Wittgenstein’s Metametaphysics and the Realism-Idealism Debate 3030733343, 9783030733346

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Wittgenstein’s Metametaphysics and the Realism-Idealism Debate Marius Bartmann

Wittgenstein’s Metametaphysics and the Realism-Idealism Debate

Marius Bartmann

Wittgenstein’s Metametaphysics and the Realism-­Idealism Debate

Marius Bartmann DRZE University of Bonn Bonn, Germany

ISBN 978-3-030-73334-6    ISBN 978-3-030-73335-3 (eBook) https://doi.org/10.1007/978-3-030-73335-3 © The Editor(s) (if applicable) and The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and ­transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Cover illustration: © Alex Linch shutterstock.com This Palgrave Macmillan imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Acknowledgments

Philosophy is about thoughts, not thinkers. Nevertheless, it’s thinkers who engage with one another by exchanging their thoughts. The best possible outcome of such exchanges is the clarification and development of thoughts. Here I’d like to acknowledge the thinkers who have helped me clarify and develop my thoughts, and the people and institutions providing me with the support and the resources to complete the research project resulting in this book. Years of extensive research at the University of Bonn went in this book. First and foremost, therefore, I’d like to thank my PhD supervisor Markus Gabriel for his continual support, from which I benefitted significantly both philosophically and personally. The innumerable productive philosophical discussions I had with him contributed substantially to sharpening my ideas. I’d also like to express my gratitude to my second supervisor, Michael Forster, whose insightful advice and constructive criticism helped in giving the manuscript a clearer shape. I owe special thanks to Hans Sluga, my supervisor during my research stay at UC Berkeley, with whom I read the Tractatus line by line; I can hardly estimate how much I learned from the precision and depth of his arguments, thoughts, and comments. Along the way I had the good fortune to benefit from enriching conversations and discussions with Julian Ernst, Philip Freytag, Marin Geier, Kevin Harrelson, Sebastian Ostritsch, Simone Maestrone, v

vi Acknowledgments

Ryan Mullins, and Moritz Müller. In particular, I want to thank Dorothee Schmitt—I discussed with her virtually every page of the manuscript, and there is not a single aspect of it that didn’t benefit from her philosophical judgment. Philosophical thoughts are not the only currency of support, however. Thus, I am very grateful to the German Academic Scholarship Foundation, which provided me generously with the resources to complete this research project. Also thanks to Brendan George, Saif Md, and Rebecca Hinsley from Palgrave Macmillan for guiding me through the publishing process. Finally, there is the kind of support that cannot be measured because it’s invaluable. I’d like to thank my family for their support, in particular my sister Leska. And, above all, I’d like to thank my Sabrina. This book is for her.

Contents

1 Introduction  1 References 16 2 Logical Form and the Unity of the Proposition 21 2.1 Moore’s Refutation of Idealism  22 2.2 Russell’s Theory of Judgment  31 2.3 Wittgenstein’s Critique  47 References 75 3 Wittgenstein’s Early Metametaphysics 79 3.1 Logic and the Fabric of the World  79 3.2 Objects, States of Affairs, and Facts  88 3.3 Names, Propositions, and the Picture Theory 103 References140 4 Case Study: The New Wittgenstein147 4.1 The Debate 147 4.2 The Resolute Reading 153 4.3 Taking Stock: Beyond Realism and Idealism 179 References201

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5 Wittgenstein’s Later Metametaphysics207 5.1 Two Roads to Idealism 208 5.2 Rules and Grammar 223 5.3 Logical Necessity, Language-Games, and the Wood-Sellers233 References254 6 Case Study: The Rule-Following Considerations257 6.1 Kripke’s Skeptical Challenge 257 6.2 Realism or Idealism? McDowell vs. Wright 269 6.3 A New Solution: Beyond Realism and Idealism Again 290 References314 Index317

Abbreviations

Unless indicated otherwise, emphases in quotes—whether taken from primary or secondary sources—have been made by their respective authors. Supplements, modifications, and ellipses in square brackets are my own. Works by Gottlob Frege FC Function and Concept. In Translations from the Philosophical Writings of Gottlob Frege, ed. P. Geach and M. Black. 2nd edition. Oxford: Basil Blackwell 1960, 21–41. GG  The Basic Laws of Arithmetic. Exposition of the System, ed. and transl. M. Furth. Berkeley: University of California Press 1964. LC Logic. In Posthumous Writings, ed. H.  Hermes, F.  Kambartel, and F.  Kaulbach, transl. P.  Long and R.  White. Oxford: Basil Blackwell 1979, 126–151. PMC  Philosophical and Mathematical Correspondence, ed. G. Gabriel et al. Oxford: Basil Blackwell 1980. Works by Bertrand Russell A Autobiography. London: Routledge 2009. MP  Introduction to Mathematical Philosophy, ed. J.H.  Muirhead. 2nd ­edition. London: Allen & Unwin 1920. ix

x Abbreviations

NT The Nature of Truth. In The Collected Papers of Bertrand Russell. Vol. 4, Foundations of Logic 1903–1905, ed. A.  Urquhart and A.  Lewis. London: Allen & Unwin 1983, 490–506. NTF On the Nature of Truth and Falsehood. In The Collected Papers of Bertrand Russell. Vol. 6, Logical and Philosophical Papers 1909–1913, ed. A.  Urquhart and A.  Lewis. London: Allen & Unwin 1983, 115–124. PLA  The Philosophy of Logical Atomism. London: Routledge Classics 2010. PM  Principia Mathematica. With A.N. Whitehead. 2nd edition. London: Cambridge University Press 1963. POM  Principles of Mathematics. London: Routledge Classics 2010. PP  The Problems of Philosophy. London: Oxford University Press 2001. SL  The Selected Letters of Bertrand Russell. The Private Years 1884–1914, ed. N. Griffin. London: Routledge 2002. TK  Theory of Knowledge: The 1913 Manuscript, ed. E.R. Eames in collaboration with K. Blackwell. London: Routledge 1984. Works by Ludwig Wittgenstein BB  The Blue and Brown Books, ed. R. Rhees. Oxford: Basil Blackwell 1958. L  Wittgenstein in Cambridge. Letters and Documents 1911–1951, ed. B.F. McGuinness. Oxford: Blackwell 2008. LFM  Wittgenstein’s Lectures on the Foundations of Mathematics. Cambridge, 1939, ed. C.  Diamond. From the Notes of R.G.  Bosanquet, N. Malcolm, R. Rhees, and Y. Smythies. Ithaca: Cornell University Press 1976. LO Letters to C.K. Ogden. Oxford: Blackwell 1973. NB  Notebooks 1914–1916, ed. G.H. von Wright and G.E.M. Anscombe, transl. G.E.M. Anscombe. Oxford: Basil Blackwell 1979. NL Notes on Logic. In Notebooks 1914–1916, Appendix I, 93–106. NM  Notes Dictated to G.E. Moore. In Notebooks 1914–1916, Appendix II, 107–118. OC  On Certainty, ed. G.E.M.  Anscombe and G.H. von Wright, transl. D. Paul and G.E.M. Anscombe. Oxford: Basil Blackwell 1977. PG  Philosophical Grammar, ed. R. Rhees, transl. A. Kenny. Oxford: Basil Blackwell 1974.

 Abbreviations 

xi

PI  Philosophical Investigations, ed. G.E.M.  Anscombe and R.  Rhees, transl. G.E.M. Anscombe. 2nd edition. Oxford: Blackwell 1997. PR  Philosophical Remarks, ed. R.  Rhees, transl. R.  Hargreaves and R. White. Oxford: Basil Blackwell 1975. RC  Remarks on Colour, ed. G.E.M. Anscombe, transl. L. McAlister and M. Schättle. Oxford: Blackwell 1978. RFM  Remarks on the Foundations of Mathematics, ed. G.H. von Wright, R.  Rhees, and G.E.M.  Anscombe, transl. G.E.M.  Anscombe. 3rd revised edition. Cambridge, MA: MIT Press 1975. RLF Some Remarks on Logical Form. Proceedings of the Aristotelian Society, Suppl. Vol. 9 (1929), 162–171. TLP  Tractatus Logico-Philosophicus, transl. D.F. Pears and B.F. McGuinness. London: Routledge Classics 2001. Tractatus Logico-­Philosophicus, transl. C.K.  Ogden. New  York: Routledge & Kegan Paul 1922. [Unless indicated otherwise, references to the Tractatus follow the Pears-McGuinness translation.] WL  Wittgenstein’s Lectures. Cambridge 1930–1932, ed. D. Lee. From the Notes of J. King and D. Lee. Totowa, N.J.: Rowman & Littlefield 1980. WVC  Wittgenstein and the Vienna Circle, conversations recorded by F.  Waismann. Ed. B.F.  McGuinness, transl. J.  Schulte and B.F. McGuinness. Oxford: Blackwell 1979. Z  Zettel, ed. G.E.M.  Anscombe and G.H. von Wright, transl. G.E.M. Anscombe. Oxford: Basil Blackwell 1967. References to the German original follow this edition: Wittgenstein, L. Werkausgabe in 8 Bänden. Frankfurt: Suhrkamp 1984. Other Abbreviations Soph. Sophist. In Plato. Complete Works, ed. and transl. J.M.  Cooper. Indianapolis: Hackett 1997. Met. Metaphysics. In The Complete Works of Aristotle. Vol. II, ed. J. Barnes. Princeton: Princeton University Press 1984. CPR Kant, I. Critique of Pure Reason, ed. and transl. P.  Guyer and A.W. Wood. Cambridge: Cambridge University Press 1998.

xii Abbreviations

AR Bradley, F.H. Appearance and Reality. A Metaphysical Essay. 9th edition. Oxford: Clarendon Press 1962. NJ Moore, G.E. The Nature of Judgment. Mind 8/30 (1899), 176–193. RI  Moore, G.E.  The Refutation of Idealism. Mind 12/48 (1903), 433–453. WRPL Kripke, S.A. Wittgenstein on Rules and Private Language. An elementary exposition. Cambridge, MA: Harvard University Press 1982.

1 Introduction

This book develops a new Wittgenstein interpretation called Wittgenstein’s Metametaphysics. The basic idea is that one major strand in Wittgenstein’s early and later philosophy can be described as undermining the dichotomy between realism and idealism. The aim of this book is to contribute to a better understanding of the relation between language and reality and to open up avenues of dialogue to overcome deep divides in the research literature. In order to clarify this idea and elaborate on what, exactly, is meant by the notoriously ambiguous terms “realism” and “idealism”, as well as what undermining these opposing positions amounts to in Wittgenstein’s writings, I’ll proceed in this introduction as follows. First, I’ll consider the broader context of Wittgenstein’s philosophical development and the still ongoing controversies over the continuity and discontinuity between his early and later writings.1 Second, by giving a synopsis of the book sections, I’ll specify in more detail how Wittgenstein’s Metametaphysics manifests itself in his two masterpieces, the Tractatus Logico-Philosophicus and the Philosophical Investigations, and connect them to a major philosophical debate each work has sparked: the debate about the resolute reading on the one hand (the so-called New Wittgenstein), and the still very controversial debate about the rule-following problem on the other. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 M. Bartmann, Wittgenstein’s Metametaphysics and the Realism-Idealism Debate, https://doi.org/10.1007/978-3-030-73335-3_1

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Philosophical and Historical Context Simply thumbing through two of the most important contributions to twentieth-century philosophy, Wittgenstein’s Tractatus and the Investigations, would already suffice to give the reader the impression that she is confronted with two extremely different books, and after closer scrutiny she may even wonder whether they were both really written by the same author. But the reader may also take Wittgenstein’s own word for it. As he explains in the preface to the Investigations: Four years ago I had occasion to re-read my first book (the Tractatus Logico-­ Philosophicus) and to explain its ideas to someone. It suddenly seemed to me that I should publish those old thoughts and the new ones together: that the latter could be seen in the right light only by contrast with and against the background of my old way of thinking. For since beginning to occupy myself with philosophy again, sixteen years ago, I have been forced to recognize grave mistakes in what I wrote in that first book. (PI: Preface)

The impression of a fundamental difference between the Tractatus and the Investigations, apparently corroborated by Wittgenstein’s own testimony, has led many commentators to conclude that Wittgenstein actually produced two radically different philosophies rather than pursuing one single philosophical agenda he later subjected to more or less substantive changes.2 This view quickly gained currency early on and is reflected in the still common distinction between “Wittgenstein I” and “Wittgenstein II” circulating in the literature. What’s more, some commentators characterize the relation between the early and later works not only as radically different but as outright adversarial, suggesting the Investigations to be “an assault upon the fundamental conceptions of Wittgenstein’s first book.”3 This narrative, sometimes called the orthodox or standard reading, often takes Wittgenstein’s change of heart to consist in a dramatic shift of the semantic theory allegedly underlying the Tractatus and the Investigations, respectively. Whereas the former is said to exhibit a truth-conditional semantics, thus representing a type of realism, the latter is viewed as displaying an assertion conditional semantics, thus representing a type of anti-realism. As Alice Crary and Rupert Read summarize the orthodoxy:

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This gives us an outline of the standard narrative about the development of Wittgenstein’s thought. Its centerpiece is a dramatic rupture between Tractarian and post-Tractarian periods which allegedly comes as Wittgenstein moves from one kind of theory of meaning to another kind of theory. The most well-known version of this narrative runs as follows: in the Tractatus Wittgenstein advocates a truth-conditional theory of meaning which has the characteristic features of realism, and later on he rejects it and embraces a theory of meaning as consisting in assertability-conditions which has the characteristic features of anti-realism.4

Of course, already early on there have been a number of dissenters from this orthodoxy, who insisted instead on a basic continuity in the philosophical aims and methods of early and later Wittgenstein. Accordingly, they suggested a “one-Wittgenstein” view as opposed to the standard “two-Wittgenstein” picture.5 And there have also been more moderate voices challenging the exegetical plausibility and fruitfulness of considering Wittgenstein’s philosophy as marked either by monolithic continuity or by clear-cut discontinuity.6 But despite the existence of these moderate voices trying to establish some common ground by urging that there are elements of both continuity and discontinuity, the literature is still far from forming even a minimal consensus. On the contrary, the emergence of the resolute reading (the so-called New Wittgenstein) has rather exacerbated the debate—about the interpretation of the Tractatus in particular and about the continuity and discontinuity of Wittgenstein’s philosophical development in general. Initiated by Cora Diamond in the 1980s and further developed by James Conant and others, the resolute reading entered the mainstream of Wittgenstein scholarship with the publication of the important collection of essays The New Wittgenstein in 2000.7 It has been gaining momentum ever since and attracting more and more supporters over the past two decades or so.8 In the footsteps of early dissenters from the orthodoxy, the resolute reading also claims to have identified a strong continuity between the Tractatus and the Investigations, though a much more radical one. The resolute reading doesn’t merely deny that Wittgenstein later on broke with his former semantic theory. Rather, it denies that early and later Wittgenstein ever put forward a philosophical theory in the first place. This, then, is supposed to be distinctive of Wittgenstein’s philosophy throughout his writings: the therapeutic aim to wean us off

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philosophical theorizing altogether, to help us steer clear of the confusions engendered by it, and eventually refer us back to our everyday life with language we already lead.9 Applied to the Tractatus, the therapeutic approach translates to the following view. Although the New Wittgensteinians oppose orthodox interpreters, the resolute readers’ main target is not the realist position defended by most standard readers, at least not in the first instance. Instead, the official target of the resolute reading is any view according to which the philosophical project of the Tractatus is “one of demarcating the bounds of sense,”10 that is, of determining the limits of language. Any such project would require, or so resolute readers argue, a semantic theory enabling us to determine whether a given sentence either complies with or violates the rules of logical syntax.11 Indeed, many standard readers think that the ineffable truths about the nature of language, thought, and reality, whose silent conveyance is taken to be the ultimate point of the Tractatus, are precisely a result of transgressions of logical syntax. That is also why the Tractarian notion of nonsense has become one of the focal points in the debate between the resolute and the standard reading. Resolute readers adamantly deny that there is such a thing as violating the rules of logical syntax and hence that there are ineffable truths. For, if there is no such thing as an illegitimate semantic content as a result of logical transgressions, then there is no need for a semantic theory to exclude such contents. In short, since according to the resolute reading Wittgenstein never was in the business of putting forward philosophical theories, it would be a misunderstanding to think the Tractatus represented a theoretical investigation into the limits of language. Rather, the Tractatus wants to show us that our everyday capacity to distinguish sense from nonsense is completely in order and doesn’t have to be supported by a philosopher’s semantic theory. Naturally, given the radical character of the resolute reading’s account of the Tractatus as well as the potentially wide-ranging implications for the understanding of Wittgenstein’s later philosophy and hence for the question of continuity and discontinuity, the New Wittgensteinians have provoked a lot of criticism. Many replies and counter-replies have been published, but although there are attempts at overcoming the deep divide in the literature, so far no common ground seems to be in sight.12

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One aim of this book is to open up avenues of dialogue and establish some common ground to make possible further discussion. Of course, if the debate about the Tractatus in particular and about the question of continuity and discontinuity in general teaches one anything, it’s surely that there won’t be any easy answers. David Stern has expressed well the need for a more nuanced approach given the dissatisfactory framework of the debate: However, this whole debate is highly problematic. For it is nearly always presupposed that either there was one Wittgenstein, that in essentials Wittgenstein’s philosophy never really changed, or that there were two Wittgensteins, that there was a fundamental change between the early and the late philosophy. Very few interpreters seem prepared to even consider the possibility that these are restrictive and constricting alternatives, or that the best interpretation might well be one that recognizes both continuities and discontinuities in Wittgenstein’s philosophical development.13

So instead of trying to find an immutable essence in all of Wittgenstein’s works, we would be well-advised to look for “family resemblances” and acknowledge that an examination of the relations between Wittgenstein’s writings will most likely yield a complicated web of similarities and dissimilarities. In keeping with the spirit of Stern’s Solomonic words, I’ll focus on one such similarity between Wittgenstein’s early and later works while leaving open the possibility of other important similarities (and dissimilarities). The similarity I take to be a central idea in early and later Wittgenstein consists in systematically undermining the dichotomy between realism and idealism. This is what I call Wittgenstein’s Metametaphysics. In examining this idea, I’ll concentrate mainly on the Tractatus and the Investigations, for three reasons. The first reason is simply that the controversies in the literature revolve mainly around Wittgenstein’s two most prominent masterpieces. The second, and more important, reason is that both works can be considered representative to a high degree of Wittgenstein’s early and later works, respectively. And the third reason, which is connected to the second, is that Wittgenstein oversaw the publication of the Tractatus; and the Investigations, although published posthumously, had almost been completed and were at least planned for publication, so that the textual basis is not as problematic as, for example, in the case of On Certainty.14 Now, what, exactly, does Wittgenstein’s

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Metametaphysics amount to in the Tractatus and the Investigations? This brings me to the synopsis of the following book sections. Logical Form and the Unity of the Proposition (Sect. 2) In my view, Wittgenstein’s starting point cannot be properly understood without reference to one of the central philosophical topics pervading the writings of Russell. This concerns what is nowadays known as the problem of the unity of the proposition.15 Russell, in turn, inherited this problem from Moore because Russell adopted central elements of Moore’s theory of judgment and his conception of propositions. It needs to be emphasized that this problem is not only of a purely semantic nature but often possesses a metaphysical aspect as well. This is particularly so if propositions are conceived of as objectively existing, mind-independent entities, which applies to the early Russell as well as Frege (who calls these entities “thoughts”). The importance of this problem and its twofold nature is not often noticed.16 Wittgenstein’s understanding of the unity problem is expressed in the following two well-known passages: “The world is the totality of facts, not of things” (TLP: 1.1) and “A proposition is not a blend of words. […] A proposition is articulate” (TLP: 3.141), respectively. In both cases Wittgenstein addresses the problem of unity by emphasizing in each case that an unstructured or unarticulated complex of isolated, self-standing entities, be they words or things, cannot account for their unity. This problem haunted Russell in many guises throughout his writings. It was Wittgenstein’s central target in his pre-Tractatus writings and one of the major logical problems he sought to resolve in the Tractatus itself. Taking together the semantic and metaphysical aspect of the unity problem, we can frame it in terms of aboutness and ask, in short, in virtue of what is a proposition about something. What makes a proposition say what it does, what makes it expressive?17 And in considering these questions it will be important not to confine the scope of Wittgenstein’s investigations to a merely linguistic undertaking.18 For Wittgenstein, the essence of language is congenial to the essence of the world, a view he already embraced in the Notebooks and is still deeply committed to in the Tractatus.19 Wittgenstein’s Early Metametaphysics (Sect. 3) Among standard readers it’s still widely held that Wittgenstein’s basic position in the Tractatus is

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some sort of variant of logical atomism as defended by Russell.20 Two basic features characterize a standard version of logical atomism, namely: first, that the existence of the complex depends on the existence of the simple and not vice versa, and, second, that the atomic entities in its ontology (universals and particulars) have their nature quite independently of the relations they bear to one another.21

Unfortunately, the giant shadow of Russell has tended to obscure an unbiased view of Wittgenstein’s own philosophical project and has made it difficult to see how radically different these thinkers are. One of the most persistent and seemingly irresolvable debates encouraged by the dominating framework of logical atomism is about the question whether the basic theoretical outlook of the Tractatus warrants either the label realism or idealism. This is no accident because in many cases attributing a variant of logical atomism to the Tractatus goes hand in hand with attributing a form of realism to it since logical atomism is taken to involve “a metaphysics of sempiternal objects constituting the substance of the world.”22 Thus, the conception of Tractarian objects is closely connected to the question whether the Tractatus represents a form of realism or a form of idealism. William Child nicely captures this connection: The debate between the realist and the idealist interpretations of the Tractatus is broadly analogous. The two interpretations agree that language and reality are isomorphic: reality is divisible into simple objects; language is analyzable into simple names; there is a 1:1 correlation between names and objects. But they disagree about the relative priority of the elements of this isomorphism. On the realist reading of the Tractatus, the division of reality into simple objects is an intrinsic feature of reality—a feature of reality as it is in itself. It is because reality has the structure it does that any language adequate to represent reality must have the same structure. […] The idealist interpretation of the Tractatus reverses that order of explanation: it takes the structure of language as basic, and sees the structure of reality as a reflection of the language we use to describe it.23

Simply put, then, the question is whether the Tractatus establishes a theory according to which “the form of the world (somehow) dictates that of

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thought” or whether “the form of thought (somehow) dictates the form of the world.”24 Even though this is a very broad characterization of the realism-idealism debate of the Tractatus, it nevertheless captures a good part of its essence. Still, it must be emphasized that the literature is vast and complex, and different commentators focus on different aspects of the debate or reframe it in slightly different terms. As a consequence, the terms “realism” and “idealism” don’t have exactly the same meaning in all contexts in which issues of realism and idealism play a role. This holds not only for the realism-idealism debate of the Tractatus, but also for the realism-idealism debate of the Investigations. So context is all-important. We must not lump together issues that need to be kept apart, which wouldn’t do justice to the complexity of the debates and the nuances of the commentators’ positions. In order to avoid painting with a broad brush that would give us only a very coarse picture of the philosophical issues, I’ll specify more precisely the meaning of the terms “realism” and “idealism” in each discussion in which they play a role so that it’s always clear what is at stake. Now, regardless of how exactly the meaning of the terms “realism” and “idealism” is spelled out, I think the realism-idealism debate of the Tractatus in almost all of its forms is insoluble as long as it’s understood as putting forward a theory informed by the view that language and the world are two different and mutually independent realms. This approach inevitably leads to the “metaphysical perplexity”25 how a connection between these two different realms is so much as possible. And indeed, the question “How can language be connected to the world?”26 is— implicitly or explicitly—widely taken to be the driving force behind Wittgenstein’s Tractatus. Unsurprisingly, then, versions of the question how a “connection,”27 “contact,”28 “bridge,”29 “link,”30 or “harmony”31 can be established between language and the world abound in the literature. I maintain that it’s one of Wittgenstein’s central tenets to expose precisely this question about how to connect language and the world as illusory. I’ll therefore argue that Wittgenstein’s early Metametaphysics consists in the rejection of establishing an a priori ontological inventory of the world as well as a logico-semantic vocabulary of language, while at the same time providing the resources to conceive of the world as that

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which is accessible to thought and expressible by language in such a way that undermines the one-sided presuppositions of realism and idealism. Case Study: The New Wittgenstein (Sect. 4) Although realist readings are still prevailing,32 the number of critics has been increasing significantly. As I’ve noted above, this is mainly due to the emergence of the resolute reading. I’ve also noted that resolute readers have as their official target not the realist position of the orthodoxy but rather any interpretation according to which the Tractatus represents a theoretical investigation into the limits of language. However, I want to show that the shift of focus away from the problem of realism and idealism to the seemingly purely semantic issues of the bounds of sense and the proper conception of Wittgenstein’s notion of nonsense is only apparent. Not only is the debate about the resolute reading a particular version of the realism-­ idealism debate, it’s also remarkably similar to the debate revolving around the alleged idealism of later Wittgenstein. For example, Bernard Williams and Jonathan Lear have developed a very influential Wittgenstein interpretation, central elements of which are also discernible in the New Wittgenstein. Williams and Lear argue that since, according to Wittgenstein, the idea of transgressing the bounds of sense constitutive of the language-games we play is problematic at best and incoherent at worst, it would be prudent for us to remain within the confines of language and explore it from the inside.33 If there were something outside language at all, it would be either inaccessible to us or incomprehensible nonsense, which is why Williams and Lear expressly attribute a form of idealism to later Wittgenstein. Although the resolute reading has a slightly different conception of the limits of language than Williams and Lear, I’ll argue, in the course of assessing the resolute reading, that it entails a similar form of idealism that is in tension with some of its premises. Wittgenstein’s Later Metametaphysics (Sect. 5) Whereas the literature is deeply divided over whether early Wittgenstein was a realist or an idealist, when it comes to later Wittgenstein the received view is that he is “one of the most important sources of contemporary idealism.”34 In the tradition of Williams and Lear, Thomas Nagel has also argued that Wittgenstein’s account of meaning entails the impossibility to get outside our language-games:

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His later views on the conditions of meaning seem to imply that nothing can make sense which purports to reach beyond the outer bounds of human experience and life, for it is only within a community of actual or possible users of the language that there can exist that possibility of agreement in its application which is a condition of the existence of rules, and of the distinction between getting it right and getting it wrong.35

This assessment is still widely shared and characterizes a form of idealism representing one of two important kinds with which later Wittgenstein is often associated. The other form of idealism often attributed to him are variants of conventionalism, according to which “some truths or realities are created by our linguistic practices.”36 The central idea is that basic cognitive processes such as inferring, calculating, and other rule-governed activities are constituted by certain conventions we have (implicitly or explicitly) adopted. Since conventions are arbitrary in the sense that it’s always possible, or at least conceivable, to adopt different conventions, it follows that our present ways of inferring and calculating could be done differently. Therefore, what counts as a correct inference or correct calculation depends on which arbitrary convention we choose to adopt. And many commentators would consider this conclusion a form of idealism. Both forms of idealism, I claim, rest on a certain understanding of Wittgenstein’s conception of grammatical rules or grammar, that is, Wittgenstein’s term for the body of rules constituting the meaning of expressions of particular language-games. A different understanding, however, may provide us with a way to overcome the realism-idealism problematic. Wittgenstein’s key insight about grammar, I believe, is the idea that the rules governing the use of linguistic expressions are neither true nor false.37 This seemingly technical insight has substantive philosophical consequences. Governed by rules, language-games cannot themselves be conceived of as true or false. Therefore, language-games are neither a mirror of nor a projection onto reality, the former leading to a form of realism and the latter to a form of idealism. This view is borne out by one of the few passages in later Wittgenstein in which he expressly addresses the realism-idealism problematic:

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For this is what disputes between Idealists, Solipsists and Realists look like. The one party attack[s] the normal form of expression as if they were attacking a statement; the others defend it, as if they were stating facts recognized by every reasonable human being. (PI: 402)

Wittgenstein points out that the disputes between realists and idealists are generated by misleadingly treating forms of expressions encoded in language-games as truth-apt statements, that is, something that could be proven or disproven. However, Wittgenstein’s central idea is precisely that grammar is autonomous, meaning that it “cannot be justified or refuted.”38 But although grammar is autonomous in this sense, and although it’s at least conceivable that there might be alternatives to grammatical principles, this doesn’t necessarily entail that grammar is merely conventional.39 I’ll therefore argue that Wittgenstein’s later Metametaphysics consists in acknowledging the (actual or possible) plurality of language-games without being committed to the standard forms of idealism usually attributed to him by showing how the vast and diverse range of factors involved in concept-formation influences and modifies the shape of grammar without compromising their autonomy. Case Study: The Rule-Following Considerations (Sect. 6) As the previous paragraphs already indicated, the realism-idealism debate is closely connected to rules and rule-following. Adrian Moore, for example, in the context of his long-standing dispute with Peter Sullivan over whether (early and later) Wittgenstein is to be considered a (transcendental) idealist, presents the connection between rule-following and idealism in the following way: It is because of ‘how we go on’ that our concepts are as they are. Hence it is because of how we go on that the necessities that hold in virtue of the interconnections of our concepts hold. But how we go on is grounded in a complex of biological and cultural contingencies to which we are subject. So the necessities in question are ultimately grounded in those same contingencies. So the limits of language and the limits of the world are indeed, at some level, limitations, set by us, those who understand language and who think about the world. And that is transcendental idealism.40

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The problem of how to go on—how to follow a rule—is therefore inextricably linked to the realism-idealism problematic. It’s central to Saul Kripke’s Wittgenstein on Rules and Private Language, which is arguably the most influential contribution to the debate revolving around this topic. Even though Kripke’s account has widely been criticized as a grave misunderstanding of the matter, many commentators nevertheless concede that it poses a threat to the concept of meaning and represents an attack on (semantic) realism so profound as to be worthy of critical study regardless of whether it’s an accurate interpretation of Wittgenstein or not. Therefore, Kripke’s exposition of the rule-following considerations has been challenged on exegetical as well as philosophical grounds, or both. There are two main types of accounts to address the rule-following problem in light of Kripke’s exposition, what may be called dispositionali sm/reductionism and primitive nonreductionism, respectively.41 Although there are sophisticated accounts of dispositionalism,42 most commentators don’t think it a feasible strategy. Kripke himself has given the main reason for dismissing dispositionalism as a viable alternative, and it concerns the normativity of meaning. Gary Ebbs sums up well Kripke’s point: Kripke’s central objection to dispositionalism applies to all versions of it. The objection is that facts about how a person is disposed to behave do not explain the rational connection that we experience between our understanding of a rule and our applications of it to new cases.43

Given the widely held belief that dispositionalism is unable to do justice to the normativity of meaning “the most promising of the two standard accounts of rule-following in the literature today is primitive nonreductionism,”44 which is why I’ll focus on this type of account. John McDowell and Crispin Wright are its two most influential proponents. While sharing the basic assessment of the problem, they notoriously differ as to how the paradox is to be treated, which is due to their taking different misconceptions to be underlying what it means to follow a rule. McDowell sees Wittgenstein as attacking what may be called the rules-as-­interpretations view, that is, the view that grasping a rule always involves interpretations. Wright, on the other hand, believes Wittgenstein is challenging what may be called the rules-as-rails view, that is, the view that rules determine

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their applications irrespective of human practice.45 As I’ll argue in detail, the dispute between Wright and McDowell can also be considered a species of the realism-idealism debate because Wright’s reflections on the rule-following considerations go hand in hand with a rejection of the Platonist autonomy of rules,46 whereas McDowell endorses a variant of the autonomy thesis he calls “naturalized platonism.”47 In my view, the root of the skeptical problem, which I also take to be generating the realism-idealism debate between McDowell and Wright, is a problematic understanding of rules. The new conception of rules developed in Sect. 5 will therefore be essential for my proposed solution of the rule-following problem that eventually allows us to overcome the dichotomy between realism and idealism.

Notes 1. Cf. Glock (2007) and Kienzler (2017) for recent overviews of positions regarding Wittgenstein’s philosophical development. For a detailed study on this topic cf. Engelmann (2013). 2. Cf. Pitcher (1964), Pears (1971), and Malcolm (1986). 3. Malcolm (1986: vii). 4. Crary and Read (2000: 2), who attribute the origin of this narrative to Dummett (1991). Other important advocates of this narrative are Pears (1971), Hintikka and Hintikka (1986), Hacker (1972) and Kripke’s WRPL. It should be added that Hacker (1986: viii), in the revised edition of his influential 1972 book Insight and Illusion, retracts the thesis about the shift from realism to anti-realism, an idea he now finds “altogether misguided as well as anachronistic.” 5. Cf. Anscombe (1963), Winch (1969), and Rhees (1970). 6. Cf. Kenny (2006), which was originally published in 1973, and Stern (1991). The exegetical situation is actually even more complicated because some commentators—for example, Stern (1991) himself and Glock (2001)—distinguish a middle or transition period in Wittgenstein’s works, and some even proposed to acknowledge a distinct fourth period after the Investigations (e.g. Stroll 1994). 7. Crary and Read (2000). The most developed version of their joint account can be found in Conant and Diamond (2004).

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8. Bronzo (2012: 46) lists more than one and a half dozen commentators subscribing to (variants of ) the resolute reading. Of course, critics of the resolute reading are not scarce either (cf. Bronzo 2012: 55). 9. Cf. Crary and Read (2000: 1). Cf. also Horwich (2012: 20), who similarly considers the opposition to traditional and theoretical philosophy an integral part of what he calls, in his eponymous book, Wittgenstein’s Metaphilosophy. However, although sympathetic to the resolute reading, he seems reluctant to fully subscribe to it (cf. Horwich 2012: 94–95). 10. Conant (2001: 45). Cf. also Diamond (2000: 151). 11. As Wittgenstein explains in his essay “Some Remarks on Logical Form”, logical syntax in general consists in “the rules which tell us in which connections only a word gives sense, thus excluding nonsensical structures” (RLF: 162). 12. Cf. the extensive bibliography in Bronzo (2012). Also, the title of a recent collection of essays on this topic, Beyond the Tractatus Wars (Read and Lavery 2011), speaks volumes. 13. Stern (2006: 211). Cf. Sluga (2011) for an excellent and balanced introduction to Wittgenstein’s thinking. 14. Cf. Hamilton (2014: 51): “The Investigations had been re-worked, polished and edited tirelessly before Wittgenstein eventually found it close to a state worthy of publication. On Certainty, in contrast, consists of something close to first thoughts on the issues it discusses.” 15. This problem, like so many others, goes back to Plato, in particular to his later dialogue Sophist (Soph.: 262d2–6), where it’s stated that, roughly, a proposition (logos) expresses something that is true or false—and doesn’t only name or refer to something—by being a synthesis (symploke) of names (onomata) and verbs (rhemata). Candlish and Damnjanovic (2012: 66) characterize the basic form of the problem as follows: “What is the difference between a proposition and a collection (or a list) of its constituents?” King (2009) helpfully distinguishes different aspects of the unity problem. For an excellent and comprehensive study on this subject cf. Gaskin (2008). 16. A recent and important exception is Zalabardo (2015, 2018). 17. Evidence for the thesis that this question is one of the main motivations behind the Tractatus is the following well-known letter to Russell: “The main point is the theory of what can be expressed (gesagt) by prop[osition]s—i.e. by language—(and, which comes to the same, what can be thought) and what can not be expressed by prop[osition]s, but

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only shown (gezeigt); which, I believe, is the cardinal problem of philosophy” (L: 98; 19 August 1919). 18. Some commentators claim that Wittgenstein’s philosophical scope in the Tractatus is limited to “clarifying our thoughts” (Hutto 2003: 86) and to the “workings of our language” (M. McGinn 2006: 9). I’ll argue against the view that Wittgenstein confines himself to an investigation of language at some length in Sect. 2 and 3. 19. Cf. NB (39): “My whole task consists in explaining the nature of the proposition. That is to say, in giving the nature of all facts, whose picture the proposition is. In giving the nature of all being.” Cf. also TLP (5.4711): “To give the essence of a proposition means to give the essence of all description, and thus the essence of the world.” 20. Cf. Fogelin (1987), Simons (1998), Proops (2011), Hacker (2013), and Cheung (2017). 21. Proops (2011: 214–215). 22. Hacker (2013: 175). 23. Child (2011: 55–56). 24. McManus (2006: 22). 25. Black (1964: 14). 26. Black (1964: 14). 27. Maslow (1961: 17), Anscombe (1963: 19), Hacker (1986: 73), and Kenny (2006: 46). 28. Mounce (1981: 20) and Dilman (2002: 207). 29. Malcolm (1986: 99). 30. Ishiguro (2001: 38). 31. Hacker (2013: 175). 32. Cf. Stern (2003: 127). 33. Cf. B. Williams (1974) and Lear (1982). For a distinct echo of this train of thought cf. Hutto (2003) and M. McGinn (2006). 34. Nagel (1986: 105). 35. Nagel (1986: 105). 36. Bloor (1996: 356). Cf. also Anscombe (1976: 200) and Hacker (1986: 195) for a similar view. 37. Cf. O’Neill (2001), Forster (2004, 2017), and Glock (2015). 38. Forster (2017: 271). 39. The thesis that alternative grammatical principles actually exist or are at least possible is known in the literature as the “diversity thesis” (Forster 2004: 107).

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40. A.W. Moore (2013: 242). Cf. also Sullivan (2013). 41. Cf. Ebbs (2017: 403). 42. Cf., for example, Ginet (1992), Soames (1998), and Horwich (2002). 43. Ebbs (2017: 403). 44. Ebbs (2017: 403). 45. Cf. McDowell (2002: 229) and Wright (2001: 39). 46. Cf. Wright (2001: 178). 47. McDowell (1994: 92).

References Anscombe, G.E.M. 1963. An Introduction to Wittgenstein’s Tractatus. 2nd ed. New York: Harper & Row. ———. 1976. The Question of Linguistic Idealism. Acta Philosophica Fennica 28: 188–215. Black, M. 1964. A Companion to Wittgenstein’s ‘Tractatus’. Cambridge: Cambridge University Press. Bloor, D. 1996. The Question of Linguistic Idealism Revisited. In The Cambridge Companion to Wittgenstein, ed. H.  Sluga and D.G.  Stern, 354–382. Cambridge: Cambridge University Press. Bronzo, S. 2012. The Resolute Reading and its Critics. An Introduction to the Literature. Wittgenstein-Studien 3 (1): 45–80. Candlish, S., and N. Damnjanovic. 2012. The Tractatus and the Unity of the Proposition. In Wittgenstein’s Early Philosophy, ed. J.L.  Zalabardo, 64–98. Oxford: Oxford University Press. Cheung, L.K.C. 2017. Logical Atomism. In A Companion to Wittgenstein, ed. H.-J. Glock and J. Hyman, 127–140. Oxford: Wiley-Blackwell. Child, W. 2011. Wittgenstein. London: Routledge. Conant, J. 2001. Two Conceptions of Die Überwindung der Metaphysik. Carnap and Early Wittgenstein. In Wittgenstein in America, ed. T.  McCarthy and S.C. Stidd, 13–61. Oxford: Clarendon Press. Conant, J., and C. Diamond. 2004. On Reading the Tractatus Resolutely: Reply to Meredith Williams and Peter Sullivan. In Wittgenstein’s Lasting Significance, ed. M. Kölbel and B. Weiss, 46–99. London: Routledge. Crary, A., and R. Read. 2000. The New Wittgenstein. London: Routledge.

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Diamond, C. 2000. Ethics, Imagination and the Method of Wittgenstein’s Tractatus. In The New Wittgenstein, ed. A.  Crary and R.  Read, 149–173. London: Routledge. Dilman, I. 2002. Wittgenstein’s Copernican Revolution. The Question of Linguistic Idealism. Basingstoke: Palgrave Macmillan. Dummett, M. 1991. The Logical Basis of Metaphysics. Cambridge, MA: Harvard University Press. Ebbs, G. 2017. Rules and Rule-Following. In A Companion to Wittgenstein, ed. H.-J. Glock and J. Hyman, 390–406. Oxford: Wiley-Blackwell. Engelmann, M.L. 2013. Wittgenstein’s Philosophical Development. Phenomenology, Grammar, Method, and the Anthropological View. New  York: Palgrave Macmillan. Fogelin, R.J. 1987. Wittgenstein. 2nd ed. London: Routledge & Kegan Paul. Forster, M.N. 2004. Wittgenstein on the Arbitrariness of Grammar. Princeton: Princeton University Press. ———. 2017. The Autonomy of Grammar. In A Companion to Wittgenstein, ed. H.-J. Glock and J. Hyman, 269–277. Oxford: Wiley-Blackwell. Gaskin, R. 2008. The Unity of the Proposition. Oxford: Oxford University Press. Ginet, C. 1992. The Dispositionalist Solution to Wittgenstein’s Problem about Understanding a Rule: Answering Kripke’s Objections. Midwest Studies in Philosophy 12: 53–73. Glock, H.-J. 2001. The Development of Wittgenstein’s Philosophy. In Wittgenstein: A Critical Reader, ed. H.-J. Glock, 1–25. Oxford: Blackwell. ———. 2007. Perspectives on Wittgenstein: An Intermittently Opinionated Survey. In Wittgenstein and His Interpreters. Essays in Memory of Gordon Baker, ed. G. Kahane, E. Kanterian, and O. Kuusela, 37–65. Oxford: Blackwell. ———. 2015. Wittgensteinian Anti-Anti Realism: One ‘Anti’ Too Many? Ethical Perspectives 22 (1): 99–129. Hacker, P.M.S. 1972. Insight and Illusion. Wittgenstein on Philosophy and the Metaphysics of Experience. Oxford: Clarendon Press. ­———. 1986. Insight and Illusion. Themes in the Philosophy of Wittgenstein. Oxford: Clarendon Press. [Substantially revised edition of Hacker’s 1972 book Insight and Illusion. Wittgenstein on Philosophy and the Metaphysics of Experience.] ———. 2013. Intentionality and the Harmony Between Thought and Reality. In Wittgenstein: Comparisons and Context, ed. P.M.S.  Hacker, 169–184. Oxford: Oxford University Press. Hamilton, A. 2014. Wittgenstein and On Certainty. London: Routledge.

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Hintikka, M.B., and J. Hintikka. 1986. Investigating Wittgenstein. Oxford: Basil Blackwell. Horwich, P. 2002. Meaning, Use and Truth. In Rule-Following and Meaning, ed. A. Miller and C. Wright, 260–273. Chesham: Acumen. ———. 2012. Wittgenstein’s Metaphilosophy. Oxford: Oxford University Press. Hutto, D.D. 2003. Wittgenstein and the End of Philosophy. Neither Theory Nor Therapy. Basingstoke: Palgrave Macmillan. Ishiguro, H. 2001. The So-Called Picture Theory: Language and the World in Tractatus Logico-Philosophicus. In Wittgenstein: A Critical Reader, ed. H.-J. Glock, 26–46. Oxford: Blackwell. Kenny, A. 2006. Wittgenstein. Revised ed. Oxford: Blackwell. Kienzler, W. 2017. Wittgenstein’s Philosophical Development. In A Companion to Wittgenstein, ed. H.-J.  Glock and J.  Hyman, 23–40. Oxford: Wiley-Blackwell. King, J.C. 2009. Questions of Unity. Proceedings of the Aristotelian Society 109: 257–277. Lear, J. 1982. Leaving the World Alone. The Journal of Philosophy 79 (7): 382–403. Malcolm, N. 1986. Nothing is Hidden. Wittgenstein’s Criticism of his Early Thought. Oxford: Basil Blackwell. Maslow, A. 1961. A Study in Wittgenstein’s Tractatus. Berkeley: University of California Press. McDowell, J. 1994. Mind and World. Cambridge, MA: Harvard University Press. ———. 2002. Mind, Value, and Reality. 2nd ed. Cambridge, MA: Harvard University Press. McGinn, M. 2006. Elucidating the Tractatus. Wittgenstein’s Early Philosophy of Logic & Language. Oxford: Clarendon Press. McManus, D. 2006. The Enchantment of Words. Wittgenstein’s Tractatus Logico-­ Philosophicus. Oxford: Clarendon Press. Moore, A.W. 2013. Was the Author of the Tractatus a Transcendental Idealist? In Wittgenstein’s Tractatus. History & Interpretation, ed. P.  Sullivan and M. Potter, 239–255. Oxford: Oxford University Press. Mounce, H.O. 1981. Wittgenstein’s Tractatus. An Introduction. Oxford: Blackwell. Nagel, Th. 1986. The View from Nowhere. New York: Oxford University Press. O’Neill, M. 2001. Explaining ‘The Hardness of the Logical Must’: Wittgenstein on Grammar, Arbitrariness, and Logical Necessity. Philosophical Investigations 24 (1): 1–29. Pears, D.F. 1971. Wittgenstein. London: Fontana.

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Pitcher, G. 1964. The Philosophy of Wittgenstein. London: Prentice-Hall. Proops, I. 2011. Logical Atomism in Russell and Wittgenstein. In The Oxford Handbook of Wittgenstein, ed. O. Kuusela and M. McGinn, 214–239. Oxford: Oxford University Press. Read, R., and M.A. Lavery. 2011. Beyond the Tractatus Wars. The New Wittgenstein Debate. London: Routledge. Rhees, R. 1970. Discussions of Wittgenstein. London: Routledge & Kegan Paul. Simons, P. 1998. Tatsache II.  In Historisches Wörterbuch der Philosophie, ed. J. Ritter, K. Gründer, and G. Gabriel, vol. 10, 913–916. Darmstadt: WBG. Sluga, H. 2011. Wittgenstein. Oxford: Wiley-Blackwell. Soames, S. 1998. Skepticism About Meaning: Indeterminacy, Normativity, and the Rule-Following Paradox. Canadian Journal of Philosophy 23: 211–249. Stern, D.G. 1991. The ‘Middle Wittgenstein’: From Logical Atomism to Practical Holism. Synthese 87 (2): 203–226. ———. 2003. The Methods of the Tractatus: Beyond Positivism and Metaphysics? In Logical Empiricism. Historical & Contemporary Perspectives, ed. P. Parrini, W.C. Salmon, and M.H. Salmon, 125–156. Pittsburgh, PA: Pittsburgh University Press. ———. 2006. How Many Wittgensteins? In Wittgenstein: The Philosopher and his Works, ed. A.  Pichler and S.  Säätelä, 2nd ed., 205–229. Frankfurt: Ontos Verlag. Stroll, A. 1994. Moore and Wittgenstein on Certainty. Oxford: Oxford University Press. Sullivan, P.M. 2013. Idealism in Wittgenstein: A Further Reply to Moore. In Wittgenstein’s Tractatus. History & Interpretation, ed. P. Sullivan and M. Potter, 256–270. Oxford: Oxford University Press. Williams, B. 1974. Wittgenstein and Idealism. In Understanding Wittgenstein, ed. G. Vesey, 76–94. London: MacMillan. Winch, P. 1969. Introduction: The Unity of Wittgenstein’s Philosophy. In Studies in the Philosophy of Wittgenstein, ed. P.  Winch, 1–19. London: Routledge. Wright, C. 2001. Rails to Infinity. Essays on Themes from Wittgenstein’s Philosophical Investigations. Cambridge, MA/London: Harvard University Press. Zalabardo, J.L. 2015. Representation and Reality in Wittgenstein’s Tractatus. Oxford: Oxford University Press. ———. 2018. The Tractatus On Unity. Australasian Philosophical Review 2 (3): 250–271.

