Bertrand Russell and the Nature of Propositions: A History and Defence of the Multiple Relation Theory of Judgement 9781138737457, 9781315185361, 1138737453

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Bertrand Russell and the Nature of Propositions

Lebens’s book makes an interesting, original, and accessible contribution both to Russell scholarship, and to current debates in the philosophy of language. It fills an important lacuna within the scholarly literature on Russell’s MRTJ, and does so admirably. —James Connelly, Trent University, Canada

Bertrand Russell and the Nature of Propositions offers the first book-length defence of the Multiple Relation Theory of Judgement (MRTJ). Although the theory was much maligned by Wittgenstein and ultimately rejected by Russell himself, Lebens shows that it provides a rich and insightful way to understand the nature of propositional content. In part I, Lebens charts the trajectory of Russell’s thought before he adopted the MRTJ. Part II reviews the historical story of the theory: what led Russell to deny the existence of propositions altogether? Why did the theory keep evolving throughout its short life? What role did G. F. Stout play in the evolution of the theory? What was Wittgenstein’s concern with the theory and, if we can’t know what his concern was exactly, then what are the best contending hypotheses? And why did Russell give the theory up? In part III, Lebens makes the case that Russell’s concerns with the theory weren’t worth its rejection. Moreover, he argues that the MRTJ does most of what we could want from an account of propositions at little philosophical cost. This book bridges the history of early analytic philosophy with work in contemporary philosophy of language. It advances a bold reading of the theory of descriptions and offers a new understanding of the role of Stout and the representation-concern in the evolution of the MRTJ. It also makes a decisive contribution to philosophy of language by demonstrating the viability of a no-proposition theory of propositions. Samuel Lebens is a Senior Research Fellow in the Philosophy Department at the University of Haifa, Israel.

Routledge Studies in Twentieth-Century Philosophy For a full list of titles in this series, please visit www.routledge.com

35 Wittgenstein and Heidegger Pathways and Provocations Edited by David Egan, Stephen Reynolds, and Aaron James Wendland 36 The Textual Genesis of Wittgenstein’s Philosophical Investigations Edited by Nuno Venturinha 37 The Early Wittgenstein on Metaphysics, Natural Science, Language and Value Chon Tejedor 38 Walter Benjamin’s Concept of the Image Alison Ross 39 Donald Davidson’s Triangulation Argument A Philosophical Inquiry Robert H. Myers and Claudine Verheggen 40 Heidegger’s Shadow Kant, Husserl, and the Transcendental Turn Chad Engelland 41 Ernst Jünger’s Philosophy of Technology Heidegger and the Poetics of the Anthropocene Vincent Blok 42 Bertrand Russell and the Nature of Propositions A History and Defence of the Multiple Relation Theory of Judgement Samuel Lebens

Bertrand Russell and the Nature of Propositions A History and Defence of the Multiple Relation Theory of Judgement Samuel Lebens

First published 2017 by Routledge 711 Third Avenue, New York, NY 10017 and by Routledge 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN Routledge is an imprint of the Taylor & Francis Group, an informa business © 2017 Taylor & Francis The right of Samuel Lebens to be identified as author of this work has been asserted in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data A catalog record for this book has been requested ISBN: 978-1-138-73745-7 (hbk) ISBN: 978-1-315-18536-1 (ebk) Typeset in Sabon by Apex CoVantage, LLC

To Dorothy Edgington and Fraser MacBride ‫ואין לך כבוד גדול מכבוד הרב ולא מורא ממורא הרב‬ There is no honour greater than that due to a teacher, and no reverence greater than that which is due to a teacher ~ Maimonides, Laws of Talmud Torah, 5:1

Contents

Acknowledgements

ix

1 Framing Our Question

1

PART I

The Philosophical and Historical Background

21

2 Moore and Russell in Rebellion

23

3 Incomplete Symbols

39

4 Semantics, Assertion and the Theory of Descriptions

59

PART II

The Rise and Fall of the MRTJ 5 The Rise of the MRTJ

93 95

6 The Stoutian Evolution of the MRTJ

119

7 The Demise of the MRTJ

131

PART III

Resurrecting the MRTJ

171

8 Significance and Representation

173

9 Molecular Propositions

191

viii

Contents

10 Explaining the Explananda

215

11 The MRTJ and Its Competitors

260

Bibliography Index

283 294

Acknowledgements

I was tremendously blessed as a graduate student at Birkbeck College to be surrounded by fabulous teachers and peers. The amount of time and guidance that my supervisors – first Fraser MacBride and then Dorothy Edgington – gave to me went far beyond what most graduate students receive, and I am so grateful to them. In fact, when I was an undergraduate at University College London, it was Fraser MacBride’s lectures on Bertrand Russell (alongside some very engaging tutorials with Colin Johnston) that first drew me in to the Multiple Relation Theory of Judgement. Susan James and Anthony Price were the faculty that encouraged me to pursue my PhD at Birkbeck. I am so glad that they did. Alongside my official supervisors at Birkbeck, I was fortunate to be able to forge a relationship with Keith Hossack, whose rich work has had a clear impact upon my own. The entire faculty there were truly engaged in creating and sustaining a supportive and invigorating intellectual environment. Furthermore, I was lucky to join Birkbeck alongside a tremendously engaging set of peers. Coffees, seminars and pub-nights with Alex Douglas, Simon Hewitt, Nick Jones, Frederique Lauret and Steven Methven were a major part of my philosophical education and certainly had an impact on the content of this book. Friendship and conversations with other graduate students in London – such as Jonny McIntosh, Arthur Schipper and Lee Walters – were also a tremendous resource to me. Facebook has made it possible to take many of these people with me over the course of the intervening years as sources of advice and friendship. Perhaps I should be thanking Mark Zuckerberg. Facebook has also allowed me to have very helpful conversations on the topics of this book with scholars I’ve not yet had the pleasure to meet, such as Christopher Menzel and Joseph Jedwab. Many thanks to them and to Lorraine Juliano Keller, a real-life and Facebook friend, who often receives random Facebook messages from me and has been a rich resource of ideas and useful references. Tom Baldwin and Mark Textor were my PhD examiners and have been a source of encouragement and advice ever since. I am very grateful to both of them.

x

Acknowledgements

Returning to professional academia after a four-year hiatus in Rabbinical School wasn’t at all easy. It was made possible by a number of people, events and programs that encouraged me to pursue a new research interest in the philosophy of religion. Thanks are particularly due to Kelly Clark, Tyron Goldschmidt, Aaron Segal, Eleonore Stump, Dani Rabinowitz, Mike Rota, Mike Rea and especially Dean Zimmerman (without whom I’m pretty certain I wouldn’t be in academia today) for making this new chapter of my philosophical career possible. My various endeavours in the philosophy of religion, over the years, have received generous support from the John Templeton Foundation, the Templeton Religion Trust and the World Templeton Charity Foundation Inc. (the views expressed in this book are not intended to represent the views of any organisation, nor was this research, in particular, funded by them – I merely acknowledge that without their support for my research in the philosophy of religion, I may not have remained in professional academia at all). The only real evidence of any philosophy of religion in this book is hidden all the way back in chapter 10, but at least I managed to sneak some in somewhere! My return to professional philosophy brought me to the University of Notre Dame and Rutgers University, before my very recent move to the University of Haifa. During this time, I was able to revisit my PhD thesis and bring it up to do date to become this book. A major feature of this process of updating was to bring the thesis more directly into conversation with contemporary philosophers of language. Rutgers, in particular, was a wonderful environment in which to perform such a task. At Rutgers, I had access to faculty who were very generous with their time, expertise and encouragement. Conversations with Bob Adams, Marilyn McCord Adams, Elisabeth Camp, Jeff King (Jeff Speaks at Notre Dame) and Ernie Lepore were invaluable to me. Andy Egan and Jonathan Schaffer were both kind enough to read long excerpts of my work and give me really helpful comments. What was most remarkable about my time at Rutgers was the invaluable help I received from the graduate students there. Much of the newest material to this book is owed to conversations with David Black, Eddy Kemming Chen, Simon Goldstein, Cameron Domenico Kirk-Giannini and Daniel Rubio. I owe a great debt to all of the graduate students at Rutgers for creating such a wonderful intellectual community to have been a part of, alongside the other research fellows, Andrew Moon and Phil Swenson. This manuscript was completed during my first semester at the University of Haifa. Even in that short time, I have learnt a tremendous amount from my colleagues here, and I look forward to continuing to work with them in such a warm and conducive intellectual environment. Thanks especially to Michael Anthony, Jonathan Berg, Ariel Meirav and Gil Sagi, who have discussed some of the contents of the book with me, as I was desperately trying to tie up loose ends, and to Saul Smilansky for being such a supportive head of department.

Acknowledgements

xi

I am honoured to have this book published alongside the other Routledge Studies in Twentieth-Century Philosophy. Indeed, I am very grateful to Andrew Weckenmann, Alexandra Simmons, and their colleagues at Routlege. They have been very encouraging, endlessly helpful and truly professional. The anonymous reviews that Routledge commissioned for this book were insightful and constructive. I extend my thanks to all concerned. In the decade that gave birth to this book, my wife and I have been blessed with three children. Together we have lived in three continents, wandering the globe, as is the lot of a number of early career academics. The body of this book is concerned with the metaphysics of meaning – but without the love of my family (near and far), and the support and companionship of my wife, there would be very little meaning left to find a metaphysics for. Finally, I dedicate this work to my teachers, Dorothy Edgington and Fraser MacBride. On a more fundamental level, and even though Bertrand Russell may have disapproved, I dedicate all of the fruits of my labour to God, the true Judge, who asserted this world into being. .‫ ָבּרוְּך הוּא‬,‫שׁאָמַר ְו ָהי ָה הָעוֹלָם‬ ֶ ‫ָבּרוְּך‬

1

Framing Our Question

Bertrand Russell once advanced a theory of assertion known as the Multiple Relation Theory of Judgement (henceforth, the MRTJ). He aired the theory, for the first time, in 1906, but didn’t adopt it until 1910. By 1919, he had rejected it. As we shall see, the theory has been thoroughly maligned by most of the philosophers who have deigned to address it at all. In this book, I defend the theory. I suggest that it provides us with a rich and insightful way to understand what propositional content really is. Wittgenstein maligned the theory for, among other reasons, its inability to rule out the possibility of asserting nonsense. However, what is nonsense, exactly? If someone was to say to you that ‘the knife is the square root of the fork’, or that ‘my toothbrush is trying to kill me’, you’d be within your rights to accuse them of speaking nonsense. However, is this the sort of nonsense that a theory of assertion should rule out any possibility of asserting? The knife isn’t the square root of the fork because it simply isn’t the sort of thing that could be the square root of anything, let alone a fork. Toothbrushes don’t and can’t have homicidal intentions.1 These sorts of assertions are not just false; they’re necessarily false. However, they do have a truth-value. If necessary falsehood is all you mean by nonsense, then we should be sure to allow the possibility of asserting it. People assert necessary falsehoods much of the time (whenever a person makes a mathematical error, for example). In this book, I argue that the MRTJ rules out the possibility of asserting the sort of nonsense that nobody could assert – since, for instance, it isn’t possible, on my reconstruction of the MRTJ, to assert that bla-bla-bla. But much of the nonsense that the MRTJ is accused of permitting, is the sort of nonsense that a theory of judgement should indeed permit, because, as it turns out, all sorts of people make all sorts of nonsensical judgements all of the time! The MRTJ has also been accused of failing to make sense of molecular propositions – propositions that contain quantification, or logical operators, like ‘and’, ‘or’, ‘if’ and ‘not’. When attempts have been made to defend the MRTJ against this charge, the costs have been off-putting, to

2

Framing Our Question

say the least. In this book, I present a new, streamlined extension of the MRTJ, to deal with molecular propositions without unsightly assumptions or costly philosophical posits. Russell was wrong to reject the MRTJ, and the history books have been unfairly dismissive of its continuing philosophical worth. In this book, I set out to right that wrong. The central philosophical question that guides this work, to which the MRTJ was designed to respond, is, what are propositions? If it turns out that propositions don’t exist, as the MRTJ actually maintains, then the question will become, how can a nominalist about propositions (i.e., somebody who thinks that propositions don’t actually exist) make sense of propositional content? In this chapter, before outlining the structure of the rest of the book, I will spend some time developing the contours of our central question – what are propositions/what is propositional content – drawing heavily from the excellent recent volume by Jeff King, Scott Soames, and Jeff Speaks, entitled New Thinking about Propositions (2014). As this book progresses, I’ll be defending some distinctly old thinking about propositions, but I think (and hope) that their discussion will help us to motivate and illuminate the way forward. After that scene setting, I’ll outline the plan for the rest of this book.

§1: What Role Are Propositions Supposed to Play? To give an account of the metaphysics of meaning has often come down to giving an account of propositions. What are they and what are they supposed to do for us? Jeff King lays out a number of reasons traditionally given for positing the existence of propositions (King et al., 2014, pp. 1–8): 1. The information content of a sentence relative to a context of utterance When you utter a sentence, especially a declarative sentence, there is something that you mean. So it seems as if sentences – at least relative to a context of utterance (because the same sentence can mean different things in different contexts) – have a meaning. Propositions are the meanings of sentences (relative to a context of utterance). 2. That which synonymous sentences have in common Since propositions are what sentences mean. If two sentences mean the same thing, then we expect to cash this out in terms of their both expressing the same proposition. 3. The object of understanding and other propositional attitudes There are a class of attitude verbs that take non-factive that-clauses as a compliment: ‘I assert that . . .’; ‘I hope that . . . .’; ‘I believe

Framing Our Question

4.

5.

6.

7.

8.

9.

10.

3

that . . .’ etc. What are the things that you stand related to when you assert something, or hope something, or believe something? Propositions are posited to be the objects of these attitudes, and philosophers tend to call them, accordingly, ‘propositional attitudes’. The primary bearers of truth and falsity Given roles one and two, a sentence, relative to a context of utterance, is only true in virtue of expressing a proposition that is true. Primary bearers of modally qualified truth-values Propositions can be necessarily true, necessarily false, contingently true or contingently false. Ultimately, what it’s going to mean for something to be contingent or necessary will be for some proposition to be contingently true or necessarily true. Indeed, under the same heading, one might think that propositions need to exist to be that which modal operators operate upon. ‘That’s not just true; that’s necessarily true!’ The representational content of experience When you see that a car is turning a corner, your experience has representational content: you experience the car as turning a corner; you see that it is turning a corner. When the verb ‘seeing’ takes a thatclause as a compliment, it seems that it’s reporting a relation between a person who sees and a proposition. The ontological foundation of possible worlds What are possible worlds? At least one account will have it that possible worlds are actually sets of propositions, whose members collectively describe how the world could have been. The content of the common ground in a conversation According to Robert Stalnaker (1978; 2002), and many linguists and philosophers in his wake, conversations operate in the presence of a common ground. A common ground is the set of propositions that all of the interlocutors in the conversation accept (at least for the sake of the conversation) and which all of the interlocutors believe that all of the other interlocutors are accepting (at least for the sake of the conversation) and which they all believe each other to be believing that everyone is accepting – iterated up to every level of belief. The semantic value of non-factive that-clauses In roles three and six, especially, we have seen that propositions are often appealed to as the semantic value of non-factive that-clauses (i.e., that-clauses that don’t obviously seem to be referring to, or describing, facts). Here we make a more general claim. Propositions are always the semantic value of non-factive that-clauses. The semantic value of certain demonstratives and anaphora Demonstratives are used to point at things. Sometimes we seem to use them to point, so to speak, at propositions: ‘I just said that’; ‘I don’t think that at all’ – if propositions didn’t exist, those demonstratives

4

Framing Our Question

would seem to be empty. In a similar vein, Peter van Elswyk argues that certain phrases are best understood as anaphora that refer to propositions. For instance, Bob says, ‘I’m hungry’. Sally replies, ‘If so, we should go to dinner soon’. Sally’s use of ‘so’ seems to make use, anaphorically, of the proposition that Bob is hungry (see chapter 1 of van Elswyk (ms)). 11. The domain for certain quantifiers About someone with whom you sometimes agree, you might utter the following sentence, ‘There are some things that she believes that I also believe.’ What is it that you’re quantifying over in that sentence? It seems that you’re quantifying over propositions. Given the Quinean criterion of ontological commitment – that to be is to be the value of a variable – the fact that we quantify over things that people believe entails that such things must exist. Propositions are the values of those variables. It’s fair to wonder whether we’re being too ambitious to hope that one type of entity will be able to play all of these diverse roles. In chapter 4, we will follow Brian Rabern (2012b) and many others, in drawing a distinction between semantic values and objects of assertion; a distinction that this list smudges over. Moreover, perhaps the informational content of experience is of a fundamentally different type to the informational content of sentences. Perhaps lived experience is of such a rich character that it can’t be neatly parcelled into the structure and stricture of sentential form, to put an experience into words is always to lose something. William Alston (1999, p. 187) raised just this concern: When I look at my front lawn, it presents much more content to my awareness than I can possibly capture in concepts. There are indefinitely complex shadings of color and texture among the leaves and branches of each of the trees. That is perceptually presented to me in all its detail, but I can make only the faintest stab at encoding it in concepts. My repertoire of visual property and visual relation concepts is much too limited and much too crude to capture more than a tiny proportion of this. This is the situation sometimes expressed by saying that while perceptual experience has an ‘analog’ character, concepts are ‘digital’. Since looks are enormously more complex than any conceptualization available to us, the former cannot consist of the latter. If that’s the case, you might think that a different sort of thing plays role 6 (if any thing can play such a role) to the sort of thing that plays role 1, even though the partial success of putting experience into words suggests that there must be an intimate relationship between the things that play these roles. Furthermore, perceiving that is often thought to be factive; whereas believing that isn’t. This might place a wedge between roles 3 and 6.

Framing Our Question

5

In short: we can at least raise the worry that it’s too ambitious to hope that one type of entity plays all 11 of these roles. We should bear in mind David Lewis’ suspicion that ‘the conception we associate with the word ‘proposition’ may be something of a jumble of conflicting desiderata’ (Lewis, 1986, p. 54). Nevertheless, the more roles that a single posit can play, the better. And thus, all things being equal, the more of these 11 roles (and perhaps more) that your theory of propositions allows for propositions to play, the better. Another question we can raise, at least for some of these roles, is whether (a) there really is a role to play, and (b) whether we really need an entity to play it. For instance, Donald Davidson (1967) famously argued that an adequate semantic theory for a language doesn’t have to think in terms of a sentence having an entity as its information content. That’s to say, he didn’t think that role 1 was a role that any thing needs to play.2 I’ll try to explain Davidson’s point as briefly as possible. One first of all needs to understand what Davidson means by a ‘meaning theory for a language’. The aim of a Davidsonian meaning theory for a language is to generate theorems that couple true sentences of that language with true sentences of the meta-language (the language that the theory is stated in). Of course, we’re not just looking to couple sentences between the object-language and the meta-language that happen to share a truth-value. Instead, we want a theory that will, without tacitly appealing to the notion of ‘identity of meaning’ – for that would be circular – couple sentences of the object-language with sentences of the meta-language that do, in fact, share the same meaning. Let’s imagine that Davidson succeeds, and that he shows us how to build a theory that can systematically specify the literal meaning of any sentence in a language; in a nutshell, he gives us a perfect version of google translate for a given object-language. You type in a sentence – his theory shoots out a perfect translation. If he could do that, he would have said everything there is to say about the meaning of that language, or so he argues. Propositions don’t seem to have any explanatory role in such a theory. The theory replaces sentences in the object-language, not with propositions, but simply with translations – that is, sentences from the meta-language. Sentences are swapped for sentences in a meaning theory. Propositions are redundant: posited as the meanings of sentences; posited to play role 1, Davidson, if his project succeeds, has shown us how to build a meaning theory for a language without them. But in a sense, Davidson isn’t just denying that we need some sort of entity to play role 1. He’s also arguing that there’s no phenomenon in the general vicinity of role 1 that calls out for explanation. This is where we should demur. Even if Davidson could provide us with a perfect translation manual for a language, he won’t have given us an account of the metaphysical nature of meaning. Propositions might be unnecessary to build Davidsonian translation manuals, but has Davidson really

6

Framing Our Question

explained what it means for a sentence to be meaningful? In this book, we’re after an account of the metaphysics of meaning!3 I think that we should be more ambitious than Davidson. We can hope for more than just translation manuals in our search for a general account of the metaphysics of meaning. And thus, even if we come to accept that we don’t need an entity to play role 1, we might still feel that there’s something in the general vicinity of role 1 calling out for explanation. What does it mean for sentences to mean something? In a sense, I have transformed role 1, which was initially a specification for an entity, into a call for an explanation of a phenomenon, with or without the aid of an ontological posit. I want to know what it means for a sentence to mean something. I want a metaphysics of meaning. Indeed, I think that all 11 of these specifications can be likewise transformed into a call for an explanation of a certain phenomenon. So even if you don’t want to posit entities to play these 11 roles, it seems to me that you should still accept that we have 11 things that call out for an explanation. For instance, we need to explain the semantic contribution of non-factive that-clauses. That is to say, role 9 represents something in need of an explanation. But it’s not clear to me that the best way to explain their semantic contribution is to give them all an entity as referent. Role 11, to turn to a different example, can be rephrased, if it turns out that there are no such entities as propositions, into what justifies this exception to Quine’s criterion, and how should we interpret these quantifiers? And thus, moving forward, I will accept (contra Davidson) that all 11 of these ‘roles’ do represent genuine explananda, but I want to be open-minded about (a) whether one class of entity will be sufficient to explain all 11, and (b) whether all, or any of these explananda require an entity as explanans. And so I repeat what I said at the outset: the question that, at least initially, drives this book is ‘what are propositions?’, but, as I said, even if it turns out that there’s no such thing as a proposition, we still have our question, which merely has to be rephrased into, ‘how else can we explain the 11 explananda listed earlier?’ Can we provide a metaphysics of meaning? I’m acutely aware that to look at meaning through the prism of these 11 explananda might well miss a really important variety of meaning. One might think that to assert a metaphor, especially a more exotic or poetic metaphor, is to engage in an act whose content isn’t the sort of well-defined and well-bounded content that propositions are supposed to model. To the extent that the metaphysics of meaning that this book develops neglects to account for the open-ended gestures that animate metaphor, I can only issue an apology. My immediate concern here is with well-bounded acts of assertion with more clearly defined truth conditions. Metaphor is critical to an exhaustive study of whatever it is that we generally mean by ‘meaning’, but it lies beyond the scope of this book,

Framing Our Question

7

whose interest lies at a more mundane, but perhaps more foundational, level of propositional meaning.

§2: What Problems Must a Theory of Propositions Avoid? As far as theories of propositions go, there are three main schools: the possible-worlders, the structured-propositioners and the primitivists. Possible-worlders think that propositions are either sets of possible worlds, or functions from sets of possible worlds, to truth-values. Obviously, possible-worlders have to deny that propositions can play role 7 – propositions can’t be the foundation of possible worlds, on their account, since possible worlds are explanatorily prior to propositions. Structured-propositioners, on the other hand, think that a proposition, p, expressed by a sentence, s, in a context, c, is a structured entity that has the semantic values of the meaningful parts of s in c as constituents.4 Here, in order to get a sense of the project of this book, I list the main problems that substantive (i.e., non-primitive) theories of propositions have to avoid – although more problems will emerge throughout the course of the book (which I’ll summarise in chapter 10); some of them are problems for possible-worlders, some for structured-propositioners – and some are problematic for both schools. These are the sorts of problems that have lead some thinkers to embrace primitivism. Primitivists claim that propositions exist as simple entities that hold their distinctive properties primitively. Primitivism is an effective way of blocking the problems that we’re going to canvas in this section, but fairly stands accused of providing us a theory lacking in explanatory power. Accordingly, primitivism might fairly be put in reserve as a refuge only of last resort. §2.1: The Problem of Unity The earliest structured-propositioners, such as Frege and Russell, were troubled by a quasi-mereological problem.5 If propositions have constituents, then you can ask how the constituent parts stick together. One reason why this problem bothered Russell so dearly was because he found it hard to conceive of a mode of composition for the parts of his structured-propositions that wouldn’t force the proposition to be true. What distinguishes the disparate ordered-many, consisting of Romeo, love and Juliet, from the proposition that Romeo loves Juliet? In the ordered-many, the property of love isn’t doing anything. It’s inert. However, in the proposition, love seems to be relating Romeo to Juliet. As we shall explore more thoroughly in the historical parts of this book, Russell feared that if the unity of the proposition derives from the fact that love is actually relating Romeo to Juliet, then there can be no unified proposition

8

Framing Our Question

unless Romeo is actually love-related to Juliet, and, if Romeo is actually love-related to Juliet, then the proposition that Romeo loves Juliet cannot fail to be true. In short: 1. For any proposition, aRb, if a is R-related to b, then it will be true. 2. For any proposition, aRb, what gives the proposition its unity is that a stands R-related to b. 3. It follows from 1 and 2 that, for any unified proposition, aRb, the proposition will be true. 4. Since all propositions have to be unified, it follows from 3 that here will be no false propositions.6 But there are false propositions. What to do? Another way of putting this problem is that a proposition, aRb, collapses into its own truth-making fact if its unity is derived from R’s actually relating a to b. For a time, as we shall see, Russell was willing to accept that there is no non-primitive distinction between true propositions and false propositions. True propositions are obtaining states of affairs. That is to say, the proposition that aRb just is the state of affairs in which a is R-related to b, and it is true because it obtains. The false proposition that cRd is just the non-obtaining state of affairs in which c is R-related to d, and is false because it is non-obtaining.7 The difference between obtaining and non-obtaining, truth and falsity, is, on this account, primitive (Russell, 1904, p. 524).8 For various reasons, which will become a central theme of the historical parts of this book, Russell came to reject this picture, not least because he was embarrassed by his ontological commitment to non-obtaining states of affairs (Russell, 1912, p. 72). Another fear that plagued Russell, a fear that had been impressed upon him by F. H. Bradley, was how to account for the unity of his complex propositions, or states of affairs, without engendering regress. The disparate many a, R, and b apparently become unified when R instantiates a and b. But now we have to explain this relation of instantiation, and how it sticks things together. In fact, we now have to consider the disparate many, a, R, b, and instantiation. Presumably, that many only becomes unified when instantiation is super-instantiated by a, R and b, which will lead us to posit super-duper-instantiation, in order to unify a, R, b, instantiation, and super-instantiation, which leads us to posit super-duperduper-instantiation, and the process proceeds ad infinitum. At his most confident, Russell was willing to brush this regress away with the recognition that instantiation is a primitive that we need not nor cannot analyse further (see Lebens (2008)). I think that this dismissive attitude was wise. Echoing that sometimes confident mood of Russell, some have argued that the problem of unity is a non-starter. There’s no regress to fear over here. Peter van Inwagen puts it thusly:

Framing Our Question

9

But is there really a puzzle here? Suppose that the fact that a certain external relation holds between two objects is a brute fact. What’s so bad about brute facts? Surely there must be some brute facts somewhere in the world? (van Inwagen, 2002, p. 36) And, as Scott Soames (King et al., 2014, p. 32) argues, there are plenty of ways to unify a, R, and b, without making R do the work for you, and without thereby creating the truth-making fact that a is R-related to b. We could appeal to a relation other than R, to be the brute explanation of the unity between a, R, and b, and, indeed, there is no shortage of options. As Soames urges us to consider: there’s the relation that unites the set {a,R,b}, and there’s the relation that unites the ordered triple , and there’s the relation that unites the tree structure: R

a

b

Soames’s insight, which he claims was little understood by Russell and Frege, was that the special quality of a proposition isn’t unity, for unity is easy to achieve, but rather their curious ability to represent: Since it would seem absurd to characterize any set, sequence, or abstract tree as inherently representing things as being certain ways – and so as being true or false – the idea that propositions are any of these structures is a non-starter. (King et al., 2014) Despite its historical pedigree, the problem of unity doesn’t necessarily strike contemporary ears as all that worrisome. §2.2: The Representation-Concern Soame’s (2010, p. 32) insight is that there is a more troubling problem hiding beneath the surface of the problem of unity: The real problem posed by [Frege and Russell’s] confused discussions of the unity of the proposition is that their conception of propositions makes it impossible to answer the question ‘What makes propositions representational, and hence capable of interpreting sentences by providing their meanings?’ The problem is how to account for the curious ability of propositions to represent, all by themselves. Sets aren’t inherently representative of anything,

10

Framing Our Question

unless we interpret them as representing something, or use them to represent something. In fact, it’s pretty hard to conceive of any entity that is representational minus an act (or a system of acts) of interpretation/use. And this problem, how to account for the inherent ability that propositions have, all by themselves, to represent, is what I’m calling the representation-concern. It is the representation-concern that really underlies the problem of unity. Soames accuses Frege and Russell of being all too dimly aware of the real nature of the problem. The historical portion of this book will contest that accusation, at least as it stands against Russell. I shall argue that Russell was acutely aware of the representation-concern (in later work, Soames haltingly comes around to realising this for himself, as we’ll see in chapter 5, §4). But for our purposes here, it’s important to note, along with Soames, that unlike the quasi-mereological problem of unity, the problem that underlies it – the representation-concern – attacks the possible-worlders as much as it attacks the structured-propositioners. Why should we think that a set of possible worlds represents something as being the case, minus an act of interpretation/use? Why should we think of a function that maps sets of worlds onto truth-values as representational, minus an act of interpretation/use? When you identify propositions with some class of entities (be they worlds, or functions, or structured-entities), you want to make sure that it’s somewhat plausible that these are the sort of entities that could have the power, all on their own, to be representational. The representation-concern is so troubling because none of the classes of entities generally identified with propositions seem to be up to this job. Are we simply to stipulate that propositions have a mysterious sui generis and unexplained, seemingly magical power to represent all by themselves? Indeed, in the words of King, ‘the traditional view of propositions, as entities that represent by their very natures and independently of minds and languages, is to be rejected as mysterious’ (King et al., 2014, p. 127): I am of course not saying that any time a thing has a property, there must be some explanation for how or why it has that property . . . But certain sorts of properties are such that we feel compelled to give an account of how/why something manages to possess them and perhaps even what the possession of them consists in . . . Perhaps it is not entirely clear what it is that makes a property such that possession of it is something that needs to be explained. But it seems utterly clear that the property of having truth conditions is the sort of property whose possession is in need of explanation. (King et al., 2014, p. 47) We might not have a good theory to explain the following datum, but the datum certainly seems to be accurate: some properties require more

Framing Our Question

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of an explanation than others. Again, this needs sharpening, justification and explanation, but it seems to be onto something. King is surely right to conclude that the power of a mind to represent things is so much less mysterious – so much less calling out for explanation – than the power of inert, inanimate abstract propositions, to represent the world. Perhaps we could put it this way: it seems appropriate in the philosophy of language to treat the power of the mind to represent as a brute primitive, even if, in the philosophy of mind, it should be explored and explained; but it is inappropriate in the philosophy of language to leave unexplained the representational power of the abstract objects that we posit there. This is a power that calls out for explanation in the philosophy of language. Propositional primitivism is the view that denies there is something here to be explained. It is the view that propositions are a sui generis type of entity which cannot be constructed out of or reduced in terms of any other sort of entity. According to the primitivist, the inner nature of a proposition is unanalysable. What is it that makes propositions representational? The primitivist doesn’t think that this is a question worthy of an answer. Propositions and their nature are primitive; as is their power to represent (that the power of propositions to represent, and to have truth conditions is primitive is defended by Michael McGlone (2012) and Trenton Merricks (2015), among others). Where King et al. see a mystery in need of an explanation, the primitivist sees a brute and primitive fact. For those of us who want more explanatory oomph from a theory of propositions, the representational-concern seems to be of central importance. §2.3: The Problem of Quantity For any theory that identifies propositions with a class of entities, the Xs, you had better be sure that for every candidate proposition there is one, and only one, X identified with that proposition, and that for every X, there is one and only one proposition identified with it. In other words, the set of Xs will need to be isomorphic with the set of propositions to be even a candidate for being co-extensive. Many theories of propositions struggle with this problem of quantity. Famously, possible-worlders are accused of falling victim to this problem because possible worlds are much more coarse-grained than we might imagine propositions to be. For instance, there are many necessarily true propositions, and yet the set of worlds in which a given necessarily true sentence is true will be a set of worlds in which all necessarily true sentences are true since they’re all true in all worlds. Accordingly, possible-worlders will end up struggling to say that there is more than one necessarily true proposition. However, it’s patently obvious that the proposition that 2 + 2 = 4 is not the same as the proposition that 5 + 5=10 (you can assert, believe, and mean one of them without asserting, believing or meaning,

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Framing Our Question

the other, for example). This is a manifestation of the quantity problem. The possible-worlder isn’t giving us enough propositions.9 Structured-propositioners can also fall victim to the quantity concern. One way in which it rears its head, even for structured-propositioners, is with relation to de se content. Presumably, when I believe that I am a philosopher, I believe something different to what I believe when I believe that Samuel Lebens is a philosopher, if, suffering from a bout of amnesia, I forget that I am Samuel Lebens. And yet, some structured-propositioners are going to say that the proposition expressed by my utterances of ‘I am a philosopher’ is a proposition composed of me and the property of being a philosopher, which will be exactly the same entity as the proposition expressed by my utterance of ‘Samuel Lebens is a philosopher.’ If we don’t have two different propositions here, then my belief that I am a philosopher cannot differ, at least not in content, from my belief that Samuel Lebens is a philosopher, even when I’m suffering from amnesia. And thus we have a problem of quantity. The problem of quantity isn’t always a function of having too few propositions. As has been pushed by Michael Jubien (2001) and Scott Soames (2010), theorists who want to define propositions as ordered sets will often suffer from an embarras de choix. If the proposition that Michael swims is the ordered set , why isn’t it the ordered set ? Or, if ordered sets are to be defined in terms of classical sets, which of the defining sets shall we chose: {{swims}, {swims, Michael}} or {{{swims}, Ø}, {{Michael}}}? There are just too many candidates!10 There are more refined views out there as to what structured-propositions might be, but even the more refined views suffer from problems of quantity. Roughly put, Soames thinks that a proposition is a complex property had by certain mental actions; a mental action type (Peter Hanks (2007b) adopts much the same view – although there are interesting differences that separate them). According to King, Soames still suffers from a problem of quantity. He generates too many propositions (King et al., 2014, p. 131). First King notes, ‘Obviously, on this view different sequences of cognitive acts yield different event types and so different propositions.’ Then he asks us to consider three different sequences of cognitive acts. (1) An agent constructs the property x loves Juliet, and then predicates it of Romeo. That sequence will yield a proposition. King calls it Romeo 1. (2) An agent constructs the property Romeo loves y and then predicates it of Juliet. This distinct sequence will yield, on Soames’ account, a distinct proposition. King calls it Romeo 2. Finally, (3) an agent predicates x loves y of the ordered pair . This third sequence will yield a third proposition, Romeo 3. And thus, where we intuitively think that there’s one proposition that Romeo loves Juliet, Soames has given us three. We’re back with an embarrass de choix. In a beautiful rhetorical flourish, King asks (King et al., 2014):

Framing Our Question

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So how does Romeo love Juliet? Let’s count the ways. It looks like there are three distinct propositions, because of the three distinct event types of agents performing sequences of cognitive acts, that are all propositions to the effect that Romeo loves Juliet. Frank Ramsey also had the concern that if you allow for the existence of complex universals, then the proposition that aRb would collapse into three propositions: one in which a is applied to the complex property Rb, one in which the complex property aR is predicated of b, and one in which R is predicated of the ordered pair . Like King, he also comes up with a witty retort: ‘So the theory of complex universals is responsible for an incomprehensible trinity, as senseless as that of theology’ (Ramsey, 1925b, p. 406).11 And so the worry that a theory of propositions will generate too many propositions has a distinguished history. I’m not here suggesting that Soames’ theory of propositions really succumbs to this problem, as King contends. I leave that issue open. I’m just delineating the sorts of problems that accounts of propositions, including Soames’, will need to avoid. Incidentally, propositional primitivists don’t have any issues with quantity. When asked what a proposition is, they will tell you that propositions are sui generis; they are just what they are. How many of them are there? Just the right amount! Of course, all of the other thinkers in the conversation are going to say that the primitivist is just evading the philosophical responsibility to provide a discursive explanation of what propositions actually are. As was the case with the representation-concern, the primitivist can avoid the issue of quantity by refusing to provide us with such an explanation. And as was the case with the representation-concern, the rest of us will be left unsatisfied. Primtivism, we continue to maintain, should be a last resort. §2.4: The Problem of Aboutness Propositions have subjects that they are about. The proposition that Socrates is wise is about Socrates. The proposition that Romeo loves Juliet is about Romeo and Juliet, and perhaps it’s also about love. A problem faced by various theories of propositions is that they fail to provide appropriate subjects for their propositions. Jeff Speaks proposes that propositions are, in fact, a certain sort of monadic property (King et al., 2014, pp. 71–90). To assert that Romeo loves Juliet is to assert that the property of being such that Romeo loves Juliet is instantiated. According to Speaks, that property is the proposition that Romeo loves Juliet. However, if it’s true, and it is instantiated, what instantiates it? Well, in a nutshell, everything. If Romeo loves Juliet, then you instantiate the property of being such that Romeo loves Juliet, and so do I, and so does the world. So what is

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Framing Our Question

your assertion about? What is the proposition about? Well, in a sense, your proposition is about nothing, because it’s a monadic property with an empty argument space. And in a sense, your assertion may as well be about anything. You could assert that the world instantiates the property, or that you instantiate it. It doesn’t really matter. It all amounts to the same thing. The world is such that Romeo loves Juliet and so are you! In fact, your assertion is probably always very general: that something instantiates the property. But this all seems wrong. The proposition, and the associated acts of assertion, should be directly about Romeo and Juliet; they shouldn’t be about nothing, and they shouldn’t be about everything (King et al., 2014, p. 143). Frege famously thought that quantification generates higher order propositions about concepts. When I judge that there’s a lion in the forest, I make a judgement about the concept being a lion and about the concept being in the forest and I judge that those two concepts have the higher order property of being co-instantiated. But is your judgement really about concepts, or is it about the domain of the quantifier – i.e., what’s in the forest? The problem of aboutness doesn’t just plague the structuredpropositioners. In what sense is a set of possible worlds in which sentence S (relative to a context) is true, about the subjects of sentence S? In what sense is a function from sets of worlds to truth-values about anything more fine-grained than entire worlds? Once again, the primitivist has an easy escape: propositions are about whatever they’re about, and that’s a brute fact that admits of no further analysis. §2.5: The Problem of Dependence In a sense, what I call the problem of dependence is just a variety, or perhaps a specific cause, of the problem of quantity. Notwithstanding, it’s a sufficiently pernicious and distinctive form of the problem to deserve its own treatment. Here’s an example of the problem: if the existence of propositions are too tightly dependent upon the acts of sentient agents, then in certain situations, where the relevant acts haven’t occurred, certain propositions that should exist won’t exist. Soames has argued, for example, that propositions are a variety of action type. So the proposition that 2 + 2 = 4 is, for Soames, something like the action type that typifies what goes on when a person asserts, or judges, or entertains the notion that 2 + 2 = 4. If such events occur in a world, then the relevant types exist. But what about a world in which no such event occurs? Are we to say that in a world in which nobody actually goes to the trouble of asserting that 2 + 2 = 4, then, in that world, there is no proposition that 2 + 2 = 4, and consequently, since propositions are the primary bearers of truth, it isn’t true that 2 + 2 = 4?

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Soames can make things a little bit better for himself. He argues that if an agent has predicated an n-adic property R, of some objects, any objects, and, if objects o1, . . ., on have all been referred to by agents, any agents, then the action type of predicating R of o1, . . . ,on exists, even if nobody has ever predicated R of those particular objects – since the raw ingredients for that action type do exist in that actions have occurred in which each of the relevant objects have been referred to and in which the relevant property has been predicated. King (King et al. 2014, p. 130) is concerned that this doesn’t go far enough. Surely, he argues, There are lots of objects that have never been referred to and properties that have never been predicated of anything. . . . [Soames doesn’t] secure the existence of event types qua propositions involving such objects and properties. Hence, on Soames’ account such propositions don’t exist. But surely, many such propositions exist and are true (e.g., the proposition that some never-referred-to molecule o is a molecule, [an example] which Soames himself considers). Eventually, Soames (King et al., 2014, p. 103) escapes this problem along a metaphysically contentious path: he argues that things that don’t exist can still have properties. His contentious examples include dead, and so, apparently, non-existent people, instantiating the properties of being dead, being referred to by me, and being admired by somebody. And so merely possible propositions that don’t exist in the actual world can still have the property of being true. According to this line of thought, if Soames’ theory generates too few existing propositions, we needn’t worry since propositions don’t need to exist to do all of the work we need them to do. As King (King et al. 2014, p. 130) points out, this line of escape is metaphysically contentious. It is out of kilter with both ‘serious actualism’ and ‘serious presentism’ (the former being the view that to have a property at a world w, a thing needs to exist at w, and the latter being the view that to have a property at time t, a thing needs to exist at t). Soames isn’t the only theorist who stands accused of generating a quantity problem in virtue of tying the existence of propositions too closely to the acts of mental agents. King himself stands accused of the same crime. King thinks that the proposition that Michael swims contains Michael and the property of swimming as constituents. But harking back to the problem of unity, we can ask, what holds them together? King’s answer appeals to a very clunky and seemingly gerrymandered relation. This relation combines Michael and swimming to create a fact: The fact that there is a context c such that Michael is the semantic value (relative to c and assignment g) of a lexical item e of some

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Framing Our Question language L and that swimming is the semantic value (relative to c and g) of a lexical item e' of L such that e occurs at the left terminal node of the sentential relation R that in L encodes ascription and e' occurs at R’s right terminal node.

This clunky fact is basically the fact that according to some context c, and some assignment of objects to variables g, there is a sentence in at least one language, say, English – e.g., the sentence ‘Michael swims’ – in which two words, ‘Michael’ and ‘swims’, stand in a sentential relation that encodes ascription of the predicate term to the subject term, and in which Michael is the semantic value of the word on the left terminal node of that sentential relation, and swims is the semantic value of the word on the right terminal node of that relation. More simply still, Michael and swimming stand in the following relation: some language or other exists with the expressive power, given a liberal assignment of objects to variables, to attribute swimming to Michael! Of course, having solved the problem of unity, in terms of this clunky relation that holds Michael and swimming together in this fact, we can now turn to the representation-concern. In what sense can this clunky fact be the proposition that Michael swims? The proposition is, after all, supposed to represent Michael as swimming, but this clunky fact can’t represent anything all by itself. It’s just a fact. The basic response is that this fact doesn’t represent on its own, but will be interpreted as representing Michael as swimming by anybody who speaks the language L; because speakers of the language L understand the significance of the sentential relation R. That relation encodes ascription, and so this fact is going to be interpreted as ascribing the property of swimming to Michael. Whether or not this response to the representation-concern suffices, we can see that there’s going to be an issue of dependence. The proposition that Michael swims cannot exist until there exists a language, any language, with a dyadic sentential relation that encodes ascription. The existence of the proposition depends upon that. To its credit, King’s view can allow for propositions about never-before referred to entities: [T]he proposition that o swims exists even where o is an object that has never been the semantic value of any expression relative to any actual context of utterance. For even if that is so, there is [an actual, and not merely possible] context c, assignment g (namely, any context and assignment that maps ‘x’ to o) and language L (English) such that for some lexical items a and b of L (‘x’ and ‘swims’, respectively), o is the semantic value of a relative to g and c and the property of swimming is the semantic value of b relative to g and c and a occurs at the left terminal node of the syntactic relation R that in L

Framing Our Question

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encodes ascription and b occurs at R’s right terminal node. And this is just to say that the proposition that o swims exists. (King et al., 2014, p. 57) Thus King’s theory seemingly steals a march on Soames. Soames cannot say that the proposition that o is a molecule exists if o has never been referred to. King, on the other hand, can allow that that proposition exists. But King’s dependence problem emerges elsewhere. What about worlds in which no sentient life evolves? King cannot generate propositions in those worlds, because there will be no languages for them to depend upon. If propositions are truth-bearers, then every world should contain the proposition that 2 + 2 = 4, because, presumably, it’s true in every world. Of course, this dependency problem also arises for King when considering pre-linguistic epochs of actual history. Were there not yet propositions before we evolved a language? Was the proposition that 2 + 2 = 4 not yet true? As King asks of his own theory, if propositions didn’t exist until languages did, and if propositions are the primary bearers of truth, then was there no truth that the universe, two seconds after the Big Bang, had a certain average temperature (King, 2007, pp. 67–8)? To these questions King has various lines of response (King, 2007, pp. 67–95; King et al., 2014, pp. 60; 191–5), which we’ll explore in chapter 10, §§4.1–4.2. As I said before, my purposes here are not to give an exhaustive account of the strengths and weaknesses of any particular theory, so much as to sketch the sorts of worry from which they’re going to have to escape.12 In laying out their shared concerns, and in criticising each other, King, Soames and Speaks have delineated an array of problems to avoid or solve: the problem of unity, the representation-concern, the problem of quantity, the problem of aboutness and the problem of dependency.

§3: The Structure of This Book We have, from §1, a sense of the sort of things that propositions, if they exist, are supposed to do. We also have, from §2, a sense of the sorts of problems that an account of propositions will have to circumnavigate. The purpose of this book is to champion an old theory, rather than the new ones put forward by King, Soames and Speaks. The theory in question has sometimes been called the no-propositions theory of propositions, since it was Bertrand Russell’s attempt to give an account of propositions – i.e., an explanation of the 11 explananda of §1 (or most of them) – without incurring ontological commitment to propositions. In short, Russell’s theory states that the judgement that Romeo loves Juliet should no longer be thought of as a relation between a mind and the proposition that Romeo loves Juliet. Instead, it should be regarded

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as a multiple relation between a mind and Romeo, Juliet and love, in a certain order. In that this theory tries to explain what goes on when a mind makes an assertion, it deserves to be called a theory of propositions. It takes the metaphysical task of a theory of propositions seriously, and doesn’t desert the undertaking, as Davidson did.13 In that it gets rid of propositions altogether, it deserves to be called a no-proposition theory. Hence: the no-proposition theory of propositions. The theory is also known as the Multiple Relation Theory of Judgement (the MRTJ). It has never been very popular. It has, admittedly, attracted a good deal of historical scholarship – which we shall engage with as the book progresses. Its main historical interest is that it marked something of a parting of the ways between Russell and his most prominent student, Ludwig Wittgenstein. The actual content of Wittgenstein’s critique, delivered in instalments over the course of a sweltering spring in Cambridge in 1913, have remained something of a mystery to scholars. This mystery has spurred something of a cottage industry – a project in intellectual archaeology – in which thinkers try to reconstruct Wittgenstein’s devastating concern from fragments of letters and notes and the like. Beyond its historical interest, very few philosophers have thought that the MRTJ was worthy of much attention. David Armstrong (1973, p. 44) notes that the MRTJ ‘seems unworkable’ and calls it ‘wasted labour to go over the ground again’ (although, as we’ll see in chapter 7, he couldn’t resist, and did end up raising certain criticisms against it). Similarly, John Mackie (1973, p. 28) notes, of the MRTJ, that ‘no one now, I think, takes it very seriously’. However, in this book, I hope to prove that taking the MRTJ seriously will not be wasted labour. I argue that a version of the MRTJ can go a long way towards explaining our explananda in a way that can also circumnavigate or at least ameliorate our concerns. I argue that the MRTJ can go a long way towards furnishing us with a metaphysics of meaning. The book divides into three parts. Part I – The Historical and Philosophical Background – charts the trajectory of Russell’s thought before he adopted the MRTJ – a trajectory that will, hopefully, motivate, in part, a contemporary defence of the theory as the book progresses. Part II – The Rise and Fall of the MRTJ – explores the following questions: what led Russell to deny the existence of propositions altogether? Why did the theory keep evolving throughout its short life? What role did G. F. Stout play in the evolution of the theory? What was Wittgenstein’s concern with the theory, and, if we can’t know what his concern was exactly, then what are the best contending hypotheses? And, why did Russell give the theory up? In part III – Resurrecting the MRTJ – I will try to argue that the MRTJ was prematurely abandoned and that the concerns that Russell had with the theory weren’t worth rejecting the theory over. Moreover, in part III, I shall try to argue that the MRTJ does most of what we could want from an account of propositions, and that it does so at little philosophical cost.

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Not much of this book is purely historical. In the first two parts, it is very much my aim to lay out the intellectual developments that lead Russell himself towards the MRTJ, but – where relevant to my overall project – I present those developments alongside contemporary considerations aimed at motivating a similar intellectual journey for the reader. In part III, I give up the task of trying to be anything of a spokesperson for Russell. By that point, I’m no longer doing history at all. Instead, I’m trying to defend and extend the MRTJ, even in ways that Russell may not have appreciated, or with arguments that he might not have liked. Part I contains three chapters. In chapter 2, I outline a number of doctrines that Russell adopted between 1899 and 1905, in his initial break from the idealism of F. H. Bradley and the other British Idealists. In chapter 3, I discuss the impact that Russell’s theory of descriptions had upon his thought in 1905 and onwards. In chapter 4, I offer a new perspective on the theory of descriptions, in order to shed new light upon the doctrines explored in chapter 2. Part II contains three chapters. In chapter 5, I document the birth of the MRTJ and explain how it arose from the philosophical background developed in part I. In chapter 6, I chart the role played by G. F. Stout in the evolution of the MRTJ between 1910 and 1913, and compare Stout’s concern with the MRTJ to the representation-concern documented in §2.2. In chapter 7, I document the demise of the theory and Wittgenstein’s alleged role in that demise. Part III contains four chapters. In chapter 8, I try to defend the MRTJ against the concerns of Stout and Wittgenstein (and others), and hope to demonstrate that the MRTJ was too quickly abandoned. In that chapter, I turn to the question of what sorts of nonsense we should be able to judge. In chapter 9, I extend the MRTJ to account for the assertion of molecular propositions – a task that, as I’ve mentioned, some people claim the MRTJ cannot handle. In chapter 10, I return to our 11 explananda, and argue that the MRTJ does a decent job of explaining what needs to be explained by a theory of propositions. In chapter 11, I compare the MRTJ to some of its contemporary contenders, and see how they all fare against the concerns we raised in §2 of this introduction (and elsewhere). I argue that the comparison is favourable. More than a hundred years have passed since Russell first adopted the MRTJ. This book seeks to breathe into this much-maligned theory a new lease of life.

Notes 1 They can in cartoons, but cartoon toothbrushes aren’t really toothbrushes (except for in the fiction of the cartoon). 2 Jeff Speaks (King et al., 2014, pp. 9–24) attacks what Davidson has to say on this issue. 3 It’s important to note: Davidson doesn’t deny that propositions exist. He denies only that they’re necessary or sufficient for a theory of meaning (1967).

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4 5

6 7 8 9 10 11 12

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Framing Our Question Technically, he’s open to the suggestion that propositions exist, if a role can be found for them to play. But it’s clear that he’s sceptical; since he sees no such role. That scepticism comes to the fore, and becomes somewhat more trenchant, in Davidson (2005), where he rejects the need for any sort of semantic universals (propositions as referents of sentences, and regular universals as referents of predicates) because not only are they not needed in a theory of meaning but also give rise to classic ‘third-man’ type regresses. Accordingly, in the rest of this book, I’m going to treat Davidson as if he denies that propositions exist. This isn’t completely fair to him, but seems to be close to the spirit of what he thought. Furthermore, even if Davidson didn’t deny the existence of propositions, it would seem to be a perfectly Davidsonian approach to go that far: to deny that propositions exist since Davidson has explained all that they were called upon to explain without positing them. So when I talk about Davidson, in this book, I’m really talking about a Davidsonian who goes further than Davidson’s own agnosticism regarding propositions, and uses Davidson’s thought to embrace a full-on denial of their existence. This neat summary of structured-propositionalism I borrow from Lorraine Keller (2014). Throughout, I call it a ‘quasi’ mereological problem, because structuredpropositioners are notoriously evasive about what it means to be a constituent of a proposition. Keller asks, rhetorically (2014): ‘Is a proposition related to its constituents as a set is to its members, or a composite object to its parts? Or are propositional constituents “parts” in some other, non-mereological sense?’ This presentation of Russell’s problem follows Weiss (1995). Russell called these non-obtaining states ‘objective non-facts’ (Russell, 1906, pp. 45–46). This presentation of Russell’s primitive distinction in terms of obtaining and non-obtaining, I owe to Landini (2007, p. 40). For the moves open to possible-worlders in response to the problem of quantity, and for a variety of counter-moves, see King et al (2014, pp. 38–44). This is, of course, an extension of the problem that Paul Benacerraf (1965) levelled against the set theoretic conception of numbers. Religious scepticism wasn’t universally a family trait, since Ramsey’s brother was later Arch-Bishop of Canterbury! There’s also a fear that King generates too many propositions, by tying them too closely to grammatical forms of language. King has something to say in order to address this concern (King et al., 2014, p. 58). I return to this issue in chapter 11. See footnote 3.

Part I

The Philosophical and Historical Background

2

Moore and Russell in Rebellion

The birthdate of analytical philosophy isn’t all that easy to pinpoint. Was Bernard Bolzano the first analytical philosopher?1 Was Hermann Lotze?2 These questions depend, in large part, upon how we might think to define ‘analytic philosophy’. One thing, however, is clear. When G. E. Moore and Bertrand Russell rebelled against the dominant idealistic philosophy that they had been taught at Cambridge – their rebellion gave rise to the first flush of English-speaking analytic philosophy. Moreover, their enthusiasm, vigour, and ingenuity, coupled with Russell’s sometimes dazzling rhetoric and polemical verve, gave the movement the momentum that would one day make it the dominant form of philosophy in the English-speaking world. British idealism, against which they strove, adopted a monism, according to which only one thing exists. That thing is the Absolute. Had the British Idealists been more religiously inclined, they may have called it the mind of God. For them, nothing else truly existed. Russell and Moore’s rebellion was to embrace a doggedly realist and common-sense metaphysics. Russell later remembered the heady days of that rebellion against the regnant Idealism of the times: I felt it, in fact, as a great liberation, as if I had escaped from a hot-house on to a wind-swept headland. I hated the stuffiness involved in supposing that space and time were only in my mind. I liked the starry heavens even better than the moral law, and could not bear Kant’s view that the one I liked best was only a subjective figment. In the first exuberance of liberation, I became a naive realist and rejoiced in the thought that grass is really green, in spite of the adverse opinion of all philosophers from Locke onwards. (Russell, 1959, p. 48) In this chapter, I develop a number of doctrines, adopted by Russell as part of his rejection of British Idealism. These doctrines evolved over time. Indeed, Russell is well known for changing his views as often as some people change their clothes. However, all of these doctrines played

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a role in motivating the MRTJ, even if he rejected some of them in the act of adopting the MRTJ. They therefore form part of the background to the story that I’m seeking to tell in this book. More generally, it is essential for any scholar who wants to chart the trajectory of Russell’s thought to understand these doctrines, their evolution, and – where applicable – Russell’s ultimate rejection of them. F. H. Bradley was the most prominent target of G. E. Moore and Bertrand Russell’s rebellion against idealism – a rebellion which was very much a joint venture.3 Accordingly, in this chapter, I will develop an account of some of the doctrines that Russell and Moore adopted, by contrasting them with the views of F. H. Bradley.

§1: Propositional Realism Bradley’s The Principles of Logic (1883) attacks the prominent empiricist view that words are meaningful, for a person, iff the meaning is bound up with ideas and experience that that person has, which seems to amount to a denial that two people can judge the same thing without having access to the same mental events/mental life. The empiricist view of meaning is therefore psychologistic, which is to say, it allows psychological notions to interfere with logic and metaphysics. Bradley was able to resist psychologism, or so he thought, with his distinction between a psychological idea and a logical idea. First, we must understand Bradley’s distinction between existence and content. All things exist, and all things exist in a certain way. We can therefore distinguish between the flower’s existence (i.e., the fact that it exists) and the flower’s content (i.e., the fact that it is red and flowery). This distinction underpins Bradley’s theory of meaning. To create a meaningful sign, Bradley says that we must concentrate on some fragment of content, cut out from its existence, and use that content as a sign. In other words, meaning is a certain sort of content considered in isolation from its existence. Perhaps this theory will become clearer as we get more details out into the open. For Bradley, meaningful content comes in two forms: original content and acquired content. To illustrate this distinction, examine the following examples. 1. In a botany class, the teacher holds up a particular flower and uses it as a symbol for a whole species. 2. In a discussion among English speakers, the word ‘table’ is used as a sign for a table. In order to allow the flower to serve as a sign for a whole species of flower, the class must ignore its particular existence, and focus on its content: its shape, size and colour, for example. The class must allow

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that content to take on some sort of general significance. In other words, they have to abstract away from the particular flower, from its particular existence, and focus on the qualities that it has in common with all flowers. Only then will the flower function as a symbol for all flowers. The content of the flower that the class concentrate on is content that is quite natural for the flower to have – e.g., colour, shape and size. The relevant content is therefore original to the flower. This is what Bradley means by ‘original content’. In order to allow the word ‘table’ to serve as a sign for a table, on the other hand, the listener must concentrate only on that part of the content that that word has in virtue of the fact that the English-speaking world has, for some reason or other, imbued it with just that meaning. There is nothing intrinsic to the word ‘table’ that makes it an appropriate sign for a table. This content is acquired. We are now well placed to understand Bradley’s distinction between logical and merely psychological ideas. A psychological idea is a mental event that takes place in someone’s mind: an experience of a red sunset, for example. A logical idea, on the other hand, is a mental event that has undergone a certain transformation and has become, via an operation of the mind, a sign with meaning. We take our red experience, and use it as a sign for redness: we ignore its merely psychological existence, and we use its content, or some of its content. In other words, logical ideas are abstracted contents divorced from the neurological happenings that happen to bear them. The fact that two people can make the same judgement can now be explained: though two people can never share the same psychological idea, two people can entertain logical ideas that are of the same thing. When you use your logical idea of redness as a sign for redness, and I use my logical idea of redness as a sign for redness, and when we both assert our logical ideas of the same ball, then we make the very same judgement: we judge that the ball is red. This was Bradley’s anti-psychologism: mental events qua mental events no longer play a role in constituting the content of an assertion. The first publication in Moore and Russell’s revolt against idealism was Moore’s ‘The Nature of Judgement’ (1899). It was an aggressive attack on Bradley’s Logic. Nevertheless, there was one noteworthy point of agreement: Now to Mr. Bradley’s argument that ‘the idea in judgment is the universal meaning’ I have nothing to add. It appears to me conclusive, as against those, of whom there have been too many, who have treated the idea as a mental state. (Moore, 1899, p. 177) But Moore and Russell didn’t think that Bradley had taken his antipsychologism far enough. If meanings really are totally public and

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mind-independent, then every meaningful sentence must have a meaning. When you assert that P, you must stand in relation to some thing – existing outside of your mind – called P: a proposition. Moore and Russell saw propositional realism (viz. ontological commitment to mind-independent propositions) as the natural conclusion to be drawn from the failures of psychologism. When two people mean the same thing, they stand in relation to the same, publicly accessible and wholly extant, meaning. Bradley didn’t accept propositional realism. His logical ideas weren’t whole propositions; they were merely the adjectival element of a proposition (ideas of redness, roundness, etc.). And even these logical ideas, Bradley would argue, have no real existence. Logical ideas were, for Bradley, abstractions. They are given rise to precisely when we ignore their existence as psychological occurrences and concentrate on their content. But if, with Russell and Moore, you reject the notion of a non-existent ‘floating adjective’, then Bradley’s own anti-psychologistic tendencies should lead quite naturally to the doctrine of propositional realism – a doctrine that Moore adopted in ‘The Nature of Judgement’ and Russell adopted in its wake (it is assumed, for example, right throughout Russell’s Principles of Mathematics (1903), though never argued for explicitly). Russell and Moore’s propositional realism is thus motivated by two factors: (1) there must exist some thing to play the role of sentence meanings – not least because we quantify over them4 – propositions are what the propositional calculus – a part of logic – deals with; just as there must be sets for set theory to deal with, and numbers for arithmetic to deal with, there must be propositions for logic to deal with and (2) meanings must be mind-external. Bradley agrees with (2). That is his anti-psychologism. However, he doesn’t agree with (1). Propositions are, in some respect at least, independent of any particular mind, but they don’t really exist, they are, rather, ‘floating adjectives’. For Russell and Moore, if you can talk about a thing, especially if you’re committed to talking about that thing, then it must exist.5 The notion of a non-existent floating adjective was a nonsense to them. In short, Russell and Moore posit the existence of propositions to play many of the roles we canvassed in §1 of chapter 1. Our first doctrine is propositional realism. The next doctrine on our tour of doctrines that Moore and Russell adopted, against Bradley, is predicate reference realism.

§2: Predicate Reference Realism I will call predicate reference realism the doctrine that universals exist and that predicates refer to them. In this section, we document why Russell and Moore adopted this doctrine.

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§2.1: Moore’s Attack on Bradley Moore’s (1899) first criticism of Bradley concerns his equivocation over the nature of logical ideas. Moore detects two distinct notions playing a role in Bradley’s Logic: (L1) A logical idea is an idea with an adjectival meaning (L2) A logical idea is an adjectival meaning (L1) is consistent with nominalism: there is no such thing as redness; but we somehow manage to generate an idea that is only true of red things. However, there are times in the Logic where Bradley equates logical ideas with adjectives and universals themselves – he calls them ‘wandering adjectives’ and ‘universal ideas’ (Bradley, 1883, §10, §7). According to such locutions, it seems as if the logical idea is no longer operating as my idea of redness or your idea of redness, but as the meaning itself, as the referent of the predicate ‘is red’: redness. (L1) arises naturally from Bradley’s account of the genesis of the logical idea from a psychological idea; an account that Moore rejects via the following reductio ad absurdum (Moore, 1899, p. 178): (1) Assume that a logical idea is created by an abstraction upon a psychological idea (2) In order to make a judgement, I need to assert a logical idea of an object (3) Before I can make the sort of abstraction demanded by (1), I need to make a judgement about some psychological idea or other: I need to judge that part of its content can serve as an appropriate sign for my current purposes (4) If (3) were not true, then there would be no way of finding an appropriate psychological idea to abstract a logical idea from (5) Given (2), (that every judgement requires a logical idea) and (3) (the creation of a logical idea requires a prior judgement): before I can make any judgement, I will first need to make a prior judgement (6) Given (5), it is impossible to make a judgement without making a judgement before it, and it is therefore impossible ever to judge (7) Given that (6) is absurd, we should reject our initial assumption. Therefore, a logical idea is not created via abstraction from a psychological idea Peter Hylton (1990, pp. 132–3) isn’t convinced by this argument. He writes that it: [P]resupposes that the abstraction by which a logical idea is formed is a conscious process, which takes place in accordance with judgement. But there is no reason why a proponent of abstractionism should admit this point, as Bradley indeed pointed out in a letter to Moore.

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There are two elements to Hylton’s response: (1) abstraction needn’t be a conscious process and (2) abstraction needn’t take place in accordance with judgment. The first response is clearly found in Bradley’s letter, but it clearly fails to hit the mark.6 Bradley’s Logic talks about the process of creating a meaningful sign (such as a logical idea) in terms of cutting off the existence from a content. In his letter to Moore, true to Hylton’s word, Bradley laments this way of putting things: I suppose my phrase ‘cut off etc.’ has been taken to imply a going about to cut off & therefore a previous idea. I never meant that. But how is a content cut off from its existence, unless we actually do the cutting? Hylton reads Bradley’s letter as a denial that the cutting off is a ‘conscious process’, but it’s wholly irrelevant whether the process of abstraction is conscious or subconscious: it still sounds like a process – a process that, because of Moore’s regress argument, can have no beginning. Hylton’s second response can’t be found (at least not clearly) in Bradley’s letter, but constitutes a powerful defence against Moore’s regress argument. Perhaps abstraction is a sui generis process: Judgements require logical ideas, but abstractions don’t. Nowhere in Bradley’s letter (or at least in what remains of it) is such an argument clearly stated, but it would certainly have some force. If abstraction can occur without any judgement taking place, then the infinite regress may be avoided (we can deny premise (3) of Moore’s argument). There are two reasons why Moore may not have been moved by such a response: first, it renders abstraction mysterious. Abstraction of original content seems to have propositional structure, since to abstract redness from something red is first of all to notice that the thing is red to begin with. Noticing that something is red has propositional structure. To deny that abstraction of original content has that form is to make it mysterious.7 Second, if meanings depend for their pseudo-existence upon abstraction, and abstraction is thought to be a cognitive act, then Bradley, though he will have escaped the regress, will not have escaped the spectre of psychologism – a spectre that can only really be avoided upon the dismissal of idealism, and the replacement of (L1) with (L2). In order to generate his regress argument, Moore assumes that the meaningful content of a logical idea was original to the psychological idea from which it was abstracted. The logical idea of redness will thus be abstracted from an experience with red content. This assumption generates a regress (or a circle) because one will have to have judged that the experience was an experience of red before knowing that it would be an appropriate target for abstraction. However, perhaps the content of a logical idea is acquired content (see §1 for the distinction between

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original and acquired content). Perhaps I can choose any experience I like – even an experience of green – and make it a sign for redness simply by choosing to use it in this way (just as the English-speaking community take a word such as ‘table’, that has nothing inherently resembling a table about it, and choose to use it as a sign for tables). On this reconstrual of Bradley, two logical ideas have shared content iff we take them to do so: we make them what we want them to be – their content is acquired in virtue of the choices we make. An experience with green original content can be abstracted so as to serve as a sign for redness whenever I take it to do so. This again allows us to deny premise (3) of Moore’s regress. Hylton thinks that Moore doesn’t appreciate this more sophisticated reading of Bradley. But Moore does appreciate this aspect of Bradley’s theory: indeed, he extends the previous argument explicitly to target the notion of taking it to be so (Moore, 1899, p. 178). The argument, as it extends, runs along the following lines: (1) Take any two people’s logical ideas of redness, call them (Id1) and (Id2) (2) Bradley suggest that (Id1) and (Id2) are logical ideas with shared meaning merely because we take them to be so (3) The operation of taking them to share meaning constitutes a judgement/stipulation (4) The judgement in question will assert/stipulate of its objects, (Id1) and (Id2), that they have a shared meaning. Given the second premise of the previous argument, this judgement/stipulation will need to invoke a logical idea (5) The logical idea needed for the judgement in question will be the idea of ‘both-being-ideas-of-redness’; call this idea (Id3) (6) One will notice that (Id3) also includes redness in its content (7) (Id1), (Id2), and (Id3) are therefore ideas with some shared content (8) What does it meant for these three ideas to share content? Bradley suggests that the three ideas share content because we take them to do so (9) Taking them to do so involves making a judgement/stipulation about all three of them, a judgement that will invoke a new logical idea – (Id4) (10) (Id4) will also include redness as a part of its content, and will thus share in the similarity between (Id1), (Id2) and (Id3) (11) The regress is infinite. The similarity is never explained, as in Plato’s third man argument Hylton misreads this argument. He misjudges its target. He takes it to be an argument against the claim that two logical ideas can have the same original content. As far as Hylton is concerned, this misses Bradley’s point entirely: it misses the point that logical ideas can have a meaning based upon acquired content. Thus Hylton accuses Moore of presupposing ‘the essential point

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The Philosophical and Historical Background

at stake between him and the Idealists – whether there are facts which are independent of the constitutive activity of the mind’ (Hylton, 1990, p. 133). However, on my analysis of the argument, Moore isn’t presupposing this essential point at all – he is, in fact, arguing forcefully for it. It seems as if Bradley (in his letter) had understood Moore’s argument as Hylton later would. He recaps it with the following words: The second argument seems to urge that in order to perceive identity of meaning in two images I must take a vivid intermediate image and then a further image to perceive my perception & so on. Bradley takes the target of the argument to be the process of noticing that two ideas have identical original content. Bradley answers Moore with appeal to the notion of acquired content (or so it seems, Bradley’s actual answer is somewhat difficult to penetrate). Interestingly, Moore took Bradley’s letter, and underlined the word ‘perceive’, as I have done. He wrote above it ‘No’. Evidently, Bradley had misunderstood. Moore’s argument has nothing to do with merely ‘perceiving’ original content. Its target is the more sophisticated notion of acquired content, of stipulating that two things should have the same meaning. As I’ve tried to demonstrate, this argument against Bradley works. Bradley could try to claim that the abstraction of acquired content is primitive and doesn’t have the propositional form of a stipulation. However, if that’s the case, we go back to reducing abstraction to a mysterious primitive. Furthermore, we would have reason still to fear the spectre of psychologism, since abstraction (whatever else it is) is a cognitive act. Logical ideas are what adjectives mean, and they cannot be generated from the content of psychological ideas (whether that content be original or acquired) without regress (or mystery). Moore thought his proof that logical ideas are not created by the mind, entailed that they were wholly mind-independent. However, in actual fact, he has only demonstrated that the mind didn’t create them. He hasn’t demonstrated that our meaningful use of adjectives can’t be cashed out in terms of a set of concepts that come innately hardwired into our brains. Moore’s full case against psychologism is, therefore, part argument and part intuition. He meets Bradley’s claim that logical ideas are created by the mind with a good argument. He is left to meet the claim that adjectival meanings are hardwired into the brain with the following intuitive assumption (which he never states explicitly): (A) The objectivity of judgement demands that what Bradley calls logical ideas are mind-independent Common sense dictates that such facts as a’s being to the right of b are wholly independent of any mind. This dictate of common sense, Moore

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and Russell seemed to think, can only be satisfied if the meaning of ‘being to the right of’ is as mind-independent as a and b. St. Augustine registered a similar concern with the notion that universals are merely concepts in the mind: why is it that some of our concepts seem to carve the beast of reality closer to the joints than other concepts? Augustine’s solution was to say that objective concepts are concepts in the mind of God.8 Moore’s theologically economical solution was to say that these concepts aren’t mental at all: they exist outside of any mind; they are the referents of predicates. §2.2: The Doctrine of Linguistic Transparency ‘[I]t must be admitted,’ Russell (1903, §46) claimed, ‘that every word occurring in a sentence must have some meaning: a perfectly meaningless sound could not be employed in the more or less fixed way in which language employs words.’ This plausible assumption, coupled with Moore’s assumption, (A), that the objectivity of meaning necessitates the existence of entities to serve as those meanings, generates the doctrine of linguistic transparency. This doctrine, which will undergo radical revision before Russell adopts the MRTJ, states that every meaningful phrase has to have a mind-independent referent,9 including predicates. Besides his doctrine of linguistic transparency, Russell had independent reasons for thinking that universals – the referents of predicates – exist. It would, of course, be possible for a nominalist to think that predicates refer, but that they refer to the sets that constitute their extension. For Russell, the realist, universals were a much more natural candidate for predicate reference. What motivated that realism? A large part of the story has to do with Russell’s rejection of Bradley’s monism. Bradley’s monism was motivated (in addition to arguments from the nature of experience) by his denial of the reality of relations. Since relations can’t be real, because of arguments like Bradley’s regress, it follows that there can’t be many things related but only one thing. Russell, while still an idealist, had hoped that he could embrace a metaphysical pluralism, whilst embracing Bradley’s denial of the reality of external relations. He hoped he could make do only with internal relations (Griffin, 2003, p. 88). Ultimately, however, Russell came to see that any way of trying to analyse asymmetric relations, like 2 > 1, which didn’t allow for the existence of external relations, would fail to respect the asymmetry of the proposition at hand (Russell, 1903, §215). For instance, you could try to recast the relation as a property held by the set that contains the numbers 1 and 2. But sets are unordered. Consequently, this analysis will ignore the asymmetry. Therefore, Russell came to think that the existence of external relations was a necessary condition for making sense out of mathematical order, including elementary propositions like 2 > 1. The

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role that realism about relations played in Russell’s move away from idealism is a well-documented story, and these paragraphs merely provide some of the headlines.10 In short, and as is well known, Russell wanted to found mathematics upon logic. He took logic to have three parts: the calculus of propositions, the calculus of relations and the calculus of classes (Russell, 1903, p.13). The subject matter of the calculus of relations is relations. Relations are said to have properties such as direction, transitivity, intransitivity, non-transitivity, symmetry, asymmetry, non-symmetry and so on. The calculus of relations, and those relational properties, were to play a fundamental role in the foundations of mathematics – so, according to Russell, upon the adoption of his logicist programme, relations must exist. Relations are universals. Beyond this well-known story, it’s also worth noting that Russell’s epistemology placed a great weight upon the relation of acquaintance (this is readily apparent in his Problems of Philosophy (1912) and later works, but is hinted to even in Principles of Mathematics (1903, p. xx)). Acquaintance is the most primitive relation between the mind and elements of the mind external world. Relations are what we are acquainted with when we notice that the same relation holds between two different collections of entities. If you weren’t acquainted with the relation, you couldn’t notice its being instantiated (singularly or multiply). Properties are what we are acquainted with when we notice the same property instantiated in more than one place (or even in one place). Russell took it for granted, for example, that we are acquainted with the taste of pineapple (1903). If we are acquainted with relations and properties, then we should admit them into our ontology – in turn, they become obvious candidates for predicate reference. Finally, Russell (Russell, 1911–1912) levelled various arguments against nominalist attempts to accommodate objective resemblances. And thus for metaphysical, epistemological, logical and linguistic reasons, Russell felt himself committed to the existence of properties and relations, which were put to work, given the doctrine of linguistic transparency, as the referents of predicates. As far as Moore was concerned, in his initial break with idealism, universals were all that existed, at least at a fundamental level. He called them ‘concepts’. Tracing his views from 1899 to 1903, Maria van der Schaar (2013, pp. 25–6) says: The idea that an individual object is a complex of concepts or qualities [the 1899 view] is modified by Moore a few years later, when Moore considers an individual thing to be nothing but a complex of particular qualities [see Moore (1901)] . . . In 1903, Moore claims again that individuals are nothing but complexes of properties, and that properties alone make up the individual.

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Moore’s (1903, p. 41) reason for this claim has to do with his dislike of the notion of a bare particular: [T]he natural properties – their existence does seem to me to be independent of the existence of . . . objects. They are, in fact, rather parts of which the object is made up than mere predicates which attach to it. If they were all taken away, no object would be left, not even a bare substance: for they are in themselves substantial and give to the object all the substance that it has. Though Russell (1940) was later to adopt a similar view, it seems that in these early days, he had no such worry about the distinction between universals and particulars, and felt no compulsion to say that particulars were somehow built up out of universals. But despite their divergent views on this matter, what Russell and Moore shared at this point was (1) an ontological commitment to universals along with (2) the belief that predicates refer to them. Again, I call this conjunction of views predicate reference realism. Eventually, and somewhat surprisingly, we’ll see that the MRTJ doesn’t really rely upon the existence of universals. Moreover, because the doctrine of linguistic transparency is going to be so thoroughly revised in the chapters ahead, I will not be asking my readers to carry forward a commitment even to the notion that predicates have semantic referents (be they universals or anything else). However, these doctrines did play an important role in the evolution of the MRTJ, and it’s interesting to note that predicate reference realism is still considered, by contemporary philosophers of language, to be a going concern (see Fraser MacBride (2006)), even if the claims of this book won’t end up relying upon it. Similarly, it’s interesting to note how, beyond the philosophy of language, metaphysical arguments in favour of the existence of universals still abound, and how those arguments still echo Russell’s original arguments (Russell, 1911–1912; 1912). Of course, more nuanced options now exist for the metaphysician to choose between: new varieties of nominalism – predicate nominalism (or ostrich nominalism),11 resemblance nominalism,12 class nominalism,13 and more – trope theory,14 and different varieties of realism about universals have developed, positing different sorts of universals for different reasons.15 And yet, reading that literature, which we don’t have the space to delve into here, one is immediately struck by the continuity with the dialectic in which Russell was involved as he argued for realism as opposed to nominalism (Russell, 1911–1912; 1912). Indeed, the lasting strength of Russell’s realism is evidenced by the ways in which the defenders of nominalism (such as Rodriguez-Pereyra (2002)) still feel duty bound to respond to Russell’s arguments. However, once again, I note that even if I continue to talk as if I’m committed, with Russell, to the existence of universals, the version of the MRTJ that I defend in part III of this book will not rely on this commitment at all.

