Roads to reference : an essay on reference fixing in natural language 9780198846277, 0198846274

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Roads to Reference

OUP CORRECTED PROOF – FINAL, 10/10/2019, SPi

OUP CORRECTED PROOF – FINAL, 10/10/2019, SPi

Roads to Reference An Essay on Reference Fixing in Natural Language MARIO GÓMEZ-TORRENTE

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Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries © Mario Gómez-Torrente 2019 The moral rights of the author have been asserted First Edition published in 2019 Impression: 1 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on any acquirer Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America British Library Cataloguing in Publication Data Data available Library of Congress Control Number: 2019944138 ISBN 978–0–19–884627–7 DOI: 10.1093/oso/9780198846277.001.0001 Printed and bound in Great Britain by Clays Ltd, Elcograf S.p.A. Links to third party websites are provided by Oxford in good faith and for information only. Oxford disclaims any responsibility for the materials contained in any third party website referenced in this work.

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Contents Preface

1. Reference: Problems and Promises What Is Reference? Why Study the Fixing of Reference? Roads to Reference: A Preview On Reference and Meaning

2. Demonstratives and Conflicting Intentions Introducing Demonstratives Kaplan’s Classical Theories The Search for Descriptivist Conditions for Demonstrative Reference Referential Indeterminacy as a Fundamental Problem for the Descriptivist Project A Picture of Demonstrative Reference Fixing

3. Proper Names and Referential Indeterminacy Some Classical Kripkean and Evansian Advances in Our Understanding of Proper Names Recent Descriptivist Views about Name Reference Fixing Referential Indeterminacy as a Fundamental Problem for Descriptivism Roots of Referential Indeterminacy Recent Theories of Jointly Necessary and Sufficient Conditions for Name Reference A Picture of Name Reference Fixing

4. Arabic Numerals and the Problem of Mathematical Sophistication

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1 1 7 11 16

19 19 21 27 36 49

60 60 64 73 80 82 90

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Verbal Numerals, Arabic Numerals, and Reference Existing Descriptivisms about Arabic Numerals and Their Problems A Picture of Reference Fixing for the Arabic Numerals What the Referents of the Numerals Could Be

111 122 130

5. Nouns for Natural Kinds and the Problem of Arbitrariness

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The “Kripke-Putnam Orthodoxy” about Nouns for Natural Kinds Challenges to the “Kripke-Putnam Orthodoxy,” with Special Attention to Arbitrariness Objections

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140 148

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 Some Unsatisfactory Responses to the Challenges A Picture of Reference Fixing for Natural Kind Nouns The Problem of Arbitrariness and the Referents of Nouns for Natural Kinds

6. Words for Sensible Qualities and the Problem of Perceptual Variation The “Secondary Quality” View of Color and Some Arguments for and against It Intersubjective Perceptual Variation Arguments and Some Implausible Objectivist Responses to Them An Account of Reference Fixing for Color Adjectives Perceptual Variation and the Referents of Color Adjectives

7. Concluding Notes The Strongest Reasons for Anti-Descriptivism, and Its Proper Reach The Referents at the End of the Roads

References Index

154 159 168

184 184 190 195 203

213 213 215

221 229

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Preface This book is my personal attempt to contribute to the theory of reference, and specifically to some of the central issues that arise when one asks how the conventional reference of some linguistic expressions or expression uses is fixed or determined (when it is). Assuming that reference is a semantic property of linguistic expressions (or expression uses), this is thus a book about what sometimes goes by the name “metasemantics,” the study of how expressions come to have the semantic properties they have. In some cases, the book basically takes for granted views about what the referents of a variety of expressions or expression uses are, and sets out to explain how they could have acquired those referents; alternative views of what the referents of the relevant expressions are are feasible, but it is hoped that the accounts of reference fixing in the book would provide the basis for interesting supplements even of those alternative views. In other cases, the book offers substantive arguments in favor of particular views of what the referents of certain expressions or expression uses are, as well as of how they have acquired those referents. But even in these latter cases the main focus is on issues of reference fixing, rather than on properly semantic or other non-“metasemantic” linguistic issues about the relevant expressions. The issues about reference fixing that the book focuses on, and the treatments of them developed below, are varied in nature, but many of them are related by several connecting threads. Thus, in chapters 2 and 3, I consider demonstratives and proper names, and seek to reject some recent views on which certain kinds of descriptivism are unavoidable as accounts of reference fixing for those expressions. In fact, I seek to provide a strong anti-descriptivist consideration about reference fixing for names and demonstratives, based on cases of referential indeterminacy, that has not, to my knowledge, been exploited in the previous literature on the topic. I then develop an account of reference fixing for these expressions which is compatible with antidescriptivism and which embraces the idea, hinted at by Kripke and others, that the relevant reference-fixing conventions need not provide necessary and sufficient conditions for reference, but only imprecise roughly sufficient conditions for reference and reference failure. A related account of reference fixing, involving only imprecise roughly sufficient conditions, is provided for

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ordinary natural kind nouns in chapter 5. Chapter 4, on Arabic numerals, argues against some views that see the reference of the numerals as unavoidably fixed by certain sophisticated descriptive structures, and develops instead a less demanding account of reference fixing for the numerals. Chapters 4, 5, and 6 all seek to reject a variety of eliminativist arguments intended to show that reference to numbers, natural kinds, and color properties is impossible— at least by means of natural language numerals, ordinary natural kind nouns, and color adjectives. According to these chapters, the reaches of reference and, accordingly, of truth extend well beyond what currently popular eliminativist considerations allow—reference fixing can take many (bumpy) roads to its destinations and surmount obstacles of all kinds. On the other hand, chapters 2, 3, and 6 all seek to reject in some way or other views which, while akin to the views of this book in being broadly anti-descriptivist and/or non-eliminativist about reference in the relevant areas, defend such anti-descriptivism and noneliminativism at the cost of postulating epistemic mysteries in the theory of reference fixing. One less theoretical but, to my mind, no less substantive thread unifying many of the discussions below is their Kripkean character. As I think will be clear after reading them, some of the main considerations in practically all of the chapters seek to establish broadly Kripkean views, often via extensions or refinements of broadly Kripkean insights. This is true in particular of chapters 2, 3, and 5 and their underlying Kripkean distrust of theories of necessary and sufficient conditions for reference; of chapters 4, 5, and 6 and their realist and objectivist views concerning numbers, ordinary natural kinds, and color properties; of the skepticism, present in all the chapters, toward views that seek to explain the existence of ordinary reference in terms of surprising epistemic resources or unexpected metaphysical targets; and of many other smaller things here and there. I have many people and institutions to thank for their reactions to ancestors of this material and for other kinds of inspiration or support for the book, and the attempt to provide a list of them would be an agonizingly incomplete exercise. I must nevertheless agonize, mentioning explicitly my gratitude to only some of them. I thank the Mexican CONACyT research project CCB 2011 166502 and the Spanish MINECO research project FFI2015-70707-P for support, and John Wiley and Sons for permission to use a part of GómezTorrente (2016) as the basis for a part of chapter 6. Thanks are also due for their help to three anonymous referees for Oxford University Press, and to Peter Momtchiloff, my editor at the Press. I wish to express a special gratitude to the teachers from whom I learned much of what I hope I know about how to

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do philosophy, especially Saul Kripke himself, Manuel García-Carpintero, and Scott Soames. I also want to thank my colleagues at the Instituto de Investigaciones Filosóficas of the Universidad Nacional Autónoma de México (UNAM), these institutions themselves, and my students, from whom I have learned so much.

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1 Reference Problems and Promises

What Is Reference? As advanced in the Preface, this book is about how the conventional reference of some linguistic expressions or expression uses is fixed or determined (when it is). But what is reference, in the sense in which we want to talk about it here? As in so many other cases where a question as to what something is is asked, in this case we can list examples that we want, at least at first sight, to count as examples of conventional linguistic reference, and we can give examples that we want, at least at first sight, to count as examples where reference to some particular thing, or reference tout court, does not take place. However, giving a general, sufficiently informative, but exceptionless characterization seems elusive, and may well be impossible—in fact, this will be one of the ideas made plausible by the discussions in this book. Still, it is possible to state some plausible general ideas about reference in the sense that interests us here, ideas that we will take as guiding in the remainder of the book. Like so many other theorists in the tradition of the theory of reference, we want to include as cases of reference some cases where a use of a linguistic expression intuitively stands for a certain thing as an effect at least in part of linguistic conventions concerning the expression, and in those same cases we want to say that there is no reference to things different from that thing; and also, we want to say that there is no reference at all in some cases where intuitively, as an effect at least in part of linguistic conventions, it turns out that there is no thing that a relevant use of an expression stands for. We want to say, for example, that “Aristotle,” as normally used in an ancient philosophy class, refers, and that it refers to Aristotle, the great ancient Greek philosopher. We want to say that the madman who believes of himself that he is Aristotle does not use “Aristotle” so that it refers to the madman himself, much as the madman believes that he is Aristotle—and much as he (as opposed to the

Roads to Reference: An Essay on Reference Fixing in Natural Language. Mario Gómez-Torrente, Oxford University Press (2019). © Mario Gómez-Torrente. DOI: 10.1093/oso/9780198846277.001.0001

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expression “Aristotle”) refers, in the sense of “refers” in which a person refers, to himself with “Aristotle.” We want to say that if I utter That is a beautiful mountain, while intentionally pointing and referring (in the personal sense of “referring”) to a mountain in plain view, with no other mountain in sight, my use of “that” refers to the mountain in question. We want to say that the agonizing man who in his delirium hallucinates a demon, and utters He is coming to get me, does not use “he” so that it refers to anyone. In all these cases, the reference, when there is such, is the object that, in an intuitive sense, the relevant expression use stands for, as a matter at least in part of what seem to be the linguistic conventions applying to that expression use. And when there is intuitively no reference, or reference is not to some particular thing, it would seem that this is because somehow those same conventions imply (together with the surrounding circumstances) these facts about the relation of standing for failing to hold between uses of linguistic expressions and objects. But beyond examples of this sort, involving uses of names and demonstratives where what we want to say about their referents or lack thereof is more or less intuitively clear, there may not be a general, informative, but exceptionless characterization that we want to accept, one determining for an arbitrary expression use whether it has a linguistic reference or not, and what that reference is to be if there is to be one. We will see in chapters 2 and 3 that in a fair number of actual and potential cases of uses of demonstratives and names, it is unclear whether there is some thing that a relevant expression use conventionally stands for, and thus unclear whether reference occurs or not. And when we move beyond names and demonstratives altogether, and consider other expressions, such as adjectives, common nouns, Arabic numerals, etc., it seems as if we can’t even rely on the intuitive idea of the thing that an expression use stands for as a guide to the question of reference. For example, is there any thing that a use of a verb, a use of “snored,” say, intuitively stands for? Well, even if there need not be a general, informative, and exceptionless characterization of reference that definitely solves questions such as this, there are probably a few things that can be said in this area, which suggest that the answer may lie in a certain direction. Frege, to whom the introduction of the modern theoretical notion of reference at stake here can be attributed in all essential respects, postulated that a variety of meaningful expressions of diverse grammatical types are susceptible of having referents. And he postulated, more specifically, that the reference of an expression use (when it has one) is the thing which constitutes the expression use’s contribution to the truth condition of the sentence in which it appears, the thing specifically contributed by the expression use on

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  ? 3 which the truth or falsehood of the sentence depends.¹ This, which we will call the Basic Fregean Idea, is an appealing idea providing a general criterion for reference, one consistent with the desired connections between the theoretical notion of reference and the intuitive notion of standing for an object in the case of names and demonstratives, and an idea that helps in the search for referents for expressions which are not demonstratives or names. If one says Aristotle snored in the ancient philosophy class, presumably the thing specifically contributed by “Aristotle,” on which the truth or falsehood of Aristotle snored depends, is Aristotle. And Frege supposed, not implausibly at first sight, that the contribution of “snored” to the truth condition of Aristotle snored was the function s assigning the truth-value truth to a thing that snored and the truth-value falsehood to a thing that didn’t snore. One can reasonably think that the thing contributed by “snored” on which the truth or falsehood of Aristotle snored depends is something that encodes the information whether Aristotle snored or not, and the function s surely does that—if Aristotle is assigned the truth-value truth by s, that means he snored; if he is assigned the truth-value falsehood, that means he didn’t. But furthermore, it is reasonable to think that the thing contributed by “snored” in the case of Plato snored ought to be the same thing, and ought to encode the information whether Plato snored or not (and mutatis mutandis for similar predications of “snored” of other things). And again the function s surely does that. Frege thus postulated that the reference of “snored” in Aristotle snored is the function s, or equivalently the set of things that snored, also known as the extension of “snored.” But the idea and its associated criterion do not solve all the questions about the reference of “snored” that one could think of. It would seem that the Basic Fregean Idea implies that “snored” does not refer to the set of things that ¹ According to a relatively uncontroversial way of reading Frege, which I am adopting here, it is his view that each well-formed complex expression arises from the application of a symbol referring to a function to symbols referring to arguments of that function. Then, in the case of a complete assertoric sentence, its reference, which is a truth value, is a function of the referents of its parts, obtained by successive applications of functions to the referents of simpler constituents. This is a principle of compositionality for referents. In this sense the truth or falsehood of a sentence depends on the referents of its constituent expressions, which thus contribute their referents to the determination of the sentence’s truth value. For example, suppose that Aristotle is the referent of “Aristotle” and that the referent of “snored” is the function s assigning the truth value truth to a thing that snored and the truth value falsehood to a thing that didn’t snore; and suppose that the sentence Aristotle snored arises from the application of “snored” to its argument “Aristotle.” Then the truth value truth is obtained as the reference of the sentence Aristotle snored by application of s to Aristotle. Like many others, I take the attribution of a principle of compositionality for referents to Frege as well-grounded, e.g. given his acceptance of the principle that substitution of co-referential expressions doesn’t alter a sentence’s referent (in Frege (1892)); see e.g. Pelletier (2001). But there are of course dissenting voices (see e.g. Janssen (2001)).

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snored when used in an utterance of Aristotle might not have snored, say. For the set of things that (actually) snored would not seem to encode enough information to determine, together with whatever reasonable referents we might assign to the other expressions in the sentence, whether Aristotle might not have snored, i.e. whether he would not have snored in other possible circumstances. It would seem that if “snored” is to have a reference here, it should be a richer thing than the set of things that actually snored; perhaps it should be the set of all pairs formed by a possible circumstance and the set of things that snored in that circumstance (a thing also known as the intension of “snored”). And this thing does also encode the information whether Aristotle (or any other actually existing thing, such as Plato) actually snored or not. So was this more complex thing the reference of “snored” in Aristotle snored, after all? And then we may also ask, was the intension of “Aristotle” (the set of all pairs formed by a possible circumstance and the thing that is Aristotle in that circumstance) the reference of “Aristotle” in Aristotle snored, after all? Frege himself pointed out that it seems as if the reference of “Hesperus” cannot be the same as the reference of “Phosphorus” in The Greeks in Homer’s times believed that Hesperus was not Phosphorus, despite the fact that they would appear to stand for the same thing, the planet Venus, which would seem to be the thing they contribute on which the truth or falsehood of simple sentences containing them depends. For The Greeks in Homer’s times believed that Hesperus was not Hesperus seems clearly false, but if “Hesperus” and “Phosphorus” contribute the same thing to the determination of truth or falsehood in The Greeks in Homer’s times believed that Hesperus was not Phosphorus, then this sentence should have the same truth value as The Greeks in Homer’s times believed that Hesperus was not Hesperus, where the two uses of “Hesperus” certainly must contribute the same thing. And yet The Greeks in Homer’s times believed that Hesperus was not Phosphorus seems intuitively true. So, what is the reference of “Hesperus,” or “Phosphorus”? Frege, as we know, postulated that their reference in simple sentences is the planet Venus, but also that their referents when embedded in verbs of psychological attitude are other things, appropriate senses containing modes of presentation of the planet Venus, each including enough information as to determine whether the subject of the attitude holds the attitude toward Venus under that mode of presentation. The same goes for “Aristotle” when embedded under verbs of psychological attitude, and a sense for Aristotle does encode the information that it is a sense for Aristotle—it determines Aristotle, in fact, on Frege’s theory. So why shouldn’t a sense, this less familiar thing conjured up by Frege, have been the reference of “Aristotle” in Aristotle snored, after all?

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  ? 5 Senses are very controversial things. Many philosophers, including perhaps most of the philosophers in the tradition of the “new theory of reference,” probably the most influential in the recent literature on reference, don’t give senses much of a role in the study of language, and think that one can do semantics, and explain the phenomena that Frege used senses to explain, using just ordinary individual objects, properties, intensions, and the like—some even doubt senses exist as such. This book shares many basic views and assumptions with the tradition of the “new theory of reference,” so perhaps we can jump onto the wave here also and just forget about senses. But even then, indeterminacies will remain. For example, why should intensions not be referents, given that they seem to be contributed by predicative expressions and (at least in many cases) they seem to encode the information needed to determine the truth or falsehood of the sentences in which those expressions occur? (Just about everybody seems to think intensions are respectable things.) It is natural to add one guiding idea about reference to the Basic Fregean Idea, one that appears to get rid of the intensions of predicative expressions as the referents of those same expressions. The reference of an expression (when it exists) must presumably be, at least in typical cases, some thing of which it can reasonably be said that some ordinary speaker has at some point (often in the early history of humankind) intended to refer (in the personal sense of “refer”) to it with the expression (or with some ancestor or relative of the expression). Linguistic referents are, we are supposing, determined in part by linguistic conventions. But these are presumably constituted, at least in some typical cases and in part, by the existence of widespread agreements regarding how speakers’ referential intentions give rise to referents for expressions or expression uses (agreements which in many cases date in some form or other from the early history of humankind).² And if this is so, it is unreasonable to suppose that the referent of an expression is its own intension, for it is unreasonable to suppose that (typically) an ordinary speaker has intended to refer to suitable intensions when she used expressions such as “Aristotle” or “snored” (let alone that someone in the early history of humankind intended to refer to the appropriate intensions with the appropriate ancestors of these words). (Though, of course, one is free to give a name to an intension if one knows what an intension is and wishes to give a name to one.) For one thing, ² For our main purpose in this book, which is to explain how reference is achieved for certain classes of expressions, we will essentially focus on this aspect of the nature of referential conventions. We will not need to say much about other aspects presumably essential to conventions in general, such as the fact that they are sustained via coordination mechanisms of certain kinds and in virtue of their successful role in the attainment of common aims.

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intensions are complicated, highly theoretical things, and ordinary people just don’t seem to be able to have intentions about them as such, certainly not explicitly, but presumably not implicitly either. If this plausible idea is accepted, names and verbs do not refer to their own intensions (at least in run-of-the-mill cases). But intensions must somehow be encoded by the real referents, if we want to respect the Basic Fregean Idea connecting reference and truth, and to respect as well the intuition that the truth or falsehood of Aristotle might not have snored depends on (something that encodes) the intensions of “snored” and “Aristotle.” Fortunately, at least for typical names and verbs, and for the other expressions we will deal with in this book (demonstratives and Arabic numerals in the case of apparent singular terms; and ordinary natural kind nouns and adjectives for sensible qualities, when we turn to apparent predicative expressions), it is reasonable to suppose that our plausible idea and the Basic Fregean Idea connecting reference and truth (as well as the initial desideratum that the reference of a demonstrative or a name should be the thing it intuitively stands for) are jointly satisfied by appropriate things. On the one hand, it is reasonable to suppose that there is a widespread, if implicit, intention to refer to Aristotle with “Aristotle” and to something such as the property of snoring (or having snored) with “snored,” an intention that may have developed in part via the formation and transmission of earlier intentions to refer to those things. It is just very natural to say that ordinary people have at some point intended to refer to Aristotle and snoring with some words, in a way in which it is not natural to say that ordinary people can have intended to refer to intensions. That this is natural is due, at least in part, to the fact that it is clear how Aristotle and snoring can have been the objects of ordinary people’s intentions; in an intuitively clear sense, both Aristotle and snoring have been the objects of representations in the minds of ordinary people in a way in which intensions have not. Ordinary people did at some point have a perceptual representation of Aristotle that formed the basis of a linguistic referential intention, later transmitted to people who did not get to see Aristotle; and ordinary people did and do have a perceptual representation of snoring that can form the basis of linguistic referential intentions concerning “snored.” But ordinary people typically have no mental representation of intensions, whether perceptual, linguistic, or of other kinds. And on the other hand, it is reasonable to suppose that the intensions of “Aristotle” and “snored” are encoded by Aristotle and (the property of ) snoring, respectively. First, the intension of “Aristotle” can be said to be encoded by Aristotle, if we accept the largely uncontroversial view that

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     ? 7 “Aristotle” is rigid, which implies that its intension is the set of all pairs formed by a possible circumstance and Aristotle himself. (And the same can be said of proper names in general, demonstratives, and Arabic numerals.) And second, the intension of “snored” can be said to be encoded by the property of snoring, as the intension of “snored” is the set of all pairs formed by a possible circumstance and the set of things that instantiate the property of having snored in that circumstance. (And the same can be said of verbs in general, and of other predicative expressions.) Accordingly, we will suppose that things in general (Aristotle being a paradigmatic example) are the referents of uses of singular terms (when they have referents), and that properties are the referents of uses of predicative expressions³ (when they have referents). This is not to say that predicative expressions refer to properties in just the same way in which singular terms refer to things in general. Presumably singular terms, in an intuitive sense, stand for the things they refer to, but the properties referred to by predicative expressions are not things that in the same intuitive sense these expressions stand for. The modes of reference of singular terms and of predicative expressions are presumably different. There are perhaps difficulties spelling out the difference in an unequivocal way, as Frege concluded in his reflections on the distinction between objects and concepts. But I think we can in any case say, without fear of erring too much, that when referred to by a predicative expression, a property is invoked in its capability or potentiality of applying to things, while when referred to by a singular term, a thing in general (including a property) is invoked simply as a thing about which something can be said, its capability of applying to things (if any) not being invoked.

Why Study the Fixing of Reference? We have now a general idea of what reference must be, in the sense that will concern us here—even if what we have said does not amount, by any stretch, to a full theory of what reference is. So we now have an idea of the sort of thing whose fixing or determination for linguistic expressions or expression uses we want to study in this book. But, it might legitimately be asked, why should a philosopher, or even a philosophy of language specialist, care about how reference gets determined? As I see things, there are two main reasons. ³ In taking properties to be the referents of predicative expressions (when they have referents), we are also following the lead of several authors from the “new theory of reference” (and from other traditions). See e.g. Salmon (1981), (1986); Soames (2002).

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The first, perhaps less important reason, is that a philosopher, and in particular a philosopher of language, should care about how communication is possible, and reference seems to have an important, if perhaps somewhat negative, role in the explanation of communication. Frege emphasized that communication, at least in the case of sentences involving names—but suitably analogous points hold for every other expression—would not work if the referent of one same name, as used by different people, were not typically the same.⁴ Why? Because if people’s knowledge of whatever it is that fixes the reference of different uses of one same name directed them to different things, or just to no thing at all, the possibility of communication would be hampered, as people would then interpret other people as talking of different things, or of no thing at all, with the resulting failures of coordination. In order to explain why this situation does not typically (seem to) arise, Frege thought it was enough to suppose that the different senses different people attached to the same name turned out to contain modes of presentation of the same thing, the thing commonly referred to by uses of the name made by different people. Along with the “new theory of reference,” I don’t think it’s plausible to suppose that it is some descriptive sense attached by a speaker to a name that fixes the name’s reference. The descriptive senses that Frege had in mind just could not do the job, as well-known arguments by Kripke, Donnellan, and others have shown. And in this book I will argue that other descriptive senses that have more recently been thought to do the job in fact cannot do it either. I think, however, and this is not a point always clearly spelled out or perhaps even conceded by “new theorists of reference,” that it is plausible to suppose that the existence of shared reference-fixing conventions plays a role in the explanation of the possibility of communication. This might be thought to lead to descriptivism, but it doesn’t, because (as I will argue) the existence of observed reference-fixing conventions does not imply the existence of reference-fixing descriptive senses. In general, it is reasonable to suppose that the ability that speakers have of following the common linguistic conventions that fix reference must play a role in the explanation of linguistic communication. When a speaker uses language in order to attempt to communicate that a certain thing (such as Aristotle) has or does not have a ⁴ In talking here of the referent of uses of “one same name,” I, like Frege, am not presupposing that the notion of two uses being uses of one same name can be understood independently of the idea that they should have the same referent. Rather, I’m using the idea of uses of one same name in an intuitive sense, deferring the question of when two uses are of one same name to ulterior theorization, theorization which should vindicate the Fregean idea in the main text. The considerations in chapter 3 will actually provide the basis for a suitable theoretical elucidation of the idea of two uses being uses of one same name.

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     ? 9 certain property (e.g. the property of having snored), which things and which properties these are is something that her hearers will plausibly often guess at least in part in virtue of their having developed an ability to follow the common conventions governing what things are being talked about by means of the expressions used by the speaker. These conventions, as the “new theory of reference” plausibly argued, and as we will emphasize many times in this book, need not be integrated into the semantic structure of the expressions that do the referring. Nevertheless, an ability to abide by the conventions governing particular expressions must be developed somehow by speakers, on pain of failures of communication—this being the thesis not always clearly spelled out by “new theorists of reference.” In this book we will propose a number of reference-fixing conventions as underlying the use of various kinds of expressions in linguistic exchanges, hoping that it will appear plausible to think that the ability to follow these conventions is manifested in relatively simple linguistic behaviors, and doesn’t require the attribution of unlikely knowledge to a normal speaker. By contrast with descriptivism, which the “new theory of reference” and the new considerations in this book show to invoke implausibly demanding reference-fixing descriptive associations on the part of speakers, it will appear plausible to think that competence with the relatively simple conventions postulated by the picture of this book does not exceed in an implausible way the capacities that we can reasonably attribute to a normal speaker. The second, perhaps more important, but at any rate related reason why a philosopher, regardless of specialty, should care about how reference gets determined, arises again from a Fregean view, the Basic Fregean Idea about the connection between reference and truth. On a natural, much reviled, but never vanquished conception of human endeavors and accomplishments, truth is something we pursue and very often achieve, of which we often fail to get as much as we want, but that we constantly get more of. Now truth depends on reference: what truths we come to get depends on what it is that is referred to when we express those truths; and if what we think are truths we have got turn out to contain expressions without reference, they will have turned out not to be truths at all. If the natural conception of human endeavors and accomplishments concerning truth is to hold its ground, it must be accompanied by a congenial view or series of views about how reference is fixed, one that makes it reasonable to believe that reference could in fact be fixed that way, consistently with human capacities and dispositions; and one that makes it also reasonable to believe that our language is not plagued by widespread failures of reference.

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10 :    There are many puzzles in discussions of reference fixing that constitute obstacles to a view congenial with the natural conception of human endeavors and accomplishments concerning truth. A first kind of puzzles make it hard to understand how reference could take place consistently with human capacities and dispositions. Some of these puzzles exploit the limitations of our epistemic capacities when it comes to singling out things by means of language and thought; others exploit our dispositions to contradict ourselves, which would often seem to get in the way of our ability to single out things by means of language and thought. A second kind of puzzles don’t necessarily exploit our epistemic limitations, but make it hard to understand how, even in some cases where our epistemic capacities are not working particularly badly, and where we are not being utterly inconsistent, the world could be such that our reference-fixing conventions manage to single out appropriate items in it. When we consider puzzles of these two kinds, we are no longer exclusively concerned with guessing what conventions may govern the assignment of reference to expressions, or with the role that referential intentions play in such conjectured conventions. We must engage in more definitely epistemological and metaphysical philosophical tasks. A tempting thought is then that such tasks go beyond the legitimate area of concern of the specialist in reference fixing or in metasemantics. However, the tempting thought must be resisted, as there is at least a strong reason for the specialist in reference fixing to concern herself with an appropriate resolution of those epistemological and metaphysical puzzles. If the puzzles are not resolved, we will be left with unchallenged reasons to believe that our language, or large and important parts of it, is plagued by widespread failures of reference. And then this will immediately constitute a challenge to whatever conjectured conventions about reference fixing the specialist may have come up with, for these conventions will not have been shown to be compatible with the natural conception of human endeavors and accomplishments concerning truth. Accordingly, from the perspective adopted in this book, which I take to be the perspective adopted by illustrious classics of the tradition of thought about reference fixing, from Frege to Kripke, the theory of reference fixing, or metasemantics, must concern itself with a relatively broad range of epistemological and metaphysical issues. For only in this way can the specialist in reference fixing be reasonably satisfied that her preferred theory of the mechanisms of reference fixing does not inappropriately disconnect reference from truth. In this book we will consider a good number of puzzles of the mentioned kinds, as problems for a theory of reference fixing, and we will often provide attempts at solutions that, if correct, will together constitute a series of views

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about reference fixing that will be congenial with the natural conception of human endeavors and accomplishments concerning truth. Some of these views are briefly previewed in the summary of the book’s contents given in the next section.

Roads to Reference: A Preview Demonstratives such as “this,” “that,” “he,” “she,” “it,” and “they” are paradigmatic, and perhaps in many ways the most basic, instruments of linguistic reference. They also turn out to give rise to phenomena closely related to those involving proper names, which are probably the most studied instruments of linguistic reference. But in the case of demonstratives, unlike in the case of proper names, and under the influence especially of Kaplan’s groundbreaking work, a certain kind of descriptivism at the reference-fixing level has not seemed difficult to swallow to originators and fans of the recent advances of the “new theory of reference.” Just about everybody writing in this area seems to imply, in some more or less explicit way, that there should be a description, provided by the reference-fixing rule for, say, “that” (by the Kaplanian character of “that”) which fixes the reference of a use of “that” in a given context, and which is known in some more or less implicit or inchoate way by a competent speaker. But the description in question has turned out to be exceedingly difficult to find, as attested by the review of the literature on reference fixing for demonstratives offered in chapter 2. This literature, as we will see, has correctly identified several difficult problems for demonstrative reference fixing, including a particularly vexing one caused by the frequent existence of conflicting referential intentions in the same speaker and occasion of use of a demonstrative. The chapter will propose, in line with similar ideas about proper names to be developed later in chapter 3, that the reason for these difficulties is that the reference-fixing conventions for demonstrative reference do not amount to necessary and sufficient conditions for reference, but only to a list of roughly sufficient conditions for reference and reference failure to take place in selected situations—a fact that is manifested in the existence of a fair number of cases where it is uncertain and presumably conventionally indeterminate whether a use of a demonstrative refers to a particular thing or not. If this is so, the chapter argues, there is little hope that a normal competent speaker could in general and invariably associate (in however an implicit or inchoate way) with a use of a demonstrative an appropriate reference-fixing description that he is aware of; for such a

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12 :    description would essentially amount to a general necessary and sufficient condition for a thing to be the referent of that use, a condition that would yield inappropriately determinate and not really known verdicts of reference failure in many cases for which the real merely sufficient conditions do not yield a determinate verdict. Thus, the demonstrative descriptivism at the reference-fixing level embraced by originators and fans of the recent advances of the “new theory of reference” is just as wrong as the corresponding descriptivism about proper names presumably is. The chapter ends by developing a picture of the reference-fixing conventions that state the conjectured roughly sufficient conditions for demonstrative reference and reference failure, and argues that the picture squares well with all the elements appealed to in the preceding discussion. Proper names like “Aristotle” are also paradigmatic instruments of reference, and it can be said that there is much that we know about them, including much about how it must be that their referents get fixed (when some referents get fixed for them). However, one fundamental worry has subsisted, I think, after all the considerable advances in our understanding of names that have been made in the last fifty years or so. Some of these fundamental advances, due especially to Kripke, have pointed to the conclusion that the referents of names, at least in typical cases, are not fixed by the ordinary descriptive information that speakers associate with them. The information that a speaker associates with a name N that seems to come out of his mouth with a certain intuitive referent r, notes Kripke among other things, will often be mostly false of r; and if it is mostly true, it will still be, to all appearances, often insufficiently detailed to pick out r. But then how is it that r comes to be the referent of N in our speaker’s mouth? Another of the relatively recent advances in our knowledge of names, again due especially to Kripke, is our current understanding that r will often have come to be the referent of N in the mouth of a speaker s as a result of the existence of a chain of transmission of the name, from some speakers who originally started using N (or an ancestor of it) with the intention to refer to r, down to its use by s. This seems right. But surely, if this happens it is as an effect of linguistic conventions that speakers should have some kind of familiarity with, however implicit and inchoate. So can’t it be held (once account is taken also of other conventions for name reference that would appear to be more easily accessible, such as conventions about the possibility of naming stipulations or “baptisms”) that s must after all know in some way some semi-occult descriptive information—the information encoded by his familiarity with referential naming conventions—fixing r as the referent of N (as it comes out of his mouth)? Chapter 3 considers this

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question, made with incisiveness especially by proponents of so-called “causal descriptivism,” and answers it negatively. The problem with this kind of idea is again that our name reference-fixing conventions do not seem to amount to a set of necessary and sufficient conditions for name reference; the conventions at work seem to give roughly sufficient conditions for reference or reference failure to take place in particular cases, but no more. Here again cases of presumable referential indeterminacy will play a role in a number of arguments for the suggestion that only roughly sufficient conditions are provided by the relevant linguistic conventions. The upshot is that no “causaldescriptivist” reference-fixing description known by normal competent speakers, not even one known in a merely implicit or inchoate way, can be plausibly built from those roughly sufficient conditions. The chapter considers also the damaging implications of these and other facts for some recent theories of name reference fixing that are not so epistemically demanding as “causal” and other descriptivisms but that propose necessary and sufficient conditions for name reference. Finally, the chapter develops a picture of the reference-fixing conventions stating roughly sufficient conditions for name reference and transmission, arguing that it explains the phenomena appealed to in the chapter. There are many other instruments of singular reference in natural language aside from names and demonstratives, mentions of which surface in the discussions of the seminal authors of the “new theory of reference,” but which are rarely treated in depth by those authors. Among these instruments one finds Arabic numerals, to which chapter 4 is devoted. In this case, as it will turn out, a certain kind of descriptivism will not seem so implausible as a consequence of what will appear as the probable relevant conventions involved in reference fixing. However, the right kind of reference-fixing conventions and descriptions can be brought to light only after a considerable work of clarification of puzzles and debunking of misleading alternatives. There is a common idea that (at least the complex, decimal) Arabic numerals must have a descriptive semantic structure, in this case one given approximately by the polynomials that detail the contribution of each digit in a numeral as the multiple of the corresponding power of ten—in the sum of multiples of powers of ten that the numeral would appear to codify. Even those who adopt the view that the Arabic numerals are semantically non-descriptive typically think of their referents as conventionally fixed by those same polynomials. But, as explained in chapter 4, there is just too much evidence against these and other ideas which seek to explain reference fixing in this area by appeal to sophisticated mathematical descriptions. The chapter proposes an alternative

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14 :    view, on which the reference of (at least the complex) Arabic numerals is fixed (“merely fixed”) by means of simple descriptions which single out the referents of later numerals in terms of the referents of earlier numerals; on the proposal, a numeral (or at any rate at least a complex one) will typically get its referent as the result of the operation of adding one as applied to the number denoted by the preceding numeral in the natural series of Arabic numerals (which is generated by principles independent of semantic interpretation). The possibility of reference for numerals, however, faces a basic problem: if numerals refer to anything, they ought to refer to numbers, and numbers have a bad press among philosophers. Some metaphysical or epistemological principles are often thought to imply that things with the properties of the numbers just could not exist, which leads directly to the view that arithmetical truths apparently containing reference to numbers via numerals, regardless of their simplicity, just cannot be literally true. What could the numbers be, if they are to be fixed as the referents of the Arabic numerals (when used as nouns) by the reference-fixing mechanism postulated in chapter 4? The chapter argues that some of the features of this reference-fixing mechanism actually point toward the view that the referents of the numerals, hence the numbers, are the finite plural cardinality properties. Chapter 5 concerns ordinary nouns for natural kinds, substances, and phenomena, which were shown by Kripke and Putnam to share many characteristics with proper names, including characteristics relevant to the fixing of their referents. In this area, a major challenge for the natural conception of human endeavors and accomplishments concerning truth and its Fregean roots comes from many recent arguments in the philosophy of biology and the philosophy of chemistry. These arguments cast serious doubts on the ability of the presumable reference-fixing conventions for ordinary language nouns for natural kinds, substances, and phenomena to fix or determine real kinds, substances, and phenomena that those terms could refer to. As in the case of names, in the case of nouns for natural kinds there is much we had wrong or that we just didn’t know about fifty years ago, but many fundamental advances have been made in the intervening years, due especially to Putnam and again to Kripke. However, the mentioned arguments from the philosophies of chemistry and biology suggest that many aspects of the KripkePutnam picture cannot be right, and in particular make it hard to believe that ordinary nouns for natural kinds, substances, and phenomena could refer to the kinds, substances, and phenomena that Kripke and Putnam thought were determined by the reference-fixing conventions they postulated for them. A tempting position, in view of the arguments, is again an

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eliminativist position, on which ordinary language discourse about natural kinds, substances, and phenomena is no more than a picturesque and pleasing fiction, but a fiction nonetheless, false or truth-valueless—the sort of view that drags along with it an undesirable conflict with the natural conception of human endeavors and accomplishments concerning truth. The issues here are complicated and require very extensive discussion, but chapter 5 sketches what I think is a sensible non-eliminativist view about the reference-fixing potentialities of the presumable reference-fixing conventions for ordinary terms for natural kinds, substances, and phenomena. These reference-fixing conventions, which again amount to lists of roughly sufficient conditions for reference, are not too different from the conventions somewhat imprecisely envisioned by Kripke and Putnam. But careful attention to their accurate formulation, and to a number of details simply overlooked by these seminal authors, leads to the mentioned non-eliminativist view, on which the referents for typical terms for natural kinds, substances, and phenomena turn out to be interestingly different from the referents assumed, somewhat uncritically, by Kripke and Putnam. The final chapter 6 deals with a more localized, but nevertheless important, challenge to the possibility of reference in large areas of discourse. The challenge arises with special force for adjectives for color properties, but if correct it must quickly generalize to all terms for what most philosophers have traditionally considered as secondary qualities, such as sound, heat, etc. There is much evidence indicating that different apparently normal people perceive the same colored thing via qualitatively different experiences. This leads them to make what appear to be incompatible color judgments, judgments which, given that the different people in question seem perfectly normal, would nevertheless appear to be equally faultless. These facts have provoked a tripartite set of implausible reactions. On a first kind of response, the judgments of some of the apparently normal people are right, and the other judgments are wrong, which is compatible with the reference of a color term being a certain objective property or phenomenon; but this brings along an epistemological mystery about how precisely that property or phenomenon has come to be referred to conventionally by all people. A second kind of response is provided by error-theoretic or eliminativist views on which color language is just not a suitable vehicle of reference and truth. And a third response is provided by less radical but somewhat ad hoc and linguistically improbable views on which color judgments (and judgments about sounds, heat, etc.) involve reference to subjective, secondary qualities. Chapter 6 develops an alternative picture on which color terms often refer to slightly different

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16 :    objective properties as they are used by different people, a picture perfectly plausible in view of the lessons of context-sensitive reference, and one which avoids both mystery views and eliminativism.

On Reference and Meaning By omission, this brief preview gives an idea of the many topics that are not covered in the book, including topics that fall to a greater or lesser extent under the scope of our self-declared subject, the question of how the conventional reference of linguistic expressions is fixed. Thus, for example, many kinds of expressions, including many expressions of traditional philosophical interest, are simply not covered—including descriptions, logical connectives, quotations, modal and other adverbs, gradable adjectives in general, “that”clauses . . . to name but a few.⁵ Some of these may not seem to present substantive problems from the point of view of reference fixing, but others do. There is not much justification for this limitation in the scope of the book aside from the obvious one, that not everything can be covered in a single midsized work. But the book covers at least most kinds of expressions of central interest to classic theorists of reference, and some feeling of relative completeness can perhaps be gathered from this fact. Mention must be made of one significant range of issues falling under our broad theme that are nevertheless not covered in the book in a substantive degree of depth. We agree with Kaplan’s distinction, recalled in chapters 2 and 3, between two senses of “meaning” relevant in discussions in the philosophy of language. In one sense, “meaning” has a fairly broad application, encompassing many conventional aspects of linguistic expressions; in particular, “meaning” in this sense includes linguistic conventions about reference fixing, so long as these are somehow accessible to or followed by competent speakers (even if they are accessible only in some implicit or inchoate way). This book is an extended essay on these conventions and thus on meaning in this sense. But there is a second sense of “meaning,” probably the most common in discussions in the philosophy of language, and certainly the most common sense of “meaning” as used in this book, in which “meaning” applies to what is often also called “content”—the information semantically encoded by an expression

⁵ For the author’s views on reference fixing for descriptions, quotations, and gradable adjectives in general, the reader is referred to Gómez-Torrente (2015b), Gómez-Torrente (2013), and GómezTorrente (2010) and (forthcoming), respectively.

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or expression use. The book does not deal in a substantive degree of depth with many questions pertaining to meaning in this focused sense. In particular, as noted in the Preface, while the book offers substantive arguments in favor of particular views of the semantic nature of certain expressions (this is especially true for color adjectives and for Arabic numerals—the view of the latter as semantically non-descriptive singular terms, favored here, has hardly any substantive defenses in the literature), in other cases views about the semantic nature of expressions are basically assumed without substantive argument. For example, in the treatment of demonstratives and names in chapters 2 and 3, we will essentially just assume that paradigmatic (uses of) demonstratives and names are semantically nondescriptive singular terms which have as referents (when they do have referents) the objects that the demonstratives and names intuitively stand for, without attempting to argue against all possible kinds of views that go against these assumptions. In particular, I will not attempt to argue against all kinds of views on which (uses of) names and demonstratives have some semantic descriptive structure or refer to properties of certain kinds in the way characteristic of predicative expressions. For example, as mentioned in chapter 3, some philosophers and linguists believe that “Aristotle” is semantically equivalent with some description broadly similar to “the thing here relevant actually called ‘Aristotle’”; and as mentioned in chapter 2, some philosophers and linguists think that a use of (the bare) “that” is semantically equivalent with a use of “that thing,” where “that thing” is understood as a quantificational phrase roughly equivalent to a description. Many of these philosophers and linguists think also that the referents of such descriptions are suitable properties, intensions, or the like, which are referred to in the way characteristic of predicative expressions. I will not attempt to argue against such views, on which the descriptions or quantificational phrases in question are rather weak and trivial, and cannot by themselves substantively determine the object that is conventionally being talked about (even if this is postulated not to be the semantic referent). In these cases, I rest content with arguing, as advanced above, that (uses of) names and demonstratives are not even known by normal competent speakers to be co-referential (let alone semantically equivalent), with strong, truly reference-fixing descriptions of any kind. As noted in chapters 2 and 3, even if the supposition that the objects that demonstratives and names intuitively stand for are their semantic referents turned out to be wrong (which I seriously doubt), the theories of reference fixing of those chapters would presumably have an appropriate version that could supplement in interesting ways the hypothetically right theory of the (weak or trivial)

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18 :    predicative semantic structure of names and demonstratives. Analogous claims hold for other expressions dealt with in the book, such as typical ordinary nouns for natural kinds. The book also doesn’t attempt to contribute to the discussion of the question of whether the reference of an expression (in our Fregean sense of the thing that the expression contributes to truth conditions) exhausts meaning in the focused sense. As made clear in the preview above, the book does heavily incline toward the view that several kinds of expressions have their meanings exhausted by their referents, and several arguments in it imply that the meanings of a number of expressions cannot be constituted, even in part, by certain descriptive contents. But the views in the book are not strictly incompatible with the possibility that there may be, even in the cases where the book rules out certain descriptive contents as parts of meaning, other aspects of meaning that go beyond reference in the sense of truth-conditional contribution. On this general issue, let me just say that I am reasonably certain that the reference of an expression must in general be at the very least the key part of its meaning. It has often been pointed out that reference must play a key role in meaning if meaning (in any reasonable sense) is to have at least many of the characteristics that it is often supposed to have, including its intersubjectivity and independence from idiosyncrasies of individual speakers’ beliefs, its relative stability through time, and its potential materialization for all kinds of expressions.⁶ However, not even the relatively weak thesis that reference must be at least the key constituent of meaning will be defended by means of any general argument in the pages that follow. Even so, the series of proposals we will soon be making amounts to an extended case that the achievement of reference is a crucial driving force in the establishment of linguistic conventions, and in the constitution of the role of language in speakers’ lives.

⁶ Once again, these are all characteristically Fregean themes. We must not forget that Frege after all identified meaning (Bedeutung) with what later would be standardly called “reference” in philosophical English, even if he evidently thought that the specifically semantic contents of expressions went beyond their Bedeutungen (not just because he viewed certain descriptive contents as in some sense part of meaning, but also because of the existence of other conventional connotations of at least many expressions). A succinct but magisterial development of these Fregean themes concerning the relationship between reference and meaning can be found in Higginbotham (2006).

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2 Demonstratives and Conflicting Intentions Introducing Demonstratives Demonstrative pronouns—in English “this” and “that” and their plural forms—are fundamental instruments of linguistic reference. Their fundamentality is manifested in several ways. Some demonstrative pronoun is invariably among the first few words learned by a child (see e.g. Clark (1978); Bloom (2000), 122), and thus among the first instruments of reference that it learns, well before personal pronouns and typically before any proper names. Evidence of a variety of sorts also suggests that demonstrative pronouns are among the first few words to have historically appeared in languages, and that when they appear they typically do not derive from other words (see e.g. Diessel (1999), 150ff. and the references therein). Presumably, these are effects of the fact that a person’s basic communicative needs involve in a preeminent way the possibility of referring to objects in the way in which one typically refers to objects by means of demonstrative pronouns. For the paradigmatic use of a demonstrative pronoun involves reference to a medium-sized physical object that is being distinctly perceived by the speaker at the time of the utterance of the demonstrative pronoun, and for which the speaker has no proper name in her repertoire. (As when a child, looking at a toy out of reach, implores Give me that!, or when a hunter calls a companion’s attention to a deer saying Look at that!) And a person’s basic communicative needs obviously involve in a preeminent way the possibility of referring to medium-sized physical objects that she is simultaneously perceiving. It is no wonder, then, that demonstrative pronouns are among the first words to appear in languages and among the first to be learned by a child. It seems very reasonable to think that in such paradigmatic cases a demonstrative pronoun has as its conventional reference the medium-sized physical object at stake. Now an important part of the literature on demonstratives seeks to argue that demonstrative pronouns are particular cases of

Roads to Reference: An Essay on Reference Fixing in Natural Language. Mario Gómez-Torrente, Oxford University Press (2019). © Mario Gómez-Torrente. DOI: 10.1093/oso/9780198846277.001.0001

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20     complex demonstratives,¹ that Give me that! is semantically equivalent to something like Give me that thing identical to itself! (see Taylor (1980)) or Give me that thing! (see King (2001), ch. 4, or Elbourne (2005), (2008)). If one holds (as at least King does, though Elbourne doesn’t) that complex demonstratives are quantificational phrases that refer in the way characteristic of predicative expressions, this opens the way to holding that the reference of the use of “that” in the utterance of Give me that! is not the toy out of reach, that that use of “that” is semantically equivalent to (a use of ) some description or at any rate to some related quantifier phrase, which is normally thought to have some property or such as its referent. (Elbourne on the other hand thinks that demonstratives are, though descriptive, singular terms that typically refer to ordinary objects.) But a majority of authors (including King; see e.g. King (2014), 234, n. 3) would grant the assumption that some individual object is conventionally talked about in paradigmatic uses of (at least) simple (or bare) demonstratives, independently of their exact semantic or syntactic properties. And at any rate we get no interesting theory of how this object comes to be conventionally talked about if we merely accept that a use of “that” is always semantically equivalent to a use of “that thing” or of “that thing identical to itself.” The question of what makes an object the thing conventionally talked about with a use of a simple demonstrative will still beg for an answer, and it is this answer that we want to attempt to provide here.² In part for these reasons, and in part because the idea that (simple) demonstratives are semantically non-descriptive singular terms that routinely have ordinary objects as referents already has many able defenders in the literature, we will not attempt to defend the idea in this chapter (aside from mentioning Kaplan’s considerations in its favor in the next section), and we will proceed under the assumption that the idea is correct. Words other than those traditionally classified as demonstrative pronouns appear to serve communicative needs essentially similar to the needs served by demonstrative pronouns. Thus, “he,” “she,” “it,” “they,” etc. clearly appear ¹ Complex demonstratives are expressions like “this chair” and “those books over there.” ² One of the reasons for thinking that uses of simple demonstratives are semantically equivalent with uses of complex demonstratives or of determiner phrases tout court is that simple demonstratives appear to have uses as bound variables, which are not clearly referential, and at any rate would not seem to be substantively explainable in terms of a purely referential semantics. (An example of such a use would seem to be Whenever an emergency comes up, the medical team have to handle that.) And simple demonstratives have other somehow anaphoric uses which have been difficult to categorize as either bound variable or referential uses (as in If Jones has an academic degree, he is not using that). But again the question of what fixes the reference of referential uses of simple demonstratives will beg for an answer independently of how we answer the question of how it is that they can work as bound variables or as problematic anaphors.

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to be like demonstrative pronouns in this respect.³ And it is also prima facie reasonable to expect that the conventions governing reference fixing for them will also be similar to the conventions governing reference fixing for demonstrative pronouns. For essentially these reasons, philosophers usually group these and other words together with demonstrative pronouns under the common label “demonstratives.” We will follow this usual practice in our discussion, in which we will almost always abstract from the semantic differences between particular words falling under our label.⁴ The observation that the basic communicative need of referring to simultaneously perceived medium-sized physical objects is well served—indeed paradigmatically well served—by demonstratives must probably be an important ingredient of any explanation of the mechanisms by which uses of demonstratives come to refer—and on the theory that we will favor in this chapter, it is. But it is also easy to observe that a comprehensive theory must account for uses of demonstratives that go beyond the mentioned basic communicative need. For one thing, demonstratives are used in order to refer, apparently in a conventional way, to physical objects that are not medium-sized (This is a doomed planet), to physical objects that are not being simultaneously perceived (as when while pointing to a spot in the map we say That’s a beautiful town), and to objects that are neither evidently physical nor perceived (as when one says That’s what I have to do, right after thinking of a possible way of acting, or when one says So that’s π, right after being introduced to the Leibniz formula for π). And there are many other kinds of examples of uses of demonstratives that go beyond the paradigmatic in some way or other, a good number of which we will come to discuss at some point in this chapter.

Kaplan’s Classical Theories Some of these examples have been thought to cast doubt on what was for some time a widely received attempt at describing the convention governing the

³ And, like demonstrative pronouns, they also appear to be able to work as bound variables (as perhaps in Whenever a policeman gets hurt, he is taken care of by the medical team) and as problematic anaphors (as in the notorious If Jones owns a donkey, he beats it). ⁴ Here are some of these differences: “this” is different from “that” in that “this” conventionally refers (when it does) to an object that is in some sense relatively close to the utterer, while “that” conventionally refers (when it does) to an object that is in some sense relatively far from the utterer; “he,” “she,” and “it” are gendered, while “this” and “that” aren’t; “these” and “those” are plural, while “this” and “that” are singular; and so on.

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22     assignment of reference to a use of a demonstrative, Kaplan’s attempt in his pioneering Demonstratives (Kaplan (1977)). It will be worth our while spending some time studying this attempt. We must recall first of all that Kaplan typically used the word “demonstrative” in an even wider sense than we have, as equivalent with “indexical,” though he made it clear that “demonstrative” was more appropriately used in our stricter sense. In general, an indexical is for Kaplan a word the referent of which varies as a function of the context of use,⁵ and such that “the meaning of the word provides a rule which determines the referent in terms of certain aspects of the context” (Kaplan (1977), 490; my emphasis). There are two notions of meaning involved with indexicals. One is the notion that Kaplan calls “content.” The content of (a use of) an expression, according to Kaplan, is the information it semantically encodes, which in the case of (uses of) an indexical, at least, Kaplan identifies with its contribution to truth conditions, its referent;⁶ in paradigmatic cases this will be an individual object—the toy out of reach, the deer seen by the hunter. The other notion of meaning is what Kaplan calls “character.” A character is a “meaning rule” (Kaplan (1977), 505), or a set of such rules, for an expression, an example

⁵ See e.g. Kaplan ((1977), 513): “it is characteristic of sentences containing demonstratives—or, for that matter, any indexical—that they may express different propositions in different contexts.” ⁶ Strictly speaking, Kaplan officially (though not invariably) postulates that the bearers of reference here are not uses or utterances, but “types” (of demonstratives) in context, something he takes to be required by his project of building a “logic of demonstratives”: Utterances take time, and utterances of distinct sentences cannot be simultaneous (i.e., in the same context). But in order to develop a logic of demonstratives we must be able to evaluate several premises and a conclusion all in the same context. We do not want arguments involving indexicals to become valid simply because there is no possible context in which all the premises are uttered, and thus no possible context in which all are uttered truthfully. (Kaplan (1977), 522) But, however expedient this may be when building a relatively simple formal semantics underpinning a “logic of demonstratives,” one problem is that it is dubious that the postulated theoretical notion of context can have any analog playing a role in the real reference-fixing conventions for demonstratives. It’s just overwhelmingly plausible that these conventions assign reference to particular utterances irrespective of whether they are related to a “context” one of whose defining characteristics is that it may include other utterances made at different times. (Some arguments in the literature that attempt to justify the Kaplanian official choice on grounds other than the convenience for the development of a “logic of demonstratives” strike me as unintuitive. Thus, Braun (1996) argues that a good consequence of the Kaplanian official choice is that it allows for the possibility of assigning contents-in-context to super-long unutterable sentences containing many occurrences of the same demonstrative, and of making true in some context sentences such as I am not talking now (in a context in which the person designated as the agent is not talking). To me, these abstruse results may seem like appropriate consequences only if one is in the grip of the mentioned theoretically charged notion of context. Also, for a convincing defense of the idea that the Kaplanian choice is not forced even as regards the logical question, see García-Carpintero (1998).) For our purposes we can proceed as if Kaplan had taken uses (or utterances) to be the bearers of demonstrative reference (as he sometimes actually does, e.g. in many of the texts we are about to cite). This is the most natural and most widely adopted choice, presumably to a large extent because it doesn’t presuppose a theoretically loaded notion of context.

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being “the rule, ‘“I” refers to the speaker or writer’” (Kaplan (1977), 505), a rule which determines the expression’s content in particular contexts: The character of an expression is set by linguistic conventions and, in turn, determines the content of the expression in every context. Because character is what is set by linguistic conventions, it is natural to think of it as meaning in the sense of what is known by the competent language user. (Kaplan (1977), 505)⁷

It’s this second notion of meaning, under which character falls, that is involved in the quotation where I emphasized “meaning” above. Kaplan’s distinction between these two notions of meaning corresponds to the distinction between two notions of semantic competence that we mentioned in chapter 1 (and to which we will turn again in our discussion of descriptivism about names in chapter 3): a restrictive notion of semantic competence involving knowledge of facts about information semantically expressed by expressions (including primordially truth-conditional information), and a notion of semantic competence about other aspects established by linguistic conventions, including in particular conventions about reference fixing. Kaplan contrasted demonstratives in the strict sense, or “true demonstratives,” with “pure indexicals.” “Pure indexicals,” such as “I,” “now,” and “today,” are words such that “the linguistic rules which govern their use fully determine the referent for each context” (Kaplan (1977), 491). In the case of “I,” the full set of linguistic rules governing their use, which are part of its meaning according to Kaplan, are these: (Dl) ‘I’ is an indexical, different utterances of which may have different contents; (D3) ‘I’ is, in each of its utterances, directly referential; (D2) In each of its utterances, ‘I’ refers to the person who utters it. (Kaplan (1977), 520)⁸

Here (D3) makes explicit a convention detected by Kaplan as governing “I”: that an utterance of “I” is directly referential means roughly that it is not semantically equivalent with a complex expression, and its truth-conditional ⁷ Again for reasons having to do with his interest in developing a “logic of demonstratives,” Kaplan says that “it is convenient to represent characters by functions from possible contexts to contents,” and sometimes these set-theoretical functions are called “characters” in a derivative sense. ⁸ As in all cases where a convention or conventional rule is merely implicit, different explicitations of the convention at work may be recognized as appropriate by different speakers (or even by a single speaker) when they consider the question reflectively. Strictly speaking, the thesis put forward by Kaplan is probably that (D1)–(D3) are good representative explicitations.

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24     content is constituted by its referent. Kaplan argues for this noting that an utterance by me of “I” is not semantically equivalent with an utterance by me of “the utterer here and now.” As Kaplan notes (following the lead of the analogous observations made by Kripke (1972) about proper names that we will review in chapter 3), if they were semantically equivalent then I am the utterer here and now would express a necessary truth as uttered by me; but it does not: I could have failed to utter anything here and now seems clearly true. Also, “I” seems rigid while “the utterer here and now” clearly isn’t: The thing that I am could not have existed without being I (and no other thing could have been I) seems intuitively true, while The thing that is the utterer here and now could not have existed without being the utterer here and now (and no other thing could have been the utterer here and now) is intuitively false.⁹ So it is not by being semantically equivalent with a description of this sort that an utterance of “I” refers (and Kaplan actually postulates that an utterance of “I” does not refer in virtue of being equivalent with a description, of any sort). Nevertheless, the additional rule (D2), which is the main part of the character of “I,” fully determines the referent of “I” for each context as the utterer of the context (without requiring that the rule itself is somehow part of the semantic structure of (an utterance of) “I”), and this rule is still part of the meaning of “I.” So if Kaplan’s picture for “I” is correct, a certain kind of pretty strong descriptivism holds for “I” (and presumably for other “pure indexicals”): an utterance of “I” refers to the person who utters it, where this description codifies (the basic part of) the character of “I,” and must thus be associated with it by a normal competent speaker (even though, as noted, this description is not semantically equivalent with “I”).¹⁰ “True demonstratives” such as “this,” “that,” “he,” and “she,” on the other hand, are words such that something else besides “the linguistic rules which govern their use” must be provided in order for a use of one of them to be endowed with a referent in a context. But only a slightly more complicated kind of descriptivism holds for them. Kaplan (1977) specifically proposed that these words “require, in order to determine their referents, an associated demonstration: typically, though not invariably, a (visual) presentation of a local object discriminated by a pointing” (Kaplan (1977), 490). Kaplan then ⁹ I have applied what Soames (2002) calls the “linguistic test” for rigidity of noun phrases. All other standard tests for rigidity would deliver the same verdict. ¹⁰ The story with other “pure indexicals” is perhaps more complicated, due to a number of phenomena, such as vagueness (will it always be completely clear what time period is the referent of a use of “now”—a second, an hour, a day, a century?). But descriptivist theses seem plausible broadly speaking in these cases as well: however vague this may be, it seems the referent of a use of “now” must be “the time of the use.”

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gave what he in effect postulated as necessary and sufficient conditions for a use of a (true) demonstrative d to have a certain object as referent in a context: “In any context c, d[δ] is a directly referential term that designates the demonstratum, if any, of δ in c, and that otherwise designates nothing” (Kaplan (1977), 527). Here, “d[δ]” stands for the demonstrative “accompanied” by a demonstration δ, and the “demonstratum” of a demonstration is the object determined by it. So Kaplan, at least in 1977, held a pretty strong descriptivist view about demonstratives: an utterance of a demonstrative refers, as we might put it, to “the demonstratum, if any, of the demonstration that accompanies the utterance in the context in which it is made,” where this description codifies (the basic part of) the character of a demonstrative, and must thus be associated with it by a normal competent speaker. Again this doesn’t mean that the description is semantically equivalent with the demonstrative: true demonstratives are also postulated by Kaplan to be “directly referential.” In particular, for example, an utterance of “that” is not semantically equivalent with an utterance of “the thing presently demonstrated” (or with any utterance of any other description). If they were semantically equivalent then That is the thing presently demonstrated would express a necessary truth whenever uttered, but it does not: That could have failed to be the thing presently demonstrated will typically seem true. And “that” seems rigid while “the thing presently demonstrated” clearly isn’t: The thing that is that could not have existed without being that (and no other thing could have been that) seems intuitively true, while The thing that is the thing presently demonstrated could not have existed without being the thing presently demonstrated (and no other thing could have been the thing presently demonstrated) is intuitively false. It is not uncommon to find many sorts of objections to Kaplan’s (1977) theory, though it is not entirely clear that all of them really cast strong doubts on the theory. Perhaps the most frequent objection is that there are uses of demonstratives which appear to be referentially successful but which are not accompanied by any demonstration (see e.g. King (2013), 289; Speaks (2017), 716). One kind of example that is normally given in this context is one of a person who is especially salient for some reason, e.g. because he is the only person shouting; in such a situation, one can say Get him out of here without doing anything special and still apparently successfully refer to the shouting guy with “him.” But it is unclear that no demonstration in Kaplan’s sense accompanies this use of “him”; the fact that the shouting guy is especially salient generates an accompanying demonstration in Kaplan’s sense—some presentation of the object. Kaplan is quite clear that

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26     a demonstration may . . . be opportune and require no special action on the speaker’s part, as when someone shouts ‘Stop that man’ while only one man is rushing toward the door. My notion of a demonstration is a theoretical concept. (Kaplan (1977), 490, n. 9)

Another objection to Kaplan’s demonstration theory that seems equally dubious is that the theory fails to account for cases of deferred reference, such as the case where we point to a spot in the map and say That’s a beautiful town. For it is unclear why pointing to the spot in the map is not to count as a demonstration of the town. Nevertheless, Kaplan himself comes to reject his necessary and sufficient conditions for demonstrative reference in his “Afterthoughts” (Kaplan (1989)), on what seem to be more substantive grounds. According to Kaplan (1989), a demonstration in his sense may fail to determine an object, or determine one that is different from the object that is in the “perceptual focus” of the user of a demonstrative, while the latter object will intuitively be the demonstrative’s referent. In his example, inspired by a famous example that Donnellan (1966) used for a different purpose, two people are at a party and, seeing an interesting-looking man who appears to be drinking a martini, one asks the other Who is that (the man with the martini)? According to Kaplan, his conditions determine no one as the referent of “that” in that utterance if the interesting-looking man is not drinking a martini, and yet “that” intuitively has the interesting-looking man as its referent. This is because the demonstration in this case is roughly the appositive utterance of the description “the man with the martini,” which according to Kaplan determines no one if the interesting-looking man is not drinking a martini,¹¹ and yet the interesting-looking man is in the “perceptual focus” of the utterer—he is the object the utterer is currently perceiving that she intends to talk about. Kaplan’s objection to his own early theory is related to another objection that one finds in the later literature, the objection that demonstrations, in any relevant sense of “demonstration,” often or sometimes would seem to demonstrate more than one thing, even in cases where it would appear that a single

¹¹ Kaplan assumes here that the appositive utterance is linguistically segregated from the main utterance, certainly semantically, but presumably syntactically as well. Otherwise he would be forced to assign a failure of reference to the use of “that” in the unified utterance. In this he is in line with what seems to be the dominant view in studies of appositives (and parentheticals in general) in syntax and pragmatics. (See Espinal (1991), Peterson (1998), and Potts (2005) for survey information and views along these lines.)

