represent. The discussion then turns to the metaphysics of attitudes under the Representational Theory of Mind. In the debate between intentional realists and their critics, the option of treating the representations of cognitive attitudes as relations to mental representations under attitudinal instrumentalism is easily overlooked. This option permits the acknowledgment of the critics’ charge of overreaching empirically— directed at those like Fodor who regard such representations of cognitive attitudes under a realist attitude—without discarding mental representations altogether from the metaphysics of mind.

Preface xvii

Chapter 7, the final chapter, applies the framework of the book to the problematics of rule-following. Rules of conduct are representations of behavior as patterned in certain ways. They may be offered either from the standpoint of an outside observer or from the standpoint of the agent, to herself or to another, for various purposes. The issue raised by Kripke’s (1982) famous discussion of Wittgenstein on rule-following can be shown to be resolved once we view arithmetical rules as representations of arithmetical behavior. Furthermore, there is no reason to suppose that representing rule-following behavior with rules discloses what the represented behavior really is at bottom. The rules representing rule-following practices are not entrusted to do this. And thinking of rules of conduct as representations of behavior dissolves yet another worry about rules that emerges from Lewis Carroll’s parable “What the Tortoise Said to Achilles” (1895). The latter worry is shown to presuppose the misbegotten notion that a rule for inferring is actually operative in the agent’s rule-governed inferential activity, which it is not. The main argument of the book can be appreciated from a variety of perspectives and backgrounds in philosophy. The book proceeds, however, via specific case studies that draw heavily on work and methodology at the core of the analytic tradition in philosophy. Consequently, some portions of the book can be more technically challenging than some readers would like them to be. Technically challenging sections of the book are marked with an asterisk and may be skipped over by those who are not interested in the technicalities. The title of Hilary Putnam’s Realism With a Human Face is meant to evoke— so we are told by James Conant, the book’s editor—the slogan “Socialism with a Human Face”, which is due, in turn, to the 1968 Prague Spring leader Alexander Dubček. Dubček’s slogan expressed a call for a renewal of socialism in light of the fact that the original aspirations of the doctrine have been undermined by its subsequent implementation in Czechoslovakia. Putnam’s corresponding idea of a realism with a human face was meant to capture a parallel call for a renewal of realism in light of the fact that the original aim of the doctrine to secure objectivity for human knowledge has been undermined by the doctrine’s eventual implementation.3 Putnam’s call for a renewal of realism can be viewed as a withdrawal in aspiration, a theoretical humility that sets its target at human eye level. Rather than aspire to establish objectivity for human knowledge from outside knowledge, as is the wont of traditional realism according to one familiar narrative, a realism with a human face aspires to establish objectivity for knowledge from within what we already know about the world and our place in it. It is a programmatic self-reflexive notion reminiscent of the Quinean procedure of naturalized epistemology—the description from within the language of science of how the creatures we happen to be can have contrived the very language within which we are attempting this very description—but with

xviii Preface special emphasis on the question of realism and without Quine’s reductive naturalism. My overall concern in this book is to contribute to what might be characterized, echoing Putnam, as a philosophy with a human face. Putnam’s original target was metaphysical realism, an insistence on mind independence for the truthmakers of our theories. My focus, by contrast, is not on any particular thematic motif in metaphysics but on the line of inquiry itself and, more generally, on the subject to which it belongs. Under a familiar self-conception, philosophy offers theories about the nature of reality in its fundamental aspects. By attending to philosophical explanation as a species of explanation, we can ask how philosophy fares as an explanatory enterprise. We can regard this or that detail of a given philosophical doctrine—and swaths of the doctrine more generally—as theoretical representations at the service of specific explanatory aims. Rather than develop an abstract theory of philosophical theorizing, a “philosophy of philosophy”, which is then applied to first-order cases, my general approach to metaphilosophical theorizing is analogous to Penelope Maddy’s (2007) vision of Second Philosophy. The Second Philosopher theorizes from within our overall theory of the world and our place in it. The methodologist, in my sense (the Second Metaphilosopher?), is guided by general reflection on first-order inquiry of any sort, taking philosophical theorizing as continuous with the rest of our overall theoretical engagement with the world around us and our place in it. Attending to metaphilosophical matters in this way can make a meaningful and timely contribution to our self-understanding as practitioners of philosophical theorizing. Lofty aspirations aside, philosophical explanation can and should be brought down to earth to answer our very real explanatory needs.4 This book is meant as a contribution to this overall effort.

Notes 1. For a useful recent survey, see Frigg and Nguyen (2016). 2. The extreme version of the position does seem doubtful, however. In saying that a realist attitude towards theoretical representations in philosophy is never justified, the extreme instrumentalist is either expressing the conviction that a realist attitude towards theoretical representations as such is never justified, or else presupposing the existence of a criterion for distinguishing philosophical explanation from other forms of explanation. Neither option seems very attractive. 3. See Putnam (1990: xv-xvii). 4. “[T]he inquiry must be turned around, but on the pivot of our real need” (Wittgenstein 2009: §108).

Acknowledgments

This book has been in the works for over six years. It is a pleasure to thank all those who helped me along the way—there are so many to thank! I hope I don’t omit anyone deserving of acknowledgment. Given the panoramic nature of the project and how long it has taken me, some omissions are probably inevitable, for which I apologize in advance. I completed the book during a sabbatical leave at the wonderful Institut Jean Nicod (IJN) in Paris. For their hospitality, collegiality, and friendship, I am especially indebted to Denis Bueller, Paul Egré, Natalie Evin, Pierre Jacob, François Recanati, and Frederique de Vignemont. During my stay at IJN, I also had the great good fortune of interacting with Frances Egan, Robert Matthews, Friederike Moltmann, and Gideon Rosen, who further influenced my thinking on some of the issues discussed here and for which I am very grateful. I would also like to thank the following individuals for their input on various aspects of the book, in one form or another: Roberta Ballarin, Avner Baz, Robin Bianchi, Philipp Blum, Simon-Pierre Chevarie-Cossette, Jordan Dopkins, Catarina Dutilh Novaes, Pascal Engel, Adam Frank, Naama Friedmann, Jade Hadley, Andrea Iacona, David Kashtan, Aviv Keren, Kathrin Koslicki, Samantha Matherne, Graham Moore, Adam Morton, Adam Murray, Nico Orlandi, Carl Posy, Diana Raffman, Gurpreet Rattan, Paul Roth, Gil Sagi, Abe Stone, Chris Tillman, Ewan Townshend, Charles Travis, Alberto Voltolini, and John Woods. Portions of the book were presented to various audiences over the past six years. I’d like to thank audiences at the Hebrew University of Jerusalem, at UC Santa Cruz, at the Cukier-Goldstein-Goren Center for Mind, Cognition, and Language at Tel Aviv University, at the Mind, Language, and Action Group at the University of Porto, at the University of Turin, at the 4th Annual TiLPS History of Analytic Philosophy Workshop at Tilburg University, at the University of Neuchâtel, and at the Logic4Peace conference at the University of Amsterdam. Anonymous readers offered me generous feedback, for which I am very grateful—the book is certainly better for their input. And I am especially grateful for the support and advice of Andrew Weckenmann, my editor at Routledge, who was a pleasure to work with from start to finish.

xx Acknowledgments Work for the book received generous support from the Social Sciences and Humanities Research Council of Canada (“Conflating Representation and Represented”, Insight Grant 435–2017–0133). Some of the material appeared in the form of standalone articles and chapters: • • • • • • •

“Instrumentalism About Structured Propositions”, in Adam Murray and Chris Tillman (eds.), The Routledge Handbook of Propositions (New York: Routledge, 2022): 90-99. “‘The bang was not as loud as I had expected’”, Philosophical Investigations 45(2022): 161–174. “The Content Program Through an Instrumentalist Lens”, Synthese 199(2021): 14599–14615. “On Performatives Being Statements Too”, Thought 10(2021): 275–281. “Modeling Truth for Semantics”, Analytic Philosophy 61(2020): 28–36. “Realism and Instrumentalism in Philosophical Explanation”, Metaphysics 2(2019): 1–15. “The Hierarchy of Fregean Senses”, Thought 7(2018): 255–261.

Finally, my loving gratitude to Shelly Rosenblum, Lila Simchen, and Milo Simchen is beyond measure. This isn’t the occasion—echoing Elizabeth Barrett Browning—to count the ways.

1

Philosophical Explanation

1.1 Realist vs. Instrumentalist Attitude Any theoretical endeavor employs representations, and philosophy is no exception. A representation for present purposes is a theoretical apparatus that stands for some subject matter within a purported explanation. So a representation in the relevant sense is, before all else, an explanatory tool. This is obviously very rough, but it helps delineate our topic and distinguish it from neighboring topics in the philosophy of mind and language. ‘Representation’ as used here applies to a plethora of explanatory devices; ‘represent’ to a plethora of explanatory activities. We do not delve into individuation conditions for theoretical representations here, leaving the matter deliberately open-ended. We assume that we represent things within our theories and that what ensues are theoretical representations of those things. We do not delve into individuation conditions for theories either. For present purposes, bits of theory doing explanatory work within a broader theoretical setting count as theoretical representations. The models of a particular model theory, for example, are representations in the relevant sense in their deployment in the course of explaining matters of interpretability for formal theories. A formal language for such a theory is itself a representation in the relevant sense in its facility for explaining syntactic properties and relations for a fragment of natural language. And the model theory for such a formal language, representing as it does word-world relations and such emergent properties and relations as truth and entailment, is a representation in the intended sense as well. Given such heterogeneity, we do well to settle for the rough characterization. For present purposes, we stay clear of the general matter of what confers representationality on representations.1 Our rough characterization is broadly functional. We regard theoretical representations either as revealing the nature of the represented themselves or else as representing the represented for other theoretical purposes without the added individual revelatory aspect. For lack of better terminology, we call the first way of regarding a representation realist and the second way instrumentalist. And we qualify ‘instrumentalism’ and ‘realism’ with ‘attitudinal’, as in ‘attitudinal realism’ and ‘attitudinal DOI: 10.4324/9781003306443-1

2 Philosophical Explanation instrumentalism’, to mark the point that our concern is with a type of attitude towards theoretical representations. This should go some way towards distinguishing the present terminology from the familiar terminology deployed in the classical philosophy of science dispute between those who regard terms for unobservables as standing for something and those who regard those terms as not standing for anything but as having some other utility within the overall theoretical context. Traditional instrumentalism is a position that concerns claims about unobservables. Very roughly, the traditional instrumentalist holds that terms for unobservables do not stand for anything because there are no such things to stand for. In other words, terms for unobservables are not representational. For example, a traditional instrumentalist about mental phenomena holds that the terms that purport to refer to such phenomena do not because, strictly speaking, there are no such things—terms for mental states and episodes do not really represent. In contra-distinction to traditional instrumentalism, attitudinal instrumentalism is an attitude towards theoretical representations according to which said representations do not themselves reveal—individually, as it were—what the represented items really are. An instrumentalist attitude, in the sense relevant to this book, presupposes that relevant theoretical representations, at least within non-superseded theories, do, in fact, represent. How they manage to do so lies, once again, outside our present concern. A clear case of attitudinal realism is the way we regard the representation of gold as a transition metal within physical chemistry. The substance is thus represented under a widespread realist attitude towards the representation: being a transition metal is part of what it is to be gold.2 It figures prominently in our account of the nature of the substance. A clear case of attitudinal instrumentalism is the way we regard the representation of gold as a standard for pre-20th-century monetary systems in economics. The substance is thus represented theoretically under a widespread instrumentalist attitude: being a standard for pre-20th-century monetary systems is not part of what it is to be gold but is nevertheless instrumental to the explanation of gold’s economic significance. Even if being a monetary standard plays a crucial role in revealing something important about the nature of the economy, it is not presumed to reveal something important about the nature of the represented substance. Again, being a standard for pre-20th-century monetary systems can represent gold theoretically, even if it doesn’t disclose the nature of the represented substance. Or so claims the instrumentalist in the relevant sense—the attitudinal instrumentalist—and common sense clearly agrees. Attitudinal realism and attitudinal instrumentalism are attitudes towards individual theoretical representations of whatever size, however they are ultimately individuated. They might concern a whole swath of theory as a special case. We might take a realist attitude towards a swath of economic theory representing a certain social arrangement. This theoretical capture might include the representation of gold as a monetary standard, which we

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regard under an instrumentalist attitude. In other words, the broader swath of theory might be regarded as revealing the nature of what it represents without the implicated representation of gold being regarded as revealing the nature of what it represents. This is analogous to the toy example mentioned in the Preface of a plastic model of connected spheres and rods representing the molecular nature of a substance without the spheres and rods themselves revealing the natures of the represented atoms and chemical bonds. The question of realist vs. instrumentalist attitude can be raised for representations wielded within various philosophical explanations as well. Philosophical explanation is often taken to reveal the nature of whatever falls within its purview, so it would seem that a realist attitude towards its representations is a natural default. My main aim in this chapter and the next is to offer reasons for doubting that such a default realist attitude is adequate, reasons that emerge from attending to several case studies of philosophical explanation pertaining to numbers, de re modality, and belief, and drawing a general metaphilosophical lesson from the foregoing. The emphasis here is on ‘default’. The upshot of the discussion is not meant to be that philosophical explanation is not, after all, in the business of uncovering the nature of things; it is rather that many familiar representations wielded within philosophical explanation should not be taken individually to reveal the nature of whatever they represent and the advantages of treating them otherwise. The question of realist vs. instrumentalist attitude towards theoretical representations demands that we regard the representations apart from what they represent. There is a special difficulty distinguishing representation and represented within various philosophical theories, a difficulty bred by the abstractness of the various subject matters of philosophical reflection inter alia. Much of this chapter will be taken up by prying apart representations and represented in several areas of philosophical pursuit, illustrating realist vs. instrumentalist choice points along the way. As will emerge, the representations deployed within the case studies of this chapter all have a distinctly logico-semantic origin. The significance of this will be brought out in the ensuing discussion of when a realist attitude towards theoretical representations is justified in the following chapter. I will argue that in none of the cases discussed is a realist attitude warranted despite the clear presence of realist purport. This has broader implications for philosophical explanation that will be explored throughout the book. A word of caution before we proceed with the case studies themselves. The history of modern philosophy is filled with debates surrounding realism. If history is to be our guide, there are good reasons to remain pessimistic when it comes to whether the question of realism can be resolved effectively via some a priori considerations. It seems unlikely that some powerful new such consideration is in the offing to resolve the matter once and for all. A promising way out is to change the terms of the discussion surrounding realism. First, rather than asking directly whether a realist thesis is true for a given factual domain, we consider whether a realist attitude towards a bit

4 Philosophical Explanation of theory concerning the domain is warranted, keeping in mind cases for which there is widespread de facto agreement. Second, and relatedly, cases for which there is widespread de facto agreement on a realist attitude provide a useful point of comparison when it comes to whether such an attitude is warranted in more controversial cases. Third, and finally, in keeping with a general avoidance of a priori considerations pertaining to the broad question of realism, the main issue of whether a realist attitude towards theoretical representations in philosophy is warranted will be approached piecemeal via case studies. In this chapter and the next we will find reasons to doubt that such representations should be taken in a realistic spirit by default. This will be achieved by examining specific cases of philosophical explanation that are both central enough to the overall enterprise and yet distant enough from one another per topic to be usefully representative.

*1.2 Case Study 1: Frege on Number We begin with what Dummett (1993) characterizes as the original site of the linguistic turn in philosophy: Frege’s ingenious construction of the natural numbers within his second-order logic as equivalence classes of first-level concepts under the relation of equinumerosity.3 In a nutshell, Fregean concepts are the semantic values of predicates. A first-level concept is a function from objects to truth-values, a second-level concept is a function from firstlevel concepts to truth-values, and so on. Equinumerosity is a second-level relational concept mapping first-level concepts φ and ψ to truth just in case there is a bijection between the φs and the ψs,4 otherwise mapping them to falsity. A number n is construed as the extension of the second-level concept equinumerous with φ, where φ is a first-level concept with an n-membered extension.5 Such is Frege’s basic construction. We now consider two distinct attitudes towards it. First, in keeping with Frege’s original attitude, we might say, ambitiously, that the extension of the second-level concept equinumerous with x ≠ x (call it 0) is what the number zero turns out to be, the extension of equinumerous with x = 0 (call it 1) is what the number one turns out to be, the extension of equinumerous with x = 0  x = 1 (call it 2) is what the number two turns out to be, and so on. With this approach, the extension of any of these secondlevel concepts reveals what the relevant natural number really is at bottom.6 As the original proposal faces well-known problems, it is consonant with the present attitude to find fixes that would salvage as much of the original idea as possible and maintain that the patched-up version does a better job at identifying what the numbers really are. Once the fixes are found, we can say what sort of things numbers are, much like water being hydrogen hydroxide or gold being the element with atomic number 79. So maintains the proponent of a realist attitude towards Frege’s original construction. There can be little doubt that Frege’s own attitude towards his construction was realist in our sense. This may initially seem difficult to maintain in

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light of certain things Frege says about definitions that would appear to make his definitions ill-suited to reveal the nature of the numbers. The definition of the number zero as the extension of the second-level concept equinumerous with x ≠ x, for example, is officially offered as laying down the meaning of the numeral ‘0’, laying bare the significance of that sign that presumably was previously implicit.7 But consider the numerical fact that zero is immediately followed by one in the number series. This fact for Frege is the fact that for some first-level concept φ and some object y, y is φ and φ is in the extension of the second-level concept equinumerous with x = 0 while the first-level concept φ-other-than-y is in the extension of the second-level concept equinumerous with x ≠ x. This depends on the explicit definitions of the individual numbers. Once we attend to such matters of dependence, it is difficult to avoid the conclusion that representing zero as the extension of equinumerous with x ≠ x reveals the nature of the number itself—it is what enables the obtaining of the posterior arithmetical facts concerning zero, including the fact that zero is immediately followed by one in the number series.8 Indeed, such facts of dependence make it implausible that Frege could think of his explicit definitions of the individual numbers as anything but revelatory of the nature of the numbers themselves. Further support for the claim that these explicit definitions of the numbers are taken by Frege to reveal the nature of the numbers individually is provided by the observation that the constructions predate the celebrated sense/reference distinction. The definitions are supposed to specify the undifferentiated content (Inhalt) of the numerals, which is both the significance of the numerals and what they stand for. Frege’s attitude towards these constructions thus seems clearly realist in our sense. Turning a familiar Quinean quip on its head, we see here that essence (of the number zero, say) is what meaning (of the numeral ‘0’) becomes when it is divorced from the word and wedded to the object of reference.9 Be that as it may, and putting Frege’s realist predilections to one side, we might say, more cautiously and out of step with Frege’s attitude, that 0 represents the number zero, 1 represents the number one, 2 represents the number two, etc.—all as part of an overall effort to show that arithmetic need not avail itself of any mathematical means beyond second-order logic. With such an approach, the extensions of the second-level concepts represent the natural numbers for a broader explanatory purpose. But like the representation of gold as the standard for pre-20th-century monetary systems in economics, they are not themselves presumed to reveal the nature of the numbers. Each of these attitudes towards Frege’s construction, the realist and the instrumentalist, has something going for it. We need not rehearse the benefits of attitudinal realism here—the grand aspirations of logicism speak for themselves and have had a momentous impact on subsequent philosophy. But the instrumentalist attitude can, while the realist attitude cannot, straightforwardly accommodate firm intuitive verdicts that both lay people and working mathematicians pass on the numbers, routine verdicts that are

6 Philosophical Explanation at odds with basic features of Frege’s construction taken realistically. For example, when we ascribe the number seventeen to a collection of things, we think of the collection as, in some sense, having this numerical attribute, of seventeen belonging to the collection or being in some sense in the collection as a whole. But on the Fregean construal taken realistically, it would be more apt to say that the collection—or rather the characteristic function of the set associated with it, the first-level concept—belongs to 17 rather than the other way around (in a different sense of ‘belong’, of course). According to an instrumentalist attitude, 17 represents the number seventeen but isn’t expected to reveal the nature of what it represents. That the characteristic function of the set of seventeen things “belongs” to 17 is an “artifact of the model” in Kaplan’s (1975) sense: When we construct a model of something, we must distinguish those features of the model which represent features of that which we model, from those features which are intrinsic to the model and play no representational role. The latter are artifacts of the model. For example, if we use string to make a model of a polygon, the shape of the model represents a feature of the polygon, and the size of the model may or may not represent a feature of the polygon, but the thickness and threedimensionality of the string is certainly an artifact of the model. (722) In short, Frege’s 17 is one thing, and the number seventeen is another—all in good Butlerian fashion.10 In the foregoing discussion, we ignored the issue of paradox that famously besets Frege’s logicism. We might, in fact, view the neo-logicist reaction to Russell’s paradox as an instrumentalist wrinkle in Frege’s overall project.11 The neo-logicist discards Frege’s Basic Law V, the offending principle that permits the derivation of unrestricted comprehension and leads to contradiction. Where ‘#(φx)’ abbreviates ‘the number of φs’ and the meaning of ‘#’ is given contextually by the relevant version of Hume’s Principle, we can regard #(x ≠ x) and #(x = 0) under an instrumentalist attitude as representing zero and one for broader theoretical aims such as establishing the logicality of 1 = S(0).12 Adopting an instrumentalist attitude towards such representations of the numbers in establishing the logicality of arithmetic comports with the research program of neo-logicism.

1.3 Case Study 2: De Re Modality A second illustration of the choice between realist and instrumentalist attitudes towards theoretical representations within philosophical explanation emerges from debates of the 1960s and 1970s surrounding the metaphysics of modality. Earlier on, in the 1950s and 1960s, logicians were developing model theories for systems of first-order quantification plus non-extensional

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operators. The basic insight in the logic of modality originated from early observations that, logically speaking, ‘possibly’ and ‘necessarily’ are duals, much like ‘some’ and ‘all’. Just as  is definable as ¬¬ or  as ¬¬, the diamond of possibility and the box of necessity are interdefinable:  as ¬¬ or  as ¬¬. This structural commonality suggested that  and  are specialized quantifiers. An index set was provided for them to range over: a set of ‘possible worlds’. p is true just in case for some possible world w, p is true at w; p is true just in case for every possible world w, p is true at w. The importance of this semantic idea for the subsequent metaphysics of modality is difficult to exaggerate. Much of the contemporary metaphysical engagement with possibility, necessity, and cognate notions (impossibility, contingency, actuality, etc.) is unfathomable without the precedent set by this basic semantic notion. It is not feasible to offer a comprehensive survey of the various ramifications of the possible world semantic apparatus for the metaphysics of modality. We focus instead on a single aspect: the quantified modal logical capture of de re modality. Sidestepping technical details, the syntactic contrast between the constructions xφx and xφx standardly receives the following treatment in the possible world semantics for quantified modal logic: xφx is true just in case for some possible world w, some individual in the domain of w is a member of the extension of φ in w; xφx is true just in case for some actual individual and some possible world w, the individual in question is a member of the extension of φ in w. The former construal may or may not require for its truth a non-actual individual φ-ing in some w.13 But our present focus is on the latter: What does it mean to say of some actual individual, say an individual who happens not to φ, that for some possible world w, that very individual is a member of the extension of φ in w? What does the identification of an individual in another possible world amount to? Take Kripke’s (1980) example of losing the 1968 US presidential election. Someone, Nixon, lacks the property—Nixon actually won the 1968 election—but might have had it—the 1968 election was a close one. So we have x(¬φx  φx), and the entailed xφx is made true by Nixon, the actual winner, losing in a counterfactual situation. But how can this be? Nixon actually lacks φ but has φ in the counterfactual situation, we are told, so by the indiscernibility of identicals, the actual Nixon is distinct from the counterfactual Nixon. And yet did we not just say that Nixon himself, despite not φ-ing, might have φ-ed? Thus goes the problem of transworld identity.14 Let us consider two different general attitudes towards the possible world representation of the de re modal fact that Nixon might have lost, a realist attitude and an instrumentalist attitude—call them A and B, respectively. Attitude A takes the possible world construal of the de re modal fact that Nixon might have lost the 1968 election to reveal the nature of the modal fact in question.15 For there to be a possible world where Nixon loses is what it is for Nixon to possibly lose. According to this attitude, the problem of

8 Philosophical Explanation transworld identity poses a genuine metaphysical puzzle demanding resolution. If inhabiting a world where he loses is what Nixon’s possible loss really amounts to, then we need to explain how his apparent transworld existence does not violate the indiscernibility of identicals. And here, there are two broad strategies to consider. The first emanates from the observation that the problem arises from the monadic character of properties the having of which needs to be relativized to worlds. On this first approach, while the property of losing the 1968 election is monadic when considered on its own, for Nixon to have the property in the counterfactual situation is for Nixon to bear the dyadic relation x-losing-in-w to the world in question. Correlatively, for Nixon to lack the property in actuality is for Nixon to fail to bear this relation to the actual world. That Nixon has the property in w and lacks it in actuality no longer speaks to the distinctness of the counterfactual Nixon and the actual Nixon, any more than my being at rest relative to the floor and in motion relative to the earth’s axis speaks to my self-distinctness. And here, once again, we can adopt two distinct attitudes towards the proposal, call them subsidiary attitudes A1 and A2. According to the realist subsidiary attitude A1, for Nixon to bear the dyadic relation to the counterfactual situation is just what it is for Nixon to have the property of losing in that situation. This is what having a monadic property in a world turns out to be upon closer theoretical scrutiny—a dyadic relation to a world. But according to the instrumentalist subsidiary attitude A2, Nixon bearing or failing to bear the x-losing-in-w relation to a world merely represents what it is for the property of losing to be itself monadic when considered on its own while for something to have it or not to have it is relativized to a world. (One might, for example, suppose on independent grounds that the relata of relations in re are particulars and deny that possible worlds are such.) According to this second attitude A2, the dyadic relation is not what the instantiation of the monadic property of losing in w really amounts to—it merely represents monadic instantiation in w for the broader theoretical purpose of capturing de re modal predication.16 Now, if we ignore the instrumentalist option encapsulated in A2 and focus only on realist subsidiary attitude A1, we might recoil from the present suggestion once the monadic properties under consideration seem sufficiently intrinsic. This gives rise to a second strategy for meeting the problem of transworld identity. Consider Lewis’s (1986) example of a five-fingered hand being possibly six-fingered. The present approach under attitude A1 would render the unactualized possibility of being six-fingered for the actually fivefingered hand to turn out to be a matter of the hand being related to a counterfactual situation. But being six-fingered seems intrinsic enough that it can seem perniciously revisionary to maintain that for the hand to have this property in a possible world is for the hand to bear a relation to the world in question. Having such a property is a matter intrinsic to the thing having it. Famously, the Lewisian recoil from the present approach—considered again under attitude A1—is to maintain that for the actually five-fingered

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hand to be possibly six-fingered is for the hand to have a six-fingered counterpart in another possible world. By extension, for Nixon to possibly lose the 1968 election despite actually winning is for Nixon to have a counterpart in another possible world who loses. Under this solution to the problem of transworld identity, any individual in any possible world is world-bound. Nixon himself inhabits one and only one world: the actual world. Unactualized possible properties for Nixon are construed as the having of those properties by Nixon’s counterparts in other possible worlds.17 And here, once again, we might consider two different attitudes towards the Lewisian proposal, a realist subsidiary attitude A3 and an instrumentalist subsidiary attitude A4. According to A3, for the actuality-bound Nixon to possibly have the property of losing the 1968 election just is for a counterpart of Nixon, Nixon, to have the property in the counterfactual situation to which Nixon is bound. This is what it is for an individual to possibly have a property lacked in actuality upon closer theoretical scrutiny. According to subsidiary instrumentalist attitude A4, by contrast, the account of Nixon’s possible loss in terms of Nixon losing represents how the actuality-bound Nixon can have the property in another possible world (“in absentia”, so to speak18). Nixon, while flesh and blood (we suppose), is a representation of Nixon within the overall explanation of the fact that Nixon satisfies the property of losing the 1968 election in absentia. Nixon losing is not itself expected to reveal the nature of Nixon’s possible loss. So much for general attitude A towards the possible world construal of de re modality and the concomitant problem of transworld identity. This general attitude is a realist attitude that considers a possible world portrayal of Nixon’s possible loss as what the relevant modal fact turns out to be upon closer theoretical scrutiny. But we saw that even under the auspices of realist attitude A, there might still be room for instrumentalist subsidiary attitudes A2 and A4, local attitudinal instrumentalisms under a more general realist attitudinal umbrella. An alternative general attitude towards the possible world construal of de re modality, attitude B, is thoroughly instrumentalist. The possible world construal is meant to represent the fact that Nixon might have lost despite actually winning. But it is not as though what it is for the de re modal fact to obtain just is for there to be a possible world according to which Nixon loses. The possible world construal plays a certain role within an overall explanation of how actual things might have had properties they do not, in fact, possess.19 The explanatory utility of possible worlds for the modal metaphysician easily outstrips the value of identifying modal facts with their possible world surrogates. The possible worlds apparatus helps represent in a more holistic manner how possibilities are connected with one another—how, say, Nixon’s possible loss is connected with Humphrey’s possible win—and how possibilities are connected with facts about actuality with certain modal implications—how, say, Nixon’s possible loss is connected with the fact that the 1968 election was fair. Such explanatory tasks

10 Philosophical Explanation can be met without treating the representation of Nixon’s possible electoral loss in terms of possible worlds as revealing the underlying nature of the fact in question, as a realist about the possible world portrayal would have it. Pace attitudinal realism, possible worlds can play a useful modeling role without telling us with regard to each modal fact what makes it the fact that it is. What makes each such fact the fact that it is need not have anything to do with possible worlds.20

1.4 Case Study 3: Indirect Reference A third illustration of the choice between realist and instrumentalist attitudes towards theoretical representations within philosophical explanation is provided by a central tenet of Frege’s philosophy of language: the theory of indirect reference. Here a default realist attitude has had far-reaching implications for the metaphysics of mind. I will return to this theory in more detail in Section 3.3 below. Very briefly, Frege’s theory of sense and reference offers a two-tiered account of semantic significance in response to a perceived need for semantic analysis to explain our epistemic rapport with linguistic expressions alongside other familiar explananda, such as productivity. If we take the contributions of subsentential expressions to the semantic significance of whole sentences to be exhausted by whatever the subsentential expressions refer to, then under commonplace assumptions, a true sentence of the form a = b will seem to have the very same semantic significance as a correlative sentence of the form a = a. And yet our epistemic rapport with sentences of the form a = b can differ greatly from our epistemic rapport with correlative sentences of the form a = a.21 Frege’s well-known response to this observation—bred by the conviction that it falls within the purview of a semantic analysis to explain our epistemic rapport with linguistic expressions—is to associate semantically significant units not only with a reference but also with a sense, a “mode of presentation”, of the reference. So while a and b are co-referential, as demanded by the truth of a sentence of the form a = b, they may be associated with distinct senses. And so, the overall semantic significance of a true sentence of the form a = b may be different from that of a correlative sentence of the form a = a. Frege’s term for the senses expressed by whole sentences, which are composed of the senses of the subsentential expressions, is Gedanken—“thoughts”. They are the objects of our intellectual grasp and the modes of presentation of the things to which our sentences refer, the two truth-values. With the apparatus of sense and reference in hand, we may now consider the theory of indirect reference. The original framework explains how the sentences ‘Danzig is pretty’ and ‘Gdansk is pretty’ might differ in overall semantic significance despite the co-referentiality of the names ‘Danzig’ and ‘Gdansk’. This might explain how Hilary can hold the sentence ‘Danzig is

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pretty’ to be true while failing to hold the sentence ‘Gdansk is pretty’ to be true.22 The explanation is that ‘Danzig’ and ‘Gdansk’ express different senses; so the whole thoughts expressed by ‘Danzig is pretty’ and ‘Gdansk is pretty’ are different; and so, Hilary can believe that Danzig is pretty without believing that Gdansk is pretty. It is this last move that merits further scrutiny. According to Frege’s theory of indirect reference, while the sentences ‘Danzig is pretty’ and ‘Gdansk is pretty’ are true or false together, the sentences ‘Hilary believes that Danzig is pretty’ and ‘Hilary believes that Gdansk is pretty’ can easily diverge in truth-value. What determines that the first belief report is true while the second is false are facts surrounding Hilary’s beliefs. Here is the situation according to the proposed semantics. Begin with the simple sentences ‘Danzig is pretty’ and ‘Gdansk is pretty’. ‘Danzig’ refers to a certain city, and ‘is pretty’ refers to a first-level concept A(x) that maps pretty objects to truth and maps other objects to falsity. The sentence ‘Danzig is pretty’ is true to the extent that the city as an argument for the concept A(x) yields truth as a value. Assuming that ‘Gdansk’ refers to the same object as ‘Danzig’, the second sentence is true to the same extent as the first. But the sentences differ in the thoughts they express to the extent that ‘Danzig’ and ‘Gdansk’ differ in the senses they express, modes of presentation of one and the same city. Now consider the belief report ‘Hilary believes that Danzig is pretty’. The name ‘Hilary’ refers to Hilary and expresses a suitable sense, a mode of presentation of the man. But the name ‘Danzig’ within the clausal complement of the belief report refers not to its ordinary reference, the city, but rather to its “indirect” reference, which is the sense of ‘Danzig’ in the simple sentence ‘Danzig is pretty’, a mode of presentation of the city.23 Similarly, the first-level predicate ‘is pretty’ within the clausal complement of the belief report refers not to its ordinary reference, A(x), but rather to its indirect reference, which is its ordinary sense, i.e., the sense of ‘is pretty’ in the simple sentence ‘Danzig is pretty’, a mode of presentation of the first-level concept. And the sentence ‘Danzig is pretty’ as the clausal complement of the belief report refers not to its ordinary reference, the truth-value, but to its indirect reference, which is its ordinary sense, i.e., the thought that Danzig is pretty, a mode of presentation of the truth-value. Accordingly, the dyadic predicate ‘believes’ refers to a dyadic relational concept B(x, y) that maps believers and thoughts believed to truth or falsity. It is thus that the sentence ‘Hilary believes that Danzig is pretty’ can be true while the sentence ‘Hilary believes that Gdansk is pretty’ is false. While ‘Danzig’ and ‘Gdansk’ are co-referential in the true identity ‘Danzig is Gdansk’, ‘Danzig’ in the first belief report need not be co-referential with ‘Gdansk’ in the second belief report. The first report truly relates Hilary to the thought that Danzig is pretty. The second falsely relates Hilary to the thought that Gdansk is pretty. Let us now step back from these details and consider the situation afresh. We wanted to explain how it is that Hilary believes that Danzig is pretty while failing to believe that Gdansk is pretty despite Danzig and Gdansk

12 Philosophical Explanation being one and the same city. Semantically ascending, we turned our attention to how it is that ‘Hilary believes that Danzig is pretty’ is true while ‘Hilary believes that Gdansk is pretty’ is false despite the truth of ‘Danzig is Gdansk’. Frege provides a semantic apparatus, the theory of indirect reference, that delivers said result by taking belief reports to relay a relation of belief that believers bear to thoughts believed. The theory offers an elegant semantic treatment of belief reports.24 Semantically descending and going back to the specific case before us, Frege’s semantic analysis represents how Hilary can believe that Danzig is pretty while failing to believe that Gdansk is pretty. The analysis in terms of the belief relation relating the believer to the thought believed is a representation wielded in the explanation of the facts surrounding Hilary’s cognitive situation. But it is all too common to regard this representation realistically as revealing what it is for Hilary to believe what he does. Indeed, the metaphysics of mind has often considered it a datum that cognitive states such as belief—the so-called propositional attitudes—are relations agents bear to the contents of whole declarative sentences (often construed via more direct relations to and from things whose contents are the contents of whole declarative sentences).25 An instrumentalist attitude, on the other hand, regards this as no datum. Relations of agents to the contents of whole declarative sentences are representations adduced for particular explanatory purposes and are not to be regarded as revealing the nature of the cognitive facts themselves. The kind of explanation for which these relations were originally adduced is a semantic account of how the significance of reports of belief and other cognitive attitudes depends on the significance of their parts and their mode of composition. Treating the pronouncements of Frege’s theory of indirect reference realistically within the metaphysics of mind emerges from (a) treating them realistically within a semantic explanation of what it is for belief reports to mean what they do while (b) treating the significance of those reports as revelatory of the nature of the facts of belief themselves. In this way, a semantic analysis of a belief report is taken to reveal the nature of the cognitive fact being reported. An instrumentalist attitude resists this two-step procedure. We note that an instrumentalist attitude, in this case, need not involve any firm conviction that belief and other cognitive states will ultimately not turn out to be relational in the way envisaged by literalizers of Frege’s semantic apparatus of indirect reference. Down the line, there might be substantive empirical reasons in favor of some such relational story. But these are early days of cognitive theorizing. From an instrumentalist standpoint, ready inference from the details of Frege’s semantic apparatus of indirect reference to the reality of the significance of belief reports, and then to the reality of beliefs themselves, is done at our peril. The theory of indirect reference captures what we say when we report beliefs by way of generating truth-conditions for our reports. An instrumentalist attitude would resist reading off of this theory a metaphysics of attitudes.26

Philosophical Explanation 13

1.5 Semantic Descent Working backward from the example of the theory of indirect reference to the previous one, the possible world construal of de re modality exhibits a strikingly similar pattern. A semantic construal of the syntactic construction xφx in the language of quantified modal logic—itself a representation of a fragment of natural language—is regarded realistically in the semantic treatment of the de re modal locution and then taken to reveal the nature of the de re modal fact thus reported. (In the Lewisian version, the nature of the modal fact is revealed by the interpretation of the counterpart-theoretic translation of the quantified modal logic construction.) Our modal discourse discloses the nature of the underlying modal facts through the prism of the formal semantic apparatus of possible worlds. Working backward still, the theme recurs in Frege’s treatment of the numbers as logical objects. Frege’s original construction is also the outcome of a semantics-first procedure. After carefully examining everyday uses of numerical expressions, Frege famously concludes that “the content of a statement of number is an assertion about a concept” (Frege 1953: §46). He then proceeds to contemplate the idea of numerical attributions as structureless second-level predicates—the so-called adjectival strategy—which is subsequently claimed to be vulnerable to insurmountable difficulties.27 Frege then turns his attention to the semantic treatment of sentences of the form ‘The number of φs is the number of ψs’. The numeral ‘four’ is claimed to be a singular term even in such adjectival constructions as ‘The King’s carriage is drawn by four horses’, which means that it refers to an object. The object in question is finally construed as an extension of a certain second-level concept, equinumerous with x = 0  x = 1  x = 2  x = 3, which is itself the reference of the second-level predicate ‘equinumerous with F’ for any firstlevel predicate F that refers to a first-level concept with exactly four objects in its extension. The proposed semantic treatment of numerical discourse is taken to reveal the numerical facts themselves—that for the King’s carriage to be drawn by four horses just is for the first-level concept horse drawing the King’s carriage to be a member of the extension of the second-level concept equinumerous with x = 0  x = 1  x = 2  x = 3. The nature of the numerical fact is thus revealed by the semantics of its report.28 As we saw earlier, Frege’s attitude towards his construction of number is clearly realist in our sense, as is the possible world metaphysician’s attitude towards the possible world capture of de re modality and the Fregean attitude towards the account of cognitive attitudes as relations to Fregean thoughts. In each case, a realist might say that the theory offers a theoretical identification, much like the identification of water as hydrogen hydroxide or gold as the element with atomic number 79. It is gratuitous to suppose that being hydrogen hydroxide only represents water for some broader theoretical purpose or other. Hydrogen hydroxide is what water turns out to be upon closer theoretical scrutiny. Similarly, it is now claimed, horse drawing the

14 Philosophical Explanation King’s carriage being a member of the extension of equinumerous with x = 0  x = 1  x = 2  x = 3 is what the King’s carriage being drawn by four horses turns out to be; Nixon losing the election in another possible world (or the counterpart Nixon* losing that election) is what possible loss for Nixon turns out to be; and Hilary bearing the attitudinal relation to the thought expressed by ‘Danzig is pretty’ while not bearing it to the thought expressed by ‘Gdansk is pretty’ is what Hilary believing Danzig to be pretty while not believing Gdansk to be pretty turns out to be. The instrumentalist, on the other hand, will point to the distinctly semantic origin of the accounts on offer and the distinctive theoretical aims of semantic explanation as compared with philosophical explanations of the facts reported by the relevant factual reports. And so, after getting a feel for the attitudinal contrast at issue, the question naturally arises whether there are general guidelines as to which attitude, realist or instrumentalist, is more apt for a proposed theoretical capture of a target subject matter in a given case.29 This is the issue to which we turn next.