2 Logical Form and the Unity of the Proposition

In this section I set the stage for Wittgenstein’s Metametaphysics by providing the necessary philosophical and historical context. I trace Wittgenstein’s philosophical starting point in the Tractatus back to his pre-Tractatus writings, particularly to the problem of logical form and unity. To understand the nature and import of these connected problems, it’s useful, as a first step (Sect. 2.1), to go back to Moore, with whom Russell was closely working together around 1900. It was Moore who supplied the theoretical basis for their common attack against idealism. Second (Sect. 2.2), I critically examine the various stages of Russell’s theory of judgment, which will help gain a deeper understanding of the starting point of Wittgenstein’s considerations. The third step (Sect. 2.3) consists in reconstructing Wittgenstein’s objections to Russell’s theory of judgment and theory of types. This will prepare the ground for an adequate interpretation of the Tractatus and offer a new resolution of a long-standing dispute in the literature, namely the question of the precise nature of Wittgenstein’s objections that eventually led Russell to abandon his Theory of Knowledge manuscript.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 M. Bartmann, Wittgenstein’s Metametaphysics and the Realism-Idealism Debate, https://doi.org/10.1007/978-3-030-73335-3_2

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2.1 Moore’s Refutation of Idealism In his two influential articles “The Refutation of Idealism” and “The Nature of Judgment” Moore launches a broad attack against idealism. Moore attributes to idealism the general thesis that the universe or reality—Moore seems to be using these terms interchangeably1—is in some sense “spiritual,” meaning “not only that it is in some sense conscious, but that it has what we recognise in ourselves as the higher forms of consciousness” (RI: 433). In “The Refutation of Idealism” Moore provides a reconstruction of what he considers the standard argument for idealism in this sense: It is said that since whatever is, is experienced by the individual, these must at least form part of some experience. Or again that, since an object necessarily implies a subject, and since the whole world must be an object, we must conceive it to belong to some subject or subjects, in the same sense in which whatever is the object of our experience belongs to us. Or again, that, since thought enters into the essence of all reality, we must conceive behind it, in it, or as its essence, a spirit akin to ours, who think: that “spirit greets spirit” in its object. (RI: 437)

However, Moore neither intends to evaluate the validity of the somewhat obscure (reconstruction of the) standard argument nor questions the idealist thesis it’s supposed to establish. In fact, Moore doesn’t even think the idealist thesis is wrong.2 Rather, his target is a fundamental assumption he considers a “necessary and essential step in all Idealistic arguments,” and by refuting this assumption Moore believes he will “have proved that Idealists have no reason whatever for their conclusion” (RI: 435) that reality is spiritual. Moore’s strategy, then, is not to attack head-on the idealist thesis and the standard argument for it but instead to combat the basic premise allegedly shared by all variants of idealism in order to undermine the central motivation for holding the idealist thesis in the first place.3 And the fundamental assumption Moore identifies as the target is nothing other than Berkeley’s (in)famous doctrine esse est percipi. Given the ambiguity of Berkeley’s doctrine, Moore explores different readings of it based

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on various possible interpretations of the key concepts involved, and the main results he arrives at are the following. The Refutation of Idealism To begin with, Moore seems to impute to idealists a position according to which reality contains at least two types of “constituents” (RI: 439), which is his catchall term to cover both objects and the experiences of those objects themselves. Moore also uses the variable “x” to range over the former kind of constituents and calls the latter kind “mental fact[s]” or “ways of experiencing” (RI: 437), a category comprising sensations as well as thoughts. Unfortunately, Moore is not very explicit about the precise meaning of either of those terms, and some of his specifications are a bit confusing.4 Ultimately, though, Moore seems to attribute to idealists the simple view that reality is composed (in a rather unclear sense of “composition”) of the aforementioned types of constituents (whatever their respective structure), and that “x” refers to whatever remains if we subtract from reality whatever contribution subjectivity makes to it. After having made these determinations, Moore eventually identifies the formula’s most important and most objectionable form: The only importance of the question whether the whole esse includes the part percipi rests therefore on the question whether the part x is necessarily connected with the part percipi. And this is (3) the third possible meaning of the assertion esse is percipi: and, as we now see, the only important one. Esse is percipi asserts that wherever you have x you also have percipi: that whatever has the property x also has the property that it is experienced. (RI: 439–440)

It’s not easy to decipher the exact meaning of the final formulation of Berkeley’s doctrine Moore puts up for debate. Moore’s reluctance to spell out the meaning of the terms “esse” and “percipi” may be due to the fact that he considers it irrelevant what exactly each term denotes because he solely focuses on the question whether there is a necessary connection between them regardless of their precise content. This seems to be borne out by the following passage: Whether x alone should or should not be called esse is not worth a dispute: what is worth dispute is whether percipi is necessarily connected with x. (RI: 440)

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And there is a similar passage in which he asks whether “object and subject are necessarily connected” (RI: 442). However, this question can be specified in two rather different ways and Moore’s elaborations waver between them. On the one hand, the necessary connection between subject and object may be conceived of as an ontological dependence, according to which objects depend on subjects for them to exist. Call this the strong idealist conception of the necessary connection between subject and object. This conception proposes as an ontological necessity that if something has the property of being an object, then it also has the property of being experienced.5 On the other hand, the necessary connection may be conceived of as a conceptual dependence, according to which any investigation into the nature of objects must take into account their relation to and the conditions of the experiencing subject(s). Call this the weak idealist conception of the necessary connection between subject and object. In the following passage in particular (and in his discussion of the nature of sensations in general) Moore seems to attribute to idealists this more moderate thesis: Idealists, we have seen, must assert that whatever is experienced, is necessarily so. And this doctrine they commonly express by saying that ‘the object of experience is inconceivable apart from the subject’. (RI: 441; second emphasis added)6

Obviously, there is a difference between the ontological claim that objects depend for their existence on subjects such that there are no objects outside the scope of actual experience; and the conceptual claim that objects depend on subjects such that all objects are within the scope of possible experience. The latter claim only implies that every investigation into the nature of objects must make reference to the subject’s conditions of experience, but not that there are no unexperienced objects. In sum, Moore seems to waver between attributing to idealists a weak and a strong conception of the necessary connection of esse and percipi, sometimes characterizing it as an ontological link between subject(s) and object(s) and sometimes as a conceptual link between subjectivity and objectivity. Fortunately, we need not decide on whether Moore attacks the weak or the strong idealist conception because what Moore mainly takes issue

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with can be reconstructed in a way that is independent of the question of whether or not there are objects outside the scope of actual experience. His point here rather concerns the relation between the distinguishable components within a particular experience. Moore assumes a very simple model of the structure of experience, what in the literature is frequently called an “act/object”7 analysis of experience or consciousness. According to this model, each experience consists of two components, namely an intentional act Moore calls “consciousness” and the object at which the intentional act is directed. The intentional act is the constant component in every experience, something “in respect of which all sensations are alike,” whereas the objects of sensations may change and are that “in respect of which one sensation differs from another” (RI: 444). In the simplest case, then, a perceptual experience of, say, the color blue is analyzed into the two components “sensation of blue” and “blue.” Now, Moore’s critique of idealism points to a certain misunderstanding of the distinction between the sensation of an object and the object itself: A distinction is asserted; but it is also asserted that the things distinguished form an ‘organic unity’. But, forming such a unity, it is held, each would not be what it is apart from its relation to the other. Hence to consider either by itself is to make an illegitimate abstraction. (RI: 442–443)

For Moore, the consequences of this view are devastating. If there is a necessary connection between sensations and objects such that this connection is constitutive of what these objects essentially are, then it’s impossible to find out what objects are apart from this relation—in fact, there wouldn’t be such things as objects apart from this relation in the first place.8 The problem is that experience seems to defeat its own purpose. Instead of providing us with the means to access what there is, the very act of accessing what there is changes it, thereby preventing us from coming to know what there really is right from the start. Even if it doesn’t strictly follow that experience is an entirely futile enterprise, this shows at least how limited our grasp of things is and, additionally, opens the door to skepticism. The boon of world-disclosing experience turns into the bane

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of King Midas, who transformed anything with which he came into contact. It’s as if our access to the world resembled a colored spotlight, actually changing the looks of everything within its scope whereas we thought it shed an illuminating light on it. In sum, we miss the intended target— reality—in principle simply by exercising our cognitive powers. The result is that we are completely cut off from reality, since what we are confronted with in experience is now by definition reality-as-experienced, not reality-in-itself. According to idealism as construed by Moore experience turns out to be inherently distorting, changing the nature of reality in the very attempt to disclose it. Moore believes that this unacceptable conclusion derives from idealism’s having confused two distinct things, namely “what is experienced” with “the experience of it” (RI: 445). Ultimately, this fallacy boils down to the simple misidentification of “blue” with the “sensation of blue” (RI: 445), a result of failing to realize that these are two distinct things even though they might form some sort of unity in the act of experience. Against this, Moore insists that the subjective and objective components within an experience are independent from each other. Both components could be separated without affecting the nature of either of them. The content of experience is objective because it bears no essential, let alone necessary, relation to experience itself: There is, therefore, no question of how we are to ‘get outside the circle of our own ideas and sensations’. Merely to have a sensation is already to be outside that circle. It is to know something which is as truly and really not a part of my experience, as anything which I can ever know. (RI: 451)

By steering clear of what Wilfrid Sellars later called the “notorious ‘ing­ed’ ambiguity of ‘experience,’”9 that is, by carefully distinguishing between experiencing (a subjective mental act) and the experienced (the objective content of judgment), idealism doesn’t even get off the ground. Based on this motivation against idealism and his zeal to preserve the independence of the objects of experience, Moore developed an account of the objective content of judgment and its unity. He therefore presents, in “The Nature of Judgment,” a new conception of propositions.10

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The Nature of Judgment The primary goal of Moore’s theory of judgment is to show that “truth and falsehood are not dependent on the relation of our ideas to reality” (NJ: 177). Moore is explicitly targeting what may be called Bradley’s version of the correspondence theory of truth.11 In a letter to Russell, Moore contrasts Bradley’s conception of truth with his own. According to Moore’s conception, truth: does not depend upon any relation between ideas and reality, nor even between concepts and reality, but is an inherent property of the whole formed by certain concepts and their relations; falsehood similarly. […] The ultimate elements of everything that is are concepts […]. (Quoted in N. Griffin 1991: 300; 11 September 1898)

More precisely, Moore’s new conception amounts to an identity theory of truth, and his theory of judgment that goes with it can be characterized by the following two closely related claims: 1. A proposition—the object of judgment—is to be conceived of as an objective complex entity, which exists absolutely independently of any judging or knowing mind and whose basic constituents (which Moore calls “concepts”) are identical with the objects the proposition is about. 2. The basic constituents making up a proposition have to be externally related in a certain way for the proposition to be true. With his new theory, Moore attacks two central theses of neo-­Hegelianism, which are also figuring prominently in Bradley.12 Moore’s theory is leveled against the thesis that the unity of propositions has its source in the mind, and against the thesis that relations between objects, if they can be considered real at all, have no independent ontological status and are therefore internal to objects themselves. Let’s examine both premises in turn. Moore opposes his first claim (1), according to which propositions are fully objective and independent entities, to Bradley’s doctrine that “when I have an idea (Vorstellung) of something, that something is itself part of the content of my idea” (NJ: 177). Moore has two worries here. Moore’s first worry concerns a version of what we already came across as the King

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Midas problem. Recall that this worry is not so much that an idea and what it is an idea of form some sort of unity. Moore doesn’t deny the unity of, say, the “sensation of blue” and “blue” within a particular experience. However, he does deny that these components are what they are only in relation to each other, and hence he denies that the nature of these components is different outside their relation to each other. Apparently, Moore sees no substantive difference between the relation of a sensing subject and the object of sensation on the one hand and the relation of a judging subject and the object of judgment on the other, and employs the same argument in both cases.13 Just as we have to distinguish sharply between sensing subjects and the objects of sensation, we also need to keep strictly apart the judging subject and the objects of judgment. When it comes to propositions it “is indifferent to their nature whether anybody thinks them or not” (NJ: 179). As we’ve seen, characterizing the objects of sensations must not make reference to sensing subjects, and the same goes for the objects of judgment. Again, the worry here is that if the objects of judgment are not entirely independent of the judging subject, then we get the familiar King Midas problem that the independence of the objects of judgment is compromised simply by the act of judging. Moore’s second worry concerns an implication of Bradley’s correspondence theory of truth. Although Bradley holds that thought (in the form of true and false judgments) aims at reality and even succeeds to latch on to it in true judgments, he nevertheless insists that reality exceeds and goes beyond it: “For I do not deny that reality is an object of thought; I deny that it is barely and merely so” (AR: 149). The resulting view is that there will always be a discrepancy between thought (true and false judgments) and reality: There will be no truth which is entirely true, just as there will be no error which is totally false. With all alike, if taken strictly, it will be a question of amount, and will be a matter of more or less. […] [T]ruth and error, measured by the Absolute, must each be subject always to degree. (AR: 320–321)

Curiously, then, while Bradley thinks that truth and reality are ideally identical, he also holds that de facto even true judgments “can never reach

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as far as perfect truth” (AR: 321). So even true judgments remain mere “representatives, worse or better, in proportion as they present us with truth affected by greater or less derangement” (ibid.), thereby condemned to infinite approximation. According to Moore, however, propositions don’t exhibit the property of truth and falsity to varying degrees in comparison to “the Absolute” but are themselves absolute properties: either a proposition is true or it is false.14 I turn now to Moore’s second claim (2) that the basic constituents of propositions have to be externally related in a certain way for the proposition to be true. The denial of internal relations between concepts here is again clearly in contradistinction to Bradley’s view that all relations belong to the concepts related. Roughly, a relation is internal if, for example, “a relation between a and b is reducible to properties held by a or b, or an aspect or attribute of a unified whole.”15 To be more precise, Bradley holds what might be called a projectivist view of relations. He doesn’t deny their existence altogether but thinks that, first, they do “not really belong to reality” (AR: 23) and have “existence only for us” (ibid.), and, second, that relations are not separate, self-standing entities regardless of what nature they turn out to have: “I still insist that for thought what is not relative is nothing” (AR: 25). Against this background, Moore introduces concepts, the basic constituents of propositions, as “possible objects of thought” (NJ: 179). Accordingly, a proposition is called a “synthesis of concepts” (NJ: 180). All concepts are equally real, objective, and immutable—they form the ultimate constituents of reality such that “[a]ll that exists is composed of concepts necessarily related to one another in specific manners, and likewise to the concept of existence” (NJ: 181). This conception is intended to obviate the need for an active subject synthesizing the concepts contained in a proposition resulting in a unified whole in the vein of a Kantian theory of judgment: It will be apparent how much this theory has in common with Kant’s theory of perception. It differs chiefly in substituting for sensations, as the data of knowledge, concepts; and in refusing to regard the relations in which they stand as, in some obscure sense, the work of the mind. (NJ: 183)16

Moore, as well as Russell in his footsteps (at least in his early phase), had to deny the functional role of the subject as a synthesizer or unifier

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because this conception runs the risk of turning the objective content of judgment into something subjective, thereby paving the way for idealism.17 Consider, for example, the proposition expressed by “This rose is red.” According to Moore, in making this judgment we don’t contribute anything whatsoever to the object being judged. Neither do we attach our ideas of being red and being a rose to a metaphysical object nor do we bundle or synthesize discrete entities into an object of experience that wouldn’t exist if there were no judging mind. The proposition expressed by “This rose is red” is therefore simply a complex entity composed of the concepts indicated by “This,” “rose,” the copula “is,” and “red,” which stand in a certain external relation to one another. If these entities are in fact so related, then  the judgment that this rose is red is true, otherwise false. This way, or so Moore thought, truth no longer had to be explained in terms of the potentially problematic relation between ideas and reality. Instead, for a proposition to be true just is for a collection of entities to stand in a certain relation to one another. The fundamental idea and motivation behind this is that propositions are discovered, not made by the mind. Any active involvement of the mind threatens the objectivity of what it tries to grasp, which is why the mind must play an entirely passive role. The question of truth and falsehood should therefore be nothing but the question of whether a particular relation is or is not obtaining between a particular class of objects. By turning truth into an obtaining relation between independently existing entities, no appeal to the judging mind is needed, and the desired objectivity of truth preserved. In short, while Moore roughly agrees with Bradley and Kant regarding the structure of a proposition as a synthesis of objects of a certain kind, he locates the source of synthesis in a different place. The mind does in no way contribute to, let alone create, the unity of the proposition, rather it’s said to be an intrinsic and fully objective property of it if the objects making up the proposition are in fact related as stated. With the Kantian option of explaining the unity ruled out, the question now arises what other element, if any, provides the unity of the proposition and how it does so. However, Moore fails to give an account of the nature of synthesis, admitting that what “kind of relation makes a proposition true, what

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false, cannot be further defined, but must be recognized immediately” (NJ: 180). Leaving the details of Moore’s theory aside, the basic motivation behind it is quite obvious. Bradley’s correspondence theory of truth still left a gap between thought and reality even in cases where judgments are true, which brought him to conclude that absolute truth is never attainable and therefore “subject always to degree” (AR: 321). For a staunch realist such as Moore, the thesis that truth (and falsehood, for that matter) is gradable was clearly unacceptable. Thus, Moore took truth and falsehood not to consist in a relation between ideas and bits of reality but as indefinable properties of propositions themselves already composed of the worldly items they are about. This way, he thought he could dispense with the judging subject and the mediating veil of ideas threatening to distort our access to reality or, even worse, fencing us off from it altogether.

2.2 Russell’s Theory of Judgment Central to Moore’s identity theory of truth is the claim that a proposition actually contains the parts of the external world it is about as opposed to potentially distorting ideas going proxy for those parts. This thesis is vital because Russell fully subscribed to it. It shows how similar their conceptual machinery is, which in turn generated similar metaphysical commitments and conclusions. Here’s how Russell, in his Principles of Mathematics, pays tribute to his philosophical ally: On fundamental questions of philosophy, my position, in all its chief features, is derived from Mr. G.E. Moore. I have accepted from him the non-­ existential nature of propositions (except such as happen to assert existence) and their independence of any knowing mind; also the pluralism which regards the world, both that of existents and that of entities, as composed of an infinite number of mutually independent entities, with relations which are ultimate, and not reducible to adjectives of their terms or of the whole which these compose. Before learning these views from him, I found myself completely unable to construct any philosophy of arithmetic, whereas their acceptance brought about an immediate liberation from a

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large number of difficulties which I believe to be otherwise insuperable. (POM: xlv–xlvi)

In this passage the basic elements of Moore’s theory of truth and judgment—(1) independence of propositions and (2) externality of relations—are clearly discernible, including the difficulties they raise. Of course, this is not to deny that there are important differences between them, and I will elaborate on them in what follows. The containment thesis jointly embodied by (1) and (2) Russell took over from Moore also brings out a fundamental disagreement with Frege regarding our access to reality. Russell expresses the containment thesis in the following way: 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 itself contain words: it contains the entities indicated by words. (POM: 51)

Both Russell and Frege agree that what we are presented with in making judgments are real objective entities, which Russell calls “propositions” and Frege calls “thoughts.” But whereas for Russell these entities are composed of the things the judgment is about, for Frege these entities are only composed of senses (i.e. abstract entities) referred to by the expressions making up the judgment. As he explains in a letter to Russell: Truth is not a component part of a thought, just as Mont Blanc with its snowfields is not itself a component part of the thought that Mont Blanc is more than 4000 metres high. […] The sense of the word ‘moon’ is a component part of the thought that the moon is smaller than the earth. The moon itself (i.e., the meaning of the word ‘moon’) is not part of the sense of the word ‘moon’; for then it would also be a component part of that thought. (PMC: 163; 13 November 1904)

Russell states his opposing view in his response to Frege’s letter, which also makes it clear that their point of contention is not so much the question of truth but rather the question of aboutness. This is the question

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what makes a proposition expressive or, put differently, “What turns a belief or judgment into a belief or judgment about the world?” Here’s Russell’s response: I believe that in spite of all its snowfields Mont Blanc itself is a component part of what is actually asserted in the proposition “Mont Blanc is more than 4000 metres high”. We do not assert the thought, for this is a private psychological matter: we assert the object of the thought, and this is, to my mind, a certain complex (an objective proposition, one might say) in which Mont Blanc is itself a component part. If we do not admit this, then we get the conclusion that we know nothing at all about Mont Blanc. (PMC: 169; 12 December 1904)

At first glance, it’s puzzling that Russell concludes that we wouldn’t know anything at all about Mont Blanc if we didn’t take it to be a genuine constituent of the proposition expressed by “Mont Blanc is 4000 metres high.” But if we understand the problem not in terms of truth and falsehood but in terms of aboutness, an answer seems to be available. If the mountain Mont Blanc weren’t itself the immediate target of our judgment but rather a Fregean sense, then our judgment, so Russell’s qualms, would not, strictly speaking, be about Mont Blanc itself. Instead, the judgment would be merely about a (perspectival) representation of Mont Blanc (a Fregean sense).18 We can say that Russell addresses the problem of unity with a conception one may call “aboutness-by-­containment”, in contrast to Frege’s approach, which can be characterized as “aboutness-by-representation”. The difference between both thinkers, then, is reflected in Russell’s denial that proper names (like “Mont Blanc”) have a sense in addition to reference. Following the literature, we can call Russell’s approach a one-­ step and Frege’s a two-step semantic theory.19 Russell’s (early) theory of propositions, like Moore’s, can therefore be characterized as an identity theory of truth. A true proposition just is identical with the fact that makes it true: a complex of entities related in a certain way. Accordingly, a false proposition is also a complex entity that merely happens to lack the property of truth.20

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The passage quoted above makes it also clear that the constituents figuring in propositions are atomistic, self-standing entities, comprising very heterogeneous objects such as “a man, a moment, a number, a class, a relation, a chimaera” (POM: 47). Put simply, an object is basically everything we can think and talk about. It’s crucial to emphasize here that this also includes logical objects like relations and forms of facts, which are viewed as being on a par with all other objects. Russell allows only for one single level of objects among which there are, from a theoretical standpoint, no substantive differences; in his universe there are facts about logical objects in the very same sense in which there are facts about lions. This view informs his philosophy beginning with his rejection of idealism, and he holds on to it despite Wittgenstein’s perseverant objections that caused him to abandon the 1913 manuscript of the Theory of Knowledge. Even five years later, in his The Philosophy of Logical Atomism, Russell’s metaphysical predilections seem not to have changed significantly: I think one might describe philosophical logic, the philosophical portion of logic which is the portion that I am concerned with in these lectures since Christmas (1917), as an inventory, or if you like a more humble word, a “zoo” containing all the different forms that facts may have. […] In accordance with the sort of realistic bias that I should put into all study of metaphysics, I should always wish to be engaged in the investigation of some actual fact or set of facts, and it seems to me that this is so in logic just as it is in zoology. In logic you are concerned with the forms of facts, with getting hold of the different logical sorts of facts, that there are in the world. (PLA: 47 f.)

In Russell’s ontological “zoo” lions as well as logical forms are held captive, and there can be no doubt that for Russell both kinds were genuine discoveries that existed all along prior to their captivity and hence are in the same way open to objective investigation. This yields an extremely pluralistic metaphysics in which all objects are virtually of the same single ontological category, namely “terms”: Whatever may be an object of thought, or may occur in any true or false proposition, or can be counted as one, I call a term. This, then, is the widest

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word in the philosophical vocabulary. I shall use as synonymous with it the words unit, individual and entity. The first two emphasize the fact that every term is one, while the third is derived from the fact that every term has being, i.e. is in some sense. A man, a moment, a number, a class, a relation, a chimaera, or anything else that can be mentioned, is sure to be a term; and to deny that such and such a thing is a term must always be false. (POM: 47)

Since terms represent Russell’s basic building blocks of which propositions are composed, and since an adequate grasp of it is essential for understanding the difficulties their conception raises in connection with the problem of unity, I’ll elaborate on it in a little more detail in what follows. Russell’s Theory of Judgment (I) Terms divide into things and concepts, the former being indicated by proper names and the latter by all other words. Concepts are further subcategorized into two kinds, predicates and relations, indicated by adjectives and verbs, respectively.21 Although terms may perform different functional roles within a proposition, all of them are to be considered objects. They are discrete entities without any intrinsic connection to one another. Russell is therefore confronted with a fundamental question. What distinguishes a mere assemblage of terms from a proposition—a complex entity having a certain structure—in virtue of which it expresses a truth-apt statement? Since the Kantian move of locating the source of unity in the judging subject was out of the question because it threatened to make propositions dependent on the subject, Russell had to look elsewhere.22 The need to account for the structure of a proposition can be illustrated by comparing the Russellian universe to the world of Lego bricks. It’s not until the unassembled parts enter into specific (spatial) relations to one another that they constitute complex objects, like houses and trees. But the resulting complex object must be more than the sum of its constituents because we are able to build very different complexes out of the very same parts. The difference in structure must somehow be explained since the objects on their own cannot account for it. And it’s no use here to appeal to different relations holding between objects in the case where two complexes have the same constituents yet are structurally

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different because relations are by definition objects themselves. This immediately raises the question how objects and relations themselves are related, and to answer it requires the invocation of an endless series of relations. This problem is known as Bradley’s regress, triggered by the conception of relations as objects on a par with all other objects.23 But there are even more troubling problems lying at the heart of Russell’s account of the problem of unity. As we’ve seen, the judging subject cannot impose any constraints on what is judged or provide the unity of a proposition on pain of making the judging subject in some sense constitutive of the proposition, a result Russell wants to avoid at all costs. The only other option is therefore to charge an element within the proposition itself with the task of unifying it. The element sought after is identified as the verb, which, besides figuring as an object-like constituent within a proposition, is to perform the additional function of relating the constituents so as to form a proposition. To illustrate this, let’s consider Russell’s own example, the proposition expressed by “A differs from B” (POM: 54). Logical analysis yields the three constituents A, difference, and B. It’s obvious that the constituents on their own, a mere collection of entities, don’t express anything. Although in both cases (before and after logical analysis) we apparently deal with the same objects, something responsible for uniting the objects so as to form a truth-apt statement has been lost in the analysis: A proposition, in fact, is essentially a unity, and when analysis has destroyed the unity, no enumeration of constituents will restore the proposition. The verb, when used as a verb, embodies the unity of the proposition, and is thus distinguishable from the verb considered as a term, though I do not know how to give a clear account of the precise nature of the distinction. (POM: 54)

Russell’s attempt at solving this problem consists in postulating that the verb has a “twofold nature” (ibid.).24 He specifies the twofold nature in terms of the difference between a “relation in itself ” and a “relation actually relating” (ibid.). Accordingly, when we consider “difference” apart from its figuring in a proposition, then it’s a relation in itself, a discrete

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object not bearing any relation to the other objects A and B. If, on the other hand, we consider the whole proposition “A differs from B,” then “difference” functions as a relation actually relating, a constituent of the proposition that in fact connects the objects involved. However, the twofold role the verb is to perform introduces several tensions into Russell’s account of the unity of the proposition. First, the twofold role of the verb, simultaneously charged with acting as an object-like constituent of a proposition and as its unifier, is at odds with Russell’s single-level metaphysics in combination with the corresponding one-step semantic theory. A relation is supposed to be “strictly the same” (POM: 55) regardless in which propositions it figures (a “relation in itself ”). Yet at the same time the relation is supposed to be different when it actually relates given pairs of terms (a “relation actually relating”). But how can the very same entity be different in the respective cases given that Russell’s theory doesn’t allow for Fregean senses? Objects, according to Russell, just are what they are and lack the perspectival character Frege tried to capture with his distinction between sense and reference. Since a “relation in itself ” differs from a “relation actually relating,” two distinct objects would have to be involved to account for this difference, which contradicts the claim that they are “strictly the same.” The source of the contradiction is that Russell tries to reconcile two categorically different things in his notion of the relation. It’s supposed to be both a bare constituent of a proposition and its logical form, an object and the structure of the connected objects of which it is itself a part.25 Second, and closely related to the first point, the twofold nature of the verb raises a fundamental difficulty that is now known as the “direction problem.”26 Most commentators discuss this problem in connection with Russell’s multiple relation theory of judgment, which he developed much later.27 But it should be emphasized—which is rarely noticed—that the direction problem not only arises already within the framework of the Principles, but also that Russell was aware of it.28 Nicholas Griffin distinguishes between two forms the direction problem can assume, wide and narrow, although the underlying difficulty it poses is in both cases the same from a theoretical perspective.29 The wide form concerns the question what distinguishes a well-formed belief such as “Othello believes that Desdemona loves Cassio” from a nonsensical

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belief such as “Othello believes that loves Desdemona Cassio.” The narrow form of the direction problem arises among well-formed beliefs with opposite or different senses such as “Othello believes that Desdemona loves Cassio” and “Othello believes that Cassio loves Desdemona.” The common denominator of both forms is the question of what accounts for the unity of the proposition, that is, what is the “ultimate source of order” (PP: 73) of the proposition. The second point (the direction problem) raises the question how it’s possible for a universal entity such as a relation to unify given pairs of terms so as to relate them in a specific way that marks a difference between such propositions as “aRb” and “bRa” (where “a” and “b” stand for objects and “R” for a relation). How can, in other words, the abstract relation difference, which is supposed to be the same in every proposition in which it occurs, contribute different contents in each case? Russell is fully aware of the need to incorporate something like Fregean senses into his theory to account for the unity of the proposition. However, his metaphysics cannot allow for them. The sense of a relation is said to be the source of order, but how this comes about is still left unexplained, which is why Russell had to concede that the notion of sense, while being a fundamental requirement, is “not capable of definition” (POM: 94). In sum, Russell’s extreme realism (or anti-idealism) forces him simultaneously to reject any involvement of the judging subject as a synthesizer or unifier of given objects and to emphasize the reality and independence of relations. This reduced Russell’s theoretical inventory to only one ontological category: the single realm of terms. His notion of a relation threatened to collapse under its theoretical burden on the one hand and made his conception of propositions vulnerable to Bradley’s regress and the direction problem on the other. What I’ve presented so far are the difficulties Russell faced in the Principles. In the ensuing years he became increasingly dissatisfied with his former account of the unity of the proposition and his problem-­ ridden theory of judgment. In his 1910 essay “On the Nature of Truth and Falsehood” Russell hoped to solve the problems by replacing his old view with the multiple relation theory of judgment. Besides the need to deal with the direction problem, Russell’s main reason for adopting a new strategy was the problem of false propositions.30

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Recall that a true proposition is identical to the fact that makes it true. It’s an objective complex composed of entities that stand in certain relations to one another. And the same goes for false propositions. They, too, are existing complexes that just happen to lack the property of being true. True and false propositions don’t differ with respect to their ontological status but only with respect to one of their properties, being true or being false. By 1910, Russell considered this view entirely unacceptable for two reasons. First, he became dissatisfied with construing true and false propositions—which he now called, with reference to Meinong, “Objectives”31— as equal denizens in the realm of reality. In assigning false propositions the very same ontological status than true ones, Russell had to accept that a false proposition such as “Mont Blanc is not the tallest mountain in Europe” is as real as its true counterpart, and that both entities exist regardless of whether there are (judging) minds or not—a view Russell now finds almost absurd.32 Russell’s second worry was that treating true and false propositions ontologically equally “leaves the difference between truth and falsehood quite inexplicable” (NTF: 119). For what is distinctive about truth if the only difference between true and false propositions is that the former class has the property of being true while the latter class has the property of being false? To call one class of propositions true and another one false is empty at best and circular at worst if there is no difference between them in the first place. But the situation is even worse. Not only does the difference between truth and falsehood become inexplicable, it collapses altogether. Since propositions, true and false ones alike, are identical with their subject matter, they both exist. But the existence of a proposition is, according to Russell, tantamount to its being true. This is because for a proposition to be true just is for the proposition’s constituents to be related in a certain way. This follows immediately from the basic premise of the identity theory, namely that propositions are identical with their truth-makers. As will become clearer in what follows, Russell’s error was to incoherently identify the unity of the proposition with what makes it true.33 For example, if A loves B, then the obtaining of the loving-relation is what makes the judgment “A loves B” true. A unified proposition must

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be true because its truth consists in nothing other than the constituents involved being related as stated. In the case where A doesn’t love B there is no such thing as the unity of A, B, and love, but merely a set of disconnected entities. But then we fail to have a proposition at all since a proposition is a certain kind of unity. And this means that there would be nothing for the false judgment to be about. The problem is thus the following. Either false propositions are not unified, in which case they cease to be propositions at all, or false propositions are unified, in which case they end up being true after all, since the truth of a proposition was defined as the unity of (i.e. the obtaining of a certain relation between) the set of the constituents it comprises. This makes false judgments impossible because now there are only true propositions—the difference between truth and falsehood collapses.34 The second point is closely connected to the first point, and they jointly generate a dilemma consisting in two equally unacceptable options. (1) Either we simply dispel false propositions from our ontology. But then, what are false judgments about? Judgment is thought to be a dual relation between a judging subject and an objective complex with which we have to be directly acquainted. But in the case of false judgments, “Caesar died of natural causes,” say, no such entity can be found because Caesar was murdered. False judgments, therefore, turn out to be a relation between a judging subject and nothing at all. (2) Or we admit of false propositions. But in this case false propositions turn inevitably into true ones according to Russell’s own premises. So the dilemma is that allowing false objectives threatens to implode the difference between truth and falsehood, whereas dismissing them renders false judgments impossible: “We must, therefore, abandon the view that judgments consist in a relation to a single object” (NTF: 120). Russell’s Theory of Judgment (II) In the same essay just quoted, Russell then presents his switch from his former dual relation theory of judgment to his new multiple relation theory of judgment: The theory of judgment which I am advocating is, that judgment is not a dual relation of the mind to a single Objective, but a multiple relation of the mind to the various other terms with which the judgment is concerned. Thus if I judge that A loves B, that is not a relation of me to ‘A’s love for B’,

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but a relation between me and A and love and B. If it were a relation of me to ‘A’s love for B’, it would be impossible unless there were such a thing as ‘A’s love for B’, i.e. unless A loved B, i.e. unless the judgment were true; but in fact false judgments are possible. (NTF: 122)

With this new approach Russell thought he was able to kill two birds with one stone. For conceiving of the judgment relation not as holding between a judging subject and a single (complex) entity but a multiple relation to non- or sub-propositional constituents removes the problematic false propositions from Russell’s ontology while at the same time allowing for false judgments. This is now possible because Russell abandoned his former identity theory in favor of a correspondence theory. The judgment that A loves B is true just in case there is a “complex corresponding to the discursive thought which is the judgment” (PM: 43). But when the judgment is false the judging subject only bears a relation to the (existing) constituents A, love, and B, and not to a false (non-existing) complex “A loves B.” According to the new theory, then, the propositional complex is broken up and replaced by their constituents to which the judging subject bears a single judging relation.35 The structure of the judgment “Othello believes that Desdemona loves Cassio” is no longer to be analyzed as a relation between Othello and the single Objective “Desdemona loves Cassio,” but rather a four-term complex (Othello, Desdemona, Cassio, and love) bound together by the judging relation. The structural difference of the respective accounts can be represented more formally in the following way. The dual relation theory of judgment holds that a judging subject, S, has a relation to a certain (relational) proposition, aRb, yielding the formula S(aRb). The multiple relation theory, however, includes the judging subject among the other propositional constituents, which are now unified by the judging relation, J, yielding the formula J(S, a, R, b). We can bring out the differences between the respective accounts by distinguishing the various roles the relation plays within a proposition. Russell’s old theory officially charges the subordinate relation—the relation other than the judging relation—with two tasks (and an implicit third one, which is a consequence of the second):

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1. the relation as a constituent of the proposition, a universal entity on a par with all other constituents regardless of status and kind, 2. the relation as the unifier of the proposition, binding together all the constituents involved, and 3. the relation as a truth-maker of the proposition, since a proposition is said to be true if the relation in fact relates the terms as the judgment says.36 Russell’s step toward his new theory consists in removing function (2) from the relation, which is now performed by the act of judgment, while still keeping (1) and (3). Plainly, this creates difficulties because, although the official doctrine has it that (2) and (3)—the matter of unity and truth—are now to be considered separately, they are still inextricably connected to each other. The connection here is, again, one of the requirements of the unity of the proposition with which Russell had been struggling since the Principles, namely that a relation actually relating the terms of a proposition must have a sense, a requirement pervading almost all his writings that concern the unity of the proposition.37 The direction problem rears its head again, and the dilemma it poses is as follows. As we’ve seen, the multiple relation theory transfers the function of providing unity from the subordinate relation to the judging relation. The subordinate relation, as Russell put it, is downgraded to being merely a “brick in the structure, not the cement. The cement is the relation ‘believing’” (PP: 74). According to an early version of the multiple relation theory, the judging relation, while providing the unity, doesn’t yet also provide the sense of the subordinate relation, that is, that feature of the subordinate relation responsible for marking the difference between asymmetrical relational propositions such as “A loves B” and “B loves A.” That is, providing the differentiating sense was still the task of the subordinate relation.38 This construction produced an outright contradiction because the subordinate relation, although officially to be considered a “brick in the structure”—a universal entity without any specific connection to all the other propositional constituents—must relate its terms in specific ways in order to contribute the necessary sense to the proposition. But in doing so, the subordinate relation unifies its terms and loses its status as a universal entity. Put in terms of Russell’s earlier terminology,

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the contradiction consists in the subordinate relation’s having to play simultaneously the two incompatible roles of a “relation in itself ” as well as a “relation actually relating.”39 By playing the former role false objectives are avoided because the subordinate relation is only one constituent among others bound together by the judging relation, but then the proposition lacks the required sense. By playing the latter role the required sense is accounted for because the subordinate relation relates A and B differently in each case, but then the constituents end up being unified in both cases regardless of whether A loves B (and vice versa). Since, according to (3), for a proposition to be true just is a complex of objects being related in a certain way, it follows that complexes involving a “relation actually relating” cannot be false. In sum, the problem is that while assigning the job of unifying the propositional constituents to the judging relation officially separates the issue of unity and truth, it nevertheless leaves them inextricably connected to each other because the subordinate relation unwillingly plays the role of a unifier owing to the requirement of sense. Hence Russell fails to disentangle unity and truth, which is why his theory is incapable of accounting for either the required sense of the proposition or the possibility of false judgments. Russell tried to repair his theory in his The Problems of Philosophy by letting the judging relation take over the function of providing the sense of the proposition in addition to the function of providing the unity.40 Does this solve the problem of unity and does the judging subject succeed in imposing constraints on the proposition judged, that is, providing its sense? The least we can say is that Russell does take a step toward a Kantian theory of judgment while at the same time shying away from going all the way because that would mean making the judging subject somehow constitutive of propositions and hence make them dependent on the subject. Russell’s appeal to the judging subject as conferring unity and sense on the proposition is driven by theoretical demands, yet in order to preserve the fully objective and independent status of them he had to reduce the judging relation to a “purely formal”41 act. But, as Stewart Candlish observed, charging the judging relation with unifying and conferring sense or direction on a proposition gives “a kind of psychokinetic power to the mind, in that simply by judging that A

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loves B I bring A and B into the relation of love.”42 The reason why Russell’s latest theory amounts to the absurdity that the judging subject creates the truth of a proposition lies in his thoroughly realistic account of subordinate relations, according to which they also function as the truth-­ makers of the proposition: What is the proof that we must understand the “form” before we can understand the proposition? I held formerly that the objects alone sufficed, and that the ‘sense’ of the relation of understanding 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 be united. (TK: 116)

This passage exhibits the fundamental problem pervading Russell’s theory of judgment as well as his theory of propositions, namely having wrongly identified what unifies a proposition with what makes it true. As I’ve noted above, this has the devastating result that there are only true propositions. For in case where A and B are not similar, “no amount of thinking can force them to be united,” but this is exactly what happens in Russell’s former theories because the judging relation unifies given terms simply by judging that they are related in a certain way. And once the terms, which are identical with the items they are about, are related in judgment they are thereby actually related as the judgment states. The underlying mistake is that in Russell’s theories unity and truth entail each other because the subordinate relation carried the burden of accounting for both; a unified proposition must be true and, conversely, a (true or false) proposition is always unified. If it weren’t, the proposition would simply cease to be a proposition. As Rosalind Carey has succinctly expressed the dilemma: “[If ] the terms of the judgement are not arranged by judging, the judgment is meaningless and fails to express anything at all, but if they are, the judgement is true.”43 The proposition that A and B are similar ends up being unified whether it is true or not, but since for Russell unity and truth entail each other, both propositions end up being

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true, which produces a contradiction. Again, Russell is faced with two equally unacceptable outcomes of his theory, namely either admitting of false objectives, which erodes the difference between truth and falsehood, or otherwise rendering false judgments impossible. Russell’s Theory of Judgment (III) Eventually, Russell came to see this point in his 1913 manuscript Theory of Knowledge, which also marks one of the last attempts at coming to terms with the recurring problem of unity and objective falsehoods. The familiar problem of unity—in this case, how the constituents A, B, and similarity form a proposition—is now being tackled from a different angle. Thus far Russell had tried to explain unity and directionality by appealing to various entities. First, the (twofold nature of the) relation involved in a proposition, second, the judging relation as a multiple relation to the constituents of a proposition, and third, the judging subject as providing both unity and directionality of a proposition. He now realized that the structure of a proposition cannot be conceived of as an entity because doing so triggers a version of Bradley’s regress and involves all the difficulties I’ve been reviewing so far.44 This, then, is Russell’s new proposal. In order to understand a proposition such as “A and B are similar” it no longer suffices to be acquainted only with its constituents A, B, and similarity but also requires being acquainted with its logical form: the way in which they are combined.45 The judging subject, confronted with a particular set of objects, must be given logical instructions to be able to put them together since the objects themselves provide us with no clue as to how to connect them with one another.46 Russell’s world of objects resembled a construction kit in which all the necessary elements are given but the possibilities of (or constraints on) correct assembly are not. Acquaintance with logical forms is now supposed to equip the judging subject with the capacity to unify given objects such that the result will always be a properly constructed proposition. The population of Russell’s universe grows and now includes logical forms in addition to all the other entities already residing there. This proposal promises to solve two problems. First, logical forms prescribe the combinatorial possibilities of given objects, which at once determine how propositional constituents form a complex and rule out nonsensical

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connections; this accounts for the source of constraints on what can be judged. Second, acquaintance with logical forms allows for dealing with false judgments. For, if an actual complex is not given, for example, when A and B are not similar and not connected in any way (or if A and B turn out to be identical), acquaintance with logical form makes it possible to (falsely) judge that A and B are similar because we now know how to combine them in thought regardless of their being actually related or not.47 This can be seen as an important step toward separating what unifies a proposition and what makes it true, which was the incoherent alliance responsible for the problems of Russell’s former theories. Logical forms provide us with the means to combine given terms without affecting the truth-value of the resulting judgment since it’s now a further and logically independent question whether there actually is a complex corresponding to the judgment. However, despite his assurance that logical forms “cannot be regarded as ‘entities’” (TK: 97), we must nevertheless be somehow acquainted with them in an act of “logical experience,” which is said to be a “kind of immediate knowledge” (ibid.). This sounds suspicious; with what could we possibly be acquainted other than entities, no matter of what kind? What is the nature and status of logical forms? Russell tells us that logical forms are obtained by replacing all constituents occurring in a proposition with appropriate variables. In our example “A and B are similar,” this procedure yields the form of a “dual complex,” which is symbolized by “xRy” or “R(x, y)” (TK: 113) and roughly corresponds to the phrase “something and something have a certain relation” (TK: 116). Now, the conjunction of the following two requirements seems to produce a contradiction: 1. Logical forms cannot be regarded as entities on pain of initiating an infinite regress. 2. Acquaintance with logical forms (“logical experience”) is a precondition of understanding any proposition on pain of making false judgments impossible. For requirement (2) forces Russell to acknowledge that in logical experience we are acquainted with something. Logical forms seem to be some sort of entity after all, which obviously violates requirement (1).48 This

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suspicion is confirmed when we consider Russell’s attempt at implementing his newly gained insights into his symbolism. According to his old version of the multiple relation theory, the judgment that A and B are similar was to be symbolized by J(S, A, B, similarity), where the judging relation was supposed to unify the given constituents so as to form a proposition. His new proposal consisted merely in adding the logical form of the judgment as a further constituent. The resulting formula is “U{S, A, B, similarity, R(x, y)}” (TK: 117) (“U” stands for the understanding relation). Russell claims that the logical form R(x, y) “enters in a different way” (ibid.) into the judgment-­ complex but nowhere does he explain how. The formula, as it stands, simply fails to account for the fundamental difference between the constituents of the complex (S, A, B, similarity) and their form because R(x, y) occupies an argument place in the formula just as the other constituents do. The problem of how the constituents are to be put together is exactly the same as before. We are still not better off than before since we are now owed an explanation as to what is to be done with A, B, similarity and the logical form R(x, y). Logical form ends up being an entity after all and turns out to be, once more, a further item in need of unification.49 The familiar dilemma ensues. To unify the constituents, we must know how to relate them with one another. And this requirement applies whether the items to be unified are objects or forms. Including the form of the judgment into the judgment itself, as in U{S, A, B, similarity, R(x, y)} is simply irrelevant for the question of unity as long as it occurs as a term in the judgment. It does nothing to prevent Bradley’s vicious regress from arising since the question remains how the objects and the logical form are to be related.

2.3 Wittgenstein’s Critique So far, I’ve been presenting the problems of Russell’s theory of judgment as being based on his problematic account of logical form, which, in my view, in turn is part and parcel of the problem of unity. After all, the unity of a proposition—what makes a proposition a proposition in the first

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place—consists in nothing but a proposition’s possessing a particular logical form; it consists in a set of objects being related in a certain way. Logical form is precisely what distinguishes a proposition (a certain kind of unity capable of being true or false) from a mere collection of objects. But is that line of argument really Wittgenstein’s objection? This is a highly controversial issue. But whatever the answer to that question, which I’ll address below, it’s at least clear that Wittgenstein’s onslaught on Russell’s theory eventually led to the abandonment of the Theory of Knowledge manuscript: Wittgenstein came to see me—we were both cross from the heat—I showed him a crucial part of what I have 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 I have missed. If I could see it too I shouldn’t mind, but as it is, it is worrying, and has rather destroyed the pleasure in my writing. (SL: 447; 27 May 1913)

And a few years later, in 1916, Russell reminisces in a letter to Ottoline Morrell: His criticism, tho’ I don’t think you realised it at the time, was an event of first-rate importance of my life, and affected everything I have done since. I saw he was right, and I saw that I could not hope ever again to do fundamental work in philosophy. (A: 267)

The reason why there is a long-standing debate in the literature over the exact nature of Wittgenstein’s critique is not only that the textual evidence in this regard is rather sparse, but also that the little evidence we do have is inconclusive. Although there is an agreement among most commentators which passages from Wittgenstein’s notebooks and his letters to Russell supposedly contain Wittgenstein’s objections—simply because Wittgenstein himself expressly intends his remarks as objections to Russell’s theory of judgment in these passages—there is much dispute over how to interpret them. There are several passages in which

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Wittgenstein addresses Russell’s theory, but his key point is taken to be expressed in the following two closely related passages: Every right theory of judgment must make it impossible for me to judge that “this table penholders the book” (Russell’s theory does not satisfy this requirement). (NL: 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.) (TLP: 5.5422)

There is broad consensus that, according to Wittgenstein, the main defect of Russell’s theory consists in its inability to rule out nonsensical judgments. But it’s far from clear which aspect of Russell’s theory Wittgenstein identified as being responsible for this defect, and hence it’s unclear exactly why nonsensical judgments are still possible within its framework. Roughly two strands of interpretation can be distinguished. The majority view (henceforth called the standard reading) taken by the vast majority of commentators connects Wittgenstein’s objection(s) to difficulties stemming from the conjunction of Russell’s theory of judgment with his theory of types, though there are sometimes differences and disputes over the precise nature of the problematic link between the two theories.50 The minority view claims that the main problem besetting the theory of judgment doesn’t originate in its combination with the theory of types but is rather internal to the theory of judgment itself (henceforth called the internal reading). Here commentators differ over whether the internal element is to be identified with Russell’s (mis-)conception of logical form or with the problem of unity.51 In the following, after having presented the standard reading, some criticism of it, and a clarification of Wittgenstein’s understanding of the relation between the theory of types and the theory of judgment, I’ll defend the internal reading, but with the important amendment that on my reading—contrary to most commentators adopting the internal reading—the problem of unity and the problem of logical form will eventually turn out to be identical, or at least as two sides of the same coin.

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The Standard Reading Now, the standard reading relies on very complex relations between the ramified type theory and Russell’s theory of judgment, but the basic idea behind the standard reading is rather straightforward and is roughly as follows. According to Russell’s theoretical edifice in his Principia Mathematica, the theory of types is supposed to be based on and emerge from the multiple relation theory of judgment and not the other way round. However, type-theoretical distinctions and restrictions are required to ensure that combinations of terms yield legitimately constructed judgments. But then, so the argument goes, the relation between the theory of types and the multiple relation theory of judgment involves a vicious circle, which is taken to be Wittgenstein’s main point in a letter to Russell: I can now express my objection to your theory of judgment exactly: I believe it is obvious that, from the proposition “A judges that (say) a is in a relation R to b”, if correctly analysed, the proposition “aRb. ∨. ¬aRb” must follow directly without the use of any other premiss. This condition is not fulfilled by your theory. (L: 40; June 1913)

Griffin explains: On Russell’s theory this belief [“a is similar to b”] is analyzed as B(S, a, R, b, Σ), where Σ is the form of an elementary dyadic complex. Does this ensure that aRb is significant? The answer is, not without further premisses. For we need to stipulate that a and b are indeed individuals, that R is a first-order relation and that Σ is the form of a first-order dyadic complex. Why won’t Wittgenstein allow us these stipulations? Because to make them would require further judgments. […] In other words, type theory will break down if the multiple relation theory is adhered to. Faced with these alternatives, Russell abandoned the multiple relation theory.52

According to the standard reading, then, the meaningfulness of first-­ order judgments such as “aRb” requires that the constituents making up the judgment be of the correct number, type, and order, to form a coherent complex. The judgment “aRb” expresses a meaningful proposition only if a and b are in fact individuals and R is in fact a dyadic relation holding between them. If R were another individual or if either a or b

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were relations, then the judgment “aRb” would be meaningless.53 But if we know the respective types of the constituents involved, then we are in a legitimate position to dismiss nonsensical judgments such as “Othello believes that Desdemona Cassio Iago” because it’s illegitimate to combine individuals without a relation of the appropriate adicity. According to the standard reading, however, the problem with this account is that the stipulation of type restrictions purportedly ensuring the legitimacy of combination of propositional constituents is expressed in further judgments, which makes the meaningfulness of first-order judgments dependent on second-order judgments.54 According to Griffin, this result is highly problematic because Russell explicitly commits himself to the requirement that “higher-order judgments are to be defined cumulatively on lower-order ones. Thus we cannot presuppose second-­ order judgments in order to analyze elementary judgments.”55 Obviously, the fact that the significance of first-order judgments depends on type distinctions expressed in second-order judgments while at the same time the latter are to be defined in terms of the former leads to a vicious circle. As a consequence, nonsensical judgments cannot be ruled out. The standard reading can claim some plausibility because, first, there are passages in which Wittgenstein doubts the very project of developing a theory of types or at least questions its necessity or usefulness; and second, it cannot be denied that the theory of types is inextricably linked to the theory of judgment.56 However, the standard reading is vulnerable to the following twofold objection. Commentators have argued that Wittgenstein’s alleged type-theoretical objection is itself either unfounded and therefore doesn’t pose a real threat to Russell’s theory or that Russell would have had at least the theoretical resources to repair his theory in such a way as to defuse the objection.57 It’s certainly true that the theory of types has significant problems of its own, but Wittgenstein, I maintain, aims primarily at deeper issues with the theory of judgment itself. On my reading, problems with the theory of types will turn out to be a byproduct of the more fundamental problem of logical form and unity. This is the problem that is actually responsible for the possibility of nonsensical judgments, which is why the theory of types must not be mistaken as its source.

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Wittgenstein on Types Wittgenstein’s objection consists in an argument that aims at the very core of Russell’s theory of types, but it actually points to a more profound disagreement between the two thinkers concerning the nature of symbols, judgments and propositions, that is, the problem of logical form and unity. I’ll reconstruct the argument first and then turn to the broader issues. Wittgenstein’s objection specifically targeting the theory of types first occurs in the Notes on Logic and resurfaces almost verbatim in the Tractatus58: Types can never be distinguished from each other by saying (as is currently done) that one has these but the other has those properties, for this presupposes that there is a meaning in asserting all these properties of both types. (NL: 106)

The purpose of Russell’s theory of types was to avoid his famous eponymous paradox by compartmentalizing the logical universe into a hierarchy of types, for example, objects, concepts, and classes. This was to preclude potentially problematic cross-categorical combinations of types, such as “the class of all classes that are not members of themselves.” But in identifying and classifying different logical types we seem to be forced to violate the very condition the theory of types imposes on us. Wittgenstein is more explicit about this problem in his Notes Dictated to G.E. Moore: This same distinction between what can be shewn by the language but not said, explains the difficulty that is felt about types—e.g., as to [the] difference between things, facts, properties, relations. That M is a thing can’t be said; it is nonsense: but something is shewn by the symbol “M”. […] Therefore a theory of types is impossible. It tries to say something about the types, when you can only talk about the symbols. But what you say about the symbols is not that this symbol has that type, which would be nonsense for [the] same reason; but you say simply: This is the symbol, to prevent misunderstanding. […] Here we have not said: this symbol is not of this type but of that, but only: This symbolizes and not that. (NM: 108)

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The reason why statements of the form “M is a thing” and “The symbol expressed by ‘M’ belongs to the type singular term” are tautological or even nonsensical (Wittgenstein wavers on this point) has to do with the fact that Wittgenstein proposes as a criterion for meaningful discourse what I’ll call the contingency requirement: Meaningful property attributions and the statements in which they are involved must essentially be contingent in that the states of affairs claimed to be the case could be (or could have been) otherwise: Whatever we can describe at all could be other than it is. (TLP: 5.634)

This is generally known as what Wittgenstein calls the bipolarity of the proposition.59 The reason why I introduce a different term is that it brings out more clearly that the defining trait of a meaningful proposition is to draw a contrast between truth and falsity and not simply to have either the property of being true or false. Tautologies (contradictions) are always true (false) yet are senseless precisely because they fail to satisfy the contingency requirement. Likewise, for a property attribution to be meaningful it must be conceivable that the property either applies to an object or not, and for a statement to be meaningful it must be intelligible that what it states either obtains or not.60 It follows that for property attributions to be meaningful it must be intelligible either to attribute a particular property to an object or deny it, and hence the statement involving the property attribution must be capable of being either true or false.61 For Wittgenstein, the necessary feature and distinctive mark of descriptive vocabulary in general and property attribution in particular is that in each case it must be possible to be (or to have been) otherwise. In other words, in each case the attribution and denial of a property as well as the truth and falsity of a statement must be intelligible.62 For example, it’s meaningful to attribute the property of being brown to a particular table simply because it’s possible that the table couldn’t have had that property. Evidently, sentences of the form “M is a thing” and “The symbol expressed by ‘M’ belongs to the type singular term” violate the contingency requirement. For “M is a thing” to be a meaningful statement it had to be capable of being either true or false, that is, its negation must also be meaningful.63 But what would it mean for M not

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to be a thing? What would it mean, for example, for a tree not to be a tree? Of course, it’s possible that the sign “M” did not refer to a particular thing (but, say, to a concept), in which case “M” wouldn’t express a symbol belonging to the logical type singular term but would rather express a different symbol belonging to a different logical type (to the type predicate). But it’s impossible that the very same symbol could have belonged to different logical types because the particular type it has is constitutive of its being the symbol it is in the same way in which it’s impossible that the thing M could be (or could have been) a concept. If “it” were to belong to a different type, “it” would simply be a different symbol and not just the same symbol with different logical properties. Here’s a crisp explanation by Adrian Moore: Imagine a sign whose sole use hitherto has been as a noun. Suppose it is now used as a verb. We must not say that the original symbol has been put to an improper use. There is now a new symbol.64

Now, according to Wittgenstein, from the contingency requirement it follows that a “theory of types” (NM: 108) is impossible. As the double emphasis indicates, what he takes issue with is the classification of types (a theory) and not so much with types themselves—Wittgenstein seems to have acknowledged that symbols belong to different types.65 However, it’s nonsensical to assert (and a theory of types is nothing but a set of assertions concerning types) that a particular symbol belongs to a particular type because this presupposes the possibility of meaningfully denying that a particular symbol belongs to a particular type. This in turn would imply that a symbol possessing a determinate type could also not possess it while remaining the same symbol. But we have seen that this makes no sense, for types are constitutive of what symbols are and they wouldn’t be the same symbols if they possessed a different type. Therefore, classifying given symbols into different kinds of logical types (or classifying given items into objects, concepts etc.) presupposes that predicates such as “x is (not) a singular term” or “y is (not) an object” can be meaningfully attributed to each symbol or item, respectively. In classifying types, we would have to say that some symbols are of the type singular term and some are not (for they may be of the type predicate) and

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that some items are objects and some are not (for they may be concepts). And this is exactly what the theory of types prohibits us to do because these type attributions would cut across different types. Therefore, the rules according to which we are to operate in the classificatory process force us to violate those very rules.66 Wittgenstein on Symbols As I’ve said, the Wittgenstein-Russell dispute over the theory of types is indicative of a larger disagreement between them regarding the nature of symbolisms in general and judgments and propositions in particular. So far, Wittgenstein’s argument revealed Russell’s theory to be problematic by demonstrating that type-theoretical attributions such as “M is a thing” are strictly speaking nonsensical. One might wonder, though, whether this is simply due to the theory’s particular design and whether it could be repaired in such a way so as to avoid the charge of contradiction. Wittgenstein is doubtful, not because he believes the theory of types cannot be made viable, but because he is suspicious of the entire framework that motivated (or forced) Russell to develop the theory in the first place. Even a coherent theory of types would seem objectionable to Wittgenstein. As he writes in the Notes, even: if there were propositions of [the] form “M is a thing” they would be superfluous (tautologous) because what it tries to say is something which is already seen when you see “M.” (NM: 109)

And this brings us to the root of their disagreement. There is a letter often quoted in support of the standard reading that Wittgenstein wrote to Russell, in which Wittgenstein presents in some detail his own analysis of judgments and the propositions they express in connection with the theory of types. This is why the letter is worth quoting at some length: I have changed my view on “atomic” complexes: I now think that qualities, relations (like love) etc. are all copulae! That means I for instance analyse a subject-predicate prop[osition], say, “Socrates is human” into “Socrates” and “something is human”, (which I think is not complex). The reason for this is a very fundamental one: I think that there cannot be different Types of things! In other words whatever can be symbolized by a simple proper

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name must belong to one type. And further: every theory of types must be rendered superfluous by a proper theory of symbolism: For instance if I analyse the prop[osition] Socrates is mortal into Socrates, mortality and (∃x, y)ε1(x, y) I want a theory of types to tell me that “Mortality is Socrates” is nonsensical, because if I treat “Mortality” as a proper name (as I did) there is nothing to prevent me to make the substitution the wrong way round. But if I analyse [it] (as I do now) into Socrates and (∃x)x is mortal or generally into x and (∃x)φ(x) it becomes impossible to substitute the wrong way round, because the two symbols are now of a different kind themselves. What I am most certain of is not however the correctness of my present way of analysis, but of the fact that all theory of types must be done away with by a theory of symbolism showing that what seem to be different kind of things are symbolised by different kinds of symbols which cannot possibly be substituted in one another’s places. (L: 38; January 1913)

Surely, Wittgenstein mentions the theory of types in the course of discussing the proper analysis of the judgment “Socrates is mortal.” But here he neither criticizes the theory of types itself nor says or even implies that its viability would in some way or other also affect the theory of judgment. It is true that Wittgenstein attacks both theories in various places, but he does so in each instance on independent grounds and nowhere claims that Russell’s problems emerge from their conjunction. Rather, what he does say in the letter (twice!) is that, while being uncertain about his own analysis, he is confident the theory of types “must be rendered superfluous” and “done away with” by a “proper theory of symbolism.” Wittgenstein’s point is that nonsensical judgments are possible within Russell’s current theory of judgment, which is why a theory of types is required to rule them out. But once we have a proper theory of symbolism (whatever its particular design) a theory of types will automatically be superfluous because a proper symbolism already reflects type-theoretical distinctions in such a way that “it becomes impossible to substitute the wrong way round, because the […] symbols are now of a different kind themselves.” The symbols used in a proper symbolism must themselves exclude the possibility of forming nonsensical judgments with them and shouldn’t have to require an extra “logical manual” instructing us how to manipulate them correctly.