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thing is somehow singled out as the referent (see e.g. Kaplan (1978) and Reimer (1992)). A visual presentation of a man, even one accompanied by a pointing, will present not just the man, but also his shirt, say, which will also be pointed at by the pointing. Considerations of this sort lead Kaplan (1989) to regard the directing intention, at least in the case of perceptual demonstratives, as criterial [for determining the referent of a demonstrative], and to regard the demonstration as a mere externalization of this inner intention. The externalization is an aid to communication, like speaking more slowly and loudly, but is of no semantic significance. (Kaplan (1989), 582)

On Kaplan’s new view, the interesting-looking man at the party is the referent of the relevant utterance of “that,” because he is the concurrently perceived object the utterer intends to refer to, and because this intention then “directs” the production of the (failed) descriptive demonstration (the utterance of the appositive “(the man with the martini)”). Something analogous happens with the man that one intends to refer to while pointing both to him and his shirt. Note however that Kaplan does not now propose a theory of jointly necessary and sufficient conditions for an utterance of a demonstrative to refer to an object, let alone one known by a normal competent speaker. He appears merely to commit himself to the claim that “in the case of perceptual demonstratives” the thing perceived and intended is the referent of a concurrent utterance of a demonstrative, because it is the object of the “directing intention.” He now has no proposal of a description that will in all cases be co-referential with an utterance of a demonstrative, let alone one associated with such an utterance by a normal competent speaker. Nevertheless, this has not deterred other writers in Kaplan’s wake from attempting to find a description of this kind. But, as we are about to see, the search has turned out to be an unexpectedly complicated enterprise.

The Search for Descriptivist Conditions for Demonstrative Reference Assuming that there must be an appropriate description which fixes the reference of a communicative use or utterance of a demonstrative and which is part of its meaning (in the second Kaplanian sense of “meaning”), where should we begin to look for it? It seems safe to say that the vast majority of

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28     theorists of demonstratives nowadays accept that referential intentions must play a key role in a correct theory of the determination of reference for demonstratives. The possibility that some “aspect of the context” (to use Kaplan’s phrase) that does not involve speaker intentions somehow can be the determining factor in reference fixing seems now considerably unlikely. One way in which this idea can be supported is by noting the problems with an alternative to the demonstration theory, the theory that what makes something the referent of a demonstrative is some fact about its special salience in the context of utterance—a view associated with Wettstein (1984) and Mount (2008). On Mount’s theory, salience is not some objective feature that can be determined independently of the mental states of conversational participants; it is essentially a minddependent matter. An object is mutually recognized as maximally salient by conversational participants when all interlocutors have focused their attention on it, and are aware that they have all focused their attention on it. Thus my claim is that a demonstrative refers to the object mutually recognized as maximally salient. When there is no such object, the demonstrative does not refer. (Mount (2008), 154–5; my emphasis)

This has the immediate problem that in many cases an object will be mutually recognized as maximally salient by a conversation’s interlocutors, and yet it will not be the referent of a demonstrative in the context. To use an example with several variants in the literature, if you and I get trapped in a zoo cage with a crocodile, the crocodile will be recognized as maximally salient by both of us. And yet, I will be able to refer to other things in the context by means of demonstratives. I can say This is a pretty bad situation and apparently get “this” to refer to our dangerous situation. The salience theorist might perhaps claim that somehow my utterance raises the salience of the situation so as to make it mutually recognized as maximally salient. This seems ad hoc, as it appears to stretch excessively the normal understanding one would have of “maximally salient.” But in any case, even if we grant that our abstract situation becomes maximally salient instead of the crocodile, it does not seem that salience is ultimately what can explain or determine the reference of my use of “this,” as presumably “this” will come out of my mouth already with a reference, before our situation is raised to (mutually recognized) maximal salience. (Couldn’t you have passed out just before I completed my utterance, and wouldn’t then our situation still be the referent of my use of “this”?) Everything points to my intention to refer to our situation as the

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determinant of reference for “this” (even if it can also determine the momentary (mutually recognized) salience of our abstract situation). Assuming, with most theorists, that referential intentions must play a key role in a correct theory of the determination of reference for demonstratives, we must wonder what exactly this role is. One simple possibility would be that the relevant reference-fixing convention were this: (Simple Intention) A use of a demonstrative refers to an object o iff o is the thing that the utterer intends to refer to with his/her use. Before we evaluate this, let me say that, along with other authors in the literature on demonstratives, I will assume that an utterer can intend to refer to an object with a demonstrative via a variety of different kinds of representations for the intended object in her intention. An utterer can intend to refer with a demonstrative to the single object having a certain property, in which case her intention will involve a descriptive representation (purportedly of an object). (When the utterer intends to refer to the single object with a certain property, we will speak of such a referential intention as a “descriptive referential intention.”) An utterer can intend to refer to an object by intending to refer to it as (apparently) represented by an (apparent) perception she is having of the object. (When the utterer intends to refer to an object as apparently represented by a perception she is apparently having of the object, we will speak of such an intention to refer to the object as a “perceptual referential intention” (to refer to the object).) An utterer can intend to refer to an object by intending to refer to it as (apparently) represented by an (apparent) memory she is (apparently) having of the object. (In such cases we will speak of such an intention to refer to the object as a “memorial referential intention” (to refer to the object).) And there are other ways in which a speaker can intend to refer to an object with a demonstrative via an apparent representation of the object in his or her intention.¹²

¹² Note that some of the representations involved in referential intentions are fully non-linguistic mental representations: perceptions (whether veridical or merely purported), memories of an imagistic sort (whether veridical or falsidical), etc. This presupposes that at least in some cases, some kinds of non-linguistic mental representation precede and play a role in the determination of conventional linguistic representation, or in the determination of failures of conventional linguistic representation (e.g. in some cases where purported perceptions or memories are in fact falsidical). I take the possibility of non-linguistic mental representation, as well as some very basic and intuitive characteristics of it presupposed here, to be nearly uncontroversial and compatible with a wide variety of theories of the mind. Unfortunately, while it would be desirable to say more in general about the mechanisms of nonlinguistic mental representation here, space limitations and the need to keep our discussion within a relatively narrow focus will prevent a fuller consideration of this topic.

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30     The Simple Intention theory certainly takes care of the This is a pretty bad situation example. Now one objection to the theory is that it makes it possible for a speaker to refer to an object by means of a demonstrative without the speaker being appropriately cooperative in communication. King (2014) develops the objection as follows: the intention account seems very strained in cases in which a speaker has the relevant intention but mounts either a poor demonstration or no demonstration. For example, suppose I am sitting on Venice beach on a crowded holiday looking south. Hundreds if not thousands of people are in sight. I fix my attention on a woman in the distance and, intending to talk about her and gesturing vaguely to the south, say ‘She is athletic.’ You, of course, have no idea who I am talking about. It seems quite implausible in such a case to say that I succeeded in securing the woman in question as the value of my demonstrative simply because I was perceiving her, and intending to talk about her. (King (2014), 223)

(See Reimer (1991) for related examples and considerations.) And the speaker may not just fail to mount a demonstration or a good demonstration. She may mount a positively misleading demonstration, even of an object she is perceiving very clearly. (See e.g. “Case 3” of Perry (2009), 190.) In view of this objection, King has developed a theory that adds to the condition in Simple Intention a requirement that the utterer make it possible for her audience to know what the referent of her use of a demonstrative is. But this seems too much to ask. As Speaks (2016) notes, using an example from Eliot Michaelson, there are cases where the utterer doesn’t make it possible for her audience to know what the referent of her use of a demonstrative is, and yet there is no intuition that there has been a failure to refer by means of the relevant demonstrative: Imagine that we are sitting on a couch in my house, and I think I see something quite surprising—like a bird quickly flying past the doorway. You do not flinch, so I am almost sure that you did not see what I think I saw. But, to be sure, I might ask you: ‘Did you see that?’ Supposing that a bird really did fly past the doorway, it seems clear that my use of ‘that’ here succeeds in referring to the bird. But did I do anything to make that referential intention clear to you? It seems pretty clear that I did not. And, indeed, we can suppose that this fact is clear to me, or would have been after a moment’s reflection—after all, I do not suppose you to be so implacable as

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to just sit there while you saw a bird flew past. None of these suppositions makes it any less plausible that my demonstrative had the bird as its semantic value. (Speaks (2016), 328)

Speaks also sensibly observes that it may well be that any impression that there is reference failure in King’s beach example and similar examples may be due precisely to an impression that the speaker has not done as much as he could to make his audience know what the referent of his demonstrative is, but not necessarily to a fact that there has been actual reference failure. Speaks reports a remark of Robert Stalnaker to the effect that this possibility cannot be excluded. Applying a well-known test from Kripke (1977), we can imagine a population speaking a version of English in which the working convention is (perhaps by explicit stipulation) that a use of a demonstrative refers to an object o iff o is the thing that the utterer intends to refer to with his/her use. In such a language, a use of “she” by an utterer of She is athletic in the circumstance described by King will conventionally refer to the woman, but the utterance will still generate a sense of inappropriateness, traceable to the failure of the utterer to make his referential intention clear, and certainly not to a failure of reference.¹³ There is an old problem identified by Kaplan as early as 1978, recently and appropriately called “the problem of conflicting intentions” by both King (2013) and Speaks (2016), a problem that every theory of the determination of reference for demonstratives must deal with. We will later come back to the sort of example originally used by Kaplan, but the problem can perhaps be initially illustrated in a most effective form with examples of the following sort. Imagine that I am sitting in my study, with my eyes closed, and it seems to me that I remember reading about a man who wrote the Iliad and also conquered Persia as king of Macedon. Then I say, intending to refer to the Greek king who conquered Persia and also intending to refer to the author of the Iliad, That was the king I read in my literature class. Now of course I am quite confused, because my two descriptive referential intentions determine different objects—Homer (let’s suppose) and Alexander. The Simple Intention theory deals with this case in a way that doesn’t seem inappropriate, at least at first sight: the theory (together with the circumstances of the utterance) implies that in this example the demonstrative does not refer, as there is no ¹³ Bach (ms.) similarly notes that the sense of inappropriateness generated by King’s examples could in principle be argued to have a pragmatic source by defenders of something like the Simple Intention theory. (He nevertheless argues for a strongly skeptical view on which (uses of ) demonstratives simply fail to have conventional referents; see note 22 below.)

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32     single object that I intend to refer to with my use of “that.”¹⁴ And, indeed, it may conceivably be that the relevant conventions operating in this case imply that my use of “that” fails to have a referent, perhaps due to some specific aspect of the nature and magnitude of the conflict involved.¹⁵ Unfortunately, the Simple Intention theory appears to deliver clearly wrong results in other cases of conflicting intentions. Imagine that you and I are looking out of my office window, watching some students play soccer in the field just beneath my office building. One of the students, the only one wearing a yellow shirt, is obviously much more gifted than the others; I also think he is the bright student who always asks the pertinent questions in my philosophy of language class. Pointing to the gifted soccer player in the yellow shirt, I say That’s a really good player, intending to refer to the guy I’m pointing at as represented by my very perception of him, and also intending to refer to the bright philosophy of language student as represented by the very description “the bright philosophy of language student.” But the guy in the yellow shirt turns out not to be the bright philosophy of language student. So according to the Simple Intention theory my use of “that” did not have a reference. But it seems pretty clear that the referent in this case is the student in the yellow shirt. In view of this, a possibility that immediately suggests itself is to avoid somehow the unique referential intention requirement of the Simple Intention theory and to propose that whenever there is demonstrative reference and conflicting intentions, there is some condition taking place that makes one referential intention override the others. But it turns out to be very difficult to think of what could be the condition that by obtaining makes one referential intention override the others. One idea is that, as in the classical Kaplanian theory, demonstrations (in some sense or other) play a role. For example, the following might be proposed: (Intention + Overriding Demonstration) A use of a demonstrative refers to an object o iff o is the x such that either 1. x is the single thing that the utterer intends to refer to with his/her use or, 2. in cases of conflicting referential ¹⁴ This will be so at least under the assumption that Homer is the thing that the utterer intends to refer to with his use of “that,” Alexander is the thing that the utterer intends to refer to with his use of “that,” etc. are all false. If we take them to be truth-valueless, then the theory will at least fail to imply that my use of “that” refers to anything. ¹⁵ Note that Kaplan’s example of the utterance of Who is that (the man with the martini)? is also an example involving conflicting referential intentions. The utterer has both the intention to refer to the man as represented by her perception of him and the intention to refer to an object as (purportedly) represented by the description “the man with the martini.” In Kaplan’s (1989) theory, however, only the first, perceptual intention is criterial for reference fixing, as it is the intention that “directs” the production of the (descriptive) demonstration.

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intentions, one of the referential intentions is to refer to x as represented by a description of the form of “the object with such and such properties that I am F’ing” (where in place of “F’ing” goes some verb for an action falling under the notion of demonstrating (in Kaplan’s broad sense, for definiteness)), and no other referential intention has this property. (This is essentially the proposal of Reimer (1992).) The Intention + Overriding Demonstration theory yields the desired result in the example of the gifted soccer player in the yellow shirt, we can suppose. (We can suppose, that is, that my perceptual referential intention goes hand in hand with a descriptive referential intention such as the intention to refer to “the guy I’m pointing at.”) But it is not difficult to find examples, related to the examples that caused problems for Kaplan’s early demonstration theory, that seem to refute the Intention + Overriding Demonstration theory. Suppose again that two people are at a party and, seeing an interesting-looking man who appears to be drinking a martini, one asks the other Who is that (the man with the martini)? But suppose that this utterer has both the intention to refer to the man as purportedly represented by the description “the guy I’m describing (as the man with the martini),” and the intention to refer to the man as represented by her concurrent perception of him (a referential intention not involving a notion of demonstration in any way). The Intention + Overriding Demonstration theory implies that the use of “that” does not refer to anything if there is no man with a martini, as the utterer will then not be describing anyone; but intuitively it does refer to the interesting-looking man. Also, in a case where the utterer has an intention to refer to an object as represented by the description “the object I’m pointing at,” but she is pointing at not just the man, but also his shirt, the Intention + Overriding Demonstration theory implies that an appropriate concurrent use of “that” does not refer to anything; but intuitively it may refer to the man, say, if he is in the “perceptual focus” of the utterer and she has an intention to refer to him as represented by a perception she has of him. A different possibility is considered by Speaks (2017) on behalf of salience theorists like Mount. The idea is that the overriding intention is one that determines an object that turns out to be maximally salient (to all conversational participants). Adapting the idea to the framework of our discussion, we might formulate a version as follows: (Intention + Overriding Salience) A use of a demonstrative refers to an object o iff o is the x such that either 1. x is the single thing that the utterer intends to

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34     refer to with his/her use or, 2. in cases of conflicting referential intentions, x is the thing determined by an intention of the utterer that is recognized as maximally salient by all conversational participants. This may well give the desired results in the examples of the preceding paragraph, for the man (as opposed to his shirt) and the interesting-looking man (as opposed to nothing) may somehow be made maximally salient, concurrently with the intentions of the utterers that determine them. But the theory has other obvious problems, again along the lines of the problems for the simpler “non-intentional” salience theory. As before, it would again seem that, in the interesting-looking man example, say, salience is not what fixes the reference of the use of “that,” as presumably “that” will come out of the utterer’s mouth already with a reference, before the man is raised to (mutually recognized) maximal salience. And there will also be cases where two conflicting referential intentions are accompanied by circumstances that make equally salient two corresponding objects (in which case the Intention + Overriding Salience theory will imply that no reference is fixed for the demonstrative) and yet only one of the objects will be the intuitive referent. For example, imagine that I am looking at an interesting-looking man holding a martini glass, with both the intention to refer to the interesting-looking man I’m looking at right now and to refer to the man with the martini; but suppose also that the man is next to his twin brother, who is drinking a martini. Presumably the two brothers are equally salient in the situation—they may even seem equally salient to me—and yet my demonstrative intuitively refers to the non-martini-drinking brother I’m focusing on if I utter That is an interesting-looking man.¹⁶ A further theoretical possibility is offered (though not determinately favored) by King (2013). The idea here is that the overriding intention is the one that is somehow last in a chain of referential intentions in which one intention explains and leads to the next, and in such a way that the last

¹⁶ Speaks (2017) offers another kind of alleged counterexample to the Intention + Overriding Salience theory: “You and I are having a conversation while jointly experiencing a quite convincing mutual hallucination of your cat Fluffy. Pointing at what I take to be the Fluffy, I say ‘That cat . . . ’ ” (727). The conflicting intentions here are the intention to refer to Fluffy (as represented by a memory of Fluffy) and the intention to refer to an object as (purportedly) represented by the description “the cat I’m pointing at” (which does not determine anything). The Intention + Overriding Salience theory implies that Speaks’s use of “that cat” refers to Fluffy, as one of his referential intentions determines Fluffy, and Fluffy is salient, but no other referential intention of his determines any other object; but, claims Speaks, his use of “that” is conventionally determined to lack a reference. I don’t share Speaks’s intuition here; to me, it is unclear whether his demonstrative refers to Fluffy or not. We will come back to examples of this sort in the final section of this chapter.

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intention is somehow closest to and explanatory of the production of the utterance. King speaks of this last intention as a “means for executing the others,” and calls it “the controlling intention.” Thus, for example, in the case of the gifted soccer player in the yellow shirt, while I may have the intention to refer to the bright philosophy of language student as represented by the very description “the bright philosophy of language student,” it is my intention to refer to the guy I’m pointing at as represented by my very perception of him that stands in a closest explanatory relation to the production of my utterance (in particular to my concurrent act of pointing), and that is therefore the overriding referential intention. One way of formulating this idea is as follows: (Intention + Overriding Control) A use of a demonstrative refers to an object o iff o is the x such that either 1. x is the single thing that the utterer intends to refer to with his/her use or, 2. in cases of conflicting referential intentions, x is determined by the intention that stands closest in explanatory terms to the production of the use. (If we abstract from his requirement that the utterer make it possible for her audience to know what the referent of her use of a demonstrative is, this is essentially the second theory of King (2013).) Unfortunately, this theory again clearly seems to propose as necessary a condition which is not in fact required for demonstrative reference in cases of conflicting intentions. Go back to the example of the interesting-looking man who appears to be drinking a martini, and suppose again that the utterer of Who is that (the man with the martini)? has both the intention to refer to the man as purportedly represented by the description “the guy I’m describing (as the man with the martini),” and the intention to refer to the man as represented by her concurrent perception of him. Presumably the first intention is the controlling intention in King’s sense, the intention closest in explanatory terms to the production of the use of “that” (which is in fact followed by the appositive use of “the man with the martini”), and we can at any rate build the case so that it just is the controlling intention. But the Intention + Overriding Control theory implies that the use of “that” does not refer to anything, and yet intuitively it does refer to the interestinglooking man.¹⁷

¹⁷ See Speaks (2017) for more considerations on and counterexamples to the Intention + Overriding Control theory.

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36    

Referential Indeterminacy as a Fundamental Problem for the Descriptivist Project One doesn’t have to reflect too hard or for too long on the problems of these theories of overriding intentions to come to the conclusion that there is a clear pattern to the fundamental counterexamples. In all of them a proposed necessary condition for demonstrative reference in cases of conflicting intentions is shown not to be in fact such; and, furthermore, it is shown that the condition in question is not necessitated by a condition that appears to be sufficient—the condition that the object referred to is the only thing intended via a referential intention that represents its object by the utterer’s concurrent perception of it. And yet this latter condition is evidently not necessary for demonstrative reference, even in cases of conflicting intentions. For it is plausible to accept that there is both straight and deferred demonstrative reference to objects that are not concurrently represented in the utterer’s perception, as noted earlier in this chapter, including cases of conflicting referential intentions. Recall the example uses of This is a doomed planet, That’s a beautiful town, and So that’s π, and for a relevantly similar example involving conflicting referential intentions, think of the following. After thinking carefully about possible courses of action I say That’s what I have to do, both with the intention to refer to my donating 1,000 dollars to my friend John’s organization as represented by this very description (“my donating 1,000 dollars to my friend John’s organization”) and with the intention to refer to my donating 1,000 dollars to the most effective charity NGO in town as represented by this very description (“my donating 1,000 dollars to the most effective charity NGO in town”); then my use of “that” will intuitively be referring to my donating 1,000 dollars to John’s organization, even if the organization in question is a fraudulent scheme having nothing to do with charity.¹⁸

¹⁸ A referee has noted that the preceding discussion of the effect of the existence of conflicting intentions on events or non-events of conventional or semantic reference evokes a number of themes in the philosophy of action. However, it is perhaps important to note some points of disconnection as well. Events of conventional or semantic reference are intuitively not actions of individual utterers, even if they may come about in part through actions of utterers, including acts of personal reference. That a use of “that” conventionally refers to a toy out of reach is not something that the child does, even if it can be said of the child that it refers to the toy with its utterance of “that,” which comes to conventionally refer to the toy as a result. A sign of this is that a use of “that” conventionally referring to some thing is not something automatically frustrated by the conflict in the intervening referential intentions, while conflicts in intervening intentions automatically frustrate or prevent rational action on most theories of action. (See, e.g., Bratman (1987).) The existence of the relevant conflicting referential intentions is compatible with the constitution of appropriate events of conventional reference, presumably because the conventions at stake determine that, at least in some cases, some referential intentions override others.

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The pattern raises a strong worry that a theory of jointly necessary and sufficient conditions for demonstrative reference in terms of overriding intentions may not be possible, let alone a theory in which such conditions are known by normal competent speakers. A theory of this kind certainly seems what is needed in view of the failure of the Simple Intention theory, at least if we want to pursue Kaplan’s project (the early Kaplan’s project, that is) of finding a description giving the character of a demonstrative—a description fixing the referent of an arbitrary use of a demonstrative (and failing to describe anything if the use has no referent) and associated with the use by a normal competent speaker (without being semantically equivalent with it). But the Kaplanian descriptivist project may just be unfeasible, in view of the counterexamples. If it is unfeasible, what would this mean for the broader, theory-neutral project of giving a theory of the conventional rules governing the reference of uses of demonstratives? In a significant and revealing paper, Speaks (2017) has argued that if the Kaplanian descriptivist project¹⁹ cannot be satisfactorily brought to completion, then a fundamental difficulty for semantic theorizing arises. It will be important for us to follow Speaks’s argument as closely as possible. Speaks notes that our knowledge of the contents of uses of simple indexicals clearly seems to be systematic and productive in some sense. In what sense is it productive, and why is it productive? Speaks says that in the same way that we know the contents of complex expressions we have never seen on the basis of our knowledge of the contents of their simpler component expressions, we know without any problem the contents of new indexical/context pairs, such as the contents of new uses of “I” by people we have never met; and the same holds for “true demonstratives”: Nor is ‘I’ at all special in this respect. . . . I have encountered the simple demonstratives ‘this’ and ‘that’ as used in any number of contexts. And yet the fact that I have never before encountered ‘this’ as used in some particular context is no bar to me figuring out what the content of ‘this’ is in that context. (Speaks (2017), 713; my emphasis)

In what sense is our knowledge of the contents of uses of simple indexicals systematic, and why is it systematic? According to Speaks, knowledge of the contents of uses of simple indexicals is systematic in the sense that if a competent speaker is able to figure out the content of one indexical in a ¹⁹ Speaks doesn’t call the project “the Kaplanian descriptivist project.”

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38     context, and also the content of another indexical in another context, then that speaker will also be able to figure out the content of the former indexical in the latter context, and the other way around. Speaks also says that if one assumes that the best explanation of the systematicity of the competent speaker’s knowledge of the contents of complex expressions in general must be provided by her grasp of a compositional theory of content, then the best explanation of the systematicity of the competent speaker’s knowledge of the contents of indexical/context pairs must be provided by an analogous, appropriately compositional theory for demonstratives. But the completion of the Kaplanian descriptivist project seems required if we are to formulate a compositional semantic theory of demonstratives that appropriately explains phenomena such as the systematicity and productivity of our linguistic competence involving demonstratives: Let’s say that a theory of character is an assignment of characters to all of the simple expressions of the language. Then . . . we can say that a theory of character is adequate if it entails, for any context, a true claim about the content of each indexical in that context, and internalizable just in case grasp of the theory could plausibly explain our knowledge of the contents of the relevant indexicals in contexts. Given these definitions, we can consider the following two principles: [S&P+] Our knowledge of the contents of simple indexicals of English in contexts is systematic and productive. [C+] If our knowledge of the contents of simple indexicals of English in contexts is productive and systematic, then there is a theory of character for English which is both adequate and internalizable. (Speaks (2017), 714)

Speaks then argues that the principles [S&P+] and [C+] are true. But note what the principles say or imply. An adequate theory of character is nothing less than an assignment of a reference-fixing description to every indexical in such a way that a use of the indexical refers to an object o just in case o is the single object satisfied by the assigned description. If there is such a single object, then the theory of character will imply, together with the relevant circumstances of the utterance, that that object is the referent of the use of the indexical. If there is no such single object, then the theory of character will imply, together with the relevant circumstances of the utterance, that the use has no referent. And if an adequate theory of character is internalizable, then

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this basically means that the assigned description is somehow known by normal competent speakers. [S&P+] and [C+] thus imply that an assignment of a reference-fixing description known by normal competent speakers to every indexical must be possible, i.e. that the Kaplanian descriptivist project must be able to be carried to completion. But Speaks argues, going through much the same terrain that we went through in the preceding section, that there seem to be great obstacles in the way to the completion of the project, and hence that an important difficulty for semantic theorizing arises. Speaks hopes that the resolution of the difficulty will come from a so far undetected theory of overriding intentions that will provide jointly necessary and sufficient conditions for demonstrative reference which are at the same time known by normal competent speakers, and hence that will also provide a descriptive character for demonstratives along Kaplan’s lines. I want to suggest, by contrast, that the correct way out of Speaks’s puzzle is probably to acknowledge that the Kaplanian descriptivist project cannot be successfully carried to completion—there is just no realistic hope of finding a theory of jointly necessary and sufficient conditions for demonstrative reference that will at the same time be known by normal competent speakers. Despite the extended implicit assumption that in the case of demonstratives descriptivism ought to fare better than in the case of proper names, the assumption is probably false. However, this will not mean that an appropriate theory of reference fixing for demonstratives should be unable to explain the phenomena of the productivity and systematicity of our knowledge of the contents of demonstratives, properly understood. Let me explain first why I think that there is no realistic hope of finding a descriptivist theory of demonstrative reference known by normal competent speakers. The basic problem is that a descriptivist project cannot give an account of knowledge of reference-fixing conventions that can provide an appropriate fit for the phenomenon of (apparent) referential indeterminacy for uses of demonstratives. Let me first argue for the apparent existence of indeterminacy, after which I will come back to Speaks’s difficulty. Perhaps the best way to introduce the phenomenon is via the promised standard illustration of the problem of conflicting intentions, (a slight variant of) an example from Kaplan (1978): Kaplan, “without turning and looking,” points to the place on his wall which has long been occupied by a picture of Rudolf Carnap and says That is a picture of one of the greatest philosophers of the twentieth century. But unbeknownst to him, someone has replaced his picture of Carnap with one of Spiro Agnew. (See Kaplan (1978), 239.) In a clear sense, Kaplan has at least two different referential intentions when he

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40     says what he says. He has the intention to refer to the picture which has long occupied his wall, the picture of Carnap, and he also intends to refer to the picture behind his back that he is pointing at. He of course has these two intentions in part because he assumes tacitly that they determine the same object, the same picture; but of course they don’t. Now what is the “true claim” (to use Speaks’s expression) about the content of the use of “that” in Kaplan’s utterance of That is a picture of one of the greatest philosophers of the twentieth century? Kaplan (1978) says that the reference of “that” in the utterance must be the picture of Agnew, but my impression is that it is unclear whether that use refers to the picture of Agnew, to the picture of Carnap, or else lacks a reference: as far as I can tell, it is unclear whether the conventions determining reference or reference failure for uses of “that” imply that that use has a particular picture as its reference, or that it lacks a reference. I also take this unclarity to be a prima facie indicator that the matter may be left indeterminate by the conventions fixing the reference of demonstratives or determining when they fail to refer. As far as I can tell, this uncertainty is not clearly exhibited by anyone in the literature I am aware of—though Kaplan (1989) may be pointing to uncertainty when he says “I now regard this [the Carnap/Agnew example] as a rather complex, atypical case” (Kaplan (1989), 582, n. 34), suggesting that his later view is that the truth about the example is more complicated than he used to think. On the other hand, and probably this is a significant fact, both the view that the use of “that” semantically refers to something and the view that it is conventionally determined to lack a referent are represented in the literature. Following Kaplan (1978), Reimer (1992) and Speaks (2016) think that “that” refers to the picture of Agnew. And King (2013), (2014) offers a number of considerations in favor of the idea that the use of “that” in Kaplan’s utterance is conventionally determined to lack a referent. I take the existence of these theoretical disagreements to provide considerable support for the view that the matter should actually appear unclear to the theoretically unprejudiced observer, presumably due to the relevant conventions failing to determine either reference or reference failure in the example. King distinguishes carefully between the case in which the audience of Kaplan’s utterance do not and the case in which they do know that the picture that used to hang on the wall was Carnap’s. In the first case, it will be natural to expect that the audience will think that Kaplan has said that the picture of Agnew is a picture of one of the greatest philosophers of the twentieth century. In the second case, the audience will not think that, and in fact someone reporting on what Kaplan said, whether in the first case or in the second, will

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not, if apprised of all the facts, report that Kaplan said that the picture of Agnew is a picture of one of the greatest philosophers of the twentieth century. As King (2013) notes, this is at least some reason for thinking that Kaplan did not in fact say that the picture of Agnew is a picture of one of the greatest philosophers of the twentieth century, and hence that his use of “that” did not refer to that picture. I agree, but I would go further: I take it as highly significant that a speaker afforded the best perspective on all the relevant facts should come to a conclusion that is incompatible with the possibility that Kaplan’s use referred to the picture of Agnew. If from the best perspective a competent speaker makes a judgment incompatible with this possibility, then this is serious reason to think that the conventions for demonstrative reference fixing (together with the relevant circumstances of the case) do not imply that Kaplan’s “that” referred to the picture of Agnew. Furthermore, the opposite judgment of audiences not afforded the best perspective could then be reasonably explained precisely as a judgment prompted by default reactions to the known circumstances of Kaplan’s utterance—in particular to the fact that Kaplan’s pointing is the only conspicuous indication of his referential intentions that these audiences have. And it’s worth noting that an application of Kripke’s (1977) already mentioned test about imaginary languages suggests in any case that the view that Kaplan’s “that” referred to the picture of Agnew may be confusing a strong pragmatic indication with a semantic fact. If a similar situation arose with speakers of an imaginary version of English where the relevant referencefixing conventions did imply that there is no reference to either picture (or where no convention implies that there is reference), audiences, or at least audiences in a non-ideal position, would still probably be led to believe that reference was to the picture of Agnew. King says that the judgment of the audience apprised of all the relevant facts would be explained on the hypothesis that the use of “that” in Kaplan’s utterance was conventionally determined to lack a reference. (Consistently with this hypothesis, he generally favors a version of the Simple Intention theory (involving an additional requirement that the utterer make it possible for her audience to know what the referent of her use of a demonstrative is), in which the constituting convention implies reference failure in cases of conflicting intentions.) But in fact the same explanation would be available to the view that the semantic conventions about “that” fail to determine a reference for Kaplan’s use and fail as well to determine that it lacked a reference. So King’s observations also support the view that the example is a case of

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42     referential indeterminacy. In fact, there is reason to think that King’s favored hypothesis that Kaplan’s use was conventionally determined to lack a reference is not right, for it is unlikely that one could elicit definite judgments of reference failure from competent speakers apprised of all the relevant facts (even if such failure does obtain). Compare some paradigm case of failure of demonstrative reference, such as the case of the agonizing man from chapter 1 who in his delirium utters He is coming to get me while he hallucinates a demon who comes to take him to hell. A doctor present at the scene, apprised of all the relevant facts, will judge that there is definitely no “he” to be talked about. But will the knowledgeable audience of Kaplan’s utterance judge that Kaplan’s use of “that,” in virtue of the conflict of his intentions, definitely did not refer to anything? I think it’s pretty clear that they will not. More importantly: if a presumably competent and knowledgeable audience of Kaplan’s utterance abstained from giving a definite judgment that Kaplan’s use of “that” either referred to something or did not refer to anything, would we reject our supposition that they were competent users of demonstratives? I think we would pretty clearly not reject the supposition. On the contrary, we might well feel that this audience showed a kind of semantic maturity and cautiousness (a cautiousness to be contrasted perhaps with the semantic theorists’ risky pronouncements about the case, reviewed above). I take this fact to indicate once more that the matter whether Kaplan’s utterance of “that” refers or not is indeterminate as far as demonstrative reference-fixing conventions go. There are quite a few other examples suggestive of indeterminacy in demonstrative reference, where considerations about competent speaker intuitions would follow a similar pattern. Suppose I am in a thick forest. My visual attention is focused on a tree top. At the same time, with my hand I’m touching what I tacitly assume to be the same tree’s trunk. As it happens, the tree top I’m seeing is the top of another tree whose trunk has its base a few yards away and which curves in the direction of the tree I’m touching, and the tree I’m touching actually has no foliage on its top—it disappeared in some way or other. I say This is a tree with such a nice trunk, with the intention of referring both to the tree I’m seeing as represented by my visual perception of it and to the tree I’m touching as represented by my tactile perception of it. What is the “true claim” about the content of the use of “this” here? Does it conventionally refer to the tree I’m touching, or to the tree my visual attention is focused on? Or is it conventionally determined that there is reference to neither? In my view, there is no clear answer. I suspect that a competent speaker apprised of all the relevant facts will not judge it appropriate to report on what I said by saying either that I said that the tree I was seeing was a tree

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with such a nice trunk or that I said that the tree I was touching was a tree with such a nice trunk. But it also seems clear that such a competent speaker will not risk with any confidence a judgment that my “this,” in virtue of the conflict of my intentions, was definitely not referring to anything. And again, more importantly, I don’t think that we would judge incompetent a speaker who did not judge it appropriate to issue a definite verdict of reference or reference failure in this case. A different kind of example, not involving conflicting intentions, is the following. I am watching a live TV show in which a person who claims to be a clairvoyant “sees” a dog in a land far away. He says, intending to refer to the dog he claims to “see,” He is now having an ear infection. All of the properties he attributes to the dog happen to be properties of my dog Joos, who was born recently and whose existence is not known to any person aside from me. And Joos is now having an ear infection. Was Joos the conventional reference of the clairvoyant’s use of “he”? I’m uncertain. I have some inclination to think that it did not refer to anything, but at the same time I cannot help feeling that it may have referred to Joos. I would not risk a definite judgment either that the clairvoyant’s use did not refer to Joos or that it did refer to Joos. As far as I can tell, it is unclear whether the clairvoyant’s use referred to Joos or not. And again I would not consider incompetent a speaker who did not issue a definite verdict of reference or reference failure in this case. Finally, consider this other case, involving again a conflict of referential intentions. Barnes is walking in the streets. A woman he vaguely sees approaching bumps into his right side, and he turns in that direction. As he does, he has a momentary hallucination. He hallucinates a woman (one very different from the woman that bumped into him), and he forms the belief that the woman that just bumped into him is the woman he believes he is seeing now. He says She gave me a good jolt, with the intention of referring both to the woman that he thinks he sees (as purportedly represented by his hallucination) and to the woman that just bumped into him (as represented by this very description, or by his memory of her). Does Barnes’s use of “she” refer to the woman that just bumped into him, or does it not? It’s not clear to me what the answer is, and I suspect that it is conventionally indeterminate whether the use in question refers to the woman or not.²⁰

²⁰ This example shares many features with Speaks’s “Fluffy” example from note 16, though I believe that the impression of uncertainty is greater in the present example. As noted there, I also see the “Fluffy” example as one of referential indeterminacy.

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44     It seems likely to me (though admittedly not certain, by any means) that the correct explanation of my impressions of uncertainty is that the conventions about demonstrative reference leave it indeterminate whether there is reference or reference failure in the cases in question. Assuming this is right, what would be the lessons of referential indeterminacy for the broad, theory-neutral project of giving a theory of the conventional rules governing the reference and reference failure of uses of demonstratives? I think one of the lessons is that such a theory is unlikely to be formulatable in terms of rules stating necessary and sufficient conditions for demonstrative reference that are at the same time known by normal competent speakers. Speaks’s requirement on the adequacy of a semantic theory for demonstratives, that it entail for every context “a true claim about the content of each indexical in that context,” amounts to a requirement that such a theory must be given in terms of necessary and sufficient conditions for an object to be the content of a demonstrative in a context. However, the existence of cases of probable indeterminacy gives reasons to think that a theory of content for demonstratives given in terms of necessary and sufficient conditions will in general not be correct, if those conditions can at the same time be said to be known by normal competent speakers. First of all, it will be hard to formulate a theory that is simply extensionally correct, as this theory must classify together cases of conventional reference failure and of referential indeterminacy, and these two kinds of cases owe their properties to circumstances which are presumably significantly different. Conventional reference failure is presumably to be explained by the existence of appropriate conventions implying it; referential indeterminacy is presumably to be explained by the inexistence of appropriate conventions implying either reference or reference failure. But second of all, even if we somehow managed to formulate extensionally correct jointly necessary and sufficient conditions for reference—implying what the reference is in cases where there is conventional reference, and implying that there is no reference when there is either conventional reference failure or a failure of conventional implications regarding reference—it is just implausible that such conditions could be known by normal competent speakers. For it is not reasonable to expect that, in cases where the conventions fail to imply a verdict of reference or reference failure, a normal competent speaker must know that there is indeterminacy, and thus ultimately reference failure; in such cases the competent speaker may be just unclear about whether there is reference, not clear that there is no reference.

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Standard theories of overriding intentions, such as the ones reviewed in the preceding section, don’t introduce suitable indeterminacies;²¹ so it would not be unclear to a speaker who had one such theory in mind either which object (a token of) the appropriate description yielded by the theory describes (if any) or that (a token of) the description yielded by the theory doesn’t describe any object (assuming that the speaker had perfect knowledge of the surrounding circumstances). For example, the Intention + Overriding Demonstration theory and the Intention + Overriding Control theory imply that Kaplan’s use of “that” in the example of the pictures refers to Agnew’s portrait, and the Intention + Overriding Salience theory implies that it does not refer (as no portrait is brought to mutually recognized maximal salience). For another example, the Intention + Overriding Demonstration theory, the Intention + Overriding Salience theory, and the Intention + Overriding Control theory all imply that my utterance of “this” in the example of the trees fails to refer, under the reasonable assumptions that my conflicting intentions in the case are symmetric as to what further referential intentions involving demonstrations they might generate, that the two trees are equally salient, and that no intention is more responsible for the production of my utterance than the other. For yet more examples, consider the clairvoyant and the Barnes examples. The Intention + Overriding Demonstration theory, the Intention + Overriding Salience theory, and the Intention + Overriding Control theory all imply that the clairvoyant’s utterance of “he” fails to refer, as there is no intention he has of referring to Joos, at least assuming that a referential intention involves some standard mental representation (perceptual, descriptive, memorial, etc.) of the intended object, which we can suppose is not the case. And Barnes’s utterance of “she” is again implied to fail to refer by all three theories: the Intention + Overriding Demonstration theory implies this because (we can suppose) there is no demonstrative intention involved; the Intention + Overriding Control theory implies it because (we can suppose) there is no controlling intention ²¹ It may be worth emphasizing that the claim I am about to defend is that the relevant theories don’t have the indeterminacies they should have, not that they are completely determinate or that they have some bad feature due to indeterminacy in general. Note for example that these theories, like any theory using vague terminology, have indeterminacies attributable to the lack of sharp boundaries in the concepts they use, but these are irrelevant for present concerns. For illustration, take a simple case of use of a demonstrative where there are no conflicting intentions, and where the relevant representation in the relevant referential intention(s) is a borderline case of a representation of the intended object, perhaps because the mental image of the object in the utterer’s mind is neither clearly complete enough nor clearly insufficiently complete (it may have a borderline number of mental “pixels,” say). This will be a case where it will be indeterminate whether the relevant referential intention(s) give rise to a fact of conventional reference, but a case that is unavoidable and harmless from the point of view of the present discussion.

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46     involved (or because we can just suppose that the hallucinatory intention is the controlling one); and the Intention + Overriding Salience theory implies that there is no reference because neither the real woman nor the hallucinated one is brought to mutually recognized maximal salience. We can try other theories of complex overriding intentions, but things don’t get better. Other conditions one could think of don’t introduce (suitable) indeterminacies, so it will not be unclear to someone having the conditions in mind either which object (a token of) the appropriate demonstrative refers to (if any) or that (a token of) the demonstrative doesn’t refer to any object. For example, suppose that the condition is that in cases of conflicting referential intentions, the referent is to be the thing intended via the relevant referential intention that the speaker would take as overriding (as suggested by Sainsbury (2005), ch. 3, for cases of conflicting intentions involved in the introduction of proper names); this would imply that the reference of Kaplan’s “that” is the Carnap portrait, and that there is a definite failure of reference in the trees case if, as we can suppose, my two intentions in that case are perfectly symmetric and I don’t take any of them to be overriding. Actually, the fact that my two intentions are symmetric in some cases of apparent unclarity/indeterminacy yields directly the strong implication that no theory of overriding intentions can introduce the appropriate indeterminacy, for in such cases such a theory will yield a verdict of definite reference failure. A speaker associating such a theory with (the token of) the appropriate demonstrative would issue definite verdicts of reference failure in the trees case (assuming she had perfect knowledge of the surrounding circumstances), but such a speaker would then have a theory of demonstrative reference fixing in mind that, even if it were extensionally correct in some sense, would not be a correct theory of the (known) conventions of demonstrative reference fixing. A speaker can evidently be a perfectly competent user of demonstratives if he merely knows what’s going on in cases where there are clear conventional implications of reference or reference failure. He can be perfectly competent if (in general and when he is afforded a good perspective) he knows what the reference of a use of a demonstrative is that has a conventional reference, and he knows that a use of a demonstrative fails to have a referent when it is conventionally determined that it so fails. A competent speaker doesn’t need to know what’s going on in cases of referential indeterminacy. He doesn’t need to know the “true fact” about such cases, i.e. the fact that it is conventionally indeterminate whether they have a referent, or the weaker fact that they don’t have a referent.

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This provides the right outlook on Speaks’s requirement that a theory of demonstrative reference known by competent speakers, an internalizable theory of character, be “adequate,” i.e. that it entail for every context “a true claim about the content of each indexical in that context.” The requirement can now be seen to be too demanding, even for a theory that aspires to explain the productivity and systematicity of our knowledge of the contents of demonstratives. This may be somewhat obscured by the fact that Speaks’s characterization of productivity is too strong (while his characterization of systematicity seems correct). For Speaks, recall, productivity is the phenomenon that a competent speaker has “no trouble at all figuring out” the content of a new use of a demonstrative. But this is too coarse, as we can see from what we said in the last paragraph. Productivity in the demonstrative case is, if anything, the phenomenon that a competent speaker (in general and when afforded a good perspective) has no trouble figuring out the referent of a use of a demonstrative when it conventionally has one and has no trouble figuring out that a use of a demonstrative has no referent when it conventionally fails to have one. But a proper understanding of productivity doesn’t involve a spurious phenomenon that a competent speaker has no trouble figuring out that a use of a demonstrative has no referent when it does not conventionally have or fail to have one. However, Speaks’s requirement that a theory of character entail for every context “a true claim about the content of each indexical in that context” surreptitiously involves the presupposition that this spurious phenomenon is real. Is there a reasonable alternative to the Kaplanian descriptivist project? I think one such alternative may be provided by a theory of merely sufficient conditions for demonstrative reference and reference failure. By contrast with a theory of jointly necessary and sufficient conditions for demonstrative reference, a theory of merely sufficient conditions for reference and failure of reference will assign semantic contents or imply verdicts of failure of reference for demonstratives in some cases, but will in all likelihood not resolve just any question concerning the content of a use of a demonstrative. The hope would then be that a theory of this kind could have the intuitively right implications concerning determinate assignments of reference and verdicts of reference failure, and also fail to imply verdicts of reference and of failure of reference precisely in cases of conventional indeterminacy such as the examples we discussed earlier. This would arguably be enough for the theory to fulfill the expectation that it should provide an explanation of systematicity and productivity, rightly understood. For the theory of sufficient conditions would imply claims

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48     concerning determinate assignments of reference and verdicts of reference failure just in cases where they follow from reference-fixing conventions and thus in cases where it can be expected from competent speakers that they can get to know the claims in question. The failure of implications of reference or reference failure in cases of indeterminacy, on the other hand, would not necessarily be knowable by competent speakers. This is entirely reasonable on the outlook inspiring such a theory. For the theory, in the sense of the conventions themselves (together with circumstances surrounding particular utterances), would fail to imply claims about the theory itself failing to imply things; these claims would thus be, according to the theory, outside the area of claims knowable on the basis of competence with the conventions. The true claims of referential indeterminacy, i.e. the claims about the inexistence of certain implications from the relevant conventions, would “lie outside” the rules themselves or their implications. They would be, if we wish, “metaclaims” knowable or conjecturable by the linguistic theorist, but not necessarily by every reflective competent speaker. And another hope for a theory of merely sufficient conditions for reference and failure of reference would be that the theory could suggest a correct picture of the difficulty that appears to lie behind attempts at providing a theory of the overriding intention in cases of conflicting intentions. The difficulty, recall, appeared to come from the fact that in the basic counterexamples to a theory it appeared to be sufficient for demonstrative reference to an object that the object was the only thing intended via a referential intention representing its object by the utterer’s concurrent perception of it, while this is compatible with the negation of a variety of proposed necessary conditions for demonstrative reference in cases of conflicting intentions. But that sufficient condition is fairly clearly not necessary for demonstrative reference, even in cases of conflicting intentions. This presents a problem for theories of necessary and sufficient conditions for demonstrative reference, because a sufficient but not necessary condition for reference appears to have been identified that is compatible with the rejection of virtually any condition that could aspire to weed out undesirable potential referents in cases of conflicting intentions. But a theory of merely sufficient conditions for reference and failure of reference would not be subject to this problem. Among the sufficient conditions for reference and failure of reference that the theory would postulate would appear the mentioned sufficient condition. But the theory would not postulate that the sufficient conditions yielded in some way an appropriate necessary condition, and thus would not be subject to the kind of counterexample exploited in the objections we saw.

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     

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A Picture of Demonstrative Reference Fixing Let us then develop a picture of demonstrative reference-fixing conventions as conventions of sufficient conditions for reference and reference failure. But let me preface the development of the picture with some caveats and clarifications. One concerns the fact, already mentioned in chapter 1, that we don’t need to postulate that the conventions we will state are known in the full sense by competent speakers (even if they might become known, after superintensive coaching), but it is reasonable to attempt to formulate conventions whose implicit familiarity to normal speakers is manifested in appropriate linguistic behaviors, behaviors that can be seen as manifesting observance of the conventions, and that don’t require the deployment of abilities that it is not sensible to attribute to a normal speaker. In this, somewhat weaker form, the broad Kaplanian project need not be given up, even if Kaplan’s descriptivist idea that the conventions give known jointly necessary and sufficient conditions for reference must in all probability be given up. Another caveat is that it need not be reasonable to demand that we be able to state all the conventions governing assignments of reference and reference failure and/or recognize that they are all the conventions, because the theorist need not be in a better position than the typical competent speaker. We have already essentially argued that the typical competent speaker need not be able to recognize that a certain set of conventions exhausts all the existing conventions of demonstrative reference—if he did recognize this, he would presumably be pretty certain that cases not resolved by the conventions are cases of reference failure. The linguistic or metasemantic theorist may not be in a much better position, and may thus be unable to state all the conventions determining demonstrative reference and reference failure, and/or recognize that the conventions she is able to state are all the extant conventions. Another clarification concerns the fact that, although we will state our postulated conventions in terms of the notion of conventional or semantic reference, which is a theoretical notion that normal competent speakers need not be familiar with, this is no objection to the postulation of the conventions, as we don’t require full knowability of the conventions as such on the part of a normal competent speaker. The notion of semantic reference can appear in the formulation of our conventions, as the conventions may be instituted in virtue of linguistic behaviors that do not require the possession of concepts needed for the formulation of the conventions themselves. Note, however, that the notion of referring for which it makes sense to say that a person refers to a

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50     certain thing by means of some other thing (such as a word), a notion which will appear in our conventions as well, is perfectly ordinary. The theoretical notion of impersonal conventional reference and this notion of personal reference (the notion involved when one says that a speaker refers to a certain thing by means of a use of a demonstrative, say) should not be confused, even though both will appear in the statement of our postulated conventions.²² Another important caveat is that the conventions for demonstrative reference fixing that we will postulate will actually be conventions for roughly sufficient conditions. This will be because they will involve conditions which should only be thought to be sufficient ceteris paribus, i.e. sufficient only under the assumption that the situation where the conditions apply is otherwise normal, relevantly similar to other situations when the conditions were taken to apply in the past. The idea of normality is imprecise, as it will not be clearly delimited what parts of the situation have to be exactly as they were in past cases. This will actually introduce a further level of indeterminacy, in those cases where some of the sufficient conditions in the extant conventions obtains, and yet some aspect of the situation is not clearly normal. For example, it is not clear that these conventions are designed to regulate demonstrative reference in a situation in which the utterer of the relevant demonstrative has all sorts of strange beliefs about the demonstrative and its function, such as that it performs some sort of magical or religious role. Nevertheless, all the examples we have been and will be dealing with can be thought to involve normal situations broadly speaking, and the conjectured conventions should give a substantive account of them. Finally, if in the case of names we will postulate, in chapter 3, that the reference-fixing conventions can be stated as conventions assigning reference or reference failure to name types, in the case of demonstratives it seems reasonable to suppose that the reference-fixing conventions assign reference or

²² Bach (ms.) emphasizes that the notion of user reference is the referential notion involved in ordinary speakers’ referential intentions about how to use demonstratives, and denies that speakers have intentions involving the notion of impersonal or conventional reference. From this he derives the skeptical conclusion that uses (or tokens, or types in a context) of demonstratives cannot be said to semantically refer, properly speaking. In my view, the conclusion is unwarranted. It seems to me evidently legitimate to postulate that speakers have intentions concerning how uses of expressions should be conventionally understood, e.g. intentions concerning what an expression should be understood as conventionally standing for. And at any rate, even if speakers did not have intentions involving notions such as the notion of conventionally standing for, the statement of the conventions themselves can perfectly reasonably contain the notion of standing for or of reference. Surely the acts of people, including people in their facet of speakers, help constitute conventions statable in terms of concepts that the people themselves need not possess.

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     

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reference failure to particular uses of demonstratives.²³ This is related to another observation distinguishing the case of names from the case of demonstratives, one that is worth making before we state any of these conventions. The observation is that the conventions about demonstrative reference will not involve any requirement that the speaker should not form intentions about how to use a demonstrative that conflict with the intentions of the community. We can suppose that, unlike in the case of names and other (presumably) context-insensitive expressions, the community conventions basically allow a speaker to endow a use of a demonstrative with its conventional reference, without need of a double-check vis-à-vis the community’s intentions, at least in some ceteris paribus sense. This is certainly in line with what we can suppose are the basic communicative needs served by uses of demonstratives, which, again by contrast with the case of names, may be quite fleeting and localized in time and space. Let us then postulate a few conventions stating (roughly) sufficient conditions for demonstrative reference, making sure that they sound intuitively correct, and after that let us consider case by case how the theory consisting of such postulated conventions fares in the treatment of the examples used in our discussion in the preceding section. Successful demonstrative reference via non-conflictive descriptive referential intentions. If a speaker S forms the intention of using a demonstrative D to refer to the object, if any, that uniquely satisfies a certain property F, and it turns out that there is such a unique satisfier of F, then S’s use of D will refer to the F, if S forms no intention conflicting with that intention. Successful demonstrative reference via non-conflictive memorial referential intentions. If a speaker S forms the intention of using a demonstrative D to refer to an object as purportedly remembered by S, and the memory in question does correspond to a certain object o, then S’s use of D will refer to o, if S forms no intention conflicting with that intention. Successful demonstrative reference via non-conflictive perceptual referential intentions. If a speaker S forms the intention of using a demonstrative D to refer to an object as purportedly perceived by S, and the perception in

²³ Note that this is not to say that the conventions for demonstratives will not be in a sense about types (of demonstrative words), nor is it to say that there will be particular conventions for each particular use of a demonstrative; it’s just to say that the conventions will have as their aim to ascribe referents or failures or reference to particular uses of the demonstrative types. Much the same could be said of nearly every other recent theory of the metasemantics of demonstratives. On the idea of taking demonstrative uses as reference bearers, as opposed to Kaplanian “types-in-context,” see note 6 above.

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52     question is in fact of a certain object o, then S’s use of D will refer to o, if S forms no intention of using D to refer to a different object p as purportedly perceived by S, with the perception in question being in fact of p. Unsuccessful demonstrative reference via descriptive referential intentions. If a speaker S forms the intention of using a demonstrative D to refer to the object, if any, that uniquely satisfies a certain property F, and it turns out that there is no such unique satisfier of F, then S’s use of D will not refer to anything, if S forms no intention conflicting with that intention. Unsuccessful demonstrative reference via non-conflictive memorial referential intentions. If a speaker S forms the intention of using a demonstrative D to refer to an object as purportedly remembered by S, and the purported memory in question does not correspond to an object, then S’s use of D will not refer to anything, if S forms no intention conflicting with that intention. Unsuccessful demonstrative reference via perceptual referential intentions. If a speaker S forms the intention of using a demonstrative D to refer to an object as purportedly perceived by S, and the purported perception in question is not of any object, then S’s use of D will not refer to anything, if S forms no intention conflicting with that intention. By postulating that these rules govern conventional assignments of reference and failure of reference to uses of demonstratives, we get a reasonable and complete picture of the phenomena and the examples involving demonstrative reference we have discussed. But the picture, it should be stressed again, leaves open the possibility that other structurally similar conventions will be identified to account for other phenomena and intuitions not discussed here. In fact, such similar conventions exist in all probability, but it may well be futile to attempt to describe all the conventions governing the phenomenon of demonstrative reference.²⁴ Unlike a theory of necessary and sufficient conditions for reference, a theory according to which referential conventions are given ²⁴ To give some more examples, two additional conventions governing demonstrative reference are probably these: Successful demonstrative reference via non-conflictive nominal referential intentions. If a speaker S forms the intention of using a demonstrative D to refer to an object as purportedly represented by a purported name of it, and the name does refer to a certain object o, then S’s use of D will refer to o, if S forms no intention conflicting with that intention. Unsuccessful demonstrative reference via non-conflictive nominal referential intentions. If a speaker S forms the intention of using a demonstrative D to refer to an object as purportedly represented by a purported name of it, and the purported name does not refer to any object, then S’s use of D will not refer to anything, if S forms no intention conflicting with that intention. See also the next note.

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     

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merely by roughly sufficient conditions for reference or reference failure assumes naturally the possibility of incompleteness in the description of the conventions. In particular, in this framework it is very natural to work under the hypothesis that a competent speaker, including a theorist reflecting on his own competence, cannot be certain that the conventions he recognizes or postulates are all the conventions that he is in principle capable of recognizing as being at work. By contrast, a theory of necessary and sufficient conditions cannot, if it is believed to codify the relevant conventions, be at the same time accepted as incomplete (as not providing, for every context, “a true claim about the content of each indexical in that context,” in Speaks’s phrase). The paradigmatic uses of a demonstrative to refer to a medium-sized physical object that is being distinctly perceived by the speaker at the time of the utterance will in most cases be covered by Successful demonstrative reference via non-conflictive perceptual referential intentions. For it is reasonable to suppose that in most cases of this kind there will not be conflicting referential intentions on the part of the speaker, and in fact that he or she will have just one basic perceptual referential intention, whose existence will then suffice for a use of a demonstrative by the speaker to refer conventionally to the intended object. (Recall the examples of the child asking Give me that!, of the hunter warning his companion with an utterance of Look at that!, and of the shouting guy who prompts my utterance of Get him out of here.) Most typical uses of demonstratives to refer to physical objects that are not medium-sized, to physical objects that are not being simultaneously perceived, and to objects that are not evidently physical or perceived, will be covered by Successful demonstrative reference via non-conflictive descriptive referential intentions, for it is again reasonable to suppose that in most cases of this kind there will not be conflicting referential intentions on the part of the speaker. There will typically be one basic referential intention, though not a simple perceptual referential intention, whose existence will suffice for a use of a demonstrative by the speaker to refer conventionally to the intended object. Thus, when uttering This is a doomed planet the speaker will normally have one basic intention, e.g. the intention to refer to the planet he lives in; when uttering That’s a beautiful town while pointing to a spot in the map, the speaker will normally have one basic referential intention, to refer to the town represented in the map by the spot she is pointing at; when uttering That’s what I have to do the speaker will normally have just one basic intention to refer to the possible way of acting that he has just considered; and when uttering So that’s π right after being introduced to the Leibniz formula, the

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54     speaker will normally have just one basic intention to refer to the sum of terms in the formula.²⁵ Other cases where the theory issues reasonable verdicts of reference via either Successful demonstrative reference via non-conflictive descriptive referential intentions, Successful demonstrative reference via non-conflictive memorial referential intentions, or Successful demonstrative reference via non-conflictive perceptual referential intentions are the examples of the utterance of This is a pretty bad situation in the crocodile cage, the utterance of Did you see that? after seeing the bird fly past the doorway, and the utterance of She is athletic used by King in order to motivate his condition on demonstrative reference (that the utterer should make it possible for her audience to know what the referent of her demonstrative is); as we argued, it is at best unclear that examples of this sort are suggestive of reference failure instead of some kind of pragmatic inaptness. Also in virtue of Successful demonstrative reference via non-conflictive perceptual referential intentions, the picture we have described yields reasonable verdicts concerning several other examples above, and in particular concerning the cases involved in the counterexamples to the theories of overriding intentions that we criticized. First, Kaplan’s original example involving an utterance of Who is that (the man with the martini)? is such that Successful demonstrative reference via non-conflictive perceptual referential intentions implies that there is reference to the man, even if he is not drinking a martini (as Kaplan and the rest of us intuited). This is because the ²⁵ The example in which I say That’s what I have to do but I have conflicting intentions appears to require the acknowledgment of a further convention, which may constitute a generalization of Successful demonstrative reference via non-conflictive perceptual referential intentions. Recall that I have both the intention to refer to my donating 1,000 dollars to my friend John’s organization as represented by this very description (“my donating 1,000 dollars to my friend John’s organization”) and the intention to refer to my donating 1,000 dollars to the most effective charity NGO in town as represented by this very description (“my donating 1,000 dollars to the most effective charity NGO in town”), and that these conflict because John’s organization is a fraudulent scheme. The reference of my use of “that” is intuitively my donating 1,000 dollars to John’s organization, which can be explained if we assume that this thing (event) is represented in my intentions by a description that allows me to go about identifying which thing (event) it is, while my donating 1,000 dollars to the most effective charity NGO in town is not represented in my intentions by a description that allows me to go about identifying which thing (event) it is, and we postulate a convention to the effect that intentions of the former kind override intentions of the second kind in successful demonstrative reference. One possibility is this: Successful demonstrative reference via non-conflictive identifying referential intentions. If a speaker S forms the intention of using a demonstrative D to refer to an object as purportedly represented by S via a representation that allows S to go about identifying the object, and the representation in question is in fact of a certain object o, then S’s use of D will refer to o, if S forms no intention of using D to refer to a different object p as purportedly represented by S via a representation that allows S to go about identifying p, with the representation in question being in fact of p.