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§3: Direct Realism Direct realism is the doctrine that a proposition contains the very entities that it is about and/or invokes as its constituents. The proposition that Socrates is wise is about Socrates and invokes wisdom. Given direct realism, the proposition in question contains Socrates and wisdom among its constituents. Frege (1892b) drew a distinction between the referent of a phrase and the sense of a phrase. ‘Hesperus’ and ‘Phosphorus’ are both names of Venus. They share a referent. Frege wanted to explain their difference in terms of sense. Frege described a sense as a mode of presenting a referent. Take the sentence that expresses a proposition: according to Frege, the proposition will not consist of the referents of the phrases that constitute the sentence; the proposition will, instead, consist of the senses of the phrases that constitute the sentence. Thus the proposition that Socrates is wise consists of the sense of the phrase ‘Socrates’ and the sense of the phrase ‘is wise’. Frege (1892b) thought that the distinction between sense and reference could solve a variety of puzzles. But one of his reasons for denying direct realism was incredulity. Frege couldn’t believe that Mont Blanc itself, along with all of its snowfields, was a constituent of the proposition that Mont Blanc is tall (McGuinness, 1980, p. 163). Part of Moore and Russell’s joint revolt against Idealism can appropriately be described as follows: they were convinced that British Idealism was an insult to common sense; that its radical distinction between appearance and Reality was at odds with our most basic intuitions; they therefore sought to adopt the most radically anti-Idealist position they could, perhaps in the hope that the position would become more refined as it was subjected to criticism. Indeed, mocking himself somewhat, Russell explains, in retrospect, that: I began to believe everything the Hegelians disbelieved . . . In my first rebellion against Hegel, I believed that a thing must exist if Hegel’s proof that it cannot is invalid. (Russell, 1959, pp. 48–9) Given this methodology, direct realism was an obvious starting place for both Russell and Moore. Russell generally lumped Bradley and Hegel together, much to Bradley’s chagrin. But it is fair to say that Bradley’s Idealism had put Reality forever beyond the reach of our minds. For Bradley a completely true thought was an impossibility. Thoughts cannot be completely true without encompassing the whole of Reality, which can’t be done as long as the proposition is something distinct from Reality, and thus truth would be thought’s ‘happy suicide’ (1893, pp. 170–3). In contrast, Direct Realism puts our minds in direct contact with the real world and allowed for our best thoughts, like the thought that 2 + 2 = 4, to be completely and utterly true. To think about x, for the direct

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realist, is to stand in direct relation to it. And thus direct realism seems like a natural starting place for a philosophy interested in believing in everything that Hegel and Bradley disbelieved! In correspondence with Frege, Russell put forward something of an argument for direct realism. Direct realism follows from the assumption that we can know things about the mind external world. If Mont Blanc itself can never be an object of our thought, ‘we get the conclusion that we [can] know nothing at all about Mont Blanc’ (McGuinness, 1980, p. 169). If all your thought is mediated via senses, how can you guarantee that it ever reaches its target? If you want to oppose psychologism, you should oppose the establishment of any sort of veil between the mind, on the one hand, and the world it perceives and forms judgements about, on the other. Direct realism is the best antidote to radical scepticism. We’ll discuss the contemporary appeal of this doctrine in chapter 4, §2.

§4: Termism Frege thought that there was a fundamental logical distinction between a complete expression and an incomplete expression (Frege, 1891; 1892a). A complete expression has no gaps in it. An incomplete expression, on the other hand, does have gaps, plugged merely by place-holding variables. Thus ‘(2 × 2) + 4’ is a complete expression that names the number 8. An example of an incomplete expression, on the other hand, would be ‘(y × 2) + 4’ – this expression names no object: the expression is incomplete – we would have to replace its variable with a number before the phrase would name an object. Corresponding to the distinction in language between complete and incomplete expressions, Frege posited an ontological distinction between, as it were, complete and incomplete entities. Complete entities are called ‘objects’. Complete expressions name objects: ‘(2 × 2) + 4’ names 8. But what do incomplete expressions name? ‘(y × 2) + 4’ names no specific number, but it can be used to plot a graph: it names a function – a specific function that yields different objects depending upon the value of ‘y’. A function isn’t an object: it is an inherently incomplete entity that is named by an inherently incomplete expression – it is the referent of a predicate.16 Take the proposition that Charles loves Camilla. As far as Frege is concerned, a proposition is constituted by senses, rather than by referents (Frege, as we’ve seen, wasn’t a direct realist). The proposition that Charles loves Camilla, is said to consist of the sense of ‘Charles’, the sense of ‘Camilla’, and the sense of ‘x loves y’. These are the three simple entities that constitute the proposition. Of those three entities, only one is incomplete: Charles and Camilla are objects, as are the senses of ‘Charles’ and ‘Camilla’, but love is a relation (i.e., a function that maps objects onto the true or onto the false) picked out by the incomplete expression, ‘x loves y’; its sense is also incomplete: it has two gaps in it (corresponding to the two variables in the incomplete phrase, ‘x loves y’); the senses of ‘Charles’ and ‘Camilla’ saturate

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these gaps and thus the complex holds together like a jigsaw puzzle. This is often said to be Frege’s solution to the problem of propositional unity. I’m far from convinced that this really was what Frege would have said in response to the problem of unity. According to Leonard Linsky’s (1992) convincing read of the primary sources, Frege’s notion of complete and incomplete entities, and his notion of saturation, were only ever intended to be metaphors (Frege, 1892a, p. 193). According to Linsky, Frege actually thought that propositions were ontologically prior to their parts, and thus the whole endeavour of sticking things together to create propositions – indeed the entire problem of unity – wouldn’t have arisen for Frege. But Frege did think that his metaphor of complete and incomplete entities was a metaphor that one couldn’t do without (Frege, 1892a, p. 193). Furthermore, it’s pretty clear that Russell understood Frege to be responding to the problem of unity not as Linsky thought, but in terms of the saturation of a jigsaw (1903, Appendix A). Russell attacked Frege’s fundamental distinction in the following way.17 ‘x is wise’ is an incomplete expression. According to the Fregean view, it names an incomplete entity: a concept. However, the following phrase, ‘the referent of “x is wise”’, is a complete expression: it names an object. However, if the referent of ‘x is wise’ is a concept, and if the referent of ‘the referent of “x is wise”’ is an object, and if whatever is an object isn’t a concept, then, the referent of ‘x is wise’ will have to be a distinct entity from the referent of ‘the referent of “x is wise”’. However, this is absurd. Frege scholars know this problem – or, at least, a very similar problem – as the concept-‘horse’ paradox (Frege, 1892a). As a result of this sort of reductio ad absurdum, Russell rejected the claim that there was a fundamental ontological distinction between the referents of predicates and the referents of other expressions. The referent of ‘x is wise’ is, of course, the same entity as the referent of ‘the referent of “x is wise”’. This leads us to our next Russellian doctrine. Russell decided, on the basis of this type of anti-Fregean argument, that every entity is a term: a doctrine which I shall call termism. What it means to be a term is to have the ability to occur as the subject of a proposition. Frege’s incomplete entities were not such that they could occur as the subject of a proposition: this is what led to absurdity. There can be no entity such that it cannot be the subject of a proposition, for the very statement that it cannot be the subject of a proposition violates the doctrine that it cannot be the subject of a proposition! This absurdity is what motivates Russell’s termism. Nevertheless, Russell thought that there was an important distinction to be drawn between different sorts of term. Russell distinguished things from concepts (Russell, 1903, Ch. IV). A thing was a term that could only occur in a proposition if it was to appear as one of its subjects (or, of course, as its only subject). A concept, on the other hand, has a ‘curious twofold use’: it can occur as a subject of a proposition (as can all terms), but is unique in that it can also appear

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in a proposition without being its subject. ‘Socrates is wise’ expresses a proposition about Socrates. The referent of ‘x is wise’ – Wisdom – also occurs in this proposition, but not as its subject. Thus wisdom is a concept: it can be spoken about – e.g., ‘wisdom is a virtue’ – but it can also feature in propositions that aren’t about it. The idea that there are things that can’t be spoken about seems like self-referential incoherence (see, for example, Alvin Plantinga’s attack on theologians who think that God cannot be spoken of (Plantinga, 2000, pp. 3–66)). If you can’t speak about something, then you shouldn’t be able to say that you can’t speak about it. And thus termism seems like an obvious truism (perhaps only an adventure in philosophy could provoke a person to deny the truth of termism – indeed, even those who argue against termism tend to recognise its initial appeal). Moreover, even if you think that quantifiers have to be restricted, and so you don’t think that it can’t actually be said, of all things, across all domains, all at once, that they can all be subjects of a proposition, you still won’t deny of any given thing that it can be spoken of. And thus, even when Russell gave up on unrestricted quantification – a story that we’ll sketch later on – he didn’t immediately give up on the notion that every entity can be the subject of a proposition. In this chapter, we have arrived at five doctrines (some of them will be amended in later parts of this book, and some of them will ultimately be rejected out of hand): (1) propositional realism, (2) predicate reference realism, (3) direct realism, (4) the doctrine of linguistic transparency and (5) termism. All but one of these doctrines arose in conversation with the great British idealist, F. H. Bradley. It is against the backdrop of these doctrines that the MRTJ was born.

Notes 1 See Künne et al. (1997) 2 It is sometimes argued that Lotze was of seminal importance in the birth of analytical philosophy, even if this influence was somewhat subconscious (Sluga, 1980; Milkov, 2000; Gabriel, 2002). 3 Russell (1904) credits Moore for leading him to analytic realism, and, in his preface to his Principles of Mathematics, Russell (1903) expresses his ‘indebtedness’ to Moore from whom Russell derived his ‘philosophical outlook’. Richard Cartwright (2003), for good reason, doubts whether Russell’s indebtedness to Moore was quite as great as these passages seem to indicate – pointing to Russell’s tendency to be over charitable in crediting others. Nevertheless, it is clear that, in his rebellion against Bradley’s Idealism, Moore was Russell’s closest ally. 4 Prior to the discovery of Frege’s quantifier-notation, they would not have said that they were ‘quantifying over propositions’ – but they were! They were talking about propositions, and logic was, for them, a science of propositions. So they considered themselves to be ontologically committed to propositions for reasons that would, under a Fregean notation, become Quine’s slogan that ‘to be is to be the value of a variable’. 5 Here I make a distinction between talking about a thing, and being committed to talking about it. I have in mind the following idea: we can and sometimes

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6 7 8

9

10 11 12 13 14 15 16 17

The Philosophical and Historical Background do talk about Harry Potter – but you might think that merely talking about him doesn’t require that he exists. The ontological status of fictional characters is, of course, a vexed issue, which I don’t want to get into here. It will come up more substantially in chapters 3 and 4 – although, even there, the discussion will not be centrally focussed upon the philosophy of fiction. But, we can at least feel the tug of the intuition that Harry Potter doesn’t exist. The mere fact that we can talk about him doesn’t immediately seem to us to imply otherwise. Sometimes, however, we don’t merely talk of a thing; rather, we are committed to talking about it. I have in mind, for example, entities that our best scientific description of the world cannot fail to refer to. If our best theory of the world commits us, in this way, to talking about a thing, then, I contend, we might feel more of an intuitive tug towards accepting that our talk generates an ontological commitment. The letter in question, dated October 10, 1899, can be found (with some missing pages) in the Cambridge University Library, Moore Archives, with the shelfmark: Add. 8330; 8B/21/1 Thanks to Gil Sagi for a useful conversation about these issues. ‘Hence in Latin we call the ideas either “forms” (formae), or “species,” (species), which are literal translations of the word. But if we call them “reasons” (rationes), we obviously depart from a literal translation of the term, for “reasons” (rationes) in Greek are called logoi, not “ideas” (ideae). Yet, nonetheless, if anyone wants to use “reason” (ratio), he will not stray from the thing in question, for in fact, the ideas are certain original and principal forms of things – i.e., reasons, fixed and unchangeable, which are not themselves formed and, being thus eternal and existing always in the same state, are contained in the Divine Intelligence’ (Augstine, 2002, pp. 79–80). Divine conceptualism will reappear in this book, as something of a live option (despite Russell’s trenchant opposition to theism), in chapter 10, §§4.2.3–4.2.4, and chapter 10, ft. 14. With few a exceptions. For example, phrases directly about the contents of a mind will not have mind independent referents. Russell also introduces, by way of exception, a small class of syncategorematic words: certain instances of ‘and’ (Russell, 1903, §71, especially p. 72), and the quantificational terms, ‘all’, ‘every’, ‘any’, ‘some’, ‘a’, and ‘the’ (Russell, 1903, §72, pp. 72–3). These exceptions were pointed out to me by Fraser MacBride. For a more in-depth telling of this story, see (Griffin, 1980; 1991; 2003; Lebens, 2017) See Devitt (1980) (Rodriguez-Pereyra, 2002) (Lewis, 1986) Trope theory was originally developed by Husserl (1900–1901) and G. F. Stout (1921; 1923) and has a number of contemporary advocates (Maurin, 2014) (Armstrong, 1989) A predicate actually picks out a sub-species of a function. Frege calls them concepts. Concepts are functions with only truth and falsehood as possible outputs. They are truth-functions. In what follows I rephrase an argument to be found in Russell (1903, §§49, 52, and 483).

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Marching forward with the five doctrines whose genesis we traced in the previous chapter, I hope to refine Russell’s doctrine of linguistic transparency in this chapter.

§1: Realism Versus Transparency The tension explored in this chapter is between the doctrines of linguistic transparency and direct realism. According to direct realism (and assuming propositional realism), a proposition always contains its subjects among its constituents. The doctrine of linguistic transparency, on the other hand, dictates that every meaningful phrase/word contributes its own distinctive and constant meaning to the proposition expressed. On many occasions, these two doctrines can live happily side by side. The proposition expressed by the sentence ‘Socrates is wise’ is about Socrates and contains him as a constituent. But on occasion, these two doctrines conflict. Take the sentence ‘I met a man’ (which is the example that Russell uses himself to describe the tension). According to the doctrine of linguistic transparency, this sentence expresses a proposition that has the same constituents every time I utter it – the same words continue to contribute the same constituents to the proposition expressed. Direct realism cannot accept this: depending on who I happened to meet today, I can use this sentence to talk about Paul, or George, or John, or Ringo etc.; when I use the sentence about John, John is a constituent of the proposition expressed; when I use it about Paul, Paul is a constituent of the proposition expressed and so on and so forth. The doctrine of direct realism demands that on these different occasions, the sentence expresses propositions with different constituents. The doctrine of linguistic transparency, on the other hand, demands that on these different occasions, and, in fact, on all occasions, the sentence expresses the same proposition with the same constituents. Russell, it seems, was aware of this tension from the outset. He knew it needed resolving.

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It’s clear that indexical words – ‘I’, ‘now’, ‘here’, ‘there’, etc. – would also give rise to this problem, although in 1903, Russell doesn’t mention the phenomenon of indexicality explicitly at all.

§2: Denoting Concepts In the Principles of Mathematics, Russell (1903) wanted us to think of the shadowy entity that seems to be the subject of our proposition – a man – as a real entity that isn’t itself any particular person – it is, instead, a logical object that functions as an aboutness shifter (to use the language of Gideon Makin (2000)): in actual fact, let’s say that Paul is the subject of the proposition even though he isn’t a constituent of it; the shadowy logical object, a man, merely sits in the logical subject position of this proposition – in normal circumstances, just as direct realism dictates, a proposition would be about that entity/those entities sitting in its logical subject position/s; but, because the entity in question is an aboutness shifter, or, in Russell’s terminology, ‘a denoting concept’, when it sits in the subject position of a proposition, it’s able to shift what that proposition is about from itself to its denotation – in this case, to Paul. Denoting concepts denote a class as many (at least when the class in question has more than one member). Russell thought there were two ways that a class can be considered (1903, p. 76). There is the class as one. In this sense, the class is itself a term. But we can also consider each class as a class as many: a class as many is basically all of the separate members of a class considered all at once. Though a class as many is a collection of terms considered collectively, it is not itself a term. It is, rather, a ‘plurality of terms’ (Russell, 1903, p. 69, footnote). And thus, in a seeming exception to his termism, Russell has to make room for something that isn’t a term – although it also doesn’t really exist at all; it is merely its members – this thing is a class as many, Russell calls it an ‘object’ (Russell, 1903, p. 55) – although we should be careful to note that Russell’s use of ‘object’ to pick out a class as many, has nothing to do with the standard English use of the word ‘object’. Russell hoped that his objects wouldn’t be a toxic exception to his termism (although he worried that it was (1903, p. 55, footnote)). I don’t think his concern was justified. It’s true that objects aren’t terms, but we also never really think about them; we may try to think of them, but all we really succeed in doing is thinking of their members collectively; or we think of the class as one, which is a term! In other words, the fact that objects are not terms is no bother – they are nothing (other than their members).1 Russell was in fact pre-empting contemporary plural logic in his comments on classes as many. On most understandings of plural logic, a plural subject isn’t an entity that somehow fails to be a term.2 A plural subject, such as ‘the even numbers’, refers to nothing above and beyond the even numbers themselves – every one of which is a term.3

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A denoting concept will denote the object (i.e., the class as many) that falls under the property alluded to in the associated denoting phrase. The denoting phrase ‘every even number’ alludes to the property of being an even number, so the denoting concept in question will denote the class as many of even numbers. The ‘quantifier’ in a denoting phrase will help us to recognise how the denoted members of the class are arranged: ‘every’ will make the proposition about the members of the class severally, ‘all’ makes the proposition about each of the members of the class collectively, ‘any’ will make a proposition about each individual member non-specifically, ‘some’ will make the proposition be ambiguously about one member of the class, ‘an’ will make the proposition be about one arbitrarily picked member of the class and the definite article picks out the only members of singleton sets. Of course, more needs to be said about what it means to be about a class as many severally, as opposed to collectively (which will, in turn, have something to do with the difference between distributive and collective predication), and more needs to be said about what it means to be non-specifically about each member, etc. But a more thorough exposition of Russell’s soon-to-be-abandoned-theory would take us too far afield. Though Russell doesn’t address indexicals in 1903, he would probably have said that their referents were also aboutness shifters. Direct realism was Russell’s ideal, at least according to Hylton (‘An unqualified version of direct realism serves as a paradigm for Russell’ (Hylton, 1990, p. 214)); why then did he accept aboutness shifters and thereby sacrifice direct realism in favour of linguistic transparency, when he could have suspended linguistic transparency to resolve the same tension? According to Hylton, the answer concerns generality. Denoting concepts were able to explain what would otherwise have been a puzzle for Russell (1903, p. 73): An infinitely complex concept, though there may be such, can certainly not be manipulated by the human intelligence; but infinite collections, owing to the notion of denoting, can be manipulated without introducing any concepts of infinite complexity. Russell the mathematician had to be able to explain generality. In particular, he had to explain how our finite minds are able to comprehend and assert things about classes as many when those classes may have an infinite number of members. Direct realism was proving to be an obstacle to this fundamental goal. As Hylton (1990) understands Russell here, the puzzle is this: we need, if we are to engage in mathematics, to say and to think, for example, that every even number is divisible by two; but direct realism would have it that every single even number would have to be a constituent of that proposition; coupled with the principle of acquaintance – the plausible notion that we must be acquainted with all

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of the constituents of a proposition before we can assert it (that, in some loose sense or other, we have to know a thing in order to be able to talk directly about it)4 – we quickly see that it becomes impossible to assert such an infinitely long proposition – I’m not acquainted with every single even number. For Russell, in his quest to put mathematics on sure footing, this state of affairs was unacceptable – we have to be able to account for generality. Direct realism had to be modified. If Hylton has understood the puzzle correctly, then denoting concepts seem to give Russell just what he was looking for: I only need to be acquainted with the (finitely complex) denoting concept every even number, which in turn can shift the aboutness of a proposition to an infinite number of numbers, without my actually having to be acquainted with any of them. Direct realism didn’t disappear entirely: only in the presence of a denoting concept would direct realism have to be suspended.

§3: ‘On Denoting’ As we’ve seen, in Principles of Mathematics (1903), Russell chose to hold on to linguistic transparency in all cases, but to suspend direct realism in the presence of denoting concepts. In 1905, Russell reverts to a more orthodox direct realism – a direct realism without exceptions (although we will need to investigate what happens to indexicals on this theory; do they remain an exception to direct realism; are they still to be treated as aboutness shifters?5). This option became available in the light of Russell’s new theory – the theory of descriptions. The theory of descriptions denies that a phrase need correspond to some entity – some meaning – in order to be meaningful (although we’ll refine our understanding of what this means in the following chapter). Take the following sentence: ‘The unicorn in Trafalgar square has a crooked horn’. When I say this sentence, what – or who – am I talking about? The sentence, seemingly, has a subject: the unicorn in Trafalgar square. However, there is no unicorn in Trafalgar square. So what does the phrase, ‘the unicorn in Trafalgar square’ mean? That is to say, what entity, according to the linguistic transparency theorist, does the phrase contribute to the proposition expressed? The only obvious candidate for the meaning of the phrase – i.e., the unicorn – doesn’t exist. We could follow Meinong and say that there is such a thing as the unicorn – that it has being even though it doesn’t exist. However, analysing this sentence so as to make it about a shadowy non-existent (but subsistent) being is, at the very least, to engage in ontological extravagance. Russell realised, by 1905, that Frege’s quantificational machinery (which he hadn’t mastered when writing Principles of Mathematics) could be used to give us a less ontologically mysterious analysis. The sentence can be analysed (ignoring the contribution of the definite article

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until later, for the sake of simplicity) – using the concepts of being a unicorn, U, and being in Trafalgar square, T, and having a crooked horn, C, as follows: (∃x)(Ux & Tx & Cx) This analysis would read as follows: there exists an x such that x is a unicorn and x is in Trafalgar square and x has a crooked horn. Though this proposition is obviously false, its meaningfulness doesn’t commit us to the subsistence of anything like a unicorn. The proposition expressed by this sentence isn’t about a unicorn at all. It’s about three properties: being a unicorn, being in Trafalgar square, and having a crooked horn; what the proposition asserts is that these three properties are co-instantiated in at least one instance. Direct realism seems to recover its centrality: though certain propositions aren’t actually about what they seem to be about – they’re never about unicorns, for example, even when they appear to be6 – propositions always do contain their actual subjects as constituents. Frege thought that the definite article is used to construct a name. ‘The unicorn in Trafalgar Square’, for Frege is simply a name – perhaps a name for the empty set, or a name with a sense but with no referent. Russell’s insight was to treat the definite article as bound up with quantification. As we’ve seen – even in the Principles of Mathematics, Russell had sought to treat the definite article as a quantifier, and in ‘On Denoting’, the majority of the discussion is focused around definite descriptions. The analysis we’ve already given of the sentence ‘The unicorn in Trafalgar square has a crooked horn’ isn’t complete. It doesn’t encode the presence of the definite article. The analysis we’ve already given really means that there is at least one unicorn in Trafalgar square with a crooked horn. In order to respect the presence of the definite article, and the claim of uniqueness that seems to come with it, the real analysis, Russell argued, should be: (∃x)((Ux & Tx & Cx) & ((∀y)((Uy & Ty) → (x = y)))) This analysis reads: there exists an x such that it is a unicorn and it is in Trafalgar square, and such that for any y, if y is such that it too is a unicorn in Trafalgar square, then it is identical to x, and it has a crooked horn. In other words, this proposition actually makes three claims: (1) there is at least one unicorn in Trafalgar square, (2) there is at most one unicorn in Trafalgar square and (3) there is no unicorn in Trafalgar square such that it doesn’t have a crooked horn. Russell’s analysis solved the following puzzle: we want it to be false that there is a unicorn in Trafalgar square with a crooked horn; but if this is false, then its horn must be straight; but we also want it to be false that there is a unicorn with a straight horn in Trafalgar square. The claim that

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‘the unicorn in Trafalgar square has a crooked horn’ is now analysed as a conjunction of three assertions; if any one of them is false, then so is the conjunction. One of the claims is the claim that there is a unicorn in Trafalgar square. This claim is false, which causes the whole conjunction to be false – which is to say, it isn’t false merely because his horn isn’t crooked! The claim that all even numbers are divisible by two, isn’t about every even number, at least not directly: it’s about the property of being an even number and the property of being divisible by two, and it says that anything instantiating the first property will instantiate the second. This might raise the aboutness problem that we discussed in chapter 1, §2.4, but it saves us from potentially more troubling instances of the aboutness problem such as (a) how can a proposition be about infinitely many numbers and yet still be graspable, and (b) how can a proposition be about non-existent objects? It avoids these problems by telling us that those propositions are actually about properties. You might now think that our proposition about even numbers is about anything/everything: it says of all things in the universe that if they are an even number then they will be divisible by two. If this is the case, then our problem hasn’t really gone away. How can we be acquainted with every single thing in the universe in order that they should all be subjects of this proposition? What we see, in fact, is that Russell, in 1905, had decided to take generality as a primitive. The proposition doesn’t tell us that all things in the world are such that if they instantiate the property of being an even number then they instantiate the property of being divisible by two – instead, these two properties are said to stand in some sort of primitive, unanalysable, relation: general co-instantiation.7 Before long, Russell began to extend his account of empty definite descriptions, to the names of non-existent beings (and in fact, to the names of anything with which the speaker isn’t acquainted). The theory suggested that all such names were somehow descriptions in disguise. The name ‘Harry Potter’, for instance, would actually be an abbreviation for a description: there is some unique x such that x is called ‘Harry Potter’, went to Hogwarts, etc., and such that. . . What the theory of descriptions has given us, is a method for paraphrasing certain phrases away with the use of quantificational machinery. On this view, the singular term, ‘a man’, in the sentence ‘I met a man’, can be meaningful without corresponding to an entity such as an aboutness shifter; rather, it is meaningful because it allows for the following eliminative paraphrase: ‘There is an x such that x is a man and . . .’ Thus the doctrine of linguistic transparency survives in part: if a phrase cannot be eliminated by paraphrasis (to borrow a phrase from Quine (1966) who in turn borrowed it from Bentham), then, and only then, must we apply the doctrine of linguistic transparency to it.

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§4: Three Views Why, in Russell’s eyes, was the theory of descriptions superior to his earlier theory of denoting concepts? In the secondary literature, there are three main avenues of response to this question. In this section, I examine them all, before coming down on the side of James Levine and his under-celebrated historical re-revision. §4.1: The Standard View The standard view, epitomised by Quine (1966), holds that even if denoting concepts (and the periodic suspension of direct realism) resolved the tension canvassed in §1, Russell (1903) still maintained the sort of cumbersome Meinongian ontology that the theory of descriptions manages to avoid. The theory of denoting concepts may allow me to rid unicorns from all of my propositions in favour of aboutness shifters – but, so the standard view maintains, it seems that unicorns must still subsist in order that aboutness shifters should be able to denote them. Thus the theory of descriptions is motivated – so says the standard view – by the desire to streamline a Meinongian ontology. Russell corroborates this view. He said the following in his later recollections: [Meinong argued that] if you say that the golden mountain does not exist, it is obvious that there is something that you are saying does not exist – namely, the golden mountain; therefore the golden mountain must subsist in some shadowy Platonic world of being, for otherwise your statement that the golden mountain does not exist would have no meaning. I confess that, until I hit upon the theory of descriptions, this argument seemed to me convincing. The essential point of the theory was that, although ‘the golden mountain’ may be grammatically the subject of a significant proposition, such a proposition when rightly analysed no longer has such a subject. (Russell, 1959, p. 64)8 In fact, whenever Russell introduced the theory of descriptions, he motivated it by his desire to get rid of shadowy subsistent entities – his desire to collapse the category of being and make do only with existence. For example: Logic, I should maintain, must no more admit a unicorn than zoology can; for logic is concerned with the real world just as truly as zoology, though with its more abstract and general features. To say that unicorns have an existence in heraldry, or in literature, or in imagination, is a most pitiful and paltry evasion. What exists in heraldry

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The Philosophical and Historical Background is not an animal, made of flesh and blood, moving and breathing of its own initiative. What exists is a picture, or a description in words. (Russell, 1919b, p. 169)

Furthermore, Principles of Mathematics is littered with instances in which Russell distinguishes, like Meinong, between existence and subsistence – a distinction which was, so the standard view opines, decisively collapsed only some years later, by the theory of descriptions in 1905. Witness the following: The distinction of Being and existence is important, and is well illustrated by the process of counting. What can be counted must be something, and must certainly be, though it need by no means be possessed of the further privilege of existence. (Russell, 1903, p. 71) And again, perhaps more famously, Being is that which belongs to every conceivable term, to every possible object of thought . . . ‘A is not’ must always be either false or meaningless. For if A were nothing, it could not be said not to be . . . Numbers, the Homeric gods, relations, chimeras and four dimensional spaces all have being . . . [if they didn’t] we could not make propositions about them. (Russell, 1903, p. 449) Given all of this textual support, it seems surprising that the standard view should ever have been revised. All of the evidence seems to point in the same direction: Russell used to be committed to a distinction between subsistence and existence; he was forced into thinking that denoting phrases such as ‘the unicorn in Trafalgar square’ actually denoted some shadowy sort of entity, and that names such as ‘Santa Claus’ (if they weren’t in fact disguised denoting concepts denoting non-existent beings) actually named non-existent beings; in 1905, Russell discovered the theory of descriptions; not only did this theory resolve the tensions canvassed in §1 and not only could it deal with generality but also with empty names and empty descriptions without succumbing to a Meinongian ontology of non-existent beings. The standard view, buttressed by all of this evidence, will take some refuting. §4.2: Hylton’s Revision Peter Hylton disputes Russell’s own recollections as hazy, and dismisses certain passages in which Russell motivates the theory of descriptions as deceptive.9 Perhaps the most important source for Hylton’s revisionary

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history is Russell’s paper entitled, ‘The Existential Import of Propositions’ (Russell, 1905a). In this paper, Russell concludes that denoting concepts can be used to avoid the Meinongian muddle of non-existent beings – the very muddle that the standard view claims as motivation for the theory of descriptions: ‘The present King of England’ is a denoting concept denoting an individual; ‘The present King of France’ is a similar complex concept denoting nothing. The phrase intends to point out an individual, but fails to do so: it does not point out an unreal individual but no individual at all. The same explanation applies to mythical personages, Apollo, Priam, etc. These words all have meaning, which can be found by looking them up in a classical dictionary; but they have no denotation; there is no individual, real or imaginary, which they point out. (Russell, 1905a, p. 399) Russell didn’t need the subsistence of the Homeric gods in order to speak about them. He only needed denoting concepts that would attempt to denote them – the fact that they wouldn’t succeed in denoting anything wouldn’t stop them from trying! And this use of denoting concepts is no real theoretical development: it was merely a realisation of latent potential. Even in Principles of Mathematics, Russell had used denoting concepts that had no denotation: he seems to make it clear that although every phrase must indicate an entity, that denoting phrases can indicate denoting concepts that in turn have no denotation; this helps him make sense of the claim that ‘in some sense nothing is something’: We may now reconsider the proposition ‘nothing is not nothing’ – a proposition plainly true, and yet, unless carefully handled, a source of apparently hopeless antinomies. Nothing is a denoting concept, which denotes nothing. The concept which denotes is of course not nothing, i.e., it is not denoted by itself. The proposition which looks so paradoxical means no more that this: Nothing, the denoting concept, is not nothing, i.e., is not what itself denotes. But it by no means follows this that there is an actual null-class: only the null class-concept and the null concept of a class are to be admitted. (Russell, 1903, §73) More succinctly, he stipulated, ‘A concept may denote although it does not denote anything’ (Russell, 1903, p. 73). Just as a Fregean sense might not need to have a referent, so too might a Russellian denoting concept fail to have a denotation. Thus Hylton’s revision amounts to two claims: 1. Russell’s recollections on this matter were deceptive: the theory of descriptions was not the discovery that stripped him of his hitherto

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Meinongian ontology; when Russell wrote ‘The Existential Import of Propositions’ he had already relieved himself of this Meinongian muddle using only the machinery of denoting concepts; this was something that Russell either subsequently forgot or covered up for one reason or another in his later reflections. 2. At the stage in Russell’s career in which he did seem sympathetic to the ontological commitments of Meinong (i.e., in 1903), he already had adequate philosophical apparatus by which to rid himself of these very commitments, in the shape of denoting concepts – though it seems only to have dawned on Russell intermittently that they could be put to this use. The standard view operates under the assumption that denoting concepts always had to denote something (or worse, the standard view simply ignores the theory of denoting concepts entirely). This assumption has been shown to be a mistake – Russell was able to dispense of the Meinongian realm of non-existent entities some time before the discovery of the theory of descriptions. Hylton, it seems, has totally undermined the standard view despite the preponderance of textual evidence in its support. Hylton thus has to find some other motivation for Russell’s change of heart. Hylton presents the following three motivations (Hylton, 2003, pp. 219–20): 1. In cases where denoting concepts don’t denote, propositions will fail to be about anything and will therefore fail to be true or false – it can’t be said to be true or false that the entity denoted in my proposition has a crooked horn, for example, if no such entity exists. Whereas, in the theory of descriptions, ‘Failure of reference is treated without recourse to truth-value gaps, which would complicate logic. No doubt these matters carried considerable weight with Russell.’ 2. The argument that Russell puts forward against denoting concepts in ‘On Denoting’ is a very enigmatic passage, known as Gray’s Elegy Argument. Properly interpreted, it displays the ‘considerable internal difficulties’ that plague the notion of a denoting concept. Difficulties such as the difficulty of talking about an aboutness shifter if they always shift what a proposition is about! 3. The theory of denoting concepts couldn’t really handle generality, even though it was specifically designed to do so. It stumbles when trying to make sense of multiple generality, whereas the Fregean quantifiers adopted in the theory of descriptions are perfectly suited for dealing with such difficulties. But it’s clear that – despite talk of the ‘considerable weight’ of these considerations – one concern weighed much more, according to Hylton, who presents us with Russell’s real reason for abandoning denoting concepts:

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Fourth, and I believe most fundamentally, is the fact that the theory of denoting concepts was an anomaly from the outset. It flatly contradicted the direct realism which issued from Russell’s most general philosophical views; it simply stipulated a class of exceptions to direct realism, with no explanation of how exceptions are possible. Hylton thinks that this fourth reason, this triumph for direct realism, is the real driving force behind the adoption of the theory of descriptions. Hylton has done Russell scholarship a great service by shaking up a complacent standard reading of ‘On Denoting’, a reading that looked well buttressed by the sources but which Hylton seems to have left vanquished.10 However, as we shall see, it’s far from clear that Hylton was actually right. For one thing, it is a strange victory for direct realism since it seems as if Russell will still have to treat indexicals as aboutness shifters – the theory of descriptions doesn’t address indexicals at all. When Russell does turn his attention to them, he treats some of them as logically proper names – i.e., words that pick out their referent – but if they refer to different things on different occasions, what’s to become of the doctrine of linguistic transparency, and if they refer in virtue of being aboutness shifters, then what becomes of the doctrine of direct realism? We’ll come back to that mystery in the next chapter, §2. Before then, we turn to James Levine’s reservations with Hylton’s view. §4.3: Levine’s Re-revision Levine (2005) invites us to take a closer look at the arguments and structure of ‘On Denoting’. The ‘initial negative argumentation’ (as Levine calls it) is clearly targeted against views that struggle with empty names and empty descriptions. A closer reading of the initial negative argumentation of ‘On Denoting’ reveals that the theory of denoting concepts falls firmly within its sights: denoting concepts couldn’t adequately deal with empty names, and Russell knew it. The initial negative argumentation has three prongs. The first prong takes on Meinong (or at least Russell’s understanding of Meinong). Meinong makes no real distinction between meaning and denotation. When faced with a definite description – such as, ‘the F’ – Meinong would take its denotation/meaning to be that entity that answers the predicate ‘F’. However, this won’t do. Sometimes there is no object that answers the description. At first, Meinong can appeal to the distinction between subsistence and existence to explain how a non-existent yet subsistent being can be the meaning of a phrase. However, Russell’s attack pushes further: Meinong will soon be forced to contravene the law of non-contradiction. Meinong accepts that sentences of the form ‘The F is F’ will always be

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The Philosophical and Historical Background

true. Not only will this commit him to the notion that ‘The present King of France’ denotes an object that is presently King of France, he will, more absurdly, have to admit that ‘the round square’ denotes an object that is, paradoxically, both round and square. As was Meinong’s wont, he went on to create another ontological category to accommodate the rise of such paradoxes: some objects merely subsist, some subsist in space and/or time and thus exist, but some objects neither subsist nor exist; objects in this last ontological category, so Meinong argued, needn’t abide by the law of non-contradiction. Round squares fit into this third category. The first prong of Russell’s argument seems to have exposed a great deal of absurdity in Meinong’s position: it’s not therefore tenable to think that the meaning/denotation of a denoting phrase is always some entity that answers to the description embedded in the phrase.11 The second prong of the argument is against one particular way of maintaining a distinction between meaning and denotation in the face of empty descriptions. Russell indicates that this particular method is suggested by the works of Frege: a phrase, such as the ‘the round square’ can have a sense without having a referent. Thus we can avoid the contradictions that Meinong walked into because contradictory descriptions never need to have a referent/denotation – there are no round squares. But, as Levine (2005) notes, this method of dealing with empty phrases is not exclusive to Frege: it is exactly what Russell tried to do with denoting concepts in ‘The Existential Import of Propositions’ (1905a): the meaning of a denoting phrase will always be a denoting concept, but not all denoting concepts have to have a denotation; thus the theory of denoting concepts, even as that theory is understood by Hylton, is squarely targeted by this second prong of argumentation. The problem that Russell levels against this method of analysis is that it will produce truth-value gaps. As Hylton himself noted, when a proposition contains a denotationless denoting concept, the proposition will fail to be true or false. Frege was, in fact, willing to countenance propositions that were neither true nor false,12 but Russell wasn’t: for Russell, what was neither true nor false was nonsense.13 But this second prong of argumentation goes further still: even if you’re happy with truth-value gaps in principle, this sort of analysis of empty denoting phrases will force you to treat propositions which are clearly true, to be neither true nor false. Russell’s (1905b, p. 419) example is the following: ‘If u is a class which has only one member, then that one member is a member of u.’ It’s clear that this should be true for every value of ‘u’. Even in cases in which the antecedent is false, it would still be true that if u is a class with one member, its member is a member of u. But what happens if u is the null-class? Surely, the sentence would still be true. Surely, it is true that if the null-class is a class with one member which, of course, it isn’t, then its member is a member of it!14 But, in this case, though we still assume that the sentence

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should be true, the words ‘that one member’ in the consequent would be a denoting phrase with no denotation – there is no member of the null-class. We seem to have been lead into a truth-value gap, even where there clearly shouldn’t be one. The second prong of this argument can therefore be summed up as follows: theories, including Russell’s own theory of denoting concepts, that distinguish between meaning and denotation and allow for phrases to have meaning without denotation, lead to truth-value gaps; Hylton may have thought that Russell wouldn’t have been too bothered by truth-value gaps, or, at least, not bothered enough for this to have been a ‘fundamental’ reason for the adoption of the theory of descriptions, but what the second prong of Russell’s own argument proves is that any such theory will create truth-value gaps where no right-minded logician would allow them. The presence of this argument in Russell’s own article undermines Hylton’s revision considerably. These truth-value gaps don’t just carry ‘considerable weight’ – they seem to be crippling. The third prong of the argument is also against the school of thought that distinguishes between meaning and denotation. This time, it targets those who try to make sense of empty descriptions, not in terms of denotationless meanings, but in terms of purely conventional denotations. According to this method, suggested at times by Frege, whenever a definite description/ name fails to denote anything, we provide it with a somewhat arbitrary denotation in order to plug up the truth-value gaps: very often, we will be able to use the null-class as our ad hoc denotation. Unlike Meinong’s account of empty names, this Fregean route avoids outright contradiction because it doesn’t adhere to the view that every sentence of the form ‘The F is F’ is true. ‘Thus, for example, “The round square is round” will be false,’ Levine explains (2005, p. 45), ‘while “The round square is not round” will be true (assuming that the null-class is not round).’ Russell has two objections to this suggestion: 1. ‘[I]t is plainly artificial, and does not give an exact analysis of the matter’ (Russell, 1905b, p. 420): Frege isn’t really arguing that the present King of France is the null-class; instead, he’s just plugging a truth-value gap in any way he can. 2. Furthermore, Russell thinks that ‘an exact analysis’ would have it that if any phrase of the form ‘the F’ did succeed in denoting an entity, then, in such cases, it would surely be true that ‘The F is F’. If ‘the golden mountain’ denotes anything, then surely it denotes something that is both golden and a mountain! However, according to this third approach, ‘the golden mountain’ has a denotation, but it’s neither golden nor a mountain. Truth-value gaps would have been a major problem for Russell’s theory of denoting concepts. This problem would have forced him to provide

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a denotation for such denoting phrases, ‘leaving him vulnerable to the criticisms he makes of Meinong’s and Frege’s methods for providing denotations in such cases’ (Levine, 2005, p. 47).15 Russell’s recollections and introductory passages can once again be read in ways that don’t make them deceptive. In fact, the three accounts of Russell’s motivation – the standard view of Quine, the revisionary view of Hylton, and the re-revision of Levine – are neatly distinguished by the ways in which they interpret the previously quoted except from My Philosophical Development (Russell, 1959, p. 64). I quote again: [Meinong argued that] if you say that the golden mountain does not exist, it is obvious that there is something that you are saying does not exist . . . I confess that, until I hit upon the theory of descriptions, this argument seemed to me convincing. The three schools of thought in question read this quote in distinct ways: 1. The Standard View takes the most literal reading: this quote should be taken at face value; until the theory of descriptions, Russell was utterly committed to the Meinongian distinction between existence and being. 2. Hylton’s revision takes the least charitable approach to this quote: it is wrong; Russell’s theory of descriptions is not what rid him of his Meinongian ontology, he had already got rid of it with recourse to denoting concepts. It was the resurrection of direct realism that really motivated the theory of descriptions. 3. Levine’s re-revision takes a middle road: the standard view is wrong to think that Russell had been totally lumbered with Meinongianism until the theory of descriptions was ‘hit upon’; in truth, Russell had already explored ways out of a Meinongian ontology using only denoting concepts; but ultimately, denoting concepts failed to help him escape from the spectre of Meinongianism, for they had left him with intolerable truth-value gaps that could only be got rid of very artificially or upon the re-acceptance of Meinongianism – it was, true to Russell’s words, only upon the discovery of the theory of descriptions that he was truly able to cast Meinongianism away once and for all. Levine’s reading of the history is the only one to take account of all the facts: of what Russell had to say for himself on the matter, of the relevant excerpt from ‘The Existential Import of Propositions’ and of all of the arguments in ‘On Denoting’. It turns out that Russell wasn’t lying to us in his old age: he truly wasn’t certain that he could rid himself of Meinongian excesses until he ‘hit upon’ the theory of descriptions. And true to what Russell himself said, it is this fact, more than any other, that answers the question set out at the outset of §4: contra Hylton, the

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restoration of direct realism wasn’t Russell’s primary concern. In some senses, as we’ll see in the next chapter, it wasn’t his concern at all.

§5: Incomplete Symbols The central development of the theory of descriptions can be thought of in terms of a new tool in Russell’s philosophical toolkit – namely, the notion of an incomplete symbol. It will be instructive to compare two competing views as to exactly what an incomplete symbol is supposed to be. §5.1: What Is an Incomplete Symbol? As G. E. Moore (1944) understands matters, an incomplete symbol is a phrase that can’t be defined outside of the context of a sentence in which it meaningfully occurs. Take the following two pairs of sentences: 1. The present King of France is wise. 2. There is at least one person such that he is presently King of France, there is at most one person such that he is presently King of France, and that person is wise. 3. Mrs. Smith is a widow. 4. Mrs. Smith was formerly wife to somebody who is now dead, and is not now wife to anyone. Moore notes that an operation can be performed upon a phrase in the latter pair of sentences that cannot be performed upon a phrase in the former. If one were to subtract ‘Mrs. Smith’ from both members of the latter pair, the remainder of both sentences would still have the same meaning – ‘is a widow’ just means ‘was formerly wife to somebody who is now dead, and is not now wife to anyone.’ For this reason, Moore argues, we are justified in saying that ‘is a widow’ is not an incomplete symbol: it can be defined outside of a sentence. The remainder of 4, once you delete ‘Mrs. Smith’ is just such a definition of ‘is a widow’. But if we try to perform the same operation upon ‘is wise’ in the first pair, in order to arrive at a definition of ‘The present King of France’ via the remainder of sentence 2, we will stumble into failure. It cannot be said that the remainder of the two sentences will have the same meaning: ‘The present King of France’ doesn’t mean the same as the ungrammatical phrase ‘There is at least one person such that he is presently King of France, there is at most one person such that he is presently King of France, and that person ________’. Thus ‘The present King of France’ (and other phrases to which the theory of descriptions similarly applies) was an incomplete symbol – i.e., a phrase that could only be defined in the context of a sentence in which it meaningfully occurs (Moore, 1944, p. 222).

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In Russell’s response to Moore (Russell, 1944b, p. 690), Russell certainly doesn’t complain that his notion of an incomplete symbol has been misunderstood. Yet, despite this, Quine (1948; 1966) put forward another interpretation of the notion of an incomplete symbol which is both incompatible with Moore’s and much more true to the sources, and to the development in Russell’s thought that was precipitated by the theory of descriptions. An incomplete symbol, according to Quine’s interpretation, is a word or phrase – meaningful within certain contexts – that can always be dispensed with in terms of a paraphrase; a complete symbol (to coin a phrase) is a word or phrase that doesn’t always allow for such paraphrasis. Moore’s example of an incomplete symbol is ‘The present King of France’, and his example of a complete symbol – so to speak – is ‘is a widow.’ By his own lights, he is quite right: ‘The present King of France’ can only be defined, given the theory of descriptions, in the context of its occurrences in sentences; whilst ‘is a widow’, as we have seen, can be defined in isolation from any particular sentential occurrence. However, on Quine’s understanding of an incomplete symbol, both phrases are (potentially) incomplete: ‘The present King of France’ can always be paraphrased away, and ‘is a widow’ can always be paraphrased away in terms of ‘being a woman who was formally married’. Both phrases are liable to paraphrasis and can thus be viewed as incomplete, according to Quine’s interpretation. What is fundamentally new to Russell, post-1905, is a method for ontological pruning: the notion of an incomplete symbol is used to transform Russell’s universe from one cluttered with all sorts of entities to one in which we need be committed only to those entities that our best description of the world cannot fail to refer to. The only phrases whose meaningfulness need come with any ontological commitment will be the most primitive predicates necessary for a complete description of the world (given the assumption that predicates refer), and logically proper names (i.e., names that contribute their bearers to the propositions that they go towards expressing). It may be true that equally expressive languages can be formed with different collections of predicates, and that equally adequate descriptions of the world can be formed which seem to quantify over different entities – in which case we will have some choice over our ontological commitment, to be made in accordance with metaphysical and epistemological best practice. Given Quine’s interpretation, it seems that we sometimes have a choice as to which terms should be treated as incomplete and which complete. §5.2: A New Methodology16 Post-1905, Russell’s philosophical method is markedly transformed. Russell now has a razor with which to prune his ontology. Part of the reason why analytic philosophy got its name was that its founders were

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interested in philosophical analysis. However, philosophical analysis as a method, pre-the-theory-of-descriptions is, as we shall see, something quite distinct from philosophical analysis post-the-theory-of-descriptions. Before the theory of descriptions, Russellian analysis consisted of two activities: (1) analysis of complexes into their simple constituents – guided by grammar, and checked by metaphysical and epistemological constraints, and (2) ‘non-sensuous’ perception of those simples (Hylton, 1990, p. 232). The first stage Russell (1903, p. 3) characterises as passing ‘from the complex to the simple’. Once the complex has been broken down, and the simples have been reached, there is no more analysis to be done. The most that the philosopher can hope to do is to perceive the simples and help others to come to perceive them too (Russell, 1903, p. xx). (Russell wants us to have the sort of acquaintance with his metaphysical simples as we already do with ‘redness or the taste of a pineapple’.) These two activities constitute the method of Russell and Moore’s analytic philosophy pre-1905: analysis as decomposition. The theory of descriptions, powered by the notion of an incomplete symbol, gives rise to an entirely distinct notion of analysis in Russell’s philosophy. ‘The present King of France is bald’ isn’t decomposed into ‘The present King of France’ and ‘is bald’. The definite description isn’t merely analysed, it’s analysed away. This analysis is transformational.17 This was key to the birth of the MRTJ, for as we shall see, the MRTJ proposes a strategy for paraphrasing commitment to propositions away – it proposes a transformational analysis of our talk about propositions. In fact, the birth of this new methodology can play a role in providing us with an additional explanation for what motivated Russell’s adoption of the theory of descriptions in the first place. It gave him the tools to dispose of troublesome entities via transformational analyses. One can immediately see how such a tool might be of help to a person trying to save set theory in the face of the Russell paradox. We’ll come around to that topic in part II of this book, but this much we can say already: if for one reason or another, the ontology of sets becomes problematic, we might be able to salvage our talk of sets without entailing ontological commitment to them. Similarly, if the ontology of propositions gets us into trouble, perhaps the theory of descriptions will allow us to make sense of our talking of propositions without committing us to that troublesome ontology. For these reasons, and with ample textual evidence to back him up, Gregory Landini (1998; 2007) claims that the goal of saving set theory from paradox was what really guided Russell to adopt the theory of descriptions. Decompositional analysis doesn’t disappear from Russell’s work post1905, but it does start to play second fiddle to transformational analysis. Before we ask what the constituents of a proposition are, we must, first of all, try to paraphrase away, via transformational analysis, any ill-defined or ontologically cumbersome phrases in terms of well-defined

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and ontologically streamlined equivalents. The theory of descriptions had massive ramifications for what we called, in the previous chapter, the doctrine of linguistic transparency. Once we allow for transformational analysis, it turns out that the structure of a sentence in a natural language can be very deceptive indeed. Only sentences of a ‘logically perfect language’ – a language in which all incomplete symbols have been analysed away – can be said to have direct structural correspondence with the propositions we express, and the facts that make true propositions true (see Russell’s second lecture, in his Lectures on the Philosophy of Logical Atomism (1918), where he argues that only a logically perfect language would be ontologically revelatory). In other words, transformational analysis helps to reveal logically perfect sentences that can then be analysed decompositionally. This, briefly put, is the new methodology given rise to by the notion of an incomplete symbol. Language isn’t transparent, but a logically perfect language would be. In addition to the doctrine of linguistic transparency, predicate reference realism has likewise to be amended (although this wasn’t immediately obvious to Russell, and it only follows from a Quinean, rather than a Moorean, understanding of an incomplete symbol): some predicates refer, because however much you paraphrase them away from a description of a world, there will still be some predicates left; but we’re no longer forced to construe every predicate as a referring term, as long as the predicate in question can be paraphrased away. We started this chapter noting a tension, within Russell’s philosophy, between his direct realism and his doctrine of linguistic transparency. The theory of descriptions resolved this tension for Russell once and for all. It replaces the doctrine of linguistic transparency with a new doctrine: the doctrine of logico-linguistic transparency: the sentences of a logically perfect language are transparent in exactly the way we used to think that language was in general. Not only does the theory of descriptions resolve our tension but also it provides our philosophy with a new tool and a new method. The tool is the notion of an incomplete symbol, which can be used as an ontological razor. The new method is that of transformational analysis. As we shall see, in chapter 5, and as I have already alluded to, these developments were keys to the birth of the MRTJ.

Notes 1 Perhaps there’s an exception for the objects that correspond to singleton sets. Since there is only one member of such a class, it’s not really possible to consider them severally, and therefore the object itself is the single member of the set. In that instance, we would have an object that is also a term. 2 See Boolos (1984, pp. 448–9)

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3 See Oliver and Smiley (2005) for a comparison between Russell’s early views and contemporary plural logic. 4 I will explore and defend this notion against an attack of Mark Sainsbury in the next chapter. 5 Note that Russell explicitly includes them, later, in his category of logically proper names (Russell, 1918). 6 That is to say, the aboutness problem from chapter 1 §2.4 potentially resurfaces here. I respond to that issue shortly. 7 This is how I cash out Russell’s talk of clauses being always true, and sometimes true, and always true together, and sometimes true together, etc. See Russell (1905b, p. 482) 8 See also Russell (1944a, p. 13) 9 Hylton isn’t the only person to have suggested this revision, but he has been the most prominent and forceful. Cartwright (1987b), acknowledging passing comments in Hylton (1980), probably gave this historical revision its first thorough working out and was among the first to explore the evolving intricacies of the theory of denoting concepts – the same revisionary history is adopted by Griffin (1996) and Stevens (2005). 10 For one thing, Hlyton’s historical revision has forced people to take greater care in reading, and to place more importance upon, the Gray’s Elegy Argument in ‘On Denoting’. For years, readings of this argument abounded in which Frege was taken to be the primary target – these readings (some of which were hostile, and some not) inevitably condemned Russell to a slew of use-mention confusions amongst other elementary errors (see Searle (1958), Geach (1959), Blackburn and Code (1978a), Geach (1978) and Blackburn and Code (1978b)). Hylton’s work has concentrated scholarship towards the theory of denoting concepts. The realisation that denoting concepts, related to Frege’s sense/reference distinction though they may be, are (most probably) the primary target of the Gray’s Elegy Argument, has resulted in new and elegant readings that are much more consistent with Russell’s philosophical aptitude – such as Noonan (1996) and Pakaluk (1993). 11 I should note again that Russell’s understanding of Meinong’s position isn’t necessarily a fair reflection of Meinong’s actual position. The notion that Meinongianism has been vanquished as a going philosophical concern is undermined by the arguments of contemporary Meimongians (see, for example (Parsons, 1980)). A further investigation of these issues falls beyond the scope of this chapter, and indeed, of this book. 12 See Frege (1892b, p. 157), but note that Frege may not have held this view consistently. Gareth Evans (Evans, 1982, p. 12) argues that Frege’s unpublished work makes it evident that, at least at some points in his career, he wasn’t happy to admit the existence of truth-value gaps at all. 13 This assertion would, of course, have been qualified. A banana isn’t nonsense just because it’s neither true nor false! We can put the principle more accurately as follows: if a putatively well-formed sentence fails to be true or false, then it fails to express any proposition whatsoever, and is therefore nonsense. 14 I was careful to phrase this argument without using counterfactuals, and restricting myself to indicatives, so as not to enter in to contemporary debates about how to assess counterfactuals with necessarily false antecedents; so-called ‘counter-possibles.’ 15 Levine goes on to demonstrate that the sort of dilemma that Russell puts forward in the initial argumentation of ‘On Denoting’ was exactly the sort of dilemma Russell had found himself in personally while dealing with the

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set-theoretic paradoxes in unpublished manuscripts. Russell, it seems, had never really been satisfied with denoting concepts in dealing with empty descriptions. 16 This section owes a great deal to Michael Beaney (2007) 17 Reck (2007) (cf. footnote 7) argues that Russell’s analysis of numbers was transformational even in Principles of Mathematics in 1903. If this is true, as it may well be, it cannot be said that transformational analyses make their debut post the theory of descriptions. And yet, even granting Reck’s claim, it is still not until 1905 that transformational analyses clearly and regularly come to the fore, as a go-to philosophical method, in the history of Russellian or analytic philosophy.

4

Semantics, Assertion and the Theory of Descriptions

Analytic philosophy of language today is host to a debate about the nature of names. One side often thinks itself to be taking Russell’s theory of descriptions to heart – adopting it, or at least adapting it, or somehow salvaging its spirit. This camp takes names such as ‘Frieda’ to be disguised descriptions, or at least disguised predicates (see Burge, 1973; Sloat, 1969; Segal, 1996; Geurts, 1997; Bach, 2002; Elbourne, 2005; Matushansky, 2006; Katz, 2001; Fara, 2011a). The other side of the debate believes that proper names are vehicles of direct reference. ‘Frieda’, according to this view, simply refers to its bearer. Context specific considerations will have to help you figure out exactly which Frieda you’re trying to refer to in any given context, but its role as a referring device exhausts its semantic contribution (see Kripke, 1972; Salmon, 1986; Soames, 1989; Heim and Kratzer, 1998 and Leckie 2013).1 The debate can be framed in terms of Russell – He thought that names of people and things with which we’re not acquainted must be disguised descriptions. He eventually came to think that we were very rarely acquainted with the bearers of names. So to what extent was he right that names (or most names) are disguised descriptions? In this chapter, I hope to show that, despite popular belief, and despite appearances to the contrary, Russell’s theory of descriptions is actually neutral on these issues. His theory of descriptions, and his account of names, actually has nothing to with semantics. Having defended that controversial claim, I then hope to show that Russell’s direct realism, as he understood it, and his doctrine of logico-linguistic transparency, are actually neutral to this ongoing debate about names.

§1: The Theory of Descriptions and Direct Realism Taken at his word, it’s pretty easy to read Russell’s theory of descriptions as a semantic theory about the semantic contribution of ‘denoting phrases’ and names, and how they get paraphrased away at the level of

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logical form. My thesis, in this section of chapter 4, boils down to the following three claims: 1. The theory of descriptions is concerned with the objects of assertion (as opposed to the semantic values) associated with the utterance of sentences containing denoting phrases and names 2. The theory of descriptions is not a semantic theory 3. The theory of descriptions has nothing explicit to say about the logical form of sentences or about the semantic values of names and denoting phrases My three claims trade upon a central distinction between semantic values and the objects of assertion. In §1.1 I will explain the philosophical motivation behind that distinction. In §1.2, I will supplement that distinction with a further distinction. In §1.3 I will utilise our various distinctions in order to draw, and to motivate, a theory of descriptions that satisfies the three claims I’ve just laid out. Those three sub-sections will not consider the historical data at all. Instead, I’ll be motivating a theory of descriptions without addressing whether it’s an accurate depiction of Russell’s theory of descriptions. Then I’ll return to the history. In §1.4, I’ll look at textual clues within ‘On Denoting’ to bolster the historical case for my three claims, and in §1.5, I’ll argue that my three claims can make historical sense of Russell’s later exchange with Peter Strawson. §1.1: The Identification Thesis The assertoric content of an expression is what is said in the utterance of that expression. In this sub-section, I look to distinguish between assertoric content and semantic value (which is often called ‘ingredient sense’). A compositional semantic theory for a language will attribute a meaning to each and every meaningful atom of that language, and provide rules that explain how those meanings can compose to generate the meaning of a sentence. Given a finite arsenal of meaningful atoms, you’ll have the power to generate a potentially infinite number of meaningful sentences. The semantic value of a sentence is just its compositional meaning – the result of combining its atoms in the appropriate way. We haven’t actually defined what we mean here by ‘the meaning of a sentence’, but it seems natural to think that it’s just what is said by that sentence. And thus, we’ve been moved to what Brian Rabern (2012b) calls the identification thesis: Identification thesis The compositional semantic value of an expression is identical to its assertoric content.

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Rabern is one of many thinkers to put pressure on this thesis. ‘In slogan form’, he puts his point as follows: ‘the problem arises when expressions that say the same thing embed differently.’ Here are some of his examples. Take the following three sentences: 1. Dave might be in Oxford 2. It is consistent with what I know that Dave is in Oxford 3. Leon said that Dave might be in Oxford Imagine that Frank uttered sentences 1 and 2. According to the contextualist, his two utterances would have the same assertoric content: that it is consistent with all that Frank knows that Dave is in Oxford. But that content – that proposition – isn’t what gets embedded in sentence 3. Sentence 3 doesn’t assert that Leon said that it is consistent with all that Frank knows that Dave is in Oxford! When Frank utters sentence 3, he’s reporting Leon to have said that it’s consistent with all that Leon knows that Dave is in Oxford. So what gets embedded in 3 isn’t the object of assertion expressed by Frank’s utterance of 1. This puts pressure on the identification thesis. Another example; take the following three sentences: 4. Licorice is tasty 5. Licorice is tasty to me 6. According to Jonathan Licorice is tasty The perspectivalist holds that utterances (by the same person) of sentence 4 and 5 assert the same thing. When Frank utters either 4 or 5, he asserts that Licorice is tasty to Frank. But, as Rabern points out, on the assumption of the identification thesis, this causes trouble for the compositional semantics of sentence 6. In response to these puzzles, we could give up our contextualism about epistemic modals and our perspectivalism about taste-predicates, or give up on the whole project or at least severely limit the scope of compositional semantics. These seem like over-reactions. Instead, we could deny that sentence 3 really embeds sentence 2 and that sentence 6 really embeds sentence 4. This seems ad hoc.2 Finally, we could do what Rabern calls ‘denying innocence’. Frege’s idea that the sense of an expression changes in certain contexts, such that the semantic value of 1 shifts when it’s embedded in the context of sentence 3, would be an example of this sort of move. Rabern hopes to motivate a different option: denying the identification thesis. According to Rabern, you can’t place too wide a gap between the semantic value of a sentence and the assertoric content of a given utterance of that sentence. If that gap was too wide, or unbridgeable, communication

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would become impossible. Rabern therefore endorses the determination principle: Determination principle The compositional value of an expression α in context c determines the assertoric content of α in c. Contextualism is just a thesis about assertoric content. It claims that utterances, by the same person, of sentences 1 and 2 have the same assertoric content; but that doesn’t mean that they have the same semantic values. The compositional semantics of 3 can perhaps be given ‘in terms of the semantic value of “Leon said” applied to the agent-neutral semantic value of ‘Dave might be in Oxford’ (Rabern, 2012b, p. 21). We can leave it to our ‘postsemantics’ to explain how the semantic value of 1 determines a particular assertoric content in a particular context of utterance, and how it determines the same assertoric content as the semantic value of 2 in similar contexts of utterance. The job of semantics proper has finished once you’ve been told what sort of contribution a sentence makes to the meaning of sentences in which it might find itself embedded. Rabern (2012a; 2012b; 2013) isn’t a lone voice. Michael Dummett (1973; 1993), David Lewis (1980), Jason Stanley (1997a; 1997b; 2000), Seth Yalcin (2007; 2012; 2014), and Dilip Ninan (2010; 2012) have all put pressure on the identification thesis for various reasons. Relatedly, a number of scholars have pointed out a certain shortfall in semantic theorising. François Récanati argues, In general, even if we know who is speaking, when, to whom, and so forth, the conventional meaning of the words falls short of supplying enough information to exploit this knowledge of the context so as to secure understanding of what is said. (Récanati, 1989, p. 298)3 Kent Bach notes that, often, ‘the conventional meaning of the sentence determines not a full proposition but merely a propositional radical; a complete proposition would be expressed, a truth condition determined, only if the sentence were elaborated somehow’ (Bach, 1994, p. 127). Yalcin (2014, p. 28) traces related themes in Sperber and Wilson (1986), Anne Bezuidenhout (2002), Robyn Carston (2002), Wilson and Sperber (2012), and ‘many others’. Drawing on these trends, Scott Soames has adopted the position that ‘the semantic content of S in a context constrains what S is used to assert, without always determining what is asserted, even when S is used with its normal literal meaning’ (Soames, 2008, p. 280). This is to go further than Rabern. Soames doesn’t adopt the determination principle; but a weaker, constraining principle. In the

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next two sub-sections, we will amend Rabern’s determination principle in stages, until it collapses, upon the adoption of the theory of descriptions, into a more Soames-like constraining principle. §1.2: The Conversational Contribution Imagine that there are only three possible worlds, a, b, and c, but none of us know which one is actual. Frank asserts, ‘This world is world b’. It’s tempting to say that the semantic value of the phrase, ‘this world’, is whichever world in which the phrase is uttered. And thus, if the sentence was uttered in world a, its semantic value would be the proposition (1) world a is world b; had it been uttered in world b, its semantic value would be the proposition (2) world b is world b, and had it been uttered in world c, its semantic value would be the proposition (3) world c is world b. Propositions (1) and (3) are necessarily false, and proposition (2) is necessarily true. However, we don’t want to say that Frank has asserted a necessary falsehood, nor a necessary truth, when he said ‘This world is world b’. Furthermore, since we don’t know which of the three worlds is the actual world, we can’t know which proposition is the semantic value of the words he’s uttered, and yet we do know what he means. Therefore, it seems right, once again, to deny the identification thesis. The assertoric content of Frank’s utterance isn’t identical to the semantic value of the sentence he uttered. Let each row of the following table represent one of the worlds in which Frank could have made his utterance. Let each column represent the world at which we assess whether Frank’s utterance is true or false:

a

b

c

a

F

F

F

b

T

T

T

c

F

F

F

The table merely illustrates that if Frank had made his utterance in world a, then (irrespective of the world from which we assess the truth or falsehood of his statement) what he said was false – since he said that world a is world b. Likewise, if he made his utterance in world c, then (irrespective of the world from which we assess the truth or falsehood of his statement) what he said was false – since he said that world c is world b. The table also illustrates that if Frank made his utterance in world b then (irrespective of the world from which we assess the truth

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or falsehood of his statement) what he said was true – since he said that world b is world b. Robert Stalnaker (1978) would argue that, since Frank didn’t assert a necessary truth or falsehood, what he asserted must have been some function that maps worlds a and c to the false, and world b to the true. That function is picked out by the diagonal row of the table:

a

b

c

a

F

F

F

b

T

T

T

c

F

F

F

Since Frank didn’t assert something necessarily true or necessarily false, he didn’t assert any of the horizontal contents on the table. He asserted the diagonal. Abstracting away from Stalnaker’s definition of propositions (in terms of functions from possible worlds to truth-values), the notion of diagonal content could be reframed as follows. When an identity statement, of the form ‘x is y’ is made, and is contextually informative, it will be informative either because (a) the common ground includes knowledge of the meaning of ‘x’, but not of ‘y’; (b) the common ground includes knowledge of the meaning of ‘y’, but not of ‘x’; or (c) even though the common ground includes knowledge of the meaning of both ‘x’ and ‘y’, it doesn’t include the realisation that ‘x’ and ‘y’ co-refer.4 Instead of thinking of propositions as functions from worlds to truth-values, we could say that the diagonal content in situation (a) would be that ‘y’ refers to x, the diagonal content in situation (b) would be that ‘x’ refers to y and the diagonal content in situation (c) would be that ‘x’ and ‘y’ co-refer.5 Presumably, we know that the phrase ‘world b’ refers to world b. Presumably we also know that the phrase ‘this world’, when uttered in this world, refers to this world! What we don’t know is whether the terms ‘this world’ and ‘world b’ co-refer. And thus we are in a situation of type (c). Consequently, the diagonal content of Frank’s utterance, which is also the object of his assertion, is that ‘this world’ and ‘world b’ co-refer. Imagine that we’re sitting in my apartment. A loud noise emanates from next door. I say, ‘He’s making a large racket next door.’ We both happen to know that it could only be Ben or Bob next door, but we don’t know which of the two it is. Who did my use of the word ‘he’ refer to? We don’t know the semantic value of my use of that word, since we don’t know whether Ben or Bob is the one making the noise next door. Even though the semantic value of the sentence I uttered is either that Bob is making a large racket next door or that Ben is making a large racket next

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door, we don’t know which of the two propositions it is. However, we do know what I asserted! I asserted the diagonal. Without thinking of content in terms of functions from worlds to truth-values, we can say that I asserted the proposition that there is a true proposition either about Bob, or about Ben, and whoever it’s about, it says that that person is currently making a large racket next door.6 The notion that we sometimes assert the horizontal, and sometimes the diagonal, presents us with an additional reason to distinguish between semantic values and the objects of assertion. Stalnaker claims that the horizontal content is always the semantic value, and that sometimes, such as in the cases that we’ve explored in this section, the horizontal content diverges from the object of assertion – i.e., in cases where we diagonalise.7 Supplementing Stalnaker’s insight with Rabern’s argument from the previous section makes matters more complicated. Rabern has given us reason to think that the semantic value isn’t even the horizontal content, since the horizontal content won’t always be able to explain the compositional semantic contribution that a sentence makes when it embeds in a larger context. For Rabern, the semantic value of a sentence isn’t identical to, but needs to determine, the horizontal content, which is generally what we assert – and then, we must add, given what we’ve said in this section, that in certain cases, where the horizontal content isn’t what we assert, we also have to diagonalise, to arrive at the assertoric content of the assertion. And yet, we still don’t have enough distinctions on the table. Consider Cameron Domenico Kirk-Giannini’s (ms) following example: Jones knows that at least one student cheated on the exam and that it was either Aimes or Barnes. Smith knows that Jones knows this; it is part of the common ground of their conversation. Smith says to Jones, ‘A certain student cheated on the exam by hiding a cheat sheet in the restroom.’ Jones has no non-parasitic way of identifying the student Smith has in mind as either Aimes or Barnes, though she knows it must be one of the two. Smith is clearly intending to restrict her description, ‘a certain student’, so as to a pick out either Aimes or Barnes. She has one of them in mind, not their disjunction. She is asserting, of a very specific individual person, that they cheated. However, she’s not updating the common ground of the conversation so as to identify who, exactly, she’s implicating. The horizontal content of Smith’s assertion (i.e., what she actually asserts) might, therefore, be very specific. However, what Jones is entitled to infer on the basis of Smith’s utterance is much less specific. Smith is being coy about sharing the full content of her assertion. Now it seems, we have to distinguish between (1) the semantic content, (2) the

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content that an utterance contributes to the conversational common ground and (3) the object of assertion. There may be times when all three types of content coincide, but Smith’s utterance to Jones certainly seems to be an example of a case in which the content of the assertion was much more specific than the content that was contributed to the conversation. Sometimes a speaker can allow only a select sub-set of her audience to infer the full specificity of her assertion whilst contributing something more coarse-grained to the common ground. Kirk-Giannini’s example is this: At the faculty meeting, Grumpy is advocating a proposal to change the course requirements for undergraduate majors. It is well-known among senior members of the faculty that Grumpy has a longstanding antagonistic relationship with his nemesis, Dopey. Junior members, however, are not aware of this relationship. With full information about how the two groups of his colleagues will interpret him, Grumpy declares, ‘A certain odious individual has written me an unsolicited letter criticizing the proposal.’ It is clear to the senior members of the faculty that Grumpy has Dopey in mind; for all the junior members of the department know, on the other hand, Grumpy could be talking about anyone. Here the semantic content might determine the horizontal content – which is that Dopey sent an unsolicited letter criticizing the proposal. Furthermore, Grumpy asserts that horizontal content, but he knows that this will be lost on some of his interlocutors (but only on some of them), and thus, what he contributes to the conversation as a whole (ignoring the sub-set of interlocutors who get to know more) is the diagonal: that someone sent an unsolicited letter criticizing the proposal. Semantic values help to determine objects of assertion in up to two stages. At the first stage, the semantic value of a sentence will determine a horizontal content. In some cases, that is what is asserted. At that point, the semantic value has already done its job for us – just as Rabern says. In some situations, however, the horizontal content isn’t what is asserted, and the process of diagonalisation is what will lead us to the asserted content (but this process will require more than just knowledge of the semantic value of the sentence and knowledge of the context of utterance, we’ll also need to know a good deal about the common ground, and about what the participants in the conversation are presupposing). Moreover, there will be times where the object of assertion will be hidden from the interlocutors. The speaker will be asserting the horizontal, as determined by the semantic value of the sentence uttered, but we won’t have enough information to know what that content is. In those situations, we’ll still be able to diagonalise, and in so doing, we’ll at least be able to arrive at the conversational contribution of the utterance.

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The object of assertion, plus the content of the common ground, should always entail the conversational contribution. For Frege, there was no route back from referent to sense, even though the sense determines a referent. Similarly, in this case, knowing the conversational contribution of an utterance, even if it is entailed by the object of assertion plus the content of the common ground, will not always give your interlocutors enough to know what you actually asserted. With this picture in hand, we can turn to the theory of descriptions. §1.3: A Theory of Descriptions Think of assertion as a binary relation. When I assert that Romeo loves Juliet, I stand related to the proposition that Romeo loves Juliet. That proposition contains Romeo and Juliet and love as constituents. I adopt the following epistemic constraint: I’m only ever in a position to assert, or even to entertain a proposition if I’m acquainted with all of the constituents of that proposition. Acquaintance is a primitive epistemic relation. Some will be liberal and some will be conservative about what sorts of objects a person can be acquainted with. A sense-data theorist, which is what Russell became, will think that you can only ever be acquainted with sense-data and phenomenal properties. A more liberal approach, to which Russell had previously subscribed, allows one to be acquainted with all sorts of garden variety objects, providing that certain conditions have been met (maybe you need to have sensed the object, or perhaps you need to stand in a certain sort of causal chain with the object, etc.). Some have argued that the principle of acquaintance demands what Howard Wettstein (2004), who doesn’t adopt the principle himself, calls a ‘cognitive fix’ on an object – furnishing you with the ability to discriminate that object from all other objects. Remaining neutral on all these questions, for now, I do insist that one can only assert, or even entertain, a proposition if one is acquainted with all of its constituents. Given this epistemic constraint, if I utter the following sentence to a group of my friends, ‘I met Gaby at the deli’, and my friends are not acquainted with Gaby, then they cannot entertain the proposition that Sam met Gaby at the deli. This might be the assertoric content of my utterance, but it’s not something my interlocutors can entertain. To arrive at the conversational contribution that I convey to my friends in this situation, we have to diagonalise. The proposition that they receive is something like there is some unique x that Sam is calling ‘Gaby’, and Sam met x at the deli. Let us further assume, on a strict construal of the acquaintance relation, that I am not even acquainted with Gaby, since I can only be acquainted with sense-data, for instance. On that assumption, even I did not assert the proposition that Sam met Gaby at the deli, though it may well be the horizontal content determined by the semantic value of the sentence I

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uttered. I am not acquainted with Gaby, so she can’t be a constituent of any proposition I assert! Perhaps I asserted that there is a unique x who stole my heart on our first date and that I met that x at the deli. But how do we determine that that’s what I asserted? It seems as if subscribing to my acquaintance principle is going to demand another slight amendment to the determination principle. This is what we had established by the end of §1.2: • • • •

The semantic content of a sentence should determine a horizontal content The horizontal content is generally the assertoric content Sometimes context makes clear that the horizontal content isn’t what was asserted, but rather the diagonal content is asserted Sometimes the horizontal content is what is asserted, but is opaque to the interlocutors, or to some of them, and therefore the conversational contribution will be the diagonal, even though the horizontal will be the object of assertion

Now we’re going to have to say that sometimes the assertoric content is neither the horizontal nor the diagonal. Rather, given the determination principle, the semantic value of a sentence will provide, for any context, a horizontal content as a candidate for the object of assertion – let us call that candidate proposition – p. If I am not acquainted with some, or any, of the constituents of p, then any analysis of the object of my assertion must replace those constituents with co-extensive descriptions. The content of those descriptions may, in some circumstances, be opaque to all but me. There’s no way that my friends could know that my assertion was about a unique x who stole my heart; that this was the exact description that I utilised; that this was the way I chose to restrict the quantifier. This is as it should be since we’ve already ascertained that one can’t always determine the object of an assertion from the contribution it makes to a conversation. In situations where descriptions have to be substituted in to our candidate for assertion, then the determination principle doesn’t quite hold – the semantic value of the sentence will place certain constraints on what the assertoric content can be – since it provides us with a candidate proposition to substitute descriptions into – but it won’t determine matters; it won’t determine which descriptions the speaker is using. This accords with Soames’ contention that semantics constrains assertoric content without determining it. And so we’ve seen the determination principle slowly evolve into a constraining principle. What value do objects of assertion have, as a theoretical posit, if they are sometimes opaque to everyone but the asserter? It seems that the conversational contribution is what really matters for any theory of communication. To this worry, there are two responses.

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First, there may be instances in which the posit does explain certain linguistic data. Imagine that the day after the meeting, a junior member of the faculty discovers that Dopey was who Grumpy had had in mind. She tells Grumpy that he had been wrong: the letter wasn’t really from Dopey, it was a forgery, from her! However, we can only say that Grumpy had been wrong if we accept that he had asserted something about Dopey, which is to accept that his assertion was more specific than what he had contributed to the conversation – a contribution which remains true – somebody did write a letter. Second, we need to be conscious of what it is that we’re hoping to explain. Donald Davidson (1967), as we noted in chapter 1, famously contended that the posit of propositions was otiose to the philosophy of language. His hope was that we could construct a theory, for any object-language, that could take a sentence of that language and specify what that sentence means by replacing it with a translation in the meta-language. The posit of propositions is unnecessary to this task. But what does a Davidsonian theory explain? It basically provides you with a translation manual. But it doesn’t explain – and can’t explain – what two people who assert the same content, using different languages, fundamentally have in common. Sure, the theory will tell you that their words mean the same thing – but we might want to explain something deeper. The posit of propositions explains how the two minds stand related to the same mind-external content, when they assert the same thing. In short: you might accept that propositions fail to ‘oil the wheels of a theory of meaning’, and yet you might think that they’re an important posit in a theory of mind-world relations. Likewise, it may be that the posit of objects of assertion – when they come apart from conversational contributions, and especially when they’re opaque to everyone but the speaker – fails to oil the wheels of a theory of communication, but they might be an important feature of a more general theory: a theory about how minds are related to the world when they make an assertion. The semantic value of ‘Romeo loves Juliet’, and knowledge of the context of its utterance, leads us to believe that the speaker who utters that sentence is asserting the proposition that Romeo loves Juliet. He’s not being coy, and we have no reason to think that the conversational contribution comes apart from the object of assertion, in this instance. The proposition that Romeo loves Juliet serves as our candidate for the object of assertion. But if, for example, the utterer is acquainted with love and with Juliet, but not with Romeo, and let’s assume for the sake of ease that she’s acquainted with the property of being a Montague, then the assertoric content becomes: there is an x such that x is called ‘Romeo’ and x is a Montague and x loves Juliet and is such that for any y, if y is called ‘Romeo’ and y is a Montague, then x = y. The constituents of the proposition are the property of being called ‘Romeo’, the property of being a Montague, love and Juliet, as well as some higher

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order properties to account for the quantificational machinery. We might know the properties that the speaker, in his idiosyncrasy, uses in order to restrict his quantifier to pick out Romeo (in this case, being a Montague, and being called ‘Romeo’). However, objects of assertion are not always discoverable; communication occurs primarily at the level of an utterance’s contribution to all of the participants of a given conversation; which is discoverable. Phrases of the form ‘the F’ generally contribute to the object of assertion (i.e., to the proposition expressed) some content of the form there is an x such that x is F and such that for any y, if y is F then x = y. But, when the speaker is using the definite description referentially, and if the speaker is acquainted with said referent, then the definite description simply contributes its denotation to the object of assertion.8 When I say that I met Gaby at the deli, and if I use ‘the deli’ referentially, and if I’m acquainted with the deli, then the deli itself will be a constituent of the proposition I assert. On the theory of descriptions that has been emerging in this section, names in a sentence contribute their bearers to the assertoric content of their utterance, and denoting phrases contribute their denotations to the assertoric content of their utterances, unless: 1. The speaker isn’t acquainted with the bearer of the name or the denotation of the denoting phrase, and/or 2. The denoting phrase is used attributively (this second condition doesn’t apply to names) If either or both of these conditions hold, then the name or denoting phrase will not contribute its bearer or denotation, instead, it will contribute some descriptive content, co-extensive with the referent of the name or the denotation of the denoting phrase, to the object of assertion. Note that this theory says nothing about the semantic value of names or denoting phrases. If you want to, you could adopt the identification thesis, and claim that objects of assertion just are semantic values and that this theory of description applies mutatis mutandis to semantic values. Or, you could be a referentialist and hold that the semantic value of a name is always its bearer. Perhaps you will hold that when a name fails to have a referent it fails to have any semantic value whatsoever. My theory of descriptions is compatible with that claim because my theory is silent about semantic values. Perhaps sentences sometimes fail to have a semantic value, because their names fail to refer, and yet you still manage to make an assertion by uttering them; your semantically deficient utterance still somehow manages to give rise to an object of assertion. Again, my theory is silent about semantics. A theory of semantics will constrain but not determine the object of any given assertion.