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Wittgenstein’s emphasis is on the need for a proper symbolism that gives us the correct view of propositions, and not on the need to modify or revise a theory of types as an auxiliary device for a theory of judgment.67 Even years later, after he had read the Tractatus, Russell still didn’t quite see Wittgenstein’s point, which manifests itself in a brief but telling exchange of letters: The theory of types, in my view, is a theory of correct symbolism: (a) a simple symbol must not be used to express anything complex: (b) more generally, a symbol must have the same structure as its meaning. (L: 96; August 1919)

Although Russell’s sketch doesn’t seem at first sight to be particularly controversial or provocative, Wittgenstein’s response is rather intense because he discerned in it a misconception pervading Russell’s view regarding the essence of a proper symbolism: That’s exactly what one can’t say. You cannot prescribe to a symbol what it may be used to express. All that a symbol can express, it may express. This is a short answer but it is true! (L: 99; August 1919)

This passage echoes a central point he already made in the Tractatus, namely, that it’s impossible to “give a sign the wrong sense” (TLP: 5.4732). The root of their disagreement is to be located in their diametrically opposed conceptions of what a proper symbolism is supposed to be, and Wittgenstein thought Russell to be guilty of what may be called, borrowing a useful term from Robert Brandom, the descriptive fallacy.68 The descriptive fallacy consists in the mistake of assimilating theoretical metavocabulary—vocabulary intended to provide a specification of essential features, that is, of structural and logical properties, of another vocabulary—to ordinary descriptive vocabulary. In short, the mistake is to construct a theoretical metavocabulary as a descriptive one. And Russell’s theory of types, so Wittgenstein’s misgivings, does precisely that. It’s a metavocabulary involving claims about which symbols possess which types, which ought to prevent us from constructing illegitimate judgments. For example, the metavocabulary might contain statements

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such as “M is a thing” and “The symbol expressed by ‘M’ belongs to the type singular term.” But according to Wittgenstein these sentences turn out to be superfluous or even nonsensical under closer inspection. They make it look as if they stated facts and thus create the false impression of being informative by providing one with true descriptions of the logical properties of types to which we are to be faithful in making judgments. Hence, when Russell says “a simple symbol must not be used to express anything complex” he gets matters back to front. You cannot prescribe a simple symbol to express only that which is also simple because expressing something simple is precisely what makes a symbol a logically simple one. If a symbol expresses something complex, then it is a logically complex symbol. Russell’s view suggests that there could be a mismatch between the logical type of a symbol and the type of its meaning (its referent), which is why philosophical theorizing is necessary to preclude our coordinating symbols and meanings in the wrong way. Now, Wittgenstein’s aim is to expose this classificatory procedure as superfluous at best and nonsensical at worst. His entire point is that identifying the meaning of a particular symbol is tantamount to identifying its logical type.69 For Russell, understanding the meaning of a symbol and knowing its logical type are two independent issues, whereas Wittgenstein insists on the impossibility (or nonsensicality) of prizing them apart. For example, if “Jones” refers to Smith’s good friend Jones, then the symbol expressed by “Jones” is already of the logical type singular term. It’s impossible (or, again, nonsense) for the symbol expressed by “Jones” to mean or refer to Jones and be of a logical type other than singular term.70 The upshot of all this is that the logical type of a symbol and the type of its meaning are essentially a package deal; you cannot have one without the other.71 And now we see clearly why it’s nonsense to categorize symbols by saying “This belongs to this type and that belongs to that type.” In order for us to do so we must already know the logical type of given symbol, but once this question is settled the question of the type of what the symbol stands for is settled as well: This is what is sought to be expressed by the nonsensical assertion: Symbols like this are of a certain type. This you can’t say, because in order to say it you must first know what the symbol is: and in knowing this you see [the]

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type and therefore [the] type of [what is] symbolized. I.e. in knowing what symbolizes, you know all that is to be known; you can’t say anything about the symbol. (NM: 109)

So far I’ve been pursuing primarily the task of reconstructing and clarifying Wittgenstein’s objection to the theory of types and its relation to the theory of judgment. The conclusion to be drawn from the discussion is that, while Russell’s theory of types struggles with difficulties, Wittgenstein is much more concerned with addressing the confused notion of symbols on which it rests. In sum, his main point consists in drawing attention to the fact that if one uses Russell’s flawed theory of judgment, then a theory of types becomes necessary to rule out nonsensical judgments because Russell’s theory of judgment, due to its problematic conception of symbols, cannot do that on its own. Wittgenstein on Judgment If a proper theory of judgment makes a theory of types superfluous, this still leaves us with the question what Wittgenstein thought was wrong with Russell’s theory of judgment and how he intended to overcome its difficulties. These questions bring us right back to the problem of logical form and unity. To answer them we need to go back to the 1913 letter I quoted at some length above because it contains Wittgenstein’s proposed solution to those problems. What Wittgenstein realized was that if the constituents of a proposition are construed as atomistic, self-standing entities bound together by copulae or logical forms (or anything else, for that matter), then there are no constraints on what can be judged because there is “nothing to prevent me to make the substitution the wrong way round.” Russell’s analysis allows for, or at least doesn’t rule out, nonsensical judgments such as “Mortality is Socrates” because for Russell both constituents are of the same kind. Therefore, swapping one term for the other should make no substantial difference in the same way the sentence “Smith is tall” remains meaningful if I replace “Smith” with “Jones.” The complexes denoted by “Socrates is mortal” and “Mortality is Socrates” contain exactly the same items, which is why it’s hard to see why only the former and not the latter should be meaningful. The view that replacing items occurring in a proposition with other items of the same kind still yields a meaningful proposition is distinctly expressed in the Principles72:

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It is a characteristic of the terms of a proposition that any one of them may be replaced by any other entity without our ceasing to have a proposition. (POM: 48)

On Russell’s analysis, the terms making up a proposition can be substituted for one another “without our ceasing to have a proposition” because they are all of the same kind (namely terms). That is why a theory of types is required to rule out illegitimate substitutions. But according to Wittgenstein, precisely because a proper symbolism meets the condition of incorporating type-theoretical distinctions anyway, a separate, additional theory of types would obviously become an idle wheel at best. All that is required is a correct account of propositions, that is, a symbolism in which “the type of a proposition can be recognized by its symbol alone” (NL: 106). And Wittgenstein tells us in his 1913 letter what such a symbolism might look like, which is roughly as follows. Wittgenstein had formerly been working with a Russellian kind of analysis, using different sorts of copulae—symbolized by the subscripted epsilon—to represent the type of connection between the constituents of a proposition. For example, a subject-predicate proposition such as “Socrates is human” was symbolized by “ε1(a, φ)” meaning that the two terms in question are bound together by the copula of the subject-­ predicate form. Accordingly, a relational proposition such as “Plato was the teacher of Aristotle” is written “ε2(a, R, b),” where the terms occurring in brackets are bound together by the copula of relational forms. Wittgenstein’s new approach introduced a distinction between names and forms in order to account for the unity of propositions and at the same time rule out nonsensical judgments.73 Accordingly, the sentence “Socrates is mortal” was now to be analyzed into the name “Socrates” and the form “something is mortal.” The use of a copula became superfluous because the form now performed the function of providing the unity. This prevents us from making “the substitution the wrong way round” because there is only one way to make the substitution. It shows that “what seem to be different kind of things are symbolized by different kinds of symbols which cannot possibly be substituted in one another’s places” (L: 38). Nothing other than a proper name can be inserted into the open formula “something is human,” which puts the desired constraints on how to substitute one thing for another and hence constitutes the possibilities on what can be judged.74

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Wittgenstein’s new analysis of judgments and the distinction between names and forms mimics Frege’s distinction between saturated and unsaturated expressions.75 Frege’s saturated and unsaturated expressions in turn refer to saturated and unsaturated entities (arguments or objects and functions or concepts, respectively): Statements in general, just like equations or inequalities or expressions in Analysis, can be imagined to be split up into two parts; one complete in itself, and the other in need of supplementation, or ‘unsaturated’. (FC: 31)

For example, in the sentence “Caesar conquered Gaul” we have the proper name “Caesar” as a saturated expression, which fills the empty place “contained” in the unsaturated expression “conquered Gaul,” thereby forming a complete sentence expressing a complete thought.76 Notoriously, Frege’s distinction is somewhat obscure and not easy to spell out.77 Whatever the details of Frege’s theory, it seems that the distinction between the saturated and the unsaturated represents his solution to “the problem of sentential (propositional) unity.”78 And it’s hard to see more than a mere difference in terminology between Wittgenstein’s name/form analysis of “Socrates is mortal” into “Socrates” and “x is mortal” and Frege’s saturated/unsaturated analysis of “Caesar conquered Gaul” into “Caesar” and “conquered Gaul.” Again, the motivation is clear. This way Wittgenstein thought he could dispense with the troubling, regress-­inducing notion of some sort of logical glue or “cement,” as Russell called it, to ensure the unity of the proposition. For, the unity is now being contributed by one of the constituents itself (the form), which eliminated the need to posit an additional entity to account for it. This had the further advantage of not having to appeal to a theory of types at all because type distinctions are now reflected in the symbolism itself. No “logical manual” is needed. The Internal Reading In the following, I’ll supply and discuss relevant further passages pertaining to Wittgenstein’s objection to Russell’s theory of judgment, which will substantiate the internal reading defended here. As a start, Russell himself expressly describes their disagreement as one about logical form in his introduction to the Tractatus:

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The problem at issue is the problem of the logical form of belief, i.e. what is the schema representing what occurs when a man believes. (TLP: xxi)

Of course, it’s well known that Wittgenstein disapproved of Russell’s introduction, which is why one should in general be cautious in taking it as a reliable guide concerning Tractatus exegesis. But, first, Wittgenstein’s disapproval should also not be taken as carte blanche to dismiss everything Russell says in the introduction, and second, and more importantly, while it’s certainly true that Russell’s outline of the Tractatus is of dubious interpretative value, one would go too far in one’s critique of Russell if one were to challenge even his mere label of their dispute. Surely, the precise nature and intricacies of Russell’s and Wittgenstein’s disagreements were presumably not fully clear to either of them. Given these facts, we shouldn’t rush to the conclusion that Russell’s characterization of their disagreement was wrong at every turn. Besides, there’s further evidence confirming his specification of the problem in terms of logical form. In the Notes on Logic, Wittgenstein writes: There is no thing which is the form of a proposition, and no name which is the name of a form. Accordingly we can also not say that a relation which in certain cases holds between things holds sometimes between forms and thing. This goes against Russell’s theory of judgment. (NL: 99)

In light of the previous discussion of Russell’s final version of his multiple relation theory of judgment in the Theory of Knowledge manuscript, Wittgenstein’s objection is quite plain. In the manuscript, Russell included the logical form of judgments into their analysis. Accordingly, the proposition “A and B are similar” was analyzed U{S, A, B, similarity, R(x, y)}. As we’ve seen, though, the problem of how the constituents yield a unified proposition was exactly the same as with his old analysis J(S, A, B, similarity) because the logical form merely occupied another argument place in the judgment. The question of how the set of objects involved in the proposition were to be combined with the form posed itself once more. The reason why the problem persisted was simply that Russell’s analysis couldn’t help treating logical forms as objects on a par with the very objects of which it was supposed to be the form. This is precisely what

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Wittgenstein objects to by saying that there “is no thing which is the form of the proposition” (and also why there are no names of forms, for names refer to things). The mistake of reification is further emphasized by pointing out that it is incoherent to think of relations (which ought also not be treated, as Russell did, as objects) as holding between objects and forms on pain of initiating a version of the familiar regress. If objects and forms have to be combined in a certain way, then the question as to what is the (second order) form of the combination of the (first order) form and the (first order) objects cannot be avoided, and so on ad  infinitum. And Russell’s latest theory exemplifies exactly this problem by construing propositions as being composed of objects (S, A, B, similarity) and forms (R (x, y)), many declarations and maneuvers on Russell’s part notwithstanding. There are some commentators among internal readers advocating the view that the thrust of Wittgenstein’s objections exhibits a “general dissatisfaction with Russell’s conception of logical form.”79 Others have argued that, while the objections to Russell’s conception of logical form point out real difficulties, these objections only pertain to the account presented in the Theory of Knowledge manuscript and “could only have undermined Russell’s confidence in the theory’s latest version” but pose “no threat to the basic idea that judgment is a multiple relation, and so they cannot account for Russell’s eventual abandonment of that basic idea.”80 Therefore, Wittgenstein’s objections are said to aim primarily at the unity problem and not at the problem of logical forms. However, it seems to me that the unity problem and the problem of logical form are simply two aspects of the very same problem. It’s precisely because Russell didn’t have the theoretical resources to make sense of the logical form of a proposition that made it impossible for him to give a coherent account of the unity of the proposition (and vice versa). It is true that Russell did not explicitly introduce logical forms until the Theory of Knowledge manuscript. But Russell’s numerous changes in the course of developing different versions of his (multiple relation) theory of judgment—tasking first the subordinate relation, then the judging relation, and finally the judging subject with imposing the required directionality and unity—already represented attempts at solving the problem of the logical form of a proposition in general. It’s because these attempts

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were unsuccessful that Russell was forced to introduce logical forms to begin with. This in turn deprived Russell’s theory of the means to impose constraints on possible judgments and left the direction problem unsolved.81 To see this, let’s consider the following passage from the Notes on Logic: When we say A judges that, etc., then we have to mention a whole proposition which A judges. It will not do either to mention only its constituents, or its constituents and form but not in the proper order. This shows that a proposition itself must occur in the statement to the effect that it is judged. For instance, however “not-p” may be explained, the question “What is negated?” must have a meaning. In “A judges (that) p”, p cannot be replaced by a proper name. […] The proposition “A judges (that) p” consists of the proper name A, the proposition with its two poles, and A’s being related to both these poles in a certain way. (NL: 96)

Wittgenstein’s fundamental point here is that the content of a judgment must be a whole proposition, something capable of being true or false. And neither Russell’s old nor his new version of the multiple relation theory satisfies this condition, for the old one mentions “only its constituents” (as in J(S, A, B, similarity)) and the new one merely lists “its constituents and form” (as in U{S, A, B, similarity, R(x, y)}). In both cases what is judged is not a proposition with a particular logical form but a disunified belief-complex composed of objects of various kinds. But a set of entities, no matter how complex and of what kind, cannot amount to something that is either true or false. The contrast between truth and falsity is simply not applicable to (sets of ) objects. This point is vividly expressed by Wittgenstein’s demand that the question “What is negated?” must make sense, a demand we’ve already come across in our discussion of his objections to the theory of types and the contingency requirement. For example, if we (truthfully) negate the judgment that Desdemona loves Cassio then, according to Russell’s multiple relation theory, Desdemona is not related to Cassio as stated and hence there is no such proposition as “Desdemona loves Cassio”, only the disconnected set of objects comprising Desdemona, love, and Cassio (and, depending on the

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theory, the logical form R(x, y)). But it makes no sense to negate (or to assert, for that matter) a set of objects. Only propositions can be asserted and negated.82 This is what Wittgenstein means when he says that in “A judges (that) p”, “p” cannot be substituted by a proper name because names refer to objects, which either fails or succeeds, whereas propositions express something that is capable of being either true or false (what he calls having “two poles”). As Wittgenstein asks rhetorically just a few pages later in the Notes on Logic: “Can we put ‘not’ before a name?” (NL: 104). Of course not, for what would it even mean if we did, such as “¬(Jones)”? However, Russell’s analysis of the negative judgment that A and B are not similar would be structurally identical to “¬(Jones)”, namely “¬(A, B, similarity).” It doesn’t matter here whether we include the judging subject and/or a logical form since we only end up with a collection of (complex) objects either way. It now becomes clear that the passage usually cited in support of the standard reading, namely, that from the judgment aRb the “proposition ‘aRb.∨.¬aRb’ must follow directly without the use of any other premiss” (L: 40), actually speaks against the standard reading and for the internal reading. According to the standard reading, “aRb” doesn’t imply “aRb.∨.¬aRb” because for the latter to follow from the former, further judgments are necessary to ensure the constituents involved in “aRb” are of the right type and of the right adicity. Given this mutual dependency of Russell’s theory of types and his theory of judgment “type theory will break down if the multiple relation theory is adhered to.”83 However, demanding that “aRb.∨.¬aRb” must be an implication of “aRb” is nothing but the contingency requirement, namely, that what is judged must be capable of being true or false (i.e. meaningful), a requirement we’ve already seen to be essential in connection with our discussion of Wittgenstein’s objection to Russell’s theory of types.84 As Peter Hanks has pointed out, Russell’s theory of judgment doesn’t meet this requirement even if the objects involved in the proposition are of the appropriate type and adicity.85 Even if the theory of types were to successfully impose restrictions on the constituents making up the content of the judgment so as to ensure that a and b are in fact individuals and that R is in fact a dyadic relation, we would still obtain no more than a set of entities (a, R, b), which is incapable of expressing something that is true or

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false regardless of types and adicity. And this is exactly what the internal reading claims, namely that the problems Wittgenstein pointed out are internal to Russell’s theory of judgment itself and pertain to his theory of types only indirectly. In conclusion, Russell’s metaphysics made it impossible for him to distinguish between two categorically different functions of language, which is the ultimate shortcoming of his theories: the function of referring to objects (the function of names) and the function of expressing truth-apt statements (the function of propositions).86 By modeling the latter on the former he couldn’t help treating sentences as (complex) names referring to (complex) objects, which is why objects and propositions only differed in complexity, but not in kind. Since logical forms turned out to be objects, too, Russell had no means at his disposal to distinguish a mere aggregate of objects from a meaningful unity expressing something capable of being true or false. This is exactly why the problem of logical form and the unity problem are two aspects of the very same problem, and they jointly pose the dilemma for Russell that, in the end, it’s still possible to judge nonsense, not only because there are no constraints on what can be judged, but also because what is judged is not capable of being true or false even if the desired constraints are met. One might have already suspected, though, that Wittgenstein’s battery of objections applies equally to his own name/form analysis. This kind of analysis may have succeeded in imposing restrictions on what can be judged by giving up a central assumption of Russell’s logical atomism, namely, that the logical universe is made up of isolated atoms that bear no intrinsic relations to one another. But Wittgenstein’s notion of logical form is still rather vague and potentially susceptible to one or the other version of Bradley’s regress. After all, insisting on the fact that logical forms are not things may be an important insight, yet this doesn’t tell us what else (if anything) they might be. To avoid falling prey to his own objections and to prevent the danger of reifying logical forms while at the same time accounting for them, Wittgenstein seemed to have no other alternative than to place logical forms in the objects themselves. This step, I maintain, is eventually taken in the Tractatus.

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Notes 1. Cf. RI (433–434). 2. Cf. RI (434): “For my own part I wish it to be clearly understood that I do not suppose that anything I shall say has the smallest tendency to prove that reality is not spiritual […]. Reality may be spiritual, for all I know; and I devoutly hope it is.” 3. Cf. Durrant (2000: 26). 4. For example, on the one hand, the variable “x” is supposed to range over objects (cf. RI: 439). On the other hand, Moore also seems to say of “x” that it expresses a property, but not a particular one (such as being green) but apparently the general property of being an object (cf. RI: 440). 5. There are various other places where Moore frames idealism in this strong sense: “Accordingly, whatever esse is percipi may mean, it does at least assert that whatever is, is experienced” (RI: 437). 6. He also says he wants to refute not that every object has the property of being experienced simply qua being an object but the claim that “what makes a thing real” is “an inseparable aspect of sentient experience” (RI: 438). 7. Cf. Crossley (1994: 4), Williford (2004: 143), and Preti (2013: 193). 8. Cf. Meillassoux (2006: 18) whose characterization of idealism as “correlationism” is structurally very similar to Moore’s, namely “l’idée suivant laquelle nous n’avons accès qu’à la corrélation de la pensée et de l’être, et jamais à l’un de ces termes pris isolément.” Both Meillassoux and Moore locate the problem in idealism’s primacy of the relation between thought and being over the relata themselves. This leads, so the objection goes, to the impossibility to access being in itself since it is by definition part of or at least constituted by thought. 9. Sellars (2003: 54). 10. It should be noted that Moore’s article “The Nature of Judgment” was published in 1899, four years before “The Refutation of Idealism.” Moore’s motivation for developing a new account of judgment (i.e. his anti-­idealism) is already present in the former article but much more explicit in the latter. For expository purposes, it was therefore sensible to present Moore’s “The Refutation of Idealism” first. 11. Of course, the characterization of Bradley’s position is more complicated. Bradley has frequently been attributed a coherence theory of truth, not only by early commentators but also by more recent ones (cf.

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Blackburn 1984: 235–243). For discussion cf. Candlish (1989: 334), who argues that Bradley actually held a variant of the identity theory of truth, and Baldwin (1991: 40), who agrees with Candlish but thinks it’s possible to reconcile Bradley’s commitment to the identity theory with a coherentist reading. 12. Preti provides a good overview over the central theses of neo-­Hegelianism (cf. Preti 2013: 189). 13. For example, Moore writes that “the distinction between sensation and thought need not detain us here. For, in whatever respects they differ, they have at least this in common, that they are both forms of consciousness or, to use a term that seems to be more in fashion just now, they are both ways of experiencing” (RI: 437). 14. Cf. Hylton (1990: 123). 15. Preti (2013: 190). 16. Kant’s dictum that synthesis is “an act of spontaneity” (CPR: B 130) can be traced back at least to Aristotle’s similar dictum, in his Metaphysics, that truth and falsehood are not to be found in the things themselves but rather in thought (cf. Met.: 1027b25). 17. Cf. Hylton (2005: 13): “The Kantian notion of synthesis can be thought of as providing a solution to a problem which structurally, at least, is very close to the Russellian problem [i.e. the problem of unity]. And given this Kantian move, the way is open, as I have tried to indicate, for an idealist metaphysics. If the necessary conditions of judgment are also necessary conditions of reality, or at least of the knowable world; and if judgment is in some sense our own act; then it is hard not to see the world as at least partially constituted by this act.” 18. Hylton (2005: 158) has already made this point: “The issue is not one of our having correct beliefs about Mont Blanc, but rather one of our having beliefs which are genuinely about that mountain at all.” 19. Cf. Potter (2008: 12). 20. Cf. NT (492). 21. Cf. POM (48). 22. Russell explicitly mentions Kant at one point: “The neglect of such objective complexes is, I think, a tradition due to the doctrine that relations are ‘the work of the mind’. It is plain that a proposition consists of a relation between its terms, and it is thought that relations are the result of the ‘synthetic unity of apperception’; […] But if the Kantian doctrine is pressed, it leads us further still, to the view that all propositions are

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meaningless, not merely false. For it involves the view that, though we have ideas of relations between things, things are incapable of having relations; hence our ideas of relations are ideas of nothing” (NT: 495). 23. Cf. AR (27–28). It should be noted that Russell addresses Bradley’s objection, albeit in a somewhat brief and unsatisfactory manner, by simply claiming that the “endless regress, though undeniable, is logically quite harmless” (POM: 99). 24. To avoid confusion, it should be noted that, first, verbs express “always or almost always relations” (POM: 48), and second, that Russell uses “verb” to refer to both the grammatical verb and its propositional counterpart. 25. Cf. Carey (2007: 13). 26. N. Griffin (1985/1986: 135). 27. Russell’s multiple relation theory of judgment is outlined and developed in “On the Nature of Truth and Falsehood” (1910), “Knowledge by Description and Knowledge by Acquaintance” (1911), The Problems of Philosophy (1912), and the Theory of Knowledge (1913) manuscript, which he abandoned after Wittgenstein’s devastating objections. I’ll discuss this in Sect. 2.3. 28. Cf. POM (94). 29. Cf. N. Griffin (1985/1986: 135). 30. That the problem of false propositions is one of the central motivations for Russell’s new account is widely held in the literature, and I will follow them here. Cf. N. Griffin (1985/1986), Linsky (1993), Weiss (1995), Candlish (1998), Hylton (2005), Cerezo (2014), and Zalabardo (2015). For different views cf. Stevens and Carey, the former arguing that developing the multiple-relation theory of judgment was primarily intended to resolve the “paradoxes of mathematical logic” (Stevens 2004: 31) and the latter that it was intended to resolve the “logical and epistemological paradoxes of propositions” (Carey 2007: 41), in particular the Liar paradox (cf. Carey 2007: 23–26). 31. Cf. NTF (118). 32. Cf. NTF (119): “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.” 33. Cf. Gaskin (2008: ch. 12), for an excellent analysis of this point.

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34. There is broad consensus on this point in the literature. Cf. Cartwright (1987: 84), Weiss (1995: 264), Candlish (1998: 114–115), Dodd (2000: 67), Stevens (2005: 130), and Zalabardo (2015: 18–19). 35. Here it is important to note that the believing or judging relation has to be understood as a single multiple relation uniting all the constituents involved in the judgment and not multiple dual relations, where the judging subject would bear separate dual relations to each of the constituents. So when we consider the judgment “Othello believes that Desdemona loves Cassio,” then believing “is not a relation which Othello has to each of the three terms concerned, but to all of them together: there is only one example of the relation of believing involved, but this one example knits together four terms” (PP: 73). 36. Cf. NTF (122): “Thus in the above illustration, love, which is a relation, is one of the objects of the judgment, and the judgment is true if love relates A and B.” 37. Cf. POM (94), NTF (123), PP (73), and TK (116). 38. Cf. NTF (123–124). 39. This objection has first been formulated by Stout (1910/1911: 202–203) and refined by Geach (1957: 51). Cf. also Stevens (2005: 98–99) on this point. 40. Cf. PP (73): “[T]he relation of judging has what is called a ‘sense’ or ‘direction.’” 41. Hylton (2005: 20). 42. Candlish (1998: 115). 43. Carey (2007: 47). There is broad consensus in the literature that this is Russell’s fundamental difficulty. Cf. Sainsbury (1979: 21–22), Candlish (1998: 111–112), Dodd (2000: 165), Gaskin (2008: 54), Bostock (2012: 213), and Zalabardo (2015: 94). What is controversial, though, is the question whether this difficulty is also (part of ) the objection made by Wittgenstein. Cf. Sect. 2.3. 44. Cf. TK (98). 45. Cf. TK (116). 46. Here it’s worth noting that Russell introduces logical forms primarily to solve the unity problem and not the direction problem. According to Russell, to understand a proposition requires being acquainted with its logical form even in cases where the relation of the constituents of a certain complex is symmetrical (as in “A and B are similar”), that is, in cases where the direction problem doesn’t occur. Cf. Hylton (1990: 345), who has put emphasis on this important point.

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47. Cf. TK (116): “The process of ‘uniting’ which we can effect in thought is the process of bringing them into relation with the general form of dual complexes.” 48. Cf. TK (130), where Russell expressly states that there is no difference between “understanding a pure form, such as ‘something has some relation to something’ and being acquainted with this object.” 49. On this point cf. Stevens (2004: 39). 50. Cf. Black (1964), Sommerville (1981), N. Griffin (1985/1986), Pears (1989), Landini (1991 and 2007), Weiss (1995), Hochberg (2000), and S. Read (2005), to name but the most prominent and influential proponents of this view. 51. Cf. Stevens (2004: 54–55), Gaskin (2008: 326), and Potter (2008: 124–125) for the former and Hanks (2007: 137–141) for the latter account. Pincock (2008: 128) has proposed yet another position in this debate, according to which the dilemma leading to the abandonment of the theory of judgment consists in Russell’s either having to “stick to ultimate constituents and so fail to define correspondence or else introduce additional constituents in the form of false propositions.” I’ll largely disregard this approach in my discussion since, as we’ll see, it will turn out that the correspondence problem and the problem of false propositions are consequences of the unity problem. Cf. Connelly (2011/2012: 166), who also concludes that Pincock’s account fails to establish “that the correspondence problem is in itself in any fundamental respect distinct from the direction/unity problems”. 52. N. Griffin (1985/1986: 144–145). 53. N.  Griffin (1985/1986: 144) takes Wittgenstein’s objection (and the “premiss” Russell is forced to resort to) to be consisting in the “dyadic analogue” of Principia’s *13.3a: “(aRb ∨ ¬aRb) → {(xRy ∨ ¬xRy) ↔ [(x=a & y=b) ∨ (x≠a & y=b) ∨ (x=a & y≠b) ∨ (x≠a & y≠b)]}.” Cf. PM (172). 54. Cf. Landini (2007: 67). 55. N. Griffin (1985/1986: 144), who is referring here to chapter 3 of the introduction of Principia, in particular PM (44–46). Cf. Hochberg (2000: 18) for a similar point. 56. Cf. L (38; January 1913): “[E]very theory of types must be rendered superfluous by a proper theory of symbolism.” Cf. also another letter, in which Wittgenstein exhibits a surprisingly strong reaction to Russell’s proposal that the theory of types be a prescriptive theory: “That’s exactly

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what one can’t say. You cannot prescribe to a symbol what it may be used to express. All that a symbol can express, it may express. This is a short answer but it is true!” (L: 99; 19 August 1919). Cf. also TLP (3.334): “The rules of logical syntax must go without saying, once we know how each individual sign signifies.” I’ll come back to these passages below. 57. Cf. Weiss (1995: 275) and Stevens (2003: 23) for the former and Hanks (2007: 129–131) for the latter line of argument. 58. Cf. TLP (4.1241). There are further discussions of the theory of types, explicitly at TLP (3.331–3.334, 5.252, and 6.123), and implicitly, by questioning the very possibility or intelligibility of rightly or wrongly attributing formal concepts, properties, and relations, at TLP (4.122, 4.124, and 4.126). 59. Cf., for example, NL (94): “Every proposition is essentially true-false.” There are countless variants of this principle in the Tractatus, in particular in the 2s, but most explicit is presumably TLP (2.21): “A picture [i.e. a meaningful proposition] agrees with reality or fails to agree; it is correct or incorrect, true or false.” 60. Barring vagueness in both cases, but as we’ll see presently, this is irrelevant to the point here. Cf. NM (112): “From this it results that ‘true’ and ‘false’ are not accidental properties of a proposition, such that, when it has meaning, we can say it is also true or false: on the contrary, to have meaning means to be true or false.” 61. Cf. Goldfarb (1997: 67): “At issue here is Wittgenstein’s contrastive view of meaning: for a sentence to have content requires a contrast between what would make the proposition true and what would make it false.” Gabriel (2008: 236) formulates the contingency requirement for predicates in general: “Man kann den minimalen Verifikationismus auch von einer Kontrasttheorie der Bedeutung aus begründen, die besagt, daß ein Prädikat X nur Bedeutung haben kann, wenn nicht ausgeschlossen ist, daß es sowohl Dinge geben kann, denen X zukommt, als auch Dinge, denen X nicht zukommt.” Wittgenstein’s contrastive view of meaning plays an important role in his later philosophy as well. Wittgenstein also applies the contingency requirement to allegedly private experiences (such as representations and pains): “And this too is clear: if as a matter of logic you exclude other people’s having something, it loses its sense to say that you have it” (PI: 398). 62. Cf. PR (V, 54): “Language can only say those things that we can also imagine otherwise.”

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63. Cf. PG (376): “Now it is a part of the nature of what we call propositions that they must be capable of being negated.” 64. A.W. Moore (2012: 230). 65. Cf. NM (109–110). Cf. also Stevens (2004: 48). 66. Cf. McManus (2006: 25). 67. This is also borne out by the only passage in which Wittgenstein actually mentions (but, unfortunately, doesn’t specify) his objection that caused Russell to abandon his theory: “I am very sorry to hear that my objection paralyses you. I think it can only be removed by a correct theory of propositions” (L: 42; 22 July 1913). Cf. Maddy (2014: 44–45). 68. Brandom (2015: 35). 69. Cf. Sullivan (2003: 217) on this point. 70. Potter (2008: 83) explains the point nicely: “The words we use can be categorized into grammatical types such as noun, verb, adjective, adverb, etc. But if I understand a word, then it already belongs to a grammatical category; and if I define a word, the definition must be such as to determine its category. I cannot later decree the word’s grammatical type when I already know what it means. It is incoherent to conceive of grammar as something that can be imposed on words when they already have a sense, since grammar is no more than a systematization of how words contribute towards the senses of the sentences that they form.” 71. Cf. RLF (169): “I have said elsewhere that a proposition ‘reaches up to reality’, and by this I meant that the forms of the entities are contained in the form of the proposition which is about these entities.” On this point cf. also Johnston (2017: 157). 72. To be clear, Wittgenstein’s attack here is not directed against Russell’s theory of judgment as presented in the Theory of Knowledge manuscript, which Russell began a few months later. By that time Russell had developed the multiple relation theory of judgment, which treated propositions as incomplete symbols. However, as we’ll see below, this change in Russell’s theoretical edifice caused more problems than it solved, and I argue that the thrust of Wittgenstein’s objections—problems about logical form and unity—was basically the same in the case of the dual relation theory as well as in the case of the various versions of the multiple relation theory. 73. Cf. NL (98), where Wittgenstein explains his motivation for the distinction between names and forms with reference to the unity problem: “Indefinables are of two sorts: names and forms. Propositions cannot

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consist of names alone, they cannot be classes of names.” Cf. also TLP (3.141–3.142), where Wittgenstein makes the very same point: “A proposition is not a blend of words. […] A proposition is articulate. Only facts can express a sense, a set of names cannot.” 74. Cf. McGuinness (2002: 109–110). 75. On this connection cf. Anscombe (1963: 93–94), McCarty (1991: 70), McGuinness (2002: 109), and Potter (2008: 82, 109–110). In a more general vein and with regard to the Tractatus, Dummett (1973: 247) correctly observes that “whether we consider Wittgenstein’s picture theory of language to be a correction of Frege’s theory or an illegitimate development of it, it had its roots in Frege’s notion of an incomplete expression.” 76. Cf. FC (31). 77. Cf. Dummett (1973: ch. 7 and 8). 78. Simons (1981: 91). Cf. also Dummett (1973: 256): “If we try to consider the predicate or the relational expression in an atomic sentence as standing for an object, as do the proper names which occupy its argument-­places, we shall be at loss to account for the unity of the sentence.” For a recent defense of the claim that Frege’s distinction was designed to solve the unity problem cf. Cerezo (2005: 89). 79. Stevens (2004: 55). Cf. also Gaskin (2008: 326) and Potter (2008: 124–125). 80. Hanks (2007: 133–134). 81. Cf. Connelly (2011/2012: 164), who seems to be an exception when he insists, against Hanks, on the inseparability of these issues. However, although Connelly (2011/2012: 158) is right that, according to Wittgenstein, “Russell’s theory cannot account for the fact that aRb.∨.¬aRb follows logically from the judgment that aRb, and so that aRb is significant, without the invocation of an additional premiss, i.e., the significance constraint,” I think that this problem is a symptom and not the cause of Russell’s difficulties. As I’ve argued above, Wittgenstein’s focus is rather on the problem of unity and logical form, the solution of which will give us at once a proper symbolism and render a theory of types superfluous since a proper symbolism incorporates type-theoretical distinctions anyway. Russell’s struggle with imposing the required constraints on judgments without resorting to additional premises is therefore simply a corollary of his inability to deal with the problem of unity and logical form.

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82. In this regard I follow the assessment of Dodd (2000: 67), Hanks (2007: 137–138), and Candlish and Damnjanovic (2012: 67). But although Hanks also identifies Wittgenstein’s objection as being about the unity problem, he seems to think that the problem of logical form is a separate issue specific to Russell’s theory in the Theory of Knowledge manuscript. As I’ve been arguing, Russell was incapable of accounting for the unity of the proposition precisely because of his failure to make sense of logical form. This failure, I think, pertains to all versions of the multiple relation theory of judgment, and not just, as Hanks claims, to the “latest theory” developed in the Theory of Knowledge manuscript. 83. N. Griffin (1985/1986: 144–145). 84. Cf. M. McGinn (2006: 38–41). 85. Cf. Hanks (2007: 138). 86. Cf. Ricketts (1996: 70), Lampert (1998: 272–273), M. McGinn (2006: 50), Potter (2008: 135), Child (2011: 45), and Cerezo (2014: 42) for a similar diagnosis. I’ll elaborate on the crucial distinction between referring and expressing in Sect. 3.3.

References Anscombe, G.E.M. 1963. An Introduction to Wittgenstein’s Tractatus. 2nd ed. New York: Harper & Row. Baldwin, T. 1991. The Identity Theory of Truth. Mind 100 (397): 35–52. Black, M. 1964. A Companion to Wittgenstein’s ‘Tractatus’. Cambridge: Cambridge University Press. Blackburn, S. 1984. Spreading the Word. Groundings in the Philosophy of Language. Oxford: Clarendon Press. Bostock, D. 2012. Russell’s Logical Atomism. New York: Oxford University Press. Brandom, R.B. 2015. From Empiricism to Expressivism. Brandom Reads Sellars. Cambridge, MA: Harvard University Press. Candlish, S. 1989. The Truth about F.H. Bradley. Mind 98 (391): 331–348. ———. 1998. The Unity of the Proposition and Russell’s Theories of Judgement. In Bertrand Russell and the Origins of Analytic Philosophy, ed. R. Monk and A. Palmer, 2nd ed., 103–135. Bristol: Thoemmes Press. Candlish, S., and N. Damnjanovic. 2012. The Tractatus and the Unity of the Proposition. In Wittgenstein’s Early Philosophy, ed. J.L.  Zalabardo, 64–98. Oxford: Oxford University Press.

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Carey, R. 2007. Russell and Wittgenstein on the Nature of Judgement. New York: Continuum. Cartwright, R. 1987. A Neglected Theory of Truth. In Philosophical Essays, ed. R. Cartwright, 71–93. Cambridge, MA: MIT Press. Cerezo, M. 2005. The Possibility of Language. Internal Tensions in Wittgenstein’s Tractatus. Stanford: CSLI Publications. ———. 2014. Russell and Wittgenstein on Proposition, Judgement, and Truth. In Philosophy of Language and Linguistics. The Legacy of Frege, Russell, and Wittgenstein, ed. P. Stalmaszczyk, 29–51. Berlin: De Gruyter. Child, W. 2011. Wittgenstein. London: Routledge. Connelly, J. 2011/2012. On ‘Props’, Wittgenstein’s June 1913 Letter, and Russell’s ‘Paralysis’. Russell: The Journal of Bertrand Russell Studies 31 (2): 141–166. Crossley, D. 1994. Moore’s Refutation of Idealism: The Debate about Sensations. Idealistic Studies 24 (1): 1–20. Dodd, J. 2000. An Identity Theory of Truth. Basingstoke: Palgrave Macmillan. Dummett, M. 1973. Frege. Philosophy of Language. New York: Harper & Row. Durrant, M. 2000. On Moore’s Refutation of Esse is Percipi. Philosophical Investigations 23 (1): 26–47. Gabriel, M. 2008. An den Grenzen der Erkenntnistheorie. Die notwendige Endlichkeit des objektiven Wissens als Lektion des Skeptizismus. Freiburg: Alber. Gaskin, R. 2008. The Unity of the Proposition. Oxford: Oxford University Press. Geach, P.T. 1957. Mental Acts. London: Routledge & Kegan Paul. Goldfarb, W. 1997. Metaphysics and Nonsense: On Cora Diamonds The Realistic Spirit. Journal of Philosophical Research 22: 57–73. Griffin, N. 1985/1986. Wittgenstein’s Criticism of Russell’s Theory of Judgment. Russell: The Journal of Bertrand Russell Studies 5 (2): 132–145. ———. 1991. Russell’s Idealist Apprenticeship. Oxford: Clarendon Press. Hanks, P.W. 2007. How Wittgenstein Defeated Russell’s Multiple Relation Theory of Judgment. Synthese 154 (1): 121–146. Hochberg, H. 2000. Propositions, Truth and Belief: The Wittgenstein-Russell Dispute. Theoria 66 (1): 3–40. Hylton, P. 1990. Russell, Idealism, and the Emergence of Analytic Philosophy. Oxford: Clarendon Press. ———. 2005. Propositions, Functions, and Analysis. Selected Essays on Russell’s Philosophy. Oxford: Clarendon Press. Johnston, C. 2017. The Picture Theory. In A Companion to Wittgenstein, ed. H.-J. Glock and J. Hyman, 141–158. Oxford: Wiley-Blackwell.

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Lampert, T. 1998. Wittgensteins Physikalismus. Die Sinnesdatenanalyse des Tractatus logico-philosophicus in ihrem historischen Kontext. Paderborn: Mentis. Landini, G. 1991. A New Interpretation of Russell’s Multiple-Relation Theory of Judgement. History and Philosophy of Logic 12: 37–69. ———. 2007. Wittgenstein’s Apprenticeship with Russell. Cambridge: Cambridge University Press. Linsky, L. 1993. Why Russell Abandoned Russellian Propositions. In Russell and Analytic Philosophy, ed. A.D. Irvine and A.G. Wedeking, 193–209. Toronto: University of Toronto Press. Maddy, P. 2014. The Logical Must: Wittgenstein on Logic. Oxford: Oxford University Press. McCarty, D.C. 1991. The Philosophy of Logical Wholism. Synthese 87 (1): 51–123. McGinn, M. 2006. Elucidating the Tractatus. Wittgenstein’s Early Philosophy of Logic & Language. Oxford: Clarendon Press. McGuinness, B.F. 2002. Approaches to Wittgenstein. Collected Papers. London: Routledge. McManus, D. 2006. The Enchantment of Words. Wittgenstein’s Tractatus Logico-­ Philosophicus. Oxford: Clarendon Press. Meillassoux, Q. 2006. Après La Finitude. Essai sur la nécessité de la contingence. Paris: Éditions Du Seuil. Moore, A.W. 2012. The Evolution of Modern Metaphysics. Making Sense of Things. Cambridge: Cambridge University Press. Pears, D.F. 1989. Russell’s 1913 Theory of Knowledge Manuscript. In Rereading Russell: Essays on Bertrand Russell’s Metaphysics and Epistemology, ed. C.W.  Savage and C.A.  Anderson, 169–182. Minneapolis: University of Minnesota Press. Pincock, C. 2008. Russell’s Last (and Best) Multiple-Relation Theory of Judgement. Mind 117 (465): 107–139. Potter, M. 2008. Wittgenstein’s Notes on Logic. Oxford: Oxford University Press. Preti, C. 2013. The Origin and Influence of G.E.  Moore’s ‘The Nature of Judgment’. In Judgement and Truth in Early Analytic Philosophy and Phenomenology, ed. M. Textor, 183–205. New York: Palgrave Macmillan. Read, S. 2005. The Unity of the Fact. Philosophy 80 (313): 317–342. Ricketts, T. 1996. Pictures, Logic, and the Limits of Sense in Wittgenstein’s Tractatus. In The Cambridge Companion to Wittgenstein, ed. H.  Sluga and D.G. Stern, 59–99. Cambridge: Cambridge University Press. Sainsbury, M. 1979. Russell. London: Routledge & Kegan Paul.

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Sellars, W. 2003. Empiricism and the Philosophy of Mind. With an Introduction by R. Rorty and a Study Guide by R. Brandom. 4th ed. Cambridge, MA: Harvard University Press. Simons, P. 1981. Unsaturatedness. Grazer Philosophische Studien 14: 73–95. Sommerville, S. 1981. Wittgenstein to Russell (July, 1913): ‘I’m Very Sorry to Hear … My Objection Paralyses You’. In Language, Logic, and Philosophy. Proceedings of the 4th International Wittgenstein Symposium, ed. R. Haller and W. Grassl, 182–188. Vienna: öbv & hpt. Stevens, G. 2003. Re-examining Russell’s Paralysis: Ramified Type-Theory and Wittgenstein’s Objection to Russell’s Theory of Judgment. Russell: The Journal of Bertrand Russell Studies 23 (1): 5–26. ———. 2004. From Russell’s Paradox to the Theory of Judgement: Wittgenstein and Russell on the Unity of the Proposition. Theoria 70 (1): 28–61. ———. 2005. The Russellian Origins of Analytical Philosophy. Bertrand Russell and the Unity of the Proposition. London: Routledge. Stout, G.F. 1910/1911. The Object of Thought and Real Being. Proceedings of the Aristotelian Society 11: 187–205. Sullivan, P.M. 2003. Ineffability and Nonsense. Proceedings of the Aristotelian Society, Suppl. Vol. 77: 195–223. Weiss, B. 1995. On the Demise of Russell’s Multiple Relations Theory of Judgement. Theoria 61 (3): 261–282. Williford, K. 2004. Moore, the Diaphanousness of Consciousness, and Physicalism. Metaphysica 5 (2): 133–155. Zalabardo, J.L. 2015. Representation and Reality in Wittgenstein’s Tractatus. Oxford: Oxford University Press.

3 Wittgenstein’s Early Metametaphysics

In this section I first develop Wittgenstein’s early Metametaphysics and address the realism-idealism problematic revolving around it, after which I examine the debate about the resolute reading (the so-called New Wittgenstein) as a case study in light of the realism-idealism problematic in section 4. In establishing Wittgenstein’s early Metametaphysics I elaborate on Wittgenstein’s conception of logic (Sect. 3.1), clarify some controversial Tractarian concepts and address central exegetical questions and philosophical problems involving them (Sect. 3.2). Finally, I give an account of the famous picture theory at the center of the realism-idealism debate and sketch how this debate may be overcome (Sect. 3.3).

3.1 Logic and the Fabric of the World In a letter to Russell Wittgenstein wrote: “Logic must turn out to be a totally different kind than any other science” (L: 30; 22 June 1912).1 We can capture what this means by contrasting Wittgenstein’s conception of logic with Russell’s because Wittgenstein specifically designed his conception to combat certain presuppositions informing Russell’s view. This © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 M. Bartmann, Wittgenstein’s Metametaphysics and the Realism-Idealism Debate, https://doi.org/10.1007/978-3-030-73335-3_3

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eventually led Wittgenstein to the realization that there cannot be logical objects (or logical facts) purportedly constituting a particular subject matter to be discovered and investigated by the logician. Russell (and also Frege) thought that logic—like any other science—covers a certain objective subject matter. According to this view, logic represents an inquiry into features of reality, although highly general ones. To be more precise, although logic doesn’t concern itself with particular empirical contents, it nevertheless has a distinct subject matter: laws of truth, inference rules, and logical objects in general. Here logical objects comprise, for Russell at least, not only the familiar logical constants such as and, or, not, but also “forms of propositions.”2 Like any other science logic is to identify, categorize, and specify the elementary constituents of its subject matter and the relations between them. So conceived, logic doesn’t differ substantially from zoology, “for logic is concerned with the real world just as truly as zoology, though with its more abstract and general features” (MP: 169). Both disciplines investigate what is, strictly speaking, out there, independent of any cognitive activities. Each discipline aims at a body of facts to be discovered, and there are facts about logical objects in the very same sense in which there are facts about lions. That lions are carnivores is as true a statement and expresses as objective a fact as a statement about logical relations, for example, the dyadic relation that “something and something have a certain relation” (TK: 116). The difference between the propositions of the empirical sciences and the propositions of logic is merely a difference in degree, and not in kind, because logical propositions are simply of higher generality.3 This immediately suggests two connected difficulties, both of which are addressed by Wittgenstein’s new conception of logic. Or rather, Wittgenstein’s new conception—which reflects a method distinctive of much of his writings—restructures the philosophical territory in such a way as to prevent the difficulties from arising in the first place. The first difficulty is that logical laws, despite being “maximally general truths,”4 turn out to be contingent.5 There seems to be no inherent contradiction in imagining a world in which different logical laws govern our way of thinking just as there could be a world in which lions are not carnivores. The source of this problem is that propositions expressing logical laws are understood as true descriptions, as expressing facts about the world. But every proposition, whatever its degree of generality, is capable of being

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true or false, and that makes their truth-value a matter of contingency. As it’s perfectly conceivable that they could be false, they are contingent. In Russell’s metaphysics, the relation between the logical realm and the empirical realm remained either unexplained or contingent.6 The second difficulty—closely related to the first—is that understanding logical laws and rules of inference as something that can be true or false leads to what Henry Sheffer has called the “logocentric predicament”: “In order to account for logic, we must presuppose and employ logic.”7 This means that “[i]nquiry into any subject matter whatsoever draws implicitly on these principles [i.e. on the principles of valid reasoning] and must conform to these standards on pain of incoherence.”8 If logic is necessarily presupposed by and serves as a foundation for any rational investigation whatsoever, then it’s all the more important for logic to rest on a solid foundation itself. Hence if the application of logical laws is the conditio sine qua non for rational discourse by providing it with the justificatory basis for the claims made within that discourse, then the application of logical laws itself stands in need of justification and calls for a foundation. Since logical laws and rules of inference are viewed as truth-­ apt statements, they have to be justified like any other scientific claim. And how is this possible without initiating an infinite regress? Now, Wittgenstein’s “fundamental idea,” namely “that the ‘logical constants’ are not representatives; that there can be no representatives of the logic of facts” (TLP: 4.0312) addresses both the problem of contingency and the logocentric predicament by radically altering the understanding of the nature of logic. The Problem of Contingency Perhaps the quickest way to see the import of Wittgenstein’s insight is to realize that “the propositions of logic are not descriptions.”9 As we’ve seen, what is essential for a proposition to be meaningful is that what it states to be the case could be otherwise, that is, a meaningful proposition draws a contrast between truth and falsity (the contingency requirement).10 This basic feature of meaningful propositions (descriptions) makes them inhabitants of logical space, that is, the realm of all possible states of affairs, obtaining and non-obtaining; logical space, we might also say, is the realm of the contingent.11 We’ve also seen that propositions attempting to say something about logical properties (“M is an object” and “The symbol expressed by ‘M’

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belongs to the type singular term”) are superfluous or nonsensical because they either fail to meet the contingency requirement or try incoherently to attribute formal concepts, properties, or relations. These propositions seemed to state facts about the deep logical structure of our language, but this turned out to be an illusion. For, expressing facts requires that it could be otherwise, that the states of affairs claimed to be the case could also not be (or could not have been) the case. Since “propositions” concerning logical properties fail to meet the contingency requirement, Wittgenstein concluded that logical properties are not really properties at all, or at least that they are not anything like ordinary properties. The diagnosis was that Russell’s mistake consisted in wrongly assimilating theoretical metavocabulary to (ordinary) descriptive vocabulary (the descriptive fallacy). Against this backdrop, Russell’s conception of logic seems to contain exactly the same mistake. If logical laws are taken to be expressed by highly general propositions, and theoretical metavocabulary in which logical laws are framed is conceived of as descriptive, then this inevitably turns what the metavocabulary expresses into a matter of facts. Logical laws, according to this understanding, are nothing but highly general facts expressed by highly general propositions. And that makes them a matter of contingency. To prevent logic from becoming a matter of contingency, Wittgenstein had to prevent logic from becoming a matter of facts. Since genuine propositions are informative by expressing what could be otherwise (by satisfying the contingency requirement), and since the propositions of logic fail to do exactly that, they don’t express truth-apt thoughts: Therefore the propositions of logic say nothing. (TLP: 6.11)

This also meant to deny that the essence of logic consists in generality: The mark of the logical proposition is not general validity. To be general means no more than to be accidentally valid for all things. (TLP: 6.1231)

Here it’s very important not to confuse universality with generality or, to be more precise, not to think of universality in terms of generality. Wittgenstein is not denying the universal character of logic in the sense of its being constitutive of the world.12 What he is denying is that the

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universal character of logic is to be identified with maximal generality. Curiously, the only way to preserve the universality of logic was for Wittgenstein to conceive of it as empty. The universality of logic can be maintained only if, in a sense, it disappears. Not only can logic not have a distinct subject matter; it cannot have a subject matter at all, for in both cases logic would be a science of (a particular body of ) facts and therefore contingent, which would compromise logic’s universality. This is the entire point of understanding the propositions of logic as tautologies because it’s the only way to avoid the descriptive fallacy. Let me briefly elaborate. Tautologies and contradictions, as is well known, are senseless (“sinnlos”) and not nonsensical (“unsinnig”) because they have no truth conditions.13 They are either always true or always false, respectively. But they are not nonsensical such as “M is an object” or “1 is a number.” Although tautologies and contradictions also fail to meet the contingency requirement, they don’t represent the misguided attempt to attribute formal concepts, properties, or relations. These propositions, recall, were nonsensical due to the underlying confusion of treating logical properties as ordinary properties, which turned out to be incoherent. But tautologies (contradictions) are not like that because they can be legitimately called true (false). Hence they are propositions in the full sense of the term. However, what is absolutely crucial is that tautologies, while being propositions, are not meaningful propositions (i.e. descriptions) for the simple reason that they fail to meet the contingency requirement.14 They don’t express a state of affairs that could either obtain or not, hence not something that could be either true or false. It would be a mistake to think of tautologies as descriptions that always happen to be true. Although tautologies are always true, they don’t exhibit the contrast between truth and falsity, which is exactly why they fail to meet the contingency requirement. It’s not as if a tautology expresses something that could be true or false but has, as chance would have it, always the truth-­ value “true.” Since they don’t express something capable of being true or false, they don’t express a possible state of affairs that could either obtain or not.15 And that is why they are not descriptions.16 In sum, whereas Russell recognized only a difference in degree between logical and non-logical propositions—a degree of generality—Wittgenstein saw a categorical difference between them.17 While both tautologies

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(contradictions) and descriptions do have truth-values, they acquire these in radically different ways. Descriptions get their truth-­value by satisfying the contingency requirement. This makes the truth-­value of descriptions a factual matter; whether a description is true or false depends on how things stand, which states of affairs actually obtain. By contrast, tautologies (contradictions) have nothing to do with factual matters. They get their truthvalue simply by virtue of the symbolism in which they are expressed, which is why their truth-value can be read straight off them. No investigation into how things stand in the world is required nor even intelligible.18 This is also why tautologies (contradictions) are not informative, “say nothing,” namely because by failing to satisfy the contingency requirement they don’t tell us how things are as opposed to how things could be. Smith would be a very poor friend if Jones told her she suspected her husband of cheating and Smith responded: “Well, I don’t know if your husband is cheating on you, but I do know that he’s either cheating on you or not.” In short, we must not identify a proposition’s having a truth-value with its being meaningful. Explaining Wittgenstein’s conception of logic as empty to avoid the descriptive fallacy now lets us also see clearly another aspect of the thrust of his fundamental thought “that the ‘logical constants’ are not representatives; that there can be no representatives of the logic of facts” (TLP: 4.0312), which corresponds to Wittgenstein’s main objection to Russell’s theories discussed in Sect. 2. There we concluded that Russell’s metaphysics couldn’t help reifying logical items, which created a host of difficulties with the problem of logical form and unity at their center. In light of Wittgenstein’s tireless onslaught on Russell’s conception of logical matters, it seems only natural that his new conception had to implement the insight that an object-based understanding of logic is a dead-end. And Wittgenstein’s fundamental thought reflects precisely this insight. Any conception of logic according to which there should or must be a distinct subject matter consisting of a body of logical objects and facts to be identified, categorized, and specified by the logician will inevitably suffer from all the inconsistent consequences of reification we’ve been discussing so far. To avoid the reification of logic prompted by the descriptive fallacy, Wittgenstein consequently had to deny that logical propositions make up a substantive descriptive vocabulary conveying maximally general truths about their subject matter. When Wittgenstein

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says “that there can be no representatives of the logic of facts,” he should not be taken as merely saying that we are to stop talking about logical objects and facts while acknowledging their existence in silence, but rather as saying that there are no such objects and facts to begin with.19 This is the entire point of conceiving of logic as empty. If Wittgenstein were to acknowledge the existence of logical objects and facts, then Wittgenstein’s persistent objections to Russell explored in Sect. 2 would become utterly unintelligible. It should therefore come as no surprise that a major theme running through the pre-Tractatus writings, namely, that the theory of types is superfluous at best and nonsensical at worst due to a misguided view on logic, resurfaces prominently in the Tractatus: The propositions of logic describe the scaffolding of the world, or rather they embody it. They are not ‘about’ anything. (TLP: 6.124; transl. am.) ‘Laws of inference’, which are supposed to justify inferences, as in the works of Frege and Russell, have no sense, and would be superfluous. (TLP: 5.132)

And this brings us to the second big issue Wittgenstein addresses with his fundamental thought. The Logocentric Predicament If logic is empty, isn’t this tantamount to eliminating logic altogether? Doesn’t it mean that there are no logical laws, no rules of inference? The logocentric predicament raises the problem that all rational discourse within which we make and justify claims— the “game of giving and asking for reasons,”20 as Brandom famously put it—possibly rests on shaky foundations, since the inference rules used to support claims of rational discourse seem themselves to stand in need of justification. As Lewis Carroll has shown, including a rule of inference into the premises of an argument in order to justify the conclusion drawn on its basis faces the question of justification itself, and an infinite regress quickly threatens.21 But conceiving of logic as empty seems to make matters even worse, since now logic not only is a fragile basis for reasoning but has vanished entirely. It seems as if logical reasoning itself has turned out to be an illusion, concealing the fact that all we actually do is at best projecting logical structures onto random statements. But no such radical conclusion needs to be drawn. On the contrary, Wittgenstein says that

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logic “pervades the world” (TLP: 5.61) and embodies “the scaffolding of the world” (TLP: 6.124).22 What does this mean? Wittgenstein’s basic point made in connection with the contingency problem applies to the logocentric predicament as well. If we treat logical laws and inference rules as truth-apt statements, that is, maximally general truths, then it’s impossible to find an answer to the logocentric predicament. Therefore, Wittgenstein abandons the entire conception of logical laws and inference rules as truths, together with the idea that the propositions of logic constitute a separate body of facts in their own right.23 In order for them to be constitutive of the inferences we make, logical laws and inference rules must be inherent in propositions and facts and therefore part of the fabric of the world itself. The idea that logical form is implicit in language (names and propositions) and the world (objects and facts) is what may be called Wittgenstein’s logical immanentism. This idea will become clearer in the following subsections, but for now I want to give a rough sketch of it in order to ward off possible misunderstandings. Let’s consider the following passage: If p follows from q, I can make an inference from q to p, deduce p from q. The nature of the inference can be gathered only from the two propositions. They themselves are the only possible justification of the inference. (TLP: 5.132)

The “nature” of inference doesn’t consist in a set of (maximally general) propositions that have to be applied to another set of propositions in order for them to be justified.24 Logical connections between propositions consist in the relations “in which the forms of the propositions stand to one another” (TLP: 5.131; emphasis added), which means they are intrinsic to them.25 Either it lies in the nature of a certain set of propositions that one follows from the other, in which case our deducing one from the other is already justified, or it doesn’t, in which case nothing can serve as a justification of their being related as stated. The confusion here is, again, to think of an inference rule as a general statement about the connection of other statements and then be puzzled about how to justify it, when in fact an inference rule is no more than an expression of formal connections.26 If a proposition can be deduced from another

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proposition, then the inferential connection holding between them is part of the structure of these propositions, and not an external bond created by inference rules.27 In other words, logic is about the possibility of what is and what is not the case—facticity—and not about what actually is the case—facts.28 Since rules of inference are not truth-apt statements, they are not something for which the question of justification can arise: If the truth of one proposition follows from the truth of others, this finds expression in relations in which the forms of the propositions stand to one another: nor is it necessary for us to set up these relations between them, by combining them with one another in a single proposition; on the contrary, the relations are internal, and their existence is an immediate result of the existence of the propositions. (TLP: 5.131)

Understanding rules of inference as facts leads directly into the logocentric predicament. For, in this case the question arises how these maximally general truths can themselves be justified (since they are facts, this implies at least the possibility that they couldn’t have been facts; hence they are contingently true). But as soon as this question arises, the justification for p and q being inferentially related breaks down, too. This can easily be seen from the infinite regress that ensues if we take rules of inference to be facts. If inferences between a certain set of propositions are justified only in virtue of another set of propositions (the rules of inference), then it’s obvious that the question of justification arises for the latter set of propositions as well. And so on. The upshot of the passage quoted above, then, is that a formula like (p ∧ (p → q) → q) is not descriptive and thus not a statement at all.29 Statements, judgments, and descriptions are essentially true or false, which is why they can be informative. They tell us how things stand while leaving open the possibility that things could have been otherwise. Statements always imply a contrast between certain possibilities among which they pick out one and present it as being the case. But the formula (p ∧ (p → q) → q) doesn’t pick out a possibility in contrast to other possibilities. It represents part of the structure of possible connections between p and q and doesn’t make a statement to the effect that a possible state of affairs among others is presented as obtaining. Calling (p ∧ (p →

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q) → q) a proposition of logic is, as we’ve seen, technically correct, but it should be kept in mind that they are not meaningful propositions because they fail to satisfy the contingency requirement: Every proposition of logic is a modus ponens represented in signs. (And one cannot express the modus ponens by means of a proposition.) (TLP: 6.1264)

Modus ponens cannot be expressed by a meaningful proposition because meaningful propositions represent possible states of affairs, something that can be the case or not.30 But (p ∧ (p → q) → q) does express a senseless (not nonsensical) tautology, which is necessarily true but not descriptive.31 And that is why the “propositions” of logic “say nothing” (TLP: 6.11) because they are not informative in the sense specified above.32 This brief outline should suffice to ward off from the outset a possible misunderstanding concerning Wittgenstein’s conception of logic and to capture a central aspect of it. For Wittgenstein, logic pervades the world without consisting in an identifiable set of objects existing in addition to what there is. Facts and propositions already have a logical structure, which is exhibited by how objects and names are connected to one another, respectively. “[L]ogic is at one and the same time built into the nature of facts and propositions”33 themselves, as Daniel Hutto nicely put it, and not the result of some sort of logical cement binding together otherwise selfstanding entities. This idea will be developed in the following subsection.