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     

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speaker, besides any other referential intentions of his, has a perceptual referential intention to refer to the man at stake, an intention that doesn’t conflict with other perceptual referential intentions of his. An example involving an utterance of the same sentence was used as a counterexample to the Intention + Overriding Demonstration theory. Here again Successful demonstrative reference via non-conflictive perceptual referential intentions implies that there is reference to the man, in this case despite the fact that, as the example was constructed, no intention of the speaker involved mention of any demonstration truly determining the man. And yet another example involving the same sentence was used against the Intention + Overriding Control theory. In this case Successful demonstrative reference via nonconflictive perceptual referential intentions implies that there is reference to the man even though the intention closest in explanatory terms to the production of the utterance of “that” is an intention to refer to the man as purportedly represented by the description “the guy I’m describing (as the man with the martini),” which does not determine any object in the envisaged situation. Similarly, in the example involving an utterance of That is an interestinglooking man, used against the Intention + Overriding Salience theory, Successful demonstrative reference via non-conflictive perceptual referential intentions implies that the proverbial man is again the conventional reference of the use of the demonstrative, despite the fact that another man is equally salient in the context. And finally, in the example involving an utterance of That is a really good player, used against the Simple Intention theory, Successful demonstrative reference via non-conflictive perceptual referential intentions implies that the gifted player in the yellow shirt is the referent of “that,” despite the fact that another man (the bright philosophy of language student) is also the target of a referential intention of the speaker in the situation. Since the present theory postulates only the existence of conventions giving roughly sufficient conditions for demonstrative reference, it also promises to deal in an intuitively appropriate way with the cases of apparent referential indeterminacy we encountered above. The idea is, of course, that the conventions provide only conditions that are at work in certain relatively simple and common situations involving uses of demonstratives, and thus that they should have no implications concerning cases not involving situations of those kinds. This is precisely what happens in the case of Kaplan’s utterance of That is a picture of one of the greatest philosophers of the twentieth century. The existence of conflicting intentions prevents the use of “that” here from getting a reference through an application of either Successful demonstrative reference

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56     via non-conflictive descriptive referential intentions or of Successful demonstrative reference via non-conflictive memorial referential intentions. Since there is no intention on Kaplan’s part of using “that” to refer to an object that he is clearly concurrently perceiving, also an application of Successful demonstrative reference via non-conflictive perceptual referential intentions is prevented. But also application of the rules yielding verdicts of reference failure is prevented. In the case of Unsuccessful demonstrative reference via descriptive referential intentions, this will be because Kaplan has at least two conflicting referential intentions, of using “that” to refer to the picture behind his back that he is pointing at, but also of using “that” to refer to the remembered Carnap picture. In the case of Unsuccessful demonstrative reference via memorial referential intentions, this will similarly be because even if Kaplan has the (non-descriptive) intention of using “that” to refer to the familiar Carnap picture as represented by a memory of it, he also has the conflicting (descriptive) intention of using “that” to refer to the picture behind his back that he is pointing at. In the case of Unsuccessful demonstrative reference via perceptual referential intentions, this again does not apply because there is no intention on Kaplan’s part of using “that” to refer to an object that he is clearly perceiving. The case of my utterance of This is a tree with such a nice trunk is also left undecided by the conventions postulated by the theory. Successful demonstrative reference via non-conflictive descriptive referential intentions does not apply because if I have any descriptive referential intention, it will conflict with one of my perceptual referential intentions. And Successful demonstrative reference via non-conflictive perceptual referential intentions does not apply either, because I have two conflicting intentions that are both perceptual, the intention of referring to the tree I’m seeing as represented by my visual perception of it and the intention of referring to the tree I’m touching as represented by my tactile perception of it. Unsuccessful demonstrative reference via perceptual referential intentions does not apply either, because the objects I intend to refer to are existing objects that I am clearly perceiving. Compare the case of the utterance by the sick man of He is coming to get me, where Unsuccessful demonstrative reference via perceptual referential intentions does apply, as the object the man intends to refer to via a purported perception of it does not really exist and is thus not being perceived by the man. In the case of the utterance of That was the king I read in my literature class in the Homer/Alexander story, once more neither the recognized conventions for successful reference nor the recognized conventions for unsuccessful reference apply, and most relevantly Successful demonstrative reference via

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     

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non-conflictive descriptive referential intentions does not apply as there are conflicting intentions at stake.²⁶ The clairvoyant’s use of “he” in his utterance of He is now having an ear infection does not receive either a verdict of reference or a verdict of reference failure from the postulated conventions. Successful demonstrative reference via non-conflictive descriptive referential intentions and Successful demonstrative reference via non-conflictive memorial referential intentions (as well as their analogues for reference failure) do not apply if we assume that the clairvoyant doesn’t have in mind any purported description or memory of a dog. Successful demonstrative reference via non-conflictive perceptual referential intentions does not apply either, because the clairvoyant’s referential intention is not perceptual, as it is not one of referring to an object that he is perceiving. And Unsuccessful demonstrative reference via perceptual referential intentions does not apply either, equally because the clairvoyant does not intend to refer via a purported perception of a dog—in fact his claim is precisely that he has established some different kind of cognitive link with the dog. Finally, let’s turn to Barnes’s utterance of She gave me a good jolt. The existence of conflicting intentions once again precludes the assignment of a determinate reference to the use of “she” through an application of Successful demonstrative reference via non-conflictive descriptive referential intentions or Successful demonstrative reference via non-conflictive memorial referential intentions. In the latter case, for example, this is because although Barnes has one referential intention that is memorial (the intention to refer to the woman that just bumped into him as represented by his perceptual memory of her), he also has the conflicting descriptive intention of referring to the woman that he believes to be seeing (as represented by his hallucination of her). Also application of the rules yielding verdicts of reference failure is prevented by the existence of conflicting intentions.²⁷ We have now seen that the present theory gives a reasonable account of many phenomena and intuitions that are problematic for existing necessaryand-sufficient conditions theories of reference fixing for demonstratives, including some phenomena involving apparent referential indeterminacy. ²⁶ In this case, as we already noted, it is perhaps not implausible to think that there is conventionally determined reference failure, even if this is not because the conventional rules we have postulated determinately imply that there is. We might try to explore possibilities as to what the relevant conventions determining reference failure here might be. However, my preferred view of the example is again the cautious one that it’s a case of indeterminacy, as I don’t think a competent speaker need reach a definite verdict of reference or reference failure in this case, rather than a state of puzzlement as to what the true situation is. ²⁷ For analogous reasons, Speaks’s use of “that cat” in the Fluffy example from note 16 is not assigned a reference nor determined to lack a reference by the postulated conventions.

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58     Furthermore, the present theory does this in a way that is fully compatible with the needs of the broad, theory-neutral project of giving a theory of the conventional rules governing the reference of uses of demonstratives. Such a theory need not aspire to “entail, for any context, a true claim about the content of each indexical in that context.” It is enough if it entails a true claim of reference for the cases where there is conventionally determined reference, and if it entails a true claim of reference failure for the cases where this is conventionally determined. A theory of the conventional rules governing the reference of uses of demonstratives need not, in fact must not, entail anything about cases of referential indeterminacy, for it is not reasonable to suppose that these entailments need be known by competent speakers. It is reasonable to require of such a theory that the conventions it postulates be conventions that competent speakers can be said to follow, as manifested in their knowledge of the conventions’ entailments for particular cases, and the rules postulated by the present theory fairly clearly satisfy this requirement. But it is not reasonable to require of such a theory that it imply claims of referential indeterminacy, for these are presumably not entailed by the conventions that competent speakers follow. A theory that entails, “for any context, a true claim about the content of each indexical in that context,” as noted above, will not be a theory whose postulated rules and entailments can reasonably be thought to be known by competent speakers. (As also noted above, theories of necessary and sufficient conditions for demonstrative reference will always have good chances of being extensionally incorrect, for they will have a hard time classifying together cases of conventional reference failure and cases of referential indeterminacy.) There was the further problem for a theory of necessary and sufficient conditions that there seemed to be a recalcitrant difficulty finding a suitable general necessary condition for overriding intentions, namely one compatible with the intuitively sufficient condition for override that takes place when the referential intention represents its object by the utterer’s concurrent perception of it. It is in combining (I hope) extensional adequacy with a suitably weak requirement of accessibility of the conventions to competent speakers, and with its avoidance of the recalcitrant difficulty of characterizing a general condition for overriding intentions, that a theory of merely roughly sufficient conditions for demonstrative reference and failure of reference succeeds where other theories fail.²⁸ ²⁸ It may be important to emphasize that the present theory doesn’t merely achieve extensional adequacy (if it does), but that it is motivated by general considerations involving the two desiderata just

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     

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In chapter 3 we will see that the phenomenon of referential indeterminacy appears also with proper names, and that a theory of roughly sufficient conditions for reference and failure of reference again provides a satisfying picture of the facts where a variety of traditional theories of jointly necessary and sufficient conditions fail to do so. This will yield further support for the theory developed in this chapter.

mentioned, to which it provides an adequate response, in my view. As a referee has pointed out, mere extensional adequacy with respect to a finite set of cases of intuitive reference or reference failure would be relatively easy to achieve for the theorist of necessary and sufficient conditions for reference, via a suitable disjunction.

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3 Proper Names and Referential Indeterminacy Some Classical Kripkean and Evansian Advances in Our Understanding of Proper Names Proper names are probably the most studied instruments of linguistic reference. The intense scrutiny to which they have been subjected has undoubtedly produced great advances in our understanding of the mechanisms by which names can refer to objects when used by speakers. However, it seems fair to say that some fundamental issues concerning reference fixing for proper names remain considerably obscure. What have been those great advances? First of all, it is clear by now that a proper name does not have the same meaning as a description that details some contingent characteristic that the speaker attributes to its intended referent, and hence that it is not in virtue of having a meaning of this kind that a use of a name refers to its referent. For example, “Aristotle” is not semantically equivalent, within the idiolect of a normal, linguistically competent speaker, with “the philosopher who first described syllogisms.” As Kripke (1972) noted, if it were, then Aristotle is the philosopher who first described syllogisms would express a necessary truth in such idiolects, but it does not. Kripke also made the closely related observation that while “Aristotle” is rigid, “the philosopher who first described syllogisms” is not: to say The thing (man) that was the philosopher who first described syllogisms could not have existed without being the philosopher who first described syllogisms (and no other thing could have been the philosopher who first described syllogisms) strikes a sufficiently reflective speaker as false, while to say The thing (man) that was Aristotle could not have existed without being Aristotle (and no other thing could have been Aristotle) strikes one as true or hard to deny.¹

¹ As in chapter 2, I have applied here what Soames (2002) calls the “linguistic test” for rigidity, but other tests for rigidity would yield the same result.

Roads to Reference: An Essay on Reference Fixing in Natural Language. Mario Gómez-Torrente, Oxford University Press (2019). © Mario Gómez-Torrente. DOI: 10.1093/oso/9780198846277.001.0001

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This firm negative conclusion is relatively weak, however; it doesn’t preclude by itself the possibility that “Aristotle” be semantically equivalent, within the idiolect of some normal speakers, with some rigid description or other. And some post-Kripkean philosophers and linguists do believe that “Aristotle” (at least when it appears in subject position) is semantically equivalent, within the idiolect of a speaker competent with “Aristotle,” with some description broadly similar to “the thing here relevant actually called ‘Aristotle.’” (Examples include Bach (1987), Recanati (1993), Geurts (1997), Katz (2001), Elbourne (2005), Matushansky (2008), and Fara (2015)— although these authors otherwise differ importantly in their theoretical presuppositions and aims.) Perhaps Aristotle is the thing here relevant actually called “Aristotle” does express a necessary truth in some or all normal speakers’ idiolects, and presumably “the thing here relevant actually called ‘Aristotle’” does pick out Aristotle. But even if all this were to turn out to be so, we would still not have an interesting account of the fact that a normal speaker’s uses of “Aristotle” manage to pick out Aristotle. The question of what would make Aristotle the (contextually relevant) thing (actually) called “Aristotle” (and of who must call him “Aristotle”) would still beg for an answer, and it is ultimately this answer that we want to attempt to provide here. In part for these reasons, and in part because the idea that names are semantically nondescriptive singular terms that refer (when they do) to the objects they intuitively stand for already has many able defenders in the literature, we will not attempt to defend the idea in this chapter against the sorts of considerations offered by the mentioned descriptivist authors, and we will proceed under the assumption that the idea is correct.² Kripke also noted that problems remain, even if we proceed under this assumption, abandon the idea that a name is semantically equivalent with a description, and adopt the weaker view that some description must be being used by a speaker to fix in a stipulative way the reference of “Aristotle” in her ² For some of the mentioned descriptivist authors (Elbourne, in particular), the description in question does have Aristotle as its referent (and “Aristotle” is thus a descriptively structured singular term), but a majority of them appear to think (and Matushansky and Fara explicitly do think) of Aristotle as merely described by the description, which, as well as the name “Aristotle,” has as its referent a property, an intension, or the like (e.g. the property that a property has when there is a single contextually relevant thing called “Aristotle” who has it). Since we will be adopting the common view that “Aristotle” refers to Aristotle, strictly speaking what we will offer in answer to the question of what would make Aristotle the (contextually relevant) thing called “Aristotle” will directly apply only to views on which the description refers to Aristotle. Nevertheless, it will also indirectly apply to views on which the description refers to something like the property that a property has when there is a single contextually relevant thing called “Aristotle” who has it. In these cases the question that arises is what makes it the case that some particular thing satisfies that property (if any thing does). The ideas in this chapter could in principle be reformulated so as to provide an answer to this question.

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62      idiolect. This description could not be one based on important biographical characteristics of Aristotle, such as “the philosopher who first described syllogisms,” for Aristotle is the philosopher who first described syllogisms does not express an a priori truth in any idiolect, and presumably it should be a priori if reference fixing by description is a kind of stipulation. Also, a normal speaker’s uses of “Aristotle” can intuitively refer to Aristotle even if she thinks that Aristotle fits some descriptions based on biographical characteristics that do not really apply to him, such as “the Athenian founder of logic.” And finally, the normal speaker’s uses of “Aristotle” can refer to Aristotle even if she does not really associate with “Aristotle” any full description based on biographical characteristics—she may think of Aristotle simply as “an ancient Greek,” for example. It thus seems clear that a normal speaker’s uses of “Aristotle” do not manage to refer to Aristotle in virtue of the speaker’s association of “Aristotle” with descriptive information based on biographical characteristics. A major insight of Kripke (1972) was that there are two fundamental ways in which a use of a proper name can come to refer to an object in the idiolect of a speaker. The case of “Aristotle” for a typical normal speaker of our time illustrates the first of these two ways. A typical normal speaker of our time inherits her capacity to refer to the Greek philosopher Aristotle with “Aristotle” from other speakers whose uses of “Aristotle” she has heard or seen, at least if she intends in some implicit way to keep using the name in the same way as those speakers. They in turn inherited their capacity from others, and so on. But when one inherits a name in this way, Kripke noted, one need not inherit also a description identifying correctly the referent that the name comes with in terms of biographically important characteristics, or even a full description purportedly of that referent. Then of course not all speakers can have inherited their capacity to refer to Aristotle with “Aristotle” from others. Presumably some speakers in Aristotle’s time came to refer to Aristotle with (an ancestor of) “Aristotle” because they developed the intention of referring with “Aristotle” to a person of whose existence they did not know merely from other speakers. Aristotle’s parents may well have chosen his name before his birth by somehow declaring or coming to accept that “Aristotle” would be the name of “the child of ours soon to be born (if a boy).” Or they may have chosen his name after seeing him by declaring or coming to accept that “Aristotle” would be the name of “that (boy).” Kripke emphasized, however, that “Aristotle’ did not thereby become semantically equivalent for his parents with “the child of ours soon to be born (if a boy),” or with “that (boy)” (however accompanied by some demonstration or presentation of the boy),

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even if for the introducers a connection that was in some sense a priori was established between the name and the introducing description/demonstrative. The presumable case of (the ancestor of) “Aristotle” for Aristotle’s parents illustrates the second of Kripke’s two fundamental ways in which a proper name can come to refer to an object in the idiolect of a speaker. This second way provides, in Kripke’s view, the initial basis of series or chains of inheritance of a name, such as the series that ends in the acquisition of “Aristotle” by a typical normal speaker of our time. It is important to stress, however, that Kripke emphasized that, in singling out these two fundamental ways in which a use of a proper name can come to refer to an object in the idiolect of a speaker, he was not claiming to have given a theory of jointly necessary and sufficient conditions for name reference; in fact, he said that he was only giving a better “picture” of the mechanism of name reference than the descriptivist picture available until then. Evans (1973), (1982) provided many important qualifications of this picture, of which we will mention just a few. Evans emphasized that when a name is transmitted from some speakers to another, reference need not be ultimately preserved even if, as required by Kripke, the inheriting speaker does intend to keep using the name in the same way as the bestowing speakers. In a historically inaccurate story often attributed to Evans, Marco Polo inherits the name “Madagascar” from Arab or Malay sailors who use it as a name of a part of continental Africa, but inherits it together with the belief that the sailors used it for the island now universally known as Madagascar,³ a fact that eventually leads somehow to the present situation in which “Madagascar” refers to that island in the idiolects of all normal competent speakers.⁴ Evans also stressed that a speaker who receives without any mediating confusion a

³ The story is attributed to Evans, e.g., by Kripke himself (in the Addenda to Naming and Necessity (Kripke (1972), 163) and in Harman et al. (1974), 513) and by Dickie (2011), 48. As far as I can tell, in his published work Evans merely quotes from Taylor (1898) a brief passage where it is only said that a misunderstanding of Marco Polo “has had the effect of transferring a corrupt form of the name of a portion of the African mainland to the great African Island” (Evans (1973), 11). Burgess (2014) stresses that the story is historically inaccurate. In fact, Marco Polo never saw Madagascar (or any part of Africa) and his misunderstanding was merely that the Arab or Malay sailors were referring to some island. Later, cartographers developed the custom of calling “Madagascar” the island we now know as “Madagascar,” inspired by Marco Polo’s earlier confusion. See also notes 10, 16, and 20 and their surrounding texts below. ⁴ Kripke had already noted a case of failure of the preservation of reference along chains of transmission of names (“Santa Claus”). But perhaps his example was not transparently one where reference is not preserved and the inheriting speakers intend to keep using the name in the same way as the bestowing speakers. In fact, Kripke conjectured that some failure to intend to keep using the name with the same referent might be responsible for the failure of reference preservation in the “Santa Claus” case ((1972), 96–7). (And it is not far-fetched to imagine some follower of Luther forming the intention of turning “Saint Nicholas” into a fictional name.)

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64      name from other speakers can have a direct, e.g. perceptual, knowledge of the referent, one not merely derived from other speakers. Aristotle’s school companions, for example, surely learned his name from other people, yet surely eventually developed an intention of referring with (the ancestor of) “Aristotle” to “the child we know from school” or “that (boy),” an intention that presumably must play a role in the explanation of the fact that their uses of “Aristotle” referred to Aristotle, besides any role that the intention of using the name in the same way as other speakers may have played. Another, essentially related point stressed by Evans is that a name may intuitively stop having the referent it started having, even among speakers who have had a direct knowledge of that referent, such as the introducers of the name and others closely linked to them (Aristotle’s parents and his school companions, in our leading example). If the child Aristotle had been replaced at some point by a very similar look-alike, it is at least unclear that after a while the companions’ and even the parents’ uses of “Aristotle” would still have referred to Aristotle, and unclear also that after a sufficiently long while these uses would not have referred to the look-alike.⁵

Recent Descriptivist Views about Name Reference Fixing These are in broad strokes the recent major advances in our understanding of reference fixing for proper names. Now these advances have had a perhaps unexpected consequence. They have lately revived the idea that a competent use of a name must after all refer in virtue of its connection in the user’s mind with an appropriate description, a description that fixes the referent of the name even if it need not provide its meaning. This description—so goes the idea—will not be based on biographical characteristics, and must instead somehow either reflect in some way or simply explicitly detail the mechanism of reference fixing for the name as elucidated by the Kripkean and postKripkean advances just reviewed. Note that the idea is not merely that the referent of a name turns out to coincide with the object described by some such description. Even if such a description existed, this would not be a ⁵ I have labeled Evans’s points as “qualifications” of Kripke’s picture, although some philosophers inspired by Evans have seen at least the point about the possibility of name-reference change along historical chains of transmission as creating a fundamental problem for that picture, and even as supporting descriptivism. Evans (1982) gave a detailed positive account of name reference, which he doesn’t seem to have seen as fundamentally opposed to Kripke’s picture, and of which we will say a bit more in the section “Recent Theories of Jointly Necessary and Sufficient Conditions for Name Reference” below.

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distinctive view. Probably some anti-descriptivists think that such a description exists, but they do not think that a normal competent speaker typically knows that the description and the name are co-referential. The additional claim that the description and the name are somehow known by a normal competent speaker to be co-referential is part of the essence of recent descriptivist views about name reference fixing. One recent view of this sort is that of McKinsey (2010). McKinsey rejects the thesis that “Aristotle” is semantically equivalent with a description in the idiolect of any normal speaker, but proposes that a competent use of “Aristotle” must have its referent fixed by a description associated by the speaker user with that use. The description will vary as a function of whether the speaker merely receives “Aristotle” from other speakers, or has a direct knowledge of Aristotle not merely derived from other speakers. In the first case, McKinsey proposes that the speaker will have the referent of her uses of “Aristotle” fixed by a description such as “the person here relevant actually called ‘Aristotle,’ of whom I have heard that he was the philosopher who first described syllogisms.” In the second case, the speaker will typically have many descriptions associated with “Aristotle,” such as “the child we know from school” and “the boy over there”; in this case, the referent of “Aristotle” will be determined (roughly) as the thing that satisfies a greater number of such descriptions. It seems fair to say that this kind of proposal is strongly discredited by the observation (with roots in Kripke) that a normal competent speaker may be wrong about whether she got a certain name from other speakers and heard what she believes about the referent from them. (See Soames (2005), 300, for a related point.) Suppose Aristotle’s father got estranged from his family shortly after his wife gave birth to Aristotle, came to believe that he had never seen Aristotle, and eventually forgot that he had introduced (the ancestor of) “Aristotle” for his son and that he knew from seeing him at birth (and only from this fact) that he was his son. In such a situation he may have developed the confused belief that he had inherited the name “Aristotle,” and the belief that he was his son, from others. Then he will (supposedly) associate with “Aristotle” a description of McKinsey’s first type, such as “the person here relevant actually called ‘Aristotle,’ of whom I have heard from others that he is my son.” However, this cannot be reference fixing, for if it is then the father will not be referring to Aristotle. And yet Aristotle will still be intuitively the referent of (the ancestor of) “Aristotle” in his idiolect. Other versions of the renewed descriptivist idea emerge in an important line of causal descriptivists, including Kroon (1987), (2009), Lewis (1997), and

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66      Jackson (1998), (2010). Some of these versions are not transparently subject to objections similar to the one just sketched. Thus, Jackson (2010) supposes that the referent of a token of “Aristotle” produced by a typical normal speaker of our time must be given by some complication of a description such as “the thing that stands at the far end of the information-preserving causal chain . . . whose near end is the person making the claim and the token they produce” (141), which might be taken to summarize at least one aspect of Kripke’s rough picture of reference fixing for names. Jackson emphasizes that the relevant complication will be hard to come by, and probably so complicated that a typical speaker would not be able to state it without intensive coaching. But the relevant complication is somehow implicit in the mind of a competent speaker, who could therefore come by it after sufficient reflection and coaching. After such sufficient reflection and coaching, which would involve consideration of phenomena such as those described by Evans and others, the competent speaker, suggests Jackson, would end up with a description that would unequivocally pick out the intuitive referent when the relevant name has one, and that would fail to refer just when the name intuitively does so fail. Jackson also suggests that the complicated descriptions in question are not only not semantically equivalent with the name, but not even a priori co-referential. And yet, he stresses that a token of “Aristotle” must be known by a competent user of it, in virtue of her linguistic competence with it, to be co-referential with a description that sufficiently complicates a description such as “the thing that stands at the far end of the information-preserving causal chain whose near end is the person producing the token.”⁶ What could the complicated description be? It would have to incorporate somehow other aspects of Kripke’s basic picture aside from the “causal chain” aspect, as well as all the complications of Kripke’s basic picture unearthed so far by theorists of reference such as Evans and others. So, to begin with, it would have to incorporate the possibility, explicitly considered by Kripke, that the referent of a name is not really at the far end of any causal chain whose near end is a use of the name; this may have happened because the referent was merely singled out by a description stipulated by the name’s introducer, without there having been causal contact between

⁶ There are many other renewed descriptivist authors who rely on similar though different ideas, but we cannot deal separately with each of them. In García-Carpintero’s ((2000), 146) and (forthcoming) especially subtle account, for example, the relevant description summarizing Kripke’s rough picture is forcefully argued to be involved in a presupposition carried by uses of the relevant name and knowable by competent users and hearers of the name. The anti-descriptivist considerations below will indifferently apply to views that postulate or imply this knowability condition.

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referent and introducer.⁷ And it may have happened in other ways. Here is one, noted by Jonathan McKeown-Green: Suppose, for example, that you know of a certain region in Ireland in which the residents of different towns see to it that there is always exactly one person bearing the name Patrick O’Grady. Learning of this curious fact, you set out to visit the region to interview the different men bearing that name. On entering a pub in a new town, you announce “I am looking for Patrick O’Grady, whom I am willing to pay for an interview for my new book.” (Soames (2005), 301)

Here you will have referred to a certain individual, even though this individual will not necessarily be in the origin of a causal chain leading up to your use of “Patrick O’Grady.” And the description would also have to spell out somehow the notion of “information-preservingness” in the uncomplicated description, so as to yield unequivocally the intuitive results in the cases of reference change without changes in intentions to refer, noted by Evans, as well as in the cases of reference change via changes in intentions to refer, noted already by Kripke. In view of this, one might think that the complicated description would have to mention somehow a long list of cases, and begin somewhat like this: the thing x such that: either (1) none of the cases later to be mentioned obtains and x stands at the far end of the causal chain of transmission of the name whose near end is the person producing the name token; or (2) there is some intermediate reference change in the causal chain of transmission of the name whose far end is the introduction of the name and whose near end is the person producing the name token, due to an inheriting speaker wrongly thinking of some object that it is referred to by the speakers from whom he inherited the name, and x is the last object with this property in the chain; or (3) the object at the far end was merely singled out by a description stipulated by the name’s introducer, without there having been causal contact between referent and introducer; or . . .

Several other known exceptions would have to be added.⁸ ⁷ In fact, such causal contact may be impossible in some cases; Kripke himself considers the case of “π” (imagined as introduced by means of the description “the ratio of the circumference of a circle to its diameter”), which he views essentially as a proper name. ⁸ Beginning with Kripke’s Santa Claus-type cases (at least if these are of a sort different from Evans’s “Madagascar” type of cases), and with McKeown-Green’s cases.

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68      Soames (2003) sensibly objects to views of this sort that they are “speculative in the extreme” (368). It does seem implausible to think that a normal speaker should know, in a reasonable sense of “know,” that “Aristotle” as she uses it is co-referential with a description of this sort. The envisaged description will be just too complicated. But, it might be argued in reply, speculative doesn’t mean impossible. And it might also be argued that the description in question might perhaps be somehow reduced to a simpler description. This might happen if it turns out that all the cases that would need to be considered can be seen as straightforward instances of just two or three appropriately described general cases, or at any rate of just few enough cases to make it reasonable to think that the resulting description is somehow known by a normal speaker for a typical use of a name. For example, it may not be initially implausible to think that all the cases in which a name appears with a new referent in a causal chain, be they cases of pure name introduction (either by description or demonstration), cases of reference change, “McKeown-Green cases,” or other cases, all respond to a single general characterization. Perhaps cases of reference change arise because the relevant speaker just comes to associate some description or demonstration with the relevant name, in a way that supersedes all previous associations; and perhaps in a “McKeown-Green case” the relevant speaker just comes to be able to use “Patrick O’Grady” because he associates with it in a way superseding previous associations an appropriate description (such as “the man named ‘Patrick O’Grady’ in this town”). If so, we might think that the description that theorists like Jackson need could be this: the thing x such that: either (1) the person producing the name token associates with the name in a way superseding previous associations a description describing x or a demonstration demonstrating x, or (2) there is some stage in a causal chain of transmission of the name whose near end is the person producing the name token, in which a speaker associated with the name in a way superseding previous associations a description describing x or a demonstration demonstrating x, and at no later stage did this happen again for a thing different from x.

But unfortunately for the descriptivist, this cannot be the whole story yet. We know, for example, that in some cases the person introducing a name introduces it via, say, a description and a demonstration that he thinks determine the same thing, but in fact don’t. Think of the following case from Kripke ((1972), 80, n. 34): someone, while watching Venus in the morning, forms the

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intention of calling “that,” “the morning star,” “Phosphorus.” Intuitively Venus becomes the referent of “Phosphorus” in the speaker’s mouth, even though there is a conflict between the intention of using “Phosphorus” for “that” and using it for “the morning star” (Venus is not a star). One problem then is that both intentions are intended to supersede previous associations, but since they don’t determine the same thing, the description we are considering on the causal descriptivist’s behalf fails to determine an object in this case, despite the fact that Venus is the intuitive referent. And another problem is that we know that causal transmission by itself, even when the receiving speakers don’t associate with the name any material that supersedes previous associations, does not always preserve reference, at least clearly (see, for example, the “George Smith” case also from Kripke ((1972), 95–6), recalled in detail in the next section). So the causal descriptivist needs some further conditions in both parts (1) and (2) of the description above—where the additional condition in (1) will have to imply somehow that some referential intentions override other conflicting intentions at the name introduction stage, and where the additional condition in (2) will have to introduce some restriction on bare name transmissions. What he needs is then a description of the following form, with the schematic parts “A” and “B” filled somehow: the thing x such that: either (1) the person producing the name token associates with the name in a way superseding previous associations (a way with characteristics A) a description describing x or a demonstration demonstrating x, or (2) there is some stage in a causal chain of transmission of the name (a chain with characteristics B) whose near end is the person producing the name token, in which a speaker associated with the name in a way superseding previous associations, and with characteristics A, a description describing x or a demonstration demonstrating x, and at no later stage did this happen again for a thing different from x.

Call this description form “D.” Perhaps it does not seem immediately implausible or too speculative to think that a description of the form D, one with the “A” and “B” parts appropriately filled, could both fix the referent of a name as used by a competent speaker and be known by the speaker, in virtue of her linguistic competence, to be co-referential with the name in her idiolect. Recent anti-descriptivists give essentially one consideration against descriptivism that would, if correct, cast strong doubts over suggestions of this kind. Soames (2003), (2005), in particular, strongly emphasizes a distinction

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70      between (i) foundational facts about a word, facts that, in the case of a name, are responsible for the name referring to what it does in a speaker’s idiolect, and to be described in whatever terms are necessary, e.g. in terms of descriptive or demonstrative introductions, preservations along causal chains of transmission, etc.; and (ii) semantic facts about a word, facts “that speakers must master in order to understand the word” ((2005), 183). With this distinction in place, the anti-descriptivist may not unreasonably claim, in the words of Soames, that when one speaks of reference fixing by historical chain, one is alluding to certain foundational facts of the sort (i) above that bring it about that a name or natural kind term comes to refer to what it does, and that play important roles in determining that the original reference is preserved over time. These foundational facts are not parts of the meanings of names or kind terms of which competent speakers must be aware. Speakers have to know what the words of their language mean and refer to, and they must know how to use them. They don’t have to know how those words got to mean and refer to what they do; nor do they have to know how the conditions for their proper use arose and are sustained. (Soames (2005), 185)

The distinction Soames describes is surely reasonable and, more importantly, it does suggest that it is perfectly conceivable, and possible, that names get to refer to what they do, and keep referring to what they do along series of transmissions, independently of whether semantically competent speakers know anything about how this happened or happens. And if it is conceivable and possible, it may well be true. In view of the fact, pointed out above, that the descriptions that the descriptivist needs must have a considerable degree of complexity, this may be all the anti-descriptivist needs to discredit the descriptivist’s apparent best shot at a theory of reference fixing for proper names. But is it really possible for names to get to refer to what they refer to, and to keep referring to what they refer to when successfully transmitted, without speakers competent with names having to know anything about how this happens? Descriptivists have flatly rejected this claim, even after taking note of distinctions similar to Soames’s. Thus Jackson, commenting precisely on the passage from Soames we just quoted, says: As against this, I insist that someone who doesn’t know that typically names get given to things and does not understand the causal informational role of names does not understand their role in English. (Jackson (2007), 21)

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Is this view defensible? It appears that there is something defensible about it. Suppose Jones is told a story about how the name “Aristotle” is heard for the first time by a student in a high school history class. The teacher, says the story, utters the sentence There were many important Greek philosophers, among them Socrates, Plato, and Aristotle. A few days after this, says the story, the student, while talking to his parents, utters the sentence Aristotle was a Greek philosopher. After being told this story, Jones says There is something wrong here; the student is not entitled to use “Aristotle” when talking to his parents; it is not enough that he heard the name from his teacher just a few days earlier. Clearly, there would be something very wrong with Jones’s linguistic knowledge involving names. And this will be so even if Jones happens to be an otherwise competent user of names like “Aristotle.” Jones may, for example, know who Aristotle was and use “Aristotle” in many ways as most people normally use it. But if Jones does not recognize that the use of “Aristotle” by the student in the story is correct, I think it’s clear that a case can be made that there is something wrong with Jones’s linguistic competence with names. Similarly, suppose that Jones is told a story about Aristotle’s father uttering We will call this boy Aristotle when seeing Aristotle for the first time after his birth. A few minutes later, continues the story, Aristotle’s father utters Aristotle will be a great man. After being told the story, Jones says There is something wrong here; Aristotle’s father is not entitled to use “Aristotle” to say that he will be a great man; it is not enough that he said that he would call him that way while seeing him. Again there would be something very wrong with Jones’s linguistic knowledge involving names, even if Jones happens to be an otherwise competent user of names like “Aristotle.” Soames would perhaps insist that semantic competence with a name includes merely knowledge of what the name refers to and knowledge of how to use the name in typical situations. And the descriptivist would probably insist that there is no pre-theoretical reason not to require semantic competence with names to include an ability to recognize that there is nothing wrong with the uses of “Aristotle” in the stories above. And I think the descriptivist would have at least a good case that “semantic competence” could be used without stretch in the encompassing way he suggests. I myself suspect that there are two notions of semantic competence underlying this discussion, closely related to the two senses of “meaning” that (following Kaplan) we distinguished in chapters 1 and 2: a restrictive notion of semantic competence, which involves knowledge of facts about semantic content in the sense of information semantically expressed by expressions or expression uses, possibly understood as truth-conditional content; and a more encompassing

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72      notion of semantic competence about both aspects of semantic content and about “foundational” aspects, which involves knowledge of more facts concerning linguistic conventions bearing on semantic content, though still facts whose knowledge is required of the normal speaker for her to count as competent in a sufficiently broad intuitive sense.⁹ At this point Soames might appeal to the not unlikely fact that the sort of ability involved is a special case of a general ability that linguistically competent speakers have: standardly, when a speaker uses any word—magenta, abode, osteopath, alphabetize, necessarily, etc.—the speaker intends to use it in accord with the linguistic conventions of the community. The speaker intends to use it to refer to, or express, whatever other competent members of the community do. In the case of proper names, it is recognized both that a given name may be used by only a subpart of the community, and that different members of the relevant subcommunity (who use the name to refer to the same individual) may associate it with very different descriptive information without the name meaning something different for each of them. Thus, the general intention that one’s use of words conform with the linguistic conventions of one’s community translates, in the case of most names, into the intention to use them to refer to whomever or whatever other relevant members of the community use them to refer to. Some such intention is a standard condition on normal language use, not a part of meaning. (Soames (2005), 301)

But the descriptivist is likely to retort that he doesn’t care whether the normal speaker’s ability to recognize that names are transmitted and are given to things is an instance of a more general ability, or whether it is a semantic ability in some restricted sense of “semantic.” He is likely to insist that, as long as he can maintain that some kind of knowledge of transmission and introduction conventions must be possessed by normal competent speakers, he can maintain that names get their reference fixed by descriptions known to normal

⁹ I suspect that Soames would ultimately be sympathetic to this distinction and to the encompassing use of “semantic competence”; see Soames (1989) for what I take to be a statement of congenial views. See also Soames (2002), 103f., where he actually speaks of a sense of “meanings” in which these are “rules mastery of which explains semantic competence,” contrasted with “meanings in the sense of semantic contents”; and where he concedes that “it is reasonable to suppose that someone who knows what a name is, has at least an implicit understanding that names standardly get their referents by stipulation, after which they are passed on to others by historical chains of transmission.” See also our comments surrounding our explanation of Kaplan’s distinction between content and character as two notions of meaning in chapter 2.

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competent speakers (even if the descriptions are not part of the names’ meanings). The descriptivist will not care much whether some of the knowledge required for knowing the appropriate descriptions is not specific about names, provided all the knowledge involved is knowledge possessed by normal speakers, linguistically competent with the expressions of their language in general.

Referential Indeterminacy as a Fundamental Problem for Descriptivism Perhaps the descriptivist can resist the battery of reviewed objections from anti-descriptivist critics by carefully treading on his high wire. Perhaps. But even assuming for the sake of argument that this is so, I think there is a more fundamental problem that shows that descriptivism cannot be right, or at least that makes it much more doubtful than the preceding objections do that descriptivism could be right. The problem, parallel to the problem we saw for descriptivist views of demonstratives, is that descriptivism cannot give an account of knowledge of reference-fixing conventions that can mesh in the right way with the phenomenon of (apparent) referential indeterminacy for names. At least some presumably competent speakers will think that many stories about the introduction and transmission of names involve cases where it is not clear whether a use of a name has a referent. This is exactly my impression when I read the following story, credited by Kripke to Richard Miller: If . . . the teacher uses the name ‘George Smith’—a man by that name is actually his next door neighbor—and says that George Smith first squared the circle, does it follow from this that the students have a false belief about the teacher’s neighbor? The teacher doesn’t tell them that Smith is his neighbor, nor does he believe Smith first squared the circle. He isn’t particularly trying to get any belief about the neighbor into the students’ heads. He tries to inculcate the belief that there was a man who squared the circle, but not a belief about any particular man—he just pulls out the first name that occurs to him—as it happens, he uses his neighbor’s name. It doesn’t seem clear in that case that the students have a false belief about the neighbor, even though there is a causal chain going back to the neighbor. (Kripke (1972), 95–6)

My impression, apparently shared by Kripke, is that, even if the students may come to use “George Smith” after having been introduced to the neighbor’s

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74      name by the teacher, it is not clear that their uses of “George Smith” come to refer to the neighbor. I am uncertain about it. I cannot say for sure that my uncertainty is not due to some kind of obtuseness, or to plain ignorance, but uncertainty it is none the less. However, more importantly, I also think that even someone with a more definite view of the situation should not judge incompetent a speaker like me, who abstained from issuing a definite verdict of reference or reference failure in this case. For another example, turn to the above (historically inaccurate) story often attributed to Evans. In the story, when Marco Polo inherits the name “Madagascar” he has both the intention of referring to whatever the Arab or Malay sailors referred to and the intention of referring to the island now known as “Madagascar”; these conflict, for they lead to different objects. At this point, it seems as if neither of those two referential intentions overrides the other, and it is intuitively uncertain whether “Madagascar,” as a matter of what the reference-fixing conventions determine, refers to either thing in the mouth of Marco Polo. (Of course, there must be a later time in the history of the transmission of the name (according to the story) in which “Madagascar” begins to refer to the island in the mouth of normal speakers.)¹⁰ Here is another story with the same characteristic. A clairvoyant who has never heard of Aristotle before (we have somehow made sure of this) “hears” someone use the name “Aristotle.” The other people in the room don’t see or hear anybody, but the clairvoyant claims he has just “heard” someone, somewhere far away, utter Aristotle was a great philosopher. Has the clairvoyant ¹⁰ Burgess (2014) appears to think that “Madagascar” in the mouth of the imagined Marco Polo conventionally refers to the island now known as Madagascar, because the imagined Marco Polo’s intention of calling a certain thing (the island) “Madagascar” is perceptually based and de re, and such intentions override non-de re intentions such as the intention of referring to whatever “Madagascar” referred to in the mouths of the sailors. But if this is Burgess’s view, I think it’s more than dubious. (Compare this case with the intuitively clearer case of overriding by a perceptually based referential intention in the imagined introduction of “Phosphorus” described above in the main text, and with the perhaps intuitively clearer case of non-overriding by a de re intention provided by the madman who calls himself “Aristotle” in chapter 1.) Perhaps Burgess is confusing here the presumable fact that the imagined Marco Polo “speaker-refers” (in the sense of Kripke (1977)) to the island he is seeing with the idea (dubious in my view) that “Madagascar” semantically and hence conventionally refers to the island in the imagined Marco Polo’s mouth. (Berger (2002), whom Burgess cites in this connection, seems to propose only the weaker view that some de re intention of referring to a new thing must always be involved in cases of reference change along chains of transmission, but I doubt that even this must always hold.) Martí (2015) emphasizes that “Madagascar” in the mouth of the imagined Marco Polo does not clearly conventionally refer either to the island or to the part of the continent the sailors called “Madagascar.” On the other hand, when we turn to the (presumable) historical facts, the question arises whether the real Marco Polo, after inheriting “Madagascar” along with the very weak belief that the sailors used it for some island, did refer to anything with “Madagascar,” and if so to what. My somewhat shaky intuition is that Marco Polo’s uses of “Madagascar” did refer to the same part of the continent that the sailors called “Madagascar”; we will come back to this case.

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inherited the name “Aristotle,” in such a way that he is now able to refer to Aristotle with his uses of it? Again, as far as I can tell, it is unclear whether the clairvoyant’s uses of “Aristotle” will from now on refer to Aristotle or not. Other stories where I am uncertain as to whether reference takes place or not involve name introductions and are parallel to the stories suggestive of referential indeterminacy that we saw in the case of demonstratives. Most of these exploit the possibility of conflictive referential intentions when names are introduced. First, suppose once more that on the wall behind Kaplan used to hang a portrait of Carnap, but now, unknown to Kaplan, the Carnap portrait has been replaced by one of Spiro Agnew. Kaplan, without looking, points behind his back and now says, with the intention of referring both to the portrait of Carnap and to the thing that he is pointing at, I will call that “Carny.” What is the reference of “Carny,” if any? The portrait of Agnew or the portrait of Carnap? Or is it clear that there is reference failure? My impression is again that it is not clear whether “Carny” has a reference or not. But again, more importantly, I don’t think that we would judge incompetent a speaker who did not think it appropriate to issue a definite verdict of reference or reference failure in the case. Now suppose I am in a thick forest, with my visual attention focused on a tree top and with my hand touching what I tacitly but wrongly assume to be the same tree’s trunk. I say I’ll call this tree “Tim,” with the intention of referring both to the tree I’m seeing as represented by my visual perception of it and to the tree I’m touching as represented by my tactile perception of it. What is the reference of “Tim,” if any? Is it the tree I’m touching, or the tree my visual attention is focused on? Or is it conventionally determined that there is reference to neither? Again I think there is no clear answer, and that a speaker should not be regarded as incompetent if he is not clear about the situation. One final example involving conflicting intentions has again Barnes walking in the streets. A woman he vaguely sees approaching bumps into his right side, and he turns in that direction. As he does, he has a momentary hallucination. He hallucinates a woman, and he forms the belief that the woman that just bumped into him is the woman he believes he is seeing now. He forms the intention of calling the woman that he thinks he sees and that he thinks just bumped into him “Nora.” Do Barnes’s uses of “Nora” from then on refer to the woman that just bumped into him, or do they not? Once more it is not clear to me what the answer is. In a final story, now not involving conflicting intentions, I am watching a live TV show in which a person who claims to be a clairvoyant “sees” a dog in a

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76      land far away. On the basis of his purported extrasensory perception, he says I will call this dog “Jeri.” All of the properties he attributes to the dog happen to be properties of my dog Joos, who was born recently and whose existence— I am reasonably certain—is not known to any person aside from me. I do some research, and I conclude that the clairvoyant cannot have known Joos, at least by standard means. But did his use of “Jeri” refer to Joos? I am uncertain. I have some inclination to think that it did not refer to anything, but at the same time I cannot help feeling that it may have referred to Joos. As far as I can tell, it is unclear whether “Jeri” referred to Joos in the mouth of the clairvoyant or not. As in the case of demonstratives, a reasonable explanation of unclarity in these cases is referential indeterminacy: the reference-fixing conventions about names, which we may grant are in some sense known by normal competent speakers, don’t determine a reference in these cases, nor do they imply that there is reference failure. Assuming that these conventions are the only thing that could determine reference of reference failure, knowledge of the conventions does not yield knowledge of reference or of reference failure in these cases, hence the unclarity for some reflective competent speakers (even if some competent speakers may not be unclear in these cases and have strong inclinations one way or the other). As in the case of demonstratives, the existence of cases of probable indeterminacy gives us reasons to think that a descriptivist theory of reference fixing for names will in general not be correct, if the description is to be known by normal competent speakers. In the first place, a description that is extensionally correct will be hard to come by, as conventional reference failure and indeterminacy will have different sources. But secondly, a normal competent speaker need not know that there is indeterminacy, and thus ultimately reference failure, in cases of indeterminacy; and yet, the standard theories of overriding intentions examined in chapter 2, when used to fill the “A” part in the description form D above, yield the result that our examples of presumable indeterminacy are classified as cases of determinate reference or reference failure, essentially for the same reasons we saw when we discussed the analogous examples in the case of demonstratives. In particular, all the fillings of the “A” part will yield a definite failure of reference in the “Tim” case of the trees if, as we can suppose, my two intentions in that case are perfectly symmetric. If they are, no theory of overriding intentions can introduce the appropriate indeterminacy. A speaker associating a description of the form D with “Tim” for an appropriate filling of the “A” part would thus issue a definite verdict of reference failure in the trees case (assuming she had perfect knowledge of the

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surrounding circumstances), but such a speaker would then have in mind a theory of name reference fixing that would not be a fully correct theory of the (knowable) conventions governing it. The situation is not greatly dissimilar with what one might expect to be the candidate fillings for the “B” part. The “George Smith” case and (the historically inaccurate) “Madagascar” case indicate that the beliefs involving the transmitted name that the receiver gets at the transmission stage cannot differ in some ways from the beliefs of the name’s bestowers if there is to be successful transmission of reference. So, if a filling for the “A” part had to imply which referential intentions are overriding at the name introduction stage, the “George Smith” case and (the historically inaccurate) “Madagascar” case indicate that a filling for the “B” part will have to resolve in some way how the body of beliefs involving the name formed by the receiver at the transmission stage should not differ from the bestowers’ body of beliefs. But again the prima facie candidates have definite implications of reference or reference failure in these cases. Consider the filling “(a chain with the characteristic that) the receivers don’t form a belief about the kind of the name’s bearer different from that of the bestowers”; this definitely implies that reference is transmitted successfully in the “George Smith” case, and that it is not in the “Madagascar” case. Or consider “(a chain with the characteristic that) the receivers don’t form beliefs involving the name too different from those of the bestowers”; this definitely implies that reference is not transmitted successfully in the “Madagascar” case or in the “George Smith” case. Or finally, consider “(a chain with the characteristic that) the receivers don’t form beliefs involving the name that on the whole conflict with the beliefs of the community of users of the name at large”; this again definitely implies that reference is not transmitted successfully either in the “Madagascar” case or in the “George Smith” case. (And we should note also that in the clairvoyant’s “Aristotle” case, any filling of the schematic parts of D will yield a definite failure of reference, as the “transmission” to the clairvoyant is not causal.) So, again, when we plug into the “B” part some of the most obvious candidates, the ensuing descriptions of the form D yield definite results as to reference or reference failure in our cases of presumable indeterminacy. Thus, if some such description were really known to be co-referential with “George Smith” as used by the students (say) by every normal competent speaker, every normal competent reflective speaker would presumably be clear about the referential status of “George Smith” in the students’ mouths (assuming he or she had perfect knowledge of the surrounding circumstances). But some normal competent reflective speakers are unclear (and they would remain so

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78      even after reflection on and explicit consideration of these descriptions of the form D), so it cannot be such a description of the form D that must be known to be co-referential with a name by a normal competent speaker. A speaker who associated such a description with a name would again have an incorrect theory of name reference fixing in mind. This conclusion about the “B” part is now perhaps less definitive than the corresponding claim about the impossibility of an appropriate filling for the “A” part, but this latter impossibility is at any rate enough to make it fairly clear that a description of the form D cannot in general be expected to be known to be co-referential with a name use by a normal competent speaker. It’s worth noting that a certain move the causal descriptivist might try would be subject to essentially the same problem. If we assume the natural explanation of referential unclarity in terms of referential indeterminacy, one option is to suppose that the right abstract form for the description is something similar to this, which we may call D0 : the x such that: either (1) [as in D]; or (2) [as in D]; or (3) the person producing the name token associates with it a description or demonstration in a way superseding previous associations, and with characteristics A, but the description or demonstration does not determine a single thing; or there is some causal chain of transmission of the name whose near end is the person producing the name token, with the characteristics B, but in the chain the speaker who associated with the name in a way superseding previous associations a description or a demonstration, so that at no later stage did this happen again, associated a description or a demonstration that does not determine a single thing; and x is nothing; or (4) neither of the circumstances (1), (2), or (3) obtains, and x is who knows what.

The idea is that here a list would appear of the circumstances giving rise to conventional reference ((1) and (2)), conventional reference failure ((3)), and indeterminacy ((4)) (once appropriate fillings were provided for the “A” and “B” parts, which would essentially codify provisos for reference). Presumably a minimally appropriate description of the form D0 will not determinately describe anything in the cases of apparent indeterminacy, these being cases in which clause (4) applies, as in them the relevant conditions described in clauses (1), (2), and (3) do not obtain. The problem, however, is that in order to know that a description of the form D0 is co-referential with (say) “George Smith” as used by the students, a normal competent speaker would have to know that the referential

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conventions cover exactly the circumstances (1), (2), and (3), leaving indeterminate what happens in circumstance (4). But if there is indeterminacy, it is too much to ask that a normal competent speaker should know exactly when there is (in)determinacy. A speaker can be competent if she knows when there is conventional reference or reference failure in cases of determinacy, but competence doesn’t require her to know that a case of indeterminacy is a case of indeterminacy. (And she might even be wrong and think that a case of indeterminacy is one of determinacy.) So it is again not credible that a competent speaker should know that a use he makes of a name should be co-referential with a description of the form D0 . It is defensible that a competent speaker should in some sense know the conventions establishing successful reference in name introduction, successful name transmission, or failure of reference. That is why Jackson’s above reply to Soames is tolerably acceptable: there is something wrong about the linguistic competence of someone who does not recognize run-of-the-mill applications of the conventions of name transmission and introduction as unproblematic. But if these conventions fail to dictate a verdict of reference or failure of reference in all circumstances, it is not reasonable to postulate that a competent speaker should also know that the conventions establishing reference or transmission of reference do so fail. For even if the competent speaker somehow knows, in the case of each particular convention of this kind, that it is a convention, he cannot reasonably be expected to know that the conventions he knows are all the conventions in which he is participating as a member of his linguistic community—he cannot reasonably be required to know that clause (4) can be straightforwardly added. This is not to deny that some speakers may have beliefs, justified to varied degrees, to the effect that a certain group of conventions of introduction, failure, and transmission of reference for names exhaust all referential conventions involving names. These speakers will presumably include speakers with substantial theoretical knowledge about language, or speakers with the abilities required to consider and evaluate linguistic hypotheses of a certain complexity. But it is not reasonable to attribute a belief in these hypotheses, let alone knowledge, to all, or even a large number of typical competent speakers. Clearly a speaker can be linguistically competent without knowing, even in an implicit way, that she is linguistically competent, essentially for the same reasons that it will not in general be true that someone who knows something will also know that she knows. For a speaker to be linguistically competent it is clearly enough that she somehow masters the conventions of her language, there being no need for her to know that they are all the conventions. This

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80      implies that the descriptivist, even when he makes this last, “causaldescriptivist” shot, cannot be right.

Roots of Referential Indeterminacy But the moral of indeterminacy is larger. The preceding considerations show that theories purporting to give jointly necessary and sufficient conditions for reference which are known to be such by normal competent speakers will be difficult or impossible to come by. But most, perhaps all theories purporting to give jointly necessary and sufficient conditions for reference, even if they are not committed to descriptivism, can also be expected to have a hard time giving extensionally correct accounts of name reference. Non-descriptivist theories are of course exempt from the descriptivist requisite that a normal competent speaker should know the relevant necessary and sufficient conditions to be such, and that’s certainly a big onus off one’s shoulders. However, it is likely that theories of jointly necessary and sufficient conditions, both those that don’t seek to reflect reference-fixing conventions in the conditions in question and those that involve conditions that can be seen as statements of the conventions, will find purely extensional troubles ultimately traceable to indeterminacy or to its presumable sources. An attractive view of referential indeterminacy is that this emerges from two sources. One source is the probable fact that the reference-fixing conventions for names give imprecise conditions for name reference, and imprecise conditions for name reference failure. Many of the notions which are probably needed in the statement of the conventions will be substantively imprecise notions. In the statement of the conjectured conventions in the final section of this chapter, for example, we’ll make use of the notions of a community of users of a name and of a conflict on the whole between the beliefs of a particular speaker and the beliefs of the community at large; and there is no way around the fact that it will in many cases be unclear or simply indeterminate who should count as a member of the relevant community, or when a speaker’s beliefs ought to be taken as conflicting on the whole with the beliefs of the community at large. A second, deeper source of indeterminacy lies in the probable fact that, as we already hypothesized for the case of demonstratives, the conventions in question adopt the form of statements of merely roughly sufficient conditions for reference and for reference failure. The list of the conditions in these statements is probably not exhaustive of the full range of relevant worldly

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possibilities, which will mean that there will be many conditions under which the conventions will simply fail to imply anything about whether reference or reference failure takes place. Furthermore, the list of such conventions of sufficient conditions is not in any case established as jointly necessary as a matter of convention. Rather, the correct picture of the list is of a collection of maxims for linguistic performance and evaluation that get established over the course of time, but without there being at any moment a concluding convention establishing the previously established sufficient conditions as jointly necessary. Moreover, as we insisted above, a normal competent speaker, even if he somehow knows the conventions, need not know that the list of them is the list of all the conventions there are, and there is even a good chance that even sophisticated linguistic theorists will not be able to know of any proposed list that it is complete; this will presumably make the right list, at any historical moment, hard to come by. Now, if the reference-fixing conventions state imprecise roughly sufficient conditions for name reference and name reference failure that are in some sense known by normal competent speakers, a linguistico-philosophical theory will have a hard time producing extensionally correct accounts of name reference in terms of jointly necessary and sufficient conditions, especially if these are not meant to reflect reference-fixing conventions. On the one hand, it will be difficult, in terms of a theoretical apparatus of conditions which don’t reflect the conventions known by competent speakers, to place the appropriate conceptual borders at the same fuzzy places as the real conventions, or even along the same dimensions of precision, in such a way that roughly the same conditions are characterized as necessary and sufficient that are let in as sufficient for reference and reference failure by the real conventions. This will mean that there will probably be both cases where reference does not occur conventionally (either because of conventionally determined reference failure or because of indeterminacy) but the theorized conditions imply that it occurs, and cases where reference takes place but the theorized conditions imply that it doesn’t—the theory will probably both overgenerate and undergenerate. On the other hand, if the conditions postulated as sufficient by a theory of jointly necessary and sufficient conditions are conditions which somehow reflect the conventions known by normal competent speakers, these will have a good chance of not being exhaustive of the full range of conditions that the conventions contemplate. This will mean that there will probably be cases where reference conventionally occurs but not in virtue of the theorized conditions; since these will have been postulated as necessary also, the theory will undergenerate.

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82      Perhaps some theory of jointly necessary and sufficient conditions for name reference can yield an extensionally correct account of reference for uses of names. But I conjecture that this could only happen by some kind of very happy random coincidence. A more promising approach is just to live with the fact that the recognizable conventions of name reference probably provide only a hard to come by list of imprecise roughly sufficient conditions for name reference and name reference failure, and to incorporate the fact directly into our picture of the situation. We will devote the last section of this chapter to the development of a picture of this sort. But before this, we will gather some evidence supporting our ominous forecasts concerning theories of jointly necessary and sufficient conditions which are not meant to reflect referencefixing conventions (somehow knowable by normal competent speakers). The evidence will come from the examination of two recent theories of this kind, those of Devitt (2015) and Dickie (2011). This will be our stepping stone toward the more appropriate picture of the final section, which will not be subject to the problems rooted in indeterminacy and which will accommodate all the other advances and desiderata that have emerged in the course of the preceding discussion.

Recent Theories of Jointly Necessary and Sufficient Conditions for Name Reference Devitt in fact proposes several different sets of necessary and sufficient conditions for name reference, based on a number of distinctions. He makes a threefold distinction between designational names, descriptive names, and names which are occasionally designational and occasionally descriptive. Designational names are “paradigm proper names,” which “have their reference fixed by causal–perceptual links in groundings” (Devitt (2015), 124); a “grounding” is “the causal link between a person and [an] object when it is the focus of that person’s perception” (Devitt (2015), 113), and there will typically be many such groundings involving different speakers and a named object after the initial naming takes place and while the named object exists. By contrast, descriptive names “get their reference fixed by what Donnellan (1966) calls an ‘attributive’ use of a description. In such a use the speaker refers to whatever uniquely fits the description, to whatever the description denotes. As a result, in my usage, the name ‘denotes’ that object” (Devitt (2015), 124). In the third category, according to Devitt, names like “Shakespeare” are found; this often functions as designational, but “in critical assessments of ‘the

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works of Shakespeare,’ however, it often seems to function as a descriptive name, so that it would not matter to the truth of these assessments if the work was actually written by Bacon” (Devitt (2015), 127). Devitt also distinguishes between “speaker designation” and “conventional designation” (for designational names), and between “speaker denotation” and “conventional denotation” (for descriptive names) (as well as between “speaker designation/denotation” and “conventional designation/denotation” (for designational/descriptive names)). The distinction is the same as Kripke’s (1977) well-known distinction between speaker’s reference and semantic reference. But Devitt contributes the plausible point that a name in a particular use may speaker-refer to more than one thing on Kripke’s characterization, in cases where the speaker has multiple referring intentions that don’t converge on the same thing. In such cases Devitt denies that there is speaker reference strictly speaking, and proposes roughly that there is reference when all the referring intentions do converge on a single thing. Then, finally, he gives characterizations of “speaker designation,” “conventional designation,” “speaker denotation,” and “conventional denotation” in terms of jointly necessary and sufficient conditions (and of “speaker designation/denotation” and “conventional designation/denotation”; but we will not be concerned with these notions), as follows: Speaker-Designation: A designational name token speaker-designates an object if and only if all the designating-chains underlying the token are grounded in the object. (Devitt (2015), 125) Conventional-Designation: A designational name token conventionally designates an object if and only if the speaker, in producing the token, is participating in a convention of speaker designating that object, and no other object, with name tokens of that type. (Devitt (2015), 126) Speaker-Denotation: A descriptive name token speaker-denotes an object if and only if all the denoting-chains underlying the token start with a description that denotes the object. (Devitt (2015), 127) Conventional-Denotation: A descriptive name token conventionally denotes an object if and only if the speaker, in producing the token, is participating in a convention of speaker-denoting that object, and no other object, with name tokens of that type. (Devitt (2015), 127)

These characterizations appeal to three notions whose use by Devitt requires some explanation. First, the notion of a “designating chain.” This is just the

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84      notion of a causal chain of transmission whose stages are either (causal) direct groundings in an object or indirect reference borrowings. Second, the notion of a “denoting chain.” This is the notion of a causal chain of transmission whose stages are either adoptions of direct descriptive stipulations or indirect reference borrowings. Third, the notion of “participating in a convention” of speaker designation or speaker denotation. Devitt says that this notion requires a complex treatment, but for present purposes it is enough to suppose that the notion satisfies two postulates, one concerned with name introductions and one with transmissions: [1] The community’s early groundings and reference borrowings establish the convention [of using a certain name to refer to a certain thing]. [2] Reference lending is the standard way of creating the mutual dependencies that spread the convention. For, a person who borrows the reference of [a certain name] from someone who is participating in the convention, from someone exercising her ability with [the name], comes thereby to participate in that convention herself. (Devitt (2015), 119)

Devitt’s characterizations of name reference both undergenerate and overgenerate, as we claimed was to be expected in general of theories of jointly necessary and sufficient conditions of name reference where the conditions don’t reflect conventions knowable by normal competent speakers. The theory does not give necessary conditions for reference, or at any rate for the main notion of conventional designation. In order for a designational name token to conventionally designate an object, the token utterer must be participating in a convention of speaker designating that object (with name tokens of that type), and in order for him to be doing this, all the designating chains underlying the token must be grounded in the object. But this is too demanding, for there may well be a few groundings of tokens of the relevant type, along the relevant designating chains, in objects different from the object in question, and yet conventional reference to the object may be taking place in the mouth of someone at the end of the chains. Perhaps some grounding of (an ancestor of) “Aristotle” was on some object that an early user of “Aristotle” mistook for Aristotle. A contemporary of Aristotle may have never actually seen him and associate the name with a different person. The contemporary may have passed along the name to someone else who also gets the name from other non-confused acquaintances of Aristotle. Even if the confused contemporary is a link in a designating chain reaching down to me now, intuitively my uses of “Aristotle” don’t thereby fail to refer (conventionally) to Aristotle.

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The theory overgenerates as well. Consider the case of “George Smith,” the teacher, and the students. Tokens of “George Smith” used by the students after exposure to the name by the teacher conventionally designate George Smith, as the students, in producing one such token, are participating in a convention of speaker-designating George Smith, and no other object, with name tokens of “George Smith”; this is so because in order to participate in a convention of speaker-designating George Smith, it is enough that the students have borrowed the name from someone who is participating in a convention of speaker-designating George Smith, as the teacher most certainly must be. Also, since all the designating chains leading to the token are grounded in George Smith (or so we can safely assume), the students’ tokens of “George Smith” will speaker-designate George Smith. So on Devitt’s theory the two relevant varieties of name reference are exemplified here, despite the appearance of indeterminacy mentioned above. The remaining cases of indeterminacy we saw are all declared cases of (determinate) reference failure by Devitt’s theory, which is fine as far as extensional adequacy is concerned. However, even here we might note that such cases point to a legitimate concern that cannot be calmed by theories such as Devitt’s. Namely, that such theories will not provide an account of the difference between cases where reference fails determinately, as a matter of what reference-fixing conventions determinately imply, and cases where no reference is determined, but merely because reference-fixing conventions fail to produce any relevant implication at all. It might legitimately be asked of an appropriate theory of name reference fixing that it distinguish in some way between the two sorts of cases. Let’s turn to Dickie’s theory of reference fixing. The theory is offered as an improvement on Evans’s theory of reference, using Evans’s own apparatus. Evans had distinguished between what he called “producers” and “consumers” of a (paradigmatic, non-descriptive¹¹) name. A producer of a name is a member of a group of people for whom the name is associated with instances of perceptual demonstration directed toward the referent; these people have a capacity to recognize the referent on later occasions on which demonstration of the referent is feasible, “have dealings with [the referent] from time to time, and use the name in those dealings” (Evans (1982), 376). A consumer, on the other hand, lacks such a privileged contact with the referent, but is nevertheless a participant in the practice of using the name to refer to its referent ¹¹ Descriptive names are for Evans roughly the names we also saw Devitt calling descriptive earlier in this section.

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86      because she ultimately derives her acquisition of the name from producers of it. In a consumer, the body of beliefs associated with the name, if any, is dominantly causally derived from the bodies of beliefs of producers of the name. Among Evans’s consumers, Dickie further distinguishes between “participating” consumers and “parasitic” consumers. Participating consumers are roughly those who have a substantive body of beliefs associated with the name, while parasitic consumers basically just intend to use the name the way others use it, and as a result need not have a substantive body of beliefs associated with the name. Dickie reconstructs Evans’s theory as involving the postulate that a use of a (paradigmatic, non-descriptive) name refers to an object just in case the user of the name is a producer of the name or a consumer of it. I myself would hesitate to attribute to Evans a theory of jointly necessary and sufficient conditions for name reference (even for paradigmatic, non-descriptive names). But it seems reasonable to think that the mentioned condition was thought of as at least necessary by Evans, and one can at any rate consider the question whether it is sufficient. Dickie objects that the participating consumers of “Chaucer” in the nineteenth century intuitively made uses of “Chaucer” that referred to Chaucer, but it is a historical fact that at that time most of the beliefs about Chaucer held by consumers were wrong beliefs, derived from fabrications of people who were not producers of “Chaucer.” If so, the bodies of beliefs associated with “Chaucer” by those consumers were not dominantly causally derived from the bodies of beliefs of producers of “Chaucer,” against Evans’s theory. This shows that the Evansian condition is not a necessary condition for reference. Dickie argues that it’s not a sufficient condition either. Her example is that of a person who hears the name of a soccer player, “Rio Ferdinand,” but from the beginning, due to a conspiracy of mistakes, associates it with some properties that could only be had by a soccer team, including the property of being a soccer team, and with other properties that can be had by both a team and a player, and which are had by Rio Ferdinand, such as the property of having moved from one city to another. Intuitively, says Dickie, the uses of “Rio Ferdinand” by this person do not refer to Rio Ferdinand, but her body of beliefs associated with the name may be dominantly derived from producers of “Rio Ferdinand.” (My own impression is not that “Rio Ferdinand” determinately fails to refer to Rio Ferdinand in the user’s mouth, but that it is unclear that it does so refer.¹²) ¹² My impression was reinforced when an anonymous referee wrote that her or his own impression was that “Rio Ferdinand” determinately refers to Rio Ferdinand in the user’s mouth.