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It’s also worth noting that my principle of acquaintance places no epistemic constraints upon what can play the role of a semantic value. Specifically, I do not say that one has to be acquainted with the referent of a name in order that it should be able to be the semantic value of that name. Mark Sainsbury (2005, pp. 20–1) imagines the following scenario. You notice that the cheese in your larder is disappearing overnight. You hypothesize that this is caused by a mouse. You imagine this mouse in some detail, which you reinforce with experiment: you leave sand near the cheese and confirm that it is a house mouse by its tracks; . . . Your behaviour becomes a little obsessive: you dignify your mouse by the name ‘Freddie’; you speculate, correctly in fact, that Freddie is the head of a large family of mice, and that he does not eat all the cheese he steals but takes some back as paternal investment in a recent brood; you get a camera and . . . replay scenes of Freddie’s activities . . . Then [finally] . . . you actually see Freddie eating your cheese. What Sainsbury thinks to be absurd is the claim that at some magical moment in your gradually coming to know Freddie, the semantic value of the name ‘Freddie’ suddenly undergoes a radical shift from having been a disguised description to being a name. Note that my principle of acquaintance, given that it is a constraint upon determining an object of assertion, but says nothing about semantics, has nothing to say about the semantic value of the name ‘Freddie’.9 My view is consistent with the claim that ‘Freddie’ is always a disguised description, or always a predicate (as Delia Graff Fara (2015) would argue), or always a vehicle of direct reference to Freddie. There is no magical semantic transformation in this story. However, I do claim that at some point, even if it’s difficult for us to isolate exactly when it happens, you come to know Freddie directly. Coming to know Freddie directly means that you can now use his name to make assertions directly about him. You can now stand in various cognitive relations to him. I’m not sure when you become acquainted with Freddie because I don’t have a fleshed out theory of acquaintance. Perhaps you stand in the right causal relation to him as soon as you’ve seen his footprints. Perhaps seeing footage of him suffices. Perhaps only when you see him in the flesh are you acquainted with him. But I do claim that you can’t make an assertion directly about him unless you are acquainted with him. My theory, silent as it is about semantic values, escapes the strange notion that his name suddenly changes its meaning. The theory is consistent with giving all names a constant semantic value. This seems to respect the following intuition: Freddie’s name undergoes no massive shift in this

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story but your epistemic relationship to Freddie does, although it might not be clear to us exactly when that shift occurs. We now have a theory of descriptions on the table that is consistent with my three claims: 1. The theory is concerned with the objects of assertion associated with the utterance of sentences containing denoting phrases and names. 2. The theory is not a semantic theory. 3. The theory has nothing explicit to say about the logical form of sentences or about the semantic values of names and denoting phrases (though it does have something to say about the logical form of the objects of assertion). I will now try to argue that this theory of descriptions is Russell’s theory of descriptions – or, at least, the best precisification of his theory. §1.4: On ‘On Denoting’ The only person I know to have read Russell’s theory as I do is Lloyd Humberstone, in an unpublished manuscript, ‘Ingredient Sense and Assertive Content’. He argues that Russell’s theory of descriptions would be unfairly accused of falling prey to problems concerning presupposition projection.10 If Russell’s theory of descriptions is supposed to provide us with the ‘ingredient sense’ (i.e., the semantic value) of (1) The king of France is bald then it’s going to struggle to explain how it embeds in: (2) If the king of France is bald then Versailles has no need for a barber Russell’s paraphrase for (1) is that there exists a unique x who is a king of France and x is bald. This gives rise to our embedding problem since nobody would suppose that (2) means ‘If there is a unique King of France and he is bald, then Versailles has no need for a barber.’ This paraphrase doesn’t presuppose that there is such a King, but sentence (2) does presuppose just that. Humberstone notes that the right response to this objection is to realise that Russell would paraphrase (2) in such a way as to import the correct presupposition. Indeed, he’d paraphrase it thusly: There is a unique King of France and, if he is bald, then Versailles has no need of a barber: Now the interesting, thing about this paraphrase [for sentence (2)] is that although it is the paraphrase of a conditional sentence, it is not got by concatenating, in a conditional construction, the paraphrase

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of that sentence’s antecedent [i.e., (1)] with the paraphrase of the sentence’s consequent. So the relation to be claimed to hold between such sentences and their Russellian paraphrases is not that of sharing the same ingredient sense [i.e., semantic value], but rather that of having the same assertive content. Humberstone’s point is that Russell has no desire to provide a uniform analysis of definite descriptions inside and outside of contexts in which they embed. Indeed, as it suits him, he will sometimes give the quantifier in his paraphrases a wide-scope, and sometimes a narrower scope, without anything like a uniform semantic rule to determine when and where the quantifier should receive which analysis. Russell calls it a distinction between primary and secondary occurrences of a denoting phrase (Russell, 1905b, p. 489). Obviously, this is bad form if your paraphrases are trying to provide a compositional semantic value for the sentences at hand; but, if you’re looking, in your paraphrases, to arrive at the object of assertion, then you won’t be required to respect the ways in which phrases embed, nor the ways in which they project or fail to project their initial presuppositions in new contexts – that would be a job for compositional semantics. It is for a semantic theory (perhaps supplemented by a pragmatic theory) to explain how presuppositions project, and to determine a candidate object of assertion. Once we have a candidate for an object of assertion, the theory of descriptions steps in, replacing some of the constituents of that proposition with descriptions – sometimes in ways that no semantic theory could in principle predict. And thus, Humberstone recognises, Russell would be best read as providing paraphrases of assertive content, rather than ingredient sense (i.e., objects of assertion rather than semantic values). A closer look at ‘On Denoting’ suggest that Humberstone’s reading was on the right lines. I should, however, make the following disclaimer about what follows. I do not seek to marshal textual proofs that my theory of descriptions, as outlined in §1.3, was exactly what Russell meant. But I’m also not claiming that my theory of descriptions is merely what Russell should have proposed. My claim is that Russell’s views about what his theory was trying to achieve, and what it was a theory of, may have been somewhat confused, vague, or inchoate but that the theory of descriptions I outlined in §1.3 would be, at least, the best precisification of those inchoate thoughts.11 This means that the burden that my textual ‘proofs’ have to meet is relatively low; they need to be suggestive rather than decisive. ‘The subject of denoting is of very great importance,’ Russell tells us (1905b, p. 479), ‘not only in logic and mathematics, but also in theory of knowledge.’ It’s noteworthy here that Russell doesn’t mention anything about the theory’s importance to language or linguistics or to any

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discipline that we might naturally associate with contemporary semantics. Zoltán Gendler Szabó (2005, p. 1199) takes ‘theory of knowledge’ to mean, ‘epistemology’. Indeed, Russell used the theory of descriptions to motivate his famous distinction between knowledge by acquaintance and knowledge by description (Russell, 1910–1911). And yet, I think that this is something of a red herring. Russell’s notion of the theory of knowledge, even though this distinction lies at its heart, doesn’t line up all that well with what most of us mean by epistemology – or, it is at least much broader than our contemporary conception of epistemology. Russell’s notion of theory of knowledge has very little to do with warrant, evidence, justification, and the like. In 1913, Russell started to write a book, to be called Theory of Knowledge (1913). The project was aborted, and other than its opening chapters, which were published in The Monist, the manuscript didn’t see the light of day until after Russell’s passing. From the outset of the book, his interest is in the nature of acquaintance, and the cognitive relations that acquaintance is said to underwrite: ‘All cognitive relations – attention, sensation, memory, imagination, believing, disbelieving, etc. – presuppose acquaintance’ (1913, p. 5). Part I of the book gives an outline of what acquaintance is and with what sorts of objects it can stand us related to, and under what circumstances. Part II of the book goes on to provide an account of how an agent is able to use the objects of her acquaintance so as to form assertions. Part III, which was never written, was supposed to extend his account of assertion to the case of molecular assertions (the assertion of conjunctions, disjunctions, conditionals and generalisations). Some years after Russell adopted his theory of descriptions, he also adopted the MRTJ. According to the new theory, when I judge that Romeo loves Juliet, I no longer stand related to a proposition. My assertion no longer has a single object. But we can still talk of the objects (in the plural) of my assertion. Russell began to think of assertion as a variably polyadic relation. When I judge that Romeo loves Juliet, I stand related to Romeo, to love, and to Juliet, in a certain order. They collectively are the objects of my assertion. The MRTJ was supposed to be the backbone of his Theory of Knowledge manuscript. That the MRTJ falls so centrally under the rubric of his Theory of Knowledge leads me to think that ‘the theory of knowledge’, as Russell understood it, even before his adoption of the MRTJ, was a discipline centrally interested in assertion, its objects, and our epistemic access to those objects.12 To echo the previous section of this paper, it was a theory interested in mind-world relations, but not (primarily) in communication. Returning to our quote from ‘On Denoting’, we can paraphrase it as follows: ‘The subject of denoting is of very great importance not only in logic and mathematics, but also in the theory of assertion and its objects.’ On page 481, Russell notes that the definite article isn’t always used, in practice, so as to ensure that some uniqueness claim is made. You might

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indicate ‘the son of so and so’ without intending to imply that so and so has only one son. Russell distinguishes between those uses of the definite article and strict uses intended to convey a uniqueness claim. This distinction between strict and loose uses of denoting phrases (much like his willingness to read denoting phrases as having either wide or narrow scope, depending merely upon seemingly pragmatic considerations) implies that Russell might not be interested in giving a general semantic account of such phrases so much as in giving an account of the assertions that those phrases can be utilised to express. Perhaps there can even be referential uses of a denoting phrase as well as attributive uses. Who knows how many different uses there may be? Russell happens to be interested, for the purposes of ‘On Denoting’, exclusively with what he calls strict uses. It’s important to note that it’s the proposition and not the sentence or the statement (i.e., the utterance) that undergoes the transformation in light of the theory of descriptions. Indeed, Russell claims that a ‘denoting phrase is essentially part of a sentence’ (Russell, 1905b, p. 488). That is to say, the theory of descriptions isn’t getting rid of denoting phrases from the analysis of sentences. What undergoes a transformation is the object of the assertion – the proposition. The denoting phrase may well be an essential feature of the semantics of the sentence, as far as Russell is concerned. His only aim has been to eliminate them from the objects of assertion. In short, a perusal of ‘On Denoting’ has given us no reason to think that Russell was trying to provide us with a general semantic account of names or denoting phrases. Russell was interested in the objects of assertion. His philosophy of mathematics and logic was interested in what it is that mathematicians assert and how the objects of those assertions are logically related. He wasn’t trying to give us a semantics of ordinary language. He was working out a theory of knowledge. I claim that the theory of descriptions that I outlined in §1.3 is, to all intents and purposes, Russell’s theory of descriptions (precisified). It’s easy to mistake a theory about the objects of assertion for a semantic theory. For instance, both types of theory will use the word ‘meaning’. But one theory means by ‘meaning’ the object of assertion, or the constituents of a proposition. The other theory means by ‘meaning’, the compositional semantic value of a phrase or sentence. When Russell says (1918, p. 253), ‘“Scott” taken as a name has a meaning all by itself. It stands for a certain person’, it sounds as if he’s adopting a semantic thesis about the meaning of a name. Instead, I’d argue that he’s talking about the contribution that that name makes to the object of assertion, when uttered by somebody acquainted with Scott. Similarly, in 1912, Russell writes (1912, p. 32): We must attach some meaning to the words we use, if we are to speak significantly and not utter mere noise; and the meaning we attach to our words must be something with which we are acquainted.

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Once again, you might think that he’s adopting a semantic thesis about names. But this all depends upon how you read the word ‘meaning’. One could consistently read this passage as saying the following: if we are actually to assert anything when we use words, then we must be acquainted with the objects of our assertion. On this reading, this passage advances no thesis about the relationship between semantics and epistemology – it’s a passage about the epistemic constrains on assertion. Any misreading of this passage, and other similar passages, likely trades on the ambiguity of the word ‘meaning’. Likewise, Russell’s talk of logically proper names and a logically perfect language might lead one to think that logically proper names have their bearers as their semantic values, and other names don’t (because their semantics has to be given in terms of disguised descriptions); that some languages only have logically proper names and therefore allow for a uniform semantics for names, and that some languages don’t. But this is to read too much into his words. I suggest that a logically proper name is one that always contributes its bearer to the object of assertion – i.e., the proposition. Russell hasn’t told us anything about the semantic difference between logically proper and improper names; perhaps there is no semantic difference. A logically perfect language, I suggest, is just one in which names always make a constant and stable contribution to the objects of assertion that they are used to assert – perhaps (although this is nowhere made explicit in Russell’s writings) whether a name is logically proper and a language is logically perfect depends upon what the speaker is acquainted with. Nothing in ‘On Denoting’ gives us reason to think otherwise. Witness the following excerpt from beyond ‘On Denoting’: It would seem that, when we make a statement about something only known by description, we often intend to make our statement, not in the form involving the description, but about the actual thing described. That is to say, when we say anything about Bismarck, we should like, if we could, to make the judgment . . . of which he himself is a constituent. In this we are necessarily defeated, since the actual Bismarck is unknown to us. (Russell, 1910–1911, p. 116) On my construal of this excerpt, we intend to make our statement about Bismarck in that we utter a sentence whose semantic value determines a proposition that contains Bismarck as a constituent, as a candidate for the object of assertion. But, since – according to Russell – only Bismarck is acquainted with Bismarck, everyone other than Bismarck fails to assert that object of assertion, and ends up asserting something with descriptions substituted in. Howard Wettstein writes about this excerpt that

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Russell, if I am not mistaken, felt a conflict between the dictates of his semantic ear, according to which names are directly referential, and his epistemological conscience. (Wettstein, 2004, p. 48) Russell’s initial semantic inclination may have been towards referentialism – a name contributes its referent as a semantic value – but his epistemological conscience couldn’t allow us to assert objects of assertion consist of constituents with which we have no acquaintance. The fix, on my reading, was to deny the identification thesis, and demand that semantic values, whatever they may be, give rise to a candidate for an object of assertion, which, in turn, can have descriptions substituted in when a person lacks acquaintance with constituents of the candidate. Why do I suggest that my theory of descriptions may only be a precisification of Russell’s somewhat inchoate thoughts on the matter? Why think there was any confusion on his part? To answer that question, I should note that in 1903, Russell is best read as committed to the identification thesis. Witness the following excerpt (Russell, 1903, p. 47): Words all have meaning in the simple sense that they are symbols which stand for something other than themselves. But a proposition, unless it happens to be linguistic, does not contain words: it contains the entities indicated by words. Here, Russell certainly seems to be relating to propositions as semantic values of sentences (although we have discovered that the word ‘meaning’ is somewhat ambiguous). And, until he gave up on his belief in the existence of propositions, he also clearly identified propositions with the objects of assertion (Russell, 1905c, p. 494): It is the things which are or may be objects of belief that I call propositions, and it is these things to which I ascribe truth or falsity. And thus Russell seems to have been committed to the view that the semantic value of a sentence is a proposition, which is identical to the object of assertion asserted upon utterance of that sentence. And thus, Russell – at least on an initial reading – seems wedded to the identification thesis, even in 1905, the year he authored ‘On Denoting’. Over time, Russell’s relationship with natural language underwent a massive change. In 1903, Russell thought that the surface grammar of natural languages was a pretty good guide for thinking about the structure, not just of objects of assertion, but of the world itself (remember that, for Russell, in 1903, the proposition expressed by a true sentence was thought to be identical to the fact that that sentence represents). In Russell’s words (1903, p. 46): ‘[G]rammar, though not our master, will

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yet be taken as our guide.’ Part of what was happening in ‘On Denoting’, was a move away from that outlook; a move towards mistrusting the grammar of natural languages, at least as a guide to understanding the ontology of what’s being asserted. By 1923, it seems as if Russell had all but given up on any interest he once had in natural languages as a guide to philosophical reflection (Russell, 1923); but there’s every reason to think that he was still interested – even once he’d given up on natural languages as a source of philosophical insight – in the relation that minds bear to the world – and thus he was still interested in thinking about objects of assertion, even though he was progressively, less and less interested in natural languages, and therefore, in their semantics. My suggestion is that I have read ‘On Denoting’ correctly, in this section, and that there really is evidence in the text that he was grappling towards the sort of theory of descriptions that I articulated in §1.3. And yet I’m willing to concede that Russell was on a philosophical journey that started with commitment to the identification thesis and ended with either its denial or simply with no interest in it whatsoever, and that in 1905, his thoughts on the matter may still have been somewhat in flux. At the very least, I suggest that the seeds of his later view are already in evidence, and that my reading provides the best precisification of his account in 1905. If I’m right, then when the older Russell looks back at his theory of descriptions, once the dust of his philosophical journey has settled, he’s all the more likely to read it as I’ve been suggesting. In the next section, we’ll see that that’s exactly what happened. §1.5: Strawson’s Char-Lady A key piece of evidence for my re-reading of Russell’s theory of descriptions stems from his acerbic response (Russell, 1957) to Peter Strawson’s ‘On Referring’ (1950). Russell’s response to Strawson has generally been written off as the senile ravings of an octogenarian. I think it would be wrong to fall for such wanton ageism. In fact, Russell’s later reflections on his early theory may represent a similar precisification to the one that I’ve provided, given that, in his old age, his views were less in flux, and perhaps less inchoate. The older Russell was perhaps better equipped at this stage to understand the import of his earlier attempts to articulate himself. Strawson understands a Russellian ‘logically proper name’ to be one whose semantic value is just its referent. On our reading of Russell, the only distinctive thing about such a name is that it contributes its referent to the object of assertion. On our reading, Russell is actually silent about the semantics of names – logically proper or otherwise. Furthermore, Strawson understands Russell to be giving a semantic account of denoting phrases. Armed with these two misunderstandings, Strawson claims,

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as a matter of semantic principle, that denoting phrases can be used in a uniquely referential way and that: Expressions used in the uniquely referring way are never either logically proper names or descriptions, if what is meant by calling them ‘descriptions’ is that they are to be analysed in accordance with the model provided by Russell’s Theory of Descriptions. (1950, pp. 323–4) On my reading of the theory of descriptions, Strawson is completely off target here. First, Russell is silent on these semantic issues. Second, Russell may well be open to a distinction between referential versus attributive descriptions, and thus, he may be open to some non-strict uses of descriptions that contribute their denotation to the proposition expressed. The non-strict use of definite descriptions that Russell explicitly recognises are ones that don’t include a uniqueness clause. However, given this admission that words can be used in all sorts of ways, we can’t rule out that Russell would allow for some truly referential uses of descriptions. These just aren’t the ‘strict’ uses he was focussing on. Strawson seems to think that Russell is denying that descriptions can ever be used in a ‘uniquely referring way’, either at the level of semantic values or at the level of assertion. This is ungrounded. Strawson proceeds to share what would later be regarded as some truisms about the semantics of natural languages. He points out that we have to distinguish carefully between a sentence and the different sorts of use to which a sentence can be put, and between particular utterances of a sentence. Consider the presence of indexical particles that shift their reference from utterance to utterance, like the word ‘I’. Think also of the presence of tense, which is going to make the truth conditions of an utterance sensitive to the time of the utterance. When you take these truisms on board, you have to become realistic about what a semantics can deliver for you. It can’t give you one proposition that will be the assertoric content for every utterance of a sentence, since a sentence can be used to say a number of different things depending on the context of utterance. In Strawson’s words (1950, p. 327), To give the meaning of an expression (in the sense in which I am using the word) is to give general directions for its use to refer to or mention particular objects or persons; to give the meaning of a sentence is to give general directions for its use in making true or false assertions. It is not to talk about any particular occasion of the use of the sentence or expression. The meaning of an expression cannot be identified with the object it is used, on a particular occasion, to refer

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The Philosophical and Historical Background to. The meaning of a sentence cannot be identified with the assertion it is used, on a particular occasion, to make.

According to Strawson, a semantic value of an expression is something like a direction: used in circumstance x, phrase ‘a’ refers to some object y related to circumstance x via some relation R. What is the semantic value of a sentence? According to Strawson, it’s also a direction. Something like: used in circumstance x, sentence S asserts some proposition p related to circumstance x via some relation R. Ironically, Strawson is accepting that there’s a distinction to be drawn between the semantic value of a sentence – a direction for use – and the objects of assertion, asserted by any particular utterance – i.e., a proposition.13 In essence, Strawson is drawing the very distinction that we drew in §1.1. What Strawson isn’t sensitive to is that Russell is only interested in claiming something about propositions – namely, that they can’t contain constituents with which the speaker isn’t acquainted, and how to substitute in descriptive content when such acquaintance fails. Russell isn’t providing us with a semantic theory at all and so cannot be accused of neglecting Strawson’s truisms about semantic values. As far as Strawson is concerned, Russell had confused semantic values with the objects of assertion and walked into the trap of thinking that you can give a semantic theory merely by associating words with referents. Strawson illustrates his point with the following example: you shouldn’t confuse the meaning (i.e., the semantic value) of ‘handkerchief’ with the handkerchief in your pocket (i.e., the object of assertion). However, in actual fact, Strawson himself has mistaken a theory about the objects of assertion for a theory about semantic values, and thereby evaluated a theory in terms of something it was never meant to be. Because of the ambiguity of the word ‘meaning’ (which can either refer to a semantic value or to a proposition) it’s easy to mistake Russell’s theory of descriptions for something it isn’t. Ironically, Strawson identifies this very ambiguity (as to the meaning of the word ‘meaning’) as the source of Russell’s confusion! Strawson’s next move is to suggest that the sentence ‘The King of France is bald’ is significant. It has a semantic value – i.e., a set of instructions telling you how to use it. You know in what circumstances it can be used to say something true (in situations where France has a King who is bald) and in what circumstances it can be used to say something false (in situations where France has a King who is not bald). According to Strawson, it happens to be that in circumstances where France has no monarchy, it can’t be used to assert anything. There is, so to speak, no proposition available in such a situation for assertion or denial. And thus, if someone uttered the sentence right now, he or she would fail to assert anything. The sentence retains its significance, since it has a semantic value, even when uttered right now, but its utterance, in these

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circumstances, would fail to pick out an object of assertion. This is the mirror image of Russell’s theory. Russell thinks that to utter that sentence right now is to succeed in asserting something, albeit something false. But, as we saw, he might well be open to the suggestion that, right now, the sentence has no semantic value (if, for instance, he held a direct reference semantics for denoting phrases, such that sentences with empty denoting phrases have no semantic value). Ultimately, Russell, in his response to Strawson, has nothing productive to say about this particular point of disagreement. It seems to be nothing more than a clash of intuitions. With Russell, I think that an utterance, right now, of ‘the King of France is bald’ gives rise to a mistake, and thus, to a falsehood. Strawson disagrees that the mistake can be cashed out in terms of being false. I can hear nothing but the dull thud of clashing intuitions. Strawson’s only real argument against Russell has been that Russell’s theory of descriptions fails as a semantic theory. But, in actual fact, that’s okay because it was never intended to be a semantic theory. As I read his response, Russell makes three key claims: 1. Strawson has confused semantics with theory of knowledge and therefore unfairly evaluated Russell’s theory of descriptions as a semantic theory, which it wasn’t intended to be. 2. Even if you were to read the theory of descriptions, erroneously, as a semantic theory, Strawson’s critique would have been incomplete. 3. Russell isn’t interested, to this day, in the semantics of natural languages, but he is interested in the objects of assertion. Let’s take each claim in turn. As Russell (1957, p. 385) understands matters: The gist of Mr. Strawson’s argument consists in identifying two problems which I have regarded as quite distinct – namely, the problem of descriptions and the problem of egocentricity. I have dealt with both of these problems at considerable length, but as I have considered them to be different problems, I have not dealt with the one when I was considering the other. This enables Mr. Strawson to pretend that I have overlooked the problem of egocentricity. This passage is cryptic, especially because it uses Russell’s idiosyncratic term for indexicality, which he calls ‘egocentricity’. Strawson attacks Russell’s theory of descriptions as a bad semantic theory. And, the grounds upon which Strawson claims the theory to be so bad is that to misidentify the semantic meaning of a sentence with the proposition it happens to assert on a given utterance is to completely ignore the semantic phenomenon of indexicality. As we shall see in what follows, Russell is annoyed

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for two reasons: (1) his theory of descriptions was never intended to be a general semantic theory for all sentences containing names and denoting phrases, and (2) subsequent to 1905, Russell had turned his attention to questions of indexicality, long before Strawson claimed to be pioneering efforts to uncover its significance.14 In order to demonstrate that Russell was not blind to the semantic truisms developed by Strawson, Russell (1957, p. 386) quotes his own Human Knowledge its Scope and Limits (1948): ‘This’ denotes whatever, at the moment when the word is used, occupies the centre of attention. With words which are not egocentric what is constant is something about the object indicated, but ‘this’ denotes a different object on each occasion of its use: what is constant is not the object denoted, but its relation to the particular use of the word. Whenever the word is used, the person using it is attending to something, and the word indicates this something. So Russell feels doubly wronged, since ‘Mr. Strawson should not expound [Russell’s own theory] as if it were a theory that he had invented’, and Mr. Strawson had clearly misunderstood the intention behind Russell’s theory of descriptions, which simply doesn’t bear on the question of ‘egocentricity’, or the semantics of natural languages. Russell had always thought semantics and ‘theory of knowledge’ to be ‘different problems’. Indexicality is a problem for semantics. The theory of descriptions is part of the the theory of knowledge. This is Russell’s first claim. Russell then goes on to make his second claim: even if you do adopt the theory of descriptions as a semantic theory, to account for the semantic value of denoting phrases, Strawson’s critique would have been incomplete (p. 387). Not all sentences that contain denoting phrases contain indexicals. How would Strawson have coped, Russell wonders, with Russell’s theory, adopted as a semantic theory, applied to descriptions that don’t have any relevant idexicality at all, such as ‘the cube of three is the interger immediately preceding the second perfect number’ (1948, p. 385)? Strawson’s semantics exagerates the extent to which indexicality pervades natural language. And yet, Russell seems to accept that his canonical example, ‘the present King of France is bald’, given the presence of the present tense, is infected with indexicality. He toys with deleting the word ‘present’, but even without the word ‘present’, the sentence is still in the present tense. He toys with adding an explicit date – e.g., ‘the King of France is bald in 1905’, but he seems sensitive to the fact that adding this clause doesn’t completely destroy Strawson’s argument – if you continue to construe the theory of descriptions, erroniously, as a semantic theory. Perhaps this is because you can’t really get rid of tense when speaking in English, and thus ‘the King of France is bald in 1905’ when uttered not in 1905 will

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seem as semantically defective as ‘I went shopping tomorrow’ uttered at any time, for there would seem to be some sort of mismatch of tense. For these sorts of reasons, Russell thought that formal languages should eradicate tense altogether (Russell, 1918, p. 248). And yet, perhaps Russell was being too charitable to Strawson here. There is certainly a reading of ‘the King of France is bald in 1905’ that utilises the historical present, and is therefore felicitious. Let’s put that to one side for the moment, and accept with Russell that you can’t easily get rid of the idexicality from his cannonical natural language example of a definite description. Does Russell therefore accept that Strawson’s critique bites against it? Does this, in turn, entail that he concedes the point that ‘the present King of France is bald’ doesn’t adhere to his theory, before moving on to descriptions about eternal entities like numbers? Russell’s response isn’t worded in the sort of concillitary tone consistent with such an interpretation. Instead, I think we should read Russell as saying the following: Look, my theory was never intended as a semantic theory of denoting phrases, and thus I won’t concede anything to Strawson’s critique, but even if my theory was intended as a semantic theory of denoting phrases, Strawson’s critique wouldn’t work against every description, but only against descriptions (like my canonical description about the king of France) embedded in sentences whose truth conditions are closely tied to the context of utterance (the critique won’t apply to descriptions about numbers, for instance). Strawson’s critique not only mistakes my theory for a semantic theory but also, as a matter of semantic fact, it over-exagerates the significance of indexicality. This, I take it, is Russell’s second key claim. Russell goes on to sound quite humbug about the fashion for ordinary language philosophy. Russell had advanced a theory about indexicals, which should form a central piece of any semantics for a natural language. However, fundamentally, Russell wasn’t interested in ordinary language, or providing a semantics adequate for natural languages. He seems to have thought that natural languages were quite ugly and unruly. See his pessimistic take on semantic indeterminacy in natural languages, for example (Russell, 1923). Russell’s transformation from 1903 was complete. Philosophy should pay no heed to ordinary language, other than being wary of the mess it can get us into if we take it too seriously! Philosophy, Russell thought, should aim to cultivate a technical and formal vocabulary, free from vagueness and from the infelicities of ordinary speech. But then, Russell seems to back-track and look quite closely at a piece of English slang, as if he were very interested in the day to day speech of English in practice (Russell, 1957, p. 388): Suppose (which God forbid) Mr. Strawson were so rash as to accuse his char-lady of thieving: she would reply indignantly, ‘I ain’t never done no harm to no one’. Assuming her a pattern of virtue, according

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The Philosophical and Historical Background to the rules of syntax which Mr. Strawson would adopt in his own speech, what she said should have meant: ‘there was at least one moment when I was injuring the whole human race’. Mr. Strawson would not have supposed that this was what she meant to assert, although he would not have used her words to express the same sentiment. Similarly, I was concerned to find a more accurate and analysed thought to replace the somewhat confused thoughts which most people at most times have in their heads.

It seems to me that Russell is here trying to make the following claims: 1. Russell’s interest applies even to relatively idiosyncratic uses of language 2. Pragmatic considerations are what would lead Russell, in the example of Mr. Strawson’s accused char-lady, to the right interpretation of her words 3. The final object of Russell’s interest here was what the char-lady was asserting. Again, Russell’s interest isn’t natural language, or the confused thoughts which people have in their heads about what it is they mean, or what their words mean. Russell’s interest is, rather, directed towards the logical form of the object of any given assertion. Szabó (2005) has a different reading of the Strawson-Russell debate, which bears important similarities to my own. First of all, he explores the possibility that Russell had hoped to distinguish semantic values from the objects of assertion, but then says, under the assumption of this proposal, that the theory of descriptions was intended to regulate the semantic value of denoting phrases whilst remaining silent about objects of assertion (p. 1191). It’s no wonder that Szabó rejects the viability of this proposal, but it strikes me as ironic, because after drawing the right distinction, Szabó’s fleeting suggestion was to place the theory of descriptions on the wrong side of it. Szabó’s own considered position is that the theory of descriptions was never intended to be a semantic theory. About that, I think he’s right. He too sees this to be evident from, among other sources of evidence, Russell’s response to Strawson. However, Szabó’s positive proposal is that Russell wasn’t interested in the meaning of assertions at all; not from the perspective of semantics nor from the perspective of an analysis of the objects of assertion. Russell’s theory is, according to Szabó, stipulative rather than descriptive. That is to say, Russell is trying to tell us what we should mean, by our confused use of language, if we want ‘to avoid formal refutation and to solve certain puzzles’ (Szabó, 2005, p. 1200). However, Russell’s theory, according to Szabó, isn’t trying to say anything about what we do actually mean.

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This reading doesn’t respect, to my mind, what Russell was after in his theory of knowledge: he was after an account of the objects of assertion; even the objects of every day assertion; as they actually are, nor merely as they should be. It also doesn’t sit well with Russell’s discussion of Strawson’s char-lady. Is Russell’s concern really to prescribe for her a revisionary way of making sense of her utterance so as to save her, ex post facto, from some sort of refutation? Or, is Russell’s concern to figure out what on earth she might actually have meant, even though she was clearly confused about how to use English correctly, and might not have been able to formulate her actual meaning in very precise language? On my reading, Russell is interested in her actual meaning, even if he’s not interested in semantics. He’s interested in the object of her assertion. I’m not claiming that I can make perfect sense of everything that Russell said in ‘On Denoting’ or in his reply to Strawson. I’m also not claiming that he had a completely clear and well-defined grasp over the distinction between semantic values and objects of assertion. Dummett claims that Frege had almost grasped the distinction, without quite going far enough (Dummett, 1973, p. 307). Similarly, perhaps Russell only had an inchoate and sometimes confused grasp over the distinction. Bear in mind that, during the time in question, linguistics and the analytic philosophy of language was still embryonic. And yet I am saying that interpreted as groping towards that disctinction, and reading the theory of descriptions as a theory ultimately about the structure of objects of assertion, rather than as a theory about semantics and the logical form of sentences, can help us to make a lot more sense of the historical data than was hitherto fore achievable. It tells a story that is consistent with his continued, and sometimes dogged defence of the theory of descpritions, despite his diminishing faith and interest in natural language. It also provides us with a theory of descpritions worthy of consideration.

§2: Refining Our Understanding of Russell’s Doctrines Armed with our distinction between semantic values and objects of assertion, we can distinguish between two doctrines of linguistic transparency. I don’t believe that this distinction would have been clear to Russell in 1903, when he first embraced the doctrine (and where he seemed more interested in natural languages than he would do later on). However, here are the two disambiguations that we can now unravel, in light of Russell’s later theory of descriptions and its denial of (or neutrality to) the identification thesis: 1. Linguistic transparency regarding semantic values: every meaningful phrase must have an entity that serves as its unique and constant semantic value

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2. Linguistic transparency regarding objects of assertion: every meaningful phrase in a sentence must contribute a unique constituent to the object of assertion asserted by the utterance of that sentence in a given context of utterance We also have to distinguish between two varieties of direct realism: 1. Direct realism regarding semantic values: the semantic value of a semantic atom is its referent, and the semantic value of a sentence is somehow constructed out of the referents of its semantic atoms 2. Direct realism regarding objects of assertion: propositions (i.e., objects of assertion) contain as constituents the very entities and properties that they are about and/or invoke. What was Russell’s account of names? Did he ever subscribe to a direct reference semantics of names? It’s really not clear. Perhaps in 1903 his theories are all consistent with his holding to the identification thesis. We’ve noted already that he wrote, in 1903, that, ‘every word occurring in a sentence must have some meaning: a perfectly meaningless sound could not be employed in the more or less fixed way in which language employs words’ (Russell, 1903, §46).15 However, it seems clear that his interest was always primarily focussed upon propositions qua the objects of assertion. Indeed, Russell’s decompositional analyses were always interested in mining down to the level of the most basic objects of our acquaintance. His interest was, even then, focussed upon the theory of knowledge. He might have thought, somewhat inchoately, in 1903, that the objects of our assertions also happen to constitute the semantic values of sentences. But if he did think this, it was because he naively used to subscribe to the identification thesis. And thus he was a direct reference theorist in those days almost by chance, because his theories hadn’t yet placed a wedge between semantic values and objects of assertion. But as his disdain for natural language begins to become pronounced, he never gives up his interest in the objects of assertion. By 1905, it’s quite clear that Russell’s direct realism is exclusively concerned with objects of assertion. If he was trying to save direct realism as a semantic theory, then he failed. Consider the following: the theory of descriptions erroneously construed as a semantic theory, presumably leaves indexicals as aboutness shifters, or disguised descriptions. However, Russell (1910–1911) explicitly maintains that a certain class of indexicals – namely, demonstratives that pick out sense-data, and the personal pronoun – are logically proper names. They contribute their referent to the proposition expressed. So they can’t contribute aboutness shifters or descriptions. However, each time you use such a word, it may refer to something else. This contradicts the view that words make a

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constant semantic contribution to the sentences in which they appear, if that contribution is supposed to be a referent. We seem to be in a mess. Until we realise that by 1905, Russell wasn’t interested in direct realism as a semantic theory. Whether or not semantic values are referents is not an issue in which Russell had a stake. I suggest that the semantic role of indexicals was being left for semantics to figure out. Russell’s direct realism was purely about objects of assertion. It’s clear what ‘I’ contributes to objects of assertion. It contributes the speaker (presuming she’s acquainted with herself). In that sense, as regards the objects of assertion, such indexicals can rightly be called names. Unlike the word ‘I’, it’s not clear what ‘the present King of France’ contributes to objects of assertion. That’s where Russell’s theory of descriptions steps in – to save direct realism about objects of assertion. Russell’s direct realism, and his doctrine of linguistic transparency, understood in this light, were always primarily concerned with objects of assertion. Direct reference theory, by contrast, is a semantic theory. The only direct realism we need to take forward with us into part II of this book, is a direct realism about the objects of assertion. And the doctrine of logico-linguistic transparency, properly understood, merely amounts to the following relatively innocuous claims: •

•

•

Natural languages are not transparent regarding the objects of assertion, even if they are, or might be transparent regarding semantic values An incomplete symbol is an expression that might have a constant semantic value, but doesn’t contribute, for one reason or another, a referent to the object of assertion (either because the speaker isn’t acquainted with the referent, or because the object has no referent, or because a description is being used attributively, etc.). Transformational analysis is all about digging beneath the semantic form of a sentence, to the object asserted by a given utterance A logically perfect language is one that has been stripped of incomplete symbols (depending upon what a speaker is acquainted with, one language might be logically perfect for speaker a without being logically perfect for speaker b).16 A logically perfect language is transparent.

For Russell, we can now say relatively confidently, propositions are not posited to be the semantic values of sentences. If we want to deny the identification thesis, we’ll have to join him in claiming that propositions, if we posit them, are destined to play the role of objects of assertion and not semantic values. This takes us back to Davidson’s claim that propositions aren’t necessary for theories of meaning (Davidson, 1967; 2005). We can now agree (if we want to)! Propositions aren’t posited to play

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that role. A semantic theory might be able to make do without propositions. And yet a metaphysics of assertion might still need them. Another doctrine that’s going to have to be amended is predicate reference realism (from chapter 2, §2). It now becomes clear that Russell’s contention wasn’t likely to be about the semantic value of a predicate, so much as what the use of a predicate generally contributes to the object of assertion. Predicate reference realism read as a semantic theory claims that the semantic role of predicates is, in part, to refer, and that their referents are universals. Predicate reference realism read as a theory about the objects of assertion is actually silent about the semantic role and the semantic value of predicates. It simply says that whatever semantics has to say about predicates, they also contribute universal properties to the objects of assertion (although, as I’ve promised, ontological commitment to universals will not, ultimately, be something upon which my reconstrual of the MRTJ will depend). Direct realism about objects of assertion is part of what Russell called the theory of knowledge: it claims that when we think about the world, and perceive it, we do so directly; not through any veil of senses – but it makes no claim about semantic values. The motivating spirit of direct realism actually stands at odds even with the sense-data epistemology that Russell was moving towards from 1905 onwards; an epistemology I don’t defend or develop in this book. The spirit of direct realism, in its purest form, doesn’t allow for a veil of sense-data any more than it allows for a veil of Fregean senses in our objects of assertion. Direct realism about objects of perception is popular today among philosophers of mind and epistemologists, for the very sorts of anti-sceptical reasons that first made direct realism about objects of assertion appealing to Russell (see Hinton (1973), Snowdon (1979–1980), McDowell (1998), and Martin (2002; 2003)). Indeed, McDowell (1998, p. 243) argues that without direct realism, and especially if you’re lumbered with a sense-data view, it becomes impossible to characterise sense-experiences in terms of what they are an experience of. This comes very close to Russell’s own arguments against Frege that if Mont Blanc, along with all of its snowfields, is not a constituent of any proposition, it becomes difficult to guarantee that we can ever have a thought that’s actually about Mont Blanc (see chapter 2, §3, and McGuinness (1980, p. 169)). As we shall see, in the next chapter, the rise of the MRTJ has to do with the relationship between the various Russellian doctrines that we’ve canvassed, clarified, and hopefully motivated in these preliminary chapters (although I’ve promised my nominalist readers that the MRTJ will end up being independent of predicate reference realism – this won’t become fully apparent until chapter 8, §3). In fact, the rise of the MRTJ was over-determined by the numerous tensions that these doctrines generate. To the extent that the MRTJ was partly motivated by direct realism, Russell’s move to a sense-data epistemology during the very years in

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which he was also developing the MRTJ, cut against some of the MRTJ’s motivation. We shall not follow that contrary thread of Russell’s thought in this book, since his sense-data epistemology is no part of the program that I’m hoping to explore in part II or defend in part III. I continue to harbour the early Russellian aversion to veils between the mind and the world, whether or not those veils are Fregean senses or sense-data. I conclude this chapter, and this part of the book, with three points. (1) Despite appearing to be a matter of controversy among philosophers of language for many years, Russell’s direct realism and his theory of descriptions, concerned as they are with the objects of assertion, are not at issue between the those who endorse and those who reject the direct reference theory as a semantic theory for names. (2) Direct realism, unrelated to the semantics of names, and as part of what Russell would call theory of knowledge, is still a going concern, with a number of contemporary adherents still attracted to its initial common-sense, anti-sceptical charm. (3) The doctrine of logico-linguistic transparency is a claim about the relationship between language, post-transformational analysis, and the objects of assertion; but not about the relationship between language and semantic values.17 With these conclusions in place, we are ready to document, and hopefully to motivate, the birth of the MRTJ.

Notes 1 These camps do not exhaust the options on offer in the philosophy of language. Even in this summary, I’m restricting myself to a broadly Russellian paradigm – some of these theories adopt what they take to be a pre-1905 Russellian view, and some adopt what they take to be a post-1905 Russellian view (or an adaptation of it), but they are all – broadly speaking – Russellian; or at least they take themselves to be. The extent to which Russell was really worried about the semantics of names in natural languages post-1905 will be a major topic of this chapter. 2 Lewis (1980, pp. 88–90) explores and dismisses this strategy. If we want to deny that sentences ever embed in other sentences, we would be forced to distinguish between the sentence ‘Dave might be in Oxford’ and the homonymous schmentence that embeds in 3! Despite Lewis’ opposition, perhaps I have been too quick to rule it off as ad hoc. Schmentences do have their supporters – such as Michael Glanzberg (2011), and Jeff King (2007). But one can’t deny how odd it is to say that ‘Dave might be in Oxford’ and ‘Dave might be in Oxford’ are homonyms. Furthermore: the embedding issues that Rabern documents are not the only reasons that might lead one to deny the identification thesis, and not the only reasons that we’ll explore in this chapter, and so even if the schmentencite option is left on the table, which I tend to doubt, we might anyway be able to marshal sufficient reasons to deny the identification thesis – which is my current concern. 3 Yalcin (2014) also points to Récanati (1993; 2010) 4 I think that this is a distinct possibility. You might think that you couldn’t know the meaning of two co-referring words without knowing that they co-refer, especially if you’re a direct realist about reference. But I think that it’s eminently possible. In that regard, I follow Tom McKay (1981). Alternatively,

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we can at least accept, as direct reference theorists, that it’s possible to know the Kaplanian character of an expression without knowing it’s content – see Kaplan (1977). 5 This paragraph was improved in the light of a very helpful conversation with Jonny McIntosh. 6 This paragraph was improved in the light of a very helpful conversation with Andy Egan. Jason Stanley (2010, p. 101) contends that you can only really make sense of diagonalisation on a possible world based account of propositional content. He says, It is a noteworthy fact about Stalnaker’s explanation of the puzzles occasioned by co-referring names that it is difficult to separate from the possible-worlds conception of content that gives rise to them. Its implementation requires something like a possible worlds conception of content. To construct a proposition that is the diagonal proposition, one needs an update operation and a set of point-wise alternatives as a representation of context, which yields a set of such points as a value. It is difficult to see how to construct a diagonal proposition in (for example) a framework that treats propositions as structured n-tuples of objects and properties. In short, Stalnaker’s pragmatic explanations seem to rely on the possible-worlds conception of proposition he advocates.

7 8

9

10

11

I don’t see why we should accept this claim. In fact, I’ve tried to show how one might go about modelling diagonal content without talking about functions from worlds to truth values. I’m concentrating on Stalnaker’s earlier view, before it was subject to various refinements (Stalnaker, 2014). I am here appealing to Donnellan’s distinction between attributive and referential uses of descriptions (Donnellan, 1966). However, I’m not entering in to whether this distinction is a good semantic distinction – perhaps our semantics should give a uniform treatment for descriptions – I merely contend that it’s a good distinction for a theory of objects of assertion. One might think it odd that semantic values are so often unknowable to people who use words meaningfully. But we saw in §1.2 that communication can occur even when people are very much in the dark as to what the horizontal content of an assertion was. Why shouldn’t the same be said about semantic values (indeed, Stalnaker identifies horizontal content with semantic content – so he certainly thought we can communicate without knowing the semantic value of what we say)? If Putnam (1975) is right about the division of linguistic labour, then there may be all sorts of technical words that I’m able to use, even though I’m completely in the dark about their semantic value. On my view, semantic values play an important role in communication, because they place constraints upon what’s being asserted, and what’s being contributed to a conversation. But there’s no reason to think that particular interlocutors need to be acquainted with the semantic values that are generating these constraints. I’m grateful to an anonymous reviewer for pointing me in the direction of this unpublished paper. For more on Humberstone’s views about the distinction between semantic values and assertive content see Davies and Humberstone (1980). I use this language of ‘precisification’ quite consciously, trying to echo the philosophical literature on vagueness. My claim isn’t that the theory of descriptions outlined in §1.3 would be the best development of Russell’s theory, but

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that it would be the best sharpening up of the somewhat inchoate thoughts that he had at the time. I mean to say that, in hindsight, Russell might recognise this theory as his own. 12 Indeed, as Jason Stanely pointed out to me, in correspondence, the fact that Russell was willing to get rid of his propositions and to think instead about the multiple relation of assertion, lends a certain weight to my claim that his interest was progressively focussing in upon assertion and its objects rather than an interest in the semantics of natural languages. 13 What Strawson is calling the meaning of a sentence, or its semantic value, is roughly what Kaplan (1977) would later call its ‘character’. 14 It seems to me that James W. Austin (1978) was close to reading Russell’s words as I have done. He says, that Strawson’s critique leaves it open for Russell to say: ‘Oh I was talking of propositions, not sentences’; but Strawson may still raise the question ‘Well what about sentences?’ After all, if Strawson’s theory can account for all the facts that Russell’s theory can, plus the issue over the difference between a sentence and the use of a sentence, then Strawson’s would seem the better theory. It is at this point that Russell’s discussion of egocentricity becomes germane. Not only can Russell account for the difference between a sentence and its use, and the difference between an expression and its use, he has accounted for these differences in at least two earlier works. 15 Although even in 1903, Russell admitted that this rule had a few exceptions. See chapter 2, footnote 9. 16 I should note that the speaker relativity of logically perfect languages is nowhere made explicit by Russell himself, but follows from his theory as I have understood it. 17 And although I’m assuming a realism about universals, it will – as I said – turn out to be inessential to my defence of the MRTJ. Accordingly, it’s worth pointing out that even a nominalist might be attracted to the idea that when the mind thinks about a concrete particular, it stands directly related to that particular, and that, when a mind is acquainted with a concrete particular, it uses its name to make some sort of direct mental reference. That’s all that direct realism and logico-linguistic transparency require.

Part II

The Rise and Fall of the MRTJ

5

The Rise of the MRTJ

My hope is that, by the end of this book, the MRTJ will seem attractive to contemporary philosophers of language because of the ways in which it can explain the explananda laid out in chapter 1. Moreover, it is my hope that, by the end of this book, the MRTJ will seem attractive to contemporary philosophers because of its favourable comparison to its rivals. However, in this chapter, my aim is to show how the MRTJ grows out of the Russellian philosophical background that was outlined in part I. Ignoring Russell’s sense-data epistemology and his logicism – which play no role in this book – the contours of Russell’s pre-MRTJ philosophical programme that emerged from part I, come down to the conjunction of: (1) propositional realism, (2) predicate reference realism, (3) direct realism about the objects of assertion, (4) the doctrine of logico-linguistic transparency (from sentences after transformational analysis to objects of assertion), and (5) termism. In §1, I explore some problems that emerge from this combination of views. In §2, I discuss the ways in which the MRTJ might be able to address those problems. In §3, I put forward a few reasons for adopting the MRTJ that emerge from the Russellian backdrop of part I, but not from problems internal to the programme. Only in §4, do I turn to the historical task of trying to figure out what ultimately pushed Russell himself to adopt the theory.

§1: Three Weak Points Within the Programme §1.1: The Truth/Falsehood Problem One problem with our philosophical programme we have already seen, in chapter 1 (§2.1). We can call it the truth/falsehood problem. Russell’s direct realism, in combination with his account of propositional unity, runs counter to the following platitude about truth: R(a, b) is a true proposition iff a is R-related to b. In the introduction, I offered a preliminary

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defence of denying this platitude. Russell and Moore had good reason for thinking that truth was a philosophical primitive. Moore wrote: [A]ll true inference must be an inference from a true proposition; and that inference must be inference from a true proposition; and that the conclusion follows from the premiss must again be a true proposition: so that here also it would appear that the nature of a true proposition is the ultimate datum. (Moore, 1899, p. 181) The idea seems to be that any argument for a theory of truth can only be judged to be valid if you already have a conception of truth – since validity itself is defined in terms of truth. Similar arguments were proffered by Russell (1904; 1905c; 1906). We only feel that the platitude should be respected because it goes some way towards describing the nature of truth: a proposition is true iff its relation relates its relata. But truth is primitive. It can’t be explained. This conclusion is supposed to minimise the cost of rejecting the platitude. However, this defence will not do. Primitivism about truth is a respectable position.1 However, primitivism doesn’t demand that we reject the platitude – as long as we don’t treat it as an explanation or definition. Without the platitude, it remains a total mystery why we should prefer true propositions over false ones. If Romeo is hate-related to Juliet as well as love-related to Juliet, why should we believe the proposition that Romeo loves Juliet and disbelieve the proposition that Romeo hates Juliet? Both relations are actually relating their relata (otherwise, the propositions would have no unity), so why believe one and not the other? Russell’s only response to this charge was that our preference must be based ‘upon an ultimate ethical proposition: “It is good to believe true propositions, and bad to believe false ones”’ (Russell, 1904, p. 76). §1.2: The Existence of Falsehoods Ordinary direct realism, given Russell’s account of propositional unity, has the following corollary: propositions are identical to the states of affairs that they purport to represent. Following Landini (2007), we could think of Russell’s true propositions as obtaining states of affairs (i.e., facts) and his false propositions as non-obtaining states of affairs: Obtaining (truth) and non-obtaining (falsehood) are accepted as primitive unanalyzable properties. States of affairs are mind – and language-independent entities that contain ordinary objects, rocks, trees, mountains, and the like, as constituents. (Landini, 2007, p. 40)

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Ontological commitment to ordinary objects, the early Russell shared with any common-sense realist. Similarly, ontological commitment to obtaining states of affairs is – at least relatively – uncontroversial. But Russell’s ontological commitments go further: he was happy to use existing ordinary objects, like you and a pair of water skis and the North Sea, to create a very peculiar sort of complex entity: a non-obtaining state of affairs, like the one in which you’re currently using those water skis to negotiate some rough waters. This leaves Russell vulnerable, even after he rids himself of the last vestiges of Meinongianism, to the charge of ontological profligacy: if propositions are identical to the states that they represent, and if we can assert false propositions (such as the proposition that you’re currently waterskiing), then non-obtaining states of affairs must exist. Ruth Barcan Marcus seems to subscribe to such a view: There is a seemingly naive as well as much maligned view, to which I subscribe, Russell’s for example, where knowing and believing are attitudes towards states of affairs (not necessarily actual), which may have individuals as constituents. (Barcan Marcus, 1981, p. 504) The combination of propositional realism and direct realism, given Russell’s account of propositional unity, does seem to give rise to the picture that Barcan Marcus sketches. But it beggars belief to think that the state of affairs in which you’re currently reading is no more a part of the fundamental furniture of reality than the non-obtaining (or non-actual) state of affairs in which you’re currently waterskiing. It invites exactly the sort of ‘incredulous stare’ that we tend to reserve for modal realism (of course, if you’re reading this while waterskiing on the North Sea, you’ll have to find some other example to illustrate my point). If we weren’t direct realists about propositional content, then the existence of falsehoods would be less problematic – false propositions would no longer constitute the very non-actual states of affairs that they attempt to represent. However, direct realism is well motivated. We have thus found ourselves in a dilemma: we must either deny direct realism about propositional content or admit an unsightly realm of non-obtaining states of affairs into our ontology. §1.3: Termism and Paradoxes Termism also brings trouble in its wake. Take the predicate of being a predicate that cannot truly be predicated of itself and call it W. W is what gives rise to the Russell-predicate paradox: W can be truly predicated of itself iff it cannot be truly predicated of itself! Frege escapes this paradox (though he can’t escape the extensional version of the paradox) precisely because Frege doesn’t subscribe to termism. If W is a Fregean concept,

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it cannot be spoken about: it cannot be the value of a variable; it cannot be the subject of predication; let alone self-predication. However, Frege’s rejection of termism commits him to the concept-‘horse’ paradox, which Russell rightly sought to avoid. A solution presents itself to the predicate paradox. We could stratify our properties into a hierarchy: things (i.e., entities that can only ever appear as the subject of a proposition) will constitute the ground-level of this hierarchy; the first-level will be occupied by properties that can only be instantiated by things; the second-level will be occupied by properties that can only be instantiated by first-level properties, and so on and so forth ad infinitum. Termism is respected by this attempted solution because, as Hylton (1980, p. 10) explains, ‘there is nothing which cannot, at some level and in some sense, be a logical subject, nothing that we cannot talk about; yet no concept can have a first-level concept attributed to it.’ A problem: it will be true of all entities, on this hierarchical view, that they occupy a level in the hierarchy; it therefore seems that the property of occupying a level in the hierarchy has no place in the hierarchy whatsoever because it can be meaningfully attributed to any entity, regardless of their level. The establishment of the hierarchy therefore invokes properties that have no place within the hierarchy. For Russell, this wasn’t good enough. Hylton (1980, pp. 2–3) explains that one of the key motivations for Russell’s termism was the doctrine of the universality of logic: the view that all reasoning ‘employs logic and is subject to logic.’ Logic is therefore the most general of all sciences and can have: ‘no meta-theory: we cannot reason about logic from outside, for all reasoning is, ipso facto, within logic’ (1980, p. 3). But if logic is host to a hierarchy, and if all reasoning employs logic and is subject to logic, we shouldn’t be able to reason with concepts that have no place within the hierarchy, such as occupying a level in the hierarchy. The philosophical programme that we’ve been sketching has therefore been placed in yet another dilemma: our commitments generate Russell-predicates such as W, which engender paradox; it seems that we must either reject our termism entirely or restrict its application in such a way as to negate the universality of logic. The first route is a dead end because it merely gives rise to properties that paradoxically cannot be spoken about. The second route, along with its hierarchy, involves a drastic re-conceptualisation of the nature of logic – if logic isn’t that which governs all reasoning then what is it? The second route also imposes a peculiar and ad hoc structure upon Russell’s ontology, according to which simple, and seemingly unrelated and distinct entities are stratified over an infinite hierarchy. In appendices to Principles of Mathematics (1903), Russell considered both routes, but was happy with neither. It was as if Russell was waiting for a third option to materialise.

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§2: The MRTJ as a Remedy to the Problems and Tensions of §1 The MRTJ denies propositional realism; it asserts that judgement (and indeed any propositional attitude) is a multiple relation between a mind, on the one hand, and the various entities that would have been the constituents of the proposition in question, had it been the case that propositions actually existed. Thus, Othello’s tragic judgement that Desdemona loves Cassio isn’t a binary relation between him and a proposition, it’s a four-place relation between Othello, Love, Desdemona and Cassio. In this section, I demonstrate the ways in which the MRTJ can be said to repair and complete the philosophical programme that we developed in the previous chapters of this book. §2.1: Solving the Truth/Falsehood Problem The MRTJ simply rejects that there is any such entity as the proposition that Desdemona loves Cassio. There is a judgement, on Othello’s part, but there is no proposition. Our talk of propositions is peppered with incomplete symbols, and our ontological commitment to propositions can be relieved via the transformational analysis of proposition-talk into talk about judgements. The judgement state of affairs doesn’t get its unity from Desdemona being love-related to Cassio; the judgement gets its unity from Othello (the subject of the judgement) being judgement-related to Love, Desdemona and Cassio (in a specific order).2 With the MRTJ in hand, we preserve our account of unity (according to which relating-relations unify states of affairs); we preserve our direct realism (no longer about the constituents of propositions, but still about the objects of assertion); we preserve a slightly reworded version of the platitude – J (s, R, x, y) is a true judgement iff x is R-related to y – and the platitude no longer implies the truth of all assertions. §2.2: Getting Rid of Objective Falsehoods By getting rid of propositions, Russell resolves the problem of existing falsehoods. If you want to judge that I’m waterskiing, I will need to exist, as will the property of waterskiing; but, given the MRTJ, you can falsely judge that I’m waterskiing without there being a non-obtaining state of affairs in which I am, and without ditching direct realism. As I pointed out in chapter 1, quoting Scott Soames, it’s pretty easy to unify the constituents of a proposition without rejecting direct realism, without collapsing propositions into truth-making facts, and without appeal to non-obtaining states of affairs. If we’re talking about the proposition that aRb, all you have to do to unify the constituents – a, R, and b – is to appeal to a relation that will create a unity that isn’t a state

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of affairs, such as the relation that creates the set {a,R,b}, or the relation that creates the ordered sequence . This route seems like a less radical fix than the MRTJ because it leaves our propositional realism intact. But there are good reasons not to adopt this route. Our theory of propositions has to answer the representation-concern – raised in chapter 1. There’s no reason to believe that sets or ordered sequences are inherently representational – propositions, on the other hand, are supposed to be. If you’re thinking of propositions as actual (obtaining or non-obtaining) states of affairs, then you might find it easier to ignore the representation-concern, since the constituents of the proposition appear in the proposition as you want to represent them to be. For example: in the false proposition that you’re currently waterskiing, on the state-of-affairs account, you yourself are actually waterskiing in the proposition; you appear, in the proposition, exactly as the proposition represents you to be – namely, waterskiing. However, it’s much harder to see how propositions thought of as sets or sequences, can be thought to overcome the representation-concern. Of course, even the state-of-affairs view of propositions probably fails to answer the concern head-on, because, in the final analysis, even if you do appear in the proposition as the proposition represents you as being, you can still ask why a state of affairs in which you’re waterskiing actually represents you as waterskiing rather than merely contains you waterskiing! Furthermore, I could use such a state of affairs to represent whatever I want. You might think that Russell never demanded of propositions that they be representational. And thus you might think that my analysis here of Russell’s motivations must be way off target. Given that propositions were, in 1903, supposed to be identical to facts, why think that they were supposed to be representational? Perhaps propositions were only supposed to be what sentences represent. However, I don’t think that’s right at all. Even in 1903, propositions were representational. There are two ways to see that this is the case. First, we can derive that Russellian propositions are representational from the exceptional cases in which Russell would appeal to denoting concepts. Denoting concepts were aboutness shifters, shifting what a proposition was about from its own constituents to some object beyond the proposition itself. And thus we can see that in the standard case, where propositions contained no denoting concepts, propositions were about their own constituents; they represented themselves. Second, Russell insists that his propositions had a peculiar property called assertedness (Russell, 1903, pp. 48–9). As we’ve explored, a proposition in 1903 was supposed to be characterised by an essential unity among its constituents. This unity was brought about by the presence of a relating-relation. The English verb ‘to murder’ can appear as a verbal

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noun, as it does in the sentence ‘Murder is wrong’, or as a verb, as it does in the sentence ‘Brutus murdered Caesar.’ Russell insists that when a verb occurs as a verb, it denotes a relation in the act of relating. When it appears as a verbal noun, it denotes that relation not in the act of relating. When a relating-relation forms a proposition, the result is that the complex whole manifests the property of assertedness, which, in this context, is supposed to be a logical and not a psychological notion (Russell, 1903). As far as I understand this somewhat obscure passage in the Principles of Mathematics, Russell is saying that when a proposition is unified, it has a non-psychological, inherent, representationality to it. It represents. What does it represent? It represents itself. It represents the state of affairs that it is. At the very least, the idea was that when we assert a proposition, we use it to represent itself and that this psychological act is made possible, or meaningful, by the non-psychological property of assertedness had by the proposition. Propositions were always supposed to be representational, for Russell. States of affairs, he thought, are inherently. The same cannot be said for sets or sequences. Consequently, it’s quite plausible that Russell preferred the MRTJ to a structured account of propositions because he thought that the MRTJ was more able to account for representation, because representation was always a concern of his. We shall soon see that people have worried that the MRTJ also struggles with the representation-concern, but you might think that the power of the human mind to represent things is a less mysterious primitive notion than the power of a set or sequence (or even a state of affairs) to represent things all by itself. To the extent that the MRTJ puts the human mind at the centre of the generation of meaningful content, in acts of judgement and assertion, one can see the kernel of a response to the representation-concern. And so the MRTJ responds to the truth/falsehood concern, and to the issue with objective falsehoods, in a way that promises to be sensitive to the representation-concern. §2.3: Addressing the Paradoxes The MRTJ solves the truth/falsehood problem and it gets rid of nonobtaining states of affairs, without ditching direct realism. I do not argue that the third issue – the paradoxes that termism threatens to give rise to – can be so easily resolved. However, I do believe that the MRTJ might be a step in the right direction. In order to see the role that the MRTJ might have to play in paradox busting, let’s briefly sketch the pre-MRTJ moves that Russell made for himself upon discovering the predicate paradox, and its set-theoretic/extensional analogue: the set of all sets that are not members of themselves.

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§2.3.1: Incomplete Symbols and Substitution Early on, Russell sought to avoid the paradoxes by writing a hierarchy of types into the grammar of his logic, without actually imposing a hierarchy upon his ontology.3 He also wanted to ensure that his grammatical conventions wouldn’t appear to be ad hoc, and that their stipulation wouldn’t invoke predicates (such as ‘occupying a place in the hierarchy’) that don’t behave according to the conventions themselves. This was indeed an ambitious project. Russell devised an entirely new logic – substitutional logic – to secure all of these desiderata (Russell, 1973a; 1973b). The theory was to work as follows. Take the proposition, Socrates is male. Russell was, given his propositional realism, committed to the existence of this proposition as an entity. Let us call it p. p is about Socrates. Russell was also committed to the existence of Socrates. Let us call him a. Call Plato b. We can now talk about what would arise from substituting all occurrences of a in p for b. This substitution would give rise to a new proposition – call it q – namely the proposition that Plato is male. We can symbolise q, the proposition that arises from substituting all occurrences b b of a in p for b, as ‘p ( )’ . ‘p ( )’ names/describes q. Russell’s substitua a tional logic is founded upon this primitive operation of substituting one entity for another in a proposition. The following symbol allows us to consider all the various propositions that we could generate by substituting Socrates for someone/something else in p: ‘p ( a )’. This symbol can therefore serve the role normally played by the propositional function, ‘x is male’. For example: if we want to say that all things are male, we don’t need to say (∀x)(x is male); x instead, reading ‘p ( a )!q’ as ‘q is the unique result of substituting x for x every occurrence of a in p’, we can say (∀x)(∀q) ((p ! q) → q is true), a which means ‘for any x, and for any q, if q is the unique proposition that results from the substitution of x for a in p, then q is true’: in other words, everything is male. When I say that the propositional function ‘x is male’ is a propositional function that is true for every value of x, it looks as if I’ve made an assertion about a propositional function; as if propositional functions are entities. By allowing what Russell called a matrix, such as ‘p ( )’, to feature a as a proxy for the propositional function ‘x is male’, it becomes clear that propositional functions needn’t have referents: they’re merely a feature of language; incomplete symbols – there are no propositional functions out there! ‘p ( a )’ is clearly an incomplete symbol, it has a space that needs fillx ing in. When I say that ‘(∀x)(∀q) ((p a ! q) → q is true)’ it’s clear that my

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assertion concerns p and Socrates; I’m saying that whatever you replace Socrates for in p, the result will be a true proposition; it isn’t an assertion about a propositional function – propositional functions aren’t entities. The property of being male is an entity. It can be spoken about. However, on a substitutional logic it becomes clear that the propositional function ‘x is male’ is an incomplete symbol in a logical notation: a matrix awaiting completion. Russell didn’t want a hierarchy of entities, since he was hoping to impose a type theory on his logic without imposing it on his ontology. Accordingly, he found that he was able to generate a hierarchy of matrices, given the grammar of substitution.4 Take a proposition about p – namely, the proposition that the-beingmale-of-Socrates was caused by his having a y chromosome. This proposition is an objective truth that has another objective truth as its logical subject – the fact/proposition that Socrates is a man. Call the proposition in question t – t is a proposition about p, which is, in turn, a proposition about a. Russell was committed to the existence of all three entities. Given these three entities, and the process of substitution, we can define the propositional function ‘x is a property caused by having a y chromosome’; we could take the proposition that Karl Marx had a beard (a proposition r about an entity c – ‘c’ here stands for Karl Marx, and not his beard, which we can ignore for the moment, concentrating only on him and his property of beardiness). We can substitute it for the proposition that Socrates was a man in proposition t. This is made posr, c sible because we can engage in simultaneous substitutions: t( ) = df p ,a r, c (lS)(t( )!S). This tells us that simultaneously substituting proposition p, a r for proposition p, and Karl Marx for Socrates, in t, results in a new proposition s – namely the proposition that the-having-of-facial-hair-ofKarl-Marx was caused by his having a y chromosome. This illustrates that just as ‘p ( a )’ is a matrix that can serve as a proxy for the first-level propositional function ‘x is male’, ‘t ( p, a )’ is a matrix that can serve as a proxy for the second-level propositional function ‘x is a property caused by having a y chromosome’. First-level matrices call for one substitution, second-level matrices call for two, and so on and so forth ad infinitum. The use of matrices has built homogeneous typing into the grammar of Russell’s logic. The troublesome propositional function was ‘x has the property of not instantiating itself’, which we abbreviated to ‘x is W.’ Paradox arose when termism forced us to allow W itself to be the value of x. On the substitutional theory, however, no ‘propositional function’ can be its own value. A matrix cannot be its own argument for two reasons: first since it ⎛ ⎞ p ⎜⎜ ⎟⎟⎟ ⎜ isn’t an entity, and second, since ‘p ⎝ a ⎠’ is ungrammatical. Type theory a

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falls out of the grammar of substitution. You needn’t stipulate that the hierarchy exists, using self-defeating concepts like ‘all properties occupy a level of the hierarchy’. Sets can also be defined away in terms of matrices, whose grammar will not allow higher level ‘sets’ to be members of lower-level ‘sets’. This is a no-set theory of sets. Sets are ‘incomplete symbols’.5 The substitutional theory of logic would have been a triumph. It adopts a logical hierarchy without any of the cumbersome ontological commitments, and without undermining the universality of logic. All properties and entities are of the same logical type, but paradoxes cannot be stated because the grammar of substitution won’t allow it. If his logic charts the structure of objects of assertion, then the paradoxes aren’t assertable, even if certain sentences of natural languages appear to suggest otherwise. Unfortunately, Russell was to find that his new logic was itself infected by a paradox of its own. §2.3.2: Ramification and Vicious Circles In 1908, Russell published his ‘Mathematical Logic as Based on The Theory of Types’. In this paper, Russell first proposes a ramified theory of types. Not only are his propositional functions and sets to be ordered in a hierarchy of logical types but also his propositions are to be divided across a hierarchy of orders. It was still clearly his hope that the hierarchy of types would have no ontological significance – since sets and propositional functions don’t really exist. He called the type part of the edifice a ‘technical convenience’, which could be translated into his ontologically type-free substitutional logic (Russell, 1908, p. 77). As we have seen, the fundamental motivation for Russell’s substitutional logic was to avoid having to say the following: ‘Every propositional function occupies a level in the hierarchy’; such a claim would undermine the universality of logic, for the propositional function x occupies a level in the hierarchy would seem to occupy no place within the hierarchy! However, what about his hierarchy of propositional orders? What was it, and how was it to be justified? Russell was worried about a family of paradoxes. The defining feature of this family is that they all contravene the following rule-of-thumb: ‘Whatever involves all of a collection must not be one of the collection’ (Russell, 1908, p. 63). I list a selection of the paradoxes that Russell had in mind: (1) The Epimenidies paradox – Epimenidies the Cretan said that all Cretans were liars. But because he was a Cretan himself, if he was telling the truth, then what he said was false. But if it was false, then Epimenidies was a liar, and perhaps what he said was true all along!

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(2) The Russell-set paradox – Let w be the class of all classes that are not members of themselves; w is a member of itself iff it is not a member of itself. (3) The Russell-predicate/relation paradox – The predicate paradox can be generated for relations: let T be the relation that holds between any two relations R and S whenever R does not have the relation R to S; given our definition of T, ‘R has the relation T to S’ will be equivalent to ‘R does not have the relation R to S’; the question is this: does T stand in the relation of T to itself? The paradoxical answer: T has the relation T to T iff T doesn’t have the relation T to T. (4) The Least Indefinable Ordinal – It can be proven that there must be indefinable ordinals. Among these indefinable ordinals, there must be a least. But this ordinal, paradoxically, is defined as ‘the least indefinable ordinal’. (5) The Burali-Forti contradiction – As Russell explains: It can be shown that every well-ordered series has an ordinal number, that the series of ordinals up to and including any given ordinal exceeds the given ordinal by 1, and (on certain very natural assumptions) that the series of all ordinals (in order of magnitude) is well ordered. It follows that the series of all ordinals has an ordinal number, Ω say. But in that case the series of all ordinals including Ω has the ordinal number Ω + 1, which must be greater than Ω, hence Ω is not the ordinal number of all ordinals. (Russell, 1908, p. 61) Russell’s hierarchy of propositional functions and sets, couched in his substitutional logic, will solve some, but not all, of these paradoxes. Paradox (1) and (4), for instance, will go through in a substitutional logic without violating any type restrictions. These paradoxes can only be solved, or so it seemed to Russell, by a hierarchy of propositional orders. This second hierarchy doesn’t just stratify grammatical matrices. This second hierarchy stratifies propositions themselves. We can see how this will help: a proposition/definition can only be about/concern propositions/ definitions of a lower order; either Epimenidies is violating the theory of orders because he attempts to make a proposition of order n about a range of other propositions of order n, and thereby slips into nonsense, or Epimenidies is making the non-contradictory claim of order n+1 that all Cretan propositions of any order ≤ n are false. But this response is clearly ad hoc, and displays none of the virtues that the simple hierarchy of types has when couched in Russell’s substitutional logic. Russell’s substitutional hierarchy of logical types has the benefit of ontological neutrality. It doesn’t maintain that entities out there in the world actually differ in type. Nor does it require us, more importantly, to violate its own theory when we state the theory: the simple

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theory of types simply falls out of the grammar of substitution, and thus we won’t need to appeal to self-defeating properties such as occupying a place in the hierarchy, when we state the theory. Indeed, the theory doesn’t even need to be stated. The grammar of substitutional logic can take care of itself. However, Russell’s ramification of the theory imposes a hierarchy upon propositions – upon independent entities. Why think that one totally independent existent entity depends in any way upon completely distinct – and seemingly unrelated – entities ‘of a lower order’? Worse still is the following: in order to generate this second hierarchy, Russell will have to stipulate that every proposition occupies a level of the hierarchy of orders, but this very proposition occupies no place within the hierarchy it establishes.6 However, without the hierarchy of orders, how can Russell solve the paradoxes that his simple theory of types leaves over? Contemporary wisdom is to draw a major distinction between the semantic and the syntactic paradoxes. This follows Ramsey, who wrote that the semantic and syntactic paradoxes were ‘unified by being both deduced in a rather sloppy way from the ‘vicious circle principle’, but it seems to me essential to consider them separately’ (Ramsey, 1925a). Paradoxes (1) and (4), for example, are semantic. They arise because they neglect to relativise truth (in (1)) and definablity (in (4)) to a language. Gödel (1944, pp. 134–5) was also influential in propagating this view: the different sorts of paradoxes should be kept apart; only the syntactic/logical ones should bother the logicist. Russell’s ramification was an unnecessary and unsightly epicycle. It’s clear that Russell wasn’t completely cognisant of the difference between the semantic and logical paradoxes. He generously credits Ramsey with the discovery that these two classes of paradox are different (Russell, 1959, p. 59). However, the standard Ramsey-Gödel view is somewhat unfair to Russell. The Ramsey-Gödel view doesn’t recognise that Russell had discovered a non-semantic paradox that motivates the ramification of his theory of types. This non-semantic paradox arises from the assumption of propositional realism: 1. Assume that propositions exist 2. Assume that every declarative sentence expresses a proposition (relative to an utterance) 3. For any set of propositions, one could utter the sentence, ‘All of the members of that set are true’ 4. Given 2 and 3, it follows that, for any set of propositions, there is a proposition that says that all of the members of the set are true 5. Call the proposition that affirms all of the members of a set, a set-affirmation 6. Presumably, some set-affirmations belong to the set that they affirm. For example, the set-affirmation of the set of set-affirmations, is a

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member of the set that it affirms. But some set-affirmations certainly don’t belong to the set that they affirm. The set-affirmation that affirms the set of propositions that are not set-affirmations, is itself a set-affirmation and so doesn’t belong to the set that it affirms Given 4, set-affirmations exist, and given 6, some of them are not members of the sets that they affirm. We can now consider the set of set-affirmations that are not members of the sets that they affirm. Call that set, S Given 4 and 7, it follows that S has its own set-affirmation, which we could call p Given 8, we can ask, is p a member of S? Given that S is the set of set-affirmations that are not members of the sets that they affirm, and given that p is the set-affirmation of that set, we’re forced to say that ‘(p ∋ S) ↔ (p ∉ S)’ – p is a member of S only if it’s not a member of S – which is a contradiction!