3.2 Objects, States of Affairs, and Facts Many commentators agree that there are substantive differences between Wittgenstein’s and Russell’s conception of logic, metaphysics, and semantics. However, the way in which the nature of these differences is to be understood is much less clear. I’ve already given an outline of Wittgenstein’s and Russell’s differences concerning the conception of logic in the preceding subsection, and I’ll investigate their disagreement concerning semantics in the next one. As regards metaphysics, the focus of this subsection, the major tendency is to conceive of Wittgenstein’s approach as a modification of Russell’s account while being by and large the same overall

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project. More often than not, the change in Wittgenstein’s theory is said to consist either in a replacement of one kind of entity (objects) for another kind of entity (facts),34 or in an expansion of the world, now including not only objects but also, over and above them, facts.35 These conceptions, I claim, are mainly due to confusions concerning two of the most important notions in the Tractatus whose precise nature is still a matter of great controversy: facts and objects. In what follows I’ll address these confusions in turn and develop my take on these notions afterward. The first confusion is conceiving of facts as (complex) objects.36 A little reflection casts doubt on this conception. For, if we think that “a fact is made up of atomic facts and an atomic fact is made up of objects or things or entities, […] then it appears that the world is, at bottom, composed of things not facts after all.”37 Hence Wittgenstein’s position would coincide with Russell’s metaphysics, a sort of “basic realism” with objects as “the ultimate constituents of the world.”38 But, as we’ve seen in Sect. 2, Russell’s objectbased metaphysics was precisely what Wittgenstein persistently inveighed against. It’s implausible that Wittgenstein would have adopted a theory he knew to be bound up with so many intractable philosophical problems. There would be no point in emphasizing that the world is the totality of facts if this were merely a differently worded expression of Russell’s metaphysics. We can avoid this confusion and bring out the radical change Wittgenstein made by distinguishing sharply, as Wittgenstein does, between states of affairs and facts: What is the case—a fact—is the obtaining [Bestehen] of a state of affairs [Sachverhalt]. A state of affairs is a connection [Verbindung] of objects (things). (TLP: 2–2.01; transl. am.)

There are at least two reasons why some commentators have either not recognized or expressly denied the categorical distinction between states of affairs and facts.39 The first is presumably to be seen in the infelicitous translation of “Sachverhalt” with “atomic fact” in Ogden’s version. The Pears-McGuinness translation is a little better in that it uses the neutral term “state of affairs,” but it’s still a misleading translation to say that a

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fact is the “existence” of a state of affairs because it suggests that facts are the sort of thing that can either exist or not.40 Against this it needs to be emphasized that a fact is the obtaining of a state of affairs, that is, that a certain connection holds between a given set of objects. The reason why this distinction is absolutely crucial is that, for Wittgenstein, a fact is not a kind of entity at all but a structure: The main stress does not lie on the point that the proposition isn’t a disordered higgledy[-]piggledy sort of combination of words, but merely on the point that it is no mixture at all but a structure. (LO: 24)41

As a consequence, both the Ogden translation and the Pears-McGuinness translation suggest that states of affairs and facts merely differ in degree or complexity, not in kind. The second reason encouraging such a view is a letter from Wittgenstein to Russell in which he answers Russell’s question concerning the difference between states of affairs and facts: Sachverhalt is, what corresponds to an Elementarsatz if it is true. Tatsache is what corresponds to the logical product of elementary propositions when this product is true. (L: 98; 19 August 1919)

Although Wittgenstein here explains states of affairs as well as facts with reference to true elementary propositions, this doesn’t cancel out the categorical distinction between them. There is still an important difference because the correspondence between states of affairs and facts to elementary propositions is categorically different in each case.42 A state of affairs is a connection of things, that this connection holds between the things is a fact. A fact is what is the case if an elementary proposition is true, a state of affairs is what exists if an elementary proposition is true. Facts concern the holding of a connection between objects, that is, the obtaining or non-obtaining of states of affairs. Facts are not objects (of whatever kind and complexity); hence they are not themselves composed of objects.43 We must distinguish between the connected things and the fact that they are so connected. The categorical distinction between states of affairs

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and facts can be brought out by the following two absurdities that would follow if the distinction were obliterated. First, the walls of Smith’s room may be white, but if the fact that these walls are white were composed of walls and whiteness, then this fact would be white itself, which is absurd.44 Second, conceiving of facts as being composed of things leads to the absurd result that there would be (almost) no facts about the past. That Caesar crossed the Rubicon is a fact (if true) although Caesar doesn’t exist anymore. How can this be if Caesar is said to be a constituent of the fact that he crossed the Rubicon?45 As Colin Johnston has pointed out, it’s essential to realize that Wittgenstein “wrote that the world is the totality of facts, and not of things.”46 The world is not layered, where objects reside at the ground level and, additionally, also happen to figure in facts at an upper level. On the contrary, facts are already the very bedrock of the world.47 Not paying attention to the full weight of the opening passage of the Tractatus is tantamount to failing to appreciate that Wittgenstein doesn’t simply amend the Russellian picture but radically breaks with it. It’s not as if Wittgenstein merely shifted the focus of metaphysics from one kind of entity to another, from objects to facts. Rather, he abandons altogether the entire tradition of conceiving of the essence of the world in terms of entities of whatever kind. The essence of the world consists neither in there being a set of discrete objects nor in there being a gigantic aggregate of connected objects. What Wittgenstein is interested in, above all, is not so much what entities there are in the world but what the structure of the connection between entities is, regardless of which kind.48 The reason for this is that an understanding of the world articulated by listing things lacks what Matthew Ostrow has aptly called “expressive power”.49 A list of things, even of things that were determinately identified and fully specified according to a Russellian-­ style analysis, would tell us nothing about how they are related to one another, and hence tells us nothing about how the world is.50 That the essence of the world should not be conceived of in terms of the existence of certain kinds of things becomes clear in the following passage of the Notebooks, which resurfaces in the Tractatus: My whole task consists in explaining the nature of the proposition. That is to say, in giving the nature of all facts, whose picture the proposition is. In

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giving the nature of all being. (And here Being does not mean existing—in that case it would be nonsensical.) (NB: 39; last emphasis added)51

The addendum that “Being does not mean existing” marks the break with Russell’s philosophical project, namely to identify and specify the ontological inventory of the world. Russell thought the world is a complex object to be decomposed by logical analysis in order to arrive at its ultimate constituents. When Wittgenstein opens the Tractatus by saying the world is everything that is the case he is rejecting exactly this kind of approach.52 The second confusion is closely related to the first one and concerns the nature and status of Tractarian objects. This issue has been generating huge amounts of commentaries because Wittgenstein says very little about them, yet they obviously play a crucial role in the Tractatus. That is why many commentators saw the need to fill in the blanks Wittgenstein left to his readers. There are two main conceptions of Tractarian objects in the literature, which I’ll call the substantial conception and the formal conception. The substantial conception holds that Tractarian objects are to be identified with a specific, determinate ontological type of object, and the task is then to find out what exact type Wittgenstein had in mind given his vague and shifting use of that term.53 Countless candidates have been proposed, but most of them fall into three categories: phenomenal entities (sense-data),54 physical entities (material points),55 and (bare or ordinary) particulars.56 Dissatisfaction with the difficulties and lack of explanatory power of the substantial conception paved the way for the formal conception of Tractarian objects. This conception was developed by Hidé Ishiguro, according to whom the objects of the Tractatus “are not particular entities in any normal sense, but entities invoked to fit into a semantic theory.”57 Therefore the term “object” is to be understood as a purely formal concept given that to “ask what kind of familiar entities correspond to the objects of the Tractatus seems to lead us nowhere.”58 Subsequently, commentators have taken Wittgenstein as advocating or at least as tacitly presupposing what has recently been dubbed the “categorical indeterminacy thesis”59 with respect to the status of objects. Roughly, the core claim

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of the formal conception is to say that the very nature of Tractarian objects is not to have a specific nature at all, and to identify them with a determinate type of entity must therefore be misleading. Although still a minority view, there is a growing number of commentators arguing in its favor.60 Nevertheless, as Christopher Campbell has pointed out, many of those subscribing to such a view content themselves with refuting the traditional approach of identifying objects with a certain ontological type but “have done less in service of explaining why the Tractatus takes this stance.”61 Later in this subsection, I will also defend a variant of the formal conception and give arguments why Wittgenstein’s “failure” to provide examples of simple objects has systematic reasons, reasons that follow from his conception of logical form as a response to the problem of unity. But first I want to focus preliminarily on a confusion I take to be at the root of the debate over simple objects. The Simplicity of Tractarian Objects The temptation to search for an answer to the question what simple objects really are is not entirely unwarranted. Especially in the Notebooks Wittgenstein toys with giving substance to the notion of a simple object and considers various candidates. The most notorious one is mentioned in the following passage: “As examples of the simple I always think of points of the visual field” (NB: 45). Remarks like that have encouraged some to identify Tractarian objects with phenomenal entities and, consequently, led them to believe “that the world of the Tractatus is a phenomenal world.”62 But the passages in the Notebooks have to be interpreted with great care, for they have to be examined within the context in which they are made and cannot simply be used to make a claim about the Tractatus, a work in its own right. The Notebooks are experimental in that they expound ideas and test them with respect to their implications, consequences, or even coherence.63 They show Wittgenstein struggling with these ideas, not stating them as definitive results. This becomes clear at a later point in the Notebooks where he concedes: “Our difficulty was that we were always talking about simple objects, however, we failed to come up with a single one” (NB: 68; transl. am.). And we can even find a passage in the Notebooks in which Wittgenstein challenges the very notion of a simple object:

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It always appears to us as if the following question made sense: “Are there simple objects?” And yet this question must be nonsensical! (NB: 45; transl. am.)

Why should Wittgenstein stick to a substantial conception of simple objects given the profound qualms he had about them?64 The reason why the nature of simple objects is still hotly disputed not only stems from the fact that commentators have picked out various of Wittgenstein’s oscillating views in the Notebooks and attributed them to the Tractatus, but from the urge to fill in the blanks left by Wittgenstein. It’s also Wittgenstein’s terse discussion of simplicity and complexity in the Tractatus itself that gives rise to confusion. In my view, the confusion consists, roughly speaking, in mistakenly treating simplicity and complexity as ordinary properties. To put it in more general terms, it consists in conflating the logical with the ontological sense of the conceptual pair simplicity/complexity. Wittgenstein doesn’t expressly distinguish between these two senses, presumably partly because he took this distinction to be self-evident, partly because his lack of interest in empirical matters led him to neglect it. Whatever his reasons, it seems clear to me that both senses have to be kept cleanly apart and are implied by the respective definitions he gives of objects and facts, names and propositions. Logical simplicity and complexity depend on whether an expression has the function of referring to an object (i.e. names) or of expressing a truth-apt statement (i.e. propositions). The expression “ambulo” (“I walk”) makes for a good example because it’s not a simple sign although it may look like one. It doesn’t entail logical simplicity.65 While “ambulo” may be regarded as lexically or typographically simple, what it expresses is nevertheless logically complex for it says something that can be true or false. Suppose someone asked me “Who was the teacher of Alexander the Great?” In answering “Aristotle,” did I simply refer to Aristotle using the name “Aristotle”? No. If “Aristotle” here were just a name I would not have said something that is either true or false (which I obviously have). By contrast, reference—the function of names—can only succeed or fail and doesn’t express a truth-apt statement. So in this example “Aristotle” is not only a name because it also expresses a proposition (which is why

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grammarians would call “Aristotle” in this case more accurately a one-­ word sentence).66 Unfortunately, Wittgenstein was less explicit with respect to the simplicity of objects. His talk of objects being “the substance of the world” (TLP: 2.021) and similar remarks have invited commentators to favor the ontological sense of the conceptual pair simplicity/complexity.67 Here’s an example from James Griffin: Can I not give this book a name, in spite of its having parts? Do the parts matter, since what I want to name, though composed of them, is nevertheless still one single thing? From this we can see that a complex is something like a book. And simples are things like the basic elements of the book.68

But these questions are illusory. In answering the question whether a book is simple or complex we need to specify first the sense in which the distinction is to be understood. Conceived of in ontological terms the question is merely an empirical matter. Furthermore, it’s not quite clear what Griffin has in mind when he speaks of the “basic elements” of a book. Does he mean pages and covers, words and sentences, atoms and quarks? Whatever the material composition of a book turns out to be, it should be clear that this question falls within the jurisdiction of science and has nothing to do with logical concerns. For the question whether a book is logically simple or complex makes no sense. The reason for this is that simplicity and complexity mark the logical roles of objects and facts, namely being referred to by a name and being expressed by a meaningful proposition, respectively.69 And that is why logical simplicity/complexity is neutral with respect to its linguistic realization. A name is simple because it has the function of referring to an object, and a proposition is complex because it has the function of expressing a possible state of affairs, which can either obtain or not. Questions such as “Can a name express something that is true or false?” and “Can a proposition refer to an object?” are nonsensical simply because if a linguistic expression refers to an object, then it’s a name and if it expresses truth-apt statement, then it expresses a proposition.70 What turns an expression into a name or proposition depends on what logical role it plays, and to perform this function it’s not important how names

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and propositions are linguistically realized (as the examples of “ambulo” and “Aristotle” show).71 Simplicity and complexity, therefore, are primarily logical distinctions that are independent of ontological composition.72 Neither are there logically complex objects and names nor are there logically simple facts and propositions. The distinction between an object and a fact (a name and a proposition) is the distinction between the simple and the complex regardless of their respective ontological composition.73 The logical roles objects and facts play are individuated by the mutually dependent relation of being referred to by a name and being expressed by a proposition. On this logical interdependency ontological concerns have no bearing.74 The Nominalist and Platonist Interpretation of Tractarian Objects Having cleared up the confusions underlying the standard conceptions of objects, states of affairs, and facts, we are now equipped with the conceptual resources to spell out Wittgenstein’s account. As is well known, there is a long-standing debate over the categorical nature of Tractarian objects and what binds them together as to form a state of affairs. Given the background of our discussions so far one might already be suspicious of the framework of such a debate. It’ll come, then, as no surprise that Wittgenstein’s conception of objects undermines the very idea that there must be something holding objects together in a particular state of affairs. Since Wittgenstein’s conception, as we’ll see, rejects the terms underlying the dispute in the literature, I’ll give a rather brief outline of it and develop Wittgenstein’s account more fully afterward. The positions of most commentators fall into two categories, which Peter Carruthers has called the narrow interpretation (a.k.a. the nominalist interpretation) and the wide interpretation (a.k.a. the Platonist interpretation).75 The narrow interpretation states that Tractarian names are restricted to proper names, that is, Tractarian names are said to refer exclusively to one single type of objects, namely individuals (particulars).76 By contrast, according to the wide interpretation, Tractarian names also subsume predicates and relational expressions in addition to proper names. On this reading, Tractarian names refer not only to individuals but also to properties and relations (universals), which they consider Tractarian objects as well.77

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More specifically, what is at issue between both parties is the question whether the relation R connecting the two objects a and b in a particular state of affairs aRb is to be counted as an object or not, that is, the question whether “R” is a Tractarian name or not. Whereas the narrow reading claims that in aRb there are only two objects a and b joined by the relation R into a possible state of affairs, the wide reading contends that, since “R” is to be regarded as a Tractarian name, R is an object as well. Hence aRb contains the three objects a, b, and R, which are said to be joined into a possible state of affairs. I’ll dismiss the wide interpretation rather swiftly. There is no need to review the arguments that have been mounted against the wide interpretation, since the entire discussion in Sect. 2 gives us ample grounds to reject, as Wittgenstein does, the idea that relations are objects connecting other objects. But what about the narrow interpretation? This seems to be a more promising candidate because narrow interpreters acknowledge the fact that treating relations as objects triggers one or the other version of Bradley’s regress.78 Furthermore, the narrow interpretation seems justified in its misgivings that “it is almost inconceivable that anyone who thought as highly of Frege as Wittgenstein did should simply have slurred over the distinction between concept and object.”79 However, although these are reasonable points, the narrow interpretation is still not quite the right one. The main flaw of the narrow interpretation is a wrong presupposition also shared by the wide interpretation, namely the idea that there is something—a relation, whether conceived of as an object (wide interpretation) or as some other kind of entity (narrow interpretation)—connecting a given set of objects in order for them to form a state of affairs.80 As we’ve seen, Wittgenstein rejected Russell’s account of the problem of unity because the constituents of a proposition always occurred as terms, which were unable to provide the required structure and unity and therefore failed to put any constraints on how objects could combine with one another. But how, then, are objects supposed to combine into a state of affairs if the only constituents making up a state of affairs are objects? What glues them together? And in light of everything we’ve discussed so far the answer will be the only possible one: nothing does. No matter what we

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posit as glue—copulae, relations, concepts, or logical forms—will inevitably lead to its reification and generate versions of Bradley’s regress. Wittgenstein’s conclusion is therefore that what binds objects together can be nothing other than the objects themselves. In order to argue for this claim, let’s return to the opening sections of the Tractatus. A state of affairs [Sachverhalt] is a connection [Verbindung] of objects (things). (TLP: 2.01) In the atomic fact [Sachverhalt] objects hang one in another, like the links of a chain. (TLP: 2.03; Ogden translation)

The chain metaphor should make it absolutely clear that the crucial feature of states of affairs is not only that they consist in a connection of objects but also that they are made up of objects alone. There is no trace of Wittgenstein’s old name/form analysis either in these or in any other passage of the Tractatus, and nowhere does he suggest further constituents of states of affairs besides objects. In a state of affairs objects “hang one in another” (“Im Sachverhalt hängen die Gegenstände ineinander”), which obviously means that they are not connected by anything else.81 A chain consists of nothing but its links and, analogously, a state of affairs consists of nothing but objects. And there is decisive evidence for this provided by Wittgenstein himself in his comments on Ogden’s translation, where he explains the chain metaphor: Here instead of “hang one on another” [Ogden’s initial translation] it should be “hang one in another” like the links of the chain do! The meaning is that there isn’t anything third that connects the links but that the links themselves make connexion with one another. So if “in” in this place is English please put it there. If one would hang on the other they might also be glued together. (LO: 23)

This passage makes it clear that it was important for Wittgenstein not to create the false impression that there might be something besides or between the links holding them together. For, if the links are said to “hang one in another” (“ineinanderhängen”) it’s clear that the links are connected without additional means of whatever kind. A state of affairs consists of objects—and objects alone.82

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Given this background, it’s now easy to see that the opening passages of the Tractatus neither present a mere replica of the Russellian picture nor a (more or less substantive) modification of it. Instead, they epitomize the exact opposite of it83: It is essential to things that they should be possible constituents of state of affairs. (TLP: 2.011) In logic nothing is accidental: if a thing can occur in a state of affairs, the possibility of the state of affairs must be written into the thing itself [muß die Möglichkeit des Sachverhaltes im Ding bereits präjudiziert sein]. (TLP: 2.012)

It’s constitutive of an object to possibly occur in states of affairs and not a logical accident, so to speak. Objects don’t form a separate ontological category where it’s indifferent whether the objects occur in states of affairs or not. Rather, they are intrinsically related to the states of affairs in which they can possibly figure. The “nature” of an object is thus determined by what may be called its occurrence space.84 The occurrence space of an object is constituted by all internal/formal properties a particular object has and represents the totality of possible connections an object can have to other objects to form a state of affairs.85 This means the occurrence space of an object determines all states of affairs in which it can possibly figure: Things are independent in so far as they can occur in all possible situations, but this form of independence is a form of connexion with states of affairs, a form of dependence. (It is impossible for words to appear in two different rôles: by themselves, and in propositions.) (TLP: 2.0122) If I know an object I also know all its possible occurrences in states of affairs. (Every one of these possibilities must be part of the nature of the object.) A new possibility cannot be discovered later. (TLP: 2.0123)

In these and the other opening passages Wittgenstein offers what may be called—in stark contrast to Russell’s atomism—ontological contextualism. Ontological contextualism is the view that the possibility of an object to occur in a state of affairs (to combine with other objects) is essential to

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it—that this possibility is, as Pears-McGuinness have aptly translated it, “written into the thing itself ”: Just as we are quite unable to imagine spatial objects outside space or temporal objects outside time, so too there is no object that we can imagine excluded from the possibility of combining with others. If I can imagine objects combined in states of affairs, I cannot imagine them excluded from the possibility of such combinations. (TLP: 2.0121)

Thus, an object is dependent in one respect, and independent in another. An object is independent insofar as it can occur in any state of affairs determined by its occurrence space, and it’s dependent insofar as it’s impossible for an object to occur outside its occurrence space. This characterization shows the mutual dependency of objects and states of affairs, which Wittgenstein intended to prevent us to think that objects and states of affairs could possibly be separated from each other. Objects are not selfstanding, self-sufficient entities; they don’t have an independent life of their own in addition to their being possibly combined with other objects. To conceive of an object as essentially being part of a possible state of affairs is to incorporate the Fregean insight into the need for unsaturatedness and to bring it to its logical conclusion.86 Accordingly, giving up the notion of objects as isolated items entails that all objects involved in a particular state of affairs are incomplete. As Johnston crisply put it, an object is “essentially copulative, dependent, unsaturated.”87 To combine into states of affairs objects require neither a copula nor a logical form nor any other kind of mediating link (whether this link is thought of as object-like or not) because the objects themselves make the connection. The occurrence space of an object, that is, the totality of possible combinations with other objects is its logical form, and by combining with other objects they yield what Wittgenstein calls the “structure” of a particular state of affairs: The possibility of its occurring in a state of affairs is the form of an object. (TLP: 2.0141) The determinate way in which objects are connected in a state of affairs is the structure of the state of affairs. Form is the possibility of structure. (TLP: 2.032–2.033)

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The structure of a state of affairs is always a concrete, determinate combination of objects, whereas the form of an object is its occurrence space, which only determines its possible occurrences in states of affairs.88 For example, the states of affairs aRb and cRd have different structures because they involve different objects. However, their form is the same (xRy) because the occurrence space of all four objects includes the same possibility, that is, the possibility of being R-related to another object. That is why the logical form of an object (its occurrence space) is the possibility of structure (a determinate combination of objects, i.e. a particular state of affairs) because its logical form determines all possible states of affairs in which an object can occur. In our example the object a includes within its occurrence space the possibility of being R-related to another object, which is why it’s possible for a to occur in the concrete state of affairs aRb.89 This possibility (of being R-related to another object) is, as I’ve stressed, written into the thing itself and not an accidental feature of it. As Wittgenstein put it: If I know an object I also know all its possible occurrences in states of affairs. (Every one of these possibilities must be part of the nature of the object.) A new possibility cannot be discovered later. (TLP: 2.0123)

How, then, are we to think, more specifically, of Tractarian objects? What exactly does it mean to say that objects are incomplete and don’t need relations or anything else to combine with one another? Let’s contrast Wittgenstein’s conception of objects with Russell’s. According to Russell, objects are the fundamental building blocks of the world, which can also agglomerate into more complex objects. There are, in principle, no constraints on how they can be put together; anything goes. Wittgenstein, on the other hand, reverses this picture by building the combinatorial possibilities into the objects themselves. A Tractarian object is therefore not a self-sufficient building block but rather a piece of a puzzle that is always already connected to the picture of which it can be a part. If we consider a piece of a puzzle in isolation it tells us nothing because it could be anything. It’s not until we assemble it with other pieces that it is revealed what it is.

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To elaborate this analogy a little, assume we are given a box containing a puzzle consisting of 1000 pieces. The whole puzzle depicts, as the box cover shows, a simple landscape with a small town in the foreground, and the sea and the sky in the background. Assume further the unassembled pieces lie in front of us and we are trying to combine them. Now, considering the pieces in isolation doesn’t yet tell us what they are. A blue piece could turn out to be part of the sky; or part of the sea; or part of the public swimming pool located at the town center. The point of this analogy is fourfold. First, that it’s only in connection with other pieces that it is revealed what they are. Second, the picture showing the landscape after we have assembled all the pieces is nothing over and above the assembled pieces. Third, there is nothing connecting the puzzle pieces other than the pieces themselves. And, fourth, the incompleteness of a puzzle piece consists in nothing other than its intrinsic connection to (its possible combinations with) other pieces. The same goes, roughly, for Tractarian objects. We cannot say anything about an object in isolation, not because it has an impenetrable, inexpressible metaphysical essence escaping the reach of thought and language, but because there are no objects in isolation.90 And if objects combine into a determinate state of affairs, then this state of affairs is nothing over and above the constituents involved. The temptation we need to resist in theorizing about objects is to ask for an object in isolation, as if we were to find out its true nature once we disregard the contingent circumstances, which are supposedly “merely” external. Wittgenstein’s point is that this is utterly wrong-headed. If we strip the occurrence space off an object, if we abstract away from the possible states of affairs in which it can occur in order to find out what it “really” is, then we have lost precisely that which made the object what it is in the first place. Someone contemplating an object in the attempt to gain insights into its true nature resembled someone picking up a piece of the puzzle and desperately wondering what “it” might be. To drive the point home, we could also compare Tractarian objects to chemical elements, in particular what is called a “radical.”91 Although an atom can be found in isolation or be isolated by some sort of (mechanical and/or chemical) procedure, the totality of possible compounds it can form with other atoms is determined by the nature of (i.e. the physical

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properties of ) the atom itself. Neither can an atom form any kind of compound nor is the totality of possible compounds it can form external to an atom (unlike Russell’s logical atoms, where anything goes). It would be absurd if chemists had to prescribe all the possible compounds each and every atom can enter into (some sort of misguided prescriptive theory of types for chemical elements) to ensure that there are no “wrong” compounds. Strictly speaking, then, it’s misleading to say objects have a determinate, essential nature because their essence is to be combinable with other objects. So conceived, their essence is their form, the totality of all possible states of affairs in which they can occur, not the totality of states of affairs in which they actually occur. The occurrence space of objects is not an accidental, additional ingredient to them but constitutive of them.92 This, then, is the variant of the formal conception of Tractarian objects I propose, which should make it clear that any version of the substantial conception, that is, any conception identifying Tractarian objects with a determinate ontological category, is misguided. This is also borne out by our discussion at the beginning of this subsection, where I attempted to show that Wittgenstein’s conception of the world as everything that is the case primarily targets the misbegotten project of trying to establish an ontological inventory of the world. There simply is “no a priori order of things” (TLP: 5.634).

3.3 Names, Propositions, and the Picture Theory Wittgenstein’s critique of Frege’s and Russell’s understanding of names and propositions is contained, in essence, in the following passage: Frege said “propositions are names”; Russell said “propositions correspond to complexes”. Both are false; and especially false is the statement “propositions are names of complexes.” (NL: 97)

For Frege a proposition is merely a “complex proper name”93 referring to either of two objects, to wit the True and the False. Russell’s semantic

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theory differed from Frege’s in many respects, but he shared with him both modeling propositions on names and, consequently, the idea that the target of propositions is an object of some kind.94 Russell, as we’ve seen, changed his mind a few times only regarding its composition and structure. We’ve also seen how this conception was fraught with problems and made for an unpleasantly powerful engine for generating new problems fueled by Russell’s object-based metaphysics. In the passage quoted above Wittgenstein’s diagnosis of the mistake underlying Russell’s and Frege’s respective theories is that both conflated two fundamentally different logical roles linguistic expressions can perform, namely referring and expressing.95 The trouble with understanding propositions as names referring to objects is that this conception makes it unintelligible how truth-apt statements are possible. Since judgments are modeled on the paradigm of names, the only relation they can have to what they are a name of is that of reference. But reference can only either succeed or fail; it cannot be true or false. As long as the logico-semantic role of propositions is assimilated to reference by understanding them in terms of names, it will be impossible to explain the characteristic function of propositions to express something capable of being true or false.96 Wittgenstein concluded from the problems besetting Russell’s theory that propositions are not objects, hence propositions don’t refer at all but express possible states of affairs, which can either obtain or not. Being true and being false are not “two properties among other properties” (TLP: 6.111) some sort of entities (propositions) turn out to have. Rather, truth-or-falsity is built into the very structure of propositions themselves. Otherwise “it would seem to be a remarkable fact that every proposition possessed one of these properties” (ibid.). In his 1931 manuscript “Complex and Fact” Wittgenstein is most explicit about these matters: Complex is not like fact. For I can, e.g., say of a complex that it moves from one place to another, but not of a fact. But that this complex is now situated here is a fact. (PG: 199) To say that a red circle is composed of redness and circularity, or is a complex with these component parts, is a misuse of these words, and is misleading. (Frege knew this and told me.) It is equally misleading to say the fact that

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this circle is red (that I am tired) is a complex with circularity and redness (I and tiredness) as constituents. (PG: 200) A chain, too, is composed of its links, not of these and their spatial relations. The fact that these links are so concatenated isn’t ‘composed’ of anything at all. The root of this muddle is the confusing use of the word ‘object’. (PG: 201)97

The distinction between complex and fact can be quickly stated. However, it has far-reaching consequences and serves to bring out a fundamental difference between Russell and Wittgenstein: “A complex is an arrangement of things; that they are arranged in this way is a fact.”98 In other words, a complex is what exists when a judgment is true, whereas a fact is what is the case when a judgment is true. This means the categorical distinction between complexes and facts is the same as between states of affairs and facts.99 Identifying complexes with facts involves a twofold mistake.100 The first aspect of it is to think facts are (complex) objects. As we’ve seen in the preceding subsection, this idea is problematic. That the circle has a determinate diameter, that it has a certain circumference, that it’s red, and so on are all facts about the red circle. However, are we therefore to conclude that the red circle is “composed” of all these things? Is it possible for a circle not to have a diameter (as one of its “constituents”)? If a circle is composed of circularity, a diameter, and a circumference, why shouldn’t there be circles lacking one or more of these constituents? These are foolish questions generated by conceiving of facts as (complex) objects. The second aspect of the mistake, closely related to the first, is to model propositions on names and hence to think propositions refer to (complex) objects.101 As we’ve also seen, objects cannot explain how propositions can be true or false simply because objects, of whatever kind and complexity, cannot be true or false. For example, Socrates considered as an object on his own can neither verify nor falsify statements about him. Socrates might be ontologically complex, but he is logically simple in that it makes no sense to predicate truth or falsity of him. Therefore, the propositions expressed by “Socrates was a philosopher,” “Socrates was Greek,” and “Socrates was snub-nosed” are true not because they refer to the complex object Socrates but because they express facts about Socrates,

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namely the fact that Socrates was a philosopher, the fact that he was Greek, and the fact that he was snub-nosed. Apart from the question how an entity can make a proposition true, it’s also hard to explain how these logically distinct propositions about Socrates should all have the very same truth-maker, which would be the case if all these propositions merely referred to Socrates.102 In sum, Wittgenstein’s overall point is that propositions express states of affairs and don’t refer to complexes.103 For Wittgenstein, all talk about objects turns out to be talk about states of affairs in disguise, that is talk about entities is really talk about connections, the obtaining and non-­ obtaining of particular arrangements of objects.104 Of course, the propositions “Socrates was a philosopher,” “Socrates was Greek,” and so on pertain to Socrates. But this must not make us forget that what these propositions express are facts about Socrates and don’t refer to Socrates. We describe Socrates by expressing states of affairs involving Socrates. Socrates dissolves, so to speak, into all the states of affairs in which he can possibly occur without being an ineffable metaphysical object behind the descriptions we can give of him. Armed with these clarifications and distinctions we can now turn to Wittgenstein’s account of names and propositions. As I’ve emphasized from the outset, in order to solve the problem of unity it must be addressed at both levels, the semantic level (propositions) and the metaphysical level (states of affairs and facts). Since both levels are structurally identical by consisting of facts it will come as no surprise that the solution turns out to be the same in both cases. The parallelism between the opening passages of the Tractatus and the picture theory spelled out in later sections is undisputed among most commentators. However, how to understand it is a matter of great controversy. Now, we’ve seen that Wittgenstein, in his pre-Tractatus writings, was acutely aware of the problem of logical form and unity, which is why he devised a Fregean style name/form analysis to solve these problems: Indefinables are of two sorts: names and forms. Propositions cannot consist of names alone, they cannot be classes of names. […] Only facts can express a sense, a class of names cannot. (NL: 98 and 105)

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The last pronouncement resurfaces almost verbatim in the Tractatus,105 and the problem of logical form and unity still keeps him preoccupied: An elementary proposition consists of names. It is a nexus, a concatenation, of names. It is obvious that the analysis of propositions must bring us to elementary propositions which consist of names in immediate combination. This raises the question how such combination into propositions comes about. (TLP: 4.22–4.221)

At first blush, this passage may strike one as a flat-out contradiction or at least a step backward on Wittgenstein’s part. He claims that a proposition is a concatenation of names—names in immediate combination—and there is no mention either here or in any other passage of further constituents (forms, concepts, etc.) being involved in the composition and structure of propositions. This suggests that propositions consist of names alone, in the same way that states of affairs consist of objects alone. How, then, do names form a proposition since a proposition now seems to be precisely what Wittgenstein denies (in the Notes on Logic as well as in the Tractatus), that is, a class or set of names? What binds names together so as to yield a proposition? In my view, the solution is identical to the problem of what binds objects together so as to yield a state of affairs: nothing does. Wittgenstein even uses the same chain metaphor we encountered in connection with states of affairs when he writes that a proposition is a “concatenation” (“Verkettung”) of names. This suggests that not only Tractarian objects but also Tractarian names are essentially incomplete.106 What this means becomes clear in the following passages, in which Wittgenstein elaborates on his notion of expressions as propositional variables: I call any part of a proposition that characterizes its sense an expression (or a symbol). […] An expression presupposes the forms of all the propositions in which it can occur. It is the common mark of a class of propositions. (TLP: 3.31–3.311) Thus an expression is presented by means of a variable whose values are the propositions that contain the expression. […] I call such a variable a ‘propositional variable’. An expression has meaning only in a proposition. All variables can be construed as propositional variables. (Even variable names.) (TLP: 3.313–3.314)

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The idea that expressions are incomplete is spelled out in terms of the notion of a propositional variable. A propositional variable is a variable whose values are the totality of all propositions in which an expression can meaningfully occur. Borrowing the notation from Elizabeth Anscombe, we can turn any expression, say “a”, into a propositional variable by replacing every other expression of the respective propositions in which “a” can meaningfully occur with “ξ,” yielding the formula “(ξ) a.”107 The formula “(ξ)a” has as its values all propositions in which “a” can meaningfully occur, that is, the formula collects all meaningful propositions containing the expression “a,” which is what Wittgenstein means by saying that an expression is the “common mark of a class of propositions.”108 For example, the formula “(ξ)identical” collects all those propositions in which “identical” can occur meaningfully. This rules out, for example, “Socrates is identical,” not because the expressions “Socrates,” “is,” and “identical” have meaning in isolation and are combined in an illegitimate way so as to express a “wrong” sense, but because it doesn’t possess the possibility of occurring as an adjective and, consequently, the possibility of expressing a property. The phrase “Socrates is identical” is nonsensical due to our having failed to “make an arbitrary determination, and not because the symbol, in itself, would be illegitimate” (TLP: 5.473).109 It’s hard not to see in Wittgenstein’s notion of a propositional variable the parallelism between the dialectics of objects and states of affairs on the one hand and the dialectics of names and propositions on the other.110 In the same way that objects are intrinsically bound up with the states of affairs in which they can possibly occur, so expressions are intrinsically bound up with the propositions in which they can possibly occur. The totality of possible occurrences within a certain class of propositions is part of the “nature” of an expression in the same way in which the totality of possible occurrences within a certain class of states of affairs is part of the “nature” of an object. Of course, it’s always possible to consider expressions apart from their figuring in particular propositions, but it’s impossible for expressions not to figure in propositions at all. This is borne out by the following crucial passage at the beginning of the Tractatus, in which Wittgenstein, seemingly dealing with ontological matters only, at once formulates what I’ve called ontological contextualism

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and foreshadows in terse form what may be called, accordingly, semantic contextualism111: The thing is independent, in so far as it can occur in all possible circumstances, but this form of independence is a form of connexion with states of affairs, a form of dependence. (It is impossible for words to appear in two different rôles: by themselves, and in propositions.) (TLP: 2.0122)

Wittgenstein’s ontological contextualism was the view that the possibility of an object to occur in a state of affairs is essential to it. Analogously, Wittgenstein’s semantic contextualism is the view that the possibility of an expression to occur in propositions is essential to it as well. And this in turn entails that expressions have an occurrence space, too, determining the totality of all possible combinations with other expressions. The incompleteness of expressions is thus no more mysterious than the incompleteness of objects. The incompleteness of an expression simply means that the possibility of occurring in particular propositions is not external to but constitutive of it, and hence that it’s impossible for an expression to have meaning in isolation. The point of Wittgenstein’s semantic contextualism is twofold. (1) It serves to bring out the essence of an expression as incomplete, that is, that an expression is also like a piece of a puzzle that is always already connected to the totality of propositions in which it can meaningfully occur, in the same way that an object is always already connected to the totality of states of affairs in which it can possibly occur. In Sect. 3.2, I said objects are states of affairs-radicals and, similarly, we can conceive of expressions as proposition-radicals. That the occurrence space of an expression is intrinsic to it simply means that the logical form of an expression is not something that needs to be imposed on it from the outside, as Russell’s theory of types would have it. Rather, the logical form of an expression is exhibited by the totality of all propositions in which it can meaningfully occur—the occurrence space of an expression is its logical form. (2) And almost more importantly, understanding expressions as incomplete symbols enables Wittgenstein to deal at once with the problem of logical form and the problem of unity. As we’ve seen in connection

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with ontological contextualism, Wittgenstein gave up the Fregean distinction between the saturated and the unsaturated with his account of incomplete objects in order to explain how objects form states of affairs without the problematic appeal to further ingredients. Now it’s easy to see how Wittgenstein solves the problem of logical form and the unity of the proposition in exactly the same way, namely by giving up the bipartite classification of expressions into saturated and unsaturated ones.112 According to Wittgenstein, all expressions are unsaturated or incomplete.113 And this includes, crucially, Tractarian names as well.114 By making names the only category of constituents composing a proposition Wittgenstein is, of course, denying neither that there are different kinds of linguistic categories nor that there are different types of symbols. His entire diagnosis of why “fundamental confusions” (TLP: 3.324) arise in philosophy is that they rest on confusing different kinds of symbols due to the misleading use of signs (using the same sign for different symbols, etc.).115 Subsuming all different kinds of expressions under the logical category name doesn’t cancel out their respective differences. It’s simply to emphasize the common nature of expressions in general, namely that all expressions (of whatever kind) are incomplete in that the possibility of occurring in propositions is essential to them. The incompleteness of an expression is constitutive of it regardless of whether we are dealing with nouns, predicates, prepositions, and what have you. And this is precisely why Wittgenstein gave up his old name/form analysis.116 As we’ve seen, Wittgenstein is not interested in what kind of objects there actually are (i.e. what kind of occurrence spaces objects actually have), and by the very same token, he’s not interested in what kind of expressions or symbols there are (i.e. what kind of occurrence spaces expressions actually have). Trying to identify, categorize, and specify all different kinds of expressions, symbols, and logical forms language does, should, or must have—establishing an a priori logico-semantic vocabulary—would be making the very same mistake underlying the project of establishing an ontological inventory: Logical forms are without number. (TLP: 4.128) It would be completely arbitrary to give any specific form. It is supposed to be possible to answer a priori the question whether I can get into a position

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in which I need the sign for a 27-termed relation in order to signify something. But is it really legitimate even to ask such a question? (TLP: 5.554–5.5542) If I cannot say a priori what elementary propositions there are, then the attempt to do so must lead to obvious nonsense. (TLP: 5.5571)

Since there is no a priori order of things, there is no telling in advance what kind of logical forms objects turn out to have and hence no telling in advance what kind of objects there will actually be.117 And since it’s a priori undecidable what kinds of objects there are, it would be arbitrary to establish a logico-semantic vocabulary listing a definitive set of forms names can have, simply because the question what logical forms names will exhibit is a contingent (empirical) matter.118 As so often, Ramsey has hit the nail on the head: Nevertheless, just as in the study of chess nothing is gained by discussing the atoms of which the chessmen are composed, so in the study of logic nothing is gained by entering into the ultimate analysis of names and the objects they signify.119

As I’ve said, what Wittgenstein is primarily concerned with is the “nature of the proposition” and the “nature of all facts.” This is the question of how a proposition says what it does and what makes it expressive, that is what I’ve called the problem of aboutness elaborated on in Sect. 2. And this brings us to the so-called picture theory of meaning. The Picture Theory First of all, whatever the details of the picture theory, Wittgenstein’s motivation for developing it and the point of comparing propositions to pictures are quite plain because the picture theory seeks to eliminate one of the fundamental problems pervading Russell’s theory of judgment. As we’ve seen, within Russell’s object-based metaphysics it was impossible to separate the unity of a proposition from its truth-value, since the subordinate relation of a proposition carried the burden of accounting for both. A proposition’s being unified entailed its being true (and vice versa), but in the case of false propositions the terms composing it were not related as stated. That is why false propositions turned out not to be propositions at all but merely a set of unrelated

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entities. Time and again, Russell foundered on the challenge to make sense of what is not the case. Now, Wittgenstein’s picture theory and his conception of propositions are designed to accomplish precisely that. The reason for likening propositions to pictures is that pictures can present a situation as being thus and so independently of what is actually the case, and we can understand what they present without knowing whether the situation thus presented obtains or not. In other words, the basic feature of the picture theory is simply to separate the unity of a proposition from its truth-value. A meaningful proposition always draws a contrast between truth and falsity regardless of whether it’s true or false, that is, a meaningful proposition always meets the contingency requirement. A meaningful proposition always presents a possible situation, such that it leaves open the possibility of the situation’s being (or having been) otherwise. At any rate, this much is largely uncontroversial among commentators because Wittgenstein makes this point in many passages,120 although the crucial background of the problem of logical form and unity has mostly gone unnoticed. However, it’s highly controversial how the picture theory actually works. Well, how does it work? Wittgenstein writes: The fact that the elements of a picture are related to one another in a determinate way represents that things are related to one another in the same way. (TLP: 2.15)

This is a distinct echo of Wittgenstein’s understanding of the essence of symbolizing in the Notes on Logic: In aRb it is not the complex that symbolizes but the fact that the symbol a stands in a certain relation to the symbol b. Thus facts are symbolized by facts, or more correctly: that a certain thing is the case in the symbol says that a certain thing is the case in the world. (NL: 105; emphasis added)

Aboutness doesn’t consist in things standing for other things, but in facts being symbolized by other facts, for otherwise truth-apt statements would be inexplicable.121 As we’ve seen at the beginning of this subsection, Wittgenstein’s critique of Frege and Russell was that both assimilated

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propositions to names and hence conflated the two different functions of referring and expressing. Wittgenstein’s insight is that what symbolizes in “aRb” (or what makes “aRb” say what it does) is neither the complex sign itself nor that the elements stand for something (“a” and “b” for objects, and “R” for a relation) but the fact that “a” and “b” are related in certain way: Instead of, ‘The complex sign “aRb” says that a stands to b in the relation R’, we ought to put, ‘That “a” stands to “b” in a certain relation says that aRb.’ (TLP: 3.1432)122

The motive of Wittgenstein’s point is that even if the constituents of “aRb” stood for something with the appropriate adicity (“a” and “b” for objects and “R” for a dyadic relation), then “aRb”, understood as a complex sign, would at best refer to something (a complex object) but not express something capable of being true or false. What makes propositions expressive doesn’t consist in names standing for objects, but that names stand in certain relations to one another says that things stand in a certain relation to one another, that is, that a possible state of affairs either obtains or not: The reason why, e.g., it seems as if “Plato Socrates” might have a meaning, while “Abracadabra Socrates” will never be suspected to have one, is because we know that “Plato” has one, and do not observe that in order that the whole phrase should have one, what is necessary is not that “Plato” should have one, but that the fact that “Plato” is to the left of a name should. (NM: 115)123

This example illustrates well the difference between referring and expressing. Names may stand for objects (“Plato” refers to Plato, “Socrates” to Socrates, etc.), but for “Plato Socrates” to be meaningful it’s not sufficient for the names to have referents. To be expressive, the fact that “Plato” stands to the left of “Socrates” must have a meaning (i.e. the possibility of a name’s occurring meaningfully next to another name must be included within its occurrence space). We could easily make the fact that two names stand next to each other say something by stipulating that the fact

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that a name stands to the left of another name expresses the fact that the person referred to by the first (left) name was the mentor of the person referred to by the second (right) name. Accordingly, propositions of the form “(name of x) (name of y)” would then express truth-apt statements. For example, “Plato Aristotle,” “Aristotle Alexander the Great,” and “Russell Wittgenstein” would all be true, but “Kant Kierkegaard” would be false. Let’s take a closer look at the picture theory. There are two central concepts playing the explanatory role in accounting for the aboutness problem: the concept of pictorial (logical) form and the concept of pictorial relationship.124 Pictorial form is “the possibility that things are related to one another in the same way as the elements of the picture” (TLP: 2.151), whereas pictorial relationship “consists in the correlation of the picture’s elements with the things” (TLP: 2.1514).125 Unfortunately, the tendency of some commentators has been to overemphasize or even to focus solely on the pictorial relationship—the idea that one kind of item (names) goes proxy for or are correlated with another kind of item (objects)—in explaining in virtue of what a picture is about that which it depicts. This has led to the question whether names or objects are the dominant partners in the pictorial relationship. The different responses to this question has produced one of the most durable debates in the literature, namely whether the Tractatus is to be viewed as taking up a realist or idealist position.126 But pictorial relationship is just one aspect of Wittgenstein’s theory; it will turn out not only that the notion of pictorial form (and, more generally, logical form) is at least as important as that of pictorial relationship but also that both notions are mutually dependent and cannot possibly be separated from each other. Now, there is a striking parallelism between the dialectics of objects and states of affairs in the opening sections of the Tractatus and the passages in which Wittgenstein specifies the relation between the elements of a picture and the picture itself. Recall how Wittgenstein characterizes the relation between objects and states of affairs: The possibility of its occurring in states of affairs is the form of an object. (TLP: 2.0141)

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In a state of affairs objects stand in a determinate relation to one another. The determinate way in which the objects are connected in a state of affairs is the structure of the state of affairs. Form is the possibility of structure. (TLP: 2.031–2.033)

And here’s the corresponding passage: What constitutes a picture is that its elements are related to one another in a determinate way. […] Let us call this connexion of its elements the structure of the picture, and let us call the possibility of this structure the pictorial form of the picture. (TLP: 2.14–2.15)

In both passages the distinction between complex and fact is crucial. To avoid confusion, I’ll call the arrangement of elements of a picture—as opposed to the fact that they are so arranged—a pictorial structure. The parallelism is thus as follows: in both states of affairs and pictorial structures objects and elements, respectively, are related to one another in a determinate way. And in both states of affairs and pictorial structures the possibility of structure, that is, the possibility of objects and elements being related in a determinate way, is called their form (what I’ve fleshed out in terms of the notion of an occurrence space). Since the notion of form is being applied to the elements of the pictorial structure as well, we can also say that the elements have occurrence spaces determining the totality of possible arrangements with other elements. Finally, since the obtaining of a particular state of affairs—that the objects composing it are related to one another in a certain way—was a fact, Wittgenstein states, as we would expect, that a picture—that the elements composing the pictorial structure are related to one another in a certain way—is a fact as well.127 At this point we have a perfect symmetry of the pictorial relationship. This symmetry simply follows from the definition of pictorial relationship as consisting “in the correlation of the picture’s elements with the things” (TLP: 2.1514). Wittgenstein also expresses this by stating that both sides of the pictorial relationship must possess the same logical multiplicity.128 For example, in order for the Paris courtroom model to adequately represent the car accident it must involve as many toy cars and

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dolls as cars and people involved in the accident. The assumption of symmetry of the pictorial relationship seems natural since it’s hardly imaginable how a model of three toy cars and five dolls could represent a situation of the actual accident where seven cars and eleven people were involved. In sum, we have on both sides of the pictorial relationship structured sets of constituents—objects composing states of affairs and elements composing pictorial structures. The question now becomes by virtue of what a picture is about what it depicts, or more generally, the question what turns a picture into a picture in the first place. Wittgenstein’s answer to this question is his notion of pictorial form129: If a fact is to be a picture, it must have something in common with what it depicts. There must be something identical in a picture and what it depicts, to enable the one to be a picture of the other at all. What a picture must have in common with reality, in order to be able to depict it—correctly or incorrectly—in the way it does, is its pictorial form. (TLP: 2.16–2.17)130

And the notion of pictorial form, in turn, is spelled out in terms of the notion of possibility: Pictorial form is the possibility that things are related to one another in the same way as the elements of the picture. (TLP: 2.151)

To be a picture and to present a particular situation as something capable of either obtaining or not, the elements of the picture and the objects of the depicted must share their possibilities of being related to one another. This requirement is not to be confused with the requirement that the elements of a picture actually have to be related in the same way as the objects in a state of affairs for the picture to be true. A false picture (a picture representing a non-obtaining situation) is still a picture, although an incorrect one because its elements are not related to one another as the objects are. However, the picture could have been true if the objects had been related to one another in the same way as the elements were, which is why false pictures are still pictures. What is essential to account for the truth-or-falsity of a picture is not that the elements of a picture are actually related to one another in the same way as the objects of a state of

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affairs, but the minimal and more fundamental requirement that the elements of a picture and the objects of a state of affairs share the same possibilities of being related to one another, respectively.131 Expressed in the terminology developed here, this simply means that for the picture and the depicted to share their pictorial form the items to be correlated with one another—elements and objects—must share their respective occurrence spaces. And if the picture and the depicted share their pictorial form, then there is the possibility of truth-or-falsity because the arrangement of elements could have been otherwise. In other words, identity of pictorial form is tantamount to a picture’s satisfying the contingency requirement. Take, for example, the Paris courtroom model. Allowing for scale and tolerating loss of (irrelevant) detail, two things are required for the aboutness of the model, that is, for the model to be a (correct or incorrect) model of the actual car accident. First, pictorial relationship, which consists in there being the same logical multiplicity on both sides of the relationship so that the model contains as many elements as the situation it presents. Second, pictorial form, which consists in the possibility that the elements of the model (toy cars, dolls, etc.) can be arranged in the same way as the objects (cars, people, trees, houses, etc.) present at or involved in the accident. What this latter requirement amounts to in our example is the minimal condition that the elements of the model be movable in the same way as the objects of the accident, which means elements and objects must share their possibilities of spatial arrangement, meaning their spatial occurrence spaces, so to speak, must be identical. As Michael Morris has nicely put it: “Movability is just possibility made vivid.”132 In sum, if the pictorial form of the model and what it’s a model of are identical, then they share their respective possibilities of arrangement (and vice versa). And if the elements of the model can be arranged in the same way as the objects in the real situation, then the elements can also be arranged otherwise. For example, toy car A can be put in front of toy car B, representing that car A in the real situation was (at a certain time) in front of car B. But we can also put toy car B in front of toy car A, which represents a possible situation regardless of whether car B was actually in front of car A. It follows that the identity of pictorial form constitutes the possibility of being otherwise, which enables the model to satisfy

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the contingency requirement. Identity of pictorial form guarantees the aboutness—the possible truth-or-falsity—of the model because it’s by virtue of the possibility of being otherwise that what the model presents as obtaining leaves open the possibility that the situation thus presented may not obtain. Accordingly, we can characterize Wittgenstein’s solution to the problem as rooted in his conception of “aboutness-by-form”, in contrast to Russell’s and Frege’s approaches addressed in Sect. 2, which appealed to “aboutness-by-containment” and “aboutness-by-­ representation”, respectively. Now, what makes the model (the pictorial structure) present a particular situation as obtaining is neither that the elements of the model are correlated with the things of the situation (pictorial relationship) nor the same possibilities of arrangement (pictorial form). These two conditions only establish aboutness (the possible truth-or-falsity) by incorporating the contrast between a situation’s possibly either obtaining or not into the model itself. But what makes the model actually present a situation as obtaining is a fact about the model, namely that the elements are related in a certain way133: The fact that the elements of a picture are related to one another in a determinate way represents that things are related to one another in the same way. (TLP: 2.15)

Again: facts are symbolized by facts.134 This idea is exactly the same as the one we previously encountered in connection with Wittgenstein’s remarks on what makes “aRb” expressive. For example, the fact that a toy car in the model turns right at an intersection represents the situation that (shortly before the accident, say) a certain real car turned right at the intersection. We may find out later that the car didn’t turn right but left, or went straight ahead. In this case the model would have been false, though it would have been a model of the car accident nevertheless because it could have been true (the real car could have turned right). Even if it were later revealed that there was no car turning left or right in the first place (or even—unlikely but possible—that there was no car accident at all), this finding would in no way affect what the model presents as obtaining. The model presents what it presents regardless of what