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In order to cope with these counterexamples, Dickie proposes a complex theory on which the body of beliefs that a participating consumer associates with a name need not be dominantly causally derived from bodies of beliefs of producers, but must in any case have inherited from them a characteristic called “governance.” Her characterization of reference is then this: A speaker’s use of a name refers to a certain object if and only if either

(i) the speaker is a producer in a practice of using the name to refer to the object; or (ii) there is a causal information chain leading from the speaker’s body of beliefs associated with the name back to the bodies of beliefs associated with the name by speakers who are producers in a practice of using the name to refer to the object, and this chain transmits governance; or (iii) the speaker is a parasitic consumer in a practice of using the name to refer to the object. (See Dickie (2011), 60) When is governance inherited? When the body of beliefs of the person who inherits the name is such that it does not give rise to ways of using the name that do not “keep faith” with the ways in which it is possible for the referent of the name to behave according to the body of beliefs of the bestowing speakers. Pending precisification of the notions of “possible ways of behaving” and of “keeping faith,” the rough idea is clear, especially when we reflect on how it deals with Dickie’s “Chaucer” and “Rio Ferdinand” counterexamples to Evans’s theory. The nineteenth-century participating consumers of “Chaucer” make uses of “Chaucer” that refer to him roughly because their bodies of beliefs associated with “Chaucer” do not lead them to use the name in ways according to which the referent of the name would have properties that would not be really possible for him to have according to the producers of the name. On the other hand, the uses by the person who got “Rio Ferdinand” along with the funny beliefs do not refer to Rio Ferdinand, roughly because her body of beliefs associated with “Rio Ferdinand” leads her to use the name in ways according to which the referent of the name would have properties that would not be really possible for him to have according to the producers: to begin with, it would not be possible for Rio Ferdinand to be a team of any sort. Dickie develops, using a complex philosophical apparatus, a full theory of what she needs to mean by “possible ways of behaving” and by “keeping faith,” which we will not enter into in any detail. But two things deserve emphasis in this connection. First, the notion of a “possible way of behaving” is

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88      “task-relative”: the discursive task in which the user of the name is engaged determines the range of properties that count, so that in some cases this may be limited to a small number of properties, in others to the whole set of metaphysically possible properties of the object, and so on. Second, the notion of “keeping faith” is relative to the importance accorded to groups of beliefs. Dickie compares the “Rio Ferdinand” story with one about “The Oracle.” She asks us to imagine that this is a name given by the priestesses of Delphi to a committee of their own ranks that is in charge of issuing the oracular pronouncements. Dickie claims that ordinary people can inherit the name “The Oracle” so that this will keep referring to the committee in their mouths, even if they develop the belief that The Oracle is a god, thus developing a mistaken belief about the basic kind that The Oracle exemplifies. According to Dickie, this is so because governance is transmitted from the priestesses to the ordinary people, and this is so in turn because the belief that The Oracle is a god is relatively secondary in the body of beliefs of the ordinary people and does not interfere very much with the great majority of their beliefs about The Oracle, which we can imagine to be mostly beliefs about the committee’s pronouncements and the ways of obtaining such pronouncements. These beliefs will ascribe properties to The Oracle that will be possible relative to the discursive tasks that they are normally engaged in with “The Oracle,” which will be just about the same as the discursive tasks of the producers (the priestesses). In these discursive tasks, the question of whether The Oracle is a god, or related questions, will not arise. (I myself don’t find this example as clear as Dickie does. One problem is that “The Oracle,” even if it can be co-opted as a proper name, has an independent life as a description in the preexisting language, one presumably roughly synonymous with “the maker of such and such pronouncements.” Surely this may lead to the impression that “The Oracle” will refer to the maker of the relevant pronouncements regardless of whether it is a god or a committee of people.¹³ See the final section of this chapter for further discussion of this example and comparison with related ones.) The “The Oracle” example suggests that Dickie’s theory does not after all give a necessary condition for reference to occur, for the belief that the referent of a name is a supernatural entity need not be a false secondary belief of participating consumers, but a correct primary belief of producers which gets eventually lost along chains of transmission. Suppose that, contrary to our ¹³ It may be worth noting that for the ancient Greeks (priestesses and ordinary people alike) the Delphic Oracle was in fact a particular priestess, the so-called Pythia.

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current belief, the producers of (the appropriate ancestor of) “Khufu” (the name of the pharaoh who commissioned the Great Pyramid of Giza) were right in thinking that he was a god.¹⁴ Suppose further that they were engaged in discursive tasks to which it was crucial that Khufu had outlandish supernatural properties. Today a typical ordinary participating consumer of the name “Khufu” will ascribe a great deal of properties to Khufu, but he will have no place for the idea that Khufu was a god, and he will straightforwardly attribute to Khufu properties such as mortality, greediness, superstition, and the like, which would have seemed outrageous to the producers of “Khufu.” So he will not be “keeping faith” with the relevant range of ways it is possible for Khufu to behave according to the beliefs of the producers of the name. And yet his uses of “Khufu” will intuitively refer to Khufu all throughout his engagement in the discursive tasks he is engaged in when he uses “Khufu.” How could this come about? Here is one possible way: It’s not hard to picture how in the situation we are imagining memory of many of Khufu’s properties was lost little by little, perhaps to the point where the name (or its other forms, like “Cheops”) subsisted in what would be for the most part “parasitic” or nearly parasitic consumers who attributed to Khufu just about the property of being the pharaoh of the Great Pyramid. At a relatively recent time, a parasitic consumer might have found substantive information about Khufu in some manuscript, but he might have found only information restricted to his human attributes or he might have chosen to reject the information about the divine attributes as a myth. The discoverer of the manuscript and others in his wake would then become fully “participating” consumers of “Khufu” centuries after the last known “participating consumers” of “Khufu” died. But such new consumers would not have inherited Dickie’s “governance” along with the name “Khufu,” despite the fact that they would clearly be “participating consumers” of “Khufu” in Dickie’s terminology. The upshot is that we have a case of intuitive reference that is wrongly classified as a case of reference failure on Dickie’s theory. Dickie’s theory overgenerates as well, as shown again by consideration of the case of “George Smith,” the teacher, and the students. The students would seem to be classifiable as parasitic consumers in a practice of using “George Smith,” as they certainly do not have a substantive body of beliefs associated with “George Smith.” If they are parasitic consumers, their uses of “George Smith” refer to George Smith on Dickie’s theory. On the other hand, if they are ¹⁴ It is perhaps not entirely clear that the ancient Egyptians believed that Khufu was a god, but we can of course imagine that they did, and more, as we are actually about to do.

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90      to be classified as participating consumers, their uses of “George Smith” again refer to George Smith, because (we can suppose) the property of being the squarer of the circle is not an impossible property according to the beliefs of the producers of the name, such as the teacher; we can suppose that they don’t know the mathematics, that they just believe that George Smith is not the squarer of the circle. Or we can change the example so that what the teacher tells the students is that George Smith has some other property he is widely known not to have but that he could come to have, such as the property of being an estimated contributor to Euclidean geometry. In the new example the impression of referential indeterminacy remains, but Dickie’s theory again implies that the students’ uses of “George Smith” refer to George Smith. So, in any case, on the theory the uses of “George Smith” by the students determinately refer to George Smith, despite the appearance that reference is indeterminate in this case. As in the case of Devitt’s theory, the remaining cases of indeterminacy above are all declared cases of determinate reference failure by Dickie’s theory. This is again acceptable from the purely extensional point of view, but again the complaint arises that the theory will not give a distinctive account, or indeed any account, of the reasons why referential indeterminacy arises in the cases where it does.

A Picture of Name Reference Fixing In this final section, we will develop the announced picture of name referencefixing conventions as conventions giving imprecise, roughly sufficient conditions for reference and reference failure. As in the case of demonstratives, we will preface the development of the picture with some caveats and clarifications, in many cases analogous to those for demonstratives. First of all, being linguistic conventions that are relied upon by the linguistic community at large, the conventions we are after must plausibly be in some sense familiar to normal competent speakers, as we have conceded to the descriptivist. However, unlike the descriptivist, we don’t require full knowability of the conventions as such, but merely that the ability to observe them should be manifested in the linguistic behavior of speakers, and specifically in behavior that it should not be unreasonable to think of as behavior that normal speakers do perform. The relevant kind of behavior might simply involve the acceptance or denial that particular objects are being talked about with specific uses of names. Such behavior certainly doesn’t require the deployment of abilities that it is unreasonable to attribute to a normal speaker.

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In any case, we can expect there to be many conventions of the kind in question, and, as we have already noted several times, it need not be reasonable to demand that we be able to state them all. Just as the typical competent speaker can only be expected to recognize particular instances of application of the conventions, but not to recognize that a certain set of conventions exhausts all the existing conventions of name reference, the theorist may not be in a much better position. But he is certainly in a better position to state the particular conventions themselves. We have been saying that the conventions are conventions about when reference and reference failure take place. Note that, if the conventions could be said to be known in the full sense by a normal competent speaker, then, insofar as the theoretical notion of reference will appear in the statement of the conventions, this knowability would involve the possibility of some effective coaching for the normal speaker involving the nature of the theoretical notion of reference. But since we don’t require knowability in the full sense of the conventions as such, we don’t need to postulate the possibility of such effective coaching. And if we don’t require knowability in the full sense of the conventions as such, there is no objection here to the conventions as we will state them. As we already noted when demonstratives were at stake, the notion of reference can appear in the formulation of our conventions, as the conventions may be instituted in virtue of linguistic behaviors that do not require the possession of concepts needed for the formulation of the conventions themselves. (Note again, however, as we did in the case of demonstratives, that the notion of referring for which it makes sense to say that a person refers to a certain thing by means of some other thing (such as a word), a notion which will appear in our conventions as well, is an ordinary notion available to normal speakers.) By contrast with the case of demonstratives, the conventions for names as we will state them will be conventions about the reference of name types (in the idiolects of particular speakers), even if when the theoretical notion of reference is involved we in all probability need an account of the reference of name uses (acts that particular speakers perform employing particular tokens for communicative purposes broadly understood). Virtually every name type (in the sense of syntactic expression type) is conventionally used to refer to different things, and our favorite example “Aristotle” is of course an example of this phenomenon as well. We probably want to say that some uses of “Aristotle” refer to the great Greek philosopher, others to other people, including the sometime famous Greek shipping magnate. However, it seems reasonable to suppose that name reference-fixing conventions concern only

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92      conditions for the reference or reference failure of name types. It’s evidently implausible to think that the possibility that a name type be used to refer to more than one object could be contemplated in the natural conventions themselves. Similarly, ambiguous words of other kinds are presumably associated with different sets of conventions, one for each acceptation of the ambiguous word, but the conventions in these different sets presumably do not specify conditions for token use reference as opposed to type reference. It is reasonable to think, in any case, and along with many other recent writers in the theory of reference, that the reference of a use of a name token (when the use in question has a reference) is the thing that in some appropriate sense is behind the body of beliefs and other thoughts that is at the origin of the use of the token, there being different bodies of thoughts for every “acceptation” of a name type in the mind of a speaker competent with all the relevant “acceptations.”¹⁵ (Note that mutatis mutandis the same ought to hold of uses of ambiguous words of other kinds.) It is also important to note, as in the case of demonstratives, that the conventions we are about to state must be understood as only roughly sufficient, as they involve conditions which are only sufficient ceteris paribus, in an appropriate sense. That they are ceteris paribus means in this case that the conditions are conventionally taken as sufficient merely under the assumption that the situation where the conditions apply is otherwise normal, that it is not unlike other situations when the conditions were accepted as applying in the past. The ensuing caveats about the idea of normality being imprecise and generating further indeterminacies will also apply here, as does the supposition that the examples we have seen involve normal situations, and so the conventions postulated by the picture we are about to give should explain the relevant facts about them. For an example of non-normality, consider this: it is not clear that the conventions are designed to regulate name reference in a situation in which the speaker introducing or inheriting a name becomes mentally incompetent in some strange way right after introducing or inheriting it, but not so incompetent as to be unable to produce some utterances of the name. One last general point deserving emphasis before we begin with the statement of our conjectured conventions is that, this time again by contrast with the case of demonstratives, the conventions concerning name introduction and adoption below incorporate as a proviso the absence of substantive conflict between the referential intentions of a certain relevant speaker and ¹⁵ Evans, Devitt, and Dickie, e.g., are all, broadly speaking, examples of this way of looking at things (which Evans (1973), 16, n. 10, traces ultimately to Grice (1969)).

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the referential intentions of the community at large. While provisos of this kind do not seem to have played a substantive role in many theories of name reference, some such condition appears clearly to play a role in name referencefixing conventions, as well as in similar conventions for other expressions (as we will see in later chapters). The kind of name reference that we are trying to understand is conventional name reference, and so it is to be expected that a large-scale conflict between the referential intentions of a speaker seeking to introduce a name and the referential intentions of the community at large concerning that name will result in reference failure or in indeterminacies as to reference. In fact, we will see how the postulation of a proviso of this kind seems to explain some intuitions of reference failure and indeterminacy. Time then to attempt to state some of the conventions relevant to name reference fixing. Successful explicit name introduction via perceptual intention. If a speaker S forms the explicit intention of using a name N that he or she introduces to refer to an object o that he or she is clearly perceiving, then N as used by S will refer to o, if S forms no intention conflicting with that intention, and if S doesn’t form intentions about how to use N that on the whole conflict with the intentions of the community of users of N at large. Successful explicit name introduction via description. If a speaker S forms the explicit intention of using a name N that he or she introduces to refer to the object, if any, that uniquely satisfies a certain property F, and it turns out that there is such a unique satisfier of F, then N as used by S will refer to the F, if S forms no intention conflicting with that intention, and if S doesn’t form intentions about how to use N that on the whole conflict with the intentions of the community of users of N at large. These conventions concern the formation of explicit intentions to refer to a certain object by means of an introduced name. They cover the basic Kripkean cases of “initial baptism” by means of explicit dubbings via demonstration and description. Note that there is a proviso to the effect that no intention of the dubber must conflict with the dubbing intention, which is just something one might expect given that the existence of conflicting intentions will introduce at the very least some unclarity as to what thing is being named.¹⁶ Note also that ¹⁶ This is not to say that there cannot be other conventions establishing that in some cases some referential intentions override other conflicting intentions, with the result that successful reference arises. Recall Kripke’s case of a speaker forming the intention of calling “that,” “the morning star,” “Phosphorus.” This suggests that, as in the case of demonstratives, there may be a convention to the

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94      the referential intentions of the community of users of N have a role relevant to the establishment of (conventional) reference even in these cases—a fact not emphasized by Kripke in his original exposition. As in all the conventions about reference establishment (as opposed to reference failure) below, a large-scale conflict between the referential intentions of S and the referential intentions of the community will result in referential indeterminacy. The community must not be opposed to the introduction of the name, so to speak, if reference is to be conventional.¹⁷ Think of two parents who intend to give a long and unpronounceable name, “Dhvmlpgnklfgmmllfrtsvansgr,” to their recently born daughter, and declare just that before the local Officer of Vital Records; if the officer, as a representative of the community, opposes their plan, it is unclear that it can be said that the parents’ uses of “Dhvmlpgnklfgmmllfrtsvansgr” will from then on refer (conventionally) to the child.¹⁸ As Kripke himself noted ((1972), 162), in many cases the initial introduction of a name will not be via the formation of an explicit referential intention. In many cases, a name will start being used in virtue of the existence of merely effect that perceptually based intentions override non-perceptually based intentions at the introduction stage (at least when the latter are relatively few or comparatively unimportant). Here is a possible statement of the convention: Successful explicit name introduction via non-conflictive perceptual referential intentions. If a speaker S forms the explicit intention of using a name N that he or she introduces to refer to an object as purportedly perceived by S, and the perception in question is in fact of a certain object o, then N as used by S will refer to o, if S forms no intention of using N to refer to a different object p as purportedly perceived by S, with the perception in question being in fact of p, and if S doesn’t form intentions about how to use N that on the whole conflict with the intentions of the community of users of N at large. (Compare the imagined introduction of “Phosphorus” with the case of the transmission of “Madagascar” to the imagined Marco Polo in the texts surrounding notes 3 and 10 above, where it was dubious that the perceptually based intention overrode other referential intentions.) It is unclear, in any case, that there is any convention that some perceptually based referential intentions override other conflicting perceptually based referential intentions at the introduction stage. (Recall that we did not postulate any such convention in the case of demonstratives.) ¹⁷ The community can even develop some positive general convention determining the proper name that is to be given to each particular individual. For example, as noted in Gómez-Torrente (2013), a practice once common in Spain and Hispanic America was to give to a child a proper name composed of a first name identical with the name of the (first) saint or angel for the child’s birthday in the calendar of Catholic saints and angels (followed by surnames also in a conventionally determined fashion)—and there are many other similar examples, some of which are also noted in Gómez-Torrente (2013) and by Evans (1982). In such a case, the intentions of the community will prevent the conventional adoption on the part of the introducer of names not sanctioned by such conventions. ¹⁸ Note that what is highlighted here is the fact that some intentions (not conventions) of the community may have the effect of blocking the fixing of reference via the implicit, naturally developed conventions for reference fixing. The question whether some legal decree can manage by itself to fix the reference of a name is an interesting question. My impression is that it cannot, precisely because such a decree cannot by itself impose the usage on the community, or eliminate automatically the existence of widespread conflicting intentions in the relevant community. The natural conventions for reference fixing are in this sense more powerful than legal decrees.

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implicit intentions to refer by means of it to a certain object as singled out, for example, by a perceptually based intention or a description. An implicit intention is just an intention that could in principle be recognized explicitly by the relevant speaker. The following might be rough statements of conventions about such implicit referential intentions, corresponding to the conventions about explicit intentions above: Successful implicit name introduction via perceptual intention. If a speaker S forms the implicit intention of using a name N that he or she introduces to refer to an object o that he or she is clearly perceiving, then N as used by S will refer to o, if S forms no intention conflicting with that intention, and if S doesn’t form intentions about how to use N that on the whole conflict with the intentions of the community of users of N at large. Successful implicit name introduction via description. If a speaker S forms the implicit intention of using a name N that he or she introduces to refer to the object, if any, that uniquely satisfies a certain property F, and it turns out that there is such a unique satisfier of F, then N as used by S will refer to the F, if S forms no intention conflicting with that intention, and if S doesn’t form intentions about how to use N that on the whole conflict with the intentions of the community of users of N at large. Other conventions about name introduction, essentially analogous to the conventions we have just seen, concern conditions for reference failure. Unsuccessful explicit name introduction via perceptual intention. If a speaker S forms the explicit intention of using a name N that he or she introduces to refer to an object that he or she believes to be perceiving, but in fact no object is being perceived by S, then N as used by S will not refer to anything, if S forms no intention conflicting with that intention. Unsuccessful explicit name introduction via description. If a speaker S forms the explicit intention of using a name N that he or she introduces to refer to the single object that satisfies a certain property F, and it turns out that there is no such single satisfier of F, then N as used by S will not refer to anything, if S forms no intention conflicting with that intention. Unsuccessful implicit name introduction via perceptual intention. If a speaker S forms the implicit intention of using a name N that he or she introduces to refer to an object that he or she believes to be perceiving, but in fact no

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96      object is being perceived by S, then N as used by S will not refer to anything, if S forms no intention conflicting with that intention. Unsuccessful implicit name introduction via description. If a speaker S forms the implicit intention of using a name N that he or she introduces to refer to the single object that satisfies a certain property F, and it turns out that there is no such single satisfier of F, then N as used by S will not refer to anything, if S forms no intention conflicting with that intention. In these cases the proviso about the lack of a conflict with the community is presumably idle, because the name is introduced via an act that the convention itself declares to be a failure without further ado. However, the proviso about the lack of conflicting referential intentions on the part of the introducer seems appropriate. S might form, at the same time as the basic intention at stake, other conflicting referential intentions that might conceivably override the basic intention according to some further conventions, being successful where the basic intention isn’t.¹⁹ A basic convention about the phenomenon of name transmission, opening the way to a codification of Kripke’s and Evans’s relevant insights, would appear to be statable in the following terms. Successful name transmission. If a name N as used by a community of speakers refers to an object o and a speaker of the community, S, clearly perceives some use of N by another speaker of the community and understands that N is used as a name, then N as used by S will refer to o, if S forms the (explicit or implicit) intention of using N as is used by the community of users of N and forms no intention conflicting with this intention, and if S doesn’t form at the transmission stage a set of beliefs involving N that on the whole conflict with the beliefs of the community of users of N at large. Here the intention of using N as is used by the community may be, in fact presumably will typically be, merely implicit in the inheriting speaker. At least some paradigmatic cases of reference change, both intended and unintended, for names that are not introduced by a speaker but that have been inherited by him or her, would appear to be covered by conventions similar to the following.

¹⁹ Compare the remarks in note 16 above.

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Successful name adoption via perceptual intention. If a speaker S forms the (explicit or implicit) intention of using a name N that he or she has inherited to refer to an object o that he or she is clearly perceiving, then N as used by S will refer to o, if S forms no intention conflicting with that intention, and if S doesn’t form intentions about how to use N that on the whole conflict with the intentions of the community of users of N at large. Successful name adoption via description. If a speaker S forms the (explicit or implicit) intention of using a name N that he or she has inherited to refer to the object, if any, that uniquely satisfies a certain property F, and it turns out that there is such a unique satisfier of F, then N as used by S will refer to the F, if S forms no intention conflicting with that intention, and if S doesn’t form intentions about how to use N that on the whole conflict with the intentions of the community of users of N at large. Then other likely conventions about name adoption, essentially analogous to the conventions we have just seen, will concern conditions for reference failure. Unsuccessful name adoption via perceptual intention. If a speaker S forms the (explicit or implicit) intention of using a name N that he or she has inherited to refer to an object that he or she believes to be perceiving, but in fact no object is being perceived by S, then N as used by S will not refer to anything, if S forms no intention conflicting with that intention. Unsuccessful name adoption via description. If a speaker forms the (explicit or implicit) intention of using a name N that he or she has inherited to refer to the single object that satisfies a certain property F, and it turns out that there is no such single satisfier of F, then N as used by S will not refer to anything, if S forms no intention conflicting with that intention. The picture that emerges from the identification of these conventions fulfills our promise to live with the fact that the recognizable conventions of name reference are given merely by a list of imprecise roughly sufficient conditions for name reference and name reference failure, thus providing a frame for indeterminacy intuitions and phenomena. The picture is also clearly compatible with the requirement that the appropriate conventions, though not necessarily fully knowable by normal competent speakers, should plausibly be observable by them, thus providing a realistic alternative to descriptivist theories with strong epistemic requirements. It remains to check that, together

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98      with the postulation of a number of plausible claims about the evolution of bodies of intentions and beliefs in relevant individual speakers and communities of speakers, the picture can provide a reasonable and complete extensionally correct account of the phenomena and the examples involving name reference discussed in this chapter, and thus a reasonably complete account of the basic phenomena surrounding name reference discussed in the recent literature. To begin with, the picture accommodates Kripke’s seminal insights about name reference, starting with the various insights about the existence of reference facts which are not due to the speaker associating a name with descriptive information of certain kinds. First of all, the operation of the conventions at no point requires that a name be synonymous with any description in the idiolect of a speaker participating in the convention. More crucially, the postulate that the Successful name transmission convention exists implies that a speaker can inherit a name from a community of speakers and come to refer to its referent by means of the name, provided merely that he or she has the (explicit or, typically, just implicit) intention of using the name in the same way as other users, and doesn’t form beliefs involving the name that conflict on the whole with the beliefs of the community of users of the name at large, at least at the transmission stage. The inheriting speaker can use the name and conventionally refer to its conventional referent without need of having inherited also a way of correctly identifying the referent via descriptive characteristics, or even a full purported description of the referent. On the other hand, the picture incorporates Kripke’s idea that names can be introduced (successfully or unsuccessfully) via description and ostension, in virtue of the postulated conventions of Successful explicit name introduction via perceptual intention, Successful explicit name introduction via description, Successful implicit name introduction via perceptual intention, Successful implicit name introduction via description, Unsuccessful explicit name introduction via perceptual intention, Unsuccessful explicit name introduction via description, Unsuccessful implicit name introduction via perceptual intention, and Unsuccessful implicit name introduction via description. (Recall, however, that the picture makes explicit what I think is a decisive role of the community even in these cases, one that was not clear in Kripke.) The picture also incorporates Evans’s insights, provided we accept a number of reasonable hypotheses about how bodies of intentions and beliefs develop when names are transmitted. But before turning to Evans’s insights, it is convenient to note that the impression that “Madagascar” as used by the Marco Polo of the (historically inaccurate) story often attributed to Evans

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does not clearly refer is explained by the fact that none of the possibly relevant conventions implies that it refers to anything. Successful name transmission does not, because the imagined Marco Polo forms beliefs at the transmission stage that on the whole conflict with the beliefs of the community of users of the name at large; he forms the belief that Madagascar is “this island” that he knows, as well as all the beliefs involving “Madagascar” that must ensue from that belief, and these clearly must on the whole conflict with the beliefs of the great majority of existing users of “Madagascar.” Successful name adoption via perceptual intention does not imply that there will be reference either, now because the imagined Marco Polo forms many intentions that on the whole clearly conflict with the intentions about how to use “Madagascar” by the existing community of users. On the other hand, Unsuccessful name adoption via perceptual intention evidently does not apply either.²⁰ Turning now to Evans’s insights, the picture provides, to begin with, a reasonable explanation of the reference change of “Madagascar.” This presumably takes place at a point when a sufficient number of speakers form the intention of referring with “Madagascar” to the island (either via perceptual intention or via description), as well as all the ensuing intentions, so that such intentions no longer conflict on the whole with the intentions of the community of users of “Madagascar” at large. (At that point, the people with those intentions constitute the community of users of “Madagascar” at large!) Under such conditions, applications of Successful name adoption via perceptual intention and of Successful name adoption via description will imply that there is conventional reference to Madagascar with “Madagascar.”²¹

²⁰ In the case of the real Marco Polo, the picture, confirming the (shaky) intuition mentioned in note 10 above, implies that his uses of “Madagascar” did refer to the continental region referred to by the sailors’ uses, at least under plausible suppositions. The real Marco Polo, as Burgess ((2014), 197) notes, reports many things about Madagascar: “It lies between Socotra and Zanzibar, the inhabitants are Muslim, they eat camels, the place is very rich, there are many elephants.” All these are properties of Mogadishu, the continental region that the Arab or Malay sailors presumably referred to (and none of them was ever true of the great African island). Assuming that Marco Polo was merely confused about the place being “some island,” not about the place being a particular island well known by him, he, at least at the transmission stage, must not have formed beliefs that on the whole conflicted with the beliefs of the community of users of “Madagascar” at large. For example, the belief that Madagascar is “some island” was compatible with the beliefs that it lies between Socotra and Zanzibar, that its inhabitants are Muslim and eat camels, that it is very rich, and that it has many elephants, all of which were presumably beliefs of the community of users of “Madagascar.” ²¹ Unsuccessful name adoption via description, on the other hand, may have been the root of the failure of the preservation of reference along the chain of transmission of “Santa Claus” if the appropriate facts about bodies of referential intentions took place at some point. Alternatively, if we suppose that Santa Claus is some kind of existing, if fictional, character (as Kripke (2013) and Salmon (1987) suggest is the case for the referents of some names), then Successful name adoption via description may provide an explanation of “Santa Claus” having changed its reference from a nonfictional object to a fictional object.

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100      Evans’s point that receivers of a name can also form explanatorily relevant perceptually based referential intentions involving the name has a natural place in the picture. Aristotle’s school companion, for example, uses “Aristotle” in such a way that it conventionally refers to Aristotle, but this is not, or not merely, because he has received the name and the convention of Successful name transmission then applies. Also the convention of Successful name adoption via perceptual intention will apply in this case, reinforcing the fact of reference, in particular because (we can presume) the school companion forms no intention conflicting with the intention of referring to the person he is familiar with, and he doesn’t form intentions about how to use “Aristotle” that on the whole conflict with the intentions of the community of users of “Aristotle” at large. Finally, Evans’s related point that a name can change reference even among people who are directly acquainted with its initial referent is also accommodated. Suppose the child Aristotle is replaced by a look-alike o. Both the introducer parents and Aristotle’s school companions will soon develop the intention of referring with “Aristotle” to o, and so will form an intention conflicting with their previous referential intentions (if these are still extant in their minds), which will mean that conventions such as Successful explicit name introduction via perceptual intention (in the parents case) and Successful name adoption via perceptual intention (in the companions case) will stop applying (if the original referential intentions are still extant). Also, after a sufficiently long while, “Aristotle” in the mouths of both parents and companions will presumably conventionally refer to o, an impression which is reasonably accounted for by the conventions of Successful implicit name introduction via perceptual intention (in the parents case) and Successful name adoption via perceptual intention (in the companions case). These conventions will apply if and when the intention of referring to o with “Aristotle” no longer conflicts with previous no longer extant referential intentions (and, as we may presume will also be the case, the relevant speakers don’t form intentions about how to use “Aristotle” that on the whole conflict with the intentions of the community of users of “Aristotle” at large). The picture deals successfully also with the cases of presumable referential indeterminacy described above. In the case of “Jeri,” Joos, and the clairvoyant, the only conventions recognized so far that could be relevant to the question whether the clairvoyant’s use of “Jeri” refers to Joos are Successful explicit name introduction via perceptual intention and Unsuccessful explicit name introduction via perceptual intention. Successful explicit name introduction via perceptual intention does not apply, because the clairvoyant is not clearly perceiving

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Joos (or anything else). But Unsuccessful explicit name introduction via perceptual intention does not apply either, because the clairvoyant does not believe he is perceiving Joos; on the contrary, he believes that he has an extrasensory power that is at work when he is “seeing” Joos. (If he were to believe that he was seeing something instead of “seeing” something, he would be simply deceived and the name introduced would have no reference.) The story of the clairvoyant who has never heard of Aristotle before but “hears” someone use the name “Aristotle” is diagnosed in the same way. The convention of Successful name transmission, the only one that could be relevant in this case, does not apply, as the clairvoyant does not perceive a use of “Aristotle” by another speaker. This is compatible with the intuition of indeterminacy. We already saw the account the picture gives of the case of “Madagascar” as used by the imagined Marco Polo.²² Let’s turn to the similar but different “George Smith” case. Here the students inherit the name from their teacher, but they also simultaneously derive from the teacher a single, rather weak belief that the teacher himself does not share, the belief that George Smith has squared the circle. This prevents this case from being an instance of Successful name transmission, for the students form a rather impoverished set of beliefs that we can presume conflicts with the beliefs of the community of users of “George Smith” at large, as we can presume that the speakers of the community at large, starting with the teacher and the neighbor himself, do not believe that George Smith has squared the circle. Hence, Successful name transmission does not imply that reference is transmitted successfully in the “George Smith” case. And clearly only Successful name transmission could be relevant here among the conventions recognized so far. Kripke ((1972), 95) compares the “George Smith” story with the case of a teacher who tells his students only that Newton was “the first man to think there’s a force pulling things to the earth” and, as Kripke plausibly claims, transmits successfully the name “Newton” to the students even if he conveys a (widespread) false belief about Newton. This makes Kripke say that the conditions for reference “seem in a way somehow different in the case of a famous man and one who isn’t so famous.” On the present picture, there is no difference, at least between the conventions governing reference fixing for names of famous people and those governing reference fixing for names of people who aren’t so famous. Certainly, a name of a famous person may be successfully transmitted even if it is transmitted along with a single false belief ²² And also of the case of “Madagascar” as used by the real Marco Polo, in note 20 above.

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102      that is widely held by the community, as this will definitely not generate in the inheriting speaker a set of beliefs that will conflict on the whole with the beliefs of the community at large. This explains the successful transmission of “Newton” to a class of students who are initially introduced to the name “Newton” in the mentioned impoverished way by a (perhaps) mischievous teacher. But the same could happen with the name of a not so famous person; if it is widely but falsely believed by the people who know him that George Smith once traveled to Antarctica, this will intuitively allow the successful transmission of “George Smith” to the students by means of an utterance by the teacher of George Smith once traveled to Antarctica. Note also that it’s not always easier to transmit “Newton” along with a falsehood about Newton than to transmit “George Smith” along with a falsehood about George Smith. If the teacher tells his students merely that Newton was the first squarer of the circle, it will be unclear that he has transmitted “Newton” successfully with its conventional reference (and Successful name transmission is evidently compatible with this). So Kripke’s impression that the case of transmission of names of famous people like Newton is different from the case of transmission of names of not so famous people does not seem very clearly or substantively true.²³ Compare these cases with a somewhat different case, though again one where a name is transmitted along with an extremely impoverished set of beliefs. To make use of a classical fictional story from Kripke (1972), imagine that Gödel was not in fact the discoverer of the incompleteness theorems, that these were in fact the discovery of a forgotten genius called “Schmidt” whom Gödel actually killed in order to steal the original manuscripts with the proofs. But suppose that otherwise the situation is much the same as it is in reality, and in particular that almost nobody has heard of Schmidt, that the theorems are universally attributed to Gödel, etc. Imagine then that the teacher, with deceitful intent, tells the students, who have never heard the names before, and many of whom will never hear them again, merely that Gödel is “the guy who killed Schmidt, the discoverer of the incompleteness theorems.” (Recall: the teacher does not believe that!) Now “Gödel” (and “Schmidt”) has been transmitted along with a true but universally disbelieved claim about Gödel (and Schmidt). Do the students’ uses of “Gödel” (“Schmidt”) from then on refer to Gödel (Schmidt)? My impression is again that it is unclear what the answer should be. In harmony with this, the picture proposed here has no implications in this case: Successful name transmission does not apply, as the students ²³ Nevertheless, Kripke’s mention of the social character of naming in the Addenda to Naming and Necessity makes him a precursor of the present view.

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form a rather impoverished set of beliefs that conflicts on the whole with the beliefs of the community of users of “Gödel” (and “Schmidt”) at large. Our final examples of apparent indeterminacy were the example of Barnes and “Nora,” the example of “Tim” and the trees, and the example of Kaplan and “Carny.” Here the only conventions from the list above that could be relevant are the conventions about successful name introduction and the conventions about unsuccessful name introduction. Neither Successful explicit name introduction via perceptual intention nor Successful implicit name introduction via perceptual intention apply in the Barnes and “Nora” case, because even if it is granted that Barnes is clearly perceiving or has just perceived the woman (via the sense of touch), it is not the case that he doesn’t have an intention that conflicts with the intention of referring with “Nora” to the woman he has perceived via the sense of touch—he also has the intention of referring with “Nora” to the woman he believes he is seeing. Unsuccessful explicit name introduction via perceptual intention and Unsuccessful implicit name introduction via perceptual intention do not apply either, because the intention of referring with “Nora” to the woman he believes he is seeing conflicts with the perceptual intention of referring with “Nora” to the woman that has just bumped into him. In the case of my attempt to give the name “Tim” to a tree, only the conventions of Successful explicit name introduction via perceptual intention and Unsuccessful explicit name introduction via perceptual intention could be relevant. But none of them applies, because of the existence of conflicting referential intentions. And in the Kaplan and “Carny” case, to make the long story even shorter, again the existence of conflicting intentions prevents the application of the possibly relevant conventions recognized so far. Our picture of the conventions governing name reference as giving only imprecise, roughly sufficient conditions for reference does deal nicely and naturally with intuitions of apparent indeterminacy. But it also accounts straightforwardly for the examples we discussed when evaluating theories of jointly necessary and sufficient conditions for reference. Recall first our counterexample to the necessity of Devitt’s conditions, involving the grounding of a use of “Aristotle” on some object that an early user of “Aristotle” mistook for Aristotle. Given the conventions recognized by our picture, this need not be an obstacle to “Aristotle” referring to Aristotle in the idiolect of a contemporary speaker at the end of a designating chain containing the speaker subject of that ancient grounding. For example, that speaker, S, might have transmitted the name to another speaker T, who might nevertheless have received the name also from other speakers who used it with

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104      its conventional reference. T will have the intention of using “Aristotle” in the same way as the community of users and need form no belief that conflicts with the community’s beliefs involving “Aristotle.” In particular, he need not form the specific belief that Aristotle is the object that causally grounded the uses of “Aristotle” by S. And at any rate, even if he forms this belief, his set of beliefs involving “Aristotle” need not conflict on the whole with the beliefs of the community at large. So T’s uses of “Aristotle” will refer to Aristotle, he will be endowed with the capacity of transmitting “Aristotle” successfully, and so on. Recall next the “Chaucer” example, in which the nineteenth-century users of “Chaucer” had most of their “Chaucer”-related beliefs consisting of fabrications from earlier times, though not by people who had directly known Chaucer. Still, intuitively their uses of “Chaucer” referred to Chaucer. On the present picture, the explanation for this is provided, in the first place, by the fact that those users inherited the name “Chaucer” in such a way that Successful name transmission applied. They inherited it from users who used it with Chaucer as referent, and formed the intention of using it in the same way as the community, without forming beliefs that on the whole conflicted with the beliefs of the community at large—we can presume that the fabrications were widely believed. In the second place, we can presume that when the fabrications were concocted, either they were not passed along at the transmission stage or, if they were passed along at the transmission stage, the inheriting speakers thereby formed beliefs that did not conflict on the whole with the beliefs of the community at large: presumably at that point the fabrications concerned matters about which the community at large held no views, such as the authorship of fabricated works and details of Chaucer’s life. Compare this case with a case in which someone has received a name successfully and, once the transmission stage is over, goes on to discover a great number of truths about the referent that were widely disbelieved at the point when the name was transmitted to her. Suppose, for example, that we are again in the fictional Kripkean story about “Gödel,” and that someone receives “Gödel” along with the usual information. Then, she goes on to discover, by means of careful historical research, that a huge deal of what the community believes about Gödel is false, including the attribution of the incompleteness theorems. Intuitively, reference to Gödel with “Gödel” in the mouth of the researcher is preserved along the whole process, despite the changes in her beliefs involving “Gödel,” which end up conflicting on the whole with the beliefs of the community at large. However, the present picture respects this intuition, as the changes in question concern stages posterior to the

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transmission stage, at which the researcher formed no beliefs about “Gödel” that conflicted with the beliefs of the community. (Later, the community at large may end up accepting the researcher’s conclusions, at which point the convention of Successful name adoption via description may apply and reinforce the implication that there is conventional reference to Gödel with “Gödel” in the mouth of the researcher.) The “Rio Ferdinand” case is different, in that the speaker forms from the beginning beliefs that on the whole conflict with the beliefs of the community at large involving the name. The belief that Rio Ferdinand is a soccer team evidently implies many other beliefs that will conflict with the fundamental beliefs of the community at large involving “Rio Ferdinand,” such as the beliefs that he is a man, that he is a player, that he is a center back, that he is an England international, and so on. So, Successful name transmission will not apply, which explains the impression that “Rio Ferdinand” does not clearly refer to Rio Ferdinand in the speaker’s mouth. Note, however, that if the example were altered, so that the inheriting speaker has simply heard the name “Rio Ferdinand” and has no view as to whether “Rio Ferdinand” refers to a soccer team or to something else, intuitively his uses of “Rio Ferdinand” will refer to the well-known soccer player. This will be accounted for on the present theory by the application of Successful name transmission in such a case. In the “The Oracle” example we are asked to suppose that ordinary people can inherit the name “The Oracle” so that they will keep referring to the committee, even if they develop the intention of referring to a god with “The Oracle.” On the present view, it is feasible that this should occur, provided that an ordinary person’s set of beliefs involving “The Oracle” formed at the transmission stage does not on the whole conflict with the beliefs of the community at large. If at the relevant transmission point the community consists of the priestesses and these transmit a good deal of information to the ordinary person about the committee’s pronouncements and the ways of obtaining such pronouncements, along with the idea of the committee’s divine nature, then it’s not implausible that there is reference to the committee in the ordinary person’s mouth with “The Oracle.” The present view is consistent with this, as the ordinary person will not have formed in such a case a set of beliefs that on the whole conflict with the beliefs of the community (the priestesses, essentially). But closely related situations in which the ordinary people come to fail to refer to the committee of priestesses are perfectly possible and intuitive. Let’s imagine the transmission of relevantly similar names under appropriately similar circumstances, and let’s ask ourselves what happens to reference

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106      then. Suppose the priestesses use the name “Koi” for the oracular committee, before any ordinary person receives the name. Then imagine that they bestow “Koi” for the first time to an ordinary person, by saying merely Koi made the pronouncement that there would be a drought last year, and Koi was right. Suppose the ordinary person receives the name and at the same time (reasonably) develops the belief that Koi is by no means a committee of people, but the god Apollo. Do the ordinary person’s uses of “Koi” from then on refer to the committee or to the god Apollo? I submit that the question is unclear, and that we are in all likelihood in the presence of a further instance of referential indeterminacy. Or suppose that the ordinary person, when receiving “Koi” for the first time in the way just mentioned, forms also the belief that Koi is a single person, not a committee. Do the person’s uses of “Koi” from then on refer to the committee? The question is perhaps even more unclear than before (even though Dickie’s theory implies that the uses will refer to the committee, as according to her roughly the same properties will be possible for the committee and for a single person, relative to the relevant discursive tasks). On the present theory, in neither example will there be clear reference to the committee; Successful name transmission does not apply, because the ordinary person forms a rather impoverished set of beliefs that conflicts on the whole with the beliefs of the priestesses concerning “Koi.” Finally, the “Khufu” example, which was seen to present problems for Dickie’s theory of reference transmission, is accommodated straightforwardly by the present theory. Khufu, we are supposing, was really a god, and the ancient Egyptians were thus quite correct in thinking so. An ordinary user of the name “Khufu” today will reject strongly any suggestion that Khufu was a god, but his uses of “Khufu” will intuitively refer to (the god) Khufu. This is explained on the present theory by the existence of a long list of applications of the convention of Successful name transmission, which will result in the ordinary contemporary speaker referring to (the god) Khufu with “Khufu.” If, as we imagined earlier, memory of the deeds of Khufu was lost little by little, the transmission of “Khufu” was nevertheless successful at each of the intervening steps, as loss of beliefs surely does not result in conflict with pre-existing community beliefs. If substantive bodies of intentions and beliefs involving “Khufu” are then developed again by relatively recent speakers, this will be no obstacle to their uses of “Khufu” still referring to Khufu, even when these speakers acquire these intentions and beliefs at the transmission stage, since by then the community at large will ascribe no divine attributes to Khufu. The present picture thus accounts, from an extensional point of view, for a great variety of phenomena and intuitions accounted for by other recent theories

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of reference fixing for proper names. And it extensionally accommodates as well a different range of intuitions and phenomena, especially having to do with referential indeterminacy, that familiar typical theories of jointly necessary and sufficient conditions for name reference simply fail to accommodate. But the picture, let’s recall, has two further satisfying features of a more abstract nature. Its postulation of mere sufficient conditions for reference and reference failure provides an explanation of the sources of referential indeterminacy for names, and indirectly of the difficulty of finding necessary and sufficient conditions for name reference. And in incorporating a suitably weak requirement of accessibility of the conventions of name reference to competent speakers, it both accounts for and overcomes the difficulties of sophisticated descriptivist theories of proper names.

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4 Arabic Numerals and the Problem of Mathematical Sophistication Verbal Numerals, Arabic Numerals, and Reference If I write 17 is a prime number I like, I would seem to have referred to a number, namely the number seventeen, and said of it that it is a prime number I like. This commonsensical view has of course been subjected to extreme pressure by many philosophers of mathematics, who have argued that things with the properties intuitively attributed to the numbers and other apparently non-physical things cannot really exist. But I think that the natural approach to questions about the nature of the numbers ought to be more or less the opposite of the skeptical or nominalist one not infrequent in discussions in the philosophy of mathematics. While these discussions often conclude, on the basis of metaphysical or epistemological assumptions, that the numbers don’t exist, and go on to develop theories of arithmetical language that don’t take linguistic intuitions about reference to numbers at face value, I think we must be ready to take more or less at face value some linguistic intuitions bearing on the question of how the referents of the numerals could get fixed, and see to what ontological or epistemological postulates they may lead us. The interesting question in this context is not, I think, whether skeptical or nominalist doubts can be assuaged to the full satisfaction of the doubters, but rather whether there is an intuitive ontology and epistemology of the numbers and the numerals that can underwrite a sensible account of reference fixing for the numerals. In this chapter we will develop such an account, relating it to a reasonable ontology and epistemology of the numbers. One thing we must emphasize before we begin is that the primary uses of the numerals are undoubtedly as adjectives and determiners, not as nouns or noun phrases. However, the question of how referents could get fixed in uses of the numerals as adjectives and determiners is essentially analogous to the corresponding question about the uses of numerals as nouns, giving rise to analogous problems and potential theoretical accounts. Thus, in focusing, as we will do in this chapter, on issues of semantic structure and reference fixing

Roads to Reference: An Essay on Reference Fixing in Natural Language. Mario Gómez-Torrente, Oxford University Press (2019). © Mario Gómez-Torrente. DOI: 10.1093/oso/9780198846277.001.0001

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concerning the uses of numerals as nouns, we will be at the same time indirectly considering abstract analogues concerning the uses of numerals as adjectives and determiners. Some of these analogies will be pointed out in brief asides or footnotes.¹ Let’s begin with some remarks on the semantics of the numerals. It’s not unreasonable to think that the verbal numerals of English and many other languages, when they are used as noun phrases (and not as adjectives or determiners), work as names or as descriptions. Simple verbal numerals, such as “one,” “two,” “three,” “ten,” “eleven,” “twenty,” “thirty,” etc. appear to work as (purported) names of corresponding numbers.² As such, their referents are presumably fixed by description or demonstration—though via descriptions or demonstratives that need not be conventionally equivalent to the simple verbal numerals. We will later see some reasonable hypotheses about what the relevant descriptions or demonstratives might be. Numerals such as “one hundred,” “one thousand,” and “one million,” which are not simple in English, consisting of a determiner and a noun, are probably not too different from simple numerals in this respect, as they presumably get their referents fixed via description or demonstration even if the nouns “hundred,” “thousand,” and “million” are semantically simple. On the other hand, truly complex verbal numerals are presumably descriptions tout court, and in fact descriptions that the numerals more or less wear on their sleeves. Thus, “twenty-one” can be seen as something like “twenty (plus) one,” “thirty-seven” as something like “thirty (plus) seven,” “seven hundred and sixty-five” as something like “(seven (times) (one) hundred) (plus) (sixty (plus) five),” and so on.³ We will later come back to verbal numerals with a bit more detail. Arabic numerals, which are nowadays employed overwhelmingly more often than verbal numerals, in uses as nouns and in other uses, are a different ¹ As noted below (in note 35), on some accounts the uses of the numerals as nouns are somehow disguised predicative uses. It is thus worth noting that the basic issues and proposals in this chapter are to a great extent independent of the issue of the relation between uses of numerals as nouns and uses of them as adjectives or determiners, and could be of use to the mentioned accounts. Nevertheless, I am confident that the use of the numerals as nouns is also semantically a use of them as singular terms for numbers. ² See e.g. Abbott (2010), where the idea is repeatedly emphasized that “some nouns that are not spelled with a capital letter nevertheless behave syntactically and semantically like proper names: words for numbers—like eight or ninety—are prominent examples” (p. 4); elsewhere (p. 49) she makes it clear that “words for numbers” include decimal Arabic numerals. ³ Related remarks hold for uses of verbal numerals as adjectives or determiners. For example, it is reasonable to think that “two” in its adjectival use may have its reference fixed as the property of being as many as the things in a certain paradigmatic two-element bunch that has been demonstrated or described at some point. And “seven hundred and sixty-five” in its adjectival use may have its reference fixed as the property of being as many as “(seven (times) (one) hundred) (plus) (sixty (plus) five)” things.

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110      story. There are many indications that the correct semantic account of at least the complex Arabic numerals, and thus the proper account of how their reference gets fixed, cannot be so simple. To begin to get a feeling of the complications, let me start by rejecting a proposal that is sometimes viewed with sympathy in the literature (e.g. in Hofweber (2005), 180) or in conversation, the proposal that the Arabic numerals either abbreviate or have their reference conventionally fixed by their corresponding verbal numerals. On a view of this kind, “765,” e.g., either abbreviates or has its reference conventionally fixed by a relatively unsophisticated description such as “(seven (times) (one) hundred) (plus) (sixty (plus) five).” To see what’s wrong with this proposal note that there are plenty more intelligible Arabic numerals than conventional verbal numerals in any typical speaker’s idiolect. Typically, speakers don’t know (whether explicitly or implicitly) how to extend the series of verbal numerals beyond some relatively small number in the range of the billions, while they would have no problem extending the series of (intelligible) Arabic numerals beyond that number. Even for linguistically sophisticated speakers who would know in principle how to produce the full series of conventionally established verbal numerals, this series ends at a relatively small number, while those same speakers would have no trouble producing a presumably contentful Arabic numeral representing a greater number.⁴ But the real problem with any view on which the referents of the Arabic numerals are fixed via corresponding verbal numerals is that, while the generation of the Arabic numerals and presumably the fixing of their referents are intuitively rule-governed, there are simply no conventional rules of any kind (explicit or implicit) for generating more verbal numerals than those conventionally existing at a given time. This creates a definitive objection to the view that the Arabic numerals either abbreviate or have their reference conventionally fixed by their corresponding conventional verbal numerals. For if N is the last verbal numeral conventionally existing at a given time, then, if n is the number N refers to, the Arabic numeral for n+1 is ⁴ If we are to trust the tongue-in-cheek Linderholm (1971), the last verbal numeral in (British) English (at least around 1970) is “nine hundred and ninety-nine thousand nine hundred and ninety-nine decillion nine hundred and ninety-nine thousand nine hundred and ninety-nine nonillion . . . nine hundred and ninety-nine thousand nine hundred and ninety-nine,” which corresponds to the Arabic numeral “999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999, 999,999,999,999,999.” (The last verbal numeral in American English is said to represent a quite smaller number, 999,999,999,999,999,999,999,999,999,999, 999,999 to be precise.) (In 2018, some time after writing the preceding, I noticed that the online Wiktionary records the words “quattuorvigintillion,” “trevigintillion,” etc., which would allow one to form the numeral “nine hundred and ninety-nine thousand nine hundred and ninety-nine quattuorvigintillion nine hundred and ninety-nine thousand nine hundred and ninetynine trevigintillion . . . nine hundred and ninety-nine thousand nine hundred and ninety-nine.” The dictionary in question doesn’t appear to record a word equivalent to “quinquevigintillion,” however.)

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intuitively generatable and will have n+1 as its reference, but surely will not acquire its reference by being the reference of a corresponding conventional verbal numeral.⁵ (A different question is whether, using conventionally established verbal numerals, and words for arithmetical operations, one could in principle fix the referents of all the Arabic numerals. The answer is positive, and this fact will actually be one ingredient in the picture of reference fixing for the Arabic numerals in this chapter.)

Existing Descriptivisms about Arabic Numerals and Their Problems There are broadly two kinds of accounts of Arabic numerals that are seriously considered in the tradition of the literature on reference. On the views of the first kind, at least the complex Arabic numerals have reference-fixing semantic structure, being semantically equivalent with certain moderately sophisticated mathematical descriptions or related phrases. Most descriptivists about proper names are naturally committed to this view, and of course even to the view that the simple Arabic numerals, or “digits” (“0,” “1,” . . . , “9”), are equivalent to descriptions of some sort (though the nature of the relevant description may be different for a complex numeral and for a digit). But also other philosophers, including some anti-descriptivists about typical proper names, have thought that at least the complex Arabic numerals must be semantically equivalent with certain descriptions (see e.g. Steiner (1975), 43; Neale (2008), 425, n. 15; these philosophers need not think of the digits as descriptions, and may well think of them as non-descriptive names of certain objects). I can also report that most people I’ve talked to about this in informal conversations view the Arabic numerals (or at least the complex ones) as mathematical descriptions of some sort, generally polynomial expansions such as “5·(9+1)⁰ + 6·(9+1)0+1 + 7·(9+1)0+1+1” in the case of “765.”⁶ (I will talk at length about these polynomials below.) One type of consideration for semantic descriptiveness is based on the obvious fact that the complex Arabic numerals ⁵ Related remarks hold for the referents of uses of Arabic numerals as adjectives or determiners. ⁶ Note that the polynomial representation requires the use of numeral notations of some sort, and in particular of notations for numbers greater than 9; and it’s at least dubious that ordinary current speakers master completely any numeral notation before they master completely the decimal Arabic one. However, I will assume that the descriptivist can get around this difficulty by supposing, first, that the digits are already available to an ordinary speaker as typical names of certain objects (whether they are also equivalent with descriptions or not), and second, that such a speaker also has available complex numerical representations formed by applying the addition sign to the digits.

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112      have a formal complexity that must somehow be relevant to their content, and are in this respect like descriptions, which are even syntactically complex, and unlike typical proper names, which are widely thought not to be formally complex in any way that is relevant to their content. A related, “Davidsonian” consideration for semantic descriptiveness is based on the intuition that Arabic numerals must get their interpretations by means of a general procedure which exploits in some way their morphological constituents and the meanings of these, unlike typical proper names, which ultimately get their interpretations via individual acts of reference fixing.⁷ On views of the second kind, held perhaps by most of the writers who have considered the question coming from the anti-descriptivist tradition about typical proper names, the Arabic numerals are not equivalent with descriptions, and are instead semantically non-descriptive singular terms, as proper names, pure indexicals, and simple demonstratives are likely to be (see Richard (1986), (1993); Soames (1987), 50; McCaffery (1999); Sullivan (2009); see also Linnebo (2009a), 227f. for an endorsement coming from a different tradition). For these authors, some remarks by Mark Richard have taken much of the sting away from the considerations for descriptiveness mentioned in the preceding paragraph. First, complex Arabic numerals certainly exhibit a morphological complexity, but this is clearly not syntactical complexity, as in the case of descriptions; the rule that constructs the Arabic numerals from the basic digits “is not one which constructs a term, given an arbitrary term, but only operates within the class of numerals” (Richard (1986), 393); a manifestation of this is that, unlike in the case of verbal numerals, intuitively one cannot “quantify into” (any proper parts of complex) Arabic numerals: There is a y such that 7y5 is odd makes no intuitive sense.⁸ Second, even if the Arabic numerals get their interpretations by means of a general procedure, and even by a procedure that assigns each of them a certain description somehow systematically related to the numeral’s morphological constituents, it is open to us to think that “[the numerals’] reference is fixed by this system of descriptions . . . but it is not the case that the terms whose reference is fixed are thereby descriptions (thus, it is a case of fixing the reference)” (Richard (1986), 403, n. 14; see also Soames (1987), 50, for an endorsement). Note that if this suggestion is correct, then the correct view of the Arabic numerals is a descriptivist, “fixes-the-reference” view, even if the numerals are not ⁷ Mutatis mutandis, essentially analogous considerations could be given in favor of the semantic “structuredness” of the uses of Arabic numerals as adjectives or determiners. ⁸ There are in fact many other interesting morpho-syntactic differences between verbal numerals and Arabic numerals. But it will not be necessary to dwell on these for our purposes here.

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semantically equivalent with descriptions. In fact, most authors of this second kind think that (at least the complex) Arabic numerals get their referents fixed via (systems of) descriptions, typically the same polynomial expansions mentioned in the preceding paragraph.⁹ I agree with the second group of writers that there is probably an implicit linguistic convention that Arabic numerals are to be taken as semantically nondescriptive. (More about my reasons for this below.) However, a remarkable feature of their writings is that they don’t contain positive arguments for the nondescriptiveness thesis. This literature is invariably defensive; that is, it always seeks to block arguments or considerations against the non-descriptiveness thesis, and doesn’t seek to give the thesis an independent justification. Richard, in particular, doesn’t construe his defensive observations as positive arguments that the (complex) Arabic numerals are not semantically equivalent with their corresponding polynomials, say. And this is as it should be, for it is perfectly open to the semantic descriptivist to claim that the numerals codify semantic descriptive structure, even polynomial semantic structure, that is hidden at the morphological surface level. Richard’s remarks only show that the numerals’ superficial morphological structure is no reliable guide to their semantic structure. There are reasons why this literature offers no positive considerations for thinking that the Arabic numerals are not semantically equivalent with descriptions. The classical Kripkean modal and epistemic arguments against descriptivism about proper names are unusable here, at least if the polynomials proposal is the main enemy: 765 = 5·(9+1)⁰ + 6·(9+1)0+1 + 7·(9+1)0+1+1 is intuitively both necessary and a priori. How about Kripkean so-called “semantic” arguments? Recall that so-called “semantic” arguments were developed by Kripke in order to undermine the idea that the intuitive referent of a typical name in the mouth of a speaker who has received the name from other speakers is determined by the properties that the speaker associates with the name. Kripke’s considerations show that in many cases these properties might turn out to fail (or do fail) to single out the object that would nevertheless be the intuitive referent, or might turn out to single out something that would not be the intuitive referent. A typical speaker, even if he associates with “Gödel” the description “the discoverer of the incompleteness of arithmetic,” would intuitively talk about the same person, Gödel, with “Gödel” even if it turned out that the proofs of incompleteness all contain a subtle mistake and formal

⁹ Mutatis mutandis, an analogous view is possible for uses of the Arabic numerals as adjectives or determiners. For example, it might be proposed that “765” in its adjectival use may have its reference fixed by “5·(9+1)⁰ + 6·(9+1)0+1 + 7·(9+1)0+1+1” in its adjectival use.

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114      arithmetic is in fact complete (or if it turned out, as in the Kripkean story we recalled in chapter 3, that Gödel was not the real discoverer of incompleteness and some other person was). This is one of the facts that suggested that the referent comes intuitively determined by the chain of transmission of the name and not by the descriptions associated with the name by the speaker at the end of the chain. The existence of this independent contact between speaker and referent makes the question whether a certain object is that referent in the speaker’s idiolect to be intuitively detached from the question of whether that object satisfies those descriptions. However, these considerations cannot be applied in general to cases in which a speaker-baptizer fixes the referent of a typical name with help from a description, for in many cases of this kind such a speaker will associate descriptive material with the name in an intuitively undetachable way. In fact, the paradigmatic cases are cases like Kripke’s “Neptune” and “Jack” (the Ripper) cases, where the speaker-baptizer uses the reference-fixing description without an independent cognitive contact with the referent and thus in a purely attributive way. Note, e.g., that intuitively Le Verrier would not have referred to anything with “Neptune” if it had turned out that there was no single planet causing the perturbations in the orbit of Uranus; and this would be so even if some other kind of thing, say a certain asteroid belt, had turned out to cause those perturbations. Now if the “fixes-the-reference” descriptivist picture of the (complex) Arabic numerals conjectured by Richard, Soames, and others is the right picture of the situation, then this will presumably be a case in which all users of Arabic numerals will be in a way “speaker-baptizers” fixing the referents of numerals by means of (a system of) descriptions without independent cognitive contact with those referents, and thus in a purely attributive way. To be sure, a typical user of the Arabic numerals cannot be a completely original stipulator; in some way she must be handed the reference-fixing descriptions by other, at that moment mathematically more knowledgeable, users. But if the mentioned picture is correct, then presumably she must implicitly take it to be a general stipulation, that she embraces for her particular idiolect, that the (complex) Arabic numerals refer to whatever it is that the corresponding descriptions describe. And if this is so, Kripkean so-called “semantic” arguments will be just as useless as modal and epistemic arguments. As McCaffery ((1999), 432) puts it, “the reason is that the referent of a given [numeral] is determined by the meanings of the parts of the [numeral] and how they are put together. The referent of the [numeral] is that thing which is the actual such-and-such” (“the actual such-and-such” is the description fixing the reference of the numeral, which McCaffery actually

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takes to be a polynomial). Just as there is no purely “semantic” argument showing that “Neptune” is not semantically equivalent in Le Verrier’s idiolect with “the planet causing the perturbations in the orbit of Uranus,” on this picture there is no purely “semantic” argument showing that “765” is not equivalent in a typical speaker’s idiolect with “5·(9+1)⁰ + 6·(9+1)0+1 + 7·(9+1)0+1+1.” McCaffery candidly concludes: “It may be that there is no way to determine . . . whether complex numerals are [non-descriptive terms] rather than definite descriptions, and that numerals, both simple and complex, are directly referential” ((1999), 435). This is why the “fixes-the-reference” descriptivist literature is always merely defensive. I think, however, that reasonable standard arguments (including so-called “semantic” arguments) can be applied with considerable intuitive force against existing descriptivisms about the Arabic numerals, and in particular against many proposals that rely on relatively sophisticated descriptions, including polynomial proposals. We will now call attention to the intuitive feasibility of some such arguments against some sophisticated descriptivist accounts. Later, we will present a “fixes-the-reference” descriptivist view for the Arabic numerals that will appeal to less sophisticated reference-fixing descriptions, a view that will be accompanied by the postulation of a significant role for certain elements that can plausibly be said to provide a kind of non-descriptive cognitive contact between speakers and numbers. The resulting picture, unlike the mentioned sophisticated descriptivist accounts, will square well with the intuitive evidence we will bring to bear against them. There are many kinds of systems of mathematical descriptions that have been or could be proposed either as giving the semantic structure of the numerals or as (merely) fixing their referents. As already noted, a widely popular candidate for the complex numerals are polynomial expansions such as “5·(9+1)⁰ + 6·(9+1)0+1 + 7·(9+1)0+1+1” in the case of “765”—on a descriptivist view the digits would have some other kind of description giving their semantic structure or fixing their referents. Another candidate is a Fregean system of descriptions where the description giving the meaning or fixing the reference of a numeral N later than “0” in the natural order would be of the form of “The number of numerals between ‘0’ and ‘M’” or “The number of numbers between 0 and M” (where for “M” one would substitute the Arabic numeral coming just before N in the natural order)—on such proposals, “0” would get its reference fixed by means of a description of some other kind. Another proposal, that would have more plausibility than the preceding ones as far as morphological structure is concerned, might be extracted from Kripke’s (1992) theory about the ontological nature of the referents of the

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116      decimal Arabic numerals. Kripke’s ontological proposal (whose motivation we will explain in the last section of this chapter) is that the referents of “0” to “9” are certain basic abstract objects, possibly the basic numerals or digits themselves, or their corresponding cardinality properties, and the numerals after “9” are finite ordered sequences whose elements are those basic objects, sequences that mirror the corresponding numerals. (See also Steiner (2011) and Marshall (2016).) For example, on this proposal the referent of “765” is the sequence (7,6,5) (where “7,” “6,” and “5” are names of the corresponding basic abstract objects).¹⁰ Now from this we might extract descriptivist proposals (neither of which is embraced by Kripke) on which “765” would be semantically equivalent with, or would at least get its reference fixed by, the presumable description “(7,6,5),” or the manifest description “the sequence of 7, 6, and 5, in this order.”¹¹ Certainly, if the descriptions postulated by these proposals are at least co-referential with their corresponding numerals, then the corresponding identifications are to be presumed necessary and a priori. As already noted, 765 = 5·(9+1)⁰ + 6·(9+1)0+1 + 7·(9+1)0+1+1 is intuitively necessary and a priori; so are The number of numerals between “0” and “764” is 765 and The number of numbers between 0 and 764 is 765; and The sequence of 7, 6, and 5, in this order, is 765 ought to be a priori and necessary if true. The application of Kripkean “modal” and “epistemic” arguments to these proposals is then precluded. Also, at least many of these descriptions are presumably ¹⁰ As Kripke notes, a sequence here is not to be understood as a function from an initial segment of the natural numbers—this would be circular. It must be understood via some other set-theoretic construction, or just taking “the sequence of . . . ” as a primitive notion. ¹¹ Probably something like the proposal that a complex Arabic numeral is semantically equivalent with such a description is what Neale ((2008), 425, n. 15) has in mind when he says that “in our base-10 system ‘0’ to ‘9’ are referring expressions whereas ‘10,’ ‘11,’ ‘12’ etc. are all definite descriptions. This is a position Saul Kripke drew me to in seminars at the University of Oslo in 1991,” evidently referring to the Kripkean ideas transcribed in Kripke (1992)—but Neale’s undeveloped claim is compatible also with the descriptions in question being the standard polynomial representations. (Neale apparently also thinks that it’s only about 0 to 9 that one can entertain genuinely singular thoughts if one represents to oneself the numbers in decimal notation (p. 425, note 15).) It’s fairly clear that Neale has drawn inadequate conclusions from Kripke’s work. It seems clear to me that for Kripke Arabic numerals are not semantically equivalent with the descriptions expressing their corresponding polynomial representations, but almost certainly also that they are not equivalent with other kinds of descriptions. (It is also clear that Kripke, unlike Neale, accepts that one can entertain singular thoughts about largish numbers that one represents to oneself in decimal Arabic notation.) An appearance of incompatibility between Kripke’s theses and the idea of semantic non-descriptiveness may have arisen from Kripke’s conjecture (with which I otherwise disagree; see the final section of this chapter) that numerals intuitively expressing the same number in different bases or notations must refer to (structurally) different sequences of basic objects. But a real incompatibility could arise only if, assuming it was a fact that certain sequences are the referents of the numerals, this implied that the numerals ought to be equivalent with descriptions describing those sequences; however, the question of whether the numerals are semantically structured is clearly independent of the question of whether the objects they refer to are ontologically structured.