Despite talking about sentences expressing propositions, this paradox isn’t, at root, a semantic paradox (although Hylton (1980) seems to think it is; a claim that Stevens (2005, p. 70) neatly dismisses, with Landini’s help). It doesn’t centrally concern the interpretation of semantic notions such as truth, falsehood, or definability (none of which appear in line 10). It is about the membership of propositions in classes of propositions. This paradox, the Appendix-B paradox – so-called after the Appendix of the Principles of Mathematics in which it appears – provides a clear logical motivation for ramification. And a similar paradox can be generated in the language of Russell’s substitutional logic.7 We have arrived at the following two conclusions: 1) Russell had good reason to ramify his theory of types; 2) the ramification was unsightly because, unlike the simple hierarchy of types, which falls out of the grammar of substitutional logic and is ontologically neutral, the hierarchy of propositional orders seems to be imposed upon Russell’s ontology. §2.3.3: The No-Proposition Theory of Propositions The first observation to make is that the MRTJ does away with propositions. If there are no propositions then any so-called theory of orders of proposition cannot really be conceived of as an ontological stratification (at least not straightforwardly). Furthermore, the MRTJ gives us an easy way to build a theory of orders into the grammar of judgement. In Principia Russell and Whitehead wrote: That the words ‘true’ and ‘false’ have many different meanings, according to the kind of proposition to which they are applied, is not difficult to see. Let us take any function φ, and let φa be one of its values. Let us call the sort of truth which is applicable to φa ‘first

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The Rise and Fall of the MRTJ truth.’ . . . Consider now the proposition (x). φx. If this has truth of the sort appropriate to it, that will mean that every value of φx has ‘first truth.’ Thus if we call the sort of truth which is appropriate to (x). φx ‘second truth,’ we may define ‘{(x). φx} has second truth’ as meaning ‘every value of φ has first truth,’ i.e. ‘(x). (φx has first truth).’ Similarly, if we denote by ‘(∃x). φx’ the proposition ‘φx sometimes,’ i.e. as we may less accurately express it, ‘φx with some value of x,’ we find that (∃x). φx has second truth if there is an x with which φx has first truth; thus we may define ‘{(∃x). φx} has second truth’ as meaning ‘some value of φ has first truth,’ i.e. ‘(∃x). (φx has first truth).’ Similar remarks apply to falsehood. (Russell and Whitehead, 1910–13, p. 42)

Russell can build this theory of orders without dividing some realm of propositions into various categories, because, in the final analysis, given his MRTJ, there are no propositions to divide. There are only judgements. But of course, my judgement that everyone is mortal can only be true if, were I to judge that Socrates is mortal and that Plato is mortal and so on and so forth, all these more basic judgements would be true. The fact that some judgements depend in this way, for their truth, upon the truth of other possible judgements,8 seems to write a theory of orders into our very notion of a proposition: Russell and Whitehead tell us, for this reason, that the truth of their theory of orders is ‘easy to see’. Propositions are to be defined away in terms of judgements, but the grammar of judgement, as it were, will order our propositions (we’ll come back to this claim, and try to flesh in out, in chapter 11, §5). Given the MRTJ, the order part of the ramified theory of types is philosophically justified: it comes for free, with no ontological impositions. Russell’s theory of types doesn’t stratify universals, or properties, or entities: it stratifies propositional functions into a hierarchy of types. Given that there are no propositions, and given that propositional functions are presented as incomplete propositions (Russell and Whitehead, 1910–13, p. 48), there is ample reason to read Russell’s 1910 theory of types as some sort of grammatical fiat, just as it was in the theory of substitution. Just as we cannot use ‘p ( )’ as its own argument, because we a yield a symbol that needs further supplementation in order to be meaningful, so too can we not use ‘x is W’ as its own argument, because we’ll yield a new symbol ‘x is W is W’ which still needs supplementation in order to say something – it still has a gap. A standard reading of Principia holds that in 1910 Russell bit a Fregean bullet: he adopted a theory of types with all of the ugly ontological consequences because he couldn’t otherwise escape the paradoxes. We cannot take a nominalistic view of propositional functions, they argue, because Russell quantifies over propositional functions throughout Principia; similarly, Russell must have been committed, in actual fact, to

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propositional realism, despite his MRTJ, because he continues to quantify over propositions throughout Principia.9 But perhaps, when Russell engages in such quantification, his quantifiers should be read as in some sense substitutional or metalinguistic. As Stevens notes: ‘The possibility of such an interpretation was first suggested by Gödel (1944) and has been explored by Sainsbury (1979) and Landini (1996; 1998).’10 On this view, even in Principia, sets and propositional functions and propositions are all incomplete symbols.11 To stratify them across a hierarchy is not to impose stratification upon your ontology; furthermore, the stratification falls out of the grammar of the transformational analyses that these incomplete symbols receive. The notion of an incomplete symbol might allow us to form a no-set theory of sets: we still have a theory of sets; we can still make assertions that putatively refer to sets; we can still talk about the relationship between sets; it merely happens to be the case that the expressions that seem to refer to sets are incomplete – sets can be defined, via a transformational analysis, in terms of their members – set talk is just a façon de parler. The MRTJ can be viewed as just an extension of this tactic: it gives rise to a no-proposition theory of propositions. I don’t deny that new logical paradoxes might arise. Nor do I deny that there are other ways to go about resolving our various paradoxes. Nor do I deny that this whole tactic seems somewhat obscure or esoteric. Nevertheless, there is certainly evidence to suggest that Russell may have thought, at least, that the MRTJ might have some role to play in paradox busting.12 Furthermore, the Appendix-B paradox is a paradox that should bother any realist about propositions (we’ll come back to this claim in chapter 11). If Russell’s no-proposition theory of propositions is a way to escape that paradox, it stands as a major consideration in its favour.

§3: The MRTJ in Its Own Right The MRTJ denies propositional realism. So in what sense can I claim that the MRTJ is motivated by the programme of part I of this book, when it seems to be at odds with it (propositional realism was supposed to be one of our doctrines)? My response is that the MRTJ is motivated by the very same considerations that motivated propositional realism in the first place: a species of anti-psychologism13 – the objects of a judgement are all mind-external – and the desire to give a fundamental account of the metaphysics of meaning. What do two people share when they make identical assertions? They stand in the same relation to the same object-terms in the same order. Given the MRTJ, we can still talk about propositions, as long as we remember that we are using incomplete symbols to be cashed out in terms of our theory of judgement. The MRTJ doesn’t abandon the project given rise to by propositional realism: it does all of the work that

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propositions were supposed to do without giving rise to the problems (it explains many of the explananda that we outlined in chapter 1, without positing the existence of propositions; a claim I come back to in chapter 10). Furthermore, the MRTJ is independently motivated by other doctrines in the philosophical programme. The fundamental motivation for direct realism is the desire to put our minds in contact with the world without any intermediary veils. Russell had tried to live up to this desire by conceiving of judgement as a binary relation between the mind and a proposition – a proposition comprised by the very things that the judgement is about or invokes. But why posit propositions? If the MRTJ can make sense of assertion without the existence of propositions, we can say that judgement puts you in direct contact with whatever it is that your judgement is about or invokes, without a veil of propositions. A veil of propositions, even if they consist of their own subjects, is still a veil. The MRTJ, in addition to any problems that it solves, gives rise to a much purer form of direct realism, without neglecting the work which we had originally delegated to propositions. To judge that Desdemona is in love is – according to the MRTJ – to stand directly related to her rather than to some complex of which she is a part. Furthermore, we have reason to believe that placing the mind at the centre of the genesis of meaning might be an important step towards overcoming the representation-concern. This is not a step towards idealism, nor does it embrace anything that should bother Russell’s brand of anti-psychologism. The mind isn’t, according to the MRTJ, constructing the world. The mind isn’t making things true or false. The mind-external world is doing that – as any good realist would demand. However, the mind is playing a role for which it seems appropriately cast – it, alone, is given the power to represent things truly or falsely. We no longer have to appeal to a realm of abstract propositions with a magical power to represent all on their own.

§4: Russell’s Motives Having looked at these issues somewhat abstractly, I now turn to the purely historical question of what were Russell’s own motivations for adopting the MRTJ. Russell (1910) levels two arguments against his former analysis of judgment as a binary relation: The first is that it is difficult to believe that there are such objects as ‘that Charles I died in his bed’, or even ‘that Charles I died on the scaffold’. It seems evident that the phrase ‘that so and so’ has no complete meaning by itself, which would enable it to denote a definite object as (e.g.) the word ‘Socrates’ does. We feel that the phrase ‘that so and so’ is essentially incomplete, and only acquires full significance when

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words are added so as to express a judgment, e.g. ‘I believe that so and so’, ‘I deny that so and so’, ‘I hope that so and so’. (Russell, 1910, p. 151) We shouldn’t be deceived into thinking that this is the same concern as expressed in §1.2 of this chapter: concern over the existence of false propositions. In this excerpt, Russell uses a true proposition as well as a false one, as examples. Given Russell’s theory of descriptions, it becomes intuitive to view ‘that’-clauses as incomplete symbols, receiving a meaning (in terms of assertive content) only in a wider context, such as ‘I judge that so and so.’ Russell’s first objection to the binary analysis of judgement is thus the observation that the theory of descriptions gives some weight to a different analysis (Carey, 2007, p. 16). The second objection is more fatal, and more germane to the consideration of truth and falsehood. If we allow that all judgments have objectives, we shall have to allow that there are objectives which are false. Thus, there will be in the world entities not dependent upon the existence of judgments, which can be described as objective falsehoods. This is in itself almost incredible: we feel that there could be no falsehood if there were no minds to make mistakes [Russell goes on to argue, that by parity of reasoning, there would be no truth either: facts, yes; but truths (i.e., true propositions), no.]. (Russell, 1910, pp. 151–2) This second objection does constitute that incredulous stare, taking us back to the problem raised in §1.2. Russell simply cannot believe that objective falsehoods exist. Hylton suggests that this discomfort with the existence of false propositions constitutes Russell’s main motivation for adopting the MRTJ. Russell’s ‘instinctive belief’ that there are no propositions, is, he admits, like ‘some of Russell’s other ‘instinctive beliefs’ . . . a flat denial of something which he had been willing to assert earlier’ (Hylton, 1990, p. 340). Hylton (1990, p. 341) goes on to admit that it is ‘hard to know how to account for the difference’ between the Russell who found objective falsehoods to be an obvious corollary of an obvious philosophy, and the Russell who instinctively found them to be deeply unintuitive. Ultimately, Hylton’s best answer to this challenge seems to run along the following lines. Russell’s philosophy, in its effort to rid itself of psychologism, had actually neglected to take account of important psychological data. In the past, Russell had simply assumed that our minds could be acquainted with all sorts of peculiar entities of which we have no direct experience. Perhaps under the influence of Meinong, Russell began to place psychological constraints upon this notion of acquaintance (Hylton, 1990, p. 357).14 How can we have any epistemic contact with non-obtaining

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states of affairs, for instance? It is this ‘step towards sanity, or a falling away from purity’ (Hylton, 1990) that explains Russell’s shift from a binary analysis of judgement to the MRTJ. Objective propositions may be the simplest way to ground logic, but, when false, they are unacceptable to a philosopher with wider concerns than logic alone. Russell (1906; 1910; 1912; 1913; 1918) presents the MRTJ as a component of a correspondence theory of truth. A judgement is true iff the order in which its object-terms are judged to be related corresponds to a fact in which those object-terms really are related in such an order by the object-relation of the judgement. As far as Hylton is concerned, at this point in Russell’s philosophical development, facts were a more plausible primitive than truth and falsehood. Richard Cartwright (1987a) argues that Russell’s main motivation for the MRTJ was the truth/falsehood problem. ‘It would be pleasant to be able to report unqualifiedly that this was Moore’s and Russell’s objection to false propositions’, Cartwright mused, but, ‘[u]nfortunately, things are not that clear-cut’ (Cartwright, 1987a, p. 82). Bernard Linsky (1993), who agrees with Cartwright, cites the following quote from Russell (1918, p. 223) as his textual evidence: Time was when I thought there were propositions, but it does not seem to me very plausible to say that in addition to facts there are also these curious shadowy things going about such as ‘That today is Wednesday’ when in fact it is Tuesday. On the surface, this looks like the problem of existent falsehoods: Russell can’t believe that in addition to obtaining states of affairs, reality is host to non-obtaining states. Cartwright also cites this quote, but sees in it nothing ‘clear-cut’. Linsky suggests an alternative reading: I propose that we read the remark about ‘That today is Wednesday’ as follows. If today is Wednesday, there is such a fact, today’s being Wednesday. There may also be a negative fact, viz today’s not being Tuesday, which contains today and being Tuesday in a special negative fashion. But there is not also a proposition of today’s being Tuesday, a complex combining today and being Tuesday . . . Indeed there is no way that objects combine except to form positive (or perhaps negative) facts. (Linsky, 1993, p. 200) As we’ve seen, the only sort of proposition-like entities that Russell’s account of unity can unify without absurdity are facts. If there were false propositions, and he had to unify them, they would become facts, and would thereupon cease to be false. Despite the truth of this, I remain unconvinced that Linsky’s interpretation accurately sums up Russell’s own point. ‘To suppose that in the

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actual world of nature,’ the quote continues, ‘there is a whole set of false propositions going about is to my mind monstrous’ (Russell, 1918, p. 223). In this particular instance, Russell’s concern seems to be the counterintuitive commitment to non-obtaining states – a commitment that conflicts with Russell’s ‘vivid sense of reality’ (Russell, 1918). His worry isn’t, at this point, that false propositions would become true.15 Nevertheless, with Cartwright and Linsky, I am convinced that the truth/ falsehood problem had some role to play in Russell’s initial motivation for the MRTJ.16 I have an independent source of textual evidence. In 1912, Russell rejected the notion that judgement was a binary relation between a subject and a singular entity because: If belief were so regarded, we should find that, like acquaintance, it would not admit of the opposition of truth and falsehood, but would always have to be true . . . We cannot say . . . [that Othello’s belief] consists in a relation to a single object, ‘Desdemona’s love for Cassio,’ for if there were such an object, the belief would be true. (Russell, 1912, p. 72) I am somewhat surprised that neither Cartwright (1987a) nor Linsky (1993) picked up on this quote as it vindicates their thesis: the truth/falsehood problem was a live concern for Russell (at least in 1912); the MRTJ was introduced (at least in part) to allow for an opposition between truth and falsehood. Russell was aware that given his direct realism, the only account he had thought to give of propositional unity would force false propositions to be true. Unlike Hylton, Cartwright and Linsky don’t need to appeal to Russell’s change of philosophical priorities in order to explain his sudden change of mind; rather, they appeal to the fact that Russell’s early philosophy was host to a major flaw: it collapsed the metaphysical distinction between truth and falsehood; the MRTJ was adopted, according to the Cartwright view, as soon as Russell became aware of this flaw in our philosophical programme, or at least when he became aware that he could resolve it. There is a third school which pushes the paradoxes to the heart of the story. Graham Stevens’ first piece of evidence for this view is biographical: From the discovery of the famous Russell paradox of 1901 until the completion of the formal system of Principia almost a decade later, Russell was single-mindedly devoted to the resolution of the paradoxes of mathematical logic. As a result, virtually every logical and philosophical innovation he produced during this remarkably fruitful period is primarily directed towards this end. (Stevens, 2005, p. 31)

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Stevens is happy to accept that various problems concerning false belief played some role in motivating the MRTJ (Stevens, 2005). Russell says so explicitly in print. But Stevens thinks it wise to pay attention to the fact that, in these years, Russell’s sole philosophical preoccupation was that of paradox busting.17 Certain posthumously published manuscripts point that way: ‘Logic In Which Propositions Are Not Entities’ and the ‘Paradox of the Liar’ both explore the option of rejecting propositional realism in order to avoid propositional paradoxes.18 These papers were written long before the MRTJ was formally adopted in print. Carey (2007) adds to these considerations a piece of evidence from Russell’s first published account of the MRTJ. After considering the binary relation theory of judgement, with its objective falsehoods, Russell writes, There are, however, difficulties in so regarding a belief. The chief of these difficulties is derived from paradoxes analogous to that of the liar, e.g., from the man who believes that all of his beliefs are mistaken, and whose beliefs are certainly all mistaken . . .We can escape this paradox if a belief cannot be validly treated as a single thing. (Russell, 1906, p. 46) Scott Soames made it sound, in his earlier work, as if Russell was insensitive to, or ‘confused’ about, the representation-concern (see, for example, Soames (2010, p. 32)). Recently Soames has come around to the view that the representation-concern played a central role in Russell’s rejection of propositions. Upon adopting the MRTJ, Russell became convinced that there can be no truth or falsehood unless there is a mind making an assertion (Russell, 1912, p. 70). Soames writes (2015, p. 440): Given his antecedent conception of what propositions would have to be (if there were any), he quite rightly saw there to be no way of explaining how such things could be the bearers of truth and falsity [and so he rejected them in favour of the MRTJ]. Soames would thus be sympathetic to the view that the representationconcern played some sort of role in pushing Russell away from propositional realism towards the MRTJ. Russell came to realise that representation only gets going when minds are put in the driving seat. The MRTJ embodies that realisation.19 What exactly motivated Russell’s adoption of the MRTJ? The following narrative seems plausible: Russell’s shifting philosophical priorities made him increasingly concerned about his inability to explain our preference for truth over falsehood and about the existence of, and our acquaintance with non-obtaining states of affairs; his theory of descriptions made the binary relation theory of judgement look less credible to him; he was slowly becoming aware of the representation-concern,

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and the paradoxes had forced him to reconsider every aspect of his philosophy; it is also likely that Russell became aware that his early views made truth and falsehood indistinguishable to the extent that falsehood threatened to collapse into truth. In short: it is likely that Russell was influenced to adopt the MRTJ by an awareness of all of the problems that I sketched in §1 and more.20 Short of any historical surety, I can at least offer a practical suggestion: there may be a lingering debate over the exact nature of Russell’s motivation for the MRTJ, but we know enough to know that, if it can be made to work, it will save the strands of Russell’s fast evolving philosophy that I have defended so far, and it will do so in such a way as to provide potential escapes from the representation-concern and the Appendix-B paradox. We know enough to know that the MRTJ, if it can be made to work, is a theory that promises to save the philosophical program of part I.

Notes 1 See Jamin Asay’s wonderful book on primitivism (Asay, 2013), which starts with an historical account of the position from the early days of analytic philosophy. 2 It’s important to note that judgement isn’t the only context in which propositions arise. Russell was keen to emphasise, as his MRTJ developed, that there are other propositional attitudes (understanding, entertaining-for-thesake-of-argument, hoping, wanting etc.). Russell’s point is that all of these attitudes are multiple relations. Propositions, conceived of as mind-independent entities, needn’t exist prior to, or outside of, these cognitive acts. Of course, Othello didn’t have to judge that Desdemona loved Cassio in order to give rise to the propositional-content that Desdemona loves Cassio: he could merely have entertained-it-for-the-sake-of-argument, or understood it in order to assert on the back of that act of understanding, a molecular proposition containing it. To see how the MRTJ is extended to molecular propositions, see chapter 9. 3 This understanding of Russell’s response to the paradoxes is owed to (Landini, 1998; 2007) and to (Stevens, 2003). 4 Once again, my reading of what Russell was hoping to achieve with his logic of substitution is heavily indebted to (Landini, 1998; 2007) and to (Stevens, 2003). 5 When I say that an entity is an incomplete symbol, I follow in a figure of speech often used by Russell. Sets are not incomplete symbols. When I say that they are, I mean that set-talk is peppered with incomplete symbols allowing for a transformational analysis that removes any ontological commitment to sets. So to say that X is an incomplete symbol is really to say that X-talk is peppered with incomplete symbols. I will continue to adopt this figure of speech throughout the rest of this book. 6 Stevens (2005, p. 63) presents an admirable account of the virtues that Russell’s substitutional logic had to sacrifice on the altar of ramification. 7 Thus there are non-semantic paradoxes left untouched by Russell’s simple type theory that seem to be awaiting the ramified type theory. Stevens (2005, chapter 3) gives a very straightforward account of the propositional paradox as it arises within Russell’s substitutional logic.

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8 Throughout I will continue to use phrases such as ‘possible judgements’. At this point, therefore, it is important to make the following disclaimer. Russell was uncomfortable talking about possibilities (see what Pears has to say in the excerpt I quote in chapter 6, §4), but my talk of possible judgements is intended as a mere façon de parle. I could, instead, talk about unjudged propositions, but that, given Russell’s denial of propositional realism, might seem equally incongruous. Rather, the thought I’m aiming for runs as follows: the world is such that certain collections of objects in certain orders (call them ‘ordered manies’) can be truly judged, whereas certain ordered manies can only be falsely judged. When I talk about a possible judgement, I really intend to talk about an ordered many – an ordered collection of object-terms waiting to be judged. A possible judgement is true iff anyone who judges it judges truly. I am really quantifying over vectors, which are ordered plurals. Just as plurals are no extra entity above and beyond their members, so too are vectors an ontologically free lunch. Of course, as I will argue extensively, vectors, or possible judgements, or unjudged propositions (which all amount to the same thing) are not, ultimately, truth bearers. Judgements are truth bearers, not vectors. Nevertheless, there is a sense in which we can talk about true possible judgements/vectors: I call a vector true when it, and the world, are such that if anyone judges that vector, they judge truly. The distinction between true judgements and true vectors echoes the sort of distinction that a Davisonian might make between true utterances and true sentences (since the Davidsonian might think that the truth of a sentence is parasitic upon the truth of associated utterances, or, at least, that truth is a relation between sentences, utterers and times) (Davidson, 1967, p. 319; 1968–9, pp. 146, ft. 14). The judgement that everything φ’s, can only be true if the following vectors/possible-judgements are true in the sense that vectors can be true: , , ,. . . , and . The judgement that everything φ’s is thus of a higher order than the judgement that a φ’s. We will develop this line of thought, and try to build a decent response to the Appendix-B paradox, in chapter 11, §5. 9 Witness Church (1956, pp. 347–348, ft. 577; 1976, pp. 748, ft. 4) 10 Landini seeks to overcome some of the problems raised by this interpretation with his compelling suggestion that first-order quantification in Principia should be read as objectual and higher-order quantification should be read substitutionally. 11 See footnote 5. 12 One paradox that we’ll particularly have to guard against is the paradoxical judgement that ‘this judgement is false’. But if a hierarchy of orders really does fall out of the MRTJ, then this judgement will be automatically excluded, as I hope to explain in chapter 11, §5. 13 In chapters 9 and 11, we’ll explore and concede to the claim that the MRTJ is actually a step towards a certain species of psychologism. But psychologism comes in many flavours and in different degrees. And thus, there’s no contradiction in contending that the MRTJ is both motivated by a type of anti-psychologism – which I argue for here – and also constitutes a step towards a (distinct and non-toxic) form of psychologism – a claim which I develop later. 14 I agree that there was such a change of mind, but I think that it probably had as much to do with the influence of Stout, and Moore, than it had to do with Meinong (see Omar Nasim (2008) and Maria van der Schaar (2013)).

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15 As we shall see in chapter 7, §2.6 and §4, long before 1918, Russell had envisaged a distinction between negative, positive and neutral modes of combination. For any n-adic relation and n entities, according to this envisaged distinction, there will either be a positive fact in which they will be combined positively, or a negative fact in which they will be combined negatively, but there may always be a neutral fact in which the same items are combined neutrally. By 1918, contra Linsky, Russell was no longer worried that the unity of a proposition would entail its truth, since a proposition could just be a neutral-fact, which would be true iff its constituents were elsewhere combined positively, and false iff its constituents were elsewhere combined negatively. In other words, he realised that propositional unity is rather easily achieved, as we argued in chapter 1, §2.1. Rather, as I have argued, Russell’s concern in 1918 with false propositions (i.e. neutral-facts, whose constituents are elsewhere combined negatively) was their ontological unsightliness, and perhaps a fear of the Appendix-B paradox. Linsky isn’t alone in making this mistake about Russell’s position in 1918; MacBride commits the same error (MacBride, 2013, p. 231). 16 Even if, contra Linsky, this motivation had dropped out of the picture by 1918. 17 Landini (2007, p. 44) downplays the role that the problem of false propositions played in motivating the MRTJ, seemingly reducing it to a foil that Russell used to make sense of his theories to a popular audience, while all the while the real motivation for abandoning propositions was the existence of propositional paradoxes. I think that this is unwarranted. The paradoxes clearly played a role in motivating the MRTJ, and it is to Landini’s credit that this is beginning to be more widely recognised, but to discount the other concerns places more weight on unpublished notes than upon the material that Russell chose to make public. The problem of false propositions is severe enough to need a response, and it’s entirely possible that many factors (including but not limited to the paradoxes) were motivating Russell simultaneously. 18 Both of these papers can be found in the McMaster University Russell Archives, where they are individually catalogued. ‘Logic In Which Propositions Are Not Entities’ is dated April-May 1906, and the ‘Paradox of the Liar’ is dated September 1906. These two papers were both published in the fifth volume of Russell’s Collected Papers (Russell, 2014). 19 Soames continues to insist that Russell didn’t truly ‘grasp’ the insight at the heart of his own MRTJ (Soames, 2015, p. 444), or ‘appreciate’ its significance (Soames, 2015, p. 472). He continues to accuse Russell of confusing the quasi-mereological problem of how to stick propositions together with the more profound representation-concern (Soames, 2015, p. xiv). I shall argue, in the next chapter, that by 1910 (at the latest) Russell was acutely aware of the representation-concern. Whether or not it pushed him in the direction of the MRTJ in the first place, it certainly played a central role in the MRTJ’s rapid evolution between 1910 and 1913. 20 One historical account of the rise of the MRTJ can certainly be discounted. Leonard Linsky (1992), with Davidson (2005) in his wake, suggests that Russell adopted the MRTJ because he had no response to Bradley’s problem of unity whatsoever. They then express their surprise that Russell should have adopted such a tactic, because the MRTJ (as a correspondence theory of truth) still relies upon the unity of facts, and the unity of the judgementcomplex. What good is it to get rid of one sort of unity, when in fact, you need to get rid of them all, since your own account of the unity of facts still leaves you with Bradley’s regress? As I hope to have made clear, this account

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is clearly mistaken. It is only the unity of propositions that Russell found difficult to accommodate. In all other respects, his response to Bradley’s regress was satisfactory. He was happy to appeal to relating-relations as the source of such unity, and he was (most of the time) happy to take that as brute. In responding to the truth/falsehood problem, Russell thereupon filled in the only gap in his response to Bradley (see Lebens (2008)).

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The Stoutian Evolution of the MRTJ

In this chapter, I sketch the rapid evolutions that the MRTJ underwent between 1910 and 1913. I argue that all of these evolutions were motivated by Russell’s continuing concern for the representation-concern – a problem that was persistently pushed on Russell by his old philosophy teacher, G. F. Stout.

§1: The 1910 MRTJ The MRTJ, as it appeared in Russell’s Philosophical Essays of 1910, included an epicycle.1 Every judgement has a subject, the person or mind making the judgement. The relation of judgement itself is the relating-relation that relates the subject to its multiple objects; those objects are called the object-terms. One of those object-terms will be a relation, which the subject is judging to be relating the other object-terms, outside of the judgement.2 When Othello judges that Desdemona loves Cassio, the object-terms are Desdemona, love and Cassio. Love is the object-relation. It isn’t relating anything in the judgement itself, but Othello is judging that it relates Desdemona to Cassio. The 1910 epicycle was the stipulation that the object-relation ‘as it enters into the judgement must have a ‘sense’ [i.e., a direction]’ (1910, p. 158). Russell wanted the object-relation to enter the judgement as an object – i.e., not as a relating-relation – but to do so along with a direction, as if a relation’s direction was somehow distinct from the relation itself. Thus Othello’s judgement would receive this analysis (which is best illustrated by my breaking with the convention that I will later adopt of listing the object-relation first among the object-terms):

(1) Judgement (Othello, Desdemona, Love, Cassio) And, had Othello judged that Cassio loved Desdemona:

(2) Judgement (Othello, Desdemona, Love, Cassio)

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In every presentation of the history of the MRTJ that I have seen, this complication is said to be a response to the ‘narrow direction problem’. The narrow direction problem, called so by Griffin (1985), demands an account of the difference between judging that aRb and judging that bRa. Russell’s own words corroborate the standard reading (Russell, 1910, p. 158): Let us take the judgement ‘A loves B’ . . . the judgement is not the same as the judgement ‘B loves A’; thus the relation must not be abstractly before the mind but . . . Thus Russell seems to introduce the direction of the object-relation precisely in order to distinguish A loves B from B loves A. However, this standard reading is surely incomplete. Russell was long committed to the view that relations relate in a direction (see, e.g., Russell, 1903, §94). Accordingly, Dorothy Wrinch (1919) ridiculed the narrow direction problem: it is resolved as soon as we note that the relation of judgement is non-symmetric. This alone distinguishes J(o, L, d, c) from J(o, L, c, d). The direction of J blocks the problem. Are we to believe that Russell, who had pioneered the study of symmetry, asymmetry and non-symmetry, took until 1912 to realise that the narrow direction problem is so easily solved? This isn’t something that Russell would likely have missed. Why did he instead, in 1910, appeal to the more complicated solution illustrated by (1) and (2)? The standard history can’t answer these questions. I suggest that the epicycle in the 1910-MRTJ was, in fact, an attempt to solve the narrow direction problem alongside a more pressing concern: the representation-concern. The question that Russell sought to answer was this: how is the appearance of unity generated among the object-terms so as to distinguish a proposition from a mere list? We’ve seen that when Russell was committed to the existence of propositions, he was troubled by a quasi-mereological problem.3 If propositions have constituents, then you can ask how the constituent parts stick together. We’ve seen the sorts of worries that this problem caused Russell. But we’ve also seen (chapter 1, §2.1) that Scott Soames (King et al., 2014, p. 32) makes a compelling case that the problem of propositional unity, conceived in terms of the quasi-mereological puzzle of sticking things together, shouldn’t really bother us at all. There are plenty of ways to unify a, R, and b, without thereby creating the truth-making fact that a is R-related to b. The real problem, once you’ve accounted for the unity of the proposition, is to explain why such a complex entity has the curious ability to represent things. Or put another way, the real problem is to explain how the constituents of the proposition stick together in such a way as to become representational. We called this the representation-concern.

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Soames made it seems as if Russell was only dimly aware of this issue – that his discussion of it is ‘confused’ (Soames, 2010, p. 32), that he ‘misdiagnoses’ what the problem is really about (Soames, 2015, p. xiv) and that, to the extent that the MRTJ encodes an insight that might help us to resolve the representation-concern – Russell didn’t really ‘grasp’ its full import (Soames, 2015, p. 444), or ‘appreciate’ its full significance (Soames, 2015, p. 472). Jeff King implies that his theory of propositions was the first account of propositions ever to address the concern (King et al., 2014, p. 48). But I claim that (whether or not it partly prompted the initial adoption of the MRTJ) Russell was acutely aware of this problem, that he tried to respond to it, and that the epicycle in the 1910-MRTJ is his first explicit gesture at a response to it. It’s true that Russell got rid of propositions, partly to avoid the quasi-mereological puzzle, but even once he’d got rid of propositions, he was worried about what he continued to call ‘the unity of the proposition’, but now the question isn’t really about sticking a proposition together, because propositions don’t really exist. Now the problem is precisely the one that bothered Soames. The problem is how to account for the curious ability of propositions (now thought of in terms of the ordered array of object-terms in a judgement) to represent, all by themselves. With the direction of the object-relation in the mix, we can explain, or at least begin to explain, in virtue of what judgements are able to represent. On the 1910-MRTJ we can judge that A loves B, and we can judge that B loves A; our theory will be able to distinguish these two judgements. But we’ll never be able to judge the list: Love, A, B (listed in any order) – for, in a list, the relation of love doesn’t have a direction, and, in a judgement, the object-relation has to have a direction. The presence of the relational direction makes the judgement truth-apt; or, representational. Reading the representation-concern into the 1910-MRTJ finally makes sense of Russell’s appeal to the direction of the object-relation, which would otherwise have been an over-reaction to the narrow direction problem. According to Stewart Candlish, the 1910-MRTJ was only trying to solve the narrow direction problem and not the representation-concern. Allegedly, Russell hoped to solve it with the stipulation that the object-relation actually relates in a specific direction. Furthermore, according to Candlish, this places Russell between the horns of a dilemma. On one horn of the dilemma, all judgements will be true. On the other horn, the mind has two mutually exclusive powers: psychokinetic and psychoinertial (Candlish, 2007, p. 67): For the mind . . . is supposed to be able to bring the real things A and B and love, not just mental or linguistic proxies, into the appropriate relation without actually making A love B.

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I think that this misunderstands the 1910-MRTJ. Russell didn’t want the object-relation to relate. He wanted the object-relation to appear as if it were relating. Notice the intentional language that Russell uses, which I embolden and italicise: Thus the relation must not be abstractly before the mind, but must be before it as proceeding from A to B. (Russell, 1910, p. 158) This appearance was supposed to be secured by allowing the object-relation to enter a judgement alongside a direction. The phenomenological language is important here. What makes the object-terms representational is how they appear to us in the act of assertion. They don’t appear as a list. The object-relation appears as if it is relating the other object-terms. This illusion is accomplished because the object-relation occurs in the judgement alongside a direction. Whether this really solves the representation-concern is beside the point. What’s important, is that we’ve isolated the problem that Russell was trying to address. G. F. Stout proves himself to be a more discerning reader of Russell than Candlish; well aware, as he was, that the object-relation is not called upon to relate (Stout, 1910–1911, p. 202). Nevertheless, Stout is concerned that, despite Russell’s best efforts, the object-terms may well collapse into a unity after all: What seems to me decisive of this point is the requirement not only that that [sic] one of the items should be itself a relation but that it should have a ‘sense’ or direction with reference to the other terms. (Stout, 1910–1911, p. 202) Perhaps the debate hangs upon what a relation’s direction is. If the direction of a relation is nothing more than the direction in which a relation happens to be relating, as Stout seems to think, then a relation has no direction unless it happens to be relating something. Perhaps Russell, on the other hand, had hoped to treat the direction of a relation as an ontologically distinct entity that can enter a complex without forcing its relation to relate. Stout reports a correspondence between himself and Russell in which the issue of the ontological status of relational direction isn’t made explicit, but in which Russell at least conceded what he hadn’t yet been willing to concede: that there ‘must never, so I now perceive, be any relation having sense in a complex except the relating-relation of that complex’ (Stout, 1910–1911, p. 203). It is exclusively the role of the relating-relation to order the terms that it relates. Relational direction isn’t some ontological entity in its own right, it is merely a part of the ideology of the relating-relation.

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§2: Stout’s Trilemma Having conceded to Stout that object-relations can’t have a sense (on my reading because he now accepts that relational direction isn’t ontologically distinct, and is part of the ideology of a relating-relation), Russell sketched, in a letter to Stout, a revision to his theory: [J]udging alone may arrange the terms in the order Mind, A, r, B, as opposed to Mind, B, r, A. This has the same effect as if r had a sense in the judgment, and gives all that one wants without being obnoxious to your objections. (Stout, 1910–1911, p. 203) This saves Russell from the narrow direction problem, but it gives renewed vigour to the representation-concern, which now becomes Stout’s over-riding concern. As Stout presents the concern, the phenomenology of judgement takes centre stage: when we judge something, we feel, at the very least, as if we’re related to a unity; if Russell can give no account of what gives rise to this feeling, then how is he able to distinguish between propositions and lists, or mere aggregations of objects; how will he be able to explain the ability of the ordered object-terms, at least in the context of a judgement, to represent? Surely Russell thought that when we judge, we apprehend some sort of unity (apparent or otherwise), but his letter to Stout left it ambiguous as to what this ‘unity’ is. Stout offers two disambiguations: (1) when we judge that A loves B, we apprehend an actual unity: not the fact that A loves B, of course, because our judgement might be false; rather, we apprehend our actual judgement; or (2) we focus upon Russell’s claim that the order imposed by the relation of judgement ‘has the same effect as if [the object-relation] had a sense in the judgment’. The first disambiguation is plainly absurd, as Stout later put it: according to this view, ‘whenever we believe, we must at the same time be aware of the state or process of believing’ (Stout, 1914–1915, p. 343). According to the second option, the order imposed by the relation of judgement is supposed to have exactly the same effect as allowing the direction of the object-relation to enter into the judgement. This amounts to saying that the relation of judgement imposes a sense upon the object-relation. But a relation can only have a sense whilst relating. On this view then, it seems as if, bizarrely, the judgement-relation is causing the object-relation to relate the remaining object-terms, which will, in turn, force all judgements to be true. Stout knows that Russell wouldn’t be happy with either of these horns. There is, instead, a third horn to the dilemma (or, trilemma) which, at this point, Stout leaves unstated. However, it’s clearly the only route left open to Russell, since Stout concedes that Russell isn’t in the business

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of positing psychokinetic and psychoinertial powers. The third horn is to accept that the MRTJ has no response to the representation-concern; we apprehend no apparent unity when we judge. There is no single thing that we judge, when we judge. On Russell’s deficient theory of judgement, propositions are no different to lists, since we have no account as to why propositions, rather than lists, are able to represent. I contend that this was Stout’s real concern.4 A number of concerns are running concurrently here. Of course, at the surface is the demand that there should be some thing, or at least an appearance of a thing, called content. However, the fact that an appearance of a thing would suffice, indicates that what we’re after here, isn’t fundamentally, a single entity to serve as an object of a belief, but that there should be some representation going on. Stout just doesn’t know how Russell can achieve that if belief doesn’t have a singular object.

§3: The 1912-MRTJ In 1912, Russell published a revised MRTJ (Russell, 1912). Here Russell imposes three adequacy constraints upon any theory of truth/judgement: 1. It must explain falsehood as well as truth. 2. Falsehood must be a property of beliefs (as must truth) – if no one believed anything, there would be no error! 3. Ultimately (unless a judgement happens to be about a mind), the mind-external world must determine whether someone’s belief is true or false. The second criterion demonstrates that Stout’s representation-concern still bothered Russell, as it had in the 1910-MRTJ, even before Stout raised it.5 An ordered series of objects is just a list; neither true, nor false. The 1912-MRTJ states that only a judgement, and not its disparate objects, can take on a truth-value. Russell’s 1912 response to Stout’s concern relied upon the notion that the act of judgement is somehow responsible for imposing the appearance of unity upon the ordered object-terms, giving rise to truth-aptness.6 This is what makes it the relation of judgement rather than the relation of listing disparate objects! You might think that an appearance of unity is only sufficient to generate the appearance of truth-aptness.7 But truth-aptness has to do with representation. The appearance of unity is, in and of itself, a mental representation before the mind of the person to whom the apparent unity appears. Using real world objects, and imposing the appearance of unity upon them, is to create a mental picture using real world objects. Russell accepts none of the horns of Stout’s trilemma: he’s trying to find a fourth way out. He does contend that the judgement-relation imposes an apparent unity upon its object-terms, but this doesn’t entail

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that it imposes a direction upon its object-relation, nor that it forces the object-relation to relate; it merely entails that the judgement-relation imposes the appearance of a direction upon the object-relation, and the appearance of relating. And this appearance, in turn, gives rise to the truth-aptness of the judgement. In the context of being judged,8 the object-terms (which include the object-relation) adopt (or, more accurately, have imposed upon them) a new found appearance: the appearance of unity, and this appearance makes the judgement itself, truth-apt. In this way, the 1912-MRTJ sought to solve Stout’s concern. Unfortunately, Stout’s 1914–1915 review of Russell’s theory doesn’t seem to recognise what Russell was attempting in 1912; that he was trying to find a fourth way out of Stout’s trilemma. First, I’ll outline how Stout responded to the 1912-MRTJ; then I’ll outline how he probably should have responded. Stout suggests three more criteria, in addition to Russell’s three criteria, for a theory of judgement/truth. First, in a correspondence theory of truth, the truth-maker may well be outside of the mind, but the proposition must be before the mind. Otherwise, ‘it would follow that truth consists in a correspondence between something which the believing mind does not think of at all and something else which it does not think of at all’ (Stout, 1914–1915, p. 335). Second, noting the similarity to Russell’s theory, Stout accepts that the object of a judgement needs to share its nature with the object that would make it true, if it’s true: When I believe ‘that A loves B,’ if in actual fact it is P instead of A that loves, or Q instead of B that is loved, or if the relation is any other instead of loving, or if it is B that loves A instead of A that loves B, my belief is false. (Stout, 1914–1915, p. 336) But he goes on to say that, despite the need for similarity between the object of a judgement and the constituents of its truth-maker, it’s also important that we don’t identify the object of a judgement with its truth-maker (he suggests that they have a different sort of being; either way, they need to be distinct). Otherwise, we’d struggle to make sense of falsehood – cases of belief where there are no truth-makers. Judgements need to be such that they could possibly have a truth-maker, but, nevertheless, some of them won’t have truth-makers. This is Stout’s second criterion. Third, Stout contends that the mind must intend to assert a correspondence between belief and the world. Stout’s claim is that the 1912-MRTJ fails to live up to his first and third criteria. To illustrate his point, Stout rehearses his trilemma of 1910–1911. On the first horn, we do apprehend a unity: bizarrely, we apprehend our

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actual judgement. On the second horn, the judgement-relation causes the object-relation to relate. This creates a unity for us to apprehend, but forces all judgements to be true. Stout, more charitable than Candlish, doesn’t imagine Russell embracing either of the first two horns of the trilemma. However, if Russell adopted neither horn, his theory would have to adopt the third horn, which Stout now makes explicit: no content appears before the mind in an act of judgement. When a person judges, no single thing appears before her mind. Thus, the 1912-MRTJ, on Stout’s reading of it, fails to meet Stout’s first criterion: ‘the correspondence [that constitutes truth will turn out to be] . . . between something which is not thought of and something else which is not thought of’ (Stout, 1914–1915, p. 344). Given the MRTJ’s ‘failure’ to meet the first criterion, the third criterion also cannot be met (Stout, 1914–1915, p. 345): The mind cannot mean or intend something to correspond with something else when one of them is not thought of by it at all. Still less can it do so when it thinks of neither of them. In short: as far as Stout is concerned, nothing that could be called representation is going on in Russell’s MRTJ – the object-terms of a judgement are just a list. Unfortunately, Stout doesn’t engage with the real project of the 1912MRTJ, which was to propose that the judgement-relation imposes the appearance of unity upon its objects without imposing anything more than the appearance of a direction upon its object-relation. This isn’t to say that Russell had done enough. In response to Stout’s representation-concern, one might think it unsatisfactory to be told that the act/relation of judgement imposes an apparent unity upon its objects, giving rise to truth-aptness. We want to know how. This is, perhaps, the critique that Stout should have levelled in his 1914–1915 review. Russell’s theory simply leaves too much unexplained.

§4: The 1913-MRTJ In his 1913 manuscript on the Theory of Knowledge, Russell realised that his 1912-MRTJ had been lacking. What had been wrong? Griffin (1985, pp. 220–1) makes the following suggestion: Russell’s reason for abandoning his 1912 version of the theory was that relying on the belief relation to order the object-terms of the judgment in the correct way implied that the act of judging itself actually arranged the terms in the way they were judged to be arranged . . . If S judged that a precedes b then either a does actually precede b, in which case the judgement contributed nothing to the order, or else a

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does not precede b, in which case no amount of judging will effect the required order. This explanation is surely mistaken. As David Pears (1967, p. 216) put it (talking directly about the 1912-MRTJ): the judgement-relation is conceived by Russell as arranging actual worldly items: But the arranging is mental [even though the items aren’t]. It is not a matter of his pushing things around outside his mind. If Russell had not been so adverse from possibilities, he could have said that what the person who makes the judgement does is to construct a possibility and judge that it is realised. We might use a remark of Wittgenstein [(1961, proposition 4.013)] . . . : ‘In a proposition a situation is, as it were, constructed by way of experiment.’ This does not mean the situation is set up in reality. Similarly, Russell’s theory does not mean that the arranging of things is actual.9 Russell and Stout were opposed to representational theories of the mind (see Nasim (2008) and van der Schaar (2013)). Neither of them wanted to acknowledge entities merely existing in the mind that the mind would then use to represent mind-external entities or states. And yet we do represent the world when we make assertions. One could explain this by appealing to some sort of inherently representational mind-external objects for the mind to latch on to. The MRTJ, on the other hand, hoped to explain how we represent the world by using the very things we want to think about, to represent themselves, so to speak, as we ‘construct possibilities’ out of them. However, as Griffin understands him, Russell was concerned that he hadn’t merely constructed possibilities, so much as constructed facts, and forced his judgements always to be true. This is the quote that Griffin’s reading seizes upon (Russell, 1913, p. 116; emphasis added): I held formerly that the objects alone sufficed, and that the ‘sense’ of the relation of understanding [or judgement] would put them in the right order; this, however, no longer seems to me to be the case. Suppose we wish to understand ‘A and B are similar’. It is essential that our thought should, as is said, ‘unite’ or ‘synthesize’ the two terms and the relation; but we cannot actually ‘unite’ them, since either A and B are similar, in which case they are already united, or they are dissimilar, in which case no amount of thinking can force them to become united. The process of ‘uniting’ which we can effect in thought is . . . [Russell then goes on to state his 1913-MRTJ which I explore in the next chapter.]10 Only a misreading of this text sees it as saying that his 1912-MRTJ had united the object-terms and forced all judgements to be true. His real

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and explicit concern is this (stated in the words that I emboldened): the 1912-MRTJ had merely put the object-terms in the right order; but we need more than mere order. This is just Stout’s representation-concern: an ordered-many is not an object of belief; it is not truth-apt; it is not inherently representational. The belief relation needs to do more: it can’t simply order its terms; it needs to unite them (without actually uniting them!),11 which is Russell’s way of saying that it needs to make them representational without collapsing them into one entity (perhaps for fear of the Appendix-B paradox), or into a truth-making fact. Accordingly, Russell’s concern wasn’t that the 1912-MRTJ had actually united object-‘complexes’ and thereby made them true: his concern was that he hadn’t given them enough unity, and that he had thereby failed to make them truth-apt. In other words, his worry was that merely putting the object-terms in the right order doesn’t explain how the appearance of a non-actual unity is imposed upon them. Now we’re in a position to amend the standard history of the MRTJ. The standard history makes three claims: 1. The epicycle of the 1910-MRTJ was exclusively designed to solve the narrow direction problem. 2. Stout himself played a role in convincing Russell to remove this peculiarity from the MRTJ. 3. Russell’s rejection of the 1912-MRTJ was down to his fear that it had unwittingly made all judgements true (that this is the standard view can be seen from the quote of Nicholas Griffin, from his widely cited paper on the MRTJ, with which this section began).12 I would respond to each claim in turn: 1. The epicycle of the 1910-MRTJ, although it was supposed to respond to the narrow direction problem, was primarily motivated by Stout’s representation-concern (independently arrived at by Russell, before it was even raised by Stout in print). 2. I agree with the second claim. This is the Stoutian influence that the standard history already acknowledges, even if the content of the discussion, which may have had a sub-text concerning the ontological status of relational direction, has been too quickly glossed over. Griffin (1985, p. 220) and Candlish (2007, pp. 67–9), for example, detail how Stout forced Russell to drop the 1910-epicycle. 3. I contend that Russell had no such fear. Rather, Russell was still bothered by Stout’s concern and was worried that the 1912-MRTJ didn’t answer it discursively enough. It’s not enough to say that the judgement-relation imposes the appearance of unity upon its objects, giving rise to the truth-aptness of a judgement; the theory also has to explain how. The 1913-MRTJ seeks to address this lacuna, as we shall see in the next chapter.

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The standard history neglects to note that the entire evolution of the MRTJ – between 1910 and 1913 – was decidedly Stoutian. From 1913 onwards, I accept that conversations with Wittgenstein, and Wittgenstein’s letters and writings, weighed more heavily on Russell than any other consideration,13 and that this burden is (at least partially) what led Russell ultimately to despair of the theory – although we’ll see that even Wittgenstein’s criticisms were not decisive for Russell. However, what hasn’t been sufficiently noted before now is that Stout’s concern was the engine that (sometimes independently of Stout himself) powered the rapid evolution of the theory before the beginning of its long Wittgensteinian demise. Stout’s concern about representation deserves a response. Perhaps we should return to Russell’s 1912 response to this problem, which we had earlier dismissed as somewhat mysterious. The 1912MRTJ argued that truth and falsehood only really emerge in the context of a propositional attitude. The seeds of this insight were already present in 1910: ‘[W]e feel that there could be no falsehood if there were no minds to make mistakes’ (Russell, 1910, p. 152), which was built upon in 1912: [T]ruth and falsehood are properties of beliefs and statements: hence a world of mere matter, since it would contain no beliefs or statements, would also contain no truth or falsehood. (Russell, 1912, p. 70) As Mark Sainsbury (1996) reconstructs the MRTJ: the mind uses a universal predicatively upon the other object-terms of the judgement – we’ll revisit this reconstruction of the MRTJ in chapter 8. Unfortunately, and unlike Sainsbury, Russell never seemed able to provide a coherent and/or discursive account of what it is that the mind must do to an ordered-many in order to make a truth-apt judgement. However, following Sainsbury, the answer probably lies in the vicinity of a theory of predication. We predicate the object-relation of the other ordered object-terms. It’s instructive to note how modern theories of propositions, such as King’s and Soames’, also respond to the representation-concern by making propositions, in some sense or other, dependent upon cognitive activity or linguistic practice (as we saw in the chapter 1). The act of predication certainly seems less mysterious than the magical inherent representational abilities of propositions, sets or ordered-manys. King and Soames are, therefore, adopting a Russellian strategy, in the face of Stout’s concern.14 What we can conclude is that (1), one way or another, Stout’s representation-concern merits a response from any theory of propositions and that (2) the way in which the mind is central to the generation of meaning, on the MRTJ, is surely going to be part of our response. We’ll return to this issue in part III. For now, we have to move on to the famous concerns that Wittgenstein raised with the MRTJ.

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Notes 1 He had proposed the theory – or a variant of it – in Russell (1906), but without decisively adopting it. 1910 was the year of its official adoption. 2 Russell sometimes called this the ‘subordinate relation.’ Following Griffin (1985), I call it the object-relation. 3 For why I call it quasi-merelogical, see chapter 1, footnote 5. 4 Maria van der Schaar would urge us to recognise a number of other concerns that Stout raises, such as the narrow direction problem, and what we’ll later call the significance constraint (2013, pp. 103–5). These other concerns were surely present in Stout’s critique, but they’re not as distinctive, since they were taken up later, by Wittgenstein. Unfortunately, she seems to miss the representation-concern altogether, in what is otherwise a very important book. 5 This second criterion is why, even Soames (2015, p. 440) accepts that the representation-concern was now, if only dimly, playing a role in Russell’s thinking. 6 My textual evidence for this claim about Russell’s 1912 theory is his insistence that truth and falsehood only emerge in the context of a judgement (Russell, 1912, p. 70), and that the judgement-relation was now supposed to do the work that had previously been delegated to the object-relation appearing ‘as if’ it had a direction. 7 I’m grateful to an anonymous reviewer for raising this concern. 8 We shall see in the next chapter that by 1913 Russell was explicit that understanding, just like enternatining-for-the-sake-of-argument, was itself a propositional-attitude, and could thus do the same work in creating truthconditions, and imposing apparent unity, as could the relation of judging. 9 I’m grateful to an anonymous referee for putting the following point to me: Pears could have said that Russell’s theory was actually close not just to Wittgenstein’s picture theory, but also to Stout’s own theory of judgement. On Stout’s binary relation theory of judgement, the object of the belief is a possibility, made true by correspondence to an actual fact (Stout, 1910–1911). Russell addresses Stout’s theory of judgement in Russell (1913, p. 152). 10 I have emboldened some text for emphasis. 11 An anonymous reviewer wrote, quoting my words, ‘“it needs to unite them (without actually uniting them!)”, This does not come across as a plausible, or even especially coherent way of describing what Russell is doing.’ In my defence, this implausible way of wording matters is merely a direct echo of Russell’s own words (from the excerpt just quoted): ‘It is essential . . .[to] “unite” or “synthesize” the two terms and the relation; but we cannot actually “unite” them’. Uniting without actually uniting. I try to explain this notion in the continuation of this sentence. 12 Or, it is sometimes contended that the 1913-MRTJ was a reaction to Wittgenstein’s significance constraint (Eames, 1989), which I introduce in the following chapter. 13 This influence continued for a long time after the conversations had ceased. In 1918, Russell is still crediting Wittgenstein with shaping his views on these matters even though they had, at that point, lost contact with one another. I should also note that Russell’s conversations with Wittgenstein began earlier than 1913, but – as we shall see in the following chapter – came to a head in that year. 14 Indeed, Soames (2015, pp. 451–464) acknowledges that despite rejecting the MRTJ, his own theory of propositions was certainly inspired by it.

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The Demise of the MRTJ

On May 7, 1913, Russell started working on his Theory of Knowledge manuscript. He worked at an astounding rate. By the 6th of June, he had written 16 chapters constituting two parts of what was supposed to be a three-part work. However, the project was abandoned in June – a month after he had started. During this period, Russell saw Wittgenstein on a number of occasions. Their discussions eventually lead Russell’s work to falter. On the 19th of June, Russell reported the following to his lover, Ottoline Morrell: All that has gone wrong with me lately comes from Wittgenstein’s attack on my work – I have only just realized this. It was very difficult to be honest about it, as it makes a large part of the book I meant to write impossible for years to come probably. (Eames and Blackwell, 1984, pp. xix–xx) This chapter asks what was the criticism that left Russell so vexed. Did it lead Russell to abandon the MRTJ, and if not, why was the theory eventually rejected by its first proponent? Perhaps it won’t be possible to arrive at any certainty about some of the key historical facts. Perhaps we’ll be left only with a number of competing candidates vying for the role of Wittgenstein’s criticism. In order to defend the MRTJ, we’ll eventually have to respond to all of these candidate concerns, whether or not they truly originated with Wittgenstein. I’ll then conclude this chapter with a brief exploration of why generations of thinkers since Russell have thought the MRTJ to be unworthy of resurrecting.

§1: The Spring of 1913 §1.1: The 14th of May 1913 On the 14th of May, Russell told Wittgenstein that he was working on a major book project which he hoped would supply firm foundations for his earlier work in logic. He wrote to Ottoline, telling her that

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Wittgenstein had been ‘shocked to hear I am writing on theory of knowledge – he thinks it will be like the shilling book, which he hates’ (Eames and Blackwell, 1984, p. xix). Wittgenstein had thoroughly disapproved of Russell’s popular The Problems of Philosophy, with its 1912-MRTJ: he had called it ‘a shilling shocker’. Wittgenstein evidently held out little hope that Russell’s next philosophical work would be any improvement. Nevertheless, as Eames and Blackwell (1984) note: the tone of Russell’s letter ‘suggests that Russell was able to bear up very well under his friend’s hatred of The Problems of Philosophy and was in no way deterred from pursuing theory of knowledge.’ §1.2: The 20th of May 1913 On the 20th of May, Wittgenstein presented what Russell described to Ottoline as a ‘refutation of the theory of judgement which I used to hold.’ He goes on to note that the refutation is ‘right’ but that ‘the correction required is not very serious’ (Carey, 2007, p. 43). The conversation of the twentieth is shrouded in mystery. What was the criticism and what was the ‘not very serious’ correction? There are various interpretations as to what was said. In order to understand them, we need to know what was new to the MRTJ as we find it in the Theory of Knowledge. In 1913, as we mentioned in the previous chapter, Russell was still bothered by Stout’s representation-concern. He recognised that simply arranging his object-terms in the right order wouldn’t enable him to distinguish between a proposition and a list. Instead, we have to find a way to ‘unite’ or ‘synthesise’ the object-terms, without actually uniting them, ‘since either A and B are similar, in which case they are already united, or they are dissimilar, in which case no amount of thinking can force them to become united’ (Russell, 1913, p. 116). In the previous chapter, we didn’t get around to describing how Russell now saw fit to solve the problem. In short, his solution was to add new constituents to judgement-complexes: logical forms. Complexes exhibit what could be called a logical form. We can distinguish, for instance, a monadic fact (a fact in which a single entity instantiates a property) from a dyadic fact (a fact in which two entities stand related) – the two complexes would have a different logical form. A logical form can be represented by a string of variables. The logical form of dyadic facts could, for example, be represented by the symbol ‘ξ(x,y)’. Russell’s 1913 innovation was this: Othello’s judgement now has another constituent: J(o, L, d, c, ξ(x,y)). The unity we’re looking for is supposed to be generated by the mind’s judging that the object-terms fit into the template of a logical form. Now we can return to the 20th of May 1913. According to Griffin (1985), Wittgenstein’s criticism, on the 20th of May, was the ‘wide direction problem’. The narrow direction problem demands that the theory

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of judgement distinguish the proposition that R(a,b), from the proposition that R(b,a). The wide direction problem demands to know why we can’t judge nonsense. If judgement is just a multiple relation between a mind and a string of disconnected entities, then why can’t we judge that Desdemona Cassios love? What ensures that the object-relation will always occur in the right slot? I think it deceptive to follow Griffin in calling this the wide direction problem. The name is owed to the fact that the direction of the judgement is more radically wrong when you judge that Desdemona Cassios love than when you judge that Cassio loves Desdemona, having meant to judge that Desdemona loves Cassio. But there are a number of reasons to resist this way of looking at the problem. First of all, it has less to do with direction than the name implies. Even if we can rely on the judgement-relation to order its terms appropriately, we still have to ask: what guarantees that each judgement will have an object-relation? Why can’t I judge that Japan celery, by standing in the multiple relation of judgement to Japan and celery? The issue wouldn’t be that I had ordered the terms inappropriately. The issue is that I don’t have the right sort of collection of terms to transform into a judgement in the first place. Second, as we shall see, there are a variety of different sorts of nonsense. The MRTJ allowing each species of nonsense to be asserted constitutes a distinct problem with the theory, but they all get banded together in the literature, under the title, ‘the wide direction problem.’ So without here getting into a debate about what to call Wittgenstein’s concern (or concerns), we can present Griffin’s view as follows. Wittgenstein demands, from a theory of judgement, that it disallows the possibility of judging (any sort of) nonsense; I shouldn’t be able to judge that Japan celery. The MRTJ doesn’t meet this constraint, which I shall call the significance constraint. This is just a version of the quantity problem that we witnessed in chapter 1. The MRTJ is allowing propositions/ judgements that shouldn’t be allowed. According to Griffin, this was the concern that Wittgenstein raised on the 20th of May. In Griffin’s view, Russell had already, and independently, introduced logical forms as constituents of the judgement-complex, prior to the 20th of May. When Russell heard Wittgenstein’s concern, he hoped that the presence of logical forms in the judgement-complex could be used to respond: Othello cannot substitute Desdemona, Love and Cassio for variables in the form so as to yield the judgement that Love Desdemonas Cassio, or that Cassio Desdemonas Love, for these substitutions are ruled out by restrictions upon the gaps of the logical form, indicated by the different styles of variables used in its notation. He also won’t be able to judge that Japan celery because there doesn’t exist a logical form that would allow for such a pattern of substitution. The presence of the logical form in the judgement-complex, it is hoped, will help the MRTJ

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to meet the significance constraint (what exactly a logical from is, and whether they can really help the MRTJ, I will come back to). According to Griffin, and consonant with Russell’s report to Ottoline, Wittgenstein’s attack, on the 20th of May, was really only relevant to the version of the theory that Russell ‘used to hold.’ This explains why Russell wasn’t so moved. He thought it attacked an old theory with a criticism he had already, somewhat unwittingly, blocked. But what were the not very serious amendments that Russell, in his letter to Ottoline, alluded to? Griffin doesn’t have a convincing reply to this important question. Elizabeth Eames argues that Russell didn’t introduce logical forms into his analysis of judgement until Wittgenstein raised his concern on the 20th of May. She thinks Russell’s logical forms exemplify his tendency to respond to Wittgenstein with ever more complicated analyses of judging and relations (Eames, 1989, p. 146). There is some good evidence for her case: along with the manuscripts of 1913, there were various notes; among these notes is a diagram of judgement-complexes that omits logical forms. Eames and Blackwell (1984) think that these sketches depict Russell’s 1913 theory of judgement at a stage prior to the introduction of logical form. This is supposed to undermine Griffin’s contention that logical forms were a part of Russell’s theory of judgement prior to Wittgenstein’s critique. Griffin isn’t impressed: There is no mention in Theory of Knowledge of logical form until parts of the manuscript written after Wittgenstein’s 20 May criticisms. This might suggest, that the doctrine of logical form was added to the theory in response to Wittgenstein. But such a major addition could hardly be described as a ‘not very serious’ correction. Moreover, we already see Russell moving logical forms toward the centre of his account of logic in an unpublished manuscript, ‘What is logic?’ . . . written the previous year.1 (Griffin, 1985, pp. 228–9) Rosalind Carey (2007) thinks that she can forge a compromise between Griffin and Eames and thereby complete the story of the 20th of May. Perhaps, until Wittgenstein’s criticisms, Russell thought that we could explain the sort of pseudo-unity that judgement imposes on its objects (that is to say, he thought he could solve Stout’s representation-concern) by stipulating that acquaintance with the relevant sort of logical form is a prerequisite to understanding, and that understanding is a prerequisite to judgement. This doesn’t mean that he had to admit logical forms into the actual judgement/understanding complex. Othello’s judgement would still relate him to Love, Desdemona and Cassio, and to nothing else; it’s just that Othello would have had to have already been acquainted with the logical

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form of a dyadic complex in order to understand the content of his own judgement – and one cannot judge without first of all understanding (on the Multiple Relation Theory of Judgement, understanding is also a multiple relation between a mind and what the propositional realist would call the constituents of the proposition). Thus Carey writes, I believe that Russell has already begun to rely on a theory of forms in order to address the flaws in his 1912 doctrine, and that his meeting with Wittgenstein on the 20th persuades him he has not gone far enough and he needs to make form an explicit component of the proposition and not merely an additional doctrine. (Carey, 2007, p. 64) Carey’s reading of the 20th of May retains the best of all the views canvassed thus far: logical forms weren’t an entirely new addition to the theory, ‘for even Russell could not integrate a new idea that thoroughly into the rest of his system in a matter of days’ (Carey, 2007, p. 45); rather, they were appealed to prior to Wittgenstein’s criticism on the 20th of May. Acquaintance with logical forms was appealed to as a prerequisite of understanding (and therefore judgement). Russell’s diagram, in his notes, didn’t contain form as a constituent of judgements because he didn’t yet think that they had to be constituents. After Wittgenstein raises his concern, Russell realises that his forms need to do even more work, so he gives them a more central role in the analysis of judgement – they move from being objects of acquaintance that make judgement possible, to being constituents of judgements themselves – this was the ‘not very serious’ correction. Once logical forms are constituents of a judgement, they will, it was hoped, provide a template that rules out the ascent of nonsense. §1.3: The 26th of May 1913: The Puzzle After what appears to be a relatively uneventful meeting with Wittgenstein on the 23rd of May, the two men met again on the twenty-sixth. Russell had just finished the chapter on understanding (the chapter which contains the new and ‘improved’ MRTJ). Russell reported this tense meeting to Ottoline: We were both cross from the heat. I showed him a crucial part of what I had been writing. He said it was all wrong, not realizing the difficulties – that he had tried my view and knew it wouldn’t work. I couldn’t understand his objection – in fact he was very inarticulate – but I feel in my bones that he must be right, and that he has seen something that I have missed. (Monk, 1997, p. 297)

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What was Wittgenstein’s criticism on the twenty-sixth? The following letter, which Russell received from Wittgenstein in early June, was almost certainly referring back to the 26th of May. Wittgenstein was attempting to make his concern more articulate: I can now express my objection to your theory of judgment exactly: I believe it is obvious that, from the prop[osition] ‘A judges that (say) a is in Rel[ation] R to b’, if correctly analysed, the prop[osition] ‘aRb.∨.~aRb’ must follow without the use of any other premiss. This condition is not fulfilled by your theory. (Wittgenstein, 2012, p. Letter 14) If I can judge that R(a,b) – that is, if ‘R(a,b)’ is a judgeable content – then it should follow that (R(a,b)) ∨ ¬(R(a,b)). This just seems to be the demand that judgeable content should be meaningful; that we shouldn’t be able to judge nonsense. It looks like Wittgenstein places a significance constraint upon a theory of judgement – a theory of judgement has to rule out the possibility of judging nonsense – and that he accuses the MRTJ of failing to meet that constraint.2 But this was, apparently, the problem that had failed to move Russell on the 20th of May. What had changed between the twentieth and the twenty-sixth? We have stumbled upon an historical puzzle.

§2: Solving the Puzzle On the 20th of May 1913, Russell hardly seemed bothered by Wittgenstein and his significance constraint (his demand that nonsense should be unjudgeable). On the 26th of May, Wittgenstein, as recorded in his letter, seems to rehearse the very same criticism, but this time it leaves Russell contemplating suicide (as he reported to Ottoline, see Monk (1997, p. 300)). How can we explain this puzzling sequence of events? §2.1: The Category Constraint As we’ve understood Wittgenstein thus far, he was placing a constraint down upon any theory of judgement. Judgements have to be meaningful. Perhaps the criticism of the twenty-sixth was deeper than the very general significance constraint (or wide direction problem) of the twentieth. The significance constraint troubles the MRTJ for two reasons: (1) what will guarantee that the object-relation will occur in the right place (so as to rule out the judgement that Cassio Desdemonas Love) and (2) what will guarantee that there will be an object-relation at all (so as to rule out the judgement that Japan celery)? Pears (1967) and Griffin (1985) argue that Wittgenstein’s criticism of the twenty-sixth piles more into the notion of

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significance: even if we guarantee that the judgement-complex always has a relation/property among its objects, and even if we guarantee that that relation will always feature in the right position, there will still be ill-formed propositions arising from the MRTJ. The MRTJ is built upon termism. Properties and relations are able to appear merely as terms of other properties and relations. In a judgement, the object-relation isn’t doing any relating – it’s merely an object; it’s somehow dormant: The difficulty about this is that, if it is dormant, it might quite well be the wrong type of relation . . . for instance, it might be the relation the-square-root-of, which could hardly relate the knife and the fork. There is nothing in the pattern of analysis suggested by Russell to prevent such a mésalliance. (Pears, 1967, p. 217) Thus, even if the object-relation were fixed in place, the MRTJ would still allow the nonsensical judgment that the knife is the square root of the fork. A satisfactory analysis of judgement, so the concern is said to run, would eliminate the possibility of such ill-formed judgements. Thus, Wittgenstein’s adequacy constraint on a satisfactory theory of judgement is supposed to be broader than the significance constraint narrowly conceived, in terms of (1) and (2). For not only does Wittgenstein require that the object-relation is fixed in place but ‘it requires also the exclusion of category mistakes’ (Griffin, 1985, p. 240). As far as Wittgenstein was concerned, a category mistake was just another form of nonsense that shouldn’t be judgeable.3 On this reading of the history, on the 26th of May, Wittgenstein adds a category constraint to his previous, more general, significance constraint; leaving Russell distraught. §2.2: Type Circularity and Regress Griffin argues that Wittgenstein’s attack of the twenty-sixth was broader and deeper than the initial significance constraint combined with the category constraint (an observation he attributes to Stephen Sommerville). More accurately, he contends that significance itself was shown, by Wittgenstein on the twenty-sixth, to be a more complicated matter: ‘for [the 1913-MRTJ] undermines some of the central doctrine of Principia’: namely, the theory of types (Griffin, 1985, p. 240). And type theory is supposed to govern significance. According to the 1913-MRTJ, the judgement that R(a,b) will receive the following analysis (where α is the logical form of a dyadic relational complex): J (s, R, a, b, α). Is this enough to ensure that R(a,b) is significant? ‘The answer’, Griffin argues, alluding to the words of Wittgenstein’s

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letter, ‘is, not without premisses’ (Griffin, 1985, p. 242). In order to ensure that R(a,b) will be significant, (i) We need to stipulate that a and b are individuals. (ii) We need to stipulate that R is a relation, and that it’s a relation of the right logical type. (iii) We need to stipulate that α is a form of the right logical type and is a form of a dyadic complex. In order to be sure about stipulations (i)–(iii), we would have to have judged (truly) that a and b were individuals; that R was a relation, and that α was a form; thus, in order to make a judgement, we would have had to have made a whole host of judgements already. If this were to be the case for every judgement, then we’re standing on the precipice of a clearly infinite regress (the sort of regress that Moore levelled against Bradley, see chapter 2, §2.1). Furthermore: the sorts of judgements that we’ll have to make will be of ‘an extremely problematic character’ (Griffin, 1985, p. 242). To judge that two entities are particulars, and to judge that an entity is a universal (and, what’s more, a universal of a specific logical type), is, Griffin argues, to make judgements of a relatively high order. But Russell made it quite clear in Principia (Russell and Whitehead, 1910–13, pp. 44–6), that higher order judgements are to be defined cumulatively in terms of lower order judgements. ‘Thus we cannot presuppose second-order judgements in order to analyse elementary judgements’ (Griffin, 1985, p. 242). Sommerville and Griffin have merely put their finger on yet another dimension of meaningfulness: initially the significance constraint asks the MRTJ how it can guarantee that (1) its object-relation will occur in the right place, that (2) its object-relation will actually be a relation – the category constraint adds to this – and asks (3) how can the MRTJ guarantee that the object-relation will be the sort of relation that can appropriately be said to relate the other object-terms. Sommerville and Griffin merely add to this a fourth question – (4) in Principia, type constraints play a role in demarcating the sense-nonsense distinction, but how can the MRTJ guarantee that its judgements will abide by the type constraints of Principia (without appeal to an infinite regress of previous judgements, judgements which, adding insult to injury, would be of a higher than elementary order and thus rob the MRTJ of its claim to be the foundation of the hierarchy of propositional orders)? Sommerville explains: Several commentators have noted already that this [i.e., Wittgenstein’s significance constraint] amounts to the condition that, whatever A judges, it be a significant proposition (either true or false). What has not been shown is that the objection that a correct analysis make

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it impossible to judge type nonsense and that ‘aRb.∨.~aRb’ follow, without further premisses, is one and the same criticism formulated in two ways. (Sommerville, 1981, p. 186) Griffin and Sommerville’s influential account of Wittgenstein’s concern has come under attack in recent years, most notably by Graham Stevens (2003; 2004). Stevens points out that Griffin and Sommerville misconstrue the relationship between the MRTJ and the ramified theory of types. As we explored in chapter 5, the MRTJ is only supposed to ground the order part of the hierarchy, and not the type part. To judge that some entity e is of logical type n isn’t necessarily to make a judgement of a particularly high order, or an order higher than n. So it’s not clear that stipulations (i)–(iii) require asserting judgements of a high order in order to make judgements of a lower order. As Stevens puts it (2003, p. 23): [T]he type part of the ramified hierarchy has no significant connection with the multiple-relation theory of judgement (which was shown to be responsible for the order part of the hierarchy). The kinds of type distinctions that Wittgenstein suggests are called for in order to prohibit nonsensical pseudo-judgements such as Othello’s belief that Love desdemonas Cassio, do not require the multiple-relation theory for their generation. If Griffin and Sommerville are wrong about type circularity infecting the MRTJ, they might still be right that a regress beckons. How can we ever judge anything if we always have to assert three stipulations first? But the problem no longer seems so devastating, especially if you’re willing to bite an admittedly unsightly bullet and accept that stipulation is somehow different to judgement.4 Stevens himself reverts to the idea that Wittgenstein’s criticism is nothing more than the demand that the MRTJ can meet the significance constraint. If that’s the case, then our puzzle is still in force. §2.3: The No Constraints Constraint James Connelly (2011–12; 2014; 2015) has developed a reading of Wittgenstein’s concern that salvages something from the apparent wreckage of Griffin and Sommerville: On my reconstruction, we should instead see the objection itself as concerning, not an incompatibility between the multiple relation theory and the theory of types (as supposed by Griffin and Sommerville), but rather an incompatibility between Russell’s deployment of a

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As Connelly conceives of things, it is Russell (and not Wittgenstein) who is imposing an external side-constraint upon the MRTJ – a significance constraint. To think that significance could be that sort of external worry for a theory of judgement to meet via stipulation is what really bothers Wittgenstein: Wittgenstein’s point in the June letter is thus that Russell’s theory cannot account for the fact that aRb .v. ∼aRb follows logically from the judgement that aRb, and so that aRb is significant, without the deployment of an additional premise i.e., the significance constraint. (Connelly, 2014) Inserting the logical form into the judgement itself doesn’t help to block the narrow or wide direction problems without further premises. How do you know which slot of the form you’re supposed to be plugging each object-term into? The judgement that Toronto is to the north of Buffalo, and the judgement that Buffalo is to the north of Toronto will have the same object-terms and the same form. Furthermore, nothing stops you from trying to plug the wrong sort of thing into the variables of the form. Connelly explains (2014): Given the unrestricted character of the variables occurring within the logical form . . . the form itself does not in any way restrict the types of the judgement’s constituents, and thus the incorporation of form, taken on its own, will fail to block the wide version of the direction problem as well. If the variables are unrestricted, why can we not plug a substantive like ‘penholder’ into the position where a verb indicating a relating-relation should be? In other words, each version of the direction problem will linger even after the incorporation of logical form, and thus together might seem to indicate the need to undertake some supplemental analysis, or incorporate some supplemental significance constraint, in order to ensure both the proper ordering of, and relevant type restrictions upon, a judgement’s constituents. These are the troubling extra premises that Wittgenstein alludes to in his letter. According to Wittgenstein, however, the inference from aRb to aRb .v. ∼aRb should not require any supplemental premises, and thus cannot require any such significance constraint on judgements. Assuming that aRb is a judgement with sense (that is, that ‘a’ and ‘b’ do in fact denote

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individuals and that ‘R’ in fact denotes a first-order dyadic relation), it should follow directly from the judgement that aRb, without having to resort to any additional premises of any kind, that aRb .v. ∼aRb. (2014, pp. 243–4) Connelly can adduce interesting pieces of evidence to suggest that this really is the concern that Wittgenstein had. For instance, in a letter of January 1913, Wittgenstein alludes to a theory that he himself had been toying with in which forms are introduced into the analysis of a proposition. In that theory, he construed forms in such a way as to forbid multiple ways of plugging things in to them – hence removing the need for any supplemental premises or constraints (Wittgenstein, 1974, pp. 19–20). Connelly’s suggestion gives pride of place to the words of Wittgenstein’s June letter too, with its dismissal of further premises. Connelly’s construal can unravel our puzzle. On the 20th of May, the concern was that the MRTJ doesn’t prevent the assertion of nonsense. The concern on the 26th of May is that the presence of logical forms isn’t going to help us unless we’re willing to rely on external stipulations and constraints. To understand Connelly’s Wittgenstein, we could borrow Robert Nozick’s distinction between a goal and a side-constraint. The goal of utilitarianism, for example, is to maximise net utility. This can often come at the expense of individual rights. For example, a crude form of utilitarianism would allow us to torture a lone individual if it would bring pleasure to the masses. One way to avoid this consequence is to place certain side-constraints upon the means by which a utilitarian is allowed to pursue their goal. So constrained, the theory might say: maximise net utility in any way possible unless it violates a person’s human rights. This is very different to adopting the promotion of human rights as your new goal. In fact, that goal, without side-constraints, will often allow for the violation of rights – if, for example, violating one person’s rights will, in the long term, promote the human rights of others. In Nozick’s words (2003, p. 29), A goal-directed view with constraints added would be: among those acts available to you that don’t violate constraints C, act so as to maximize goal G. To borrow this terminology, we can present Connelly’s Wittgenstein as follows. A theory of judgement has to have meanings as its goal, or output. In Russell’s hands, the theory of judgement seems to have strings of objects and forms as its output (or goal), with meaning only arising out of respect for certain side-constraints placed upon the theory. Put this way, Wittgenstein isn’t the one placing a significance constraint upon a theory of judgement; Russell is. And that’s the problem – a theory of judgement

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shouldn’t yield meaningful objects merely as a result of a side-constraint; it should yield meaningful objects unadorned by side-constraints. We can still talk about Wittgenstein’s significance constraint, but it’s a constraint on a theory of judgement, rather than a side-constraint within a theory of judgement. The constraint on a theory of judgement is that it forbids the assertion of nonsense, but Wittgenstein wants it do so without recourse to side-constraints within the theory of judgement itself. In other words, Wittgenstein’s constraint on a suitable theory of assertion is that the theory generates only meaningful content without relying upon side-constraints in order to do so. Wittgenstein’s constraint, on this reading, is something like a no side-constraints constraint. The problem with a side-constraint bolted on to a theory of judgement isn’t that it will lead to a regress of prior judgements. Perhaps that regress can be blocked on the assumption (dubious though it may be) that the stipulations needed to meet the significance constraint are stipulations and not judgements. The problem isn’t that we generate some sort of tension with type theory. As Connelly puts it (2011–12, p. 142), [T]he supplemental premiss is problematic not . . . because it poses an incompatibility with the theory of types, but because it runs afoul of basic intuitions about logical inference. What are those basic intuitions? Take any proposition that you can assert, for example, ‘The ball is red’. If that is a proposition that you can assert, then it should follow that ‘The ball is red or the ball is not red.’ In fact, any tautology should follow from any proposition. This entailment should go through without any supplemental premises or constraints. You shouldn’t need to stipulate, before licensing the entailment of a tautology from your judgement, that your judgement has ordered its objects in deference to some side-constraint. Tautologies should follow automatically. These intuitions are not respected by the MRTJ. As Wittgenstein’s puts it (1914–1916, p. 96): Russell’s theory ‘does not satisfy this requirement’. What requirement? The no constraints constraint. I said at the outset of this chapter that my real concern isn’t to reconstruct Wittgenstein’s actual criticism. Any such reconstruction would be relying upon inarticulate letters, truncated diary entries and reconstructions of conversations, theories, and thought processes that have all been lost to history. My real concern is, rather, to lay out all of the most philosophically worthy reconstructions of Wittgenstein’s concern, because my defence of the MRTJ will have to answer all of them, irrespective of their historical provenance. For what it’s worth, Connelly’s reconstruction of Wittgenstein is about as a good a reconstruction as can be found in the literature. Even so, I’m not convinced that any single account conveys every nuance of Wittgenstein’s concern. In this light, I continue the survey of options.