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really happened. Whether the situation is other than the model presents it as being or whether the presented situation actually exists at all has no bearing on the model’s symbolizing what it does because this depends only on the facts about the model itself. Even in the latter case the model doesn’t become meaningless because, first, it would still be a fact about the model that the toy car turned left and, second, there could have been a car turning left.135 By making the representational character of the model a feature of the model itself (i.e. the facts about it) instead of conceiving of it as merely consisting in a correlation of the elements with the objects of the situation (the pictorial relationship), the model acquires the capacity to present a situation as obtaining independently of what actually is the case. Observers in the Paris courtroom following the reenactment can understand perfectly well what (allegedly) happened without having been present at the actual accident. As I’ve emphasized, the notions of pictorial (logical) form and pictorial relationship are integral parts of Wittgenstein’s picture theory. One might wonder though whether either of these notions plays a more basic role than the other, and if so, which one enjoys a privileged status within the picture theory. This question is not unjustified because Wittgenstein says of both notions that they are responsible for making something into a picture. He does so explicitly with regard to pictorial relationship and implicitly, but no less clearly, with regard to pictorial form.136 The only way to reconcile these seemingly contradictory statements is to acknowledge, as I’ve urged, that both notions are mutually dependent and cannot possibly be separated from each other. Realism vs. Idealism Failure to recognize this mutual dependency of pictorial (logical) form on the one hand and pictorial relationship on the other has been the root cause for one of the most controversial and persistent debates about the Tractatus. In most general terms, this debate is about the question whether the structure of the world determines the structure of language or rather the other way round. What is at stake is nothing other than the question whether the Tractatus is at bottom either realist or idealist.137 This debate has assumed different forms and therefore revolves around different points of disagreements. But there are also structural

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similarities. In any event, the point of departure of the debate between realism and idealism has traditionally been an argument over the function of Tractarian names famously started by Hidé Ishiguro. Brian McGuinness later joined her position, whereas David Pears and Norman Malcolm objected vigorously. Since their respective positions are very similar, I’ll refer to the opposing parties as the Ishiguro-McGuinness position and the Pears-Malcolm position, respectively.138 The starting point of the debate may be at first sight somewhat surprising given that an argument over Tractarian names doesn’t seem to go beyond the boundaries of semantics. According to Ishiguro, the question is “whether the meaning of a name can be secured independently of its use in propositions by some method which links it to an object.”139 Pears attacks Ishiguro’s view and adopts the opposite position, namely that there “is no reason to deny, and there are many reasons to assert, that names in the Tractatus do make independent references.”140 Thus, the basic question is whether establishing the reference of a name necessarily involves its employment in propositions or not. In other words, is it possible for names to refer to objects simply in virtue of there being a “direct linkage”141 (e.g. through ostensive acts) between a name and an object, or does reference depend on the propositional contexts in which names are meaningfully used? As we’ll see, the debate over which notion plays the dominant role—“direct linkage” or “use”—is simply the explicitly linguistic analogue of the debate over the question whether the notion of pictorial relationship or pictorial (logical) form is more significant within the picture theory. However, the case seems straightforwardly decidable. The textual evidence strongly supports the Ishiguro-McGuinness position: “Only propositions have sense; only in the nexus of a proposition does a name have meaning” (TLP: 3.3). But, of course, the Pears-Malcolm position is aware of this passage and the need to account for it, which is why it readily concedes that the propositional contexts of a name (its having a particular use and a determinate logical form) are essential for a name to have reference; but it still insists on prioritizing direct linkage over use, thereby assimilating Wittgenstein’s view to Russell’s basic picture of reference:

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[A] name may first be attached to an object in something like the way envisaged by Russell, but thereafter it will represent the object only so long as the possibilities presented by the propositions in which it occurs are real possibilities for that object. If [TLP] 3.3 is taken in this way, it qualifies the direct attachment of names to objects but does not replace it with something completely different. The initial act of attachment is necessary for a representation but not sufficient.142

Why does the Pears-Malcolm position insist on this prioritization, and how does the debate over the logical role of Tractarian names connect to the realism-idealism debate? To see this, it’s important to get clear on what exactly is at issue. Both sides agree that the meaning of a Tractarian name is the object it refers to and that the use of a name is an essential part of fixing and maintaining that reference. What is highly contested, though, is what determines that use, that is, what governs the logical form of a name. Put differently, the question is whether the logical form of a name is being governed by the totality of propositional contexts in which that name can meaningfully occur or whether the logical form of a name is being prescribed by the totality of states of affairs in which the object the name refers to can possibly occur. Consequently, at issue is the determination of the relata of the reference relation, namely whether the combinatorial possibilities of objects (their metaphysical occurrence spaces) are prior to and hence determine the combinatorial possibilities of names (their logical occurrence spaces) or vice versa.143 Given this background it now becomes clear how the initially semantic disagreement over the logical role of Tractarian names has turned into a metaphysical dispute. The reason is that the source of the determination of the logical form of a name corresponds to the (anti-) metaphysical commitments underlying the wider philosophical picture within which the different semantic views are embedded. According to the Ishiguro-­ McGuinness position, considering the logical form of a name as a function of the propositional contexts in which it can meaningfully occur makes the reference relation dependent on the meaningful use of names and thus primarily a linguistic affair. Reference to objects becomes a mere

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byproduct of language use, which is why they not only have no significant role to play in a logical theory but are even superfluous.144 A conception threatening to compromise the idea of a world of independently constituted objects, on the other hand, is clearly anathema to a realist position such as Pears-Malcolm’s. That is why according to them the reference relation is to be conceived of in the first instance as a matter of direct linkage between a name and an object, which makes the logical form of the name dependent on the intrinsic nature of the object and thus primarily a metaphysical affair.145 And it also incorporates the importance of propositional contexts for reference because the combinatorial possibilities of a name—once the name has been attached to an object— must reflect the combinatorial possibilities of the object for the former to refer to the latter. The Pears-Malcolm position promises to respect the spirit of the context principle (TLP: 3.3) while preserving a realist view of the world.146 In sum, the Ishiguro-McGuinness position claims it’s the use of a name determining the “direction of fit” so that a name refers to whatever object fits the semantic bill, whereas the Pears-Malcolm position maintains it’s the object determining the “direction of fit” so that a name refers to an object if and only if it fits the metaphysical bill. One of the things keeping the question concerning the “direction of fit” alive is undoubtedly connected to the still widespread notion of “isomorphism” used to characterize Wittgenstein’s alleged position regarding the relation between language and the world. This notion has been perpetuating the imagery of language and the world as two mutually independent realms and cemented the picture theory as a theory about what conditions have to be fulfilled in order for either the linguistic possibilities (the occurrence space of names) to match the metaphysical possibilities (the occurrence space of objects) or the other way round.147 Given that many commentators have taken this philosophical project to be at the heart of the Tractatus, it comes as no surprise that they consequently attributed either a form of realism or idealism to it, depending on which realm of possibilities they viewed as determining the other. Against this, I’ve tried to show how the notions of pictorial relationship and pictorial (logical) form are mutually dependent on each other

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and render any attempt at prioritization inappropriate. It’s not as if we correlate certain items with one another first and then make sure their occurrence spaces match, nor vice versa. Rather, if certain items are correlated with one another, then their occurrence spaces match automatically, and if certain items share their occurrence space, then they can be correlated with one another.148 To illustrate this point, consider a chess game in which some pieces are missing (a bishop, say), and we want to replace them using ordinary objects of the appropriate size available in the vicinity (corks or whatever). Now, if we stipulate that a particular object is going proxy for the (missing) bishop, then that object will automatically be subject to the rules governing the bishop (the diagonal rule, among others). Conversely, if we stipulate that a particular object is going to be subject to the rules governing the bishop, then that object will automatically go proxy for the bishop. It would be impossible—or, once again, nonsensical—for an object to stand for the bishop and not be subject to the corresponding rules, and vice versa. There is simply no room for a possible mismatch between a chess piece an object is supposed to stand for and the role it’s supposed to play within the chess game. And the same goes for the items to be correlated and their respective occurrence spaces within the framework of the picture theory. Where one might discern two steps in the aboutness of a picture—correlating items and matching their occurrence spaces—there is only one. Hence there can be no question of prioritizing or privileging either pictorial form or pictorial relationship, simply because both notions are two sides of the same coin. Now we can also see how the mutual dependency of pictorial relationship and pictorial (logical) form undermines the two-worlds-view underlying the isomorphism thesis and the realism-idealism debate it leads to. The key to understanding the picture theory is to realize that the structure of language and the structure of the world are not two numerically different structures that are aligned with each other as a result of one realm conforming to the other. Rather, the picture theory spells out the idea that if something is to be a picture of something else, then they need to have their structure in common, and, conversely, if a picture depicts something, then they share a common structure:

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There must be something identical in a picture and what it depicts, to enable the one to be a picture of the other at all. (TLP: 2.161) A gramophone record, the musical idea, the written notes, and the soundwaves, all stand to one another in the same internal relation of depicting that holds between language and the world. They all have the same logical structure in common. (Like the two youths in the fairy-tale, their two horses, and their lilies. They are all in a certain sense one.) (TLP: 4.014; transl. am.)

Logical space is not to be reduced to or identified with language, and thus is not opposed to the world but rather comprises it.149 As we’ve seen, propositions are (linguistic) facts, and they are used to represent other (worldly) facts. The picture theory can be understood as an articulation of the internal differentiation of the one single domain of possible states of affairs (logical space) into two subdomains, in which one type of fact (the linguistic ones) serves to picture the other type (the worldly ones).150 It is this sense in which both subdomains are “one.” This is ultimately the reason why the limits of language and the world are said to coincide, namely because they are identical and not because one domain imposes its limits on the other.151 And since language and the world don’t merely possess numerically distinct structures that happen to coincide but rather are identical in structure, the question of a “direction of fit” becomes simply unintelligible and the need to establish a connection between language and the world becomes superfluous. And yet—even if we acknowledge the identity of structure, isn’t it still legitimate to insist on the priority of worldly facts, that is, that which is depicted? After all, doesn’t the very idea of representation imply that there have to be facts prior to their being represented? What else would a representation be a representation of? Commenting on Wittgenstein’s example of the gramophone record quoted above, Anthony Kenny has voiced a concern or puzzlement shared by many interpreters: This example is helpful, but not altogether clear since it is not obvious what is supposed to be a picture of what. The derivation rules connect score, record and sound: is each supposed to be a picture of the other? Surely not: score and record must surely be supposed to be a picture of the sound: it is

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the sound, at least, which we are most interested in. But Wittgenstein does not here make clear what, in addition to A’s having logical structure, and pictorial relation to B, is needed for A to be a picture of B rather than the other way round.152

That is exactly Wittgenstein’s point! Since A and B share the same logical structure if one is a picture of the other, there is indeed no intrinsic structural feature of either A or B that would distinguish it as the representing item rather than the represented one. In principle, at least, it’s possible for A to be a picture of B as well as it is possible for B to be a picture of A if their structure is identical, that is, if the mutually dependent conditions of pictorial relationship and pictorial (logical) form are fulfilled. But, Kenny objects, score and record have to be a picture of the sound because the sound is our primary object of interest. From this he concludes “that the pictorial relationship which makes the picture into a picture (the correlation of the elements) is in some way a one-way correlation.”153 This doesn’t follow, though. Why, after all, should we be more interested in the sound rather than the score or the record? Besides, Wittgenstein’s elaboration of his account of picturing in the following passage makes it quite clear that the relation between a picture and what it depicts cannot be a one-way street: There is a general rule by means of which the musician can obtain the symphony from the score, and which makes it possible to derive the ­symphony from the groove on the gramophone record, and, using the first rule, to derive the score again. That is what constitutes the inner similarity between these things which seem to be constructed in such entirely different ways. And that rule is the law of projection which projects the symphony into the language of musical notation. It is the rule for translating this language into the language of gramophone records. (TLP: 4.0141; emphasis added)

Record, score, and symphony are very different domains. But there is an “inner similarity” between them constituted by there being derivation rules by virtue of which one domain is translatable into another. “Inner similarity” here is by no means a mysterious notion but simply another

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name for the fact that these domains share the same logical form. And if their form is identical, then it’s possible to translate these domains into one another. The idea of translatability makes it also clear why it’s wrong trying to single out a special feature or criterion in settling the question what is a picture of what. A skilled musician can play a symphony by looking at the corresponding score as well as obtaining that very score by listening to the symphony. The symphony will be a “picture” of the score if the musician gets the structure right, that is, if her musical performance accurately reflects pitch and duration of each individual note according to the score. The same goes for the opposite case. The score the musician writes down will only be a “picture” of the symphony if the former reproduces the structure of the latter. What is a picture of what is indeed dependent on what use is being made of the relata of the picturing relation, and therefore dependent on various pragmatic factors such as interest and the like.154 But these factors are external to and don’t belong to the logic of depiction. The logic of depiction only establishes—through identity of form—the possibility of translating certain kinds of domains. This relation is neutral with respect to the question which domain is supposed to be a picture of the other, and that is why Wittgenstein is deliberatively silent on it. The question what is a picture of what cannot be generalized because it can be answered only on a case-by-case basis. With these considerations in mind, we can now give a clear diagnosis of where the realism-idealism dispute went awry. Both parties involved commit, wittingly or not, the same mistake, namely to confound two aspects of the picturing relation that should be strictly kept apart, which may be called logical symmetry and ontological asymmetry. Ontological asymmetry reflects the simple point that the depicted is prior to the picture because there have to be facts prior to their being represented. Of course, the facts of the car accident precede their representation by the Paris courtroom model. It’s precisely in that sense that the model has to “conform” to reality—satisfying the conditions set by pictorial relationship and pictorial (logical) form—in order for it to be a (true or false) picture of the accident. But, as the example with the score and the symphony has shown, the picturing relation is not a one-way street. In this regard, the picturing relation exhibits logical symmetry, which can be characterized by the following biconditional: if two domains share the

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same logical form, then they are translatable into each other, and if two domains are translatable into each other, then they share the same logical form. Now, Wittgenstein’s fundamental point is that, regardless of how the ontological asymmetry manifests itself in the difference between the picture and the depicted, there is a logical symmetry between them in each case. For example, regardless of whether the toy car model is being used as a picture to reenact the car accident or whether the toy car model functions itself as the depicted, something that is supposed to be depicted by something else—in both cases there has to be logical symmetry in order for one thing to be a picture of the other. This is why the picture theory only concerns itself with logical symmetry because ontological asymmetry, unlike logical symmetry, is dependent on the particular case. Nevertheless, both notions have to be sharply distinguished. The realists in the debate overemphasize ontological asymmetry, leading them to the metaphysical divide of language and the world and all the problems of bridging the gap between them we’ve been discussing so far. The idealists, on the other hand, give too much weight to logical symmetry, which threatens to reduce the world to a mere projection of logico-­ semantic structures. But by keeping ontological asymmetry and logical symmetry cleanly apart and understanding the picture theory as a metaphysically neutral articulation of the logic of depiction, we can avoid these problems, and the realism-idealism debate vanishes.

Notes 1. Cf. also TLP (4.111): “Philosophy is not one of the natural sciences. (The word ‘philosophy’ must mean something whose place is above or below the natural sciences, not beside them.)” 2. McGuinness (2002: 104). All forms of propositions such as “the general notion of predicate, the general notion of dual relation, triple relation, and any other forms there might be of whatever complexity and level had been supposed to be logical objects, and Wittgenstein was denying them that status” (ibid.).

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3. As Frege put it in his essay “Logic”: “[T]he task we assign logic is only that of saying what holds with the utmost generality for all thinking, whatever its subject-matter. We must assume that the rules for our thinking and for our holding something to be true are prescribed by the laws of truth. The former are given along with the latter. Consequently we can also say: logic is the science of the most general laws of truth” (LC: 128). However, Frege’s views on this matter are less clear. Cf. Putnam (2000). But we need not explore these exegetical questions here since Wittgenstein’s attack is, as we’ll see, directed against a conception of logic in terms of generality, and thus it’s only of secondary importance whether Frege propounds it or not. At any rate, Russell’s case seems clear enough. 4. Ricketts (1996: 59). Cf. also Goldfarb (1997: 62). 5. Cf. McGuinness (2002: 109) and Hutto (2003: 30). 6. Cf. Potter (2008: 57): “Russell’s assumption of the existence of a logical realm existing somehow alongside the physical one rendered it inexplicable why the laws obeyed by the former should be applicable to the latter.” 7. Sheffer (1926: 228). 8. Ricketts (1985: 3). 9. Hyman (2001: 1). 10. Cf. Sect. 2.3. I’ll come back to this topic in Sect. 3.3. 11. Cf. Tejedor (2015: 22). Cf. also WVC (260; transl. am.): “The totality of these obtaining and non-obtaining states of affairs is called logical space. Logical space is the possibility for the obtaining and non-­ obtaining of states of affairs.” As is well known, Wittgenstein makes a conjunction of three statements in the Tractatus that seem to be incompatible with one another: “The totality of obtaining states of affairs is the world” (TLP: 2.04; transl. am.), “The obtaining and non-obtaining of states of affairs is reality” (TLP: 2.06; transl. am.), and “The sumtotal of reality is the world” (TLP: 2.063). This conjunction leaves one wondering whether the world is the totality of obtaining states of affairs alone or whether the world also includes non-obtaining states of affairs. Though Wittgenstein’s wording is indeed somewhat ambiguous, I think it’s clear that he intended the latter, if only for the simple reason that between the first two statements Wittgenstein claims: “The totality of obtaining states of affairs also determines which states of affairs do not obtain” (TLP: 2.05; transl. am.). Obtaining and non-obtaining

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states of affairs come essentially as a package deal and cannot possibly be separated from one another  (like meaning and logical form). Wittgenstein’s idea here is, as Potter (2008: 143) nicely put it, “that reality might be characterizable as much by the absence of something as by its presence.” What is not the case shapes reality inasmuch as does what is the case. 12. Cf. TLP (5.61 and 6.124). Cf. also Tang (2011: 601): “[L]ogic is always already the logic of the world.” 13. Cf. TLP (4.461). 14. This and the following remarks apply, of course, to contradictions as well. 15. Cf. TLP (4.462): “Tautologies and contradictions are not pictures of reality. They do not represent any possible situations.” 16. In the Notebooks Wittgenstein writes somewhat confusingly: “One cannot say of a tautology that it is true, for it is made so as to be true” (NB: 55). But in the Tractatus Wittgenstein clearly states that tautologies are “unconditionally true” (TLP: 4.461). For discussion cf. Kenny (2006: 54–55), who denies and A.W. Moore (2012: 229), who defends the thesis that tautologies (contradictions) are really true (false). For further discussion of the various categories of sentences in the Tractatus cf. A.W. Moore (2020). 17. Cf. TLP (6.112): “The correct explanation of the propositions of logic must assign to them a unique status among all propositions.” 18. Cf. TLP (6.113): “It is the peculiar mark of logical propositions that one can recognize that they are true from the symbol alone, and this fact contains in itself the whole philosophy of logic. And so too it is a very important fact that the truth or falsity of non-logical propositions cannot be recognized from the propositions alone.” 19. Cf. NB (66): “There doesn’t after all seem to be any setting up of a kind of logical inventory as I formerly imagined it.” 20. Brandom (1994: 648). 21. Carroll (1895). 22. Cf. also TLP (6.1264): “Every proposition of logic is a modus ponens represented in signs. (And one cannot express the modus ponens by means of a proposition.)” 23. Cf. Glock (1996: 203) and Künne (2003: 124). 24. Cf. TLP (6.123): “Clearly the laws of logic cannot in their turn be subject to laws of logic.”

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25. Cf. Tejedor (2015: 35). 26. Cf. Baker and Hacker (2009: 90): “In short, a rule of inference does not engineer a fit between independently given propositions. Rather, it makes perspicuous the fact that a pair of propositions belong to one another, that they are internally related.” The idea that rules in general are not assertions (i.e. that they are neither true nor false) is also the fundamental thought underlying (the solution of ) Wittgenstein’s rulefollowing considerations and will be dealt with at length in Sect. 5 and 6. 27. Cf. Hacker (1986: 48). 28. Cf. Ostrow (2004: 22). 29. Cf. Glock (1992: 19). 30. Cf. Glock (1992: 20). 31. Cf. Hacker (2017: 215). 32. Cf. Ryle (2009: 245): “But ‘Today is Monday, so tomorrow is Tuesday’ is not a statement. It is an argument, of which we can ask whether it is valid or fallacious; it is not an assertion or doctrine or announcement of which we can ask whether it is true or false. We can, indeed, ask whether its premiss is true, and whether its conclusion is true; but there is no third question ‘Is it true that today is Monday so tomorrow is Tuesday?’ An argument is not the expression of a proposition, though it embodies the expressions of two propositions.” 33. Cf. Hutto (2003: 45). 34. Cf. Maslow (1961: 4), Black (1964: 3), and Mounce (1981: 18). 35. Cf. J. Griffin (1964: 30), Künne (2003: 120, n. 98), and Sullivan (2005: 59). The view that there are both objects and their combinations (complexes or facts) is essentially Russell’s own: “[T]he only other sort of object you come across in the world is what we call facts” (PLA: 111). Cf. against this Wittgenstein’s clarification: “[t]he world does not consist of a catalogue of things and facts about them […]” (WL: 119). 36. Cf. also Stenius (1960: 28), Stern (1995: 53), McGuinness (2002: 77), M. McGinn (2006: 138), and Priest (2014: 199), who consider things components of facts. 37. Ostrow (2004: 24). 38. Pears (1987: 8–9). 39. Commentators composing the first group are legion. For the latter group cf. Stenius (1960: 31), who thinks states of affairs are simply possible (but non-actual) facts, and Black (1964: 45).

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40. Among the commentators recognizing the distinction between existing and holding/obtaining are McGuinness (2002: 84) and Palmer (1998: 172–173). Wittgenstein makes the same point about relations when commenting on Ogden’s translation of TLP (4.122): “That a relation exists cannot be asserted at all. What we can assert is that it holds between certain objects” (LO, 28). 41. Wittgenstein speaks here of propositions, but it’s clear that what he says applies to facts as well because propositions are facts, a claim Wittgenstein makes repeatedly. Cf. TLP (3.14–3.143). 42. Cf. Lampert (1998: 281). 43. Cf. Kenny (2006: 51) and Johnston (2011: 72) who have observed this important point. This is also why Wittgenstein distinguishes between positive and negative facts but not between positive and negative states of affairs. A positive fact is the obtaining of a state of affairs, a negative fact is the non-obtaining of a state of affairs (cf. TLP: 2.06). For example, to say that the watch doesn’t lie on the table expresses a negative fact (if true), that is, that a certain connection between certain objects doesn’t hold; but this doesn’t say anything about the existence or nonexistence of (a set of ) objects. States of affairs are connections of objects, and if certain objects are not connected in a particular way, then there simply is no such state of affairs. 44. Cf. PG (200): “It is just as misleading to say the fact that this circle is red (that I am tired) is a complex whose component parts are a circle and redness (myself and tiredness).” This passage is taken from a small manuscript entitled “Complex and Fact” Wittgenstein wrote years after the Tractatus. Some commentators believe this manuscript to be a critique of his conception in the Tractatus, whereas I’ll argue in Sect. 3.3 that his passage is merely a clarification of his former views and hence that the distinction between complex and fact is already operative in the Tractatus. 45. Cf. Lampert (1998: 282). 46. Johnston (2007: 245). 47. Cf. Skyrms (1981: 199) and Zalabardo (2015: 116). 48. Cf. Genova (1995: 66). 49. Ostrow (2004: 50). 50. Cf. WL (119): “What the world is is given by description and not by a list of objects.”

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51. Cf. TLP (5.4711): “To give the essence of a proposition means to give the essence of all description, and thus the essence of the world.” 52. Cf. WL (119): “‘The world is everything that is the case’. This is intended to recall and correct the statement ‘The world is everything that there is’; the world does not consist of a catalogue of things and facts about them (like the catalogue of a show).” 53. R. Bradley (1992: 67) lists over a dozen uses. 54. Cf. Hintikka and Hintikka (1986: ch. 3) and Cook (1994: 31). 55. Cf. R. Bradley (1992: 74) and Lampert (1998: 241). 56. Sellars (1962), Anscombe (1963), J. Griffin (1964), Copi (1966), and Carruthers (1989). 57. Ishiguro (1969: 21). 58. Ishiguro (1969: 47). 59. Campbell (2011: 140). 60. Cf. Winch (1987), McCarty (1991), Blank (2000), McGuinness (2002), Cerezo (2005), Johnston (2009), Campbell (2011), and Zalabardo (2015). 61. Campbell (2011: 139). 62. Cook (1994: 31). 63. Cf. White (2006: 20). 64. For a thorough analysis regarding Wittgenstein’s views on this matter in the Notebooks cf. Sluga (2012). He convincingly argues against the substantial conception and concludes: “Wittgenstein’s notebooks already contained everything necessary for the destruction of the theory of simple objects and of the whole edifice to which it belongs” (Sluga 2012: 114). 65. Cf. TLP (4.032), where Wittgenstein expressly calls “ambulo” a proposition. 66. Here’s Wittgenstein’s own example: “[…] how is it possible for ‘kilo’ in a code to mean: ‘I’m all right’? Here surely a simple sign does assert something and is used to give information to others.—For can’t the word ‘kilo’, with that meaning, be true or false?” (NB: 8). 67. Cf. TLP (2.024). 68. J. Griffin (1964: 49). 69. Cf. TLP (3.144 and 3.221; transl. am.): “Situations can be described but not named. […] Objects can only be named. […] I cannot express them.” Cf. Winch (1987: 8–10) and Johnston (2009: 151). I’ll come back to this in Sect. 3.3.

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70. Cf. Palmer (1998: 179). 71. Cf. TLP (3.323), where Wittgenstein makes the same point with the proposition “Green is green.” The first and third words are the same sign yet express “different symbols” because they have different logical roles, the first one being a proper name (referring to an object) and the third one being an adjective (expressing a property). The fact that both symbols share the same sign is logically irrelevant. 72. Cf. NB (69): “But logic as it stands, e.g., in Principia Mathematica can quite well be applied to our ordinary propositions, e.g., from ‘All men are mortal’ and ‘Socrates is a man’ there follows according to this logic ‘Socrates is mortal’ which is obviously correct although I equally obviously do not know what structure is possessed by the thing Socrates or the property of mortality. Here they just function as simple objects.” And a page later Wittgenstein writes: “And it is clear that the object must be of a particular logical kind, it may be as complex or as simple as it is” (NB: 70). 73. Cf. NB (69): “The simple sign is essentially simple. It functions as a simple object. […] Its composition becomes completely indifferent.” 74. Cf. WVC (252): “Elements are simple. For that reason they cannot be described. What can be described? Whatever is complex.” 75. Carruthers (1989: 108). 76. Proponents of the narrow interpretation include Sellars (1962), Anscombe (1963), J. Griffin (1964), Copi (1966), Carruthers (1989, 1990), and Mácha (2015). Since Carruthers has developed the most elaborate account of the narrow interpretation, I’ll focus primarily on his writings. 77. Stenius (1960), Mounce (1981), Maury (1983), Hintikka and Hintikka (1986), Hacker (1986), and Potter (2008) are the main advocates of the wide reading. 78. Cf. Copi (1966: 180). 79. Carruthers (1989: 109). 80. Cf. Carruthers (1989: 110), according to whom “a state of affairs will consist of individuals standing in some material relation to one another.” I share the diagnosis that the terms of the debate between the narrow and the wide interpretation are misguided with Lampert (1998: 241), Cerezo (2005: 92), and Johnston (2009: 149). 81. Cf. Johnston (2007: 240) and Candlish and Damnjanovic (2012: 87). One of the commentators who had understood all this right from the

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beginning was Ramsey (2013: 133): “As regards the tie, I cannot understand what sort of a thing it could be, and prefer Wittgenstein’s view that in the atomic fact the objects are connected together without the help of any mediator. This does not mean that the fact is simply the collection of its constituents but that it consists in their union without any mediating tie.” 82. Cf. NL (101): “Logical indefinables cannot be predicates or relations, because propositions, owing to sense, cannot have predicates or relations.” The same point is made in the Cambridge Lectures, in which Wittgenstein explains TLP (2.01) to Desmond Lee: “[A] proposition is not two things connected by a relation. […] The objects hang as it were in a chain” (WL, 120). Consider also the following passage, in which Wittgenstein comments on Frege’s famous distinction between concepts and objects after having identified it as that which is, for Frege, responsible for the unity of the proposition: “Frege held that what connected the words within a proposition—that which made a proposition a proposition, so to speak—was its predicate. He called possible predicates concepts and distinguished accordingly between concept and object. It might then be thought that in describing the phenomena we encountered an analogous difference, i.e. that there was something in a state of affairs which constituted its form, which connected the other elements, as well as something thing-like which was to be connected. The predicate would then signify the form-­like part of the state of affairs and the other elements of a proposition its thing-like part. Thus this whole distinction arises when we ask, What connects the elements of a situation [Sachlage] together? But have we any right to ask this question? The elements are not connected with one another by anything. They simply are connected, and that concatenation [Verkettung] just is the state of affairs in question. After all, does the other conception explain anything? If cement [Kitt] is needed to hold the elements together—what is it that connects the cement and the elements?” (WVC: 251–252; transl. am.). The thesis that in a state of affairs there are objects and objects only is also perfectly consistent with Wittgenstein’s remarks on propositions later in the Tractatus, where he even makes use of the chain metaphor again: “An elementary proposition consists of names. It is a nexus, a concatenation [Verkettung], of names” (TLP: 4.22). In the same way that states of affairs are made up of objects only, so propositions are made up of names only. How this analysis works will be discussed in Sect. 3.3.

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83. Cf. Palmer (1998: 170, 179). 84. This term is inspired by TLP (2.013): “Each thing is, as it were, in a space of possible states of affairs. This space I can imagine empty, but I cannot imagine the thing without the space.” 85. Cf. Mácha (2015: 57): “The internal properties which make up the form of an object are always relational properties, because they involve the possibility of being combined with other objects.” 86. For Frege’s influence on Wittgenstein, particularly with respect to the context principle, cf. Reck (1997). 87. Johnston (2007: 242). 88. Cf. McGuinness (2002: 68) and Tejedor (2015: 31–32). 89. Cf. Hochberg (2000: 18) and Cerezo (2005: 103). 90. Cf. Friedlander (2001: 35). 91. I borrow this apt metaphor from Anscombe (1963: 38), who uses it to explain Wittgenstein’s notion of linguistic expressions in terms of incompleteness. Anscombe, in turn, may have gotten this metaphor from Wittgenstein (she doesn’t make any references in the cited passage) because it appears prominently in the Philosophical Investigations: “Imagine a picture representing a boxer in a particular stance. Now, this picture can be used to tell someone how he should stand, should hold himself; or how he should not hold himself; or how a particular man did stand in such-and-­such a place; and so on. One might (using the language of chemistry) call this picture a proposition-radical” (PI: p. 12). While I agree with Anscombe about Wittgenstein’s notion of (Tractarian) expressions (I’ll go into that in Sect. 3.3), I disagree with her about Wittgenstein’s notion of (Tractarian) objects, which she takes to belong to a determinate ontological category, to wit particulars. 92. Cf. Johnston (2017: 148). 93. Dummett (1973: 246). 94. Cf. Hanks (2012: 42). 95. Russell came to see this point much later and credited Wittgenstein with this insight (PLA: 12–13): “It is very important to realize such things, for instance, as that propositions are not names for facts. It is quite obvious as soon as it is pointed out to you, but as a matter of fact I never had ­realized it until it was pointed out to me by a former pupil of mine, Wittgenstein.” 96. Davidson (2005: 103) succinctly captures what is wrong with Russell’s theory in particular and with its ilk in general: “The trouble is that

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propositions are entities, and Russell has maintained that any entity can be a logical subject. But if we say that some proposition is true or false, we are saying that an entity is true or false, which makes no sense. […] The problem apparently arises if we take a sentence to express a thing, whether that thing is a proposition, a meaning, or anything else.” 97. Unlike Geach (1976: 67), Simons (1992: 335), and Künne (2003: 142, n. 162), I don’t think Wittgenstein was confused about the distinction between complexes and facts in the Tractatus. The following passage in the Notebooks shows that Wittgenstein was aware of this crucial distinction quite early on: “The old problem of complex and fact. The theory of the complex is expressed in such propositions as: ‘If a proposition is true then Something exists’; there seems to be a difference between the fact expressed by the proposition: a stands in the relation R to b, and the complex: a in the relation R to b, which is just that which ‘exists’ if that proposition is true. It seems as if we could designate this Something, and with a ‘complex sign’ at that” (NB: 48; transl. am.). 98. Potter (2008: 102). 99. This raises the question whether complexes and states of affairs are the same. Lampert (1998: 290) argues that they are not: while both complexes and states of affairs are determinate connections of things, the constituents of the former are homogeneous, whereas the constituents of the latter are heterogeneous. Be that as it may, for our purposes we can disregard this subtlety here. 100. Cf. Potter (2008: 135) and Hanks (2012: 38). 101. Cf. Child (2011: 27). 102. Cf. Gaskin (2008: 122). 103. Cf. TLP (3.144 and 3.221; transl. am.): “Situations can be described but not named. […] Objects can only be named. […] I cannot express them.” Cf. also WVC (252). Anscombe (1963: 17) has seen this clearly when she writes that Wittgenstein “held that names had no sense but only reference, and propositions no reference but only sense.” Cf. also Ishiguro (2001: 31) and Glock (2004: 225) for a similar point. 104. Cf. Ostrow (2004: 28). 105. Cf. TLP (3.141–3.142): “A proposition is not a blend of words. […] A proposition is articulate. Only facts can express a sense, a set of names cannot.” 106. Cf. Textor (2009: 61–62). Once again, no one has seen this more clearly than Ramsey (2013: 121): “There is a sense in which any object is incomplete; namely that it can only occur in a fact by connection

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with an object or objects of suitable type: just as any name is incomplete, because to form a proposition we have to join to it certain other names of suitable type.” 107. Cf. Anscombe (1963: 93). 108. Cf. Diamond (2010: 551). 109. The crucial issue of Tractarian nonsense will be addressed in Sect. 4. 110. Bronzo (2011: 104–105) also emphasizes the interdependence of objects and states of affairs on the one hand as well as expressions and propositions on the other. 111. The most prominent expression of Wittgenstein’s semantic contextualism is, of course, TLP (3.3): “Only propositions have sense; only in the nexus of a proposition does a name have meaning.” 112. Cf. WVC (251–252). 113. Cf. White (2006: 64) and Zalabardo (2015: 127). 114. Cf. TLP (3.314). With this claim I follow Ramsey (2013: 121), Anscombe (1963: 98), and Lampert (1998: 258). 115. Cf. TLP (3.323): “In everyday language it very frequently happens that the same word has different modes of signification—and so belongs to different symbols—or that two words that have different modes of signification are employed in propositions in what is superficially the same way. Thus the word ‘is’ figures as the copula, as a sign for identity, and as an expression for existence; ‘exist’ figures as an intransitive verb like ‘go’, and ‘identical’ as an adjective; we speak of something, but also of something’s happening. (In the proposition, ‘Green is green’—where the first word is the proper name of a person and the last an adjective— these words do not merely have different meanings: they are different symbols.)” 116. Cf. McGuinness (2002: 114). 117. Cf. the anecdote told by Malcolm (2001: 70): “I asked Wittgenstein whether, when he wrote the Tractatus, he had ever decided upon anything as an example of a ‘simple object’. His reply was that at that time his thought had been that he was a logician; and that it was not his business, as a logician, to try to decide whether this thing or that was a simple thing or a complex thing, that being a purely empirical matter!” 118. Cf. Marion (1998: 114). 119. Ramsey (2013: 145). 120. Cf. TLP (2.22): “What a picture represents it represents independently of its truth and falsity, by means of its pictorial form.” Cf. also TLP

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(2.224–2.225): “It is impossible to tell from the picture alone whether it is true or false. There are no pictures that are true a priori.” The same point is made about propositions because they are pictures: “A proposition can be true or false only in virtue of being a picture of reality” (TLP: 4.06). And again, the same point is made about thoughts: “If a thought were correct a priori, it would be a thought whose possibility ensured its truth” (TLP: 3.04). 121. Cf. Cerezo (2005: 261) and Hanks (2012: 51). 122. This passage can also be found virtually verbatim in the Notes on Logic (cf. NL: 105). 123. In the same passage Wittgenstein expresses his idea more formally in the following way: “What symbolizes in φξ is that φ stands to the left of a proper name […].” 124. Cf. Frascolla (2007: 46). 125. Cf. NB (7): “In the proposition a world is as it were put together experimentally. (As when in the law-court in Paris a motor-car accident is represented by means of dolls etc.)” Cf. also TLP (4.031–4.0311): “In a proposition a situation is, as it were, constructed by way of experiment. Instead of, ‘This proposition has such and such a sense’, we can simply say, ‘This proposition represents such and such a situation’. One name stands for one thing, another for another thing, and they are combined with one another. In this way the whole group—like a tableau vivant—presents a state of affairs.” 126. Highly influential representatives of the realist position are Malcolm (1986) and Pears (1987). Leading proponents of the anti-realist or idealist position are Ishiguro (1969) and McGuinness (2002). I’ll discuss the Malcolm-Pears position as well as the Ishiguro-McGuinness counter-­position below. 127. Cf. TLP (2.14–2.141). 128. Cf. TLP (4.04): “In a proposition there must be exactly as many distinguishable parts as in the situation that it represents. The two must possess the same logical (mathematical) multiplicity.” 129. Cf. Cerezo (2005: 98) and Hacker (2013: 174–175). 130. Cf. also TLP (2.18). 131. Cf. Morris (2008: 120): “The possibilities of arrangement of the movable bits of the model are exactly the same as the possibilities of arrangement of the movable things—the real cars and people—in reality. This makes it possible for us to use the model to construct, experimentally,

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a way in which the real things might have been arranged.” For similar points cf. Ricketts (1996: 78), Hutto (2003: 59), and Frascolla (2007: 43). 132. Morris (2008: 121). 133. Cf. Hacker (1986: 59) and Frascolla (2007: 24). 134. Cf. Candlish (1998: 128), Cerezo (2005: 261), and Hacker (2013: 174). 135. Cf. TLP (3.24): “A proposition that mentions a complex will not be nonsensical, if the complex does not exist, but simply false.” 136. Compare TLP (2.1513): “So a picture, conceived in this way, also includes the pictorial relationship, which makes it into a picture” with TLP (2.16): “If a fact is to be a picture it must have something in common with what it depicts,” which common “ingredient” is identified immediately afterward (TLP: 2.17) as pictorial form. 137. Cf. Dilman (2002: 206) and McManus (2006: 22). 138. Of course, both parties have had both predecessors and successors, but Ishiguro-McGuinness and Pears-Malcolm have developed the most elaborate accounts for the respective positions. That is why I’ll focus mainly on their views. Notable predecessors of the Ishiguro-McGuinness position are Rhees (1966, 1969) and Winch (1969), and important predecessors of the Pears-Malcolm position are Black (1964) and Kenny (2006). A more recent defense of (a modified version of ) the Ishiguro-McGuinness position can be found in Diamond (2006), whereas Hacker (2001) advocates the opposite view. 139. Ishiguro (1969: 20–21). Cf. McGuinness (2002: 96) for a similar statement. 140. Pears (1987: 114). 141. Pears (1987: 110). 142. Pears (1987: 102–103). Cf. also Pears (1987: 110). The same concession can be found in Malcolm (1986: 29). 143. Tejedor (2015: 30) has aptly categorized this debate as belonging to a series of very similar debates about the Tractatus she groups together under the umbrella term “Determination Question.” Other such debates include the debate whether “meaning determines sense (or vice versa)” and whether “content determines form (or vice versa)” (Tejedor 2015: 31). These debates are not only very similar in structure but also characterized by the divide between realists and idealists. 144. Cf. Ishiguro (1969: 40): “[T]he simple objects, whose existence was posited were not so much a kind of metaphysical entity conjured up to

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support a logical theory as something whose existence adds no extra content to the logical theory.” Cf. also McGuinness (2002: 87) and McGuinness (2002: 98). 145. Cf. Pears (1987: 88): “Once a name has been attached to an object, the nature of the object takes over and controls the logical behaviour of the name, causing it to make sense in some sentential contexts but not in others.” 146. Pears (1987: 111): “This interpretation still distances Wittgenstein from Russell, but not so far. […] It understands Wittgenstein’s words, ‘Only in the context of a proposition does a name have meaning’, in the same general way as Ishiguro and McGuinness, but reverses the direction of fit, so that the Tractatus comes out as basically realistic.” 147. The notion “isomorphism” has been introduced by Stenius (1960: 91). His highly influential commentary concludes with attributing to the Tractatus a strong version of Kantianism: “Wittgenstein’s philosophical system could be called ‘Critical Lingualism’ or ‘Transcendental Lingualism’ or even ‘Lingualistic Idealism’. […] The limits of the world of the metaphysical subject, or rather, the limits of the metaphysical subject’s ‘logical space’ of possible worlds, is determined by the limits of language” (Stenius 1960: 220–221). 148. Cf. Morris (2008: 131). 149. Cf. TLP (5.61): “Logic pervades [erfüllt] the world: the limits of the world are also its limits.” 150. Cf. Tejedor (2015: 86). 151. Cf. Wilke (2006: 106) and Travis (2011: 169), who also put emphasis on the identity of structure. 152. Kenny (2006: 56). 153. Kenny (2006: 56). 154. Cf. Tejedor (2015: 85).

References Anscombe, G.E.M. 1963. An Introduction to Wittgenstein’s Tractatus. 2nd ed. New York: Harper & Row. Baker, G.P., and P.M.S.  Hacker. 2009. Wittgenstein: Rules, Grammar and Necessity. Vol. 2 of an Analytical Commentary on the Philosophical Investigations. 2nd ed. Oxford: Wiley-Blackwell.

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Black, M. 1964. A Companion to Wittgenstein’s ‘Tractatus’. Cambridge: Cambridge University Press. Blank, A. 2000. Die kategoriale Unbestimmtheit der Gegenstände in Wittgensteins ‘Tractatus’. Grazer Philosophische Studien 60: 197–215. Bradley, R. 1992. The Nature of All Being. A Study of Wittgenstein’s Modal Atomism. Oxford: Oxford University Press. Brandom, R.B. 1994. Making It Explicit. Reasoning, Representing, and Discursive Commitment. Cambridge, MA: Harvard University Press. Bronzo, S. 2011. Context, Compositionality, and Nonsense in Wittgenstein’s Tractatus. In Beyond the Tractatus Wars. The New Wittgenstein Debate, ed. R. Read and M.A. Lavery, 84–111. London: Routledge. Campbell, C. 2011. Categorical Indeterminacy, Generality and Logical Form in Wittgenstein’s Tractatus. European Journal of Philosophy 22 (1): 138–158. Candlish, S. 1998. The Unity of the Proposition and Russell’s Theories of Judgement. In Bertrand Russell and the Origins of Analytic Philosophy, ed. R. Monk and A. Palmer, 2nd ed., 103–135. Bristol: Thoemmes Press. Candlish, S., and N. Damnjanovic. 2012. The Tractatus and the Unity of the Proposition. In Wittgenstein’s Early Philosophy, ed. J.L.  Zalabardo, 64–98. Oxford: Oxford University Press. Carroll, L. 1895. What the Tortoise said to Achilles. Mind 4 (14): 278–280. Carruthers, P. 1989. Tractarian Semantics. Finding Sense in Wittgenstein’s Tractatus. Oxford: Blackwell. ———. 1990. The Metaphysics of the Tractatus. Cambridge: Cambridge University Press. Cerezo, M. 2005. The Possibility of Language. Internal Tensions in Wittgenstein’s Tractatus. Stanford: CSLI Publications. Child, W. 2011. Wittgenstein. London: Routledge. Cook, J.W. 1994. Wittgenstein’s Metaphysics. Cambridge: Cambridge University Press. Copi, I.M. 1966. Objects, Properties, and Relations in the ‘Tractatus’. In Essays on Wittgenstein’s Tractatus, ed. I.M.  Copi and R.W.  Beard, 167–186. New York: The Macmillan Company. Davidson, D. 2005. Truth and Predication. Cambridge, MA: Harvard University Press. Diamond, C. 2006. Peter Winch on the Tractatus and the unity of Wittgenstein’s philosophy. In Wittgenstein: The Philosopher and his Works, ed. A. Pichler and S. Säätelä, 2nd ed., 141–171. Frankfurt: Ontos Verlag.

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———. 2010. Inheriting from Frege: The work of reception, as Wittgenstein did it. In The Cambridge Companion to Frege, ed. M. Potter and T. Ricketts, 550–601. Cambridge: Cambridge University Press. Dilman, I. 2002. Wittgenstein’s Copernican Revolution. The Question of Linguistic Idealism. Basingstoke: Palgrave Macmillan. Dummett, M. 1973. Frege. Philosophy of Language. New York: Harper & Row. Frascolla, P. 2007. Understanding Wittgenstein’s Tractatus. London: Routledge. Friedlander, E. 2001. Signs of Sense. Reading Wittgenstein’s Tractatus. Cambridge, MA: Harvard University Press. Gaskin, R. 2008. The Unity of the Proposition. Oxford: Oxford University Press. Geach, P.T. 1976. Saying and Showing in Frege and Wittgenstein. Acta Philosophica Fennica 28: 54–70. Genova, J. 1995. Wittgenstein. A Way of Seeing. London: Routledge. Glock, H.-J. 1992. Cambridge, Jena, or Vienna? The Roots of the Tractatus. Ratio V (1): 1–23. ———. 1996. Necessity and Normativity. In The Cambridge Companion to Wittgenstein, ed. H. Sluga and D.G. Stern, 198–225. Cambridge: Cambridge University Press. ———. 2004. All Kinds of Nonsense. In Wittgenstein At Work. Method in the Philosophical Investigations, ed. E.  Ammereller and E.  Fischer, 221–245. London: Routledge. Goldfarb, W. 1997. Metaphysics and Nonsense: On Cora Diamond’s The Realistic Spirit. Journal of Philosophical Research 22: 57–73. Griffin, J. 1964. Wittgenstein’s Logical Atomism. Oxford: Oxford University Press. Hacker, P.M.S. 1986. Insight and Illusion. Themes in the Philosophy of Wittgenstein. Oxford: Clarendon Press. ———. 2001. Naming, Thinking, and Meaning in the Tractatus. In Wittgenstein: Connections and Controversies, ed. P.M.S.  Hacker, 170–184. Oxford: Clarendon Press. ———. 2013. Intentionality and the Harmony between Thought and Reality. In Wittgenstein: Comparisons and Context, ed. P.M.S.  Hacker, 169–184. Oxford: Oxford University Press. ———. 2017. Metaphysics: From Ineffability to Normativity. In A Companion to Wittgenstein, ed. H.-J.  Glock and J.  Hyman, 209–227. Oxford: Wiley-Blackwell. Hanks, P.W. 2012. Early Wittgenstein on Judgement. In Wittgenstein’s Early Philosophy, ed. J.L. Zalabardo, 37–63. Oxford: Oxford University Press.

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Hintikka, M.B., and J. Hintikka. 1986. Investigating Wittgenstein. Oxford: Basil Blackwell. Hochberg, H. 2000. Propositions, Truth and Belief: The Wittgenstein-Russell Dispute. Theoria 66 (1): 3–40. Hutto, D.D. 2003. Wittgenstein and the End of Philosophy. Neither Theory nor Therapy. Basingstoke: Palgrave Macmillan. Hyman, J. 2001. The Gospel According to Wittgenstein. In Wittgenstein and Philosophy of Religion, ed. R.L.  Arrington and M.  Addis, 1–11. London: Routledge. Ishiguro, H. 1969. Use and Reference of Names. In Studies in the Philosophy of Wittgenstein, ed. P. Winch, 20–50. London: Routledge & Kegan Paul. ———. 2001. The So-Called Picture Theory: Language and the World in Tractatus Logico-Philosophicus. In Wittgenstein: A Critical Reader, ed. H.-J. Glock, 26–46. Oxford: Blackwell. Johnston, C. 2007. The Unity of a Tractarian Fact. Synthese 156 (2): 231–251. ———. 2009. Tractarian Objects and Logical Categories. Synthese 167: 145–161. ———. 2011. Assertion, Saying, and Propositional Complexity in Wittgenstein’s Tractatus. In The Oxford Handbook of Wittgenstein, ed. O.  Kuusela and M. McGinn, 60–78. Oxford: Oxford University Press. ———. 2017. The Picture Theory. In A Companion to Wittgenstein, ed. H.-J. Glock and J. Hyman, 141–158. Oxford: Wiley-Blackwell. Kenny, A. 2006. Wittgenstein. Rev. ed. Oxford: Blackwell. Künne, W. 2003. Conceptions of Truth. Oxford: Clarendon Press. Lampert, T. 1998. Wittgensteins Physikalismus. Die Sinnesdatenanalyse des Tractatus logico-philosophicus in ihrem historischen Kontext. Paderborn: Mentis. Mácha, J. 2015. Wittgenstein on Internal and External Relations. Tracing all the Connections. London: Bloomsbury Academic. Malcolm, N. 1986. Nothing is Hidden. Wittgenstein’s Criticism of his Early Thought. Oxford: Basil Blackwell. ———. 2001. Ludwig Wittgenstein. A memoir by Norman Malcolm with a Biographical Sketch by G.H. von Wright. 2nd ed. Oxford: Clarendon Press. Marion, M. 1998. Wittgenstein, Finitism, and the Foundations of Mathematics. Oxford: Clarendon Press. Maslow, A. 1961. A Study in Wittgenstein’s Tractatus. Berkeley: University of California Press. Maury, A. 1983. Reality and Logical Form. Synthese 56 (2): 171–180. McCarty, D.C. 1991. The Philosophy of Logical Wholism. Synthese 87 (1): 51–123.

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McGinn, M. 2006. Elucidating the Tractatus. Wittgenstein’s Early Philosophy of Logic & Language. Oxford: Clarendon Press. McGuinness, B.F. 2002. Approaches to Wittgenstein. Collected Papers. London: Routledge. McManus, D. 2006. The Enchantment of Words: Wittgenstein’s Tractatus Logico-­ Philosophicus. Oxford: Clarendon Press. Moore, A.W. 2012. The Evolution of Modern Metaphysics. Making Sense of Things. Cambridge: Cambridge University Press. ———. 2020. The Bounds of Nonsense. In Wittgenstein and the Limits of Language, ed. H. Appelqvist, 27–45. London: Routledge. Morris, M. 2008. Wittgenstein and the Tractatus. London: Routledge. Mounce, H.O. 1981. Wittgenstein’s Tractatus. An Introduction. Oxford: Blackwell. Ostrow, M.B. 2004. Wittgenstein’s Tractatus. A Dialectical Interpretation. Cambridge: Cambridge University Press. Palmer, A. 1998. The Complex Problem and the Theory of Symbolism. In Bertrand Russell and the Origins of Analytic Philosophy, ed. R.  Monk and A. Palmer, 2nd ed., 155–182. Bristol: Thoemmes Press. Pears, D.F. 1987. The False Prison. Vol. 1. Oxford: Clarendon Press. Potter, M. 2008. Wittgenstein’s Notes on Logic. Oxford: Oxford University Press. Priest, G. 2014. One. Being an Investigation of the Unity of Reality and of its Parts, including the Singular Object which is Nothingness. Oxford: Oxford University Press. Putnam, H. 2000. Rethinking Mathematical Necessity. In The New Wittgenstein, ed. A. Crary and R. Read, 218–231. London: Routledge. Ramsey, F.P. 2013. The Foundations of Mathematics and other Logical Essays. Edited by R.B. Braithwaite. Mansfield Centre: Martino. Reck, E. 1997. Frege’s Influence on Wittgenstein: Reversing Metaphysics via the Context Principle. In Early Analytic Philosophy. Frege, Russell, Wittgenstein. Essays in Honor of Leonard Linsky, ed. W.W. Tait, 123–185. Chicago/La Salle, IL: Open Court. Rhees, R. 1966. The Philosophy of Wittgenstein. Ratio 8: 180–193. ———. 1969. ‘Ontology’ and Identity in the Tractatus. In Studies in the Philosophy of Wittgenstein, ed. P.  Winch, 51–65. London: Routledge & Kegan Paul. Ricketts, T. 1985. Frege, The Tractatus, and the Logocentric Predicament. Noûs 19 (1): 3–15.

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———. 1996. Pictures, logic, and the limits of sense in Wittgenstein’s Tractatus. In The Cambridge Companion to Wittgenstein, ed. H. Sluga and D.G. Stern, 59–99. Cambridge: Cambridge University Press. Ryle, G. 2009. If ’, ‘So’, and ‘Because. In Collected Papers. Vol. II: Collected Essays 1929–1968, ed. G. Ryle, 244–260. London: Routledge. Sellars, W. 1962. Naming and Saying. Philosophy of Science 29 (1): 7–26. Sheffer, H. 1926. Review of Principia Mathematica, Volume 1, 2nd ed. Isis 8: 226–231. Simons, P. 1992. The Old Problem of Complex and Fact. In Philosophy and Logic in Central Europe from Bolzano to Tarski. Selected Essays, ed. P. Simons, 319–338. Dordrecht: Springer. Skyrms, B. 1981. Tractarian Nominalism (for Wilfrid Sellars). Philosophical Studies 40 (2): 199–206. Sluga, H. 2012. Simple Objects: Complex Questions. In Wittgenstein’s Early Philosophy, ed. J.L. Zalabardo, 99–118. Oxford: Oxford University Press. Stenius, E. 1960. Wittgenstein’s Tractatus. A Critical Exposition of its Main Lines of Thought. Oxford: Basil Blackwell. Stern, D.G. 1995. Wittgenstein on Mind and Language. New  York: Oxford University Press. Sullivan, P.M. 2005. Identity Theories of Truth and the Tractatus. Philosophical Investigations 28 (1): 43–62. Tang, H. 2011. Transcendental Idealism in Wittgenstein’s Tractatus. The Philosophical Quarterly 61 (244): 598–607. Tejedor, C. 2015. The Early Wittgenstein on Metaphysics, Natural Science, Language and Value. London: Routledge. Textor, M. 2009. Unsaturatedness: Wittgenstein’s Challenge, Frege’s Answer. Proceedings of the Aristotelian Society 109: 61–82. Travis, Ch. 2011. Objectivity and the Parochial. New York: Oxford University Press. White, R.M. 2006. Wittgenstein’s Tractatus Logico-Philosophicus. New  York: Continuum. Wilke, A.-U. 2006. Philosophie und Stil. Eine Verhältnisbestimmung dargestellt an Berkeley, Kant und Wittgenstein. Göttingen: V&R unipress. Winch, P. 1969. Introduction: The Unity of Wittgenstein’s Philosophy. In Studies in the Philosophy of Wittgenstein, ed. P.  Winch, 1–19. London: Routledge. ———. 1987. Language, Thought and World in Wittgenstein’s Tractatus. In Trying to Make Sense, ed. P. Winch, 3–17. Oxford: Blackwell. Zalabardo, J.L. 2015. Representation and Reality in Wittgenstein’s Tractatus. Oxford: Oxford University Press.

4 Case Study: The New Wittgenstein

This section consists in a critical examination of the resolute reading (the so-called New Wittgenstein). First, I give a logical geography of the current debate (Sect. 4.1). Next, I review the three main challenges the resolute reading is facing, against the backdrop of which I develop my own argument intended to show that the resolute reading is both exegetically and philosophically problematic (Sect. 4.2). Finally, I provide a summary and synthesis of the results reached so far in light of the realism-idealism problematic (Sect. 4.3).