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descriptions whose satisfaction would be intuitively undetachable from the referents of the corresponding numerals, even after appeal to far-fetched epistemic possibilities, the possibility of Kripkean so-called “semantic” arguments being then also prevented in these cases. But other considerations can be used to undermine these descriptivist proposals. For example, a number of intuitions about de re attitudes toward natural numbers seriously discredit at least many of the semantic descriptivist views. This kind of intuitions has been adverted to by Ackerman (1978) and Kripke (1992) among others. They are intuitions to the effect that typical English speakers seem to have de re attitudes involving the natural numbers when they entertain those attitudes via Arabic numeral representations (at least when the numerals are not too long), but not when they entertain them via other representations which are more clearly descriptive. If I know that there are, say, 765 dollars in my account, then intuitively there is a number of which I know that it is the number of dollars in my account; if I only know that there are 5·(9+1)⁰ + 6·(9+1)0+1 + 7·(9+1)0+1+1 dollars in my account, then it cannot be intuitively said that there is a number of which I know that it is the number of dollars in my account (if I only know that, I have to engage in a little bit of calculation if I want to know what’s the number of dollars in my account). Also: I know what’s the number of dollars in my account if I know that there are, say, 765 dollars in my account; but intuitively I don’t know what’s the number of dollars in my account if I only know that there are 5·(9+1)⁰ + 6·(9+1)0+1 + 7·(9+1)0+1+1 dollars in my account. Similar remarks hold for “The number of numerals between ‘0’ and ‘764,’” “The number of numbers between 0 and 764,” and in my view even for “The sequence of 7, 6, and 5, in this order.”¹² The corresponding views on which the (complex) Arabic ¹² Arabic numerals seem even to give rise to de re attitudes in many more cases than verbal numerals. I feel a difference of “proximity” even between “765” and “seven hundred and sixty-five.” And compare “seventy-two thousand, eight hundred and forty-seven” with “72,847.” Does the reader get a feeling of greater “proximity” when looking at the Arabic numerals in note 4, but not when she looks at the corresponding (not fully written) verbal numerals? I’m sure many readers had not heard the words “decillion,” “nonillion,” etc., but have some sense of what number 999,999,999,999,999,999,999,999,999,999,999,999,999 is, and of how (in principle) one would get to it by counting or by multiplication. Another interesting set of data comes from experiments on the psychological processing of numerals. It has been shown experimentally that the realization of which particular quantity is named by a given Arabic numeral is much faster than the realization of which quantity is named in the case of a given verbal numeral; see Henik and Tzelgov (1982) and Pavese and Umiltà (1998). In fact, this literature shows that it’s almost impossible to ignore the meaning or referent of a given Arabic numeral when asked to perform tasks with it, suggesting a special directness of the connection between Arabic numeral and numerical referent. This has led a number of psychologists to suggest that “the processing of arabic numerals resembles more the processing of pictures than the processing of words” (Brysbaert (2005), 35; see Brysbaert, Fias, and Reynvoet (2000), and Fias, Reynvoet, and Brysbaert (2001)).

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118      numerals are semantically equivalent with descriptions of these forms are thus greatly weakened.¹³ The alternative “fixes-the-reference” views for these descriptions are, however, consistent (if barely) with these intuitions; for it might be held that, even though the numerals’ referents are fixed by the descriptions, some other mechanism, perhaps one of substantively non-descriptive acquaintance with the numbers via their numerals, is responsible for the fact that through the numerals I am able to entertain de re attitudes toward the numbers—while if the numerals are just semantically equivalent with the descriptions then they ought not to be different in this respect. However, no concrete proposal in this direction seems to exist in the “fixes-the-reference” literature. Also, it seems clear to me that plausible considerations about conceptual competence strongly discredit both semantic and “fixes-the-reference” proposals using the mentioned systems of descriptions. For example, many, probably most typical speakers who have irreproachable competence with the numerals, and who presumably use them in their idiolects with the numbers as their semantic referents, have little or no knowledge of exponentiation (and indeed, in many cases, only marginally better knowledge of multiplication or at least of the possibility of forming complex arithmetical terms by composition of many operations). This places under great strain both the view that the (complex) numerals are simply disguised polynomials such as “5·(9+1)⁰ + 6·(9+1)0+1 + 7·(9+1)0+1+1” and the view that they get their referents fixed in the idiolect of a typical speaker by means of such polynomials.¹⁴ It’s also just hard to believe that concepts like the general concept of a numeral, which are required for an understanding of the Fregean descriptions, are really part of the semantic structure behind the numerals or even of the conceptual wherewithal of the users of the numerals as reference fixers.¹⁵ Arguably, for example, people can be competent with the numerals for specific numbers (even very large ones) without having the general concept of a numeral. Perhaps more importantly, even if people probably need to have some concept of number or quantity if they are to be irreproachably competent ¹³ The same can be said of “structuredness” views of the adjectival and determiner uses of the Arabic numerals. ¹⁴ There is evidence coming from the psychological literature suggesting that the Arabic numerals are processed and compared digit by digit. From this psychologists sometimes extract the conclusion that they are somehow processed as polynomials in powers of 10; but I think that this conclusion is manifestly unwarranted. What the digit-by-digit processing of an Arabic numeral suggests is simply that the event or process involved in the realization of which number is the content of a given numeral involves non-descriptive psychological processing of the numeral’s digits and their relative positions, rather than of any description, including polynomial ones. This suggestion will be vindicated by the proposal in this chapter. ¹⁵ Related considerations can be applied against the proposal in Linnebo (2009b), even though for him the reference fixers are not strictly speaking descriptions.

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with numerals, they clearly need not have a sophisticated conception of the numbers or quantities underlying the numerals which includes a view of them as things that can themselves be counted (and of concepts, sets or pluralities of numbers as themselves having numbers) (see related remarks in Heck (2000), 201, and Linnebo (2009a), 227). Related considerations are also intuitively applicable against the mentioned descriptivist proposals inspired by Kripke’s ontological view of the numbers. In order to be competent with “(7,6,5)” or with “the sequence of 7, 6, and 5, in this order,” one must possess a sophisticated conception of numbers as things that can form sequences; but I think it’s doubtful that ordinary people who are competent with “765” really need to have any notion of an ordered sequence of numbers or cardinalities, even if they need to be acquainted or familiar with things that can be taken to form sequences, and perhaps even with sequences formed by more ordinary things than the numbers. And on the proposal below, it will indeed be at least conceivable that one may be competent with the numerals without thereby having any sophisticated conception of the cardinalities or the numbers as things that can themselves be counted or form sequences.¹⁶ It will be good to note at this point that a certain potential “conceptual poverty” objection to descriptivist views is unsuccessful, and I don’t subscribe to it. The objection can be put as follows: “Even moderately sophisticated speakers who have the ability to associate suitable polynomials with Arabic numerals don’t have this ability for all the Arabic numerals: some numerals are just too big. If all the numerals are to get referents under such a proposal, then it must be in virtue of the speaker having somehow embraced a general rule for assigning a polynomial to each numeral. But the formulation of such a general rule is way too complicated mathematically for even moderately sophisticated speakers to grasp it, even implicitly. Hence polynomial numeral descriptivism is wrong.” It is certainly true that if all the numerals are to get referents, then it must be in virtue of the speaker having mastered a general rule for assigning a referent to each numeral. And it is also true that the formulation of a general rule for transforming each Arabic numeral into its corresponding polynomial is mathematically complicated and unavailable even to moderately sophisticated speakers. But I don’t think the availability ¹⁶ Once more, analogous considerations discredit views of the adjectival and determiner uses of Arabic numerals as having complex semantic structure or as having their content fixed by complex semantic structures. The polynomial “5·(9+1)⁰ + 6·(9+1)0+1 + 7·(9+1)0+1+1” could be proposed as giving the semantic structure of adjectival and determiner uses of “765,” or as fixing their contents. Similarly, a complex adjectival phrase or determiner phrase corresponding to the Fregean description might be proposed to give the semantic structure or fix the content of “765,” e.g. “as many things as numbers between 0 and 764.” Again the arguments above would plausibly discredit such proposals.

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120      of such a general rule is necessary in order for a speaker to be said to follow the rule, just as the non-availability to a speaker of the rules of grammar, or of complex semantic rules, doesn’t mean that he is not following these rules when he speaks or writes. In particular, I think we must grant that a speaker who knew how to assign suitable polynomials to sufficiently many Arabic numerals could be said to be following a procedure that has fixed the referents of all the Arabic numerals in his idiolect, even if he did not know how to describe the procedure itself. We will later see that analogous remarks are important also for the proposal favored in this chapter. Considerations about linguistic or conceptual competence should perhaps have stared numeral descriptivist theorists in the face, though one obstacle to this may have lain in the appearance of inevitability of a relatively sophisticated mathematical descriptivist conception of the Arabic numerals. But further, I think that also an appreciation of the intuitive possibility of the so-called “semantic” arguments against at least some descriptivist proposals, even as applied to conceptually sophisticated speakers, may have been neglected due to that appearance of inevitability. An argument of the so-called “semantic” kind against the view that the Arabic numerals are disguised polynomials, even in the idiolects of typical arithmetically sophisticated speakers, might be as follows. One can surely imagine that it came to turn out that our usual way of making some elementary arithmetical computations is meaningless, due to some subtle and hitherto unimagined problem making, say, exponentiation ill-defined. As a matter of fact, the usual reasoning leading to the conclusion that the 0th power of any number must be 1 is somewhat involved;¹⁷ who is to say that no mistake has been made in this reasoning? Or who is to say that it could not turn out that we became convinced that there is some substantive and uncontroversial ground for thinking that “fast-growing” functions like exponentiation are somehow problematic and “unreal” in a way in which “slow-growing” functions like addition and multiplication are not?¹⁸ ¹⁷ To quote from a popular mathematics reference book: The more natural we make our generalization, the more interesting and useful it is likely to be. And the way we make it natural is to ensure that at all costs we keep the property of ‘turning addition into multiplication.’ This, it turns out, leaves us with only one sensible choice for what 23/2 should be. If the fundamental property is to be preserved, then we must have 23/2 · 23/2 = 23/2 +3/2 = 2³ = 8. Therefore, 23/2 has to be √8. It turns out to be convenient to take 23/2 to be positive, so we define 23/2 to be √8. A similar argument shows that 2⁰ should be defined to be 1: if we wish to keep the fundamental property, then 2 = 2¹ = 21+0 = 2¹ · 2⁰ = 2 · 2⁰. Dividing both sides by 2 gives the answer 2⁰ = 1. (Gowers (2008), 200) ¹⁸ As a matter of fact, some radical constructivists think that exponentiation is only partially defined (see e.g. Nelson (1986)), but even more radical views about the meaningfulness (or rather meaninglessness) of exponentiation are surely epistemically possible.

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Of course these may well be (in my view, they are) no more than epistemic possibilities; of course there may well be no such problems, just as there is (probably) no flaw in Gödel’s proof of the incompleteness of arithmetic that makes it the case that the description “the discoverer of the incompleteness of arithmetic” is not satisfied. But (a certain kind of) epistemic possibility is all that we need in “semantic” detachment arguments. If one of those things came to happen, would the reader think that a typical user of the Arabic numerals would have never referred to 765 with “765,” given that the description “5·(9+1)⁰ + 6·(9+1)0+1 + 7·(9+1)0+1+1,” insofar as it mentions exponentiation, would have turned out to determine no number? I think that in such cases we would not say that “765” did not refer or was meaningless in the idiolect of that user, provided merely that, on closer inspection, we uncovered no additional reason to impugn other parts of his and our typical arithmetical education and practice not involving exponentiation, and especially our practice of counting with the numerals. In fact, as already noted, many typical speakers competent with the Arabic numerals have little or no knowledge of exponentiation. I myself would think that in the envisaged circumstances we would just say that, however strong our idea might have been that the Arabic numerals were polynomials in the idiolects of (at least) conceptually sophisticated users, the fact that exponentiation had turned out to be problematic but our overall arithmetical practice remained sustainable would have shown that even those sophisticated users ultimately relied on some other mechanism to get the referents of their Arabic numerals fixed.¹⁹ Undoubtedly some mathematically sophisticated descriptivist proposals (including some of the proposals considered above that were vulnerable to “conceptual poverty” objections) will not be vulnerable to detachment considerations. Some of these may feature descriptions whose satisfaction is intuitively undetachable from whatever things turn out to be the referents of the corresponding numerals, even after appeal to far-fetched epistemic possibilities. If there were an a priori correct theory of the conditions determining the reference of an Arabic numeral, then one kind of descriptivist proposal that would presumably be invulnerable to the so-called “semantic” arguments would be one that postulated that the appropriate description recapitulates that condition. Also the Fregean proposals above would seem invulnerable to detachment considerations, for the epistemic possibilities one would need would be possibilities in which the existing notions of number or counting ¹⁹ Analogous “semantic” considerations could be given against both “structuredness” and “fix-thereference” accounts of the adjectival and determiner uses of Arabic numerals.

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122      themselves would be put in jeopardy. Similarly, the Kripke-inspired proposal above would seem invulnerable to detachment considerations: probably the relevant notion of a sequence is just too intertwined with the notions of number and counting for us to feel the intuitive pull of a detachment argument in this case. It’s fortunate that “conceptual poverty” arguments are available in these cases. But even if they were not available against all conceivable mathematical descriptivist proposals, I think that a strong consideration against other sophisticated descriptivist views one might concoct would be provided by the plausibility of the alternative picture described in the next section.

A Picture of Reference Fixing for the Arabic Numerals Existing descriptivist theories (whether semantic or “fixes-the-reference”) respond to the intuition that the Arabic numerals get interpreted via a general procedure which exploits their morphological constitution, conjecturing that there is indeed a system of moderately sophisticated mathematical descriptions conventionally associated with the numerals, descriptions that exploit in some way the morphological structure of the numerals whose reference they fix. The preceding considerations, however, suggest that, even if such a system of descriptions plays some role in the cognitive lives of some sophisticated users, the referents of the Arabic numerals are probably fixed in some other way in the idiolects of typical users, and in fact even in the idiolects of sophisticated users. But what could that way be? In view of the considerations we just reviewed, it is natural to conjecture that the Arabic numerals have their referents fixed in a typical speaker’s idiolect when she masters some kind of systematic correspondence between the numerals and some reference-fixing descriptions that employ relatively unsophisticated conceptual resources. But it is also natural to conjecture that these associations are accompanied by independent non-descriptive cognitive connections with the numbers eventually represented by the Arabic numerals. In the pages that follow, I will make a specific proposal with these characteristics. In order to state the proposal, we will need to have in mind some basic facts about the typical speaker’s arithmetical education which are presumably relevant to her capacity to single out numbers in thought and language. By the time a typical speaker is exposed in earnest to the Arabic numerals, she has learned to recite at least a moderately large initial segment of the sequence of existing verbal numerals and has learned to count bunches of objects with it, even though this recitation and this counting are initially

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“mindless,” i.e. are not accompanied by any sort of realization of what meaning or reference the numerals have in the common language or are susceptible of having in the speaker’s idiolect. The development of these “mindless” abilities precedes as a matter of psychological fact the grasp of any sophisticated mathematical concepts. Indeed, it precedes even the grasp of the concept of quantity or number as such.²⁰ However, the mastery of these abilities eventually induces the appearance of particular conceptions of the numbers in a progressively larger set, and also of a minimal conception of the general notion of number. The minimal conception of the general notion of number includes a number of implicit ideas. Among them, the idea that the number of a bunch of things is an aspect of it that is common to other bunches that can be counted by means of the same verbal numeral; the idea that a bunch of individual objects have the number they have as a matter of intrinsic fact, i.e. independently of the relations of the bunch or the objects in it to other individual objects; and the idea that to each new verbal numeral corresponds in the natural order a number that is greater by one than the number corresponding to the preceding verbal numeral in that same order.²¹ The conceptions of the particular numbers include identifications of them, presumably by means of descriptions or demonstratives of various kinds. In the case of the very small numbers, examples would be “the number of these things” or “this number,” supplemented with suitable intentions to refer to paradigmatic bunches of things, or to mental models of such bunches.²² In the case of bigger numbers, whether with simple or complex verbal numerals, the descriptions will involve simple arithmetical operations, for example “six times ten” in the case of “sixty,” “ten times ten” in the case of “(one) hundred,” “ten times one hundred” in the case of “(one) thousand,” “seven times one hundred plus sixty plus five” in the case of “seven hundred and sixty-five,” etc.

²⁰ Three-year-olds have the ability of putting sets in correspondence with initial segments of the verbal numerals in a fairly developed way, but it’s doubtful that they can be said to know that the procedure gives indication that sets have specific quantities (see Gelman and Gallistel (1978), 198ff. and Wynn (1992); see also Heck (2000) in the philosophical literature). This knowledge requires the development of an ability additional to that of “mindless counting”; it plausibly requires some level of competence with the concept of number or quantity, or of “how many.” ²¹ Concerning this latter idea, see Carey (2009a), 251: children who have come to understand that counting yields cardinality develop, according to Carey, “a (tacit) appreciation of how counting implements the successor function . . . [those children] judged that if a hidden array they were told consisted of 5 objects had another added to it, the resultant array must have 6 not 4 or 7.” See also Carey (2009b), ch. 8. ²² See Carey (2009a), 249: “the child may create a long-term memory model of a set of one individual and map it to the linguistic expression ‘a’ or ‘one’. Similarly, a long-term memory model of a set of two individuals could be created and mapped to the linguistic expression for a dual marker or ‘two’, and so on for ‘three’ and ‘four’.” Again, see also Carey (2009b), ch. 8.

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124      A typical speaker then (often concurrently) acquires similar abilities and implicit ideas concerning the sequence of Arabic numerals. These include first of all similar descriptive associations with the small numerals. Also, and crucially, they include the ability to generate mechanically the sequence of Arabic numerals and to count with it, apparently without the intervention of any sophisticated knowledge of polynomial representation.²³ This is a fairly non-conceptual ability, as in exercising it the typical speaker does not appear to be relying on a conceptual grasp of the rule of generation of the Arabic numerals, let alone applying it to each particular step. The typical speaker, in counting, does not compute the next step by means of a composition of concepts. Surely, once one becomes (quite) sophisticated, one may become able to formulate more or less mathematically clever rules for the generation of the series of the Arabic numerals.²⁴ But surely these are rules which are not conceptually grasped by the typical speaker, even if they can be reasonably said to code his behavior. The ability to generate the Arabic numerals, at least for a good initial segment, is acquired before the concepts necessary to formulate these rules are acquired, and certainly well before mastery of polynomial representation is acquired (by those who actually acquire it). The typical speaker also acquires the additional implicit idea that any given number is “notation-independent,” at least in the sense that it indifferently corresponds to a certain verbal numeral (if the number has a verbal numeral, that is) and to a certain Arabic numeral. She extends her implicit conception of number correspondingly: in particular, she adopts the implicit idea that the number of a bunch of things is an aspect of it that is common to other bunches that can be counted by means of the same Arabic numeral, the idea that a bunch of individual objects have the number they have as a matter of intrinsic fact, i.e. independently of the relations of the bunch or the objects in it to other individual objects, and the idea that to each new Arabic numeral corresponds in the natural order of generation a number that is greater by one than the number corresponding to the preceding Arabic numeral in that same natural order. However, since the rule of generation for the Arabic numerals that the speaker masters does generate infinitely many numerals (while in the case of

²³ Compare the psychological experiments with six- to ten-year-olds reported in Fayol and Seron (2005), 17. ²⁴ If one is considerably sophisticated mathematically, one may eventually note, e.g., that the counting order of the Arabic numerals is roughly their lexicographical order, in the sense that it’s the order where first come the digits “0,” “1,” “2,” “3,” “4,” “5,” “6,” “7,” “8,” “9,” in this order; and then, for sequences of digits of more than one member and not beginning with zero, a sequence of digits d₁d₂ . . . dn comes before a sequence d₁’d₂’ . . . dk’ iff n is less than k or n=k and, at the first i where di and di’ differ, di comes before di’ in the initial list of the digits.

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verbal numerals there is no such rule), this last idea will contain the potential for fixing the reference of at least vastly many more Arabic numerals than verbal numerals in the speaker’s idiolect.²⁵ That all these ideas are implicit in the typical speaker’s mind is a reasonable postulate given the existence of certain dispositions to verbal behavior on the part of typical speakers. Thus, the idea that the number of a bunch of things is an aspect of it that is common to other bunches that can be counted by means of the same verbal or Arabic numeral is manifested in the disposition to assent to utterances of The number of these things is the same as the number of those things or similar sentences, accompanied by realizations that the intended bunches can be counted by means of the same verbal or Arabic numeral. The idea that any given number is “notation-independent” is manifested in the disposition to assent to utterances of sentences such as 17 is seventeen, or to appropriate utterances of This number is the same as this number, said by pointing to an Arabic numeral and a verbal numeral which occupy the same places in the natural order of their respective sequences. The idea that a bunch of individual objects have the number they have as a matter of intrinsic fact, i.e. independently of the relations of the bunch or the objects in it to other individual objects, is manifested in dispositions to reject utterances of sentences such as If this stone had not existed, the number of these people would not have existed, or would have been different, or If Julius Caesar had not existed, the number of these stones would not have been the same, or there would have been no such number. Finally, the idea that to each new verbal or Arabic numeral corresponds in the natural order of generation a number that is greater by one than the number corresponding to the preceding verbal or Arabic numeral in that same natural order is manifested in the disposition to assent to sufficiently many sentences of the form of 17 is greater by one than 16, or to appropriate utterances of sentences such as This number is greater by one than this number, said by pointing to two verbal or Arabic numerals the first of which follows the second in the natural order.²⁶ ²⁵ All these abilities, conceptions, and implicit ideas have appropriate analogues for adjectival and determiner uses of the numerals. For example, a speaker may associate with the adjectival use of “2” the adjectival phrase “as many as things in this bunch,” and will acquire the implicit idea that to each new Arabic numeral used as an adjective corresponds in the natural order of generation a property that ascribes a quantity greater by one than the quantity corresponding to the preceding adjectival Arabic numeral in that same natural order. ²⁶ It may be worth noting that these implicit ideas about number parallel other implicit ideas concerning the notion of an expression, involved in reference fixing for quotations (see GómezTorrente (2013)). For example, a typical speaker will think of an expression as an aspect common to different tokens (as manifested e.g. in the disposition to assent to appropriate utterances of This expression is the same as that expression); she will think of a token’s being a token of a certain expression as a matter of intrinsic fact, i.e. one independent of the relations of the token to other

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126      It is not implausible to suppose that these and related implicit ideas acquired by typical speakers manage to determine in some way the kind of things that the numbers are. Later we will offer some considerations in support of the thesis that the implicit ideas about number acquired by typical speakers probably manage to determine that the numbers are the finite plural cardinality properties. For the moment, we will just suppose that, whatever the conception of number acquired by a typical speaker, this conception, possibly together with other elements, determines an extension for the concept of number in the speaker’s idiolect. In doing this we work under an assumption that is also tacitly made in the sophisticated descriptivist proposals we rejected. Under this assumption, we will proceed to offer our proposal about how the reference of individual Arabic numerals gets fixed in the idiolects of typical users. The proposal is based on the thought that the existence of the ability to generate the series of Arabic numerals without recourse to sophisticated arithmetical knowledge, plus the mentioned implicit ideas and corresponding dispositions to verbal behavior, suffice to establish in a typical speaker’s idiolect an association between the Arabic numerals and a system of relatively unsophisticated reference-fixing phrases that successfully single out the corresponding numbers. The ability to generate the series of the Arabic numerals underlies this association and is responsible for providing speakers with the non-descriptive cognitive contact with the referents of the Arabic numerals that would seem required in view of the existence of de re attitudes about the natural numbers via those numerals. The proposal is, first, that small Arabic numerals, like “1,” get their referents either via translation to their corresponding verbal numerals, or directly via descriptions similar to those that presumably fix the referents of small verbal numerals, such as “the number of these fingers,” or “this number,” said or thought while intending a paradigmatic bunch of objects or a mental model of a bunch of objects having the number in question. And second, that bigger Arabic numerals get their referents fixed in a typical speaker’s idiolect when she masters systematic ways to identify those referents in terms of the referents of the smaller numerals. There may be many such ways. Perhaps the simplest one would be manifested in the speaker’s disposition to associate with sufficiently many Arabic numerals, coming after “1” and following an Arabic numeral M in the natural order, the description of the form of “the number individual objects (as manifested in dispositions to reject utterances of sentences such as If Julius Caesar had not existed, the expression here would not have existed, or would have been different); etc.

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greater by one than M.” Surely a description such as “the number greater by one than 9” fixes the reference of “10” if we can suppose that the reference of “9” has already been fixed, a description such as “the number greater by one than 10” fixes the reference of “11,” and so on.²⁷ Other ways to identify numeral referents in terms of the referents of smaller numerals presumably exploit the speaker’s knowledge of verbal numerals and his ability to translate Arabic numerals into corresponding verbal numerals, plus the ability to compute numbers for which there is no verbal numeral on the basis of large numerals for which there is. For example, “1,000,000,000,000,000” may be associated, in the idiolect of a speaker who has no verbal numeral for this, with the description “one million billions.” “10,000,000,000,000,000” may be associated, in the idiolect of a speaker who has no verbal numeral for this, with the description “ten million billions,” and so on. Note then that the proposal concedes that some descriptive material is involved in numeral reference fixing—the general meanings of “number” and of “being greater by one,” in the simplest case. But the proposal has it that no part of the work will be done by even moderately sophisticated mathematical (or metamathematical) concepts. In essence, only the speaker’s general conception of number and of adding one need be involved. (Note in particular that no general conception of numeral need be involved.) It is, I think, a mechanism such as this that singles out the referent of an Arabic numeral, rather than a descriptive composition of moderately sophisticated mathematical (or metamathematical) operations. This mechanism also provides a speaker with the intuitive idea that the sophisticated descriptions postulated by the “fixes-the-reference” views reviewed above are not really semantically undetachable from the corresponding numerals. The ability to generate and interpret bigger and bigger numbers via the mechanism is, not coincidentally, essentially related to the ability to count; it is ultimately this ability that provides our most basic conceptions of number. Note also that the emergence of systematic ways of identifying the referents of the bigger numerals in terms of the referents of the smaller ones is made possible by the systematicity of the generation of the series of Arabic numerals, which was ²⁷ Analogously, it might reasonably be held, first, that small Arabic numerals used as adjectives get their referents via adjectival phrases such as “as many as beds in my bedroom,” or “as many as these,” said or thought while attending to a paradigmatic bunch of objects or a mental model of a bunch of objects having the number in question. And second, that bigger Arabic numerals used as adjectives get their referents fixed in a typical speaker’s idiolect when she masters systematic ways to identify those referents in terms of the referents of the smaller numerals, for example by learning to associate with the numeral following an Arabic numeral M in the natural order the adjectival phrase of the form of “as many as M plus one.”

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128      ultimately lacking in the case of the series of verbal numerals. Nevertheless, this systematicity doesn’t require or presuppose anything like knowledge of the polynomials corresponding systematically to the Arabic numerals. The postulated system of implicitly associated reference-fixing descriptions must be finite for each particular speaker. Nevertheless, the association at stake can be naturally coded by general rules encompassing an infinite number of cases, and it is just as natural to postulate, leaving meaning-skeptical worries aside for our purposes, that some such rules are in fact determined by the speaker’s finite practice and dispositions—in particular the dispositions to associate numerals with phrases of the form of “the number greater by one than M,” or similar. In this way, it can reasonably be said that an infinity of numerals get their referents fixed in a typical competent speaker’s idiolect. Let’s make this clear by making completely explicit the simple rule postulated above: Number rule. The Arabic numeral “1” refers to the number one; and whenever an Arabic numeral refers to a certain number, the Arabic numeral that follows it in the generating order refers to the number greater by one than that number. A competent user could in principle associate with each Arabic numeral he gets acquainted with one or more particular (utterances of) reference-fixing descriptions for that numeral which intuitively follow from the Number rule. For example, such a competent user, when shown an utterance of “765,” could in principle associate with that utterance (an utterance of) the description “the number greater by one than 764,” or similar, which fixes the referent of that numeral, provided “764” already has a reference (as it will). All these descriptive associations follow from the universal quantification constituting (the second part of) the Number rule, and by hypothesis all of them fix 765 as the referent of “765.” Full explicit grasp of the Number rule by a typical speaker is not really necessary for the referents of the numerals to be fixed in her idiolect. While there is a rule encompassing the variety of phrases that could be associated with the Arabic numerals, there is really no obstacle to the possibility that users of the numerals don’t learn the associations by conceptually grasping the rule; it’s enough that one learns to make the relevant particular associations governed by the rule, even if one cannot describe how this takes place in general.²⁸ (Nevertheless, it is worth observing that the Number rule can be ²⁸ Note that similarly, proponents of sophisticated descriptivism about the numerals, e.g. polynomial descriptivism, cannot plausibly claim that even speakers who know how to associate each Arabic

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formulated employing relatively unsophisticated concepts, certainly less sophisticated than the polynomials postulated by standard sophisticated descriptivist theories (not to speak of the concepts required in a formulation of a general rule for assigning each such polynomial to its corresponding numeral).) The picture of reference fixing for the Arabic numerals that we have developed has a number of welcome consequences. First, the appeal of “conceptual poverty” arguments against sophisticated descriptivist views is very naturally explained: for, on the proposal, speakers would have (in principle) no need to have at their disposal a sophisticated conceptual apparatus in order for the referents of the Arabic numerals to get fixed in their idiolects. There is presumably a minimal conceptual wherewithal required. This includes some sortal like “number” or “quantity” or at any rate a related locution like “how many.” It also includes the concept of being greater by one. But these are all arguably concepts available from very early on to all typical speakers, and in fact their possession amounts in a way to a realization that what numerals are for is signaling cardinality. Second, the possibility of the so-called “semantic” arguments against a number of descriptivist proposals about the numerals is also naturally explained under the present proposal. For the question of whether a decimal Arabic numeral gets a certain thing as referent (in the idiolect of a typical English-speaking user) will be intuitively independent of the question of whether that thing has the descriptive characteristics postulated by the descriptive proposals in question.²⁹ The descriptions of the form of “the number greater by one than M” (among others) are responsible for the numerals’ acquiring their referents as referents in the speaker’s idiolect, rather than the associated system of moderately sophisticated mathematical descriptions (which must have, in the speakers in whom it exists, only a negligible, at best auxiliary role in reference fixing). A speaker of English will typically be able to refer to 765 in

numeral with its corresponding polynomial know explicitly a general rule that describes how to generate each such polynomial; as already noted in the main text, the rule in question can only be formulated by sophisticated mathematicians. ²⁹ The situation may be different with binary Arabic numerals; we don’t learn to count with them, and our knowledge of their meanings and referents is presumably strongly associated with polynomial descriptions; perhaps these are (for typical English speakers) semantically equivalent with the corresponding polynomials (absent any implicit convention that they are unstructured).

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130      a way that exploits her familiarity with the way “765” is generated in the series of Arabic numerals, thus independently of any knowledge of polynomial representation.³⁰ The picture is also compatible with other intuitions and desiderata. In particular, the intuition that the numerals get interpreted via a general procedure which exploits their morphological constitution is respected—though in a way very different from the way sophisticated mathematical descriptivist proposals respect it. The reason is that the referent of a numeral is fixed, as it were, by a recursion that exploits the order of generation of the Arabic numerals, and this exploits their morphological structure, which undoubtedly plays a role in the singling out and the identification of their corresponding numbers on the part of the speaker. It is the morphological structure of an Arabic numeral that determines its place in the counting sequence, as generated by the lexicographic procedure. Moreover, the picture is fully compatible with the view of the Arabic numerals as not semantically equivalent with the phrases that fix their reference. The fact that the referents of numerals are plausibly fixed by descriptions extractable from the general Number rule does not imply that a numeral should have the semantic structure of some particular description provided by the rule, or that it should have any other kind of reference-fixing semantic structure. The descriptions plausibly work only at the reference-fixing level, and the numerals otherwise function under a convention of nondescriptiveness, an implicit agreement that the Number rule merely helps fix their reference, without providing a description constituting the semantic structure of a numeral and fixing its reference.

What the Referents of the Numerals Could Be How could the typical speaker’s conception of number determine an extension for this notion? A reasonable idea is that the principles or preconceptions that we may see as constitutive of this conception constrain the nature of the entities that the numbers can be, via some implicit reference-fixing intention concerning “number,” to the effect that these entities must satisfy those preconceptions, and that if some entities (are the only ones to) satisfy them,

³⁰ Burge (2007) can be read as having a similar view, but only for the single digits. He seems to think (wrongly, in my view) that counting up to complex numerals like “765” implies some kind of sophisticated conceptual manipulation, though he concedes that the opposite view is feasible.

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then they are the things to which “number” applies. And the nature of the numbers is, I think, considerably constrained by those preconceptions— indeed, considerably more constrained than the dominant literature in the philosophy of mathematics might lead one to expect.³¹ We have already mentioned the preconception that any given number is “notation-independent,” in the sense that it indifferently corresponds to a certain verbal numeral (when it has one) and to a certain Arabic numeral, being thus independent for its existence from the existence of the notation. This preconception excludes identifying the numbers with things which are not notation-independent, such as the corresponding numerals, or related things such as sequences of basic objects corresponding to the Arabic digits, as in the Kripkean theory mentioned above.³² We also mentioned the implicit ideas that the number of a bunch of things is an aspect of it that is common to other bunches that can be counted by means of the same Arabic numeral, and that to each new Arabic numeral corresponds in the natural order of generation a number that is greater by one than the number corresponding to the preceding Arabic numeral in that same natural order. These ideas exclude identifying the numbers with aspects which are highly specific to particular bunches, or with things which are not homogeneous in nature—all of the same kind—or that cannot reasonably be seen as generatable from an initial item by recursive application of a homogeneous operation—one applying to things of a kind to yield things of that kind—corresponding to the intuitive operation of adding one. Yet another preconception forming part of the typical conception of number—if a neglected one—is that the number of a bunch of individual objects is an aspect of that bunch which is intrinsic to that bunch. This is manifested in the typical speaker’s disposition to accept that a given bunch of individual objects would have the number they have even if other individual objects extrinsic to the bunch had not existed. Thus, intuitively the number of coins in my pocket would have been five even if Julius Caesar had not existed, or even if (per impossibile) Zermelo five or Von Neumann five had not

³¹ In chapter 5 we will appeal again to “preconceptions” in the moderately theoretical sense at stake here. The basic idea I have in mind is that preconceptions may be very strongly adhered to, but are not perforce constitutive of the meaning of the relevant expressions. Still, they have an auxiliary role in the fixing of their reference. (This notion is inspired by the notion of a “prejudice” introduced by Kripke, as discussed in Gómez-Torrente (2011).) For other intuitive preconceptions constraining the nature of numbers, which perhaps go somewhat beyond those attributable to every typical speaker, see GómezTorrente (2015a). ³² We still owe the reader a description of Kripke’s motivation for his proposal. We will give it below, together with an explanation of how he handles the objection of notation dependence.

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132      existed; also intuitively, the number of coins in my pocket would have been five even if (again per impossibile) Kripke five or the verbal numeral “five” had not existed: the non-existence of all these things would intuitively leave untouched the fact that the number of coins in my pocket would be five, so five cannot—at least as far as the common conception of number is concerned—be any of these things. By contrast with the relationships we intuitively think to hold between the bunch of coins in my pocket and Zermelo 5, Von Neumann 5, Kripke 5, etc., the coins in my pocket have the number five as an intrinsic aspect—as far as the common conception of number is concerned. I think this constrains considerably the nature of the things that can be the numbers as far as the common conception allows. In fact, they probably require the number five to be an intrinsic property of the bunch of coins in my pocket, and mutatis mutandis for the other numbers. The intuitions that underwrite ideas about the possibility of de re thought via the Arabic numerals can also be seen as providing further constraints on the nature of the numbers on the common conception. For the intuition that one can often entertain de re thoughts about numbers via their Arabic representations but not via their verbal representations is plausibly interpreted as an intuition that one can often identify in a fairly non-conceptual or nondescriptive way a number if one is presented with its Arabic representation (and that one must employ descriptive or conceptual resources if one is to identify it via its verbal representation); so, that intuition plausibly imposes on numbers the constraint that they must be things that in some sense are susceptible of being identified non-descriptively via a process that significantly involves their corresponding Arabic numerals. An idea that is quite congenial with the preconceptions of the common conception of number is that the res that the numbers are are probably to be identified with certain high-order properties.³³ (Furthermore, I think it’s fair to say that the idea that numbers are abstract individuals of a certain kind has been widely discredited by a variety of independent considerations, to which a few more were actually added above.) My own more specific view is, following Yi (1999) and Gutiérrez Vivanco (2018), that the numbers of the common conception are probably to be identified with plural cardinality properties or numerosities, or, to say it in a somewhat misleading way, with cardinality properties of pluralities; for example, the property that the coins in my pocket ³³ Cognitive scientists also make this assumption quite generally (“Numbers are properties of objects in the external world that are mentally represented as abstract concepts” (Semenza and Granà (2006), 731)), though often with disarming philosophical ingenuousness; it is especially they who call cardinalities “numerosities,” as we are about to do.

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have of being five is the number five.³⁴ I thus postulate that the numerosities or cardinality properties of pluralities are the referents of the Arabic numerals in their uses as nouns.³⁵ (They are also the referents of verbal numerals when used as nouns, and they are the things described by those verbal numerals which are analyzable as descriptions.) We will now see that this postulate squares very well with the array of preconceptions constituting the common conception of number that we identified above.³⁶ First, plural cardinality properties are clearly notation-independent, as manifested in the fact that, if the typical numeral notations had not existed, intuitively the cardinality properties would still have been properties of bunches of things of the corresponding cardinalities. Second, the cardinality property of a bunch of things is an aspect of it that is common to other bunches that can be counted by means of the same Arabic numeral, and certainly not an aspect highly specific to particular bunches. Third, to each new Arabic numeral corresponds in the natural order of generation a cardinality property that ascribes one more element to a bunch of things than the property corresponding to the preceding Arabic numeral in that same natural order. The cardinality properties are, as expected, homogeneous in nature and things that are generatable from an initial item by recursive application of a homogeneous operation that can plausibly be seen to correspond to the intuitive operation of adding one—the operation yielding the property of ascribing one more element than a given cardinality property. Fourth, the cardinality property of a bunch of individual objects is an aspect of that bunch which is intrinsic to that bunch. A typical speaker will expectably be disposed ³⁴ This view seems to square better with linguistic evidence than other related views on which the numbers come out as high-order properties, such as the view that they are properties of concepts (as in an intensional version of Frege’s historical view), or the view that they are properties of sets (as in Maddy (1981), (1990)). For example, it seems more appropriate to speak of the number of coins in my pocket than of the number of the set of coins in my pocket or of the number of the concept of being a coin in my pocket. Nevertheless, if some more conclusive argument favored one of these alternative hypotheses, much of what we are about to say would still apply to the alternative proposal. ³⁵ Philosophers of mathematics who assign a basic role to cardinality properties in the interpretation of number words typically don’t think of them also as referents of the numerals in their apparent use as nouns. Thus Hodes (1984), e.g., sees sentences in which numerals appear as nouns as having a deep logical form in which apparent singular reference to numbers has disappeared and has been replaced with essentially predicative uses. Hofweber (2005) sees those sentences as a kind of cognitive helpers without real content, but which are easier to deal with than corresponding contentful sentences in which numerals have their basic predicative use. I do think that the Arabic numerals have a use as genuine singular terms, and that they probably refer to cardinality properties or related entities. Nevertheless, as I have already emphasized, many of the basic points in this chapter could be made for predicative, presumably “undisguised” uses of the Arabic numerals as well. ³⁶ It may be worth noting that our postulate is not in conflict with the views in the recent paper Moltmann (2013), which despite its title is more about the author’s thesis that some natural language expressions do not refer to numbers that might seem to. Moltmann concedes that when used as nouns the numerals, especially the Arabic ones, do refer to numbers.

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134      to accept that a given bunch would have the cardinality property it has even if other individual objects extrinsic to the bunch had not existed, including Julius Caesar, Zermelo five, Von Neumann five, and Kripke five. Perhaps most importantly, if the numbers are numerosities typical speakers can plausibly identify them non-descriptively in ways that involve their corresponding Arabic numerals. In order to argue for this claim, let me first propose what I take to be a plausible general model of how some properties could be non-descriptively identified by speakers. While writers in the theory of reference typically presuppose that at least many properties must be things about which one can have non-descriptive thoughts, or things susceptible of non-descriptive acquaintance, there is little discussion in the literature of how this could be so. A plausible idea, in any case, is that at least sometimes a speaker can non-descriptively identify a certain empirical property when she possesses the ability of telling apart, in principle and without the use of procedures involving in some way an appeal to compositions of concepts or descriptions, the property’s instances from instances of related properties (at least in all cases in which there is no gross mistake in perceptual judgment involved). That is, the ability (in principle) to tell in some non-descriptive way the property’s instances from instances of other properties that lie on some common intuitive array or continuum (in all cases in which there is no gross mistake in perceptual judgment involved). For example, abilities of this kind include my ability to distinguish non-descriptively circles from squares and ellipses, my ability to distinguish non-descriptively things that are red from things that are orange or purple, etc. What kind of non-descriptive recognitional abilities allow speakers with a typical arithmetical education to identify the numbers, on the hypothesis that these are indeed numerosities, cardinality properties of pluralities? On the mentioned model, the development of some basic abilities to tell pluralities having a certain cardinality property from pluralities having other cardinality properties (at least in cases in which there is no gross mistake in perceptual judgment involved), should play a key role in the typical speaker’s capacity to identify these properties in a non-descriptive way. Now, to complete the case that numerosities are thus capable of being non-descriptively identified by typical speakers, we must make it clear that they in fact develop some such recognitional abilities involving cardinality properties, and furthermore that these abilities are saliently connected with the corresponding numerals. But at this stage nothing could be easier, for it’s reasonable to think that the ability to tell pluralities having a certain cardinality property from pluralities having other cardinality properties is typically strongly linked, at least for numbers

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that are not too small and cannot be grasped “in a flash,” with abilities involving the decimal Arabic numerals themselves, and in particular with the ability to count, in the sense of the ability to put an initial segment of the series of Arabic numerals in correspondence with a (possibly very large) set of things; this is surely a highly non-descriptive ability. In this way, the intuitions underwriting the possibility of de re attitudes about natural numbers are in their turn satisfied under the hypothesis that the numbers are plural cardinality properties. It’s worthwhile comparing the present proposal about the nature of the numbers with a proposal made by Kripke in unpublished work, and motivated also by intuitions about de re attitudes toward natural numbers. According to Kripke, as we advanced above, the referents of the basic decimal Arabic digits are some corresponding basic abstract objects, e.g. the digits themselves, or the corresponding basic cardinalities, and the referents of the complex decimal Arabic numerals are ordered sequences of these objects. These ideas suggest a view on which the numbers are susceptible of being non-descriptively identified by a typical speaker: if a number is conceived as a sequence of digits, for example, this will surely allow the speaker to “see” such sequences and slightly indirectly to identify non-descriptively the numbers that correspond to the corresponding numerals. This is surely a tempting view. To see why it is tempting, let me recall some of the facts that led Kripke to postulate it. Recall that the intuitions about de re attitudes pointed out by Kripke and Ackerman indicate cognitive or broadly epistemic differences between Arabic numerals and polynomial descriptions. Ackerman sought to account for intuitions about de re attitudes by relying on a general distinction between numerals and other kinds of numerical expressions, and postulating that the de re attitudes toward natural numbers are those which are entertained via numeral representations forming part of a numeral system for which the subject of the attitude knows how to generate its sequence of numerals in order, and how to count with it. Kripke noted that this seems too undemanding; we may, e.g., calculate in some clever way, without going through the answer in Arabic decimal notation, that the answer to a certain problem in Arabic binary notation is “1011111101” and hence entertain a belief that that’s the answer to the problem via that numeral representation; but it cannot intuitively be said that we know what number is the answer, or that there is a number of which we know that it is the answer, even if we know how to generate the sequence of binary Arabic numerals and thus count with it. (“1011111101” is the (palindromic) binary representation of 765.)

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136      It is in view of this that Kripke proposes to account for de re attitudes involving natural numbers by means of an ontological idea that has immediate cognitive or epistemic repercussions. On Kripke’s view, the things named by the numerals (i.e. the sequences of basic abstract objects) are in a close natural relation with the numerals, a relation not unlike the relation of picturing. In this way, if some creature believes of a certain number that it has a certain property via the representation “1011111101,” it believes of the sequence (1,0,1,1,1,1,1,1,0,1) that it has that property, and it has not come to believe that 765, i.e. the sequence (7,6,5), has that property. On Kripke’s proposal, the explanation for de re attitudes relies on the fact that a numeral like “765” would be something really close to a picture of what it refers to, and this could reasonably be taken as the ground for the sort of acquaintance with numbers that plausibly underlies the intuitively de re nature of the attitudes specified in terms of Arabic numerals. Let me emphasize again that he has not explicitly developed his ideas into a view of reference fixing for the numerals. What he says explicitly is compatible with, at the very least, a “fixes-the-reference” sophisticated descriptivism about the Arabic numerals. But it is only natural to think that a substantively non-sophisticated descriptivist reference-fixing version of his proposal would be a natural companion of Kripke’s explicit views. While I obviously sympathize with the spirit of these ideas, and I concede that the Kripke-inspired view can at least be argued to meet our epistemic constraint, I think it’s clear that it is vulnerable to other very serious objections. Let me mention them in what I take to be their order of increasing seriousness. First, the proposal needs to postulate that there is a relation of structural similarity between numbers and numerals. But one would have expected numbers to be strongly metaphysically independent from notations, i.e. not to have their nature co-varying with the nature of notations in any way. In fact, numeral notations might appear to depend for their existence on the existence of their concrete tokens (they may well be “quasi-concrete” abstract objects, in the terminology of Parsons (2008)); but one would not have expected this of the numbers, which would appear not to depend in any way on the existence of concrete instances of the numerosities (bunches of abstract objects should also have numbers). Second, the proposal requires a suspicious heterogeneity in the ontological natures of the numbers less than ten and the greater numbers (in the primordial case of decimal notation), as well as in the appropriate operation of adding one; and mutatis mutandis for other Arabic notations.

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Third, the proposal postulates an unintuitive difference in the natures of the referents of numerals in different notations, and in particular it postulates different referents for numerals which are intuitive translations of one another. Kripke accepts that there is a sort of double-think in our practice of use of the numerals, for usually we don’t require the things they name to be different from the things named by other numerical notations; this is the use exemplified when we say things like DCCLXV is 765. However, even if there is such double-think (and I think Kripke is right to say that there is), and even if we concede that Kripke’s account may explain well the use of numerals on which we sort of identify the numbers with the numerals themselves, the fact remains that there is another use of the numerals on which we don’t require the things they name to be different from the things named by other numerical notations. If some explanation could be given of this use, I believe we would be much better off. As against the Kripkean view, on the present proposal all the numbers are uniformly taken to be cardinality properties, which need not stand in any quasi-graphical structural relationship with the numerals—but our cognitive contact with these properties is effected partly via processes or states involving the numerals themselves. This contact does not exploit a supposed relation of structural similarity between numerals and numbers, but a relation (roughly the relation of usability of the numerals in the constitution of several numerical abilities) that plausibly suffices for the establishment of close cognitive connections between speakers and numbers via abilities involving the numerals. Also, the present proposal, as against the Kripke-inspired view, is compatible with the view that the referents of numerals can be the same in alternative notations, even in alternative Arabic notations employing different bases; for the cardinality properties one would get acquainted with via the development of sufficiently analogous abilities involving different numeral notations are plausibly the same. I’m thinking of, say, people who used binary Arabic notation from the beginning in their education and managed to employ it as efficiently as we employ decimal notation. In their idiolects (unlike perhaps in our idiolects), binary numerals would be non-descriptive. Let me finish by addressing one potential objection to the proposal in this chapter, modeled precisely on the objection we saw Kripke making to Ackerman’s account of de re attitudes toward natural numbers, an account that bears some initial similarities to the present account. On Ackerman’s account, in order to have a de re attitude toward a natural number it’s enough to have it under some numeral. Ackerman does not attempt to give a detailed account of what is to count as a numeral, but she makes it clear that she

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138      doesn’t include mathematical descriptions constructible by means of the usual arithmetical operations, and that numerals belong to systems that can be “mastered.” “Mastering” a numeral notation is in turn something one accomplishes when one becomes able to generate the sequence of the notation’s numerals in their natural order. As we saw, Kripke objected that, pretty clearly, in order to have a de re attitude toward a natural number it’s not enough to have it under some numeral. I think his objection to Ackerman’s account is correct, as far as the account goes. Now the related objection to our account would be that it doesn’t explain de re attitudes, because “mastering” a notation is not enough for acquaintance with the natural numbers, nor hence for de re attitudes. But this objection is not correct, because one can require more of “mastering” a notation than Ackerman did. Clearly there is a continuum of levels of ability and ease with the numerals of a notation, from a clumsy level at which a speaker only knows how to generate the numeral series and compare numerals as to the relative size of their numbers in slow and indirect ways, to a level at which a speaker can generate the series and make numeral comparisons in a direct and relatively effortless way. In our account, we may simply require the development of direct and effortless counting and comparing abilities for acquaintance with the numbers via a numeral notation. This is clearly much more than simply possessing an ability to translate (via computation) numerals in, say, binary representation, into numerals in decimal representation, and vice versa. While in some sense one has a “mastery” of binary representation if one has this ability, having this ability involves much less than having the abilities to count directly and effortlessly in binary notation and to compare directly and effortlessly binary numerals as to their relative positions in the natural order. Someone having these abilities would presumably be susceptible of having de re attitudes toward the natural numbers when having them under their binary representations. Kripke (1992) is very worried by the possibility that if we are forced to reject an Ackerman-style account of de re attitudes, then we must yield to a sort of relativism on which different people, or different groups of intelligent beings, can become acquainted with the numbers via different notations, while it seems to him that there is a mystery as to what could make some people acquainted with the numbers via one notation and other people acquainted with the same numbers via a different notation. This is what leads Kripke to his “middle ground” proposal that the mastery of different notations determines different numbers as referents for the numerals. But I think that there is no real mystery, and that the present proposal avoids the obvious problem of

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the Ackerman proposal and at the same time provides at least the beginnings of an explanation of the fact that the development of a strong familiarity with a particular numeral notation yields acquaintance with the same numbers in each case. The truth is that one can get acquainted with the same number via different processes of mastery of different notations, say decimal and binary. On the proposal, the reason is that one can identify non-descriptively the instantiation of a cardinality property as a result of a strong familiarity with a particular notation, while another person or an intelligent being of a different species could identify non-descriptively the instantiation of that same cardinality property as a result of having acquired a strong familiarity with a different notation. This is just as one can get acquainted with Venus via different states or processes of cognitive rapport with the planet, say looking at it in the morning and looking at it in the evening. The fact that the same object can be an object of acquaintance via different “acquainters” certainly generates no particular mystery. To be sure, the accessibility of one “acquainter” to someone who is exclusively familiar with another one may be more difficult in some cases than in others. For example, the accessibility of the “acquainters” provided by mastery of binary notation to someone who has exclusively mastered decimal notation is undoubtedly hard, because the abilities involved are really complex and not that easy to develop. (They might actually be impossibly hard to develop for beings with the cognitive resources of typical humans.) By contrast, the state of looking at Venus in the evening is typically readily accessible to someone who has only seen it in the morning. Still, we can imagine cases in which some special circumstance makes it hard for some people to get acquainted with Venus in the evening, say. We can imagine, for example, that some seriously impaired nyctalopes may have difficulty seeing Venus in the evening, while they have no such difficulty seeing it in the morning. These differences between “acquainters” are perfectly expectable and indicate that there is no special mystery for the existence of connections of acquaintance between speakers and cardinality properties on the basis of different notations (or for the lack thereof).

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5 Nouns for Natural Kinds and the Problem of Arbitrariness The “Kripke-Putnam Orthodoxy” about Nouns for Natural Kinds Ever since Kripke claimed, and persuasively argued, that “terms for natural kinds are much closer to proper names than is ordinarily supposed” (Kripke (1972), 127), nouns for what appear to be natural kinds have been studied against the background of Kripke’s ideas—and of related ideas of Hilary Putnam (especially in Putnam (1973) and (1975)). Kripke has particularly in mind nouns from ordinary, pre-scientific language for what appear to be natural substances (such as “water” and “gold”), biological species (such as “tiger” and “lemon tree”), and natural physical phenomena (such as “heat” and “lightning”). And his claim that these are close to proper names has certainly been vindicated by all that has followed. As in the case of proper names, some of the basic Kripkean ideas on natural kind nouns, including a basic kind of anti-descriptivism, have largely appeared to constitute incontrovertible advances in our understanding of them. And as in the case of proper names, there has been an analogous controversy between sophisticated descriptivists about natural kind nouns and sophisticated anti-descriptivists who take their inspiration from Kripke but embrace other, generally stronger forms of anti-descriptivism than his. However, perhaps the fact that descriptivists and anti-descriptivists alike have typically discussed the Kripkean and Putnamian ideas about natural kind nouns only in afterthoughts, added to discussions of proper names, has made these ideas appear as even more widely accepted than the basic Kripkean ideas about proper names—it is not infrequent to find references to “the Kripke-Putnam orthodoxy” about natural kind nouns, while one would probably have some difficulty finding the phrase “the Kripke orthodoxy” when proper names are concerned. But things seem to be changing, or perhaps have already changed: by now a considerable literature, in many cases inspired by ideas from the philosophies of chemistry and of biology, has produced a number of arguments designed to cast doubts over at

Roads to Reference: An Essay on Reference Fixing in Natural Language. Mario Gómez-Torrente, Oxford University Press (2019). © Mario Gómez-Torrente. DOI: 10.1093/oso/9780198846277.001.0001

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least some main aspects of the “Kripke-Putnam orthodoxy.” As we will see, these doubts do not point, at least directly, to arguments for descriptivism about natural kind nouns. But the strongest among these arguments aim at the conclusion that the mechanisms Kripke and Putnam postulated for the fixing of reference of natural kind nouns do not really deliver, or perhaps just cannot deliver, any referents. The arguments in question thus challenge the ability of the “Kripke-Putnam orthodoxy” to provide an account of reference and reference fixing for natural kind nouns that preserves the idea that there is no generalized failure of reference and of truth conditions in central linguistic domains. In this chapter we will assess these challenges, and will come to the conclusion that they do point to the need to reformulate the Kripkean and Putnamian models. It will be suggested that the needed reformulation does not differ in nuclear respects from Kripke’s account of the mechanism of reference fixing for natural kind nouns. However, the reformulation will be more explicit and detailed than Kripke’s account about what the operation of the mechanism itself requires and doesn’t require. Crucially, our reformulation in this chapter, unlike the Kripke and Putnam writings, will make it thoroughly clear that the correctness of the corresponding picture of reference fixing does not presuppose certain specific views about the nature of the referents of particular natural kind nouns, such as “water,” “gold,” “tiger,” etc. And, more positively, our reformulation will suggest that, as regards the nature of their referents, terms for natural kinds are much closer to proper names than even Kripke supposed. We need to know first what the “Kripke-Putnam orthodoxy” is, so that we can see also how the challenges in question aim to undermine it. As we will mention in brief notes and asides here and there, Kripke’s ideas are different from Putnam’s, and both sets of ideas are more complex than most critical expositions suggest. This will uglify our exposition a little, as we need to separate what is taken to be the “Kripke-Putnam orthodoxy” from other aspects of the Kripkean and Putnamian ideas. But it is important to isolate the ideas that people usually have in mind when they criticize the “KripkePutnam orthodoxy,” for these are the influential, if simplified and sometimes attributed with undue simplification, ideas to which criticisms are always directed. We should also note that the “Kripke-Putnam orthodoxy” includes many ideas, correctly attributable to Kripke and Putnam, that the critics generally don’t question. Before we start with the exposition of the “Kripke-Putnam orthodoxy,” let me note that we will assume that natural kind nouns must function at least as predicative expressions, and hence that when they function as such, they must

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142       refer to suitable properties, in the characteristic manner in which predicative expressions refer.¹ This is compatible with accepting also that natural kind nouns may have uses as singular terms (as in Gold is a metal, Lightning came down from the clouds, and perhaps in The tiger lives in Asia), in which reference is made (or intended) to the relevant kind in the characteristic manner in which singular terms refer to or stand for things in general. We will often run together our remarks about the predicative and singular term uses, for, as with predicative expressions quite generally, it is natural to postulate a close connection between the singular term use and the predicative use. In the singular term use the nouns refer (if they do) to the relevant substances, species, etc. (viewed as properties that the terms stand for, in the characteristic way in which singular terms stand for things in general), and in the predicative use they refer to those same kinds (though in the manner characteristic of predicative expressions). One basic idea of the “Kripke-Putnam orthodoxy,” which as far as I can tell is rarely if ever questioned by the critics, is that a natural kind noun, or at any rate a typical natural kind noun from ordinary, pre-scientific language, does not have the same meaning as a descriptive predicative expression that details some well-known but contingent a posteriori characteristics that the speaker attributes to the objects instantiating the corresponding natural kind. This implies that it is not in virtue of having a meaning of this sort that a natural kind noun has the referent it has (if it has any). For example, “water” is not synonymous, within the idiolect of a normal speaker, either with “transparent, odorless, tasteless liquid filling rivers, lakes, and oceans” (in predicative uses) or with “the transparent, odorless, tasteless liquid filling rivers, lakes, and oceans” (in singular term uses).² As both Kripke (1972) and Putnam (1975) ¹ This assumption would, as far as I know, be universally conceded for natural kind nouns that function typically as count nouns. And it would hold also under most views of the semantics of mass terms; this would be so independently of the particular form that predicative theories of mass nouns adopt (whether they cash out the relation of predication in mereological terms (Burge (1977)), or as set membership (Montague (1973)), or in terms of the relation of being one of many (Nicolas (2008)), or in some other way). The assumption would only be disputed by an exiguous minority of writers in the case of natural kind nouns that function typically as mass terms (an example being Sidelle (1989)). ² Although both Kripke and Putnam hold that “water” is not synonymous with “transparent, odorless, tasteless liquid filling rivers, lakes, and oceans,” for Putnam these characteristics play a definite constitutive role in what he identifies as the meaning of “water” (or strictly speaking in its “predominant sense”; see note 4 below), and specifically in the part of the meaning that he calls the “stereotype” (see Putnam (1975), 269); this part however doesn’t play a role in fixing the reference of “water.” (Similarly for other ordinary natural kind terms.) Kripke on the other hand doesn’t really have a theory of the meaning of “water.” In particular, Kripke at no point holds that “transparent, odorless, tasteless liquid filling rivers, lakes, and oceans” has any role in the meaning of “water,” but neither does he hold that the meaning of “water” is entirely non-descriptive, contrary to what is sometimes thought. In fact, he thinks that that meaning must be at least a priori connected with that of “substance,” as we will soon mention in the main text.