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§2.4: The Failure of Logical Forms Russell conceives of the logical form of an n-adic complex as the completely general fact that there exist some n objects that are somewhere and somehow n-adically related. The generalised facts that constitute logical forms are so general, we are told, as to have no constituents. This makes them simple rather than complex. If they are simple, then to judge that they are the case isn’t to stand in a multiple relation but a dyadic one: this rules out the possibility of error because the binary relation theory of judgement allowed for no falsehood (as we saw in chapter 5). Logical truths are, we are told, self-evident. Logical forms are truths of logic. However, if truth is supposed to be a structural correspondence between the ordered objects of a judgement and a fact, then how can these simple, structureless, objects be true?5 More importantly, this tortured account of logical truth undermines the 1913-MRTJ’s response to the significance constraint: if logical forms are simple, then they cannot play the role that the 1913-MRTJ gives them. Forms, in the early stages of Theory of Knowledge had gaps in them reserved for different sorts of entities. These gaps helped us to impose a template upon our judgements to rule out nonsense. You can only plug certain entities into certain sorts of gap.6 The later accounts of logical forms, in the same manuscripts, treat them as simple in order to explain their self-evidence and to avoid a certain regress, as Griffin explains: Suppose that forms have constituents. Then these constituents must be strung together in some way to yield the form. But forms themselves are merely ways in which items can be strung together to from complexes. Thus in order to yield forms from their constituents one needs a form, which in turn has constituents and requires a further form, and so on indefinitely . . . At some stage, therefore, it seems we need forms without constituents. (Griffin, 1985, p. 223) But if logical forms are simple, we have no response to the significance constraint. We were supposed to conceive of logical forms as a string of gaps reserved for different sorts of entities. ‘It was the incomplete nature of the substitutional forms . . . which made them useful in solving the wide direction problem’ (Griffin, 1985, p. 224). But in order to avoid regress and in order to give an account of how these logical forms, that look like contingent facts, could be self-evident truths belonging to a higher world, Russell had to make logical forms simple. Perhaps, on the 26th of May, Wittgenstein attacked Russell’s appeal to logical forms. Both meetings centred on the straightforward significance constraint, but where Russell, with his logical forms, thought he had an

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answer on the twentieth, was left devastated and bereft of a response on the twenty-sixth : Russell’s logical forms don’t work. §2.5: The Independence Constraint Pears (1977) elaborates upon Wittgenstein’s dislike for Russell’s logical forms. He recovers the following concern from Wittgenstein’s notebooks: how can there be such a thing as the logical form of the false proposition, p, when there doesn’t happen to be any state of affairs instantiating that form? Given Russell’s account of a logical form as a completely general fact, it seems that Russell can provide no answer to this question. This line of reasoning leads Wittgenstein to the following conclusion: The reality that corresponds to the sense of the proposition can surely be nothing but its component parts, since we are surely ignorant of everything else. If the reality consists in anything else as well, this can at any rate neither be denoted nor expressed; for in the first case it would be a further component, in the second, the expression would be a proposition, for which the same problem would exist in turn as for the original one. (Wittgenstein (1914–1916) 20/11/14) Wittgenstein’s concern isn’t merely that propositions need to make sense. His concern is, Pears (1977, p. 190) concludes, that propositions should ‘achieve . . . sense without the help of any apparatus of truths, either about the referents of its names or about its form.’ To see how the 1913-MRTJ fails in this respect, consider the following: if you wanted to judge the false proposition that relation R relates one thousand particles, you could only do so if there exists the logical form of a one-thousandplace-complex – a chiliadic logical form – and a chiliadic logical form is a fact that can only exist if somewhere in the world there really are one thousand things that stand related to one another by a chiliadic relation. However, what if there isn’t? Does that mean I can’t make my judgement? Is my false judgement so dependent upon the obtaining of what seems to be a completely unrelated fact? This conception of an independence constraint, like Connelly’s very different no constraints constraint puts appropriate weight upon Wittgenstein’s statement that: ‘‘aRb. V ~aRb’ must follow directly without the use of any premiss’. §2.6: The 20th of May According to Carey As far as Carey (2007) is concerned, Wittgenstein’s worries were broader than meaningfulness, even on the 20th of May. Wittgenstein, Carey argues, was convinced that propositions have to be prior to any cognitive act: p needs to have a meaning prior to the proposition that not-p

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(Wittgenstein, 1914–1916, p. 94), for how can you deny something if that thing isn’t meaningful independently of your denial, and, for that matter, how can you assert something if that thing isn’t meaningful independently of your assertion? The MRTJ seems to undermine this fact: the fact that what we understand is prior to any act of belief or denial. This, according to Carey, is Wittgenstein’s real concern on the 20th of May. As we know, Russell wasn’t fazed by Wittgenstein’s first attack. The addition of logical forms was supposed to help. Carey explains: a logical form is the structure embodied by a ‘proposition’, and this structure exists independently of any cognitive act. Carey tells us how, in order to make his theory completely safe from Wittgenstein’s attack, Russell made two small amendments after the 20th of May. First, he decided to place logical forms within each judgement-complex. Second, he decides to focus on the multiple relation of understanding, before focusing on the relation of judgement/assertion: By defining propositions in terms of the relation of understanding, Russell hopes to do justice to the fact that a proposition is what is common to a variety of contexts: belief, doubt, affirmation, denial etc. By abstracting from all the particular terms constituting the understanding fact, he hopes to arrive at something that no longer has an essential reference to a particular subject at a particular moment in time. The resulting fact or form is therefore objective, not subjective, and common to all other cognitive acts having the same form. That is, ‘there is a U and an S such that U(S, x, R, y, γ)’ is an objective proposition, not a mere incomplete symbol, and is ‘the same for all subjects and for all propositional relations . . . concerned with the same proposition.7 (Carey, 2007, pp. 64–2) With these two moves, Russell thinks he can accommodate Wittgenstein’s demands within the MRTJ. Carey suggests that Russell made one more move in response to Wittgenstein: his notes suggest that he had intended to divide the later parts of the manuscript into a part about belief and a part about inference; at some point (between the twentieth and twenty-sixth), he changed his mind and decided to divide it instead into a part on atomic propositional cognitive acts and a part on molecular propositional cognitive acts – ‘This decision shows,’ Carey (2007, p. 81) thinks, that Russell ‘has become persuaded that a proper account of judgement should show that something, a proposition, is significant apart from those contexts in which it is asserted or denied, and that it is logically prior to notions like ‘not’ [and ‘and’ and ‘or’].’ In short, Russell is trying to adopt a Wittgensteinian notion of a bi-polar proposition, within the rubric of his MRTJ.

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To this end, Russell introduces the pair of relations, believing and disbelieving, towards the same objects-terms. These relations are presented as being secondary to the relation of understanding. After the 26th of May, as the whole project seems to be falling apart, Russell holds out little hope of extending the MRTJ to give an analysis of molecular propositions. His theory seems to demand: [A] mode of analyzing molecular propositions which requires the admission that they may contain false atomic propositions as constituents, and therefore to demand the admission of false propositions in an objective sense. This is a real difficulty, but as it belongs to the theory of molecular propositions [which was to be dealt with in the part of the book that was never written] we will not consider it further at present. (Russell, 1913, p. 154) What was this ‘real difficulty’? And how was it related to Wittgenstein’s concerns? According to the 1913-MRTJ, when I judge that a is similar to b, I stand in relation to a, b, similarity, and to the logical form of dyadic-complexes. Only one proposition can arise from this judgement: similarity only fits into one of the slots of the logical form (putting to one side the worry that we’d first of all have to judge that it is a universal), and it doesn’t matter which way round we plug a and b into the form because the relation in question is symmetrical: a is similar to b is equivalent to b is similar to a. Russell’s quoted concern centres upon molecular propositions. When I judge that a is similar to b or c is similar to d, I stand related to a, b, c, d, similarity, and, perhaps, to the logical form, ξ(x,y) V ξ(w,z). However, this time, what ensures that I’ll plug the right entities into the right spaces? I could equally well substitute into this form so as to yield the proposition that b is similar to c or a is similar d. We could appeal to the direction of the judgement-relation in order to help us plug the right relata into the right slots, in the right order, but (as we’ll see in §5.1) in 1913, Russell no longer thought that relations (including the judgement-relation) relate in any direction at all. Seemingly, the only way to guarantee that we generate the right molecular proposition, short of reintroducing the notion of relational direction, is to allow the atomic propositions (a is similar to b and c is similar to d) to enter the judgement as constituents. Russell was thus led to the self-defeating admission that molecular propositional judgements ‘contain false atomic propositions as constituents, and therefore to . . . the admission of false propositions in an objective sense’ – the very notion that the MRTJ sought to avoid. Christopher Pincock (2008) views this to be Wittgenstein’s damming concern of the 26th of May. Russell may have got rid of atomic propositions in his analysis of atomic propositional judgements, but it seems that he would

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need to readmit atomic propositions in order to complete his analysis of molecular propositional judgements. Contra Pincock, the problem really doesn’t seem to be all that damning: it evaporates upon the re-assumption that the judgement-relation relates in a given order.8 Nevertheless, the fact that Russell was moved by this problem does corroborate Carey’s view: Russell was struggling to accommodate the bipolarity of propositions – their priority to any logical operation. Having said all of this, the puzzle hasn’t dissolved. To say that worries about molecular propositions was the new and devastating concern can hardly convince us when we realise that Russell was aware that these concerns lay in wait for him, even before he formally adopted the theory, but merely explored it, in 1906. As early as then, he wrote (Russell, 1906, pp. 47–8): There is . . . another argument in favour of objective falsehood [and therefore against the MRTJ], derived from the case of true propositions which contain false ones as constituent parts. Take, e.g., ‘Either the earth goes round the sun, or it does not.’ Here, Russell was already aware that molecular propositions were going to pose problems for the MRTJ downstream.9 According to Carey, the best way to appreciate Wittgenstein’s final attack is via Russell’s three-paged sketch entitled ‘Props’. There is good reason to believe that these notes were written in the direct aftermath of Wittgenstein’s final assault: the notes begin on the back of a page that Russell drafted and rejected in the third week of May; Russell, apparently, wasn’t in the habit of keeping pages around for long periods of time, and the content sketched in these notes overlaps the concerns that Russell raises as his Theory of Knowledge sputters out. Carey (2007, p. 96) therefore concludes, with Blackwell (1974, p. 85), that these notes originate in May ‘very soon after Wittgenstein’s second visit’. ‘Props’ rejects Russell’s 1913-MRTJ out of hand. Surely, given the moment in which it was drafted, it embodies the scent of Wittgenstein’s attack. The theory of judgement that Russell sketches in these notes has a lot in common with his earlier, binary, theory of judgement. Here he distinguishes between positive and negative facts. Whenever we have two individuals (a and b) and a dyadic relation (R), there will, according to this theory, either be the fact that R(a, b), or the fact that not-R(a, b). Furthermore, we shouldn’t imagine that the negative fact includes an extra constituent, corresponding to the negation. The difference between the positive and negative fact is primitive: in the first case the three constituents are combined positively; in the second case, negatively. Then, Russell conceives of a neutral fact: a complex consisting of the same constituents, united in a neutral, as opposed to a positive or negative, fashion.

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Judgement, in this sketch, as Carey represents it, seems to be a binary relation between a mind and a neutral fact.10 The neutral fact is bi-polar: it points in both a negative and a positive direction. To assert the neutral fact is to believe that its constituents are positively combined, elsewhere, in a positive fact. To deny the same neutral fact is to believe that its constituents are negatively combined in a negative fact. Russell had taken to heart the point that Soames would later urge: there are plenty of ways to combine constituents of a proposition, and doing so doesn’t have to generate a positive fact that makes the proposition true. In neutral facts, relations actually appear as relations, neutrally relating: they don’t appear as object-terms.11 This will block most of the concerns raised in Wittgenstein’s name: these problems only seem to arise when the object-relation is ‘dormant’. In this theory of judgement, the object-relation relates, but not in such a way that it forces the judgement to be true.12 Appealing to ‘Props’ to explain Wittgenstein’s critique might encourage us to construe Wittgenstein’s concern as being very closely related to Stout’s representation-concern. On some construals of Wittgenstein’s critique, once you’ve guaranteed that every judgement has an object-relation of the right type, occupying the right position in the judgement, then you’ve met all of his constraints. However, Peter Hanks argues as follows: Wittgenstein’s point is that judging that p is always judging that p is true. This means that we can rephrase the question ‘What does A judge?’ as ‘What does A judge to be true?’. And now the answer that A judges that a, b and R are true obviously makes no sense. The collection of a, b, and R is not the sort of thing that can be true or false. Only a proposition can be judged to be true – a collection of items, even if they are of the right number and variety of types, is not the sort of thing that can be true or false and hence not the sort of thing that can be judged. (Hanks, 2007a, pp. 137–8) Demanding that the object-relation of a judgement actually relates (in a neutral way), as Russell did in ‘Props’, seems to answer Hanks’s construal of Wittgenstein’s concern: a concern that clearly echoes Stout’s demand for a distinction between propositions, which should be truth-apt, and collections/lists, which shouldn’t be.13 Furthermore, our appeal to ‘Props’ as a response to Wittgenstein, reveals how Fregean Wittgenstein’s critique may have been. On the 26th of December 1912, Wittgenstein wrote Russell a report of an important meeting: I had a long discussion with Frege about our theory of symbolism of which, I think, he roughly understood the general outline. He said he

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would think the matter over. The complex-problem is now clearer to me and I hope very much that I may solve It. (Beaney, 2009, p. 456) Michael Beaney concludes, [A] full account of Wittgenstein’s critique of Russell’s work must elucidate the way that Wittgenstein draws upon and transforms Fregean ideas, most notably, Frege’s distinction between ‘saturated’ objects and ‘unsaturated’ concepts. (Beaney, 2009, p. 567) The demand that relations always relate (whether positively, negatively or neutrally) – that they never occur merely as object-terms – clearly echoes Frege’s insistence that relations are unsaturated. If ‘Props’ is responding to Wittgenstein’s concern, Frege’s potential influence over this story becomes more and more apparent.

§3: Transcending the Puzzle Why did Wittgenstein’s criticism move Russell so little on the 20th of May, when, on the twenty-sixth, the very same criticism leaves him feeling suicidal? This puzzle can be looked at in one of two ways: philosophically or historically. Taking the historical puzzle seriously has given rise to a variety of concerns, each of which have been attributed to Wittgenstein. As philosophers embarking upon a defence of the MRTJ, this puzzle has served us well: thinking about it has provided us with a whole battery of concerns that need to be fended off. As historians, however, I worry that we have reached a dead end. Our only account of Russell’s immediate reaction to his meetings with Wittgenstein are gleaned from letters to his lover, Ottoline Morrell. At this stage in their relationship, Russell had a clear agenda: he wanted to evoke sympathy from Ottoline, for he knew that he was less and less an object of her amorous desire. The notion that the meeting of the 26th of May left him suicidal, and the notion, which he later expressed to Ottoline, that Wittgenstein had made him see that he was no longer capable of serious philosophy (Monk, 1997, pp. 301–2), should be treated with suspicion. Russell had a strong motive to engage in hyperbole (Landini (2007, pp. 8–9) and MacBride (2013, p. 207) both make this point). Indeed, whatever it was (and I believe it was probably a combination of some of the concerns canvassed earlier), I’m sympathetic to the view that Russell was nowhere near as moved by Wittgenstein’s 1913 critique as has often been portrayed. After all, he continued to subscribe to the MRTJ until 1919. It’s true that the 1913 manuscripts sputter out when Russell was supposed to turn his attention to molecular propositions, but

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this might not have had all that much to do with Wittgenstein. It may have been down to Russell’s realisation that his 1913 denial that relations relate in a direction (see §5.1) was incompatible with the MRTJ’s extending to account for molecular propositions (as we saw in §2.6). As soon as he resumed his belief in relations having directions, he was able to and did continue on in his allegiance to the MRTJ (this point is advanced by MacBride (2013, p. 209)). Furthermore, even if we take the letters to Ottoline seriously, and even if we accept that Wittgenstein’s criticisms devastated Russell, we needn’t believe that Russell’s changing reaction was based purely upon the philosophical give and take between him and Wittgenstein. Wittgenstein had a certain hypnotic hold on many of his associates. Russell was no exception. In fact, around this time, Russell spoke of his profound love for Wittgenstein and his deep faith in Wittgenstein’s abilities (Monk, 1997, p. 252). By Russell’s own admission, he didn’t really grasp what Wittgenstein’s charge against the MRTJ was: he just ‘felt in his bones’ that Wittgenstein must be right. In this light, the puzzle seems less pressing: we can’t be certain that Russell’s changing reaction was as radical as he presents, and we can’t be certain that if it was, it was due to a change in Wittgenstein’s actual argument so much as a corollary of the powerful psychological hold that Wittgenstein allegedly had upon Russell at that time. Finally, there is no primary source with a discursive account of the content of any of the May meetings between Wittgenstein and Russell. All of the attempts to reconstruct these conversations therefore embrace the spirit of a particularly adventurous form of philosophical archaeology. Nevertheless, some things are clear. Over the years, when it came to Russell’s MRTJ, Wittgenstein was consistently worried about the significance and category constraints (even if he thought that they were constraints on a theory of judgement and that they shouldn’t be met by supplemental premises and side-constraints within the theory): Every right theory of judgment must make it impossible for me to judge that ‘this table penholders do the book’. (Russell’s theory does not satisfy this requirement.) (Wittgenstein, 1914–1916, p. 96) The correct explanation of the form of the proposition, ‘A makes the judgement p’, must show that it is impossible for a judgement to be a piece of nonsense. (Russell’s theory does not satisfy this requirement.) (Wittgenstein, 1961, 5.422) We also know that Russell’s 1913 attempt to block this concern with logical forms was unsuccessful. To do the work required of them, logical forms would have to be, paradoxically, both simple and complex.

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So we do know what some of Wittgenstein’s ongoing concerns were even if we can’t reconstruct the conversations he had with Russell in May 1913. The next section deals with an historical question that is much easier to answer: why did Russell eventually abandon the MRTJ? The question is easier to answer because it has less to do with Wittgenstein than is generally noted.

§4: The MRTJ on Its Last Legs In his Lectures on Logical Atomism (1918), Russell rehearsed some of his old arguments against a binary relation theory of judgement. He could now accept, since the authorship of ‘props’, that a false proposition could be unified without being true: a false proposition might just be a neutral fact whose neutrally united constituents are elsewhere united negatively and not elsewhere united positively. However, Russell was still uncomfortable with ontological commitment to propositions: he could stomach facts, even negative facts, but not neutral facts! Russell’s (1918, p. 223) ‘vivid sense of reality’ preferred the MRTJ to a realm of propositions, in addition to his positive and negative facts. He may also have feared the revival of the Appendix-B paradox.14 Furthermore, what guarantees that the neutral fact will represent anything, inherently, and all by itself. Surely, if I want to, I can use the neutral fact that snow is white, to represent snow being green. Representation is up to me, not to the neutral facts I use. Despite rejecting neutral facts, and holding fast to his MRTJ, Russell renounced his termism in 1918; now he accepts that some entities simply cannot be the subject of a proposition. If a thing is a ‘verb’ (by which he means a relation), ‘it cannot occur otherwise than as a verb’ (Russell, 1918, p. 225). If relations could sometimes occur as relata, then the question would arise, within the MRTJ, as to which of the object-terms should be treated as object-relation; but if relations always occur as relations, there will be no such question – many of Wittgenstein’s constraints will be met automatically. This development lends credence to Beaney’s claim that Wittgenstein’s critique had a Fregean undercurrent, since part of Russell’s response to Wittgenstein seems to be the denial of termism, and the denial of termism is, in itself, a retreat to a more Fregean position. MacBride (2013, pp. 233–5) makes it sound as if Russell rejected his termism because, upon the adoption of the theory of types, it seemed to him that the rejection of termism was the best way of responding to Bradley’s regress: A number of factors had led to this change of heart [regarding termism] – most notably, a shift in his thinking about Bradley’s Regress and the various paradoxes that had occupied his attention after completing the Principles. Russell had come to the view that

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On MacBride’s account, as I understand it, it was only once Russell had rejected termism to better respond to Bradley’s regress, that he found that it would also help to bolster the MRTJ against Wittgenstein’s significance constraint. Though I think that this is plausible, it’s not all that clear to me how heavily Bradley’s regress weighed upon Russell’s shoulders by 1918. It’s true that Russell had told Bradley, in a letter, of 1914, that he would search for a solution to the problem of unity for as long as he lived (Griffin, 1993, p. 159). But this was a letter to Bradley – he may have been overstating matters somewhat – and there are times where Russell seems to be quite comfortable with the solution to the regress that I have already advocated: namely, resolutely insisting that the relation’s power to relate its relata is a brute and primitive power (Lebens, 2008). It seems equally plausible to me, therefore, that Russell beat his Fregean retreat solely in order to save his theory of judgement from Wittgenstein’s critique. Whatever Russell’s reasons were, he soon found that his denial of termism generated new problems for the MRTJ – take the judgement that Desdemona loves Cassio: You have this odd state of affairs that the verb ‘loves’ occurs in that proposition and seems to occur as relating Desdemona to Cassio whereas in fact it does not do so, but yet it does occur as a verb, it does occur in the sort of way that a verb should do. (Russell, 1918, p. 225)

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The object-relation has to occur as a verb if it is to meet Wittgenstein’s various constraints, but now the judgement-complex seems to be unstable: it has two relating-relations and is thus unlike any other complex; what is the source of this complex’s unity? Russell is confused, and he admits it. If you were to symbolise, map or draw a diagram of Othello’s judgement-complex, you would arrive at a diagram that makes it look as if the false proposition existed. Russell shares this diagram with his audience as an example:

This is a multiple relation theory. There are no neutral facts, or propositions. There are just judgement-complexes that have two relations as constituents. Russell grants: no other sort of complex contains two relating-relations (remember: on this account, all relations are relating-relations), and it seems a complete mystery how the occurrence of love in this complex doesn’t generate a subordinate fact (even a neutral one) that Desdemona loves Cassio. Russell concludes his discussion hoping that he has helped us to notice two things: (1) that it is implausible to treat propositions as independent entities – the binary relation theory of judgement is wrong (not for fear of making false propositions true – Russell had overcome that fear already – but because of their ontological unsightliness, and perhaps because of the Appendix-B paradox, and the representation-concern), and (2) the subordinate relation in a judgement cannot appear ‘on a level with its terms as an object-term in a belief’ (Russell, 1918, p. 226). Whatever Russell’s reasons for rejecting his termism, and whatever his reason for conceiving of the judgement-complex as one in which there are two relations somehow relating, the 1918 presentation of the MRTJ seems halting and hesitant. Nevertheless, Fraser MacBride has suggested (MacBride, 2013, pp. 235–6) an ingenious speculative precisification of the 1918-MRTJ, which transforms it into a theory worthy of our attention: [W]hat Russell may have been tentatively edging towards . . . is an appreciation of a far more radical version of the multiple relation theory of judgment than hitherto countenanced. According to this version, the relating-relation of a judgment complex is neither the relation expressed by the subordinate verb (so avoiding the problem

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The Rise and Fall of the MRTJ of falsehood), nor the ascription relation (thereby side-stepping Witttgenstein’s criticism): it is the relation expressed by the compound verb ‘. . . ascribes R to . . . and . . .’. It follows from this that judgment cannot, as Russell declared, ‘strictly be logically one’ because what constitutes the unity of a judgment act will vary depending upon the character of the compound relation that is responsible for relating the other constituents of the complex together.

This theory asks us to imagine that judgement is something like a function that operates upon relations. Love, for instance, is a two-place relation. The function of judgement takes that relation and turns it into a new three-place relation: judges-Love. If I stand in this relation to Romeo and Juliet (in this order), then I judge that Romeo loves Juliet. In fact, judgement takes any n-adic relation and turns it into a new n+1-adic relation. No longer does the subordinate relation have to appear as an object – rather, the relation is transformed by the judgement function: after being transformed it does relate, but it neither creates a proposition nor forces the judgement to be true – judges-love isn’t the same relation as love. We’ll come back to MacBride’s suggestion in the next chapter – he rightly (MacBride, 2013, p. 207) characterises this ‘more radical version of the multiple relation theory’ as ‘an intriguing conception of judgment that continues to merit our attention.’ Indeed, I shall argue, in the next chapter, that MacBride’s precisification of the 1918-MRTJ doesn’t just obviate Wittgenstein’s concerns with the MRTJ, but also Stout’s. In the meantime, we can note that Russell’s 1918 statement of the MRTJ needed more fleshing out, and that, as it stands, without MacBride’s precisification, it sounds more like a promissory note, or even an apology, than an argument. By 1919, Russell had given up on the MRTJ entirely. Russell’s (1919a) new theory of propositions rejects direct realism about propositional content: when you believe that A is to the left of B, you have ‘an image of A which is to the left of your image of B’ (Russell, 1919a, p. 319); your belief will be true iff the real A is to the left of the real B. Once Russell had given up direct realism about propositional content, many of the puzzles that lead us to the MRTJ evaporate. Even the representation-concern can be met. If you accept that propositions are something like mental images, then of course they get their representational power from the mind (although clearly, you might find this intolerably pyschologistic, and you might also worry that the Appendix-B paradox will raise its head again). I have already mentioned that Russell, soon after 1905, began to drift away from the spirit of his direct realism in his adoption of a sense-data theory of perception (which isn’t among the topics of this book). The spirit of his original direct realism was the desire to put minds in direct

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contact with the everyday objects of the world around us. Sense-data epistemology, on the other hand, puts a veil of sense-data between our minds and those objects. For this reason, and in many other ways, the MRTJ never really sat so easily within Russell’s fast changing world-view. Griffin (1985, pp. 243–4) puts this point neatly: During the period of 1903–1913 Russell’s views on logic and metaphysics were undergoing a major transformation . . . The multiple relation theory (more properly considered a theory of propositions instead of belief) and the related doctrine of logical forms . . . [as] bridges between Russell’s old [direct realist] philosophy and his new [sense-data epistemology] . . . were torn to pieces by the tension between the two. As his realism became less direct, the MRTJ was less important to him. However, Russell tells us that he gave up the MRTJ, primarily, because he no longer believes that there is a particular thing called the self. He had to give up the MRTJ for he had lost his belief in the mental subjects of beliefs. His rejection of the subject as a particular entity has to do with his increasingly Humean tendencies, and the sense-data epistemology that accompanies it. The self, Russell complains, ‘isn’t empirically discoverable’ (Russell, 1919a, p. 305). We never perceive ourselves, nor do we perceive our acts of perception: Such things [as selves] may exist, but we have no reason to suppose they do, and therefore our theories ought to avoid assuming either that they exist or that they do not exist . . . The first effect of the rejection of the subject is to render necessary a less relational theory of mental occurrences. (Russell, 1919a, pp. 305–6) Initially, at least, it’s not entirely convincing that this was the sole reason that Russell had for abandoning the MRTJ. For already in 1913, while Russell was still trying hard to develop the theory, he had already given up on the idea that we have any acquaintance with persisting subjects of judgements (Russell, 1913, p. 35): It is to be observed that we do not identify a mind with a subject. A mind is something which persists through a certain period of time, but it must not be assumed that the subject persists. So far as our arguments have hitherto carried us, they give no evidence as to whether the subject of one experience is the same as the subject of another experience or not. For the present, nothing is to be assumed as to the identity of the subjects of different experiences belonging to the same person.

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And yet, it’s fair to say that Russell’s rejection of subjects had become more severe. In 1913, he wasn’t willing to assume that they persist through time (even if minds do). By 1919, he wasn’t willing to adopt a theory that assumes that they exist at all.15 This rejection of the self pre-empts Wittgenstein’s crystallised rejection of the MRTJ in the Tractatus. Peter Hacker (1972, p. 59) notes that Wittgenstein, for standard Humean reasons concerning the ‘non-encounterability of the self in experience’, didn’t believe that there was such a thing as the ‘thinking, representing subject.’ Hacker accepts that Wittgenstein’s ‘central’ concern with the MRTJ was that it didn’t meet the significance constraint. However, Wittgenstein makes the following elusive comment: It is clear, however, that ‘A believes p’, ‘A has the thought p’, and ‘A says p’ are of the form ‘“p” says p’: and this does not involve a correlation of a fact with an object, but rather the correlation of facts by means of the correlation of their objects. (Wittgenstein, 1961, 5.542) Hacker takes this comment to be illustrative of Wittgenstein’s commitment to the complexity of the ‘soul’:16 when someone judges that p, some parts of what we take to be the person in question are arranged in a way that pictures p: The apparent unitary subject A which seemed related to a fact is a multiplicity of objects some of which are structured into a fact that pictures the fact or possible fact that p. (Hacker, 1972, p. 61) By 1919, the MRTJ was dead – a victim of Russell’s Humean rejection of the self; a rejection that he and Wittgenstein came to independently. Russell had held onto the theory for many years, despite Wittgenstein’s criticisms of 1913. And when he rejected it, he did so because of his developing Humeanism; not because of any of the constraints on a theory of judgement that we discussed in §2. This all constitutes compelling evidence that Wittgenstein’s 1913 concerns with the MRTJ weighed less heavily on Russell’s shoulders than his letters to Ottoline Morell make out.17

§5: The Legacy of the MRTJ Given that I believe that I exist, and that you probably believe that you do too, I’m not going to discuss Russell’s Humean scepticism about the self, which, as we’ve seen, was the straw that broke the MRTJ’s back. I’m also going to ignore any concerns that have to do with reified logical forms since I have no interest in defending the 1913-MRTJ, per se.

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Instead, we’ve been left with Stout’s representation-concern, and the following concerns associated with Wittgenstein: the significance constraint (which has also to deal with both category and type concerns, and should ideally be met without supplemental premises, so as to meet the no constraints constraint) and concerns about extending the theory to account for molecular propositions. Since the death of the MRTJ, there haven’t been many thinkers queueing up to resuscitate it.18 I already noted how David Armstrong (1973, p. 44) called the theory ‘unworkable’ and dubbed it ‘wasted labour to go over the ground again’. But a number of philosophers – including Armstrong – have been willing to go over the ground again – generally only in order to subject it to further criticisms in addition to those of Wittgenstein and Stout. In what remains of this chapter, I summarise (and dismiss) some of the most distinctive of those criticisms. §5.1: Peter Geach One of the most sustained attacks upon the MRTJ occurs in Peter Geach’s Mental Acts (1971). Here I discuss his most distinctive criticism. The act of judging that a bears some relation to b, Geach argues, is ‘the very same act as judging that b bears the converse relation to a’ (Geach, 1971, p. 52). The MRTJ fails to respect this fact. For any non/a-symmetric relation R, there will be a distinct converse relation R*.19 When R is a relation that holds between a and b in one order, R* is that relation that thereby holds between them in the opposite order. The converse of larger than is smaller than: whenever a is larger than b, it will be the case that b is smaller than a. Symmetric relations could either be thought to have no converse – because they relate in both directions at once, or because they don’t relate in any direction at all – or they could be thought of as their own converse: a is similar to b is equivalent to b is similar to a. Geach’s claim is that the judgement that aRb should be indistinguishable from the judgement that bR*a. This seems to be right: how could we judge that a is larger than b without thereby judging that b is smaller than a? How can we judge that a is similar to b without thereby judging that b is similar to a? The 1912MRTJ dictates that these two pairs of judgements constitute four distinct cognitive acts: 1. 2. 3. 4.

J(s, larger than, a, b) J(s, smaller than, b, a) J(s, similar to, a, b) J(s, similar to, b, a)

The MRTJ gives us no reason to think that the first two judgements should always take place together or that the second pair should always

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come together. In fact, it seems to entail that they don’t have to, and that even if the judgements in question always do come together, they would still constitute distinct mental acts. This is Geach’s most distinctive concern. In 1903, Russell was already aware of a certain puzzle to do with relational direction. The puzzle is this: are aRb and bR*a ‘really different propositions, or do they only differ linguistically?’ (Russell, 1903, §219). On the one hand, Russell was sensitive to the sort of concern later raised by Geach. When we judge that aRb, it seems to us that we’re also judging that bR*a, and more broadly, the two judgements, when true, seem to pick out the very same fact. But on the other hand, Russell couldn’t make sense of the view that the difference between greater and less than is down merely to the ‘exigencies of speech and writing’ (Russell, 1903). Each of the words ‘greater’ and ‘less’ have a meaning. Given Russell’s early doctrine of linguistic transparency, he couldn’t make sense of the view that these words should have a distinct meaning unless they both have a distinct referent. Thus, the view that ‘a is greater than b’ expresses the same proposition as ‘b is less than a’ has to be committed, given Russell’s doctrine of linguistic transparency, to one of the following: (a) ‘greater’ and ‘less’ refer to different relations, but the proposition expressed by ‘a is greater than b’ and ‘b is less than a’ contains both relations as constituents (b) ‘greater’ and ‘less’ actually co-refer, albeit in slightly different ways, to the same directionally neutral relation; thereby cashing out their difference in meaning, in terms of different ways of picking out the same referent Russell couldn’t accept (a). Which one of the two relations in the proposition should be viewed as the relating-relation? Surely one complex doesn’t have or need more than one relating-relation. The view collapses into oddity (an oddity that Russell wasn’t willing to accept, until his 1918-MRTJ – and even then, he didn’t accept it for long); that one complex could host two relating-relations. Russell also couldn’t accept (b). If a and b were related by some directionally neutral relation of relative-quantity, and if ‘a is greater than b’ and ‘b is less than a’ were just different linguistic means of getting at the same state, a problem arises: what does it mean to be the greater in this complex, and what does it mean to be the lesser? The only way of answering this question will have to appeal to the different argument places of the neutral relation: which term occupies the first argument place and which the second? However, this view, Russell concludes, ‘cannot be maintained without circularity’, for neither the greater nor the lesser is inherently the occupant of the first argument place of the neutral relation. We can only say that when the greater is in the first argument

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place, the relation is greater, and when the lesser is in the first argument place, the relation is lesser. Russell, not satisfied with (a) or (b), gives up on his intuition that ‘aRb’ and ‘aR*b’ express the same proposition. Consequently, for a time, Russell wouldn’t have thought Geach’s concern to be too pressing against the MRTJ. It was simply a consequence of the fact that relations relate in a direction: relations give rise to distinct converses; hence, the judgement that aRb has to be distinct from the judgement that bR*a, just as the fact that aRb will have to be distinct from the fact that bR*a. This may be embarrassing, but it is forced on the theory of judgement by the best response to a puzzling metaphysical riddle. Dorothy Edgington has pointed out to me (in conversation) that we shouldn’t be too perturbed by Geach’s argument: just because two propositions are logically equivalent doesn’t mean that to judge one is to judge the other. ‘2 + 2 = 4’ is logically equivalent to ‘1 + 2 = 3’, but the two assertions require distinct cognitive acts. Most humans are so advanced that aRb and bR*a are usually judged simultaneously, but we can imagine a less cognitively able mind judging one without judging the other. Russell’s position in 1903 was simple: aRb and bR*a are logically equivalent, but quite distinct; requiring two acts of assertion. By 1913, Russell thought that he could make sense of (b). Finally, Russell could adopt the view that had seemed so tempting in 1903. Russell sought to escape circularity as follows: in a complex with a neutral relation such as relative-time-sequence, we can define two relational positions, before and after. If we want to draw attention to the occupant of the before position, we use the word ‘precedes’ for the relation in question, and mention the object of our attention first, and the other relatum last; if we want to draw attention to the occupant of the after position, we use the word ‘after’ for the same relation, and mention this other relatum first. Then the question arises as to how we define these positions.20 Russell thinks the two positions in the relational complex can be defined without circularity in terms of the following relations: let us say that A precedes B, and let us call this fact α; A and B are both related to α via distinct relations – A precedes in the complex α whereas B succeeds in the complex α. These two relations (preceding and succeeding in a complex) define our positions. To occupy the before position in the complex is to be related to it by the first relation. To occupy the after position in the complex is to be related to it by the second relation. Of course, there is a threat of circularity. We have to give an account of the direction of the relations precedes in the complex and succeeds in the complex; won’t these relations have directions and converses, and won’t the problems that we were trying to avoid simply reappear? Russell’s (1913, pp. 111–2) response to the circularity charge is this: he distinguishes between homogeneity and heterogeneity.

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The Homogeneous case 1. 2. 3. 4.

We start with the complex A-is-before-B We attempt to swap the positions of A and B in that complex We arrive at a new complex: B-is-before-A Because swapping A and B in the first complex yields another possible (though in this case incompatible) complex (and because swapping them back will yield the old one), we call A and B homogeneous with respect to one another in both complexes

The Heterogeneous case 1. We start with the complex A-is-a-constituent-of- α 2. We attempt to swap the positions of A and α in that complex 3. We find this to be impossible because α is more complex than A, which rules out the possibility of α-is-a-constituent-of-A (in the same way that it’s not possible for the labour party to be a member of a politician, for example) 4. Because swapping A and α in the first complex fails to yield another possible complex, we can call them heterogeneous with respect to one another in that complex Relational direction was only ever posited to explain the difference between two homogeneous complexes with the same constituents in a different arrangement. Because heterogeneous complexes don’t admit of a multiplicity of arrangements, direction doesn’t need to be posited to explain anything in their case. The notion of relational position defined in terms of heterogeneous relations, such as A-precedes-in-α, allows Russell to give a transformational analysis of any homogeneous relation in terms of a collection of heterogeneous relations. The judgement that aRb and the judgement that bR*a can now be thought of as the same judgement. They are both the judgement that there exists a complex to which a is heterogeneously related in one way, and b in another. Geach’s most distinctive concern with the MRTJ disappears, and Russell is allowed to return to his intuition that ‘aRb’ and ‘bR*a’ name the same fact.21 Unfortunately, it’s not clear that relational direction really can be abandoned in the way that Russell had hoped. MacBride (2007) claims, convincingly, that the denial of relational direction rules out complex forms of symmetry that we shouldn’t want to rule out. We don’t have space to examine this worry at length, but consider the relation that holds between a, b, c, and d, when they form a circle. This is a symmetric relation – forming a circle – but how many positions does it have? Perhaps it has only one position, open to many objects at once. Russell would model this in terms of a, b, c and d all standing to the complex in question in the same heterogeneous relation. But this won’t do. The state of affairs is more complex than that because one thing cannot form a circle

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on its own; it needs a critical mass of peers with which to form a circle together. Modelling these sorts of relations with the resources provided by Russell’s non-directional analysis will be a challenge. MacBride demonstrates that we shouldn’t be too quick to rid ourselves of the notion of relational direction. Furthermore, we’ve already seen reason to reinstate relational direction, if we want to save the MRTJ from the concerns of Pincock (see §2.6). Pincock fears that the MRTJ can’t distinguish the judgement that ‘a is similar to b or c is similar to d’ from other judgements that arrange the same object-terms in different orders. This seems right when we deny that the judgement-relation has a direction. The problem evaporates once we reinstate that direction. If relations do need to have a direction, as I tend to think they do, then Geach’s objection is a bullet that we’ll all have to bite, whatever our theory of judgement. But it’s interesting to note that if the project of abandoning direction in favour of heterogeneity, or in terms of the various options canvassed by Kit Fine (2000) for getting rid of relational direction can be made to work, then, whatever other problems may arise, the 1913 solution to Geach’s concern will be effective. §5.2: John Mackie Mackie asks, ‘[How is] the fact that it would be Desdemona’s loving Cassio, not Cassio’s loving Desdemona . . . mirrored in the more complex belief-relation?’ (Mackie, 1973, p. 29). This isn’t simply the narrow direction problem. Even if the judgement-relation can be trusted to order its arguments, what is it, given the fact that the terms do not form a unity, which makes this the proper correspondence: Judgement:

Judgement (Othello, Love, Desdemona, Cassio)

Fact:

Love (Desdemona, Cassio)

rather than this?

Judgement:

Judgement (Othello, Love, Desdemona, Cassio)

Fact:

Love (Cassio, Desdemona)

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Thus even when the internal order of the judgement-complex is secured, there are numerous problems facing the specification of the correspondence necessary for truth, and for determining just one fact. This correspondence concern shouldn’t bother us. We accept that relations, when they relate, relate in a direction. The direction in which the relation of judgement relates its relata establishes an easy convention to learn: a judgement is true iff outside of the judgement-complex, the object-relation relates the object-terms in the order that they appear in the judgement. Another reason why the concern shouldn’t bother us is this: as A. J. Ayer (1971, pp. 205–6) and Anthony Woozley (1976)22 have both argued, Russell was ill-advised to characterise his own MRTJ as a classic correspondence theory of truth when it was, in fact, quite compatible with a more primitivist and Aristotelian definition of truth: the act of judgement that relates a subject to R and then a and then b is true iff a is R-related to b; we needn’t quantify over facts and posit a correspondence relation at all, even though Russell did. Thus, for various reasons, Mackie’s correspondence concern can be dismissed. §5.3: David Armstrong Despite saying that it would be wasted labour to go over the ground again, Armstrong does spell out some of his concerns with the MRTJ (Armstrong, 1973, pp. 44–5), the most pressing of which he shares with Geach (1971), Prior (1971), and Mackie (1973): universals don’t exist except in their instances. Armstrong explains, ‘if, as is the case, there is no loving except where individuals love, then it seems impossible to give any concrete account of the required relation between loving and the three particulars [in the case of Othello’s false judgement that Desdemona loves Cassio].’ Armstrong seems to have adopted a quasi-Fregean conception of a relation that forbids it from appearing in any complex except as a relating-relation. This line of criticism shouldn’t bother us in the slightest. First, realism about universals and a principled termism is prima facie well motivated – we may well have very good reason to believe in the existence of relations, such as love, and every reason to think that, if they exist at all, they can occur as subjects just as easily as they can occur as relating-relations. Moreover, as I noted in chapter 1, the MRTJ doesn’t actually end up depending upon realism or upon the adoption of termism, at all. Now we can begin to see why (although we’ll arrive at a more full account in the next chapter, §3). MacBride’s precisification of the 1918-MRTJ can allow for the rejection of termism and even a rejection of universals altogether, since it doesn’t require any relation to appear as an object of a judgement (a claim we’ll revisit, and expand upon, in the next chapter, §3), and so even if we were predisposed to reject termism, along with Armstrong, or

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universals, along with the nominalists, we still wouldn’t have demolished the prospects of adopting a version of the MRTJ. §5.4: Arthur Prior One concern, shared by Geach (1971), Prior (1971), and Russell (1918) himself, runs as follows. According to the MRTJ, the relation of judgement will have a different number of argument positions depending upon the adicity of its object-relation. A judgement with a monadic objectrelation, such as the judgement that Socrates is wise, will be triadic: it will relate a subject to Socrates and wisdom. A judgement with a dyadic object-relation will have four argument positions: it will relate a subject to a dyadic object-relation and two further object-terms. For any n-adic object-relation, a judgement will be n+2-adic. If the relation of judgement changes its adicity so frequently, what right do we have to think that it is the same judgement-relation each time? Russell (1918) raises this concern and hopes to avoid it simply by conceding that there are a multiplicity of judgment-relations corresponding to all the various adicities but that we have the right to call them all ‘judgement’ because they all have so much in common.23 I see no need to be so concessive towards this concern. Why can’t we accept that relations are able to be variably polyadic? MacBride (2005) appeals to Armstrong as one of the few thinkers who have actually provided an argument for, rather than dogmatically asserting, the thesis that relations are unigrade (which is to say that they have a fixed adicity). Armstrong asks us to suppose, for the purposes of a reductio, that Rm is actually multigrade (that is to say variably polyadic). In that case, it must really be the same relation in each of the following facts: Rm(x), Rm(x, y), Rm(x, y, z), . . . By the Indiscernibility of Identicals, Rm must have the same properties in each of its instantiations. But Rm has different properties in each: in one it is monadic, in another dyadic, in another triadic etc. Thus Rm cannot be the same relation in each one of those facts. We are therefore lead to conclude that Rm cannot be multigrade. This argument relies upon the assumption that relations that have different adicities, ‘differ in their essential natures’ (Armstrong, 1997, p. 85). If each universal is essentially n-adic (for some n), then Armstrong’s argument follows. An n-adic universal cannot be identical to a k-adic universal where n≠k. But as MacBride (2005, p. 574) responds, Armstrong’s assumption is question-begging in two respects: 1) the thesis that some relations are multigrade is just the thesis that some relations lack an essential adicity, ‘So the argument simply presupposes what it is intended to prove’ (MacBride, 2005); 2) it assumes (in order to draw a distinction between universals and particulars) that particulars can occur in facts with different numbers of constituents

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without differing in their essential natures – thus, x, the very same particular, is thought to occur in each of the facts Rm(x), Rm(x, y), Rm(x, y, z), . . . It seems that there is no good reason to think that relations have to be unigrade. If our best theory of judgement makes it a multigrade relation, then so be it. We are under no pressure to concede that the relation of judgement divides into an infinite number of distinct relations simply because its adicity varies. A similar worry can be raised concerning the logical type of the relation of judgement. Its logical type will seemingly change in tandem with the logical type of its object-relation, and it seems plausible that a logical type, according to type theory, really is part of the essence of a relation. Consequently, logical type – unlike adicity – isn’t the sort of thing that should be subject to change from instance to instance of the same relation. This is a concern that I’ll come back to, and dismiss, in the next chapter. §5.5: Arthur Prior and Frank Ramsey Russell subscribed to an ontology of facts and to the notion that the mind can stand in a dyadic relation to a fact: a mind can know a fact; a mind can perceive a fact etc. Prior (1971) argues that the MRTJ is incompatible with such theories of perception and knowledge. He leaves Russell with a choice: he must either reject his theory of facts, or reject his theory of judgement. Prior’s argument runs as follows. Take the fact that the knife is to the left of the book. Call that fact p. Now, imagine that Joe perceives this fact – Joe perceives that the knife is to the left of the book. On Russell’s view, that the mind can be dyadically related to facts, we could symbolise the relation involved in Joe’s perception as follows: Perception(Joe, p). Perception is a dyadic relation between the perceiver and the perceived. In this case, it relates Joe to the fact in question. Now, imagine that Felix, conveniently standing nearby, judges that Joe perceives that the knife is to the left of the book. Felix’s judgment would – according to the MRTJ – receive the following analysis: (1) Judgement (Felix, Perception, Joe, p) Nevertheless, let’s not forget that judgements can be false. This judgement could be false for one of two reasons: either because Joe doesn’t perceive p, or because there is no fact that p – the knife isn’t to the left of the book after all! However, if there is no p, then Felix’s judgement will have to receive a different analysis. Prior concludes dismissively: [W]hat a belief consists in surely cannot depend in this way upon what is true; indeed, one of the main motivations of Russell’s theory

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is to give an account of belief which doesn’t make what is believed depend on the belief’s truth or falsehood. (Prior, 1971, p. 10) The MRTJ doesn’t want to give a different analysis to a judgement merely because it’s false. We could try to fix this concern. We could assert that Felix’s judgement (whether true or false) receives the following analysis: (2) Judgement (Felix, Perception, Joe, Left, knife, book) However, Perception is, ex hypothesi, supposed to be dyadic – it’s supposed to relate perceivers to the perceived – and sometimes to facts. How can we judge that it takes four arguments (Joe, Left, knife and book)? If Russell wants to adopt the MRTJ, then it seems he will have to give up his conviction that perception and knowledge are dyadic relations that are able to relate a mind to a fact. As we shall see in chapter 10, §3, I would be quite happy to give up the idea that perception relates minds to facts, but it would be a shame to have this choice forced upon one by the MRTJ. Thankfully for Russell, Prior’s argument doesn’t really go through. Reflection upon Frank Ramsey’s work suggests a solution. Prior seems to think that he was repeating an argument of Ramsey’s, but he was mistaken. Prior introduces ‘Ramsey’s argument’ as an argument against the MRTJ. However, Ramsey, in the text that Prior cites, clearly views his argument as an argument in favour of the MRTJ. Ramsey (1927) can only see two options for a theory of judgement, both are due to Russell: on the one hand, we are presented with the MRTJ option; on the other hand, we are presented with the view that Russell (1921) later came to accept in which ‘Mr Russell speaks of beliefs as either pointing to or pointing away from facts’ (Ramsey, 1927, p. 155). On this view, Ramsey tells us, ‘a judgment that Caesar was murdered and a judgement that Caesar was not murdered would have the same object, [namely] the fact that Caesar was murdered, but differ in respect of the relations between the mental factor and this object’ (Ramsey, 1927). Ramsey wants to reject the latter option, in favour of the MRTJ, claiming that there are no dyadic relations whatsoever between minds and facts. He tries to demonstrate that there are no dyadic relations between minds and facts with the following argument: in the sentence, ‘Joe perceives that the knife is to the left of the book’, the phrase, ‘that the knife is to the left of the book’ cannot be a name for the fact that the knife is to the left of the book, because this sentence will still be meaningful even if there is no such fact. Given that this sentence doesn’t simply name two relata and assert that they are related, Ramsey wants us to conclude that perception isn’t simply a dyadic relation between a mind and fact. Once we have given up the notion that minds can be dyadically related to facts,

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we will be ‘driven, therefore, to Mr Russell’s [earlier] conclusion that a judgement has not one object but many’ (Ramsey, 1927, p. 157). It turns out that Prior’s argument against the MRTJ fails precisely because Ramsey’s argument in favour of the MRTJ fails! Ramsey recognises that his argument admits of a response: we could say that the assertion in question doesn’t name a fact, but that it describes one, and then asserts a dyadic relation between the fact described and a mind. The assertion in question would then receive the following analysis: (3) (∃p)((p is constituted by the relation of Left relating the knife to the book) & (Perception (Joe, p))) Thus, when I assert that ‘Joe perceives that the knife is to the left of the book’, I really assert a conjunction: that there exists a particular fact such that it can properly be described as the fact that the knife is to the left of the book, and that the perceiver in question perceives that particular fact. This analysis seems perfect: it allows us to continue to think that fact-perception is a dyadic relation, and it gives the assertion a meaning and a constant analysis even when false. Ramsey says of this analysis that it is ‘plausible but not, in my opinion, valid’. Ramsey wants to make do without an ontology of facts. Fundamentally, it is for this reason that he cannot accept (3), which quantifies over facts. Ramsey’s argument, it seems, wasn’t supposed to demonstrate that belief isn’t a relation to facts, since he recognises that his argument presupposes the non-existence of facts. I take it that his ‘argument’ was really an attempt to illicit anti-fact intuitions even though he knew his ‘argument’ was open to a straightforward response. The anti-fact intuition was rooted in the observation that ‘the fact that x’ can’t be the name of a fact. However, even granting this, if you doggedly subscribe to an ontology of facts, even Ramsey accepts that his argument fails. Now we can respond to Prior: we can give Felix’s judgement an MRTJ analysis even when the knife is to the right of the book. When Felix judges that Joe perceives that the knife is to the left of the book, Felix in actual fact, asserts a very complex judgement: he asserts that there is a fact that contains Left, a knife, and a fork (in a certain arrangement), and he asserts that Joe perceives this fact. Such a conjunction can still be asserted even when no such fact exists. I happen to prefer Ramsey’s approach to facts over Russell’s. Why think that there are such things in existence as facts if we can do without them? Why say that people ever perceive facts? Nonetheless, Prior’s argument fails to force any conclusion upon Russell: the MRTJ is, as Ramsey was aware, perfectly consistent with Russell’s reification of facts, even if that reification was unnecessary or unwise (and even if the denial of the existence of facts might convince one – as it convinced Ramsey – to embrace the MRTJ).

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Scott Soames (2015) has raised some forceful criticisms against the MRTJ, which I shall explore, and respond to, in passing, in chapters 10 and 11. Besides those criticisms, I know of no worthy critique that should particularly bother a champion of the MRTJ other than those already owed to Stout and Wittgenstein. Stout provides us with the representation-concern. Wittgenstein, and the various reconstructions of Wittgenstein provide us with ‘the wide direction problem’, which, I hope to have demonstrated, is more complicated than a simple syntactic worry about order: the worry concerns syntax and semantics and more. The worry places a significance constraint, a category constraint, a type constraint, and an independence constraint upon a theory of meaning, potentially at the same time as requiring that these constraints are met automatically, by a theory of judgement, with no supplementary premises. It is those concerns that I hope to ameliorate in part III of this book, as we move away from history, in the hope of securing an account of the metaphysics of meaning.

Notes 1 ‘What is Logic?’ can be found in The Collected Papers of Bertrand Russell (Russell, 1992). Griffin also cites a letter from Wittgenstein to Russell, dated January of 1913 (Wittgenstein, 1974, pp. 19–20), in which Wittgenstein seems to place logical forms within his own construal of a proposition/judgement. Doesn’t this imply that logical form was a feature of Russell’s MRTJ prior to the Theory of Knowledge manuscripts? I’m not so certain. It only proves that they were once a part of Wittgenstein’s analysis of propositions. This letter plays a role in James Connelly’s reconstruction of Wittgenstein’s concern in §2.3. 2 We will explore what it means for a theory to be under a constraint when we turn to the work of James Connelly later on in this chapter, §2.3. 3 An anonymous reviewer put to me the concern that Wittgenstein was worried about the syntax of judgement rather than the semantics, and that to read Wittgenstein as being concerned with category mistakes (as Pears and Griffin do) is to superimpose Gilbert Ryle (1949) – who coined the term ‘category mistake’ – upon Wittgenstein. I can respond to this in one of two ways. My most concessive response is to admit that my primary concern is less focussed upon what Wittgenstein’s actual concern was, so much as what people have understood his concern to be. This is because I’m unsure that his actual concern can ever be reconstructed with any certainty. Consequently, a contemporary defence of the MRTJ will have to respond not only to Wittgenstein (and perhaps not even to Wittgenstein) but also to all of the complaints raised in his name. Whether or not it is anachronistic, the category constraint is raised in his name prominently in the literature. It therefore merits attention. My more strident response is to deny any anachronism. Even though Wittgenstein clearly does have syntactic concerns, that doesn’t mean that he doesn’t also have semantic concerns with the MRTJ. And, even though Ryle coined the term ‘category mistake’, it’s clear that one of the prominent features of Wittgenstein’s own picture theory of meaning, developed as a response to the MRTJ, is that it blocks category errors.

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It contends that a name loses its meaning as soon as it combines with other names in ways that don’t reflect the modal profile of its referent. Wittgenstein doesn’t use this terminology, but when he talks about an object’s ‘form’ (Wittgenstein 1961, 2.0141), he is referring to its modal profile, which is what the ‘logical form’ of an object’s name needs to echo in order to be a name for that object. David Pears (1967, p. 218) explains this Tractarian picture according to which names draw their meaning from their referents by mirroring their form – only combining with other names in ways that respect the form of the objects to which they refer: ‘Consequently, if they are combined in a way which the things cannot be combined, they will snap the lines which connect them with the things and lose their meanings, and the result will be not a proposition but a piece of nonsense.’ Even without the terminology, it’s clear that Wittgenstein was worried about ‘category mistakes’. His theory of meaning doesn’t allow for them to arise. As we said in chapter 2, §2.1, Bradley could bite a similar bullet in response to a regress threatened by his theory of judgement, and discovered by G. E. Moore. An anonymous reviewer asks, ‘Why are logical forms truths of logic rather than the facts stated by these truths or the facts believed to obtain?’ This is a fair question. I think that the answer is that even if they are the facts themselves, the associated judgements need to be self-evident. This is reason enough to make them simple, so as to make their assertion binary, rather than multiple, and therefore, apparently, immune to error. An anonymous reviewer asks, ‘Does the notion of substitution require a gap? It’s . . . not as though the fact that Love(a,b) is the form Rxy filled with constituents. For that would make it seem as though the form is a constituent, when it seems to be more of an “aspect” of the fact.’ Again, this seems like a fair point to raise. It seems as if Russell was somewhat confused as to whether the form was an ‘aspect’ rather than a constituent of a fact, or even whether that distinction could be coherently drawn. Even if it turns out that forms don’t have to be gappy in order to allow for substitution, plenty more problems with forms will arise. Carey is here quoting Russell (1913, p. 115) This response to Pincock occurred immediately to Fraser MacBride and myself in conversation. MacBride (2013) later put this response forward in print, and argued that it had occurred to Russell himself to respond this way; hence Russell’s later reversion to the theory that relations relate in a direction, and his continued allegiance to the MRTJ. Thanks are due to an anonymous reviewer for reminding me of this excerpt. The accompanying diagrams seem to back this up. But it’s important to note that Carey misquotes ‘Props’. In Russell’s essay, it seems that judgement is still to be viewed as a multiple relation, but that the logical form is supposed to be replaced by the relevant neutral fact. In Russell’s words, ‘It will still be a multiple relation, but its terms will not be the same as in my old theory’ (Russell, 1995, p. 197). Carey misquotes this crucial passage replacing ‘multiple’ with ‘neutral’. This theory doesn’t have to deny the platitude about truth. It merely needs amending: R(a, b) is a true proposition iff a is positively R-related to b; R(a, b) is a false proposition iff a is negatively R-related to b. a’s being neutrally R-related to b will not force anything to be true or false. Even granting, as we did in footnote 10, that judgement is still a multiple relation, it is plausible that a neutral fact will only allow for one order of substitution (unlike a more general logical form, with its free and unregimented variables). This might even help the theory to meet Connelly’s no constraints

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constraint, were it not for the problems that neutral facts throw up in their wake (see §4). Hanks isn’t the only person to interpret Wittgenstein’s critique so as to bring it closer to Stout’s representation-concern. Other examples include Maire McGinn (2006, p. 38) and, to some extent, Michael Potter (2009, pp. 118–29), who also appeals to ‘Props’ in his historical account of the debate between Russell and Wittgenstein in the spring of 1913. See chapter 5, footnote 15. I document there how Bernard Linsky and Fraser MacBride have both made the mistake of thinking that Russell was still, in 1918, worried about forcing all propositions to be true. In actual fact, the possibility of neutral combination had alleviated Russell of this worry. Thanks to an anonymous reviewer for helping me notice the need to clarify this point. In actual fact, more needs to be said about Wittgenstein and the soul. In 5.5421, of the Tractatus¸ Wittgenstein denies that the soul is composite, but on Hacker’s reading of 5.5421, he is asserting that the soul is complex. Somewhat confusingly, Hacker writes, ‘The claim should be interpreted thus: the soul conceived of as a unitary simple subject does not exist. But conceived of as a manifold, it is the legitimate subject-matter of psychology’ (Hacker, 1986, p. 62). MacBride (2013) develops this point at length. A noteworthy exception is Friederike Moltmann (2003). She doesn’t deny that propositions exist – and in that respect, she can’t be considered a full adherent to the MRTJ. But she does deny that propositions are the objects of propositional attitudes and she accepts that the MRTJ provides us with, broadly speaking, the right analysis of assertion. Keith Hossack (2007) also adopts the MRTJ – but his version of the theory will be scrutinised in part III. To illustrate the difference between symmetric, non-symmetric and a-symmetric relations, let’s restrict our attention to dyadic relations. A dyadic relation R, is symmetric iff, when it relates a and b in one direction, it also relates them in the other direction; it is a-symmetric if its relating a and b in one direction rules out its simultaneously relating them in the other direction. R is non-symmetric if it is neither symmetric nor a-symmetric. Kit Fine (2000) makes two suggestions as to how define positions for neutral relations: one makes positions ontologically distinct constituents of the complex; the second suggestion treats them as a resemblance nominalist might treat universals. For more on Fine, and this comparison to resemblance nominalism, see MacBride’s (2007) response. Neither of Fine’s suggestions are quite the same as Russell’s. Note that in our presentation of the 1913-MRTJ earlier, I suggested, following Russell, that the judgement that a is similar to b will turn out to be same as the judgement that b is similar to a – this, we can now see, is a consequence of his 1913 rejection of relational direction. Woozley doesn’t make this argument as explicitly as Ayer. He merely defends Russell’s MRTJ in chapter 5 and then goes on to argue for a very primitivist account of truth in the following two chapters. He clearly sees the two positions as compatible (Woozley, 1976, p. 124, ft. 1). MacBride (2013, p. 236) accepts that Russell shared this concern but argues that his expression of this concern may well have been grappling towards the insight that, if judgement is a function that creates new compound relations out of its object-relation, then judgement cannot ‘strictly be logically one’ because what constitutes the unity of a judgment act will vary depending upon the character of the compound relation that is responsible for relating the other constituents of the complex together. There will be one judgement function, that yields many different judgement-relations.

Part III

Resurrecting the MRTJ

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Significance and Representation

Between them, Stout and Wittgenstein left the MRTJ with a number of criticisms to overcome. Stout brought the representation-concern to the table (although Russell was aware of the problem before Stout raised it). The representation-concern is a problem that any account of propositional content will have to answer. Wittgenstein’s independence constraint that we raised, in the last chapter (§2.5), can thankfully be put to one side, since it only had any bite against the 1913-MRTJ, with its idiosyncratic appeal to reified logical forms. But Wittgenstein has left us with the significance constraint, the category constraint, and type constraints, which the MRTJ might struggle to meet, and he is also said to have raised the challenge of extending the MRTJ to account for molecular propositions. Finally, he raises the issue that a theory of judgement should be able to meet theses constraints without supplemental premises – i.e., not in virtue of side-constraints within the theory. In this chapter, I hope to solve all of these problems, except for the issue of molecular propositions, which I leave for the next chapter.

§1: Wittgenstein’s Constraints It is my contention that none of the issues that Wittgenstein raised, or is said to have raised, with the MRTJ are anywhere near as difficult to overcome as Stout’s representation-concern. In this section, I will try to rescue the MRTJ from Wittgenstein’s various concerns, and in doing so, I also hope to illustrate the ways in which Stout’s concern is more fundamental. §1.1: Dismissing Category Constraints In part III of this book, my concern is no longer with history, but with defending the MRTJ as a philosophical theory. The wide direction problem, as classically conceived, has to do with syntax – putting the wrong types of objects together, or putting the right objects together in the wrong sorts of ways. The category constraint, on the other hand, is a

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purely semantic concern – attributed to Wittgenstein most explicitly by David Pears. Whether or not Wittgenstein actually had this concern is no longer my concern.1 The MRTJ can certainly stand accused, if not by Wittgenstein, then by some proxy, of allowing the assertion of category mistakes. How should we respond? Richard Larson and Gabriel Segal (1995, p. 47) present the following Tarski style T-theorems: a) ‘John’s toothbrush is trying to kill him’ is true iff John’s toothbrush is trying to kill John. b) ‘Max went to the pictures tomorrow’ is true iff Max went to the pictures tomorrow. c) ‘Colourless green ideas sleep furiously’ is true iff colourless green ideas sleep furiously. If you know the truth conditions of a sentence, then you could be said to know its meaning. Thus, knowledge of a), b) and c) is sufficient for knowing the meanings of the sentences: ‘John’s toothbrush is trying to kill him’. ‘Max went to the pictures tomorrow’. ‘Colourless green ideas sleep furiously’. There is certainly something odd about these sentences, but that doesn’t make them nonsensical. Because their argument is dependent upon a somewhat Davidsonian understanding of meaning, Ofra Magidor (2013, p. 59) provides us with independent arguments for the same conclusion. Magidor considers the following three ascriptions of propositional attitudes, all of which embed category mistakes (I use her numbering, Magidor, 2013): (3) John said that the theory of relativity is eating breakfast. (4) John believes that the number two is green. (5) John dreamt that his toothbrush was pregnant. She then asks us to consider the following claims (Magidor, 2013): (M): (3)–(5) are meaningful sentences. (T): For each of (3)–(5), there is some possible circumstance in which it is true. (M-entailment): If M is true, then the category mistakes embedded in (3)–(5) are meaningful. (T-entailment): If T is true, then the category mistakes embedded in (3)–(5) are meaningful. Either M and M-entailment or T and T-entailment are sufficient to prove that category mistakes are meaningful, and all four claims are plausible. Against T, Magidor envisages an argument for the claim that (4) can

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never be true: anyone who possesses the concepts ‘two’ and ‘green’ will never believe that the number two is green. Magidor responds, asking us to consider the following scenario (Magidor, 2013, p. 61): Jane is a philosopher. She recently developed a new theory in the philosophy of mathematics according to which numbers are coloured, and the colour of the number two is green. To flesh out the example a bit more, suppose Jane holds some naturalist position according to which the number two is the set of all pairs of physical objects in the world. In addition, Jane holds that if most such pairs have a certain colour, then the set – and therefore the corresponding number – has this colour . . . Suppose that following some empirical investigation Jane concludes that . . . most pairs of objects are green and so, following her theory, she forms the belief that the number two is green. There’s no reason, in such a case, to think that Jane lacks any of the relevant concepts. ‘Jane knows a lot of mathematics, and clearly possesses the concept ‘two’.’ And, she ‘generally does a perfectly good job telling which things are green and which are not’ (Magidor, 2013). M-entailment and T-entailment are both plausible. The only reason why ‘John believes that bla-bla-bla’ is nonsense while ‘John believes that the theory of relativity is eating his breakfast’ isn’t, is because ‘bla-bla-bla’ has no meaning whereas ‘The theory of relativity is eating my breakfast’ does. Surely, these sentences, (3)–(5), ascribing propositional attitudes, can only ever be true if such category mistaken assertions are possible. Magidor brings many more arguments to bear on this issue, including an argument from synonymy: if ‘two is green’ is synonymous with ‘deux est vert’, and if synonymy entails shared meaning, then both of these category mistakes – the English and the French one – must have a meaning; a meaning that they share. Without exploring her full array of arguments, we can safely conclude that it is more than reasonable for us to dispense with the category constraint in any future defence of the MRTJ. It is possible to assert category mistakes. The only consequence of doing so is that you will have asserted a necessary falsehood; not only is your toothbrush not trying to kill you, it isn’t even the sort of thing that could try to kill you. If you assert that it is, you’re asserting something necessarily false – your assertion might be ‘nonsensical’ in some colloquial sense of the word, but it isn’t strictly speaking nonsense. I know and understand what you said, it’s just necessarily false. The same could be said for the assertion that the knife is the square root of the fork. There’s no need for a theory of judgement to make such judgements impossible. People believe impossible thing all the time! One is reminded of the Queen of Hearts. Category mistakes are merely a species of necessary falsehood, and necessary falsehood is, unfortunately, the stuff of a great many everyday assertions!

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§1.2: Dismissing Type Constraints Whether or not there really is some sort of tension between the MRTJ and the ramified theory of types, one could simply worry: what in the MRTJ makes it the case that a person can’t assert a type-confused proposition? According to the theory of types, properties are supposed to be regimented according to types, such that certain properties can’t be meaningfully predicated of certain entities. What in the MRTJ guarantees that this is the case? We could defend the MRTJ against type constraints by rejecting Russell’s theory of types. Perhaps the paradoxes that gave rise to type theory are simply non-existence proofs for the paradoxical sets, properties and relations in question – leaving us without any need to regiment those sets and universals that do exist, into a hierarchy of types. Alternatively, adhering more to Russell’s philosophical outlook, we could accept that type restrictions are necessary, but insist that type confusions give rise only to falsehood instead of nonsense and, therefore, impose no constraints upon a theory of judgement. A type mistake might just be a species of category mistake, which is, in turn, just a species of necessary falsehood, and necessary falsehoods can be asserted. Finally, if we wanted to tie ourselves to a particularly robust and ontologically serious type theory, and if we wanted to ban the assertion of type-confused propositions, we could say that the judgement-relation has type-restricted argument places. It isn’t that we, ourselves, paradoxically, have to make judgements about the suitability of the objects of our judgement before we can judge; it’s just that the relation of judgement will only take certain objects in certain argument positions. The relation does the work for you. Just as a chair can’t marry a table, because the relation of marriage (as that culturally constructed relation is currently configured) has argument places reserved only for human beings; the relation of judgement could have certain restrictions on its argument places, to rule out the possibility of type-confused judgements. Of course, to place type restrictions on argument places in the judgement-relation is to rely upon the sort of supplemental premises that Connelly’s Wittgenstein, and his no constraints constraint would abhor. However, if you don’t adopt the no constraints constraint, this option will be a live one. In the previous chapter, we raised a concern about the logical type of the judgement-relation itself. Its logical type will seemingly change in tandem with the logical type of its object-relation. If the object-relation is of type n, then the judgement-relation will have to be of type n+1, but a relation can’t keep shifting its place in the type hierarchy. We can make sense of the notion of variable polyadicity, but it’s not clear that we could make sense of a relation that’s flexible with regard to its logical type, given the strictures of type theory.

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But as we’ve seen, we have a number of options open to us: (1) we can deny type theory, and solve our paradoxes in some other way, and thereby accept that judgement is the same relation whatever its relata, or (2) we can deny type theory only as it applies to propositional attitudes; this shouldn’t be a problem, and in fact seems to follow from saying that type violations aren’t meaningless, but merely false. If type violations can be meaningful but false, then they should be the sorts of things that are able to occur in the context of a propositional attitude, and only in the context of a propositional attitude. On the second option then, type theory applies to all sets and universals, except for the propositional attitudes. §1.2: The Significance Constraint Having dealt with the category constraint and the various constraints imposed on the MRTJ by type theory, our conception of ‘significance’ reduces merely to the classical wide direction problem. In response to this concern, one has merely to make a couple of stipulations: first, that the second argument place of a judgement be reserved for universals; second, that the judgement-relation never takes more or less than n +2 relata when its object-relation is n-adic (the count includes the subject of the judgement, the n-adic object-relation in question, in addition to n further object-terms).2 Allowing for the meaningfulness of category mistakes and type confusions, these stipulations will only make room for judgements that have a truth-value (even if the value is necessarily false); no nonsense will be tolerated (unless, colloquially, you call category mistakes ‘nonsense’ – but then that’s the sort of nonsense that can be asserted)! Of course, if you adhere to the no constraints constraint, you will be disappointed by a tactic of stipulating our way out of trouble. And, indeed, we will do better as the chapter progresses. However, these stipulations are relatively easy to understand, nor do they require any sort of regress of judgements having to take place before judgements. As far as stipulations go, these seem relatively tame. Indeed, the sorts of stipulations we’re engaging in here seem inherently reasonable ones to make about relations in general. As I’ve said before, the relation of marriage is reserved for human beings, it cannot relate tables to chairs. The relation of x being between y and z is reserved for spatially located entities, or regions of space. The relation of x being a member of y only allows sets or set-like abstracta into the y position. Why can’t we say that the relation of judgement is reserved for minds, n-adic relations and n further objects? Keith Hossack (2007) adopts a related strategy. He posits a realm of negative facts in addition to positive facts. He thinks of assertion as a relation between a mind and a vector. A vector is just a plural-many in an order. In other words, Hosack adopts a version of the MRTJ. But because

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he has an ontology replete with positive and negative facts, he will have truth-makers, and false-makers. Vectors that, when judged, constitute true judgements, correspond to a truth-making fact. Vectors that, when judged, constitute false judgements, correspond to a false-making fact. This allows Hossack to stipulate that vectors with no truth-maker or false-maker simply cannot feature in a judgement. Russell had no false-making principle, since he had no negative facts, and so he had no way to distinguish between falsehood and nonsense (neither correspond in any way, for Russell, to a fact). By the time that Russell was willing to entertain the existence of negative facts (Russell, 1918), he had already adopted the 1918-MRTJ, which (as we’ll see in §2) had its own response to the significance constraint. Without negative facts, Russell was ill equipped to make the sorts of stipulations that allow Hossack to meet the significance constraint. Hossack can say the following: a nonsensical vector (i.e., one that cannot feature as the ordered objects-terms of a judgement) is one with no truth-maker and no false-maker. With these resources in hand, we can stipulate: the relation of judgment only relates minds to vectors with a truth-maker or a false-maker. In either the form of the double-stipulation strategy (which doesn’t require an ontology of facts) or in the form of Hossack’s MRTJ, we have a straightforward response to the significance constraint (albeit, one that disregards the no constraints constraint).3 One problem does arise, however, for both of these responses. They depend upon our being able to draw a clear distinction between universals and particulars and to talk with authority about each category – as if we know of what we talk! Hossack uses the distinction between universals and particulars to define facts, which he thinks always ‘combine’ an n-adic universal and n further entities.4 Unfortunately, in a series of compelling articles, MacBride (1999; 2004; 2005) has made it abundantly clear that the universal/particular distinction is not an easy distinction to draw.5 MacBride (2011) attacks Hossack on just this point. It’s no surprise, therefore, that Landini (2007, pp. 8, 65–72) should argue that Wittgenstein’s real concern with the MRTJ was that it depended upon a universal/particular distinction, which, Landini’s Wittgenstein claims, cannot be drawn in language.6 According to this Wittgenstein, supplemental premises are not a problem for a theory of judgement, per se, but the premises required here are not assertable. I don’t seek to defend either the double-stipulation strategy or Hossack’s strategy. However, without adopting these strategies, I do want to point out that neither of them brings us anywhere nearer to solving Stout’s concern. These versions of the MRTJ view judgement as a relation between a subject and an ordered-many, albeit subject to certain stipulations; but an ordered-many is like a list of objects. What makes an ordered-many inherently representational? In order to meet all of Wittgenstein’s alleged

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concerns, other than the no constraints constraint, we’ve been able to guarantee that all judgements will be assigned a truth-value; but we still haven’t explained what makes certain ordered-manys judgeable in the first place; nor have we explained how judgement manages to represent.7 This already alludes to the fact that Stout’s concern is just more fundamental than many of the concerns attributed to Wittgenstein. What I hope to demonstrate in the remainder of this chapter is that to solve Stout’s concern is to solve the significance concern in its wake – even in a way that respects the trenchant no constraints constraint. The same does not hold, as we’ve just seen, in the reverse order. This is what ultimately underlines how fundamental Stout’s representation-concern really is for the MRTJ, and for the metaphysics of meaning in general.