4.1 The Debate The resolute reading has its roots in Cora Diamond’s essay “Throwing Away the Ladder,” in which she presents a rigorous interpretation of the Tractarian notion of nonsense, a focus that has been dominating the agenda of the debate ever since.1 The controversy revolves around the notoriously opaque ending of Wittgenstein’s early masterpiece: My propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when he has © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 M. Bartmann, Wittgenstein’s Metametaphysics and the Realism-Idealism Debate, https://doi.org/10.1007/978-3-030-73335-3_4

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used them—as steps—to climb up beyond them. (He must, so to speak, throw away the ladder after he has climbed up it.) (TLP: 6.54)

This remark is one of many examples in Wittgenstein’s work displaying his seismographic sense of the logico-semantic status of his own statements. The reason why this passage is essential consists in its generating a paradox, or at least a fundamental tension that threatens to rescind the entire book’s very intelligibility. The metatheoretical statement expressed in this passage—that at the end of the book the propositions contained therein are to be recognized as nonsensical—therefore poses the serious problem as to how we are to assess the apparently meaningful theses and arguments given prior to this declaration. The “frame” of the Tractatus (comprising metatheoretical statements as well as remarks on philosophizing in general, paradigmatically occurring in the Preface and the Conclusion) appears to be at odds with its “body” (comprising all other statements, i.e. those making up the actual theory putatively developed in the Tractatus).2 Two main lines of response have been developed to account for this enigmatic conclusion, both of which rest in turn mainly on the question whether or not Wittgenstein is advancing a philosophical theory. So-called standard readers (roughly those commentators not subscribing to the resolute reading) answer this question in the affirmative, whereas resolute readers do not. Both standard and resolute readers can be further subcategorized into two variants. I will follow the literature with slight modifications and call the first variant of the standard reading realist and the second one idealist. Accordingly, the first variant of the resolute reading is known as weak resolutism (which is the Diamond-Conant position) and the second one as strong resolutism. But regardless of whether resolute readers defend the weak or strong variant, almost all resolute readings deny the following two claims: 1. The propositions of which Wittgenstein famously says that they are “nonsensical” (TLP: 6.54) somehow “convey ineffable insights.”3 2. Recognizing those propositions as nonsensical requires “the application of a theory of meaning” specifying “the conditions under which a sentence makes sense and the conditions under which it does not.”4

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That is why most resolute readers have homed in on Peter Hacker, who is not only the most influential proponent of the targeted view but also the most outspoken critic of the resolute reading.5 As we’ve seen in Sect. 3, according to the realist reading (such as Pears-­ Malcolm’s ) Wittgenstein still engages in the traditional philosophy-as-­ theory project, purporting to explain how language “hooks on” to a transcendent world that has a structure of its own in the strictest possible sense.6 This sort of theoretical undertaking quickly follows once we have accepted the notion of a mind-independent reality unaffected by the emergence or presence of concept-mongering creatures like us. For, if we conceive of language and reality as being mutually independent, the question naturally arises how it’s possible to forge a link between the two. Since the realist view holds that the structure of reality dictates the structure of language, the question becomes “What must the structure of language be like in order for it to represent reality?” The realist reading, therefore, starts with an analysis of the structure of the world (as does, apparently, the opening of the Tractatus) and deduces from it the conditions any language has to meet if it is to represent the world. The idealist reading, however, rejects the presuppositions of the realist reading and turns around the order of analysis. One way of doing this, as we’ve seen in connection with the Ishiguro-McGuinness position, is to reverse the “direction of fit” so that the reference relation is determined by language use. Another but similar way proceeds in a more Kantian fashion, according to which Wittgenstein is said to develop a theory that draws “the limits of what can be represented. By considering the essence of representation he attempts to say what the world must be like in order to be represented at all.”7 From this the (transcendental) idealist character becomes quite clear. Assuming that the world’s logical form is not to be found in the world itself leads to the conclusion that the mind is responsible for the desired unity “in which everything is held together, an abstract, logical unity which contributes nothing to what the world is like but constrains what it could be like.”8 Representational content so conceived is the result of a joint venture in which the mind contributes the form and the world provides the content. The so-called picture theory of meaning in the Tractatus is then viewed as a transcendental argument that deduces the structure of the world by analyzing the structure of language.9

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By inverting the “direction of fit” between language and reality, idealist readings abandon the notion of a mind-independent reality set over against us by emphasizing the active role language and the mind plays in the constitution of reality. Although idealist readings appear superior to realist readings in that they account for the involvement of subjectivity, they run the risk of turning logic into something that is transcendentally ideal and hence subjective—and there are, as I argued in Sect. 3.1, good reasons to deny that Wittgenstein ever conceived of logic as being merely a formal ingredient of the mind. As Hutto rightly observes, instead of adhering to the Kantian project “Wittgenstein’s position was closer to Hegel’s in this regard.”10 Regardless of their diametrically opposed views when it comes to the “direction of fit” between language and reality, both the realist and the idealist reading agree on their answer to Wittgenstein’s problematic concluding remarks by allowing for some form of inexpressible content.11 Whereas, strictly speaking, the propositions of the Tractatus are plain, mere nonsense, they nevertheless succeed in gesturing or hinting at that which cannot be expressed but still be grasped. Theoretical propositions concerning the structure of language may turn out to be nonsensical under closer logical inspection, but they are nevertheless capable of conveying otherwise ineffable philosophical insights, which is why the standard reading is sometimes also called the “ineffability reading”.12 To account for this kind of inexpressible content, Hacker introduced a distinction between misleading nonsense and illuminating nonsense by implicitly drawing on the distinction between saying and showing established in the Tractatus: Philosophers try to say what can only be shown, and what they say, being nonsense, does not even show what they try to say. Nevertheless, even within the range of philosophical, covert nonsense we can distinguish, as we shall see, between what might (somewhat outrageously) be called illuminating nonsense, and misleading nonsense. Illuminating nonsense will guide the attentive hearer or reader to apprehend what is shown by other propositions which do not purport to be philosophical; moreover it will intimate, to those who grasp what is meant, its own illegitimacy.13

Deploying this distinction between misleading and illuminating nonsense enables the standard reading to preserve the traditional conception of the Tractatus as advocating a substantive philosophical theory. Once we are

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brought to recognize the depth of the difference between that which can be said and that which can only be shown, traditional metaphysics can be dispensed with altogether. If we acknowledge that a theory of meaningful discourse necessarily violates its own conditions, we come to realize that all endeavors to put into words the fundamental features of language are misguided. According to the standard reading, there is something that in principle outruns the limits of language—the inexpressible—but this something can still be “apprehended” or “grasped” by virtue of the Tractarian propositions that “hint” or “gesture” at the intended but inexpressible content. The crucial point of the standard reading is not so much to eliminate the insights of traditional metaphysics but rather the doomed-to-failure attempt to express them. The standard reading, although concluding that it’s in general impossible to frame meaningful propositions regarding facts about the essential features of language and reality, insists that we, after having carefully read the Tractatus, are being “left holding on to some ineffable truths about reality after one has thrown away the ladder.”14 In trying to express the fundamental features of language we inevitably end up producing nonsense. The logical structure of language cannot provide the resources for the articulation of its own analysis because its very nature is to point to something other than itself—reality. The expressive character of language is thus essentially limited. It resembles a spotlight in that it can only illuminate its surroundings, never itself: Categorical necessities are reflected in the formation-rules of language, but cannot be expressed in language. Any attempt to express them involves the use of formal concepts and hence the violation of rules of logical syntax.15

A big part of the reason why the notion of a theory being put forward in the Tractatus is anathema to resolute readers lies in the fact that theorizing seems to imply certain commitments that cannot be reconciled with what they believe is the very point of the Tractatus. One of these commitments is supposed to be that a theory of meaning demarcating the bounds of sense or determining the limits of language—understood as a body of doctrines specifying criteria under which a sentence makes sense—entails the possibility of an illegitimate but still informative kind of semantic content resulting from a violation of the rules of logical syntax laid down by the theory.16 Candidates for this logically illegitimate yet illuminating kind of

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nonsense are the ineffable truths putatively shown but not said in the Tractatus, which is exactly what resolute readers deny.17 For resolute readers there is no such thing as nonsense that is somehow illuminating. Resolute readers hold that, from a logical point of view, there is only one kind of nonsense, namely plain nonsense—mere gibberish such as “piggly wiggle.”18 A nonsensical sentence is always the result of “a failure of determination of sense”19 owing to “our failing to mean anything by these words”20 and never of the “incompatible senses the words already have.”21 That is why the resolute reading endorses what is sometimes called the “austere” conception of nonsense as opposed to a “substantial” conception of nonsense usually endorsed by (or allegedly implied by) the standard reading.22 The question of the possibility of an illegitimate semantic content resulting from a violation of logical syntax is vital because with it the need for a theory of meaning falls as well. If there is no illegitimate semantic content to be ruled out by a theory of meaning, then all we have to do is to rely on our ordinary capacity for distinguishing between sense and nonsense: The Tractatus seeks to bring its reader to the point where he can recognize sentences within the body of the work as nonsensical, not by means of a theory which legislates certain sentences out of the realm of sense, but rather by bringing more clearly into view for the reader the life with language he already leads—by harnessing the capacities for distinguishing sense from nonsense (for recognizing the symbol in the sign and for recognizing when no method of symbolizing has yet been conferred upon a sign) implicit in the everyday practical mastery of language which the reader already possesses.23

Another commitment seemingly implied by a philosophical theory is the presupposition of an external standpoint from which it’s judged how things are independently of us. And this is unacceptable for resolute readers given that such a “view from sideways on” is supposed to be one of the main targets throughout Wittgenstein’s writings. Denying that Wittgenstein ever harbored theoretical intentions is essential, for, if we: cast Wittgenstein as advancing some form of theory, even modestly defined, it follows that he must have been offering proposals about how things stand independently of us. But if so, then we cannot take seriously some of

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his most important insights about how philosophy must be pursued, given our place in the world.24

As a consequence, resolute readers conclude that Wittgenstein’s task was purely therapeutic and hence never intended to gain substantive theoretical insights into the nature of language, thought, and reality. Reading the Tractatus is more similar to attending a therapy session in which the patient is, unbeknownst to her, under the spell of a host of philosophical illusions and confused preconceptions that are being worked through in the healing process and eventually recognized as such. Really throwing away the ladder and not “chickening out,”25 then, means letting go of philosophy as a positive, constructive discipline and realizing that it’s nothing but a therapeutic activity trying to liberate us from intellectual pseudo-problems. Resolute readers go even further than that. For, admitting that there are pseudo-problems tricking our philosophical mind presupposes their meaningfulness, that there was something intelligible yet misleading that had put us on the wrong track. But, strictly speaking, even that turns out to have been an illusion all along. A sentence like “The world is everything that is the case” neither advances a philosophical thesis, nor is it the cornerstone of a wrong metaphysics to be eventually overcome, nor does it express a confused notion philosophers are prone to—it simply doesn’t express anything because we have failed to make sense of it by having failed to attribute meaning to (parts of ) this particular combination of signs. At the end of the book, we are therefore not left with any metaphysical knowledge of the structure of language, thought, and reality but rather gain a certain insight into ourselves—the insight into our susceptibility to get lost in philosophical reflection. The only way “to free oneself from such illusions is to enter into them and explore them from the inside.”26

4.2 The Resolute Reading Before turning to the critique of the resolute reading advocated by Cora Diamond and James Conant, I’ll briefly present and assess the elucidatory reading by Marie McGinn and Daniel Hutto. This reading has been developed as a response to the dissatisfaction with the standard reading

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on the one hand and as a critique of the resolute reading on the other.27 This will help sharpen the framework of the debate and prepare the ground for evaluating the resolute reading. The Elucidatory Reading On the face of it, the elucidatory reading satisfies the basic requirements for qualifying as (a version of ) the resolute reading because it also denies, first, that the nonsensical propositions of the Tractatus convey ineffable insights and, second, that the Tractatus puts forward a theory of meaning by means of which these nonsensical propositions can be recognized as such (both of which claims run counter to the standard reading). But although the elucidatory reading shares with the resolute reading the rejection of any type of theoretical reading, it doesn’t draw the conclusion that the bulk of the Tractatus must be regarded as plain nonsense. That is why the elucidatory reading is also sometimes called a middle or third way. McGinn characterizes her approach as follows: The metaphysical [i.e. standard] and therapeutic [i.e. resolute] approaches to TLP offer us an unappealing alternative between reading Wittgenstein’s remarks as nonsense that conveys ineffable truths about the world and as nonsense that conveys nothing. […] The elucidatory reading is intended to enable us to find a way between these two alternatives, one which allows the remarks to achieve something, while stopping short of holding that they convey ineffable truths about reality.28

And in a very similar vein Hutto writes that philosophy, according to Wittgenstein, “clarifies our understanding of important philosophical matters,”29 which is why the apparently theoretical remarks in the Tractatus are “in fact meant to be nothing more, or less, than a non-­ explanatory working out of what is required if we are to represent the world to ourselves.”30 Instead of “throwing away the baby together with the bathwater”31 and dispense altogether with what the resolute reading deems plain nonsense, both McGinn and Hutto try to extract from the Tractatus valuable insights about language, logic, and thought, while at the same time denying any metaphysical or ontological ambitions on Wittgenstein’s part. The opening of the Tractatus ought to be reinterpreted as exposing an “ontological myth,”32 a declaration of “the bankruptcy of the very idea of philosophical theorising itself.”33 Rather, its purpose is to gain clarity about the essence of language.

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Taking this route seems to offer the possibility of having one’s cake and eat it, too. It allows us to preserve much of the Tractatus as a non-­ theoretical investigation into the very conditions of representation while resisting the temptation of metaphysics. Wittgenstein’s project is said to consist in laying bare the structure of language, logic, and thought—but not reality. The idea: that we are getting outside the symbolism and saying something about its relation to a transcendent realm with an intrinsic structure is indeed an illusion, but the illusion lies in our taking what belongs to the logic of the language in which we express propositions that can be tested for truth or falsity, for substantial doctrine. What we come to see is that what Wittgenstein is doing in these remarks is not metaphysics but logic.34

The insight into the impossibility of transcending language and of an external standpoint is, according to the elucidatory reading, to prevent us from committing the fallacy of deriving metaphysics from logic. The Tractatus is nothing more than an inquiry into the essential features of language, logic, and thought, which in no way licenses drawing any metaphysical conclusions, the ontological tone of the book notwithstanding. Regarding the relation between language and the world, we ought to take heed of Wittgenstein’s warning (allegedly) issued in the Preface, namely that it’s “not possible to leave our side of the fence […].”35 Various commentators have pointed out that the elucidatory reading turns out to be unstable because it threatens to collapse into either the standard or the resolute reading.36 The challenge for the elucidatory reading is to reconcile its claim that the Tractatus contains elucidations and clarifications about the essential features of language, logic, and thought (in contrast to the resolute reading) with its claim that these elucidations and clarifications don’t amount to a philosophical theory demarcating the bounds of sense (in contrast to the standard reading). Hutto addresses this problem with reference to Wittgenstein’s later works and suggests understanding the elucidatory remarks of the Tractatus as fulfilling the same role as the “grammatical remarks” in the Philosophical Investigations: the propositions of the Tractatus neither express substantial theses nor convey new information. Instead, they simply serve as

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“reminders of what we ought already to know.”37 Like truth-tables, which only display the space of logical possibilities in which propositions can interrelate, the propositions of the Tractatus convey no information at all, but in “elucidating and clarifying, they show what cannot be said. They tell us nothing new. Rather, they merely, and quite literally, re-present that which is already immanent in our use of logic.”38 This is why “philosophy can at best clarify and make perspicuous that which is already known to us.”39 And McGinn writes that Wittgenstein’s remarks, though containing substantive insights into language, logic, and thought, are “entirely transitional: they do not express propositions with sense, and nor do they convey truths that cannot be expressed in propositions with sense, but they serve to bring about a clarified vision of the logical order […].”40 Given the background of the standard and resolute reading characterized above, the tension running through the elucidatory reading becomes quite evident. For, as we’ve seen, it insists on the constructive, positive (non-therapeutic) approach of the Tractatus, claiming that it contains a large number of valuable insights into the nature of language, logic, and thought (against the resolute reading), without adding up to a philosophical theory because these insights are supposed to be nothing but non-explanatory reminders and elucidations of the obvious (against the standard reading). It’s doubtful, though, whether the elucidatory reading manages to navigate these waters without running aground on the reef of either the standard or the resolute reading. First of all, it should be noted how curious it is that the question “Theory or no Theory?” continues to be one of the most controversial subject-matters separating resolute (and elucidatory) readers from standard readers considering that, in the literature, not much substance is being given to what actually constitutes putting forward a theory, and what the implications are of doing so (as opposed to “mere” elucidations, clarifications, and reminders). What’s more, some standard readers have also protested against being committed to attributing to Wittgenstein a theory of meaning as well as thinking of Tractarian nonsense as violations of logical syntax in a way that entails substantial but ineffable semantic contents.41 Be that as it may, when talking about a theory Wittgenstein is allegedly holding, most resolute readers seem to have in mind Hacker’s terse slogan

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of the Tractatus as setting forth a body of doctrines “clarifying the bounds of sense.”42 Resolute readers take this to mean that Wittgenstein develops a theory of meaning that specifies the “conditions under which a sentence makes sense and the conditions under which it does not.”43 Understood this way, the Tractatus purportedly provides us with definite semantic criteria, which results in the command of a clear view of the workings of language enabling us to distinguish between sense and nonsense. And providing such criteria was tantamount to offering a theory.44 But even if the elucidatory reading succeeds in quashing the theory objection leveled against it, on the grounds that the objection is based on a mere terminological quibble over whether the elucidations, clarifications, and reminders of the Tractatus should be taken as constituting a theory or not, there still remain other central features of the elucidatory reading that make it difficult to distinguish it from both the standard and the resolute reading. There are, in particular, several passages in which McGinn and Hutto articulate their respective views in a way that seems like a clear commitment to ineffable contents, which is obviously among the defining traits of the standard reading, proximity to which they are at pains to avoid. Here’s Hutto on the status of logical syntax: Thus logico-syntactic rules for permissible combinations inherently mirror the logical form of the world and permit us to make sense of it, but they are revealed only retrospectively and on specific occasions of use. It is not possible to anticipate them or give them a general characterization. In no way can they be specified or codified.45

Although Hutto explicitly rejects all proposals trying to explain how, according to the Tractatus, language “‘hook[s] on’ to reality”46 (because this would constitute advancing a theory), this passage seems to outline just such a proposal. Not only is the claim that language has to “mirror the logical form of the world” a traditional expression of the realist stripe of isomorphism, which in itself already casts doubt on Hutto’s claim that Wittgenstein’s “reminders” don’t constitute a theory.47 But he also claims that the rules of logical syntax grounding all acts of sense-making cannot “be specified or codified.” This seems merely another way of taking the rules of logical syntax to be inexpressible, which is a cornerstone of the standard reading.

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A similar dissonance can be detected in McGinn’s account. Although she reassures us that on her reading Wittgenstein’s “remarks are indeed plain nonsense,”48 they nevertheless possess a transitional character elucidating the workings of language, logic, and thought, in such a way as to allow us “to acknowledge that, once Wittgenstein’s remarks have achieved what they are intended to achieve, they can be completely left behind.”49 This understanding of Tractarian nonsense is exactly what resolute readers criticize the standard reading for, namely simultaneously taking the propositions of the Tractatus to be nonsense and yet be somehow expressive of something, regardless of how subtle their being expressive might be construed.50 In sum, the elucidatory reading seems to oscillate between the standard and the resolute reading owing to its difficulties to reconcile the conflicting features of the standard and the resolute reading it’s eager to preserve. On the one hand, its attempt to invest the nonsensicality of Tractarian propositions with an elucidatory function (McGinn), and the near-acknowledgment of inexpressible contents (Hutto), respectively, makes the elucidatory reading come dangerously close to the standard reading.51 On the other hand, if the elucidatory reading were to cut all ties with the standard reading by eliminating the last remnants of ineffable contents still lingering in its approach, then the elucidatory reading threatens to coincide with the resolute reading. It therefore seems there can be no middle ground between standard and resolute readings. Whether the resolute reading itself succeeds in formulating a coherent account of what goes on in the Tractatus is a question to which I’ll now turn. The Resolute Reading Arguments made and objections raised against the resolute reading can be categorized broadly into two types: internal and external criticism.52 External criticism is based on source material other than but surrounding the Tractatus (before and after), and critics try to establish that the resolute reading is inconsistent with the views (and sometimes explicit comments on the Tractatus) Wittgenstein expressed in this source material.53 Internal criticism pertains to the resolute reading itself, and here critics try to establish either that the resolute reading is inconsistent with (various aspects of ) the Tractatus or that the resolute reading is itself inconsistent because it holds contradictory views or puts forward flawed arguments (or both).

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In what follows, I’ll exclusively focus on and develop an internal criticism of the resolute reading and try to show that it’s inconsistent or at least committed to incompatible views. I have two main reasons for disregarding external criticism. First, a lot of arguments and objections resting on external evidence have already been meticulously detailed in the literature.54 Second, and more importantly, even if one finds (as I do) the evidence of the external criticism compelling, this is in itself not enough to yield a decisive verdict on the viability of the resolute reading. For, the assessment of external evidence is itself open to interpretation and requires the context of an account of Wittgenstein’s wider philosophical approach (early and later) in order to determine the status of particular writings and their connection to one another. And resolute readers have proved to be very adept at explaining the external evidence seemingly contradicting their approach by supplying just such a kind of context.55 This is a huge topic in the literature, where the debate revolving around the resolute reading has also provoked a larger debate about the continuity between early and later Wittgenstein and, as a consequence, about how to understand Wittgenstein’s philosophy in general. Since the evaluation of external evidence is dependent on one’s big picture view on Wittgenstein, the development and defense of which is beyond the scope and purpose of this subsection, I’ll confine myself to internal criticism. But this is no disadvantage. On the contrary, if the resolute reading can be shown to be inconsistent according to its own premises, no further (external) evidence is needed to reject it. Since my argument is related to and builds on points already made in the literature, I’ll review what I consider the three most challenging objections to the resolute reading before developing my own. The Frame-and-Body Objection The first objection consists in a methodological point concerning one of the key distinctions on which the resolute reading depends to articulate its view, namely the distinction between the “frame” and the “body” of the Tractatus. Obviously, some such distinction is needed because the penultimate Tractarian claim that all its propositions are nonsensical is paradoxical. The frame, then, is exempt from the verdict of nonsensicality and encompasses all those propositions outlining the aim and method of the book as well as providing instructions for how it is to be read. The body is simply defined as

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composing those propositions not belonging to the frame. But unlike the (meaningful) propositions of the frame, the (nonsensical) propositions of the body constituting the rungs of the ladder have to be thrown away after having served as elucidations.56 The resolute reading in its early stages restricted the frame to the Preface and the concluding remarks.57 But in elaborating their account, partly in response to waxing resistance to it, resolute readers were forced over the years to resort to more and more propositions of the Tractatus not occurring in the Preface and the concluding remarks. To bolster their case, resolute readers added to the frame a wide variety of propositions ranging from linguistic principles and distinctions58 to metaphilosophical remarks59 and important concepts.60 Naturally, this provoked critics to raise objections against this form of hermeneutic cherry picking. Whenever a proposition of the Tractatus could be used in support of their interpretation, critics complained, the resolute reading saved it from nonsensicality by putting it into the frame as a further meaningful instruction for how to read the book. The distinction between frame and body seemed arbitrary because it didn’t appear to be based on textual evidence but rather on ad hoc interpretative needs.61 Resolute readers have addressed this issue by clarifying that the distinction between frame and body must not be understood as a spatial but as a functional one: it is “its role within the work”62 and not the place of occurrence determining whether a particular remark is part of the frame or the body. At first sight, this seems to be begging the question since we are now simply owed an answer to the question according to which semantic criteria we are to decide what role a certain proposition plays. Worse yet, resolute readers cannot appeal to semantic criteria distinguishing between meaningful (frame) and nonsensical (body) propositions because they reject the very idea that the Tractatus offers a theory of meaning establishing a distinction between sense and nonsense by means of semantic criteria. But resolute readers have made a virtue of necessity and replied that there “can be no fixed answer to the question what kind of work a given remark within the text accomplishes. It will depend on the kind of sense a reader of the text will (be tempted to) make of it.”63 Instead, recognizing whether a particular remark is meaningful or nonsensical is an

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“inherently piecemeal”64 process, such that a decision on the matter can be made only on a case-by-case basis. As we’ve seen, this process of recognition is supposed to merely involve our ordinary, non-theoretical capacity for distinguishing between sense and nonsense, a practical ability the reader already possesses qua language user anyways.65 Critics have retorted, however, that now it would be dependent on the reader of the Tractatus whether a certain proposition was part of the frame or the body. And since this may vary from reader to reader, depending on her respective semantic and philosophical skills, the objection of arbitrariness can be raised again. One reader may wrest sense from a given remark and keep it as a meaningful part of the frame, whereas another reader may take the very same remark to be nonsensical and discard it as part of the body. So the decision whether a particular proposition in the Tractatus belongs to the frame or the body cannot be made without reference to a reader’s individual abilities and preferences. But then the inevitable follow-up question how to adjudicate between conflicting decisions from different readers seems next to impossible to answer. This introduces a certain amount of instability into the distinction between frame and body.66 The Elucidation Objection The problem of whether a given remark in the Tractatus is to be considered nonsensical or not is related to another problem regarding nonsensical propositions, and this brings us to the second objection. For, even if we bracket for the moment the difficulties with determining the status of Tractarian propositions and pretend, for the sake of argument, that this problem can somehow be solved, the next question then is how the nonsensical propositions accomplish their task of elucidation without falling into the ineffabilism for which the standard reading is criticized. We’ve already seen how resolute readers pointed out the difficulties and tensions underlying the elucidatory reading’s struggle with reconciling its anti-theoretical thrust and the willingness to take seriously that the propositions of the Tractatus are plain nonsense with its claim that these propositions can somehow serve as elucidations, clarifications, and reminders. Naturally, since the resolute reading also claims that the propositions of the body are plain nonsense yet serve as elucidations, one might wonder how this process is supposed to work without being

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affected by the same problems attributed to the elucidatory reading. The suspicion here is that the resolute reading, its emphatic reassurances notwithstanding, is also committed to attributing meaning in some form or other to the allegedly nonsensical propositions in order to account for their elucidatory function. This suspicion seems to be corroborated by some passages in Diamond, where she calls Wittgenstein’s propositions “transitional remark[s],”67 which in their entirety make up a “‘transitional’ vocabulary, the before-you-throw-away-the-ladder mode of speaking.”68 This suggests that the allegedly nonsensical propositions have some sort of semantic content after all, and critics have quickly pointed out this tension in the resolute reading’s account of elucidation: There are two ways to treat them [i.e. the transitional passages]. They can be taken to offer sound arguments against metaphysical enticement, in which case they are indeed meaningful sentences. Or they themselves have only an illusory meaningfulness, which is seen through as one progresses higher up the ladder in the escape from philosophical theorizing. These two possibilities pose a dilemma for the austere reading. If the transitional passages are meaningful, then the nonsense thesis is seriously compromised. […] If the passages, on the other hand, are themselves plain nonsense, then there is no argument or rational defense for the austere reading.69

Much like the elucidatory reading, the resolute reading is charged with being incapable of reconciling their austere conception of nonsense (the view that the nonsensical propositions are plain nonsense, mere gibberish) with the elucidatory function the nonsensical sentences are supposed to perform. But resolute readers have rejected this kind of objection because they believe it to be based on a misrepresentation of their position.70 First, they re-emphasized that the nonsensical propositions are indeed plain nonsense and don’t differ, from a logical point of view, from mere gibberish such as “piggly wiggle.” Nonsensical propositions “are as it were internally all the same: all are einfach Unsinn, simply nonsense.”71 The semantic content of every nonsensical proposition is exactly the same, to wit: nil. But doesn’t this view imply the possibility to replace each and every nonsensical proposition of the Tractatus with instances of “piggly wiggle” without changing one semantic iota of the book? This

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clearly seems absurd. And it’s at this point where resolute readers, as a second step, appeal to a non-semantic kind of content purportedly also involved in the process of making or failing to make sense of a proposition, namely psychological content. Logically speaking, all nonsensical propositions belong to the same kind of nonsense (mere nonsense), but psychologically speaking they may belong to different kinds of nonsense. To which kind it belongs depends on both the potential of a particular nonsensical proposition to generate certain psychological effects and the receptiveness of a reader’s mind to those effects. For example, whereas for resolute readers “The world is all that is the case” and “piggly wiggle” are indistinguishable regarding their semantic content (there is none because they are mere nonsense), they are nevertheless different regarding their power to induce a particular psychological content in the recipient since the former (unlike the latter) may give rise to the appearance of expressing a philosophical thesis. As Diamond writes: That, then, is one of the ideas in the Tractatus about the role of imagination in the producing of metaphysical nonsense. We are attracted by certain sentences, certain forms of words, and imagine that we mean something by them. We are satisfied that we mean something by them because they have the mental accompaniments of meaningful sentences.72

Psychological contents accompany the engagement with both meaningful and nonsensical propositions, which is why the reader is prone to falsely attribute meaning to propositions lacking in semantic content. In such cases, the reader falls prey to an “illusion”73 or even “hallucination”74 of meaning because she mistakes her own psychological content for an allegedly semantic content by projecting the products of her confused imagination into propositions that are actually void of any semantic content. Nonsense has nothing to do with the proposition itself and everything to do with the reader’s relation to the proposition. The “nonsensicality is to be traced, not to the logical structure of the sentence, but to our failure to mean something by it.”75 Given this diagnosis of the origin of nonsense (the confused reader), resolute readers characterize the purpose of the Tractatus in general, and

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the aim of its conception of nonsense in particular, as consisting in guiding the reader through a piecemeal process of disillusionment. Accordingly, the realization that the propositions of the body of the Tractatus are nonsensical doesn’t yield any so-called ineffable truths, but rather results in the reader’s becoming disabused of certain philosophical misconceptions: Thus the elucidatory strategy of the Tractatus depends on the reader’s provisionally taking himself to be participating in the traditional philosophical activity of establishing theses through a procedure of reasoned argument; but it only succeeds if the reader fully comes to understand what the work means to say about itself when it says that philosophy, as this work seeks to practice it, results not in doctrine but in elucidations.76

The reader seemingly engages with philosophical theses and arguments presented and defended by Wittgenstein, thereby climbing one rung of the ladder after another. The Tractatus has accomplished its goal if the reader realizes that, at the end of the book and after being confronted with the nonsensicality of its propositions, she didn’t gain any philosophical insights but got rid of a particular illusion, the illusion that she was engaging with meaningful propositions conveying philosophical theses and arguments in the first place. The reader doesn’t acquire knowledge about language, thought, and reality, but clarity about herself, which she achieves once she recognizes that “the aim of Tractarian elucidation is to reveal (through the employment of mere nonsense) that what appears to be substantial nonsense is mere nonsense.”77 In short, Wittgenstein’s remarks serve as elucidations simply “by enabling us to recognize them as nonsense.”78 Unsurprisingly, commentators have focused in their critique on the somewhat obscure notion of psychological content, which is barely elaborated on by resolute readers. Here’s Roger White expressing his sheer incredulity about the plausibility of such an account: One reply that is wholly inadequate here is to say that, whereas it is the business of logic and philosophy to explain significant propositions, the illusion of a significant proposition is a psychological matter, and that there

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is a purely psychological difference between different kinds of nonsense. ‘Psychological’ here is a weasel word. […] What we need to understand is what it is about these words which creates this wide-ranging illusion, and that it is a question about language and the words, and not the psychology of the individual reader of the book.79

White’s point here is that establishing an asymmetry between sense and nonsense, the former being a purely logical matter (a property of meaningful propositions) and the latter being a purely psychological matter (a property of a confused state of mind), is simply without adequate justification. On what is this asymmetry based, and how exactly is the difference to be conceived? The problem is not the existence of psychological content per se; few would deny it. Rather, the psychological contents accompanying the processing of meaningful and nonsensical propositions alike (of whatever nature these psychological contents may actually be) are a highly individual affair, and they may vary from reader to reader. On the one hand, psychological contents are supposed to be completely dissociated from and unlike semantic contents because they are nothing but the fleeting goings-on in a particular reader’s mind accompanying the (apparent) understanding of propositions. On the other hand, however, psychological contents are apparently so deceptively similar to semantic contents as to trick almost every reader of the Tractatus into believing that philosophical theses and arguments are being expounded there. The “illusion” that the Tractatus presents a series of philosophical theses and arguments, including criticism of positions held by other philosophers, appears to be quite ubiquitous. It seems utterly mysterious how it’s possible for meaningless linguistic strings to have such uniform psychological effects. At the very least, then, much more needs to be said to explain the peculiar quality of the Tractatus to trigger a virtually universal and homogeneous semantic hallucination.80 The Compositionality Objection The distinction between semantic and psychological content on which the resolute reading’s account of Tractarian elucidation is built is deeply connected to the third problematic issue critics have raised and concerns the very core of its approach: the austere conception of nonsense itself. This conception is critical

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because it’s of a piece with the overall claim that the Tractatus does not pursue the philosophical project of “demarcating the bounds of sense”— that it does not develop a theory of meaning enabling us to distinguish between sense and nonsense by means of semantic criteria. The austere conception of nonsense and the no-theory view of the Tractatus are two sides of the same coin.81 Hence if the austere conception of meaning cannot be maintained, neither can the resolute reading itself. Recall the contentious issue, outlined in Sect. 4.1, between standard and resolute readers with respect to the nature of nonsense, which is predicated on whether or not it’s possible to violate the rules of logical syntax. Standard readers conceive of the rules of logical syntax as a specification of the logical roles of linguistic expressions together with their respective possibilities to combine into meaningful propositions. Nonsense is then considered to be the result of using meaningful expressions in a way that violates or at least doesn’t accord with the rules of logical syntax.82 The conception of nonsense underlying the standard reading may be called the clash-theory of nonsense because it holds a view of meaning according to which a proposition is nonsensical if meaningful expressions are put together in such a way as to bring about a conflict between their logical roles due to the misuse of one or more of the meaningful expressions involved. Resolute readers, by contrast, don’t believe there is such a thing as violating the rules of logical syntax at all. As we’ve seen in connection with the second objection to the resolute reading, nonsense is always a psychological and not a semantic matter. The reason for this is that nonsensical propositions are not the product of the clash of the logical roles the expressions already possessed prior to their combination into a supposedly meaningful proposition. Rather, we have failed to assign logical roles to those expressions in the first place: “If a sentence is nonsensical, then, on the view of nonsense that forms a part of any resolute reading, it contains a word or words to which no meaning has been given.”83 Take, for example, the proposition “Caesar is a prime number.” According to standard readers, this proposition is nonsense because of the collision of the incompatible logical roles of the respective expressions. Logical syntax dictates that expressions standing for numbers cannot meaningfully be predicated of expressions standing for persons. “Caesar”

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and “is a prime number” considered individually are perfectly meaningful expressions. However, in the combination “Caesar is a prime number” the phrase “is a prime number” is being misused because it’s not being used in accordance with the rules of logical syntax.84 Since the logical roles of the parts of the proposition are combined in a way prohibited by logical syntax, they clash with each other and produce nonsense. The proposition “Caesar is a prime number” is not void of meaning but composed of meaningful parts in the wrong way. Resolute readers object that the nonsensicality of “Caesar is a prime number” is not to be traced to a clash of incompatible logical roles, simply because the expressions contained in it don’t have logical roles. Instead, we are under the psychologically induced illusion to have given meaning to all the constituent parts of the meaningless string of signs “Caesar is a prime number” when in fact we have failed “to mean anything determinate by our words.”85 The disagreement between standard and resolute readers over the proper place of nonsense in general, that is, whether to locate nonsense in logically flawed propositions or in the psychological states of a confused mind, and the possibility of violating the rules of logical syntax in particular, is rooted in another prominent dispute in semantics. This is the dispute between atomism and wholism, of which the standard and resolute readings are representatives, respectively.86 The clash-theory underlying the standard reading represents a version of semantic atomism, since the notion of a clash between the logical roles of expressions clearly presupposes that the logical roles of the parts of a proposition can be identified independently of, and prior to, the formation of the proposition in question. As the example above makes clear, standard readers think the logical roles of the expressions “Caesar” and “is a prime number” are fixed before a logically untrained mind committed a category mistake by misusing these expressions and illegitimately putting them together. Conversely, the austere conception of nonsense advocated by the resolute reading rejects the clash-theory precisely because it’s implied by semantic atomism and embraces a version of semantic wholism instead. The background of the resolute reading’s wholism is derived from a very strong interpretation of the Tractarian version of Frege’s context principle:

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Only propositions have sense; only in the nexus of a proposition does a name have meaning. (TLP: 3.3)

Resolute readers take this to mean that the logical roles of expressions can only be individuated as parts of whole meaningful propositions. Since expressions are meaningful only when they figure as parts of a meaningful proposition, their logical role can therefore not be determined in isolation. Expressions occurring outside meaningful propositions or as “part” of nonsensical propositions cannot, by definition, possess any logical role. In short: One can identify the contribution the senses of the parts of a proposition make to the sense of the whole only if the whole has a sense—if it stands in some identifiable location with respect to the other occupants of logical space. According to the Tractatus, there are no examples of a proposition’s failing to make sense because its parts do not “fit” together.87

Given this rather strong version of semantic wholism, it didn’t take very long until critics have pointed out its Achilles’ heel. They argue that the semantic wholism of the resolute reading is incapable of explaining an essential feature of language every conception of meaning must account for: the compositionality of meaning.88 Here critics have attacked the resolute reading not only on exegetical grounds but on philosophical grounds as well because resolute readers defend semantic wholism both as a view held by Wittgenstein and also as a philosophically correct view of meaning. Regarding textual evidence, critics cite the following passages in the Tractatus purporting to be indicative of a compositionalist view of meaning and hence of an underlying semantic atomism: The meanings of simple signs (words) must be explained to us if we are to understand them. With propositions, however, we make ourselves understood. It belongs to the essence of a proposition that it should be able to communicate a new sense to us. A proposition must use old expressions to communicate a new sense. (TLP: 4.026–4.03)

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The capacity to form “new” propositions out of “old” constituents as well as the corresponding capacity to understand hitherto unknown propositions on the basis of their known constituents seems to speak heavily in favor of a compositionalist view of meaning. The “building block” model on which this view depends—the idea according to which we operate with independently meaningful expressions consonant with the rules of logical syntax—can then aptly be regarded as a version of semantic atomism. Regarding philosophical reasons telling against semantic wholism, critics try to establish that the context principle frequently invoked by resolute readers must be given a laxer interpretation, an interpretation that allows for words to have meaning outside the context of a proposition. Critics rely mostly on two types of examples to make their case. The first type of examples concerns encyclopedic entries, which are clearly cases in which words don’t occur as parts of a proposition. Here critics simply point out the absurdity of considering such isolated expressions as meaningless, in particular given that the definition or paraphrase following encyclopedic entries are a specification of their meaning, which would, again, be absurd if they had none.89 The second type of examples concerns translations. Not only do we not have the slightest difficulties in translating individual expressions such as “house” or “green,” which are also obvious cases in which words don’t occur as parts of propositions; dictionary entries are as meaningful as encyclopedic entries. But we can even translate nonsensical propositions. “Caesar is a prime number,” “César est un nombre premier,” and “Cäsar ist eine Primzahl” all seem perfect translations of one another. How is that possible if the constituent expressions are all equally meaningless?90 As we’ve seen, according to the semantic wholism of the resolute reading there is no such thing as meaningful expressions in isolation and hence no such thing as operating with semantic building blocks to form propositions because this would imply the possibility of semantic clashes in cases in which the operation with the building blocks goes wrong. Since semantic wholism acknowledges only whole propositions, it seems indeed difficult how it can muster the resources to explain the compositionality of meaning. The strategy of the resolute reading here is to deny the incompatibility of semantic wholism with compositionality by

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appealing to Frege’s context principle and its guiding notion of the primacy of judgment. According to their interpretation of Frege’s context principle (which they also attribute to Wittgenstein’s context principle in the Tractatus), a proposition does have meaningful parts contributing to the meaning of the proposition as a whole, but they function only as parts if the whole proposition is meaningful. In short: no whole, no parts.91 Whereas semantic atomism represents a bottom-up approach where antecedently meaningful expressions are (correctly or incorrectly) combined into (meaningful or nonsensical) propositions according to the prescriptions of logical syntax, semantic wholism exhibits a top-down model where meaningful expressions exist only as parts of propositions whose meaningfulness is an antecedent requirement for there to be and for us to identify the logical roles of the expressions composing them. Having reviewed the three biggest challenges the resolute reading is facing—which are, I believe, not decisive despite raising profound difficulties—the ground is prepared for my own argument. It consists of two parts. The first part is concerned with exegetical matters intended to show that the resolute reading is committed to views on the Tractatus that seem incompatible with one another. The second part is concerned with internal matters of the resolute reading itself intended to show that it’s based on premises that seem in tension with one another. The Exegetical Objection Let’s begin with the exegetical point and consider the two passages in the Tractatus serving as key witnesses (apart from the context principle) on which resolute readers build their case for the austere conception of nonsense. I’ll try to show that their analysis of these passages and the austere conception of nonsense attributed to it are incompatible with their semantic wholism. Here are the two passages in question: Logic must look after itself. If a sign is possible, then it is also capable of signifying. Whatever is possible in logic is also permitted. (The reason why ‘Socrates is identical’ means nothing is that there is no property called ‘identical’. The proposition is nonsensical because we have failed to make an arbitrary determination, and not because the symbol, in itself, would be illegitimate.) In a certain sense, we cannot make mistakes in logic. (TLP: 5.473)

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Frege says that any legitimately constructed proposition must have a sense. And I say that any possible proposition is legitimately constructed, and, if it has no sense, that can only be because we have failed to give a meaning to some of its constituents. (Even if we think that we have done so.) Thus the reason why ‘Socrates is identical’ says nothing is that we have not given any adjectival meaning to the word ‘identical’. For when it appears as a sign for identity, it symbolizes in an entirely different way—the signifying relation is a different one—therefore the symbols also are entirely different in the two cases: the two symbols have only the sign in common, and that is an accident. (TLP: 5.4733)

At first sight, these passages seem to reflect the austere conception of nonsense. Not only is there no mention of violations of logical syntax, category clashes, and the like (nor anywhere else in the Tractatus). It’s also expressly stated that nonsense, in general, arises out of a failure to give meaning to certain constituents of a supposedly meaningful proposition. In particular, the reason why “Socrates is identical” is nonsensical lies in our failure to have given an adjectival meaning to the word “identical,” such that the correct diagnosis of the nonsensicality is the absence of meaning due to lacking meaning determinations and not the presence of an illegitimate proposition composed of wrongly combined constituents.92 The resolute reading seems to be right in assuming that, according to Wittgenstein, nonsense is essentially a sin of omission: the result of having failed to do something (making meaning determinations) rather than the result of having done something wrong (putting together meanings contrary to logical syntax). Let’s take a closer look. According to the austere conception, a proposition is nonsensical if “it contains a word or words to which no meaning has been given,”93 echoing Wittgenstein’s words that a nonsensical proposition is the result of a failure to “give a meaning to some of its constituents.” As I’ve already mentioned, resolute readers put the utmost emphasis on this point and make it repeatedly.94 Perhaps most explicit is Diamond in commenting on Wittgenstein’s example: What I am emphasizing is that on Wittgenstein’s view, the only thing wrong with ‘Socrates is identical’ is the absence of an adjectival meaning for ‘identical’, where the need for a meaning may be hidden from us by the fact that the word ‘identical’ has other uses in which it is meaningful.95

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Resolute readers stress that in a nonsensical proposition there is at least one expression to which no meaning has been given. But this implies that the proposition contains expressions that, in some sense, do have meaning. For, if nonsensical propositions only contained exclusively meaningless expressions, why say only some of them are meaningless? As opposed to which ones? More precisely, what is the point of singling out some of the meaningless expressions as the source of the nonsensicality of a proposition given that they all are supposed to be meaningless? The problem is, however, that this is exactly the thesis of semantic wholism defended by resolute readers. Expressions are meaningful only as parts of a meaningful proposition. Hence where we don’t have a meaningful proposition there are no meaningful expressions either. None whatsoever. If the resolute reading were to admit of the possibility that a nonsensical proposition is composed of meaningful as well as meaningless expressions, then it would endorse a version of the clash-theory. As we’ve seen, resolute readers are unequivocal about this: Again, what is being excluded [by Wittgenstein’s context principle] is the idea of meaningful symbols being combined in such a way that the whole itself has no sense or has the wrong kind of sense: unless the sentence we are dealing with has a sense, we do not really have meaningful constituents at all.96

And there are numerous other passages where resolute readers give distinct expression to their semantic wholism. They claim that “the Tractatus is centrally concerned to repudiate […] the possibility of identifying the logical (or grammatical) category of a term outside the context of legitimate combination”97 and that one “can identify the contribution the senses of the parts of a proposition make to the sense of the whole only if the whole has a sense.”98 Again: no whole, no parts. However, the unmistakable commitment to semantic wholism is impossible to square with the austere conception of nonsense, according to which nonsense arises out of a failure to give meaning to some of the expressions occurring in a supposedly meaningful proposition. For, why would Wittgenstein say that the only thing wrong with “Socrates is identical” is that we have failed to give an adjectival meaning to “identical” if,

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as semantic wholism implies, it is equally meaningless as “Socrates” and “is”? Why focus on “identical” rather than the other meaningless expressions? In fact, why give any specific explanation for the meaninglessness of any nonsensical proposition if the reason for its meaninglessness is always the same, namely that all (and not only some) expressions occurring in a nonsensical proposition are meaningless? It’s simply futile to charge one or more expressions of a nonsensical proposition with meaninglessness, as the austere conception of nonsense has it, if, in such cases, all expressions are meaningless. Yet this is exactly what semantic wholism states. The contradiction is thus the following. On the one hand, the resolute reading is wedded to semantic wholism according to which expressions have no meaning except as parts of meaningful propositions. On the other hand, the austere conception of nonsense, according to which nonsense arises when certain expressions of a proposition haven’t been given meaning, implies a distinction between meaningful and meaningless expressions within nonsensical propositions, for otherwise it would be incoherent (or at least pointless) to claim that nonsense consists in the lack of meaning of some expressions. But one implication of semantic wholism is precisely the denial of any such distinction. Hence semantic wholism implies the negation of the austere conception of nonsense and vice versa. However, the resolute reading is committed to both. The specifically exegetical problem here becomes clear by reflecting that semantic wholism has, almost by definition, no resources to explain why a proposition is meaningless. Any such explanation presupposes that we be able to identify a “linguistic culprit” responsible for the lack of meaning (like “identical” in “Socrates is identical”). But for semantic wholism there can be no such thing as a linguistic culprit. Since nonsensical propositions don’t constitute a meaningful whole there are no meaningful parts to begin with, which means that in any such case all expressions are equally meaningless. It would be entirely arbitrary, or rather pointless, to pick out any one expression as the meaningless one since all expressions equally “contribute” to the meaninglessness. However, when Wittgenstein singles out “identical” as the linguistic culprit in “Socrates is identical,” he does precisely that. He seems to be giving exactly the kind of explanation from which a semantic wholist would be barred. Consequently, it’s impossible, without contradiction, to jointly

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attribute to Wittgenstein semantic wholism and the austere conception of nonsense in the way resolute readers do. The Internal Objection Let’s turn now to the internal conflict of the resolute reading. In presenting and discussing the third objection (the compositionality objection focusing on the austere conception of nonsense) I noted at the beginning a deep connection between this and the second objection (the elucidation objection involving the distinction between semantic and psychological content). We are now in a position to specify this connection in a way that poses a problem for the resolute reading. As we’ve seen, the austere conception of nonsense is motivated by a strong interpretation of Wittgenstein’s context principle I spelled out as semantic wholism, whose implications turned out to undermine the austere conception itself, at least insofar as both conceptions are being attributed to the Tractatus. The rejection of the clash-theory of nonsense with its underlying semantic atomism excludes the possibility of locating the source of nonsense in semantics, which is why resolute readers were forced to introduce the category of psychological content to account for the source of nonsense. As resolute readers frequently point out, “the charge of nonsense is directed not at the propositional sign itself, but rather at the character of the relation in which a particular speaker stands to a propositional sign.”99 Nonsense always refers to a form of illusion “generated through an inability on part of a speaker to command a clear view of what he is doing with his words.”100 Whereas sense is an objective, or at least supra-individual, property of a legitimate proposition, nonsense is a subjective property of a confused state of mind. Here critics pointed out the obscurity of the notion of psychological content and raised questions regarding its potential to explain the uniform illusion of sense to which so many readers of the Tractatus seem to have succumbed. But, I claim, the situation is even more problematic because the psychological account of nonsense brings with it severe problems even if we grant it the explanatory status it’s supposed to have. Broadly speaking, the problem is that a psychological account of nonsense, at least in the form the resolute reading is advocating, threatens to collapse into a psychological account of sense as well. If so, then the question whether a Tractarian proposition is meaningful becomes entirely a

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psychological matter. In this case the resolute reading would be sawing off the branch it’s sitting on because it would then, according to its own premises, have no resources whatsoever to say of any proposition (not only the Tractarian ones) objectively, or at least supra-individually, that it’s meaningful or nonsensical. This would be a devastating result given that the claim that the propositions of the Tractatus are nonsensical (at least those belonging to the body, whichever they are) in the strictest possible sense is the main thesis of the resolute reading. To substantiate this train of thought, consider the following passage containing the resolute reading in a nutshell: What criteria govern whether a given remark is Unsinn or not? This question presupposes that certain strings of signs are intrinsically either cases of Unsinn or cases of Sinn. But the Tractatus teaches that this depends on us: on our managing (or failing) to perceive (erkennen) a symbol in the sign. There can be no fixed answer to the question what kind of work a given remark within the text accomplishes. It will depend on the kind of sense a reader of the text will (be tempted to) make of it.101

Semantic criteria as a means to decide on whether or not a Tractarian proposition is nonsense are being rejected because this would turn nonsense into a property of semantically flawed propositions and thus a semantic matter. In the same breath, it’s pointed out that signs are not only not intrinsically nonsense, they are not intrinsically meaningful either. Now, if this were simply a reminder of the arbitrariness of signs there would be no problem. But the passage goes much further than that. It’s crystal clear in its claim that the meaningfulness of any given Tractarian proposition depends “on the kind of sense a reader of the text will (be tempted to) make of it.” In connection with the frame-body objection regarding the methodology of the resolute reading, we’ve already seen how this conception makes the outcome of the decision on whether a particular Tractarian proposition belongs to the body or the frame somewhat arbitrary because this decision was dependent on the reader. Now we see that the problem goes much deeper than that. Consider again the passage quoted above. If nonsense is always the result of a reader’s failing to make certain meaning determinations, then

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it inevitably follows that sense is always the result of a reader’s making certain meaning determinations. This much is explicitly acknowledged by saying that whether we are confronted with cases of “Sinn” or “Unsinn” depends on us, on our ability to “perceive (erkennen) a symbol in the sign.” But this poses a dilemma. On the first horn of the dilemma, the resolute reading must concede that the strings of signs in the Tractatus express (or don’t express) symbols objectively, or at least supra-individually, such that it’s independent of the reader (and thus a semantic matter) as to whether there is or is not a symbol for us to perceive and hence whether there is a meaningful proposition or not. But in that case there would be semantic criteria by virtue of which we could address the question of whether a given proposition is meaningful or nonsensical. However, resolute readers clearly reject the idea of there being semantic criteria governing whether a certain remark is nonsense. On the second horn of the dilemma, the resolute reading insists that the strings of signs in the Tractatus express (or don’t express) symbols non-objectively, such that it’s dependent on the reader (and thus a psychological matter) as to whether there is or is not a symbol for us to perceive and hence whether there is a meaningful proposition or not. But if the presence (or absence) of a symbol were dependent on the reader, it would be more accurate to say we (subjectively) “project” the symbol into the sign rather than (objectively) “perceiving” it.102 However, if the question whether a given Tractarian proposition is meaningful depends on whether a particular reader succeeds in projecting a symbol into it or not, then it becomes impossible to non-arbitrarily decide on this question, and resolute readers are not justified in claiming that a given proposition is objectively, or at least supra-individually, nonsensical. To be clear, the problem is not so much that, according to the resolute reading’s account, there may be a form of dependency of the semantic content of the Tractatus on the interpretation of its reader (any non-­ dogmatic approach would probably readily concede this point to a certain degree). The real problem is that the resolute reading wants to claim that certain propositions of the Tractatus (at least those of the body, whichever they are) are nonsensical and that the process of elucidation consists in realizing this. But this is precisely what resolute readers cannot

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claim since nonsensicality is said not to be a property of propositions, but rather depends on our failing to make sense of a given linguistic string of signs. And here nothing prevents us from making certain meaning determinations by means of which we would be capable of making sense of any given proposition. The irony here is that the resolute reading’s main thesis—that there is only one kind of nonsense (failing to make sense by failing to make meaning determinations)—leads to the conclusion that there is no nonsense at all. Anything goes. To illustrate, take, for example, the proposition “The world is all that is the case.” Is it nonsense? Well, here’s how resolute readers advise us to decide the case: […] Wittgenstein’s procedure is one in which we simply have to look at the sentence, in the context in which it is apparently being put to use, and determine from that whether or not the signs really do have a significant use.103

We “simply have to look at the sentence” and go from there. Obviously, the thinness of this recommendation is by design since we have nothing but our “capacities for distinguishing sense from nonsense […] implicit in the everyday practical mastery of language”104 to rely on. This may be unsatisfactory on its own, given that the Tractatus is an enormously difficult book with a vast technical vocabulary, in the face of which our ordinary capacity to distinguish sense from nonsense soon gives out. But again, the problem is not that the meaning of “The world is all that is the case” may vary depending on the respective interpretations commentators attribute to it. The problem is that resolute readers cannot claim “The world is all that is the case” is nonsense according to their own premises. I’ve devoted a lot of space (Sect. 3) to developing an account of what this proposition means—so have many other commentators of the Tractatus. My, or any other interpretation of this proposition, may be contested, but according to the resolute reading’s own premises the proposition cannot be nonsensical because this depends “on the kind of sense a reader of the text will (be tempted to) make of it.” And the same goes for each and every proposition of the Tractatus. The resolute reading cannot say of any proposition of the Tractatus that it is nonsensical because there is always

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the possibility to make meaning determinations, in the course of exegesis, so as to render it meaningful (the rich history of extremely diverse Tractatus exegesis testifies to that). And that is why the thesis that there is only psychological nonsense leads to the conclusion that there is no nonsense at all. Confronted with an interpretation of a particular proposition of the Tractatus the resolute reading has no resources to convince one of its nonsensicality because this verdict presupposes that the nonsensicality of a proposition is somehow rooted in the proposition itself, which is exactly what resolute readers deny.105 Since the aim of the Tractatus, according to resolute readers, was to elucidate the reader by enabling her to recognize the propositions of the Tractatus as nonsense, the contradiction becomes quite obvious: the resolute reading claims that the propositions of the Tractatus (at least those of the body, whichever they are) are nonsensical and are to be recognized as such, when in fact their account of nonsense rules out the very possibility of issuing such a verdict. The entire debate began with resolute readers’ claiming that a lot of propositions in the Tractatus standard readers took to be meaningful (the “ontological” opening remarks, the picture theory, etc.) are in fact nonsensical, but under closer inspection it now turns out that the resolute reading is prevented by its own lights from making judgments of this form. There are passages in which resolute readers seem to be aware of the need to mitigate the problematic implications of a psychological account of nonsense: The attempt at clarification can bring out that no use has been fixed on for some or other sign, or indeed that we have been in an unclear way trying to run together two quite different sorts of use, wanting neither the one nor the other but both. [emphasis added]106

The “use” of a sign here seems to be a deflated, more malleable successor of the “logical role” of a sign. Now, in order to be able to claim that a certain proposition is nonsensical, resolute readers point out that in the case of nonsensical propositions (which are to illuminate us by our recognizing their being nonsense) some signs lack a fixed use. Apart from the implication here of a distinction between signs with and signs without

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fixed uses, which is again problematic in itself because it conflicts with semantic wholism, the explanation of nonsense as arising out of “running together different sorts of use” sounds very much like a version of the clash-theory. What is the difference between standard readers saying in the proposition “Caesar is a prime number” expressions with incompatible logical roles are being put together and resolute readers saying expressions with incompatible uses are being run together? This is not surprising because resolute readers need some sort of minimally objective semantic conflict in a proposition they can point to in order to substantiate their claim that it’s nonsensical. If resolute readers were to retreat to considering conflicting uses of signs a mere psychological matter, then they would get, again, into the predicament of not being able to issue the verdict of nonsensicality given that it’s always possible to find suitable uses of signs so as to produce a meaningful proposition. Eventually, the resolute reading’s view of nonsense either turns out to be a variant of the clash-theory of nonsense, representing a version of the standard reading, or has no justification for considering any Tractarian proposition nonsensical.