Notes 1. For my considered take on such questions in the philosophy of mind and language, see Simchen (2017). 2. It is also part of what it is to be palladium, part of what it is to be iridium, part of what it is to be silver, etc. 3. The construction is found in Frege’s Grundlagen (1953). Later, in Grundgesetze (2013), Frege defines the numbers as equivalence classes of classes under equinumerosity, but this change has little bearing on our discussion. 4. So just in case ξ(x(φx  !y(ψyξxy))x(ψx  !y(φyξyx))), where !vFv abbreviates v(Fv  u(Fu  u = v)). 5. I use italics for mentioning concepts—a difficult matter broached in Frege (1952) and contemplated ever since—and underlining for the mentioning of concepts within the mentioning of concepts (double concept-quoting, as it were). I mostly set aside well-known problems with logicist reductions, such as the notorious contradiction arising from Frege’s Basic Law V or the violations of the axiom of foundation engendered by the variant proposal that identifies the number n with the class of n-membered classes, even though I do discuss briefly the neo-logicist reaction to the aforementioned contradiction towards the end of this section. 6. For a contrasting reading of Frege that emphasizes a more pragmatic strain in his thinking, see Reck (2007). My present focus is on the more common reading of Frege’s project as endorsed by much of the philosophical tradition it subsequently spawned. 7. “The definition of an object does not, as such, really assert anything about the object, but only lays down the meaning of a symbol. After this has been done, the definition transforms itself into a judgment, which does assert about the object; but now it no longer introduces the object, it is exactly on a level with other assertions made about it” (Frege 1953: §67). 8. The claimed logicality of one immediately following zero in the number series dovetails the logicist construction of zero and one as the logical objects 0 and 1, respectively. The construal Frege (1953: §76) offers of the relation of immediate succession in the number series, n = S(m), is: (S) φy(φy Xˆ (x (Xx, φx)) = n Xˆ (x (Xx, φx x  y)) = m).

Philosophical Explanation 15 (In words: for some first-level concept φ and some object y, n is the number belonging to φ and m the number belonging to φ-other-than-y.) From this definition, together with the explicit definition of zero as the extension of equinumerous with x ≠ x, i.e. Xˆ (x (Xx, x  x)), and of one as the extension of equinumerous with x = 0, i.e. Xˆ (x (Xx, x  0)), it easily follows that 1 = S(0). For Frege (1953: §73) proves what is now known as Hume’s Principle, (HP) Xˆ (x (Xx, φx)) = Xˆ (x (Xx, ψx)) x (φx, ψx). (In words: the extension of equinumerous with φ is identical with the extension of equinumerous with ψ just in case φ and ψ are equinumerous.) He then proves that ≈x (x = 0  x ≠ 0, x ≠ x). From the definitional Xˆ (x (Xx, x  x)) = 0 and (HP) it then follows that Xˆ (x (Xx, x  0 x  0)) = 0. Taking φ as x = 0 and y as 0, the relevant instance of (S) follows immediately from the definitional Xˆ (x (Xx, x  0)) = 1: φy(φy Xˆ (x (Xx, φx)) = 1 Xˆ (x (Xx, φx x ≠ y)) = 0). 9. “Meaning is what essence becomes when it is divorced from the object of reference and wedded to the word” (Quine 1951: 22). 10. “Everything is what it is, and not another thing”—Bishop Butler. 11. See Heck (2011) for a comprehensive assessment of the current state of neo-logicism, a project inspired by Geach (1955) and initially carried out in further detail by Parsons (1965) and Wright (1983). 12. The fundamental move is to treat the following version of Hume’s Principle as an axiom schema: (HPneo)

(φx) = (ψx)  x (φx, ψx).

With suitable adjustments to Frege’s definitions we can then prove the axioms of arithmetic without relying on Basic Law V. To establish 1 = S(0) as in Grundlagen §§76–7 we define immediate succession analogously as (Sneo)

13. 14. 15. 16.

17.

φy(φy (φx)= n (φx x  y) = m)

and proceed as in footnote 8 under the representation of zero as #(x ≠ x) and one as #(x = 0). For example, the proof Frege offers (1953: §75) for the intermediary claim that ≈x (x = 0 x ≠ 0, x ≠ x) nowhere relies on Frege’s explicit definitions of the numbers. (The proof is that, given that no object falls under x = 0  x ≠ 0, and given that no object falls under x ≠ x, every relational concept is such that every object falling under the one is so related to a unique object falling under the other, and vice versa. So some relational concept is such. And so, the concepts are equinumerous.) Much ink has been spilled over cases where φ seems neither instantiated by anything actual nor possibly instantiated by anything actual while xφx seems true. I set this aside for now, but see Section 2.2 for further discussion of the issue. A further development of the issue is the epistemological concern with identifying the individual in the counterfactual situation, which we can set aside. Such an attitude is clearly exhibited in what Plantinga (1976) calls “the canonical conception of possible worlds”. The situation under A2 may thus seem quite different from the situation regarding my being in motion relative to the earth’s axis but at rest relative to the floor. In the latter case it is often supposed, realistically, that the properties of being in motion or being at rest, while apparently monadic, are revealed upon closer theoretical scrutiny to be relations borne to reference frames. Whether or not in this case there is wiggle room for preserving the monadic character of being in motion or being at rest while maintaining relativity as per the formalism of SR is an interesting question that cannot be pursued here. See, however, some preliminary discussion in the next chapter concerning theoretical identifications in natural science. We ignore the further Lewisian emphasis on the inconstancy of counterparthood.

16 Philosophical Explanation 18. See Lewis (1986: 9–10). 19. It might be maintained, for example, that things possibly have just those properties tolerated by what those things are in the most demanding sense—by their natures or essences. See Simchen (2012: Chs. 1–2) for one development of this line of thought. A possible world construal could still act as a heuristic for such an account. 20. Attitude B is exhibited throughout Kripke’s (1980) and leads Kripke to regard the problem of transworld identity as a pseudo-problem engendered by the wrong attitude towards possible worlds. 21. The classic statement of the problem is in the opening paragraph of Frege (1948). 22. In conversation once Hilary Putnam expressed genuine astonishment at the fact that Danzig is Gdansk. Such cognitive dissonance is familiar from Kripke’s (1979) influential discussion of puzzling Pierre. 23. The indirect sense of ‘Danzig’ is the mode of presentation of the indirect reference and is other than the sense of ‘Danzig’ in the simple sentence, but we leave indirect senses aside for now. We return to this matter in more detail in Section 3.3. 24. But we set aside the issue of semantic innocence and its significance for semantic theorizing. Further features of the account qua being a semantic theory will be taken up in Section 3.3. 25. Examples of such an approach abound, including Davies (1991), Lycan (1993), and Rey (1995). See also the discussion of Fodor’s RTM in Section 6.4. 26. We return to this topic at greater detail in Section 6.4. 27. Of particular note here is the so-called Julius Caesar problem. See Heck (2011) for an extensive discussion of the issue. 28. See Steiner (1995) for an interesting discussion of Frege’s methodology in the context of problems of applicability in the philosophy of mathematics. Given my characterization of Frege’s methodology as semantics-first, I disagree with Steiner’s suggestion that Frege solves the metaphysical problem of how applied mathematics is possible. Under Frege’s construal, when all is said and done mathematical applicability boils down to a matter of membership of a referent of a first-level predicate in the extension of a referent of a second-level predicate. This mislocates the problem of how abstracta can apply to worldly concreta as a problem to be solved within the background semantic apparatus. 29. By ‘subject matter’ here and elsewhere I mean the facts or portions thereof portrayed by claims without further commitment to a specific theoretical articulation of the pre-theoretical notion, such as the one offered in Lewis (1988) or the more recent one offered in Yablo (2014). This should be borne in mind for the remainder of the discussion.

2

Justified Attitudinal Realism

2.1 Theoretical Identifications Consider familiar cases of theoretical identification, such as water being hydrogen hydroxide or gold being the chemical element with atomic number 79. Theoretical identifications in natural science provide paradigm examples for when a realist attitude towards a representation is justified. Hydrogen hydroxide is what water really is. Being hydrogen hydroxide is not only a representation of water at the service of a broader theoretical purpose, but it is also what water turns out to be upon closer theoretical scrutiny.1 Something similar may be said of other theoretical characterizations in physical chemistry that are less definite. When we represent water as a chemical compound, for example, or gold as a metal, we are clearly not presuming to reveal the nature of the substance in its entirety. But being a chemical compound and being a metal are clearly parts of what it is to be water and gold, respectively, in the most demanding sense. We regard such representations realistically. This may be contrasted, once again, with gold being represented as a standard for monetary systems within economic explanation. Being such a standard is no part of what gold itself is in the relevant sense. We treat the latter representation as having a theoretical role to play within a broader explanatory context but not as itself revealing the nature of gold individually, so to speak. The question to be tackled in this chapter is when we are justified in adopting a realist attitude towards theoretical representations. We might take for granted such warrant for theoretical identifications in natural science and consider whether we can isolate certain central features of such cases as necessary conditions. This will then provide a template of sorts to hold up against more controversial cases, especially those afforded by philosophical explanation. The present strategy will seem of limited reach from a more traditional mindset on the question of realism, especially given that the ur-concern of truth or falsity for the thesis of realism is not being directly addressed here. For example, there is widespread agreement on a realist attitude when it comes to the representation of water as hydrogen hydroxide within physical chemistry. A traditionalist might insist that this fact by itself is inconsequential DOI: 10.4324/9781003306443-2

18 Justified Attitudinal Realism when it comes to the question of whether water really does have the particular molecular nature alleged by physical chemistry. From the present point of view, however, the fact that being hydrogen hydroxide is revelatory of the true nature of water is on a surer footing than the doubts of the traditionalist on the question of realism. We do well to ask after characteristics present in a theoretical identification, such as water being hydrogen hydroxide, and use them as a measure for explanations proffered in philosophy. This is what I propose to do here. A related doubt about the present methodology is the thought that, strictly speaking, warrant for a realist attitude towards a theoretical representation ultimately rests on the representation getting the facts straight. All other considerations, such as various commonalities across cases we tend to regard under a realist attitude, are beside the point. This concern runs deep and betrays a basic misunderstanding of the question being pondered here, namely, when a realist attitude towards a representation is justified. The question of justification is raised from a “deliberative” epistemic standpoint, addressed to a deliberating doxastic agent.2 On the present approach, the warrant for adopting a realist attitude towards a theoretical representation is compatible with bad epistemic luck—that despite conducting ourselves impeccably as would-be knowers, for example, it turns out that water just isn’t hydrogen hydroxide after all. Asking whether a realist attitude towards a philosophical theoretical representation is justified is likewise undertaken from a deliberative standpoint. To short-circuit the issue by suggesting that such an attitude is justified only when the representation gets the facts straight about whatever is represented is to misunderstand the present quest. We are looking to cases where a realist attitude towards a theoretical representation seems clearly justified to see if we can identify central features as markers for such warrant, which we can then deploy as measures for our philosophical theoretical representations. The task is circumscribed by our perspective as deliberators. A first salient feature of theoretical representations for which a realist attitude seems clearly justified is the presence of realist purport—a pretension to uncover the underlying nature of the represented. In representing gold as the element with atomic number 79, we aim to uncover the nature of gold. But there are cases of representing gold for other theoretical purposes that lack such pretension. The representation of gold as a standard for pre-20thcentury monetary systems within economic explanation is widely regarded under an instrumentalist attitude—to be the gold standard is not presumed to be part of what it is to be gold. The latter case is distinctly unlike the identification of gold as the element with atomic number 79 when it comes to realist purport. Or consider Gresham’s law in economics that says that between two forms of currency for the same nominal value, the currency whose commodity value is higher will tend to get pushed out of circulation by the one whose commodity value is lower (presumably because the first will get hoarded and taken out of circulation for its higher commodity

Justified Attitudinal Realism 19

value). When we consider such generalizations with an eye to the theoretical representations deployed therein—say being a currency of some commodity/nominal value ratio—we see that the representations are not themselves meant to reveal the nature of whatever they represent. What they represent are currencies, a range of real-world phenomena. But they have a very different role to play in economic explanation than the role played by representing those same currencies in metallurgy or physical chemistry. Revealing the nature of material coins is not the point of representing forms of currency when formulating economic laws. Realist purport is not a feature of such theoretical representations. A second important feature of representations for which a realist attitude seems clearly justified is that the surrounding theory does not require us to switch from the subject matters of basic everyday claims regarding the target phenomena to something other than what those claims are pre-theoretically about—unless of course such switching is demanded by some clear theoretical benefit. Conservatism as to subject matter is a natural default. Quine (1957) memorably puts the larger point as follows: We imbibe an archaic natural philosophy with our mother’s milk. In the fullness of time, what with catching up on current literature and making some supplementary observations of our own, we become clearer on things. But the process is one of growth and gradual change: we do not break with the past, nor do we attain to standards of evidence and reality different in kind from the vague standards of children and laymen. Science is not a substitute for common sense, but an extension of it. (2) This does not mean that properties previously unheeded and unexplained have not emerged in the course of identifying water as hydrogen hydroxide, say. But the subject matters of our basic pre-theoretical water-claims are recognizably what we initially set out to explain even in the advent of the theory: they are water-facts. There are certainly cases that require us to revisit and revise subject matters of basic everyday claims. Pre-theoretically we distinguish thunder from lightning when we afrm such claims as that the lightning preceded the thunder or when we afrm that the thunder was loud and the lightning bright and deny that the lightning was loud and the thunder bright. It might thus seem that the thunder and the lightning are not at bottom one and the same event of electrical discharge, which is what they are. The right thing to say about such cases is that the identification of thunder and lightning as one and the same event of electrical discharge does entail revision of pre-theoretical subject matter of everyday thunderand-lightning discourse, but that such revision is clearly warranted by gained theoretical dividends overall. A third salient feature of representations for which a realist attitude seems clearly justified is that the facts of theoretical representation fall within the

20 Justified Attitudinal Realism purview of the surrounding theory. How water is represented as hydrogen hydroxide or gold as the element with atomic number 79 are matters that are presumed to fall within our grasp. This is due to our handle on how microstructure is linked to macro-features in light of the achievements of physical chemistry. The point extends beyond theoretical identification and beyond physical-chemical representation. Consider the representation of nasonite (Pb6Ca4Si6O21Cl2) as hexagonal-dipyramidal within crystallography. Crystallography details how it is that nasonite, given its chemical nature, should be so represented geometrically. Being hexagonal-dipyramidal is a denomination originating from solid geometry. But the fact that nasonite is theoretically represented in this way does not raise perplexities beyond those already tackled by the surrounding theory. We thus identify three salient features of representations for which a realist attitude seems clearly justified. The first is the presence of realist purport—a pretension to reveal the nature of the represented individually (clearly lacking in the gold standard case, for example). A second is conservatism as to the subject matter—the preservation of pre-theoretical subject matter (as in the water case) not come-what-may but in such a way as to be sensitive to substantial theoretical benefits gained by potential revision (as in the thunder/lightning case). A third is that the facts of theoretical representation should themselves be covered by the surrounding theory (as in the nasonite case). I propose to treat these features as conjectured necessary conditions for when a realist attitude towards theoretical representations is justified. Realist purport is plausible as a condition for such warrant insofar as reality disclosure isn’t an unintended side-effect of our theories but an explanatory aim in its own right. And what goes for theories goes for theoretical representations on a smaller scale. Justified attitudinal instrumentalism with respect to a given theoretical representation requires, at the very least, that the representation be intended to disclose the nature of the represented. As for subject matter conservatism and the theoretical explicability of the facts of representation, both are hallmarks of nature disclosure. We theoretically represent aspects of an underlying reality with which we maintain antecedent rapport. Our gradual theoretical refinements pertaining to an extant subject matter gain their theoretical significance from their extant theoretical contexts, allowing us to peer further and further into what those represented aspects of reality really are at bottom. Armed with these conditions, we can turn to consider theoretical representations wielded within various philosophical theories. Is a realist attitude towards such representations justified? They typically meet the first condition. As noted in the previous chapter, realist purport associated with particular theoretical representations in philosophy is prevalent, likely fuelled by the common understanding of the philosophical enterprise as entrusted with the task of revealing the nature of whatever falls within its purview.3 But what about the other two conditions? According to the second condition, the representations of philosophical explanation should not require

Justified Attitudinal Realism 21

substantial revision as to the subject matter of everyday claims unless such revision is warranted by clear theoretical benefits gained by the revision. According to the third condition, such representations should apply to the represented in a manner that is itself well-understood in light of the surrounding philosophical theory. It now appears that for the three case studies of the previous chapter, the second and third conditions for when a realist attitude is justified are not met. Regarding the third condition, in particular, we have witnessed that in each case the proposed representation was originally devised to serve distinctly semantic aims within an explanation of the significance of our reports of the relevant facts—arithmetical, modal, or cognitive. Take again the possible world capture of a de re modal fact, a piece of applied mathematics, and compare it to the applied mathematics in the nasonite case just mentioned. Why the possible world representation should apply to the modal fact that Nixon might have lost the 1968 election surely does not enjoy the transparency of the applicability of the solid geometrical denomination of hexagonal-dipyramidality to nasonite. In the latter case, the theory offers a detailed account of why the solid geometrical shape should apply to the substance, given its composition. Nothing remotely similar can be said of the possible world capture of the de re modal fact. This is not to deny that the general applicability of mathematics—of which the applicability of hexagonal-dipyramidality to nasonite is a special case—can seem perplexing. But why, beyond the general perplexity of mathematical applicability, the formal semantic analyses of various factual reports should apply to the explananda of philosophical explanation as pertaining to the facts being reported seems mysterious. Those formal semantic representations seem like alien transplants from a remote theoretical endeavor. Regarding the second condition of preservation of pre-theoretical subject matter unless revision is demanded by clear theoretical dividends—conservatism as to subject matter—we register some further observations. Consider, again, arithmetical discourse. Numerical attributions figure prominently among basic claims we make in everyday life. Frege insists that the subject matter of ‘The King’s carriage is drawn by four horses’ is not the carriage and the plurality of horses drawing it being four, as we might ordinarily expect, but a first-level concept horse drawing the King’s carriage belonging to the extension of the second-level concept equinumerous with x = 0  x = 1  x = 2  x = 3. The same revisionism as to subject matter is exhibited vividly regarding such universal claims as ‘All whales are mammals’, which Frege (1953: §47) claims to be about concepts rather than animals. The Fregean analysis effectively swaps the everyday subject matter—the carriage being drawn by a plurality of horses numbering four—for a theoretical proxy— one concept belonging in the extension of another. Or consider, again, the de re modal claim that Nixon might have lost. Under one realist construal, possible loss for Nixon is loss for Nixon*, a counterpart. The subject matter of the everyday claim that Nixon might have lost, a modal fact concerning

22 Justified Attitudinal Realism Nixon, is swapped for another, a fact concerning the counterpart.4 Or consider, finally, the everyday attribution that Hilary believes Danzig is pretty while not believing Gdansk is pretty. The pre-theoretical subject matter is Hilary’s beliefs. And yet relations to abstracta—Fregean thoughts—are again something else altogether.5 Now, theoretical advances can surely exact the toll of revision when it comes to subject matters of basic pre-theoretical everyday claims, as noted above. A familiar example is Putnam’s (1975) case of jade, which upon closer theoretical scrutiny was revealed to be not one but two distinct minerals, jadeite and nephrite. That the jade phenomena lack the unity we were pre-theoretically inclined to confer upon them is a price incurred by theoretical progress.6 So in keeping with the second conjectured necessary condition for when a realist attitude is justified, we need to ask about the cases we have been considering whether revisions of pre-theoretical subject matters of basic everyday claims are indeed warranted by significant theoretical achievement. A radical departure from pre-theoretical subject matters of basic everyday claims that is not accompanied by clear theoretical progress should rouse the suspicion that a representation has taken on a life of its own. It should certainly incline us to resist the tendency to regard the representation realistically. In keeping with a general conservatism as to subject matter, I conclude that such is the case for all three examples we have been considering—arithmetical facts, de re modal facts, and cognitive attitudinal facts. The revision of pre-theoretical subject matters of basic everyday claims, coupled with scant evidence for clear theoretical dividends demanding such revisionism, should disincline us to regard the relevant theoretical representations realistically. The representations of these facts within their respective philosophical theories should not be regarded as revealing the nature of the represented facts.

2.2 Semantic Representations in Metaphysics A recurring theme so far has been the migration of theoretical representations from their original semantic habitat to various extra-semantic philosophical pursuits. In this section, I would like to illustrate this general tendency within contemporary discussions surrounding necessitism in the metaphysics of modality. The case provides a particularly vivid illustration of the philosophical tendency to bring semantic representational details to bear on an extra-semantic subject matter without paying sufficient heed to the distinctness in aims and scope of the semantic and extrasemantic theoretical contexts. Necessitism is the view that what there is is necessary, often expressed as the claim that necessarily, everything is necessarily something. This is meant to be compatible with modal variability in how things are, or modal qualitative variability. While how things are may vary, what things there are may not. Contingentism, by contrast, is the view that what there is is contingent

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rather than necessary. Specifically, there could have been more things than there are or fewer. Necessitism implies two modal quantitative theses. The first is that there couldn’t be more things than there are: the things there are are the most there could be. The second is that there couldn’t be fewer things than there are: the things there are are the least there could be. Call the first thesis atmost-ism and the second thesis at-least-ism. Pre-theoretically, both at-mostism and at-least-ism are difficult to motivate. This hardly settles the dispute surrounding necessitism, however. As Williamson (2013) insists, the dispute is theoretical. This brings us to the question of how the issue is supposed to be resolved theoretically. As we are about to see, the necessitist strategy of reading a necessitist ontology off of a preferred semantics for a system of modal logic is dubious as a point of general methodology. Towards the end of the section, I will sketch an alternative methodology and, with it, a conception of the metaphysics of modality that implies at-most-ism but for a different reason from the one provided by necessitist considerations. Atleast-ism, on the other hand, plausibly fails under this alternative approach. What can be said pre-theoretically on behalf of at-most-ism? Let us consider the pre-theoretical appeal of a restricted version of the thesis in the case of mathematical things. It can be shown that this appeal drives Kripke’s famous argument for the conditional claim that if the Goldbach conjecture is true, then it is necessarily true.7 Now, the Goldbach conjecture is the conjecture that every even number greater than two is the sum of two primes. Kripke’s argument is that under the assumption that the conjecture is true, each number can be shown by direct computation to have the Goldbach property of being the sum of two primes if even and greater than two. So on the assumption in question, it is necessary for each number to have this property. Now suppose for reductio that the Goldbach conjecture isn’t necessarily true. Then possibly some number doesn’t have the Goldbach property. It follows, then, that for some number it is possible not to have the Goldbach property. But this is ω-inconsistent with each number having the Goldbach property necessarily. Therefore, if the Goldbach conjecture is true, it is necessarily true. A crucial step in this argument is the transition from the general (or de dicto) possibility that some number does not have the Goldbach property to the specific (or de re) possibility for some number of not having the property.8 The legitimacy of this step rests on the simple observation that what makes the general possibility of a number not having the property obtain can only be a specific possibility for some number of not having the property.9 In the absence of a specific possibility for each number of not having the property, the general possibility can obtain only due to some non-actual number possibly not having the property. But this latter idea is independently repugnant, regardless of the specifics of the case. In general, it seems that for every general possibility that a number has (or lacks) a mathematical property, there is a “witness” in the form of a specific possibility for a

24 Justified Attitudinal Realism number of having (or lacking) the property. This is because there couldn’t be merely possible numbers to sustain the general possibility of a number having (or lacking) a certain mathematical property in the absence of a specific possibility for each of the actual numbers of having (or lacking) it. None of the numbers could fail to exist. So merely possible numbers attesting to the general possibility would have to be extra numbers beyond those already existing. And yet the realm of the numbers is necessarily a plenum in the sense that it must be fully saturated with its entities—the individual numbers—not leaving room for the possibility of an extra number beyond those that already must exist. Such considerations, while pre-theoretical as regarding the nature of possibility, clearly support numerical at-most-ism: the numbers there are, are the most there can be.10 There couldn’t be more numbers than there already are. Analogous pretheoretical considerations support mathematical at-most-ism more generally. There couldn’t be more mathematicals than there already are. Do such considerations generalize to logical at-most-ism, i.e., the idea that there couldn’t be more things in the widest sense than there are? The trouble here is that with things in general, unlike mathematical things, how they are seems modally variable. At least on the most common views, the configuration of things isn’t modally fixed. (As mentioned earlier, necessitism, in particular, is supposed to be compatible with such modal qualitative variability.) When a structure is fully saturated with its entities and modally fixed, as in the mathematical case, it seems pre-theoretically plausible that there couldn’t be any room in the structure for an extra node. For where is an extra node supposed to go if the structure is the way it is necessarily? But with modally variable structures of things more generally, we don’t get any pre-theoretical purchase on the thought that there isn’t room for an extra thing. Why couldn’t a possible alternative structure accommodate an extra thing? And yet the logical at-most-ist claims that while how things are is modally variable, what things there are isn’t. At-most-ism is thus difficult to motivate pre-theoretically. What about at-least-ism? Perhaps the pre-theoretical appeal of the view in the case of mathematical things can be motivated along similar lines. Suppose we manage to prove Goldbach’s conjecture. Then every even number greater than two is indeed the sum of two primes. And so, it couldn’t be otherwise, as we just saw. Now someone comes along and says, “While I concede that it’s necessary that every number has the Goldbach property of being the sum of two primes if even and greater than two as a general matter, perhaps for some number in particular, it isn’t necessary to have this property.” As noted above, some number not having the Goldbach property necessarily is ω-inconsistent with each of the numbers having the property necessarily. So it seems that the only way for some number not to have the property necessarily, as per the mooted suggestion, is for some number to

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possibly fail to exist. But the idea of one of the actual numbers possibly failing to exist is prima facie repugnant. The structure of the numbers must be exactly the way it is, including all of its nodes occupied by the actual occupants. If seventeen were not to exist, then sixteen wouldn’t exist either, lest every number having an immediate successor would be violated, in which case fifteen wouldn’t exist either for the same reason and so on. Alternatively, if seventeen were not to exist, then perhaps sixteen would exist but have an immediate successor other than seventeen. Suppose eighteen were the immediate successor of sixteen in that scenario, in which case an even number would be the immediate successor of an even number, which would also violate a basic mathematical truth. Such examples could be multiplied as needed and would ramify without limit. The upshot is the overall plausibility of numerical at-least-ism: the numbers there are, are the least there could be. There couldn’t be any fewer of them. And this plausibly extends to mathematical things in general. There couldn’t be any fewer mathematicals than there are. Do such considerations generalize to logical at-least-ism, i.e., the idea that there couldn’t be fewer things in the widest sense than there are? Once again, this is hard to motivate pre-theoretically once the configuration of things in general is acknowledged to be contingent. For it seems plausible that the structure of things, being modally variable, could do with fewer things. After all, it seems plausible that things are intertwined with other things to varying degrees. The thought that some of them are modally extricable—that had things gone otherwise, they wouldn’t exist—is pre-theoretically appealing. The general case for logical at-least-ism doesn’t enjoy the pre-theoretical appeal of its mathematical kin. Again, given that mathematical structure is necessary, it is very hard to see how any node in the structure might have gone missing. Not so, it seems, for things in general. I conclude that at-leastism is difficult to motivate pre-theoretically as well. Williamson (2013) contends that the necessitism vs. contingentism dispute is to be resolved theoretically: “However strange the consequences of necessitism . . . common sense has limited authority over such claims. We can properly evaluate them only by theoretical inquiry” (9). The evaluation of the consequences of necessitism is to be conducted by attending to systems of (higher-order) modal logic. Suppose it turns out that a straightforward semantics for a system of modal logic that best combines certain theoretical virtues such as strength, naturalness, and simplicity looks very much like it includes a necessitist ontology. That would then provide, according to Williamson, a compelling reason to uphold necessitism. And indeed, this is exactly how things turn out. Necessitism becomes a metaphysical corollary of a fixed-domain semantics for a preferred system of modal logic that is recommended by certain theoretical virtues as befitting formal systems. So when it comes to the theoretical resolution of the metaphysical dispute between necessitism and contingentism, Williamson’s strategy is to turn to the logic.11 But this methodology, despite its relative popularity, is dubious.

26 Justified Attitudinal Realism Methodological differences are, in general, difficult to assess and very difficult to resolve. Anecdotal evidence suggests that the criteria underlying the adoption of a method in philosophy are not well understood. To keep Williamson’s stance in view, however, suppose one adheres to a logic-first methodology in metaphysics because of its fruitfulness in yielding theoretical results. Set aside the interesting question of why fruitfulness in yielding theoretical results is something we should prize in philosophy. Even if we assume such a criterion to be operative in the adoption of a logic-first methodology in metaphysics, it had better turn out that the fruitfulness in question isn’t merely in the underlying logic but rather in the metaphysics itself. For, otherwise, it can seem mystifying that yielding valuable logical results should have anything to do with suitability for yielding valuable metaphysical results. I submit that it is far from clear that the logic-first methodology behind necessitism is indeed fruitful in yielding theoretical results that contribute to our understanding of the nature of metaphysical modality. But I want to turn to a more pressing issue. Insofar as necessitism is tightly interwoven with a fixed-domain semantics for a certain preferred system of modal logic, it is worth pausing to reflect on the explanatory purview of the semantics. In general, a semantics for a formal system captures logical consequence in terms of relations between bits of a given theory and portions of the theory’s universe of discourse. This is supposed to contrast with capturing logical consequence in intratheoretical terms (i.e., syntactically). If the formal system for modality theoretically represents modal reasoning, its semantics theoretically represents real word-world relations that undergird modal reasoning truly or falsely, thus explicating the meaningfulness of modal discourse. This is, of course, very rough and subject to numerous qualifications, but it serves the purpose of reminding us that a fixed-domain semantics for a system of modal logic is, in the first instance, a theoretical representation of real word-world relations in our modal reasoning about reality. In such light, the idea of reading a necessitist ontology off of a fixed-domain semantics seems independently questionable. Even if the semantics represents real word-world relations in a way that reveals something important about those relations and, ultimately, about the meaningfulness of modal discourse, there is little reason to suppose that every working part of the semantics is revelatory of whatever it represents on its own. Consider the cartoonish analog mentioned in the Preface: a plastic model of a molecule consisting of balls and connecting rods revealing the nature of a certain molecular structure but without the rods themselves revealing what the represented chemical bonds really are or the balls themselves revealing what the represented atoms really are. The success of such a representation in revealing molecular structure in no way depends on each of its representational parts being revelatory of what it represents. We can only make sense of the explanatory role of the rods representing chemical bonds and the balls representing atoms by keeping the larger representation in view. It is

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no part of the plastic model revealing what the molecular structure really is that the balls reveal what the represented atoms really are and the rods reveal what the represented chemical bonds really are. Similarly, in the case before us, even if a preferred fixed-domain semantics as a whole provides a revelatory theoretical representation of the meaningfulness of modal discourse, there is little reason to suppose that the fixed-domain aspect of that larger theoretical representation is itself revelatory of what reality is really like. We are simply not justified in reading off of the preferred fixed-domain semantics a necessitist ontology. The fixed-domain aspect of the larger theoretical representation—the semantics as a whole—can stand for reality without thereby disclosing its underlying nature as consisting of a totality of necessary existents.12 Similarly, in the FOL case, we don’t read off of the standard model theory that reality is fundamentally discrete or that properties in re are sets. The inclination to suppose otherwise is based on an illicit assumption that theoretical representations inevitably disclose the nature of what they represent. The fixed-domain aspect of the preferred semantics for modal logic theoretically represents whatever our discourse is about, reality. But this doesn’t require that the representation disclose what reality is really like at bottom. The present critique is far more general than Stalnaker’s (2016) focused critique of Williamson’s methodology. Stalnaker’s efforts are directed at providing a realistic semantic interpretation for modal discourse that can be squared with a contingentist metaphysics. A semantics is realistic in Stalnaker’s sense insofar as assignments of semantic values to expressions correspond appropriately to the things within the subject matter of the language. This is compatible, according to Stalnaker, with nonrealistic model structures that are utilized to study the compositional structure of the language. Those structures are nonrealistic insofar as some of their aspects may not correspond to reality. An important case in point is the model structures of a variable-domain (Kripkean) semantics for modal logic. The present critique, on the other hand, is more global and gains plausibility from the wider methodological setting of how we should regard theoretical representations quite generally. Reflecting on the explanatory aims and achievements of formal semantics disinclines us to suppose that the fixed-domain aspect of a semantics for modal logic should disclose the nature of reality. We do not have a reason to regard the fixed-domain aspect of Williamson’s preferred semantics for modal logic under a realist attitude as revealing the nature of reality as a totality of necessary existents. But do we have some positive reason not to regard this theoretical representation of reality under a realist attitude? Call the theoretical representation of reality as a totality of necessary existents R. We show that a realist attitude towards R as deployed within the metaphysics of modality isn’t justified by holding up the case against the three conjectured necessary conditions for justified attitudinal realism articulated in the previous section, namely, (1) realist purport, (2) conservatism

28 Justified Attitudinal Realism as to subject matter, and (3) intelligibility of representation in light of surrounding theory. When it comes to (1), there can hardly be any doubt that R is put forward by the proponent of necessitism as revealing the nature of reality. The theorist engaged in the metaphysics of modality is typically concerned with revealing the nature of reality in its modal aspect. Deploying R within the larger theory is thus not merely for the sake of some broader explanatory purpose, as might be the case in deploying an index set to represent the meaning of a sentence in formal semantics. R is clearly put forward by the necessitist with realist purport. But the situation surrounding (2) is complicated by the fact that a totality of necessary existents is pretty clearly distinct from the apparent subject matter of everyday claims about reality. So whether or not R meets (2) depends on whether or not revisionism as to subject matter is warranted in this case by clear theoretical benefit. The matter is surely controversial. But there is nothing controversial about R failing to meet (3). The possible world metaphysics surrounding R doesn’t contribute to our understanding of how it is that R represents reality. The arguments in favor of R are all abductive, based on considerations of strength, explanatory power, simplicity, elegance, and the like. It isn’t as if details provided by the surrounding possible world metaphysics contribute to our appreciation of why reality should be represented as a totality of necessary existents in the manner that the details provided by crystallography explain why nasonite should be represented as hexagonaldipyramidal. That nasonite is so represented theoretically emerges directly from the surrounding theory. Not so, however, for R representing reality as a totality of necessary existents. The surrounding theory is compatible with contingentism—at a high cost perhaps, if the necessitist is to be believed, but compatible nonetheless. This means that the surrounding theory does not itself provide an articulation of how R represents reality. Rather, the necessitist claims that R representing reality better comports with the straightforward applicability of the usual possible world semantics for quantified modal logic than contingentism, an abductive claim.13 Given the failure of R to meet condition (3), we conclude that we have a positive reason not to regard R under a realist attitude as revealing what reality is really like. What becomes of the quantitative modal theses of at-least-ism and atmost-ism without their pre-theoretical appeal and without a proper justification for the necessitist’s “reading-off ” methodology? Do the theses reasonably extend beyond mathematical cases? I want to close this section by suggesting that at-most-ism does while at-least-ism doesn’t. The reason at-most-ism holds, in general, has to do with the nature of possibility itself rather than because of a metaphysical downstream effect of adopting a certain semantic framework. At-most-ism holds on an alternative conception of metaphysical possibility that regards what is generally possible as determined by what is specifically possible for particular things. Here is a brief articulation of such an alternative conception of metaphysical possibility.14

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We begin with the natural thought that metaphysical modality is, in the first instance, about configurations of actual things. Marcus (1993) puts the point as follows: “[M]odalities in their primary use concern counterfactuals about actual objects, and to reintroduce possibilia is to run counter to the admonition of Russell that we ‘retain our robust sense of reality’” (197).15 Possibilities never obtain due to the vicissitudes of merely possible things. One way to spell out such a conception of metaphysical modality is to think of general possibilities, or possibilities de dicto, as beholden to what is specifically possible for particular things, or possibilities de re. In paradigm cases where we consider something to be generally possible, say the general possibility that a Progressive replace Clarence Thomas on the bench of the US Supreme Court, we take it for granted that it is possible for something or other—a person, presumably— to be such a replacement for Thomas. The general possibility obtains only in virtue of the specific possibility obtaining. General possibilities do not float free from specific possibilities as their witnesses. Such a conception, however otherwise congenial in its Russellian “robustness”, famously runs up against cases of general possibility that seem not to be beholden to specific possibilities in this way. It might seem plausible that there could have been an additional carbon atom to those already existing or having existed at some point in the past. But it might not seem plausible that being an additional carbon atom is possible for anything in particular because anything for which it is possible to be a carbon atom would already have to be a carbon atom. In other words, being a carbon atom cannot be had contingently. There are different ways of handling such cases without countenancing merely possible things. One way is to give up on the essentialist idea that being a carbon atom cannot be had contingently, in which case it would be possible for some existing boron atom, for example, to be a carbon atom by the possible addition of a proton to its nucleus.16 Another way is to uphold the essentialism while denying that the troublemakers are genuine possibilities after all. There couldn’t have been an additional carbon atom after all. This requires providing an explainer for our natural inclination to suppose otherwise.17 On such a view (which is the one I myself favor), being a carbon atom cannot be had contingently. Nothing that isn’t already a carbon atom could be a carbon atom, so nothing could be a carbon atom that is additional to those that are or were. And so, while it isn’t really possible that there be an additional carbon atom because it isn’t possible for anything to be an additional carbon atom due to essentialist considerations, it is nevertheless possible that something becomes an additional carbon atom. This depends, in turn, on it being possible for something or other—a boron atom, perhaps—to become something else, an additional carbon atom. On the understanding of potentiality as possible becoming, we could say of the boron atom that it is a potential carbon atom rather than a possible carbon atom (on the model of an oak seed being a potential oak tree rather than a possible oak tree). Be that as it may, specific possibilities on this way of thinking are prior in the order of

30 Justified Attitudinal Realism metaphysical explanation to general possibilities. The latter obtains only in virtue of the former obtaining. From this standpoint, at-most-ism with respect to things in general obtains because any possibility that there be an additional thing to the things there are or were would require something other than anything there is or was for which it is possible to be. Under the assumption that things are what they are by their natures, an additional thing would have to be of some particular nature or other. For example, an additional number would have to be a number, an additional carbon atom would have to be a carbon atom, an additional human would have to be a human, and so on. But then, the considerations adduced above regarding being an additional carbon atom would kick in for the kind of thing at issue. If it is possible that there be an additional human, then there is something for which it is possible to be an additional human. But being human isn’t something that can be had contingently. So there is nothing for which it is possible to be an additional human. Therefore, it is not really possible that there be an additional human (even if it is possible that something become an additional human because it is possible for something to become an additional human). And so it goes. In sum, at-most-ism is justified by the present alternative conception of metaphysical modality. And while earlier we characterized at-most-ism as a modal quantitative consequence of necessitism, under the present conception it is revealed to be deeply qualitative. The reason there couldn’t be more things than there are is that such things would have natures that couldn’t be had contingently. The thesis of atmost-ism follows from the alternative conception of metaphysical modality just sketched as a theoretical outcome. Finally, when it comes to at-least-ism, the present conception is compatible with its failure. It just isn’t obvious why there couldn’t be fewer things than there are. Suppose it is generally possible that someone fail to exist. All that is required for this to obtain in the present conception is the specific possibility of someone not existing. And here we have our usual pretheoretical verdicts. As Kripke (1980) puts it: “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” (48). The significant bits here are the ‘of course’ and the ‘certainly’. We may indeed treat such verdicts of possible non-existence for things as data for subsequent metaphysical theorizing. In the absence of countervailing theoretical considerations, it seems safe to assume that at-least-ism fails.