§2 Responding to the Representation-Concern The representation-concern has been solved for the MRTJ by Mark Sainsbury (who doesn’t go on to adopt the MRTJ for himself, but who still did it a great favour), and in a related fashion by Fraser MacBride’s precisification of the 1918-MRTJ. What’s distinctive about both of their accounts is that they also meet what’s left of Wittgenstein’s significance constraint. §2.1: Sainsbury’s MRTJ Mark Sainsbury (1996, p. 104) lays out what he takes to be the main problems to face the MRTJ, some of these will be familiar to us, but it’s worth laying them out as he sees them; I paraphrase his presentation: (i)

Only some collections of entities can be arranged, by the relation of judgement, so as to say something (such as the collection of Romeo, Juliet and love). What distinguishes these collections from collections that cannot be arranged (without supplementation) so as to say anything (such as the collection of Japan and celery)? (ii) Given a collection of entities that can be meaningfully arranged, what distinguishes a meaningful arrangement from a meaningless arrangement? (iii) What distinguishes two arrangements of the same collection that each say different things? (iv) What is this seemingly extra ingredient, hitherto referred to as an ‘arrangement,’ that has to be added to a collection in order that it should be able to say something? What is the cement that binds propositional content? Problems (i) and (ii) are clearly the sort of concern that we’ve been attributing to Wittgenstein: in order to rule out the possibility of nonsensical judgements, we’ll need to be able to account for the difference between

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a collection of objects that can be arranged, in a certain order, so as to say something meaningful, and a collection, or an order, that cannot give rise to meaning – this is the significance constraint. Problem (iii) is the narrow direction problem: if the judgement that Romeo loves Juliet relates me to the same three entities as the judgement that Juliet loves Romeo, then what distinguishes between these two judgements? Problem (iv), on the other hand, is clearly the sort of concern repeatedly raised by Stout: what distinguishes a proposition, which is truth-apt, from a mere ordered-many? Sainsbury is right to regard this fourth problem as fundamental: the other problems merely ‘serve to illustrate that (iv) is genuinely puzzling’ (Sainsbury, 1996, p. 105). The so-called ‘extra ingredient’ at the heart of problem (iv) is only shared by meaningful arrangements of entities. If we can solve (iv), we have a good chance of solving the other problems in its wake. The first move that Sainsbury makes in the direction of saving the MRTJ is merely to recognise that the fourfold problem that it faces is analogous to a central fourfold problem in the philosophy of language: (Li)

What distinguishes a collection of words that can be arranged meaningfully (i.e., to form a meaningful sentence) from a collection that cannot be so arranged (without supplementation)? (Lii) Given a collection of words that can be arranged so as to say something, what distinguishes a meaningful arrangement from a non-meaningful arrangement (a well-formed sentence from an illformed sentence)? (Liii) Given a collection of words that can be meaningfully arranged, what distinguishes one meaningful arrangement (a sentence) from another (a distinct sentence comprised by the same words)? (Liv) What is the extra ingredient, hitherto referred to as an ‘arrangement,’ that takes a mere collection of words and allows them to say something? Sainsbury contends that Donald Davidson has been able to solve this fourfold problem for the philosophy of language. And though, for various reasons, Davidson might see no need for propositions or for a Russellian theory of judgement, Sainsbury argues that the structure of Davidson’s theory can be superimposed upon the MRTJ in order to solve our original four-part problem: (i)–(iv). In the next two sub-sections, I first explore how Davidson attempts to solve (Li)–(Liv), and then present Sainsbury’s related attempt to save the MRTJ from some of its most significant criticisms. §2.1.1 Davidson, Truth and Predication8 According to Davidson, Frege was the first thinker to provide us with a syntax and a logic for predicates anywhere near precise enough ‘to invite

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a precise semantics’ (Davidson, 2005, p. 139). Frege also noticed that most meaningful sentences have truth conditions: they have associated conditions that would make them true (and even sentences that don’t – such as questions and commands – seem to be inherently and importantly related to sentences that do). To understand a sentence, it seems, is to know what would make it (or a closely related sentence) true. These observations led Frege to see that a meaningful string of words has (or is significantly related to a sentence that has) two watermarks: 1) a predicate and 2) truth conditions. These insights took Frege close to a solution to (Li)–(Liv). A predicative expression doesn’t merely refer (if it refers at all). Such expressions play a special role in determining the truth conditions of the sentences in which they occur: ‘loves’ doesn’t just refer to love (if there is such a thing as a universal to be referred to), it also makes sentences true iff the referent of its left-flanking name loves the referent of its right-flanking name. This role, above and beyond any notion of reference, is its semantic value. Predicates are the watermark of a meaningful string of words because predicates determine truth conditions. We’re getting close to our solution. As far as Frege was concerned, the next step was a general theory of predication, so that we can explain how it is that predicates determine truth conditions. According to Davidson, this is where Frege’s account flounders. Frege spoke of predicates as functions. Just as the function of addition takes two numbers as arguments and yields a third number, their sum, as its value; n-adic predicates take the referents of n names as their arguments and yield the true or the false as their value. But a function takes objects as arguments and yield objects as values. Unless we buy Frege’s commitment to these peculiar objects called the true and the false, it becomes increasingly implausible to think that predicates are some sort of function, however valid the analogy may be. Given all of this, Frege’s general theory of predication, if we delete the objectionable ontological commitments, seems to boil down to the following: a predicate is such that when appended to the right number of names ‘it constitutes a sentence that is true or false’: In other words, the predicate does just what we know predicates do. I do not question that predicates and functional expressions are in a way syntactically similar, or that the many metaphors (‘mapping’, ‘falling under’, etc.) appeal to genuine intuitions. What I do question is whether predication has now been explained. (Davidson, 2005, p. 139) In the light of the failure of Frege’s attempt, Davidson thinks that we should learn to shy away from a general account of predication. The history of the subject suggests to Davidson (2005, p. 161) that, in this

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case at least, less is more. Rather, following Tarski’s lead, we should, noting that any language only has a finite number of predicates, specify the semantic role of each and every predicate one by one. Take the predicate ‘x loves y’. We can specify its role in just a few steps. It forms a sentence when flanked by two names. One name needs to left-flank and one needs to right-flank. The resulting sentences will be true iff the referent of the left-flanking name loves the referent of the right-flanking name. The predicate ‘x is white’ can also have its role specified. It forms a sentence when left-flanked by one name. The resulting sentences will be true iff the referent of the flanking name is white. Once we have run through every predicate in a language and specified, in this way, the role it plays in forming sentences and determining truth-values, we will have said all that we can say about predication in that language: we will have an axiomatic theory of predication for the language in question. This, of course, falls short of a general account of predication: It is true that no general explanation emerges. What does emerge is a method for specifying the role of each and every predicate in a specific language; this role is given by a non-recursive axiom which says under what conditions it is true of any number of entities taken in the order in which its blanks occur. What more can we demand? (Davidson, 2005, p. 161) These Davidsonian insights, Sainsbury argues, solve the fourfold problem with which we started this section. (Li)

What distinguishes a mere collection of words from a collection that can say something is that collections that can say something must contain an n-adic predicate and n names. (Lii) Given such a collection, what makes for a meaningful arrangement is the application of names to predicates in accordance with the flanking conventions specified by the axiom for the predicate in question in the theory of meaning. (Liii) The axioms of our meaning theory, and the truth conditions they impose upon strings of words, are sensitive to the order in which predicates are flanked by names. (Liv) What distinguishes a mere collection from a meaningful arrangement is a truth condition; truth conditions are given rise to by predicates, whose role can be recursively specified, if not explained, by our axiomatic theory of predication. We cannot really criticise Davidson for using predicates in the meta-language in order to give an account of predication in the object-language because it’s

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not possible for an account of language to break free from language itself: the theory needs to be stated in some language or other, and every language utilises predicates! Davidson’s axiomatic accounts of the predicates of a given language are theories of language stated in a language. For this reason, you might think that no theory of meaning can be completely explanatory, but we can demand, at the very least, the sort of systematic specifications that Davidson’s theories provide us with. Davidson’s theory is modest, but this is no fault. Furthermore: it is as discursive as modesty allows. One might think that Davidson has been so successful that there’s no longer any need to give an account of propositional attitudes. Propositions were posited as the meanings of sentences. But Davidson thinks he can provide you with a theory of meaning for any language that you like, in which propositions play no role. According to Davidson, propositions are neither sufficient for, nor necessary to, a theory of meaning. They’re not sufficient because one isn’t told very much when one is told ‘Snow is white’ means the proposition expressed by the sentence ‘Snow is white’ (Davidson, 1967, p. 306). And they’re not necessary because a Davidsonian theory of meaning can systematically specify the meaning of any sentence in a language without recourse to propositions or to propositional attitudes. Ultimately, however, as I tried to spell out in chapter 1, and repeated in chapter 4, Davidson doesn’t so much provide an account of the metaphysical nature of meaning as to provide an account of how systematically to translate one language (the object-language) into another (the meta-language). That propositions are unnecessary to this task, I readily accept. However, we might want to give a more general account of the metaphysical nature of meaning (within the bounds of modesty). When I make an assertion about the world, even if I use language to express it, what relation does that assertion place me in to the world around me? The MRTJ answers: I stand in a multiple relation to the entities that my assertion is about and invokes. What do two people share when they make identical assertions, even when they do so in different languages? The MRTJ answers: they stand in the same relation to the same object-terms and to the same object-relation in the same order. We shouldn’t think that Davidson has undermined the metaphysical project that Russell was engaged in. Even if propositions, or propositional attitudes, don’t ‘oil the wheels of a theory of meaning’ (Davidson, 1967, p. 307), they still have plenty of philosophical work to do, and our no-proposition theory of propositions tries to do that work, if only we can avoid the representation-concern, and solve problems (i)–(iv). §2.1.2: Sainsbury’s Davidsonian MRTJ Davidson’s success at the linguistic level gives us every hope that a theory can be constructed so as to distinguish between sense and nonsense at

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the level of Russellian judgements. In fact, Sainsbury’s whole defence is predicated upon the notion that anything that words can do, referents can do too. Certainly, names can be used to represent their referents, but why can’t their referents be used to represent themselves? To illustrate Sainsbury’s point, imagine a language in which speakers pick up objects in order to refer to them. In such a language, objects would be used to signify themselves.9 Imagine that we extend the absurd language in which things are lifted when we want to speak about them. How would we make predications and thereby say things? Perhaps a variety of flags could be used as predicates. If someone waved a red flag before picking up Romeo and then Juliet (in that order), she would have said that Romeo loves Juliet. The waving of the red flag predicates love. But if objects can be used to refer to themselves, as this language illustrates, and if the mind is acquainted with universals (properties and relations), then why can’t the mind use them, just as we can use the flag, as predicates? By ordering Love, Romeo and Juliet in my mind, in a certain order, why can’t I thereby predicate Love of Juliet and Romeo? I can do this without sticking anything together to create a unified propositional entity. I can do this even when Love doesn’t actually relate the object-terms in question. As Sainsbury (1996, p. 106) puts it: if the fact that ‘a’ and ‘b’ flanking an occurrence of ‘loves’ can say that a loves b; then a and b themselves, flanking an occurrence of the actual relation of love in a judgement, can be used to say that a loves b – if you don’t believe that universals exist – bear with me until §3. A mind can use anything it likes to represent anything else that it likes, but surely the insight at the heart of direct realism is that the most fundamental way in which the mind reaches out to the world is to form thoughts directly about it; using things in the mind-external environment to represent themselves. Just as a Davidsonian theory can specify the role of every predicate in a language, we could create an analogous theory of predication for directly realistic judgement which would specify the role of every property in determining the truth conditions of the judgements in which they can feature. For example, our axiom for the relation of love, would read as follows: The relation of love is such that it can only be used predicatively of two further object-terms, and will generate a judgement that is true iff the first of the two loves the second. The same trick could be performed for every universal with which a person is acquainted; she can use it in a directly realistic judgement only if she knows how to use it predicatively, and a theory of predication for judgement would specify, for each universal, just how to use it in a judgement. Such a theory will solve problems (i)–(iv). (i)

Our theory, like Davidson’s meaning theory for a language, will stipulate that a collection of entities that can be meaningfully arranged

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by a (directly realistic)10 propositional attitude such as the relation of judgement will have to include an n-adic property and n individuals: this stipulation solves (i). And we won’t require (that which MacBride and Landini’s-Wittgenstein would find objectionable, namely) a general definition of what it means to be an n-adic property. Rather, each property has an axiom in the theory that stipulates what its role is in a judgement. (ii) Given such a collection, our theory will specify, as Davidson’s did at the level of language, that what makes for a meaningful arrangement is the application of individuals to properties in accordance with the flanking conventions specified for the property in question by its axiom in the theory of predication for judgement: (ii) is solved just as (Lii) was. (iii) The axioms of our theory of predication (for judgement) stipulate that the predicative role of object-properties is sensitive to the order in which they are flanked by the remaining object-terms. This solves (iii) just as (Liii) was solved. (iv) What makes an ordered collection of objects in a judgement meaningful, despite just being a disparate list of entities, is the act of predication which gives the judgement a truth condition; the truth condition is determined by the object-relation whose ‘semantic’ role within a judgement is specified, if not explained, by an axiomatic theory of predication in judgement. This solves (iv) just as (Liv) was solved. Sainsbury’s defence of the MRTJ is relatively simple. Judgement is a relation that confers truth conditions upon a vector (an ordered-many). Why can’t you judge nonsense? Well, nonsense is the lack of a truth condition, and judgement is what, by definition, confers truth conditions. Note that judgement just does this. It doesn’t do it out of deference to some sort of side-constraint. However many stipulations seem to be made in our theory of judgement, our theory only really describes something that judgement simply does all by itself. In this way, we have arrived at the first version of the MRTJ to meet the significance constraint without violating the no constraints constraint. Despite appearances, this theory isn’t vacuous: it’s just modest. Sainsbury grants that ‘the approach is firmly non-reductive’ (Sainsbury, 1996, p. 109), but the theory is certainly discursive: we can say what it means for judgement to confer truth conditions in that we can specify what the truth conditions will be for any arrangement of objects. We can also say for any arrangement of objects that cannot be judged, that it cannot be judged, by feeding the sequence through our set of axioms and seeing that they don’t generate a truth condition. Sainsbury simply echoes Davidson’s sentiment: we might not be able to give a general explanation of how judgement works, but we can, at least, explain what it means for

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a collection of entities to say something, in the sense that we can supply a ‘systematic provision of the saying in question. What else could one expect?’(Sainsbury, 1996). In a judgement, a mind predicates its object-relation of its object-terms. The object-relation doesn’t occur as a relating-relation, nor does it occur merely as an object: it appears predicatively. And the power that the mind has to predicate a property of some individuals isn’t a ‘mysterious power’ (Sainsbury, 1996, p. 110), because we can specify the predicative role that each property can play when so judged, just as Davidson can specify the predicative role that each predicate in a language can play in the utterance of sentences in which they occur. That Sainsbury doesn’t fully appreciate what he’s achieved is a claim that I will explore and justify in chapter 11, §1. But what’s important for our purposes is that, whether he realises it or not, Sainsbury’s MRTJ really does save us from Stout. Hossack thinks that vectors themselves have truth-values. Those that correspond to positive facts are true, and those that correspond to negative facts are false. However, that doesn’t respond to Stout’s representation-concern at all. What gives a vector the power to represent? By writing a theory of predication into the MRTJ, you relieve us of this mystery. As I pointed out, in the name of King, in chapter 1, the ability of people to use their minds to represent the world seems far less mysterious and in need of explanation (at least in the philosophy of language),11 than the ability of abstract objects, or vectors, to represent, all on their own. Sainsbury’s MRTJ puts the mind in the driving seat. It is the mind that performs the truth condition conferring act of predication. Comparing Hossack and Sainsbury’s defence of the MRTJ demonstrates that to solve the representation-concern will suffice to meet the significance constraint (and the no constraints constraint), but meeting the significance constraint will not always suffice for responding to the representation-concern (or to the no constraints constraint). Finally, I think it fair to say that Sainsbury’s defence of the MRTJ, cuts to the heart of what Russell was probably after, with his insistence that ‘there could be no falsehood if there were no minds to make mistakes’ (Russell, 1910, p. 152). In 1912, he elaborated upon the same theme: ‘It seems fairly evident that if there were no beliefs there could be no falsehood, and no truth either, in the sense in which truth is correlative to falsehood’ (Russell, 1912, p. 70). Russell was concerned, as we saw right throughout chapter 6, that judgement shouldn’t merely place its objects in the right order, because that would make them a mere list rather than a meaningful arrangement. The meaningfulness of a judgement comes from a sort of pseudo-unity that the mind imposes (a unity but not an actual unity, to paraphrase Russell’s confusing language).12 Now, with the help of Sainsbury, we’re

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finally in a position to say, better than Russell ever did, what that pseudo-unity is: it’s a truth condition. And we know how the mind does what it does. It uses its object-relation as a predicate. And though we can give no general account of predication, we can specify, for each and every universal (even if we can’t give a general account of what a universal is), what predicative role it can play in a judgement. In chapter 11, §1, I’ll return to Sainsbury and critically explore why he doesn’t end up adopting the MRTJ for himself. It comes back to my claim that he doesn’t fully appreciate the difference between Stout’s concern and Wittgenstein’s constraints, even though he gave us the resources to solve them both.

§3: MacBride’s MRTJ Before moving on to the next chapter, it’s worth expanding upon MacBride’s suggested precisification of Russell’s 1918-MRTJ, for it shares certain merits with Sainsbury’s MRTJ, and has certain advantages over it, at the cost, perhaps, of certain disadvantages. MacBride’s (2013) suggested precisification of Russell’s 1918-MRTJ, if you recall from the previous chapter, runs as follows. Instead of having a relation, judgement, that relates a subject to an n-adic relation, and n further objects, we posit a distinct judgement-relation for every predicate, or property. So when Othello judges that Desdemona loves Cassio, he doesn’t stand multiply related, by the relation of judgement to love, Desdemona and Cassio – instead, he stands related to Desdemona and Cassio by the relation x judges that y loves z. Scott Soames imagines that the 1918-MRTJ was a retreat from the central insight that the mind is what generates representation. Insisting that the object-relation appears in the judgement as a relating-relation is, Soames insists, a retreat to the view that the object-relation is responsible for creating the illusive unity of the proposition – this was a failure to respect or to ‘appreciate the significance’ of the central insight of the MRTJ (Soames, 2015, p. 472). But on MacBride’s construal of the 1918MRTJ, that’s not what’s happening at all. On MacBride’s account, the 1918-MRTJ very much shares in the spirit of Sainsbury’s reconstrual of the MRTJ. To assert something is to engage in an act of predication. If there were no minds to judge, there would be no such acts. In fact, you might think that the 1918-MRTJ more emphatically embraces the notion that the act of predication is what gives rise to truth conditions and representation. On Sainsbury’s account of the MRTJ, Othello stands related to Love, Desdemona, and Cassio. But this might lead you to obscure the fact that he doesn’t merely stand related to those three relata, but that he is engaged in predicating love of the other two. MacBride’s version of the 1918-MRTJ makes this perspicuous – of course that’s what he’s doing, since he stands in the judging x and y to be

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love-related relation to Desdemona and Cassio! Once again, we meet the no constraints constraint because judgement imposes truth conditions on ordered manies without recourse to supplementary premises. This is just what judgement does. Furthermore, MacBride’s 1918-MRTJ, unlike Sainsbury’s version, is compatible with the rejection of termism. There are realists, who accept that universals exist, but deny that they can ever occur as terms of another relation. Of course, this denial of termism throws up new problems since, if there are such entities, how are we able to talk about them? However, the fact that the 1918-MRTJ is compatible with the rejection of termism certainly makes the theory stronger, since it’s able to stay neutral on the issue of termism and its rejection. In the previous chapter, §5.3, I noted how certain thinkers had rejected the MRTJ, in part, on the basis of its incompatibility with the rejection of some form of termism. David Armstrong, for instance (1973, pp. 44–5), wrote, If, as is the case, there is no loving except where individuals love, then it seems impossible to give any concrete account of the required relation between loving and the three particulars [in the case of Othello’s false judgement that Desdemona loves Cassio]. This concern seems to have been shared by Geach (1971), Prior (1971), and Mackie (1973). MacBride’s 1918-MRTJ shows them that the MRTJ is quite capable of being stated in such a way as to stay neutral on the issue of termism. Furthermore, MacBride’s 1918-MRTJ can even be adopted by nominalists about universals – as I promised way back in chapter 1. You can deny that properties and relations exist, and yet still think that Othello stands related to Desdmona and Cassio in a certain distinctive way when he judges that Desdemona loves Cassio. What it means for Othello to stand so related to Desdemona and Cassio can be cashed out in terms of any nominalistic treatment of relations. But if relations are themselves supposed to be objects of the judgement-relation, then the nominalist might be forced to get off the boat (depending on the form of nominalism). Because MacBride’s MRTJ needn’t make properties or relations the object of any other relation, it not only remains neutral on the issue of termism but also can be neutral on the existence of universals and thus allow nominalists to adopt the theory in search of a more robust metaphysics of meaning than could be provided by, say, a Davidsonian translation manual. Having said all of this, and given the fact that I subscribe to termism and have no problem with realism about universals, it seems to me that Sainsbury’s reconstrual of the MRTJ is a more workable theory than

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MacBride’s ingenious precisification of Russell’s confused presentation of the 1918-MRTJ. Why prefer Sainsbury’s theory (bear in mind that when I call it Sainsbury’s theory, it doesn’t mean that Sainsbury actually adopted it – he didn’t, and bear in mind that when I call it MacBride’s 1918-MRTJ, I also don’t mean that MacBride adopted it!)? I prefer Sainsbury’s theory for two reasons. 1. MacBride’s 1918-MRTJ forces us to deny that there is one single attitude called assertion. Instead, for every single property that could ever be predicated of anything else, we have to posit a distinct assertion that R is instantiated relation. It’s true that, even on Sainsbury’s theory, for every property we could ever predicate of anything else, our meaning theory for judgement will have to include a separate axiom to explain how that property could be used as a predicate in a meaningful judgement. In essence, then, we have a choice between the ideological economy of MacBride’s theory, that won’t require all of these axioms, and the ontological economy of Sainsbury’s theory, that won’t require a proliferation of distinct assertion relations – of course, the nominalist will say that MacBride’s theory is also ontologically more economical since it doesn’t even require the reification of object-relations, and assertion relations can also be understood in nominalistic ways – but since I’m already a realist, I already have those universals in my ontology – what I don’t want is a proliferation of distinct assertion relations. I prefer the economy offered by Sainsbury’s theory. 2. As a termist, a realist about universals, and a direct realist, it make sense to me to say that when Othello judges that Desdemona loves Cassio, he doesn’t just stand related to Desdemona and Cassio – he also stands related to love. Sainsbury makes sense of that. He stands related in a relation that predicates it of Desdemona and Cassio. For that reason, I think that Sainsbury’s theory stays truer to the spirit of the philosophical program from which the MRTJ initially arose; a program that I tried to motivate in part I. In fact, if you do have these philosophical commitments, you might regard MacBride’s theory as little more than a notational variant of Sainsbury’s theory – focussing on a compound verb ‘. . . judges that . . . is R-related to . . .’ rather than the simple verb ‘. . . judges that . . .’ Moving forward, I adopt Sainsbury’s response to the representationconcern. However, it’s worth nothing that my extension of the MRTJ to molecular propositions – which I develop in the next chapter – can easily be stated in accord with MacBride’s version of the MRTJ. I can therefore say this: to people less convinced than I am about termism, or about the existence of universals, I offer MacBride’s intriguing precisification of Russell’s 1918-MRTJ as a viable alternative.

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Notes 1 You might think that this sort of concern is better attributed to Gilbert Ryle. See footnote 3, in the previous chapter for a response to such a thought. But whoever this concern should be attributed to – Wittgenstein, or Ryle, or both of them – it’s a concern that demands a response. 2 We should allow that some object-relations will be variably polyadic, allowing for a range of adicities from n to k. We would then merely have to add that to judge that such a relation holds is to stand in a relation of adicity no greater than k+2. 3 Another, much more radical, strategy is to attack the significance constraint itself—see Magidor (2009). On her view even syntactical confusions don’t generate nonsense (even if they generate ambiguity). 4 ‘Combine’ is Hossack’s technical term, since he rejects the notion that facts are merelogically complex and therefore constituted by universals and particulars – instead, every fact instantiates a primitive combination relation to such entities. 5 See also his book (MacBride, 2017). 6 See also (Stevens, 2003) 7 For more on the difference between the provision of truth-conditions and the explanation of representation, see chapter 11, §1. 8 In this section, I make extensive use of Davidson’s first and last ‘proper book’ (as its sleeve notes describe it): Truth and Predication (2005). The book brings together old lectures of Davidson’s and serves to explain his account of predication in the context of the problem of unity more thoroughly than many of his other texts. Though it hadn’t been written when Sainsbury (1996) defended Russell’s MRTJ, it still serves as a good introduction to the insights that Sainsbury was helping himself to. 9 This is the sort of language that Lewis calls ‘Lagadonian’ – (Lewis, 1986, pp. 145–6) 10 I’m now going to drop the constant qualification that I’m talking about directly realistic judgement. Of course, a mind can use anything it wants to represent anything else that it wants. But if a judgement is going to live up to the doctrine of direct realism, it will have to adhere to the sort of Lagadonian language for judgement that these Davidsonian style axioms set out, see footnote 9. In what follows, when I talk about judgements, I’m talking about judgements that embody the doctrine of direct realism, which I suggest, along with that doctrine, are cognitively fundamental. 11 The philosophy of mind, presumably, might not want to leave this mental power as a primitive one, but it does seem to be a power that the philosophy of language can take for granted more readily than the power of words or non-mental entities to represent all on their own. 12 See chapter 6, footnote 11.

9

Molecular Propositions

The only recurring historical critique of the MRTJ that we’re yet to have found a response for, is the concern that it cannot extend to account for molecular judgements. This concern has generally taken the form of two accusations. The first, which I call the fundamental concern, is that the MRTJ can’t explain away molecular propositions without readmitting atomic propositions into its ontology .1 A less common variation, which I shall call the cosmetic concern, admits that the MRTJ can escape ontological commitment to all varieties of proposition, but that it only gets rid of molecular propositions at an unsightly metaphysical and/or epistemological cost (Sainsbury , for instance, raises just such a worry). This chapter aims to demonstrate that neither of these accusations is grounded or fair.

§1: Motivating the Fundamental Concern We need to distinguish between two sorts of molecular proposition. One variety is constructed by linking other propositions together with one of the logical connectives (the limiting case of this variety of molecularity doesn’t actually link propositions together but takes a proposition and prefaces it with the negation). I call this first variety molecularity1. Molecular2 propositions, the second variety, are any proposition in which a variable is bound by a quantifier. An atomic proposition is one that is neither moelcular1 nor molecular2. What I have called the fundamental concern is the claim that the MRTJ can deal with neither sort of molecularity. We saw in chapter 7, that Russell was worried in 1913 that his MRTJ would struggle to account for molecularity1. This may even be why he abandoned his Theory of Knowledge manuscript. But as we saw there, this worry seemed to stem merely from the eccentric conception of relational direction that he had accepted in that year. As soon as we allow that the relation of judgement orders its relata, then the fundamental concern with molecularity1 seems to evaporate (see chapter 7, §§2.6, 3 and 5.1).2 Indeed, Russell soon reverted to the view that relations do relate in

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a direction,3 and this may be why he continued to subscribe to the MRTJ for a number of years after the collapse of the 1913 manuscripts. However, there are other routes to the fundamental concern. We feel that when we assert a disjunction, for example, that Ga or Fb, the atomic constituents of that disjunction exist prior to the cognitive act of my asserting their disjunction. It seems to us that when we make such a judgement, we stand related to the disjuncts, (Ga and Fb) not merely to their disjointed parts (G, F, a, b) – it is their disjunction that we assert. The MRTJ has to ignore this phenomenology entirely. To respect the phenomenology of molecular judgement, we would seemingly have to readmit atomic propositions into our ontology. This is, as we saw, the powerful criticism that Rosalind Carey (2007, p. 47) puts forward in Wittgenstein’s name. The other side of our fundamental concern is that the MRTJ completely fails to deal with molecuarlity2. According to Tom Baldwin (2003, p. 431), this is the decisive failure of the MRTJ. Soames (2015, pp. 447–8) calls it a ‘devastating problem’. When I assert that ‘Desdemona loves Cassio’, I stand related to the referents of the expressions that form my sentence. However, what happens when I judge that ‘(∃x) (x is immortal)?’ What is the referent of ‘x’? These problems seem intractable, and they are only compounded when we introduce multiple generality. When I assert that ‘(∃x) (∀y) (x loves y)’, how do the referents of ‘x’ and ‘y’ differ? In the next two sections, I look at attempts of others to overcome the fundamental concern, attempts that, if they work at all, merely serve to motivate cosmetic concerns. If you’re less interested in the history of the fundamental concern, and more interested to hear a new, ontologically economic and (hopefully) epistemically plausible solution to it, you may want to skip straight to section §4.

§2: The Cosmetic Concern: Metaphysical Ramifications As early as 1919, Dorothy Wrinch levelled the first challenge against our fundamental concern (Wrinch, 1919). Unfortunately, her defence lumbers the MRTJ, at the very least, with what I have called the cosmetic concern. Wrinch’s attempt is historically significant as she had been Russell’s research assistant whilst he was incarcerated for his anti-war agitations.4 At that time, Russell was still grappling with the MRTJ, in the hope that he could find a way of salvaging it. Though circumstantial, this historical consideration suggests that her work on this topic may bear some relation to Russell’s own deliberations. With recourse to a dizzying variety of logical forms and hitherto unheard of universals, Wrinch tries to demonstrate that the MRTJ can deal with molecular propositions, but is this theory worth the cost? Think of a logical form as a strange kind of entity: a concatenation of gaps, or spaces. Wrinch, following in Russell’s 1913 wake, wanted

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us to think that such entities exist, however hard it might be to conceive of such a thing. Furthermore, we are told that, ‘Each of the spaces is guarded by one type so that only arguments of certain types can be put in certain spaces’ (Wrinch, 1919, p. 321). When we make a judgement of a certain logical form we are, in a sense, Wrinch argues, plugging certain entities into the spaces of that logical form. There are, of course, different ways in which a form can be filled in. Ways of filling in a form are called evaluations. Wrinch wants to reify each and every way that a form can be evaluated. She calls these universals, evaluators. So the way that we fill in the gaps to yield ‘a loves b’ is an evaluator that exists in Plato’s heaven, as is the way that we would fill in the gaps to yield ‘b loves a’. So far, our theory is ontologically committed to entities consisting of nothing more than gaps, and to a huge array of these new evaluator properties. These are enough resources, Wrinch argues, to deal with molecularity1. When I judge that Ga or Fb, Wrinch accepts that I needn’t actually stand directly related to G, F, a, or to b. Instead, my judgement stands me related to the logical form – – V – –, and to the evaluator that would fill that form in so as to yield Ga or Fb. The judgement that Fa or Gb involves a completely different evaluator. In summation: atomic propositions and molecular1 propositions don’t have to exist; molecular1 propositional attitudes are multiple relations between a mind, a form and an evaluator. To deal with molecularity2, Wrinch needs to introduce the notion of a partial evaluation. We can arrive at the formula ‘x is wise’ by partially evaluating the form ‘– –’ (plugging wisdom into the second slot, whilst leaving the first slot vacant). Wrinch calls that way of filling in a form, a partial evaluation. Wrinch then introduces two more universals – generalisation and particularisation (henceforth G and P). When you generalise a partially evaluated form, you assert that any way of completing the evaluation will yield a true judgement. When you particuarlise a partially evaluated form, you assert that there is at least one way of completing the evaluation so as to yield a true judgement. Molecular2 judgements relate minds to forms, partial evaluators and to G or to P. It would go beyond the remit of this chapter to explain, in any level of detail, how Wrinch tries to deal with multiple generality. However, I should point out that, in order to explain the difference between judging that ‘(∃x)(∀y)(xRy)’ and judging that ‘(∃x)(∀y)(yRx)’, Wrinch is eventually forced to accept that xξy is a distinct logical form from yξx. Given my declared comfort with the existence of universals, I might not credibly be able to deny that partial and complete ways of filling in strings are the sort of things that can exist. But the ontological profligacy and quixotic posits don’t end with the reification of these ways of filling things in. A much more pressing ontological concern, even for realists about universals, would focus on what these strings are. What is a string of gaps? What is a type-restricted gap? How do two equally long stings of

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gaps with identical type restrictions differ from one another? These are, at the very least, cosmetic worries about the ontological commitments of Wrinch’s MRTJ. In addition to our cosmetic worries about the nature of strings of gaps, we have to reintroduce all of the other issues with logical forms that we were hoping to have left behind in chapter 7. These issues threaten to saddle us not merely with cosmetic concerns but with outright incoherence. For instance, if logical forms are a string of type-restricted gaps, then they are complex. They have constituent parts. However, if a logical form is defined as the way in which a complex is strung together, then logical forms, being complex, will themselves need to have logical forms. This generates a regress. We should like to say that logical forms are simple, so as to avoid this regress, but if they’re simple, then they can’t play the role that Wrinch requires them to play, since they won’t have the parts in to which we can plug things.5 If Wrinch’s theory can answer these questions, and thereby overcome the fundamental concern that we raised with the MRTJ, then the metaphysical picture that emerges, with its strange gappy entities, is likely to offend against all sorts of metaphysical intuitions (not to mention the epistemological issues of being acquainted with these strange entities) – even for realists about universals. This fact gives succour to the cosmetic concern. Nino Cocchiarella (1980, p. 104) suggests that Russell’s own (sketchy and incomplete) extension of the MRTJ to deal with molecularity (Russell and Whitehead, 1910–13, pp. 44–5), would have relied upon a massive ontology of propositional functions, understood as a species of universal. This supports my contention that Wrinch’s extension is a good approximation of the direction in which Russell’s own thought was leading. Universals wouldn’t have been enough. He would have had to posit strange gappy entities, such that the universals could be ways of plugging them in. Russell’s own preferred account, so understood, would seem to suffer from similar cosmetic worries to those that beset Wrinch’s account (in fact, I assume that the two accounts would have been, to all intents and purposes, the same).

§3: The Cosmetic Concern: Epistemological Ramifications Keith Hossack (2007) has demonstrated that the MRTJ can reach complete expressive adequacy with a good deal of ontological economy in comparison to Wrinch. He can do without her strings of gaps. Unfortunately, as we shall see, the epistemic commitments that Hossack’s theory eventually forces us into are, at best, unsightly and improbable. Hossack’s MRTJ is related to his firm commitment to the existence of facts. I want to ignore that commitment in the following

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presentation – as we’ve seen (chapter 7, §5.2), the MRTJ itself doesn’t really demand an ontology of facts despite Russell’s (and Hossack’s) own views on the matter. The Hossakian commitment that I do want to explore is his commitment to ten logical universals and to the epistemological claim that we’re actually acquainted with all of them. §3.1: Hossack and Molecular1 Propositions Five universals are appealed to by Hossack’s MRTJ to account for molecular1 propositions. Each of the five classical logical connectives are treated, by Hossack, as universals. Four of them are relations that can hold between vectors. Negation, on the other hand, is a property held by one vector at a time. Vectors, of course, are not to be confused with propositions. A proposition would be an entity that exists in its own right. The MRTJ does away with propositions. A vector is just a disparate plurality, with an order – like a queue of people, which we needn’t think of as an entity in its own right, so much as people lined up. Here are the five universals that Hossack appeals to, with their associated rules for appearing in judgements: Conjunction 1. This universal can appear as the object-relation of a judgement only if followed by an n-adic property, n futher entities; then by an m-adic property and m futher entities. 2. Any judgement that features conjunction as its object-relation will be true iff the n entities instantiate (in their order) the n-adic property, and, the m entities instantiate (in their order) the m-adic property. Disjunction 1. This universal can appear as the object-relation of a judgement only if followed by an n-adic property, n futher entities, and then by an m-adic property, and m futher entities. 2. Any judgement that features disjunction as its object-relation will be true iff the n entities instantiate (in their order) the n-adic property, or, the m entities instantiate (in their order) the m-adic property. Conditional 1. This universal can appear as the object-relation of a judgement only if followed by an n-adic property, n futher entities, and then by an m-adic property, and m futher entities. 2. Any judgement that features conditional as its object-relation will be true iff, if the n entities instantiate (in their order) the n-adic property, then the m entities instantiate (in their order) the m-adic property.

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Equivalence 1. This universal can appear as the object-relation of a judgement only if followed by an n-adic property, n futher entities, and then by an m-adic property, and m futher entities. 2. Any judgement that features equivalence as its object-relation will be true iff, the n entities instantiate (in their order) the n-adic property iff the m entities instantiate (in their order) the m-adic property. Negation 1. This universal can appear as the object-relation of a judgement only if followed by an n-adic property and n futher entities. 2. Any judgement that features negation as its object-relation will be true iff the n entities do not instantiate (in their order) the n-adic property. It’s clear from this treatment that the assertion of any molecular1 proposition can be analysed as a multiple relation with recourse to these five universals. Because the five logical operators are just universals in their own right, universals that relate vectors, the aforementioned rules allow for the recursive application of logical operators. The ordered-many, disjunction, G, a, F, b, when judged, is what gives rise to the assertion that Ga⌵Fb. But if you judge that that ordered-many is itself related by disjunction to the vector, H, c, then you give rise to the assertion that ((Ga⌵Fb)⌵Hc) (although, as we’ll see in §4.2, Hossack’s theory doesn’t seem to escape from certain ambiguities of scope – at least, not without further ado6). Wrinch gives rise to the cosmetic concern when she, like Russell before her, relies upon the weird and wonderful, if at all coherent, world of logical forms. Hossack seems to have no such problem. A realist about universals, which any adherent of the classical MRTJ will be (ignoring, for the moment, MacBride’s 1918-MRTJ), is likely to have little problem accepting the existence of the five logical universals that we’ve just listed. Furthermore, if you’re capable of asserting a conditional proposition, then you must already have the cognitive ability to grasp the relation of being an antecedent to a consequent. Thus the epistemology is quite straightforward too. If these universals exist, then we probably are acquainted with them, which in turn allows us to make molecular1 assertions. In dealing with molecularity1, Hossack avoids the fundamental concern and the cosmetic concern.7 Unfortunately, when Hossack turns to molecularity2, the waters quickly become murkier, if not metaphysically speaking, then epistemologically. §3.2: Quine and the Variable When I assert that (∀x)(x is wise), what are the constituents of my judgement? What entity corresponds to the variable, ‘x’ and what to the

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quantifier? Quine (1960) argues that variables and their quantifiers can always be paraphrased away. Thus, according to Quine, we have no reason to think that variables contribute any specific entity to a judgement. This is an insight that Hossack hoped to help himself to. In order to paraphrase variables away, Quine found reason to posit four logical operators. The first operator, Quine calls ‘derelitivisation’ or ‘Der’. This operator turns two placed predicates into one placed predicates. Take the two-place predicate ‘B’ – the transitive verb ‘bites’ – Der transforms B(xy) into Der-B(x) – it transform the verb ‘bites’ into the verb ‘bites something’ – literally ‘x bites something’. Der can be recursively applied. It can turn one placed predicates into zero placed predicates (i.e., sentences). Der-Der-B is the sentence ‘something bites something’. The following two propositions are quite distinct: ‘(∃x)(∃y)(B(xy))’; ‘(∃x)(∃y) (B(yx))’. One says that something bites something; the other says that something is bitten by something. Thus the order of the variables matter. Wrinch needed different logical forms, with different arrangements of variables, to account for this sort of difference, which led her to the somewhat bizarre conclusion that xξy and yξx are different entities. Quine accounts for the difference without using variables. Quine adds an operator of inversion. ‘Inv-B(xy)’ means that B(yx), thus Inv transforms the verb from ‘bites’ to ‘is bitten by’. We can now paraphrase away the variables from both of the distinct propositions without losing what the order of the variables seemed to designate: (∃x)(∃y)(B(xy)) has, as we have already seen, become ‘Der-Der-B’, and (∃x)(∃y) (B(yx)) has become ‘Der-Der-Inv-B’. A variable repeated can have special significance. ‘(∃y)(B(yy))’ states that something bites itself. This example prompts the adoption of a third operator, reflection. This operator turns the two-place predicate ‘bites’ into the one-place predicate ‘bites self.’ ‘Der-Ref-B’ will mean that something bites itself. When there are more than two variables, things become a little more complicated. Our three operators have to become four: Derelativisation: Der-P(x1, . . ., xn-1) if and only if there is something, xn, such that P(x1, . . ., xn-1, xn). Major Inversion: Inv-P(x1, . . ., xn), if and only if P(xn, x1, . . ., xn-1). Minor Inversion: inv-P(x1, . . ., xn), if and only if P(x1, . . ., xn-2, xn, xn-1). Reflection: Ref-P(x1, . . ., xn-1) if and only if P(x1, . . ., xn-1, xn-1). Major Inversion has the effect of pushing the first variable to the end of the list of variables. Minor Inversion simply swaps the last two variables round: It is easily seen that major and minor inversion suffice to permute any number of subjects into any desired order; and then reflection suffices to resolve repetitions, when they are permuted to terminal

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Once Quine has shown us that variables and the machinery that binds them can be eliminated, the door has been opened for an account of molecular2 propositions in terms of the MRTJ. Hossack saw this door and walked right through it. §3.3: Hossack and Molecular2 Propositions Hossack takes Quine’s four innovations and reifies them. They are properties. When I judge that someone invented the toaster, for example, my judgement is about the property being the inventor of the toaster: I judge that this first property instantiates the further property of derelitivisation. My judgement has two objects: Der and the property of being the inventor of the toaster. Derelitivisation only gets rid of variables bound by existential quantifiers. Hossack introduces an extra operator to eliminate variables bound by universal quantifiers. Even though the two quantifiers can be inter-defined, it would be arbitrary to think that reality itself contained one but not the other.8 Unfortunately, Hossack’s method for getting rid of molecular propositions gives rise to new manifestations of the cosmetic concern: the metaphysical tools to which Hossack’s theory appeals may strike one to be readily acceptable to a realist (although you might worry that Major Inversion, Minor Inversion and Reflection seem a little too gerrymandered to be viable contenders for the status of logically and metaphysically basic universals9); but even if you accept all of this metaphysical machinery, new epistemic concerns arise. It is generally contended that you have to be acquainted with each of the constituents of your judgements. To believe that anyone who is capable of forming molecular2 judgements must be directly acquainted with all of Hossack’s logical universals beggars belief. Does the fact that I can deal with multiple generality mean that I was already acquainted with major and minor inversion? This is a strange epistemological commitment indeed. I didn’t think that I had ever come across these logical objects until I read about them in Hossack’s book, but apparently, I’ve been acquainted with them ever since I mastered the semantic ability to talk and think in generalities! Nobody, as far as I’m aware, had thought about these logical operations before Quine, and we’re now supposed to believe that people have always been epistemically acquainted with their corresponding logical objects. This is easier to accept regarding some of the operators than others. Indeed, it may seem plausible to say that acquaintance with a relation entails acquaintance with its inverse. To know the relation x

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bites y, might be sufficient for knowing the relation y was bitten by x, and vice versa. To understand that you can’t be acquainted with the one, without being acquainted with the other, and to understand the relationship between these two relations, might be all that we need in order to be acquainted with the universal inversion. But are we all cognisant of the distinction between major and minor inversion? And, do we really have to be in order to deal in multiple generalities? This certainly seems to be an epistemological cost to Hossack’s reduction of molecular propositions. Hossack might argue that his theory is worth this cost. He might say, ‘So you didn’t know that you were always acquainted with major inversion, but, it turns out, you were!’ This becomes a somewhat subjective question. Do you think that the theory is worth such an epistemological price? You might think that I’m being unfair to Hossack. Acquaintance with these logical objects isn’t the horrific price that I’ve turned it into – or, you might reject the principle that one needs to be acquainted with the constituents of one’s own judgements. But let us not forget, that there’s a good chance that I’ve been too charitable to both Wrinch and Hossack. If Wrinch’s gappy metaphysical posits really turn out to engender regress or to host some other form of incoherence, then her theory doesn’t just fail cosmetically, it fails fundamentally. Likewise, if Hossack’s theory cannot avoid the scope ambiguities that I shall develop in §4.2, then whether or not his theory suffers from unsightly epistemological commitments, and thereby fails cosmetically, it will turn out to have failed fundamentally. Wrinch’s extension is perhaps the most faithful to Russell’s own developing thoughts on the matter. Hossack’s extension is perhaps the most elegant in the subsequent literature. But neither of them provides us with a theory that clearly escapes the dual problem of the fundamental and the cosmetic concern.

§4: A New Extension of the MRTJ10 In this section, I develop the claim that the MRTJ can deal with molecularity without any peculiar metaphysical or epistemological commitments. §4.1: Molecularity1 If we take Carey’s phenomenological critique seriously, we’ll want to guarantee that, in some sense or other, the propositions Ga and Fb are prior to any act of asserting their disjunction. Surely, you can’t truly assert a disjunction unless you already understand both of the disjuncts.11 But accepting this much doesn’t mean that we have to accept that atomic propositions exist. Understanding is, itself, a propositional attitude. According to the MRTJ, this attitude isn’t a binary relation that stands minds related to propositions. It is, instead, a multiple relation.

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The multiple relation of understanding relates a mind, in a specific order, to the constituents of the ‘proposition’ it understands. It predicates, for the sake of understanding, its object-relation of the remaining objects in a specific order. So when you understand the proposition Ga, you stand related, via the relation of understanding, to G and to a. You predicate, for the sake of understanding, G of a. This gives rise to a state of affairs: the state of your understanding Ga, in which you are related, by the relation of understanding, to G and to a. Call this state of affairs A. You also understand the proposition Fb. That is to say, there is a state of affairs, call it state of affairs B, in which you stand related by the relation of understanding to F and to b. All that Carey has forced us to accept is that states of affairs A and B have to exist before you can assert the disjunction, Ga or Fb. She hasn’t yet forced us to accept that any atomic propositions have to exist. All that we’ve been forced to accept, so far, into our ontology, are states of affairs in which a mind is related to various object-terms, by the multiple relation of understanding. Let’s call this type of state, an understanding-state. Once we accept that these states of affairs exist, a path opens out before us. Understanding-states exist and are now available to play the role of object-terms in judgements. I want to posit ten new cognitive acts: conjunctive-judgement, conjunctive-understanding, disjunctive-judgement, disjunctive-understanding, conditional-judgement, conditional-understanding, equivalence-judgement, equivalenceunderstanding, negation-judgement and negation-understanding.12 I define them as follows: Conjunction 1. Conjunctive-understanding is a multiple relation between a mind and two of its understanding-states. When a mind stands related by this relation to state A and to state B, which I defined earlier, that mind thereby understands the conjunction Ga & Fb. This relation gives rise to a new understanding-state. 2. Conjunctive-judgement is a multiple relation between a mind and two of its understanding-states. When a mind stands related by this relation to state A and to state B, that mind thereby asserts the conjunction Ga & Fb. Disjunction 1. Disjunctive-understanding is a multiple relation between a mind and two of its understanding-states. When a mind stands related by this relation to state A and to state B, that mind thereby understands the disjunction Ga ∨ Fb. This relation gives rise to a new understanding-state.

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2. Disjunctive-judgement is a multiple relation between a mind and two of its understanding-states. When a mind stands related by this relation to state A and to state B, that mind thereby asserts the disjunction Ga ∨ Fb. Conditional 1. Conditional-understanding is a multiple relation between a mind and two of its understanding-states. When a mind stands related by this relation to state A and to state B, in that order, that mind thereby understands the conditional Ga → Fb. This relation gives rise to a new understanding-state. 2. Conditional-judgement is a multiple relation between a mind and two of its understanding-states. When a mind stands related by this relation to state A and to state B, in that order, that mind thereby asserts the conditional Ga → Fb. Equivalence 1. Equivalence-understanding is a multiple relation between a mind and two of its understanding-states. When a mind stands related by this relation to state A and to state B, that mind thereby understands the claim Ga ↔ Fb. This relation gives rise to a new understanding-state. 2. Conditional-judgement is a multiple relation between a mind and two of its understanding-states. When a mind stands related by this relation to state A and to state B, that mind thereby asserts the claim Ga ↔ Fb. Negation 1. Negation-understanding is a binary relation between a mind and one of its understanding-states. When a mind stands related by this relation to state A, that mind thereby understands the claim ¬Ga. This relation gives rise to a new understanding-state. 2. Negation-judgement is a binary relation between a mind and one of its understanding-states. When a mind stands related by this relation to state A, that mind thereby asserts the claim ¬Ga. When one looks at a claim such as ‘(Ga ∨ Fb) & Rc’, one has to notice the role played by the brackets. The brackets indicate that the proposition has to be constructed in stages and in a certain order. First, you have to construct the disjunction in the brackets, only then can you go about building the conjunction. If you go about trying to build this proposition in a different order, you’ll end up with a different proposition, such as Ga ∨ (Fb & Rc). My suggestion that each of the logical connectives be

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analysed in terms of the aforementioned ten cognitive acts has two major benefits: (1) it meets Carey’s phenomenological concern – the disjuncts pre-exist the disjunction in the sense that you have to understand the disjuncts separately before you can use those understanding-states to create the disjunction; (2) it respects the fact, indicated by brackets in our modern logical notation, that complex molecular propositions have to be built up in stages, as I will now briefly illustrate. To judge that (Ga ∨ Fb) & Rs, on my account, is to perform the following sequence of cognitive acts: one first needs to stand in the multiple relation of understanding to the ordered constituents of the first disjunct; this, as we have seen, is what gives rise to what we’ve called state of affairs A; then one needs to stand in the multiple relation of understanding to the ordered constituents of the second disjunct; this, as we have seen, is what gives rise to what we’ve called state of affairs B; then one has to stand in the disjunctive-understanding relation to A and B; this gives rise to a new understanding-state, call it C; one then has to stand in the relation of understanding to R and s, in that order; this gives rise to yet another understanding-state, call it D; only then can one assert the conjunction, by standing in the relation of conjunctive-judgement to understanding-states C and D. We have now accounted for molecularity1 within the rubric of the MRTJ. At no point have we had to admit propositions into our ontology. In fact, we’ve improved upon previous attempts in two respects: (1) we’ve replaced metaphysically and/or epistemologically unsightly logical objects with plausible cognitive acts and (2) we’ve been able to respect Carey’s phenomenological concern that when we judge, we feel as if we stand related to the pre-existent atoms of the molecular proposition; we recognise that this phenomenology is given rise to by the fact that understanding-states have to proceed molecular judgements. This isn’t some ad hoc stipulation, equivalent to a side-constraint. This is, rather, a feature of the nature of molecular propositional content. The account certainly raises some concerns of its own. To what extent is it true to the spirit that is supposed to motivate the MRTJ in the first place? To what extent is it a retreat into psychologism? To what extent is the process of stage-by-stage judgement construction consonant with the phenomenology of judging? These concerns I will address later. One concern I’ll try to respond to now is this: there are all sorts of ways of defining the logical connectives. The five that I’m using can be defined in terms of each other, and they can be reduced to a single Scheffer stroke or dagger. Why should I believe that the mind has these five pairs of cognitive attitudes, corresponding to the five classical operators, when other combinations of attitudes, modelled on different sets of operators, would be equally expressive? My response is that this is an empirical question for the cognitive sciences to answer. My theory is merely that, instead of using logical objects to

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make molecular judgements, we have a number of cognitive attitudes that do the same work. Which of those attitudes are basic (i.e., which we’re born with), is a question for the empirical sciences. I assume that we have the five pairs of attitudes I canvassed earlier, at least by the time that we master the use of the logical connectives that they’re modelled upon. In fact, I imagine that we have more pairs of attitudes to correspond to other operators that we use (such as the counterfactual conditional). The exact number of attitudes used might differ from mind to mind depending upon the extent to which our cognitive architectures can differ from birth, and upon the various things that we learn as we develop. Perhaps some of these attitudes only go online later on in our cognitive development. Alternatively, perhaps we’re all born with a Scheffer stroke (understanding and judgement) attitude in our cognitive toolkit, and that’s all we ever use (or a Wittgenstein-like N-operator that can model the quantifiers as well). However, even if that were the case, my basic extension of the MRTJ would still be the right one: an extension that replaces logical objects with cognitive attitudes. For the sake of illustration, I’m taking the five classical logical connectives, in order to showcase how any putative logical relation could be replaced with a cognitive act. Nothing much really hangs on how many pairs of attitudes we actually have, as long as they are modelled on some sufficiently expressive set of logical operators.13 Assuming that the quantifiers are modelled by distinct attitudes (an assumption that can be discharged if the cognitive sciences discover that we actually use something like an N-operator module), I now move on to make sense of molecularity2. §4.2: Molecularity2 Michael Dummett (1973) celebrates the genius of Frege’s quantifier-variable notation. Focusing on the phrase ‘(2 + 3) × 6’, Dummett notes what we’ve already noted regarding the role of brackets, and how they teach us that it ‘is necessary to jettison the original natural idea that the linear ordering of symbols is a true guide to the process of formation of complex expressions’ (Dummett, 1973, p. 10). Complex expressions have to be built up in successive stages, and in a particular order. Frege’s quantifier-variable notation, with which he expressed general claims, made an unprecedented advance. It made apparent the correct constructional history of general sentences. Take the sentence, ‘Everybody envies somebody’. Multiple generality is involved, and it’s not clear which general term should be afforded the greater scope. Historically, difficulty arose in such cases because, unlike Frege, earlier thinkers didn’t try to build this proposition up in stages. They considered it as ‘being constructed simultaneously out of its three components, the relational expression here represented by the verb, and the two signs of generality’

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(Dummett, 1973). Russell was aware, even before he discovered, understood or adopted, Frege’s quantifier-variable notation, that his difficulties with multiple generality would be alleviated if we were to conceive of such phrases as ‘obtained by successive steps’ (Russell, 1903, p. 94). The advance that Frege had made beyond Russell was to fill in the detail of these successive steps. According to Frege, we have to start with a sentence with no generality. Dummett’s example is ‘Peter envies John.’ From this sentence, we can extract a one-place predicate, ‘Peter envies ξ’. We then combine this predicate with the sign of generality, ‘somebody’, to yield the sentence, ‘Peter envies somebody.’ Only then can we form the predicate ‘ξ envies somebody’, by removing the remaining proper name. Combining this predicate with another sign of generality, ‘everybody’, yields the sentence ‘everybody envies somebody’. This order of construction is made perspicuous by Frege’s notation: (∀x)(∃y)(Exy).14 The universal quantifier is applied last. It has widest scope. This is signified by its being the most left flanking of the quantifiers. The existential quantifier needs to be applied first. If we constructed this expression in a different order, it would have had a different meaning: instead of claiming that everyone has someone that they envy, we would have claimed that there is someone who is envied by everyone, and the order of Frege’s quantificational symbols would have signalled this fact: (∃y)(∀x)(Exy). Propositions involving generality really are molecular. They really are constructed out of atomic propositions in successive stages. Molecular2 propositions have a constructional history, displayed unambiguously by Frege’s notation. You cannot understand a molecular2 proposition – you cannot know its truth conditions – without understanding (i.e., knowing the truth conditions) of at least one atomic proposition from which it could be constructed. This is why it makes sense to call molecular2 propositions molecular: they are, indeed, constructed out of atomic ones. Taking these lessons to heart, we can now extend our account of judgement to account for molecularity2 with the addition of four new cognitive acts: existential-understanding, existential-judgement, universalunderstanding and universal-judgement: one pair of acts for each of the quantifiers.15 When I understand that Peter envies John, the following relation obtains: Understanding (Me, Envy, Peter, John), or for short: U(m,E,p,j). That relation, the relation of understanding, relating me to those three objects, gives rise to an understanding-state. Its constituents are Understanding, me, Envy, Peter and John. Its source of unity is the relating-relation of understanding. Take the state, U(m,E,p,j) . I can perform the following operation upon it: I can say that what I understood is true for at least one substitution instance of John. This operation corresponds to removing the name ‘John’ from ‘Peter envies John’ and replacing it by a variable bound by the existential quantifier. This operation is a relation between me, the

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understanding-state in question and John. Call the operation in question existential-judgement: ‘∃j’. It is a triadic relation between a mind, an understanding-state, and one of the constituents in the constructional history of that state, in this case: ∃j(m, U(m,E,p,j) , j). This operation can be recursively applied. ‘∃u’ symbolises the relation of existential-understanding. This is the operation of understanding the truth conditions imposed by ∃j. When I understand the proposition that someone is envied by Peter, I stand in the following relation: ∃u(m, U(m,E,p,j) , j). This relation gives rise to a new understanding-state. The triadic operation of existential-judgement can be re-applied to this new understanding-state so as to yield: ∃j(m, ∃u(m, U(m,E,p,j) , j , p); this is the judgement that somebody envies somebody. It was constructed in successive stages, from an act of atomic understanding, that mirror Frege’s insight. The relations of universal-judgement (∀j) and universal-understanding u (∀ ) exactly mirror the relations of existential-judgement and existentialunderstanding, but they replace the universal quantifier instead of replacing the existential quantifier. The MRTJ gets rid of all propositions. However, regarding molecular propositions, there isn’t just one cognitive act responsible for doing so. When I said, at the end of the last chapter, that we only want to posit one assertion relation – that was at the level of atomic assertion. At the molecular level, each logical operator (connectives and quantifiers alike – or each logical operator that we actually use) will correspond to a unique cognitive act which can be recursively applied. Molecular propositions arise from cognitive acts performed upon previous states of understanding. This seems right: how could one assert a molecular proposition unless one already understands its atomic constituents? How can one assert a general proposition, if one understands none of its substitution instances? Writing the constructional history of molecular propositions into our theory of judgement will also help us to guard against ambiguities of scope; just as Frege’s notation helped him to steer clear of quantifier scope ambiguity. It’s not clear to me that Hossack, for example, can escape from scope ambiguity. Hossack accepts the existence of multigrade universals that accept other universals as objects. The relation of judgement, on Hossack’s account, would be one of them. Another one, coming from his account of facts, is his relation of combination – the relation that holds between a fact and its ‘constituents’.16 Now consider the following two conjunctions (using Greek letters as variables for universals): 1. (Φ(Ψ, Ξ, Γ) & Θ(Σ)) 2. (Φ(Ψ, Ξ) & Γ(Θ, Σ)) To assert either of these conjunctions, of a form that Hossack – with his multigrade universals that accept other universals as objects, would have

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to accept – requires a judgement between a subject and the following vector: &, Φ, Ψ, Ξ, Γ, Θ, Σ – a vector which turns out to be ambiguous as between 1 and 2. You might think we could avoid this problem by putting the relation of conjunction in the middle of the vector; as it were, between the two conjuncts; shifting its position between 1 and 2. This wouldn’t remove ambiguity, it would, rather, make things worse. Hossack needs the logical universals to be at the beginning of the vector in order to illustrate which logical connective has the widest scope when the proposition in question contains more than one connective. Even if there is only one logical connective in the judgement, if it wasn’t first in the list, how would we know if it was appearing as a logical connective or as one of the regular objects of the judgement (perhaps conjunction is one of the universals that is being judged to instantiate the property Φ, alongside Ψ, Ξ, Γ, Θ, and Σ))? This problem arises, like pre-Fregean problems with generality, because we’re trying to stick all of the pieces of the puzzle together at once. Given that some of the items in this ordered-many are variably polyadic, it really isn’t clear how to put them all together. On my suggestion, we begin with atomic judgements, which don’t admit of scope ambiguity, and only then do we build molecular propositions up in stages – that is to say, we build our conjuncts first, and only then do we go about building conjunctions. Failure to avoid scope ambiguity might entail that Hossack’s MRTJ fails to avoid the fundamental concern after all.17 One might raise the following concern:18 it simply isn’t plausible to say that I arrive at a molecular judgement in a succession of distinct cognitive acts. Is it really plausible that understanding a quantified proposition requires a previous act of understanding of one of its substitution instances? When I assert that everyone loves someone, I have no inclination that I have, first of all, searched through my mind for a substitution instance from which to build up this claim. Fortunately, I can defend my theory on the following lines. Given the stunning success of Frege’s quantifier-variable notation, it seems to be a truism that one cannot build, let alone understand, a general claim, if one cannot understand any of its substitution instances. My claim regarding molecularity2 reduces to the following: when you make a general claim, you are unconsciously utilising your own states of understanding. You build your general claims up out of substitution instances that you already understand. You don’t think about doing this, and you don’t pay attention to which substitution instance you use because it’s totally arbitrary which one you use; to pay attention would be to miss the point. The cosmetic concern states that the MRTJ cannot get rid of molecular propositions without nasty ramifications. Wrinch’s theory, if it survives the fundamental concern, posits weird gappy objects. Hossack’s theory, if it survives the fundamental concern, forces us to accept that all lay-people are actually acquainted with some of the most surprising

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posits of Quine’s logical imagination, reified. My claim is this: exchanging weird and wonderful objects and universals for an array of plausible cognitive powers is enough to save the MRTJ from both the fundamental concern and the cosmetic concern.19 Contrary to generations of scholarship that have dogmatically taught otherwise, the MRTJ has no problem accounting for molecularity, and can do so at no extra cost.20

§5: Criticism and Reply Having presented these ideas to a number of audiences, and having benefited from the comments of anonymous reviewers, I include a final section, in this chapter, in which I list and reply to criticisms that could be made of my extension of the MRTJ. Criticism 1 The main reason that you reject Hossack’s theory is because of its appeal to universals with which we’re not acquainted. But it’s not obvious that we are acquainted with our own cognitive states of understanding, conceived of as single items to which we then adopt differential judgemental attitudes. It’s not at all obvious that we can introspect and see such states within. Reply 1 Anybody who really asserts a molecular proposition, say, that if P then Q, upon introspection, will tell you that they understand both P and Q.21 If they didn’t, how could they really claim to be able to assert that if P then Q? Upon introspection, people know that these states of understanding exist. If they know that they exist, even though that knowledge is unconscious until they turn an introspective light inwards, then they must be acquainted with them. Criticism 2 In reply #1, you resort to the unconscious. We are acquainted with these states, you urged, even if we don’t know that we are. But if you can appeal to the ‘unconscious’ to get out of epistemological difficulties, why can’t Hossack? We might not know that we’re acquainted with his special universals, but we are, unconsciously. Reply 2 Anybody who knows what the word ‘Socrates’ means, and who asserts that all men are mortal, already understands the claim ‘Socrates is mortal’

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even if there was no act in which they entertained it. There was a still a state, even if it was only dispositional. That this state is discoverable by introspection is what helps us to steal a march upon Hossack. Introspect however much I might, I will not come to realise that I had a prior acquaintance with his logical universals. But anyone who makes a general claim will realise, upon introspection, that they already understood any substitution, providing they’re already acquainted with the substitute. Criticism 3 On you theory, as stated, when S judges that aRb or bRa, he or she isn’t, as one might suppose, thinking about the manner that a, R and b are arranged in the world, but rather about cognitive states of S. Reply 3 When I judge that P or Q, I’m saying that either the content of what I understand when I understand P, or the content of what I understand when I understand Q, is true. So the molecular judgement really is about the content of, P, and Q, but, we’re not here reifying content, because ‘content’ is a façon de parle cashed out by the multiple relation theory of understanding. Criticism 4 On you view, S’s judging that something is F is conceived of as indexed to a state of S’s understanding that this, that or the other is F. But other thinkers, T and R, cannot similarly judge the exact same thought that something is F because even if we grant that they do have corresponding states of singular understanding, they may concern different individuals, or they may have built them up in slightly different orders, and they cannot anyway be the same states because they belong to different thinkers. So it’s unclear how thinkers can share general thoughts. Reply 4 Criticism 4 maintains that if two molecular propositions have a different constructional history, then they can’t really have the same content. However, the whole beauty of the Fregean quantifier-variable notation is that it doesn’t matter what names you started with once they’ve been deleted and replaced by bound variables. When two people assert the same atomic proposition (using whatever language), they stand related to the world in exactly the same way. The MRTJ can capture that shared metaphysics of meaning. But since molecular propositions have to be built up in stages from things that agents

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already understand, the same is not true for the assertion of molecular propositions – two people’s judgements that (∀x)(∃y)(x envies y), will have distinct constructional histories, but the theory explains how those two histories converge upon the same end result. Given Frege’s insight into the nature of molecularity, this seems right and proper. The complete answer to criticism 4 is this: although the initial starting blocks will likely differ – you start with John envies Paul, and I might start with George envies Ringo – and the second building blocks will certainly differ, given that we cannot share understanding-states – nevertheless, by operating upon what you understand, you generate the predicate John envies x, and existentially quantity over x, while I create the predicate George envies x and existentially quantify over x. At the next stage, we both arrive at the same predicate – that x envies someone – from then on in, it’s clear how we’re entertaining the same thought and saying the same thing about the world. To assert the same molecular proposition is to assert the same thing, but it isn’t automatically to have engaged in the same history of construction; this is a difference between molecular and atomic assertion that falls out of Frege’s insight. Criticism 5 Consider the judgment that Peter envies someone. You might arrive at this judgment by thinking that Peter envies John and generalizing on John. You might also think that Peter envies Kylie and generalise from there, on Kylie. Are we to believe, from the reply to criticism 4 that these end states are the same? That is are we to accept that ∃j(m, U(m,E,p,j) , j) = ∃j(m, U(m,E,p,k) , k)? What is being claimed to be the same? Notice that in Frege’s case, we can say it is the output formula. That is, the same formula results from substituting ‘x’ for ‘a’ in ‘Fa’ (and prefixing by ‘∃x’) as substituting ‘x’ for ‘b’ in ‘Fb’ (and prefixing by ‘∃x’). But I don’t see anything analogous in this case.22 Reply 5 We have two states of assertion: ∃j(m, U(m,E,p,j) , j) and ∃j(m, U(m,E,p,k) , k). In some important sense, my theory requires that they be the same. In what sense? It’s clear that having the same truth conditions won’t be enough. The judgement that 2 + 2 = 4 has the same truth conditions as the judgement that 2 + 3=5, but the two judgements don’t say the same thing. Instead, we require that ∃j(m, U(m,E,p,j) , j) and ∃j(m, U(m,E,p,k) , k) say the same thing. And yet, I think that the fact that we can model the constructional history of both states, using Fregean notation, and that doing so will yield the same formula – namely, ‘(∃x) E(p,x)’ is enough to illustrate that these two states, despite not being identical in terms of their constructional history, do say the same thing.

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Criticism 6 This extension of the MRTJ puts the mind at the heart of logic. The mind creates molecular propositions. Logical connectives get reduced into ways of thinking. This is psychologism. Reply 6 Yes, in a limited sense, this is psychologism; a step back from Frege’s insistence that thoughts are things out there that can be shared (Frege, 1918). However, it’s essential to note that the MRTJ itself, even without my extension to account for molecular proposition, was always a concession to a slightly more psychologistic way of thinking (though Russell wouldn’t have put it that way). Russell now accepts, upon the adoption of the standard MRTJ, that the mind has a special role to play in the genesis of content. And in fact, any metaphysics of meaning has to accept this if it wants to respond to the representation-concern – this is Russell’s key insight. We can defend ourselves against the negative connotations of psychologism when we realise that this mentally created content has objective truth conditions that objectively hold, or objectively fail to hold, quite independently of any mind. This is supposed to remove the sting of ‘psychologism’ – a label that has meant different things to different people at different times, and needn’t always be as toxic as people make out (Jacquette, 1997). According to the MRTJ, people create content, but that content has objective truth conditions. This is all consistent with Russell’s brand of anti-psychologism, even if it constitutes a step towards an alternative and non-toxic form of psychologism in and of itself. I will even accept that Russell would have preferred to cash out my cognitive acts in terms of Platonic universals and mind-independent logical forms, a la Hossack or Wrinch. However, it’s not clear that the fundamental concern can be overcome in that way, or that the cosmetic costs would be worth doing so even if it were possible. After tentative starts, Russell gave up on the project of extending the MRTJ with reference to more and more universals and mind-independent forms. Ultimately, he gave up on the MRTJ altogether. My suggestion is to exchange logical operators and logical forms for cognitive acts, and to recognise that this isn’t really any more psychologistic than the insight that already lay at the heart of the MRTJ: that minds are responsible for the genesis of meaning.23 I hope to have met, in the first two chapters of part III, all of the famous criticisms that have hitherto been thought to make the MRTJ unworkable. In the remainder of this book, I hope to argue that the MRTJ isn’t just free from obvious defect, but deserves to be considered as a strong contender in the contemporary contest to provide a robust metaphysics of meaning.

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Notes 1 In fact, as we noted in the previous chapter, Russell himself raised this concern with the MRTJ before he adopted it (Russell, 1906), and as it was stumbling (Russell, 1913). 2 This sentence evoked an interesting response from an anonymous reviewer. ‘How can a mental thing, [such as] judgement, order non-mental things? The constituents of a judgement are not in the mind and thus cannot be moved around in the mind. Short of mastering the art of [the] Jedi, moreover, they can’t be moved around by the mind outside the mind either.’ I think that this is a worry that a number of readers might share. The best that I can do is to refer them back to what David Pears (1967, p. 216) is quoted as saying in chapter 6, §4, ‘The arranging is mental [even though the items aren’t]. It is not a matter of his pushing things around outside his mind . . . Russell’s theory does not mean that the arranging of things is actual.’ I don’t see why merely mental arranging has to use merely mental items. Why can’t my mind mentally order actual things – not by moving them around in the actual world, but by, so to speak, passing over them in a certain order? 3 Of course, the object-relation of a judgment doesn’t relate in an order, because it doesn’t relate at all, but the judgement relation relates in an order, and its doing so can block our fundamental concern as it applies to molecular1 propositions. 4 She had been his research assistant in that she was his source of books from Cambridge. She had also been in a very select group of students who had remained under his tutelage, before his time in prison, after he had been sacked by Cambridge for his anti-war activism (Monk, 1997, p. 525 ft.). 5 Russell, in his 1913 manuscripts, and Wrinch, both struggle with this problem, but neither of them find a satisfactory solution. 6 See footnote 17. 7 An anonymous reviewer raises a concern that’s neither to do with unsightly ontological commitments, nor peculiar epistemological consequences, but could still be labelled a cosmetic concern. The worry is this: by saying that these are the five logical universals that we use to assert molecular1 judgements, Hossack is making an unwarranted claim that these five operators are privileged. But, as the reviewer writes, the ‘logical connectives identified have no ontological status and import. They are not universals. They are merely symbols, selected by authors of logic textbooks for pedagogical purposes. Hence, they are interdefinable and so eliminable. They are all reducible to a single connective, either the Scheffer stroke or dagger. Wittgenstein’s generalization of the Scheffer dagger, the N operator, brings quantification in under the umbrella, too.’ Even if I resist the reviewer’s conclusion that no logical connectives are universals, we could ask: why should we think that the five operators that Hossack choses are the ones that exist out there in Plato’s heaven, when there may only be one big Platonic Scheffer stroke (or N-operator)? Hossack could say that there is a fact of the matter which logical connectives are the real ones (out of which the others are constructed), but that since we can’t know which ones are the real ones, we will treat these five standard ones as if they’re the real ones, as a heuristic, and construct a theory that could easily be adapted if only we knew which of the connectives were the ones with real ontological feet. But this raises the epistemological concern that I’m eventually going to level against Hossack myself. If we don’t know which of the operators are real, but we’re using them in our judgements, as objects, then we will have violated the principle of acquaintance, according to which you can only use entities in judgements if you are already acquainted with them. As we shall see when we confront molecularity2, Hossack seems

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to make unrealistic epistemological demands of people who make molecular judgements. This consideration re-raises the worry discussed in footnote 7. Again, see footnote 7; perhaps a different set of operators could have done this work equally well. I’m grateful to Dorothy Edgington for her mentorship in general, but for her guidance on this section in particular. I believe that I wouldn’t have come up with this new extension for the MRTJ had she not encouraged me to read Dummett, and to read him with an eye to thinking about the way in which molecular propositions are built with a constructional history. An anonymous reviewer sought to raise a pressing objection against this claim: Suppose you know nothing about hockey, but you’ve been invited to a game. The person who invited you to come told you that you should come because it is game 7 of the finals and ‘either the Oilers or the Maple Leafs will win the Stanley Cup tonight.’ You don’t know anything about the Oilers or [the] Maple Leafs other than what your friend told you. Now, you’re going to invite a friend, and try to persuade them to come. All you know about either team is this disjunction: one or the other of them is going to win the Stanley Cup tonight. As far as what it would mean if the Leafs won the cup, you don’t even really understand that. This is your first game.

In this case, so the reviewer is pressing on me, you are asserting a disjunction, but you don’t really or fully understand either of the disjuncts. In truth, I’m ashamed to admit it, I didn’t even know that there was something called a Stanley Cup. Had I not been told that it was a Hockey game, I wouldn’t even have understood that. And yet I admit that I would have been able to assert that ‘either the Oiler or the Maple Leafs will win’, even in the face of such a lack of understanding. But I don’t think that this is really a counterexample to my claim. I still maintain that in order to assert a disjunction you have to understand both disjuncts. This case is not a counterexample because, given the philosophy of language I developed in chapter 4, it’s clear that when I repeat my friend’s words, I’m not asserting the same content that he asserted when he used them. He asserted the horizontal content. I’m asserting the diagonal. I’m saying something like, there is a team that my friend called ‘the Oilers’ and another one that he called ‘the Maples’, and they’re playing a game tonight, and one of them will win something that my friend called ‘the Stanley cup’. This is a molecular proposition, and when I assert it, despite my lack of Hockey knowledge, I do understand each and every atomic constituent that builds it up. 12 This temporarily opens me up to the criticism levelled against Hossack in footnote 7, but I will turn to that problem later. 13 My view can allow for ignorance here. We don’t yet know enough about our cognitive architecture to know how many logical operators we deploy in the language of thought, so to speak. Hossack claims that there are ten logical operators and we’re acquainted with them. If, as I think is the case, it turns out that we don’t know how many Platonic logical operators there are in our fundamental ontology, then his whole theory seems to be in trouble. How can we use these operators as objects in our judgements if we’re not acquainted with them? But in my theory, the cognitive attitudes that model the logical connectives are not objects of our everyday judgements, and so it

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doesn’t matter if we’re not yet acquainted with them. We are acquainted with our understanding states, but that doesn’t mean we have to be acquainted with the cognitive attitudes that give rise to them. To be acquainted with a complex whole doesn’t entail acquaintance with all of its constituents. And thus, even though the objection raised in footnote 7 can be raised against my account, I think I can escape the objection, and that Hossack can’t. This isn’t actually Frege’s notation, but our modern notation encodes exactly the same information vis-à-vis constructional history as Frege’s notation does. My disclaimer from earlier should apply here too: I’m not really claiming that I know how many logical operators we actually use in our language of thought. I leave that to the cognitive scientists. Here I use the standard operators of quantification in order to illustrate how pairs of attitudes can be modelled on them, and on operators like them. I’m grateful to Fraser MacBride for helping me to sharpen this criticism by concentrating on relations that even Hossack accepts as multigrade. Hossack can escape this problem if he denies that relations can be variably polyadic; if he stipulates that all universals have a rigidly fixed adicity. Then we’ll be able to work out where the first conjunct ends and the next one begins. When a universal seems to have a variable polyadicity, on this view, there must actually be a range of rigid relations hiding behind the fictional façade of a variably polyadic one. As we saw in chapter 7, §5.4, Russell makes a similar suggestion regarding judgement. He was unhappy, for various reasons, accepting variably polyadic universals into his ontology, and yet recognized that, according to the MRTJ, the relation of judgement itself turns out to be variably polyadic – he therefore suggested that there are an indefinitely large number of distinct judgement relations corresponding to all of the different numbers of entities that can enter into a particular judgement. I find this line of escape unattractive. I’d rather have variably polyadic relations in my ontology; as would Hossack, but he can’t have his cake and eat it. Variably polyadic relations will create scope ambiguities, given his version of the MRTJ. I’m grateful to an anonymous referee for pointing out that if I’m not careful, my theory will have to face this concern. For full expressive power, we might need a few more cognitive acts than the ones I’ve already surveyed – not merely because our language of thought might have a wealth of distinct logical operators. In chapter 11, we’ll discuss the possibility of a special cognitive act of self-ascription, in order to give rise to de se content. We might also want to appeal to cognitive acts that model our use of plural quantifiers, and other types of quantifier. But the general strategy should be clear from what I’ve already presented. Thank you to Daniel Rubio for conversation on these issues. The idea of replacing reified logical operators with distinct cognitive acts is similar to the strategy employed by Peter Hanks. See, for example Hanks (2011). But it’s worth noting that, for him, it’s very important to reify the act-types that he multiples. On my account, those types play no role in the analysis of assertion or understanding. Apparent counter-examples abound, but they tend to be cases where the molecular proposition isn’t really asserted, but in which some diagonal content is asserted in its place. Content cannot be asserted where atomic constituents of that content are not understood. See footnote 11. And just to be clear. I don’t deny that you can understand, or even know, a general claim without knowing any of its instances. You can, for example, know that football players are overpaid even if you don’t know the name of a single football player.

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My claim is merely this. If you know the meaning of the name ‘Sarah’, and you know the meaning of the phrase ‘All football players are overpaid’, then you must understand the meaning of the phrase ‘Sarah is a football player who is overpaid,’ whether or not Sarah is actually a football player, or known by you to be one. 22 This criticism is almost taken verbatim from an anonymous reviewer. 23 In his first critique of Russell’s theory of judgement, Stout’s final jibe is selfavowedly ad hominem (Stout, 1910–1911, p. 205). It is the claim that the theory constitutes a concession to idealism. If the mind is an essential feature of a judgement, and if there are no propositions outside of judgements, then Russell seems to be retreating from his trenchant anti-idealism: I do not myself regard the idealistic tendency of a theory as a reductio ad absurdum. But so far as Mr. Russell is concerned, it certainly seems to me that, from the present position, the hard and unsympathetic treatment which he has given to. . . idealistic doctrines. . . ought no longer to be possible. Rosalind Carey echoes this concern with her claim that Russell’s theory of judgement (especially in its 1912 incarnation) placed too much of a burden upon cognitive acts; overall, she disapproves (or at the very least, expresses what she takes to be Wittgenstein’s disapproval) of making ‘judging critical to the meaning of propositions’ (Carey, 2007, p. 47). So we see that criticism 5 hasn’t just been levelled against my extension of the MRTJ. It was also levelled against the original theory. But I don’t take either of these concerns, Stout’s or Carey’s, to be criticisms. I see them as strengths of the theory. To Carey, I would say, indeed, there can be no meaning or representation without intention, and, as it turns out, long after Russell came to this conclusion, it was finally arrived at by Wittgenstein – meaning is use! To Stout I would say: thankfully, Russell is able to jettison the noxious claim of the idealists that the mind plays some sort of role in shaping reality itself, but he should be praised for prizing this notion away from, and salvaging, the single most profound insight of the transcendental idealists – namely, that truth, falsity, and meaning, emerge at the interface between mind and the world.

10 Explaining the Explananda

In chapter 1, §1, I outlined 11 roles that propositions have classically been posited to play. The MRTJ eliminates propositions from our ontology. This means that propositions can no longer play any of those roles. However, to the extent that the MRTJ is supposed to be a no-proposition theory of propositions, it owes us an explanation of the 11 explananda that the posit of propositions was once supposed to explain – or, at the very least, we’re owed an account as to why a theory of propositions doesn’t really have to explain a given explanandum. Furthermore, throughout the course of this book, certain distinctions have been drawn – such as the distinction between semantic values and objects of assertion (which we drew in chapter 4). Some of those distinctions will lead us to additional explananda to the 11 that arose in the introduction – those 11 explananda are coarse-grained in a way that some of our newfound distinctions enable us to refine. In this chapter, I therefore return to our 11 explananda, refining them and drawing distinctions where necessary, before offering the MRTJ’s explanation (or deflation) of each of them. For ease of reference, I reproduce, here, the 11 explananda that we arrived at in chapter 1, worded now as questions for a theory to resolve: 1. What is the information content of a sentence relative to a context of utterance? 2. What do synonymous sentences have in common? 3. What are the objects of understanding and other propositional attitudes? 4. What are the primary bearers of truth and falsity? 5. What are the primary bearers of modally qualified truth-values? 6. What are the representational contents of experience? 7. How should we understand the ontological foundation of possible worlds? 8. What is the common ground in a conversation? 9. What are the semantic values of non-factive that-clauses? 10. What are the semantic values of ‘propositional’ demonstratives and anaphora? 11. How should we understand quantification seemingly over propositions?