4.3 T  aking Stock: Beyond Realism and Idealism Let’s take stock, recapitulate the results we’ve reached so far and situate them in the broader context of the debate between realism and idealism. In Sect. 3 I developed what I called Wittgenstein’s early Metametaphysics. This view consists in an attempt to address the aboutness problem: how can we account for the world’s being accessible to thought and expressible by language? And the challenge was to do it without engaging in the traditional enterprise of establishing an ontological as well as a logico-­ semantic inventory of the world and language, respectively, an enterprise that more often than not runs the risk of falling prey to the pitfalls of realism and idealism. I traced the roots of Wittgenstein’s philosophical project, in Sect. 2, to his distinct opposition to Russell’s object-based metaphysics, specifically his logical atomism and its lacking resources to deal with the inextricably linked problems of logical form and unity.

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According to Russell’s logical atomism, the fundamental building blocks of reality are isolated elements, which are ontologically all on a par but bear no essential relation to one another. This view also informed his theory of judgment and gave rise to a fundamental problem that is part and parcel of the problem of logical form and unity: the possibility of nonsensical judgments. This problem affected all versions of Russell’s theory of judgment, and he tried to find a remedy for it by appealing to various devices and entities, such as the subordinate relation, the judging relation and the judging subject, and, finally, logical forms. All of these devices and entities were, in one form or other, in the service of providing what I called a logical manual, a means to put constraints on what can be judged. Developing a combinatorics for logical atoms promised to deliver specifications for how to combine given constituents so as to yield legitimate propositions and exclude illegitimate ones. As we’ve seen, Wittgenstein took issue with the very idea of a logical manual, for two closely related reasons. Wittgenstein’s first objection pointed out an inconsistency in the classificatory procedure employed by the theory of types. In order to sort symbols and items by their logical category, we are forced to make claims involving the use of predicates such as “x is (not) a singular term” and “y is (not) an object.” But the meaningful application of such predicates presupposes the possibility of applying them to each symbol or item, which is exactly what is prohibited by the theory of types because we would be applying them to symbols and items of different categories. As Wittgenstein elaborates, the underlying mistake is that the claims involving type attributions violate what I called the contingency requirement, according to which it’s a necessary condition for the meaningfulness of a proposition that what it claims to be case could be (or could have been) otherwise. To assert (or deny) that a certain symbol or item possesses a particular logical type is nonsensical because the logical type it possesses is constitutive of it and can therefore not be (or could not have been) otherwise without changing what the symbol or item essentially is. The second objection consisted in Wittgenstein’s demand that “every theory of types must be rendered superfluous by a proper theory of symbolism” (L: 38). Although the theory of types suffers from a flawed theoretical design, there is no need to focus on fixing it because once we’ve

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developed an adequate symbolism based on a correct view of propositions a theory of types will automatically be obsolete. The reason is simply that a correct symbolism incorporates type theoretical distinctions in such a way as to be reflected by the different kinds of symbols themselves. The constraints required for meaningful statements are built into the symbols and prevent the formation of nonsensical statements without our having to devise a logical manual of any kind for accomplishing this purpose, an undertaking Wittgenstein’s first objection showed to be problematic anyways. Wittgenstein’s disagreement with Russell regarding the nature of judgments and propositions in particular (the problem of logical form and unity) and the design of a proper symbolism in general (the problem of type specifications) is symptomatic of a fundamental difference concerning their respective understanding of logic. This fundamental difference is epitomized in Wittgenstein’s accusation that Russell had reified logic by committing what I called the descriptive fallacy. Russell’s theoretical metavocabulary contains claims involving type attributions purportedly enabling us to construct only legitimate judgments by providing us with the resources to pair symbols and meanings correctly. However, construing theoretical metavocabulary descriptively in this way is problematic not only because of the contingency requirement but also because it doesn’t recognize that the specific type of a symbol and the type of what it symbolizes is necessarily a “package deal”: if a particular sign expresses a particular symbol, for example, one that refers to an object, then it is thereby of the same logical type as that to which it refers; and if the same sign were to symbolize something else, for example, one that expresses a concept, then it would thereby express a different symbol. It’s incoherent to think a symbol of the type singular term could wrongly express a concept simply because referring to an object is what a symbol of the type singular term consists in. Again, the logical type of a symbol is constitutive of it so that if it were to express something else, then it would simply be of another logical type and not of the “wrong” type, as Russell thought. There is no such thing as correlating symbols and meanings in the wrong way, and it’s precisely this sense in which “we cannot make mistakes in logic” (TLP: 5.473). Hence identifying the type of a symbol is tantamount to identifying the type of what it symbolizes. Since there is no

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room for the possibility of a mismatch between a symbol and what it symbolizes, it’s superfluous (or rather nonsensical) to prescribe symbols their logical type. As Wittgenstein wrote to Russell: “You cannot prescribe to a symbol what it may be used to express. All that a symbol can express, it may express. This is a short answer but it is true!” (L: 99). Wittgenstein’s “fundamental idea” in the Tractatus “that the ‘logical constants’ are not representatives; that there can be no representatives of the logic of facts” (TLP: 4.0312), then, consequently implemented his insights and avoided the descriptive fallacy and the reification of logic it generates. By conceiving of logic as essentially composed of non-­ descriptive tautologies—which is why the “propositions of logic say nothing” (TLP: 6.11)—Wittgenstein is able to kill two birds with one stone. It dissolves two major problems affecting Russell’s descriptive logic, namely the problem of contingency (the problem that the “maximally general truths” of logic turn out to be only contingently and not necessarily true) and the logocentric predicament (the problem of how to justify these “maximally general truths”). Against the background of this radically different conception of logic I fleshed out Wittgenstein’s logical immanentism, according to which logical form pervades language and the world by being implicit in names and propositions, objects and states of affairs. Logical immanentism was then further articulated through what I called Wittgenstein’s ontological and semantic contextualism. This means objects and expressions are essentially unsaturated or incomplete in that the totality of possible occurrences (i.e. their occurrence spaces) within a certain set of states of affairs and propositions, respectively, are part of the nature of objects and expressions themselves. Wittgenstein’s emphasis on the incompleteness of objects and expressions marked a radical break with Russell’s logical atomism in two important respects. First, objects and expressions are no longer viewed as isolated, self-standing entities but rather as potential constituents of states of affairs and propositions with which they are inextricably bound up. And, second, conceiving of objects and expressions as incomplete also meant to reject establishing an ontological inventory as well as a logico-­ semantic vocabulary of the world and language, respectively. This undertaking became superfluous once Wittgenstein realized that the essence of

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objects and expressions consisted not in some sort of substance but in their possible connection with one another. The focus on the dialectics between objects and state of affairs as well as between names and propositions turned the study of which logical forms objects and expressions actually exhibit into a contingent and hence empirical matter. Since there is “no a priori order of things” (TLP: 5.634) it would be “completely arbitrary to give any specific form” (TLP: 5.554). In reconstructing the so-called picture theory, I’ve put emphasis on the mutual dependency of pictorial form (the respective possibilities of arrangement of the elements of the picture and the depicted) and pictorial relationship (the correlation of those respective elements), which jointly constitute the aboutness (the possible truth-and-falsity) of a picture. We’ve also seen that not realizing this mutual dependency led to the long-standing debate between realist and idealist accounts of the Tractatus. The question about whether the dominating part in the name-object relation is to be identified with either the “direct linkage” or the “use” of a name turned out to be the linguistic analogue of the question about whether pictorial relationship takes precedence over pictorial form or vice versa. The Pears-Malcolm position argued that the logical form of a name is being prescribed by the totality of states of affairs in which the object the name refers to can possibly occur, whereas the Ishiguro-McGuinness position held that the logical form of a name is being governed by the totality of propositional contexts in which that name can meaningfully occur. The basic issue of whether it’s the combinatorial possibilities (the occurrence space) of objects determining the combinatorial possibilities (the occurrence space) of names or whether it’s the other way round is nothing other than a dispute about whether language has to conform to the world or whether it imposes its structure on it. The resolution of this debate consisted in conceiving of language and the world not as two mutually exclusive realms but, rather, as being “in a certain sense one” (TLP: 4.014), namely in the sense that language and the world are simply to be understood as an internal differentiation of the one single realm called logical space. The common logical structure of language and the world is neither a logical accident nor something that needs to be engineered by some sort of “isomorphism” against the possibility of a mismatch, but simply a manifestation of the relation between

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the denizens of logical space, in which pictures/propositions are facts serving to represent other facts. Thus, the debate about whether language must mirror the structure of the world or whether it projects its own structure on to it can be dropped. Of course, the thesis that logical space comprises both language and the world may raise the suspicion that, according to my interpretation, Wittgenstein is envisioning a form of idealism after all, given that language and the world now appear to be “inseparable.” But this suspicion is only justified as long as we don’t distinguish sharply between what I’ve called logical symmetry (the mutual entailment of shared logical structure and translatability of domains) and ontological asymmetry (the context-­dependent circumstances determining pictorial relationship and form as well as what is a picture of what in the particular case). Language and the world are mutually dependent only on the level of logical symmetry but, of course, not on the level of ontological asymmetry. Logical symmetry is always involved in a picturing relationship, that is, in case pictorial relationship and form constitute the aboutness of a picture. Interestingly, the mutual dependency of pictorial relationship and form actually harks back to and is a reflection of the relation between the type of a certain symbol and the type of what it symbolizes. In the same way in which the logical type and meaning of a symbol are to be considered a package deal, pictorial form and pictorial relationship are to be considered a package deal, too. What Wittgenstein says of symbols could be said of pictures as well, namely that whatever a picture can express it may express. This means the idea of our having to correlate pictures and what they depict in the right way is incoherent for the very same reason it’s incoherent to correlate symbols and what they symbolize in the right way: there simply is no room for a possible mismatch between a picture and what it depicts because the expressive resources of a picture are a matter of its internal structure. Much like symbols, either pictures are meaningful, in which case they are already about something by virtue of pictorial relationship and form, or they are not, in which case the question of aboutness cannot even intelligibly be asked. A picture simply expresses what it expresses; it cannot wrongly express something. “We cannot give a sign the wrong sense” (TLP: 5.4732) although, of course, a picture can be false, but that is a matter of its truth-value, and not of what

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it’s about. The logic of depiction articulated by the picture theory is neither a mirror (realism), nor a projection (idealism), but rather a metaphysically neutral expression of the logical structure of the world. With these considerations in mind, we can now fend off the charge of idealism. What is essential here is that we must not conflate the status of the picturing relation (which is logically symmetrical) with the source of determination of pictorial relationship and form responsible for the aboutness of a picture (which is ontologically asymmetrical). As I’ve tried to illustrate with the relation between the score and the symphony, there may be an ontological asymmetry due to various sources determining pictorial relationship and pictorial form. For example, depending on our interests the score can be considered as a picture of the symphony or vice versa. It’s on this level that the question may legitimately arise as to what is a picture of what, and therefore what has to “conform” to what in order to reproduce logical structure. Ontological asymmetry is an empirical and hence a contingent matter, and must be considered on a case-by-case basis. But, regardless of how ontologically asymmetrical circumstances enter into determinations of pictorial relationship and form, there is a logical symmetry in each case of a picturing relationship. So conceived, Wittgenstein provides us with an account of aboutness without lapsing into either realism or idealism. In the introduction to this book, I maintained that the seemingly purely semantic debate about whether the Tractatus pursues the philosophical project of a determination of the limits of language, which was revived by the emergence of the resolute reading, represents in fact a version of the realism-idealism dichotomy. In particular, I noted a significant similarity to the debate about the alleged idealism of later Wittgenstein, and now we are in a position to flesh out more fully what exactly this similarity consists in. To begin with, it’s not quite clear where, exactly, resolute readers stand on this issue. Just as the Ishiguro-McGuinness position, resolute readers also clearly reject realist positions such as Pears-Malcolm’s. On the one hand, Diamond seems to express this rejection distinctly when she writes that “to throw the ladder away is, among other things, to throw away in the end the attempt to take seriously the language of ‘features of reality.’”107 On the other hand, there are also passages in which she and other

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resolute readers show signs of wanting to overcome the realism-idealism dispute.108 Be that as it may, let’s examine the actual stance to which the implications of the resolute reading eventually commit them. To do this, it will prove helpful to make use of the distinction between limits and limitations, which was introduced by Sullivan in connection with Wittgenstein’s explicitly stated aim in the Preface of the Tractatus to draw a limit to (the expression of ) thought: The notion of a ‘limit’ […] is a non-contrastive, non-excluding one: limits have no ‘other side’; there is nothing ‘beyond’ them. ‘Limitation’, on the other hand, is a contrastive, excluding notion: limitations are boundaries separating what qualifies for inclusion within them from what does not. The previous discussion takes the construal of limits as limitations to be symptomatic of idealism, and then asks what place that construal has in Wittgenstein’s thought.109

Moore, with whom Sullivan has been having a long-standing discussion over whether early Wittgenstein was an idealist, elaborates on the distinction between limits and limitations and how it relates to idealism in the following way: There are, in the Tractatus, notably in the 5.6s, remarks in which the limits of language and the limits of the world appear not merely as limits, not merely as essential features, but as limitations, as features that at some level exclude certain possibilities. Because these features appear to exclude certain possibilities, they also appear to admit the question why they are as they are. The answer implied in those same remarks involves the subject, who both understands language and has thoughts about the world, and who somehow sets the limits—is a limit—of each.110

The limits of something are its essential features; they are constitutive of its very nature and form. According to Sullivan, who rejects reading (early) Wittgenstein as an idealist, to say that thought has limits doesn’t necessarily mean thought is constrained by or barred from something (e.g. constrained by logic or barred from the structure of the world as it is in itself ). Rather, it means that thought has certain characteristics

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without which it wouldn’t be what it essentially is. One example Sullivan mentions is Wittgenstein’s comparison of the relation between language and its logic to the relation between space and its geometry111: It is as impossible to represent in language anything that ‘contradicts logic’ as it is in geometry to represent by its co-ordinates a figure that contradicts the laws of space, or to give the co-ordinates of a point that does not exist. (TLP: 3.032)

Drawing a point without coordinates and framing an illogical thought are not possibilities that happen to be excluded by geometry and language, respectively, but are simply not possibilities. As Hacker nicely put the point: A “logical or metaphysical ‘impossibility’ is not a possibility that is impossible.”112 Language is limited by logic in that it is constitutive of it. This limit manifests itself in the fact that there is no contrast between logical and illogical thoughts because being logical is an essential feature of being a thought. It’t impossible for a thought not to be logically structured. An “illogical thought” is an oxymoron because a thought that contradicted logic would simply not be a thought, and it’s in this sense that the limits of language and thought are said to be “non-contrastive.”113 Limitations, on the other hand, are contrastive. They impose constraints on something by excluding certain possibilities in comparison to others. Put differently, limitations satisfy the contingency requirement in that they always leave room for the possibility of being otherwise. This sharply sets limitations apart from limits, where being otherwise doesn’t constitute excluded possibilities but is rather incoherent (like a geometrical point without coordinates). Here it’s worth noting that, like idealism, realism also construes the limits of language and thought as limitations, differing from it only with respect to the source of those limitations.114 The realist Pears-Malcolm position—much like Russell’s logical atomism—conceives of the world as an autonomous structure composed of an antecedently given stock of various entities and their fixed logical categories “set over against us in mysterious independence.”115 For language and thought to accurately represent this ontological inventory the logico-semantic vocabulary must be attuned accordingly. Here the world is the source of limitations

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imposing constraints on the structure of language and thought, violations of which result in a disconnection of both realms. Realism, then, can be seen as the exact mirror-image of idealism, which locates the source of limitations instead either in the resources of language (e.g. the overt linguistic idealism of Stenius or in the covert linguistic idealism of the Ishiguro-McGuinness position) or in the world-constituting subject (e.g. the idealism of A.W. Moore). The resolute reading, with the austere conception of nonsense occupying center stage, doesn’t construe the limits of language and thought as limitations. On the contrary, the “illusion the Tractatus wants to explode, above all, is that we can run up against the limits of language.”116 Like the Ishiguro-McGuinness position, the resolute reading also recoils from the kind of realism usually defended by standard readers, but it does so in a much more radical way. Recall that realism goes hand in hand with semantic atomism, according to which an expression can play a certain logical role and hence can have a meaning outside the context of a proposition. Semantic atomism, then, views meaningful propositions as the result of combining antecedently given and independently meaningful expressions according to the combinatorial prescriptions of logical syntax. This compositional model of meaning implies what I’ve called the clash-theory of nonsense because nonsense is considered to be the result of combining already meaningful expressions contrary to or in violation of the combinatorial prescriptions of logical syntax, causing a clash between incompatible logical roles. Now, as we’ve seen, in rejecting the clash-theory the resolute reading automatically rejects the semantic atomism by which it is implied and espouses a form of semantic wholism. This doctrine, which resolute readers derive from a strong interpretation of Wittgenstein’s context principle, acknowledges meaningful expressions only as parts of meaningful propositions, without or apart from which expressions have neither logical roles nor meanings. Since for the resolute reading’s semantic wholism there can be no such thing as semantic clashes (because for semantic wholism there are only meaningful wholes) it instead resorts to psychological content to account for nonsense. According to this conception, nonsense is always an illusion of sense on the reader’s part, namely the result of having failed to make certain meaning determinations. Nonsense

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is not the property of a logically flawed proposition (as semantic atomism has it), but rather the property of a confused mind not in command of its linguistic resources. As I’ve argued in the previous subsection, the psychological account of nonsense threatens to collapse into a psychological account of sense as well. Since nonsense has nothing to do with propositions per se but rather with a particular reader’s relation to propositions—having failed to make meaning determinations—sense can be produced simply by making the appropriate determinations. Because the question whether a proposition is meaningful or not now “depends on the kind of sense a reader of the text will (be tempted to) make of it,”117 the individual reader becomes the source of the meaningfulness or nonsensicality of any given proposition. The wider picture emerging from this conception is one according to which the Tractatus wants to enable us to realize the nonsensicality of its propositions by harnessing the capacities for distinguishing sense from nonsense (for recognizing the symbol in the sign and for recognizing when no method of symbolizing has yet been conferred upon a sign) implicit in the everyday practical mastery of language which the reader already possesses.118

This passage exemplifies well how the recoil from realism with its underlying semantic atomism has landed the resolute reading in the opposite extreme. Semantic atomism tries to establish a logical manual that provides semantic criteria prescribing which combinations of expressions make sense and which do not, criteria that are being derived from a prior classification of the ontological inventory of the world. Semantic wholism rejects this realist metaphysics and with it the very idea of combining expressions according (or contrary) to the semantic criteria of a logical manual. Now, given the rejection of semantic criteria, the inevitable question arises where semantic constraints, if any, on meaningful discourse are supposed to be coming from. It’s precisely the inability to answer this question that is manifest in the resolute reading’s oscillation between “projecting”119 and “perceiving”120 a symbol in(to) the propositional sign generated by the psychological account of nonsense on the one hand, and the need for some sort of semantic constraints on the

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other. Here all that resolute reading has to offer is the retreat to our “capacities for distinguishing sense from nonsense […] implicit in the everyday practical mastery of language […].” But this retreat is problematic even if we disregard that the “capacities for distinguishing sense from nonsense” sound suspiciously like watered-­ down semantic criteria in the guise of ordinary capacities, and disregard that this account suggests a uniformity of these implicit ordinary capacities among people that is most likely an illusion, such that appeal to these capacities are hardly a viable means to decide on the meaningfulness (or nonsensicality) of Tractarian propositions. Even then, the major problem still remains that the psychological account of nonsense (and hence, inadvertently, of sense too) leads to the problematic outcome that the resolute reading loses its grip on semantic constraints altogether. Since the reader is the main source of making (or failing to make) sense of any given propositional sign, there are no objective, or at least supra-­ individual, constraints on projecting symbols into it other than the individual’s power of imagination. Any concession of objective constraints, even minimally construed, would be a step toward semantic atomism, which the strong semantic wholism of the resolute reading cannot allow for. In the end, by resorting to our “everyday practical mastery of language,” the resolute reading seems to relocate the source of limitations on the process of sense-making and places it wholly in the participants of ordinary language-games. Whereas the semantic atomism of the standard reading turns the limits of language and thought into the limitations of a transcendent world, thereby running into all the difficulties of devising and applying a logical manual to secure the connection between language, thought, and the world, the semantic wholism of the resolute reading denies that language and thought have any limits, thereby running the risk of turning sense-making into a more or less arbitrary function of ordinary language-games, beyond which there is simply nonsense and nothing else. Interestingly, the resolute reading exhibits exactly the kind of idealism attributed to later Wittgenstein by Nagel. He characterizes his own realist position as the thesis that in “a very strong sense, the world extends beyond our minds” and then contrasts it with a form of idealism whose

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main source he takes to be later Wittgenstein. Incidentally, rather than being an accurate description of later Wittgenstein’s position, this characterization instead applies perfectly to the resolute reading’s austere conception of nonsense: The idealism to which this is opposed holds that what there is is what we can think about or conceive of, or what we or our descendants could come to be able to think about or conceive of—and that this is necessarily true because the idea of something that we could not think about or conceive of makes no sense.121

In sum, whereas standard readers always face the danger of a fundamental disconnect between language and thought from the world, resolute readers with their psychological account of sense and nonsense are always on the verge of transforming our ordinary linguistic practices into a “frictionless spinning in a void.”122 Fortunately, there is a way to dismount the seesaw of semantic atomism and semantic wholism and their respective metaphysics. As the discussion in the previous subsection showed, standard readers are eager to find cases of meaningful expressions literally occurring outside propositions in order to justify their weakening of the context principle in favor of semantic atomism, and simultaneously to make a case for the possibility of semantic clashes to counter the semantic wholism of resolute readers.123 This debate revolves around the question whether typographically isolated expressions (such as dictionary entries and the like) can have logical roles and thereby meaning. But it’s questionable whether it’s this problem Wittgenstein had in mind. Consider again the following passage: Things are independent in so far as they can occur in all possible situations, but this form of independence is a form of connexion with states of affairs, a form of dependence. (It is impossible for words to appear in two different rôles: by themselves, and in propositions.) (TLP: 2.0122)

Wittgenstein’s claim about the impossibility for words to appear “by themselves” doesn’t seem to refer to a typographical impossibility. In this passage as well as in the passage articulating the context principle, in

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which Wittgenstein makes the converse claim that expressions have meaning “only in the nexus of a proposition,” the nexus he’s talking about is a logical one. As I’ve argued at length, regardless of whether expressions literally and actually occur in propositions or not, if they are meaningful at all they are logically connected to propositions in that the possibility of being a constituent in the totality of propositions determined by their occurrence spaces is essential to the meaning of these expressions. The impossibility to which Wittgenstein is referring is the impossibility for expressions to have meaning and not be a possible constituent of a particular class of propositions (and vice versa). Conversely, having a meaning and being a possible constituent of a particular class of propositions mutually entail each other. And this logical interconnectedness holds for all expressions, even for those that may occur typographically isolated. Some expressions (such as dictionary entries) may occur isolated in that they are not actually being used in a proposition but, of course, that is not proof that expressions have meaning “outside” propositions (as semantic atomism has it). Their meaning, if they have any, is still inextricably bound up with the possible propositions in which these expressions may occur. But neither is it proof that expressions occurring in isolation are mere noise or marks on paper (as semantic wholism has it). Insofar as we identify them as expressions at all we are identifying them simultaneously as possible constituents of a particular class of propositions. In short, Wittgenstein readily concedes the possibility for expressions to occur typographically outside propositions, but he vigorously denies the possibility for expressions to occur logically outside propositions. In contrast to semantic atomism and wholism, then, semantic contextualism, as I’ve developed it as part of Wittgenstein’s early Metametaphysics, neither privileges expressions nor propositions but rather understands them in terms of one another by acknowledging their mutual dependency. On the one hand, the bottom-up approach of semantic atomism faces all the problems a logical manual brings with it in imposing constraints on isolated elements so as to allow only the formation of meaningful propositions and prevent nonsensical ones. The top-down approach of semantic wholism, on the other hand, makes it mysterious how constraints on the formation of propositions are possible given that it rejects

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semantic criteria and provides only a problematic substitute in the form of the ordinary capacity to distinguish sense from nonsense. It is true, the Tractatus doesn’t put forward a theory of meaning, a logical manual prescribing the correct combinability of expressions. The reason for this, though, is not because Wittgenstein is a quietist therapist, who wants to redirect our confused minds away from harmful, illusion-­ generating philosophical discourse back to the alleged clarity of our ordinary thought and talk, but because of a reason all too familiar by now: a logical manual is superfluous because the combinatorial possibilities of expressions are built into expressions themselves. If anything, a logical manual in the form of a logical syntax encodes in a perspicuous way the constitutive rules for the use of expressions, but these rules are neither descriptive nor prescriptive, but simply expressive of the logico-semantic relations between them. As I’ve emphasized, expressions are like puzzle pieces already containing the form of possible connections to other pieces. Of course, considered apart from figuring in actual combinations expressions have no determinate meaning, in the same way a piece of a puzzle doesn’t reveal what it is unless it’s part of a larger picture. However, from this mutual dependency of the whole and the parts it comprises it doesn’t follow that expressions considered in isolation have no logical form at all, in the same way a piece of a puzzle has a particular form constraining the possibilities of combining it with other pieces. Expressions are neither semantic atoms that are placed in propositional contexts according to a logical manual, nor are expressions considered apart from semantic wholes mere noises or marks on paper. Rather, the propositional contexts in which they possibly figure are written into expressions themselves. In conclusion one might say language and thought, though they have indeed no limits in the sense that language and thought are not in any way barred, in principle, from accessing and articulating worldly states of affairs, there are still objective, or at least supra-individual, limitations implicit in the very vocabulary used to access and articulate those states of affairs. Semantic atomism and wholism together with their respective metaphysics present us with the false dichotomy between realism and idealism, at the root of which lies a conflation very similar to the one we came across in connection with the picture theory. The debate makes it

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appear as if we must choose between conceiving of logical syntax either as a (correct or incorrect) description of the fundamental structure of the world or as an arbitrary projection of our logico-semantic vocabulary. But again, we must not conflate the status of the rules of logical syntax with the source of determination of the constitution of those rules. This means we must not infer from the fact that these rules are not a reflection of the fundamental structure of the world (because they are not descriptive) that they are arbitrary products of our contingent cognitive equipment instead. The determinations entering into the constitution of the concepts making up the rules of logical syntax may have their source “in the world” or “in language,” but that leaves their status as non-descriptive untouched. The misconception characteristic of the debate over the status of logical syntax is also operative, or so I claim, in the debate over the status of grammatical rules—the successors of the rules of logical syntax124—as part of the central issue of following a rule occupying later Wittgenstein. Unsurprisingly, then, the literature on later Wittgenstein in general and the rule-following considerations in particular has produced their own versions of the dichotomy between realism and idealism.

Notes 1. Diamond (1991). It’s worth noting that the resolute reading was partly anticipated in the writings of Rhees (1966, 1969), Winch (1969), Ishiguro (1969), and McGuinness (2002). 2. Initially, the resolute reading restricted the frame to the Preface and the closing sentences (cf. Conant 1993: 216 and Diamond 2000: 149). The difficulties arising from this narrow frame-body distinction, frequently pointed out and attacked by standard readers, have forced Diamond and Conant to substantially revise this distinction (cf. Conant and Diamond 2004: 68–69). I’ll discuss this issue in the next subsection. 3. Conant and Diamond (2004: 47). 4. Conant and Diamond (2004: 47). Given that these two interrelated commitments form the common denominator of virtually all resolute readings, I’ll focus mainly on the Diamond-Conant position. It should

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be noted, however, that Conant and Diamond emphasize that there is no such thing as “the” resolute reading because their position “is better thought of as a program for reading the book” (Conant and Diamond 2004: 47) rather than an actual reading of it. Since the differences between weak and strong resolutism are not particularly substantive, suffice it here to give a short characterization by citing two of the most prominent defenders of strong resolutism, namely R. Read and Deans (2003: 249–250): “A key difference between the weak and strong versions of resolutism is that the weak version thinks that Wittgenstein attempted to demonstrate in the Tractatus just what a deflationary and therapeutic conception of logical analysis amounts to,” whereas the strong version maintains “that the Tractatus is a deliberatively ‘selfrefuting’ attempt to establish that no logical system is powerful enough to fully express in a general way the meaningfulness or meaninglessness of any possible configuration of signs, and that the attempt to do so, including the attempt of the Tractatus, will inevitably result in nonsense.” Another important proponent of strong resolutism is Floyd (2007). 5. Hacker (1986: 23, n. 31) writes indeed that like “the Critical philosophy of Kant, the Tractatus is concerned with clarifying the bounds of sense” and he also maintains that “one is left holding on to some ineffable truths about reality after one has thrown away the ladder” (Hacker 2000: 357). But Hacker’s position, in particular with regard to the question whether the Tractatus puts forward a theory (of meaning), is much more subtle and nuanced than it’s usually portrayed in the literature. I’ll come back to this below. 6. Cf. Malcolm (1986: 14) and Pears (1987: 8). 7. A.W. Moore (1997: 149). 8. A.W. Moore (1997: 150). 9. Cf. Stenius (1960: 220–221). 10. Hutto (2003: 15). 11. Since Hacker has introduced this category and is the main target of resolute readers, I’ll focus mainly on his writings in what follows. But it’s important to note that the notion of an inexpressible content also figures prominently in Wittgenstein’s alleged idealism. A.W. Moore (2013: 245) takes Wittgenstein’s account to be a version of transcendental idealism because it’s supposed to be an “attempt to say, not how things are, nor yet how things must be, but what it is, in some deep

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metaphysical sense, for things to be how they are.” But “our knowing an object does not itself consist in our thinking anything: we cannot say what we know when we know an object. That our thinking depends on our having such inexpressible knowledge is therefore another fundamental mark of its finitude” (A.W. Moore 2013: 244–245). 12. Conant (2002: 374). 13. Hacker (1986: 18–19). 14. Hacker (2000: 357). 15. Hacker (1986: 106). 16. By “logical syntax” Wittgenstein generally means “the rules which tell us in which connections only a word gives sense, thus excluding nonsensical structures” (RLF: 162). How exactly to understand the status of logical syntax and in what sense it excludes “nonsensical structures” is a highly controversial matter and will be central to the following discussions. 17. Cf. Costello (2004: 104). 18. Diamond (2000: 155). 19. Conant and Bronzo (2017: 180). 20. Conant (2002: 419). This is directed, again, against Hacker (1986: 18), who explicitly argues that “[n]onsensical pseudo-propositions violate the rules of logical syntax.” Cf. Hacker (2003: 13), where he defends his claim with slight modifications. 21. Conant (2002: 419). Cf. also Conant (2011: 630). 22. Conant and Bronzo (2017: 180). 23. Conant (2002: 423–424). Cf. also Mulhall (2007: 7) for a similar view. 24. Hutto (2003: 51–52). Cf. also Conant (2002: 422) for a similar point. 25. Diamond (1991: 181). 26. Conant (2004: 185). 27. M. McGinn (2006: 9) and Hutto (2003: 86) also describe their position as “anti-metaphysical” and “anti-theoretical,” respectively, intending this label mainly to capture the anti-realist thrust of their approach. To distinguish M. McGinn’s and Hutto’s position from other stripes of the anti-realist reading (such as the Ishiguro-McGuinness position) I’ll follow the literature and use the term elucidatory reading. 28. M. McGinn (1999: 498). 29. Hutto (2003: 1). 30. Hutto (2003: 70). 31. Hacker (2000: 369).

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32. M. McGinn (2006: 135). This term was coined, as far as I can see, by McGuinness (2002: 85). 33. Hutto (2003: 57). 34. M. McGinn (2006: 137). 35. Hutto (2003: 70). For a similar statement cf. also M. McGinn (2006: 161). 36. Cf. R. Read (2006), Hutchinson (2006), Hutchinson and R. Read (2006), and Kuusela (2007). 37. Hutto (2004: 129). Cf. also Hutto (2003: 101). 38. Hutto (2003: 48). 39. Hutto (2003: 48). 40. M. McGinn (2006: 253). Cf. also M. McGinn (1999: 502). 41. For the former protest cf. Hacker (2003: 11): “I agree with Conant that logical syntax is not a combinatorial theory, since logical syntax is not a theory. It is a set of rules for the use of expressions, and a set of rules is not a theory about anything, not even a theory about expressions.” For the latter protest cf. White (2011: 35): “The most natural interpretation of phrases such as ‘violations of logical syntax’ is to take them to apply to a sentence that is void of any sense whatever because it incorporates a word or phrase that has been assigned a significant use only when combined in other sentences but not in this one.” Cf. also Cheung (2008: 205) for a defense of Hacker’s claim that the “violations-oflogical syntax-view” doesn’t require attributing to Wittgenstein a theory of meaning. 42. Hacker (1986: 23, n. 31). 43. Conant and Diamond (2004: 47). 44. Cf. R. Read (2006: 76). 45. Hutto (2003: 69). 46. Hutto (2003: 64). 47. Cf. Kuusela (2008: 479). 48. M. McGinn (2006: 159). 49. M. McGinn (2006: 253). 50. Cf. Hutchinson and R. Read (2006: 7): “Although we still cannot, strictu sensu, say what that something is, we can show (by elucidating) what ‘it’ is. But the question arises once again. If that ‘something’ is not ineffable, then why not simply say it?” 51. Cf. Hutchinson and R. Read (2006: 7) for this assessment of the elucidatory reading. For a reply cf. Hutto (2006).

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52. Cf. Hacker (2000: 360, 371). 53. Typically, this includes (but is not restricted to) the pre-Tractatus writings, letters as well as documented discussions and lectures, post-1929 manuscripts and, in particular, Wittgenstein’s essay “Some Remarks on Logical Form”, in which he addresses the so-called color exclusion problem. The main (rhetorical) question regarding most external criticism is why Wittgenstein elaborated on concepts, commented on mistakes, and even attempted to repair some of the arguments in the Tractatus if, according to the resolute reading, all of the passages in the Tractatus on which Wittgenstein remarks had been intended as plain nonsense all along. 54. Cf. Hacker (2000: 371–382) and Proops (2001: 383–395). 55. The overall strategy for reconciling their position with external evidence is “to distinguish between taking Wittgenstein to have unwittingly failed to have got free of metaphysical preconceptions (as resolute readers may) and taking him to have intended to put forward a metaphysical view (as standard readers do)” (Conant and Diamond 2004: 64). For a detailed deployment of that strategy cf. Conant (2006, 2007). 56. Cf. Conant and Diamond (2004: 68). 57. Cf. Conant (1993: 216) and Diamond (2000: 149). 58. For example, the context principle (TLP: 3.3) and the sign/symbol distinction (TLP: 3.32–3.323). 59. E.g. TLP (4.003–4.0031 and 4.111–4.116). 60. E.g. the concept of nonsense (TLP: 5.473 and 5.4733). 61. Cf. Hacker (2000: 360). 62. Conant (2002: 457, n. 135). 63. Conant (2002: 457, n. 135). 64. Conant (2002: 423). 65. Cf. Kremer (2001: 41). 66. Cf. Proops (2001: 380). Resolute readers reply by turning the objection into a feature of their dialectical interpretation of the Tractatus: “There is no forced choice between fixing upon an antecedent interpretation of Wittgenstein’s more general hints and instructions for the reader […] and ignoring Wittgenstein’s more general remarks about how the work is to be read […]. Rather they—the remarks about the book and the book that they are about—must be interpreted in the light of each other” (Conant and Diamond 2004: 68–69). 67. Diamond (1991: 183).

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68. Diamond (1991: 185). 69. M. Williams (2004: 18). For similar points cf. also M. McGinn (1999: 496), Hacker (2000: 361), and Koethe (2003: 198). 70. Cf. Conant and Diamond (2004: 56–69) for a reply to M. Williams. 71. Diamond (2000: 159). 72. Diamond (2000: 159). 73. Conant (2002: 381). 74. Conant (1998: 247). 75. Conant (2002: 419). 76. Conant (2002: 422). 77. Conant (2002: 421). 78. Conant (2004: 185). 79. White (2011: 40). On this point cf. also Hutto and Lippitt (1998: 273). 80. Cf. Hutto (2006: 565). 81. Cf. Conant and Diamond (2004: 61) and Conant and Bronzo (2017: 180). 82. Cf. Hacker (2003: 15–16), where he writes that “nonsensical pseudo-­ propositions […] do indeed involve transgressions of logical syntax, i.e., failures to accord with the rules for the use of these expressions […].” 83. Conant and Diamond (2004: 58–59). The formulation of the austere conception of nonsense is nearly always the same. Cf. Conant (1998: 245), Conant (2001: 23), Conant (2002: 380), Conant and Dain (2011: 67), and Conant and Bronzo (2017: 180). 84. Cf. Hacker (2003: 9–10). 85. Conant (2002: 418). Cf. also Conant (2002: 419): “Wittgenstein’s teaching is that the problem lies not in the words, but in our confused relation to the words […].” 86. I borrow the expression “wholism” from McCarty (1991), but I’ll use it somewhat differently to distinguish it from my account of semantic contextualism developed in Sect. 3.3. I’ll highlight the differences between wholism and contextualism in the next subsection. 87. Conant (2002: 404). Cf. also Conant (2001: 40). 88. Cf. Hacker (2003) and Glock (2004). 89. Cf. Glock (2004: 226). 90. Cf. Hacker (2003: 9). 91. Cf. Conant (2002: 432, n. 34). 92. Cf. Conant (2002: 419).

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93. Conant and Diamond (2004: 59). 94. Cf. Conant (2001: 23), Conant (2002: 419), Conant and Dain (2011: 75), and Conant and Bronzo (2017: 180). 95. Diamond (1991: 197). Cf. also Diamond (2011: 247), where she reaffirms her basic point. 96. Conant and Dain (2011: 76). 97. Conant (2001: 40). 98. Conant (2002: 404). 99. Conant (2011: 630). 100. Conant (2011: 630). 101. Conant (2002: 458, n. 135). 102. In one remarkable passage, Conant (2002: 424), in the course of elaborating on the Tractarian notion of elucidation, even characterizes successful sense-making as the result of a reader’s projection: “The work seeks to do this, not by instructing us in how to identify determinate cases of nonsense, but by enabling us to see more clearly what it is we do with language when we succeed in achieving determinate forms of sense (when we succeed in projecting a symbol into the sign) and what it is we fall short of doing when we fail to achieve such forms of sense (when we fail to confer a determinate method of symbolizing on a propositional sign).” 103. Conant and Dain (2011: 76). 104. Conant (2002: 423–424). 105. Here’s how Kremer (2001: 43), a prominent resolute reader, conceives of the process of elucidation: “Some of the propositions of the Tractatus, then, do not succumb to the corrosive effect of the self-refuting ‘theory’ and ‘argument’ putatively developed therein. The propositions which survive this disintegration of an illusion of sense, then, are simply those that we can still make sense of at the end of the day.” This seems circular because the question how we decide which propositions we can make sense of is exactly what is at issue here. 106. Conant and Diamond (2004: 64). 107. Diamond (1991: 181). Conant (1991: 152–153) also attacks the language of “features of reality.” 108. Cf. Diamond (1984: 367) and Conant (2007: 58). 109. Sullivan (2013: 257–258). For a recent volume on the role of the limits of language in Wittgenstein’s philosophy cf. Appelqvist (2020). 110. A.W. Moore (2013: 240–241).

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111. Sullivan (2011: 171–172). 112. Hacker (2000: 366). 113. Cf. TLP (5.4731): “What makes logic a priori is the impossibility of illogical thought.” Cf. also TLP (3.03 and 3.031). 114. An important exception is the kind of idealism Nagel, Williams, and Lear attribute to early and later Wittgenstein. More on that below and in Sect. 5. 115. Pears (1987: 8). Cf. also Malcolm (1986: 14). 116. Conant (2002: 424). Cf. also Conant (2002: 423). 117. Conant (2002: 458, n. 135). 118. Conant (2002: 423–424). 119. Cf. Conant (2002: 424). 120. Cf. Conant (2002: 458, n. 135). 121. Nagel (1986: 90). Nagel takes over this kind of idealism from Williams and Lear. I’ll elaborate on it in Sect. 5. 122. McDowell (1994: 11). 123. Cf. Glock (2004: 226–228). 124. I share this view with Glock (2004: 232–233) and Hacker (2017: 217–218). Compare Wittgenstein’s rough definition of logical syntax as “the rules which tell us in which connections only a word gives sense, thus excluding nonsensical structures” (RLF: 162) with his equally rough definition of grammar (WL: 46–47): “Grammar (rules and vocabulary) is the description of language, and it consists in giving the rules for the ­combination of symbols, i.e. which combinations make sense and which don’t, which are allowed and which are not allowed.”

References Appelqvist, H. 2020. Wittgenstein and the Limits of Language. London: Routledge. Cheung, L.K.C. 2008. The Disenchantment of Nonsense: Understanding Wittgenstein’s Tractatus. Philosophical Investigations 31 (3): 197–226. Conant, J. 1991. The Search for Logically Alien Thought: Descartes, Kant, Frege, and the Tractatus. Philosophical Topics 20 (1): 115–180. ———. 1993. Kierkegaard, Wittgenstein, and Nonsense. In Pursuits of Reason. Essays in Honor of Stanley Cavell, ed. T. Cohen, P. Guyer, and H. Putnam, 195–224. Lubbock: Texas Tech University Press.

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———. 1998. Wittgenstein on Meaning and Use. Philosophical Investigations 21 (3): 222–250. ———. 2001. Two Conceptions of Die Überwindung der Metaphysik. Carnap and Early Wittgenstein. In Wittgenstein in America, ed. T.  McCarthy and S.C. Stidd, 13–61. Oxford: Clarendon Press. ———. 2002. The Method of the Tractatus. In From Frege to Wittgenstein. Perspectives on Early Analytic Philosophy, ed. E.H. Reck, 374–462. Oxford: Oxford University Press. ———. 2004. Why Worry about the Tractatus? In Post-Analytic Tractatus, ed. B. Stocker, 167–192. Aldershot: Ashgate. ———. 2006. Wittgenstein’s Later Criticism of the Tractatus. In Wittgenstein: The Philosopher and his Works, ed. A. Pichler and S. Säätelä, 2nd ed., 172–204. Frankfurt: Ontos Verlag. ———. 2007. Mild Mono-Wittgensteinianism. In Wittgenstein and the Moral Life. Essays in Honor of Cora Diamond, ed. A. Crary, 31–142. Cambridge, MA: MIT Press. ———. 2011. Wittgenstein’s Methods. In The Oxford Handbook of Wittgenstein, ed. O. Kuusela and M. McGinn, 620–645. Oxford: Oxford University Press. Conant, J., and S.  Bronzo. 2017. Resolute Readings of the Tractatus. In A Companion to Wittgenstein, ed. H.-J. Glock and J. Hyman, 175–194. Oxford: Wiley-Blackwell. Conant, J., and E.  Dain. 2011. Throwing the Baby Out: A Reply to Roger White. In Beyond the Tractatus Wars. The New Wittgenstein Debate, ed. R. Read and M.A. Lavery, 66–83. London: Routledge. Conant, J., and C. Diamond. 2004. On Reading the Tractatus Resolutely: Reply to Meredith Williams and Peter Sullivan. In Wittgenstein’s Lasting Significance, ed. M. Kölbel and B. Weiss, 46–99. London: Routledge. Costello, D. 2004. ‘Making Sense’ of Nonsense: Conant and Diamond Read Wittgenstein’s Tractatus. In In Post-Analytic Tractatus, ed. B. Stocker, 99–125. Aldershot: Ashgate. Diamond, C. 1984. What Does a Concept Script Do? The Philosophical Quarterly 34 (136): 343–368. ———. 1991. Throwing Away the Ladder: How to Read the Tractatus. In The Realistic Spirit. Wittgenstein, Philosophy, and the Mind, ed. C.  Diamond, 179–204. Cambridge, MA: MIT Press. ———. 2000. Ethics, Imagination and the Method of Wittgenstein’s Tractatus. In The New Wittgenstein, ed. A.  Crary and R.  Read, 149–173. London: Routledge.

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———. 2011. The Tractatus and The Limits of Sense. In The Oxford Handbook of Wittgenstein, ed. O. Kuusela and M. McGinn, 240–275. Oxford: Oxford University Press. Floyd, J. 2007. Wittgenstein and the Inexpressible. In Wittgenstein and the Moral Life. Essays in Honor of Cora Diamond, ed. A. Crary, 177–234. Cambridge, MA: MIT Press. Glock, H.-J. 2004. All Kinds of Nonsense. In Wittgenstein At Work. Method in the Philosophical Investigations, ed. E. Ammereller and E. Fischer, 221–245. London: Routledge. Hacker, P.M.S. 1986. Insight and Illusion. Themes in the Philosophy of Wittgenstein. Oxford: Clarendon Press. ———. 2000. Was He Trying to Whistle It? In The New Wittgenstein, ed. A. Crary and R. Read, 353–388. London: Routledge. ———. 2003. Wittgenstein, Carnap and the New American Wittgensteinians. The Philosophical Quarterly 53 (210): 1–23. ———. 2017. Metaphysics: From Ineffability to Normativity. In A Companion to Wittgenstein, ed. H.-J.  Glock and J.  Hyman, 209–227. Oxford: Wiley-Blackwell. Hutchinson, P. 2006. Unsinnig: A Reply to Hutto. International Journal of Philosophical Studies 14 (4): 569–577. Hutchinson, P., and R. Read. 2006. An Elucidatory Reading of Wittgenstein’s Tractatus: A Critique of Daniel D. Hutto’s and Marie McGinn’s Reading of Tractatus 6.54. International Journal of Philosophical Studies 14 (1): 1–29. Hutto, D.D. 2003. Wittgenstein and the End of Philosophy. Neither Theory nor Therapy. Basingstoke: Palgrave Macmillan. ———. 2004. More Making Sense of Nonsense: From Logical Forms to Forms of Life. In Post-Analytic Tractatus, ed. B. Stocker, 127–149. Aldershot: Ashgate. ———. 2006. Misreadings, Clarifications, and Reminders: A Reply to Hutchinson and Read. International Journal of Philosophical Studies 14 (4): 561–567. Hutto, D.D., and J. Lippitt. 1998. Making Sense of Nonsense: Kierkegaard and Wittgenstein. Proceedings of the Aristotelian Society 98: 263–286. Ishiguro, H. 1969. Use and Reference of Names. In Studies in the Philosophy of Wittgenstein, ed. P. Winch, 20–50. London: Routledge & Kegan Paul. Koethe, J. 2003. On the ‘Resolute’ Reading of the Tractatus. Philosophical Investigations 26 (3): 187–204. Kremer, M. 2001. The Purpose of Tractarian Nonsense. Noûs 35 (1): 39–71.

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Kuusela, O. 2007. Review of Marie McGinn: Elucidating the Tractatus. Notre Dame Philosophical Reviews 21. http://ndpr.nd.edu/news/23051/?id=10524. Accessed 12 Jan 2021. ———. 2008. Review of Barry Stocker (ed.): Post-Analytic Tractatus. European Journal of Philosophy 16 (3): 478–482. Malcolm, N. 1986. Nothing is Hidden. Wittgenstein’s Criticism of his Early Thought. Oxford: Basil Blackwell. McCarty, D.C. 1991. The Philosophy of Logical Wholism. Synthese 87 (1): 51–123. McDowell, J. 1994. Mind and World. Cambridge, MA: Harvard University Press. McGinn, M. 1999. Between Metaphysics and Nonsense: Elucidation in Wittgenstein’s Tractatus. The Philosophical Quarterly 49 (197): 491–513. ———. 2006. Elucidating the Tractatus. Wittgenstein’s Early Philosophy of Logic & Language. Oxford: Clarendon Press. McGuinness, B.F. 2002. Approaches to Wittgenstein. Collected Papers. London: Routledge. Moore, A.W. 1997. Points of View. Oxford: Oxford University Press. ———. 2013. Was the Author of the Tractatus a Transcendental Idealist? In Wittgenstein’s Tractatus. History & Interpretation, ed. P. Sullivan and M. Potter, 239–255. Oxford: Oxford University Press. Mulhall, S. 2007. Wittgenstein’s Private Language. Grammar, Nonsense, and Imagination in Philosophical Investigations, §§243–315. Oxford: Clarendon Press. Nagel, Th. 1986. The View from Nowhere. New York: Oxford University Press. Pears, D.F. 1987. The False Prison. Vol. One. Oxford: Clarendon Press. Proops, I. 2001. The New Wittgenstein: A Critique. European Journal of Philosophy 9 (3): 375–404. Read, R. 2006. A No-Theory?: Against Hutto on Wittgenstein. Philosophical Investigations 29 (1): 73–81. Read, R., and R. Deans. 2003. ‘Nothing is shown’: A ‘Resolute’ Response to Mounce, Emiliani, Koethe and Vilhauer. Philosophical Investigations 26 (3): 239–268. Rhees, R. 1966. The Philosophy of Wittgenstein. Ratio 8: 180–193. ———. 1969. ‘Ontology’ and Identity in the Tractatus. In Studies in the Philosophy of Wittgenstein, ed. P.  Winch, 51–65. London: Routledge & Kegan Paul. Stenius, E. 1960. Wittgenstein’s Tractatus. A Critical Exposition of its Main Lines of Thought. Oxford: Basil Blackwell.

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Sullivan, P.M. 2011. Synthesizing Without Concepts. In Beyond the Tractatus Wars. The New Wittgenstein Debate, ed. R. Read and M.A. Lavery, 171–189. London: Routledge. ———. 2013. Idealism in Wittgenstein: a Further Reply to Moore. In Wittgenstein’s Tractatus. History & Interpretation, ed. P. Sullivan and M. Potter, 256–270. Oxford: Oxford University Press. White, R.M. 2011. Throwing the Baby Out with the Ladder: On ‘Therapeutic’ Readings of Wittgenstein’s Tractatus. In Beyond the Tractatus Wars. The New Wittgenstein Debate, ed. R.  Read and M.A.  Lavery, 22–65. London: Routledge. Williams, M. 2004. Nonsense and Cosmic Exile: The Austere Reading of the Tractatus. In Wittgenstein’s Lasting Significance, ed. M. Kölbel and B. Weiss, 6–31. London: Routledge. Winch, P. 1969. Introduction: The Unity of Wittgenstein’s Philosophy. In Studies in the Philosophy of Wittgenstein, ed. P.  Winch, 1–19. London: Routledge.

5 Wittgenstein’s Later Metametaphysics

In this and the next section I proceed in the same way as in Sect. 3 and 4. I first establish Wittgenstein’s Metametaphysics and address the realism-idealism problematic revolving around it (Sect. 5), after which I examine the rule-following considerations as a case study in light of the realism-idealism problematic (Sect. 6). To begin with, I lay out and discuss two common ways in which later Wittgenstein has been taken to be an idealist (Sect. 5.1). The first is a kind of conventionalism, according to which the structure of reality is nothing but a shadow of grammar, and the second one maintains that it’s in principle impossible to transcend the language-games we play. I then go on to elaborate on Wittgenstein’s notions of rules and grammar (Sect. 5.2), with particular focus on grammar being autonomous and rules being constitutive and non-descriptive. Finally, I synthesize the previous results and sketch my own account of Wittgenstein’s approach, according to which the autonomy of grammar and the plurality of language-games don’t imply the forms of idealism usually attributed to him (Sect. 5.3).