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observed, if those synonymies obtained, then Something is water just in case it is a transparent, odorless, tasteless liquid filling rivers, lakes, and oceans and Water is the transparent, odorless, tasteless liquid filling rivers, lakes, and oceans would express necessary and a priori truths in such idiolects, but they do not.³ In particular, Putnam famously elicited from most of his readers the intuition that neither statement is necessary or a priori with the help of the following thought experiment. Imagine a traveler from Earth in a planet (an existing planet in Putnam’s thought experiment, but we may also think of it as a merely possible planet) where a transparent, odorless, tasteless liquid fills rivers, lakes, and oceans but has a nature thoroughly different from that of the liquid on Earth (we may think of it as an elemental substance with these characteristics implanted there by God, though in Putnam’s example it is a regular composite substance with a chemical structure very different from the structure of samples of the liquid on Earth). Even if the traveler will presumably be inclined at first to call the liquid in the planet “water” (assuming of course that she intends to use the word type “water” with the meaning and reference it presumably has in her idiolect), she will abstain from calling it “water” once she discovers that the nature of this liquid is thoroughly different from the nature of the superficially similar liquid on Earth.⁴ (Let us note, however, that while Putnam’s thought experiment has shown to the satisfaction of virtually everybody that “water” is not synonymous with “transparent, odorless, tasteless liquid filling rivers, lakes, and oceans,” for some of the critics this does not happen exactly in the way Putnam says. ³ “Water” also seems to be rigid in its singular term use, while “the transparent, odorless, tasteless liquid filling rivers, lakes, and oceans” clearly isn’t: The substance that is water could not have existed without being water (and no other substance could have been water) seems intuitively true and The substance that is the transparent, odorless, tasteless liquid filling rivers, lakes, and oceans could not have existed without being the transparent, odorless, tasteless liquid filling rivers, lakes, and oceans (and no other substance could have been the transparent, odorless, tasteless liquid filling rivers, lakes, and oceans) is intuitively false. Also, “water” seems to possess a property analogous to rigidity in its predicative use, while “transparent, odorless, tasteless liquid filling rivers, lakes, and oceans” doesn’t: Every thing that is an instance of water could not have existed without being an instance of water seems intuitively true, while Every thing that is an instance of the transparent, odorless, tasteless liquid filling rivers, lakes, and oceans could not have existed without being an instance of the transparent, odorless, tasteless liquid filling rivers, lakes, and oceans is intuitively false. (See Gómez-Torrente (2006) for development of the idea of predicative rigidity using versions of this test.) ⁴ Strictly speaking, Putnam holds only that when the speaker has in mind “the predominant sense” of “water” (Putnam (1975), 239), she will have that reaction. But Putnam claims that there are other “senses” of “water” which can be in operation as a function of “context.” One of these is simply a sense in which “water” means the same as “transparent, odorless, tasteless liquid filling rivers, lakes and oceans” (see Putnam (1975), 239). Kripke on the other hand doesn’t give any indication that he thinks that “water” is somehow ambiguous, not even as a function of “context.” He does say, however, that the vagueness of the notion of substance used in the fixing of the reference of “water” implies a corresponding vagueness in the notion of water (see Kripke (1972), 136, and our discussion in the main text surrounding note 21 below).

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144       For these critics, the traveler need not definitely abstain from calling the extraterrestrial liquid “water.” She can so abstain without breaking any semantic rules about “water,” which does show that there is no synonymy. But according to these critics she can also choose to call the extraterrestrial liquid “water,” without thereby breaking any semantic rules about “water.” This critical view definitely conflicts with the intuition apparently elicited by Putnam that the existence of great differences in the nature of two things implies that they are not made up of the same substance.⁵ We will come back to this.) As in the case of proper names, Kripke also noted that it seems clear that a normal speaker’s uses of a natural kind noun can refer to a natural kind even if she thinks that its instances fit some descriptive predicate framed in terms of superficial characteristics that does not really apply to the instances. Suppose that it is only due to some bizarre optical illusion that the liquid filling rivers, lakes, and oceans appears transparent (appears transparent, that is, when relatively pure and in small quantities); then a normal speaker who associates with water (and with “water”) the property of transparency will nevertheless intuitively refer to the liquid with “water.” Another Kripkean point in the case of proper names was that speakers’ uses of them can refer even if the speakers do not associate with them full descriptions based on biographical characteristics. Similarly, a normal speaker’s uses of “sulfur” refer (if they do) to sulfur even if she does not really associate with “sulfur” any descriptive predicate framed in terms of well-known superficial characteristics that she takes to be necessary and sufficient for membership in the kind—she may think of sulfur simply as “some substance or other,” for example. It thus seems abundantly clear that a normal speaker’s uses of “water” or “sulfur” do not refer to water or sulfur in virtue of “water” or “sulfur” being associated by her with a descriptive predicate of the kind in question. As Kripke did in the case of names, both Kripke and Putnam postulate two fundamental ways in which a natural kind noun can come to have a reference in the idiolect of a speaker. The case of “sulfur” for many typical normal speakers illustrates the first of these two ways. A typical normal speaker, who will often have had no direct observational contact with sulfur, inherits her (apparent) capacity to refer to sulfur with “sulfur” from other speakers whose uses of “sulfur” she has heard or seen, at least if she intends to keep using the noun with ⁵ Strictly speaking (see the preceding note), Putnam claims only that that’s the intuition when “the predominant sense” of “water” is in play, so he might reject this criticism on the grounds that the critics have an optional non-predominant sense of “water” in mind. Kripke on the other hand would appear not to contemplate such different senses of “water,” so he presumably ought to deal with this sort of criticism in a different way; we will reply to the criticism on his behalf in the main text below.

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the same referent as those speakers. They in turn inherited their capacity from others, and so on. Then of course not all speakers can have inherited their capacity to refer to sulfur with “sulfur” from others. Some speakers’ uses of “sulfur” (or of some ancestor or translation of the word) come to refer to sulfur because the speakers develop the intention to refer with “sulfur” to a substance of whose existence they do not know merely from other speakers. Individuals with hands-on experience with sulfur, including the first people who began to use the term “sulfur” (or some ancestor or translation) for the newly discovered (or suspected) substance, develop such an intention. Specifically, on the pictures of Kripke and Putnam, these people develop the intention to refer with “sulfur” to the substance of which all or most of these are examples (while attending in perception or in thought to suspected instances or indicators of sulfur). (The qualification “or most” is intended to contemplate the possibility that the bunch of paradigmatic suspected instances contains a few spurious cases.) Equivalently, they develop the intention to call “sulfur” any sample of the same substance as the paradigmatic suspected instances. This illustrates the second, and more fundamental, of the two fundamental ways in which a natural kind noun can come to have a reference in the idiolect of a speaker. The case of nouns for more familiar ordinary natural kinds, such as “water,” will for typical speakers fall under this second way; nearly every speaker has hands-on experience with water, and on the pictures of Kripke and Putnam, a typical speaker will develop the intention to refer with “water” to the substance of which all or most of these are examples (while attending in perception or in thought to alleged instances or indicators of water). Equivalently, they develop the intention to call “water” (any sample of) the same substance as their paradigmatic suspected instances. When we come to biological species, the appropriate intention will be a suitable one of applying a certain noun to (individuals of) the same species as their paradigmatic suspected instances; and when we come to physical phenomena, the appropriate intention will be a suitable one of applying a certain noun to (instances of) the same phenomenon as their paradigmatic suspected instances. Note that, as in the case of names, the development of the intention to refer with “water” to “the substance of which all or most of these are examples” does not by itself establish a relation of synonymy between “water” and “(instance of) the substance of which all or most of these are examples.” For Kripke, however, it establishes at the very least an a priori connection between “water” and a phrase of that sort, and thus an a priori connection between “water” and the concept of substance. From the exposition so far, we see that the analogies between names and natural kind nouns postulated by (the largely unquestioned part of) the

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146       pictures of Kripke and Putnam are indeed wide-ranging, as we saw Kripke claimed. And it is worth noting at this point that there are surely many other analogies that one can reasonably expect will hold, even if they don’t form part of the “Kripke-Putnam orthodoxy” or of the original thoughts of Kripke and Putnam. Thus, for example, Evans’s emphasis on the possibility (and actuality) of reference change for a name (even when transmission always occurs with an accompanying intention to use it in the same way as the bestowing speakers) is presumably appropriate when natural kind nouns are concerned. As noted by Evans (1982) himself, the noun “turkey” for the North American bird eaten on Thanksgiving day provides, on the most widely accepted theory of its etymology, an example similar to (the historically inaccurate story about) “Madagascar” in the case of proper names. A bird now called the guinea fowl, which came from Western Africa, was imported and eaten by the English well before Columbus traveled to America; it was called “turkey cock,” and later just “turkey” by the English, apparently because it was usually bought from Turkish merchants. When English settlers in America saw the first North American birds they mistook them for the birds they called turkeys, and so called them turkeys as well, fully intending to keep using the noun as they had always done. The same general intention can presumably be attributed to their descendants and to other speakers of English, and yet, eventually, “turkey” became an English noun exclusively for the North American bird. And it is presumably equally appropriate to think, as Evans did for names, that a speaker who receives a natural kind noun from other speakers, and who keeps using the noun for the same kind for which they use it, can come to have a direct knowledge of things of that kind and thus plausibly of the kind itself, one not merely derived from other speakers. Thus someone may come to have direct hands-on experience with sulfur associated with the noun “sulfur,” even if he had inherited the noun before having had any such experience. In such cases, a newly developed intention to refer to “this substance” must presumably play a role in the explanation of the fact that the speaker’s uses of “sulfur” refer to sulfur, besides the initial intention to keep using the word as it was used by the bestowers. Other predictable analogies concern cases of introduction and transmission of natural kind nouns where it will be intuitively indeterminate whether a use of such a noun has a referent. In a story analogous to the “George Smith” story from chapter 3, a mischievous teacher tells his students, who have never heard the word “sulfur” before, merely that sulfur effects the transmutation of lead into gold. My impression here is again that even if the students may come to use “sulfur” after having been introduced to the substance’s name by the

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teacher, it is not clear that their uses of “sulfur” come to refer to sulfur. Or suppose I am watching a live TV show in which a person who claims to be a clairvoyant “sees” a liquid in a land far away. Merely on the basis of his purported extra-sensory perception, he develops the intention to refer to “this liquid” with the noun “tonicum.” All of the properties he attributes to the liquid happen to be properties of a liquid—I call it “vigorium”—which I have just concocted in my laboratory, which I intend to commercialize soon, and whose existence—I am reasonably certain—is not known to any person aside from me. But did the clairvoyant’s uses of “tonicum” refer to vigorium? As far as I can tell, it is unclear whether they did so refer or not. And analogies with other cases of apparent indeterminacy exist as well. It is thus natural to expect that reference fixing for natural kind terms will be governed, as in the case of names, by a system of conventions amounting to roughly sufficient conditions for natural kind noun reference, reference failure, and successful transmission, which fail to have implications of reference or reference failure in the cases of presumed indeterminacy. We will in fact propose such a system in this chapter. It is important to separate the theses we have seen so far from a different part of the “Kripke-Putnam orthodoxy,”⁶ in particular from Kripke’s and Putnam’s adoption of certain specific views concerning the nature of the referents of certain nouns for natural substances and biological kinds. Thus, both Kripke (1972) and Putnam (1975) adopt the specific view that modern chemistry has shown that water is identical with H₂O, i.e. that something is water if and only if it is H₂O; Putnam (1975), at least, accepts that modern biochemistry has shown that the lemon trees are exactly the plants with a certain appropriately specified genetic code;⁷ and both Kripke (1972) and Putnam (1975) accept that modern chemistry has shown gold to be identical with the element with atomic number 79.⁸ More generally, Kripke and Putnam appear to accept a wide-ranging conception of the natures of natural ⁶ And from other parts of the doctrines of Kripke and Putnam that we have mentioned and will mention in notes and asides (see e.g. notes 2 and 4 above). ⁷ As far as I can tell, Kripke does not explicitly accept that the nature of animal or vegetable species is given by the specification of a microstructure of any kind, but he may have had the view implicitly in mind. (All of his remarks about things not having the “internal structure” of paradigmatic tigers not being tigers (in (1972), 120ff.) are compatible with the relatively weak view that having certain internal features, such as bones or muscles, is a necessary condition of being a tiger.) It is also worth noting that in publications after “The Meaning of ‘Meaning’ ” (Putnam (1975)), Putnam sets aside the thesis that the nature of biological species has been identified via genetic descriptions (see e.g. Putnam (1988), ch. 2, and Putnam (2015)). ⁸ Other widely accepted “theoretical identifications” especially emphasized by Kripke involve physical phenomena such as heat and light. These identifications are apparently not questioned in the critical literature we will discuss later, though it doesn’t appear difficult to question them, for example, by constructing arbitrariness arguments of the kind discussed below. We will offer bits of discussion relevant to nouns and adjectives for physical phenomena in chapter 6.

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148       substances and biological species as given by the specification of appropriate microstructures (chemical and genetic) that their instances must possess. These views, we will insist later, are independent of the views concerning reference fixing we sketched in the preceding paragraphs. It is conceivable, for example, that Kripke and Putnam are mistaken in their belief (apparently shared by the scientific community at large) that modern chemistry has shown the referent of the ordinary word “water” to be H₂O,⁹ and yet that the reference-fixing mechanism they postulate does deliver some other reference for “water.” In fact, I will argue that this is precisely the actual situation.

Challenges to the “Kripke-Putnam Orthodoxy,” with Special Attention to Arbitrariness Objections What would become the “Kripke-Putnam orthodoxy” was subjected to criticism from very early on. The two earliest objections are perhaps the ones often called “the impurities problem” and “the qua problem.” The impurities problem (Zemach (1976); Sterelny (1983)) (also called “the composition problem” by Brown (1998)) arises from the fact that the (alleged) samples of a substance that are available to speakers when forming their referential intentions will typically contain many substances and other items. Thus, naturally occurring (alleged) instances of water come together with calcium and magnesium salts, sulfates, nitrates, silica, iron, sodium, aluminum, nucleases, and bacteria, to name but a few of the things they come together with. Since the alleged instances or indicators of water available to ordinary speakers thus do not instantiate a (single) substance, the critics say, no substance is fixed by the speakers’ referential intention to refer with “water” to “the substance of which all or most of these are examples” (while attending in perception or in thought to the alleged instances).¹⁰ The qua problem (Papineau (1979), ch. 5; Dupré (1981); Platts (1983), (1997), ch. 11; Sterelny (1983); Devitt and Sterelny (1987), ch. 5) (also called ⁹ Just as Putnam eventually acknowledged something analogous in the case of his original identification of lemon trees (see note 7), without for that reason giving up the core of his theory of reference fixing for “lemon tree” (see especially Putnam 2015). ¹⁰ A different kind of criticism of Kripke and Putnam having to do with impurities was offered by Malt (1994) and Chomsky (1995). Both Kripke (1972) and Putnam (1975) had said that we call “water” a substance (H₂O) that typically comes together with impurities, thus implying that “water” is flexible enough that it can be correctly applied to H₂O with impurities. Malt and Chomsky claim that being H₂O with impurities is not a sufficient condition for being water, since we would not call tea (say) “water,” despite being H₂O with relatively few impurities. See note 18 for a brief comment on this criticism.

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   “- ”

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“the higher-level natural kinds problem” by Brown (1998)) is that an instance of a certain natural kind will at the same time be an instance of many other natural kinds, in particular other “higher-level,” or just “different-level” but still ordinary natural kinds. Thus, for example, instances of water are also instances of the kind liquid, instances of gold are also instances of the kind metal, particular tigers are also instances of the kinds feline and mammal, and instances of lightning are also instances of electricity. If a speaker forms the intention to refer with “lightning” to “the phenomenon of which all or most of these are instances” (while attending in perception or in thought to a few alleged instances), it is unclear that he will have formed an intention to refer to lightning with “lightning,” rather than an intention to refer to electricity instead.¹¹ (As we will soon see, there is a related but different (and to my mind more serious) problem in the vicinity of the qua problem, which we will call “the arbitrariness problem.”) Proponents of the “impurities” and “qua” objections doubt that the KripkePutnam mechanism for reference fixing can be the real mechanism at work with natural kind words, while not typically questioning the possibility that these words have appropriate referents, or even the referents conjectured by Kripke and Putnam. By contrast, more recent criticisms inspired by ideas from the philosophy of chemistry and the philosophy of biology do not really question the common core of the ideas of Kripke and Putnam that concern the mechanism of reference fixing. The aspects of the “Kripke-Putnam orthodoxy” questioned by critics inspired by the philosophy of chemistry and the philosophy of biology include, instead, Kripke’s and Putnam’s adoption of their specific views concerning the nature of the referents of particular nouns for natural substances and biological kinds. While chemists and biochemists often claim, or give the impression of claiming, that water is identical with H₂O, that a species is characterized by a certain kind of genome, and that gold is the element with atomic number 79 (which is surely part of the explanation for Kripke and Putnam making these same claims), critics inspired by the philosophy of chemistry and the philosophy of biology have seen many reasons to question Kripke’s and Putnam’s identifications.¹² And, more ¹¹ One qua objection involving not higher-level but lower-level ordinary kinds is that “tiger” need not refer to tigers instead of (just) to Bengal tigers if only Bengal tigers appear in the paradigm sample. ¹² As we will see, we will eventually agree with these critics at least in their negative claim that science has not shown that the usual identifications are true. The fact will remain that the scientific community at large, and not just the philosophers influenced by Kripke and Putnam, appear to believe in the truth of those identifications. The critics appear to explain this belief simply by a confusion on the part of the scientific community at large: the community confuses the discovery of the identification with a partly arbitrary choice of identification of the ordinary kind with one of several possible scientific

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150       fundamentally, the critics have seen reasons to question the possibility that natural kind nouns originating in ordinary use can have a reference identified by science, at least if their reference is supposed to be fixed in the way postulated by Kripke and Putnam (which is something not explicitly questioned by the critics, as we mentioned). Note that this implies that, if the conventional mechanisms for reference fixing postulated by Kripke and Putnam are in fact the mechanisms at work in natural language, then these critics’ arguments lead to the conclusion that ordinary natural kind nouns lack referents. Let us survey some of the main considerations of these critics, beginning with the case of “water” and H₂O. One kind of consideration is based on the observation that “H₂O” is a compositional, not a structural formula: it details a proportion of hydrogen to oxygen, not the structure by which they are joined. A compositional formula often corresponds to many intuitively different substances in which the component atoms are arranged differently, these substances being then structural isomers. “H₂O” does not correspond to several isomers, there being only one kind of H₂O molecule. But since merely compositional formulas cannot in general be said to give the reference of substance terms (they arguably do not in cases of isomerism), why should “H₂O” give the reference of “water” (van Brakel (1986); Leslie (2013))? Assuming that “H₂O” does not give the reference of “water,” what could? If we seek a detailed microstructural description of water, in the not purely compositional sense, as we might perhaps suspect that Kripke and Putnam would ask us to do, we will run into difficulty, as we will find many different microstructures and no obvious unifying microstructural description. In its liquid phase water contains H₂O molecules, dissociated ions of hydrogen and oxygen, polymers of H₂O molecules, and recurrent combinations of all these. Why are there not many substances here instead of a single one, and what unified microstructural description could be given of them (van Brakel (1986); Needham (2000), (2011))? If this question cannot be answered, it would seem that whoever forms the intention to refer with “water” to the substance of which all or most of these are examples (while attending in perception or in thought to alleged instances of liquid water) is not really thereby singling out any substance to refer to with “water.” We might call this sort of consideration, insofar as it is based on a claim that there is no (obvious) unifying description of a certain sort, a “disunity” consideration.

correlates. The story is probably more complex than that in each particular case, but we can agree with the critics that some kind of confusion underlies the usual perfect identifications of an ordinary kind with a scientific kind.

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   “- ”

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A different kind of criticism inspired by the philosophy of chemistry involves several considerations. One of these appeals to the so-called spin-isomers of H₂O (Needham (2011); Leslie (2013)). In orthowater, the spins of the protons in the hydrogen atoms of the H₂O molecules are parallel, while in parawater they are not. Paradigmatic water has a 3:1 ratio of orthowater to parawater, but they can be separated by physical means, and while each of them returns to the 3:1 ratio after a while, it is conceivable that under appropriate circumstances orthowater (or parawater) stayed stably as such. In view of this, what determines whether a certain sample is one of the same substance as some paradigms of water? Is a certain sample of the same substance as the paradigms of water when it is in the 3:1 ratio of orthowater to parawater? When it is composed of orthowater and parawater? When it is composed of orthowater or parawater? If this question cannot be answered in a principled way, the Kripke-Putnam mechanism is not singling out any substance as the reference of “water.” A related kind of consideration involves isotopic variations of H₂O (Donnellan (1983); LaPorte (2004), ch. 4; Needham (2011); Leslie (2013)). Elements come in different isotopes, depending on the number of neutrons in the nucleus. The most common isotope of hydrogen, protium, has atoms with just one proton and no neutrons in the nucleus, while another of its isotopes, deuterium, has atoms with one neutron besides the proton. There are isotopic variations of H₂O corresponding to these isotopes: protium oxide, P₂O, is H₂O where the hydrogen atoms are protium atoms, and deuterium oxide, D₂O, is H₂O where the hydrogen atoms are deuterium atoms. Paradigmatic water is basically composed of P₂O, but contains extremely small amounts of D₂O (and very small amounts of many other things as well, as we noted). Is there a principled reason why water should be identified with H₂O instead of with P₂O? To ask a different but closely related question: is there a principled reason why D₂O instances are or are not the same substance as alleged paradigms of water? The critics suggest no such reason can arise from the Kripke-Putnam story about reference fixing. If they are right, it would seem, the Kripke-Putnam mechanism of reference fixing for natural kind words fails for one more reason to fix a reference for “water.” We may call considerations of this sort “arbitrariness” considerations, as they are based on a claim that there is no principled reason singling out one among several feasible options. (Arbitrariness considerations are thus in a sense related to the qua problem, but they deal not with “higher-level” kinds or with “different-level” ordinary kinds, but with “lower-level” scientific kinds, and, as we will note later, they are not amenable to certain natural responses that appear fairly reasonable as Kripkean-Putnamian responses to the qua problem.)

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152       If we leave the case of water and turn to other examples of substances that figure prominently in the discussions of Kripke and Putnam, the situation, according to the critics, is not very different. The cases of gold and other substances considered as elements by modern chemistry generate arbitrariness objections not dissimilar to the ones generated by the case of water. There is again the fact of the existence of isotopes of all the elements, including gold (Brown (1998); Hughes (2004), ch. 1). Also, some elements come in different varieties called allotropes, each allotrope being characterized by a peculiar pattern of bonding between the element’s atoms. As it happens, gold has a single allotrope in standard conditions of temperature and pressure (call it “Auα”), but at high pressures its atoms form a different allotrope (call it “Auβ”) (Leslie (2013)). Is there a principled reason why gold should be identified with Au (the element with atomic number 79) instead of with ¹⁹⁷Au (the single naturally occurring isotope of Au)? Or a principled reason why it should be identified with Au instead of with Auα? To ask different but closely related questions: is it determinate that ¹⁹⁹Au or Auβ instances are or are not the same substance as alleged paradigms of gold? Similar questions can be pressed for other (apparent) names of elements coming from ordinary language, in many cases with allotropes that can exist under standard conditions, such as tin. In the context of critical discussion of the “Kripke-Putnam orthodoxy,” the case of jade (and “jade”) has also played a prominent, though somewhat different, role in arguments for arbitrariness. Putnam ((1975), 241) had said that “although the Chinese do not recognize a difference,” it has turned out that “the term ‘jade’ applies to two minerals: jadeite and nephrite. Chemically, there is a marked difference. Jadeite is a combination of sodium and aluminum. Nephrite is made of calcium, magnesium, and iron.” Putnam went on to say ((1975), 241) that when the things grouped under one natural substance noun turn out to have “two or more hidden structures—or so many that ‘hidden structure’ becomes irrelevant,” then “superficial characteristics become the decisive ones” (as determinative of the reference or extension). LaPorte (2004, ch. 4) has explained that Putnam’s brief note on jade gives a misleading impression. The Chinese had known nephrite for millennia, under the name “yü,” and then came across jadeite toward the end of the eighteenth century . They (or their jade artisans, at least) knew from the beginning that the two substances were different. The Chinese, including their artisans, do now call both substances “jade” (“yü,” that is)—although this usage, as LaPorte explains, was not initially adopted when the Chinese came across jadeite. Both LaPorte and Leslie (2013) have seen here a refutation of Putnam’s

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   “- ”

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view of “jade.”¹³ Didn’t Putnam elicit the intuition that the traveler to the planet of the water-looking liquid would abstain from calling it “water” once she learned that it had a different nature from that of the Earth’s water? Well, the Chinese when coming across jadeite did not abstain from calling it “jade,” so Putnam (and Kripke, who presumably would follow him here) cannot have been quite right. LaPorte concludes that the planetary traveler, just as the Chinese actually did with “jade,” could have chosen to call the extraterrestrial liquid “water,” without thereby breaking any semantic rules about “water.” (This is the criticism of the Putnam planetary thought experiment that we mentioned above.) The critics’ considerations concerning nouns for biological species share basic analogies with their considerations concerning nouns for natural substances; in particular, we find here again both disunity and arbitrariness considerations. As we saw, Putnam (1975), at least, said that what determines that a plant is a lemon tree is its sharing a certain specific “genetic code” with paradigm lemon trees. But we are told that conventional biologists, as a matter of practical fact, do not seek to classify species via genetic descriptions, but in other ways (see e.g. LaPorte (2004), chs. 3 and 5; we will come back to these ways presently). Furthermore, from a more theoretical point of view, the critics claim that if we seek a “genetic code” common to all the members of a given species, as Putnam (and, we may suspect, Kripke) would ask us to do, we will run into difficulty, as we will find many different “codes” among members of the species and no obvious unifying genetic description (Ferguson (2002); Leslie (2013)). An evolutionary explanation is often given for this difficulty, namely that mutation and DNA recombination will all the time introduce genetic differences between organisms and their descendants of the next generation (see e.g. Hull (1965); Ereshefsky (2014)). There are also problems for the “Kripke-Putnam orthodoxy” arising from what would appear to be a different indeterminacy of the same species relation. In current biological science there are several proposed theories of what the same species relation is. Before stating the objection to the “Kripke-Putnam orthodoxy” that this gives rise to, let me explain the main characteristics of three of these theories (or, strictly speaking, kinds of theories) (see e.g. Sterelny and Griffiths (1999), ch. 9; Ereshefsky (2014)). A first kind of theories, paradigmatically illustrated by Mayr (1969), understand a species as a group of organisms that can interbreed and is “reproductively isolated” from other groups; these are often called “biological theories.” A second kind of theories, sometimes called “ecological theories,” see a species as a lineage of organisms ¹³ Or strictly speaking, of the simplified version of Putnam’s view. Recall notes 2 and 4.

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154       that occupies a peculiar ecological niche, in the sense of a habitat where evolutionary forces minimally different from those of other habitats are in play (van Valen (1976) is one main reference). A third kind of theories, which has apparently become the dominant one over the last few decades, are the “phylogenetic thories” arising from cladistic taxonomy (originating in Hennig (1966)). On a view of this sort, “a species is a lineage of organisms, distinguished from other lineages by its distinctive evolutionary trajectory, and bounded in time by its origin in a speciation event and its disappearance by further speciation or extinction” (Sterelny and Griffiths (1999), 193); a phylogenetic theory presupposes some account of speciation, for which purpose it may appeal to a biological species theory, an ecological species theory, or to some different theory of the same species relation. The different species theories proposed by biologists need not coincide extensionally in general. Then, given that the theories in this plurality would all seem to have equal claim to scientific correctness or value, the critics say, it is dubious that science gives a principled, non-arbitrary response to the question whether a certain animal is of the same species as some paradigms of tigers, say (see e.g. Dupré ((1981), (1993), ch. 2); Kitcher (1984)). It is then tempting to draw the conclusion that “biological science has not uncovered such hidden conditions that properly govern our use of the term “tiger” . . . At best it has uncovered a multitude of distinct sets of conditions . . . each with equal claim” (Leslie (2013), 142). It would then once more seem that, if questions concerning the membership of one organism in a specific group cannot be answered in a principled way, the Kripke-Putnam postulated reference-fixing mechanism does not determine any group of organisms as the reference of, say, “tiger” or “lemon tree.”¹⁴

Some Unsatisfactory Responses to the Challenges So far the criticisms. Let’s now turn to possible replies. A number of postKripke-Putnam theorists have provided accounts of reference fixing for natural kind terms that propose more or less extensive refinements of the Kripke-Putnam picture. These accounts are especially designed to deal with ¹⁴ In the vicinity of arbitrariness objections one also finds the different objection that most biological kinds named in ordinary language do not correspond to kinds accepted by biological science (Dupré (1981); (1993), ch. 1). LaPorte (2004), ch. 1, powerfully questions this claim (see also Boyd (1999), 161), but from our perspective the claim might be correct, though for reasons different from Dupré’s—as we will eventually see.

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     

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the impurities and qua objections. Among these theories we find the accounts offered by Sterelny (1983), Brown (1998), and Stanford and Kitcher (2000). Sterelny (1983) proposes a theory on which the basic Kripke-Putnam mechanism for the introduction of reference to a natural kind is preserved, but he adds some necessary conditions as requirements on the introducer of the term and his referential intentions. In particular, the introducer must “identify causal powers of the sample” (Sterelny (1983), 117), and the referential intention will be that the term is to apply to all the things “that have a structure that is the same as that in the paradigm . . . responsible for the causal powers associated with the exemplar” (Sterelny (1983), 121). In the case of “cat,” for example, the introducer must have in mind a set of causal powers of the creature. If it has those powers in virtue of a structure common and peculiar to cathood, “cat” is grounded on the kind cat. This will be the case if the powers are mouse catcher, cockroach killer, and the like. (Sterelny (1983), 116)

This yields immediately the result that in such a case the introducer will not refer, e.g., to the kind mammal with “cat,” as the powers the introducer has in mind are not explained by a “structure” common to mammals; he will refer to cats, because (by hypothesis) these powers are explained by a structure common to cats. Thus the requirement that the introducer have in mind a particular set of causal powers can be presumed to provide a solution to the qua problem. And according to Sterelny, it also provides a solution to the impurities problem, the idea being that the introducer will typically associate a set of causal powers with the kind he seeks to refer to that will be explained by the structure of the kind, not of any of the impurities. On Brown’s (1998) related account, someone can introduce successfully a term for a natural kind if she (or at any rate some members of her community) possesses a “recognitional capacity” for that kind and “associates” the term with that recognitional capacity, which presumably means that she develops the intention to refer with the term to the kind for which she has the capacity. A recognitional capacity is a capacity the speaker has to identify reliably instances of the kind and to discriminate them from instances of other kinds, or at any rate from instances of other natural kinds “instantiated in her local, actual environment” (Brown (1998), 292).¹⁵ (The idea behind this ¹⁵ Brown adds also the requirement that the speaker must have “a grasp of the metaphysical nature of natural kinds and associate this with the discriminatory capacity in question” (Brown (1998), 292),

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156       weakening is that a recognitional capacity for a kind need not be a capacity to discriminate instances of the kind from instances of just any kind superficially similar to the kind in question, in particular of kinds like the one imagined in Putnam’s planetary thought experiment above; otherwise, a recognitional capacity would not serve to single out a kind.) According to Brown, this proposal evades the qua or “higher-level natural kinds” problem because the set of superficial properties that will trigger a speaker’s recognitional capacity for a kind will typically be superficial properties only of instances of the desired kind and not of all instances of “higher-level” kinds. For example, “it might be that the relevant set consists in the properties of being silvery and metallic. If that were the case, then it seems very plausible that the recognitional capacity is for silver, not metal” (Brown (1998), 293). Brown considers also in this context the case of gold and its isotopes (even though these are not kinds of a “higher level” than gold), and says that, even though all the isotopes of gold are associated with the same set of superficial characteristics and thus one might think that her account cannot imply that a normal speaker will refer to Au instead of to its naturally occurring isotope, ¹⁹⁷Au, in fact the account implies that reference will be to the element, not the isotope. The idea is that the property which distinguishes each isotope from the others, and from the element, namely the number of atomic neutrons, does not need to be cited in explaining the appearance of the isotopes. Instead, their shared appearance is explained by fundamental properties which they all share, and share with the element gold. Given this, it is plausible that if members of a scientifically ignorant community have a recognitional capacity which is triggered by items of the naturally occurring isotope of gold, then the recognitional capacity is for gold, not for the isotope. (Brown (1998), 294–5)

About the impurities problem, Brown says that this is solved on her account because the superficial properties that trigger a recognitional capacity will typically be properties explained by the presence of the desired kind, and thus the recognitional capacity will in fact be for the desired kind. Stanford and Kitcher (2000) offer an account that shares some features with Sterelny’s and Brown’s, but without appealing to the notion of a recognitional capacity. On their account, a speaker-introducer has in mind a set of superficial properties of the paradigmatic sample, for “gold,” say. Then his but the requirement of the association of a recognitional capacity plays the main theoretical role in the cases that interest us.

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     

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referential intention is one to refer to the kind characterized by “that feature of the minute parts (whatever it is and whatever they are) that is a common part of the total causes of each of the distinct ascertainable properties” (Stanford and Kitcher (2000), 113). In the case of “gold,” provided the superficial properties are the yellow color, malleability, ductility, and the like, “atomic number 79 looks like just the thing that is going to have to show up in the total cause of each of the stereotypical properties in the samples” (Stanford and Kitcher (2000), 113), and thus reference will be to Au. This is supposed to solve the qua problem because, on the one hand, “the common part of the total causes of each of the distinct ascertainable properties” of an appropriate sample will not be a part of the total causes of higher-level kinds (think of the case of gold vs. metal); and, on the other hand, this common part will not include properties characteristic of lower-level kinds, if these do not essentially contribute to the explanation of the superficial properties; think again, as in Brown, of the case of gold vs. its naturally occurring isotope. Stanford and Kitcher don’t explicitly consider the impurities problem, but presumably they would deal with it in a similar way: the superficial properties of the paradigmatic sample for “gold,” for example, will typically be properties explained in all cases by a common part, which we can presume to characterize Au, and not any of the impurities it comes with. One moderately serious problem with views of this sort is that they attribute relatively sophisticated referential intentions to speakers, intentions involving relatively sophisticated notions of explanation and causality (and others). Sterelny requires the referential intention to be one in which the notion of responsibility for the causal powers of the paradigm sample appears. Brown appears to require the referential intention to be one mentioning the notion of a recognitional capacity for a kind, and this notion is itself apparently spelled out as a capacity for recognizing the kind that needs to be cited in the explanation of certain specific superficial properties of the paradigm sample. Stanford and Kitcher’s proposal involves referential intentions containing the notion of (the common part of) the total causes of certain superficial properties. While the original proposal of the “Kripke-Putnam orthodoxy” did not require speakers to possess conceptually demanding referential intentions, the proposals we are examining evidently impose conceptual demands on the referential intentions appropriate to natural kind terms that we might not want to impose on all speakers to whom we attribute the ability to refer to natural kinds. Another, perhaps more serious, problem with these views is that they don’t seem able to escape appropriate versions of the objection of arbitrariness. One

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158       problem of arbitrariness for these views arises from the fact that the questions of what is the cause and what is the explanation of a certain property, at least outside the most basic physics, are widely thought to be relative to a background of assumptions. The assumptions in a particular background need not be fully explicit, and may take the form of a vague ceteris paribus clause. Thus, to come to examples relevant in our present situation, it is surely only ceteris paribus (in some appropriately understood sense) that the possession of atomic number 79 will cause or explain the possession of malleability, ductility, and the like. Some isotopes of Au are extremely unstable, decaying in just a few microseconds (millionths of a second), and thus cannot properly be said to be malleable or ductile, if by “malleable” and “ductile” one means what is usually meant, i.e. certain properties that one can observe when one performs certain macroscopic physical operations on pieces of gold. Thus, even if speakers had the sorts of referential intentions postulated by Sterelny, Brown, and Stanford and Kitcher, there would be a question as to whether “gold” refers to Au (the element with atomic number 79) or to something like observationally stable (isotopes of) Au. The first option would be reasonable on account of the possibility that one assume a ceteris paribus clause that excludes from consideration precisely the highly unstable isotopes of Au; while the second option would be reasonable on account of the possibility that one not assume any such thing. The Sterelny, Brown, and Stanford and Kitcher proposals don’t imply that the referential intentions of speakers should determine one of these options over the other. (In fact, as already noted, it is dubious that many speakers who intuitively might be referring to Au with “gold” can form, however implicitly, complex intentions involving the notions of explanation and cause, let alone the even more complex intentions that would be needed in order to make a distinction between Au and observationally stable Au.) If so, then the mechanisms postulated by Sterelny, Brown, and Stanford and Kitcher don’t really fix a particular kind of substance in the case of “gold.” Similar observations surely hold in the case of biological species. It is surely only ceteris paribus (in some appropriately understood sense) that membership in a species will cause or explain the possession of the properties of, say, being a mouse catcher, a cockroach killer, and the like. Cathood (however we spell this out) presumably causes or explains these properties only if some appropriate ceteris paribus clause is assumed; after all, presumably cats suffering from congenital anophthalmia will not have a tendency to catch mice or to kill cockroaches. But membership in other less inclusive kinds presumably can explain the possession of these properties as well, under an appropriate

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        

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ceteris paribus clause. Being a cat with normal eyes causes and explains, ceteris paribus, being a mouse catcher and a cockroach killer. Again there doesn’t seem to be any reason why the referential intentions of speakers postulated by the Sterelny, Brown, and Stanford and Kitcher accounts should determine one of these options over the other, so on these accounts no particular kind of animal is really fixed in the case of “cat.”

A Picture of Reference Fixing for Natural Kind Nouns The most prominent post-Kripke-Putnam accounts of reference fixing for natural kind terms that attempt to refine the “Kripke-Putnam orthodoxy” thus seem to fall prey to a version of the objection of arbitrariness, and in any case they are not designed to deal with the disunity objection. However, as noted above, the recent literature inspired by the philosophy of chemistry and the philosophy of biology, which stresses these problems, does not question the idea that the reference of natural kind terms is fixed in the way postulated by Kripke and Putnam. These critics’ arguments thus suggest the conclusion that ordinary natural kind nouns lack a reference (or at best have only “fictional referents”), and this appears to be the idea that is on the way to becoming the new orthodoxy in this area. After all, as Leslie says, the objections indicate that “the extensions and truth conditions of our thought and talk are governed more by our false quintessentialist mindset [the alleged set of ideas underlying our ordinary thought and talk, according to which the apparent natural kinds of ordinary thought and talk are characterized by hidden microstructural essences] than by any ‘scientifically discoverable’ essentialism, contrary to what philosophers often suppose” (Leslie (2013), 144).¹⁶ Is this the unavoidable conclusion that should replace the “Kripke-Putnam orthodoxy”? I don’t think it is, and in the remainder of this chapter I will endeavor to explain why. The issue is a large one that deserves at least a full book, but here I will attempt to give a compressed outline of the view that I think is correct. This will involve us in a task of reformulating and reconceiving the basic ideas of the “Kripke-Putnam orthodoxy.” ¹⁶ Elsewhere Leslie explicitly refrains from categorically drawing the conclusion that there is widespread reference failure in the case of ordinary natural kind terms, but this nevertheless appears to her as the almost inescapable consequence: Science shows there are not in general good candidates to be the common quintessences, so what happens to reference under this assumption? It is either much less determinate than the work of Kripke and Putnam led us to suppose or, if this is different, it is determinate only relative to a quintessentialist fiction that we all tend to share. (Leslie (2013), 158, my emphases)

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160       Just as the critics who use arguments from the philosophy of biology and the philosophy of chemistry appear to concede, the basic mechanism of reference fixing for natural kind nouns is essentially the one postulated by the “KripkePutnam orthodoxy,” but the details of the mechanism must be seen under a magnifying lens, and in some cases modified appropriately. First of all, with a view especially to accounting for cases of relatively benign referential indeterminacy analogous to the ones we described in chapter 3, but also for other intuitions and desiderata uncovered by Kripke, Putnam, Evans and others, we must begin by stating some conventions of imprecise roughly sufficient conditions for natural kind noun reference, reference failure, and successful transmission. As in the case of names, a number of preliminary notes concerning these conventions are worth bearing in mind. First, the conventions will be conventions that in a fairly clear sense will be plausibly recoverable from the linguistic behaviors of normal speakers, who can be said to be familiar with the conventions, in some appropriately weak sense. Second, they will be conventions about the reference of noun types, even if different uses of the same noun type may conventionally refer to different kinds; we can suppose again that the reference of a use of a noun is the kind appropriately related to the body of beliefs that underlies that use of the noun. Third, the conditions in the conventions are to be understood as sufficient for reference, reference failure, or transmission, only ceteris paribus, in some appropriate sense, and thus are only roughly sufficient. Finally, there is little hope that we can state all the extant conventions, but we can hope to be able to give rough statements of some of the most important conventions relevant to natural kind noun reference. As we might expect from the Kripkean basic insight with which we started this chapter, the main conventions about reference for natural kind nouns will be greatly analogous to the conventions concerning names that we saw in chapter 3 (and also, to a lesser extent, to the conventions concerning demonstratives that we saw in chapter 2). They will include the following. Successful explicit natural kind noun introduction via perceptual intention. If a speaker S forms the explicit intention of using a noun N that he or she introduces to refer to the natural substance (/species/ phenomenon) exemplified by (most of) a bunch of items that he or she has clearly perceived, and most of the items in question do exemplify a single substance (/species/ phenomenon) A, then N as used by S will refer to A, if S forms no intention conflicting with that intention, and if S doesn’t form intentions about how to use N that on the whole conflict with the intentions of the community of users of N at large.

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        

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Successful explicit natural kind noun introduction via description. If a speaker S forms the explicit intention of using a noun N that he or she introduces to refer to the natural substance (/species/ phenomenon), if any, that uniquely satisfies a certain property F, and it turns out that there is such a unique satisfier of F, then N as used by S will refer to the F, if S forms no intention conflicting with that intention, and if S doesn’t form intentions about how to use N that on the whole conflict with the intentions of the community of users of N at large. Successful implicit natural kind noun introduction via perceptual intention. If a speaker S forms the implicit intention of using a noun N that he or she introduces to refer to the natural substance (/species/ phenomenon) exemplified by (most of) a bunch of items that he or she has clearly perceived, and most of the items in question do exemplify a single substance (/species/ phenomenon) A, then N as used by S will refer to A, if S forms no intention conflicting with that intention, and if S doesn’t form intentions about how to use N that on the whole conflict with the intentions of the community of users of N at large. Successful implicit natural kind noun introduction via description. If a speaker S forms the implicit intention of using a noun N that he or she introduces to refer to the natural substance (/species/ phenomenon), if any, that uniquely satisfies a certain property F, and it turns out that there is such a unique satisfier of F, then N as used by S will refer to the F, if S forms no intention conflicting with that intention, and if S doesn’t form intentions about how to use N that on the whole conflict with the intentions of the community of users of N at large. Unsuccessful explicit natural kind noun introduction via perceptual intention I. If a speaker S forms the explicit intention of using a noun N that he or she introduces to refer to the natural substance (/species/ phenomenon) exemplified by (most of) a bunch of items that he or she believes to have clearly perceived, but in fact no such items have been perceived by S, then N as used by S will not refer to anything, if S forms no intention conflicting with that intention. Unsuccessful explicit natural kind noun introduction via perceptual intention II. If a speaker S forms the explicit intention of using a noun N that he or she introduces to refer to the natural substance (/species/ phenomenon) exemplified by (most of) a bunch of items that he or she has clearly perceived, but it is not the case that most of the items in question do exemplify a single substance (/species/ phenomenon), then N as used

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162       by S will not refer to anything, if S forms no intention conflicting with that intention. Unsuccessful explicit natural kind noun introduction via description. If a speaker S forms the explicit intention of using a noun N that he or she introduces to refer to the natural substance (/species/phenomenon), if any, that uniquely satisfies a certain property F, and it turns out that there is no such single satisfier of F, then N as used by S will not refer to anything, if S forms no intention conflicting with that intention. Unsuccessful implicit natural kind noun introduction via perceptual intention I. If a speaker S forms the implicit intention of using a noun N that he or she introduces to refer to the natural substance (/species/ phenomenon) exemplified by (most of) a bunch of items that he or she believes to have clearly perceived, but in fact no such items have been perceived by S, then N as used by S will not refer to anything, if S forms no intention conflicting with that intention. Unsuccessful implicit natural kind noun introduction via perceptual intention II. If a speaker S forms the implicit intention of using a noun N that he or she introduces to refer to the natural substance (/species/ phenomenon) exemplified by (most of) a bunch of items that he or she has clearly perceived, but it is not the case that most of the items in question do exemplify a single substance (/species/ phenomenon), then N as used by S will not refer to anything, if S forms no intention conflicting with that intention. Unsuccessful implicit natural kind noun introduction via description. If a speaker S forms the implicit intention of using a noun N that he or she introduces to refer to the natural substance (/species/phenomenon), if any, that uniquely satisfies a certain property F, and it turns out that there is no such single satisfier of F, then N as used by S will not refer to anything, if S forms no intention conflicting with that intention. Successful natural kind noun transmission. If a natural kind noun N as used by a community of speakers refers to a certain substance (/species/ phenomenon) A and a speaker of the community, S, clearly perceives some use of N by another speaker of the community and understands that N is used as a noun for a natural kind, then N as used by S will refer to A, if S forms the (explicit or implicit) intention of using N as is used by the community of users of N and forms no intention conflicting with this intention, and if S doesn’t form at the transmission stage a set of beliefs involving N that on the whole conflict with the beliefs of the community of users of N at large.

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        

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Successful natural kind noun adoption via perceptual intention. If a speaker S forms the (explicit or implicit) intention of using a noun N that he or she has inherited to refer to the natural substance (/species/ phenomenon) exemplified by (most of) a bunch of items that he or she has clearly perceived, and most of the items in question do exemplify a single substance (/species/ phenomenon) A, then N as used by S will refer to A, if S forms no intention conflicting with that intention, and if S doesn’t form intentions about how to use N that on the whole conflict with the intentions of the community of users of N at large. Successful natural kind noun adoption via description. If a speaker S forms the (explicit or implicit) intention of using a noun N that he or she has inherited to refer to the natural substance (/species/ phenomenon), if any, that uniquely satisfies a certain property F, and it turns out that there is such a unique satisfier of F, then N as used by S will refer to the F, if S forms no intention conflicting with that intention, and if S doesn’t form intentions about how to use N that on the whole conflict with the intentions of the community of users of N at large. Unsuccessful natural kind noun adoption via perceptual intention I. If a speaker S forms the (explicit or implicit) intention of using a noun N that he or she has inherited to refer to the natural substance (/species/ phenomenon) exemplified by (most of) a bunch of items that he or she believes to have clearly perceived, but in fact no such items have been perceived by S, then N as used by S will not refer to anything, if S forms no intention conflicting with that intention. Unsuccessful natural kind noun adoption via perceptual intention II. If a speaker S forms the (explicit or implicit) intention of using a noun N that he or she has inherited to refer to the natural substance (/species/ phenomenon) exemplified by (most of) a bunch of items that he or she has clearly perceived, but it is not the case that most of the items in question do exemplify a single substance (/species/ phenomenon), then N as used by S will not refer to anything, if S forms no intention conflicting with that intention. Unsuccessful natural kind noun adoption via description. If a speaker S forms the intention of using a noun N that he or she has inherited to refer to the natural substance (/species/ phenomenon), if any, that uniquely satisfies a certain property F, and it turns out that there is no such single satisfier of F, then N as used by S will not refer to anything, if S forms no intention conflicting with that intention.

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164       The supposition that these conventions are in place accommodates or directly implies the uncontroverted aspects of the “Kripke-Putnam orthodoxy,” as well as other analogies with the case of proper names. Insofar as the identified conventions regulating the successful introduction and transmission of natural kind nouns do not require that the nouns be synonymous with descriptive predicative expressions, the conventions are compatible with the remark that a typical natural kind noun from ordinary, pre-scientific language does not have the same meaning as a descriptive predicate that details contingent a posteriori characteristics of members of the kind (in the predicative use), or the same meaning as a corresponding description (in the singular term use). Also, the convention about successful transmission allows that uses of a natural kind noun by a speaker who inherits a natural kind noun can refer to a relevant natural kind even if she is wrong about the superficial characteristics that its instances possess. Additionally, that convention allows that a natural kind noun as used by a speaker can refer to a natural kind even if she does not really associate with the noun any descriptive predicate that she takes to give necessary and sufficient conditions for the application of the noun. The picture that emerges from the identification of the conventions nevertheless contemplates ways of introducing natural kind nouns via referential intentions with some appropriate descriptive content involving the notions of substance, species, and phenomenon, as well as via referential intentions with descriptive content involving superficial characteristics. The Evansian emphasis on the possibility of unintended reference change, in this case for natural kind nouns, is also accommodated by the picture suggested by the identification of the referential conventions above. “Turkey” presumably did not change reference immediately after the English colonists came across the North American bird. After all, the colonists themselves had the conflicting intention of calling “turkey” also the bird they had seen in England, and the conflict probably introduced some referential unclarity or just determinate reference failure in their uses of “turkey” by application of Unsuccessful natural kind noun adoption via perceptual intention II (once the colonists were exposed to a sufficient number of paradigms of the North American bird). “Turkey” probably came to refer conventionally to the North American bird when a sufficient number of speakers of English formed the intention of referring with “turkey” to the North American bird (either via perceptual intention or via description) and failed to form any intention conflicting with this. At that point, the intentions of typical speaker users of “turkey” did no longer conflict on the whole with the intentions of the community of users of “turkey” at large. Under such conditions, applications

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of Successful natural kind noun adoption via perceptual intention and of Successful natural kind noun adoption via description would have implied that there was conventional reference to the turkey with “turkey.” The proposed conventions accommodate as well Evans’s point that speakers who inherit a noun can form perceptually based referential intentions involving the noun which are relevant to the explanation of reference facts. The person who inherits “sulfur” but eventually comes to have hands-on experience of sulfur makes uses of “sulfur” which refer to sulfur (if they do) in part because the convention of Successful natural kind noun adoption via perceptual intention will apply, not merely because the convention of Successful natural kind noun transmission applies in his case. (We can presume that the speaker in question forms no intention conflicting with the intention of referring to the substance he has come to be familiar with, and that he doesn’t form intentions about how to use “sulfur” that on the whole conflict with the intentions of the community of users of “sulfur” at large.) As in the case of names, the picture of conventions for roughly sufficient conditions for reference (and lack thereof) deals smoothly with cases of apparent referential indeterminacy, for it has no implications concerning those cases. Thus, in the case of the mischievous transmission of “sulfur,” the students inherit the noun from their teacher, but they also inherit a single false idea about sulfur not shared by the teacher or by the community at large, according to which sulfur effects the transmutation of lead into gold, an idea which essentially comes to constitute the students’ meager view of “sulfur.” This prevents this case from being an instance of Successful natural kind noun transmission, as the students form a rather poor set of beliefs that presumably conflicts with the beliefs of the community of users of “sulfur” at large: these speakers (by and large) believe that sulfur does not effect the transmutation of lead into gold. Hence, Successful natural kind noun transmission, the only possibly relevant convention in this case among those we have recognized, does not imply that reference is transmitted successfully in the imagined “sulfur” case. In the case of “tonicum,” vigorium, and the clairvoyant, the only conventions we have postulated that could be relevant to the question whether the clairvoyant refers to vigorium with “tonicum” are Successful explicit natural kind noun introduction via perceptual intention and Unsuccessful explicit natural kind noun introduction via perceptual intention I and II. Successful explicit natural kind noun introduction via perceptual intention does not apply, because the clairvoyant has not clearly perceived (instances of) vigorium (or anything else). But Unsuccessful explicit natural kind noun introduction via perceptual intention I and II do not apply either, because

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166       the clairvoyant does not believe he is perceiving vigorium, as he at best believes that it is an extra-sensory power that produces his representations of the substance. We have stressed that the conventions we have identified do not establish synonymies or meaning connections between introduced or transmitted natural kind nouns and descriptive contents. Also, the referential intentions contemplated in these conventions can in some cases be extremely meager in content, in that they need not contain mention of superficial characteristics of the members of the relevant kind. However, the concepts of substance, species, and phenomenon involved in the referential intentions, the involved concept of exemplification (of being a case or example), and the introduced concepts for particular substances, species, and phenomena (insofar as they are precisely concepts of substances, species, and phenomena) do possess contents and a priori connections that are moderately rich and complex. Note that the picture respects the Kripkean idea that the development of the intention to refer with “gold” (say) to “the substance of which all or most of these are examples” does establish at the very least an a priori connection between “gold” and that description,¹⁷ and thus an a priori connection between “gold” and the concept of substance (mutatis mutandis for other intended names of substances, species, and natural phenomena). These contents and connections play a decisive role in constraining the field of candidates for reference, thereby blocking the impurities, qua, and arbitrariness objections, as we will argue in what follows. (Once we have seen this, we will take a fresh look at disunity objections toward the end of the chapter.) Thus, to begin with, it is arguably a consequence of the ordinary meaning of “exemplification” (or of “being a case” or “being an example”) and of the contents or a priori connections that particular substance nouns come to have (in virtue of being substance nouns) that the items typically thought of as exemplifying a particular substance will not also exemplify its impurities. For example, the (alleged) instances of water (and “water”) available to ordinary speakers are not things that, given the ordinary meaning of “exemplify,” exemplify also the kinds calcium salt, magnesium salt, sulfate, nitrate, silica, iron, sodium, aluminum, etc. A sample of water (let’s assume for the sake of

¹⁷ Despite the a priori connection between “gold” and that description, the introduction or adoption of a natural kind noun such as “gold” via a referential intention of the relevant sort is based on what in chapter 4 we called “preconceptions” on the part of the introducing speaker. In the case of “gold,” these include a preconception that the paradigms are gold, and a preconception that the paradigms exemplify a single substance. These are not themselves a priori or analytic, although they are strongly believed ideas which work as conditional props in the mechanism of reference fixing.

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argument that there is such a thing) simply does not exemplify the kind aluminum; something would have to have a much higher proportion of aluminum than a sample of water has in order to exemplify the kind aluminum. Thus, the impurities objector’s claim that the apparent instances of a substance available to ordinary speakers do not exemplify a single substance, and that no substance is fixed by the speakers’ referential intention to refer with “water” to “the substance of which all or most of these are examples” is simply not defensible on the basis merely of the existence of impurities.¹⁸ Similar attention to the meanings of “substance,” “species,” and “phenomenon,” as well as to the meanings and a priori connections of particular substance, species, and phenomenon terms and to the meanings of other kind terms, take the bite out of the qua problem, at least in its relatively weak version involving just a “higher-level natural kinds problem” (in Brown’s (1998) expression). While it is undoubtedly true that an instance of a given natural kind will at the same time be an instance of “higher-level” natural kinds, these kinds will in general be implied not to be substances, species, or phenomena by appropriate meaning-constituting or a priori principles. For example, though instances of water are also instances of the kind liquid, liquid is not a substance, as it is compatible with the meanings of “substance” and “liquid” that different liquids may be different substances—and in fact, there are liquids with very different natures, which in no sense can be said to belong to one same substance. Though instances of gold are also instances of the kind metal, metal is not a substance, as it is compatible with the meanings of “substance’ and “metal” that different metals may be different substances. Though particular tigers are also instances of the kinds feline and mammal, feline and mammal are not species, as it is compatible with the meanings of “species,” “feline,” and “mammal” that different felines and different mammals may be of different species.¹⁹ The case of “lightning” is a bit different, for ¹⁸ The Malt and Chomsky criticism of Kripke and Putnam, based on the claim that being H₂O with impurities is not a sufficient condition for being water (see note 10), turns on a different aspect of ordinary concepts. Assuming for the sake of argument that the referent of “water” has been fixed to be H₂O, then instances of H₂O coming together with impurities will be naturally called “water” if the context doesn’t require that a liquid should be constituted by an extremely high proportion of H₂O in order to count as water (as both Kripke and Putnam implied). It is to say the least unclear that we will not be ready to call tea “water” in perfectly normal contexts (think of an utterance of Well, this liquid over here is just H₂O with a few impurities, so you are drinking just a fancy kind of water, my friend). Malt’s and Chomsky’s observations at most indicate that “tea” may not typically be called “water,” presumably because it will typically be more informative to call a certain liquid “tea” than to call it “water.” “Tea” is presumably precisely a name for water with impurities of certain kinds. (See Abbott (1997) for related remarks.) ¹⁹ One “lower-level” qua objection was that it is not clear why “tiger” (say) does not refer (just) to Bengal tigers if only Bengal tigers appear in the paradigm sample. This is not a consideration involving higher-level kinds, but the objection is dissolved in much the same way as the objections involving

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168       (perhaps unlike “water,” “gold,” and “tiger”) this is not a term entirely devoid of descriptive content involving superficial characteristics. It is surely part of the meaning of “lightning” that lightning comes from a cloud, and so “lightning” must be thought of as introduced via the formation of a minimally qualitative descriptive intention, such as “call ‘lightning’ a phenomenon always coming from clouds of which (most of) these are examples” (as formed in conjunction with an act of having in mind a perceived paradigm sample, either in simultaneous perception or in thought). If so, then even though instances of lightning are also instances of electricity, electricity is not singled out by the referential intention, just because many instances of electricity do not come from a cloud. (See LaPorte (2004), 6–7, and Leslie (2013), 128–9, for related dissolutions of the qua problem for the “Kripke-Putnam orthodoxy” by critics of the orthodoxy, also appealing to broadly conceptual features of the relevant kind concepts.) Note that these solutions to the impurities and qua problems do not appeal in any way to referential intentions involving complex concepts of cause and explanation, unlike the accounts of Sterelny, Brown, and Stanford and Kitcher; they only appeal to the original Kripkean and Putnamian idea that “water” (say) is a priori connected with something like the description “the substance of which all or most of these are examples,” as well as to the idea that the concept of substance has a minimal content.

The Problem of Arbitrariness and the Referents of Nouns for Natural Kinds The arbitrariness objections can be seen as deeper versions of the qua problem, versions that do not concern higher-level kinds, or even different-level ordinary kinds, but lower-level kinds typically discoverable only by scientific investigation. These objections are therefore unlikely to be resoluble merely by attending to the ordinary concepts of higher- or lower-level kinds. Nevertheless, I want to suggest that close attention to the meanings of “substance,” “species,” and “phenomenon,” as well as to the meanings and a priori connections of particular ordinary substance, species, and phenomenon terms as compared with the meanings of scientific kind terms, again provides a resolution of the arbitrariness worry. higher-level kinds in the main text. As long as it can be held that the ordinary meaning of “species” is such that members of the same species are typically broadly similar and can typically interbreed, there will be a principled reason for assuming that the reference of “tiger” is not determined to be one of the groups ordinarily taken to be races of tigers.

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Much of the perceived force of the arbitrariness objections comes from a number of background presuppositions that the arbitrariness objectors see as essential parts of the accounts of Kripke and Putnam. Thus, the objectors assume that it is an essential part of these accounts that “there are scientifically discoverable necessary and sufficient conditions for belonging to a natural kind [referred to by an ordinary natural kind noun]” (Leslie (2013), 124); that “in particular, these necessary and sufficient conditions consist in a specification of the kind’s hidden underlying structure” (Leslie (2013), 124); and that “membership in these kinds ought to be close to an all-or-nothing matter . . . real kinds should have sharp boundaries” (Leslie (2013), 112). These presuppositions do indeed lend a great force to the arbitrariness objections. But, as we will now see, the presuppositions cannot be said to constitute an essential part, or in some cases even a part, of the Kripke and Putnam accounts; and in any case they cannot be said to constitute a part required by the mechanism of reference fixing that the accounts can be said to have envisioned. As we noted, it is certainly true that Kripke and Putnam adopted certain specific views concerning the nature of the referents of certain nouns for natural substances and biological kinds, according to which these referents could be specified in terms of scientifically discovered necessary and sufficient conditions consisting in the possession of hidden underlying structures (e.g. something is water if and only if it is H₂O;²⁰ the tigers are exactly the animals with a certain appropriately specified genetic code; something is a gold instance just in case it is an instance of the element with atomic number 79; etc.). But it is important to emphasize that these views are independent of their views concerning the mechanism of reference fixing, and also independent from our refined version of the mechanism detailed in the preceding pages. In fact, in just a bit we will be arguing that this type of mechanisms probably deliver referents of other sorts for “water,” “tiger,” and “gold.” Why are the specific views of Kripke and Putnam, concerning the specific referents of “water,” “tiger,” and “gold,” independent of the sort of mechanism of reference fixing that they (and I, with some refinements) postulate? It’s again a question of what is included in the ordinary, pre-scientific meanings of “substance,” “species,” and “phenomenon,” and in the meanings and a priori connections of particular ordinary substance, species, and phenomenon terms. Is it required by the ordinary meanings of “substance” and “water,” for ²⁰ Here and in what follows I will write as if “H₂O” referred to a structural kind, even though the philosophers of chemistry have remarked that (at least in a certain technical, by no means ordinary sense of “structural”) it does not. We will eventually come back to the disunity consideration motivated by that remark.