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§1: Information Contents and Synonymous Sentences The first traditional role that propositions are posited to play is to provide the information content for the utterance of a sentence. When you utter a sentence, especially a declarative sentence, there is something that you mean. So it seems as if sentences – at least relative to a context of utterance (because the same sentence can mean different things in different contexts) – have a meaning. In the wake of chapter 4, we can disambiguate what had hitherto been ambiguous. There are, at least, two things we could be talking about when we talk about the meaning of a sentence. There is the compositional semantic value of the sentence and the object of assertion of the utterance of a sentence. The semantic value of a sentence plays two theoretical roles. First of all, it determines a candidate for the object of assertion, in a given context. Second, it will explain the contribution that the sentence would make to the compositional semantic value of sentences in which it is embedded as a syntactic part. The object of assertion, on the other hand, is what is said in a given utterance of a sentence (and, as we saw, this can sometimes come apart from what is contributed to the common ground of a conversation). The word ‘meaning’ can sometimes refer to a semantic value, and sometimes to an object of assertion (and sometimes to a conversational contribution). Staying true to what I take to be a Russellian spirit, I’ve tried to stay relatively quiet as to what I think semantic values are. I leave that to the semanticists. If the identification thesis can be defended, then semantic values will receive the same sort of philosophical analysis as objects of assertion. But perhaps semantic values are something completely distinct from objects of assertion. I’m agnostic concerning the identification thesis. When I say that I’m leaving semantics for the semanticists, I am, in fact, trying to draw a distinction that philosophers of language are sometimes too quick to smudge over. Theories of meaning, theories of communication, and formal semantics, are often trying to explain the following: they try to specify what a given utterance means. They do this by replacing an item of the object-language with a translation in the meta-language. To produce a formal theory that always gets such specifications right is important, and no mean feat. But there’s something else to explain, as I’ve been at pains to point out. Beyond the production of a systematic translation manual, we might want to explain what goes on, at the most fundamental level of mind-world relations, when a person makes an assertion about the world – and we might want to explain, at that same fundamental level, what two people have in common when they make the same assertion.1 Davidsonian inspired semantics strikes me as a going concern. For that reason, I dare say he’s right that propositions don’t oil the wheels of

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a theory of meaning. But even without propositions, I do think we should try to explain something that his theories don’t attempt to tackle: what is a mind related to, at a fundamental level, when it makes an assertion? We’re asking for an analysis of the objects of assertion – even if they play no role in a semantic theory, or a theory of communication. The first explanandum is asking for an analysis of the objects of assertion. The propositional realist suggests that propositions are objects of assertion (and sometimes they are posited to be semantic values too). This is what they mean when they suggest that propositions are the informational content of a given utterance of a sentence. The MRTJ, on the other hand, offers a transformational analysis of objects of assertion. In the final analysis, singular objects of assertion don’t exist. However, when a person asserts that Romeo loves Juliet (providing that they’re acquainted with the following objects), they stand multiply related to Romeo, love and Juliet (in a certain order). Under the rubric of the MRTJ, we could even say that the object of assertion is the ordered-many (not a thing in its own right, but just a plural in an order): . That ordered-many only becomes representational when a mind stands related to it, and predicates its first item of the remaining two. The MRTJ therefore explains our first explanandum just as well as the posit of propositions would have done. Our second explanandum is intimately related. We had said that ‘Since propositions are what sentences mean. If two sentences mean the same thing, then we expect to cash this out in terms of their both expressing the same proposition.’ We now know that this is ambiguous, because of the ambiguity of the word ‘meaning.’ One way in which two sentences can mean the same thing is if they make the same (or somehow analogous) contributions to wider contexts in which they embed, and if they always determine the same (or somehow analogous) candidates for object of assertion in any given context. Another way in which two sentences can mean the same thing, in a given context, is if they are used to assert the same thing. Frank utters the following two sentences: 1. Dave might be in Oxford. 2. For all Frank knows, Dave is in Oxford. In the first sense of meaning the same thing – i.e., having the same semantic value – these two sentences do not mean the same thing. In the second sense of meaning the same thing – i.e., being used to assert the same thing – when uttered by Frank, they do mean the same thing. To the extent that propositions might not be necessary for an account of semantic values, they might also be otiose to an account of sameness of meaning, in the sense of having the same semantic value. But there’s still something to explain – of course: what do two people who assert the same thing have

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in common, at that fundamental level that concerns us? Indeed, what does it mean for two utterances to mean the same thing, in terms of the second sense of sameness of meaning – sameness of assertoric content? The propositional realist explains this second explanandum with appeal to propositions. Sentences that are used to say the same thing, are being used to express the same proposition. Two people who make the same assertion stand related to the same proposition. The MRTJ does just as well without positing propositions. Two sentences are used to say the same thing if their speakers use these sentences to express that they stand judgement-related to the same object-terms in the same order.2 Two people make the same assertion when they stand judgement-related to the same object-terms in the same order. The second explanandum therefore receives an explanation. This is one of the places where Scott Soames (2015, p. 447) puts pressure on the MRTJ. As he understands it, the MRTJ tries to do away with reifying propositional content, and instead employs particular acts of assertion or understanding to play the role traditionally given to propositional content. This seems, on the surface, to be a fair paraphrase of the position. But it actually leads to an absurdity. We want to say that Mary and John said the same thing. Look where the MRTJ is said to lead us: 1. According to the MRTJ, acts of assertion stand in the place traditionally given to propositions. 2. According to 1, the proposition that John asserts = John’s act of assertion 3. According to 1, the proposition that Mary asserts = Mary’s act of assertion 4. John and Mary asserted the same content. 5. Traditionally, therefore, we’d want to say that John and Marry asserted the same proposition. 6. Therefore, given 1 and 5: John’s act of assertion = Mary’s act of assertion We’ve been lead to the crazy claim that John and Mary’s distinct mental acts were actually one and the same act. That can’t be right! However, that’s where the MRTJ leads us. This whole argument is, however, based upon a misunderstanding of the sorts of transformational analyses licenced by the MRTJ. The way that premise 1 reads, and functions in the argument to 6, is that it licences a simple substitution of mental acts for propositions. However, the transformational analysis at the heart of the MRTJ is supposed to be more complex than that. What it means for John and Mary to assert the same proposition isn’t that they are subjects of numerically identical mental acts, but merely that they stand in the same relation to the same object-terms in the same order. Accordingly, the argument should read as follows:

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1* According to the MRTJ, talk of a proposition can be replaced with talk of standing multiply related to an ordered array of objects. 2* According to 1*, John doesn’t assert a proposition but stands related to an ordered array of objects. 3* According to 1*, Mary doesn’t assert a proposition but stands related to an ordered array of objects. 4* John and Mary asserted the same content. 5* Traditionally, therefore, we’d want to say that John and Marry asserted the same proposition. 6* Therefore, given 1* and 5*: John and Mary stand related to the same ordered array of objects. Thankfully, 6* isn’t absurd at all. It is merely the MRTJ’s explanation of our second explanandum, namely, how two people can mean the same thing.3

§2 : Objects of Propositional Attitudes and Bearers of Propositional Properties The next role that propositions are posited to play is that of objects to propositional attitudes. The MRTJ maintains that propositional attitudes don’t have singular objects. This is what distinguishes the MRTJ from binary theories of assertion. Propositional attitudes are not dyadic but variably polyadic. The mind-world relations in question – the propositional attitudes – are still explained, and they’re still explained in terms of a relation between the mind and mind-independent entities (in line with the degree of anti-psychologism that we still embrace). But these relations relate you to what were hitherto regarded to be the constituents of the propositional realist’s propositions. Our third explanandum is explained, once again, without the need for propositions. Related to the third explanandum is the desire to posit ultimate bearers of truth and falsehood. According to the propositional realists, sentences are true when, and only when, they are used to express true propositions. Propositions are the ultimate bearers of truth and falsehood. But the propositional realist has problems explaining the mysterious ability of propositions to represent. And surely, propositions are only true if they represent the world as being as it is, and false if they represent the world as being as it isn’t. But if the representational nature of propositions hasn’t been explained, then it’s hard to accept that they can be bearers of truth or falsehood.4 We’ll come back to this concern in the next chapter, §1. The MRTJ escapes this concern entirely. In chapter 1, I suggested, along with King, that the power of the mind to represent is less mysterious than the power of mind-external entities to do the same. At the very least, I suggested that while the power of the mind to represent

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could be taken as a primitive in the philosophy of language (even if not in the philosophy of mind), the representational power of metaphysical entities posited by philosophers of language would have to be explained by philosophers of language. Representation needs to occur before we can talk about truth or falsehood. Representation is mysterious for most propositional realists. It isn’t mysterious for the MRTJ. It is minds which represent, and it is mental acts that serve as the ultimate bearers of truth and falsehood. Imagine that a proposition is an ordered set of its constituents – this is how Kaplan sometimes seems to characterise propositions. It’s not enough that ordered set x bears some sort of correspondence to state of affairs y. In order for x to represent y, someone needs to capitalise on the latent correspondence in order to use x to represent y. A photo of my face succeeds in representing my face because of the structural analogy between the elements of my face and the elements of the photo. But what is it that makes the photo a representation of my face when it’s equally possible that my face is a representation of the photo? If there are two photos of my face, what makes them both representations of my face when it’s equally possible that photo A is a representation, not of my face but of photo B? Once again, the missing ingredient is use. The photos are representations of my face because that’s what we’re using them to be; moreover, that’s what they were intended to be when the photographer took them and had them printed. Our theories of judgement need to recognise that objects will only succeed in representing themselves, and ordered-manys or ordered sets will only succeed in representing certain situations, if we intentionally use them to do so. This is a key insight of the MRTJ. Russell’s idea is that assertion is a mental act that directly utilises that which it’s about. This act is, in some sense, more basic than languages that use words to refer to objects. Even if we express our thoughts to ourselves in a conventional language (of words); what we do when we think is to arrange worldly items in our mind; to picture possible states of affairs.5 Even if we express our thoughts to ourselves and to others in words; when we think, we are, in some fundamental sense, reaching out directly to the referents of our thoughts, constructing pictures of possible situations out of them. Remember: Russell is incorrectly interpreted as thinking that the mind has some Jedi like power to move items around outside of the mind, or some paradoxical combination of magical psychokinetic and psychoinertial capabilities. Russell’s idea is much more in tune with what would later become Wittgenstein’s picture theory. The mind reaches out to the referents of its thoughts, and organises them, mentally, so as to construct pictures of possible situations out of them. The arrangements are mental, even if the things arranged are not. The difference between the MRTJ and Wittgenstein’s picture theory, is that the MRTJ doesn’t

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require that the pictures be drawn with linguistic or mental tokens, nor does it require the existence of propositions; rather, the mind reaches out directly to the things it thinks about. It’s as if the MRTJ gives rise to a Lagadonian language of assertion (Lewis, 1986, pp. 145–6). To provide a theory of meaning for this language, as Sainsbury helped us to do in chapter 8, is to provide the most general account of meaning that we can achieve. Just as use and intention are significant in normal languages, so too will they be significant in this more fundamental language of propositional attitudes. I think of Hilary Putnam’s ant, coincidentally leaving tracks in the sand that are reminiscent of a caricature of Winston Churchill (Putnam, 1981, p. 1). On reflection, we conclude that the line in the sand doesn’t, in actual fact, depict Churchill, because (over and above Putnam’s own point that the ant’s tracks don’t stand in the right causal connection to Churchill) there was no intent on the part of the ant. And even if you want to say that, for you, it is a caricature of Churchill, that’s because you are a rational mind capable of reading meaning into things. Without minds to invest meaning into the inanimate world, there can be no meaning. Davidson was keen to emphasise that sentences are not really the bearers of truth. For Davidson, truth is either a relation between sentences, speakers, and times, or, the real bearers of truth are particular utterances (Davidson, 1967, p. 319; 1968–9, pp. 146, ft. 14). This stipulation carries certain technical advantages. It allows for a systematic account of certain indexical phrases. By tying truth to utterances rather than to sentences (or making truth a relation between sentences, speakers, and times), I can build up a theory that will yield theorems such as (T): (T) For any utterance x by speaker y at time z of the sentence, ‘I am tired’, utterance x will be true (in English) iff y is tired at time z. But Davidson’s insistence also allows him to respond to a Stout-like concern. A collection of words arranged randomly doesn’t say anything until someone, at a certain time, and in a certain place, uses them to say something.6 The English language (which is determined by evolving conventions of communal use) places certain constraints upon what words I can use to say which things, but use is still key to generating meaning. Davidson’s emphasis on the centrality of utterances over abstract sentences encodes this fundamental insight. As far as Davidson is concerned, in a world where no one makes an utterance, there will be no truth. We can add: in a world where no one makes an utterance, thinks a thought, or makes any kind of assertion, there will be no truth. The MRTJ agrees. It is acts of minds, and not abstract propositions, that ultimately bear truth and falsehood. As we shall explore in §4, holding fast to this insight will create certain problems for us downstream: it will effectively heighten what we have called,

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in chapter 1, the problem of dependence. However, we’ll cross that bridge when we come to it! Explaining our fourth explanandum: it is judgements that bear truth and falsehood. Explaining our fifth explanandum: it is judgements – rather than abstract propositions that can be contingently true, or necessarily true. Having said that, some have argued that propositions are the wrong sorts of things for modal operators to operate upon. You might think that if these arguments are sound, then they also wouldn’t operate upon judgements. David Lewis (1980) – as he has generally been understood – made a clear distinction between semantic values and objects of assertion. In the language of chapter 4: Lewis denies the identification thesis. Once that thesis has been denied, Lewis can say that all of our operators – tense, location and modal – operate upon the semantic value of the embedded sentence, but they don’t have to operate on propositions – which are objects of assertion. This seems to make sense. We don’t want what we assert to have truth-values that shift from location to location, and from time to time, so we shouldn’t want what we assert to shift in truth-value from world to world. If Lewis’ picture is correct, then propositions are needed to be the objects of propositional attitudes, for example, but they are not required to be objects upon which modal operators operate. Assimilated into the MRTJ, the view would be that modal operators operate upon semantic values of sentences, but they do not operate upon judgements. Jeff King (2007, pp. 165–6), on the other hand, maintains the identification thesis. He admits of no bifurcation between semantic values and objects of assertion. If modal operators operate on one, then they operate on both, because – according to King – they are the same thing! King nevertheless manages to escape the conclusion that propositions change their truth-value from time to time and from place to place, even though he does think that they shift their truth-value from world to world. King’s argument is simple: tense and location operators are not really operators at all. They don’t operate on sentences, nor do they operate on propositions. Instead, King defends a quantificational analysis of so-called tense and location operators (these analyses are given empirical weight from linguists, such as Barbara Partee (1973) and David Dowty (1982)). As far as King is concerned, modal operators are different, because they really are operators and they operate not just on semantic values, but on objects of assertion (i.e., propositions) – since, for King, semantic values are objects of assertion. I don’t want to enter in to the debate between King and Lewis. Either, we can take ourselves to have strong reasons, based upon Lewis’ arguments, to deny that propositions are what modal operators operate upon (this route is adopted by Jason Stanley (1997a; 1997b)). This relieves our theory of propositions of one more explanandum to explain. We needn’t

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posit their existence for modal operators to have something to operate upon. Or, we can follow King and say that modal operators do need something to operate on. But we can ask, must they really operate upon propositions? Can they not operate upon judgements? For Davidson, remember, when we say that a sentence is true, it’s something of a shorthand for saying that the sentence is such that its utterances are true. On the MRTJ view, we have to go further. To say that a sentence is true, is to say that its utterances are true, which is to say that the utterances express judgements which are true. Likewise, to say that a sentence is possibly true, or necessarily true, is to say that its utterances are, which is to say that they express judgements which are. If we want to say, with King, that a modal operator operates upon a proposition, we can give that talk a transformational analysis in terms of its operating upon the acts of assertion that give rise to that proposition. On this view, then, it really is judgements which are the ultimate bearers of modally qualified truth-values, and, it is in terms of judgements that we might want to explain the operation of modal operators.

§3: The Multiple Relation Theory of Appearances I mentioned, in chapter 1, that propositions are sometimes posited to be the content of representational experience. I appealed to the following example. When you see that a car is turning a corner, your experience has representational content: you experience the car as turning a corner; you see that it is turning a corner. I expressed an almost instinctive – and somewhat pre-philosophical – doubt that propositional content and experiential content, however related the two might be, should really turn out to be exactly the same kind of thing. I illustrated that concern with a quote from William Alston. The idea that ‘seeing’ should ever pick out a relation between a proposition and a mind continues to make me uncomfortable. When I see that a car is turning a corner, I don’t see a proposition. Propositions – whether they’re functions from worlds to truth-values, or structured abstracta – may have visible constituents, but they are not, themselves, visible! I see the car. I see that it’s turning the corner. I don’t see a proposition. I am therefore unconvinced that a theory of propositions – even a no-proposition theory of propositions like the MRTJ – should be compelled to explain experiential content. Consequently, I wouldn’t count it against the MRTJ if it offered no explanation of this explanandum. Nevertheless, there certainly seems to be some sort of relationship – however attenuated – between propositional and experiential content. They are both forms of content after all. Furthermore, we’re able to represent what we see – to various degrees of success – in what we assert. Finally, it sometimes seems as if experience, like an assertion, can be accurate or inaccurate – true, or false (this turns out to be contentious, but we

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certainly talk as if it’s true – ‘The shirt looked red to me, but it turned out that it was actually blue’). And thus, in what follows, I’m going to sketch a theory of perception in which seeing that is a multiple relation. I’m not personally committed to this view of perception, and I don’t think that the MRTJ should be rejected if it fails. However, if it works, it will quite naturally explain the similarity between the two types of content – both assertoric and perceptual content emerge in a multiple relation between mind and world. The most straightforward extension of the MRTJ to the case of seeing that was explored by C. D. Broad who – clearly aware of the similarity it bore to Russell’s theory of judgement – called it the Multiple Relation Theory of Sensible Appearances. Let’s call it the MRTA. Broad’s discussion starts with the observation that we ‘constantly make such judgements as: “This seems to me elliptical, or red, or hot” as the case may be’. He also notes that we feel no doubt about the truth of these judgements even though we may ‘at the same time doubt or positively disbelieve that this is elliptical, or red, or hot’ (Broad, 1965, p. 87). The MRTA takes the view that ‘appearing to be so and so’ is a multiple relation between an object, a mind and a characteristic. As Broad puts it (Broad, 1965, p. 88): On this type of theory to say that the penny looks elliptical to me is to say that the unique and not further analysable relation of ‘appearing’ holds between the penny, my mind, and the general characteristic of ellipticity. There are reasons to be uncomfortable with the MRTA. It makes seeing that far too much like judging that! If the mind is active in predicating the object-relation of the other object-terms, even as it passively sees something, then the mind really seems to be given too much responsibility. We start to collapse into an intolerable form of idealism. According to this theory, you see the knife as being to the right of the fork only because your mind is actively predicating ‘being to the right of’, of the knife and the fork, in that order. Surely, in seeing that, a mind is more passive – even if it is just that active in the act of assertion. Surely it’s more attractive to say, with Thomas Reid, that sensory experiences have a sensory component that is nothing more than a raw feel, independent of judgments about how things are around you (see, for example, Reid (1785, pp. 295, §4.1)). Surely those judgements happen somehow downstream. And even if those judgements are actually a component of visual experience itself, surely they can be isolated from the purely sensory component. William Alston defends the MRTA. As we shall see, it’s clear that he wouldn’t abide by any of these reservations. Alston defends the MRTA, but tacitly rejects the MRTJ. He thinks that one of the things that distinguishes perception from judgement is that, in seeing or perceiving an object x, we stand directly related to x without any sort of cognitive

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intermediary. He thinks that thinking about x is different. In merely thinking about something, that thing is not directly related to the mind. Assertion might, instead, stand you related to a proposition, and the thing that you’re thinking about might be a constituent of that. But the relation is not direct. Nevertheless, we can hold on to both the MRTA and the MRTJ, and utilise the resources of Alston’s arguments to draw a clear distinction between perception and assertion nevertheless. As Alston (1999, p. 184) argues: X’s looking P to S does not involve S’s applying the concept of P to X, or thinking of X as P, or using the concept of P to ‘classify’ X, or anything of the sort. There is no such deployment of concepts ‘between’ S and X. S is simply aware of X as looking a certain way, and that’s all there is to it. So the threat of idealism – the worry that the mind is too active in constructing what we perceive – is discounted. The difference between judging that something is the case and perceiving that something is the case is that in judging, the mind actively predicates the object-relation of the other object-terms. In seeing that something is the case, or at least, in seeing that X appears P-ishly, you stand multiply related to X and to P, but your mind is passive. X appears to you to be characterised by P. The world, so to speak, is acting on you! Alston draws further distinctions between assertion and perception (Alston, 1999): I am not so pre-Kantian as to suppose that concepts play no role in perception. When I look out my study window my visual experience bears marks, obvious on reflection, of being structured by concepts of house, tree, grass, pavement, etc. I see various parts of the scene as houses, trees, etc., employing the appropriate concepts in doing so. But just because our perceptions relate us to concepts/universal properties – such as being a house – we shouldn’t think that we can’t distinguish between pure experience and judgements about those perceptions – as Thomas Reid insists that we should. For example, in judgement, we need to be acquainted with the universals that we effectively use as predicates, and we need to know (in some sense of ‘knowing’) how to use the universal as a predicate in judgement (or we need to know how to judge each predicate-judgement, on MacBride’s reconstruction of the 1918-MRTJ). No such epistemic constraints impinge upon what we can perceive. This explains why perception is so much richer, in content, than what we can judge. X can look P to S even if S lacks the concept of P. Where that happens, there is the look without the corresponding concept application.

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In that case, S perceives that X looks P-ish, but wouldn’t be in a position to assert that that’s the case – that that’s how X looks – since they lack the concept P. This brings us back to the quote I used in in chapter 1 to motivate the claim that perceptual content isn’t propositional. It warrants repeating (Alston, 1999): When I look at my front lawn, it presents much more content to my awareness than I can possibly capture in concepts. There are indefinitely complex shadings of color and texture among the leaves and branches of each of the trees. That is perceptually presented to me in all its detail, but I can make only the faintest stab at encoding it in concepts. My repertoire of visual property and visual relation concepts is much too limited and much too crude to capture more than a tiny proportion of this. This is the situation sometimes expressed by saying that while perceptual experience has an ‘analog’ character, concepts are ‘digital’. Since looks are enormously more complex than any conceptualization available to us, the former cannot consist of the latter. The MRTA is a plausible theory of perception and perceptual content. Alston does a masterful job comparing it to more naive forms of direct realism (that struggle to account for visual illusions), and to sense-data theories and adverbialism, which struggle to make sense of the epistemic connection to extra-mental objects that perception often facilitates. He also sketches ways that the MRTA could respond to the problem cases of hallucination. I refer interested readers to Alston’s paper. In short, the MRTA seems like a workable theory of perception. The MRTA demonstrates that we don’t need propositional realism to account for perceptual experience, but also makes clear what perception does have in common with assertion, for those who (unlike Alston) subscribe to the MRTJ. Assertion and perception are both multiple relations between a mind and an ordered array of object-terms. The relations are different in various ways, but they are structurally analogous, and what it takes for a judgement to be true will directly correspond to what it takes for a perceptual appearance to be accurate. One problem with the MRTA is that it commits us to realism about universals. When a ball appears to me to be red, I stand related to the ball and to the property of redness. Realist as I am, I have no problem with this commitment. But I promised my readers that the positive theories

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that I’d eventually end up proposing would be neutral about the existence of universals and would be open to nominalists. The fact that MacBride’s MRTJ is on the table alongside Sainsbury’s MRTJ means that I’ve hopefully been true to my promise. But if, in explaining our explananda, I commit the MRTJ to the MRTA, it looks as if I’ve broken my promise. Matthew Conduct (2008) suggests a revised version of adverbialism which, to my mind, constitutes a version of the MRTA that should be acceptable even to a nominalist. It might help to present the orthodox version of adverbialism before turning to Conduct’s revision. On the orthodox account, a perceptual experience shouldn’t be thought of as a mind-world relation at all. Experiences are, rather, modifications of a mental subject that can be characterised by sometimes somewhat gerrymandered adverbs. When you see a red ball, for example, you are appeared to redly and roundly. Defenders of this orthodox adverbialism include C. J. Ducasse (1942) and Roderick Chisholm (1957). Adverbialism – quite unlike the MRTA – seems to undercut the direct realist desire to put the mind in unmediated contact with the things that it thinks about and the things that it perceives. Conduct’s revision of adverbialism, however, generates no such conflict with the dictates of our direct realism. If X looks P to S, Conduct would say that S stands related to X. He doesn’t also stand related to P. This will be good news to the nominalist, since she thinks that P doesn’t exist. But the relation that relates S to X is modified by an adverb. X stands related in the appearing-P-ishly relation to S. Of course, the appearing-P-ishly relation doesn’t exist, according to nominalism. But we can give a nominalistic account of what it means for two things to stand in this relation. If the fork appears to be to the right of the knife, to S, then the fork and the knife stand multiply related to S (in that order) in the appearing-to-the-right-ishly relation. This modified adverbialism therefore agrees with Alston, at least when more than one object is appearing to the subject, that the relevant relation is a multiple (rather than a binary relation). They only disagree about whether one of the relata has to be the perceptual characteristic which appears to be instantiated by the other objects, or whether the characteristic merely modifies the relation itself as an adverb. And thus, this modified adverbialism also seems to be a modified MRTA. Conduct’s modified MRTA stands to Alston’s MRTA as MacBride’s MRTJ stands to Sainsbury’s MRTJ. Indeed, one way of thinking about MacBride’s MRTJ is as an adverbial theory of judgement. When Othello judges that Desdemona loves Cassio, according to the MacBride version of the theory, he stands judgement-related to Desdemona and to Cassio, but the judgement-relation is modified by an adverb so as to become the judging-that-love-obtains-between relation. MacBride’s MRTJ can be adopted even by a nominalist because it never demands that universals exist as relata of the nominalistically construed judgement-relation. Conduct’s modified MRTA, likewise, can be adopted even by a nominliast.

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Conduct argues that his theory of perception shouldn’t be confused with the multiple relation theory, but just as MacBride’s theory might strike the realist as nothing more than a notational variation on Sainsbury’s theory, Conduct’s theory might well strike the realist as nothing more than a notational variation on Alston’s theory. Either way, I offer Conduct’s theory to my nominalist readers. We have a theory of perception that denies that propositions are required to play any role, but also can explain what judgement and perception have in common – they are both relations of variable adicity between the mind and the world. To the extent that perceptual content is something that a theory of propositions should explain, it seems that the MRTJ has a natural ally in the MRTA. The MRTA explains the representational nature of experience in virtue of the mind’s power to represent, when acted on by the world. The MRTJ explains the representational nature of assertion in virtue of the mind’s power to represent when acting on the world.

§4: Common Ground and Possible Worlds The seventh and eight explananda had to do with the common ground of conversations and the ontological foundation of possible worlds. The common ground explanandum is easier to accommodate for the MRTJ than the possible world explanandum. The intuitive idea behind the notion of a common ground is that, in any conversation, there is some set of propositions that everyone is accepting (at least for the sake of the conversation), and which everyone believes everyone else to be accepting, and which everyone believes that everyone believes that everyone is accepting, and so on and so forth, iterated up to every level of belief. At the root of this notion, then, is a set of propositions – the set that everyone’s accepting. The propositional realist can explain what such a set of propositions is because, according to their theory, propositions exist and can serve as the members of such a set. The MRTJ denies that propositions exist. Can it explain what a common ground is? The answer is relatively straightforward. Although the MRTJ doesn’t posit the existence of propositions, it does allow us, as a façon de parle, to talk about propositions. All such talk receives a transformational analysis in terms of judgements or other cognitive acts – such as acts of understanding. We likewise know how to analyse talk of two people making the same judgement, or judging the same thing. It really means that they stand in the judgement-relation to the same object-terms in the same order. We know how to analyse talk of two people accepting the same thing, it means that they stand in the acceptance relation to the same object-terms in the same order. All of this paves the way for a transformational analysis of a set of propositions accepted in a certain conversational context. The analysis will proceed in terms of each of the interlocutors standing in a number of acceptance relations to the same

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objects, in the same orders. Accordingly, the MRTJ can explain what a conversational common ground is without reifying propositions and creating sets of them. The relationship between the MRTJ and the ontology of possible worlds is going to be much more complicated. It will throw up a number of difficulties. These difficulties stem from what I called the dependence problem in chapter 1. In what follows, I lay out the problem of dependence and how it might be escaped by the MRTJ (§4.1). I then lay out the ways in which this problem is harder to solve when we focus upon certain modal facts (§4.2). I then canvas some of the options for escaping the modal version of the dependence problem – none of which are going to be comfortable to everyone. Despite this discomfort, I argue (§4.3) that the difficulty has to arise, for any theory that takes the representation-concern seriously. §4.1: Escaping the Dependence Problem In chapter 1, §2.5, I defined the dependence problem as follows: if the existence of propositions is too tightly dependent upon the acts of sentient agents, then in certain situations, where the relevant acts haven’t occurred, then certain propositions that should exist won’t exist. Soames and King, we discovered, are both held hostage by the dependence problem. If propositions are types of mental acts, as Soames thinks that they are, then they don’t exist in worlds with no minds, and indeed, in this world, they didn’t exist before there were minds. Alternatively, if propositions are parasitic on certain linguistic facts or conventions, as King thinks them to be, then there will be no propositions in worlds with no languages, and indeed, even in this world, before there was language there were no propositions. Before there were minds or languages, was the proposition that 2 + 2 = 4 not yet true? Soames, we saw, escaped this problem along a metaphysically contentious path; arguing that things that don’t exist can still have properties. So in a pre-mental world, the non-existent proposition that 2 + 2 = 4 can still be true! Surely, this is an unsightly response to the problem. It is out of kilter with ‘serious actualism’ and ‘serious presentism’ – and therefore, at the very least, metaphysically contentious. Soames doesn’t regard conflict with serious actualism as a cost, because he denies ‘serious actualism’.7 I think it fair to say that many philosophers would regard it as a cost, and that his theory of representation would be stronger if it could remain neutral on these questions.8 King adopts a route out of the problem that Russell had endorsed beforehand. Russell (1912, p. 70) writes, It seems fairly evident that if there were no beliefs there could be no falsehood, and no truth either, in the sense in which truth is correlative

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Russell appears here to be bullet biting, but in fact he’s explaining why the dependence problem isn’t a bullet at all; it can actually be presented as an intuitive corollary of our theory of judgement. The idea is that we only call judgements and assertions and ideas true . . . but it would be strange to call a fact true. You might think that calling a fact true is redundant, since its being a fact guarantees that it’s true. However, Russell’s point is that it isn’t redundant, it’s a category mistake. Facts aren’t the sorts of things that can be true; they are, rather, the sort of things that can make judgements and assertions and thoughts true; those mental acts are true when they are true to the facts! When you put it that way, it becomes natural to say that in a world with no minds, there is nothing you could point to and say, ‘Gosh, that’s true’, and ‘Look here, that’s false!’ Non-mental bits of a world can’t be true or false – only mental acts can be! So the dependence problem isn’t a problem after all, it’s an intuitive corollary of our theory. And the embarrassment we feel when we have to concede that there are no arithmetical truths in a world without minds is immediately rescinded when we realise that there would still be arithmentical facts in that world. Even without Russell’s ontological commitment to facts, we could adopt his general attitude to the corollary. You might think that all true sentences, or propositions, are made true by the one and only truth-maker – namely, the world.9 You might call this the one big fact, or, upon realising that the world itself is all that’s needed to make true sentences/ propositions true, you might not like to talk of a realm of facts at all. On this view, the world makes the proposition that 2 + 2 = 4 true. The world could still have that property – the disposition to make such a proposition true – even if the proposition didn’t exist, or didn’t yet exist. So even if you don’t like facts, the world’s having this disposition prior to the existence of minds might be enough to remove the sting from the corollary to the mind-dependent views of representation. For the remainder of this chapter, I’ll frame this response in terms of facts, but it would work equally well in terms of the world’s disposition to make certain propositions true and others false. King follows in Russell’s footsteps. He writes (King, 2007, p. 72), [A] particle’s possessing a certain charge property did not make any proposition true back then; but the particle’s possessing the charge

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property was nevertheless a fact back then. This takes a lot of sting out of the claim that nothing was true in the remote past. As long as there were particles standing in relations, and, later, planets orbiting stars, that nothing was true despite this seems rather harmless. King offers this Russellian response, but only if you’re a presentist. If you’re an eternalist, King thinks you can do better. You can say that propositions, though they’re only temporally located at times where languages are located, since they depend upon language, they still exist – as per eternalism – atemporally. And since propositions – like everything else, for the eternalist – always exist in this atemporal sense, they can have the property of being true at t1, even if they’re not temporally located at t1, just as, for an eternalist, we can say that reference to Socrates, even after he dies, is still reference to an existing thing; an existing thing that isn’t temporally located at the moment of the act of reference, but still has the property of being referred to in that moment. So if you’re an eternalist, you can say that propositions are true eternally, even though they’re only located in stretches of time after the evolution of minds or languages. If you’re a presentist, you have to bite a bullet and say that there were no truths until there were minds/languages, but since there were still facts, the bullet doesn’t end up hurting anybody. Russell’s response is neutral to the philosophy of time. The first thing to note about Russell’s response – even though I think that it’s the right response to the dependence problem – is that it puts a spanner in the works for explanandum seven. One role that has sometimes been given to propositions is to explain what possible worlds are. A possible world is just a consistent set of propositions, containing, for every proposition p, either p or its negation (Adams, 1974). Possible-worlders, however, can’t define possible worlds in terms of propositions, because they define propositions in terms of possible worlds. And thus, a special benefit of structured-propositions is the way in which they open the door to a promising account of the nature of possible worlds: possible worlds are sets of propositions.10 The Russell-King response to the dependence problem, however, closes this door, and rules out an account of possible worlds in terms of propositions. Why? As Lorraine Juliano Keller (2016) has pointed out: according to the Russell-King response to the dependence problem, at some points in our world’s history, at least, there were more facts in the actual world than propositions. The facts of the world outstripped the propositions available to us. But, if that’s the case, then, at such times, there will be no set of propositions rich enough to describe what is actual. The actual world is certainly a possible world, and yet – on the Russell-King response to the dependence problem – it provides a counter-example to the claim that every possible world can be defined in terms of or modelled by a set of propositions. A theory of propositions that embraces the

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Russell-King response to the dependence problem can no longer explain explanandum seven. Keller seems to think that this is a major problem. At times before the existence of minds or languages, the Russell-King response to the dependence problem will deny that the proposition that 2 + 2 = 4 exists. Keller responds to this sort of strategy (Keller, 2016, p. 11): Of course, it is always open to the defender of a theory of propositions, when faced with recalcitrant examples, simply to deny that the problematic propositions exist. If such denials involve relinquishing roles that propositions were introduced to play [such as explanandum seven], however, the view starts to look less like a theory of propositions and more like a view that has given up on propositions. If the theory of propositions gives up on explanandum seven, then – according to Keller – it’s giving up on being a theory of propositions. I’m not completely convinced. Perhaps explanandum seven simply isn’t the sort of thing that a theory of propositions owed us in the first place. The possible-worlders certainly never thought that this explanandum should be on the list of things for propositions to explain, and in the early history of analytic philosophy, neither Frege, Moore, Russell nor Wittgenstein were ever positing propositions in order to make sense of modal metaphysics. Sure, it would be nice. But it shouldn’t be a deal breaker on a theory of propositions, especially one that can explain all of the other explananda. As it turns out, and as I shall argue, it is actually possible to resurrect the view that possible worlds are sets of propositions, even on (a supplemented version of) the Russell-King response to the dependence problem.11 But even without such an act of resurrection, failure to explain our seventh explanandum needn’t be a death knell for a theory of propositions. Unfortunately, with or without explanandum seven, the RussellKing response (in isolation) won’t be sufficient to block the dependence problem in all of its forms. I turn now to an underappreciated, and more recalcitrant, version of the dependence problem. I call it the modal dependence problem. §4.2: The Modal Dependence Problem Turn your mind to a world with no sentient life. Or, turn your mind to the epochs of this world’s history before there was sentient life. You’re now regarding a world in which – to echo Russell’s way of presenting matters – there are facts – even eternally existing facts like the fact that 2 + 2 = 4 – but there are no truths. The fact that 2 + 2 = 4, for a realist, is going to consist in the number 2 standing in a certain relationship to the number 4 – a relationship that 2 and 4 stand in in every world. Presumably, in the

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world that we’re considering, it’s a fact that human life might one day evolve – we’re certainly going to want to accept that that was a fact in our world before human life evolved! If it wasn’t a fact back then, then it wouldn’t have been possible for us to evolve, and we wouldn’t be here today. The fact that we’re considering is a modal fact – that human life might evolve. In what does that fact (or world-disposition) consist, in worlds before or otherwise without sentient life? The modal realist thinks that every possible world exists just as concretely as our own world does. Of course, they are spatio-temporally discontinuous from each other, so you can’t visit other possible worlds, but they do exist. Ours is the only world that we can truly call ‘actual’, just as this moment of time is the only time that we can currently truly call ‘now’ and the place in which we’re currently located is the only place that we can currently truly call ‘here’; but other worlds are just as truly actual to their denizens as ours is to us; just as every other time is equally now to those who are in it as ours is to us, and other places are equally here to those that are there as ours is to us! Possible worlds are real. According to the modal realist, a world, w, is such that possibly-p iff there is some world y at which p is actual, and y is accessible to w.12 What is actual at possible worlds accessible from here will determine what is possible here. Accordingly, the modal realist can make sense of how our world contained the modal fact that we might evolve (or how our world could have had the relevant disposition), before there were minds to make assertions, since there were accessible possible worlds in which minds would evolve to make assertions (in fact, our world turned out to be one of them). Accordingly, the modal version of the dependence problem wouldn’t worry a modal realist. Possible-worlders are (like most people) inclined to deny modal realism (Stalnaker, 2012). Be that as it may, the possible-worlder is at least committed to possible worlds being more basic than propositions. Even so, they needn’t be concrete places! Modal realism is simply too incredible for most people to accept. Structured-propositioners often think that their view is superior because it can allow for propositions to be more basic than worlds. Worlds, on their view, can be constructed out of sets of propositions – providing us with a definitive alternative to modal realism. We have already concluded that the Russell-King response to the regular dependence problem leaves us unable to say that possible worlds are sets of propositions. However, let’s imagine that we had some way around that problem. Let’s imagine that we really can construct possible worlds out of propositions. According to the views on the table, there are no propositions before there are minds or languages. So there are no sets of propositions before there are minds or languages. So there are no possible worlds before there are minds and languages. Accordingly, before the evolution of minds or languages, there was nothing to make it true that human beings might evolve.

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You might hope to respond as follows: in our post-linguistic world, we can construct propositions that describe a world in which there are no minds. Indeed, we can construct propositions that describe this world before language evolved. We can say that, though no propositions exist in those worlds, there are some propositions available to us, in our post-linguistic situation, that are true at those worlds. The response that emerges runs as follows: the relevant possible worlds exist now, even if they didn’t exist before minds evolved. Those worlds now ground the fact that it was possible then for human life to evolve; those worlds also ground the fact, at worlds which never evolve life, that life is possible there, even though there are no possible worlds in those worlds. This sort of view has a number of serious drawbacks. 1. It creates a counterintuitive mirror image of Russell’s intuitive distinction of a world containing facts but no truths. On this account, there are no modal facts and no modal dispositions in the pre-linguistic world, but there are modal truths about that world, only stated and state-able from way over here. But if there were neither modal facts nor world-dispositions, over there, what makes our statements over here, true? And, if this modal fact, or disposition, didn’t exist before we evolved, then how was our evolution possible, since the fact in question is the very possibility of our evolution? 2. If possible worlds are sets of propositions, and propositions only come to exist when minds/languages do, then there’s a massive modal explosion once minds/languages evolve. Of course, King explicitly accepts that when languages come onto the scene there is an explosion of propositions coming into existence. That’s fine. But our new account has to say that there’s also an explosion of modal facts or historical modal dispositions. Only when there are languages can there be modal facts or modal world-dispositions, which all burst onto the scene once we have the relevant linguistic capabilities. And, some of these modal facts and/or dispositions are somehow retroactive. There was no modal fact about the possibility of human evolution at t0, nor was the world disposed to allow for such evolution, but there starts to be a modal truth at t1 about the possibility of human evolution at t0, which, in turn, creates a modal fact, or disposition, at t0. This view beggars belief.13 You might think that the adoption of eternalism will help us here. Assume eternalism. Since mind/language does evolve, the relevant sets of propositions always exist atemporally – as do all things, for the eternalist. If possible worlds are sets of eternally existing propositions, then possible worlds exist eternally. But, according to the views in question, nothing has any representational power at times where there are no minds. So possible worlds, for such an eternalist, might exist atemporally, but at

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times before minds are located, they are not located. Accordingly, at those times, the propositions which collectively characterise possible worlds, will have no power to represent ways that the world could be, and therefore they won’t have the power, at those times, to ground modal facts. Eternalism doesn’t help us to escape these worries. How can we escape the modal version of the dependence problem without embracing modal realism? There are a number of options. §4.2.1: Option 1: Combinatorialism The first option is to adopt a combinatorial view of modality. According to combinatorialism, a world is possible if it could be constructed, somehow, out of the raw materials of the actual world. In our world, even before human life evolved, the raw material out of which human beings are formed, existed. And thus, our modal fact – that human life might evolve – could have consisted in the existence of those raw materials and their combinatorial profiles. Unfortunately, combinatorialism comes at various costs. Modal logic is host to a debate as to which axioms should be allowed to govern modal thought. Accordingly, different systems of modal logic have been suggested, which compete with one another – so to speak. According to the dictates of the most powerful modal logic – S5 – if p is possible, then it’s necessary that p is possible. Combinatorialism seems to be incompatible with S5. Indeed, David Armstrong, a key proponent of combinatorialism concedes that he has to reject S5 (Armstrong, 1986, p. 585). Imagine: we could recombine some, but not all, of the raw material of this world, in order to construct a world that’s smaller than our own. That world is a possible world. But our world isn’t accessible to that world. That world doesn’t contain enough material to recombine back into our world. Our world is too big for it. So our world isn’t accessible – our world isn’t possible – from that world. This is where the conflict emerges with S5. Unless you can complicate the picture so as to give every world enough material to recreate every other world, combinatorialism forces our hand in the competition between different modal logics. Logical issues aside, combinatorialism rules out the possibility of worlds that are larger than our own – worlds with completely alien properties (not recombined from properties that exist in this world). Why should those worlds not be possible? This is another prima facie cost of combinatorialism. §4.2.2: Option 2: Rationalism The second option would be to follow Keith Hossack (2007). For reasons unrelated to our project, and unrelated to his own version of the MRTJ, Hossack adopts a theory of modality that could help us. He calls

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it a ‘rationalist’ theory of modality. Hossack argues that modality is, at root, an epistemic, and not a metaphysical issue. A fact is necessary iff it’s knowable a priori, and a fact is contingent iff it isn’t knowable a priori. On this view, the fact that humans would one day evolve was always possible since it wasn’t discoverable a priori. Unfortunately, this view comes with a number of costs. First of all, it too forces our hand into rejecting S5. S5 follows from a slightly weaker logic, S4, in addition to the Brouwerian axiom: B: ⊢ ♢□A → A (in plainer English: if it’s possible that it’s necessary that A, then – as a matter of fact – A). Given’s Hossack’s rationalist account of modality, B is unacceptable to him. To see why, notice that an equivalent form of B is: B': ⊢ A → □♢A (in plainer English: if A, then it’s necessarily possible that A). B', given the rationalist theory of modality, amounts to the claim that ‘if A, then it is a priori that it is not a priori that ¬A.’ But it’s clearly not right that, for any true proposition p, it’s a priori that the negation of p is not a priori! Accordingly, the rationalist has to deny B. S5 entails B, so the rationalist has to deny S5. The strongest modal logic open to the rationalist will be S4. The characteristic axiom of S4 is ⊢ □A → □□A (in plainer English: if A is necessary, then it’s necessary that A is necessary). Hossack (2007, pp. 135–6) does his best to motivate the denial of S5, appealing to various strange consequences that he thinks it entails (such as a sound ontological argument for the claim that God probably exists, that allegedly goes through on S5, and the surprising claim that if Socrates is possibly foolish then his possible foolishness exists necessarily). Despite these arguments against S5, I can’t help shake the feeling that tying ourselves to the rejection of S5 would be an over-reaction to the modal dependence problem. Furthermore, B has a certain intuitive appeal. Despite forcing our hand in the realm of modal logic, Hosaack’s ‘rationalism’ allows that there could be larger worlds – worlds containing truly alien properties – this possibility is closed off to the combinatorialist. But unfortunately, we generate new costs: we now have to respond to all of the compelling examples that Saul Kripke (1972) popularised; examples that seem to demonstrate the existence of a priori contingencies and a posteriori necessities. Hossack tries to fight that fight, with characteristic ingenuity. To that end, he is actually aided by his denial of S5 (Hossack, 2007, pp. 137–61). But we might be happier if we could avoid such a scuffle with Kripke.

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§4.2.3: Option 3: Worlds as Properties In correspondence, King maintains that this modal variety of the dependence problem needn’t worry him. He suggests that possible words are not sets of propositions, but maximal properties that the world could have had. The proposition that human beings could have evolved comes into existence when language does, but that proposition is made true by the existence of a mind-independent property. And thus, without modal realism, and without future possible worlds acting on the past with a magical backwards causation, King shows us that we’re able to avoid the modal version of the dependence problem, if only we accept that possible worlds are some sort of eternally existing property that the actual world could instantiate. But there are problems with thinking of possible worlds as maximal properties. You might worry about a massive inflation in one’s ontology. Are we really to believe that every way the world could have been, but isn’t, exists as a property? Realism about universals is one thing (I’m committed to it, but I want the MRTJ to be neutral on the issue). But many realists start to get queasy when you reify properties that are not, never have been, and never will be instantiated in, or by, the actual world. You might think that the relevant maximal properties are kosher because they are simply built up out of more pedestrian properties – properties that are instantiated, even if the complex property isn’t instantiated. For example, a possible world that has unicorns in it would be a property constructed out of the properties (among other properties) of being a horse, being white, and having a horn. All of these properties are instantiated in the actual world, even if the actual world doesn’t instantiate the complex property of being a world with unicorns in it. According to this proposal, there are no maximal properties who have, among their constituent properties, properties that are uninstantiated. This will make fewer people queasy. But, it follows, from this limitation, that there are no possible worlds where truly alien properties are instantiated. Why limit modal space so radically as to rule out the possibility of truly alien properties? And, how can this approach to modality allow for the possibility of truly alien properties without reverting to an inflated ontology, according to which every way the world could have been, but isn’t, exists as a property, many of which are not constructed out of actually instantiated properties? More worrying for King is the concern that worlds constructed out of properties, can no better do the work than sets of propositions can, before the evolution of minds – as I shall endeavour to explain. The central conviction shared by the MRTJ, King, Hanks and Soames, is that there can be no representation without minds (or without languages developed by minds). If propositions existed, and had the power to represent the world as being a certain way all by themselves, then they

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would be intentional entities. What would make them ‘intensional’ is, as George Bealer (1998) explains, That they violate the principle of extensionality; the principle that equivalence implies identity . . . [A]lthough the proposition that creatures with kidneys have kidneys and the proposition that creatures with hearts have kidneys are equivalent (both are true), they are not identical. Unless you’re a possible-worlder, you’ll think that some propositions are hyper-intentional – the proposition that 2 + 2 = 4 has the same intension as the proposition that 2 + 3 = 5 – and yet the two propositions are distinct. Accordingly, some propositions will be individuated not by intensions, but by hyper-intensions. Nevertheless, there are some (nay, many) propositions – like the propositions noted earlier about kidneys and hearts – that are individuated by their intensions. One reason you might have for thinking that nothing can have meaning unless a mind bestows a meaning upon it is if you think that nothing can have an intension (or indeed a hyper-intension) unless a mind bestows one upon it. An intension is a function from a possible world to an extension. The extension of a proposition is its truth-value. What makes a proposition meaningful is that it has an intension that maps it onto a truth-value in any given world (although hyper-intensions will be required to individuate necessarily truth-functionally equivalent meanings). Accordingly, you might well think that if propositions require minds before they can acquire truth conditions, or meaning, or representation, then you’re also saying that they require minds before they can acquire an intension (or a hyper-intension). The problem is that possible worlds thought of as abstracta, whether they are sets of propositions, or structured universals, will be intentional entities. This follows quite simply – on the assumption that worlds are properties – from the fact that properties are intentional entities. That two properties have the same extension in a given world is no proof that they are the same property (such as the properties of being renate and cordate, which have the same extension in this world, but come apart in other possible worlds, where there are beings with kidneys and no hearts, and vice versa). If worlds are properties, then worlds have intensions. More formally, Christopher Menzel (2016) demonstrates that abstract possible worlds (unlike the concrete worlds of a modal realist) are irreducibly modal, and allow for no reductive analysis of modality in terms of worlds. Instead, they understand worlds in terms of modality. A world is just a property that the world could have had, or a set of propositions that all could have been true together. So, in fact, the abstractionist has to give a different analysis of intensions to the one we’ve been working

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with. An intension isn’t a function from world to extension. On the contrary, worlds themselves are defined in terms of intentional entities. However, if possible, worlds are intentional entities, and no entity can have an intension before one is bestowed upon it by a mind, then there can be no possible worlds before there are minds. King’s suggested response to the modal variety of the dependence problem is no better off than the suggestion that possible worlds are sets of propositions. King could try to respond in the following way. He could deny that he has a problem with mind-independent intensions. When I put this problem to King, this, indeed was his reaction. He sees a basic difference between entities being representational and entities having an intension independently of a mind. What he finds objectionably mysterious is that one thing X could represent another thing Y as being a certain way merely in virtue of X’s nature, independently of minds and languages. However, since properties don’t represent anything as being a certain way, it doesn’t matter that they (or some of them) are intensional, they simply aren’t related to King’s concern. I don’t think that it’s so easy to make the distinction that he’s gunning for. I agree with him, full heartedly, that it’s objectionably mysterious to posit some entity, X, with the ability to represent another thing Y as being a certain way, purely in virtue of X’s nature, independently of minds and languages. But this seems to be so structurally analogous to the ability of some property X to map some other thing Y onto a truth-value at a world, independently of minds and languages, that it remains unclear why the latter ability shouldn’t be objectionably mysterious if the former is. I think that both phenomena are objectionably mysterious because I don’t see how abstracta are able to act on their own, and it seems as if representing and mapping really are a sort of action. They require minds. King could push back. The genesis of meaning might require minds, but nobody wants to say that the existence and proper function of properties require the existence of minds, even though properties have intensions (and, possibly hyper-intensions). To this, I would say the following: (1) If properties can indeed have intensions all on their own, then why can’t propositions, and if propositions can have intensions, why can’t they have meaning and representation? Because, if propositions do have intensions, all by themselves, then – without the aid of any mental activity – they are mapping worlds onto truth-values. Doesn’t that make them representational already? Are we not undermining ourselves here? (2) Since I am committed to the thesis that there can be no representation without minds, and since I can’t so easily force a large enough gap between meanings and intensions, perhaps I should be willing, simply to give up my commitment to the existence of mind-independent universals altogether. But that would certainly scupper the project of building mind-independent worlds out of properties. (3) If I don’t want to give up

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on the existence of universals, and I don’t want to give up on the dependence of intensions on minds, perhaps I have to choose between some form of Divine conceptualism or activism, according to which the objectively existing properties are the ones who derive their intension from the activity of the mind of God.14 If King doesn’t want to give up on the existence of objective properties, and he wants to maintain that mind-independent representation is mysterious, it would seem that he really needs to hang on to his distinction between mind-independent representation, and mind-independent possession of an intension, unless he wants to become a Divine conceptualist/activist. Unfortunately, I don’t see the distinction that he wants to draw as starkly as he does. To be fair to him, I’m more than open to the possibility that I’m simply not seeing something here. §4.2.4: Option 4: Theism If there’s a necessarily existing mind – let’s call it God (even though it needn’t have many of the properties traditionally associated with God) – and if that mind entertains all possible propositions, then, even on minddependent views of propositional content, there always exists every proposition conceivable. God is entertaining every proposition. In this way, we can make sense of talk about eternally existing propositions, eternally existing sets of propositions, and eternally existing ersatz possible worlds – defined in terms of sets of propositions. We can make sense of the claim that these worlds eternally, and at every moment, represent ways the world could be. They get their representational power from God’s mental acts. These ersatz worlds can ground eternally existing modal facts and help us to resolve our modal version of the dependence problem, and the traditional dependence problem too, without having to give up on explanandum seven. Of course, this God, that we’ve been forced to posit, only has to have the property of necessary existence and to entertain all propositions – for all our posit says, this God may not be omnipotent, benevolent, nor even omniscient, since this God only needs to entertain propositions, but doesn’t need to know their truth-values. I’m going to call this view theism even though I know that the job description of this God falls far short of the job description generally given to God by theists (and it’s not even clear to me that the work we’re giving here to God couldn’t be performed by a necessarily existent committee of minds who divide the work up). Nevertheless, one reason for this less than standard designation is that an entity that grounds all possibility might be sufficiently awesome to be worthy of worship; another reason for this designation is that the only people likely to find this option a plausible escape route from the problems that we’ve developed in this chapter are going to be theists to begin with. Theists – like me – already believe in the existence of a mind capable of doing the work called for here.

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Instead of positing an infinite number of concrete possible worlds (at least some of which anyway have a God, or God-like entities in them), we posit just one – albeit pretty awesome – mind. And instead of taking a stance on issues of modal logic, the theistic posit allows us to remain neutral as between S4 and S5. If God is acquainted with uninstantiated properties, existing only in Plato’s heaven (or in God’s mind), or if God has a vocabulary that includes predicates not to be found in any human language, and which can’t be truly predicated of anything actual, then larger possible worlds, with instantiated alien properties can be made sense of. The theistic way out of this problem isn’t completely free from complication. Direct realism entails that when God entertains a thought about you, he stands directly related to you, or that you should somehow be a constituent of the proposition entertained. But before you exist, it doesn’t seem as if he could entertain such thoughts. If that’s the case, then there won’t be modal facts about human beings before there were at least some human beings for God to be thinking about. I don’t see this worry as presenting a major obstacle since there are numerous ways out, depending upon your metaphysics of time, and/or your theology. For instance, if eternalism is true, then we are always available for God to think about, and for God to represent, even before our time comes, so to speak. Alternatively, if we don’t want to take a stance on the metaphysics of time, we could say that from God’s atemporal present, all times are equally accessible – you might think that you could make sense of such a claim irrespective of your metaphysics of time – and therefore God can think about things and people – irrespective of their location on the timeline – from his atemporal present.15 On this view, it will turn out that it is only in God’s atemporal present, so to speak, that our ersatz possible worlds eternally exist, and eternally represent ways that the world might be. Alternatively, if you’re a presentist, and/or you don’t want to take a stance on God’s relationship to time, you could appeal to general possibilities that become progressively more specific. Before any particular humans exist, God is thinking that it’s possible for humans to evolve, without thinking about any specific human. So the first possible worlds that God constructs would contain only general facts. On this view, only when particular humans come on to the scene, as was always possible for them to do, given the general modal fact that they could evolve, will God be able to construct possible worlds that contain particular human individuals. This general tactic could preserve every modal fact that needs to exist before non-Divine minds come onto the scene and also has a certain intuitive appeal – how could you yourself be a denizen of a possible world before you were even born? General modal facts, like the fact that humans like you could evolve are all that need exist eternally.

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Arthur Prior, as a consequence of his presentism,16 developed a conception of modality, according to which there are always general possibilities, and then more specific de re possibilities pop into existence when the relevant objects come into existence.17 I don’t think that this is at all an ugly consequence of the theistic response to the problem of modal dependence. Robert Adams defends the same sort of view (Adams, 1981). The view restrict de re possibilities to objects that presently actually exist. Even an eternalist might want to restrict de re possibilities to objects that actually exist atemporally. Leibniz writes, in his Monadology (as translated by Robert Adams (1994, p. 177)): It is true . . . that in God is not only the source of existences, but also that of essences, insofar as they are real, or of what is real in possibility. That’s because the Understanding of God is the region of eternal truths, or of the ideas on which they depend, and because without him there would be nothing real in the possibilities, and not only nothing existing, but also nothing possible. For if there is a reality in the essences or possibilities, or indeed in the eternal truths, that reality must be founded in something existing and Actual; and consequently in the Existence of the necessary Being, in which Essence includes Existence, or in which being possible is sufficient for being Actual. Adams unpacks this argument, and finds a very similar dialectic to the one that has led us to the same theistic hypothesis. One of the underlying premises is that, as Michael Dummett has stated, ‘It is certainly part of the meaning of the word ‘true’ that if a statement is true, there must be something by virtue of which it is true’ (Dummett, 1959, p. 335). At the very least, Adams suggests that this is a ‘philosophically respectable premise’ (Adams, 1994, p. 178). Before there were minds to represent things like numbers, what were their ontological grounds, and in what did arithmetical facts consist (or how did the world have the disposition to make arithmetical propositions true)? Leibniz’s answer is that there is always a mind to represent things: the mind of God. That mind grounds arithmetic. Russell prefers to appeal to a realm of Platonic facts. We saw that this Russell-King response works just fine for arithmetical facts. If the numbers 2 and 4 exist eternally, as Platonic abstracta, then so can the fact that 2 + 2 = 4. However, when we examine modal facts, and if we want to retain S5, and also to deny modal realism, then we struggle to account for their obtaining prior to the existence of some mind or other. This is where we might be tempted to join with Leibniz and give the work of sustaining eternal modal facts to the eternally and necessarily existing mind of God. Adams is sympathetic to this argument himself (Adams, 1983, p. 751).

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The role that God has to play on this theistic account is incompatible with some theologies according to which God’s thought and knowledge is not propositional.18 But many theologians would be happy to think of God’s knowledge and thought as propositional, and I’m anyway not here trying to defend any form of classical theism. I have already acknowledged that I’m using the label of ‘theism’ in a somewhat non-standard way. In fact, I’m not even defending any form of theism. I’m merely pointing out the various escape routes available from the modal variety of the dependence problem. This theistic route is just one of them. It happens to be my favourite because I’m independently a theist. We should note, however, that I’m not here advancing the view that propositions are thoughts in the mind of God (or any other mind). Nathan Shannon (2015) fears that if that was what propositions were, then our epistemic access to them would be severely restricted.19 Rather, this theistic option is proposed as an escape route for the MRTJ, or for any of the views of propositions put forward by Hanks, Soames or King. Whatever propositions are, and even if the MRTJ is right to paraphrase away their existence, it will turn out that God always entertains all possible thoughts. §4.3: The Underlying Cause of the Dependence Problem Possible-worlders do not suffer from dependence problems. For them, propositions are sets of worlds, or functions from worlds to truth-values. Accordingly, for them, propositions exist eternally and independently of the action of any mind. Structured-propositioners don’t have to be burdened with this problem either. If a proposition is just a set, or an ordered n-tuple, then they too can exist independently of mental activity. But the reason why the MRTJ, Soames, Hanks and King find themselves in this predicament is because all of them, in their various ways, make truth-bearers dependent upon mental acts, or upon the existence of linguistic communities. Russell’s distinction between facts and truths helps us to escape from almost every manifestation of the dependence problem, but we get stuck when we consider the existence of pre-mental, or pre-linguistic modal facts. However, there’s a reason why the MRTJ, Soames, Hanks, and King make their propositions dependent upon mental activity. The reason is that their theories are the only ones on the market really to take seriously the representation-concern. The idea that propositions can represent all on their own – whether they’re sets of worlds, or sets of objects – is mysterious. The idea that minds have the ability to represent the world, strikes us as less mysterious. We answer the representation-concern by demanding that representation and truth-bearing depends upon minds. This, in turn, gives rise to the dependence problem. But if you don’t make this move, you never get

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past the representation-concern. So, in a sense, it’s a good thing that we face this problem. It’s sign that we’re making progress! Furthermore, the dependence problem has a number of solutions: • • • • •

modal realism combinatorialism rationalism the possible worlds as properties view theism20

I’m independently a theist, and so theism strikes me here as the least costly option. It explains modal metaphysics in terms of sets of propositions (which are analysed away by the MRTJ). And thus, this option maintains that a theory of propositions really can explain the ontological foundation of possible worlds. Sets of propositions (which are analysed away in terms of judgements), of course depend upon the existence of a mind, but we avoid the modal dependence problem because we posit a necessarily existing mind entertaining all possible thoughts, which undergirds the metaphysics of modality. All of the other options threaten to inflate our ontology intolerably, restrict modal space so as to rule out the instantiation of alien properties, tie us to a weakened modal logic, and/or to give up hope of explaining explanandum seven with our theory of propositions. In light of all of this, the theistic option looks attractive to me (once you have God on the scene, you can also appeal to the activity of his mind to explain how inert abstracta, like objectively existing properties, are able to map objects from worlds to truth-values). Winding up this section, I can say this. The MRTJ, like any view that makes propositional content dependent upon the activities of minds, has to make the following choice. It can abandon explanandum seven. Unlike Keller, I don’t think that that is a huge sacrifice. To block the modal form of the dependence problem, it can then adopt modal realism, combinatorialism, rationalism, or (perhaps) the view that worlds are properties. Alternatively, the MRTJ can escape all of the problems associated with those views, embrace theism, and thereby resolve the modal form of the dependence problem whilst, at the very same time, explaining explanandum seven in terms of the propositional attitudes of the Divine mind.21

§5: Semantic Values The last three explananda that we surveyed in the introduction had to do with semantic values. The basic idea was that propositions have to exist in order to be the referent, or the semantic value, of certain expressions. The MRTJ, of course, doesn’t accept that propositions exist. Accordingly, it cannot seek to explain any semantic phenomenon with reference to propositions. The MRTJ is therefore stronger to the extent that one

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can provide well-motivated analyses of these phenomena that make no appeal to propositions. In the remainder of this chapter, I’ll address the issues in order of ease. Once all of these issues have been resolved, I turn to a certain puzzle about belief that should receive a solution (or at least, some sort of deflation) in terms of what we develop in this section. §5.1: Propositional Quantifiers We quantify over propositions. To be is to be the value of a variable. Therefore, propositions exist. Arthur Prior (1971), however, goes so far as to say: ‘I doubt whether any dogma, even of empiricism, has ever been quite so muddling as the dogma that to be is to be the value of a variable’ (quoted by MacBride (2006, p. 445)). Prior (1971, p. 37) provides us with the following inference. We infer from ‘I hurt him treading on his toe’ to ‘I hurt him somehow.’ However, there are no grounds upon which to think that we can infer from ‘I hurt him somehow’ that there exists some thing called ‘the way in which I hurt him’. MacBride (2006) charts the development of a view, which he calls Neutralism, that followed Prior’s lead. This view, proposed by Ruth Barcan Marcus and Wilfrid Sellars, argues that whether the use of a quantifier implies ontological commitment ‘will depend upon whether the class of constants that provide substitution instances for the variables it binds are referential expressions’ (MacBride, 2006, pp. 445–6). Since the adverbial phrase in the original derivation, ‘by treading on his toe’, isn’t even implicitly referring, ‘there is no need to construe the quantifier phrase “somehow” that replaces it as ontologically committing either’ (MacBride, 2006). Accordingly, if you want to prove that propositions exist, it’s not going to be as easy as observing the following sort of sound argument, and inferring from the conclusion that propositions exist: 1. Everything that Hilary believes, Bill believes. 2. There is something that Barak believes that Hilary believes. 3. Therefore, there is something that Barak believes that Bill believes. The premises and the conclusion seem to be quantifying over a domain of entities. The conclusion seems to be an existential quantification over that domain of entities. The argument is sound. So do we have to accept that something exists, such that it is what Barak and Bill both believe? What sort of entity would that be? Isn’t that obviously a proposition? No! We can accept the soundness of this argument without accepting that true quantification always comes at an ontological price. Premise 1 of the Hilary and Bill argument seems to be saying the following: 1

It is the case that for every x such that Hilary believes that x, Bill believes that x

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What this slightly clumsy paraphrase of 1 makes explicit is that the quantifier is really binding variables here that appear in the context of that-clauses. According to the Marcus-Sellars view then, whether or not these true quantifications really bring with them an ontological commitment to some realm of entities suitable to be the xs in this argument, is really a question as to whether that-clauses are referential expressions. So that brings us to the next sub-section! §5.2: That-Clauses and Contexts of Sentential Display Propositions are sometimes appealed to as the semantic value, or the referent, or the assertoric content (take your pick) of non-factive that-clauses. Non-factive that-clauses appear in one of two contexts. They appear in belief-reports: ‘Sally believes that Paris is in France’, and they can appear outside of belief-reports: ‘that someone is trying to kill her, keeps Sally up at night’. In what follows, I will try to argue, against appearances, that the linguistic significance of that-clauses give us no independent reason to believe that propositions exist. I will start by considering that-clauses as they appear in belief-reports, before moving on to a much briefer discussion of non-factive that-clauses outside of belief-reports. Howard Wettstein (2004, p. 176) directs his attention to a revealing sort of puzzle. Sam doesn’t know that John Wayne was the son of Mary Morrison. But everyone in John Wayne’s hometown – Winterset, Iowa – knows it. Sam thinks that John Wayne was a great actor. If people in Winterset, Iowa, care a great deal about Sam’s opinion of Mary Morrison’s son, it seems appropriate, and true to report, ‘Sam believes that the son of Mary Morrison was a great actor’. But in actual fact, Sam’s never heard of Mary Morrison! How can the report be true? And yet, in the right context, ‘such a report is unproblematically true’ (Wettstein, 2004). This kind of example demonstrates how ‘latitudinarian our practices are’ in the domain of belief ascription. However, there are other examples, Wettstein is quick to point out, that pull in the opposite direction. He here points to a family of well-known examples in which synonyms are not always intersubstitutable, in the context of a belief-report: [S]omeone can wonder whether a fortnight is a period of two weeks while being certain that a fortnight is a fortnight, someone can be certain that all (medical) doctors are (medical) doctors without being certain that all (medical) doctors are physicians. (Wettstein, 2004, p. 177) There are various well-trodden ways of making sense of these phenomena. The pragmatic route: When we report Sam’s belief that Marion

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Morrison was a great actor – if you’re a direct reference theorist – then you’re right. Sam does hold that belief, even if he doesn’t recognise that that’s the belief he holds, since ‘Marion Morrison’ and ‘John Wayne’ co-refer. In that case, the reason that that belief-report, in some contexts, sounds wrong (despite its truth), is because it might pragmatically convey, in some contexts, the false proposition that Sam knows that ‘Marion Morrison’ and ‘John Wayne’ co-refer. Alternatively, if you’re a Fregean or a descriptivist about names, it’s always false to report Sam’s belief as a belief about Marion Morrison, since, ‘Marion Morrison’ encodes a different description from, or has a different sense than, ‘John Wayne’. Nevertheless, this belief-report (despite it falsehood) might sometimes seem appropriate to us when, pragmatically, it conveys the information that Sam thinks, of the person that some people knew as ‘Marion Morrison’, that he was a great actor. A semantic route, for a Fregean, would look like this. Usually, when a name appears in a belief ascription, it needs to carry the sense that that name has for the believer in question. If Frank has a belief about Bob, for example, and I report this belief, then the word ‘Bob’ in my belief-report needs to carry the sense that Frank associates with that name. Otherwise, I’ll be reporting his belief incorrectly. But perhaps we can amend the Fregean view and say that when a reporter uses an embedded name, she attaches her own favored sense to it, in order to let it refer to its ordinary referent. A semantic route for the referentialist, might look like this. Where substitution fails, in a belief-report, it’s because the belief-report in question is doing two things – it reports a relation of belief obtaining between a believer and a proposition, and it also states that the embedded sentence is the sentence by means of which the proposition in question is believed – or to which the believer would assent. Because ‘Marion Morrision is a great actor’ is not the sentence by means of which Sam believes the proposition in question, and because it’s not a sentence to which he would assent, the belief-report is false if it’s doing two jobs, but true when it’s only doing one.22 Wettstein presents an alternative to these well-trodden routes. He contends that, belief-reporting is putting a sentence in somebody’s mouth. When you’re quoting somebody directly, you have to use the very sentences that they did. If you’re quoting them indirectly, or attributing a belief to them, then you have to present a sentence that, in the context of utterance, they might agree to be a fair representation of what they said, or what they believe. A belief-report, if it isn’t a direct quotation, is in the business of paraphrase. And to paraphrase is to provide a sentence that the original speaker would think fairly represents them in the context in which the paraphrase was uttered. Providing necessary and sufficient conditions for being an appropriate paraphrase is no easy task. However, one way to think about

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the appropriateness-conditions of a paraphrase is to think about the appropriateness-conditions of a translation. The two primary and often divergent goals of translation are also primary and often divergent goals of indirect reports. The reporter must be faithful to the original speaker’s remark. At the same time the reporter needs to choose a sentence that in the current context conveys the original speaker’s point. And there may well be no uniquely correct way to satisfy both desiderata. (Wettstein, 2004, p. 196) Wettstein’s next move is to suggest that phrases like ‘thinks that’, ‘says that’, believes that’, create a context of sentential display. A context of sentential display is one that, so to speak, displays a sentence. When something is displayed, you are encouraged to look at it, and to entertain it, perhaps for the sake of argument, but you needn’t assert it. When a sentence is displayed, it comes along with its normal semantic properties – its truth conditions remain intact, as do facts about what its parts refer to, etc. Wettstein sums up his view as follows: My idea about indirect discourse is that ‘says that’ creates just such a context. It’s like [a] display in that the embedded sentence occurs unasserted but with its semantics intact . . . I don’t take the embedded sentence of an indirect discourse report as a device of reference, nor do I take an indirect discourse sentence to be relational. ‘Says that’ rather creates the sort of context just described—display or quasidisplay—and signals that what follows is a contextually appropriate paraphrase. (Wettstein, 2004, p. 202) What would be a good paraphrase of a Shakespeare plot to a five-year-old might be a horrible paraphrase to somebody older. And thus, Wettstein’s account writes context-sensitivity into the heart of belief-reporting, seemingly where it should be, which in turn makes sure that our practices will be latitudinarian where appropriate, and strict where appropriate. By writing context-sensitivity into the heart of belief-reporting, one feels as if the right truth conditions of belief-reports are secured, not by way of epicycle, but in virtue of a real insight about what we’re doing when we report a belief. This is why, on reflection, Wettstein’s account seems stronger than the alternatives. To display a paraphrase is to display a sentence. If that-clauses within belief-reports simply generate contexts of sentential display, then thatclauses do not refer to anything other than the sentences that they display, and even then, they don’t refer to those sentence; they display them. That-clauses, on this account, do not refer to propositions. Propositions

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are not needed to explain the semantics of that-clauses; they do not oil the wheels of a theory of meaning for that-clauses. Of course, Wettstein’s account of belief-reporting doesn’t explain the mind-world relation that obtains when a belief ascription is true. That’s what the MRTJ can add to this picture. If you provide an appropriate paraphrase, you have provided a sentence that, in context, would be accepted by the person whose beliefs you’re describing. Now, of course, if they did accept that sentence, then they would stand in a multiple relation of assertion to the world. But that’s not what you’re saying, in any direct way, with a belief-report. You’re just presenting a sentence as a suitable paraphrase. We’re now left to account for non-factive that-clauses that occur outside of belief ascription. ‘That monsters were under her bed was what kept Sally up at night’. Note that if this sentence is true, then any appropriate paraphrase of ‘monsters were under her bed’ would be just as good, substituted in. If Sally lived in a world in which monsters were always thought of as green and hairy, then in some contexts, in that world, it might be just as good to say, ‘That something green and hairy was under her bed, was what kept Sally up at night.’ This gives one reason to think that the word ‘that’ even outside of a belief-report, in cases where the that-clause is non-factive, is still functioning so as to create a context of sentential display. Witness the following sentence: ‘That monsters were nearby is what kept Sally up at night.’ How do we interpret the word ‘nearby’: nearby to us, in the context of the utterance, or nearby to her at the time that she’s described lying awake? The fact that the salient location is nearby to her should lead us to conclude that the context is one that tries to represent things from her point of view.23 We’re finding sentences that apparently paraphrase her perspective. We have a context of sentential display on our hands. Wettstein’s account plausibly extends to all cases of non-factive that-clauses. Now we can return to the issue of quantification. If non-factive that-clauses are not referential expressions, then it also follows that quantification into such contexts doesn’t generate ontological commitment. You’re quantifying into a context of sentential display. It’s fairly clear then, that the values of those variables will be sentences – and not propositions. The quantification in question is going to be substitutional quantification. The idea that propositional quantification is something akin to substitutional quantification has been forcefully advocated by Thomas Hofweber (2005; 2006; Forthcoming).24 I think that this sort of view follows quite naturally from Wettstein’s promising account about the nature of contexts of sentential display. What’s more, if you’re not moved by Wettstein’s account of that-clauses, Hofweber proposes his own non-referential account. There’s no reason to think that that-clauses or so-called propositional quantification demand the reification of propositions.

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§5.3: Anaphora Peter van Elsywk explains: An anaphor is a context–sensitive expression whose meaning depends on a prior expression from the conversation in which it is used. The prior expressions are their antecedents and the range of meanings an anaphor can have is limited to the antecedents on offer in a context. The paradigm example of an anaphor is a pronoun like she, he, or they. When used anaphorically, she receives its meaning from an antecedent introducing an individual gendered as female.25 Van Elsywk goes on to argue that there are a class of expression that act like anaphoric pronouns for antecedently salient propositions. He goes as far as to say that even if you can explain propositional attitudes, and that-clauses, and propositional quantification, without reference to propositions, you will still be forced to reify propositions once you realise that there’s a class of anaphoric pronoun that can only be construed as referring to them. The three classes of anaphor that van Elswyk offers as pure propositional anaphora are (1) the word so; (2) response markers, like yes and no; and (3) ‘inference markers’, such as thus, therefore, accordingly, consequently, etc. van Elswyk develops a plausible tripartite test for being an anaphor. All three of his candidate classes of expression pass all three tests. The three tests are as follows: 1. Anaphors are infelicitous if antecedentless. 2. Anaphors can occur in donkey sentences. 3. Anaphors can be used strictly or sloppily. If I say, ‘It will rain soon’, you can say, ‘I think so too’. However, if there’s no antecedent, and you just blurt out, ‘I think so too’, then your statement will be infelicitous. Nobody will have a clue what you’re saying. You can’t use a response marker if you’re not responding to something, and you can’t use an inference marker unless you’re drawing an inference from something already said. A donkey sentence is a sentence that includes an anaphor which depends upon an antecedent that lies beyond its syntactic scope. ‘Every woman who owns a donkey treats it kindly.’ The word it in that sentence is an anaphor. And yet, a relative clause, such as who owns a donkey, is supposed to be a so-called ‘scope island’: ‘scope–taking expressions like quantifiers cannot take scope outside of [scope islands]. Nevertheless, indefinites, commonly viewed as existential quantifiers, can bind pronouns outside of a relative clause.’ We therefore see that it in our donkey sentence varies with every woman but receives its meaning from the

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antecedent indefinite (who owns a donkey) in the relative clause. Van Elswyk demonstrates that all of his expressions can occur in donkey sentences, varying with the quantifier phrase, but receiving meaning from an indefinite in a relative clause. For instance: 4. Not every lawyer who knows that a cop is corrupt says so ⎧⎪yes⎫⎪ 5. Not every lawyer who is publicly asked if a cop is corrupt says ⎪⎨ ⎪⎬ ⎪⎪⎩ no ⎪⎪⎭ ⎪⎧⎪ therefore ⎪⎫⎪ ⎪ ⎪ 6. Every lawyer who knows that a cop is corrupt ⎪⎨consequently⎪⎬ ⎪⎪ ⎪ believes that a cop is corrupt. ⎪⎪⎩ accordingly ⎪⎪⎭⎪ Van Elswyk’s expressions pass his second test. The strict and sloppy distinction, regarding anaphors runs as follows. ‘Ari saved her paycheck. Betty banked it’. Did Betty bank Ari’s check, or did she receive her own, and bank her own? The possibility for this type of ambiguity is characteristic of anaphora. Witness the following: 7. (a) Ari hopes that her paycheck was deposited on time. (b) Betty hopes so too. 8. (a) Ari hopes that her paycheck was deposited on time. (b) Yes, me too. ⎪⎧⎪ Therefore ⎪⎫⎪ ⎪ ⎪ 9. (a) Ari deposited her check. (b) Betty too. (c) ⎪⎨Consequently⎪⎬, Betty ⎪⎪ ⎪ had money to spend. ⎪⎪⎩ Accordingly ⎪⎪⎭⎪ It’s easy to see the ambiguity in 7 and 8. Does Betty hope that her paycheck was deposited on time, or that Ari’s paycheck was deposited on time? In 9, the sloppy reading is easiest to see. It’s because Betty deposited her own check that she has money to spend. And yet, a strict reading can be teased out as follows: Imagine Ari and Betty are partners sharing a checking account, Betty is unemployed, and Ari is regularly cut two paychecks due to an error in the payroll department at her work. Then the marker can be strictly interpreted as marking that Betty had money to spend follows from Betty depositing one of Ari’s paychecks. All of van Elswyk’s expressions seem to pass the tests for being anaphoric pronouns. This becomes especially compelling, once you look for, and fail to find, good counter-theories for the function of these expressions. Even on van Elswyk’s account, the response markers don’t merely refer to a proposition, they refer back to a proposition and then affirm or deny it.