2.3 A Brief Aetiology I began the Preface with a passage from Wittgenstein’s Philosophical Investigations that urges us to replace explanation in philosophy with description alone (2009: §109). I found value in the Wittgensteinian sentiment for the metaphilosophical study of theoretical representations in philosophy. Instead

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of proposing a theory of philosophical representation—a theory whose subject matter is philosophical theories, a “philosophy of philosophy”—I resorted to observing some philosophical theories with some importance for contemporary philosophy and drawing general morals from these observations. In the Preface I called the default inclination to regard theoretical representations in philosophy as revealing the nature of what they represent metaphilosophical realism. I contrasted this with a preferred stance of metaphilosophical instrumentalism. I tried to make a case for the latter by offering instrumentalist takes on various substantive philosophical theories as plausible alternatives. I also offered general guidelines for when attitudinal realism might be justified vis-à-vis particular theoretical representations. I would now like to turn to the wider historical context of the general methodological theme illustrated in this chapter of semantic theoretical representations being deployed within extra-semantic theoretical contexts I will venture a broad conjecture as to the origins of the tendency to regard semantic theoretical representations as metaphysically revealing when it comes to the facts portrayed in language and thought. Explaining the appeal of metaphilosophical realism is a very tall order. Such appeal is likely the outcome of overlapping metaphilosophical tendencies. For example, it seems natural to suppose that if a declared aim of philosophical inquiry into Y is to reveal the underlying nature of Y, the specific theoretical representations deployed within the theory should themselves reveal the nature of whatever they represent. The tendency to suppose something like this is bred by the intuitive appeal of a simple view of theoretical representation whereby theoretically representing Y is like picturing it, with various parts of the picture corresponding to various parts of Y, each revealing the part for which it stands. This idea, coupled with the elevated status of natural scientific theories in post-Quinean analytic philosophy and the occurrence therein of theoretical identifications, is surely partly responsible for a default realist attitude when it comes to theoretical representations in philosophy. In the way the astrophysicist is identifying the sun as a sphere of hot plasma converting hydrogen into helium, the philosopher—so the thought goes—is identifying the belief that the sun is hot as a computational relation to a sentence in mentalese, say.18 While the widespread general appeal of metaphilosophical realism is a very high-level phenomenon, some of its manifestations seem more tractable. I have been arguing against taking a realist attitude towards particular theoretical representations within various philosophical theories by pointing out that the representations in question originate from semantics and should, therefore, not be expected to reveal the nature of what they represent within an extra-semantic explanatory context. We can perhaps gain a better understanding of this migration of theoretical representations from semantic to extra-semantic explanatory contexts by attending to some of the historical background. It is noteworthy that work in the formal semantic tradition has often tacitly assumed that semantic analyses disclose the nature of the facts conveyed

32 Justified Attitudinal Realism in language and thought. Examples throughout the writings of the pioneers of formal semantic tradition, notably Carnap and Montague, abound.19 Carnap (1947) explicitly characterizes, within his proposed formal semantic method of extension and intension, semantic values as continuous with the subject matter of the natural sciences. After identifying properties as the intensions of predicators, for example, he writes: Whatever is said in this book about properties may be wrong, but it has at least cognitive content. This follows from the fact that our statements belong to, or can be translated into, the general language of science. We use the term ‘property’ in that sense in which it is used by scientists in statements of the following form: “These two bodies have the same chemical properties, but there are certain physical properties in which they differ”; “Let us express the property . . ., which is exemplified by the one but not by the other of these two bodies, ‘P’”. (22) According to this view, properties as semantic values assigned to predicates in the proposed formal semantics are the very worldly properties studied by the natural scientist. And what goes for properties goes for other elements in the formal semantic apparatus. Small wonder that semantic analyses should be taken as guides to the nature of the facts represented in language. In a similar vein, in the course of arguing for the indispensability of events in the formal semantic analysis of such sentences as ‘Not all psychological events have physiological correlates’, Montague (1969) identifies events as properties of moments and writes: One advantage of identifying events with properties of moments is that it is easy to analyze the notion of occurrence. To say that an event P occurs at a moment t is simply to say that t possesses (or partakes of, or participates in) the property P. (161) One would have thought that the notion of occurrence isn’t an explanandum for semantic theory. But the formal semantic identification—or “explication”, in Carnap’s (1947: §2) terminology—of events with (or as) properties can be utilized, according to Montague, in the extra-semantic explanation of what it is for an event to occur at a time. Later work in the formal semantic tradition has often also aligned itself with Strawson’s project of descriptive metaphysics.20 Both tributaries, the Carnapian-Montagovian and the Strawsonian, can ultimately be traced back, via Frege, to Kantian influences. But doing justice to such complexities and the ways they inform the contemporary predilection to regard formal models of language and thought as revelatory of the nature of the facts represented in language

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and thought is a large and difcult project. Here is a rough preliminary sketch of how such a project might proceed. First, to suggest that the formal semantic tradition is shaped by Kantian influences is to suggest that it can be ultimately traced back to transcendental idealism. And while establishing this ambitious claim in full generality is out of the question here, we can get a sense of how a historical argument to such effect might go by considering a distinctly Kantian theme running through what Dummett (1993) identifies as the birth of the analytic tradition in philosophy: Frege’s (1953) construction of number with which we began. The theme emerges directly from Kant’s so-called Copernican revolution. A rough outline of Kant’s basic idea is that to be an object of experience is to be constituted by our forms of sensible intuition and categories of understanding. Experience is “receptive” rather than merely “spontaneous”, but what we receive in experience are already products of our faculties of sensibility and understanding. Smoothing over important differences between forms of intuition and categories of understanding, the overall picture is that of objects constituted (“transcendentally”, not “empirically”—a point to which we return below) by preconditions for judgments about them. Cognition does not just conform to its objects as the empiricists would have it. Objects conform to cognition. To appreciate the impact of such ideas on Frege’s construction of number, we consider meaningful speech for Frege as expressive of judgment. The preconditions for meaningful numerical speech are given by Frege’s secondorder logic, the Begriffsschrift, starting with the primitive logical categories of concept and object. Numbers are logical objects; they are extensions of certain second-level concepts, as we saw earlier. The objects of meaningful number talk—the numbers themselves—are thus constituted by logical preconditions for such talk. And what goes for the objects of arithmetic goes for arithmetical properties and relations as well. Consider, again, the relation of immediate succession in the number series discussed in Section 1.2. The Fregean construal of the number one immediately succeeding the number zero in the number series is that for some first-level concept φ and some object y, φ is in the extension of the second-level concept equinumerous with x = 0 while the first-level concept φ- other-than-y is in the extension of the second-level concept equinumerous with x ≠ x. But functions from objects to truth-values belonging in the extensions of functions from such functions to truth-values is a radical semantics-based departure from the intuitive and pre-theoretical notion that the number one immediately follows the number zero in the number series. For example, the latter claim is in no way existential, let alone doubly so or second-order. But more significantly for our purposes, that the number one is the successor of the number zero seems on the face of it—that is to say, pre-theoretically—to have nothing to do with extensions or truth values. It is an arithmetical matter. And yet in Frege’s hands it becomes a logico-semantic matter.

34 Justified Attitudinal Realism The dispute between Frege and Kant as to whether arithmetical judgments are synthetic and presuppose intuition is often emphasized—notably by Frege himself—to the detriment of appreciating deep structural affinities between their respective views. Frege’s basic point contra Kant is that arithmetical judgments are not synthetic and do not presuppose a form of intuition. The numbers are purely logical objects. But in Kant’s framework, to deny that arithmetical judgments are synthetic is to affirm that they’re analytic and, therefore, not about any objects at all. For Frege, the judgments of arithmetic are indeed analytic but under a different conception of analyticity.21 But the emphasis on such differences between Frege and Kant obscures an important underlying commonality: the idea that if numbers are objects, then they are constituted by preconditions for judgments about them. Kant thinks that if numbers are objects, then they are constituted by forms of intuition, which are required for all judgments about objects alongside the categories of understanding. Frege thinks that numbers can be objects without requiring intuition but that they are nevertheless constituted by logico-semantic preconditions for arithmetical judgment. Viewed this way, we have a relatively local dispute against the background of broad agreement: objects constituted by preconditions for judgments about them. The idea that whatever we represent in language and thought is constituted by preconditions underlying the possibility of meaningful language and thought lies, I believe, at the root of the widespread tendency to regard semantic theoretical representations of the significance of our factual reports as revealing the nature of the facts reported by them. I have not established this larger claim, however. I have merely indicated a direction for establishing it by tracing an obvious line of influence from basic Kantian doctrine to Frege’s semantics-first construction of numbers as logical objects. A fuller demonstration in the arithmetical case would include at least a more systematic exploration of the logico-semantic underpinnings of arithmetical properties and relations. Be that as it may, given such background and given Frege’s singular importance for both the linguistic turn in philosophy and the subsequent project of formal semantics, it is hardly surprising that semantic theoretical representations have been treated as revelatory of the nature of the facts conveyed in language and thought. I note that whatever can be said for or against the Kantianism inherent in the work of the pioneers of the formal semantic tradition, the situation is complicated in a contemporary setting due to the distinctly empirical aspirations both in more recent work in semantics and in contemporary postQuinean philosophy. For the Kantian tradition, talk of preconditions for judgment informing subject matter is from a “transcendental” rather than an “empirical” standpoint. It isn’t assumed that the objects confronted in experience are somehow constituted by mentality as a matter to be studied by empirical psychology.22 Similarly, logico-semantic preconditions for arithmetical judgments informing arithmetical subject matter in Frege are not offered from an empirical standpoint on logic as specifying laws governing

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thought processes (a “psychologistic logic”, as it were). It isn’t as if Fregean numbers are supposed to be constituted somehow by the elements of our actual thinking. What I am identifying as a Kant-inspired attitude towards semantic theoretical representations within contemporary philosophical theories regarding extra-semantic matters typically fails to heed the Kantian distinction between the transcendental and empirical standpoints. This opens up a large and complex topic that I hope to broach elsewhere.

2.4 Philosophical Theoretical Representations We have been considering the choice of attitude towards representations deployed within philosophical explanation. We looked at some familiar cases outside philosophy for which a realist attitude seems clearly warranted and identified conjectured necessary conditions for such a warrant. We concluded that for the philosophical theoretical representations discussed in Chapter 1, the second and third conditions aren’t met. Regarding the third condition, in particular, we noted that in all the cases discussed, it appears that a realist attitude treats semantic representations originally adduced to explain the significance of certain factual reports as revealing the nature of the facts being reported. This was further illustrated in the case of necessitism in Section 2.2. Let us now draw some broader implications from the foregoing for general philosophical methodology. Any teacher of philosophy is familiar with the incredulity exhibited by students regarding theoretical constructions deployed within putative philosophical explanations. “Numbers are sets.”—“But we don’t count with sets!” (the student’s reaction, voicing perhaps the sentiment that numbers are inherently quantitative while sets are not). “Possibilities are possible worlds.”—“But what do possible worlds have to do with the world?” (voicing perhaps the worry that unactualized possibilities are aspects of actuality whereas non-actual possible worlds are in some sense alternatives to actuality). “Beliefs are relations to the semantic contents of whole declarative sentences.”—“But believing doesn’t require language!” (voicing perhaps the thought that mental states such as belief are exhibited by non-linguistic animals too). “God is that than which nothing greater can be thought.”—“But what does our ability to think have to do with what God is?” (voicing perhaps the concern that the nature of the divine should float free from matters of conceivability). In all such exchanges, the student may be expressing a correct idea under a certain reading of the teacher’s claim. The teacher, on the other hand, need not be committed to the ascribed reading. The student complains that the being such that nothing greater can be thought isn’t what God really is at bottom. The teacher could reply: Being such that nothing greater can be thought is a representation of God within an ingenious argument for God’s existence. Anselm may have thought that being such that nothing greater can be thought reveals

36 Justified Attitudinal Realism the nature of the divine. We need not follow him in this to appreciate his achievement. The representation of God as that than which nothing greater can be thought is still serviceable within the broader effort to show how God’s existence is the sort of thing that might be proved and the resources needed for such a proof. The teacher’s point can also be put like this: Even if we assume that a particular theoretical representation (Anselm’s definition of God) deployed within an overall explanatory effort (the ontological argument) doesn’t reveal the nature of what it represents (God), it can still have a more general or holistic explanatory utility, illustrating how something like God’s existence can admit of proof in the first place.23 Philosophical explanation is a human enterprise, not an exercise in divine revelation. It deploys representations of its various subject matters in an effort to shed light on them. But reasons for deploying theoretical representations within our various theories are many and varied. We philosophers might imagine our representations as invariably tapping into the nature of what they represent, imagining ourselves to be undertaking the physical chemistry of reality, so to speak, taking each of our representations as offering something on par with the representation of gold as the element with atomic number 79 or of water as hydrogen hydroxide. In point of fact, even if there is something to this aspiration on a larger scale, for a great many cases of philosophical explanation there is very little to support the contention regarding the particular theoretical representations deployed therein. Theoretical representations deployed in philosophy are often closer to such cases as representing the meaning of a sentence as its truth-condition in truthconditional semantics. In the latter case, it is not assumed by the working semanticist that the truth-condition is what the meaning of the sentence turns out to be upon closer theoretical scrutiny, along the lines of water turning out to be hydrogen hydroxide. Rather, the meaning of the sentence is so represented within a more holistic effort to explain the compositionality of meaning—how the meanings of complex expressions depend on the meanings of their parts—which in turn ultimately contributes to the theoretical exploration of our capacity to produce and understand novel sentences. That the meaning of a sentence should be theoretically identified with its truth-condition is no part of such broad explanatory aims. In the next couple of chapters, we turn to examine the appeal of attitudinal instrumentalism regarding theoretical representations deployed in semantics in greater detail.

Notes 1. There is in fact a growing consensus among philosophers of chemistry that this picture is grossly oversimplified if not downright false. See e.g. Weisberg and Needham (2010). And yet the currency and influence of this picture on contemporary

Justified Attitudinal Realism 37

2.

3.

4. 5. 6.

7.

philosophical culture is difficult to exaggerate. Its dialectical role in this book is as a point of contrast with the recommended attitude towards many theoretical representations within philosophical theories to be discussed below. The terminology is borrowed from discussions in Kantian ethics. See, for example, Korsgaard (1996): “It is from within the deliberative perspective that we see our desires as providing suggestions which we may take or leave” (96). The general point in the ethical case is that on a Kantian (“practical”) conception, ethics is supposed to tell us how we should reason in deliberating what to do (or refrain from doing), whereas on the competing (“theoretical”) conception, the business of ethics is to outline the moral facts, which actions are right and which are wrong, etc. This is not to deny that some philosophers—David Lewis chief among them—have resisted drawing a default implication from the global revelatory pretension of a philosophical theory to the more specific revelatory pretensions associated with particular theoretical representations deployed therein. The point in the text targets a common tendency nonetheless. This appears to be the crux of Kripke’s so-called Humphrey objection against Lewis’s Counterpart Theory. See Kripke (1980: 45 n.13). In Simchen (2012: Ch.5) I explore this particular distinctness in some detail. See also Section 6.4. Unlike the lightning/thunder case, where apparently bifurcated phenomena are revealed by our theories to be unified, in the jade case apparently unified phenomena are revealed by our theories to be bifurcated. For an illuminating discussion of the jade case, see Hacking (2007). The argument is found in Kripke (1980: 36–37). Kripke’s attitude of prioritizing common sense considerations over theoretical ones is in keeping with such passages as the following: Of course, some philosophers think that something’s having intuitive content is very inconclusive evidence in favor of it. I think it is very heavy evidence in favor of anything, myself. I really don’t know, in a way, what more conclusive evidence one can have about anything, ultimately speaking. (42)

8. For more on this contrast, see Simchen (2012, 2013a). The contrast is commonly represented as the scopal difference between ◊xφx and x◊φx, where φ represents not having the Goldbach property and quantification is restricted to numbers. 9. As Kripke puts it: Could it then be the case that, although in fact every such even number is the sum of two primes, there might have been such an even number which was not the sum of two primes? What would that mean? Such a number would have to be one of 4, 6, 8, 10, . . .; and, by hypothesis, since we are assuming Goldbach’s conjecture to be true, each of these can be shown, again by direct computation, to be the sum of two primes. (Kripke 1980: 36–37) 10. Being pre-theoretical as regarding possibility is clearly compatible with being theoretically informed as regarding the numbers. 11. Williamson’s logic-first methodology, whether explicitly endorsed or not, has many other adherents. Here is an explicit endorsement by Sider (2016): “I believe that Williamson’s general methodology—his view of how to choose a logic, and of the bearing of this choice on metaphysics and ontology in general—is correct” (689). 12. Being such a totality might be an “artifact of the model” in Kaplan’s (1975: 722) lucid phrase. 13. One of the main arguments in Williamson (2013) is that contingentism is incompatible with there being an intended model structure. But whether or not there is an

38 Justified Attitudinal Realism intended model structure is itself negotiable, given the declared aims of the semantics at issue. 14. The conception belongs to a family of views known as “the new actualism”. For a useful early survey, see Vetter (2011). See also Simchen (2012, 2013a). 15. The Russell reference is to the following famous passage from Russell’s Introduction to Mathematical Philosophy (1919):

16. 17. 18. 19. 20. 21.

22.

23.

If no one thought about Hamlet, there would be nothing left of him; if no one had thought about Napoleon, he would have soon seen to it that some one did. The sense of reality is vital in logic, and whoever juggles with it by pretending that Hamlet has another kind of reality is doing a disservice to thought. A robust sense of reality is very necessary in framing a correct analysis of propositions about unicorns, golden mountains, round squares, and other such pseudo-objects. (169–170) See Parsons (1995) for this line of thought. See Simchen (2013a) for this line of thought. For further discussion of this particular case, see Section 6.4. For a representative sampling of this tendency, see, in particular, the informal discussion in Carnap (1947: §4) and the opening pages of Montague (1969) (the latter evocatively titled ‘On the Nature of Certain Philosophical Entities’). See Strawson (1959). For the Strawsonian thread in formal semantics, see, e.g., Pelletier (2011) and Moltmann (2013). Kantian analyticity is a matter intrinsic to the judgment—containment of the predicate in the subject—whereas Fregean analyticity is the extrinsic matter of being fully grounded in definitions and logic rather than partially grounded in a special science. See Frege (1953: §3). That idea is regarded by the Kantian as a detail of an objectionable “empirical idealism”. See Kant’s (1998: A366-A380) discussion of the Fourth Paralogism. Kant characterizes his own position as a transcendental idealism and an empirical realism, distancing himself from what he characterizes as a transcendental realism that becomes an empirical idealism. The latter is the view that affirms the reality of space but denies that we directly encounter things in space, affirming that we can only know non-inferentially our own minds and their temporally ordered contents. I am ignoring well known problems with Anselm’s argument, the most striking being the “exportation” fallacy pointed out by Gaunilo that from the fool’s concession that it is thought that the x such that for all y it is impossible to think that y > x exists, it doesn’t follow that the x such that for all y it is impossible to think that y > x is such that it is thought that x exists.

3

Attitudinal Instrumentalism in Semantics

3.1 Formal Semantic Evaluation In previous chapters, we witnessed the migration of certain theoretical representations in the formal study of meaning in language and thought from semantics to metaphysics. In Section 1.3, and then again in Section 2.2, we saw, for example, how semantic representations of the significance of modal locutions within a possible world semantics for quantified modal logic can become a guide to the metaphysics of modality. In this chapter and the next we turn our attention to the semantic side of things. We will explore ways in which an instrumentalist attitude towards theoretical representations becomes relevant in the formal study of meaning itself. The significance and reach of an instrumentalist attitude in semantics will be illustrated through several case studies: the formal capture of sentential truth (Section 3.2), the Fregean theory of indirect reference (Section 3.3), the semantic analysis of comparisons (Section 4.1), and the delineation of the purview of semantic theory relative to that of speech act theory (Section 4.2). In the next chapter we will consider the main theme of this book, attitudinal instrumentalism, in relation to work by two central figures of the “ordinary language” movement in 20th-century philosophy, Wittgenstein and Austin. In this chapter we consider this theme in relation to the project of formal semantics. We begin with a certain ambiguity in how we regard linguistic phenomena that stems from the various theoretical settings in which we study them. Human language is part of human nature, which is part of nature entire. It is a species of natural phenomena. We can study it phonetically, attending to the mechanisms underlying articulation on the production side of speech, or attending to the mechanisms underlying auditory perception on the consumption side of speech. We can then dig deeper into the neurophysiological bases for such mechanisms. By contrast, we can study the phenomena phonologically, with an eye to patterns of language-specific phonemes, abstracting from the physical mechanisms underlying speech production and consumption. We can thus formulate general phonological generalizations without particular regard to actual physical implementation, which is studied separately under phonetics. The contrast between the DOI: 10.4324/9781003306443-3

40 Attitudinal Instrumentalism in Semantics phonetic and the phonological study of linguistic phenomena is a contrast between theoretically attending to the phenomena using descriptive natural scientific methods and attending to the same phenomena using broadly formal ones. The range of phenomena is the same; the theoretical means for studying it are different.1 An analogous ambiguity exists when it comes to the study of meaning. The focus of this chapter is on the formal side of the contrast.2 The first order of business is to get a feel for the kind of evaluation of linguistic phenomena at issue in formal semantics. In keeping with our discussion so far, we need to distinguish formal semantic theorizing from metaphysical theorizing and, more specifically, distinguish formal semantic evaluation from metaphysical evaluation (the kind of evaluation of the facts portrayed in language and thought). In an effort to get a better handle on the scope of semantic issues and their distinction from neighboring metaphysical ones, we draw on a familiar theme from Carnap, one of the early architects of formal semantics. This should pave the way for further explorations of how theoretical representations in semantics should be treated on their own terms. Carnap (1937) famously introduces the distinction between the material and formal modes of speech: Material Mode: Is there a whole number between 5 and 7? Formal Mode: Is ‘There is a whole number between 5 and 7’ true? The former is a question about whole numbers, targeting an arithmetical fact. The latter is a question about the sentence ‘There is a whole number between 5 and 7’. There is clearly a close connection between the two questions insofar as an answer to the latter depends on an answer to the former together with various semantic facts about the language at issue, such as that ‘whole number’ denotes a certain function from individuals to truth-values, ‘5’ and ‘7’ denote certain individuals, and so on. But the material mode and formal mode questions are clearly distinct insofar as an answer to the former question does not require the latter question to be settled. This might not be obvious when the formal mode existence question concerns the very language in which the material mode existence question is raised, as in the present case. But it becomes obvious once we consider the translation of the two questions into another language. The language-reality connection queried in the second question—truth for a sentence—depends on subsentential language-reality connections of denotation, an intra-linguistic structure of functional application, and the number-theoretic state of affairs queried in the first question. Factors other than the state of affairs factor are language-specific. The material mode question, on the other hand, queries the state of affairs factor alone. We can draw an analogous distinction between material and formal mode questions when it comes to existence per possible world. There is a familiar

Attitudinal Instrumentalism in Semantics 41

hurdle of ambiguity when it comes to possible world talk—whether ‘possible world’ is meant to apply to indices (or parameters within indices) within a formal semantic apparatus or whether it is meant to apply to global alternatives to reality as a whole as studied by the possible world metaphysician. The way to resolve such ambiguity is to attend to the role played by the notion within a wider theoretical context.3 With this caveat in mind, we can distinguish three ways of raising existence questions per possible world w: Material Mode: Are there people in w? Formal Mode:

Is ‘There are people’ true in w? {Internal: Atternal: Is ‘There are people’ true at w?

The material mode question concerns people in w. The answer is affirmative if there are such things in w and negative if there aren’t. One might think that asking such a question about a possible world is a category mistake if ‘in’ is understood in the usual spatiotemporal containment sense. Suppose one thinks of possible worlds as abstracta of some sort, say maximal states of affairs. Then the question of whether there are people in such a thing will seem ill-formed under the spatiotemporal containment sense of ‘in’. Analogously, it would seem ill-formed to ask, under the spatiotemporal containment sense of ‘in’, whether Socrates is in the impure set {Socrates}. In the latter case, we revise our understanding of ‘in’ along the lines of whatever ‘’ means in some preferred theory of sets, so the question of whether Socrates is in {Socrates} becomes whether Socrates  {Socrates}. So, too, in the present case, we revise our understanding of the material mode question of whether there are people in w to mean whether the maximal state of affairs w includes the state of affairs of there being people (perhaps with some requisite revision in the case of ‘include’.) Let us turn to the formal mode questions. Starting with the internal question, given the standard English interpretation of the quoted sentence in w minimizes the contrast between this question and the material mode question. An affirmative answer to each turns on the existence of people in w. Assuming that in w ‘there are’ means what it does in English, assuming that in w ‘people’ means what it does in English, and assuming that the compositional rules of English hold in w, ‘There are people’ in w will mean that there are people in w. The material mode question asks whether this is indeed so. And it is so just in case the sentence ‘There are people’ means what it does in English in w and is true in w. Whether ‘There are people’ means what it does in English in w depends on there being English speakers in w, speakers for whom ‘There are people’ means what it does in English. If there are no English speakers in w, then the answer to the formal mode internal question will depend on what ‘There are people’ means in w, if it means anything at all. No English sentence—‘There are people’ included—will be true in w in such a case on account of English not being spoken in w. If there are

42 Attitudinal Instrumentalism in Semantics no English speakers in w and if the quotation in the formal mode internal question refers to an English sentence, then the answer to that question is negative even if there are people in w. If there are no English speakers in w, the English sentence ‘There are people’ will not be true in w despite the existence of people in w. This brings us to the formal mode atternal question. When we raise this question, we raise a question about the English sentence ‘There are people’, meaning what it does for us English speakers and evaluated with respect to possible world w. All that’s required for the truth of ‘There are people’ at w is that there be people in w. (Here, we read the ‘in’ in the phrase ‘people in w’ as ‘according to’ or something similar.) To consider what obtains in a possible world is to consider what obtains according to a possible world, where the possible world encodes information, actual or counterfactual, relevant for semantic evaluation. When answering the formal mode atternal question, whether or not there are English speakers in w is beside the point and not determinative as such of whether the sentence in question is true at w.4 It is determinative, on the other hand, of whether or not the English sentence ‘There are people’ is true in w, as we just saw. So there are at least two sorts of relativization of linguistic phenomena to possible worlds. When we relativize linguistic phenomena to counterfactual world w, the contrast between the formal mode internal question and the formal mode atternal question turns on the difference between considering a language employed in w and considering our language as evaluated against the counterfactual situation at issue: Does ‘Moses’ name anyone in w? { Internal: Atternal: Does ‘Moses’ name anyone at w? Who does ‘Moses’ name in w? { Internal: Atternal: Who does ‘Moses’ name at w? And so on. We have a contrast between linguistic phenomena in w and linguistic phenomena evaluated at w. In the former case, we have the factualemergent relations true-in, refer-in, apply-in—all world-internal. In the latter case, we have the formal-semantic relations true-at, refer-at, applyat—all world-atternal. With these remarks on formal semantic evaluation as background and setting aside the special case of relativization to possible worlds, we can now see that claims such as ‘N refers to o’ are, in fact, ambiguous. On the one hand, they report natural facts, facts pertaining to bits of language standing for particular things, however such facts ultimately emerge from the surrounding factual ooze.5 On the other hand, such claims report facts that figure in formal-semantic modeling. That an expression refers to something in this sense means that it stands for (“denotes”) the thing relative to an assignment of semantic values to expressions for the purpose

Attitudinal Instrumentalism in Semantics 43

of formal-semantic evaluation. What the expression stands for in this way is what partakes in semantic computation.6 The ambiguity in ‘N refers to o’ is an ambiguity in the relation at issue, an ambiguity that, in fact, carries a difference in arity: R(N, o) { R(N, o, m), where R stands for the factual-emergent relation of reference, R stands for the formal-semantic relation of denotation, and m stands for a model, which is a pairing of a domain, i.e., a universe of discourse, and an assignment to linguistic expressions of semantic values drawn from the domain, i.e., an interpretation in the formal sense. Analogous remarks apply to claims of the form ‘S is true’. On the one hand, we have reports of the factual-emergent property of sentential truth— a kind of agreement with reality according to one prominent way of thinking. On the other hand, we have a formal-semantic relation to a model. The ambiguity has the form T(S) { T(S, m), where T stands for the factual-emergent property of sentential truth and T stands for the formal-semantic relation to a model. The latter is a formal capture of the former pre-theoretical subject matter. Once we see this contrast clearly, we can begin to consider the purposes served by the formalsemantic notion of truth-in-a-model.7 In keeping with the general theme of this book, we need not consider truth-in-a-model under a realist interpretation as revealing the nature of truth. Truth-in-a-model is a theoretical representation of truth within a larger explanatory setting. We can ask how truth should be modeled for the express explanatory purposes of semantic theory. We turn to explore this question next.

*3.2

Representing Truth

The notion most fundamental to the truth-conditional semantic enterprise is sentential truth. The received paradigm in semantics for modeling truth is Tarski’s work.8 Given the work’s prominence and centrality for subsequent semantic theorizing, it is easy to forget that what Tarski did was offer a certain theoretical capture of an everyday notion, the notion of sentential truth. Holding the theoretical capture apart from the everyday notion allows us to reflect on the achievement by asking what makes a theoretical representation of truth especially suited for semantics. The general question of how sentential truth should be modeled for semantic purposes is neither trivial nor uninteresting and yet seldom discussed in its own right.

44 Attitudinal Instrumentalism in Semantics In Simchen (2017), I begin to develop an answer to this question against a background discussion of metasemantics and its relation to formal semantics. My purpose in this section is to make further progress on the issue by way of illustrating the general utility of an instrumentalist attitude in semantics. The question of realist vs. instrumentalist attitude towards truth-in-a-model as a representation of sentential truth will not be undertaken directly here, but the reader is invited to consider the case against the conjectured necessary conditions articulated in Section 2.1.9 On the other hand, asking why truth-in-a-model is so well-suited for its theoretical role within the explanatory context of truth-conditional semantics will be shown to yield some interesting results. The first order of business is to explain the context in which the question of how truth should be modeled arises, particularly in metasemantics. Think of metasemantics as the study of what determines that expressions have their semantic significance. There is a fault line in metasemantics between positions that portray semantic endowment as determined directly by conditions surrounding the production or employment of the items thus endowed on the one hand, and positions that portray semantic endowment as determined directly by conditions surrounding the interpretive consumption of such items on the other. Examples of metasemantic views of the former sort are Donnellan’s (1966) views on how certain uses of descriptions refer (by having a putative referent “in mind”), Kripke’s (1980) views on how proper names refer (by initial acts of naming and subsequent causal-historical chains of communication), Kaplan’s (1989) views on how demonstrative pronouns refer (by directing intentions), and Putnam’s (1975) views on how kind terms come to apply to instances of the relevant kinds (by intending the term to apply to anything relevantly similar to paradigmatic instances). Examples of metasemantic views of the latter sort are Davidson’s (1977) interpretationist notion that expressions are assigned semantic values so as to generate the right (“interpretive”) truthconditions for sentences in context, and Lewis’s (1983, 1984) interpretationist doctrine of reference magnetism according to which expressions are assigned semantic values so as to maximize truth for the total theory in which they are embedded while respecting objective joints in nature. Views of the former sort prioritize semantic endowment for subsentential expressions over semantic endowment for whole sentences in the order of metasemantic explanation. Views of the latter sort prioritize semantic endowment for sentences over semantic endowment for subsentential expressions. In Simchen (2017), I develop an extended argument against interpretationism in metasemantics that aims to show that any such position is vulnerable to radical indeterminacy in singular reference. Whether or not the argument succeeds in its broad metasemantic aims is beyond our immediate concerns. What is of immediate interest here is the argument’s deployment of an alternative construal of sentential truth. The argument considers a simple first-order extensional language L that contains, besides the usual logical vocabulary, only constants and predicate

Attitudinal Instrumentalism in Semantics 45

letters of various arities. A model m is understood in the usual way as a pairing of a domain and an interpretation function that assigns to each constant a member of the domain and to each predicate letter of arity n a subset of the domain’s nth Cartesian power. The standard Tarskian construction of truth-in-a-model (Ï) includes the following clause for the atomic cases: m Ï ϕv1, ..., vi , t1, ..., tjs ⇐⇒ 〈sv1, ..., svi, σ t, ..., σ t1, ..., σ tj〉 ∈ σ ϕ, where s is an assignment function that assigns members of the domain to the free variables v1, ..., and vi, t1, ..., and tj are constants, σ is the model’s interpretation function, and ϕ is an n-place predicate letter (n = i + j ≥ 1). We now consider an alternative construal of sentential truth—scrambledtruth-in-a-model (Ïρ)—that agrees with the standard Tarskian construal in all respects except for the atomic clause. For any m = M, σ , a scrambler ρ : M → M is a permutation on the domain M: m Ïρ ϕ(v1, ..., vi, t1 ..., tj)s ⇐⇒ 〈ρs(v1)), ..., ρs(vi)), ρσ (t1)), ..., ρσ (tj))〉 ∈ σ (ϕ). Scrambled-truth-in-a-model, in effect, generalizes the two-place Tarskian notion of truth-in-a-model by adding a scrambler ρ as a third parameter. Truth-in-a-model thus becomes a special case of scrambled-truth-in-amodel when ρ is identity. Of course, ‘become’ is to be understood here as heuristic flourish and not only because of the temporal connotation. Strictly speaking, truth-in-a-model and scrambled-truth-in-a-model are considered here as alternative theoretical representations of one and the same pretheoretical subject matter of sentential truth. Now, it is easily observed that for any model m = M, σ, if mμ = M, σ μ is the same as m but for the fact that for any constant t of L, σ μ(t) = μ(σ(t)) where μ is a permutation on M, then for any sentence S of L, m Ï S ⇐⇒ mμ Ïμ−1 S.10 μ and μ−1 simply “cancel each other out”. This simple fact can be deployed to undermine a familiar Lewisian interpretationist attempt to disarm semantic indeterminacy arguments due to Putnam and others. Here is some relevant background. In a number of writings from the late 1970s and early 1980s, Putnam has argued that a distinction held dear by metaphysical realists between epistemic ideality and realist truth collapses under minimal assumptions.11 The metaphysical realist would like to maintain that epistemic ideality might, if we happen to be epistemically unlucky, fall short of realist truth. Putnam’s argument, in a nutshell, is that an epistemically ideal theory would be, at the very least, consistent. So under minimal assumptions, it would have a model of the same size as the world. And so, it would have a model with the world itself as its domain. Hence the theory in question is guaranteed to be true of

46 Attitudinal Instrumentalism in Semantics the world itself. This is the notorious model-theoretic argument. Lewis’s response to the argument is to say that not every interpretation of the theory’s language into the world is on par with any other. Some interpretations are more eligible than others, given the way the world is. An interpretation is more eligible in Lewis’s sense the more it respects objective joints in nature. And there is no guarantee that the epistemically ideal theory would be rendered true by a reasonably eligible interpretation. Thus, according to Lewis, we can restore the idea that epistemic ideality is one thing and realist truth another. More broadly, what determines that expressions have the meanings they do is not just truth for the overall theory in which they partake, as assumed by Putnam’s argument. That would leave language largely semantically indeterminate. What determines that expressions have the meanings they do is truth for the overall theory that respects the world’s pre-existing structure. This is the Lewisian idea of reference magnetism.12 Unfortunately, the idea is ineffective in blocking semantic indeterminacy. Turning to indeterminacy in singular reference first, let mL be the Lewisian intended model ML, σ L, where ML is the intended domain. Let us first assume that for any σ, σ ≠ σ L, σ is no more eligible in Lewis’s sense than σ L as an overall interpretation of the language when it comes to the predicates. σ L is thus maximally eligible by Lewisian standards—the interpretations of predicate letters are maximally natural in Lewis’s sense. Next, an alternative model m = M L, σ  is considered, where σ (ϕ) = σ L(ϕ) for every ϕ so that maximal naturalness for the predicates is preserved. Letting f : M L → M L be a nontrivial permutation such that for some constant t, f(σ L(t)) ≠ σ L(t), σ(t) is defined as f (σ L(t)) for every constant t. It is then an immediate application of the general observation above that for any sentence S of L, mL Ï S iff m Ï f−1 S. The metasemantic upshot is that nothing the reference magnetist can offer here will decide which of mL and m is intended. σ L and σ  are equally maximally eligible by Lewisian standards and can differ as radically as we like on the interpretation of the singular terms. Semantic indeterminacy is thus fully restored. Before moving on, we note that this kind of indeterminacy in singular reference is not a simple rehashing of standard semantic indeterminacy arguments. In this version, the interpretation of predicate letters can remain fixed while the interpretation of the singular terms varies by utilizing the triadic scrambled-truth-in-a-model construction. That is why reference magnetism, despite its insistence on relative fixity in the interpretation of predicate letters, is incapable of blocking the argument without special pleading. But now stepping back and considering scrambled-truth-in-a-model in its own right raises a question of independent interest: What advantage does Tarski’s apparatus of truth-in-a-model enjoy over scrambled-truthin-a-model as a formal capture of sentential truth for semantic purposes?—For clearly we cannot take scrambled-truth-in-a-model seriously

Attitudinal Instrumentalism in Semantics 47

as an alternative to truth-in-a-model for the purposes of truth-conditional semantics. The qualification ‘for the purposes of truth-conditional semantics’ is important because even if we discern some significant abstract model theoretic difference between the two alternative captures of sentential truth, this by itself does not, without argument, entail a decisive advantage for one construction over the other for the purposes of semantic theory.13 The Simchen (2017) answer to the advantage question is that the original Tarskian construction respects a natural and intuitive locality-perreference requirement on modeling sentential truth: truth for singular sentences must be directly dependent on reference for singular terms. Tarskian truth-in-a-model clearly abides by the requirement while scrambled-truth-in-a-model clearly flouts it—truth in the atomic cases on that alternative scheme depends on reference for singular terms only as mediated by a scrambler. This turns out to be important in the metasemantic context. Interpretationism as a metasemantic orientation makes semantic endowment for singular terms beholden to semantic endowment for whole sentences: truth and falsity come first in the order of metasemantic explanation, while subsentential reference is derived. The requirement of locality-per-reference, on the other hand, allots priority to subsentential reference over sentential truth and falsity. It is thus the natural accompaniment to non-interpretationist metasemantic views that recognize reference as fixed prior to truth. It is, of course, open to a metasemantic interpretationist to insist on locality-per-reference as a constraint on modeling truth in order to block the new indeterminacy argument. But such insistence seems ad hoc in comparison with the noninterpretationist justification for the constraint. Non-interpretationist views seem at a clear advantage here, already having resources to account for the fact that scrambled-truth-in-a-model is not what we want from a formal capture of sentential truth. Theory choice in semantics, it appears, is not metasemantically neutral. The focus of the indeterminacy argument in Simchen (2017) is metasemantics, the study of how it is that expressions become “loaded” with their contributions to truth-conditions. But the proposed requirement of locality-per-reference on modeling truth for semantics raises a concern of independent interest. Tarski’s “straight” notion of truth-in-a-model, as compared with my “bent” notion of scrambled-truth-in-a-model, is so very clearly superior in modeling the everyday notion of sentential truth for semantic purposes. A pressing question is what accounts for this phenomenology. Regardless of what we are inclined to think about the prospects of metasemantics as a field of inquiry, the comparison of Tarski’s notion with neighboring notions seems important to the philosophy of (the science of) formal semantics. For given the prominence of Tarski’s work for subsequent semantic theorizing, such a comparison enables us to achieve a better understanding of theoretical choices that lie at the core of the truthconditional semantic enterprise.