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170       example, that water must be (if it is anything) a substance specifiable in terms of scientifically (chemically, that is) discovered necessary and sufficient conditions consisting in the possession of a hidden underlying structure? Or that “water,” or water, should have sharp boundaries? It seems pretty clear that it is not. First of all, as Johnston (1997) once put it, the introduction of “water” by way of a referential intention involving a notion of substance on which substances are conceptually required to be scientifically (chemically) specifiable is a performance possible only at a comparatively late stage of human history, since the notion of a chemical kind, a kind individuated by its chemical properties, probably postdates alchemy and may even require some anticipation of the classification of elements found in the periodic table. Therefore, the semantic account associated with that model of introducing ‘water’ can hardly be the right account of the meaning of ancient ordinary language names for the manifest stuff which we drink, bathe in, and use to irrigate land. (Johnston (1997), 576)

Johnston actually attributes to Kripke “the semantic account associated with that model of introducing ‘water’,” and thus a view of the ordinary meaning of “substance” on which substances are conceptually required to be scientifically characterizable. But I think this is confused. Kripke does at no point I can see hold the (otherwise clearly absurd) view that the ordinary meaning of “substance” is or ever was so demanding. The fact that Kripke adopts the view that it has been discovered that water is identical with H₂O is explained quite simply in a way compatible with a view that the meaning of “substance” is relatively meager: Kripke believes that the meager meaning of “substance” is such that no other substances than the scientific kind H₂O have turned out to be instantiated by the (majority of) paradigms in the “water” samples of typical ordinary speakers. Kripke is probably wrong about this, but his mistake need not be due to a mistaken view of the ordinary meaning of “substance.” Whatever the truth about Kripke’s views on the ordinary meaning of “substance,” we must surely follow Johnston in supposing that this meaning involves no requirement that a substance be characterizable as a scientific kind. Similarly, it is no part of the ordinary meaning of “substance” or “species” that a substance or species ought to be specifiable in terms of scientific necessary and sufficient conditions consisting in the possession of hidden underlying structures. It is natural, for example, to suppose that it is part of the meaning or the a priori connections of “species” that a species must have a certain nature or essence, if by this we simply understand a

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characterization, which may well require the use of properties hidden from ordinary knowledge. But it is unclear, to say the least, that the meaning of “species” requires by itself that such a characterization be given in terms of necessary and sufficient conditions consisting in the possession of a scientifically specified hidden underlying structure. It is unclear that it is part of the ordinary meaning of “species” that a species, such as the conjectured species that the tiger is, ought to be reducible to scientific conditions detailing underlying structures. For it would seem that it is compatible with the meaning of “species” and “tiger” that the tigers might have a hidden underlying structure and yet that this hidden underlying structure might not be enough to characterize tigers. Anyone tempted by the contrary view ought to recall that it was not so long ago that it was generally thought that living beings had a crucial characteristic (life) which was not reducible to scientific conditions, let alone to conditions specifying hidden underlying structures. Presumably vitalists did not have in mind non-ordinary meanings for “species” and “tiger.” Surely, similar views about the nature of water were possible (and probably actual, especially among people for whom water had religious purifying powers of some sort). I also think it is evidently not part of the ordinary meaning of “substance” or “water” that these should have sharp boundaries, and in particular that they should be precise along the dimensions along which scientific chemical kinds are precise. In fact, the intuitive reaction of critics of the “Kripke-Putnam orthodoxy” to arbitrariness arguments concerning the relationship between water and H₂O suggests precisely that the ordinary meaning of “water” is vague along dimensions along which “H₂O” is not. There is no principled reason, the critics note, why water should be identified with H₂O instead of with P₂O, no principled reason why D₂O should or should not be the same substance as alleged paradigms of water. A sample of D₂O molecules is not determinately water, in the ordinary sense of “water,” even if it is determinately H₂O (and determinately not P₂O). But if this is so, “water” has blurry boundaries along dimensions along which “H₂O” does not.²¹ Commentators on the “Kripke-Putnam orthodoxy,” whether critical or not, have often referred to experimental psychological evidence in support of the view that people, even very small children, have implicit beliefs to the effect that the referents of ordinary natural kind nouns must be specifiable in terms ²¹ Recall that Kripke explicitly noted that the vagueness of the notion of substance used in referential intentions concerning “water” induces a corresponding vagueness in the notion of water (see Kripke (1972), 136). He was probably not fully aware, however, of the potential implications of this vagueness for the coming apart of ordinary and scientific kinds, to which we will soon turn in the main text.

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172       of scientifically precise necessary and sufficient conditions consisting in the possession of hidden underlying structures (see e.g. Gelman (2003), Leslie (2013)). And they have reasonably observed that ordinary people, if they have such beliefs, may be unaware that they have them, or that they have dispositions to act as if they had them (see e.g. Leslie (2013), 155–6). However, I don’t think considerations of this sort can show in any way that the meanings or a priori connections of “substance,” “species,” and “phenomenon,” and of particular ordinary substance, species, and phenomenon terms are as rich as the critics of the “Kripke-Putnam orthodoxy” must presuppose. First, the cited experimental psychological evidence does probably show that ordinary people usually believe in the existence of hidden necessary conditions for natural kind membership, and reject sufficient conditions for membership based on merely superficial characteristics. But I strongly doubt that the evidence shows (let alone that it conclusively shows) that they believe in jointly necessary and sufficient scientifically precise hidden structural conditions for natural kind membership.²² Second, and more important, even if people had the relevant beliefs, however implicitly, this in itself would show nothing about the meanings or a priori connections they ascribe to “substance,” “species,” “phenomenon,” and to particular ordinary substance, species, and phenomenon terms. What is relevant to the constitution of these meanings are in any case the reflectively held views concerning them, and surely the reflectively held view will be that, for example, there need not be scientifically precise sufficient structural conditions for natural kind membership—as our considerations about vitalism and the purifying powers of water illustrate. Surely only reflectively held views concerning word function are relevant to semantic theorizing, and the experimental psychological evidence cited in this context does not involve evidence concerning reflectively held linguistic views. The upshot is that we have no argument from experimental psychological evidence against the natural thesis that it is not part of the meanings or a priori connections of “substance,” “species,” “water,” “tiger,” etc., that there should be scientifically precise necessary and sufficient structural conditions for membership in the corresponding kinds.²³

²² Unfortunately, I cannot attempt here to justify this claim with a review of the cited psychological literature; otherwise I would stray too far from the argumentative line of this chapter. But I invite the reader to evaluate my claim by confronting it with a review of the psychological literature such as Leslie’s (2013), sec. 1.2. ²³ At any rate, even if there was some evidence that ordinary people have reflectively held views that support the thesis of appropriate rich meanings for “substance,” “species,” “water,” “tiger,” etc., it is unclear that this would decisively show that the meanings would have the relevant properties. Ordinary people are well known to give confused accounts of their semantic intuitions, about which the expert semanticists will generally be more reliable.

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Once we see that the meanings and other a priori notes of “substance,” “species,” “water,” “tiger,” etc., do not require the existence of scientifically precise necessary and sufficient structural conditions for natural kind membership, we see also that the corresponding presuppositions of the critics of the “Kripke-Putnam orthodoxy” are not an essential part of the mechanism of reference fixing postulated by Kripke and Putnam and refined here. And this in turn affords us a better perspective on what arbitrariness objections can and cannot show. Even if we grant that arbitrariness objections show that a KripkeanPutnamian mechanism of reference fixing cannot determine that, say, the referent of “water” is H₂O instead of P₂O, or vice versa, the objections cannot show that the referent of “water” is not some natural kind irreducible to precise structural scientific kinds. They could show this only if the meanings or a priori connections of “substance” and “water” required that the referent of “water” ought to be characterizable in terms of scientifically precise necessary and sufficient structural conditions; if this were the case, then the possible referents would be limited to precise structural scientific kinds such as H₂O and P₂O, among which the choice would presumably be arbitrary. But if the meanings and a priori connections of “substance” and “water” impose no such requirement, then the possibility is left open that the referent of “water” is an appropriately irreducible kind. But is it? Could it be? How reasonable could the mere thought be that “water,” and “gold,” and “tiger,” etc., could have a referent of this sort? And doesn’t the mere thought imply an abandonment of some of the features that made the Kripke and Putnam accounts seem so attractive as views of scientific progress, and in particular an abandonment of their view that science may and does discover the nature of water, gold, and the tiger? When one thinks carefully about it, it actually appears very reasonable to conclude that the conjectured ordinary kinds water, gold, tiger, etc. are, if anything, kinds not reducible to scientifically precise necessary and sufficient conditions given in terms of underlying structures. One reason is in fact provided by a gestalt switch, as it were: we can see arbitrariness arguments not as eliminativist arguments showing that no reference is fixed because the choice among scientifically precise structural kinds is arbitrary, but as revealing intuitive constraints on the kinds possibly referred to. And once one sees this, the constraints in question point toward the view that the kinds referred to, if they exist, are in fact kinds irreducible to scientifically precise structural kinds. Arbitrariness arguments can be thought of as showing that the properties that are the potential referents of “water,” “gold,” “tiger,” etc. have determinacy

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174       profiles different from those of the properties which are the presumable referents of “H₂O,” “P₂O,” “Au,” “¹⁹⁷Au,” “animal with GenT,” etc.—where “GenT” abbreviates some genomic description detailing a common part of the descriptions of the genomes of various individual tigers. A sample of liquid may be determinately H₂O and yet not be determinately water, because it is a sample of D₂O and paradigmatic water is not D₂O but P₂O. But a sample of P₂O may not be determinately water either, if it is a sample of “½ orthowater, ½ parawater”— recall that paradigmatic water samples are “3/4 orthowater, ¼ parawater.” Is water then to be identified with “P₂O, 3/4 orthowater, ¼ parawater”? No, because even if we assumed that “P₂O, 3/4 orthowater, ¼ parawater” is a determinate sufficient condition for being water (which is probably too much to assume), it is unclear that all water must be “P₂O, 3/4 orthowater, ¼ parawater” (or even that all water must be composed of “P₂O, 3/4 orthowater, ¼ parawater”); what exactly would determinately disqualify “½ orthowater, ½ parawater” from being water? Similarly, a little grain may be determinately Au and yet not be determinately gold, because it is a sample of ¹⁹⁹Au and naturally existing gold is all ¹⁹⁷Au. But a sample of ¹⁹⁷Au may not be determinately gold either, if it is a sample of an abnormal allotrope of ¹⁹⁷Au. Is then the normal allotrope of ¹⁹⁷Au to be identified with gold? No, because even if we assume that being of the normal allotrope of ¹⁹⁷Au is a determinate sufficient condition for being gold (which is probably too much to assume), it is unclear that all gold must be of the normal allotrope of ¹⁹⁷Au; what exactly would determinately disqualify ¹⁹⁹Au or abnormal allotropes from being gold? An animal a may determinately have a genome falling under the GenT description, and yet not be determinately a tiger, if its genome strikes us as sufficiently different from the genomes of several paradigmatic tigers. Perhaps there is some further biochemical description GenT’ under which fall only the paradigms but not the animal a. But some further animal b may fall under GenT’ and yet not be determinately a tiger if its genome is sufficiently different from the genomes of the paradigmatic tigers. Is then the possession of a genome with some appropriate description GenT’’ which is possessed by the paradigms but which excludes b to be identified with tigerhood? No, because even if we assume that the possession of GenT’’ is a determinate sufficient condition for being a tiger (which is probably too much to assume), it is unclear that all tigers must have a genome falling under the description GenT’’; what exactly would determinately disqualify a or b from being tigers? The conclusion that a precise structural biochemical, chemical, or physical kind will typically not be identifiable with an ordinary kind seems hard to avoid.

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And it is indeed probably too much to assume that, say, “P₂O, 3/4 orthowater, ¼ parawater” is a determinate sufficient condition for being water. A sample of “P₂O, 3/4 orthowater, ¼ parawater” need not be determinately water, for it is conceivable, for example, that the orthowater in paradigmatic water samples belongs to a yet more fundamental subkind of orthowater, O1: if O2 were one of the other fundamental subkinds of orthowater, a sample of “P₂O, 3/4 O2 orthowater, ¼ parawater” would arguably not be determinately water, even though it would of course be determinately “P₂O, 3/4 orthowater, ¼ parawater.” (Similar arguments could be given for analogous identifications of gold and tigerhood.) In fact, I suppose that for all we know, every biochemical, chemical, or physical precise structural scientific kind PSSK underlying the paradigms of an ordinary kind OK may be a heterogeneous kind such that the paradigms of OK are underlain by just one of the more fundamental scientific subkinds of PSSK. There may be an appropriate branching of precise structural scientific subkinds “all the way down.” If this “all the way down” branching is a fact, we will have one more reason why no precise structural scientific kind is an ordinary kind. And since such “all the way down” branching presumably cannot typically be excluded in principle for candidate biochemical, chemical, and physical kinds, no identification or reduction of an ordinary kind to a precise structural biochemical, chemical, or physical kind will typically be warranted. But if no identification or reduction of an ordinary kind to a precise structural biochemical, chemical, or physical kind will typically be warranted, then we will have in principle not much of a reason to think that an ordinary kind OK will be identifiable with any precise structural scientific kind PSSK. But then do ordinary kinds really exist? The fact that they cannot be identified with precise structural biochemical, chemical, or physical kinds might suggest that ordinary kinds cannot exist, as the eliminativist will be happy to conclude. But this failure of identification is by no means a good argument for the non-existence of ordinary kinds. One way to see this is by observing that roughly analogous failures of identification in the case of ordinary objects (the intuitive referents of typical proper names) have not tempted too many thinkers into the analogous conclusion that ordinary objects don’t really exist, and instead have led some to think that an ordinary object is an entity that is just different from a variety of related entities that one might think of as responding to properly scientific descriptions. Some arguments for the impossibility of identifying ordinary objects with more scientifically describable objects actually have Kripkean roots. Kripke suggests ((1972), 145, n. 74) that a given statue is not the same object as the

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176       matter that constitutes it through its life history, however scientifically described, as the thing that the statue is is essentially a statue, but the matter is not essentially a statue. And reports of Kripke’s unpublished lectures on “Time and Identity” speak of related arguments. A given plant which is plucked up from the ground and killed early in its development—Kripke is said to have argued—cannot be identified with the matter that constitutes it through its life history, as the plant had dispositions and other modal properties that the matter didn’t have: the plant had the disposition to become constituted by different matter, for example, but the matter that actually constituted it didn’t. Significantly, Johnston (1997) provides analogous arguments for ordinary natural kinds. For example, he claims, basically, that the kind water cannot be the kind H₂O because the instances of water must be essentially instances of liquid water, water vapor, ice, or perhaps of some other manifest subkind of the manifest kind water, while an instance of H₂O—a single H₂O molecule, for example—is not essentially any of those things. Yet Kripke sees his arguments as showing that ordinary objects exist and are simply different from the aggregates of matter that constitute them, and Johnston sees his arguments as showing that ordinary kinds exist and are simply different from the scientific kinds with which they are typically identified. The gestalt switch I’m recommending concerning arbitrariness arguments similarly suggests distinguishing ordinary kinds from precise structural scientific kinds, in this case not by differences in their modal profiles, but by differences in their determinacy profiles. Water has the property that it is not determinately true or false that there can be instances of it which are at the same time instances of D₂O, say; but H₂O certainly doesn’t have that property, for it is determinately true or false (it is determinately true) that there can be instances of it which are at the same time instances of D₂O. The conclusion I suggest we can draw is, as in Johnston, that ordinary kinds are not to be thought of as fictions of some sort, but as kinds which are simply different from the precise structural scientific kinds with which they are typically identified. Significantly, arbitrariness arguments again have analogues involving ordinary objects. If G is a given statue made of ¹⁹⁷Au throughout its life history, G has the property that it is not determinately true or false that after a series of replacements of its matter it could come to be constituted completely by ¹⁹⁹Au (without losing its identity).²⁴ The matter actually constituting ²⁴ The reader may recall that Kripke ((1972), 114, n. 57) considers sympathetically the thesis that being made up of the substance of which an object is made up is a property essential to it. Even so, note that the thesis that it is indeterminate whether ¹⁹⁹Au is the same substance as ¹⁹⁷Au implies that it is not determinately true or false that after a series of replacements of G’s matter, G could come to be

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G through its history, however, has the property that it is determinately true or false (it is determinately false) that it could come to be constituted completely by ¹⁹⁹Au. So once again we reach the conclusion that G and its matter (however scientifically described) cannot be identified, but this fact shouldn’t tempt us into thinking that G doesn’t exist. If, as these arguments suggest, ordinary objects have determinacy profiles different from those of objects described in certain more scientifically fundamental ways, the differences in determinacy profiles between ordinary kinds and kinds described in terms of precise structural scientific conditions, tacitly exploited by arbitrariness objections, cannot provide arguments against the existence of ordinary kinds or against the existence of referents for ordinary natural kind nouns. In fact, the basic analogy between ordinary objects and ordinary kinds suggests that ordinary kinds, the kinds we are envisioning as potential referents for ordinary natural kind nouns, are kinds irreducible to precise structural biochemical-chemical-physical kinds. Provided we are inclined to believe in the existence of ordinary objects, we should presumably be just as inclined to believe in the existence of kinds irreducible to precise structural biochemical-chemical-physical kinds, and to believe that ordinary natural kinds are of this sort. There are other analogies between ordinary objects and ordinary kinds. Many have insisted that the implicit ordinary postulations of ordinary objects and of ordinary kinds are alike, in that they play a key role in our ordinary ability to generalize inductively from known to new cases. Just as the implicit ordinary postulation of an ordinary object “unifies” certain different temporal “stages,” making us expect the instantiation of certain properties across a range of such “stages,” an ordinary kind “unifies” certain different spatiotemporal “segments,” making us expect the instantiation of certain properties across a range of such “segments.” Relatedly, our system of folk beliefs involving ordinary objects seems just “too good to be false,” just as our system of folk beliefs involving ordinary natural kinds seems just “too good to be false.” To take a basic example, it sounds just as absurd to claim that water (and gold, and the tiger) doesn’t really exist as it sounds absurd to claim that Barack Obama (and my mother, and my son) doesn’t really exist. It is hard, and it requires a lot of philosophical sophistication, to make sense of the idea that these apparently absurd claims could be true, as this would thoroughly disrupt our ways of facing the world. constituted completely by ¹⁹⁹Au, i.e. the principle used in the text. See Salmon (1981), }}21–3, for discussion bearing on the thesis considered sympathetically by Kripke.

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178       Many analogies thus suggest a strong case for the existence of kinds irreducible to precise structural biochemical-chemical-physical kinds. In fact, views related to the present view are represented in the literature. Besides Johnston, and via different motivations which in some ways are closer to the present motivations, Boyd (1999) and Hawley and Bird (2011) defend views on which many natural kinds are vague or indeterminate kinds. Both Boyd and Hawley and Bird emphasize that many natural kinds must be understood so that membership in them is indeterminate in ways in which membership in many scientific kinds is not. Nevertheless, there are differences between these views and the view I would be tempted to adopt. In particular, both Boyd and Hawley and Bird seek to understand vague or indeterminate natural kinds as clusters of individually non-necessary but jointly sufficient properties for membership. I find the idea of clusters of individually non-necessary but jointly sufficient properties somewhat dubious; for one thing, some of the properties that will presumably appear in the clusters may turn out to be necessary (perhaps being composed of H₂O is an example in the case of the kind water, as we are about to mention); and the idea of jointly sufficient properties seems dubious as well. Also, the cluster idea introduces a worry about the exact nature of the composition or unifying principle turning the composing kinds into one composed kind, a question not resolved by either Boyd or Hawley and Bird. On the view I’m inclined to adopt, ordinary kinds need not be ontologically composed out of other kinds, and may well be sui generis kinds—even if the nature of some ordinary kinds may be such that membership in them turns out to involve possession of some necessary but typically non-sufficient structural scientific condition.²⁵ For present purposes, these differences don’t matter so much as the affinities showing that the view of at least some natural kinds as vague or indeterminate is intrinsically attractive, and has been largely independently arrived at via indeterminacy considerations by several authors.²⁶

²⁵ This view is to be contrasted with the view of Lowe (2006), on which kinds are entirely sui generis, and in particular are not universals of any sort. On the view I am inclined to adopt, ordinary kinds are sui generis universals. ²⁶ I can also report that Kripke himself, in an intervention at a conference in Mexico City in August of 2016, suggested that he was ready to acknowledge that an ordinary natural kind word had some inherent “flexibility” preventing a full identification of its referent with a fundamental scientific kind, even if such identifications could be made at late stages of scientific development, to some degree arbitrarily. I take this view to be congenial with the view suggested here, of the referents of ordinary natural kind words as ordinary kinds not reducible to precise structural scientific kinds. It may also be noted that in his unpublished work on natural phenomena such as color, sound, heat, etc., Kripke has emphasized that these may be phenomena pertaining not to fundamental science, but to other levels of scientific representation and knowledge (see Gómez-Torrente (2011) for a brief exposition).

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The existence of ordinary kinds irreducible to precise structural biochemical-chemical-physical kinds is thus a reasonable thing to believe in. But how reasonable is it to think that such kinds are the referents of ordinary natural kind nouns? Very reasonable, I think. In order for Successful explicit natural kind noun introduction via perceptual intention, Successful implicit natural kind noun introduction via perceptual intention, or Successful natural kind noun adoption via perceptual intention to operate and yield the ordinary kind water, say, as referent of “water,” the ordinary kind water must be the single substance that the items in a typical paradigm sample for “water” exemplify, making it the case that each of them is “of the same substance” as another. We must note first that the fact that many fundamental-scientific substances underlie the paradigms is not an obstacle to reference, for in the sense of “substance” and of “exemplify” relevant to ordinary referential intentions it is strictly speaking false that the typical paradigms exemplify those substances. Those senses are, as we have argued, vague along dimensions along which the concepts of fundamental-scientific substances are not: exemplification of the would-be referents offered by fundamental science is not indeterminate in the way dictated by the ordinary meaning of “substance”—and the typical paradigms contain just too many things to count as exemplifying a precise, fundamental-scientific substance. This is just another way of saying that the reference of “water” must be an ordinary substance, if anything. But then the crucial question is: is there a single ordinary substance that is exemplified by the items in a typical paradigm sample for “water”? That the answer is “yes” can be argued in two steps. Scientific facts will play a role in the first step. They will determine that the members of the paradigm sample for “water” share a homogeneous nature. In order for this to happen, it is not required that the scientific facts reveal by themselves an identification of water in terms of necessary and sufficient conditions. It is enough that the members of the sample will be revealed to share some necessary properties at the appropriate level. In the case of water, these may include being composed of H₂O, being composed of P₂O and being composed of “3/4 orthowater, ¼ parawater.” In the second step, the meaning of “substance” involved in the relevant referential intention will operate in order to “abstract away” a single ordinary, irreducible kind from the precise structural scientific kinds underlain in the paradigm sample. This will happen because in virtue of the ordinary notion of substance, the things exemplifying a substance will be the things which are not too different, in a suitably vague sense, from the paradigms as regards the necessary properties of the latter. These will of course include

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180       determinately the paradigms, and will include indeterminately things composed of some of the kinds but not others (things composed of H₂O but not of P₂O, say) (and will determinately exclude things which are just too different from the paradigms). A single ordinary kind will be referred to, because there are not two kinds satisfying the requisite that what exemplifies them are the things which are not too different, in a suitably vague sense, from the paradigms as regards the necessary properties of the latter. This is nothing less than a characterization, in terms of vague, not precise-structural-scientific necessary and sufficient conditions, of a single ordinary kind.²⁷ We get a hint here of how to view the worry whether the idea of ordinary natural kinds as irreducible to precise structural scientific kinds gets into an unsatisfactory conflict with the Kripke-Putnam view that science discovers the nature of water, gold, and tigers. In my view it does not. While the view suggested here precludes the possibility of reductions of ordinary natural kinds to precise structural biochemical-chemical-physical kinds, it does by no means preclude scientific discoveries concerning ordinary kinds, nor the reference to and study of ordinary kinds in science, both at non-fundamental and fundamental levels. In particular, the view is fully compatible with the possibility of science discovering basic aspects of the nature of an ordinary kind, in the sense of the structural scientific properties involved in the description of some necessary properties of the items in the paradigm sample, that serve as the basis for the vague characterization of that ordinary kind. In fact, the view is also compatible with the possibility of science discovering necessary scientific properties of all instances of the kind, in cases in which science discovers properties the lack of which would make a thing too different from the paradigms as regards their necessary properties. Thus, for example, science can probably be said to have discovered that paradigms of water (the ordinary kind water) are composed of H₂O; and probably also that all water must be composed of H₂O, as not being composed of H₂O probably makes something just too different from paradigms of water to count as water (the converse, that being composed of H₂O is sufficient for being water, of course need not be true, or at least determinately true). Similarly, science can probably be said to

²⁷ Needless to say, the fact that the nature of an ordinary natural kind is vague doesn’t mean that “anything goes,” and in particular it doesn’t mean that any purported natural kind noun will get some imprecise reference or other. For example, a necessary condition for two things being of the same substance in the ordinary sense is that they must not be too different in nature. This prevents a set of paradigms containing things of very different natures from giving rise to a successful introduction of a corresponding natural kind noun via Successful explicit natural kind noun introduction via perceptual intention, Successful implicit natural kind noun introduction via perceptual intention, or Successful natural kind noun adoption via perceptual intention.

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have discovered that gold chunks, paradigm or not, are chunks composed of Au (the element with atomic number 79) (even if the converse is not determinately true); and that tigers, paradigm or not, have a genome of a certain sufficiently abstract kind, even if it will not be determinately true, and may even be determinately false, that all the animals with a genome of that kind are tigers. On the view sketched here, science does play a key role in uncovering the nature of ordinary kinds. This helps make it clear that the present view is in principle compatible with two other aspects of the Kripke-Putnam ideas that were always thought to be attractive from the time those ideas became known. One is that ordinary natural kind nouns need not change their meaning after scientific discoveries concerning the nature of the kinds they refer to take place. A change of meaning was once a popular hypothesis designed to account for the fact that, at least after the scientific discoveries concerning water, say, whether a liquid is (composed of) H₂O became a touchstone for the question whether it is water. On the present account, being composed of H₂O may have always been a necessary condition of being water, even if this was not known, because there was always reference to the ordinary kind water, which may include being composed of H₂O as a necessary property. Another aspect of the KripkePutnam picture that the present picture is compatible with is then that ordinary natural kind nouns need not change their extension through history, at least if one understands this to mean that a noun referring to a vague kind will not change its connections to the more precise kinds it is related to. This is one way in which scientific discoveries concerning ordinary kinds would be possible, and the idea that there are advances in our knowledge concerning kinds might be accommodated in this way. We saw that some arbitrariness arguments in the biological case arose from an apparent indeterminacy of the same species relation, allegedly revealed by attention to the largish number of theories of that relation that have been proposed by theoretical biologists. Key here is the presupposition that the proposed theories of the same species relation all have equal claim to scientific correctness or value. But it is unclear in this particular case that this impression is not due to the transitory state of theoretical biology rather than to deep facts of indeterminacy. In fact, if we are to believe several philosophers of biology (see e.g. Sterelny and Griffiths (1999), 194) there are indications that phylogenetic theories have been becoming the dominant ones, presumably because they seek to reflect robust facts about evolutionary history. There may be somewhat deeper indeterminacies within phylogenetic theories themselves, generated by the embedded concept of speciation. Presumably there is no

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182       sharp boundary in the processes of formation of a new group that does not interbreed with an old one, of acquisition of a new habitat, etc. at which new species emerge from old ones. If so, there will not be a sharp boundary along the relevant dimensions drawing the line between tigers and non-tigers, say. But the vagueness responsible for this sort of indeterminacy may be compatible with the species of ordinary language being vague along similar dimensions as the species ultimately recognized by theoretical biology (which will not attempt to provide precise structural biochemical-chemical-physical characterizations of particular species). If so, the corresponding arbitrariness argument cannot show by itself that the species of theoretical biology will not be the species referred to by ordinary species nouns (though other considerations might eventually show this). The reader will recall the case of jade (and “jade”) and the special kind of argument for arbitrariness in which it played a role in LaPorte (2004) and Leslie (2013). If correct, this argument would undermine a very basic and largely uncontroverted thesis which is a part of the “Kripke-Putnam orthodoxy,” namely that the existence of great differences in the natures of two things implies that they are not made up of the same substance. In my view, the argument is defective quite independently of the right view of ordinary natural kinds. Note that, before the Chinese started calling jadeite “jade” without qualification, there was a time when jadeite had special names and was not called “jade” without qualification, because artisans knew it was not exactly like nephrite. The natural view is that the establishment of the use of calling jadeite and nephrite “jade” just amounts to the consolidation of a new, disjunctive non-natural-kind meaning of the word (if it was a name for a natural kind before). LaPorte says that a view of this sort “seems ill supported and motivated only by a desire to save a theory” (LaPorte (2004), 97). But it’s hard not to think that in this case it’s LaPorte who is in the grip of his own desired view, for the natural view is not ill-supported at all. The aspects of the “jade” story that support the anti-Putnamian view are just too unlike the corresponding aspects of the Putnam planetary story about “water” for the dispassionate reader to see the “jade” story as a minimally convincing refutation. In particular, a long time elapsed between the discovery of jadeite and the establishment of the use of calling jadeite “jade” without qualification. Vice versa: there are aspects of the story that support the Putnam view, specifically the use of qualifiers of “jade” when it was initially realized that jadeite was not quite like nephrite. In conclusion we can finally return to disunity considerations and, in the light of what we have said so far, see that they don’t cast serious doubts on the

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picture we have developed in this chapter. The first consideration was that “H₂O” is a compositional, not a structural formula, and the second was that obtaining a structural formula for water seemed a vain hope. We can now see that this has no force against the picture of reference fixing for ordinary natural kind nouns in this chapter (nor, indeed, against the Kripke-Putnam view of the pure mechanism of reference fixing—as opposed to their specific view of the relevant referent of “water”). For as we have argued, there is no constraint imposed by the relevant referential intentions requiring that the characterization of the ordinary kind water, or even any necessary property of it that science may come upon, be given in terms of underlying scientific structural conditions. For all that the ordinary meaning and a priori notes of “substance” and “water” require, the characterization of the ordinary kind water need not include underlying structural conditions, and in particular, if science finds some necessary property of the instances of the kind, such properties need not be structural. Being composed of H₂O may be, probably is, one such necessary condition of the instances of the ordinary kind water. A third disunity consideration, coming from the philosophy of biology, was provided by the claim that there is no obvious unifying genetic description even of the paradigmatic members of an ordinary biological kind. Here again we must note that the reference-fixing mechanism postulated in this chapter (and the coarser mechanism of Kripke and Putnam) does not require the existence of unifying genetic descriptions for ordinary biological kind reference. But this said, we may also note that it is to say the least unclear that informative unifying descriptions coming from genomics and molecular biology do not exist in the case of the vast majority of species, including many that are named in ordinary use. Geneticists routinely speak of the genomes of particular species, by which of course they mean genome descriptions “in which individual differences are ignored” (Slack (2014), 25). Some such descriptions, when they abstract sufficiently from individual differences, might well provide merely necessary properties of the corresponding ordinary species (though the situation here looks less clear than in the case of natural substances). But it cannot be overemphasized that not even this is required for the picture of the present chapter to be correct.

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6 Words for Sensible Qualities and the Problem of Perceptual Variation The “Secondary Quality” View of Color and Some Arguments for and against It One of the notorious conclusions that Kripke extracted from his account of terms for natural kinds was that sensible properties such as (determinate) properties of color, sound, heat, etc., which had been regarded as “secondary qualities”—mere dispositions to produce sensory effects—by a dominant tradition of thought about the topic, could be and probably were in fact “primary qualities.” His account, he thought, could be used to dispel at least one confusion which had provided one main source of support for the view of color, sound, heat, etc. as secondary qualities, namely the confusion between nouns synonymous with descriptions and nouns that merely get their referents fixed by means of descriptions: Many philosophers for want of any other theory of the meaning of the term ‘yellow’, have been inclined to regard it as expressing a dispositional property. At the same time, I suspect many have been bothered by the ‘gut feeling’ that yellowness is a manifest property, just as much ‘right out there’ as hardness or spherical shape. The proper account, on the present conception is, of course, that the reference of ‘yellowness’ is fixed by the description ‘that (manifest) property of objects which causes them, under normal circumstances, to be seen as yellow (i.e., to be sensed by certain visual impressions)’; ‘yellow’, of course, does not mean ‘tends to produce such and such a sensation’; if we had had different neural structures, if atmospheric conditions had been different, if we had been blind, and so on, then yellow objects would have done no such thing . . . . If we take the ‘fixes a reference’ view, then it is up to the physical scientist to identify the property so marked out in any more fundamental physical terms that he wishes. (Kripke (1972), 140, n. 71)

Roads to Reference: An Essay on Reference Fixing in Natural Language. Mario Gómez-Torrente, Oxford University Press (2019). © Mario Gómez-Torrente. DOI: 10.1093/oso/9780198846277.001.0001

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To be sure, proponents of the view of color, sound, heat, etc. as “secondary qualities” had other reasons for their view, and a few more emerged precisely in discussions partly sparked by Kripke’s account. Kripke would consider and rebut some of these other reasons in work of the 1980s and 1990s that, unfortunately, remains unpublished at the time of writing; however, an exposition of this work, along with some extensions of Kripke’s arguments, can be found in Gómez-Torrente (2011). Still other related but more sophisticated arguments against the Kripkean view, especially concerning the central case of color qualities or properties, have emerged more recently, though this time as arguments that some authors see as reasons for some kind of eliminativism about those qualities and other authors see as reasons for some kind of linguistically improbable subjectivism (including subjectivist dispositionalism) about them. The main purpose of this chapter is to explain how a natural view of reference fixing for color terms, and especially for color adjectives, provides an account of color language (and by extension of the language for other sensible properties) that respects the objectivist intuitions mentioned by Kripke and that rejects eliminativism, being thus in harmony with the natural conception of human endeavors and accomplishments concerning truth. Let’s first be clear about terminology. Eliminativist accounts of color language postulate that color nouns and adjectives refer to no kinds or properties at all, or at any rate refer to properties that always have the empty extension. Subjectivist accounts of color language, as we will use the term “subjectivist,” postulate that color nouns and adjectives refer to properties that are metaphysically constituted by perceptual relations between objects and perceiving subjects. (Thus, views of color properties as dispositions to produce certain sensory effects are subjectivist views in this sense.) Non-eliminativist objectivist accounts, on the other hand, postulate that color nouns and adjectives refer to properties that are not metaphysically constituted by perceptual relations between objects and perceiving subjects, and which yield reasonable extensions for them. (Note that an objectivist view of the color properties can in principle be coupled with an eliminativist theory of them, but I will practically always reserve “objectivist” for non-eliminativist views.)¹ ¹ Jonathan Cohen ((2004), (2009)) has recently used the label “relationalist” for the views I call “subjectivist.” Classical dispositionalist theories such as those of McGinn (1983), Peacocke (1984), Wright (1988), and Johnston (1992) and recent theories such as Cohen’s come out subjectivist on the present understanding. Physicalist theories such as those of Smart (1963), Armstrong (1968), Hilbert (1987), Matthen (1988), Byrne and Hilbert (1997), (2003), and Tye (2000) come out objectivist. Eliminativist views include those of Hardin (1988), Boghossian and Velleman (1989), Maund (1995), and Averill (2005).

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186       The recent sophisticated arguments for eliminativism and subjectivism that I have in mind appeal to several kinds of variations in the perception of color. In particular, there are intrasubjective, interspecies, and intersubjective perceptual variation arguments. In this chapter we will especially focus on offering a (non-eliminativist) objectivist theory of the reference-fixing conventions and the referents of color adjectives that aims to compare favorably to standard objectivist theories, especially as an account of what intersubjective variation shows about those contents.² But first we will say a few words about intrasubjective and interspecies arguments. In intrasubjective perceptual variation arguments appeal is made to wellknown differences in the ways one single perceiver can have a chromatic perception of the same object depending on distance, background, illumination, etc. If a geranium leaf is illuminated exclusively with monochromatic red light, I will see it the way I see a ripe tomato under normal solar light. Or if I see it against a suitable yellow background, I will see it looking somewhat blue. These perceptual differences are not grounded on differences in perceptual apparatuses, so they cannot be used to establish directly any conclusion that the color properties are constituted subjectively. But they have been used to suggest in indirect ways that color attributions are either erroneous or implicitly relative to an arbitrary choice of conditions in which objects are perceived as having the attributed properties, in some way in which attributions of paradigmatically objective sensible properties, e.g. of shape and length, are not. Note first that the perceptual differences in question don’t normally give rise to natural intuitively contradictory color attributions. We wouldn’t normally say This geranium leaf is red or This geranium leaf is not green (or even This geranium leaf is red in these conditions) just because the leaf is being illuminated exclusively with monochromatic red light. And we wouldn’t say This geranium leaf is somewhat blue just because we are seeing it against a suitable yellow background. As often noted by objectivist theorists, in many of the cases appealed to in intrasubjective arguments the relevant perceptions will be intuitively erroneous or illusory, and the (often unnatural) attributions that could be made on their basis will often be intuitively false (see e.g. Tye (2000), ch. 7). In the vast majority of cases appealed to in intrasubjective arguments, ² This account also suggests a companion account of a relevant part of the contents of chromatic experiences, but here I can only focus on the complex issues concerning the contents of color language, which ultimately motivate the development of the present theory, and which require their own extended independent treatment. See note 44 and Gómez-Torrente (2016), section 5, for a sketch of the mentioned account of the contents of chromatic experiences.

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some conditions of observation, however vaguely specified, are intuitively or arguably privileged when it comes to revealing the colors of things.³ In this respect, there would seem to be no difference with the cases of shape or length. Nevertheless, in other examples there are no clear intuitions that some conditions of observation are privileged in the color case. A chocolate bonbon, e.g., looks brown when seen against a background that is lighter overall, but looks orange when seen through a black reduction tube. Here it might perhaps be argued that only the second perception is non-illusory, and that of the two attributions The bonbon is brown and The bonbon is orange only the second is true; or alternatively, that since the second situation is not quite as normal as the former, the orange perception is illusory while the brown perception is veridical (with Byrne and Hilbert (2003), 13). But the eliminativist theorist and the subjectivist may press the point that the conditions of observation that yield intuitively veridical perceptions of the color of an object are definitely vague in many cases, and allow for what seem clearly incompatible perceptions or attributions. For example, slightly different lights with a roughly flat power distribution (including different samples of solar light) can all be considered normal illuminants, and yet they will give rise to different perceived determinate colors for a single object. It’s unintuitive to claim that one of these illuminants is privileged, the eliminativist and the subjectivist will say.⁴ In my view, however, it is very clear that this sort of consideration cannot support eliminativist or subjectivist treatments of the color properties. Although such treatments often proceed as if paradigmatically objective properties are not constituted by conditions of observation or measurement, this is simply false. For example, it should by now be pretty clear that “the” length or shape of a sensible object can be determined only with respect to a level of resolution. To take a famous case in point, you will get different lengths (and shapes) for the coastline of Britain if you measure it from an airplane flying at 30,000 ft by using a scaling factor of the perceptions (or the photographs) you get, and if you measure it by adding a large number of measurements made with a 1-yard-long stick while you walk all around the coast. As the resolution of your observations gets more and more fine-grained, you get larger and ³ These facts create a strong pressure for the subjectivist to explain why we don’t have relativistic intuitions in most intrasubjective variation cases (as opposed to the normal intersubjective variation case described in the next section). Of course, subjectivists have attempted to meet this challenge; see e.g. Cohen (2009), 111ff. ⁴ Compare e.g. Hardin (1988), 67ff., or Cohen (2004), 464ff. Sometimes this intuition is backed by the more theoretical remark that the viewing conditions stipulated by the existing colorimetric systems, developed especially for industrial purposes, are not intuitively special or preferred.

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188       larger lengths for the coastline of Britain (and more and more complicated shapes for it). Among many of these levels of resolution there is intuitively no privileged one, and consequently there is no such thing as “the” length or “the” shape of the coastline of Britain. But this doesn’t mean that the different length and shape properties that you get in these different measurements are subjective. Presumably they are properties somehow constituted by specific (objectively specifiable) conditions of observation or measurement in each case, but objective properties nonetheless.⁵ There thus seems to be an underlying confusion in this kind of considerations for subjectivist or eliminativist views about color. As Cohen ((2004), 461) puts things, color is supposed to be distinct from paradigmatically objective sensible properties, like shape, in that there are intuitively “perception-independent criteria for deciding” whether an object is, say, square; but there are no intuitively perception-independent criteria for telling whether an object is, say, green. Allegedly, the criterion of having four right interior angles and sides of equal length is a perception-independent criterion for telling whether an object is square, but there is intuitively no such criterion for deciding whether an object is green. The confusion is that while we can of course view the words in “having four right interior angles and sides of equal length” as standing for abstract geometric properties, perhaps defined in terms of the primitives of analytic geometry, there is no reason to view criteria of this sort as allowing us to decide the shapes of sensible objects (like concrete square-looking objects, or the coastline of Britain).⁶ For this to be the case, the properties of, say, being a right angle, of being a side, and of being of equal ⁵ So the remark alluded to in the preceding note is quite true, but I find perplexing the frequent implicit suggestion that the situation is different in the case of shape or length. Just as in the case of colorimetry, sophisticated length metrology stipulates conditions for the measurement of lengths that in no sense are intuitively special or preferred. These conditions, just as in the case of color, are conventionally stipulated, and are specified because our best theories postulate that there are factors whose variation would produce differences in the results of length measurement, e.g. quality of air, rust, temperature, etc. For example, the International Organization of Legal Metrology stipulates that uses of length measurement instruments must be performed at a “temperature of 10  C to +40  C and a relative humidity of 65%  10%” (Organisation Internationale de Métrologie Légale (1985), 4). The truth is that, indeed, no viewing conditions are intuitively singled out with scientific detail as the appropriate conditions for determining whether an object has a certain color. But there are no such conditions in the case of paradigmatically objective sensible properties like shape or length, either. ⁶ As is well known, perceptual color space can be mapped in a number of ways onto a threedimensional geometric space, with the axes representing values of hue, saturation, and brightness. (See e.g. Hardin (1988), 113ff.) One can also assume for the sake of argument that these values represent objective properties. So one can assume a correspondence between three-dimensional geometric space and objective color properties, and derivatively view color words as standing in a technical use for (some of the) abstract geometric properties of the geometric space. A criterion of, say, “greenness,” expressed purely in terms of these abstract geometric properties, would again be unusable in determining whether a sensible object is green. There is again no dissimilarity here between the cases of shape and color.

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length must be sensible, pre-abstract-geometric properties. But surely the sensible property of being a right angle is not characterizable without appeal to conditions of observation, including resolution scales. The case of color need not be different. In neither case does the constitution by conditions of measurement or observation imply any eliminativist or subjectivist conclusion. So-called interspecies variation arguments, on the other hand, might seem more relevant to the issue of objectivity vs. subjectivity. They appeal to partitions of the dimension of hue by means of fewer or more different types of perceptual qualities than in normal humans. One such argument might be as follows: Elephants seem to be dichromats with color vision similar to that of human deuteranopes. The photoreceptors in their retinas are of two kinds, ones with an absorption similar to that of normal human S-cones and ones with an absorption similar to that of normal human L-cones. Assuming that a yellow-blue opponent process is the only chromatic channel processing photoreceptor information that is in operation in their visual system, presumably the qualities of their color perceptions reduce to those that normal humans experience when they see blue and yellow objects. If elephants developed a verbal language, they would presumably have names for only two unique colors, say “bblue” and “yyellow.” They would see tomatoes the way we see yellow things, and they would say things like Ttomatoes aare yyellow. The existence or possibility of these differences can be used to suggest that ordinary human color experiences and attributions (like Tomatoes are not yellow) are either erroneous (because not veridical or true to the exclusion of the corresponding experiences and attributions of elephants) or just as veridical or true as the corresponding superficially incompatible color experiences and attributions of elephants (because implicitly relativized in each case to the pertinent class of perceivers), as suggested by subjectivist theories.⁷ But it’s unclear that this argument can support eliminativist theories or subjectivist theories with much force. When we use “yellow” and the elephants use “yyellow,” it’s overwhelmingly plausible to think that the two words have different meanings. For one thing, the elephants will not have a structurally similar color vocabulary, and hence there will be no sense in which the properties referred to by their color adjectives will stand for them in the same intuitive relations as our properties stand for us. For another thing, when we restrict ourselves to the color words of their language that would

⁷ We can quite naturally make non-monadic attributions such as Tomatoes are yellow for elephants and Tomatoes are not yellow for humans. But this naturalness shows nothing about subjectivity. We can also say Motorcycles are light for elephants, but there is no suspicion that lightness is subjective.

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190       seem to correspond to the color words in ours, clearly different intuitively analytic or necessary truths would seem to be generated; Dumbo could say perfectly sincerely Eeverything ccolored hhas tto bbe eeither bbluish oor yyellowish, indicating that the meaning he attaches to his words “bblue” and “yyellow” is very different from the meaning we attach to our words “blue” and “yellow.” Also the properties represented in Dumbo’s experience are plausibly just different from the properties represented in the experiences of normal humans:⁸ Dumbo’s experience presumably represents tomatoes as having one of two possible unique colors, while our experience represents tomatoes as having one of four possible unique colors. If our words and the elephants’ words plausibly differ in meaning and the properties represented in our respective experiences are structurally different, the error theorist and the subjectivist lose the argumentative ground they need.

Intersubjective Perceptual Variation Arguments and Some Implausible Objectivist Responses to Them It is the recent consideration of facts of normal intersubjective variation in color perception that has led to the formulation of the most difficult problems for existing (non-eliminativist) objectivist theories of the contents of color language and color experience. Intersubjective variation is strikingly illustrated by a famous kind of psychological experiments. In one experiment of this kind, a large group of normal subjects⁹ are presented with several chips that when illuminated with some fixed normal illuminant reflect lights of distinct dominant wavelengths in the 490–520 nm zone of the spectrum, and are asked to point to the one that is (closest to) unique green, i.e. a shade of green that is neither somewhat yellow nor somewhat blue, and classify the others as either somewhat yellow or somewhat blue.¹⁰ The answers vary considerably. There are, for example, chips that a considerable group of normal subjects classify as green but neither somewhat yellow nor somewhat blue, and another ⁸ Compare the related view defended in Byrne and Hilbert (2003), 16, though on grounds somewhat dependent on the details of their particular theory of color properties as sets of reflectances. ⁹ The tests of normality for chromatic perception (such as the Farnsworth test) are based essentially on the idea that the vast majority of subjects (the normal subjects) ought to order in the same way a series of objects along the dimensions of their apparent color (especially hue). (Not all subjects who are normal by these tests are able to make side-by-side color distinctions with the same apparent acuity. However, the differences in linguistic classification about to be mentioned are robustly independent of the apparent acuity of the subjects.) ¹⁰ “Yellowish” is also used instead of “somewhat yellow” (and similarly for the other color adjectives). I take these to be synonymous in the relevant contexts.

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considerable group of normal subjects classify as green but somewhat blue; there is even a large group of subjects who classify those same chips as blue but neither somewhat green nor somewhat red (i.e. as unique blue).¹¹ All this suggests that there are phenomenal differences among the experiences that different normal subjects have of the same chip in the same normal viewing conditions, which in turn induce the differences in their linguistic classifications. Those phenomenal differences are in all probability caused by a number of physiological factors resulting in minute interpersonal differences in the absorption curves of cones (see e.g. De Valois and De Valois 2000, 135ff.). One main argument against non-eliminativist objectivism based on these facts goes as follows: It seems natural to think that, if χ is a chip that a subject UG perceives and classifies as green but neither somewhat yellow nor somewhat blue and another subject BG perceives and classifies as green but somewhat blue, there is no reason why one of these experiences or attributions should be veridical or correct to the exclusion of the other. After all, the subjects are both normal according to reasonable tests, and the differences between them appear to be traceable merely to their cones having slightly different absorption curves, neither of which would seem to be “better” in any sense than the other. It does seem natural to suppose that either both UG and BG have veridical experiences and make true attributions or both have falsidical experiences and make false attributions. If the latter, then an eliminativist theory must be correct. And if the former, then the properties of being green but neither somewhat yellow nor somewhat blue and of being green but somewhat blue must be subjective. For “green but neither somewhat yellow nor somewhat blue” and “green but somewhat blue” are incompatible unless they refer to subjective properties. If we suppose that they do, then both BG’s and UG’s experiences and attributions can be taken to be correct: BG perceives and implicitly classifies χ as something like looking green but somewhat blue to BG and UG perceives and implicitly classifies χ as ¹¹ The classic reference for experiments of this kind is Hurvich et al. (1968). There are especially accessible descriptions in Hardin (1988), 79ff. and Block (1999); see also Kuehni (2014) for a somewhat technical presentation of a large range of experiments of this kind. In a related kind of experiment (Malkoc et al. (2005)), subjects are asked to classify chips as either “red,” “orange,” “yellow,” “greenyellow,” “green,” “blue-green,” “blue,” or “purple”; some classify some chips as red and not orange and others classify those same chips as orange but not red; some classify some chips as orange but not yellow and others classify those same chips as yellow but not orange, and so on. (For discussion see Tye (2006), Cohen et al. (2006), and Byrne and Hilbert (2007).) Although I will focus on the classifications involving the unique hues, the theory in this chapter is designed as an account of the classifications in this latter experiment as well.

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192       something like looking green but neither somewhat yellow nor somewhat blue to UG. There is no contradiction between UG and BG because the properties they talk about come constituted by perceptual relations involving UG and BG; if we don’t assume such constitutive relationality, e.g. if we suppose that those properties are objective, the contradiction is inevitable.¹²

To be sure, this argument can seem convincing (or at least convincing at first sight) only to moderately sophisticated language users with knowledge of the spectrum of wavelengths, of cone absorption curves, of what counts as a normal perceiver according to reasonable tests, etc. At least some language users lacking this information or unable to digest it think, when presented with the raw data of the subjects’ classifications in the mentioned psychological experiments, that at most one of UG or BG can be correct. The eliminativist option carries with it the usual undesirable conflict with the natural conception of human endeavors and accomplishments concerning truth, and creates the accompanying tension for whatever our preferred view of reference fixing for color language may be. But subjectivism is also not without its counterintuitive consequences. One of them lies in what I take to be an extended Kripkean impression that the color properties are properties “out there,” not involving subjects or perceptual relations at all. A companion difficulty involves a related idea that can be somewhat more precisely stated, the idea that color predicates have what we might call “objective modal stability,” a property closely related to rigidity. Say that a (possibly contextsensitive) monadic predicate P is objectively modally stable iff, for any given object o and context c, there are no two different worlds w and w’ which are the same as to the objective properties of o but are such that o is in the extension of P with respect to (c, w) but fails to be in the extension of P with respect to (c, w’). If UG says If my eyes were just a bit different, χ would stop being green and neither somewhat yellow nor somewhat blue, what he says will probably sound false to him (it did sound false to all my informants). This is plausibly explained under the supposition that “green and neither somewhat yellow nor somewhat blue” is objectively modally stable: the antecedent of the counterfactual takes UG to a world w’ that is at most subjectively different from the actual world w, and UG thinks that in w’ (and with respect to the same context of his utterance) “green and neither somewhat yellow nor somewhat blue” doesn’t change extension. But UG’s utterance is true ¹² For places where forms of this argument are developed and embraced, see Cohen (2004), (2009), ch. 2, Hardin (1988), 79ff., (2003). Cohen chooses the subjectivist horn, Hardin the eliminativist one.

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on a standard unsophisticated subjectivist view, on which what he says is something like If my eyes were just a bit different, χ would stop being green-but-neither-somewhat-yellow-nor-somewhat-blue-looking (to me). On a standard unsophisticated subjectivist view, “green but neither somewhat yellow nor somewhat blue” is not objectively modally stable.¹³ Problematic as eliminativist and subjectivist theories may be, existing noneliminativist objectivist theories and their reactions to intersubjective variation arguments seem to me to incur unreasonable costs. Let me now briefly review some of these theories and the costs they incur, so that I can later indicate how the account suggested in this chapter avoids those costs. The theories in question obviously cannot be dismissed merely on the basis of the following brief discussion. But my main concern in this chapter will not be to give knockdown arguments against rival views, but just to note that my view compares favorably to them in a few key respects. A prominent reaction can be found in Alex Byrne and David Hilbert (2003), (2004) and Michael Tye (2006), among other authors. They reject the idea that either both UG and BG must have veridical perceptions or both must have falsidical perceptions, and thus the assumption that either both UG and BG must make true attributions or both must make false attributions. On this view, it may well be that at most one of either BG or UG has a veridical perception of χ’s objective chromatic property, and thus that at most one of either BG or UG makes a true attribution about χ. It may well be that we just don’t know at present, and perhaps will never know, who among BG or UG or the other normal subjects with phenomenally different experiences is right about χ. It seems fair to say that this sort of reply is very unconvincing in view of what we know about the physical and physiological phenomena underlying color perception. We have no clue as to what fact of the matter, if this is to be describable in terms of the relevant known physics and physiology, could make BG or UG or some other subject be in the right to the exclusion of the others. Moreover, in part because of this, but also insofar as purely linguistic ¹³ On some sophisticated subjectivist views, color predicates are objectively modally stable. “Rigidified” properties like being disposed to look green but neither somewhat yellow nor somewhat blue to UG as actually constituted in the actual experimental conditions C are subjective, but a predicate that refers to this property is presumably modally stable. (See e.g. Shoemaker (1986), or Cohen (2009), ch. 7 on “role-functionalism,” for essentially similar proposals.) But an explanation on which “green but neither somewhat yellow nor somewhat blue” stands for a non-rigidified objective property is arguably simpler (ceteris paribus), much in the same way in which an explanation of the rigidity of proper names or demonstratives in terms of their being semantically unstructured is simpler (ceteris paribus) than one on which their content is given by sophisticated rigidified descriptions. Further, the “rigidifying” explanation needs to postulate that speakers with stability intuitions who do not have at their disposal rigidifying concepts are not really competent users of color concepts; I think this is implausible. See also note 19 and the surrounding text below for further criticism of related views.

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194       judgments are concerned, neither BG nor UG would seem to have made any mistake in their use of color words. It is hard to avoid the conclusion that objectivist accounts that respected the impression that all the subjects are equally right would enjoy a definite advantage over this kind of reaction. One such objectivist account has been proposed by Mark Eli Kalderon (2007).¹⁴ He concedes that both UG and BG have veridical perceptions and make true attributions, but rejects the assumption that “green but neither somewhat yellow nor somewhat blue” and “green but somewhat blue” as used by UG and BG must refer to incompatible properties unless they refer to subjective properties. Kalderon claims that being green but neither somewhat yellow nor somewhat blue and being green but somewhat blue must in some way be compatible properties, and that while UG is able to see how χ possesses the first of these properties but not how it possesses the second, BG is able to see how χ possesses the second but not how it possesses the first. I agree that the weakest spot in the argument is the transition from the compatibility of the attributed properties to their subjectivity, and the theory in this chapter can be seen as one possible way of fleshing out Kalderon’s abstract idea, as it will propose that UG and BG do indeed refer to two different chromatic properties of χ. A main problem with Kalderon’s abstract idea, however, is how it can adequately deal with the fact that “not somewhat blue” in UG’s attribution χ is green but neither somewhat yellow nor somewhat blue and “somewhat blue” in BG’s attribution χ is green but somewhat blue are contradictory predicates.¹⁵ Kalderon’s proposal doesn’t appeal to any sort of relativization that could make the properties referred to by those predicates compatible. But if no relativization of any sort is invoked, it’s hard to see what fact of the matter could make it the case that “not somewhat blue” in the first attribution and “somewhat blue” in the second are not contradictory.¹⁶ An objectivist reaction that invokes one kind of relativization is one favorably considered by Brian McLaughlin (2003).¹⁷ The idea is that the reference of the predicate “somewhat blue” when used by UG is fixed by the a priori equivalent descriptive predicate “has the physical property that in normal

¹⁴ See also Mizrahi (2007) and Allen (2009). ¹⁵ See the related objection in Hardin (2006), 343. ¹⁶ Cohen (2009), 81, on behalf of Kalderon, considers as a way of avoiding the contradiction the possibility of denying that “not somewhat blue” in the first attribution and “somewhat blue” in the second are both intended to apply to χ. But I take this way out to lack independent motivation, and should hope that Kalderon would not be tempted by it. ¹⁷ It is also closely related to an objectivist reaction to other subjectivist considerations, favorably considered by Frank Jackson (1996). Compare the discussion of these views, under the label “realizer functionalism,” in Cohen (2009), ch. 7.

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conditions makes something look somewhat blue to UG” (mutatis mutandis for BG),¹⁸ but this doesn’t imply that that predicate stands for the subjective property of having the physical property that in normal conditions makes something look somewhat blue to UG; in fact, it stands for the physical property that in normal conditions makes something look somewhat blue to UG, which we can suppose to be objective (mutatis mutandis for BG). This is consistent with UG’s attribution χ is green but neither somewhat yellow nor somewhat blue and BG’s attribution χ is green but somewhat blue being true attributions of compatible objective properties. And it suggests an explanation of why “not somewhat blue” in UG’s attribution χ is green but neither somewhat yellow nor somewhat blue and “somewhat blue” in BG’s attribution χ is green but somewhat blue are not contradictory predicates, as “somewhat blue” is postulated to be a priori equivalent with different descriptive predicates in the two cases. But one serious problem with this view is that “somewhat blue” and “has the physical property that in normal conditions makes something look somewhat blue to UG” are not a priori equivalent. It’s imaginable to UG that some things that are somewhat blue are in some way precluded from looking somewhat blue to him in certain conditions he could not have excluded a priori as abnormal.¹⁹ It’s just implausible that the conventions governing a color predicate should stipulate an a priori equivalence between it and a predicate ascribing the association in normal conditions of a certain perceptual quality with a certain property in a particular person, even if this person is the speaker. An account that used some kind of relativization without yielding such equivalences would thus be preferable.

An Account of Reference Fixing for Color Adjectives Gradable adjectives in general are plausibly context-sensitive. A gradable adjective like “hot” or “big” seems susceptible of receiving different referents as a function of the contextual determinants at play, which we can see as ¹⁸ Actually, in McLaughlin’s preferred view, the idea is that the predicate “somewhat blue” when used by UG means something like “has the physical property that in normal conditions makes something look somewhat blue to UG.” One problem with this is that it implies that UG’s predicate “somewhat blue” is objectively modally unstable. McLaughlin is not too worried about this, as he doesn’t take the intuition of objective modal stability to be robust. Another problem is that this view implies that a color predicate like “somewhat blue” means different things in the idiolects of different speakers, which I take to be fairly implausible. But there is another, in my view more basic, problem with all views of this sort, as noted in the text. ¹⁹ This objection is Kripke’s; see Gómez-Torrente (2011). Accounts such as the subjectivist “rigidifying” accounts mentioned above in note 13 are liable to a related criticism.

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196       contextual standards necessary for the interpretation of the adjective relative to its associated dimension or dimensions of variation. On standards appropriate when we are thinking of washing some clothes, the heated water that comes out of the tap counts as hot, but on standards appropriate when we are thinking of scalding a chicken, that same water doesn’t count as hot and even counts as cold. On a set of standards appropriate when I’m thinking of an apartment where I can live with my extended family, the micro-apartment I once occupied in a visit to Seoul counts as not big and even as (very) small, but on standards appropriate when I’m thinking of a short touristic visit to that crowded city, that same apartment counts as big. In the case of “hot” the relevant dimension is probably identical with a physical dimension of temperature, and in the case of “big” the relevant dimension (at least for the case of apartments) is that of area.²⁰ The relevant standards are usually taken to be fixed by contextual aspects of the use of the gradable adjective, fundamentally by the utterer’s generally vague and often merely implicit intentions determining such standards. There are several theories in the literature, but a general feature of these theories is that they imply that in a particular context of use of “hot,” a thermal property gets contextually determined as the content of “hot” by some implicit convention that operates on the contextually determined standards and delivers a corresponding property, which will be constituted in part by those standards.²¹ In my

²⁰ In my presentation in the text I make a fairly non-technical use of the apparatus of standards. It may be good to note, however, that the claims made using this apparatus in what follows are compatible with all of a variety of standard theories in the semantics of gradability and comparison. All these theories analyze gradable predicates as providing mappings of objects into values on suitable scales, which in turn are composed of degrees, or values along a dimension (temperature, area, etc.) ordered in a particular way. When applied in particular cases, a gradable predicate as thus analyzed takes as arguments an object to which the predicate may intuitively apply or not apply, and a contextually determined standard, in such a way that the predicate is said to apply to the object when the value that the relevant mapping assigns to the object is greater than or equal to the standard in the relevant ordering. For examples of views sharing this abstract structure also presupposed in the text, see Bartsch and Vennemann (1972), Bierwisch (1989), Kennedy (2007), and Bale (2011), among many others. (These theories nevertheless differ substantively as to the characteristics of the procedure that yields the contextually relevant standard.) ²¹ These are orthodox assumptions that I again share with the literature alluded to in the preceding note. More specifically, I will be assuming that the reference of a gradable adjective at a context of utterance (of a sentence S containing the adjective) is a property which is partially constituted by standards determined by the context of utterance. This property then partly constitutes a proposition (expressed by S at the context) which is evaluable at indices partly constituted by times and worlds. Though this format is the one I favor for the influence of context on content in the case of standards for gradable adjectives, some of the views in this chapter might conceivably be applied under other formats for such influence explored in the recent literature. (See e.g. Lasersohn (2005) and MacFarlane (2014) for representative examples.) For example, standards might appear along times and worlds as elements of the indices with respect to which the proposition is evaluated; and they might be postulated to be provided by some context different from the context of utterance. Here I cannot fully argue that my orthodox framework is more adequate than other alternatives, but see note 30.

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view, for each gradable adjective there are typically several such conventions that can deliver such properties as contextual referents. For present purposes, it will be enough to focus on conventions of a central sort, which handle assignments of reference in occasions of use where the speaker intends more or less directly some rough minimum or maximum standards along the relevant dimensions of variation.²² In the case of “hot,” this central convention exploits the possibility of intending minimum values in a fixed dimension of temperature²³ and looks like this: Successful reference fixing for “hot” via a minimum temperature. For an occasion of use O, where the speaker S intends to refer with “hot” to the property of having at least the temperature r, “hot” as used by S in O will refer to the property of being a thing with at least the temperature r. (All this subject to the condition that S forms no intention conflicting with his or her intentions concerning the precise minimum temperature r.)²⁴ This convention will determine, in occasions where it applies, that the speaker’s uses of “hot” will refer to a particular thermal property constituted by a particular standard.²⁵ For example, in one appropriate occasion where Successful reference fixing for “hot” via a precise minimum temperature is in operation and the speaker intends, say, the heated water from the tap (with the temperature h, say) to provide the very minimum acceptable standard of hotness, the speaker will refer with “hot” to the property of being a thing having at least the minimum temperature h. An analogous convention of Successful reference fixing for “big” via a precise minimum area holds for “big,” for which similar examples could be given, involving apartments, say. The possibility of different contextual standards is compatible with the objectivity of the properties characterized and constituted by such standards. To begin with, the determinable properties of hotness and bigness are ²² For conventions of other kinds involving gradable adjectives see Gómez-Torrente (2010) and (forthcoming). ²³ In line with the ideas in chapter 5, this dimension of temperature ought presumably to be an ordinary vague dimension, in the sense of that chapter, not one definable in terms of highly fundamental physics. ²⁴ I take it to be clear that, consistently with our general requirements on reference-fixing conventions, this convention can be plausibly said to be accessible to normal competent speakers, and manifested in unsophisticated linguistic behaviors. ²⁵ When this convention applies, there must also be at work overarching meaning restrictions on how the properties referred to by uses in the same context of “hot” and “cold” must be related. Fundamentally, those properties must be incompatible, which imposes, say, the restriction that the contextual minimum value for “hot” must be a value higher than the value that is the maximum value for “cold.”