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But using the term loosely, we can say, that these anaphora are vehicles of reference. And we can ask, to what do they refer? van Elswyk’s response is that they refer to propositions. I think he has made a compelling case for these expressions to be regarded as anaphoric pronouns. But do I have to accept that propositions are their referents? So far, we have found that all of our explananda for a theory of propositions can be explained without reifying propositions. Are we really going to fall at this last hurdle? And, if we do, is that not a large price to play for the explanation of one explanandum? We’re going to generate the quantity problem, the representation-concern, the Appendix-B paradox, and all sorts of other issues, simply in order to provide this small class of anaphoric pronouns with referents? I think we can do better, helping ourselves to the insight of Wettstein, regarding contexts of sentential display. I would argue that we should treat van Elswyk’s anaphora as metalinguistic pronouns that refer back (in a loose sense of reference), in order to re-display antecedent sentences.26 We’ve already surveyed good reasons for thinking that indirect quotation, and indirect discourse has contexts of display into which sentences are inserted as appropriate paraphrases of a person’s speech, belief, or attitude. Let’s take each type of expression in turn: 10. (a) Ari hopes her paycheck was deposited on time. (b) Betty hopes so too. 11. (a) Ari hopes that her paycheck was deposited on time. (b) Yes, me too. ⎧⎪ Therefore ⎪⎫ ⎪⎪ ⎪⎪ 12. (a) Ari deposited her check. (b) Betty too. (c) ⎪⎨Consequently⎪⎬, Betty ⎪⎪ ⎪ ⎪⎪⎩ Accordingly ⎪⎪⎪⎭ had money to spend. In 10(a), the phrase ‘her paycheck was deposited on time’ was displayed as an appropriate paraphrase, given the context, of a sentence that Ari would hope to be true. In 10(b), the word so redisplays that sentence, as a paraphrase of a sentence that Betty would hope to be true, but, because of the anaphoric her in the sentence, and the anaphoric way in which the sentence is being redisplayed, we’re not sure if her in the second display is supposed to refer to Ari or to Betty. The same basic analysis applies to 11(a) and (b), where a sentence is redisplayed – put into another person’s mouth, so to speak, and affirmed. Where our Wettstein-inspired analysis seems to get stuck, is when we look at the inference markers in 12(c). Nobody is being quoted, directly or indirectly in 12. There are no belief or attitude reports here. But still it’s not clear to me why we can’t adopt a metalinguistic analysis, even if we have no context of display. What these inference markers are marking is that the truth, in context, of the succeeding sentence is a consequence of the truth, in context, of the anaphorically referred to antecedent sentence

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(though of course, what it means for a sentence to be true is, eventually, cashed out in terms of judgements). I don’t see why these anaphora, beautifully identified as anaphora by van Elswyk, force us to posit an entirely new realm of entities, called propositions, to serve as referents, when all of the other explananda of a theory of propositions can be explained without them, and when even these anaphora can receive some sort of metalinguistic analysis. Finally, you might worry that certain non-anaphoric demonstratives function as vehicles of reference to propositions. Phrases like ‘that which she said’, ‘the thing he asserted’, ‘what you were thinking’, all seem to be referring to the content of assertions. We might think that there’s something quantificational going on here. However, it’s not going to be convincing that we’re quantifying over sentences, since no sentence may have been uttered, and the quantification doesn’t seem to be quantifying into contexts of sentential display – for instance, these phrases don’t all quantify into the midst of a that-clause. Are we to say that propositions must exist, in order to be the referents of such terms? I think we can develop a compelling semantic account of these phrases – following the general lead of Thomas Hofweber – that will leave us uncommitted to the existence of propositions. Take the following sentence for example: 13. She said something beautiful. Given what we’ve said so far in this chapter, it seems plausible that, in 13, we’re simply quantifying over contextually appropriate paraphrases of the sentence she said. If the example had to do with something she thought or asserted, then we’d be quantifying over contextually appropriate paraphrases of sentences she’d have been willing to endorse in her act of thought or assertion. Sentences like 13 don’t generate a worry for us. Now we’re worried about sentences like the following: 14. That which she said was beautiful. Note, however that 14 seems to follow from 13. We’re in the ballpark of what Stephen Schiffer calls a ‘something-from-nothing transformation’. A more classic example would be the inference from the following: 15. Jupiter has four moons. to 16. The number of moons of Jupiter is four. Sentence 16, in turn seems to imply that there is something that is the number of moons that Jupiter has – namely, 4. In other words, 15 is acceptable

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to a nominalist about numbers, but it seems to imply 16 which seems to wear ontological commitment to numbers on its sleeve. We’re in a similar situation with 13 and 14. We have a reading of 13 that allows a nominalist about propositions to accept it, but 13 entails 14, and 14 seems to wear ontological commitment to propositions on its sleeve. It is because commitment to propositions can be generated by such something-from-nothing transformations, that Schiffer feels compelled to admit that propositions exist, as what he calls ‘pleonastic entities’ (Schiffer, 2003). A pleonastic entity is one that falls under a pleonastic concept. A concept, F, is pleonastic if it implies true something-fromnothing transformations. The concept of being a proposition is pleonastic since it is implicated in true something-from-nothing transformations, and therefore propositions are pleonastic entities. Schiffer thinks that these things really exist, since our semantics seem to commit us to them, but that they come at barely any price. Their existence doesn’t interfere with anything else. They are merely pleonastic. However, with Hofweber, I don’t think that we should be compelled into any such ontology by the sorts of linguistic transformations that we’ve been talking about. The move from 13 to 14 doesn’t really generate a new ontological commitment. To see this, witness the fact that a language can contain syntactic devices for directing focus. Hofweber (2005, p. 264) presents the following sentences: 17. Johan likes soccer. 18. It is Johan that likes soccer. 19. It is soccer than Johan likes. It’s tempting to say that all three sentences express the same proposition (although King would probably have to deny this). The difference here is merely a function of focus. Using only 17, you could have the same effect as 18 by stressing the word Johan, and you could have the same effect as 19 by stressing the world soccer. In short, Hofweber’s advice would be to deny that 14 says anything different to 13. Sentence 14 is just a syntactical transformation of 13 designed to concentrate focus in a different way. If we have a reading of 13 that’s ontologically neutral as to whether propositions exist, then we can say that 14 says the same thing, but with a different focus. Don’t be deceived by the singular term in 14, that seems to be referring to a proposition: ‘These singular terms are the result of movement and extraction that places particular parts of the syntactic material of the sentence in special positions’ for the purposes of focus (Hofweber, 2005, p., 267). The semantic considerations which are supposed to generate ontological commitment to propositions don’t generate ontological commitment to propositions at all. This paves the way for our no-proposition theory of propositions.

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§5.4: Solving Kripke’s Puzzle It’s interesting, and instructive to note, that placing a wedge between that-clauses and propositions helps us to solve a famous puzzle. ‘Sam believes that Marion Morris is a great actor’ can only be true if Sam stands multiply related, by the relation of belief, to Marion Morris and being a great actor. But it’s important to note that, on my defence of the MRTJ, I’m making no claim that that belief-report refers to any such judgement. Instead, that report merely displays a sentence, and says that it’s a contextually appropriate paraphrase of a sentence that Sam would accept. To deny that that-clauses refer to propositions, or even – in any direct way – to judgements is what saves us from Kripke’s puzzle about belief (Kripke, 1979). Kripke asks us to imagine a young Frenchman called Pierre. As a child, his parents took him on an overseas trip to a town called Londres. He thought it was very pretty. As an adult, he spent some time living in London. He only got to see the miserable parts of the town, and came to the conclusion that London is ugly. At no point did Pierre realise that London and Londres are the same place. He thinks that Londres is pretty and that London is ugly. This is a troubling state of affairs whatever your philosophy of language. Because ‘Londres’ is a precise French translation of ‘London’, the Fregean will think that they have the same sense, the descriptivist will think that they encode the same description, and the direct reference theorist will say that they refer to the same thing. So how are we supposed to describe Pierre’s beliefs about London, without attributing an obviously contradictory belief to him; so obvious that he should have been able to figure it out for himself? Note, that for Wettstein, belief-reports don’t refer to propositions believed. They provide appropriate paraphrases of what the believer might be willing to accept. However, on Wettstein’s account, we should predict that there will be contexts in which belief-reporting breaks down: Think about cases in which the goals of reporting speech cannot be simultaneously met, in which faithful paraphrase seems to be incompatible with making the original speaker’s point accessible. Every good paraphrase seems obscure in the new context, and every one that adequately communicates misses something important about the speaker’s point. (Wettstein, 2004, p. 208) Kripke’s view is that the norms of belief-reporting break down in cases like Pierre’s belief. Wettstein’s account of belief-reporting explains why that should be the case.

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Unlike Wettstein, I do endorse a theory of propositions – even if only a no-proposition theory of propositions. Again, unlike Wettstein, I do endorse a principle of acquaintance. You have to be acquainted with the objects of your assertion. However, I do not demand much from the relation of acquaintance. I think of it as something like direct epistemic contact. I don’t think that it gives rise to a power of discrimination – to what Wettstein calls a ‘cognitive fix’. I think that Pierre is acquainted with London. He asserts that it’s ugly, and therefore stands multiply related to London and ugliness. He also thinks that it’s pretty, but because he doesn’t have a cognitive fix on London, but is merely acquainted with it, he is able to fall into the mistake of not realising that the thing he thinks is pretty is one and the same as the thing that he thinks is ugly. He does have a contradictory set of beliefs, but he’s falling into this situation unwittingly. Reporting this belief state, in most contexts, is going to be very difficult, if not impossible. We don’t want to make it sound as if he’s consciously endorsing a contradiction – since that’s not what he’s doing. Accordingly, we shouldn’t say that he thinks that London is pretty and not ugly, nor that it’s ugly and not pretty. The best that we can do is to tell the whole story as to how Pierre fell into the mistake that he’s fallen into. Simple belief-reporting, short of that, is going to get us into trouble, since it will make it look like Pierre is wittingly contradicting himself – which he isn’t. Either way, the MRTJ shouldn’t be fazed by the Kripke puzzle. It turns out that the puzzle has more to do with belief-reporting than with belief. The combination of the MRTJ with a Wettstein style account of belief-reporting seems particularly well placed to explain the puzzle away. According to this nexus of view, that-clauses (at least at the level of semantics) don’t refer to propositions, or to judgements (of course, they might refer to judgements, or possible judgements, at the level of assertion – but that’s not our interest right now). The failure of belief-reporting in our Kripke puzzle doesn’t mean that Pierre isn’t making judgements. We can even explain the contradictory judgements that he’s making, if we’re willing to tell the whole story; but the norms of simple belief-reporting may well break down in certain contexts. We start to see that placing a wedge between the semantic significance of that-clauses and our theory of propositions is exactly what gives us the room to free the MRTJ from somehow being implicated by Kripke’s puzzle. I hope to have shown that the MRTJ can do a good job generating explanations of all the explananda that a theory of propositions should ideally provide, whilst avoiding the explananda that a theory of propositions needn’t bother with. Explaining the explananda of a theory of propositions, without reifying propositions, is what warrants for the MRTJ, its renown, as a no-proposition theory of propositions.

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Notes 1 An anonymous reviewer points out that in order ‘to understand assertion and communication you are going to have to go beyond ‘mind-world’ relations, to look at the broader social and natural historical context into which human beings are ‘thrown’ to use Heidegger’s phrase’. But note that I’m not talking here about communication. I’m merely talking about the mind-world relation that minds stand in to the world when they make an assertion about it. No doubt that a theory of communication would have to look at broader social and historical context, but I don’t see that that’s relevant to the narrower metaphysical program at issue here. 2 An anonymous reviewer insisted again at this point, that ‘Short of mastering the art of [the] Jedi, the mind cannot put mind-external objects in an order.’ But that misses my point, and indeed, it misses Russell’s point. I refer people who share this concern to footnote 2, in the previous chapter. 3 Furthermore, if Soames is insistent that the MRTJ leave us with propositional objects – we can define them as Russell did (Russell, 1913, pp. 114–5) – see chapter 7, § 2.6. As should be clear, I just don’t see the need for any such ‘objects’. 4 An anonymous reviewer, at this point of the book, asked the following insightful question: ‘Why think that propositions represent rather than that they are what is represented for the early Russell? Surely the early Russell thought something like this when he held that true facts are propositions. . . Is it not natural that a similar view should carry over to the MRTJ?’ I hope to have rejected that claim in chapter 5, §2.2. I argue there, based on an analysis of what denoting concepts were supposed to achieve, in 1903, and on what ‘assertedness’ amounts to, that even when Russell thought that true propositions were identical to facts, he still thought that propositions represented. He just thought that they most often represented themselves! At the very least, he thought that we use them to represent themselves (except for the exceptional case of propositions containing denoting concepts). For Russell, propositions were always representational, or, at the very least, representation was always a concern of his. 5 See the instructive David Pears quote, in chapter 6, §4. He too describes the MRTJ as a theory in which the mind constructs pictures of possibilities using the very items that it’s thinking about. 6 Following Sainsbury, we called this concern (Liv) in chapter 8. 7 See (King et al., 2014, p. 237) 8 Soames claims (King et al., 2014) that his student, Justin Dallmann is able (in unpublished work) to reconcile his account with actualism, but without investigating Dallmann’s account, it remains true to say that there is work to be done here. 9 This view was proposed by, among others, Donald Davidson (1969; 2005). 10 Soames (King et al., 2014, pp. 34–5; 239) explicitly says that possible worlds are to be defined in terms of sets of propositions (although, in conversation, he seems to have changed his mind on this matter). And though King never explicitly went so far as to define possible worlds in terms of sets of propositions, he did celebrate the fact that such an option was open to him, given his denial of the possible-worder’s account of propositions (King et al., 2014, p. 57). 11 Spoiler alert: it’s going to require something like the adoption of theism. Keller (2016) also anticipates that belief in an infinite intellect would allow the views she targets to explain explanandum seven (although the views that call themselves naturalistic will then have become super-naturalistic).

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12 A world being such that possibly-p means that there is a fact, in that world, that makes the proposition ‘possibly-p’ true at that world, or it means that the world in question has the disposition to make the proposition that possibly-p true. The accessibility relation is a primitive relation that holds between worlds. I’m not going to say anything about the relation in this paper. Think of it, for the time being, as an epistemic relation – a world w is accessible from world y if a mind situated at y is able to conceive of world w. This is just a heuristic, it does a bad job describing what accessibility really is, but gives you something to work with, for our purposes. We will see another notion of accessibility, when we come to assess the view known as combinatorialism. 13 Thanks to Daniel Rubio for this worry 14 For the distinction between Divine conceptualism, and the closely related school of Divine activism, see (Gould, 2014). Stalnaker is reported to have raised the following objection at a talk given by Peter Hanks (Hanks, 2015, pp. 46, ft. 3). Propositions have objective truth-conditions. Similarly, properties have objective instantiation conditions. Those instantiations conditions don’t depend upon the activity of any mind. For example, the property of redness is such that it applies to all and only the red things. That’s just a brute fact about the property. The property doesn’t inherit that quality from any mind. If properties can have brute instantiation conditions independently of us, then why – Stalnaker asks – can’t propositions have brute truth-conditions independently of us? King tells us that propositions are different because they represent and properties don’t. Many people don’t find this to be a satisfactory response. These concerns occurred independently to Lorraine Juliano Keller in work of hers, in progress. I find myself torn here. On the one hand, I agree with King that representation does seem to be the sort of thing that requires explanation. But I also see why a proposition’s capacity to represent is so similar to a property’s capacity to be instantiated – perhaps, as I have argued, this similarity is bound up with their intensionality. Perhaps the best response for a person with my philosophical commitments is to accept (with Stalnaker) that there is no salient difference between a proposition’s capacity to represent, and a property’s capacity to be instantiated, but then to demand (contra Stalnaker and King) that both phenomena require the activity of a mind. If properties are to retain their objectivity, and to do their work, before the evolution of creaturely minds, perhaps we’ll have to defer to the activity of a Divine mind. As promised in chapter 2, footnote 8, Divine conceptualism (or activism) now seems to be a live option! Of course, this option gives rise to its own peculiar concerns. If properties depend upon God, what about God’s own essential properties? This bootstrapping concern, among other worries, is addressed in (Gould, 2014). Thanks to Keller, and Tyron Goldschmidt for discussing these issues with me. 15 You might think that Divine atemporalism is only really compatible with an eternalist metaphysics, since all times have to exist to be eternally present to God. Brian Leftow, however, develops a Divine atemporalism despite his presentist metaphysics of time (Leftow, 2009). Eleonore Stump has also told me that her conception of Divine atemporalism is supposed to be neutral over the question of the metaphysics of our time line. 16 To be clear, this view about de re possibilities was not a consequence of Prior’s theism. 17 See Arthur Prior (1968, pp. 78–87, ch. 8), the view has recently been defended against criticism by Márta Ujvári (2012). 18 For discussion of this issue, see Wes Morriston (2002, pp. 157–60). 19 For the record, I don’t share his fears, but, as I’ll go on to say, I also don’t think that my account falls into the category of views that he’s discussing.

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20 Perhaps the powers conception of modality presents us with another way out. The basic attitude of the powers conception of modality is to take modal dispositions to be primitive (Jacobs, 2010). It’s simply a brute fact – not to be cashed out in terms of possible worlds – that the pre-linguistic world had the relevant disposition to make human evolution possible. The powers conception of modality, like some of the other options we’ve sketched, struggles to account for the possibility of alien properties: it has to deny them, or inflate our ontology in order to make room for them. It’s worth noting that Jonathan Jacobs (2010) and Alex Pruss (2002; 2011) suggests a response to this problem that’s grounded in the existence of an omnipotent God. So this view of modality is, in itself, committed to a choice between a restricted realm of possibility, an inflated ontology, or to the existence of an omnipotent God. It’s interesting to note that this theistic response doesn’t demand a God who entertains propositional thoughts. It rather demands an omnipotent God. This is more squarely in line with all forms of classical theism than is my preferred theistic route. For similar reasons, to the argument developed in this part of this chapter, Keller (Forthcoming) also thinks that there is some sort of hypothetical argument to be had from a theory of propositions that represent on the back of mental activity, to the existence of an infinite intellect. 21 I imagine that Russell is turning in his grave at this combination of his MRTJ and my theism. Marilyn McCord Adams, on the other hand, has assured me that Russell no longer minds. 22 This is, broadly speaking, the view defended by Tom McKay (1981). I found McKay’s account deeply compelling, until I read Wettstein, who I think does an even better job making sense of belief-ascription. 23 Thanks to Mark C. Baker for discussing this case with me 24 The final of these three papers is particularly interesting since it summarises a lot of Hofweber’s work on these topics but also engages in a careful study of the changing attitudes of Stephen Schiffer on the question of the semantic and ontological significance of that-clauses and quantification over them. 25 All quotes in this section are from Peter van Elswyk (ms). 26 That I’m amenable to such a meta-linguistic analysis shouldn’t lead you to think that I’m replacing sentences for propositions wholesale. The MRTJ is what really does the work explaining the majority of our eleven original explananda. Sentences just help out with a few of them!

11 The MRTJ and Its Competitors

It should be clear by now that the considerations that might motivate the MRTJ today are not exactly what motivated Russell. For instance, we’re not worried about the truth-falsehood problem that seemed to motivate him, or by the existence of objective falsehoods. Those worries only get going if you adopt Russell’s somewhat idiosyncratic conception of propositional unity in which a constituent relation is required to relate the other constituents. Absent that theory of unity, you could unify the constituents of a proposition by the relation of set-formation or the relation of ordered-n-tuple-formation. If you did that, your propositions wouldn’t collapse into truth-making facts, and, your false propositions won’t look like non-obtaining states of affairs. Some of Russell’s concerns, however, do still stand. The MRTJ is motivated by direct realism. Indeed, a realism so direct that what you’re thinking about is directly before your mind without – even – the mediation of a proposition. The MRTJ is motivated by a brand of anti-psychologism that wants to make the objects of assertion completely mind-independent – even if the mind is given the responsibility of generating representation. Sainsbury’s MRTJ is also motivated by its dogged termism and its realism about universals (although MacBride’s MRTJ is neutral on those issues). More than anything, the MRTJ is motivated by the fact that it explains all of the explananda that a theory of propositions really owes us. It does this without positing the existence of propositions, but without neglecting the explananda, as Davidsonian meaning theories do – and thus the MRTJ, despite its denial of propositional realism, really is a theory of propositions: a no-proposition theory of propositions. In this final chapter, I revisit the various concerns that I raised in chapter 1 that theories of propositions need to avoid. I add to that toxic mix of problems the specter of the Appendix-B paradox. I compare and contrast the fate of the MRTJ and its various competitors against these concerns. Ultimately, in the light of this comparison, I claim that the MRTJ is a strong contender in the race to unlock the metaphysics of meaning.

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§1: The Representation-Concern Throughout this book, we have seen that the representation-concern is a major motivating factor for certain theories of propositions, and seemingly ignored by others. The concern is how the theory of propositions can explain the otherwise mysterious property that propositions are said to have, namely, the power to represent. Jeff King implies that his theory of propositions was the first – perhaps in the history of philosophy – to take this concern seriously (King et al., 2014, p. 48). I’ve argued that that’s not true. Russell’s MRTJ took it seriously. If this were a different (and longer book), I’d like to argue that Wittgenstein, in the Tractatus, took it seriously too.1 But before we return to King, let’s look at the theories that clearly don’t meet the concern. Sets of possible worlds don’t inherently represent anything. Why should they be thought as somehow representing the inhabitants of their members? The best route that a possible-worlder can take, in order to address the representation-concern, is to argue that to have truth conditions is to be representational. A possible-worlder can give a very clear account of what truth conditions any set of worlds should receive. Or, if they think of propositions as functions from worlds to truth-values, it’s relatively easy to give each function a clear definition – the proposition will be true if the function maps our world to the truth, and false otherwise. If your theory can divvy out appropriate truth conditions, then representation has been explained. The same tactic could be adopted by a structured-propositioner who thinks of propositions as structured sets, or ordered n-tuples. A convention will stipulate how they would have to correspond to a fact in order to be true. They therefore receive truth conditions, and they therefore represent. The idea that the divvying out of truth conditions is sufficient to generate representation is one that Mark Sainsbury seems to cling to. As Sainsbury understands matters, two competing theories arise from his defence of the MRTJ. The first theory to arise from Sainsbury’s defence is the traditional MRTJ, refined and padded out as we explored in chapter 8. On this theory, judgement is a multiple relation between a mind and an ordered-many. An axiomatic theory of judgement will state, for every universal, what roles that universal can play in determining the truth conditions of a judgement. The theory has the power to determine, in advance, which ordered-manys can receive a truth-value (and therefore, which can be judged) and the power to provide the truth conditions of any such ordered-many. The second theory to arise from Sainsbury’s analysis will allegedly do all that the MRTJ can do, but it won’t eradicate propositions. Think of a sentence as a concatenation of words. Now, think of a proposition as a concatenation of meanings. Why not say that such concatenations exist? Unlike the early Russell’s propositions, these propositions seem

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inoffensive. They’re not forced to be true, since their object-relations are not doing any relating in the concatenation itself – they’re just concatenated alongside other entities in a specific order. On this view, judgement is a relation between a mind and an ordered set. Judgement is a binary relation. Sainsbury’s axiomatic theory of judgement plays the same role here. It will distinguish between ordered sets that receive no truth conditions (and are not, therefore, propositions), and ordered sets which do receive truth conditions: namely, propositions. The theory will specify, for any proposition, what its truth condition will be. And in answer to the Stoutian concern – what distinguishes a proposition from a list – Sainsbury will say: just as an ordered ensemble of words receives a truth condition, and therefore a meaning, within the context of a language – as stipulated by the language’s Davidsonian meaning theory; so too can an ordered set of entities receive a truth condition as stipulated by a theory of propositional meaning. Sainsbury writes, Russell wanted a multiple relation theory because he thought that if judgement related one who judged falsely to a single thing, it would have to be an unpalatable ‘objective falsehood’. On my proposal [i.e., assertion as a binary relation to a concatenation of entities], there is no such problem, so the most obvious theory of judgement would relate thinkers to concatenations of meanings. (Sainsbury, 1996, p. 110) According to Sainsbury, theory two – the binary relation theory of judgement – is more obvious, and therefore preferable, to theory one – the MRTJ. Sainsbury can adopt concatenations of meanings as propositions – essentially, ordered n-tuples. However, this defence of a binary theory over the MRTJ seems to conflate the systematic provision of truth conditions with an explanation of representation. The MRTJ puts the mind in the driving seat as the originator of representation. Sainsbury’s binary alternative doesn’t do that, and therefore his concatenations may well receive a truth condition from his theory, but does that mean that they are inherently representational? It doesn’t seem that way to me. There is a tendency among some philosophers to say that a theory is good if it makes all the right predictions and makes sentences that should clearly be true come out true. If the theory does that work for you, then it’s a good theory. A case in point: David Lewis would argue that to have free will is to have counterparts in other worlds who make different choices than you do. Were you free when you chose to do X? Yes, because you had a counterpart who chose otherwise. Some would respond that this isn’t what they meant by freedom. They want their freedom to consist in what they could have done, and not in what their counterparts do do! This is the sort of concern that Kripke raises with counterpart theory and

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has been called the Humphrey-objection (although his concern wasn’t with free will so much as with contingency in general). The Lewisian response is simple: my theory preserves all the things you want to say. You want to say that you’re free. My theory says that it’s true that you’re free. Tough luck if it turns out that the metaphysics that preserves that semantic data isn’t what you had hoped for. Likewise, here, the possible-worlder and Mark Sainsbury’s concatenation theory can say, my propositions are representational because they have truth-values. This response maintains that receiving a truth condition from a theory is what it means to be representational. The Humphrey-like response would be to say that that isn’t what we meant when we said that something is inherently representational. To those people inclined to take the Humphrey concern seriously, it should be clear that possible-worlders, and most conceptions of structured-propositions, have given their propositions truth conditions but haven’t explained their representational power. Even if having an intension is a prerequisite for being a representation, the possible-worlder can’t be right that intensions themselves are representational. If I want to, I can use a mapping from our world onto the false to represent something true. I could use it to represent snow being white. It’s up to me what I use to represent what. If propositional representation is nothing more than having a truth-value systematically specified by a theory, but you can’t explain why propositions are such as to deserve such a specification, and you reach for some excuse such as ‘well, that’s what propositions do’, then your account of propositional representation seems no more explanatory than the account offered by a propositional primitivist.2 When I say that propositions are representational, I mean something more than that your theory happens to divvy out truth conditions to them. I think that those who are unmoved by the Humphrey concern will probably be unmoved here. Nevertheless, I hope that two further considerations could help to win some people over from the Lewis to the Kripke camp on this particular issue; into taking the representation-concern more seriously. The first consideration is to reflect upon the history that we explored in part II of this book, and the constructive proposals for saving the MRTJ that we explored in the earlier parts of part III. It was possible to answer Wittgenstein’s concerns with the MRTJ without touching upon Stout’s concern, but it was barely possibly to solve Stout’s concern without meeting Wittgenstein’s constraints (including the no constraints constraint) in the same breath. This went to indicate that Stout’s concern was somehow more fundamental. Wittgenstein was merely concerned with giving every proposition a well-defined truth condition (without recourse to supplemental premises). Stout’s concern was the representation-concern. A wide-eyed appreciation of the history might help to wake some people up to the fact that securing truth conditions isn’t enough; securing representation is.

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A second consideration is to reflect once more upon Jeff King’s words (King et al., 2014, p. 47): I am of course not saying that any time a thing has a property, there must be some explanation for how or why it has that property . . . But certain sorts of properties are such that we feel compelled to give an account of how/why something manages to possess them and perhaps even what the possession of them consists in . . . Perhaps it is not entirely clear what it is that makes a property such that possession of it is something that needs to be explained. But it seems utterly clear that the property of having truth conditions is the sort of property whose possession is in need of explanation. I have argued repeatedly, throughout this book, that King is surely right to conclude that the power of a mind to represent things is so much less mysterious – so much less calling out for explanation – than the power of inert, inanimate abstract propositions, to represent the world. It seems appropriate in the philosophy of language to treat the power of the mind to represent as a brute primitive, even if, in the philosophy of mind, it should be explored and explained; but it is inappropriate in the philosophy of language to leave unexplained the representational power of the abstract objects that we posit. The reason I have repeatedly reverted to King, Soames and Speaks as the putative competition for the MRTJ is that they’re in a small niche of thinkers about the nature of propositions who take the representation-concern deeply seriously. Peter Hanks also takes this concern very seriously (his account of propositions, which he’s been championing since 2007, is very similar to the view adopted by Soames (Hanks, 2007b)). And yet it’s my contention that all of them fail to mollify the representation-concern, despite their taking it seriously. Indeed, in the face of this concern, the MRTJ is the only theory of propositions left standing. Speaks’ account of propositions brings his view of assertion into territory close to the MRTJ. It’s quite conceivable that assertion might be, for Speaks, a multiple relation. For instance, Speaks seems comfortable with the idea that to assert that the ball is red is to predicate being such that the ball is red of the entire world. That means, in the act of asserting this, you stand related to the property of being such that the ball is red, and to the world. You predicate the first of these relata of the second. This all sounds like the MRTJ. We get why this is representation. This is an act of predication. But Speaks goes further than the MRTJ because he thinks that the monadic properties that we predicate of the world are propositions. These properties seem ill suited to be propositions since they’re not obviously representational. We use them as predicates, and that use generates representation. However, they are not representational in and of themselves. In fact, they are like reified versions of Bradley’s

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floating adjectives. Speaks wholeheartedly accepts that they are not representational – but why say that they are propositions? They are more like predicates. Soames takes himself to have met the representation-concern because he places the mind at centre stage. We can see, intuitively, why this might help. However, it’s as if he gets confused between the properties of a token and the properties of a type. He thinks that propositions are mental event types. I can see why an act of predication generates representation, but I don’t see why the event type is representational. At times, Soames argues that the type inherits this property from its tokens (Soames, 2010, p. 107). Peter Hanks once endorsed the same view: propositions are mental event types that inherit their representational power from their tokens (Hanks, 2007b; 2011). This seems like a confusion. We need a solid account as to why and when a type inherits the properties of its tokens. Sometimes properties are inherited in this way; sometimes not. A token of a $5 bill is worth $5. The type of being a $5 bill, on the other hand, is worth nothing on the open market. Why think that the event type of asserting something is inherently representational, just because the tokens of that type are?3 Soamesian propositions are not representational – or at least he hasn’t given us sufficient reason to think that they are. When pressed on this issue, Soames changed his view somewhat. He now argues that regular representation is possessed not by event/action tokens, not by event/action types, but by the agents themselves, and that in virtue of that, the relevant event types inherit, not the same property, but some extended or derivative version of the property of representation (King et al., 2014, p. 231). But one is left scratching one’s head. What is this extended sense of representation, and is it really representation? Caplan et al. (2013) pile on other concerns to this new theory of Soames. I remain unconvinced that Soames has really answered the representation-concern. We’ll come back to Hanks shortly. King also seems to stumble here. He accepts that his propositions – which are the strange sort of linguistic fact that we described in the chapter 1, §2.5 – are not inherently representational, but he thinks that speakers of a language will naturally interpret them. It is the act of interpretation that bestows representation upon King’s propositions. I think that, in many ways, this is the best account of the proposition’s power to represent.4 But I actually think it leads to a very particular, new problem. Let’s imagine that p is the proposition that Michael swims. The proposition contains Michael and the property of swimming as constituents. The syntactic machinery of property-ascription, contained in the fact, leads all speakers of a language, who are perhaps born with an innate stock of syntactical knowledge, which naturally leads them to interpret certain structures in certain ways, upon acquaintance with p, to interpret it as representing Michael as swimming. Let’s grant King all of that – even

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if we have our doubts. Here comes the problem. The act of interpretation seems to have propositional content: (i) I interpret p to be representing Michael as swimming It seems fair to me to represent (i) as equivalent to (ii): (ii) I assert that p represents Michael swimming But (ii) can only be true if I have available to me the proposition that p represents Michael swimming. That proposition, according to King, is also a fact, call it q, which speakers will naturally interpret as representing p to be representing Michael to be swimming! But the act of so interpreting q has propositional content too. We seem to be on the edge of an infinite regress; exactly the sort of regress that Moore alleged against Bradley’s theory of judgement. You can never interpret a proposition, since you need to complete an infinite sequence of acts before you can. King is aware of this sort of concern (King, 2007, pp. 65–7; King et al., 2014, p. 60). One option, he considers, is that we’re born, and our pre-linguistic ancestors were born, already understanding some sort of language of thought. So we human beings came equipped somehow, already acquainted with, and understanding, certain propositions, from which we could build up the rest, and, from our meagre beginnings, we’d have the mental vocabulary necessary for attaching semantic significance to syntactic structure, in order to develop public languages, and allow new, meaningful, propositions to blossom into existence. King isn’t satisfied resting his theory upon the existence of such a hardwired language of thought. However, even if he did rest his case upon it, it’s not clear that it would work. How would we understand the propositions that we’re born acquainted with? What would make them representational, unless we were interpreting them? And, even if we interpret them in a pre-programmed, instinctive way, that act of interpretation still has content, and that content is propositional, and needs interpretation, which introduces new content that also needs interpretation, and before we can understand any proposition (tied to a private or a public language), it seems as if we need to have completed an infinite sequence of interpretative acts. I just don’t see how its being a language of thought, or its being pre-programmed into us, can help us to escape the regress. The other route that King appeals to is to suggest that, our ancestors, at least, were born with ‘proto-intentional-states’, these proto-beliefs and proto-intensions were somehow sufficient to bestow semantic significance upon lexical items, and ‘more generally to do what had to be done to bring propositions into existence’ (King, 2007, p. 67). I just don’t think I have a good enough grip on what these proto-intensions and proto-beliefs must

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have been, in order to have the power to bestow semantic significance, and the power to represent, without requiring content or representation in the first place. And if you too think you don’t have a good grip on what these states must have been, you’ll worry that King hasn’t solved any problem here, but waived his hands at it. Furthermore, even if our proto-intensions, and those of our ancestors, were enough to bring full blown propositions into existence, isn’t it important that we all, each in our own day and age, continue to interpret those propositions? Do we have an account as to how we do this without infinite regress? To block the regress, you might think that moving from (i) to (ii) is unwarranted. Interpreting p to be representing Michael as swimming isn’t to assert anything about p. Perhaps this is the sort of move that King intends with his talk of proto-intensions. But as we saw in chapter 2, §2.1, Bradley tried a similar move to escape Moore’s regress, and it didn’t work. Even if interpreting p is stipulative, or unconscious, or primitive or ‘proto-intentional’, it still seems to be an act with propositional content. Where did that content, and its power to represent, come from? Who interpreted that? And why didn’t that act of interpretation require its own content? And so on and so forth forever more. This regress will be difficult to escape. The MRTJ is the only theory to meet the representation-concern because it doesn’t seek to reify bits of representational information that exist outside of mental acts. There are no propositions. There are merely acts of assertion. And yet, we still have a theory of propositions on our hands – a no-proposition theory of propositions – since the MRTJ manages to explain all of the explananda that a theory of propositions ought to explain. It also makes no mystery of representation. Scott Soames thinks that it’s an ‘incredible’ corollary of the MRTJ that you can’t straightforwardly talk about that which is believed (Soames, 2015, p. 445). Instead, all such talk receives a transformational analysis in terms of acts of assertion (and, I would add, a semantic interpretation in terms of focus constructions and contexts of sentential display). But what we see now is that if you want to reify that which is believed, you’re never going to be able to secure for it the property that it should have if it exists at all – the power of representation. We’re better off without any such reification; for only that way can we ensure that mental acts, rather than abstract objects, remain the seat of each and every variety of representation. Soames would argue that a mental act can be strong, or halting, or deliberate, but that it can’t be true or false (Soames, 2015, p. 446). Truth and falsehood are properties of the content of the act, but not of the act itself. But this once again falls into the trap of thinking that you can peel off some abstract entity called a content that has the power to represent all by itself. What we learn when we realise that representation is firmly anchored in acts of representation, is that mental acts are indeed the only things that can be, ultimately, true or false.

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Hanks has come round somewhat, and actually agrees with Russell that mental event tokens are what play the role of ultimate bearers of truth and falsehood. Unlike Soames, he accepts that an act of judgement can be true or false. When he says that his propositions, construed as mental event/action types, inherit truth-values and representation, he really means that they inherit some sort of derivative, or second-hand truth-value and power to represent (Hanks, 2013). But why make this move? Once we’ve realised that it is acts of representation that are the bearers of truth and falsehood, and once we’ve realised that all of the other explananda of chapter 10 can be explained without reifying propositions, why not rest satisfied with the MRTJ?

§2: The Problem of Quantity She tasted the largest bowl, which belonged to the Big Bear, and found it too cold; then she tasted the middle-sized bowl, which belonged to the Middle-sized Bear, and found it too hot; then she tasted the smallest bowl, which belonged to the Little Bear, and it was just right, and she ate it all. Robert Southey, The Three Bears

The problem of quantity faced by theories of propositions challenges us to make sure that we don’t generate too many propositions, and that we don’t generate too few propositions, but that the quantity of propositions we generate should be just right. In other words, it’s a goldilocks conundrum. The problem is most closely associated with possible-worlders. As we saw, in chapter 1, the identification of propositions with sets of worlds at which a certain sentence would be true, or with functions of worlds to truth-values, makes it look as if every necessarily true sentence will express the same proposition. It’s clear that a possible-worlder could respond in various ways. They could bite the bullet and say that we’re not always in a position to know that two sentences actually end up expressing the same proposition, think of Pierre, in the previous chapter; but once we realise that two sentences are necessarily true, that’s what we come to know, in spite of strong and lingering appearances to the contrary. Alternatively, the possible-worlder could appeal to the existence of impossible worlds. Perhaps there’s an impossible world in which ‘2 + 2 = 4’ is true, and all other sentences that we call necessarily true, are false. That world isn’t possible, of course, but if you accept that impossible worlds exist, then it can serve to make the set of worlds in which 2 + 2 = 4 sufficiently fine-grained so as to distinguish the proposition that ‘2 + 2 = 4’ from all other propositions. Perhaps, even without appealing to impossible worlds, you could impose certain structure upon your modal space in order to model the fine-grained structure of propositions.

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I’m not sure that impossible worlds are a coherent notion. It depends what worlds are, I suppose. But Adriane Rini and Max Cresswell are of the opinion that they’re not coherent at all (Rini and Cresswell, 2013, p. 31): A proposition is impossible if it is true in no worlds—that is to say the impossible proposition is the empty set ∅. From this we see that there can be no impossible worlds. For, on the assumption that an impossible world w is a world at which an impossible proposition is true, we have that if w is an impossible world then w ∋ ∅. But since ∅ is empty there can be no such w. But even if we accept that we can formulate a coherent notion of impossible worlds, or we bite the bullet and accept that all necessarily true propositions are identical to each other; I still can’t believe that what we actually assert, when we assert something, is a set of worlds, or a function. I simply can’t believe that standing related to such a thing explains the mind-world relation that obtains when someone makes an assertion. This instinctive reaction of disbelief is probably fuelled, in part, by the representation-concern. I know that this will fall on deaf ears among many supporters of a possible world conception of propositions, but, as I said in the previous section, having the right truth conditions imposed upon you by a theory doesn’t make you, inherently, a representation. To summarise: perhaps possible-worlders can escape the quantity problem, but only at the cost of a more unsightly ontology, and even if you’re willing to pay that price, you haven’t answered the representation-concern. We’ve seen – in chapter 1 – how Soames seems to generate too many propositions. King accuses him of generating three propositions that all say that Romeo loves Juliet. King also can’t escape this problem because for him, as soon as there’s a syntactic difference between two sentences, there must be more than one proposition, since propositions are, in part, individuated, on his account, by the syntax they inherit from the sentences that express them. In chapter 4, we saw cases of sentences that intuitively seem to express the same proposition when uttered by Frank, even though the syntax of the two sentences are significantly different. One example we saw was the following: 1. Dave might be in Oxford. 2. For all Frank knows, Dave might be in Oxford. Uttered by Frank, it seems as if either of these sentences would assert the same thing. King has to argue that there are two distinct objects of assertion here since the syntax of 1 and 2 are so different. Small syntactic differences will pose less of a challenge to King, who can appeal to more and more generalised linguistic facts that abstract away from minor syntactic

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differences between instances of the general fact (King et al., 2014, p. 58). But the differences between 1 and 2 will leave King with different propositions, or with a vacuously general theory. You might side with King in this case, because you might think that 2 gets the analysis of epistemic modals wrong. 1 and 2 simply say different things. But to rule out the possibility of two sentences ever expressing the same object of assertion despite significant differences in syntax seems like a case of excessive deference to syntax. Take for example the two sentences contrasted by Frege in the Grundlagen: 1. Jupiter has four moons 2. The number of moons that Jupiter has is four How can King escape the conclusion that these sentences express distinct propositions, even though most people would think that they say the same thing? The MRTJ has no such problem. It’s consistent with the denial of the identification thesis (see chapter 4, §1.1), which allows an agent to be making the very same assertion when they utter 1 and 2, even if 1 and 2 have distinct semantic values.5 King also generates too few propositions. He seems bound to accept that the following two sentences, when uttered by Frank, express the same proposition: 3. I am a philosopher. 4. Frank is a philosopher. That seems wrong, since it’s possible for Frank to know the truth of 4 but not the truth of 3. He may be an amnesiac, reading a philosophy book by Frank, without remembering that he, himself, is Frank. Other theories do a better job of accounting for the sui generis content of de se predication. On Jeff Speaks’ account, for example, when Frank utters 3, he self-ascribes the property of being a philosopher. When he utters 4, he self-ascribes the property of being such that Frank is a philosopher.6 Those two properties – the property of being a philosopher and the property of being such that Frank is a philosopher – are clearly non-identical. Since Speaks identifies the propositions expressed by 3 and 4 with those two properties, respectively, he can explain why we have two propositions on our hands. Soames can also make the necessary differentiation here, since he maintains that self-ascription is a different type of mental act, to general assertion. The MRTJ can make the very same move. We can appeal to the multiple relation of self-ascription to make sense of de se content. When Frank asserts 4, he stands related by the multiple relation of judgement to Frank (i.e., himself) and to the property of being a philosopher.7 When Frank asserts 3, he stands related by the multiple relation of

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self-ascription (which is, in this case, dyadic) to the property of being a philosopher.8 King can’t make a differentiation here, since both sentences have words that refer to Frank at their left terminal node. And though Speaks is well placed to account for the special nature of de se assertion, he ends up generating too many propositions elsewhere. He calls this a problem of demarcation (King et al., 2014, pp. 89–90). He maintains that propositions are monadic properties – like the property of being such that Frank is a philosopher. But he also maintains that not every monadic property is a proposition. Until he can give us sufficient conditions for being a proposition, he doesn’t yet have a fully-fledged theory. Furthermore, a person should be able to self-ascribe any monadic property, if they’re sufficiently deranged – for example, I might assert that I am the square root of 49. This means that being the square root of 49 needs to be a proposition, available for self-ascription, since it’s the proposition I assert in my moment of madness. But being the square root of 49 isn’t the sort of thing that even Speaks wants to call a proposition. The MRTJ escapes this problem. It allows that you can self-ascribe that property. But the MRTJ denies that propositions exist, so it doesn’t feel compelled to say that that property that you might self-ascribe is itself a proposition. In fact, Speak’s theory would almost collapse into the MRTJ if only he would recognise that the predicates he has the mind use to generate meaning are just that – predicates – and not propositions.

§3: The Problem of Aboutness The aboutness concern arises automatically for any view that doesn’t answer the representation-concern. It’s somewhat mysterious how a set of worlds in which ‘2 + 2 = 4’ is about the number 2 and the number 4. Worlds aren’t inherently about their inhabitants, and sets of worlds are not inherently about the inhabitants of their members. However, the aboutness concern has other ways of rearing its head. We saw, in chapter 1, that for Speaks, assertions all end up being about either everything or nothing, or any arbitrary thing. The MRTJ is free from these manifestations of the aboutness concern because the MRTJ recognises that judgement has particular and specific objects of predication. In fact, at least when we consider atomic propositions, the MRTJ provides us with the purest version of aboutness on offer. Most structuredpropositioners can probably give you a formal account, given any structured proposition, of what that proposition is about. Despite the worry I raised in the previous paragraph, Speaks could probably generate such an account too. Maybe a possible-worlder could even generate an account that provides a formal definition for any set of worlds, what that set is about, and provided their partition of modal space imposes lots of

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structure, perhaps they’ll make every proposition about what it’s really about! However, not only might this strike some readers as artificial, these moves also impose a veil between the mind that asserts and the things that those assertions are about. On all of these accounts, assertion is a relation between a mind and a thing – a set of worlds, or a structured proposition – and on all of these accounts, the thing you stand related to isn’t what your assertion is about. Instead, the thing that you stand related to is about what your assertion is about. Your assertion, so to speak, inherits aboutness from the proposition. Only the MRTJ stands you directly related to the things that you’re thinking about. Only the MRTJ rids us of this veil of propositions. Incidentally, we can see that Speaks’ account would complete its evolution into the MRTJ if, after accepting that its predicates are not propositions, it realised that we are able to use more fine grained predicates to make judgements about specific entities, rather than every judgement having the whole world, or nothing in particular, as its object. Things get a little murkier for the MRTJ when we consider molecular propositions. I had said, in chapter 1, that the judgement that there’s a lion in the forest doesn’t appear to be a judgement merely about the properties of being in the forest, and being a lion – asserting that the two properties are co-instantiated. On the contrary, it either seems to be a judgement about the lion, or the possibility of there being a lion, or about the domain of the quantifier – i.e., the things in the forest. By those lights, my extension of the MRTJ seems to get things wrong too. But the fact that aboutness is somehow diluted when we ascend to the level of molecular propositions has now been explained. It is merely a corollary of Frege’s insight about the nature of molecular propositions, and the fact that they require construction in stages; that there are built, in a specific order, from atomic constituents. Without Frege’s insight, logicians were unable to escape from interminable cases of scope ambiguity as they tried to throw all of their quantificational machinery at a proposition all at once, without writing a constructional history into it. We saw how this scope ambiguity re-arose for Hossack’s version of the MRTJ (chapter 9, §4.2), because he didn’t build molecular propositions up in stages (and even then, his generalised propositions also all ended up being about properties). The order-sensitive construction of a molecular proposition is part of the essence of its molecularity; the diluted aboutness of the MRTJ when extended to molecular cases is nothing more than a downstream consequence of that insight. On further reflection, this consequence seems intuitive. Take the proposition, ¬(∃x)(x is immortal and x is a man). What should we say that that proposition is about? Aboutness at a molecular level is simply more dilute than at the atomic level.

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§4: The Dependence Problem We saw in the previous chapter that the dependence problem, as its name implies, only arises for views that make propositions, or truth-bearers, dependent upon mental acts, or the evolution of language. If propositions are independent of minds – as the possible-worlders would insists, and as would many structured-propositioners, who think of propositions as ordered n-tuples, or sets – then the problem doesn’t arise. However, as I argued there, propositions (or at least, truth-bearing) should depend upon minds. If it doesn’t depend upon minds, then the representation-concern will never be answered. So it’s a good thing that this problem arises for the MRTJ (and for Soames and Hanks and King) – it indicates that we’re on the right track. And the problem loses its sting, once you’re happy to accept the distinction between truths and facts (or world-dispositions). The existence of truths might depend upon there being minds to judge, but the existence of the facts that would make those judgements true or false can be completely independent. Of course, we also saw that the problem becomes more vicious if you want to make sense of modal facts obtaining before the rise of sentient life, or in ‘a world of mere matter’. But this problem too, only arises because we’re taking the representation-concern seriously, and the problem has a number of potential solutions (in terms of (1) biting the bullet of modal realism, whilst insisting that propositions can’t be defined in terms of possible worlds, (2) combinatorialism, (3) Hossack’s rationalism, (4) the view that possible worlds are constructed out of universals or (5) theism). Finally, I should note that there is one manifestation of the dependence problem that holds Soames hostage but doesn’t touch the MRTJ. Even in a world where minds and language exist, Soames cannot make room for the proposition that molecule o is a molecule until somebody, somewhere, has referred to molecule o. Lacking that mental event, there will be no mental event type – referring to o – to play a role in constructing the mental event type – asserting that o is a molecule. However, the MRTJ doesn’t have propositions in its ontology. We talk about propositions, but all such talk receives a transformational analysis in terms of judgements (or, more accurately, cognitive acts). As soon as o exists, it’s possible to stand in any variety of multiple relations to it. And, therefore, we can talk about propositions containing o as a constituent, subject to a transformational analysis, as soon as o exists, irrespective of whether anybody has ever referred to it. We saw, in chapter 1, §2.5, that King’s theory can also accommodate this proposition pre-reference to o. The fact that Soames can’t accommodate this proposition pre-reference to o when other theories that take representation seriously can is a serious problem for Soames. And though Soames and King take representation seriously, giving rise to the various

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manifestations of the dependence problem, we have also argued that, in the final analysis, only the MRTJ really escapes the representation-concern. Other theories take that concern seriously, fail to meet it, and consequently give rise to the dependence problem. The MRTJ gives rise to the problem as a consequence of actually meeting the representation-concern head-on; furthermore, the problem can be overcome.

§5: The Appendix-B Paradox Let’s recap the Appendix-B Paradox since I fear that it might be the Achilles heel of a number of theories of propositions: 1. Assume that propositions exist. 2. Assume that every declarative sentence expresses a proposition (relative to an utterance). 3. For any set of propositions, one could utter the sentence, ‘All of the members of that set are true’. 4. Given 2 and 3, it follows that, for any set of propositions, there is a proposition that says that all of the members of that set are true. 5. Call the proposition that affirms all of the members of a set, a set-affirmation. 6. Presumably, some set-affirmations belong to the set that they affirm. For example, the set-affirmation of the set of set-affirmations is a member of the set that it affirms. However, some set-affirmations certainly don’t belong to the set that they affirm. The set-affirmation that affirms the set of non-set-affirming propositions doesn’t belong to the set that it affirms. 7. Given 4, set-affirmations exist, and given 6, some of them are not members of the sets that they affirm. We can now consider the set of set-affirmations that are not members of the sets that they affirm. Call that set, S. 8. Given 4 and 7, it follows that S has its own set-affirmation, which we could call p. 9. Given 8, we can ask, is p a member of S? 10. Given that S is the set of set-affirmations that are not members of the sets that they affirm, and given that p is the set-affirmation of that set, we’re forced to say that (p ∋ S) ↔ (p ∉ S), which is a contradiction! You might try to escape the paradox by denying that sets exist. You might think this route to be particularly attractive given the trouble that sets get us into elsewhere – think of the Russell set! Unfortunately, Russell discovered a variant of our paradox that doesn’t require any talk of sets at all. Consider a property W that a proposition p has just in case there is some property F for which p states that all propositions with F are true but which p does not itself have. Now consider the proposition, call

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it r, which states that all propositions with property W are true. Does proposition r have property W? Given that r is the proposition that all propositions with W are true, and that W is the property that all propositions have when they affirm of all other propositions that they have some property that they don’t have, then r has W iff r doesn’t have W. We haven’t escaped the paradox. Sets are not causing the trouble here! Indeed, Gabriel Uzquiano notes that you can generate the paradox with plurals of propositions (Uzquiano, 2015, p. 330). Clearly, sets are not necessary for this paradox to get going. You might think that we can restrict the individuation of propositions such that they are sufficiently coarse-grained to avoid the paradox. The paradox seems to require the following assumption: (A) If n and m are names of different things, but are of the same type, and a declarative sentence is altered by replacing one occurrence of n by m, the original sentence and the altered sentence represent different propositions. Without that assumption, propositions will exist, but they won’t be fine-grained enough to ensure that every single set of propositions gets its own unique set-affirmation. Put it this way: if a and b are different sets of propositions, then (A) is what entails that the set-affirmation of a is not the same proposition as the set-affirmation of b. If you get rid of (A), you get rid of the idea that each set has its own unique set-affirmation – and you therefore get rid of the paradox. This line of response is defended by Uzquiano (2015). And yet, in order to respect what I have called the quantity problem, we might very well require propositions to be at least sufficiently fine-grained to guarantee the truth of (A). I hope to show in the remainder of this chapter that Uzquiano’s response is an over-reaction. The initial threat of the Appendix-B paradox is that what’s really causing the trouble is the very posit of propositions. If Davidson, for example, can really do without propositions, then he doesn’t need set-affirmations to be members of sets, because set-affirmations don’t exist. He can’t ask whether proposition r instantiates property W because he doesn’t think that there’s any such thing as proposition r. However, this won’t do. Surely you could generate analogous paradoxes about sets of sentences that affirm sets of sentences of which they are not members, or about sets of possible utterances that affirm the truth of sets of possible utterances of which they are not members, etc., and of course, the Appendix-B paradox is related to the standard semantic paradoxes that Davidson will anyway have to consider, with or without commitment to propositions. Accordingly, one grounds for hope is that this isn’t really a problem that’s particular to the propositional realist, and that it isn’t really the

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posit of propositions that’s creating the problem. Notwithstanding, I think that the Appendix-B paradox does potentially pose more trouble for the propositional realist than similar paradoxes pose for others, as I shall try to explain. Let’s start with an ad hoc solution. Russell’s ramified theory of types can look more or less ad hoc, as a solution to the Appendix-B paradox, depending upon one’s background metaphysics. Imagine that you believe in propositions, but that, unlike Russell, you’re a propositional primitivist, so you have no story to tell about the internal structure of propositions. They are simple. What makes one proposition the proposition that Paris is the capital of France, and another proposition the proposition that London is the capital of England? The difference is primitive. There’s nothing more to say. Assume that that’s your account of propositions. Now add in Russell’s ramified theory of types. The result is going to look intolerably ad hoc. Why think that some of these simple and primitive entities exist on a completely different storey of a logical hierarchy to their peers?9 Or, if propositions are sets of worlds, why think that some of these sets are higher or lower than others, on a hierarchy – worlds, surely, are all of the same logical type. We saw, in chapter 5, §2.3, that such a stratification of propositions along a hierarchy would deflate the paradox, but we saw that Russell was reluctant to stratify his actual ontology. That reluctance was well placed. Furthermore, we saw that, by saying that every proposition has to occupy a place in the hierarchy, you seem to be quantifying over all propositions, and predicating something of all of them, including the proposition that you’re asserting, which is to violate the theory that you’re stating! These sorts of expressibility concerns plague all types of type theory, and it may be that the type-theorist simply has to bite that bullet and say that certain things that look like they can be said, actually can’t be said. But expressibility concerns aside, what I want to note is that the ramification of type theory looks much less ad hoc, if you’re ramifying sentences, or utterances, or truth predicates, instead of propositions. Let me explain. Imagine that you go Davidsonian. You don’t believe in propositions.10 I concede that you’re still going to have a paradox similar to the Appendix-B paradox, alongside the regular semantic paradoxes. However, my claim is that type-theoretic responses to those paradoxes are going to look less ad hoc. Davidson makes a somewhat elusive claim that natural languages don’t allow for universal quantification and therefore don’t allow the semantic paradoxes to arise without violating the constraints set down by the language itself. He recognises that he has no conclusive argument to counter ‘the claim that natural languages are universal. But it seems to me that this claim, now that we know such universality leads to paradox, is suspect’ (Davidson, 1967, p. 314).

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As Lepore and Ludwig (2007, p. 133) read him, Davidson is here claiming that ‘natural languages should not be regarded as having the expressive resources required to generate the paradoxes, despite appearances to the contrary’. Lepore and Ludwig try to make sense of this claim but ultimately find it lacking in motivation. Without trying to engage in Davidson exegesis, I think I can provide a reason for thinking that Davidson must have been right that natural languages are not universal. For a Davidsonian, whether your theory of meaning is merely intended to be a model of what speakers are able to do when interpreting a language, or an empirical theory about what speakers actually do when interpreting a language, you need to make sure that your theory makes the language, in principle, learnable. If your theory had an infinite number of axioms, for example, you might think that you’ve violated this constraint. The theory, and thus the language, would be unlearnable. On the other hand, perhaps we could allow an infinite number of axioms, as long as there was a learnable schema for generating them. Either way, the theory must be learnable in some sense or other. I think we should add a further qualification. It needs to be that each and every axiom – or each and every schema – in the theory of language is, in and of itself, learnable; such that it could, in theory be understood. So take the axiom, in your theory of meaning for English that explains the semantic contribution of the truth predicate. It’s going to look something roughly like this: ‘is true’: for any sentence α, and context c, ⌜α is true⌝ is true iff α, uttered in context c, is true I think it fair to say that if the sentence ‘“snow is white” is true’ can serve as one of the values for the variable α in this axiom, then there’s a real sense in which this axiom would be difficult to understand. Let us remember the Fregean insight encoded in his quantifier-variable notation (which we discussed in chapter 9): molecular2 propositions, like this axiom, have a constructional history. You have to construct them out of an atomic proposition that you’re able to understand. You cannot understand a quantified proposition/sentence – you cannot know its truth conditions – if you don’t have the capability to understand arbitrary substitution instances of its bound variables (providing, of course, that you understand the phrases that you’re using as substitutes). And thus, providing that I understand the phrases ‘snow is white’ and ‘James is tall’, it cannot be that I understand our axiom, unless I also understand the following phrases: 1. ‘Snow is white’ is true. 2. ‘James is tall’ is true.

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That seems right. However, providing I know what ‘“Snow is white” is true’ means, I don’t understand the ‘is true’ axiom, unless I also understand: 3. ‘“Snow is white” is true’ is true. However, how could I ever come to know what ‘is true’ means, if I didn’t understand the axiom? And, how can I come to understand the axiom, if there’s a substitution instance – 3 – that I can’t understand before I’ve actually learnt the axiom? There seems to be a vicious circle here, and that circle seems to make it prohibitively difficult to learn the axiom, or to learn the meaning of ‘is true’. However, we do know the meaning of ‘is true’, and English is learnable. If there isn’t one truth predicate, but an infinite number, stratified over a hierarchy, then we avoid these circles, and explain how the language is learnable. On this view, sentence 3 is only meaningful if the truth predicate outside of the mentioned sentence is of a higher type to (and is therefore a different predicate from) the one within the mentioned sentence. You might then worry that having an infinite number of truth predicates raises a new learnability concern. How could you learn the meaning of an infinite number of truth predicates? But we don’t need to learn the whole language; we only need to learn the axioms of the truth predicates that we end up using. The presence of an infinity of axioms shouldn’t bother us if only a finite number of axioms are required for the fragment of the language we end up using.11 One might now worry that antinomies will rear their head in the following – sneaky – way.12 Take the truth axiom for truthn – the nth placed truth axiom in the hierarchy of truth predicates. The axiom looks like this: ‘is truen’: for any sentence α, and context c, ⌜α is truen⌝ is true iff α, uttered in context c, is truen The hope is that you won’t be able to understand or use the axiom if you allow sentences containing the truthn predicate or any predicate above it on the hierarchy into the domain of the axiom’s quantifier. Since you won’t be able to understand it, if you violate this rule, the axiom effectively prohibits certain sentences from being substituted in for the variable, α. But take a paradoxical sentence – one that will generate a paradox when said to be true – and call that sentence Bob. You can understand the word ‘Bob’ – which simply refers to a paradox generating sentence; plug it into our truth predicate – understand the result, since you understand the name – and generate what will ultimately be a semantic paradox, that ‘Bob is true’. However, we can evaporate this worry. If I’m right, then predicates – or at least the potentially toxic ones – come arranged in a hierarchy.

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Paradoxical sentences can’t be generated in the first place. So there are no paradoxical sentences that we could sneak in, under a pseudonym, because there are no paradoxical sentences. My suggestion is that Davidson has the resources to explain why we’re forced to interpret the truth predicate as ambiguous between different types of truth, in a hierarchy of truth predicates. This isn’t something too sophisticated for most speakers. In fact, it’s the only way to learn the language. But then, why do the so-called ‘paradoxes’ even have the appearance of a paradox? Why isn’t our type-theoretic interpretation of the truth predicate, if it’s the only possible interpretation, salient enough to block even the appearance of paradox? I think that Davidson would have to say, here, that interpreting a sentence in a certain way doesn’t always entail that you completely and self-consciously understand your interpretation, which allows for the possibility of illusions of understanding, and the appearance of paradoxes even where there are none. The liar sentence, for instance, certainly looks to be paradoxical, but really, on our new theory, it utilises type distinctions between different truth/falsehood predicates in order to make itself coherent. However, that’s clearly not how it looks. It looks like a paradox. If you buy Davidson’s account of language and meaning, you can explain, in a principled fashion, why the truth predicate has to be divided across a hierarchy of truth predicates and why the quantifiers have to be restricted so that no sentence can be about all sentences. And thus, your solution to the paradoxes won’t be ad hoc. On the contrary, something like the ramified theory of types falls out of Davidson’s account. So having propositions in your ontology can make ramified type theory seem more ad hoc than it would otherwise needs to be. The propositional primitivist and the possible-worlder, for example, will struggle to explain why we should divide propositions, which all seem to be metaphysically similar to one another, across an infinite hierarchy. The metaphysical account of propositions provided by these views gives us no reason to think that some propositions, or worlds, are more logically fundamental than others. Davidson, by contrast, has given us a good reason to stratify the truth predicate, and, in turn, sentences. If your commitment to propositions isn’t generating the Appendix-B paradox, you might still think that it’s making the solution less attractive. We should note that some structured-propositioners might be able to tell a similar story to Davidson about the solution to the paradox. If you adopt a theory like King or Soames, you’ll be able to tell a principled story about why some propositions should be seen as more foundational than others. King’s propositions are, as we’ve seen, parasitical on the existence of languages. Just as some sentences in a natural language, given what we’ve seen in our Davidsonian detour, can be thought to be more fundamental than others, so can the corresponding Kingian propositions, which are parasitic upon sentences and can be said to inherit their logical type.

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Soames’ propositions are mental act types. And since you can’t assert a quantified proposition if you don’t already have the ability to assert its substitution instances, you might be able to tell a similar story about why some of these mental act types are cognitively more fundamental than others. On either account, it’s plausible that your hierarchy will be generated quite naturally by your metaphysics of propositions. This strikes me as a major benefit for both theories, despite being un-championed by their proponents. But of course, the MRTJ also escapes the Appendix-B paradox, and it does so because it also requires an axiomatic theory of predication, as we saw in chapter 8. Sainsbury’s version of the MRTJ has a completely Davidsonian structure. A theory of orders will likewise fall out of the structure of the theory. The axioms of a Sainsbury style judgement theory also need to be learnable. We learn how to use universals as predicates.13 Each axiom, just as for Davidson, needs to be understandable. This will give rise to a hierarchy of types. You don’t need to stipulate that all propositions, or judgements, occupy a position in a hierarchy. To make that stipulation is to violate the theory of types. It’s another example of an illusion. You think you’ve asserted something, when you assert that every proposition occupies a position in the hierarchy, but you haven’t – or, at least, if you have, you haven’t asserted what you think you have! You think you’ve asserted something when you assert that ‘this judgement is false’, but if you have, you didn’t assert what you think you did! This is guaranteed to us, not by a theory of types that we stipulate into existence, but by the grammar of judgement itself, which falls out of our MRTJ account of assertion. Alongside the theories of King and Soames, the MRTJ is one of the only theories of propositions that can escape the Appendix-B paradox in this non-ad hoc fashion. I don’t suggest that other propositional realists can find no escape. I don’t doubt the power of philosophical and logical ingenuity to get people out of tight spots,14 but I do think that the solution open to the MRTJ (and to King and Soames) has a certain elegance to it; it constitutes the sort of ramified type theory for free that Russell was always searching for. When stood side by side with its peers in the face of other potential problems, the MRTJ more than stands its ground. It’s been almost a century since the Multiple Relation Theory of Judgement was abandoned by its founder. I claim that the time has come to resurrect this neglected account of the metaphysics of meaning.

Notes 1 Here, I’ll merely sketch the direction in which a study of Wittgenstein might lead us. Much as King thinks that we inject his propositions with their power to represent, via an act of interpretation, Wittgenstein (in both later and earlier phases) seems to adopt a similar strategy. Howard Wettstein (2004, p. 107) summarises as follows:

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Wittgenstein argues forcefully that photographs, no less than other representations, stand in need of interpretation; they require a method of projection. Perhaps we have some such methods that are natural to us—although training may be relevant—methods that we employ effortlessly, naturally. But this is not intrinsic intentionality. This is projection by us.

2 3 4

5 6

7

8

9

I would go so far as to say that even in the Tractatus, propositions have only the potential to represent facts because of the structural similarities laid out by the picture theory, but it still takes an act of using a proposition in order to complete the transaction, so to speak, and to give rise to representation. I urge readers to consider proposition 4.0141 of the Tractatus – in which it looks as if the grooves on the record are as much a representation of the symphony, as the symphony is a representation of the grooves on the record. All that’s going to decide what really represents what, will be dictated by human interests and human use. We use the grooves to represent the symphony, and not the other way round, because we’re interested in the symphony, and not shapes upon vinyl. If this comparison seems rash, see Keller (2014), who argues for such a comparison to great effect. This concern is raised by Jeff Speaks (King et al., 2014, pp. 164–5), and by Caplan et al. (2013). In fact, it may have been Russell’s strategy too, in 1903. As I argue in chapter 5, §2.2, Russell may have thought that we use propositions, which he thought of as states of affairs, in order to represent themselves. Presumably, if that’s the right reading of Russell, we are supposed to recognise, or to interpret propositions, as being well suited to represent themselves! As I’ve indicated, King does try to address this concern (King et al., 2014, p. 58), but he’ll want to ensure that the linguistic facts he identifies with propositions are not too general. Speaks’ account is clearly inspired by Lewis (1979). But we should note that for Lewis, the properties that we self-ascribe, even if they are ‘propositional properties’, are not propositions. For Lewis, propositions are sets of worlds. For Speaks, propositions are properties. It might well be that the relation of self-ascription, like the relations of existential and universal judgement will have to operate on previous acts of judgement (as detailed in chapter 9). In order for Juliet to judge that Romeo loves her, she might first of all have to build up the predicate Romeo loves x, by understanding some substitution instance, which she can then operate upon, using the relation of self-ascription, to form the judgement that Romeo loves her. However, I relegate this consideration to a footnote, since I think the general idea is clear enough. Also, this epicycle won’t be necessary if you allow that there are complex properties, or, on the MacBride MRTJ, if you allow sufficiently complex adverbs to modify the judgement relation. We might need to posit a distinct attitude to model the time-indexicals – to judge that the meeting is now, and to judge that the meeting is at 12 o’clock, is not to judge the same thing, even if now is 12 o’clock. This difference too, could be cashed out with appeal to different sorts of multiple relations. The multiple relation of judging to be now, is different to the multiple relation of judging. This is, of course, merely a sketch of a theory – nothing more than a promissory note, but one can see why these indexicals (and others like them) would pose no significant burden. Of course, you could say that the paradox itself is motivation enough for ramified type theory. But even if this is your response, it would clearly be

282

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11

12 13

14

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better to have external motivation for ramification. More motivation is always better! Davidson doesn’t actually deny the existence of propositions, but only that they’re necessary or sufficient for a theory of meaning. He does also worry that their existence might generate various sorts of regress (like Bradley’s regress). See footnote 3 of chapter 1, for more details, and some clarification. Alternatively, you might be able to make sense of learning a schema for generating an infinite number of axioms for all of the truth predicates, although this strategy seems like it might be more complicated and fraught with potential landmines. The following worry was Ernie Lepore’s initial response – in conversation – to my strategy for escaping the semantic paradoxes. I’m grateful to him for helping me to explore my way around these thoughts. Presumably, if the MRTJ somehow represents our most fundamental mental language, then we come equipped with knowledge of how to use some of its vocabulary innately, but we certainly learn how to use new universals as predicates as our competence to express ourselves and to understand our surroundings expands. Furthermore, to fend off regress, we must insist that our know-how regarding the fundamental axioms isn’t reducible to propositional knowledge. Indeed, there’s a burgeoning technical literature about the appendix-B paradox and how best to escape it. Uzquiano (2015) cites much of it, but a real survey of that literature would take us too far afield.

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Index

acquaintance 32, 55, 67, 74, 77, 80, 86, 111, 113–14, 134–5, 198–9, 208, 213; knowledge by 74; principle of 41, 67–68, 71, 211, 256; with self 155 Adams, Robert 231, 242 adverbialism 226–7 Alston, William 4, 223–8 anaphora 3–4, 215, 250–3 appendix-B paradox see paradox Armstrong, David 18, 38, 157, 162–3, 188, 235 Augustine 31 Ayer, A. J. 162, 169 Barcan-Marcus, Ruth 97, 245–6 Bradley, F. H. 19, 34–5, 37, 138, 168; his regress 8, 31, 117–8, 151–2, 282; his theory of judgement/meaning (floating adjectives) 24–30, 264–7 Broad, C. D. 224 Candlish, Stewart 121–2, 126, 128 Carey, Rosaline 111, 114, 132, 134–5, 144–5, 147–8, 168, 192, 199–200, 202, 214 category mistakes/errors 136–7, 167–8, 173–7, 230 combinatorialism 235, 244, 258, 273 common ground 3, 64–7, 215–16, 228–9 communication 61–2, 68–70, 74, 90, 216–17, 257 Connelly, James 139–42, 144, 167–8, 176 Davidson, Donald 5–6, 18, 19–20, 69, 87, 116–17, 174, 180–6, 188,

190, 216, 221, 223, 257, 260, 262, 275–7, 279–80, 282 denoting concepts 40–2, 45–52, 57–8, 100, 257 de se attitudes 12, 213, 270–1 direction (or sense of a relation) 32, 119, 121–3, 125–6, 146, 157, 162, 168–9, 191; narrow problem of 120–1, 123, 128, 130, 132, 140, 161, 180; neutral relations and the denial of 146, 150, 158–161, 169, 191; wide problem of 132–3, 136, 140, 143, 167, 173, 177 direct realism 34–5, 37, 39–43, 45, 49, 52–3, 56, 59, 86–9, 91, 95–7, 99, 101, 110, 113, 154, 184, 190, 226–7, 241, 260 divine conceptualism see God Dummett, Michael 62, 85, 203–4, 212, 242 Eames, Elizabeth 130, 132, 134 Edgington, Dorothy 159, 212 focus 254, 267 Frege, Gottlob 7, 9–10, 14, 34–8, 42–3, 47–8, 50–2, 57, 61, 67, 85, 88–9, 97–8, 108, 148–9, 151–2, 162, 180–1, 203–6, 208–10, 213, 232, 247, 255, 270, 272, 277 Geach, Peter 57, 157–63, 188 generality 41–2, 44, 46, 48, 204, 206; multiple generality 48, 192–3, 198, 203–4 God 23, 31, 37, 236, 240–4, 258–9; divine activism 240, 258; divine conceptualism 38, 240, 258 Gödel, Kurt 106, 109

Index Griffin, Nicholas 31, 38, 57, 120, 126–8, 130, 132–4, 136–9, 143, 152, 155, 167 Hanks, Peter 12, 148, 169, 213, 237, 243, 258, 264–5, 268, 273 Hofwebber, Thomas 249, 253–4, 259 Hossack, Keith 169, 177–8, 186, 190, 194–9, 205–7, 210–13, 235–6, 272–3 Hylton, Peter 27–30, 41–2, 46–52, 55, 57, 98, 107, 111–13 intensionality 238–40, 258, 263; proto-intensions 266–7 Jedi powers 211, 220, 257 Keller, Lorraine 20, 231–2, 244, 257–9, 281 King, Jeff 2, 10–13, 15–17, 20, 89, 121, 129, 186, 219, 222–3, 229–34, 237, 239–40, 242–3, 254, 257–8, 261, 264–7, 269–71, 273, 279–81 Kirk-Giannini, Cameron Domenico 65–6 Kripke, Saul 59, 236, 255–6, 262–3 Lagadonian language 190, 221 Landini, Gregory 20, 55, 96, 107, 109, 115–7, 149, 178, 185 Leibniz, Gottlieb 242 Levine, James 45, 49–52, 57 Lewis, David 5, 38, 62, 89, 190, 221–2, 262–3, 281 logical forms 60, 72, 84–5, 132–5, 137, 140–1, 143–6, 150, 155–6, 167–8, 173, 192–4, 196–7, 210 logically perfect language 56, 76, 87, 91 logically proper names 49, 54, 57, 76, 78–9, 86 MacBride, Fraser 33, 38, 117, 149–54, 160–3, 168–9, 178–9, 185, 187–9, 190, 196, 213, 225, 227–8, 245, 260, 281 Mackie, John 18, 161–2, 188 Magidor, Ofra 174–5, 190 Meinong, Alexius 42, 45–52, 57, 97, 111, 116 modal realism 97, 233, 235, 237, 242, 244, 273

295

Moore, G. E. 23–34, 37–8, 53–6, 96, 112, 116, 138, 168, 232, 266–7 multiple generality see generality Multiple Relation Theory of Sensible Appearances 224 names 34–6, 43–4, 46, 49, 51, 59–60, 70–2, 75–78, 82, 86, 89–90, 167–8, 184, 247; see also logically proper names narrow direction problem see direction neutral relations see direction nominalism 27, 33, 169, 188, 227 nonsense 1, 19, 50, 57, 105, 133, 135–9, 141–3, 150, 168, 175–8, 183, 185, 190 paradox 50, 102–9, 113–6, 151–2, 176–7, 274–80; appendix-B paradox 106–7, 109, 116–7, 128, 151, 153–4, 252, 260, 274–80, 282; the concept-‘horse’ paradox 36, 98; Russell’s (set) paradox 55, 58, 101; Russell’s predicate paradox 97–8, 101, 105 Pears, David 116, 127, 130, 136–7, 144, 167–8, 174, 211, 257 Pincock, Christopher 146–7, 161, 168 pleonastic entities 254 plurals and plural logic 40, 57, 116, 177, 195, 213, 217, 275 possible-worlders 7, 10–11, 20, 231–3, 243, 263, 268–9, 273 possible worlds 3, 7, 10–11, 14, 63–4, 90, 215, 228–9, 231–5, 237–41, 244, 257, 259, 261, 273; impossible worlds 268–9 pragmatics 73, 75, 84, 90, 246–7 primitivism: about propositions 7, 11, 13–14, 263, 276, 279; about truth 8, 96, 115, 162, 169 principle of acquaintance see acquaintance Prior, Arthur 162–7, 188, 242, 245, 258 psychologism 24–8, 30, 35, 109–11, 116, 202, 210, 219, 260 quantification 1, 14, 37–8, 42–4, 70, 109, 116, 204, 211, 213, 215, 222, 245–6, 249–50, 253, 259, 272, 276

296

Index

Quine, W. V. O. 44–5, 52, 54, 56, 196–8, 207; Quine’s criterion 4, 6, 37, 245 Ramsey, Frank 13, 20, 106, 164–6 rationalism 235–6, 244, 273 representation 3, 9–11, 100–1, 119–30, 151, 178–9, 184, 187, 190, 214–15, 217, 219–20, 223, 228, 235, 237–44, 257–69, 273, 280–1; the representation-concern 9–11, 13, 16–17, 19, 100–1, 110, 114–15, 117, 119–30, 132, 134, 148, 153–4, 157, 167, 169, 173, 179, 183, 186, 189, 210, 229, 244, 252, 261–9, 271, 273–4 Russell’s paradox see Sainsbury, Mark 57, 71, 109, 129, 179–91, 221, 227–8, 257, 260–3, 280 Schiffer, Stephen 253–4, 259 Sellars, Wilfred 245–6 sense-data 67, 86, 88–9, 95, 154–5, 226 sense/direction of a relation see direction Soames, Scott 2, 9–10, 12–15, 17, 59, 62–3, 68, 99, 114, 117, 120–1, 129–30, 148, 167, 187, 192, 218, 229, 237, 243, 257, 264–5, 267–70, 273, 279–80 Speaks, Jeff 2, 13, 17, 19, 264–5, 270–2, 281 Stalnaker, Robert 3, 64–5, 90, 233, 258 Stanley, Jason 62, 90, 222 Stevens, Graham 57, 107, 109, 113–15, 139, 190

Stout, G. F. 18–19, 38, 116, 119–30, 132, 134, 148, 154, 157, 167, 169, 173, 178–80, 186–7, 214, 221, 262–3 Strawson, Peter 60, 78–85, 91 structured-propositioners 7, 10, 12, 14, 20, 233, 243, 261, 271, 273, 279 structured propositions 7, 10, 12, 90, 101, 156, 223, 231, 238, 261, 263, 271–2 substitutional logic 102–8, 115 syntax 16, 84, 106, 167, 173, 180–1, 190, 216, 250, 254, 265–6, 269–70 termism 35–7, 40, 95, 97–8, 101, 103, 137, 151–3, 162, 188–9, 260 unity of the proposition 7–9, 10, 15–17, 36, 95–7, 99–100, 112–13, 117–18, 120–6, 128, 130, 132, 134, 152–3, 169, 186–7, 190, 260; see also Bradley, F. H. van Elswyk, Peter 4, 250–3, 259 vectors and vector logic 116, 177–8, 185–6, 195–6, 206 Wettstein, Howard 67, 76–7, 246–9, 252, 255–6, 259, 280 wide direction problem see direction Wittgenstein, Ludwig 1, 18–19, 127, 129–54, 156–7, 167–9, 173–4, 176, 178–9, 185, 187, 190, 192, 203, 211, 214, 220, 232, 261, 263, 280–1 Wrinch, Dorothy 120, 192–4, 196–7, 199, 206, 210–11