48 Attitudinal Instrumentalism in Semantics With this in mind, let us now ask: what other requirements might there be for modeling truth beyond locality-per-reference? My aim for the remainder of this section is to articulate another such requirement. We begin with another alternative construal of sentential truth—jumbled-truthin-a-model (Ïτ)—which again agrees with the standard Tarskian construal in all respects except for the atomic clause. For any m = M, σ , a jumbler τ is a permutation on P(M n) (the power set of M ’s nth Cartesian power) for every n: m Ïτ ϕ(v1, ..., vi, t1, ..., tj)s ⇐⇒ 〈s(v1), ..., s(vi), σ (t1), ..., σ (tj)〉 ∈ τ (σ (ϕ)) Truth-in-a-model becomes a special case of jumbled-truth-in-a-model when τ is identity. Now, it is easily observed that for any model m = M, σ, if mπ = M, σπ is the same as m, but for the fact that for any n and any predicate letter P n of L, σπ(P n) = π(σ(P n)) where π is a permutation on P(M n), then for any sentence S of L, m Ï S ⇐⇒ mπ Ïπ−1 S. We see this by focusing on atomic sentences ϕ(t1, ..., tn)—generalizing to atomic formulas is trivial and full generality follows by induction on syntactic complexity: mπ Ïπ−1 ϕ(t1, ..., tn) ⇐⇒ 〈σπ(t1), ..., σπ(tn)〉 ∈ π−1(σπ(ϕ)) ⇐⇒ 〈σ (t1), ..., σ(tn)〉 ∈ π−1(π(σ(ϕ))) ⇐⇒ 〈σ (t1), ..., σ(tn)〉 ∈ σ(ϕ) ⇐⇒ m Ï ϕ(t1, ..., tn). This construction can be deployed to undermine Lewisian reference magnetism even further by enabling indeterminacy in the application of predicates, which is again immune to the magnetist proposal. Consider, again, the Lewisian intended model m L = M L, σ L with the maximally eligible σ L. Let us define an interpretation σ , σ  ≠ σ L, that agrees with σ L on the assignments to every constant but potentially disagrees on the assignments to the predicate letters. For each n for which L contains a predicate letter of that arity, we consider a nontrivial permutation gn on the set {σL (P1n), σL (P2n), σL (P3n), ...} of assignments to all of L’s predicate letters P1n, P2n, P3n, ... (if no such nontrivial permutation exists, we let gn go trivial).14 Now, for any arity n and any predicate letter ϕ of this arity, we define g(σ L(ϕ)) = gn(σ L(ϕ)) and define σ (ϕ) = g(σ L(ϕ)) for each ϕ and σ (t) = σ L(t) for each constant t. From this definition of g it is clear that there is a −1 mapping G : P( M n ) - P(M n ) for every n that extends g. Clearly G is a jumbler. Where m = M L, σ , it follows from the above that for any sentence S of L, m L E S iff m′′ EG −1 S. We note that mL and m are equally maximally eligible by Lewisian standards. So under the minimal assumption that there is an n for which L contains

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more than a single predicate letter of that arity, the upshot is indeterminacy in the application of predicates sustained by the availability of an alternative construal of sentential truth, jumbled-truth-in-a-model. It is yet another form of semantic indeterminacy that passes under the radar of reference magnetism. Jumbled-truth-in-a-model presents yet another challenge: What advantage does truth-in-a-model have over jumbled-truth-in-a-model as a formal capture of sentential truth?—For surely jumbled-truth-in-a-model cannot be taken seriously for semantic purposes despite the fact that, unlike scrambled-truth-in-a-model, jumbled-truth-in-a-model does not violate the aforementioned locality-per-reference constraint. And yet jumbledtruth-in-a-model is as unsuitable for modeling sentential truth as the other construction. Echoing an analogous point made in Simchen (2017), I note that an answer to this new advantage question cannot merely point to some abstract feature truth-in-a-model has and jumbled-truth-in-a-model lacks without further argument as to why having this feature should matter to semantics. For example, truth-in-a-model exhibits invariance under isomorphism: (IUI)

If m Ï S and m  m•, then m• ÏS.

But it is surely not the case that for any m = M, σ, if m Ïτ S and m  m•, then m• Ïτ S. For suppose that m Ïτ  ϕ(t1, ..., tn). Then for any m• = M •, σ • for which M  M• = , τ(σ•(ϕ)) will be undefined, and so m• Ïτ ϕ(t1, ..., tn) will be undefined. Indeed, jumbled-truth-in-a-model has the following feature instead: (IUI)

If m Ïτ S and m  m•, then m• Ïτ • S,

where τ • = I • ◦ τ ◦ I •−1 and I • is a mapping such that for each s  M n, → M • is the I •(s) = {〈I(o1), ..., I(on)〉 | o1, ..., on  s} where I : M → 15 isomorphism. But why exactly (IUI) should be important for semantic purposes—as opposed to (IUI), say—is a question that must be faced by anyone who wishes to tackle the contrast between truth-in-a-model and neighboring notions such as jumbled-truth-in-a-model “in the abstract”, as it were. It is a difficult question. An answer would seem to require, at a bare minimum, an exploration of the scope of semantic theory in relation to the logicality of its fundamental notions. But there is a far more obvious and direct route to why jumbled-truthin-a-model is unsuitable for semantic purposes: jumbled-truth-in-a-model fails to respect a natural and intuitive locality-per-application requirement on modeling sentential truth that truth-in-a-model clearly respects. Locality-per-application is the requirement that sentential truth for singular

50 Attitudinal Instrumentalism in Semantics sentences should depend directly on the application of the predicates. In jumbled-truth-in-a-model this requirement is clearly flouted: for an atomic sentence to be jumbledly true in a model is not for the predicate to apply to the referents of the singular terms but for its jumbling to thus apply. This is obviously not so for Tarksi’s original construction of truth-in-a-model where truth for atomic cases depends directly on the application of the predicates. As a side note, locality-per-application is a challenge to the metasemantic interpretationist just as much as locality-per-reference and for the same reason. The interpretationist orientation to metasemantics renders semantic endowment for subsentential expressions beholden to the semantic endowment for the sentences in which they partake. For non-interpretationist views, on the other hand, the situation is reversed. The non-interpretationist can and must insist not only on reference for singular terms as settled prior to truth but also on predicate applicability as settled prior to truth. Once again, non-interpretationism is at a clear advantage over interpretationism as a metasemantic orientation to accompany truth-conditional semantic theory. It is the natural metasemantic partner to the two requirements on modeling sentential truth we have been considering—locality-per-reference and locality-per-application. On one level, it is hardly surprising that scrambled-truth-in-a-model and jumbled-truth-in-a-model should be inferior to standard truth-in-a-model as theoretical captures of sentential truth. The requirements of localityper-reference and locality-per-application are, after all, natural and intuitive. They are to be respected by any theoretical articulation of our everyday notion of truth. Insofar as semantics concerns itself with the formal modeling of language-world relations (a widespread, even if not universally shared, conception), it is hardly surprising that truth-in-a-model should be found suitable for semantics—so suitable, in fact, that we tend to overlook the features that render it so. It is perhaps more surprising that semantics, as it is widely understood, is difficult to reconcile with interpretationism as a metasemantic orientation. Teasing out further lessons from this last observation, especially lessons for the history of formal semantics and the seminal contributions made to it by leading metasemantic interpretationists, is a larger project for another day. In the meantime, we note that comparing the Tarskian notion of truth-in-a-model with neighboring notions affords us a better understanding than was hitherto available of pre-theoretical requirements that shape theoretical choices at the basis of contemporary semantic theory. That the issue can so much as be raised is testimony to a clear instrumentalist streak in theory construction in semantics. The question of how to theoretically represent the pre-theoretical notion of truth for semantic purposes is not answered in the way we might initially be inclined to answer a parallel question in the metaphysics of truth.16 The question of whether truth-in-a-model reveals what truth really is, at bottom, is beside the semantic point. We could represent truth by deploying

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the Tarskian construction of truth-in-a-model (Ï) under the stipulation of an intended model. Or we could represent truth by deploying the more general scrambled-truth-in-a-model construction (Ïρ ) under the stipulation of an intended model and the further stipulation that the scrambler go trivial. Or we could represent truth by deploying the jumbled-truth-in-amodel construction (Ïτ) under the stipulation of an intended model and the further stipulation that the jumbler go trivial. Or we could represent truth by deploying the most general construction of scrambled-and-jumbledtruth-in-a-model (Ïτρ) under all three stipulations (intended model, trivial scrambler, trivial jumbler). It could then be argued that the advantage of truth-in-a-model over the alternative constructions is obvious, given the need for the extra stipulations to approximate answerability to the requirements of locality-per-reference and locality-per-application in the other cases. But the issue would not be settled by an emphatic insistence that truth-in-a-model is revelatory of the nature of truth while the alternative constructions are not, as is the wont of the attitudinal realist.

*3.3

Indirect Reference Again

In Section 1.4, we considered Frege’s theory of indirect reference as another example of the inclination to regard semantic analyses of certain factual reports as revealing the nature of the facts being reported, quite apart from their utility within semantic theorizing. We saw that a realist attitude towards such theoretical representations in the metaphysics of attitudes isn’t properly motivated, given the distinctive theoretical aims of semantics. And we concluded that there is, in fact, little reason to regard a semantic theoretical representation whereby a certain relation obtains between a believer and the content of the complement clause of the belief reports as a good guide to the metaphysics of the cognitive state of belief being reported. This conclusion is at odds with much of the metaphysics of mind inspired by Frege’s theory, as we will see in Chapter 6. In this section, we return to Frege’s theory of indirect reference as a strictly semantic theory. It is often assumed that the theory of indirect reference requires an infinite hierarchy of Fregean senses. Recall that the basic thought behind the theory is that attitude verbs create an environment where reference gets shifted. Frege’s suggestion is that expressions in those clausal complements refer not to what they would refer to outside that context but rather to what they would otherwise express—Fregean senses, which are modes of presentation of what the expressions would otherwise refer to. But then it appears that attitude reports with clausal complements that are themselves attitude reports would require yet further reference shifting to modes of presentation of modes of presentation of what the expressions would refer to, and so on without apparent end in sight. This immediately raises two issues. The first is whether Frege’s theory of indirect reference on its own terms does indeed launch an infinite hierarchy of Fregean senses. The second is the larger methodological question

52 Attitudinal Instrumentalism in Semantics of how to think of such a theory in light of the express goals of formal semantic explanation, which is an issue that will occupy us in the next chapter as well. When it comes to the first issue, the theory of indirect reference is often presumed to require an infinite hierarchy of senses. This is commonly thought to be a substantial cost for any semantic theory and is widely considered a major flaw in Frege’s semantic outlook. Perhaps the most influential treatment of the hierarchy of Fregean senses is that of Burge (1979), who offers an argument for the existence of the hierarchy from rather minimal Fregean assumptions. I will now show that this argument, endorsed by many, does not itself enforce an infinite hierarchy of senses. When it comes to the second issue, I aim to show that an instrumentalist attitude towards semantic theoretical representations allows the semanticist who wishes to utilize Frege’s theory of indirect reference to circumvent the need to posit an infinite hierarchy of senses. The general theme of attitudinal instrumentalism towards semantic theoretical representations will then be elaborated further in the next chapter. Consider the occurrence of ‘Opus 132 is a masterpiece’ in (1) Bela believes Opus 132 is a masterpiece and compare it with its occurrence in (2) Igor believes Bela believes Opus 132 is a masterpiece.17 Fregean doctrine tells us that in (1), ‘Opus 132 is a masterpiece’ refers to the ordinary sense of ‘Opus 132 is a masterpiece’, a mode of presentation of the truth-value of ‘Opus 132 is a masterpiece’ as it occurs unembedded, the thought that Opus 132 is a masterpiece. And the doctrine is often taken to suggest that in (2), ‘Opus 132 is a masterpiece’ refers to the sense of ‘Opus 132 is a masterpiece’ in (1), a mode of presentation of a mode of presentation of the truth-value of ‘Opus 132 is a masterpiece’ as it occurs unembedded, a mode of presentation of the thought that Opus 132 is a masterpiece. Question: Might the referent of ‘Opus 132 is a masterpiece’ in (2) be the same as the referent of ‘Opus 132 is a masterpiece’ in (1), namely, the thought that Opus 132 is a masterpiece? There is an influential argument due to Burge that is meant to show that it can’t be. For any expression α, let ‘sα s’ refer to the sense of α and assume for reductio that ssα ss = sα s. (We treat single quotes as corners and assume the sense-of relation to be a one-many relation to expressions.) Call this reductio assumption SC for “Sense Collapse”. Also, assume a Sense Functionality principle SF that for any expressions α, β1, ..., βn of a suitable type, s α(β1, ..., βn)s = sα s(sβ1s, ... sβns); assume a Sense Identity principle SI that for any expressions α, β, if α is synonymous with β, then sα s = sβ s; and assume the extensionality principle that for any expressions α, β, if α = β, then ... α ...  ... β ... .

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Now, the Fregean analysis of (1) is: (3) Believes(Bela, sOpus 132 is a masterpieces). And (2) is analyzed as (4) Believes(Igor, sBela believes Opus 132 is a masterpieces), from which, by the synonymy of (1) and (3), SI, and extensionality, we get (5) Believes(Igor, sBelieves(Bela, sOpus 132 is a masterpieces)s), from which, by SF and extensionality, we get (6) Believes(Igor, sBelievess(sBelas, ssOpus 132 is a masterpiecess)), from which, by SC and extensionality, we get (7) Believes(Igor, sBelievess(sBelas, sOpus 132 is a masterpieces)). But assuming Bela isn’t believed to believe everything with the truthvalue of Opus 132 being a masterpiece, if (5) is correct, then (7) isn’t. For call what sBelievess refers to ‘Believes’ (a dyadic first-level concept), call what sBelas refers to ‘Bela’ (an individual), and call what sOpus 132 is a masterpieces refers to ‘truth-value’ (a truth-value). Let ‘Believes’ express s Believess, ‘Bela’ express sBelas, and ‘truth-value’ express sOpus 132 is a masterpieces. Then, (8) Believes(Bela, truth-value) expresses sBelievess(sBelas, sOpus 132 is a masterpieces), the second relatum for Igor’s belief according to (7), purportedly a thought about what Bela believes. But then, for any δ for which ‘δ = truth-value’ is true, we get (9) Believes(Bela, δ ) by extensionality. Such a consequence does not follow from (3), which expresses sBelieves(Bela, sOpus 132 is a masterpieces)s, the second relatum of Igor’s belief according to (5). So assuming the correctness of (5), SC should be given up. SC enables the further derivation of (7), which is incompatible with Igor not believing Bela to believe everything, with the truth-value of Opus 132 being a masterpiece. SC says that for any α, ssα ss = sα s. The foregoing shows that for some α (i.e., ‘Opus 132 is a masterpiece’), ssα ss ≠ sα s. And so, SC is false.

54 Attitudinal Instrumentalism in Semantics Let us now assume that Burge’s argument supports the generalization that for any α, ssα ss ≠ sα s. Question: Does this argument force upon us a hierarchy of senses? Burge (1979) concludes his presentation of the argument as follows (passage adjusted to the terminology and numbering of the reconstruction above and supplemented accordingly): The argument shows that on these assumptions ‘Opus 132 is a masterpiece’ in [(2)] cannot be represented by a term [‘sOpus 132 is a masterpieces’] denoting the [thought] that Opus 132 is a masterpiece. It is prima facie plausible to assume with Frege that the expression as it occurs in [(2)] should be represented by a term [‘ssOpus 132 is a masterpiecess’] denoting the sense of the expression [‘Opus 132 is a masterpiece’] that represents [‘Opus 132 is a masterpiece’] as it occurs in unembedded belief contexts [e.g. (1)]. Given this assumption, the argument can be replicated to show that the sentential expression [‘Opus 132 is a masterpiece’] as it occurs in doubly embedded oblique contexts must be represented by yet another term [i.e., a term other than ‘ssOpus 132 is a masterpiecess’]—and so on. (272) It is often assumed that Burge’s argument establishes a hierarchy of senses. Indeed, Burge writes: “In summary, the argument for a hierarchy ... seems very powerful” (274). The assumption makes an appearance in a recent discussion by Salmon (2005: 1100 n. 31). And in an even more recent discussion Kripke (2008) writes: “I agree with Burge ... that the hierarchy is an actual consequence of Frege’s theory” (184 n. 9). This, I will now argue, is a mistake. Call an expression without s-quote marks an expression of level 0. Independently of Burge’s argument, it seems plausible on Fregean grounds to suppose that for any expression α of level 0, α ≠ sα s. (Think here of the example of Mont Blanc in the famous exchange between Frege and Russell.18) Similar considerations could extend to α ≠ s(×n)α s(×n) for any n ≥ 1, where ‘s(×n)’ designates n occurrences of ‘s’. And we assume that Burge’s argument can be given for any n ≥ 1 to the effect that s(×n)α s(×n) ≠ s(×n + 1)α s(×n + 1). But such an argument would still not launch a hierarchy of senses per α. For a hierarchy per α, we would need to show that for any n ≥ 1, the following conjunction is true: (10) ∧1in s(×i) α s(×i) ≠s(×n + 1) α s(×n + 1). Now consider the following instance of (10) for n = 2:

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(11) sαs≠sssαsss∧ssαss ≠sssαsss. Burge’s argument establishes, we suppose: (12) sαs≠ssαss∧ssαss≠sssαsss. Mont Blanc-type considerations establish: (13) α≠sαs∧α≠ssαss∧α≠sssαsss. But we can see that the theory {(12), (13), ¬(11)} is consistent by constructing a simple model m = {o, o, o},σ, where {o, o, o} is the domain and σ is the interpretation function: σ(α) = o σ(sαs) = o σ(ssαss) = o σ(sssαsss) = o It is easily verified that m Ï{(12), (13), ¬(11)}. So now consider the following model m = {o, o, o},σ interpreting every expression of the form s ... sα s ... s, where n ≥ 1: σ α = o σ s(×2n - 1) α s(×2n - 1)) = o σ * (s(×2n) α s(×2n)) = o Let the Burge set B be {s(×n)α s(×n) ≠ s(×n + 1)α s(×n + 1) | n ≥ 1} and let the Mont Blanc set M be {α ≠ s(×n)α s(×n)| n ≥ 1}. Clearly for any n ≥ 2, mÏ ¬(10). And for any n ≥ 1, m Ï s(×n)α s(×n) ≠ s(×n + 1)α s(×n + 1) and mÏ α ≠ s(×n)α s(×n). So m Ï {B, M}. I conclude that Burge’s argument does not enforce a hierarchy of senses per α after all. In light of the foregoing, consider the following triply embedded occurrence of ‘Opus 132 is a masterpiece’: (14) Zoltan believes Igor believes Bela believes Opus 132 is a masterpiece. Fregean doctrine analyzes it as

56 Attitudinal Instrumentalism in Semantics (15) Believes(Zoltan, sIgor believes Bela believes Opus 132 is a masterpieces), which, by the synonymy of (2) and (5), SI, and extensionality, gets us (16) Believes(Zoltan, masterpieces)s)s),

s

Believes(Igor,

s

Believes(Bela,

s

Opus 132 is a

Which, by repeated applications of SF and extensionality, gets us (17) Believes(Zoltan, sBelievess(sIgor s, ssBelievesss(ssBelass, masterpiecesss))).

sss

Opus 132 is a

Now, according to interpretation σ  above, σ (sssα sss) = σ (sα s). Let us consider such an interpretation for ‘Opus 132 is a masterpiece’ and assume, accordingly, that (18)

Opus 132 is a masterpiecesss = sOpus 132 is a masterpieces.

sss

From (17), (18), and extensionality, we get (19) Believes(Zoltan, sBelievess(sIgors, ssBelievesss(ssBelass, sOpus 132 is a masterpieces))). Can we say here, as we did in the case of Burge’s original argument, that assuming Bela isn’t believed to believe everything with the truth-value of Opus 132 being a masterpiece, if (16) is correct, then (19) isn’t? Call what ss Believesss refers to ‘Believes’ (a mode of presentation of the relational concept Believes), call what ssBelass refers to ‘Bela’ (a mode of presentation of the individual Bela), and call what sOpus 132 is a masterpieces refers to ‘truth-value’ as before. Let ‘Believes’ express ssbelievesss, ‘Bela’ express ssBelass, and ‘truth-value’ express sOpus 132 is a masterpieces as before. Then (20) Believes(Bela, truth-value) expresses ssBelievesss(ssBelass, sOpus 132 is a masterpieces)), which is the second relatum for Igor’s belief according to Zoltan’s belief according to analysis (19). Now, it does follow from (20) by extensionality that (21) Believes(Bela, δ ) for any δ that agrees in truth-value with ‘Opus 132 is a masterpiece’. But notice that (20) does not purport to express any thought about what Bela believes. With (20), we are in pre-theoretically unfamiliar territory. What

Attitudinal Instrumentalism in Semantics 57

(20) expresses is a complex consisting of a mode of presentation of a mode of presentation of a relational concept, a mode of presentation of a mode of presentation of an individual, and the thought that Opus 132 is a masterpiece. To simply insist that while (21) follows from (20), it does not follow from whatever would express ssBelievesss(ssBelass, sssOpus 132 is a masterpiecesss), the second relatum for Igor’s belief according to Zoltan’s belief according to (17), and so to conclude that the latter complex is distinct from the second relatum of Igor’s belief according to Zoltan’s belief according to (19), is to beg the issue at hand. There might well be other theoretical reasons to resist (18) and, more generally, reasons to resist the collapse of third-level senses to first-level senses, fourth-level senses to second-level senses, fifth-level senses to first-level senses, sixth-level senses to second-level senses, and so on. For example, under the present scheme, the usual Fregean assumption whereby for each n > 1, s(×n)αs(×n) refers to s(×n− 1)αs(×n− 1) entails that for any even number k, s(×k)αs(×k) refers to and is referred by s(×k− 1)αs(×k− 1), whereas for any odd number m, s(×m)αs(×m) will refer to both s(×m + 1)αs(×m + 1) and the direct referent of α (however this is to be modeled, ultimately). The present point isn’t that we in fact need only two levels of sense. That is a question pending further theoretical development. The present point is that the familiar argument for the hierarchy fails to establish an infinite hierarchy of senses. And once we view the theory of indirect reference through an instrumentalist lens, various aspects of the position become negotiable as part of an overall theoretical effort to explain the target phenomena. In an important paper on Frege’s theory of indirect reference, Parsons (1981) argues that a hierarchy of senses is not an inevitable outcome of basic Fregean doctrine. He considers a Carnapian version that resorts to a single level of sense by revisiting the commonly held assumption that the referent of a complex expression is invariably a function of the referents of its parts. In this version, where X( ) is an indirect sentential context, the referent of X(Y ) is the application of the referent of X to sY s rather than the application of the referent of X to the referent of Y.19 (The Sense Functionality principle SF remains unaltered.) This allows us to maintain that for any α and any n ≥ 1, sα s = s(×n)αs(×n). And it blocks the transition from (8) to (9) in the above reconstruction of Burge’s argument. In response, however, it might be claimed that extensionality is too fundamental to the Fregean outlook to be amenable to revision as required by such an approach. The argument presented here, by contrast, does not depend on tinkering with extensionality in any way. In a more recent paper on the hierarchy, Parsons (2009) considers a semantic framework that avoids a hierarchy of senses by introducing a function symbol ‘’ into the metalanguage (and a new governing logical principle) that stands for the function that for any sentence α takes sα s to sthat α s. But such

58 Attitudinal Instrumentalism in Semantics enrichment of the metalanguage, with the presupposed object-level/ meta-level distinction, is difficult to motivate within a more orthodox Fregean outlook. Whether Frege’s theory of indirect reference is committed to an infinite hierarchy of senses is a question that is usually handled under the tacit assumption that the theory’s pronouncements are to be taken in a realistic spirit. This is certainly Frege’s original approach to the topic. What the assumption amounts to, at the very least, is the idea that the theory of indirect reference is to reveal the very meaning of attitude reports as they are “in the wild”, so to speak. By extension, the theory is often also presumed to reveal the nature of the reported cognitive facts themselves, the facts of belief, for example. But such large methodological assumptions are not inevitable. When thinking of the theory in a more instrumentalist spirit, we can ask what explanatory work the theory can be expected to achieve in the first place and how much of the pre-theoretical situation surrounding the meaning of attitude reports should be captured. Under such attitudinal instrumentalism, it is at least not obvious that finitely many levels of sense could not suffice for the theory’s explanatory success. Perhaps, for example, we need as many levels of sense per α as there are humanly parsable embeddings of α and no more. The foregoing discussion opens up a more general issue: What should we expect of semantic analyses of our sentences? Specifically, should we expect such an analysis to reveal the nature of what it represents, to wit, the meaning of the analysandum? Or should we, rather, evaluate semantic analyses without the further demand that such theoretical representations of the significance of natural language expressions reveal the nature of what they represent individually? The next chapter will explore the second option as part of a wider pitch for the utility of attitudinal instrumentalism in the formal semantic study of natural language. Once an instrumentalist attitude towards theoretical representations in semantics is in view, we can also gain a better understanding of formal semantics in relation to the aspirations and procedures of ordinary language philosophy, which is the topic we turn to next.

Notes 1. In Section 4.2 we will encounter the same dynamic of a single range of linguistic phenomena theoretically pursued in two different ways at play in the case of semantics and speech act theory. 2. In the study of meaning the closest analog to phonetics would be a “productivist” approach to metasemantics. See Simchen (2017: Ch.3) for an extended discussion of productivist metasemantics in relation to formal semantics. 3. I study this ambiguity in more detail in Simchen (2012, 2013a).

Attitudinal Instrumentalism in Semantics 59 4. I set aside the distracting complication that w may contain people all of whom are speakers of English, in which case there being English speakers in w will be determinative of whether or not the sentence ‘There are people’ is true at w. 5. ‘Natural’ here should not be read as a tacit endorsement of a reductive naturalism. Even if semantic facts are inherently social, and social facts aren’t reducible to natural facts according to some favored interpretation of ‘reducible’, semantic facts count as natural in the sense of obtaining in nature, as opposed to obtaining super-naturally (whatever that might be). 6. I explore this particular contrast between the two readings of reference claims as they pertain to linguistic reflexivity in Simchen (2013b). 7. From the present perspective ‘truth-in-a-model’ is a misnomer—the relation should be termed ‘truth-at-a-model’—but we keep the familiar nomenclature. 8. See, in particular, Tarski’s classic (1983). 9. Given the difference in arity between the theoretical and pre-theoretical notions discussed in the previous section, it would be interesting to compare this case with other cases where the theoretical representation of a pre-theoretical subject matter includes an extra parameter, as in the SR-based representation of being in motion as a relation to a reference frame (where pre-theoretically being in motion is monadic rather than dyadic). See discussion in Section 1.3, especially at 15 n.16. 10. Details can be found in Simchen (2017: 2.3). 11. See, for example, Putnam (1977, 1978, 1981). 12. See Lewis (1983, 1984) for the original articulation of the idea and some of its ramifications. No claim is being made here as to the earlier metasemantic position articulated in Lewis (1975), but the idea of tacking eligibility of interpretation in terms of naturalness onto the earlier metasemantic position is difficult to motivate. See further discussion of the issue in Simchen (2017: Appendix I). 13. See discussion of this point as it pertains to the alternative construction discussed below. 14. Clearly for any n for which L contains only a single predicate letter of that arity the requirement of nontriviality cannot be met. 15. We can see that jumbled-truth-in-a-model has (IUI) by focusing again on atomic sentences—generalizing to atomic formulas is once again trivial and full generality follows by induction on syntactic complexity. Thus,

m Ïτ ϕ t1, ..., tn⇐⇒ σ (t1), ..., σ (tn)(σ ϕ)⇐⇒ I (σ (t1)), ..., I (σ (tn)) I •(τ σ ϕ⇐⇒ σ•(t1), ..., σ•(tn)I •(τ σ ϕ On the other hand, for each ϕwe have σ •(ϕ) = I •(σ(ϕ)), so that I •−1(σ •(ϕ)) = σ(ϕ). Substituting in the last clause gets us:

σ • (t1), ..., σ • (tn)I •(τ I •-1 σ • ϕ We see that I • ◦ τ ◦ I •−1 is a jumbler on M•, from which we conclude that m• Ïτ • ϕ(t1, ..., tn),

60 Attitudinal Instrumentalism in Semantics where τ • = I • ◦ τ ◦ I •−1. 16. Although even here, judging by the situation in neighboring metaphysical pursuits, how we might initially be inclined to answer such a question can easily come apart from how we should answer it upon reflection. See Chapter 5 for a related discussion of these matters in the metaphysics of what is said. 17. The example is from Burge (1979). 18. Frege (1980) writes: Mont Blanc with its snowfields is not itself a component part of the thought that Mont Blanc is more than 4,000 metres high ... The sense of the word ‘moon’ is a component part of the thought that the moon is smaller than the earth. The moon itself (i.e. the reference of the word ‘moon’) is not part of the sense of the word ‘moon’; for then it would also be a component part of that thought. (163) 19. For the original version of the view in terms of the Carnapian notions of extension and intension, see Carnap (1947: §§13–15). It is interesting to note in this context that Carnap also claims that Frege’s theory of indirect reference leads to a hierarchy of senses but without providing an explicit argument for the claim. See Carnap (1947: §30).

4

Semantics and Ordinary Language

*4.1 Attitudinal Instrumentalism and Analysis Whatever else divided them, practitioners of ordinary language philosophy during the middle third of the 20th century tended to exhibit a shared animadversion against formal methods in the study of natural language. In such spirit, Strawson (1950), for example, concluded his famous critique of Russell’s theory of descriptions by saying: “Neither Aristotelian nor Russellian rules give the exact logic of any expression of ordinary language; for ordinary language has no exact logic” (344). This type of sentiment engendered a false dichotomy: either we theorize about natural language using formal means, thereby distorting and oversimplifying the phenomena we set out to explain at our peril, or else we refrain from theorizing about language altogether. In this chapter, I would like to illustrate the falsity of the dichotomy as it pertains to the work of two important figures of ordinary language philosophy: Wittgenstein and Austin. In this section, I will illustrate how attitudinal instrumentalism can help us form a more nuanced understanding of Wittgenstein’s critique of extant semantic doctrines due to Frege and Russell. In Section 4.2, I will illustrate how attitudinal instrumentalism allows us to arrive at a better appreciation of the methodological innovation introduced by Austin in his influential treatment of performative utterances and the relation between his project and the semantic one. As noted in the Preface, it is widely appreciated that a major theme in Wittgenstein’s Philosophical Investigations is a programmatic call for philosophy’s reorientation from “explanation” to “description alone”.1 It is also generally acknowledged that much of that work unfolds in reaction to doctrines propounded by Frege, Russell, and notably Wittgenstein himself in an earlier phase of his thought. But given the vast programmatic ambition of the work, it is, in fact, easy to overlook the details of Wittgenstein’s many critical discussions of extant doctrines, particularly those of his contemporaries and immediate predecessors within the then-emerging enterprise of formal semantics. Attending to those details is worthwhile in its own right but can also provide a fresh outlook on the explanatory aims of semantics in DOI: 10.4324/9781003306443-4

62 Semantics and Ordinary Language relation to the phenomenology of meaning in natural language. As we will see, the prevailing attitude towards formal semantic analyses that forms the backdrop to Wittgenstein’s critique is the thought that semantic paraphrases should be synonymous with what they paraphrase. This is clearly assumed by the founders of the analytic tradition in philosophy. In the terms set by the present investigation, the synonymy assumption is just that we should regard semantic paraphrases as theoretical representations of the meanings of the paraphrased sentences under a realist interpretation as revealing what those target meanings really are at bottom. The assumption is clearly not compulsory. In Russell (1905), we encounter the following famous passage: I have heard of a touchy owner of a yacht to whom a guest, on first seeing it, remarked, “I thought your yacht was larger than it is”; and the owner replied, “No, my yacht is not larger than it is”. What the guest meant was, “The size that I thought your yacht was is greater than the size your yacht is”; the meaning attributed to him is, “I thought the size of your yacht was greater than the size of your yacht”. (489) Russell is concerned with illustrating the power of his theory of descriptions here, particularly the theory’s capacity to deal with scope distinctions. The theory accommodates ambiguities in such sentences as (1) I thought your yacht was larger than it is. Ignoring, for now, the analysis of the denoting phrase ‘your yacht’ and treating ‘size of ’ as a functor S(x), we have the intended reading (2) [the x : x = S(your yacht)](I THOUGHT: [the z : z = S(your yacht)] (z > x)) (i.e., ‘The size of your yacht is such that I thought your yacht’s size is greater than that’), as opposed to the unintended one (3) I THOUGHT: [the x : x = S(your yacht)](x > x) (i.e., ‘I thought the size of your yacht is greater than itself ’). These, in turn, receive the following respective analyses: (4) x(y(y = S(your yacht) ↔ y = x) I THOUGHT: z(y(y = S(your yacht) ↔ y = z)  z > x)) (5) I THOUGHT: x(y(y = S(your yacht) ↔ y = x)  x > x).

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It has been claimed that this construal of the ambiguity is inapt on the grounds that (2) and (4) suggest that the guest had some definite size z in mind for the yacht.2 This might not be what we mean when we say of something that we thought it was larger than it is. We might just mean that the size of the thing is smaller than whatever we took its size to be. With this in mind, perhaps a better approximation of the Russellian contrast between the intended and the unintended readings of (1) is (6) [the x : x = S(your yacht)](I THOUGHT: S(your yacht) > x) (3) I THOUGHT: [the x : x = S(your yacht)](x > x), which would be analyzed, in turn, as (7) x(y(y = S(your yacht) ↔ y = x) I THOUGHT: S(your yacht) > x) (5) I THOUGHT: x(y(y = S(your yacht) ↔ y = x)  x > x). In (6) and (7), there is no implication that somehow there is an exact measure of the yacht’s size in the guest’s thought. Of course, there is still the occurrence of ‘S(your yacht)’ inside the attitude context, but this need not be seen as incurring a commitment to an ascribed definite value for ‘S(your yacht)’. Along similar lines, I can also say ‘Paul thought 289 is the most arbitrary number’ without committing Paul to the thought that 17 is the most arbitrary number.3 In fact, this point regarding the occurrence of the functor ‘S(x)’ in (6) and (7) applies equally to occurrences of descriptions in attitude contexts. With the right contextual setup, I can truly say, ‘I thought the third planet from the sun was larger than the fourth’ without ascribing to myself the thought that Earth was larger than Mars. If this is correct, the detour through (6) and (7) in order to avoid ascribing to the guest having some definite size z in mind for the yacht is not really necessary. (2) and (4) can be apt even if the guest couldn’t specify the size he thought the yacht was. Be that as it may, we can provide a Russellian treatment of the ambiguity without changing the apparent subject matter from the yacht to its size. We utilize a dyadic predicate ‘greater in size than’ (or ‘>S’): (8) [the x : x = your yacht](I THOUGHT: your yacht >S x) (9) I THOUGHT: [the x : x = your yacht](x >S x). These would be rendered, in turn, as (10) x(y(y = your yacht ↔ y = x) I THOUGHT: your yacht >S x) (11) I THOUGHT: x(y(y = your yacht ↔ y = x)  x >S x). We could also analyze ‘your yacht’ as ‘the x: x is a salient yacht belonging to TYO’, where ‘TYO’ names the touchy yacht owner, in which case the

64 Semantics and Ordinary Language condition of being identical with the yacht would be replaced by being a salient yacht belonging to TYO. We would then get the following two readings: (12) [the x : x is a salient yacht belonging to TYO](I THOUGHT: [the z : z is a salient yacht belonging to TYO](z >S x)) (13) I THOUGHT: [the x : x is a salient yacht belonging to TYO](x >S x). And these would be rendered, in turn, as the intended (14) x(y(y is a salient yacht belonging to TYO ↔ y = x) I THOUGHT: z(y(y is a salient yacht belonging to TYO ↔ y = z)  z >S x)) and the unintended (15) I THOUGHT: x(y(y is a salient yacht belonging to TYO ↔ y = x)  x >S x). So much for the Russellian background. In Wittgenstein (2009), we read: I see someone aiming a gun and say “I expect a bang”. The shot is fired.— What?—was that what you expected? So did that bang somehow already exist in your expectation? Or is it just that your expectation agrees in some other respect with what occurred; that that noise was not contained in your expectation, and merely supervened as an accidental property when the expectation was being fulfilled?—But no, if the noise had not occurred, my expectation would not have been fulfilled; the noise fulfilled it; it was not an accompaniment of the fulfilment like a second guest accompanying the one I expected. Was the feature of the event that was not also in the expectation something accidental, an extra provided by fate?—But then, what was not an extra? Did something of the shot already occur in my expectation?— Then what was extra? for wasn’t I expecting the whole shot. “The bang was not as loud as I had expected.”—“Then was there a louder bang in your expectation?” (§442) The context of the discussion is future-oriented mental states, specifically expectations. Along the way, Wittgenstein is responding to familiar doctrines due to Russell and Frege. So far, we’ve only considered the Russellian background, the theory of descriptions. The Fregean background is Frege’s theory of indirect reference discussed in Section 1.4 and then again in Section 3.3. We will see that Wittgenstein is pinpointing an important interpretive issue with the application of the theory of descriptions to attitude

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reports, a difficulty that arises when we attempt to utilize some variant of Frege’s theory of indirect reference as well. Consider the locution at the end of §442, ‘The bang was not as loud as I had expected’. This is the intended disambiguation of another case along Russellian lines: (16) I expected the bang to be louder than it was. Letting ‘>L’ stand for the dyadic ‘louder than’, Russell’s theory delivers the following ambiguity for (16): (17) [the x : x is a salient bang](I EXPECTED: [the z : z is a salient bang] (z >L x)) (18) I EXPECTED: [the x : x is a salient bang](x >L x). These, in turn, receive the following Russellian analyses: (19) x(y(y is a salient bang ↔ y = x) I EXPECTED: z(y(y is a salient bang ↔ y = z)  z >L x)) (20) I EXPECTED: x(y(y is a salient bang ↔ y = x)  x >L x). It is then (17) and (19) that capture ‘The bang was not as loud as I had expected’ according to the Russellian treatment. What is the significance of Wittgenstein’s response, “Then was there a louder bang in your expectation?” To appreciate this requires a short detour through further mid-20th-century theoretical developments in the semantics of attitude reports. (19) includes a description taking wide scope over the attitude verb, with a variable in the scope of that verb bound from outside the attitude context. This gives rise to an interpretive issue much discussed in the literature following Quine (1956) concerning the very idea of quantification into attitude contexts. Quine tells us that it makes sense to quantify into the position of ‘Cicero’ in (21) Cicero denounced Catiline to yield (22) x(x denounced Catiline) insofar as that position is open to substitution salva veritate. And indeed, it follows from (21) and (23) Cicero is Tully that

66 Semantics and Ordinary Language (24) Tully denounced Catiline. By parity, if it makes sense to quantify into the position of ‘Cicero’ in the belief report (25) Tom believes Cicero denounced Catiline to yield (26) x(Tom believes x denounced Catiline), then the latter position must also be open to substitution salva veritate. But it is not. Despite the truth of (23), (25) can be true without it being true that (27) Tom believes Tully denounced Catiline.4 It thus seems illegitimate to generalize from (25) to (26). If it were, such legitimacy would be attested by salva veritate substitutivity. An extensive literature arose in response to this issue, the issue now known as quantifying in. An influential treatment of quantifying in due to Kaplan (1969) recasts the logical form of so-called de re belief reports to include meta-representational quantification. On this account, the analysis of (28) Someone is such that Tom believes that person to have denounced Catiline includes meta-representational quantification marked by the variable ‘α’, a special autonymous quotation device marked by ‘F’ and ‘F’ (after Frege) that creates an environment in which expressions stand for themselves, a dyadic attitude verb ‘B’ standing for the relation between a believer and a sentence expressing what the believer believes, and a triadic predicate ‘R’ standing for the relation of de re representation among a singular term, a res, and a believer.5 Kaplan’s analysis of (28) is (29) xα(R(α, x, Tom)  Tom B Fα denounced Catiline F). Now, in (1905), Russell doesn’t discuss the problem of quantifying in, focusing instead on a superficially similar problem that arises from treating the denoting phrase ‘the author of Waverley’ as a singular term. Russell’s claim is that from the intended reading of (30) George IV wondered whether Scott is the author of Waverley and

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(31) Scott is the author Waverley it doesn’t follow that (32) George IV wondered whether Scott is Scott. This is due to the fact that the denoting phrase ‘the author of Waverley’ is not a singular term. The intended reading of (30) has the description take narrow scope under the attitude verb. What George IV wanted to know is not to be construed with an identity complement clause at all but with an existentially quantified one. To suppose otherwise, according to Russell, is to mistake the denoting phrase for a singular term. The literature following Quine (1956), on the other hand, addresses the problem of substitutivity into attitude contexts even when only genuine singular terms are at play. Quantifying in is a separate matter from an issue that arises when quantifiers take narrow scope under attitude verbs, what we might call quantifying within. Consider (33) Tom believes someone denounced Catiline as regimented by (34) Tom believes x(x denounced Catiline). How are we to interpret ‘someone’ in (33), or the quantification in (34)? The principal source of inspiration for work on quantifying within is Frege’s (1948) theory of indirect reference. On this view, the verb ‘believes’ stands for a dyadic function—a relational Fregean concept—that takes pairs of objects to truth just in case the first object is a believer and the second object is the sense of the clausal complement taken on its own, which is a Fregean thought. Expressions in the scope of attitude verbs undergo a reference shift from their ordinary reference to their indirect reference, which is their ordinary sense. In the Fregean analysis of (33), ‘someone’ will stand for a certain sense that would compose the whole Fregean thought expressed by (35) Someone denounced Catiline. In (35), ‘someone’ stands for a certain second-level Fregean concept—a function from first-level Fregean concepts (which are themselves functions from objects to truth-values) to truth-values—and expresses whatever ‘someone’ in (33) stands for. Similarly, in (35), ‘Catiline’ stands for a certain object, a man. But in (33), ‘Catiline’ stands for a different object, the sense expressed by ‘Catiline’ in (35), which is a mode of presentation of the man.