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198       presumably not constituted by perceptual relations between objects and subjects. Furthermore, the more determinate properties referred to by contextual uses of “hot” and “big” are presumably objective, even if standards of application for “hot” and “big” are somehow selected by subjects (utterers). Moreover, and crucially, these determinate properties are presumably objective even though these standards are often selected by an utterer via intentions formed with the help of perceptual qualities as felt, remembered, or imagined by him.²⁶ For example, the utterer in the just mentioned example involving “hot” may intend the tap water with the temperature h as having the minimum level of hotness because he has felt the temperature that the water has. But this is no obstacle to the objectivity of the selected property: the determinate hotness property referred to by the utterer in such an example presumably consists in the possession of a temperature equal to or greater than h (the value corresponding to the felt temperature), and is thus a property uncontroversially not constituted by perceptual relations. In the case of “big,” a determinate bigness property presumably consists (in an example involving apartments) in the possession of an area that equals or surpasses a particular area, say 70 square meters, and is thus a property uncontroversially not constituted by perceptual relations. And this is so even if speakers can refer to such properties via whatever mechanisms are involved in the fixing of area standards, and even if these mechanisms allow them to fix the relevant standards via appeals to the ways those standards are sensed, remembered, or imagined by them. If the determinate properties referred to by utterances of “hot” and “big” are objective, then it is to be expected that both “hot” and “big” are objectively modally stable. And this is in fact the case. If I am in a context in which the water is not hot according to my minimum washing standard h, and I say If my nerve endings were more sensitive, the water would be hot, what I say sounds false. And in any typical context where I say of a small apartment If my vision were microscopic, this apartment would be big, what I say will equally sound false.²⁷ ²⁶ Often but certainly not always. Nowadays most of us feel comfortable hearing astronomers speak of stars as hot when their temperature is above 10,000 C, and cold when it is below 4000 C (which in usual contexts would count as hot). These standards are intended via theoretical descriptions of those temperatures, not via felt, remembered, or even imagined perceptual qualities. ²⁷ But think of a context in which the water is not hot on my standards for taking a bath. Doesn’t it sound true to say here If my nerve endings were more sensitive, the water would be hot? Maybe, but this is probably due to the fact that here “hot” is used to mean (non-semantically) something like “causing impressions as of heat,” presumably because in this context I’m especially interested in effects on my nerve endings. There are similar examples with “big.” Suppose I’m calmly contemplating a small apartment of a reasonable area, without any very practical purpose in mind such as calculating if my old furniture or my extended family will fit inside, but rather with some vague aesthetic attitude. Then it sounds true to say If my vision were microscopic, this apartment would be big.

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Like “hot” (and “cold”) and “big” (and “small”), also “green,” “blue,” “red,” and “yellow”²⁸ are susceptible of different standards of application along the dimensions of variation presupposed by our use of them, especially hue.²⁹ On some standards, an aquamarine jewel counts as green, but on others it counts as blue. Imagine that you are shopping for a jewel you want to give as a present to a friend who loves all kinds of greenish jewelry. If you ask the jeweler Show me some green jewels, you intend “green” as you are using it to apply both to emeralds and to aquamarine beryl gems of substantively different hues. However, if you are shopping for a jewel for a pickier friend, who likes only the pure greens of the gem stones that you often see in the jewels he wears, then for you given your interests, the aquamarines count as not green and even blue, while the emeralds count as green and not blue. Plausibly, you intend matching standards in the physical dimension of hue, via some seen or remembered perceptual qualities that you take to correspond to those standards. These intentions are again aspects of the context of use of the color adjective, and the corresponding intended standards are presumably constituents of the contextually determined color properties.³⁰ There are of course important differences between the use of contextually set standards for “hot” and their use for “green.” A use of “hot” presupposes

²⁸ Much of what I will say will hold also, with appropriate modifications, for many words for nonunique colors, like “orange,” “olive,” etc. But I will only deal explicitly with terms for the unique colors. ²⁹ It may not be clear that the dimension of variation is the same for “red” and “green,” or for “hot” and “cold.” We wouldn’t normally say that water frozen at 0 C is hotter than water frozen at 10 C, or that tomatoes are redder than geranium leaves. But there is a clear continuity between the corresponding dimensions of variation, and they jointly form all-embracing dimensions. ³⁰ That standards of application are constitutive of the properties referred to by utterances of color and other gradable adjectives is also made compelling by a number of tests for the existence of covert syntactic arguments. Standards for color adjectives arguably pass, e.g., the binding, licensing, and sluicing tests. (See e.g. the useful presentation in Schaffer (2011).) It sounds natural to say At this jeweler’s, you can find something green for all standards of greenness, which suggests a bindable tuple of standards argument projected by “green.” It also sounds natural to say Aquamarines are green on these standards, which indicates that the existence of a tuple of standards argument licenses the explicitation of some such standards; further, “on these standards” is arguably not an optional prepositional adjunct, as naturalness is not preserved when a clear adjunct is interposed: Aquamarines are green when not industrially manipulated, on these standards sounds odd, as opposed to Aquamarines are green on these standards, when not industrially manipulated. Finally, sluicing constructions targeting standards arguments are natural, as in If aquamarines are green, on what standards is this so? By contrast, as Jonathan Cohen has remarked to me, perceiver arguments for color adjectives fail these tests. To use an example of Schaffer’s, to say The stinky cheese is blue, but to whom? sounds odd, which suggests failure of the sluicing test. Cohen says this has led him to abandon his subjectivist account as an account of ordinary color language, and to think of it as a revisionary proposal on which the subjectivist contents of color experience are properly captured. This seems to me to detract from the value of his proposal, for, along with most of the literature on the philosophy of color, I take it to be a natural assumption that experience represents the color properties referred to by color words. (See e.g. Byrne and Hilbert (2003), 4: “it is natural to suppose that there are intimate connections between a certain salient property that tomatoes appear to have, the word ‘red’ and the concept RED; in particular, the word ‘red’ refers to this property.”)

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200       only the setting of contextual standards relative to a single dimension of temperature. The use of “green” requires the operation, however implicit, of standards relative to at least three dimensions—hue, saturation, and brightness. These standards must delimit an interval in the dimension of hue establishing dividing lines between blue and green and between green and yellow, a rough level in the dimension of saturation establishing a dividing line between green and white (or gray or black), and an interval in the dimension of brightness establishing dividing lines between white and (bright) green and between (dark) green and black. Presumably, at least in typical cases, something counts as green in a context when its hue is in the contextual hue interval, its saturation meets at least the contextual saturation minimum value, and its brightness is in the contextual brightness interval.³¹ Thus, analogously to “hot” and “big,” in contexts of use of “green” the particular property that gets contextually determined is presumably determined by one of several conventions that can deliver such properties as contextual referents. For example, the central abstract convention exploiting the possibility of intending directly some minimum and/or maximum values in the dimensions of hue, saturation, and brightness would look like this: Successful reference fixing for “green” via minimum and/or maximum values of hue, saturation, and brightness. For an occasion of use O, where a speaker S intends to refer with “green” to the property of having a hue between or equaling one of the hue values rmin and rmax, a saturation greater than or equal to the saturation value rmin’, and a brightness between or equaling one of the brightness values rmin’’ and rmax’’, “green” as used by S in O will refer to the property of being a thing with a hue between or equaling rmin and rmax, a saturation greater than or equal to rmin’, and a brightness between or equaling rmin’’ and rmax’’. (All this subject to the condition that S forms no intention conflicting with his or her intentions concerning the precise values rmin, rmax, rmin’, rmin,’’ and rmax’’.)³²

³¹ This may be the place to add that I see little justification in recent attempts to argue that color adjectives are sensitive to a contextually filled argument specifying the part of an object that the adjective is intended to apply to (see e.g. Szabó (2001) and Rothschild and Segal (2009)), or that they are semantically ambiguous in some related way (see e.g. Kennedy and McNally (2010) and Hansen (2011)). I cannot go into this here, but let me stress that these proposals have nothing to do with the more established idea that standards for gradable adjectives contextually fill syntactically real arguments. (Perhaps I should also note that I see equally little or less justification in other recent views, such as that in Travis (1994), on which the data that motivate the mentioned proposals raise a challenge to orthodox truth-conditional semantics.) ³² Once more this convention can plausibly be said to be observed by normal competent speakers, and their observance of it to be manifested in simple linguistic behaviors.

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This convention will determine, in appropriate occasions of use, that the speaker’s uses of “green” will refer to particular chromatic properties constituted by particular standards.³³ For example, in one appropriate occasion where Successful reference fixing for “green” via minimum and/or maximum values of hue, saturation, and brightness is in operation and the speaker intends, say, the hues h₁ and h₂ as the minimum and maximum hue values for something to count as green, s₁ as the minimum saturation value, and b₂ and b₁ as the minimum and maximum brightness values, the speaker’s uses of “green” will refer to the property of being a thing with a hue between or equaling h₁ and h₂, a saturation greater than or equal to s₁, and a brightness between or equaling b₂ and b₁. What are the dimensions presupposed by our use of “green” and the other color adjectives? The present account will work under any reasonable answer to these questions, provided we grant two suppositions that will sound plausible to any objectivist: (1) The supposition that the relevant reference-fixing mechanisms manage to determine that the dimensions in question, which we can see as natural dimensions intended as referents for “hue,” “saturation,” and “brightness,” are certain objective dimensions—just as those mechanisms presumably determine that the dimension presupposed by our use of “hot,” “cold,” “warm,” etc. is an objective dimension of temperature, and that the dimension presupposed by our use (in apartment examples, say) of “big,” “small,” etc. is the dimension of area. (2) The supposition that the relevant reference-fixing mechanisms manage to determine that the relation of having a hue value, a saturation value, and a brightness value is objective. The main ideas of the present account will be applicable under any objectivist conception of the dimensions of hue, saturation, and brightness, and of the relation of having values in these dimensions, provided it is a conception that satisfies these suppositions. In this sense, the basic ideas of the present account will be just as abstract as the basic ideas of the objectivist accounts reviewed above.

³³ When this convention applies, there must also be at work some presumable complex meaning restrictions on how the properties referred to by uses in the same context of “green,” “blue,” “yellow,” etc. are to be related. Fundamentally, the properties referred to by “blue” and “yellow” must be incompatible, as must be the properties referred to by “red” and “green”; the property referred to by “green” can be compatible with the property referred to by “blue” and the property referred to by “yellow,” but it may also be compatible with just one of these, or with neither (in contexts where “green” is intended to stand for the same property as “green but neither somewhat yellow nor somewhat blue”); and so on. This imposes the restriction that the standards for “blue” and the standards for “yellow” must delimit disjoint hue intervals, and likewise for “red” and “green”; that the standards for “green” in a context can in principle delimit a hue interval that overlaps the interval delimited by the hue standards for “blue,” or the interval delimited by the hue standards for “yellow,” or both, or neither; and so on.

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202       This is not to say that we cannot make some reasonable conjectures as to the nature of the dimensions of hue, saturation, and brightness, and as to the nature of the relation of having values in these dimensions. The dimensions in question must be closely related to the colorimetric dimensions of dominant wavelength, purity, and luminance factor, though literally understood these ultimately qualify as subjective dimensions, for they are defined by reference to perceivers. One objectivist possibility, though a rather artificial one, is to identify, e.g., the hue dimension with the dimension of values singled out by the notion of dominant wavelength, taken as a purely extensional function from types of light to real numbers, and similarly for saturation and purity, and for brightness and luminance factor.³⁴ There are less artificial possibilities, however, as it’s not so difficult to define in objective physical terms functions with values in approximate correlation with the standard colorimetric dimensions. On the other hand, for a thing to “have” a particular hue value (and a particular saturation value, and a particular brightness value) may just be for the thing to have the disposition to irradiate light with precisely the corresponding values in the appropriate objective dimensions, in the condition of illumination which is typical or paradigmatic for that thing, which may be fairly vaguely specified. My guess, in line with the ideas of chapter 5, is that the appropriate chromatic dimensions will be suitable ordinary dimensions related to those physical functions, but not definable exclusively in terms of fundamental physics; and that the appropriate relation of having values in these dimensions will be the relation of having the disposition to irradiate light with the corresponding values in these dimensions.³⁵ As already noted, and again analogously to the case of “hot,” in the case of “green” the contextual dividing lines in the dimension of hue between blue and green and between green and yellow, the contextual level in the dimension of saturation establishing a dividing line between green and white (or gray or black), and the contextual dividing lines between white and (bright) green and between (dark) green and black (all generally vaguely and often merely implicitly intended by the utterer in a context of use of “green”) will typically be set by the utterer with the help of some seen, remembered, or imagined

³⁴ Perhaps this purely tabular understanding provides the way some philosophers of color and color scientists actually understand the colorimetric dimensions. ³⁵ One motivation for this set of hypotheses comes from the suspicion that it compares favorably to reflectance proposals as an account also of the contents of color experiences. It’s implausible to suppose that color experience represents the full spectral reflectance information of an object (let alone the full information concerning its possession of one of the reflectances in a complex set of reflectances). By contrast, I see great plausibility in the hypothesis that a color experience represents an object as having values in certain intervals in the chromatic dimensions, as mentioned in note 44.

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chromatic perceptual qualities. The intention to fix the relevant standards as those corresponding to the perceptual qualities the utterer has in mind is again a contextual aspect that together with the reference-fixing conventions for “green” fixes a fairly determinate chromatic property as the reference of “green” in the context. But crucially, these determinate properties are presumably objective even if the standards set by an utterer are often selected via intentions formed with the help of perceptual qualities. For example, the utterer may implicitly intend the contextual reference of “green” to be fixed by “the property of having a hue of the color green between these, a saturation of at least this, and a brightness between these,” where the demonstratives pick out hue, saturation, and brightness values via a deferred demonstration in which the directly demonstrated things are certain remembered qualities. But this is presumably no obstacle to the objectivity of the selected property. The determinate greenness property referred to by the utterer in the example above, e.g., presumably consists in the possession of an objective hue value between (or equaling one of) the two hue values the utterer fixes on (h₁ and h₂), an objective saturation value greater than or equal to the minimum saturation value the utterer fixes on (s₁), and an objective brightness value between (or equaling one of) the two brightness values the utterer fixes on (b₂ and b₁) (whatever the objective hue, saturation, and brightness dimensions turn out to be). This is thus a property that (under basic objectivist assumptions) is not constituted by perceptual relations.

Perceptual Variation and the Referents of Color Adjectives Now that we have a fairly developed (if abstract) picture of reference fixing for (utterances of) color adjectives, we can begin to see how it throws light on intersubjective variation arguments for the subjectivity of the contents of color language. In order to see this, it’s heuristically useful to construct and consider first a perceptual variation argument analogous to the argument above but about hotness and coldness. We could conduct the following experiment on a large group of subjects, all with unimpaired thermal perception on any reasonable criteria. We would present them with several objects of different temperatures around 33o C (roughly the average temperature of the human skin); and we would ask them to touch the objects and point to the one that is thermally neutral, i.e. the one that is (closest to being) neither somewhat cold nor somewhat

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204       hot, and classify the others as either somewhat hot or somewhat cold. The answers will predictably vary a great deal,³⁶ to all appearances as a function of a number of intersubjective physiological variations, including minute differences in the activation thresholds of the coldness and hotness thermoreceptors of the subjects.³⁷ It seems natural to suppose that, if ψ is an object that a normal subject N perceives and classifies as neither somewhat hot nor somewhat cold, and another normal subject H perceives and classifies as somewhat hot and not somewhat cold, then either both N and H have veridical perceptions of ψ and make true attributions about it or both have erroneous perceptions and make false attributions. If the latter, then an eliminativist theory must hold. If the former, H must perceive and implicitly classify ψ as something like feeling somewhat hot and not somewhat cold to H and N as feeling neither somewhat hot nor somewhat cold to N.

Presumably this thermal perceptual variation argument will not shake the view, by now apparently the majority view, that thermal properties are objective. Why? The reason will certainly not be that most philosophers will be inclined to embrace an (objectivist) eliminativist theory or a theory that at most one of N and H is right. Nor will it be that philosophers will suppose that “hot” is a priori equivalent with “feels hot to me” in N’s and H’s idiolects. I submit that the reason why this argument will not impress objectivists about thermal properties will be captured by the account of reference fixing for thermal adjectives sketched above. A thermal adjective is susceptible of being used by an utterer together with default (implicit) intentions determining contextual standards for the adjective which may diverge from the standards fixed on by default (vaguely and implicitly) by another person, including listeners of that utterer. It is this fact that makes certain superficially incompatible attributions involving complex thermal predicates composed by thermal adjectives compatible, and also compatible with objectivism. Let’s see this in a bit more detail, drawing on the account above. Suppose, as is reasonable, that the property referred to by an utterance of “(somewhat) hot” in the context of the imagined experiment is picked on the ³⁶ “Predictably,” because a variety of experiments have shown that there are robust, wide intersubjective variations in thermal sensation thresholds even among subjects who have unimpaired thermal perception on any reasonable criteria. (It may be noted that the differences are so wide in normal subjects that they cannot be attributed to differences in capacities for thermal discrimination, which are very fine-grained in subjects with unimpaired thermal perception.) See e.g. Fruhstorfer et al. (1976) and Harju (2002). ³⁷ Coldness thermoreceptors seem to be the free endings of thin myelinated (Aδ) fibers, and hotness thermoreceptors the free endings of unmyelinated (C) fibers (see e.g. Brodal (2010), 169).

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basis of an application of Successful reference fixing for “hot” via a minimum temperature.³⁸ This is reasonable, in particular, because the subjects are essentially asked to use a minimum temperature as a standard, a temperature that the utterer will think of via a felt, remembered, or imagined perceptual quality. And similarly for “(somewhat) cold.” N’s attribution of the complex predicate “is neither somewhat hot nor somewhat cold” is presumably made as he implicitly fixes on a set of default standards that he thinks of via certain remembered perceptual qualities of “minimal hotness” and “minimal coldness.” But what standards correspond to these qualities in N’s perception is something determined by peculiarities of N’s thermoceptive apparatus, in particular by the specific tuning of his thermoreceptors. The default standards for “hot” and “cold” that correspond to the qualities of “minimal hotness” and “minimal coldness” are simply the activation thresholds t₁ and t₂ of N’s hotness and coldness thermoreceptors: t₁ is the minimum temperature a thing must have to feel hot to N (and below which a thing does not feel hot), and t₂ is the maximum temperature a thing must have to feel cold to N (and above which a thing does not feel cold). The temperature t of ψ that N feels as neither somewhat hot nor somewhat cold will then be precisely between t₁ and t₂. (See Fig. 6.1.) So the property picked out by N’s use of “(somewhat) hot” will be the property of having at least the temperature t₁; and the property picked out by N’s use of “(somewhat) cold” is the property of having at most the temperature t₂. And by simple compositionality and intuitive meaning restrictions, the property picked out by N’s use of “neither somewhat hot nor somewhat cold” will be the property of having a temperature between t₁ and t₂. Given N’s default standards, then, ψ counts as neither (somewhat) hot nor (somewhat) cold, and N’s attribution is true.³⁹ ³⁸ I will assume that “somewhat” is a “vacuous” modifier, in the sense that it doesn’t affect the extension of a gradable adjective it modifies, though its use will often pragmatically convey something beyond the satisfaction conditions of the adjective. If we say that something is somewhat hot, we typically mean that it’s not very hot. Similarly, with Some philosophers from the university protested against budget cuts we say the same as with Philosophers from the university protested against budget cuts; but we would avoid saying either of those things if we could have said All the philosophers from the university protested against budget cuts. If I say Some philosophers from the university protested against budget cuts: all did, I’m not contradicting myself. Similarly, if I say This is somewhat hot: it is very hot, I’m not contradicting myself. Alternatively, “somewhat” might be treated as non-vacuous, as “very” often is: an object counts as “very hot” in a context when its temperature is not only at least the minimum temperature contextually intended for “hot,” but also above some other higher standard contextually associated with “very” (see e.g. Kennedy and McNally (2005)). On a treatment of this sort, the semantics of “somewhat” would require the introduction of further standards, in this case of closeness to the thermally neutral. In any case, the account in the text could be straightforwardly adapted to this more complex semantics. ³⁹ Note that the predicate “is neither somewhat hot nor somewhat cold” (or equivalently, the adjectival predicate “is thermally neutral”) is not a gradable predicate, but still its conditions of application and its extension obviously vary as a function of the standards of application for the

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t2

t

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t1 hot

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t4 cold

t3

t2

t

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Fig. 6.1 N’s and H’s standards along the dimension of temperature.

In H’s case, by contrast, the set of standards fixed on by default is induced by H’s thermoceptive apparatus, which again surely determines his default intentions concerning minimal hotness and coldness. Here the standard that is the minimum temperature a thing must have to count as (somewhat) hot is a rough level t₃ below t₂, t, and t₁; and the standard that is the maximum temperature a thing must have to count as (somewhat) cold is a rough level t₄ slightly below t₃. (See again Fig. 6.1.) So the property picked by H’s use of “somewhat hot” is the property of having a temperature greater than or equal to t₃, and the property picked by H’s use of “somewhat cold” is the property of having a temperature lower than or equal to t₄. And by simple compositionality and intuitive meaning restrictions, the property picked out by H’s use of “somewhat hot and not somewhat cold” is the property of having a temperature greater than or equal to t₃. On H’s default standards, then, ψ counts as (somewhat) hot and not (somewhat) cold, and H’s attribution is true. As advanced above for the case of many simple adjectives, the hotness properties that this account assigns to thermal adjectives and to many predicative expressions composed of them are obviously objective, even though the properties can be different for (utterances of) subjects with different default intentions determining different default standards, as illustrated in the case of N and H. A further key to seeing why the picture is not some kind of “thermal subjectivism” is appreciating the distinction between adjectives or predicates (or utterances thereof) referring to subjective properties and

adjectives that compose it. For another example of non-gradability accompanied by dependence on standards induced by the dependence on standards of the composing adjectives, compare the predicate “is neither big nor small.”

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adjectives or predicates that merely get to refer to certain (objective) properties as a function of aspects of the occasion of use which may be prompted in turn by peculiar properties of subjects (e.g. through default contextual intentions involving certain perceptual qualities). The latter adjectives or predicates are simply ones such that for some object o and some contexts c, c’, o has the property referred to in c but fails to have the property referred to in c’. An indication of the objectivist nature of the account is that this is compatible with “hot,” “cold,” “neither hot nor cold,” etc. being objectively modally stable, as opposed to the prediction of an (unsophisticated) subjectivist account on which (an utterance by H of) “hot,” say, refers to something like the property of feeling hot to H. Given any context c, there are not two different worlds w and w’ which are the same as to the objective properties of o but are such that o has the property of having a temperature greater than or equal to the contextually set standard with respect to (c, w) but fails to have it with respect to (c, w’). It may be good to stress again at this point that N and H do fix on different standards for “hot” and “cold,” even if in a certain purely phenomenological sense they might have been loosely said to intend “the same standards”: N and H both intend to call “hot” those things which feel hot, and presumably the “hotness feeling” is phenomenologically the same for both. But this is indeed only a loose criterion for identity of standards. The present account, like usual theories of standards for gradable adjectives, takes these standards to yield values in certain objective dimensions which need not be the immediate phenomenological dimensions used in reference fixing: in appropriate cases, for example, N (implicitly) intends to use “hot” for the property of having at least this temperature, where “this temperature” refers to a degree t₁ that N is disposed to think of via the remembered phenomenological quality (of “minimal hotness”) that he takes to correspond to that degree; by contrast, H intends to use “hot” for the property of having at least this temperature, where “this temperature” refers to a degree t₃ different from t₁ even if H is disposed to think of it via the same phenomenologically felt quality (of “minimal hotness”) that N associates with t₁. Given these intentions, N and H fix on different objective standards for “hot,” even if in some way they form their corresponding intentions with the help of the same remembered quality. It may also be good to stress at this point that the objective standards that speakers fix on for “hot” and “cold” need not be publicly available, or be part of a “context” understood as an already publicly available common ground. The notion of contextual determinant at play is a Kaplanian one on which such things need not be immediately publicly available, in the same way in which

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208       (as argued in chapter 2) the referent of an utterance of a demonstrative need not be immediately publicly available. Of course, if there is to be successful communication between N and H (and between each of them and the experimenter or other language users) they will each have to guess in some way which thermal properties and consequently which objective standards the other intended. But these guesses of standards, of referential intentions, and, in general, of contextual determinants and of contextual aspects fixing the referents of context-sensitive words, need not always be successful, and may be prevented by false beliefs of several kinds.⁴⁰ Now, an account analogous to this account of superficially incompatible thermal attributions can also be reasonably given in the case of superficially incompatible color attributions. The property referred to by an utterance of, say, “(somewhat) green” in a context may, for example, be implicitly picked on the basis of the convention of Successful reference fixing for “green” via minimum and/or maximum values of hue, saturation, and brightness.⁴¹ This will happen through the utterer’s implicit association of his utterance with a couple of objective hue values, an objective saturation value, and a couple of objective brightness values. Such an association will typically occur as the values are associated in the utterer’s perception with certain sensed, remembered, or imagined chromatic perceptual qualities. And similarly for “(somewhat) blue,” “(somewhat) yellow,” etc. (For the sake of brevity and perspicuity, I will henceforth often omit mention of saturation and brightness, supposing, as will typically be the case, that the truth or falsity of the color attributions we are interested in depends just on hue values—saturation and brightness values being assumed to be fixed and irrelevant to the question.) Second, turn to the UG and BG case—a case where we can again reasonably suppose that Successful reference fixing for “green” via minimum and/or maximum values of hue, saturation, and brightness is in operation, with

⁴⁰ Elsewhere I have shown that the case of intersubjective perceptual variation in linguistic thermal and color classifications, as well as other cases involving context-sensitive expressions, involve in some special cases interesting obstacles to the correct guessing of contextual determinants and thus of contextual content. See Gómez-Torrente (2016), section 4. ⁴¹ Again I am assuming that “somewhat” is a “vacuous” modifier (see note 38), but again the account in the text could be easily adapted to a more complex semantics. On an alternative view, “somewhat” would be treated as a non-vacuous modifier like “very”: something should count as “very green” in a context when its degree in the dimension of hue levels is not only between (or equaling one of) the standards contextually intended for “green,” but also between (or equaling one of) some other standards closer to unique green and contextually associated with “very” as applied to “green.” (Closeness to unique green should also provide the key element in the truth conditions of comparative color statements; at least for things a, b which are both bluish green or both yellowish green, a is greener than b when a’s hue degree is closer to unique green than b’s. See Hansen (2017a) and (2017b) and Gómez-Torrente (2017) for discussion.)

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saturation and brightness values assumed to be fixed over the relevant universe of discourse. Just as utterers’ default standards in the thermal case were induced by thermoreceptoral activation thresholds, UG’s default intentions to fix standards, and thus the standards themselves, are presumably induced by his visual apparatus, and in particular by the idiosyncratic absorption curve of his cones. In his case the hue value h of χ is precisely between the “lower” hue standard h₁ for “yellow” from which things start looking (somewhat) yellow to UG and the “upper” hue standard h₂ for “blue” from which things start looking (somewhat) blue to UG;⁴² and all these standards lie between the two contextual hue standards, h₃ and h₄, for “green.” (See Fig. 6.2.) So the property picked out by UG’s use of “(somewhat) yellow” is a property consisting in part in the possession of a hue value of at least h₁, the property picked out by his use of “(somewhat) blue” is a property consisting in part in the possession of a hue value of at most h₂, and the property picked out by his use of “green” is the property of having a hue value between the hue values h₃ and h₄. And by simple compositionality and intuitive meaning restrictions, the property picked out by UG’s use of “green but neither somewhat yellow nor somewhat blue” is the property of having a hue value between h₁ and h₂. So, in context, UG’s attribution is true.⁴³ By contrast, BG’s attribution is made as he implicitly intends default hue standards induced by his visual apparatus, by the idiosyncratic absorption curve of his cones. This is such that the hue value h of χ is below the “upper” hue standard h₅ for “blue” from which things start looking (somewhat) blue to BG, below the “lower” hue standard h₆ for “yellow” from which things start looking (somewhat) yellow to BG, and finally also between the two contextual hue standards, h₇ and h₈, for “green.” (See again Fig. 6.2.) So the property picked out by BG’s use of “(somewhat) yellow” is a property consisting in part in the possession of a hue value of at least h₆, the property picked out by his use of “(somewhat) blue” is a property consisting in part in the possession of a hue value of at most h₅, and the property picked out by his use of “green” is the property of having a hue value between the hue values h₇ and h₈. And by ⁴² Since the hues presumably constitute a circumference, talk of “lower” and “upper” standards is strictly speaking misleading, even if it is clear what is meant when only the non-purple hues are involved. More exactly expressed, and assuming that in the hue circumference the blue, green, yellow, and red hues appear in this order in clockwise direction, the idea is that h₁ is the initial standard for “yellow” in this direction, and that h₂ is the initial standard for “blue” in counterclockwise direction. Mutatis mutandis for the standards mentioned later. ⁴³ Much as before, it may be noted that the predicate “is green but neither somewhat yellow nor somewhat blue” (or equivalently, the adjectival predicate “is unique green”) is not a gradable predicate, but still its conditions of application and its extension obviously vary as a function of the standards of application for the adjectives that compose it.

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210      

h4

h2 h h1 blue

h3

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h h5 h6 blue

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Fig. 6.2 UG’s and BG’s standards along the dimension of hue.

simple compositionality and intuitive meaning restrictions, the property picked out by BG’s use of “green but somewhat blue” is the property of having a hue value between h₅ and h₈. So, in context, BG’s attribution is true. Just as in the thermal case, no implication that the relevant properties must be subjective is warranted, provided we grant our assumption that the dimension of hues is objective and that the relation of having a certain hue is also objective.⁴⁴ As in the thermal case, it may be good to stress that UG and BG do fix on different standards for their color adjectives and the complex color predicates composed of them, even if in a loose sense they might be said to intend “the same standards”: UG and BG both intend to apply “green but neither somewhat yellow nor somewhat blue” to those things which look green and do not look yellow or blue at all, and presumably the looks of the green that is neither somewhat yellow nor somewhat blue are the same for both. However, UG intends to refer with “green but neither somewhat yellow nor somewhat blue” to the property of having a hue value between this and that, where this hue ⁴⁴ The present account of the contents of color language suggests also an account of a relevant part of the contents of color experiences, an account that I think is also susceptible of independent motivation. On this account, a typical color experience represents at least some objective chromatic properties, including the properties that are the contents of color expressions in the typical color attributions that could be made by the experiencer on the basis of the experience. The account postulates, in particular, that a color experience by a typical perceiver represents an object as lying on certain hue intervals—that if I am a typical perceiver, I see an object not merely as occupying a particular hue locus, but also as occupying a locus between, or above, or below certain other significant hue loci (mutatis mutandis for the other dimensions). See Gómez-Torrente (2016), section 5, for details.

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value is a value h₁ that UG is disposed to think of via the remembered phenomenological quality (of “greenness with minimal yellowness”) that he takes to correspond to that value, and where that hue value is a value h₂ that UG is disposed to think of via the remembered phenomenological quality (of “greenness with minimal blueness”) that he takes to correspond to that value. By contrast, BG intends to refer with “green but neither somewhat yellow nor somewhat blue” to the property of having a hue value between this and that, where this hue value is a value h₆ different from h₁ that BG is disposed to think of via the same remembered phenomenological quality (of “greenness with minimal yellowness”) that UG associates with h₁, and where that hue value is a value h₅ different from h₂ that BG is disposed to think of via the same remembered phenomenological quality (of “greenness with minimal blueness”) that UG associates with h₂. Given these intentions, UG and BG fix on different objective standards determining different properties and extensions for “green but neither somewhat yellow nor somewhat blue,” even if they do so via the same remembered qualities. Let me conclude this chapter by offering some further support for the present account, observing how it respects the desiderata violated by the objectivist theories mentioned in the second section of this chapter. First, the account does respect the impression that all the attributions involved in the eliminativist/subjectivist intersubjective perceptual variation argument are true, unlike the accounts of Byrne and Hilbert and Tye. And it does so respecting objectivism too. The fact that what is responsible for the truth of UG’s and BG’s attributions is the implicit operation of two sets of contextually intended standards, ultimately induced by peculiarities of the visual apparatuses of the two subjects, doesn’t imply the subjectivity of the properties they refer to, just as the fact that “hot” and “big” apply or fail to apply under the operation of (sets of) standards somehow selected by (and in some cases induced by peculiarities of the perceptual apparatuses of) subjects doesn’t imply that the properties referred to by (utterances of) “hot” or “big” are subjective. Note also that on the present account neither UG nor BG (nor the experimenter) makes any mistake, either purely linguistic or factual, when offering their classifications; they just set their standards via their default referential intentions, as they surely are allowed to do by the reference-fixing conventions for context-sensitive adjectives. Second, the account respects the desideratum that Kalderon’s abstract account did not deal with. “Not somewhat blue” in UG’s attribution χ is green but neither somewhat yellow nor somewhat blue and “somewhat blue” in BG’s attribution χ is green but somewhat blue do refer to compatible

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212       properties in virtue of a relativization having to do with contextual effects. Since the standards involved are different in the two cases, “somewhat blue” in UG’s attribution and “somewhat blue” in BG’s attribution stand for different chromatic properties. Hence there is no problem in holding that “not somewhat blue” in the first attribution and “somewhat blue” in the second are not contradictory.⁴⁵ Third, unlike the account viewed favorably by McLaughlin, on which UG’s predicate “is (somewhat) blue” is a priori equivalent with the reference-fixing descriptive predicate “has the physical property that in normal conditions makes something look (somewhat) blue to UG,” the present account is compatible with the absence of a priori connections between being of a certain color and looking that color to a particular person. A speaker may implicitly rely on a reference-fixing convention for “(somewhat) blue” and on some referential intentions ultimately determining some hue standards corresponding to perceptual qualities produced in him. But this doesn’t require it to be a priori that these qualities are associated with the corresponding property in the utterer’s perception, even in normal conditions (though they may be so associated as a pure matter of fact). Reference fixing via a reference-fixing convention will be successful when some feasible values working as hue standards do actually correspond to the perceptual qualities intended by the utterer in context; but the existence of the correspondence need not be a priori for the mechanism to work. The upshot of this chapter is that what appear to be the main recent considerations for subjectivism or eliminativism about color words—and by extension about the words for other properties traditionally regarded as “secondary qualities”—don’t create fatal trouble for an objectivist, noneliminativist view of the referents of those words. In particular, this moderately large linguistic domain is, like others we have surveyed before, safe from the eliminativists’ assaults on reference, at least for now.⁴⁶

⁴⁵ And in particular, no problem in doing this without denying that both are predicates that apply to χ, as in Cohen’s half-hearted supplement to Kalderon’s theory. ⁴⁶ A part of this chapter is based on a part of Gómez-Torrente (2016). The reader is referred to this paper for consideration of a good number of additional issues surrounding the proposal in this chapter.

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7 Concluding Notes The Strongest Reasons for Anti-Descriptivism, and Its Proper Reach By way of conclusion, it is worthwhile revisiting two of the main themes of this book, from a synoptic perspective now available after the more analytic expositions in the previous chapters. The first theme concerns the right picture of the reasons for a broadly antidescriptivist conception of reference fixing in the case of demonstratives, proper names, and nouns for natural kinds. Now one issue is the issue of in what cases are descriptivist and anti-descriptivist reference-fixing procedures applied across the field of expressions considered in the book, which can probably be taken as in many ways representative of the field of linguistic expressions in general. The analyses in the previous chapters confirm the Kripkean diagnosis that the reference of some expressions or expression uses is essentially fixed in a descriptive way, while the reference of many typical and abundant cases or uses of some central expressions is fixed non-descriptively, that is in virtue of mechanisms which do not require the existence of a correct description of the eventual referent taken as reference-fixing in the mind of a user. But we have provided some novel reasons why descriptivism does not provide the right picture of typical cases, reasons which serve also to vindicate Kripke’s evident but practically unargued skepticism about the possibility of providing a theory of necessary and sufficient conditions for reference. Descriptivism as a theory of reference fixing for proper names and nouns for natural kinds has stayed alive even after Kripkean and post-Kripkean criticisms. This has been largely because of the suggestion of “causal descriptivists,” that the conventions for successful name and kind noun introduction and transmission, which presumably underlie Kripkean intuitions, can be represented in a description that identifies the referent of a particular use of a proper name or kind noun and that is knowable by a typical competent speaker. However, we have seen, especially in chapter 3, that we cannot expect a “causal description” to exist that correctly identifies in general and in a knowable way the referent of an arbitrary use of a proper name. This cannot be

Roads to Reference: An Essay on Reference Fixing in Natural Language. Mario Gómez-Torrente, Oxford University Press (2019). © Mario Gómez-Torrente. DOI: 10.1093/oso/9780198846277.001.0001

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214   expected because, even if typical competent speakers know somehow the name introduction and transmission conventions, we cannot expect to have a knowable set of necessary and sufficient conditions for reference that puts together the cases where there is conventionally determined reference failure and the cases where no reference or reference failure is determined by any relevant convention. The latter cases will be cases of reference failure as well, but they need not be, and are not, known to be such by typical competent speakers. The existence of examples of referential indeterminacy in the case of names and nouns for natural kinds suggests strongly that the extant conventions for name and natural kind noun reference and reference failure are not codifiable into a suitable knowable description, and form instead sets of conventions stating roughly sufficient conditions for reference and reference failure. For if the relevant conventions adopt this form, then the existence of many cases left undecided by the conventions is naturally explained. As a bonus, we get then a reason for reaffirming Kripke’s skepticism about theories of necessary and sufficient conditions for reference. Such skepticism was quite justified if, as argued in the previous chapters, the natural view of the relevant conventions is as sets of sufficient conditions for reference and reference failure. While the possibility of a set of necessary and sufficient conditions for name reference, which could be turned into a knowable “causal descriptivist” reference-fixing description, was not fully excluded by his considerations, as he himself emphasized,¹ the present picture and the support it receives from cases of referential indeterminacy confirm Kripke’s suspicion that the possibility was an unlikely one. Another nice implication of the consideration of cases of referential indeterminacy is that it recommends a broadly unified picture of the conventions of reference fixing for names and demonstratives. It has been standard to suppose that, even if descriptivism is not right in the case of names, it has to be ¹ The reader may recall footnote 38 of Naming and Necessity, where Kripke says: As Robert Nozick pointed out to me, there is a sense in which a description theory must be trivially true if any theory of the reference of names, spelled out in terms independent of the notion of reference, is available. For if such a theory gives conditions under which an object is to be the referent of a name, then it of course uniquely satisfies these conditions. Since I am not pretending to give any theory which eliminates the notion of reference in this sense, I am not aware of any such trivial fulfillment of the description theory and doubt that one exists. (Kripke (1972), 88) Nozick’s remark of course applies whether the available theory of the reference of names is spelled out in terms of the notion of reference or not. Kripke is especially skeptical of the possibility that one can give an appropriate theory that does not use any notion of reference, including the notion of personal reference or of intending to refer. But even the possibility of a knowable theory of necessary and sufficient conditions for name reference stated in terms of a personal notion of reference or of referential intentions appears unlikely in view of the considerations of the previous chapters.

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right in the case of demonstratives, uses of which presumably have their referents fixed by simple principles governing the mechanism of ostensions which yields those referents. If the considerations in chapter 2 are right, however, descriptivism must be the wrong conception of reference fixing even in the case of demonstratives, and the right picture must again be one involving a set of rough sufficient conditions for reference and reference failure of demonstratives’ uses, a set having no implications concerning cases of indeterminacy. Occasionally one gets the impression from writers in the tradition of the “new theory of reference” (though not from Kripke) that they believe that antidescriptivist arguments by Kripke and others establish that nothing in the mind of speakers can in any sense fix the reference of proper names not introduced descriptively (though, as noted, the usual view, even among these writers, is typically different for the case of demonstratives). But if they believe this, I think they have gone wrong. What shows itself to be true when one pursues natural Kripkean lines of thought is that no accessible description can do the job of generally singling out the referent of a proper name in the linguistic repertoire of a typical competent speaker (and similarly in the case of demonstratives). This doesn’t exclude the possibility that the set of conventions for name reference that that speaker has access to does imply, together with relevant and often highly complex and unknowable historical facts, that a name she borrowed from others has the reference it has or that it fails to have a referent; in fact, it’s very plausible to think that in many cases this will just be so. But even if this is so, a typical competent speaker doesn’t know, of any reference-fixing material that is somehow in her mind, that that material provides necessary and sufficient conditions for a typical name in her repertoire to have the reference it has. This is a strong enough anti-descriptivist conclusion.

The Referents at the End of the Roads The second main theme of the book that we will revisit here by way of conclusion concerns the connection between the theory of reference fixing and the determination of the exact natures of the referents fixed or purportedly fixed for natural language expressions (including especially expressions discussed, either centrally or in supporting roles, in the theory of reference). The theory of reference fixing is inseparable from metaphysical and epistemological considerations. Kripke’s modal and epistemic arguments against

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216   descriptivism are just one example of this. Another example of the metaphysical involvement of the theory of reference brought out by Kripke (and Putnam) is provided by their claims that the reference-fixing conventions governing ordinary kind nouns such as “water” or “tiger” determine for them referents that are also singled out by highly precise scientific descriptions, such as “H₂O” and “species with the genome GenT.” Yet other, but now negative examples are provided by claims, such as those mentioned in chapters 4 and 6, that epistemological and metaphysical considerations preclude the fixing of real referents for numerals and color terms—claims that have been opposed by Kripke among others. In this book, I have sought to follow the principle that the theory of reference should provide a series of views about reference fixing that is congenial with what I have called “the natural conception of human endeavors and accomplishments concerning truth.” This is essentially the natural view that truth (and falsehood) are pervasive in our languages and that our languages are thus not plagued by widespread failures of reference. A view of reference fixing congenial with this natural conception must thus provide a picture consistent with the possibility that our linguistic and epistemic capacities and dispositions do determine referents for most terms in important areas of our languages. But there are significant challenges to this project, such as the mentioned epistemological and metaphysical challenges to the natural impression that numerals and color terms must have referents of some kinds, and some notably deep challenges, reviewed in chapter 5, to the mentioned Kripke-Putnam view that science provides precise structural biochemical, chemical, or physical descriptions of the referents of ordinary kind nouns like “water” or “tiger” (such as “H₂O” and “species with the genome GenT”)— which are also in fact challenges to the view that the conventions governing reference fixing for ordinary natural kind nouns can provide any referents for them at all. A common recipe for resisting these challenges involves the realization that the referents singled out for the expressions in question by their referencefixing conventions need not be, and in fact presumably are not, identifiable in exclusively precise scientific terms, or otherwise extra-ordinary terms. In the case of nouns for natural kinds, the deepest challenges reviewed in chapter 5 arise because an initial baptism for such a noun doesn’t appear to manage to identify a unique precise scientific kind among the many ones involved in the relevant paradigms. For example, a Kripke-Putnam baptism for “water” doesn’t appear to discriminate between H₂O and P₂O (H₂O where the isotope of hydrogen involved is protium oxide, as in regular paradigms of water),

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making arbitrary any idea that H₂O rather than P₂O is the kind fixed as referent for “water.” On our refinement of the Kripke-Putnam picture, which involved again appeal to sets of rough sufficient conditions for reference and reference failure, the referents of ordinary natural kind nouns such as “water” turn out to be what I called “ordinary kinds,” kinds which are not as precise as extremely precise scientific kinds and which are vague along dimensions along which such scientific kinds are precise. The reference of “water,” for example, turns out to be “the ordinary kind water,” the kind of the things not too different from the paradigms as regards the necessary properties of the latter— rather than H₂O or other precise scientifically identified kinds. This is enough to dispose of the deep arbitrariness challenge on a broadly Kripkean view. That a view along these lines must be the correct view of the reference of ordinary natural kind nouns is suggested with special force by the amply confirmed Kripkean thesis of the analogy between proper names and ordinary natural kind terms. While there are apparently no substantive dissimilarities between the reference-fixing conventions for ordinary natural kind terms and for proper names, no requirement that the referents of proper names be objects identified by precise structural biochemical, chemical, or physical descriptions is imposed by Kripke (or Putnam) or perceived by him as emerging from considerations on the reference-fixing mechanism for names. (And consequently no significant arbitrariness worry has emerged in the literature concerning the referents fixed for proper names.) In fact, on the most natural view, the objects that we take intuitively as referents of typical proper names (and of typical uses of demonstratives), such as persons, cities, rivers, etc., do not respond to descriptions taken from precise structural biochemistry, chemistry, or physics, and are instead objects whose identity conditions are vague along dimensions along which objects describable exclusively in precise structural biochemical, chemical, or physical terms would be precise. That this is the natural view is in fact supported by a number of arguments in the metaphysical literature on ordinary objects, to which we added some novel considerations in chapter 5. It is therefore also natural to postulate that the referents of ordinary natural kind nouns have similarly vague identity conditions along dimensions picked out by precise structural biochemistry, chemistry, or physics, even if on this point Kripke didn’t heed his own suggestion that the cases of ordinary natural kind nouns and proper names are analogous. The case of color terms greatly worried Kripke, but he did not reach a definite view on the nature of their referents. A widely popular argument for the view that these terms lack referents is based on the fact that different

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218   normal speakers give apparently incompatible classifications of the same chromatic stimulus in the same physical conditions of observation. If A calls a stimulus s “red, without trace of yellow” and B calls it “orange,” then (the argument goes) there is nothing that their color terms really refer to, in particular there is no precise physical property of s that either A or B is pointing to—and their attributions are both false or truth-valueless. Noneliminativist responses have often adopted implausible forms, e.g. in the proposal that a color term does pick out a precise physical property, such as the possession of a reflectance in a certain complex set of reflectances, and one of A and B is simply wrong, for reasons that are epistemically opaque. On the view defended in chapter 6, the kind of reasoning behind the eliminativist argument overlooks the fact that ordinary color terms have in part the role of making possible classifications of stimuli that will vary as a function of the particular perspective of the speaker, and do not seek to categorize them ascribing to them an absolute property, physical or otherwise. And proposals such as the reflectances theory involve us not just in the mystery of why some particular precise set of precise reflectances should be picked out as the referent of a color term, but also in the mystery of why some normal speakers classify correctly according to this referent and others don’t. By contrast, on the picture proposed in chapter 6, the relevant referencefixing conventions fix the referents of color terms as properties that ascribe to stimuli the possession of values in appropriate intervals in the chromatic dimensions, especially that of hue. These dimensions are again not exactly identifiable with dimensions describable in extremely precise terms of fundamental physics, but correspond to physical dimensions and are fully objective. That such dimensions are involved allows color terms to be used with different intended standards in different contexts provided by different perspectives, and this explains the possibility that different equally normal people classify the same object by means of apparently incompatible color terms. Finally, the also problematic case of numerals—one of those classes of terms often appealed to as referring terms in works in the theory of reference, including Naming and Necessity itself, but rarely studied in depth from the point of view of reference fixing—illustrates once again the dangers of assuming that the referents of terms of ordinary discourse ought to be given by sophisticated descriptions from extra-ordinary discourses. Here again we find in the first place a strong camp of eliminativist philosophers, who, often working under the assumption that the numbers are implicitly postulated in ordinary discourse to be sui generis individuals inhabiting an extra-ordinary world disconnected from our ordinary world, justifiably reach the conclusion

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that such individuals are neither metaphysically plausible nor epistemically accessible if existent at all. But we also find views on which the numbers are remarkably extra-ordinary entities characterizable only via somewhat sophisticated resources of set theory, such as sets of equipollent sets and settheoretical sequences of various kinds. On the view defended in chapter 4, by contrast, the relevant reference-fixing conventions determine as referents of the numerals perfectly ordinary properties—the property some things have of being five, the property some things have of being seventeen, etc.—which can furthermore be argued to satisfy the ordinary conception of what the numbers should be. The two themes of the book that we have revisited in these concluding notes are related, and related to something I see as an important part of the spirit of Kripke’s work on reference. Reference appears to be a pervasive phenomenon, and indeed, in a sense, a basis for all kinds of increasingly complex human endeavors that rely on our linguistic capabilities. It would be strange if the existence of ordinary reference required suspicious extra-ordinary epistemic resources or involved suspicious metaphysically extra-ordinary targets. Kripke’s work, and the work of others in his wake, made it plausible to think that our reference-fixing resources, our roads to reference, could reach the desired destinations without requirements of those kinds being involved. This book has attempted to follow in the footsteps of this Kripkean tradition.

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Index Abbott, B. 109n.2, 167n.18 Ackerman, D. 117–18, 135, 137–9 Adjectives color 199–211 gradable 195–201 numerals as 108–9, 113n.9, 119n.16, 121n.19, 125n.25, 126–7n.27 for sensible qualities 15–16, 184–212 standards for 195–201 Allen, K. 194n.14 Anaphors 20n.2, 21n.3 Anti-descriptivism 44–8, 57–63, 69–72, 76–80, 98, 106–7, 112–22, 129–30, 142–4, 164, 213–15 Arbitrariness problem 151–4, 168–83 Armstrong, D. M. 185n.1 Averill, E. W. 185n.1 Bach, K. 31n.13, 50n.22, 61 Bale, A. C. 196n.20 Baptisms 62–3, 93–6, 144–5, 164 Bartsch, R. 196n.20 Berger, A. 74n.10 Bierwisch, M. 196n.20 Bird, A. 178 Block, N. 191n.11 Bloom, P. 19 Bodies of beliefs 85–8, 91–2 Boghossian, P. 185n.1 Boyd, R. 154n.14, 178 Bratman, M. 36n.18 Braun, D. 22n.6 Brodal, P. 204n.37 Brown, J. 148–9, 152, 154–9 Brysbaert, M. 117n.12 Burge, T. 130n.30, 142n.1 Burgess, J. P. 63n.3, 74n.10, 99n.20 Byrne, A. 185n.1, 187, 190n.8, 191n.11, 193–4, 199n.30, 211

Cardinality properties 132–5 Carey, S. 123nn.21–22 Causal chains of transmission 62–3, 84, 96, 144–5 Change of reference 63–4, 74, 98–9, 145–6, 164–5 Character 11–12, 21–3 Chomsky, N. 148n.10, 167n.18 Clark, E. V. 19 Cohen, J. 185n.1, 187nn.3–4, 188–9, 191n.11, 192n.12, 193n.13, 194nn.16–17, 199n.30, 212n.45 Communication 8–9 Compositionality 2–3 Convention 5–6 Conventions of reference 5–6, 8–9, 51–3, 128, 160–3, 196–7, 200–1 Demonstrations 24–7, 32–3 Demonstratives 11–12, 19–59 as anaphors and as bound variables 20n.2, 21n.3 anti-descriptivism about 44–8, 57–9 character of 21–3 and conflicting intentions 31–5, 39–48, 55–7 and controlling intentions 34–5 and demonstrations 24–7, 32–3 descriptivism about 11–12, 24–5, 27–39 and directing intentions 27 historical appearance 19 vs. indexicals 23–5 Kaplan’s early theory 24–7 learning 19 logic of 22n.6, 23n.7 and overriding intentions 32–5, 54–5 paradigmatic uses 19 referential conventions about 51–3 and referential indeterminacy 36–48, 55–7

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230  Demonstratives (cont.) and referential intentions 27–35, 51–7 referents of 19–21 rigidity of 23–5 and salience 27–9, 33–4 systematicity and productivity of 37–9, 47–8 theories of sufficient conditions for reference and reference failure of 47–59 types in context vs. utterances of 22n.6 De re attitudes 74n.10, 117–18, 132, 134–9 Descriptivism 11–14, 24–5, 27–39, 61, 64–73, 109–22, 126–30 De Valois, K. K. 190–1 De Valois, R. L. 190–1 Devitt, M. 82–5, 90, 92n.15, 103–4, 148–9 Dickie, I. 63n.3, 82, 85–90, 92n.15, 105–6 Diessel, H. 19 Disunity problem 150, 153, 182–3 Donnellan, K. 8–9, 26, 82–3, 151 Dupré, J. 148–9, 154 Elbourne, P. 19–20, 61 Eliminativism 14–16, 159, 185–93, 203–4 Ereshefsky, M. 153 Espinal, T. 26n.11 Evans, G. 63–7, 67n.8, 74, 85–7, 92n.15, 94n.17, 96, 98–100, 145–6, 160, 164–5 Fara, D. G. 61 Fayol, M. 124n.23 Ferguson, J. 153 Fias, W. 117n.12 Folk essentialism 171–2 Frege, G. 2–10, 14–15, 18n.6, 115–16, 118–19, 119n.16, 133n.34 Basic Fregean Idea 2–3 on compositionality 3n.1 on sense 4–5 Fruhstorfer, H. 204n.36 Gallistel, C. R. 123n.20 García-Carpintero, M. 22n.6, 66n.6 Gelman, R. 123n.20 Gelman, S. 171–2 Geurts, B. 61 Gowers, T. 120n.17

Granà, A. 132n.33 Grice, H. P. 92n.15 Griffiths, P. E. 153–4, 181–2 Gutiérrez Vivanco, M. 132–3 Hansen, N. 200n.31, 208n.41 Hardin, C. L. 185n.1, 187n.4, 188n.6, 191n.11, 192n.12, 194n.15 Harju, E.-L. 204n.36 Hawley, K. 178 Heck, R. 118–19, 123n.20 Henik, A. 117n.12 Hennig, W. 153–4 Higginbotham, J. 18n.6 Hilbert, D. 185n.1, 187, 190n.8, 191n.11, 193–4, 199n.30, 211 Hodes, H. 202n.35 Hofweber, T. 109–10, 202n.35 Hughes, C. 152 Hull, D. 153 Hurvich, L. M. 191n.11 Impurities problem 148, 154–7, 166–7 Indeterminacy, referential 39–48, 55–8, 73–82, 100–3, 146–7, 165–6 Indexicals 21–5, 37–9 Intensions 3–7 Intentions, conflicting 31–5, 39–48, 55–7, 68–9, 74–5, 92–4, 98–9 Intentions, referential 5–6, 27–36, 45–6, 51–8, 74–7, 92–6, 160–8 Jackson, F. 65–6, 68, 70, 79, 194n.17 Janssen, T. M. V. 3n.1 Johnston, M. 169–71, 175–8, 185n.1 Kalderon, M. E. 194, 211–12 Kaplan, D. 11–12, 16–17, 19–28, 31–3, 37, 39–42, 45–6, 49, 54–6, 71–2, 75, 103 Katz, J. J. 61 Kennedy, C. 196n.20, 200n.31, 205n.38 King, J. C. 19–20, 25, 30–2, 34–5, 40–2, 54 Kitcher, P. 154–9, 167–8 Kripke, S. 8–10, 12–15, 23–4, 31, 41, 60–7, 67n.8, 68–9, 73–4, 83, 93–6, 98–9, 101–3, 113–19, 121–2, 131nn.31–32, 135–55, 157, 159–60, 166–73, 175–7, 178n.26, 180–5, 195n.19, 213–19

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 Kroon, F. 65–6 Kuehni, R. G. 191n.11 LaPorte, J. 151–3, 154n.14, 167–8, 182 Lasersohn, P. 196n.21 Leibniz, G. W. 21, 53–4 Leslie, S.-J. 150–4, 159, 167–9, 171–2, 182 Lewis, D. K. 65–6 Linderholm, C. E. 110n.4 Linnebo, Ø. 112–13, 118–19 Lowe, E. J. 178n.25 MacFarlane, J. 196n.21 Maddy, P. 133n.34 Malkoc, G. 191n.11 Malt, B. C. 148n.10, 167n.18 Marshall, O. 115–16 Martí, G. 74n.10 Matthen, M. 185n.1 Matushansky, O. 61 Maund, B. 185n.1 Mayr, E. 153–4 McCaffery, S. 112–15 McGinn, C. 185n.1 McKeown-Green, J. 66–8, 67n.8 McKinsey, M. 65 McLaughlin, B. P. 194–5, 212 McNally, L. 200n.31, 205n.38 Meaning as knowable conventions 16–17, 23, 71–2 as semantically encoded information 17–18, 21–3, 71–2 Michaelson, E. 30 Miller, R. 73 Mizrahi, V. 194n.14 Moltmann, F. 133n.36 Montague, R. 142n.1 Mount, A. 27–8, 33 Names 12–13, 60–107 anti-descriptivism about 60–3, 69–72, 76–80, 98, 106–7 baptisms 62–3, 93–6 and bodies of beliefs 85–8, 91–2 causal chains of transmission of 62–3, 84, 96 causal descriptivism about 12–13, 65–73, 76–80

231

change of reference of 63–4, 74, 98–9 and community intentions 93–4 and conflicting intentions 68–9, 74–5, 92–4, 98–9 descriptivism about 61, 64–73 and governance 87–8 and overriding intentions 93n.16 producers and consumers of 85–6 referential conventions about 93–7 and referential indeterminacy 73–82, 100–3 referential intentions about 92–7 theories of necessary and sufficient conditions for reference of 82–90, 103–6 theories of sufficient conditions for reference and reference failure of 80–1, 90–107 types vs. utterances of 91–2 Natural kind nouns 14–15, 140–83 anti-descriptivism about 142–4, 164 arbitrariness problem about 151–4, 168–83 baptisms 144–5, 164 causal chains of transmission of 144–5 change of reference of 145–6, 164–5 disunity problem about 150, 153, 182–3 eliminativism about 14–15, 159 and folk essentialism 171–2 impurities problem about 148, 154–7, 166–7 indeterminacy from vagueness 171–8 Kripke-Putnam “orthodoxy” about 140–8 and ordinary kinds 173–82 and ordinary notions of substance, species and phenomenon 169–73 and names of ordinary objects 175–6, 217 as predicative 141–2 qua problem about 148–9, 154–7, 167–8 referential conventions about 160–3 and referential indeterminacy 146–7, 165–6 referential intentions about 160–8 referents of 147–50, 173–82 rigidity for 143n.3 and science and scientific progress 179–81

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232  Natural kind nouns (cont.) as singular terms 141–2 Twin Earth thought experiments involving 142–4, 152–3, 182 Neale, S. 111–12, 116n.11 Needham, P. 150–1 Nelson, E. 120n.18 “New theory” of reference 5, 7n.3, 8–9, 11–12 Nicolas, D. 142n.1 Nozick, R. 214n.1 Numerals, decimal Arabic 13–14, 108–39 as adjectives and determiners 108–9, 113n.9, 119n.16, 121n.19, 125n.25, 126–7n.27 anti-descriptivism about 112–22, 129–30 vs. binary Arabic 135–6 and cardinality properties 132–5 counting with 124, 134–5 de re attitudes via 117–18, 132, 134–9 descriptivism about 13–14, 109–22, 126–30 generation of the sequence of 124, 127–8, 130 implicit ideas involving 124–6, 130–3 nominalism about 108 and polynomial expansions 111–21, 128n.28 referential convention about 128 referents of 130–9 semantic arguments and 114–15, 120–2, 129–30 vs. verbal numerals 109–11 Objectivism 193–5, 203–12 Ordinary kinds 173–82 Ordinary objects 175–6, 217 Papineau, D. 148–9 Parsons, C. 136 Pavese, A. 117n.12 Peacocke, C. 185n.1 Pelletier, F. J. 3n.1 Perry, J. 30 Peterson, P. 26n.11 Platts, M. 148–9 Potts, C. 26n.11 Polynomial expansions 111–21, 128n.28

Preconceptions 130–3, 166n.17 Productivity and systematicity 37–9, 47–8 Properties 6–7, 132–5 Putnam, H. 14–15, 140–57, 159–60, 164, 167–8, 167n.18, 169–73, 180–3, 215–17 Qua problem 148–9, 154–7, 167–8 Recanati, F. 61 Reference and Bedeutung 18n.6 and communication 8–9 compositionality of 2–3 as contribution to truth conditions 2–7 conventions of 5–6, 8–9, 51–3, 128, 160–3, 196–7, 200–1 direct 23–4 general characterization 1–7 and meaning 16–18 “new theory” of 5, 7n.3, 8–9, 11–12 paradigmatic examples 1–2 semantic vs. speaker’s 49–50, 83 and truth 9–11, 216 Reimer, M. 26–7, 30, 33, 40 Reynvoet, B. 117n.12 Richard, M. 112–15 Rigidity 6–7, 23–5, 60–1, 143n.3, 192–3, 195n.18 Rothschild, D. 200n.31 Sainsbury, M. 46 Salience 27–9, 33–4 Salmon, N. 7n.3, 99n.21, 176n.24 Schaffer, J. 199n.30 Science and scientific progress 179–81 Segal, G. 200n.31 Semantic competence 23, 71–2 Semenza, C. 132n.33 Sense 4–5, 8–9 Sensible qualities, adjectives for 15–16, 184–212, 217–18 color adjectives 199–203, 208–11 and contents of color experiences 210n.44 eliminativism about 15–16, 185–93, 203–4 intersubjective perceptual variation arguments about 190–5, 203–11

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 intrasubjective and interspecies perceptual variation arguments about 186–91 modal stability of 192–5, 198, 206–7 objectivism about 193–5, 203–12 referential conventions about 196–7, 200–1 referents of 197, 201, 204–11 secondary quality views about 15–16, 184–5 standards for 195–201 subjectivism about 185–90, 192–3, 194n.17, 195n.19, 199n.30, 206–7, 211 Seron, X. 124n.23 Shoemaker, S. 193n.13 Sidelle, A. 142n.1 Slack, J. 183 Smart, J. J. C. 185n.1 Soames, S. 7n.3, 24n.9, 60n.1, 65, 67–72, 79, 112–15 Speaks, J. 25, 30–3, 34n.16, 35n.17, 37–40, 44, 47, 52–3, 57n.27 Stalnaker, R. 31 Stanford, P. K. 154–9, 167–8 Steiner, M. 111–12, 115–16 Sterelny, K. 148–9, 153–9, 167–8, 181–2 Subjectivism 185–90, 192–3, 194n.17, 195n.19, 199n.30, 206–7, 211 Sufficient conditions for reference and reference failure, theories of 47–8, 51–3, 80–2, 93–8, 160–3, 214–15

233

Sullivan, A. 112–13 Systematicity and productivity 37–9, 47–8 Szabó, Z. G. 200n.31 Taylor, B. 19–20 Taylor, S. 63n.3 Travis, C. 200n.31 Truth and reference 9–11, 216 Twin Earth thought experiments 142–4, 152–3, 182 Tye, M. 185n.1, 186–7, 191n.11, 193–4, 211 Types vs. utterances 22n.6, 91–2 Tzelgov, J. 117n.12 Umiltà, C. 117n.12 Van Brakel, J. 150 Van Valen, L. 153–4 Variation, perceptual 186–95, 203–11 Velleman, D. 185n.1 Vennemann, T. 196n.20 Wettstein, H. 27–8 Wright, C. 185n.1 Wynn, K. 123n.20 Yi, B. 132–3 Zemach, E. 148