68 Semantics and Ordinary Language We are now finally in a position to appreciate Wittgenstein’s critique in §442. We note that (4), (14), and (19) are all combined cases of quantifying in and quantifying within. This raises a pressing interpretive issue. Consider, for example, the embedded clause ‘z >L x’ in (19) x(y(y is a salient bang ↔ y = x) I EXPECTED: z(y(y is a salient bang ↔ y = z)  z >L x)). That clause is within the attitude context ‘I EXPECTED’. The variable on the left is bound by a quantifier within that context, but the variable on the right is bound by a quantifier outside that context. What are we to make of this for the interpretation of ‘>L’? Suppose we name the bang that actually occurred ‘b’. Then (19) is entailed by (36) y(y is a salient bang ↔ y = b) I EXPECTED: z(y(y is a salient bang ↔ y = z)  z >L b). Setting aside the first conjunct, we have an expected comparison as to loudness between the actual bang b and an expected unique instance of a salient bang, a “bang in your expectation”. But how can such a comparison reach out to both an actual bang and a bang in your expectation? Assume along Fregean lines that the comparison as to loudness is in your expectation in the sense that it is the mode of presentation of the relation >L that composes the content of that expectation, the Fregean thought. It is then unclear how the expected comparison can be applied to b at all, given that b is an actual event and not a mode of presentation of one. (Hence Wittgenstein’s query, “So did that bang somehow already exist in your expectation?”) On the other hand, assume along Russellian lines that the comparison as to loudness is the relation >L itself. It is then unclear how such predication with respect to the audibility of events can be applied to the bang in your expectation, given that whatever is contained in your expectation isn’t a suitable candidate for audibility at all. (Hence Wittgenstein’s query, “Or is it just that your expectation agrees in some other respect with what occurred; that that noise was not contained in your expectation, and merely supervened as an accidental property when the expectation was being fulfilled?”6) So ‘>L’ in (36) and (19) can’t stand for the relation >L as per Russell. Nor can it stand for a mode of presentation of >L, as per Frege. This is the problem Wittgenstein is pointing to in §442. The difficulty can be handled in a contemporary setting but at an apparent cost. Consider, again, Kaplan’s (1969) theory of quantifying in. On this view, the correct rendering of the second conjunct of (36), assuming Russell’s theory of descriptions, would be (37) α(R(α, b, I)  I EXPECTED: Fz(y(y is a salient bang ↔ y = z)  z >L α)F).

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Recall that in the Kaplanian analysis, ‘F’ and ‘F’ are atonymous quotation marks indicating an environment in which expressions stand for themselves. In (37), the occurrence of ‘>L’ is only within the F-quotation context, which means that the predicate stands for itself and contributes neither the louder-than relation >L (á la Russell) nor a mode of presentation of that relation (á la Frege) to the truth-condition of the whole. Instead, it simply contributes itself. The apparent cost is that while in the original report, ‘The bang was not as loud as I had expected’, my expectation seems to involve a comparison between b—an actual event—and something expectation-internal, in (37), the actual event b falls outside the expectation altogether. The complement of an attitude verb on this view stands for a sentence, which is meant to capture the idea that the object of the attitude is the content of the complement clause. If what we want from our semantic analysis is a close approximation of the pre-theoretical significance of the original report, which includes a comparison of something expectationexternal and something expectation-internal, then (37) is not what we want. What we seem to need is the Russellian idea that b can somehow occur within the expectation in propria persona. Kaplan’s (1969) analysis doesn’t deliver that. Let us turn, then, to Kaplan’s (1986) later and more Russellian theory of quantifying in. This later theory draws heavily on simultaneity of use and mention, as exhibited by Quine’s famous example (38) Giorgione was so-called because of his size, which is standardly understood to mean that (39) Giorgione was called ‘Giorgione’ because of his size. Kaplan extends the basic idea of such simultaneity of use and mention to occurrences of free variables in open formulas. This involves introducing a new quotation device—“arc-quotation”—and providing a coherent interpretation for it. A sentence (i.e., a closed formula) enclosed in arc-quotes

◜F(a◝) is defined as the ordinary quotation of the sentence ‘F(a)’. But an arc-quoted open formula

◜F(x◝) is defined as ‘F(x)’ with respect to x as value of ‘x’. Employing this device, the analysis of ‘The bang was not as loud as I had expected’, assuming Russell’s theory of descriptions, would be (40) x(y(y is a salient bang ↔ y = x) I EXPECTED: z(y(y is a salient bang ↔ y = z)  z >L x) ).

◜

◝

70 Semantics and Ordinary Language On this semantic proposal, the complements of attitude verbs stand for what Kaplan calls $entences, which consist of sentences (when the attitudes reported are de dicto) and valuated formulas (when the attitudes reported are de re). The latter are the linguistic analogs of Russellian singular propositions: partly linguistic and partly non-linguistic entities.7 The complement of ‘I EXPECTED’ in (40) stands for the valuated formula ‘z(y(y is a salient bang ↔ y = z)  z >L x)’ with actual bang b as value of ‘x’. But in the entailing (41) y(y is a salient bang ↔ y = b)  I EXPECTED: z(y(y is a salient bang ↔ y = z)  z >L b))

◜

◝

the complement of the verb stands for ‘z(y(y is a salient bang ↔ y = z)z >L b)’. In neither case does ‘>L’ stand for the louder-than relation. But here we have the oddity that while in (40) the attitudinal relation of expectation to the actual bang b is represented by the role b plays in the valuated formula interpreting the complement clause, in (41) b plays no such role: the entire arc-quotation stands for the arc-quoted sentence. Consider an obvious candidate analysandum for (41): (42) Salient bang b and no other was not as loud as I had expected. (41) would seem ill-suited as an analysis of (42) insofar as in (41), the event b itself drops outside the expectation altogether. The complement of the attitude verb stands for a sentence. The difculty here exactly mirrors the problem with the earlier Kaplanian analysis (37). Let us step back from all these details and reflect on what semantic analyses are supposed to do for us in the first place. Under the most common conception of the formal semantic modeling of meaning in natural language, semantic analyses are charged with delivering truth-conditions. In this way, the analyses are meant to model what the locutions mean. What the locutions mean is a pre-theoretical matter, something the analyses are meant to capture to a certain degree. But not every aspect of a formal semantic analysis should be taken to play a representational role; not every cog in the formal semantic machinery needs to stand for something pretheoretical. Some such aspects are merely “artifacts of the model”, to use Kaplan’s (1975: 722) phrase. Seen this way, assessing the achievement of the various semantic analyses considered in this section is more nuanced. Successful modeling of meaning—or of anything else, for that matter—is a multivalent affair. Consider an analysis of ‘The bang was not as loud as I had expected’ along the lines of Kaplan’s (1969) theory: (43) x(y(y is a salient bang ↔ y = x)  α(R(α, x, I)  I EXPECTED: Fz(y(y is a salient bang ↔ y = z)  z >L α)F)).

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To complain that (43) doesn’t capture the meaning of the original because, pretheoretically, the original involves a comparison between something expectation-external and something expectation-internal, whereas ‘>L’ in (43) doesn’t is to mislocate the theoretical import of the analysis. The likes of (43) should be viewed more holistically. Not every working part of a semantic analysis need stand for something pre-theoretical in the meaning of the original, as we might expect if the analysis were meant to be synonymous with the analysandum. Specifically, ‘>L’ doesn’t contribute to (43) a comparison between an expectation-external event and something expectation-internal (a “bang in your expectation”). On the other hand, ‘not’ in the original locution ‘The bang was not as loud as I had expected’ isn’t captured by any occurrence of negation in (43) either, as we might also expect if (43) were synonymous with the analysandum. Rather, the analysis is supposed to deliver the meaning of the original by way of generating the right truth-conditions for it. Synonymy is no part of the theoretical achievement here. The pioneers of analytic philosophy did not see things this way. Frege and Russell thought of their paraphrases as revealing the underlying meaning of the locutions those paraphrases are meant to model even when the latter depart considerably from everyday usage. Those analyses were clearly meant to be synonymous with their analysanda. This is how Frege (1953) can say that even though “at first sight . . . ‘All whales are mammals’ seems to be not about concepts but about animals” (§47), it nevertheless is about concepts and not about animals. And this is how Russell (1905) can positively identify what the guest meant in saying what he said to the touchy yacht owner while casually swapping the apparent subject matter of (1)—the yacht itself—for its size. Such attitudes towards semantic paraphrases smack of revisionism, of changing the subject, and much of the later Wittgenstein’s efforts are directed against them. His critique in §442 and elsewhere throughout the Philosophical Investigations assumes such attitudes towards semantic paraphrases as a given. The proposed paraphrases are meant to reveal what the original locations really mean by providing synonyms for them that are semantically more perspicuous. But in point of fact, we need not regard formal semantic paraphrases in this way. In considering the theoretical role semantic paraphrases play in the formal modeling of meaning, it behooves us to avoid Frege and Russell’s original attitudes. It is open to us to consider formal semantic paraphrases in terms of how well they fare relative to a variety of theoretical desiderata, chief among them perhaps the generation of the right truth-conditions, but coherence with syntax and overall simplicity are crucially important as well. Generating the right truth-conditions is only the beginning. Preferring certain semantic paraphrases over alternatives that are perhaps equally successful in delivering the right truth-conditions but do not cohere as well with neighboring paraphrases is the stuff of which formal semantic inquiry is made. We should relax the additional requirement imposed by early analytic philosophy that

72 Semantics and Ordinary Language semantic paraphrases be synonymous with their analysanda. The prospects for such a requirement are as dim now as they were in the early days of semantic theorizing. This is how nowadays a formal semantic paraphrase can represent ‘The bang was not as loud as I had expected’ as saying that the maximal degree of a set of degrees for loudness I expected the bang to have is greater than the maximal degree of a set of degrees the loudness of the bang exceeded.8 To suppose that the original sentence is synonymous with an analysis that includes sets of degrees and maximality is gratuitous and isn’t required for such a paraphrase to achieve its theoretical purpose. Wittgenstein’s admonition in §442 of semantic paraphrases informed by the theories of Russell and Frege can be taken in various ways. A familiar way is to regard the lesson of this type of critique as damning for the project of formal semantics as a whole. The idea is that natural language does not admit of a formal semantic analysis because any such analysis is inherently distortive of the phenomenology of meaning. This is perhaps the most familiar reception of later Wittgensteinian ideas. But there is another, and, to my mind, more satisfying way to think of the lesson of this type of critique: Pace Russell and Frege et al., semantic paraphrases, including that of ‘The bang was not as loud as I had expected’, should never have been expected to be synonymous with what they paraphrase to begin with. An individual semantic paraphrase stands for the meaning it represents within a broader theoretical setting. The achievement of formal semantic paraphrases ultimately rests on the capacity of the broader theory to meet various desiderata that include overall systematicity and the meshing with neighboring areas of inquiry in fruitful ways. Revealing the very meaning of the target sentences individually, as it were, one paraphrase at a time, should never have been considered one of those desiderata.

4.2 Performativity In this section, I would like to illustrate the way in which an instrumentalist attitude in the study of natural language can also resolve an old dispute surrounding performative utterances. Performative utterances such as ‘I promise you to φ’, issued under suitable conditions, have been claimed by Austin (1962) to constitute the enactment of something, such as a promise, as opposed to the stating of something. They are thus not to be assessed in terms of truth and falsity but rather in terms of felicity and infelicity. Subsequent theorists have typically contested half of this Austinian view, agreeing that a performative utterance such as ‘I promise you to φ’ is the enactment of a promise but claiming that it is also a statement to the effect that the promise is issued. I will now illustrate that considered speech-acttheoretically, uttering ‘I promise you to φ’ under suitable conditions is not also the statement that the promise is issued. This is compatible, however, with the fact that considered semantically, ‘I promise you to φ’ is true if my promise to you to φ is issued. Neither speech act theory nor semantics can

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claim primacy in revealing the underlying nature of performativity. Each approach can achieve its distinctive explanatory aims without conflict with the other. Attitudinal instrumentalism holds the key to such reconciliation. In Austin (1962), we get a characterization of certain utterances as the doing, or enacting, of certain things—such as marrying (‘I do’), promising (‘I promise you to . . .’), naming (‘I name the ship . . .’), and bequeathing (‘I give and bequeath . . .’)—as opposed to describing or stating whatever was so done or enacted: In these examples it seems clear that to utter the sentence (in, of course, the appropriate circumstances) is not to describe my doing of what I should be said in so uttering to be doing [footnote: Still less anything that I have already done or have yet to do.] or to state that I am doing it: it is to do it. None of the utterances cited is either true or false: I assert this as obvious and do not argue for it. (6) Austin does, however, marshal some considerations against a particular descriptivist view that seeks to assimilate performatives to statements.9 He rejects the idea that in issuing a performative utterance along the lines of ‘I do’ or ‘I promise you to φ’ the speaker describes an “inward and spiritual act” rather than simply undertaking the marriage or commitment: For one who says “promising is not merely a matter of uttering words! It is an inward and spiritual act!” is apt to appear as a solid moralist standing out against a generation of superficial theorizers: we see him as he sees himself, surveying the invisible depths of ethical space, with all the distinction of a specialist in the sui generis. Yet he provides Hippolytus with a let-out, the bigamist with an excuse for his ‘I do’ and the welsher with a defence for his ‘I bet’. Accuracy and morality alike are on the side of the plain saying that our word is our bond. (10) Both ‘accuracy’ and ‘morality’ speak against the view that when I say ‘I promise you to φ’, I am only describing some inner undertaking of the commitment to you to φ. Regarding accuracy, it is presumably plainly obvious that issuing a promise in speech is itself the enactment of the promise, the undertaking of the commitment. Regarding morality, the situation is more complicated, but the gist of Austin’s complaint is that there is a good moral (or “practical” in the wide sense) reason to suppose that in saying ‘I promise you to φ’ I am undertaking the commitment to you to φ, pure and simple. If the words themselves, in the appropriate circumstances, couldn’t bind me in issuing the promise, requiring some inner accompaniment to make them true, then I could always get out of my commitment by pleading that the requisite inner accompaniment was missing. This would make a

74 Semantics and Ordinary Language hash of promising. But, counters Austin, our word is our bond. Performative utterances are not in the business of reporting or stating “inward” acts because they are not statements at all. Their proper assessment is in terms of felicity and infelicity rather than in terms of truth and falsity. It is widely held that Austin’s foundational treatment of performative utterances as the doing of certain things (promising, wedding, bequeathing, naming, etc.), as opposed to the stating that they are done, is right about the doing but wrong about the stating. Yes, the performative ‘I promise you to φ’ is the doing of something, the issuing of a promise. But pace Austin, the self-same performative utterance is also the stating of something made true by what was thereby done, the issuing of that very promise. The Austinian view that performative utterances are not statements has been widely contested. Here is Lewis (1970): I have assumed that performatives themselves do have truth values, but that also has been denied. (Austin 1962, Lecture I.) I would wish to say that to say that ‘I bet you sixpence it will rain tomorrow’ is true on an occasion of utterance if the utterer does then bet his audience that it will rain on the following day; and, if the occasion is normal in certain respects, the utterer does so bet; therefore his utterance is true. Austin says it is obviously neither true nor false, apparently because to utter the sentence (in normal circumstances) is to bet. Granted; but why is that a reason to deny that the utterance is true? To utter ‘I am speaking’ is to speak, but it is also to speak the truth. (59) Here is Bach (1975): I wish to argue that the negative side of Austin’s doctrine—that performative utterances do not constate, are not true or false—is mistaken. Since I accept the positive side—that they are, or are part of, the doing of an action—my position is that performative utterances (other than conventionalized ones) are both doings and statings. (229) And here is Ginet (1979): One must, of course, agree that to utter one of Austin’s sentences in the appropriate circumstances (and with the right intentions) is to perform the act signified by the verb phrase in it. But I do not see why it should be thought, as Austin apparently takes for granted, that this is a reason to deny that in uttering one of those sentences in order to perform the associated act one also states that one thereby performs that act. As far as I know, no good reason has been offered by Austin or anyone else for denying this. (246)

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None of these theorists claims that what the performative states or reports is something ‘inward’. On the contrary, the performative states what it enacts while enacting it. In other words, the performative is self-stating or selfdescriptive. In saying ‘I promise you to φ’ (in the right circumstances), (i) I issue a promise to you to φ, while (ii) I truly state that (i). At least this is the normal case. False performative utterances are admitted in cases where some of the conditions for bringing about the performed act aren’t met, as in the case of ordering on the stage: [I]t is hard for a performative to be anything but true on an occasion of its utterance. Hard but possible: you can be play-acting, practicing elocution, or impersonating an officer and say ‘I command that you be late’ falsely, that is, say it without thereby commanding your audience to be late. (Lewis 1970: 59) But the prevailing wisdom is that performative utterances are normally selfverifying, enacting that which verifies them.10 Does this mean that “performatives are statements too”, as Bach (1975) puts it? There is a straightforward argument that suggests a negative answer here and goes some way to fill the lacuna mentioned in the passage from Ginet (1979). This will be laid out next. The implications of the argument, however, are not straightforward. The moral to draw, I want to suggest, is broadly methodological: While there is an important speech-act-theoretic sense in which the issuing of the performative is not also the issuing of the corresponding statement, there is a semantic sense in which the performative utterance is plausibly regarded in the normal case as self-verifyingly true. Whether a performative utterance is a statement too is a speech-acttheoretic issue; whether the utterance is true or false is a semantic one. Neither the speech-act-theoretic representation of the utterance nor its semantic representation are entrusted to reveal the nature of performativity on its own, as we will see. By way of introduction to the speech-act-theoretic argument that performatives aren’t statements too, it is useful to consider a parallel metasemantic argument regarding the possibility of self-reference. Elsewhere I raise the question of when an expression could be used to refer to itself.11 Plausibly, (1) a referring expression is produced by its utterer loaded with its contribution to truth-conditions. This is supported by empirical considerations regarding humdrum cases of truncated speech production, such as the uttering of ‘Joe Biden is . . .’ without ever completing the utterance. The utterer in such cases succeeds in referring to Biden despite the absence of a larger sentential context. The name is produced as standing for Biden.12 Next, it is a familiar lesson of the so-called new theory of reference that to employ an expression to refer to something requires some sort of causal-historical connection to the referent. If I demonstratively refer to an apple in my hand, I do so in

76 Semantics and Ordinary Language virtue of being somehow in the apple’s causal wake, so to speak, through various sensory modalities. If I refer to Bismarck in using his name, I do so in virtue of a worldly relation, however complex, to the man. And so it goes: (2) an expression employed to refer to something refers to something existing at some point in the past, perhaps the very recent past and perhaps persisting into the present and the future, but something existing in the past nonetheless.13 Finally, (3) a referring expression contributes its referent to truth-conditions. This is supported by familiar considerations that favor Millianism. The trio of commitments (1)-(3) precludes self-reference insofar as self-reference would require the purported self-referential item to exist before coming into existence. That item would be produced loaded with its contribution to truth-conditions, as opposed to its contribution to truth-conditions being determined after the fact of its production, as per (1). Qua self-referential, it itself would constitute its own contribution to truth-conditions, as per (3). But its referent, namely, it itself, would have to exist at some point before being produced to refer to itself, as per (2). None of this precludes, of course, anyone from regarding a linguistic expression, once produced, as self-denotative. But it does preclude the production of a self-referential expression, an item standing for itself In the way that a speaker might, say, produce a demonstrative pronoun to refer to an intended demonstratum.14 Turning to the view that performatives are self-stating or self-descriptive, we face an analogous situation. For any p, in order to truly state that p, it has to be the case that p. For the case at hand, in order to truly state that I promise you to φ, it has to be the case that I promise you to φ. Now suppose that (i) I only complete the issuing of my promise to you to φ by saying ‘I promise you to φ’ at t0, in the sense that for any time interval ϵ > 0, I have not yet issued the promise to you to φ by saying ‘I promise you to φ’ at t0−ϵ. Let Rc be the triadic relation of commitment created by the issued promise among speaker S (me), audience A (you), and φ-ing. Then Rc(A, S, φ) obtains at t0 but does not obtain at t0−ϵ for any ϵ > 0. Now, under ordinary circumstances, for a speaker to sincerely state that p, where p recounts the speaker’s doing something, requires that the speaker believe that p. Indeed, it seems plausible that (ii) to sincerely state that p at t, where p recounts the speaker’s doing something, requires the speaker to believe that p at t − δ for some time interval δ > 0 that is at least as long as is needed fo the registration of the act by the speaker to culminate in the act’s report. In other words, we state that we do something after registering, or forming the belief, that we do it. This seems especially clear when we recount acts conducted by us in the past, but it is also the case for present-tense and future-tense reports regarding what we are doing at present and what we will do in the future. When the realtor does the remote walk-through on FaceTime and says, ‘I am now walking into the dining room’, she says what she is doing after she registers that she is doing it, however close the time of registration or belief formation is to the later time at which she reports

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that she is walking into the dining room. Similar considerations apply to her saying, ‘I will next show you the front balcony’. Saying that she will show her audience the front balcony follows her forming the belief that she will show her audience the front balcony. If this is generally correct, then sincerely and truly stating that p at t, where p recounts the speaker’s doing something, requires that the speaker truly believe that p at t−δ for some δ > 0. And when p is present-tense, the speaker truly believing that p at t −δ requires that it be the case that p at t − δ  for some δ  ≥ δ.15 Now suppose that in promising you to φ by saying ‘I promise you to φ’, as per (i), I am also sincerely and truly stating that I promise you to φ. Truly stating that I promise you to φ at t0 requires that it be the case that I promise you to φ at t0 − δ  for some time interval δ  > 0 that is at least as long as is required for me to (promise you to φ and to) register that I promise you to φ, as per (ii). In other words, Rc(S, A, φ) obtains at t0−δ . But this contradicts the choice of t0 above: simply set ϵ to δ . So in promising you to φ, I do not also truly state that I promise you to φ. Assuming the argument is sound, what is the moral to draw here? Consider the crucial step that to sincerely state that p at t, where p recounts the speaker’s doing something, requires the speaker to believe that p at t−δ for some δ > 0. What sort of requirement is this? We might say it is a basic fact about our linguistic practices when it comes to sincerely reporting our own conduct, part of the phenomenology of stating “in the wild”, a fact of language as studied by speech act theory. Why would such a fact be set aside by the theorist who wishes to argue that in saying ‘I promise you to φ’, I am also issuing a truth made true by what my words enact, namely the promise to you to φ? The latter position is taken from the standpoint of semantics. For semantics, the idea that the likes of ‘I promise you to φ’ are to be assessed radically differently from the likes of ‘I promised you to φ’ or ‘She promises you to φ’ introduces a theoretically intolerable discrepancy in the assignment of truth-conditions. Davidson (1979) puts it as follows: Austin held that performatives have no truth value on the ground that uttering a sentence like ‘I order you to go’ is not typically to describe one’s own speech act but rather to issue an order. This is perhaps an accurate account of how we would characterize many speech acts that consist in uttering explicit performatives. But as a description of what the words that are uttered mean, this view introduces an intolerable discrepancy between the semantics of certain first-person present-tense verbs and their other-person other-tense variants. (16) From a semantic-theoretic standpoint, the first-person pronoun is another pronoun, among others. In extensional contexts, it contributes the speaker to the truth-conditions of sentences in which it partakes. How can it be that the truth-conditions of ‘She promises you to φ’ should be determined by

78 Semantics and Ordinary Language what the third-person pronoun ‘she’ stands for inter alia, whereas replacing that pronoun with the first-person pronoun—and adjusting the presenttense verb accordingly—results in the loss of truth-conditions altogether? This seems incredible. In an important paper on methodology in the study of language, Lewis (1975) asks what languages as assignments of truth-conditions (in the form of intentions) to sentences have to do with language as a social practice. The answer he offers draws on his earlier work on convention: there is a convention of truthfulness and trust in such an assignment of truth-conditions to sentences—where truthfulness is trying not to utter a falsehood, and trust is imputing truthfulness to others—within the population of speakers. In the background of this picture is a methodological divergence between semantics as the study of truth-conditions and speech act theory as the study of linguistic action. When Lewis (1970) insists that ‘I bet you sixpence it will rain tomorrow’ is true on an occasion of utterance if the utterer does then bet his audience that it will rain on the following day; and, if the occasion is normal in certain respects, the utterer does so bet; therefore his utterance is true. (59) his insistence falls within a proposed semantics. When Austin (1962) insists that it seems clear that to utter the [performative] sentence (in, of course, the appropriate circumstances) is not to describe my doing of what I should be said in so uttering to be doing or to state that I am doing it: it is to do it. (6) his insistence doesn’t fall within a proposed semantics but within the rather different explanatory enterprise of (what is to become) speech act theory. The question of whether performatives are self-verifying statements is a useful prism through which to view the methodological contrast between these two distinct theoretical endeavors in the study of natural language. The contrast offers a more satisfying assessment of the dispute over the workings of performativity in natural language than alternative assessments. The phenomenology of performativity is one and the same, we might say; the theoretical standpoints for handling it are different. Even if speech-acttheoretically in promising to φ, we are not also stating that we are, as Austin suggests, this does not entail that it isn’t the case that ‘I promise you to φ’ is true just in case the promise to you to φ is issued. Even if semantically ‘I promise you to φ’ is true just in case the promise to you to φ is issued, as Lewis and others contend, this doesn’t entail that in enacting the promise,

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we are also enacting a statement to the effect that this very promise is issued. Statements as such are not the subject matter for semantic theorizing.16 The theoretical purview of speech act theory is the agentive production of speech. The theoretical purview of semantics is its post hoc evaluation in terms of truth-conditions (or context change potential within dynamic approaches). There is no inference from the performative utterance not constituting an act of stating to its lacking truth-conditions. There is no inference from the performative having truth-conditions to its utterance constituting an act of stating alongside its other enactment. Neither theoretical framework should be viewed as entrusted with revealing the underlying nature of performativity.

Notes 1. See Wittgenstein (2009: §109). The theme is explored extensively throughout §§92–137. 2. See, for example, Kripke (2005: 1022–1023). 3. We may assume that ‘√’ is a functor while ‘±√’ isn’t. 4. Or so it is often claimed. Much ink has been spilled over whether the truth of (23)  (25) is compatible with the falsity of (27). The ultimate merit of the claim lies outside my present concern. 5. I make the simplifying assumption, here and elsewhere, that ordinary objectual quantification is already properly restricted, in this case to persons. The three conditions for the obtaining of the de re representation relation—“denotation”, “of ness”, and “vividness”—need not concern us. I also assume that Tom’s belief isn’t de re with respect to Catiline. 6. The verb ‘supervene’ here should not be taken to mean what it does in contemporary philosophical parlance. The German original is a form of the verb ‘hinzukommen’, which in context could be translated as ‘added’. 7. For simplicity we can ignore de re attitudes towards linguistic items. We will return to Russellian propositions in detail in the next chapter. 8. See von Stechow (1984) for a survey of some of the theoretical options here. 9. Interestingly, he later assimilates statements to performatives before supplanting the earlier distinction between performatives and constatives with the mature theory of the locutionary, illocutionary, and perlocutionary aspects of the total speech act. 10. For a comprehensive articulation of this point of view, see García-Carpintero (2013) and many of the references contained therein. 11. See Simchen (2013b: §IV). 12. There is of course much more to say in behalf of (1), which cannot be undertaken here. 13. The point of the previous footnote clearly applies to (2) as well. For the purpose of introducing the argument to follow we can safely avoid the tangled issue of reference to things commonly regarded as non-spatiotemporal, such as fictional characters (according to some views) or mathematical entities (according to many views). 14. Crucial here is the distinction between reference as the worldly relation between an expression and what it is deployed to stand for, and denotation as the formal relation of semantic evaluation. See also Section 3.1. A topic that cannot be broached here is purported reference to future entities, such as Kaplan’s (1969) famous example of ‘Newman 1’ purportedly referring to the first child to be born in the 22nd century. Such examples arguably depend on illicitly combining elements of the two relations. 15. ‘≥’ rather than ‘>’ to allow for the belief formation to be simultaneous with the act. If such simultaneity is allowed, then in the stating of p, where p recounts the act

80 Semantics and Ordinary Language of stating that p, the stating that p might be simultaneous with the belief that one is stating that p after all, flouting (ii). This, however, concerns the enactment of statements and is beside the present concern with whether performative utterances such as ‘I promise you to φ’ or ‘I do’ are statements too. 16. Consider, for example, the following passage from the opening section of Heim and Kratzer (1998): A theory of meaning, then, pairs sentences with their truth-conditions. The results are statements of the following form: Truth-conditions The sentence “There is a bag of potatoes in my pantry” is true if and only if there is a bag of potatoes in my pantry. (1) Statements constitute semantic theory itself, but it is sentences rather than statements that are included within its purview.

5

Propositions and What Is Said

5.1 The Metaphysics of What Is Said In Chapters 1–2, we considered various doctrines in philosophy as explanatory endeavors and asked how they fare compared with explanatory endeavors outside philosophy. We saw that a pertinent question to ask about theoretical representations, in general, is whether to regard them as revealing the nature of what they represent, i.e., realistically, or whether to regard them as serving certain explanatory ends without the additional revelatory aspect, i.e., instrumentally. We explored the question of realist vs. instrumentalist attitudes in various cases of philosophical theorizing. The modal metaphysician represents Nixon’s possible loss in the 1968 US presidential elections as Nixon losing in another possible world. We can ask whether Nixon in a possible world where he loses is what the fact of Nixon’s possible loss amounts to upon closer theoretical scrutiny, as per attitudinal realism, or whether Nixon in a possible world where he loses merely represents Nixon’s possible loss for some explanatory purpose other than revealing what that possibility really is at bottom, as per attitudinal instrumentalism. The set-theorist represents the individual numbers as pure sets. We can ask whether these sets are what the individual numbers turn out to be upon closer theoretical scrutiny, as per attitudinal realism, or whether they represent the numbers for the broader purpose of reducing number theory to some first-order theory of sets without propounding further what the represented numbers really are at bottom, as per attitudinal instrumentalism. In this chapter, we consider structured propositions as theoretical representations deployed within yet another explanatory context—the metaphysics of what is said—with the aim of exploring whether a realist attitude towards these representations is justified. In keeping with the book’s general approach, we avoid the grand topic of realism as traditionally construed. We compare the case at hand to the cases where a realist attitude towards a representation is clearly warranted and ask whether central features of such cases are present here as well. I will argue that they are not. After briefly outlining the doctrine of propositions in its bare form, I will proceed to offer general reasons for not regarding propositions under a realist attitude, DOI: 10.4324/9781003306443-5

82 Propositions and What Is Said reasons outlined in Chapter 2. This will be followed by a discussion of a special reason emerging from a problem originally raised by Russell, the originator of the doctrine of structured propositions, to refrain from treating propositions realistically. The conclusion will be that the case for an instrumentalist attitude towards structured propositions is particularly strong. The first order of business is to understand the various theoretical roles played by structured propositions. (Henceforth, I leave the qualification ‘structured’ implicit.) The literature here is vast, but in a nutshell, propositions are presumed to be the semantic contents of sentences in context, the bearers of truth and falsity, the objects of the so-called propositional attitudes, and the operands for modal operators. As is customary, we abbreviate all these roles under a single rubric: what is said. Propositions theoretically represent what is said. They are purported to be structurally akin to the sentences expressing them and to be constituted by whatever the significant subsentential expressions stand for, held together in some structure. It has been a matter of dispute whether any single thing performs all the tasks included under the rubric of what is said—semantic content, bearer of truth-value, object of attitude, and modal operand. But work in the area typically proceeds by arguing for the existence of something performing at least one of those tasks and subsequently arguing for the thing’s suitability to perform the other tasks as well. And here, the tendency to treat the representations realistically as revealing the nature of whatever is individually represented drives much of the current discussion and gives rise to special difficulties. At the closing of a recent book on propositions (King et al. 2014), Soames, one of the book’s three co-authors, summarizes the authors’ combined efforts as follows: As I see it, success in our common enterprise will be success in identifying what agents have been referring to all along when speaking of propositions, and what properties they have ascribed to these entities when characterizing them as having been asserted or believed, or as having truth-conditions—even if little of the theoretical detail about what these entities are, or how precisely we or they manage to represent the world, is something we are in a position to know without careful theory construction. (244) The point here is that even if there are multiple extant theories of what is said—the co-authors’ theories are all quite different from one another—such a theory (“our common enterprise”) is expected to tell us what we’ve been referring to all along in speaking of what is said. Soames seems to consider propositions, rather than what is said, as the pre-theoretical subject matter for the kind of theory the authors aim to provide. As will emerge shortly, it is better to think of propositions as theoretical representations of what is

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said rather than as comprising the pre-theoretical subject matter. Be that as it may, in contrast with the attitude exhibited in this passage, I will argue here that we should regard propositions under an instrumentalist attitude rather than think of them under a realist attitude as revealing the nature of what they represent, namely, what is said. But a realist attitude is undoubtedly the more prevalent one within the metaphysics of what is said. The historical precedent to contemporary discussions of propositions is Russell’s early doctrine of The Principles of Mathematics (1903). According to this view, there is no principled distinction between true propositions— what is truly said to be the case—and their truthmakers—what is the case. Given the lack of distinction here, there is also no distinction between constituents of propositions and what they are about. The Russellian default is that propositions are constituted by what they are about.1 A principal issue that bedevils the doctrine of propositions is the problem known as the unity of the proposition. The problem, in a nutshell, is that if we regard propositions as constituted by semantic contributions of subsentential expressions to the significance of whole sentences, it is difficult to see how the propositions themselves are anything beyond itemizations of propositional constituents. And yet when we speak of the significance of a sentence, we speak in the singular. Take the sentence ‘Amy loves Mary’. What is said by it, let us suppose, is a structure constituted by Amy, the LOVE relation, and Mary. But Amy, LOVE, and Mary do not themselves provide a unified something to act as what is said by the entire sentence. What might otherwise confer such unity? It is hard to know what to say here. Regarding ‘A is different from B’, Russell (1903) writes: “[T]he difference which occurs in the proposition actually relates A and B, whereas the difference after analysis is a notion which has no connection with A and B” (49). And after contemplating the unhelpful suggestion that what is contributed to the proposition by ‘is’ and ‘from’ provides the requisite glue between A and DIFFERENCE and between DIFFERENCE and B, Russell concludes: [A] proposition, in fact, is essentially a unity, and when analysis has destroyed the unity, no enumeration of constituents will restore the proposition. . . . The verb, when used as a verb, embodies the unity of the proposition, and is thus distinguishable from the verb considered as a term, though I do not know how to give a clear account of the precise nature of the distinction. (50) Thus goes the problem of the unity of the proposition. A second problem often raised for the doctrine of propositions is a problem of indeterminacy that can be traced back to Benacerraf ’s (1965) familiar discussion of set-theoretical reductions of numbers. There are two familiar, equally workable, and mutually incompatible total reductions of numbers to pure sets, one due to Zermelo and the other due to von Neumann. What

84 Propositions and What Is Said determines which is to stand for the number two, say, Zermelo’s {{}} or von Neumann’s {,{}}? While these are distinct sets, each does just as well as the other as the set-theoretical representation of the number two. An analogous worry can be raised for propositions. Propositions, we assume, are structures of propositional constituents. What determines that what is said by ‘Amy loves Mary’ is represented by the structure Amy, Mary, LOVE, say, as opposed to LOVE, Amy, Mary? While these are distinct structures of propositional constituents, each does just as well as the other in representing what is said by the sentence. A third familiar problem often raised for the doctrine of propositions is suitability for semantic evaluation. If propositions are structures of propositional constituents, such as the individuals Amy and Mary and the LOVE relation, how is such a structure supposed to be suitable for truth or falsity? What is said by the sentence ‘Amy loves Mary’ is plausibly associated with a truth-condition, the condition of Amy loving Mary. Yet even if we set the indeterminacy problem of the previous paragraph aside and assume there to be a unique structure of propositional constituents representing what is said by ‘Amy loves Mary’, what sense can be made of the idea that that very item, the structure, might be true? The structure is just an arrangement of the individuals Amy and Mary and the LOVE relation, much like the arrangement of a fork, a plate, and a knife in a place setting. It can thus seem unsuitable for truth or falsity. We think it categorically inapt to associate the fork being to the left of the plate and the knife being to the right with being true or false. From such a mindset it can also seem categorically inapt to associate the structure of propositional constituents, Amy, Mary, and LOVE, with being true or false. Now, without prejudging whether to regard propositions under a realist or an instrumentalist attitude, let us register how these three problems fare under attitudinal instrumentalism. Consider, again, the proposition representing what is said by the sentence ‘Amy loves Mary’. The propositional constituents, Amy, LOVE, and Mary, are to be held together in a structure that represents the unified semantic significance of the sentence while attesting to the semantic contributions of the subsentential components. Any representational means for capturing what is said by our sentence would work here as long as the individual contributions of significant subsentential components are discernible in the resultant representation. There may be other explananda for the overall account that favor one representation over a potential competitor, but all else being equal, under attitudinal instrumentalism nothing of significance to the nature of what is said turns on the choice of representational means. Structures represented by iterated sequencing are a natural choice here, but syntactic trees with semantic values assigned to terminal nodes are another, and there are other options as well. The specter of the unity of the proposition is laid to rest by treating propositions instrumentally as performing certain explanatory tasks without the further demand that they reveal the nature of what they represent. To

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treat the unity of a structure over a plurality of its elements as a deep worry about what is said is to regard the structure as revealing the nature of what is said. From an instrumentalist standpoint this is a mistake. A similar instrumentalist treatment extends to the Benacerraf-style worry about propositions and to the same deflationary effect. Here is the Benacerrafstyle worry again: What determines that the proposition expressed by ‘Amy loves Mary’ has the structure Amy, Mary, LOVE rather than the structure LOVE, Amy, Mary? The instrumentalist answer is that propositions are meant to play certain explanatory roles and that either structure works for our explanatory purposes as long as we adhere to a single choice throughout the explanation. The representational suitability of either option (all else equal) should not occasion any deep anxiety about the indeterminacy of what is said if we do not regard such representations realistically. An instrumentalist deflation extends to the problem of suitability for truth or falsity as well. It can seem categorically inapt to attribute truth-values to a structure of propositional constituents and, so, inapt to associate it with truth-conditions. The instrumentalist response is that the structure is meant to represent what is said for certain explanatory purposes. It is part of the nature of what is said that it is capable of semantic evaluation. To demand of the theoretical representation of what is said, the proposition, to be intrinsically true or false in the relevant sense, is to treat the representation as revealing the nature of what is said. By contrast, under an instrumentalist attitude, we stipulate that propositions are associated with truth-conditions.2 As with other explanatory endeavors, the question of representational adequacy assumes, at the very least, consistency for the representational means at issue. This requirement will eventually lead us to consider a specific and, to my mind, decisive consideration against adopting a realist attitude towards propositions. But first, having noted how an instrumentalist attitude handles the three problems outlined above, we approach the question of realist vs. instrumentalist attitude towards propositions by utilizing the framework introduced in Chapter 2.

5.2 Attitudinal Instrumentalism and Propositions Is a realist attitude towards propositions warranted? While the traditional question of realism for a given domain is fraught with controversy, we can approach the larger issue indirectly by comparison with cases where a realist attitude towards theoretical representations is clearly warranted. This is the general methodology pursued throughout the book for other cases of philosophical explanation. Take again the worn example of water being H2O. We represent water within physical chemistry as H2O under a widespread realist attitude. Being H2O is widely assumed to reveal the nature of the substance. It is not merely a representation of water for some theoretical purpose or other. It is what water itself turns out to be upon close theoretical scrutiny.3 Now, instead of seeking some ur-consideration that might decide

86 Propositions and What Is Said the question of realism vs. instrumentalism in general and then apply it to the case of propositions, we take for granted the aptness of a realist attitude towards physical-chemical representations of substances, for example, and ask whether such an attitude might be warranted towards propositions as representations of what is said. In Section 2.1 we identified three salient features of such cases of theoretical identification (or TID, for short) as conjectured necessary conditions for when a realist attitude is justified. First and foremost, TIDs exhibit realist purport. When representing gold as the element with atomic number 79, we clearly intend to reveal what gold itself really is. This familiarly extends beyond TIDs. Representing the material composition of a certain currency as 94% steel, 1.5% nickel, and 4.5% copper for the purpose of metallurgical or physical-chemical analysis is associated with a clear pretension to identify the underlying nature of the items in question, saying what those things are at bottom. Such a case is quite unlike representing the selfsame currency as one exhibiting a certain discrepancy between nominal and commodity value in applying Gresham’s law in economics. In the latter case, there is no realist purport to identify the underlying nature of the represented items. The explanatory purpose behind the representation in applying economic generalization is quite different. Revealing the underlying nature of physical coins is no part of it. Second, TIDs are formulated against an overall background of conservatism as to subject matter: a general inclination to preserve the pre-theoretical subject matter of basic everyday claims unless a radical revision is called for by genuine theoretical progress. Even in the advent of physical chemistry, we consider the subject matter of basic pre-theoretical water claims to be water. The identification of water as H2O does not require us to say that those water claims are really about something other than what we pre-theoretically take them to be about. Even if some revisions regarding the subject matter of basic pre-theoretical claims are required by certain theoretical advances, conservation of pre-theoretical subject matter is the general rule. Third, how the theoretical representations deployed in TIDs are supposed to represent whatever they do is presumed to be well understood in light of the surrounding theory. The facts of theoretical representation are themselves made intelligible by the theory. If we think of water or gold as substances that we track pre-theoretically via their macro-features, then given our overall understanding of how micro-structure is related to macrofeatures, it is relatively well understood how being H2O represents water or being the element with atomic number 79 represents gold for the purpose of physical-chemical analysis. The representation of water as H2O or of gold as the element with atomic number 79 does not raise further perplexity as to how it is that water or gold should be so represented theoretically. That they are so represented is made intelligible by the surrounding theory. We have, then, three salient features of TIDs, and we put them forward as conjectured necessary conditions for when a realist attitude towards theoretical representations is justified: (1) realist purport, (2) conservatism as to

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subject matter, and (3) intelligibility of representation in light of surrounding theory. Let us now turn to propositions as deployed within the metaphysics of what is said and examine how they fare when considered against them. When it comes to (1), there can hardly be any doubt that propositions are typically put forward as revealing the nature of what is said. The proposition theorist engages in the metaphysics of what is said and is typically concerned with revealing the very nature of what is said in particular cases. Going by anecdotal evidence, propositions as representations of what is said clearly meet condition (1).4 When it comes to condition (2), however, the situation is far from clear. Even granting that pre-theoretical claims about what is said are less firmly rooted in common opinion than pre-theoretical claims about water or gold, it is highly doubtful that basic claims about what is said are claims about any structure of propositional constituents. What happens in the advent of any of the proposed theories of propositions is pretty clearly a significant departure from whatever we pre-theoretically take ourselves to be talking about, however dimly, when making claims about what is said. Recall, for example, that what is said provides objects for the attitudes. The idea that in believing that p, we bear a cognitive relation to something that has the content of the complement clause p is not a pre-theoretical idea.5 So whether or not condition (2) is met in this case will depend on whether or not revisionism as to subject matter is demanded by genuine theoretical progress. And here we must admit that the evidence for such progress is scant. It surely does not compare even remotely with whatever warrants revision as to the subject matter in the natural sciences. Finally, turning to condition (3), we very clearly come up short. Even putting aside worries raised in the previous section, it remains unclear why a certain structure of the constituents, Amy, Mary, and LOVE, should represent what is said by ‘Amy loves Mary’. Again, what is said covers the significance of the sentence, the bearer of truth and falsity, the object of attitudes, and the modal operand. How the proposition is supposed to represent all that does not follow from facts articulated by the surrounding theory. This is certainly the case for theories that identify propositions with ordered n-tuples of propositional constituents. But it extends to more recent views as well. Consider a position such as King’s (2007), according to which the proposition expressed by ‘Amy loves Mary’ is roughly the fact that Amy, LOVE, and Mary are the semantic values at the terminal nodes of the relevant syntactic structure. How this is supposed to capture what is believed in believing that Amy loves Mary—one of the hallmarks of what is said—is left officially unaccounted for by such a view. One might perhaps couch the theory in some language-centered account of belief such as RTM, but arguably this only delays the complaint.6 It is no clearer by the lights of the surrounding extended theory how the relevant structure per mentalese is supposed to capture what is believed in believing that Amy loves Mary. The situation here is thus unlike that of the typical TID. Propositional structures seem to encode what is said as covering these various roles. There is

88 Propositions and What Is Said an unmistakable feel of stipulation here, which bespeaks an instrumentalist attitude towards the representation. In short, judging by the conditions set forth by cases where a realist attitude towards theoretical representations seems clearly warranted, the case for a realist attitude towards propositions is weak. The weakness is compounded by a special problem afflicting propositions, a paradox first presented and discussed by Russell himself, the chief progenitor of the doctrine of propositions. The rest of the chapter will be devoted to this problem and its ramifications for the issue at hand.

*5.3 The Russell-Myhill Paradox In a review of King’s (2007) theory of propositions, Deutsch (2008) admonishes the literature surrounding propositions quite generally for its failure to engage with the paradox of propositions presented in Russell (1903: Appendix B), a problem also known as the Russell-Myhill paradox. I would now like to channel some of Deutsch’s sentiment as a further pitch for adopting an instrumentalist attitude towards propositions as theoretical representations of what is said. The paradox of propositions is originally formulated as follows: If m be a class of propositions, the proposition ‘every m is true’ may or may not be itself an m. But there is a one-one relation of this proposition to m: if n be different from m, ‘every n is true’ is not the same proposition as ‘every m is true’. Consider now the whole class of propositions of the form ‘every m is true’, and having the property of not being members of their respective ms. Let this class be w, and let p be the proposition ‘every w is true’. If p is a w, it must possess the defining property of w; but this property demands that p should not be a w. On the other hand, if p be not a w, then p does possess the defining property of w, and therefore is a w. Thus the contradiction appears unavoidable. (527) The claim “there is a one-one relation of this proposition to m: if n be different from m, ‘every n is true’ is not the same proposition as ‘every m is true’” can be generalized to the uncontroversial claim that where P and P´ range over propositions, (P=) if P = P , then for any o, o where o occupies the same position in P as o occupies in P , o = o. Now, for any class of propositions m, the proposition q(q  m  q) is taken as the claim that every proposition in m is true.7 Such a proposition may or may not be a member of m. Consider the class w of propositions, each saying with respect to some class m of propositions that all the propositions

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in m are true, but which do not themselves belong to m: w = {r | m (r = q(q  m  q)  r  m}. Let p be the proposition that says that every member of w is true: p = q(q  w  q). It turns out that p  w just in case p  w. For suppose that p  w. Then for some class of propositions, m, p = q(q  m  q) and p  m. But given that p = q(q  w  q) and given (P=), m = w. So from p  m, we get p  w. Other way, if p  w, then, given that p = q(q  w  q), it follows that for some m or other, p = q(q  m  q) and p  m. So by the definition of w, p  w.8 When facing paradox, we naturally tinker with our extant theories and the representations they deploy in search of better theories and representations that would evade the problem. When naïve set theory saddles us with Russell’s paradox, we conclude that our naïve set-theoretical capture of sets, with its principle of unrestricted comprehension, is faulty. We do not conclude, as per attitudinal realism about naïve sets, that somehow sets or collections themselves are revealed upon closer theoretical scrutiny to have a paradoxical nature. Otherwise, it would make little sense to search for a theory of sets such as ZF to supplant the naïve theory. We look for a different theoretical capture of an extra-theoretical subject matter, a theoretical capture of sets or collections that is paradox-free. Or consider the Liar paradox in a metamathematical setting. Tarski’s Theorem says that no language sufficiently rich (i.e., in which the diagonal function is definable) may contain its own truth predicate. The proof of the theorem is a formalization of the Liar. But the metamathematical limitative result concerns a particular formal capture, a truth predicate, that is, a formal representation of the property of sentential truth. It is not generally maintained that sentential truth itself is paradoxical—otherwise, the various proposed formal captures of sentential truth in the wake of Tarski’s limitative result would not have been proposed as alternative formal captures of sentential truth. When a paradox-free theoretical capture of a pre-theoretical subject matter is proposed, there is a perfectly understandable tendency to regard the new representation under a realist attitude as revealing the nature of whatever it purports to represent. Here, however, we must exercise caution. The proposed theoretical capture must not introduce elements that are prima facie too alien to the represented subject matter to be plausibly regarded under a realist attitude as revealing its nature. As we are about to witness, this requirement can be overlooked. Russell himself evades the paradox of propositions with his ramified theory of types, disallowing such propositions that include quantification over all propositions, themselves included, and more generally, prohibiting impredicative definitions (definitions that include quantification over a universe containing the defined entity). This puts to rest the paradox of propositions as representations of what is said. But when it comes to what is said itself, ramification seems mysterious and unmotivated. Let S be a sentence that says something I take to be the cleverest. Why in the world would there not be anything said by the sentence ‘Of all things said, what is said by S is the cleverest’? Even if we accept some prohibition on

90 Propositions and What Is Said quantifying overall propositions ‘a’ la Russell to block the paradox, our acceptance does not easily extend from the specific theoretical means for representing what is said—propositions—to what is said by our sentences.9 Under a realist attitude that regards propositions as disclosing the nature of what is said, to deny the existence of certain propositional complexes is to withhold significance from sentences that appear for all the world to be significant in their apparent form. Suppose I say, “Anything said is either grasped by someone or could be grasped by someone time and energy permitting”. The realist about propositions who seeks to block the paradox by disallowing quantification over all propositions will maintain either that nothing is literally said here, or else that the sentence says something rather different from what it appears to say. Neither option is attractive. What I said seems to make perfectly good sense as it stands—it seems for all the world to speak of anything said without qualification. Indeed, it might even be true. It is a very tall order to deny significance for natural language locutions that seem perfectly meaningful as they stand. On the other hand, revisionism with respect to what such sentences appear to say in light of their apparent form is unmotivated, given our current understanding of their syntax and semantics. In this respect, the situation here is unlike parallel situations with attempted solutions to neighboring paradoxes. Consider Russell’s more familiar paradox of the class of non-self-membered classes. To block the latter, we typically either enter a provision into the transformation rules of a proposed formal system by swapping one axiom schema (unrestricted comprehension) for another (separation), as in ZF; or else we enter a provision into the formation rules of a proposed formal language that disallows certain syntactic constructions, as in the theory of types. But in neither case need it be maintained that the ordinary phrase ‘is non-selfmembered’ is literally insignificant or has significance other than its apparent one.10 I repeat the upshot of the present discussion regarding another suggested response to the paradox of propositions. According to Deutsch’s (2014) proposed Morse-Kelley-based solution to the paradox, we would recast my sentence as saying that any proposition that is a member of some class is either grasped by someone or could be grasped by someone time and energy permitting. While such revisionism may be warranted as a stipulation about propositions as theoretical representations of what is said, it should not, I submit, be taken to reveal what the original English sentence says. Nothing in the original sentence bespeaks class membership. The sentence says what it says, and what it says would be represented—assuming Deutsch’s solution to the paradox is preferred over others—by a proposition that includes the condition of class membership. This final consideration offers, I believe, a compelling reason to regard propositions under the auspices of an instrumentalist attitude even beyond the general guidelines discussed in the previous section. Accordingly, I propose not to regard these representations of what is said under a realist attitude.

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Propositions, we may suppose, have some explanatory utility. But we should not treat them realistically lest we be saddled with an empirically unmotivated revisionism regarding apparently significant sentences, or worse, the radical idea that those sentences lack significance altogether. Together with the instrumentalist deflation noted in Section 5.1 of worries about propositional unity, Benacerraf-style indeterminacy, and suitability for truth and falsity, I conclude that we have an overriding reason to regard propositions as representations wielded for specific explanatory purposes but not regard them as revealing the nature of what is said. Attitudinal instrumentalism is the right attitude to adopt towards them. Finally, in a number of writings on the topic, Soames objects to traditional conceptions that characterize propositions as formal structures of propositional constituents on the grounds that such structures are not inherently representational. As against a proponent of the traditional view, Soames (2010a, 2010b) insists that structures of constituents do not have representational properties intrinsically, so it is incumbent on their advocate (Soames’s opponent) to explain how those properties emerge from cognitive relations cognizers bear to those structures—an undischarged explanatory burden. The key here is that propositions are presumed to reveal the nature of what is said. If propositions are identified as structures of constituents, as per Soames’s opponent, then those structures are to reveal the nature of what is said. But then, claims Soames, we are owed some explanation of how the representational properties of those structures of constituents, specifically their having truth-conditions, emerge from our cognitive relations to them. On the present way of looking at things, by contrast, propositions are theoretical representations that are not to be regarded as revealing the nature of what is said to begin with (pace both Soames’s target and Soames’s complaint). We associate propositions with truth-conditions by stipulation. Perhaps an analogy is in order. Consider, again, Frege’s (1953) representation of the number n as the extension of the second-level concept equinumerous with F, where F is a first-level concept with an n-membered extension.11 A critic might object that this cannot be right because the Fregean construction—the extension of the second-level concept—is not intrinsically applicable to quantities. And so, we are owed some explanation of how the applicability of the construction to quantities emerges from our interactions with the number, our counting practices, or whatnot. Frege and this critic share the assumption that whatever theoretical account is being offered here is to be regarded as revealing the nature of the number. But an instrumentalist about Frege’s construction would demur: Frege’s construction represents n for a certain broad theoretical purpose—showing that arithmetic need not avail itself of any logical means beyond secondorder logic. But the construction should not be expected to reveal the nature of the number it represents. The applicability of the construction to quantities can be stipulated.

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Notes 1. Except in cases involving denoting concepts. Denoting concepts are introduced and discussed in Russell (1903: Ch.V) before being subjected to criticism in the Gray’s Elegy passage in Russell (1905), where they are misleadingly identified with Fregean senses. Importantly, denoting concepts allow the early Russell to introduce generality into propositions. Regarding ‘I met a man’, for example, there is a distinction between the proposition expressed, one that contains the a-man denoting concept, and whatever makes it true, my having met Jones, say. See Simchen (2010) for further discussion of this early and lesser known Russellian theory. 2. There is another sense in which the representation may be true or false—by adequately or inadequately capturing what is said, i.e. by being true or false to what is said—but this is a very different matter from the one discussed in the text concerning truth or falsity for what is said. 3. But see p.  36 n.1 above for an important qualification. The relevance of subtleties in the philosophy of chemistry to the overall theme of this book is rather limited insofar as cases regarding which attitudinal realism is prevalent are discussed here as points of contrast with the main cases of interest, which are theoretical representations in philosophy, in this case the metaphysics of what is said. 4. See, for example, the evidence cited in the previous section from the concluding discussion of King et al. (2014). 5. See Chapter 6 for further articulation of this point. 6. See Section 6.4 for an extended discussion of RTM in a related context. 7. We can represent this as a complex consisting of the property of universality for propositional functions ALLpf, the truth-function IF-THEN, and the relational property MEMBER relating things to the classes that include them. The proposition can then be taken as ALLpf, h where h is a propositional function that takes proposition q to IF-THEN, MEMBER, q,m,q. 8. For further discussion of this argument, see Urquhart (2003). 9. There may be other reasons to dislike the ramified theory of types. Logicians have tended to dislike the theory’s attendant axiom of reducibility, which is difficult to accept as a logical principle. For further discussion of the issue, see Goldfarb (1989). 10. Russell himself assumes otherwise for reasons discussed in van Heijenoort (1967) and which would take us too far afield. Suffice it to say that Russell’s predilection to the contrary is based on a conception of logic and language that is markedly different from our own. 11. See Section 1.2.

6

The Content Program

6.1 Significance and Content Contemporary philosophy of language and mind is replete with appeals to content, both in philosophical semantics and elsewhere in the philosophy of mind broadly construed. Contents are theoretical representations of the significance of linguistic expressions and mental states and episodes. It is sometimes assumed that the notion of content is pre-theoretical. This is testimony to how entrenched content has become in philosophical discussions of linguistic and mental phenomena. But the idea that what accounts for the significance of linguistic expressions is also what is true or false, which is also what provides objects for cognitive attitudes such as beliefs, hopes, fears, and so on, is certainly not a pre-theoretical idea but a basic tenet of what might be called the content program in the philosophy of language and mind. The notion of content may have different roles to play in different explanatory settings. Whether or not it should ultimately be one and the same posit across distinct theoretical contexts is an interesting question I will not attempt to settle. My aim in this chapter is to make an extended case for an instrumentalist interpretation of familiar swaths of theory within the content program. Consider, again, the contrast between attitudinal realism and attitudinal instrumentalism. In contra-distinction to how we treat certain individual theoretical representations in the natural sciences, where we can regard a given representation as itself disclosing what the represented item really is in the most demanding sense, there are explanatory settings where such an attitude seems clearly inappropriate. These are cases where the individual theoretical representation isn’t entrusted with revealing the nature of the represented item but is rather called upon to perform some other theoretical role within the overall explanatory context. In such cases, we do not treat the representation under a realist attitude but treat it under an instrumentalist attitude instead. Examples that come to mind are the representation of real numbers as Dedekind cuts in the foundations of mathematics, for example, or the representation of the meaning of a sentence as a set of indices in formal semantics. In the latter cases, we do not presume that the DOI: 10.4324/9781003306443-6

94 The Content Program representation should itself disclose what the represented item really is. We don’t expect, for example, that a certain set of indices should capture what the meaning of ‘There is a bag of potatoes in my pantry’ really is.1 Whatever that meaning is, it surely isn’t that. Rather, the set of indices represents the meaning within a broader theoretical context of formal semantic explanation that includes generating truth-conditions for whole sentences in a way that comports with structural requirements introduced by generative syntax. In a very different setting, we don’t generally suppose that the Dedekind cut tells us what the real number really is; we assume, rather, that the real is represented by—or “constructed” as—a Dedekind cut of rationals. As I have been arguing throughout, the distinction between a realist and an instrumentalist attitude towards theoretical representations has important implications for philosophical theorizing. Without a default commitment to philosophy’s theoretical representations revealing the nature of what they represent individually, we can pause and ask what explanatory work those representations are called upon to do. I will now explore the central aspects of the content program through an instrumentalist lens as a further pitch for metaphilosophical instrumentalism. I am not going to argue directly against the adoption of a realist attitude and in favor of the adoption of an instrumentalist attitude towards theoretical representations within the content program, however. My aim, rather, is to illustrate the explanatory advantage of adopting an instrumentalist stance by focusing on central aspects of the program and viewing them from an outlook that is superior to the realist one. In Chapter 2, we considered some general guidelines for warrant in adopting a realist attitude towards theoretical representations. The basic idea was to take for granted such warrant in uncontroversial cases outside philosophy—geometrical solids representing minerals in crystallography, for example—identify central aspects of those cases and apply them as necessary conditions for such warrant in the more controversial cases of philosophical theorizing. Implementing such a strategy here would require showing that some of those hypothesized necessary conditions fail. As we saw earlier, in uncontroversial cases of a justified realist attitude towards a theoretical representation, the fact of representation itself falls within the purview of the surrounding theory. That gold is theoretically represented as being the element with atomic number 79, for example, is covered by a broad physical-chemical account that ties together macro and micro-features of the substance. It can explain, for example, why it is that atomic number 79 absorbs a lot of the low wavelengths and, therefore, presents as yellow. Nothing like this can be said about familiar theoretical representations within the content program. But my aim in this chapter is the more modest one of providing an instrumentalist interpretation of basic aspects of the content program by focusing on familiar foundational work within it. I aim to show that an instrumentalist stance enjoys greater plausibility than its realist rival when it comes to theoretical representations of meaning, of meaning-determination, and of the cognitive attitudes within the content

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program. Swaths of theory to be discussed here are commonly viewed under a realist interpretation. This is a fundamental oversight about the explanatory work and achievement of various familiar aspects of the content program, as we will see. Some of the criticisms of realist interpretations offered below may seem familiar to those who have been following relevant debates in the philosophy of mind and language. The instrumentalist takes on the various doctrines offered in this chapter gain their significance from the larger context of the book’s overall case against a default adoption of a realist attitude towards philosophical theoretical representations. Taken together, a broader methodological theme can emerge.

6.2 Attitudinal Instrumentalism and Content Discussions surrounding content within the philosophy of language and mind are generally framed by engagement, positive or negative, with the socalled new theory of reference of the 1970s. The influence of the new theorists’ work on subsequent philosophy has been nothing short of profound. Before this work, it was commonly assumed that the terms of language and thought are associated with conditions that fix what the terms are about. For example, singular terms such as ‘Elizabeth Warren’ were thought to be associated with conditions specifying the term’s referent; general terms such as ‘Democrat’ or ‘progressive’ were thought to be associated with conditions specifying the term’s range of application. Treating referents for singular terms and ranges of applications for general terms as the terms’ extensions, endowment with semantic content was thought to consist in the association of terms with extension-fixing conditions. And knowledge of such conditions was thought to comprise semantic competence. All this changed following the work of Donnellan (1966, 1970), Putnam (1975), Kripke (1980), and others, work that convinced philosophers that the old view of semantic endowment and competence was wrong not only on this or that detail but fundamentally. An average speaker may be proficient with ‘Cicero’ and use it to refer to Cicero without being able to identify Cicero beyond being some famous Roman orator or being some famous Roman, or perhaps even just being some famous guy. An average speaker may be proficient with ‘elm’ and ‘beech’ and use them to specify the elms and the beeches, respectively, without having in her cognitive possession a condition associated with each term that allows her to distinguish the elms from the beeches. Pre-1750 Oscar here on Earth may think a thought he would express by saying ‘Water is abundant’ while his pre-1750 Doppelgänger on Twin-Earth may think a thought he would express by saying ‘Water is abundant’. Oscar and his twin are in every relevant way the same. But the stuff surrounding Oscar is H2O, while the stuff surrounding his twin is some alien but superficially similar stuff XYZ. So Oscar’s thought and his term ‘water’ are about H2O; his twin’s thought and his term ‘water’ are about XYZ. Such examples may be multiplied as needed. The negative upshot

96 The Content Program is that semantic endowment isn’t the association of terms with extensionfixing conditions, and semantic competence isn’t knowledge of such conditions. But in the wake of this important body of work, the question remains how to think positively about semantic significance.2 Putnam’s classic “The Meaning of ‘Meaning’” (1975), a cornerstone of the new theory of reference, exhibits heightened sensitivity to methodological issues that lie at the heart of the theoretical study of meaning and are easily overlooked. There is a clear instrumentalist streak running through Putnam’s thinking about semantic significance: Briefly, my proposal is to define “meaning” not by picking out an object which will be identified with the meaning (although that might be done in the usual set-theoretic style if one insists), but by specifying a normal form (or, rather, a type of normal form) for the description of meaning. If we know what a “normal form description” of the meaning of a word should be, then, as far as I am concerned, we know what meaning is in any scientifically interesting sense. (190) And a little later, regarding a normal form description of the meaning of ‘water’ that includes specifying H2O as the term’s extension, alongside other parameters such as syntactic marker, semantic marker, and stereotype, we read: [T]his does not mean that knowledge of the fact that water is H2O is being imputed to the individual speaker or even to the society. It means that (we say) the extension of the term ‘water’ as they (the speakers in question) use it is in fact H2O. (191) The picture that emerges from such passages is that in characterizing the meaning of ‘water’, we are not offering a theoretical identification that would tell us what that meaning is in the way imagined perhaps by the metaphysician of meaning and modeled after theoretical identifications in natural science, such as water being H2O. We can say what we need to say theoretically about meaning by giving a normal form description of the meaning of the term. We do this without providing a theoretical representation that would itself be entrusted to reveal what that meaning really is, as one might theoretically capture the constitution of a substance in physical chemistry by representing it as a certain chemical compound. Putnam’s talk of not picking out some object to be the meaning while leaving room for its set-theoretical representation (“although that might be done in the usual set-theoretic style if one insists”) is reminiscent of a similar point urged by Lewis regarding a related explanatory enterprise. The point merits a brief digression on Lewis’s own instrumentalist predilections in the study of language and thought.

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Lewis (1975) identifies language use in a given population as the existence of a convention of truthfulness and trust in £, where £ is a mapping of strings of signs onto sets of possible worlds (indices). To be truthful in £ is to try not to issue a false sentence—construed as a string of signs σ for which @  £(σ), where @ is the actual world—and to be trusting in £ is to impute truthfulness to others. This convention of truthfulness and trust in £ is a kind of regularity in linguistic behavior within the population, a regularity of not uttering sentences believed to be false and expecting others to do the same. Lewis’s six conditions for such a regularity to qualify as a convention need not concern us. What is of present concern, however, are the levels upon levels of theoretical representations within this work, none of which needs to be treated under a realist attitude. First and foremost, we have the language used by the population, represented as a function £ from strings of signs to sets of possible worlds. This function is represented set-theoretically as a set of ordered pairs. The strings of signs making up the first members of those pairs represent sentences; the sets of possible worlds making up the second members of those pairs represent sentence-meanings (“propositions”). A sentence represented by the string σ being true or false is represented by the actuality-representing @ being a member or not of the set £(σ). Lewis considers many objections to his theory of language use and offers detailed replies. An important objection runs as follows: Unless a language user is also a set-theorist, he cannot expect his fellows to conform to a regularity of truthfulness and trust in a certain language £. For to conform to this regularity is to bear a relation to a certain esoteric entity: a set of ordered pairs of sequences of sound-types or of mark-types and sets of possible worlds. . . . The common man has no concept of any such entity. Hence he can have no expectations regarding such an entity. (24–5) Insofar as a language is a pairing of sentences with their meanings, it would appear that a language user would need to have some cognitive rapport with the pairing in question, the set-theoretical entity. This would require, in turn, rapport with sentences construed as strings, which are further settheoretical entities, and rapport with the meanings of sentences, construed as yet further set-theoretical entities. Does it not follow that the language user would need to be cognitively en rapport with an elaborate set-theoretical construction? Lewis replies: The common man need not have any concept of £ in order to expect his fellows to be truthful and trusting in £. He need only have suitable particular expectations about how they might act, and how they might form beliefs, in various situations. . . . He expects them to conform to

98 The Content Program a regularity of truthfulness and trust in £ if any particular activity or belief-formation that would fit his expectations would fall under what we—but not he—could describe as conformity to that regularity. (25) £ is a formal object representing a language, just as the non-membership of @ in £(σ) represents falsity for the sentence represented by the string σ. It isn’t a representation that we should be treating as itself telling us what a language is in the most demanding sense, what issuing a meaningful sentence is, or what interpretation amounts to. Nor does the representation of sentences as strings of signs in the set-theoretical sense tell us what sentences themselves really are at bottom. Whatever sentences are, it’s unlikely they’re sets. Nor does the representation of the meaning of a given sentence as a set of possible worlds tell us what that meaning really is. Lewis’s theory of language use deploys various theoretical representations in an effort to shed explanatory light on a wide-ranging, multi-faceted phenomenon. Treating those representations individually in a realistic spirit is no part of this explanatory endeavor. Similarly, those who are expecting the new theory of reference to represent meanings in a way that reveals what those meanings really are at bottom are bound to come away disappointed. One of the easily missed lessons of the new theory of reference is that we need not be beholden to a conception whereby representations of meaning are themselves revelatory of the nature of the pre-theoretical subject matter. A question often raised in reaction to the now familiar arguments in Donnellan (1966, 1970), Kripke (1980), and Putnam (1975) is: “So what is the meaning of a referentially used description, or of a proper name, or of a kind term?” Such questions belie a misunderstanding. The correct response to such questions is to say that it really depends on the broader theoretical purpose at hand. There may be good theoretical reasons to treat descriptions and proper names, for example, as denoting individuals for formal semantic purposes. Those denotations are no more meant to tell us what the meanings of those expressions really are than the representation of the meaning of a sentence as a set of indices is meant to tell what the meaning of the sentence really is. Specific theoretical representations of meaning—that particular descriptions denote in the formal semantic sense particular individuals, for example—are not themselves entrusted with revealing the nature of the pre-theoretical subject matter—what the meaning of the given description ultimately is.

6.3 Attitudinal Instrumentalism and Metasemantics The new theory of reference shouldn’t be taken as offering theoretical identifications along the lines of gold being the element with atomic number 79 or water being H2O when it comes to semantic significance. Treating the theory’s pronouncements as purporting to reveal what semantic significance

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really is in given cases misconstrues the theory’s scope and achievement. But philosophers have also looked to this body of work for how best to think of the determination of semantic facts, specifically how language and thought “hook onto the world”. Subsentential expressions make various contributions to the truth-conditions of the sentences in which they partake. Semantics specifies those contributions, whereas metasemantics inquires after how those particular contributions get determined. Before the advent of the new theory of reference, the distinction between semantics and metasemantics was not clearly drawn. But once semantic contributions of subsentential expressions to truth-conditions of sentences became more austere—individuals in the case of proper names, for example—a separate line of inquiry could emerge targeting the determinants of semantic relations—how, for example, a particular name came to name a particular individual. Such metasemantic matters, with a common way of looking at them, form a branch of metaphysical inquiry, and the question I turn to next is how to regard theoretical representations within this branch of inquiry in the wake of the new theory of reference. I aim to show that an instrumentalist attitude can play an important role within a defensible variant of the metasemantic picture handed down to us by the new theorists. The situation here is complicated by certain entrenched ways the theory has often been received, but I will illustrate the need for an instrumentalist attitude in appreciating the work’s real explanatory power. The need for an instrumentalist attitude towards theoretical representations in metasemantics can be usefully illustrated by considering some of the details surrounding extension-fixing for general terms. An important component of Putnam’s (1975) overall conception, for example, is the suggestion that extension-fixing for a general term such as ‘water’ is crucially demonstrative (or ‘indexical’). After presenting his sociolinguistic hypothesis of the division of linguistic labor, Putnam (1975: 148–149) compares two alternative characterizations of demonstrative extension-fixing for ‘water’ and opts for the second: (1) for any world w and any x in w, x is water just in case x is the sameL as the referent of ‘this’ in w, (2) for any world w and any x in w, x is water just in case x is the sameL as the referent of ‘this’ in actuality. According to (1), to be water in any world is to be the sameL as a sample of local watery stuff—clear, potable liquid, raining from the sky, filling the lakes, etc.—demonstratively referred to in the world in question. According to (2), to be water in any world is to be the sameL as a sample of watery stuff demonstratively referred to in the actual world. SamenessL is a cross-world relation of sameness for liquids that prominently features chemical composition. It is (2) rather than (1) that comports with our referential intentions as users of ‘water’, says Putnam. We intend ‘water’ to apply to all and only

100 The Content Program samples of water, i.e., H2O plus or minus impurities, in any world. A world where H2O is entirely absent and a superficially similar alien substance XYZ occupies the role played by H2O in actuality is a world where there is no water at all despite the abundance of the superficial look-alike. That ‘water’ applies to water and only to water in any possible world is characterized by Putnam, using Kripke’s terminology, as rigidity:3 If we extend the notion of rigidity to substance names, then we may express Kripke’s theory and mine by saying that the term ‘water’ is rigid. The rigidity of the term ‘water’ follows from the fact that when I give the ostensive definition “this (liquid) is water” I intend (2) and not (1). (149) Speakers wield ‘water’ with the intention to specify anything, in any possible world, relevantly similar to this (as deployed in the presence of a paradigm actual sample of water). The rigidity effect appears to depend on the behavior of the implicated sameness relation.4 The account we’ve been considering is part of an overall metasemantic story offered to counter a traditional view according to which the terms we use in language and thought are associated with extension-fixing conditions, knowledge of which accounts for semantic competence. An important consequence of the older view is that it makes fixity of subject matter across radical changes in theory and belief unlikely. As such, the older view isn’t as well equipped to handle theoretical progress. On the older view, in order for a contemporary theoretically-informed speaker and an ancient speaker using a substance term to be on the same page when it comes to the substance at issue, the conditions associated with the term in each of their mouths are required to specify one and the same substance. This is unlikely, to say the least. The belief-set of contemporary speakers when it comes to water is quite different from the corresponding belief-set of ancient speakers. But on the account of extension-fixing we’ve been discussing, speakers intend to use ‘water’ for anything relevantly similar to paradigmatic samples. Insofar as contemporary and ancient samples are samples of the same substance, the term ‘water’ in the mouth of contemporary speakers can have the same range of application as the term in the mouth of ancient speakers despite significant disparities in beliefs and theory. What counts as a relevant similarity for water is something that inquiry homes in on in the fullness of time. The important point is that according to the new view, what counts as water doesn’t pose an undue burden on speakers and thinkers about the substance. We may think of Putnam’s endorsement of (2) over (1) as filling in some of the implications of speakers’ referential intentions in light of this last point. How to think of referential intentions is vexing.5 Referential intention attribution is intention attribution, which is a type of cognitive attitude attribution. We shouldn’t expect the representations deployed in characterizing cognitive attitudes to reveal the nature of the represented attitudes at

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this early stage of inquiry into such cognitive matters.6 And we certainly shouldn’t expect such representations to reveal the nature of extra-cognitive matters of fact, such as individuation conditions for water. In characterizing referential intentions, ‘sameL’ represents whatever relevant similarity for liquids happens to be by the lights of the attributor, the theorist, not the attributee. There is considerable metaphysical controversy over how to think of relevant similarity of substances, but the outcome of this controversy is largely irrelevant to the proposed metasemantics for ‘water’. The metasemantics stands on its own even in the absence of a satisfying metaphysical story about sameness for substances.7 SamenessL is invoked here as part of a theoretical capture of speakers’ referential intentions. We are told that the average speaker deploys ‘water’ with the intention to specify anything relevantly similar—i.e., anything that is the same as befitting liquids—to samples in the speaker’s environment. Think of samenessL in the characterization of an average speaker’s referential intention along the lines of £ as it figures in Lewis’s characterization of language use discussed in the previous section. Lewis characterizes language use in terms of an attitude of expecting fellow speakers to be truthful in £ inter alia, where £ is an elaborate settheoretical construction. The relevant objection considered by Lewis we discussed earlier, is that the average speaker cannot be expected to be able to form attitudes towards £-such attitudes would require the speaker to be a set-theorist. Lewis’s reply to the objection is that it isn’t incumbent on the agent of the attitude to be capable of characterizing the attitude by appealing to £. Such an appeal is something we theorists do. To suppose that £ should be taken as a realistic theoretical representation of an aspect of the cognitive attitude of trust in a language is to misunderstand its explanatory role in the overall theory. Along similar instrumentalist lines, Putnam’s proposal that speakers intend their ‘water’ to pick out anything that is the sameL as actual samples of water can be apt without making unreasonable predictions under a realist interpretation of what goes on within speakers’ mentality as they deploy the term. Moreover, just as the controversy surrounding the metaphysics of sets is beside the theoretical point when it comes to Lewis’s appeal to £ within his theory of language use, the controversy surrounding what counts as the same substance is beside the theoretical point when it comes to Putnam’s appeal to samenessL within his proposed metasemantics. Differences among various metaphysical takes on sets—platonism vs. nominalism, for example—are largely irrelevant when it comes to the explanatory achievement of Lewis’s theory, even if it utilizes sets. Differences among various metaphysical takes on sameness for substances—realism vs. nominalism about natural kinds, for example—are likewise irrelevant when it comes to utilizing sameness for substances within the target metasemantics.8

6.4 Attitudinal Instrumentalism and RTM Let us now turn to the deployment of content within the metaphysics of cognitive attitudes. We saw that positing contents need not be committed

102 The Content Program to the idea that such representations of semantic significance are themselves revelatory of the nature of what they represent. We also saw that positing a particular demonstrative-cum-comparative structure for referential intentions need not be taken to reveal the underlying nature of the mental set required for the acquisition of and proficiency with general terms. We will next witness how positing certain mental particulars with a syntax and semantics as relata for cognitive states and episodes quite generally need not be taken to reveal what it is to be in such states and undergo such episodes. And yet the entire system of such theoretical representations may reveal something important about the nature of cognition. To fix on an image here, think of Mendel’s theory of inheritance and his notion of “factor” as the unit of inheritance in formulating Mendelian principles. The Mendelian factor represents the gene, with its different “forms” representing different alleles. But we wouldn’t say that the Mendelian factor individually reveals what the represented gene really is. In the course of subsequent genetic inquiry, that story gets filled in, but Mendelian factors represented genes within a larger theoretical context that didn’t include delving deeper into what the represented genes really are. Such explanatory holism (for lack of a better term) is especially important to keep in mind when considering leading theories in the metaphysics of cognitive attitudes, views according to which being in a cognitive state such as believing that p consists in bearing a certain relation to something—a “mental representation”—that carries the semantic content that p. The most developed and influential of those views is Fodor’s Representational Theory of Mind (RTM). Fodor (1987) summarizes his position as follows: At the heart of the theory is the postulation of a language of thought: an infinite set of ‘mental representations’ which function both as the immediate objects of propositional attitudes and as the domains of mental processes. More precisely, RTM is the conjunction of two claims: Claim 1 (the nature of propositional attitudes): For any organism O, and any attitude A towards the proposition that P, there is a (“computational”/“functional”) relation R and a mental representation MP such that MP means that P, and O has A iff O bears R to MP. . . . Claim 2 (the nature of mental processes): Mental processes are causal sequences of tokenings of mental representations. (17) RTM has been subjected to many criticisms and subsequent refinements over the years. The general tenor of Fodor’s overall position is an abductive

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“only game in town” stance. What comparable alternative might there be, given what we aim to explain? Indeed, RTM has an unmistakable reach when compared with some of its alternatives. How can we understand, for example, what it is for someone to believe the universe began with the Big Bang without positing a relation between the believer and something that behaves like the sentence ‘The universe began with the Big Bang’, with an attendant syntax and semantics? Such a posit easily figures in further explanations of systematicity in the agent’s thinking. It can help explain why, for example, believing the universe began with the Big Bang plausibly gives rise to the belief that the universe had a beginning, that the Big Bang was in the past, and much else besides. Alternative accounts that seek to avoid such posits are in a difcult spot. Consider, for example, Marcus’s (1990) dispositionalism. Marcus contrasts “language centered” theories of belief, such as RTM, with the “object centered” accounts she favors. In her view, an agent believes that p just in case under various agent-centered circumstances, the agent is disposed to act as if the state of affairs that p obtains. We might understand “disposition to act” on this view as a way station in the quest after something more comprehensive and theoretically satisfying down the road of inquiry. Dispositionalism might seem like a reasonable reaction to certain perceived shortcomings of language-centered accounts, such as the construal of beliefs for nonlinguistic or prelinguistic creatures as relations to sentence-like things, and the construal of Kripke’s (1979) logically blameless Peter believing Paderewski had musical talent while believing Paderewski had no musical talent as someone who believes a contradiction. Nevertheless, a dispositional story will be hard-pressed to distinguish believing the universe began with the Big Bang from believing the universe will end with the Big Crunch or anything else without obvious ramifications for behavior. This is so unless the “disposition to act” on the right-hand side of the proposed account includes linguistic behavior. But then it seems reasonable to want to know why the disposition to utter ‘The universe began with the Big Bang’ is correlated with believing the universe began with the Big Bang, while the disposition to utter ‘The universe will end with the Big Crunch’ is correlated with believing the universe will end with the Big Crunch. It is a tall explanatory order. RTM, on the other hand, can enlist the gamut of syntax and semantics to distinguish such beliefs. The dispositionalist story, by comparison, seems ill-equipped to track such cognitive fineness of grain. A shortcoming of theories such as RTM not discussed by Marcus directly is the general matter of sheer theoretical overreaching, given the paucity of the evidence. Such theories seem to overreach empirically, which can easily incline critics to dismiss them as fanciful. Language-like intermediaries for cognitive attitudes can easily be regarded as theoretical wishful thinking. But one can accept the general tenor of such criticism while wondering whether there isn’t a less radical alternative to doing away with language-like intermediaries in the metaphysics of cognitive attitudes altogether.9

104 The Content Program Fodor (1975) considers RTM’s representations of cognitive states and episodes in terms of relations to such intermediaries as revealing the very nature of those states and episodes: To have a certain propositional attitude is to be in a certain relation to an internal representation. That is, for each of the (typically infinitely many) propositional attitudes that an organism can entertain, there exist an internal representation and a relation such that being in that relation to that representation is nomologically necessary and sufficient for (or nomologically identical to) having the propositional attitude. The least that an empirically adequate cognitive psychology is therefore required to do is to specify, for each propositional attitude, the internal representation and the relation which, in this sense, correspond to it. Attitudes to propositions are, to that extent, ‘reduced’ to attitudes to formulae, though the formulae are couched in a proprietary inner code. (198) When Fodor describes himself as an intentional realist and takes RTM to be the only game in town, the upshot for him is that the representation of a given cognitive fact within the theory reveals the very nature of this fact. But this need not be the only option. Might not RTM as a whole reveal something important about the nature of cognition without each of its theoretical representations doing so individually? Here we might take our clue from a related theoretical setting: the semantics of belief reports and the sententialist view that the truth-condition for ‘A believes that p’ is the agent bearing a certain relation of ‘believing-true’ to the complement clause. In an illuminating discussion of sententialism about belief reports, Quine (1956) writes: This semantical reformulation is not, of course, intended to suggest that the subject of the propositional attitude speaks the language of the quotation, or any language. We may treat a mouse’s fear of a cat as his fearing true a certain English sentence. This is unnatural without being therefore wrong. It is a little like describing a prehistoric ocean current as clockwise. (186) To say that the mouse fears the cat is about to pounce is to say, according to the sententialist, that the mouse fears-true the English sentence ‘The cat is about to pounce’. This, we are told, no more requires us to attribute the speaking of English to the mouse than describing a prehistoric ocean current as clockwise requires us to postulate some interesting relation between the prehistoric ocean and clocks. The theorist is offering truth-conditions for the likes of ‘The mouse fears the cat is about to pounce’. It is no part of the theoretical effort here to get deeper into the cognitive facts being reported

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beyond delivering the right truth-conditions for the reports. However the mouse happens to be tracking the cat’s readiness to pounce, its fact-directed fear is the truth-condition for ‘The mouse fears the cat is about to pounce’. And this fact-directed fear may be construed by the theorist as a relation to an English sentence without misconstruing the cognitive facts. Switching from sententialism in the semantics of attitude reports to the metaphysics of the attitudes themselves, we can deny the realist interpretation of the deliveries of RTM with respect to our mouse’s fear along analogous lines. RTM represents the fear in question as a functional relation R obtaining between the mouse and a mental representation MP that means that the cat is about to pounce. But we need not think of this theoretical representation as itself revealing the nature of the represented fear. What we aim to lay bare with RTM is a general cognitive architecture for the mouse. We might consider the mouse’s fear that the cat is about to pounce as interestingly related to the more generic fear that something or other is about to pounce. We might characterize the mouse’s fear as interestingly related to the mouse’s belief that there is a cat in front of it, or to the belief that there is a cat in front of it about to pounce, or perhaps to the highly specific belief that this very cat—the proximal source of pheromones—is about to pounce. What the individual attitudes really are at bottom, the nodes in the overall structure of mouse mentality, need not be part of this explanatory enterprise. To evoke, again, the image from the Preface, we may represent a substance with a plastic model of its molecular structure, consisting of spheres and connecting rods that, in turn, represent atoms and chemical bonds. The model as a whole may reveal the molecular nature of the represented substance without the spheres and rods individually revealing the natures of the represented atoms and bonds. These are early days of cognitive theorizing. Perhaps instead of starting to theorize from scratch under various idealizations in order to avoid empirical overreaching, we ought to take a more cautious attitude towards what we’ve already got.10 Such conservatism in theory-choice, coupled with an instrumentalist stance in theory-interpretation, need not be viewed as abandoning the main tenet of Fodorian intentional realism. There is a fact of the matter about cognitive states and processes, but it is revealed by larger swaths of theory rather than by individual representations of particular manifestations of mentality. A healthy instrumentalist attitude in the metaphysics of mind allows us not to throw out the baby with the bath water here.11 Fodor (1975) famously introduces his Language of Thought Hypothesis with a critique of reductionism. He discusses the special sciences vis-á-vis physics; economics, in particular, is offered as a salient example of an implausible reduction to physics. But there is a general lesson regarding special scientific explanation that Fodor fails to heed. Economists can insist that there is a fact of the matter about the nature of monetary systems vis-á-vis the gold standard, or about the circulation of currencies in formulating Gresham’s Law without having anything interesting to say about the underlying nature of gold

106 The Content Program or the underlying nature of currencies represented by ratios of commodity value to nominal value. Something similar, I claim, can be said about representing a cognitive state such as a belief as a relation to a sentence in mentalese. The intentional realist need not adopt a realist attitude towards RTM’s individual theoretical representations to maintain that there is a fact of the matter about cognition. The further realist insistence is just not realistic given the general form and reach of cognitive psychological explanation. The functional relation to a sentence in mentalese representing a given attitude should not be regarded as disclosing the nature of the represented attitude at issue. Theoretical representations in the philosophy of mind and language can easily be mistaken for theoretical representations in the natural sciences that give rise to theoretical identifications à la gold being the element with atomic number 79 and water being hydrogen hydroxide. It can easily seem that when we theoretically represent things or facts pertaining to semantic significance, we are somehow purporting to lay bare what those things or facts really are at the end of the day. It can easily seem that when we theoretically represent mental states and episodes as involving mental representations, we are somehow disclosing what those aspects of mentality really are at bottom. But this is a myopic outlook on how theoretical representations function within our theories. Within the content program, we model wideranging phenomena by appealing to various theoretical representations that need not, and should not, be viewed as disclosing the nature of what they represent individually. When we theoretically represent a referential intention within a metasemantic explanation as the intention to specify anything relevantly similar to samples in the environment of the speaker, we need not and should not assume that our representation itself reveals the nature of the attitudinal state in question. Rather, representing the intention figures within a broader explanatory effort to delve into the nature of aboutness for language and thought. When we represent a belief along Fodorian lines as the bearing of a relation to a sentence in mentalese, we should not expect of such a representation to disclose (individually, as it were) what it is for the belief state to obtain. Such cases within the content program are distorted by adopting a realist attitude towards the relevant theoretical representations, which in such light can seem fanciful. Instead of simply discarding those representations for not being sufficiently well grounded in the more experimental reaches of cognitive science, we can view them more holistically as having larger roles to play within their respective theories that do not include disclosing the nature of whatever they represent individually.

Notes 1. The point is familiar to semanticists and illustrated nicely in the opening sections of Heim and Kratzer (1998). 2. I set aside the question of narrow content. See Simchen (2004, 2022) for a discussion of narrow content in relation to the explanatory achievements of the new theory of reference.

The Content Program 107 3. Kripke (1980: 48) characterizes rigidity for singular terms as the designation of the same individual in any world in which the individual exists. How to extend the notion of rigidity to general terms such as ‘water’ has spawned a sizable secondary literature. Let us assume, however, that for a general term to be rigid is for the term to apply to an individual member or sample of an associated kind at any world in which the individual or sample exists. See Gòmez-Torrente (2006) for a discussion of this construal of rigidity for general terms. 4. To see this, consider extension-fixing for a non-rigid general term along Putnamian lines. What my favorite color happens to be might have been different, so the complex singular term ‘my favorite color’ is presumably non-rigid—it doesn’t designate the same color at every world in which the color exists. Accordingly, the general term ‘sample of my favorite color’ should presumably come out non-rigid as well in the sense given in the previous footnote. Let samenessFC be the relation among samples of color such that o is the sameFC as o just in case each is a sample of my favorite color in its respective world. (Such a cross-world relation prominently features, let us suppose, psychological goings-on associated with certain types of response-dependence.) If o and o are worldmates, then they sample the single color that happens to be my favorite in their shared world, whereas if they’re not worldmates, each samples my favorite color in its respective world. We can characterize extension-fixing for ‘sample of my favorite color’ as follows: (3) for any world w and any x in w, x is a sample of my favorite color just in case x is the sameFC as the referent of ‘this’ in actuality.

5. 6. 7.

8.

The structure of (3) is the same as that of (2). And yet ‘water’ is rigid whereas ‘sample of my favorite color’ is not. A sample of blue in the actual world is a sample of my favorite color, blue, whereas that very sample in a world in which my favorite color is red will not be a sample of my favorite color in that world. So ‘sample of my favorite color’ will not apply to that sample at every world in which the sample exists. See Simchen (2012: Ch.3) for an extended discussion of the issue. See next section for further elaboration of this point. For a contrasting view, see Häggqvist and Wikforss (2018), who hold that metaphysical troubles concerning what counts as a given substance have dire consequences for the metasemantic picture outlined here. See also Needham (2017), who takes the notion of demonstrative extension-fixing for substance terms to be of limited reach. These discussions seem to miss relevant aspects of Putnam’s metasemantic proposal under an instrumentalist interpretation. In characterizing the relevant referential intention, the role of the demonstrative pronoun ‘this’ is simply to highlight the environmental aspect of extension-fixing for a substance term by whichever means—that the term is intended for stuff of the kind found “around here”. Whether or not demonstrative reference plays any role in how substances are in fact named is beside the metasemantic point; the choice of particular semantic means is incidental. This choice should also not be taken to imply that mastery with ‘water’ depends on antecedent mastery with ‘this’, an empirical matter to be settled separately. For yet another striking example of Lewisian attitudinal instrumentalism in the philosophy of mind and language, consider Lewis’s (1979) view according to which believing is represented as the self-ascription of a certain property, which is construed as self-location within the property, which is construed, in turn, as selflocation within a set of possibilia. Such theoretical representations of the attitudes are clearly not to be taken under a realist interpretation. Lewis’s account of the attitudes as the self-ascription of properties is not to be mistaken for the misbegotten idea that the cognizing agent is somehow invariably the topic of all her attitudes. On the latter point, see also an interesting discussion by Nolan (2006). At first

108 The Content Program blush, Nolan’s critique appears to target the inevitable self-involvingness of attitudes under the Lewisian scheme, which would presuppose an independently unmotivated realist interpretation of the deliveries of the theory. But on a closer look, Nolan’s complaint is the more subtle one that Lewis’s failure to distinguish between self-involving and selfless attitudes is a shortcoming of the framework in its express explanatory aims. This does seem like a fair consideration against the Lewisian view. 9. In previous work (2012) I try to counteract the Fodorian “only game in town” idea by developing a template for an alternative I call Cognitive Relations Theory (CRT). The theory avoids positing linguistically structured mental representations. It views cognitive attitudes such as hunting, wanting, and worshipping, but also believing and the rest of the so-called propositional attitudes, as in the first instance direct relations to objects such as lions, sloops, and people. It is thus very clearly an object centered theory in Marcus’s sense. CRT treats specific attitudes—cognitive states directed at particular things such as Ernst hunting a particular lion or Ralph believing Ortcutt in particular to be a spy—as primary in the order of explanation, and conceives of such attitudes as putting agents in direct, unmediated contact with their objects without language-like intermediaries. For non-specific (“generic”) attitudes such as hunting a lion but no lion in particular, or believing every spy is dangerous without believing any spy in particular to be such, CRT goes subjunctive. For Ralph to believe every spy is dangerous, for example, is roughly for the following to obtain: Had Ralph believed anything in particular to be a spy (given his actual mental set), Ralph would believe that thing to be dangerous. For further details, see Simchen (2012: Ch.5). 10. See previous footnote and the reference contained therein for a contrasting approach. CRT proceeds by way of the idealization that complement clauses for attitude reports are fully regimentable without loss into first-order logic. The theory is then put to a formal test via a proof, within a quantificational extension of Lewis’s counterfactual logic VC, that the set comprising the deliveries of CRT with respect to an omniscient believer—a believer whose belief states are reported with complement clauses that themselves comprise a consistent set of sentences—is consistent. See Simchen (2012: Appendix II) for details. 11. A promising reinterpretation of RTM along such lines is provided by Rescorla (2020) whereby mental representations are conceived as abstracta that theoretically represent actual representational capacities. Those abstracta are clearly not meant to disclose what the represented representational capacities really are at bottom. A system of such abstracta, however, can offer a genuine step forward within the metaphysics of mind.

7

Rules and Representation

7.1 Representing Behavior Rules of behavior are representations of behavior as patterned. In this final chapter I want to explore some of the mischief that results from treating such representations as revealing part of the underlying nature of the behavior they represent. Under such a realist attitude, the rule represents a component or ingredient of the represented behavior. There is a naïve view according to which an agent following a rule somehow actively incorporates the rule into her conduct by wielding or deploying it. Whatever “wielding” or “deploying” amounts to here, let’s assume it includes bringing the rule to the forefront of conscious attention and thereby having it exert causal influence on the ensuing behavior. The assumption is that the rule is, therefore, available for introspection. The view is tailor-made for distinguishing actually following a rule for adding integers, for example, from merely guessing the right answers. Only in the former case is the rule supposedly operative in the relevant bit of arithmetical behavior. In the latter case it supposedly plays no such role. Problems with the view are familiar. For one thing, phenomenologically speaking it is spurious to suppose that in humdrum cases of rule-following, the agent really does wield or deploy a rule in the relevant sense. On the contrary, when we consider actual cases of rule-following without bias, we see that such wielding or deploying of rules is, for the most part, a myth. When peering into our own minds as we follow rules, we typically see nothing of particular note. What goes on phenomenologically in rule-following is, for the majority of cases, completely ‘dark’ as far as actively deploying rules goes. And even when we perform elaborate problem-solving tasks and find ourselves reminding ourselves of general strategies for their solution, those strategies are, for the most part, very different from the official rules we would be deploying according to the naïve view. Other problems with the naïve view aren’t as vivid but are no less pressing. One such problem is the one that will occupy us in this chapter: treating rules within rule-governed activities as actual ingredients or components of those activities easily engenders pernicious forms of skepticism. We should be thinking instead of rules of DOI: 10.4324/9781003306443-7

110 Rules and Representation conduct as representing rule-governed behavior, or so I will argue. Insofar as rules are representations of behavior, they have many roles to play, some theoretical and others practical. But revealing the nature of the rule-governed behaviors they represent is not among them. I will have little to say about the phenomenological situation surrounding rule-following other than to appeal to it as prima facie evidence for the absence of operative rules in rule-governed behavior. My main aim is to trace how the idea of rules as ingredients in rule-governed behavior engenders two forms of rule-skepticism: one articulated in Kripke’s (1982) famous discussion of the rule-following passages in Wittgenstein (2009), the other a rule-skeptical position personified in the character of the Tortoise in Lewis Carroll’s (1895) famous parable “What the Tortoise Said to Achilles”. I will show that both types of rule-skepticism presuppose the questionable idea of a rule follower wielding or deploying the rule in her own behavior. The outrageousness of the engendered forms of skepticism is sufficient for a root-and-branch rejection of the presupposed notion. If the naïve view of rule-following is indeed naïve, why discuss it? The main reason is that alternative and more sophisticated accounts of rulefollowing do not typically venture to say what the rules themselves are vis-àvis the regulated behavior. Consider a dispositional story according to which rule-following is the manifestation of a disposition to behave in accordance with the rule, where behaving in accordance with the rule is the result of a certain kind of training, as opposed to being the result of an accidental but psychologically ingrained habit. Even if such a dispositionalist story is correct, it ultimately explains rule-following in terms of behaving according to the rule inter alia, leaving us officially none the wiser as to what the rule itself is and its relation to the behavior. The naïve view, by contrast, brings to the fore a particular—if under-specified and ultimately objectionable—account according to which the rule is an ingredient or component in the relevant behavior by being an object of conscious attention that thereby exerts causal influence. The view is wrong, but at least it presents a concrete if partial suggestion as to what the rule itself is vis-à-vis the behavior: something we can attend to and that can thereby influence our behavior, presumably a thought of some kind or (on certain views) the content of one. In what follows, I will highlight an important reason for rejecting the naïve view, which is the forms of skepticism it spawns. If we discard the naïve view in favor of the view that rules of behavior are representations of behavior as patterned and nothing more, given either from the outside by an observer or by the behaving agent herself—to herself or to another—and if we steer clear of attitudinal realism towards those representations, the two pernicious forms of rule-skepticism to be discussed will not get off the ground. And as an added bonus, we will not be inclined to suppose that the rule, while somehow an ingredient in a natural process, determines its own implementation in behavior in some non-natural way. Rather, and more straightforwardly, the rule represents the behavioral output as patterned. The relation between the

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rule and the behavior is a relation of representation. This nicely complements the more sophisticated alternative accounts of rule-following just mentioned. To follow a rule can indeed be the manifestation of a disposition to behave according to the rule as a result of a certain kind of training, where the rule itself is simply the representation of the behavior as patterned, and behaving accordingly is just being amenable to being so represented.

7.2 Calculating The rule-following considerations discussed by Kripke (1982) have received a great deal of attention over the past several decades. The rule-skeptic of the Kripke-Wittgenstein (KW) variety alleges that nothing determines the wrongness of answering ‘5’ in response to the arithmetical query ‘What is 68 plus 57?’. Assuming that the subject has never added numbers greater than or equal to 57, and letting the quaddition of X and Y be the addition of X and Y if X, Y < 57 and otherwise be 5, the challenge is to say what determines that the rule associated with ‘plus’ is really the rule for addition rather than the rule for quaddition. For if the rule associated with ‘plus’ is the rule for quaddition, then ‘5’ is the correct answer to ‘What is 68 plus 57?’ after all.1 The obvious reply to the challenge is to say that the wouldbe adder associates the rule for addition with ‘plus’ rather than the rule for quaddition. This determines the answer to the arithmetical query as 125 rather than 5. Suppose the rule the would-be adder gives herself according to the obvious reply is: the value of X plus Y is the sum of X and Y. This would seem to sufce in ruling out the association of a deviant rule with ‘plus’, according to which ‘5’ is the correct answer to the arithmetical query. But the skeptic famously presses on. Perhaps the ‘sum’ that the would-be adder deploys in giving herself the rule associated with ‘plus’ is itself associated with the rule for calculating quums rather than sums, where to be the quum of X and Y is to be their sum if X, Y < 57 and be 5 otherwise. Even if we could look into the head of the would-be adder, claims the skeptic, the rule she gives herself wouldn’t settle the matter because it’s just as open to associations with deviant rules as was the ‘plus’ of the original query. The KW skeptical stance clearly depends on the idea that arithmetical behavior incorporates an arithmetical rule as an ingredient that determines subsequent performance. But the idea has little to recommend it. First, as noted above, the view that in performing the task of addition, the would-be adder simultaneously deploys the rule for addition isn’t borne by the phenomenology of what actually happens. Post hoc unbiased reflection on a recent performance of addition does not reveal subvocalized citation of or consultation with any such canonical rule. Commonly, the task of adding small numbers is performed automatically and without unnecessary reflection.

112 Rules and Representation The task for larger numbers is broken down into simpler and largely automatic subtasks ordered by the deployment of short-term memory. The task for negative integers may involve subtraction and sign reversal. And so on. Second, the idea that the performance of addition invariably requires the simultaneous deployment of a rule for addition isn’t borne by the psychology of adding more generally. Attending to a rule while performing the primary cognitive task at hand is cognitively taxing and unlikely in the general case. If, in adding numbers, I must somehow consciously bring a rule for addition to bear on my task, it would seem that I would be acting on distinct cognitive fronts, which seems implausible for the general case. And even if, on occasion, we consciously deploy a rule while performing an arithmetical task, it certainly isn’t inevitably so. Pre-theoretically, the absence of such deployment hardly disqualifies the activity from being recognized as an instance of the relevant kind of rule-following. Many of us have memorized our multiplication tables up to 12 × 12. For us, performing a simple multiplication task X × Y where X, Y ≤ 12 is just as much an instance of multiplying as step-by-step multiplication. Of course, someone might dig in their heels and insist that all this shows is that arithmetical behavior isn’t generally rule-governed in the intended sense. But then one worries that being rule-governed becomes a theoretical denomination that doesn’t correspond to what is otherwise widely and pre-theoretically recognized as paradigmatic rule-following behavior. Third, even when a rule is consciously and deliberately brought to bear on a cognitive task, the rule is silent on how it is, in fact, to be implemented in practice, a fact exploited by the KW skeptic. And yet, without such further details, the rule for addition could hardly perform its role in regulating the relevant cognitive task of addition, requiring yet a further specification of how the original rule is to be implemented in practice, and so on. For all these reasons, it appears that arithmetical behavior need not generally incorporate arithmetical rules as operative ingredients. Treating rules as representations of behavior and refraining from treating them under a realist interpretation upends the KW skeptical stance. The arithmetical behavior of the student who adds 2 as we do up to 1000 and then deviates from us with 1004, 1008, 1012, etc., is simply not correctly represented by the rule for adding 2.2 Which rule adequately represents the student’s arithmetical behavior may or may not be settled by subsequent performance and observation. An outside observer may accumulate enough information to infer the regularity at play in the student’s performance. Perhaps the student belongs to a culture where adding by 2 beyond 1000 is considered profane and for whom adding even numbers is strongly preferred to adding odd numbers. Given further information about the student’s psychology—e.g., that it is cognitively less taxing to add by 4 past 1000 than to add 4 from 1000 to 2000, by 6 from 2000 to 3000, by 8 from 3000 to 4000, and so on—it may be possible to adequately represent the student’s behavior by one rule (‘add 2 up to 1000 and 4 thereafter’) to the exclusion of another (‘add 2n between (n − 1) × 1000 and n × 1000’). As far as the

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rule with which the student represents her behavioral pattern to herself or to another goes, the student can report the regularity in her behavior in her own words, vocalized or subvocalized. It is tempting to think that insofar as the student’s words are meaningful, their meaning is given by further rules, in which case it would seem that the question of which rules are operative is merely pushed back, this time to the rules for meaning rather than the rules for adding. But the idea of meaningfulness as involving rules in this way is independently unmotivated. The words ‘add 2’ mean what they do—that the addressee should add 2—and how they manage to mean that is an interesting question, an object of study for metasemantics. But the thought that somehow rules of use wielded by the speaker inevitably enter the story of how those words mean what they mean is controversial.3 A rule for addition represents arithmetical behavior. Wittgenstein (2009) paints a vivid picture of rules as representations in such passages as the following: We use a machine, or a picture of a machine, as a symbol of a particular mode of operation. For instance, we give someone such a picture and assume that he will derive the successive movements of the parts from it. (Just as we can give someone a number by telling him that it is the twenty-fifth in the series 1, 4, 9, 16, . . .) (§193)4 The picture of the machine, by analogy to the rule, represents the real-world movement of the machine, the behavioral output, as patterned. To infuse the machine’s performance with the picture of the machine, and by analogy to infuse the behavior of the person continuing the ascending series of perfect squares with the rule for continuing the series, is to mistake the representation for what it represents—a use-mention conflation of sorts.

7.3 Inferring Let us now turn to a second form of rule-skepticism. Lewis Carroll’s “What the Tortoise Said to Achilles” has been a philosophical favorite ever since its publication in Mind in 1895. A parable of sorts, it is a dialog between Zeno’s familiar characters of Achilles and the Tortoise concerning what is described as “a race-course, that most people fancy they can get to the end of in two or three steps, while it really consists of an infinite number of distances, each one longer than the previous one” (278). The upshot is a form of rule-skepticism personified in the character of the Tortoise. As is common, we can streamline the original presentation of the problem by looking at a schema of an argument in MP form:5 (1) (2) (3)

p if p, then q q.

114 Rules and Representation The Tortoise of the story concedes the truth of (1) and (2) and resists drawing the conclusion (3). Why the Tortoise so resists has been the topic of much speculation.6 What is relatively uncontroversial, however, is that the Tortoise raises the possibility of not accepting the conclusion despite its obvious entailment by the premises. The claim that the conclusion does, in fact, follow from the premises is then added, upon the Tortoise’s insistence, as an additional premise, yielding: (1) p (2) if p, then q (2.1) from (1) and (2), (3) follows (3) q. The Tortoise next concedes the truth of the premises but resists drawing the conclusion in an analogous way, yielding the further enriched variant: (1) (2) (2.1) (2.11) (3)

p if p, then q from (1) and (2), (3) follows from (1) and (2) and (2.1), (3) follows q.

And so it goes, on to the next variant: (1) (2) (2.1) (2.11) (2.111) (3)

p if p, then q from (1) and (2), (3) follows from (1) and (2) and (2.1), (3) follows from (1) and (2) and (2.1) and (2.11), (3) follows q.

And so on. It appears that the Tortoise’s repeated demand for further and further inferential licenses to legitimate drawing conclusion (3) cannot be met. The rule-skeptical generalization is that drawing conclusions is never fully legitimate. There is always room for failing or refusing to draw a conclusion entailed by accepted premises while accepting the claim that the conclusion indeed follows from them. Now, there is a neglected response to the skeptic that would spell trouble for the Tortoise’s deliberative stance straight away. Intuitively, if a premise addressing an argument’s premise-set is added to an argument, we would expect it to address the extant premise-set in its entirety, itself included. An added inferential license is just such an added premise. The Tortoise ignores this intuitive requirement of self-inclusion for the added premise, however, thus launching a regress. So with this in mind, let us begin, as before, with the Tortoise failing or refusing to draw conclusion (3) from

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accepted premises (1) and (2). This time, however, we enrich the original premise-set with a premise that includes its own citation: (1) p (2) if p, then q (2.1) from (1), (2), and (2.1), (3) follows (3) q. The self-citation of (2.1) is achieved via self-denotation.7 What can be said about the Tortoise’s reticence when it comes to this enriched variant (1)(2.1)/(3)? By analogy to the original case, we would have to ascribe to the Tortoise the acceptance of (1) and (2) and (2.1) without accepting that from (1) and (2) and (2.1), (3) follows.8 But if the Tortoise accepts (1), (2), and (2.1) without accepting that (3) follows from (1), (2), and (2.1), this can only mean that the Tortoise accepts (1), (2), and (2.1) without accepting (2.1) itself: (3) following from (1), (2), and (2.1) is just what (2.1) ‘says’. And this entails that the Tortoise accepts (2.1) and does not accept (2.1), which is impossible. Before moving on, let us bring these observations to bear on the argument of the original story: (A) things that are equal to the same are equal to each other (B) the two sides of this triangle are things that are equal to the same (Z) the two sides of this triangle are equal to each other. With the addition of the premise (C) if A and B are true, Z must be true,9 we get an argument whose conclusion the Tortoise maddeningly resists: “If A and B and C are true, Z must be true,” the Tortoise thoughtfully repeated. “That’s another Hypothetical, isn’t it? And, if I failed to see its truth, I might accept A and B and C, and still not accept Z, mightn’t I?” (Carroll 1895: 279) But if we substitute (C) if A and B and C are true, Z must be true for the original C, Achilles can answer the Tortoise’s second question with a resounding no and walk away. For if the Tortoise accepts A, B, and C and still fails to accept Z, this can only mean, in the terms set by the original story, that the Tortoise doesn’t accept that if A, B, and C are true, Z must be true.

116 Rules and Representation But this last claim is just C itself, which the Tortoise accepts. In other words, the Tortoise both accepts C and does not accept C, which is impossible. We note that (2.1) is distinct from the conditional (2.1) if (1), (2), and (2.1) are true, then (3) is true, which is problematic in a way dramatized by Curry’s paradox. A (2.1)-type conditional seems to allow us to infer anything from (1) and (2). Consider, for example, (2.1†) if (1) and (2) and (2.1†) are true, then the moon is made of green cheese. Assuming the truth of (1), (2), and (2.1†) as premises, we may conclude that the moon is made of green cheese by truth-functional implication due to the equivalence of the truth of (2.1†) and (2.1†) itself. Discharging the premises from the conclusion, we get (2.1†) from no premises whatsoever. So if we assume (1) and (2) and then add (2.1†), we may conclude that the moon is made of green cheese from (1) and (2) alone due to the equivalence of each of (1), (2), and (2.1†) and its truth. The relevance of all this for the case at hand of adding (2.1) to (1) and (2) is limited, however, due to the fact that (2.1), unlike (2.1) or (2.1†), isn’t Curry-paradoxical. But going back to the self-citational version of the original story, we do have the Curry-paradoxical C. We can prove that the moon is made of green cheese from A and B alone with the aid of the following C-type conditional: (C†) if A, B, and C† are true, then the moon is made of green cheese. We need only assume the truth of A, B, and C† as premises, rely on the equivalence of the truth of C† and C† itself, detach the latter’s consequent, and then discharge the premises from the conclusion to yield C† from no premises whatsoever. Assuming next A and B as premises, and adding C†, allows us to draw C†’s consequent as a conclusion via the equivalence of each of A, B, and C† and its truth from A and B alone. It would appear that, at least in the original argumentative setting, the Tortoise can resist our proposed regress blocker in terms of the self-citational C by citing its Curry-paradoxicality. We can replicate, however, the regress-stopping effect of self-citationality without actually indulging in it. Begin again with the Tortoise failing or refusing to draw conclusion (3) from accepted premises (1) and (2). This time enrich the original premise-set with two premises, each including the other’s citation: (1) (2)

p if p, then q

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(2.1) from (1), (2), and (2.1), (3) follows (2.1) from (1), (2), and (2.1), (3) follows (3) q. Suppose the Tortoise in this strengthened version accepts (1), (2), (2.1), and (2.1) but doesn’t accept that (3) follows from (1), (2), (2.1), and (2.1).10 Then, given the kind of entailment at issue, the Tortoise will not accept that (3) follows from any subset of this premise-set. And so, the Tortoise will not accept that (3) follows from (1), (2), and (2.1) and will not accept that (3) follows from (1), (2), and (2.1). But that means that the Tortoise doesn’t accept (2.1) and (2.1) after all, which contradicts their acceptance. Going back to the original argumentative setting, we observe the same pattern: (A) (B) (C) (C) (Z)

things that are equal to the same are equal to each other the two sides of this triangle are things that are equal to the same if A, B, and C are true, Z must be true if A, B, and C are true, Z must be true the two sides of this triangle are equal to each other.

Given that the ‘must’ expresses deducibility, if the Tortoise accepts A, B, C, and C without accepting that if A, B, C, and C are true, Z must be true, then the Tortoise will not accept that if A and B and C are true, Z must be true—i.e., C—and will not accept that if A and B and C are true, Z must be true—i.e., C. And this entails that the Tortoise both accepts C and C and doesn’t accept them, which is impossible. Curry’s paradox doesn’t afflict C and C. Consider the attempt to deduce the claim that the moon is made of green cheese from A and B alone with the aid of the following conditionals: (C) if A, B, and C are true, then the moon is made of green cheese (C) if A, B, and C are true, then the moon is made of green cheese. Assuming the truth of A, B, C, and C, the shared consequent of C and C follows by truth-functional implication due to the equivalence of the truth of C and C itself and that of the truth of C and C itself. Discharging the premises from this conclusion gets us (C) if A and B and C and C are true, then the moon is made of green cheese from no premises whatsoever. But if we now attempt to detach C’s consequent by adducing premises A, B, C, and C, we get the conclusion that the moon is made of green cheese but from the four premises. In particular, we don’t get this conclusion from A and B alone.

118 Rules and Representation These considerations can assuage our concerns about the Tortoise’s stance. The Tortoise is revealed as accepting (2.1) while not accepting it (or accepting (2.1) and (2.1) while not accepting them, but we set this more complex argumentative setting aside in everything that follows). But if the description of the Tortoise’s stance regarding (1)-(2.1)/(3) implies a contradiction, then that stance loses much of its interest. All that remains is a failure or refusal to draw the relevant conclusion. The relevance of these observations to our overall assessment of the Tortoise’s stance in the original story is as follows. By tweaking the inferential license added to the premise-set of the original argument, our description of the Tortoise’s stance is shown to entail a contradiction. The stance in the tweaked version is thus shown to be impossible. But then it seems that the Tortoise’s stance in the original story is saved from impossibility by a fluke, as it were. We have a strong pre-theoretical sense that it isn’t possible to acknowledge an inferential license as applying to one’s inferential behavior without regarding the behavior as thereby licensed. What is it to acknowledge such a license as obtaining, after all, if not to regard it as licensing behavior? The Tortoise’s stance in the original version is made possible by the fact that the inferential license added to the premiseset doesn’t include its own citation. But the issue of self-citationality seems otherwise irrelevant to the stance in question. As such, the Tortoise’s stance in the original case loses much of its interest as well. Consider an analogy. We have a strong pre-theoretical sense that it isn’t possible to sip a thirst-quenching, transparent, odorless, tasteless (henceforth TTOT) liquid without sipping water because a TTOT liquid is just water as far as our sipping behavior goes.11 Now suppose an argument is given, the upshot of which is someone sipping a glass of TTOT liquid while not sipping a glass of water. It happens that there is no possibility of sipping a glass of TTOT liquid that naturally occurs in three states without sipping a glass of water because a TTOT liquid that naturally occurs in three states is water as a matter of metaphysical necessity. It also happens that there is exactly one possible liquid other than water that is TTOT, which happens to occur only on the other side of the known universe and naturally occurs in two states. Then the original case of sipping a glass of TTOT liquid without sipping a glass of water is saved from impossibility by a metaphysical fluke that happens to occur on the other side of the known universe and which seems otherwise completely irrelevant to our sipping behavior. In other words, but for the existence of the TTOT liquid on the other side of the universe, sipping a glass of TTOT liquid while not sipping a glass of water would have turned out to be impossible, exactly in accordance with our pre-theoretical verdict on the matter. Similarly, in the present case, we have a strong pre-theoretical sense that it isn’t possible to acknowledge an inferential license as obtaining without treating inferential behavior as licensed. The tweaked version of the story invoking the selfcitational (2.1) bears this out, showing that the target stance in the tweaked case is indeed impossible. As mentioned earlier, an added premise addressing an extant premise-set should intuitively address the entire set, itself included,

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and this intuitive requirement of self-inclusion is expressly flouted by the Tortoise’s (2.1) (or C) and subsequent iterations. So now it seems that the original story narrowly escapes impossibility by the absence of self-citationality, getting off on a technicality that is otherwise irrelevant when it comes to the Tortoise’s stance towards inferential licenses. I submit that the Tortoise’s stance in the original story thus loses much of its interest as well. It doesn’t culminate in a threatening skepticism about rules after all. The regress blocker we’ve been considering is open to an obvious response. The so-called impossibility in the Tortoise’s stance, it is now claimed, arises from a superficial take on the issue of acceptance. The Tortoise can accept (2.1) (or accept C) in one sense—as a premise, as true—while failing to accept it in another sense—as a rule, as action-guiding. With proper disambiguation, the apparent contradiction of accepting the self-citational premise while not accepting it is revealed as merely apparent. Let us turn to explore this response in more detail. A familiar take on the original story maintains that the Tortoise’s repeated demand for more and more rules licensing the transition from premises to conclusion exhibits a failure or refusal to attend to an important distinction between premises and rules within one’s reasoning. The distinction is allegedly between what inferential behavior turns on, the stuff upon which the thinker is acting in reasoning, the premises, and what makes the behavior a case of genuine reasoning, the rule as incorporated into the relevant bit of inferential behavior. The Tortoise, it is claimed, accepts the rule as an extra premise. But this is shown to be irrelevant to the inferential task at hand, which requires the thinker to incorporate or accept the rule in a different sense into inferential conduct and thereby proceed to the conclusion. Thus Ryle (1946) concludes: “Acknowledging the maxims of a practice presupposes knowing how to perform it. Rules, like birds, must live before they can be stuffed” (11). And Sellars (1949) adds that “a rule, properly speaking, isn’t a rule unless it lives in behavior, rule-regulated behavior, even rule-violating behavior . . . A rule is lived, not described” (315). The skeptical response we are now considering utilizes this distinction between rules as lived and rules as described. Call acceptance of a rule as described acceptance and acceptance of a rule as lived acceptance. Rather than conclude that the Tortoise accepts (2.1) and doesn’t accept (2.1), which is impossible, we now say that the Tortoise accepts (2.1) and doesn’t accept (2.1). Impossibility averted. The skeptical upshot is that one can always fail to comply with the rule, even while acknowledging it as being in force. Acknowledgment that a rule holds is powerless in the face of skeptical reticence. But the question remains how, on this way of thinking, we are supposed to think of the incorporation of rules into inferential behavior other than as being acknowledged to hold. Consider, again, what the Tortoise in the original story is supposed to be doing wrong. The Tortoise fails or refuses to draw a conclusion without the relevant license, which is then cited as an additional premise. The Tortoise then proceeds to raise an analogous concern in the new inferential setting,

120 Rules and Representation thus launching the regress. At each step, the Tortoise supposedly accepts the rule. And yet, at each step, the Tortoise fails or refuses to draw the conclusion licensed by the rule. It is incumbent on a proponent of the present response to the challenge of the self-citational license to explain what it is to accept the rule while failing to accept it. How can anyone acknowledge an inferential license as a truth about one’s inferential behavior without treating it as licensing one’s behavior? There is little use in saying “by behaving in a Tortoise-like fashion”, which is what we are trying to explain.12 To accept a license as a truth about one’s behavior is to treat the behavior as thereby licensed. Similarly, to accept the naming of a ship as a truth about the ship is to treat the ship as so named; to accept my promising you to φ as a truth about us is to regard me as having so promised and you as the promisee; to accept a description of France as hexagonal as a truth about France is to treat France as so described. We seem to lack an independently motivated distinction between acknowledging a license as being in effect and regarding it as licensing the behavior. Of course, to claim that one acknowledges a license as being in effect isn’t to acknowledge the license as being in effect. We can mouth the words that the license is in effect without acknowledging that the license is in effect, as evidenced by our behavior. And we can acknowledge a license as being in effect without expressing our acknowledgment. What we cannot do, however, is acknowledge the license as being in effect (as a truth about one’s behavior) without acknowledging it as being in effect (as licensing the behavior). When asked why we behave in certain ways, we often cite rules at various levels of specificity. When asked why (3) is entered as a conclusion upon the acceptance of (1) and (2) as premises, for example, we might answer by citing the fact that from (1) and (2), (3) follows. A fuller answer might include the fact of our acknowledgment of the fact that from (1) and (2), (3) follows. Such answers to the why question offer reasons for the inferential behavior at issue. The fact that (3) follows from (1) and (2), or the fact of acknowledgment of the fact that (3) follows from (1) and (2), answers the question of why the behavior culminates in entering (3) as a conclusion. So in what sense can it still be maintained that the license has to be incorporated into the behavior in some way other than acknowledging that it obtains? There is an unmistakable air of mystery here.13

7.4 Rules as Representations The mystery dissipates as soon as we reorient our thinking about rules and discard the assumption that inferential rules must somehow be incorporated into inferential behavior as ingredients, so to speak. A rule of conduct is a representation of behavior as patterned in a certain way. To say that the rule is a representation isn’t to say that it should be thought of as merely stating or describing that the behavior occurs. Far from it. We use such representations of behavior for a variety of purposes, from explaining and predicting to instructing and enjoining would-be practitioners to engage in the relevant

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practice. Whatever our purposes for using rules of conduct may be, a rule for adding integers is a representation of arithmetical behavior, a traffic rule is a representation of the behavioral negotiation of traffic, a rule for inferring is a representation of inferential behavior, and so on. If rules of conduct are representations of behavior as patterned, the license captured by (2.1) in the first iteration of Carroll’s regress represents a certain pattern of proceeding from (1) and (2). The argument (1)-(2.1)/(3) is the same as (1)-(2)/(3) but for the inclusion in the former of (2.1). The mode of inference is the same in both, the only difference being that (1)-(2.1)/ (3) includes (2.1) as an additional (and idle) premise. Once we see the rules as representations of inferential behavior, we no longer need to assume that they require incorporation into behavior in some mysterious way or that described rules aren’t really rules, as Sellars puts it. The truth of the matter, on the contrary, is that insofar as rules are representations of behavior, they can also be described in turn. To speak of rules as “lived” is to skirt dangerously close to mistaking the representation for what it represents. The behavior is lived, of course, but it, in turn, is represented by the rule. As a response to the Tortoise of the original story, the emphasis on rules as lived is unsuccessful. At each stage of the regress, the Tortoise supposedly accepts a rule that enjoins that the desired conclusion follows from the extant premiseset. The explanatory burden then shifts to the skeptical proponent of the Ryle-Sellars line to say why such acceptance is ineffective. In his Presidential Address before the Aristotelian Society, Ryle (1946) describes the perils of failing to heed the distinction between knowing that and knowing how, and more specifically, between “accept[ing] rules in theory” and “apply[ing] them in practice”, by adding, parenthetically: “This is Lewis Carroll’s puzzle in ‘What the Tortoise said to Achilles’. I have met no successful attempt to solve it” (6). Treating Carroll’s regress as a serious difficulty is predicated on succumbing to a mythology of rules as somehow operative in behavior. Regarding rules as representations of behavior instead defuses such worries. The Tortoise fails to conclude (3). Why the Tortoise so fails may be an interesting question about tortoise psychology but need not culminate in a worrisome skeptical threat about rules. The Tortoise’s failure is the failure to draw the relevant conclusion—end of story.14 An inferential license qua rule of inferential conduct is a representation of inferential behavior. But rules of inference also play a crucial role in setting up formal systems in logic. A formal language is specified by providing an inventory of basic signs and “formation rules” that specify which strings of signs qualify as formulas. A formal system is specified by providing “transformation rules” of two kinds: axioms and rules of inference. A formal system as a whole can represent a type of real-world reasoning. The axioms can represent where the reasoning of the represented type may begin without further justification. The rules of inference can represent how the reasoning may, in fact, proceed. Once we attend to such matters of representation, we are less likely to suppose that rules of inference are somehow invariably

122 Rules and Representation operative in the inferential behavior being modeled by the formal system as a whole. The thought that rules of inference are operative in this way blurs the distinction in level between the representation and what it represents. Lewis Carroll and his contemporaries, including, notably, the Russell of The Principles of Mathematics (1903: Ch.3), did not see things in this way. The attempt to meet the Tortoise’s reticence by enriching the set of premises of an obviously valid argument to include the relevant inferential license is but one detail of their shared commitment to a single-level approach to logic. The fully mature idea of a formal system had to wait until the transformative work of Carnap, Gödel, and others in the ensuing decades.15 But once the idea of a formal system became prominent in logic, another idea became prominent in philosophy—that insofar as formal systems represent swaths of reasoning, each significant aspect of those representations is itself representational.16 It is but a short step from here to the thought that a rule of inference of a formal system stands for something operative in the reasoning represented by the system as a whole. The view then impels the further insistence that whatever is thus operative must not be included as a mere premise on pain of regress. But this, as we saw, including as it does the problematic idea of rules as somehow incorporated into rule-governed behavior, is not independently motivated. Finally, there may be yet another thought lurking behind the insistence that rules must somehow be operative in rule-governed behavior. It is the conviction that whatever else rule-governed behavior may be, surely the rule discloses an essential aspect of the behavior, part of its very nature, what makes rule-governed behavior what it is. Consider, for example, the following passage from Sellars (1949): We distinguished above between action which merely conforms to a rule and action which occurs because of a rule and pointed out that in so far as actions merely conform to it, a rule is not a rule but a mere generalization. On the other hand, we must not say that a rule is something completely other than a generalization. The mode of existence of a rule is as a generalization written in flesh and blood, or nerve and sinew, rather than in pen and ink. (299) The rule is supposed to disclose the nature of the behavior it governs, not unlike the way the physiology of a bodily process reveals what it really is at bottom. But why think the rule should so reveal what the behavior it governs really is remains unclear. We may study various forms of behavior and identify rules that govern them. The rules we identify are representations used for a variety of purposes. The idea that those representations are inevitably entrusted with more than their theoretical or practical roles as representations of behavior, namely, with nature-disclosure when it comes to being governed by rules, has little to recommend it.

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There is, in fact, little reason to suppose that representing behavior by specifying a rule tells us what the behavior is in the most demanding sense. A behavioral pattern is a regularity in human behavior; it can be studied from a variety of explanatory perspectives at various scales. Nothing suggests that the rule we describe ourselves as operating under, to ourselves or to others, in performing simple addition reveals what the practice of addition really is at bottom. The same goes for inferential behavior. What those behaviors are can be approached from a variety of angles, some personal (as when we explore matters of justification, for example), some sub-personal (as when we explore implicated cognitive processes at the individual level), and yet others super-personal (as when we explore advantages of certain practices over alternatives at a social level). The standard rule for addition often belongs to the first person take on the practice, perhaps a representation for pedagogical purposes. It isn’t the job of such a representation to tell us what the practice of adding really is in the most demanding sense. Indeed, even for standard scenes of instruction, where rules are given to novices as means of initiating them into and guiding them through the practice, the rules don’t disclose what exactly is to be done in the most demanding sense. A rule for addition, for example, doesn’t tell us whether in adding 57 to 68, we should first add the tens, then the units, and then add the results, or add the units first and carry the one over to the tens; or add from left to right (or top to bottom in a column) or from right to left (bottom to top); or what. Rules for inferring likewise don’t tell us the order in which we should take multiple premises into account. Rules are silent, as can only be expected, on the many ancillary details that are relevant for actual behavior that accords with them. Be that as it may, thinking of rules as representations of behavior doesn’t allow the skeptical problems we’ve been discussing to get off the ground.

Notes 1. A further challenge is to offer an answer to the first challenge that justifies answering 125 rather than 5. I set aside this extra demand for justification in everything that follows. Also, in speaking of the rule as “associated” with ‘plus’, I am deliberately sidestepping the question whether the meaning of ‘plus’ is given by the rule. Our primary concern here is with rule-following itself rather than with its downstream implications for meaning. 2. See Wittgenstein (2009: §185). 3. I am setting aside the sort of use-conditional theory of meaning espoused by Kaplan (2003) and others whereby rules of use enter the determination of meaning at a different level—from the perspective of what Kaplan calls “description from above” as opposed to “expression from below”—because such rules are emphatically not ingredients of linguistic behavior in the relevant sense. 4. See also the surrounding discussion in Wittgenstein (2009: §§193–194) and (1978: §§I:122–130). 5. We treat argument-schemas as arguments throughout as a matter of terminological convenience. 6. For my own take on the issue, see Simchen (2001). My earlier work was concerned to show that the Tortoise’s deliberative stance, which inspires a distinct form of

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7.

8.

9. 10. 11.

12.

normative skepticism, isn’t necessary. In what follows I argue that, appearances to the contrary notwithstanding, the stance in question isn’t really possible after all. For a useful bibliography of the secondary literature, see Imholtz and Moktefi (2016). ‘Self-denotation’ rather than ‘self-reference’ for reasons that would take us too far afield. Suffice it to say that in the real time production of (2.1), the token so produced wouldn’t be available (yet) to act as a referent for the produced constituent token of ‘(2.1)’. See Simchen (2013b) for further discussion of the contrast between self-denotation and self-reference and its ramifications. If a rationale for accepting (2.1) is needed (a big ‘if ’—see below) it’s that the Tortoise accepts the claim that (3) follows from (1) and (2) alone, which is just (2.1), in which case the Tortoise already accepts the claim that (3) follows from (1) and (2) and any additional premise, including (2.1), which is just (2.1). This assumes that the Tortoise understands that for the kind of entailment at issue, anything following from a set of premises follows from any premise-superset of that set (monotonicity). Given the Tortoise’s original stance, there is no reason to think this rationale for accepting (2.1) isn’t available. Having said that, in the terms introduced by the original story it isn’t clear that a rationale for accepting (2.1) is needed in the first place. After all, no rationale is provided in the original story for the Tortoise’s acceptance of the equivalent of (2.1) other than being asked by Achilles to do so. See Carroll (1895: 279). The ‘must’ expresses deducibility. We set aside the occurrences of ‘this’ in B and Z. See footnote 8. The Tortoise accepting (2.1) will accept (2.1) and (2.1) as well. If (3) follows from (1) and (2) alone, then, in particular, it follows from (1), (2), and any additional premise. Pack into being TTOT all the superficial characteristics of water and abstract from the case the philosophical lore surrounding theoretical identifications in natural science. The sense of impossibility here is meant to be pre-theoretical. To make the example more “attitudinal”, the reader is invited to substitute de re wanting for sipping and keep everything else the same. Ryle (1946) comments on the contrast between acceptance and acceptance by saying: What has gone wrong? Just this, that knowing how to reason was assumed to be analysable into the knowledge or supposal of some propositions, namely, (1) the special premisses, (2) the conclusion, plus (3) some extra propositions about the implication of the conclusion by the premisses, etc., etc., ad infinitum. (6–7)

This in effect answers the question how one can acknowledge an inferential licence as a truth about one’s inferential behavior without incorporating it as a license into one’s inferential behavior by citing the Tortoise’s behavior as a case in point. 13. In his Presidential Address before the Pacific Division of the American Philosophical Association, Albritton (1985) persuasively argues that the will’s freedom isn’t restricted by the inability to act accordingly. It is easy to mistake constraints on what we do for constraints on our deciding what to do. If I’m prevented from moving around freely by being held down, this by itself doesn’t prevent me from choosing to move around freely. A deficiency or inability to do something shouldn’t be read backwards, as it were, into an alleged earlier deficiency or inability to choose to do it. Along similar lines, a deficiency or inability to behave according to an inferential license shouldn’t be read backwards into some deficiency or inability in the earlier acceptance of the license in question. 14. A sophisticated reading of Ryle’s distinction between intelligent behavior and mechanical habit due to Bäckström and Gustaffsson (2017) characterizes the Rylean distinction as a formal distinction in category, where a category delineates the range of claims and questions that make sense regarding the item at issue. Such a reading

Rules and Representation 125 renders the Tortoise as someone who, appearances to the contrary notwithstanding, is simply not behaving intelligently. Why Ryle (1946: 26) says, regarding the problem we’ve been discussing, “I have met no successful attempt to solve it”, remains unclear. 15. Further details on the contrast between the later focus on formal systems in logic and the earlier conception of the subject may be found in van Heijenoort (1967) and Goldfarb (2005). 16. But see Kaplan’s (1975: 722) notion of “artifact of a model” for a compelling critique of this move from a model being representational to every aspect of the model being representational.

Postscript

When I first started working on this material, I thought of it under the rubric “Conflating Representation and Represented”. This, in fact, is the title of the research grant from the Social Sciences and Humanities Research Council of Canada under which the work was conducted. The rubric was meant as a diagnostic and not very generous catchall for a broad tendency to underplay the epistemic situation of the philosopher. It was meant as a metaphilosophical counterpart to the infamous conflation of use and mention. What I noticed in contemporary work in the areas of philosophy I was most immersed in is an inclination to regard the products of philosophical theorizing—theoretical representations—as if they were the subject matter of such theorizing—what those representations represent. The philosopher contemplates some pre-theoretical subject matter, say properties in re, and then proceeds to offer some theoretical capture of said subject matter, say properties as classes of tropes, which is meant to resolve a longstanding quandary, say the problem of how distinct worldly things can exhibit real (as opposed to merely nominal) commonalities. The conflationary tendency is then to suppose that being a class of tropes is what properties turn out to be upon closer theoretical scrutiny, much like being element 79 is what gold turns out to be and being a sphere of hot plasma converting hydrogen into helium is what the sun turns out to be. The philosopher is thus imagined to reveal what is really behind our pre-theoretical talk of properties. This picture portrays philosophical activity as peering directly into what things are in the widest sense with the authority of natural science but armed with nothing but an expert use of reason (beyond what science itself already provides). While the picture elevates the philosopher to the questionable status of an expert rational “seer” into the fabric of being, it also tends to overlook the great conceptual innovations behind so many philosophical theories, their very real explanatory achievements, and how those achievements dovetail the intricacies of theoretical structure. It is as if philosophy’s theoretical interventions, if successful, drop out of the picture altogether, and all that remains is the achieved revelation of reality in all its nakedness. Philosophical representation, on this way of looking at things, is just reality disclosure, pure and simple, one representation at a time. The aim of

Postscript 127

philosophical activity is for its representations to fade into transparency, so to speak, leaving behind what is represented in its truest form. The diagnostic rubric of conflating representation and represented is fine as far as it goes but doesn’t go quite to the heart of the matter that interests me. I have come to regard such conflation as a downstream effect of the contemporary tendency to treat theoretical representations as revelatory of the nature of whatever they represent. Perhaps in earlier times, the treatment of philosophical representations as portals for nature disclosure could be chalked up to the philosophical aspiration to “become like god” (Theaetetus 176a-b). Nowadays, it has a more proximal source in natural science envy, in what recent pragmatists such as Hilary Putnam have decried as the pervasiveness of scientism within contemporary philosophical culture. (Of course, it might just be that natural science envy is nothing but a further iteration of the philosopher’s more traditional aspiration, but I don’t feel qualified to speculate further on this.) If we think of being hydrogen hydroxide as revelatory of what water really is, so the thought goes, why not think of a metaphysically possible world as revelatory of what metaphysical possibility really is; or of a computational relation to a mental representation as revelatory of what a belief really is; or of being an equivalence class under equinumerosity as revelatory of what a number really is; or of being an ordered sequence of things and properties as revelatory of what what is said by a sentence really is? But such an attitude easily misses what is most interesting about theoretical representations generally and philosophical ones in particular. Theoretical representations are a motley, and they gain their explanatory significance from their wider theoretical contexts in various ways. There is no reason to think in a one-size-fits-all manner that all theoretical representations behave in the way some theoretical representations seem to behave within certain reaches of natural science. Our explanatory needs are many and varied; it stands to reason that the ways theoretical representations behave are many and varied too. Only by attending to this multiplicity can philosophical theoretical representations be appreciated for their utility, elegance, and yes, beauty. The emphasis for us is—and should have always been—on explaining rather than revealing or disclosing. Or perhaps on disclosing through explaining. An explanation is a messy multi-modal affair bound up in the messiness of human aims and needs. Philosophy is at its best while keeping those in clear view.

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Index

abstracta 16n28, 22, 41, 108n11 Achilles: “What the Tortoise Said to Achilles” (Carroll), analysis of 110, 113–122 actualism: “new actualism, the” 38n14; see also Plantinga agentive production of speech see speech agents xiv, 82, 101, 103–104; behaving 110; cognizing 107n8; deliberating doxastic 18; relations 12; rulefollowing 109 Albritton, Rogers 124n13 ambiguity, linguistic 40–41, 43, 62–63, 65; construal of 63 ‘Amy loves Mary,’ analysis of 83–85, 87 “artifact of the model” 6, 37, 125n16 at-least-ism 23, 24, 25, 28, 30 at-most-ism 23, 24, 28, 30 atternal question 41, 42 attitude reports: clausal components 52; meaning of 58; semantics of 65, 105 attitude verb 69–70 attitudinal contrast 14 attitudinal instrumentalism ix, xi–xiii, 1–2, 84, 91; analysis and 61–72; appeal of 36; content and 95–98; contrast between attitudinal realism and 93; Lewisian 107n8; local 9; metasemantics and 98–101; propositions and 85–88; RTM and 101–106; semantics and 36, 39–60 attitudinal realism viii, 1–2, 81; benefits of 5; contrast between attitudinal instrumentalism and 93; justified 17–36; naïve sets and 89; possible worlds and 10; see also realist attitude attitudinal relation of expectation 70 Austin, J. L. xiii, 39, 61, 72–74, 77–78 axiom of foundation 14n5

axiom of reducibility 92n9 axiom schema 15n12, 90 axioms 121 Bach, Kent 74–75 Bäckström, Stina, and Gustafsson, Martin 124n14 ‘bang’ example (“the bang was not as loud as I had expected”) see gun-bang example belief: ‘Amy loves Mary,’ analysis of 87; case studies xii; ‘Cicero denounced Tully,’ analysis of 65–66; as cognitive attitude 93; as cognitive state 106; de re 79n5; facts of 58; language-centered 87, 103–104; as mental state 35; ‘Opus 132 is a masterpiece’ in Bela believes Opus 132 is a masterpiece,’ analysis of 53–54, 56–58; what belief really is 127 belief formation 76–77, 97–98 belief report 11, 12, 51; de re 66; semantics of 104–105 belief-set 100 ‘believe’ as dyadic relational concept 11 believer 11, 12, 51, 66, 67, 103, 108n10 Benacerraf, Paul 83, 85, 91 Biden, Joe x; “Joe Biden is…” utterance 75 Big Bang 103 Burge, Tyler 52, 54–57 Carnap, Rudolph (or Rudolf) 32, 38n19, 40, 122; extension and intension 60n19; Parsons and 57 Carnapian-Montagovian semantic tradition 32 Carroll, Lewis: “What the Tortoise Said to Achilles” xiv, 110, 113–122 ‘Cataline,’ example of 65–67, 79n5

134 Index Cavell, Stanley vii ‘Cicero,’ example of 65–66, 95 cognitive attitude xiii, 93, 94–95; Fregean thought in relationship to 12–13; metaphysics of 102, 103 cognitive attitude attribution 100 cognitive dissonance 16n22 cognitive facts 21, 22, 58, 105; cognitive matters of fact 101 cognitive processes 123 cognitive rapport 97 cognitive relations 87, 91 Cognitive Relations Theory (CRT) 108n9, 108n10 cognitive states 104, 106; of belief 51, 106 cognitive tasks 112 cognitive theorizing 105 contingency 7 contingentism 22–23, 28–30, 37n13; necessitism vs. 25; see also necessitism contingentist metaphysics 27 Copernican Revolution of Kant 33 counterfactual situation 7–9, 15 counterfactuals 29, 42 counterpart 9, 13–14, 21–22 Counterpart Theory 13, 37n4 CRT see Cognitive Relations Theory Curry’s paradox 116–117 ‘Danzig is pretty’ and ‘Gdansk is pretty,’ example and analysis of 10–12, 14, 16, 22 Davidson, Donald 44, 77 Davies, Martin 16n25 demonstrative extension-fixing 99, 107 demonstrative pronouns 44, 76 demonstrative reference 75 denoting concepts 54, 92n1 denoting phrases 62, 66, 67 denoting proper names 98 de re belief: logical form of 66; Tom, with respect to ‘Cataline’ 79n5 de re modality 3, 6–10, 13 Deutsch, Harry 88, 90 dispositionalism 103, 110–111 Donnellan, Keith 44, 91, 98 Dubček, Alexander xiv Dummett, Michael 4, 33 epistemic ideality 45, 46 epistemic rapport 10 epistemology: naturalized xiv; philosophers and 126 extension-fixing 96, 99, 100, 107

extensionality principle 53, 56, 57 extension and intension 32, 60n19 fixed-domain semantics 26–27; see also semantics Fodor, Jerry xiii; Language of Thought Hypothesis 105; Representational Theory of Mind (RTM) 16n25, 87, 101–106, 108n11 formal capture of sentential truth 46–47, 89; see also sentential truth formalism: of SR 15n16 formal language 1, 90, 121 formal methods in study of natural language 61 formal modeling: of language-world relations 50; of meaning 70 formal semantic analysis 70; prevailing attitudes toward 62 formal semantic apparatus 13, 41 formal semantic explanation 52 formal semantic evaluation 39–43, 79 formal semantic paraphrase 71–72 formal semantics ix, xiii, 40; analyses 21; descriptions and proper names in 98; explanatory aims and achievements of 27; index sets and meaning of sentences in 28, 94; lessons for the history of 50; metasemantics and 44; ordinary language philosophy and 58; representations 21; Strawsonian thread in 38n20 formal semantic tradition 31; Kantian influence on 33, 34; pioneers of 32; see also Carnap; Montague formal systems 121; Carnap and others, work on 122; necessiticism and 25; semantics for 26 formal theories 1 Fregean analysis 21, 53, 56 Fregean analyticity 34, 38n21 Fregean concepts 4, 67 Fregean construal 6, 33 Fregean logicism xi Fregean numbers 35 Fregean senses 51–52, 92n1; see also hierarchy of senses Fregean theory of indirect reference see Frege Fregean thought 13, 22, 67–68 Frege, Gottlob xiii, 32; analysis of phrase, ‘Hilary believes …’ 11–12, 14, 22; analysis of phrase, ‘The King’s carriage is drawn by four horses’ 21; analyticity

Index 135 of 34, 38n21; Basic Law V 14n5; Gedanken of 10; Grundlagen 14n3; Grundgesetze 14n3; Kant, dispute with 34; on modal claim that Nixon might have lost 21–22; on number 4–7, 13, 33–35, 91; philosophy of language 10–11; semantic analysis 12; Steiner’s discussion of 16n28; theory of indirect reference 11, 39, 51–54, 56–58, 60n19, 61, 64–69, 71; Wittgenstein’s critique of 61, 72 Frigg, Roman, and Nguyen, James xv note 1

indeterminacy argument 47 indexical 99 index set 7, 28 indirect reference 51–58; case study 10–12; theory of (Frege) 10, 11–13, 39, 51–52, 54, 57–58, 60n19, 65, 67 indirect sentential context 57 inferring 113–120 instrumentalism 1–2; see also attitudinal instrumentalism instrumentalist attitude: realist attitude vs. 1–4, 44, 84, 94 jade, Putnam’s case of 22, 37n6

García-Carpintero, Manuel 79n10 ‘Gdansk is pretty,’ example and analysis of 10–12, 14, 16, 22 Geach, Peter 15n11 Ginet, Carl 74–75 ‘Giorgone,’ meaning of 69 Goldbach conjecture 23–24, 37n9 Goldfarb, Warren 92n9, 125n15 gold, representations of vii, ix–xi, 2–5; atomic number 4, 13, 17, 18, 20, 36, 86, 94, 98, 106, 126; attitudinal realism and 2–3; as monetary standard 5, 18; pre-theoretical claims regarding 87; realist purport and 86 gold standard, the 105 Gòmez-Torrente, Mario 107n3 gun-bang example (“the bang was not as loud as expected”) 64–72 Gresham’s Law 18, 86, 105 Hacking, Ian 37n6 Häggqvist, Sören and Wikforss, Åsa 107n7 Heck, Richard Kimberly 15n11, 16n27 Heim, Irene, and Kratzer, Angelika 80n16, 106n1 hierarchy of senses: Burgean 54, 55; Fregean 51–52, 57–58, 60n19 ‘horses drawing the king’s carriage,’ example and analysis of 13–14, 21 Humphrey objection 9, 37 Imholz, Clare, and Moktefi, Amirouche 124n6 impossibility (Anselm’s proof) 38n23; Tortoise’s stance 115, 116, 117, 118, 119 indeterminacy 85, 91; Bencerraf-style 83, 91; enabling 48; problem of 83–84; radical 44; semantic 45, 46, 49

Kant, Immanuel 32–35, 37n2, 38n21; Fourth Paralogism 38n22 Kaplan, David: “artifact of the model” of 6, 37, 125n16; on de re belief reports, logical form of 66; on how demonstrative pronouns refer 44; ‘Newman 1’ of 79n14; on $entences 70; theory of quantifying in 68–69; useconditional theory of meaning 123n3 King, Jeffrey 88, 92n4 ‘King’s carriage is drawn by four horses, The,’ example and analysis of 13–14, 21 Korsgaard, Christine 37n2 Kripke, Saul 98; on Goldbach conjecture 23, 37n9; on hierarchy according to Frege 54; on how proper names refer 44; Humphrey objection against Lewis’ Counterpart Theory 37n4; on losing the 1968 US presidential election 7, 30; on problem of transworld identity 16n20; on Peter believing Padarewski 103; on puzzling Pierre 16n22; on rigidity 100, 107n3; rule-following considerations of 110, 111; on semantic competence and endowment 95; variable-domain semantics of 27; on Wittgenstein on rule-following xiv, 110 Kripke-Wittgenstein (KW) 111 Language of Thought Hypothesis 105 Lewis, David 37n3; attitudinal instrumentalism of 96–98 107n8; counterparthood of 15n17; epistemic ideality of 46; five-fingered/sixfingered hand 8–9; interpretationist doctrine 44, 45; metasemantic position of 59n12; on methodology in the study of language 78; on performative

136 Index utterances 74–75; reference magnetism 44, 48; theory of language use 98, 101 Liar paradox 89 linguistic action 78 linguistic and partly non-linguistic entities 70 linguistic behavior 97, 103, 123n3 linguistic expression 10, 43, 76, 93 linguistic items, de re attitudes toward 79n7 linguistic labor, division of 99 linguistic phenomena 39, 40; relativization of 42 linguistic practices 77 linguistic reflexivity 59n6 linguistic turn in philosophy 4, 34 Lycan, William 16n25 machine, analogy of 113 Maddy, Penelope xv Marcus, Ruth Barcan 29, 103, 108 Mendel’s theory of inheritance 102 mentalese 31, 87, 106 mental phenomena 2, 93 mental representation xiii, 102, 105, 127; linguistically structure 108n9 mental states 35, 93, 106; futureoriented 64 metaphilosophical instrumentalism xi–xii, 94 metaphilosophical realism x–xi, 31 metaphilosophy vii, 126 metaphysical evaluation: semantic evaluation vs. 40 metaphysical inquiry 99 metaphysical/metaphysics of modality see modality metaphysical realism/realist xv, 45 metaphysical theorizing: semantic theorizing vs. 40 metaphysician: possible world 13, 41 metaphysician of meaning 96 metaphysics: descriptive 32; dispute between necessitism and contingentism 25, 27; essentialist doctrine in viii; logic-first methodology in 26; semantic representations in 22–30 metaphysics of cognitive attitudes 102–103, 105, 112 metaphysics of mind 10, 12 metaphysics of possible world 127 metaphysics of sets 101 metaphysics of truth 51 metaphysics of what is said 81–85, 87, 92n3

metasemantics 44, 47, 50, 113; attitudinal instrumentalism and 98–101; productivist 58n2 Millanism 76 modality: de re 3, 6–10, 13; metaphysical/metaphysics of x, xii, xiii, 6–8, 22–23, 28–30, 39 modes of presentation 52 Moltmann, Friederike 38n20 Montague, Richard 32, 38n19; Carnapian-Montagovian semantic tradition 32 ‘moon,’ Frege’s analysis of word 60n18 ‘moon is made of green cheese’ as truthconditional proposition 116–117 Morse-Kelley set theory 90 naming 73, 74, 120; acts of 44 natural kinds 101 naturalized epistemology xiv necessitism 28; at-most-ism and at-leastism as modal consequences of 23-24; contingentism vs. 25; definition of 22–23; fixed-domain semantics and 26; metaphysics of modality and xiii, 22, 30 Needham, Paul 107n7 ‘Newman 1’ 79n13 nephrite 22 Nixon, Richard 7–10, 14, 21–22, 30, 81 Nolan, Daniel 107n8 non-actual individual 7 non-actual number 23 non-existence 30 non-interpretationist views, noninterpretationism 47, 50 nonrealistic model structures 27 non-linguistic creatures 103 non-rigidity 107n4 non-self-membered classes, paradox of 90 non-specific attitudes 108n9 non-spatiotemporal things 79 nontriviality 46, 48, 59n14 object centered theory 103, 108n9 objectivity xiv ontology 36, 37; necessitist 23, 25, 26, 27 ordinary language: semantics and 61–79; attitudinal instrumentalism and 61–72; performativity/performative utterances and 72–79 “ordinary language” movement in philosophy xiii, 39, 58, 61 ordinary reference 111 Oscar and his twin 95

Index 137 paradox 90; Curry’s paradox 116–117; Frege and 6; theory construction, implications of xiii; see also RussellMyhill Paradox Parsons, Terence 38n16, 57 performativity/performative utterances 61, 72–79; Austin on 77; Bach on 75; descriptivist assimilation of 73; Lewis on 74; as self-stating or self-descriptive 76; as statements 73, 75, 78; truthvalue of 77 Plantinga, Alvin 15n15 Prague Spring xiv possible numbers 24 possible things 29–30 possible world metaphysics/metaphysician 28, 41, 127 possible world semantics 28, 39 possible worlds x, 7–10; canonical conception of 15n15; capture of de re modal fact by 21; existence per 40; indexical signs and sets of 97–98; rigidity and 100; two sorts of relativization of linguistic phenomena to 42; world, the, and 35; see also Twin Earth pre-theoretical subject matter see subject matter proper names 44, 98, 99 propositional attitudes 12, 102, 104, 108n9 propositional constituents 83, 84, 85, 87, 91 propositional unity 83, 85 propositions: doctrine of 81–82, 84; explanatory utility of 91; paradox of 89; Russellian 70, 79n7, 83, 90; structured xiii, 82, 91; theory of 87, 88; unity of 83; what is said and xiii, 81–92 Putnam, Hilary 95; on case of jade 22; on Danzig as Gdansk 16n22; demonstrative extension-fixing for ‘water’ 99–101; on epistemically ideal theory and semantic indeterminism 45–46; on kind terms and instances of relevant kind 44, 98; “Meaning of ‘Meaning’, The” 96, 98; Realism with a Human Face xiv–xv; on scientism in philosophical culture 127 quaddition 111 quantification 38, 65, 67, 89, 90; first order 6; meta-representational 66

quantified modal logic xii, 7, 13, 28, 39, 67 quantifiers 7 quantifying in 66, 67, 68, 69 quantifying over all propositions 90 quantifying within 67, 68 Quine, W. V. 5, 15n9, 19; ‘Giorgione’ example 69; naturalized epistemology of xiv; post-Quinean analytic philosophy 31, 34; quantification into attitude context, idea of 65; on sententialism about belief reports 104, 105; on substitutivity 67 realist attitude viii, ix–xiii, xv, 7–10, 17–22; as default 31; instrumentalist attitude vs. 1–4, 44, 84, 94; prevalence of 83; towards propositions 85, 90; towards theoretical representations 86, 88; see also attitudinal realism realist interpretation 62, 101; criticism of 95 realist purport 19, 28, 86 realist truth 45–46 Reck, Erich 14n6 reductionism 105 Representational Theory of Mind (RTM) 16n25, 87; attitudinal instrumentalism and 101–106; Rescorla’s reinterpretation of 108n11 Rescorla, Michael 108n11 Rey, Georges 16n25 rigidity 100, 107n3 RTM see Representational Theory of Mind rule-following 109–112; deployment of 109; problematics of xiii; representing xiv rule-governed behavior 110–112; rules and 122 rule-regulated behavior 119 rules: arithmetical 112; of English 41; formation 90; as “lived” 121; as representations of behavior 110, 112–113, 121; Russellian 61; as silence 123; in theory versus practice 121; transformation 90 rules and representation 109–125; rules of conduct as representations of behavior xiii–xiv rules as representation 110, 113, 120–123 rule-skepticism 110, 111, 113–114 rules of behavior 109, 110 rules of conduct xiii, 121

138 Index rules of inference 122 rule-violating behavior 119 Russell, Bertrand xiii, 29, 92n1; Introduction to Mathematical Philosophy 38n15; paradox of propositions of 88; theory of descriptions 61, 62; theory of quantifying in 69; ‘your yacht,’ analysis of readings of 62–72 Russellian: assumptions 68; background 64; contracts 63; idea 69; propositions 70, 79n7, 83; ‘robustness’ 29; rules 61 Russell-Myhill Paradox 88–91 Russell’s paradox xi, 6, 90 Ryle, Gilbert 119; on acceptance and acceptance, distinction between 124n12; on intelligent behavior and mechanical habit, distinction between 125n14 Ryle-Sellars line 121 Salmon, Nathan 54 salva vertitate substitutivity 65–66 Second Philosophy xv self-ascription of properties 107n8 self-citationality 115, 116, 118, 119, 120 self-denotation 115, 124n7 self-distinctness 8 self-involvingness 108n8 self-location 107n8 self-reference 76, 124n7 self-reflexivity xiv self-stating or self-descriptive, performative as 75 self-understanding vii self-verifying, performatives as 78 Sellars, Wilfrid 119, 121, 122 semantic descent 13–14 semantic representations: in metaphysics 22–30 semantics: attitudinal instrumentalism in 36, 39–60; fixed-domain 26–27; of modal discourse xii; ordinary language and 61–79; philosophical 93; possible world 7, 39; realistic 27; syntax and 90, 103; theoretical purview of 79; theoretical representations in xiii, 40; truth-conditional ix, 36, 43, 44, 47; truth-values 33; see also formal semantics; metasemantics semantics-first: Frege’s methodology of 13, 16n28, 34 semantics for a system of modal logic 23, 25, 26

semantics of attitude reports 65, 105 $entences (Kaplan) 70 sentential context 75; indirect 57 sentential expression 54; see also subsentential expressions sentential truth 43–50; paradoxical nature of 89 sententialism 104, 105 set-theoretical reductions of numbers 83 Sider, Theodore 37n11 Simchen, Ori 14n1, 16n19; on denoting concepts per Russell 92n1; indeterminacy argument of 47; on metasemantics in relation to formal semantics 44, 47, 58n2; on narrow content in relation to theory of reference 106n2; on ‘new actualism’ 38n14; on new advantage question 49; on productivist metasemantics 58n2; on reference claims as they pertain to linguistic reflexivity 59n6; on scopal difference between ◊xϕx and x◊ϕx 37n8; on self-denotation and selfreference 124n7; on Tortoise’ stance 123n6; on truth-in-a-model 49; see also Cognitive Relations Theory (CRT) Soames, Scott 82, 91 sociolinguistic hypothesis 99 Socrates 41 speech: agentive production of 79; formal modes of 40; meaningful numerical 33; promises issued in 73 speech act theory xiii, 39, 58, 72, 75, 77–79 Stalnaker, Robert 27 Steiner, Mark 16n28 Strawson, Peter xiii, 32, 38n20, 61 Strawsonian semantic tradition 32 subject matter xii, 1; apparent (yacht example) 63, 71; of basic everyday claims 19, 21, 22, 28; definition of 16n29; conservativism as to 19, 20; of the language, Stalnaker’s views regarding 27; of metaphysical theory vii; of natural sciences 32, 87; of philosophical reflection 3; of philosophical theory 31; pre-theoretical 19–22, 43, 45, 59n9, 82–83, 86–87, 89, 98; representations of 36; of sentential truth 45; statements not subject matter for semantic theorizing 79; theoretical capture of 14; transcendental standpoint on 34, 35

Index 139 subsentential components 84 subsentential expressions 10, 44, 50, 82, 83 subsentential reference 47 subsentential language-reality connections 40 substance: nature of ix, 3, 17, 85; metasemantics and metaphysics of 101; relative similarity of 101; representations of 86; represented viii, ix, 2, 21 substance terms 100, 107n7 substitutivity 66, 67 Tarski, Alfred 43, 45–51 Tarski’s theorem 89 theoretical identification (TID) 13, 18, 20, 31, 86, 96; justified attitudinal realism and 17–22; in natural science 15n16, 17, 124n11 theoretical representations: migration of 22; in natural sciences 106; in philosophy of mind and language 106; realist attitude toward 18–20, 31, 106; semantic 31; TIDs and 86; see also metaphilosophical realism theory: accepting rules in theory 121; economic 2; metaphilosophical xvii; model 1, 27; number 81; object centered 121n9; philosophical 37; semantic 16n24, 32, 39, 43, 47, 49–51; speech act xiii, 39, 77–79; surrounding 19–21, 28, 86, 87, 94; see also Cognitive Relations Theory theory-choice 105 theory construction 82 theory-interpretation 105 theory of descriptions (Russell) 61–62, 64, 68 theory of indirect reference (Frege) 10, 11–13, 39, 51–52, 54, 57–58, 60n19, 65, 67 theory of inheritance (Mendel) 102 theory of language use (Lewis) 97–98, 101 theory of meaning 80n16; useconditional 123n3 theory of mind see Representational Theory of Mind theory of philosophical representation 31 theory of philosophical theorizing xv theory of propositions (King) 88 theory of quantifying in (Kaplan) 66, 68–70 theory of reference xiii, 75, 95–96, 99, 106n2

theory of sense and reference (Frege) 10 theory of sets 41, 81; naïve 89; see also Morse-Kelley set theory theory of types 90, 92n9 thirst-quenching, transparent, odorless, tasteless (TTOT) liquid 118, 124n11 TID see theoretical identification Thomas, Clarence 29 Tortoise: “What the Tortoise Said to Achilles” (Carroll), analysis of 110, 113–122 transcendental idealism 33, 38 transcendental standpoint on subject matter 34, 35 truth-conditional semantics ix, 36, 43, 44, 47 truth-conditional semantic theory 50 truth conditions 12, 70–71, 75–79, 82; propositions associated with 84–85, 91; sententialist view of 104–105; subsentential expressions’ contribution to 99; theory of meaning and 80n16 truth-at-a-model 59n7 truth-in-a-model: jumbled 48–51, 59n15; scrambled 45–51; Tarskian 43–51, 59n7 truth-values 33 TTOT see thirst-quenching, transparent, odorless, tasteless (TTOT) liquid Tully 65–66 Twin-Earth 95 Urquhart, Alasdair 92n8 use and mention, conflation of 126 valued formulas 70 van Heijenoort, Jean 92n10, 125n15 Vetter, Barbara 38n14 von Neumann, [John] 83–84 von Stechow, Armin 79n8 water, representations of: extension-fixing 99; as hydrogen hydroxide viii, 4, 13, 17–20, 36, 85–87, 95–96, 98, 106, 127; metasemantics of 101; Oscar’s thoughts regarding 95–96; rigidity of semantic claims regarding 101–101, 107n3; TTOT liquids and 118, 124 water-claims 19 Weisberg, Michael 36n1 Williamson, Timothy 23, 25–27, 37n11, 37n13 Wittgenstein, Ludwig vi–vii, xiii–xiv, xv note 4; gun-bang example 64–65,

140 Index 68; Kripke-Wittgenstein (KW) 111; machine analogy of 113; “ordinary language” movement in philosophy and 39, 61; Philosophical Investigations vi, 30, 61, 71; on rule-following xiv, 110; on rules as representation 113; rule-skepticism of 111; on semantic paraphrasing 62, 72; theory of

descriptions as applied by 64–65 Wright, Crispin 15n11 Yablo, Stephen 16n29 yacht, example of 62–64, 71 Zermelo, [Ernst] 83–84