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 M. Bartmann, Wittgenstein’s Metametaphysics and the Realism-Idealism Debate, https://doi.org/10.1007/978-3-030-73335-3_5

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5.1 Two Roads to Idealism In the last section I elaborated on how a different understanding of Wittgenstein’s conception of logical syntax and the picture theory, of which it’s an integral part, enables us to sidestep the realism-idealism dichotomy. According to my analysis, what generated the debate between realists (such as the Pears-Malcolm position) and idealists (such as the Ishiguro-McGuinness and A.W. Moore’s position) was a particular construal of the limits of language as limitations. Both positions share the assumption that language and the world are two different and mutually independent realms but disagree over which realm is to be recognized as the source of limitations. More specifically, at issue was whether logical syntax has to reflect the independent structure of the world in order to represent it correctly, or whether the seemingly independent structure of the world is nothing but a projection of logical syntax. As we’ve seen, the framework of this debate turned out to be misguided because for Wittgenstein the structure of language and the structure of the world are identical. Logical syntax, therefore, is better understood as a nondescriptive, metaphysically neutral expression of the structure of the world— neither mirror nor projection. The crucial point was to distinguish between the status and the source of determination of the picturing relationship, the former being logically symmetrical and the latter being ontologically asymmetrical. This way, we could conceive of the totality of obtaining and nonobtaining states of affairs—logical space—as already comprising language and the world, while simultaneously acknowledging a significant distinction between what represents and what is represented. In a certain sense, then, no contrast between language and world can be drawn, and the assumption of two different and mutually independent realms can be abandoned without falling prey to the pitfalls of either realism or idealism. As we’ve also seen, the resolute reading, too, entailed a tacit commitment to a version of idealism, although for different reasons. In general, realist readings take the Tractatus to be a theoretical philosophical project determining the limits of language by determining the metaphysical structure of the world. However, the resolute reading views the fundamental aim of the Tractatus as diametrically opposed to such a project and rejects the very idea of language’s having limits in the first place. But with the need to make

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room in some way or other for semantic constraints on the one hand, and with the world as a potential source for these constraints ruled out on the other, the resolute reading instead deflates the notion of logical syntax by reinterpreting it as our ordinary “capacities for distinguishing sense from nonsense […] implicit in the everyday practical mastery of language […].”1 By placing the source of semantic constraints mainly in the practices of our ordinary language-­games, together with its austere conception of nonsense, the resolute reading implicitly commits itself to the conclusion that the notion of something’s being outside our language-games is ultimately inconceivable. Therefore, this conception of the limits of language revealed itself to be a form of idealism because it’s essentially the same kind of conception believed to be at work in later Wittgenstein by Nagel. Nagel, in turn, has largely adopted the Wittgenstein interpretation developed by Williams.2 I’ll present this position, which I’ll refer to as the Williams-Lear position given their close philosophical kinship on this matter, in greater detail below. But first I want to draw attention to the profound methodological consequences of this position for any philosophical account of the relation between language and the world because they are also reflected in the resolute reading (although implicitly) and the elucidatory reading (rather expressly). Williams and Lear themselves make these consequences quite explicit. Since, according to the Wittgenstein of the Williams-Lear position, it’s impossible to get outside language in order to analyze its underlying conditions, we are left with making language: clearer to ourselves, by reflecting on it, as it were self-consciously exercising it; not indeed by considering alternatives—for what I am presently considering can have no comprehensible alternatives to it—but by moving around reflectively inside our view of things and sensing when one began to be near the edge by the increasing incomprehensibility of things regarded from whatever way-out point of view one had moved into.3

As noted, the resolute reading doesn’t make this implication of its conception of the limits of language explicit, but it’s interesting to see that the elucidatory reading of the Tractatus reaches the same methodological conclusion as the Williams-Lear position. This shouldn’t be particularly surprising because the elucidatory reading, although it differs from the resolute reading in some respects, also subscribes to a similar conception

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of the limits of language. For example, according to Hutto, Wittgenstein tells us “that it is not possible to leave our side of the fence, as it were, so as to think both sides of the ‘limits’ of thought.”4 Consequently, as: the bounds of sense are set internally, by the very topics about which we can think, philosophy can at best clarify and make perspicuous that which is already known to us. This is what it means to stake out the limits of thought from the inside.5

Reflecting on the foregoing considerations, we can now describe in more detail two basic ways in which the Tractatus has been taken to embody a form of idealism. Both ways depend on a certain conception of the limits of language, which is why it will be useful to recall Sullivan’s distinction between limits and limitations introduced in Sect. 4.3. “Limitation” is a contrastive notion, referring to boundaries separating different things or regions (concrete or abstract). Limitations always have two sides regardless of what they separate. “Limit,” on the other hand, is a non-contrastive notion, referring to essential or constitutive features of something. Limits have no other side. In short, the idea of transgressing, going beyond, or violating something can be meaningfully applied only to limitations, but not to limits.6 As I mentioned at the beginning of this section, it’s characteristic of the idealist positions of Ishiguro-McGuinness and A.W. Moore to construe the limits of language as limitations, and now we can couch this assessment in more precise terms. According to Ishiguro-McGuinness and Moore, logical syntax consists of a set of rules providing the conceptual resources for representing the world. But logical syntax could be (or could have been) other than it is. It’s in this specific sense that logical syntax is understood as a limitation of language, simply by being one possible set of rules among others. This has metaphysical consequences because the shape of logical syntax also determines the shape of how the world is represented. The world would be represented differently if logical syntax were other than it is. So the structure of the world depends on the kind of logical syntax we have, and that is why commentators such as Moore conclude that the Wittgenstein of the Tractatus was an idealist.7 To illustrate, consider Wittgenstein’s famous opening of the Tractatus: “The world is the totality of facts, not of things” (TLP: 1.1). According

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to Moore, what Wittgenstein is doing here is characterizing the actual fundamental structure of the world by contrasting it with a certain way the fundamental structure of the world could be (or could have been). Our world is the totality of facts, but that is merely one possibility among others. There could have been, so the argument goes, creatures in the universe whose world were one of things (or we could have been such creatures). Therefore, Moore takes the proposition that the world is the totality of facts to express certain limitations, as a claim that is only contingently true of our world due to our conceptual resources. However, this claim would have been false if we had had the conceptual resources allowing for the possibility to access a world of things. Since we ourselves are the source of limitations of the structure of the world by excluding possibilities “not consonant with the nature of our thinking,”8 we subscribe to a version of idealism. Let’s compare Moore’s position with the Williams-Lear position. Williams draws a distinction between two categorically different interpretations of the limits of language that yield two very different kinds of idealism. The limits of language can be understood either empirically or transcendentally.9 The empirical interpretation here roughly corresponds to Moore’s construal of the limits of language as limitations, as empirically contingent constraints that could be (or could have been) other than they actually are. For Moore, our having been endowed with different conceptual capacities is perfectly imaginable, at least in principle. And since our conceptual capacities determine the structure of the world, it also becomes intelligible how differences concerning the former constitute differences regarding the latter. Williams spells out this empirical form of idealism in the following way: Thus the claim that the limits of our language mean the limits of our world might be construed empirically this way, by taking language narrowly, to refer to one’s system of communication, its grammatical categories, etc., and world widely, to mean how in general the world appears to one, the general framework of comprehension one applies to things, etc.; and then, taking ‘we’ relatively to various linguistic groups, one would have the hypothesis, perhaps ascribed to Whorf, that the way things look to different groups profoundly depends on what their language is like.10

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In sharp contrast to this, Williams believes Wittgenstein conceives of the limits of language transcendentally and takes him to subscribe to a form of transcendental idealism: Under the idealist interpretation, it is not a question of our recognizing that we are one lot in the world among others, and (in principle at least) coming to understand and explain how our language conditions our view of the world, while that of others conditions theirs differently. Rather, what the world is for us is shown by the fact that we can make sense of some things and not of others.11

Contrary to Moore, who sees the limits of language as relative limitations, as empirically contingent constraints shaping our world-view that may contrast with other conceivable alternatives, Williams-Lear see the limits of language as an absolute limit, as a world-view that cannot contrast with other possibilities. For the position of Williams-Lear, every insight we could possibly gain into the conditions of our access to the world, or into the allegedly radically different conditions of imagined others, would, necessarily, itself be subject to our conditions.12 The intuitively plausible idea of a radically different access to the world now becomes unintelligible, because we cannot break the vicious circle of being conditioned by our world-view—our world-view simply has no alternative. Since, according to Williams-Lear, for Wittgenstein “everything can be expressed only via human interests and concerns,” they conclude that this provides strong evidence for “calling such a view a kind of idealism.”13 What deserves emphasis at this point is that the two kinds of idealism I distinguished in the preceding paragraphs are not only most commonly attributed to the Tractatus but also frequently attributed to later Wittgenstein, in particular to the Investigations. Let’s have a closer look at both forms of idealism, which I’ll call, for reasons that will become clear shortly, mindedness idealism and convention idealism. Mindedness idealism is the kind of idealism advocated by Williams-­ Lear, Nagel, and others. Since the resolute and elucidatory readings of the Tractatus subscribe to a very similar conception of the limits of language that led Williams-Lear to their position, we can categorize both readings as a version of mindedness idealism as well.

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The positions of Ishiguro-McGuinness and A.W. Moore, on the other hand, represent a species of convention idealism, and the simple reason for classifying them in this way is that this position is structurally very similar to conventionalist readings of later Wittgenstein, which more often than not end up taking Wittgenstein to be a kind of idealist. I’ll start with elaborating on convention idealism and then turn to mindedness idealism. As we’ll see in the course of this section, although both forms of idealism seem very different, they share what I take to be a misunderstanding regarding Wittgenstein’s conception of rules. This misunderstanding will then be cleared up in the following subsection. Convention Idealism Attributing to later Wittgenstein a form of conventionalism enjoys a long and still popular tradition, going back at least to Michael Dummett. In a famous essay he characterizes Wittgenstein as going in: for a full-blooded conventionalism; for him the logical necessity of any statement is always the direct expression of a linguistic convention. That a given statement is necessary consists always in our having expressly decided to treat that very statement as unassailable.14

And a little later in the same essay he writes: He appears to hold that it is up to us to decide to regard any statement we happen to pick on as holding necessarily, if we choose to do so. The idea behind this appears to be that, by laying down that something is to be regarded as holding necessarily, we thereby in part determine the sense of the words it contains; since we have the right to attach what sense we choose to the words we employ, we have the right to lay down as necessary any statement we choose to regard as such.15

Dummett’s account of Wittgenstein’s (alleged) conventionalism focuses primarily on the case of logic (e.g. inference rules and logical laws such as modus ponens and the law of excluded middle) and on the case of mathematics (mathematical statements such as “7 + 5 = 12”). There are two salient components of Dummett’s conventionalism reflected in the quoted passages, components that can also be frequently encountered in the accounts of subsequent proponents of conventionalism:

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1. The necessity of logical and mathematical statements is somehow rooted in linguistic conventions consisting in semantic rules that constitute the meaning of linguistic expressions. 2. Since we are at liberty to associate linguistic expressions with whatever semantic rules we want, we can thereby also determine as necessary any statement we want. The logical or mathematical necessity of a statement is always the result of linguistic choices, whether made deliberately or not. Concerning the first component (1), many Wittgenstein commentators would presumably accept it regardless of whether they would also endorse the second component, and with it “full-blooded conventionalism” itself. Very few would deny that, according to Wittgenstein, there is a close connection between the logical and mathematical necessity of statements and semantic rules expressed by linguistic conventions, even though it’s not uncontroversial exactly how the connection is to be understood. Not only does Wittgenstein state at one point that there is a “deep need for the convention” (RFM: I, 74), but he also considers concrete mathematical and logical examples to explain his account: If it is not to be an empirical sentence that the rule [+ 1] leads from 4 to 5, then this, the result itself, must be taken as a criterion for someone’s having followed the rule. (RFM: VI, 16) In mathematics the result itself is a criterion for calculating correctly. Therefore, it is impossible to follow the rule correctly and generate different calculations. (RFM: VII, 27) The steps which are not brought in question are logical inferences. But the reason why they are not brought in question is not that they “certainly correspond to the truth”—or something of the sort—no, it is just this that is called “thinking,” “speaking,” “inferring,” “arguing.” (RFM: I, 155)

Wittgenstein maintains that certain kinds of rule-governed practices such as calculating and inferring are defined—and not merely described—by the respective rules involved in these practices. Mathematical and logical rules are constitutive of calculating and inferring in the sense that a practice in which rule-followers didn’t follow the respective rules correctly couldn’t adequately be described as calculating or inferring. The

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definitional character of these constitutive rules is also precisely what makes for mathematical and logical necessity. Since the correct result of calculations involving the rule “+ 1” is an essential part of the definition of the rule “+ 1,” it follows that if someone were to give any other response than “5” when asked to calculate “4 + 1,” then she would automatically not count as having followed correctly the rule “+ 1.” Similarly in the case of inference rules. Modus ponens is simply defined as implying “Q” given “P” and “If P, then Q,” so that any response other than “Q” wouldn’t count as having inferred correctly. In both the mathematical and logical cases, the correct result of the respective operations is part of the identity conditions of the operations itself.16 As we’ll see in more detail in the next subsection, Wittgenstein’s idea behind this conception, adumbrated in the last of the quotes above, is that the constitutive rules governing certain kind of practices enjoy a special status, not because they cannot but be taken as true or cannot reasonably be denied, but because constitutive rules are not candidates for truth and falsity in the first place. Concerning the second component of conventionalism (2), the idea that we can declare any sentence as necessary because we are free to adopt any linguistic convention we want by associating linguistic expressions with whatever semantic rules we want is highly controversial.17 But it’s easy to see how one may arrive at such a conclusion. If logical and mathematical necessity are based on linguistic conventions, and if linguistic conventions are the product of our associating linguistic expressions with semantic rules, then it quickly follows that the set of sentences possessing the property of necessity co-varies with the set of rules we adopt. Unlike the laws of physics, linguistic conventions are the product of human linguistic activity not set in stone, and it seems therefore perfectly possible to adopt different linguistic conventions by choosing different rules. This makes it plausible how one may get the impression that conferring necessity on statements is in the end arbitrary, the result of choices we could have made otherwise. What is important to note here is that a conventionalist account of Wittgenstein along these lines leads commentators in many cases to attributing a kind of idealism to his position, which is why I’ll call such accounts convention idealism. The connection between conventionalism and idealism is rather straightforward, and Wittgenstein seems at times to make the connection himself. Not only seems the possibility of

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interpreting and following rules in different ways to be a prominent and recurring theme in later Wittgenstein, particularly in the Investigations.18 He also characterizes his notion of grammar—which “consists of conventions” (PG: 138), that is, semantic rules governing the use of linguistic expressions—in the following way19: Essence is expressed by grammar. Consider: “The only correlate in language to an intrinsic necessity is an arbitrary rule. It is the only think which one can milk out of this intrinsic necessity into a proposition.” Grammar tells what kind of object anything is. (PI: 371–373)20

The two components of conventionalism I’ve identified in Dummett’s account seem to be discernible in this passage as well. First, Wittgenstein not only connects grammar and rules to essence and necessity, but also links it to the categorization of objects. Second, necessity is being presented as correlating with arbitrary rules. Now, if grammar plays a decisive role in logical and mathematical necessity, as well as in the categorization of objects, and if grammar is a product of arbitrary human conventions, then it’s indeed difficult to see how this kind of conventionalism is not tantamount to a kind of idealism. Take, for example, Anscombe’s recapitulation of Wittgenstein’s view: To sum up: Essence is expressed by grammar. But we can conceive of different concepts, i.e. of language without the same grammar. People using this would then not be using language whose grammar expressed the same essences.21

Again, both components of conventionalism are present: the connection between grammar and essence, and the possibility of alternative concepts and hence the possibility of alternative grammars. In light of this fact, it comes as no surprise that Anscombe concludes shortly thereafter that Wittgenstein was a linguistic idealist: However this may be if there is such a thing as idealism about rules and about necessity of doing this if you are to be in conformity with this rule, then here Wittgenstein was a linguistic idealist.22

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Bloor is thus perfectly right in his assessment of Anscombe’s reading of Wittgenstein when he asks rhetorically: “For what is Anscombe’s ‘linguistic idealism’ other than a way of acknowledging the operation of convention?”23 Even more explicit is Hacker’s account of later Wittgenstein, which is presumably one of the most refined expressions of convention idealism in the literature, even though Hacker is careful not to label Wittgenstein as an idealist. Nevertheless, reviewing Hacker’s account of “the conventionalism of the later philosophy”24 leaves one wondering if Wittgenstein may be an idealist after all. For example, Hacker not only states pointedly that, according to Wittgenstein, “the apparent ‘structure of reality’ is merely the shadow cast by grammar,”25 but he is also perfectly clear about the role conventions play in Wittgenstein’s account of grammar: What is logically possible or impossible just is: what makes sense. And what makes sense in a given language is determined by the grammar of the language, by the arbitrary rules for the use of expressions (and their manner of application in practice). Essences are reflections of forms of representation, marks of concepts, and thus made rather than found. […] Essences are a product of convention, not a discovery of reason. All talk of essence is talk of conventions, and what seems to us to be the ‘depth’ of the essences is the fact of the depth of our need for the conventions.26

Together with the emphasis on essences being the arbitrary product of human convention, it’s difficult not to see this account of Wittgenstein’s later philosophy as a kind of idealism. Hacker’s account of Wittgenstein’s notion of grammar also shares with the (expressly idealist) Williams-Lear account the very same methodological consequence. Since essences are determined by grammar, which in turn is confined to being a purely linguistic affair, “conceptual investigation will not produce insights into the nature of the world, but only into the grammar of our descriptions of the world.”27 But regardless of whether Hacker’s account of later Wittgenstein amounts to a kind of idealism, at least the Williams-Lear position definitely does, and this brings me to mindedness idealism. Mindedness Idealism The notion of being minded a certain way—or mindedness for short—has been introduced by Lear, stating that Wittgenstein sees philosophy’s main job in drawing attention to and

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systematically exploring our own mindedness.28 Lear defines this notion in the following way: Let us say that a person is minded in a certain way, if he has the perceptions of salience, routes of interest, feelings of naturalness in following a rule, etc. that constitute being part of a certain form of life.29

According to Lear, mindedness comprises various sets of preferences a person must necessarily possess in order to be a member of a particular form of life. Unfortunately, Lear does not specify in more detail his interpretation of Wittgenstein’s notoriously vague notion of a form of life. However, from the context of Lear’s discussion it seems safe to count beliefs, customs, and practices as important aspects of a particular form of life, which in their entirety shape a person’s world-view.30 At first sight, then, Lear’s conception seems to suggest that mindedness, just as the notion of a convention, is a genuinely pluralist notion. Just as it seems possible for persons to adopt different linguistic conventions, so it seems possible for persons to be minded in different ways, for them to be part of different forms of life, and hence for them to have different worldviews. After all, isn’t it perfectly imaginable for persons to differ with regard to their perceptions of salience, routes of interest, and feelings of naturalness in following a rule? And aren’t the existence of different forms of life and different world-views not simply a plain fact of life itself? As noted above, this is exactly what the Williams-Lear position denies. For now, however, we can bracket this issue and state that if these preferences are constitutive for being part of a particular form of life, then it follows that a person possessing different preferences also entails her being part of a different form of life and consequently having a different world-view. In other words, preferences such as perceptions of salience, routes of interest, and feelings of naturalness in following a rule form part of a person’s “cognitive hardware,” so to speak, which manifest themselves in the person’s membership of a particular form of life, which in turn also determines a person’s “cognitive software,” that is, her having a particular world-view. Lear illustrates this connection, the determination relation between a person’s hard- and software, by considering the following two examples:

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What does 7 + 5 equal? (a) 12. (b) Anything at all, just as long as everyone is so minded. What follows from P and If P, then Q? (a) Q. (b) Anything at all, just as long as everyone is so minded.31

These are extreme examples of two persons or two groups of persons following mathematical and logical rules, respectively, in radically different ways, and consequently arriving at very different results. The point Lear wants to make with these examples is this. Usually, while we would in both cases consider any answer other than (a) as plainly false, commentators attributing to Wittgenstein a radical form of conventionalism like Dummett would have to concede that (b) might under certain circumstances also be true. As we’ve seen, for convention idealism alternative grammars are always possible if we imagine following rules differently and thereby adopting linguistic conventions other than those we actually have. Since rules making up linguistic conventions are the source of logical and mathematical necessity, following different rules and adopting different linguistic conventions would also generate a different set of logically and mathematically necessary sentences. Convention idealism, then, is committed to the claim that questions such as “What does 7 + 5 equal?” and “What follows from P and If P, then Q” don’t have one determinate and correct answer, but instead depend on the arbitrary rules we follow and the conventions we adopt. It depends, as Lear puts it, on how we are minded. I want to pause here for a moment to point out that Lear’s initial conception of mindedness, which he uses as a starting point in his efforts to paint Wittgenstein as an idealist, bears a striking resemblance to convention idealism. The common denominator of convention and mindedness idealism is that both single out rule-following as one of the essential elements among the factors shaping our access to the world and hence our world-view. For Lear, a person’s various dispositions to follow a rule in certain ways enter into the calibration of a particular form of life and subsequently form the person’s world-view. In a very similar way, convention idealism states that the particular ways in which we follow rules at the same time establish the concepts we use, which in turn structures our access to the world given that language is our primary means of

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representing it. Moore succinctly describes how the combination of rule-­ following and arbitrariness may lead to a form of idealism: It is because of ‘how we go on’ that our concepts are as they are. Hence it is because of how we go on that the necessities that hold in virtue of the interconnections of our concepts hold. But how we go on is grounded in a complex of biological and cultural contingencies to which we are subject. So the necessities in question are ultimately grounded in those same contingencies. So the limits of language and the limits of the world are indeed, at some level, limitations, set by us, those who understand language and who think about the world.32

What convention and mindedness idealism agree on is the overall importance of rule-following for logical and mathematical necessity in particular and for determining a certain kind of form of life in general, that is, the role rule-following plays in the formation of our beliefs, customs, and practices—in short: in shaping our world-view. Convention and mindedness idealism’s common theoretical ground is summed up in the following thesis: Only because we are minded as we are do we see the world the way we do.33

The point at which mindedness idealism parts company with convention idealism is the next step conventionalists are naturally inclined to take: If we were other-minded, we would see the world differently.34

The possibility of being other-minded is exactly what Williams-Lear deny. Mindedness idealism doesn’t claim that the structure of reality depends on our particular mode of access to it while conceding that our mode of access—and hence the structure of reality—is but one contingent possibility among others. This position, rather characteristic of convention idealism, would admit the possibility of creatures being other-minded and playing language-games radically different from our own. However, the Wittgenstein of Williams-Lear fervently denies this possibility. They wouldn’t consider a world in which “7 + 5” equaled anything other than 12 and in which anything other than Q followed from “P” and “If P, then Q” a possible world at all, as if that world were

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imaginable in principle, but inaccessible to us because of our limited conceptual resources. Such counterfactuals: cannot for us express real possibilities; for the notion of people being “other-minded” is not something on which we can get any grasp. The possibility of there being persons who are minded in any way at all is the possibility of their being minded as we are. Our problem is that being minded as we are is not one possibility we can explore among others. We explore what it is to be minded as we are by moving around self-consciously and determining what makes more or less sense. There is no getting a glimpse of what it might be like to be other-minded, for as we move toward the outer bounds of our mindedness we verge on incoherence and nonsense.35

In sum, according to Williams-Lear, Wittgenstein’s idealism is supposed to be the thesis that it’s impossible to transcend the limits of our language-­ games, meaning that what is outside the language-games we play is perforce unintelligible, and every attempt to go beyond the limits of language must therefore result in nonsense. Whereas convention idealism emphasizes the possibility of a world-view radically different from ours, mindedness idealism insists on the impossibility of getting outside one’s own world-view without falling into incoherence.36 Regardless of the philosophical consistency of mindedness idealism as presented by Williams-Lear, it seems at least exegetically problematic to attribute it to Wittgenstein. As has been pointed out in the literature, it’s surprising how scarce the textual evidence is on which Williams-Lear base their reading.37 Hardly any examples are being discussed, only a few scattered remarks by Wittgenstein are mentioned. However, even those remarks are far from being unambiguous and are rather in need of careful interpretation. For example, Williams-Lear see mindedness idealism at work in both early and later Wittgenstein. The only difference consists in a shift of focus from the first-person singular to the first-person plural, so to speak. According to Williams-Lear, for early Wittgenstein the absolute limit of language is established by the solipsistic “I,” whereas for later Wittgenstein the very same limit is established by the collective “we.” In both cases, though, there is nothing contrasting with the limit of language thus constituted because in both cases the limit is a transcendental one. Just as the

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solipsistic “I” is not a particular person in the world among others, so the collective “we” is not a particular group in the world among others. Rather, they are simply names for the uncrossable border of the realm of sense, the point of no return before the realm of nonsense. However, several commentators have pointed out that Wittgenstein in many cases does refer to particular empirical groups by the use of “we” instead of intending to mark an absolute, transcendental limit.38 A particularly relevant and interesting case in point is Wittgenstein’s wood-­ sellers, people whose method of measurement and payment is so different that it raises the question whether their practice can be understood at all. I’ll examine the case of the wood-sellers in Sect. 5.3 because it lends itself to showing how Wittgenstein is steering between realism and idealism. For now, I want to point out what I take to be a misunderstanding common to convention and mindedness idealism that is rooted in a particular misconception of Wittgenstein’s account of rules. This misunderstanding is best illustrated by a disagreement between Lear and Dummett about the law of excluded middle, the law according to which all instances of the schema “P or Non-P” are true. The details of Dummett’s arguments against the validity of the law of excluded middle are complex and sophisticated. However, the thrust of these arguments is rather straightforward.39 Dummett draws attention to a class of sentences he calls “undecidable sentences.” These are sentences whose truth-value is effectively undecidable, that is, sentences about the remote past and future, about infinity, and about regions of space-time in principle inaccessible to us. Dummett argues that, since in the case of undecidable sentences we have no justification for either asserting or denying them, it would follow that we also have no justification for either asserting or denying that an undecidable sentence is either true or false because we are justified only in asserting or denying a disjunction if we have a justification for asserting or denying either of the disjuncts. Interestingly, what Lear takes issue with is not Dummett’s attack on the law of excluded middle per se, but rather with Dummett’s demand of a justification for it. Lear himself thinks that the law of excluded middle is a belief so fundamental and so deeply entrenched in our form of life that it’s incapable of justification. Therefore, Lear agrees with Dummett that no justification for the law of excluded middle can be given, but he criticizes him for not accepting it as an inexplicable fact about our mindedness:

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When we come to view our linguistic practices correctly, we will see that there is no defense of the law of excluded middle beyond the fact that we are minded as we are. And the fact of our being so minded as we are is no defense at all. So Wittgenstein is not trying to impugn our belief in the law of excluded middle; his aim is to undermine the belief that we can provide explanation, justification, defense or foundation for our belief in it.40

Whereas Dummett demands a justification for the law of excluded middle, Lear claims that the law is unjustifiable. The convention idealism of Dummett ends up taking logical and mathematical statements such as “P or Non-P” and “7 + 5 equals 12” to be a contingent possibility among others, whereas the mindedness idealism of Williams-Lear states that any answer deviating from our own is unintelligible. In my view, both seem to be making the same mistake. Dummett and Lear are treating the law of excluded middle as a descriptive statement, something that can be true or false, which is why for both the question of justification arises. Once we realize that the law is not a truth-apt statement but a non-descriptive rule governing certain regions of rational discourse, then the question of justification disappears. The question “Is belief in the law of excluded middle justified or (un)justifiable?” can then be transformed into the question “Which regions of rational discourse are governed by the law of excluded middle?” To substantiate this view, we therefore need to have a closer look at Wittgenstein’s conception of rules and grammar.

5.2 Rules and Grammar For Wittgenstein, semantic rules are like the rules of a game (hence his ubiquitous notion and examples of language-games), and in their entirety, they make up what he calls grammar. Maybe the shortest way to capture the essence of semantic rules is by borrowing a phrase Georg Henrik von Wright used to characterize the laws of logic: they “neither describe nor prescribe, but determine something.”41 This means grammatical rules are constitutive in character, that is, they are neither descriptions of nor prescriptions for certain linguistic practices but partially define these

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practices—they wouldn’t be the same practices without these rules. These rules establish what counts as a move within certain linguistic practices and make them possible in the first place. Rather than being descriptions of the “true-false games” (PG: V, 68) we play, grammatical rules instead constitute the games within which descriptions are being made. Michael Forster succinctly captures Wittgenstein’s conception of grammar: Wittgenstein’s most basic conception of grammar is that it consists in rules which govern the use of words and which thereby constitute meanings or concepts. […] Just as the rules of a game constitute the game and first make possible the moves which occur within it, likewise grammar constitutes an area of language and first makes possible the linguistic moves which occur within it.42

Wittgenstein’s conception of grammatical rules is closely related to his conception of the rules of logical syntax on which I elaborated in Sect. 3. In this regard, constitutive rules are similar to tautologies in that they fail to meet the contingency requirement because they don’t describe something (truly or falsely) but rather determine that which they are about. As so often, Wittgenstein illustrates his conception of grammatical rules with reference to chess: You cook badly if you are guided in your cooking by rules other than the right ones; but if you follow other rules than those of chess you are playing another game; and if you follow grammatical rules other than such and such ones, that does not mean you say something wrong, no, you are speaking of something else. (PG: X, 133)

The point of this passage is that constitutive rules such as grammatical ones cannot be changed without simultaneously changing that of which they are constitutive. Not following the proper cooking rules will most likely result in unpalatable meals, but the activity producing these meals could still justifiably be called cooking. On the other hand, not following the rules of chess or following significantly different rules wouldn’t result in playing chess badly but rather in an activity that can no longer be

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characterized as playing chess. We can bring out the categorical difference between the rules of cooking and the rules of a game using John Searle’s distinction between “regulative” and “constitutive” rules: Regulative rules regulate a pre-existing activity, an activity whose existence is logically independent of the rules. Constitutive rules constitute […] an activity the existence of which is logically dependent on the rules.43

Regulative rules paradigmatically assume the form of imperatives such as “Do X” or “If Y do X,”44 whereas constitutive rules paradigmatically assume the form of quasi-definitional specifications such as “X counts as Y in context C.”45 Regulative rules are prescriptive in that they tell us what activities we ought to perform, whereas constitutive rules specify what it is to perform a certain activity, or what you have to do in order to perform it.46 For example, the regulative rules of dinner etiquette tell us how we ought (not) to behave at the dinner table, but these rules are not constitutive for the activity of eating. They can be flouted without ceasing to eat. The constitutive rules of chess, on the other hand, specify which actions count as moving the chess pieces, castling, check mate, and so forth. If we stop following them, we thereby cease to play chess. In other words, the rules of a game (i.e. grammatical rules) are constitutive in that they represent conditions for the possibility of the game itself.47 In sum, changing the constitutive rules of a game, unlike changing the regulative rules, is always tantamount to a change of the game itself. Wittgenstein describes this result of his considerations rather expressly. According to his view, a change in grammar is quite literally a game changer: The thing that’s so difficult to understand can be expressed like this. As long as we remain in the province of the true-false games a change in the grammar can only lead us from one such game to another, and never from something true to something false. (PG: V, 68)48

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One must resist the temptation to conceive of grammatical rules as being of the same kind as, or a species of, assertions because their surface grammar is deceptively similar. Compare the following two sentences: 1. Moving the bishop diagonally counts as a move in the context of chess. 2. It is true (correct) that moving the bishop diagonally counts as a move in the context of chess. Both sentences seem to be assertions about what the rule is for the bishop in chess, only that (2) makes explicit what (1) merely implies, namely that they are both either true or false, or, in other words, that they are both candidates for truth and falsity. But appearances are deceptive, and Wittgenstein clearly saw this ambiguity: “Every instruction can be construed as a description, every description as an instruction” (PR: II, 14). Following this distinction, we can call sentence (2) a description, whereas sentence (1) expresses an instruction, that is, an expression of the rule itself.49 Sentence (1) can, unlike (2), be considered constitutive. This becomes clearer if we rephrase (1) as follows: When you engage in playing chess and want to make a move with the bishop, then move only diagonally. This suggests that (1) is more aptly characterized as a conditional order or command, rather than an assertion, because it tells you what you have to do in order to make a move with the bishop.50 Therefore, sentence (1)—as opposed to sentence (2)—is, like an order, neither true nor false. Why exactly? Suppose I overhear a conversation in which Smith explains to Jones the rules of chess. Smith says “Moving the bishop orthogonally counts as a move in the context of chess.” Surely, Smith is saying something false here, but the sense in which she does is important. In ordinary circumstances, it would be perfectly fine to say that Smith is wrong because she cited the wrong rule for the bishop. But this should not mislead us to think that there are two kinds of chess rules, right ones and wrong ones. The only sense in which the rule expressed by Smith is a wrong one is that it’s not a rule constitutive of the bishop (but rather constitutive of the rook). More specifically, Smith simply represented a certain chess piece as being subject to a certain rule, when in fact the chess piece is subject to a

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different rule. The  appropriate contrast is  thus not between right and wrong, correct and incorrect, true or false rules. Rather, it would be less confusing simply to draw a contrast between those rules that are part of a game and those that are not. We can fix this contrast terminologically and call those rules that are actually a constitutive part of the game the rules that are in force, where being in force roughly consists in rules being “accepted and enforced by sanctions.”51 Of course, the orthogonal rule (or some other rule) could have been the rule for the “bishop” (i.e. other rules could have been in force).52 Would we say, then, that we now have the correct (or incorrect) rule for the bishop? Did, hypothetically, people who played chess with the orthogonal rule for the bishop play chess correctly (or incorrectly)? I think it would be natural to say these people would have had a different rule than we have today (and played a chess variant, if you will). And the simple reason for this is that the rules for chess pieces are not descriptions of wooden pieces but express what it means for the wooden pieces to be chess pieces.53 That is also why any item associated with the respective rule will be a chess piece, that is, any item subject to a particular chess rule. If we made the chess board big enough, for example, we could even play with pears, people, planes, whatever—as long as those items are subject to the respective rules. Practicality is the only limit here. Strictly speaking, then, there is no answer to questions such as “Why is it true that moving the bishop diagonally counts as a move in the context of chess?” or “What are the correct rules of chess?” These questions make sense only if we understand them descriptively, not instructively, so to speak. To ask what the “correct” rules for chess are is no more than to ask what the rules of chess are. But the rules that make up the game of chess are neither true nor false, neither correct nor incorrect. There are no “wrong” rules of chess, only the rules of chess. But if there are no wrong rules, then there are no right ones either. There is simply no fact in the world that could make a rule true because a rule is not an assertion about a possible state of affairs that might or might not obtain—though there are facts about which rules are in force.

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It’s true to say that the diagonal rule is the rule for the bishop in our current game of chess (i.e. is the rule in force), but the diagonal rule itself is neither true nor false. And the same goes for those grammatical rules constitutive of the meaning of particular expressions: There cannot be a question whether these or other rules are the correct ones for the use of ‘not’ (that is, whether they accord with its meaning.) For without these rules the word has as yet no meaning; and if we change the rules, it now has another meaning (or none), and in that case we may just as well change the word too. (PG: X, 133)54

Now, Wittgenstein’s conception of grammatical rules as constitutive has a consequence that is as surprising as it’s profound. As we’ve seen, constitutive rules, unlike prescriptive (regulative) rules, determine actions or practices by specifying the conditions under which certain activities count as those very actions or practices. These actions or practices are logically dependent on those constitutive rules such that without them the actions or practices would cease to be the very actions or practices they are. Chess without the (constitutive) chess rules ceases to be the game that it is because the chess rules simply define what the game essentially is. If we change the rules of chess, we simultaneously change the game itself. This conception has the consequence that constitutive rules cannot be violated and that, in a certain sense, there is no such thing as an incorrect or wrong application of a rule. Let me elaborate. Take our example from before and suppose Jones, due to the misinformation given to her by Smith, moves the bishop orthogonally in a chess game. We would ordinarily call that a mistake and say she had made a wrong move. But from the point of view of constitutive rules there can be no such thing. Given the constitutive rule for the bishop, Jones wouldn’t have violated this rule had she moved the bishop orthogonally. The reason is this: constitutive rules, recall, specify certain kind of actions performance of which counts as performing other kinds of actions. In our example, moving the bishop diagonally counts as making a chess move with the bishop (in the context of chess). But not moving the bishop diagonally is not violating the constitutive rule for the bishop—that is, not misapplying the diagonal rule—but rather is simply doing something

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that doesn’t qualify as moving the bishop. She wouldn’t have made a wrong move but no move at all, because the diagonal rule for the bishop defined what is required to make a move with the bishop in the first place. Strictly speaking, then, moving the bishop orthogonally cannot even be considered as moving the bishop at all.55 Hence, moving the bishop orthogonally is not violating—that is, not misapplying—the diagonal rule but simply either applying a different rule (e.g. the rule for the rook) or none (e.g. if Jones randomly moves chess pieces around).56 Similar considerations apply to constitutive rules with respect to expressions. If Jones associates and follows rules for certain expressions other than those of her speech community, then she is not saying something wrong or violating a semantic rule; rather she is speaking of something else. For example, if Jones, for whatever reason, associates in her idiolect the expression “cow” with the rule that is usually associated by her speech community with the expression “horse,” then of course Jones makes a linguistic mistake. But the point is that when Jones, in front of a horse under epistemically ideal conditions, says “That’s a cow,” then the mistake doesn’t consist in misapplying “cow” (in fact, in her idiolect she even said something true). Rather, it consists in following the wrong rule for “cow” in the sense specified above, namely in following a rule not in force in her speech community. Again: “if you follow grammatical rules other than such and such ones, that does not mean you say something wrong, no, you are speaking of something else” (PG: X, 133). In sum, a constitutive rule cannot be misapplied—that is, cannot be violated—because a constitutive rule defines what counts as an application of it in the first place. This means an allegedly “wrong” application of a constitutive rule is simply not an application of it. In other words, whereas a regulative (prescriptive) rule draws a contrast between correct and incorrect applications—that is, violations of it—a constitutive rule is non-contrastive in that it only specifies what counts as an application of it, which is why there is no such thing as violating it.57 To avoid confusion, I therefore propose, with regard to constitutive rules, to replace the usual term “correctness conditions” with what Amie Thomasson has called “application conditions,” which are simply “certain basic rules of use that are among those that are meaning-constituting for the term.”58 I’ll roughly follow Thomasson’s use so that application

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conditions are conceived of as specifying conditions under which a particular rule, word, or concept applies, but with the crucial modification that there is no contrast between correct/incorrect (or true/false). Instead, application conditions constitute what it is for something to be an application of a rule. Hence, if constitutive rules mark a contrast at all it’s one between, as it were, applications and non-applications. Strictly speaking, though, there is no such thing as an incorrect or wrong application of a constitutive rule and to say that an application of it is correct is pleonastic at best.59 The upshot of all this is that, according to Wittgenstein, grammar— conceived of as composed of non-descriptive, constitutive rules incapable of being true or false—is essentially “arbitrary” or “autonomous,” which “amounts to a claim that grammar cannot be justified or refuted (discredited).”60 Of course, we may argue that a rule such as the diagonal rule for the bishop is a good one, balances the game, enhances strategic possibilities, and combines nicely with the other rules of the game. But it makes no sense to ask whether the diagonal rule is true, as if our chess game somehow mirrored an antecedent metaphysical nature of chess. Nothing “corresponds” to the rules of chess because they themselves create the game of chess. And to ask why we have or should have a particular chess rule (rather than another) is an entirely different question. As Wittgenstein puts it: Grammar is not accountable to any reality. It is grammatical rules that determine meaning (constitute it) and so they themselves are not answerable to any meaning and to that extent are arbitrary. (PG: X, 133)61

But does that really mean that there is absolutely no sense in which grammatical rules can be justified and hence that we are at liberty to choose and adopt grammatical rules on a whim? Is Wittgenstein a convention idealist after all? To clarify this question, it will be useful to introduce a distinction between two different kinds of justification regarding rules and rule-following. The first kind is what may be called pragmatic justifications and the second kind is what may be called logical justifications. This distinction will also be important in Sect. 6.3 because it will enable us to sidestep Kripke’s skeptical challenge by showing in what sense sign usage may be justified even when faced with the skeptical paradox.

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The two kinds of justification are expressed by the difference between “justifying a practice as a system of rules to be applied and enforced, and justifying a particular action which falls under these rules.”62 Stated in more Wittgensteinian terms, there is a distinction between justifying a rule of a game and justifying a particular move falling under it (i.e. a particular application of it). Again, constitutive rules—whether the rules of a board game or the semantic rules of a language (game)—are neither true nor false, neither correct nor incorrect because they are essential to the domain they determine and don’t correspond to facts. But now it seems impossible to justify rules since justifying something is usually being done with reference to facts. For something to be a candidate for justification it must be capable of being true or false. But, as I’ve been arguing, the contrast between truth and falsity is not applicable to constitutive rules. Constitutive rules cannot be justified with reference to facts simply because they are not descriptive, and hence there are no facts corresponding to them.63 There is, though, a weak sense in which rules can be justified, and that concerns pragmatic justifications. A pragmatic justification consists of reasons for adopting one rule rather than another that are not based on facts, but on a diversity of pragmatic principles regarding a particular practice such as simplicity, fairness, balance, and propriety. These reasons are always highly context-sensitive and presumably never decisive. For example, suppose Jones asks Smith why we should play according to the diagonal rule in chess. And here all that Smith, a proponent of the rule, may say in its defense is that it’s a reasonable rule because it balances the game, enhances strategic possibilities, combines nicely with other rules, and so forth. But there simply is no conclusive argument neither for keeping it, nor for changing it, nor for having adopted it in the first place. Jones may accept these reasons or not, and if not, she may submit a petition to FIDE (the World Chess Federation) in which she requests adopting a different rule, or quit playing chess, or whatever. But there is no one true rule for the bishop (nor is there a false one either!). Ultimately, the diagonal rule is arbitrary: The danger here, I believe, is one of giving a justification of our procedure where there is no such thing as a justification and we ought simply to have said: that’s how we do it. (RFM: II, 74)64

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The phrase “That’s how we do it” here is a fundamental expression of the arbitrariness of rules, and we may as well say: “Those are simply the rules in force.” And all we can do is to appeal to pragmatic justifications to persuade others. But in the end, we reach bedrock, and our spade will turn simply on the grounds that there are no facts to decide the matter. The case is different with logical justifications. Logical justifications, as opposed to pragmatic ones, don’t concern the rules of a (language) game but the moves that are made within it (the application of the rules). Logical justifications are available if a move is made in compliance with or according to a rule (or a larger set of rules) of the game. For example, Smith is justified in moving the bishop diagonally simply because moving the bishop diagonally is in compliance with the rules of chess. If Jones asks Smith why she moved the bishop diagonally, the only justification for doing so is the fact that the diagonal rule is in force, that is, is a rule of chess. Whereas the rules of chess are arbitrary in the sense described above, the moves that are made within it are not. It follows that the question of whether a move is justified is decidable, at least in principle, because there are facts about which rule is supposed to be in force, even if the rule in force is, as a matter of fact, not being followed. The rule that is in force does not have to be identical to the rule that is actually being followed (an example here would be legal rules, i.e. laws). Complying with a rule (that is in force) is tantamount to having a logical justification for applying it, regardless of whether one can cite the rule in question or not. And the same thing goes for word usage: To use a word without justification does not mean to use it without right. (PI: 289)

The “right” to use a word simply derives from its being in accordance with the rule that is in force for its use and is logically independent from my ability to make that rule explicit. If my use of a word complies with its rule of use, then I am justified in applying the word in this way, whether I know the rule for its use or not. That’s why I don’t need to be able to cite a rule for being justified in my word usage (provided it’s in accordance with the rule).

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The distinction between the rules of a game on the one hand and the moves (applications) that are made within it on the other hand, and, correspondingly, the distinction between pragmatic and logical justifications, is important as it creates profound confusions if it goes unnoticed. It shows that a question such as “Why should I move the bishop diagonally?” must be treated in fundamentally different ways (and must receive completely different answers, i.e. pragmatic or logical ones) depending on whether we operate on the level of rules or applications. But is it really conceivable for people to play (language) games and follow rules radically different from our own? Are profoundly deviating grammars possible, as convention idealism would have it, or is the possibility of an alternative grammar simply incoherent, as mindedness idealism would have it? These questions will be explored in the next subsection.

5.3 L ogical Necessity, Language-Games, and the Wood-Sellers There are several passages in Wittgenstein’s writings in which he imagines people with language-games and practices that are different in some way or other. The differences Wittgenstein presents us with are very diverse. They range from different sensory and mental capabilities to the employment of more or less unusual concepts, and even entirely different practices. For example, in Zettel Wittgenstein imagines the following case: What would a society consisting only of deaf people be like? Or a society of the mentally challenged [Geistesschwachen]? An important question! That is, what of a society that never played many of our customary language-­games? (Z: 371; transl. am.)

In Remarks on Colour, Wittgenstein explores another thought experiment: There could very easily be a tribe of people who are all color-blind and who nonetheless live very well; but would they have developed our color names, and how would their nomenclature correspond to ours? What would their

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natural language be like?? Do we know? Would they perhaps have three primary colors, blue, yellow, and a third which takes the place of red and green?—What if we were to encounter such a tribe and wanted to learn their language? We would no doubt run into certain difficulties. (RC: III, 128)

Also in Zettel, Wittgenstein invites us to consider a tribe with a different concept of pain: A tribe has two concepts, related to our “pain”. One of them is used in connection with visible injuries and entails care, compassion etc. The other one is used in connection with stomach pain and entails, for example, ridicule of the person lamenting. “But don’t they see the similarity?”—Do we have a concept for every case where there is a similarity? The question is: Is the similarity important to them? Does it have to be? And why shouldn’t their concept overlap with our concept of “pain”? (Z: 380)

And in On Certainty, Wittgenstein imagines a courtroom situation in which a physicist “testifies” that water boils at 100 degree Celsius, a testimony everyone in the courtroom treats as an unassailable truth.65 He then goes on to contemplate the possibility of a people who don’t place their confidence in physicists in these matters but have a rather different practice of gathering evidence and recognizing reasons: Suppose we met people who do not regard this [the physicist’s testimony] as a compelling reason. Well, how would we imagine such a case? They consult an oracle instead of a physicist. (And because of that we think they are primitive.) Is it wrong for them to consult an oracle and act accordingly?—If we called that “wrong”, don’t we already presuppose our language-­game and combat theirs? (OC: 609)

There are several points we need to be mindful of in interpreting and assessing Wittgenstein’s examples. First, most of Wittgenstein’s hypothetical and counterfactual cases occur in posthumously published writings that haven’t been thoroughly revised. We must keep in mind that Wittgenstein’s examples are rather exploratory and tentative. The character of these passages often strikes one as that of a first draft, as raising

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issues and opening up lines of thought in a somewhat piecemeal fashion rather than illustrating and summarizing definitive results. We have to take into account that Wittgenstein might have refined or revised these passages if he had had the opportunity to rework these writings in preparing them for publication. This is also connected to the second point. The thought experiments Wittgenstein presents us with are extremely compressed. In many cases, Wittgenstein’s train of thought often spans no more than a few paragraphs, giving us only a very rough and vague outline of the situation he has in mind. This makes it difficult to assess Wittgenstein’s thoughts in depth because the reader has not much to go on. However, the third and most important point to realize about Wittgenstein’s examples is the following. The most salient feature of Wittgenstein’s thought experiments—not only of the passages quoted above but also of other such passages in which Wittgenstein is more explicit—is that he is asking questions rather than giving answers. The questions Wittgenstein raises are real questions, not rhetorical ones. They reflect genuine unclarity, ambiguity, and even indecisiveness concerning the case at hand. This exegetical fact alone should caution us against rash judgment. Just as with Wittgenstein’s considerations about simple objects in the Notebooks, we need to be very careful in attributing theses or positions based on Wittgenstein’s experimental explorations of other-­ mindedness. This is in stark contrast with the interpretation of Williams-Lear, who instead deliver an unequivocal verdict about Wittgenstein’s intentions: The chief [an imaginary character who rejects modus ponens] is a mere posit, a heuristic device to help us in our exploration of our mindedness. Wittgenstein occasionally postulates a tribe whose interests and activities differ from ours. Their function is to help us see how our activities are dependent upon the interests we have. But it is a mistake to think of these tribes as providing concrete examples of other-mindedness. Insofar as we can make sense of their activities and interests, that is, insofar as we can fill out the picture, they do not turn out to be other-minded. We are discovering more about what our form of life is like, not what another form of life would be like. Insofar as we cannot fill out the picture, as in the case of our chief, we have not reached a case of other-mindedness; we have simply passed beyond the outer bounds of our mindedness into incoherence.66

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For Williams-Lear, the point Wittgenstein wants to make with his examples is quite clear. Every seemingly possible alternative to our own mindedness with its particular world-view is revealed to be either a form of our own mindedness in disguise, or simply an illusion. Accordingly, Wittgenstein’s method is understood as proceeding in two phases, a destructive and a constructive one. In the first phase, Wittgenstein presents us with a thought experiment about seeming other-mindedness, only to show us in the course of philosophical scrutiny that what looked like a genuine alternative to our ways of doing things is not really an alternative at all but rather incoherent nonsense we did not recognize as such. In the second phase, after having realized that we had been the victim of an illusion, we are thrown back into our own mindedness but see more clearly its inner workings, how our world-view is conditioned by our form of life—a form of life that exists necessarily only in the singular.67 It seems as if we are on the horns of a dilemma. Either the Williams-­ Lear reading is correct, and Wittgenstein wants to persuade us that the examples allegedly presenting us with alternative concepts and practices are ultimately unintelligible, which is why we are to conclude that our own mindedness is the only one there could be. On this reading, Wittgenstein is a clear proponent of mindedness idealism. Or Dummett’s interpretation is on track, and Wittgenstein wants us to see alternative concepts and practices as genuine possibilities, which is why we are to conclude not only that there are or could be forms of other-mindedness, but also that the forms other-mindedness may assume depend on arbitrarily adopted conventions. On this reading, Wittgenstein turns out to be strong defender of convention idealism. Both kinds of idealism, mindedness idealism and convention idealism, are somewhat unattractive positions both as Wittgenstein exegesis and as philosophical accounts. Mindedness idealism has the tendency toward intolerance since the account has narrow-mindedness quite literally written into it. When confronted with (imaginary or real) social groups exhibiting what we take as substantially different practices, mindedness idealism must either dismiss these practices as in the end unintelligible or as versions of our own practices in disguise. Both conclusions don’t seem to be very promising and helpful ways to engage cultural differences.

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Convention idealism, on the other hand, seems to represent the opposite extreme by embracing a very strong form of relativism, according to which there are no constraints on practices such as calculating and inferring. Concerns stemming from realist intuitions aside, this conclusion seems not very plausible on its own given that we are not inclined to accept any answer to queries such as “5 + 7” and “P” and “If P, then Q” merely on the grounds of arbitrary conventions. However, mindedness idealism and convention idealism are not the only options. Barry Stroud, for example, proposes to conceive of Wittgenstein’s examples in a different way: Even if we founder when we try to understand in some detail what it would be like to think in one or another of those ways, so that we do not find fully intelligible any particular way of thinking different from ours, Wittgenstein does seem to be suggesting that we can nevertheless be brought to see the contingency of our thinking in the ways we do, or the contingency of anyone’s being ‘minded’ as we are rather than in some other way.68

And Michael Forster has further elaborated and refined this line of Wittgenstein interpretation, defending what he calls the “diversity thesis”: the thesis that for every grammatical principle in every area of the grammar that constitutes our ‘true-false games,’ alternative but in some degree ­similar grammatical principles, and hence alternative but in some degree similar concepts, either actually exist or are at least possible and conceivable.69

Here it’s important to note that Forster doesn’t subscribe to convention idealism, arguing instead against Dummett that, according to Wittgenstein, “a person’s adoption of a particular grammar, and the ability of sentences to serve as grammatical principles, are heavily constrained.”70 Even though I disagree with Stroud about certain details of his analysis (to which I’ll come back below), I think the “third way” outlined by Stroud and Forster is essentially correct. In my view, the reason why Wittgenstein presents his examples in the way he does is connected to the dilemma outlined above. In exploring

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possible forms of other-mindedness, Wittgenstein finds himself in an unstable philosophical position. Williams and Lear are aware of this instability, as can be seen from a passage in Lear quoted above, namely that “insofar as we can fill out the picture, they do not turn out to be other-minded,” and “insofar we cannot fill out the picture, as in the case of our chief, we have not reached a case of other-mindedness.”71 If Wittgenstein were to succeed in characterizing an allegedly substantially different practice by tracing out in detail all the ways in which the practice differed from ours, and were to unearth all the interests and desires, motivations and reasons the participants of the alternative language-game have for deviating from our practice in the way they do, then doubts would arise if the practice so characterized could really be considered an example of other-mindedness. For, if such an account gave an exhaustive answer regarding all questions about the what, the how, and the why of their behavior, that is, if we completely understood their practice, then it seems the allegedly substantially different practice wouldn’t be so different after all. The attempt to show the possibility of an other-minded people by making their substantially different practices intelligible would defeat its own purpose because the conceivability of substantially different practices undermines the claim that they are being followed by other-­ minded people. If, on the other hand, these practices really turn out to be ultimately unintelligible, then how can they be proof of the possibility of other-mindedness? The only way out of this dilemma seems to be exactly the kind of approach Stroud and Forster take Wittgenstein to be pursuing. In the following, I want therefore to consider and discuss in a little more detail one of Wittgenstein’s examples I think is particularly instructive for this approach: the wood-sellers. This example at once illustrates well Wittgenstein’s general approach to other-mindedness and also provides valuable insights into how to overcome the dichotomy between realism and idealism. Wittgenstein discusses the wood-sellers in two places, in the Remarks on the Foundations of Mathematics (RFM: I, 142–152) and the Lectures on the Foundations of Mathematics (LFM: XXI, 202–204). Interestingly, in both cases Wittgenstein references a famous passage in Frege’s The Basic Laws of Arithmetic in the immediate vicinity of describing the wood-seller example. Since Wittgenstein gives only part of the quote or paraphrases it, I’ll reproduce Frege’s quote here in full:

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But what if beings were even found whose laws of thought flatly contradicted ours and therefore frequently led to contrary results even in practice? The psychological logician could only acknowledge the fact and say simply: those laws hold for them, these laws hold for us. I should say: we have here a hitherto unknown type of madness. (GG: XVI)

This passage is one of many in which Frege fights his well-known battle against a psychologist conception of logic. Psychologism about logic was indeed widespread among Frege’s contemporaries. One of its representatives, the logician and psychologist Benno Erdmann, was the primary target of Frege’s critique. Erdmann defended a radically epistemic theory of truth, according to which the truth of a judgment depends in some way or other on our ability to recognize its truth. He also argued for a descriptivist conception of logic, according to which logical laws merely describe how humans actually think. Erdmann’s epistemic theory of truth and his descriptivist theory of logic turned truth and logic into something subjective and relative. For Frege, however, logical laws are completely objective, normative truths about the way we ought to think if we are to think correctly.72 What is interesting to note with respect to our discussion is that the psychologism characterized by Frege is very similar to Dummett’s radical conventionalism. For the psychologist about logic, the laws of logic simply reflect our mode of thought, which is why the psychologist readily concedes the possibility of substantially different modes of thought. This position, again, undermines there being one correct answer to the question what follows from the premises “P” and “If P, then Q,” because the answer depends on the psychological settings of the person making the inference. That is why Frege admonishes that the psychological logician has no resources to adjudicate between logical disputes because there is no one right answer. All that the psychological logician can do is state that different people infer in different ways, and that is the end of the matter. For a staunch realist such as Frege, this kind of convention idealism about logic is clearly anathema. Now, what is Wittgenstein’s reaction to Frege’s harsh judgment that obeying logical laws and following rules of inference substantially different from ours amounted to an “unknown type of madness”? Here’s Wittgenstein’s response, immediately after which (in the Lectures) he presents the case of the wood-sellers:

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This is queer. We wouldn’t call a man mad who denied the law of contradiction—or would we? (LFM: XXI, 202)

Imagine a community in which people buy and sell wood by cubic measure to calculate the price. Of course, other ways of calculating the price of wood are possible, and Wittgenstein points out some of them: conditions of labor such as the time it takes to fell the timber, or the physical shape, strength, and experience of the woodsman. Also, wood could be sold by weight, or there could be a fixed sum in the context of an “All-­ You-­Can-Carry” special offer. And why not give the wood away for free, for example, as a publicity stunt to attract customers? So far, so good. It doesn’t seem very difficult to make sense of any of these ways of buying and selling wood provided some context like background information and additional premises. Now, Wittgenstein considers a strange method the wood-sellers could be using in their calculations. They could calculate the price of wood proportionate to the area covered by the wood—independently of the height of the pile. This means that two piles of wood consisting of exactly the same amount of logs but arranged in different ways so that the pile that is of less height but covers a bigger area costs more than the other pile, even though in both cases you end up with exactly the same amount of logs. This is strange indeed. Wittgenstein then deliberates if and how these people could be convinced that their way of measuring wood is somewhat awry. And here things get really strange: How could I shew them that—as I should say—you don’t really buy more wood if you buy a pile covering a bigger area?—I should, for instance, take a pile which was small by their ideas and, by laying the logs around, change it into a ‘big’ one. This might convince them—but perhaps they would say: ‘Yes, now it’s a lot of wood and costs more’—and that would be the end of the matter. (RFM: I, 149)

The fact that the wood-sellers take only the covered area into account and disregard the height may somehow be explained or simply chalked up to indifference, whim, or eccentricity. But their insistence on a pile’s becoming bigger simply by rearranging the logs doesn’t seem to be simply a

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peculiar way of measuring wood. Rather, there seems to be something wrong with it. In the Lectures, Wittgenstein apparently shares Frege’s assessment when he says that we might call the practice of the wood-­ sellers “a kind of logical madness” (LFM: XXI, 202). In the Remarks, however, he is much more cautious, dryly concluding that the wood-­ sellers “simply do not mean the same by ‘a lot of wood’ and ‘a little wood’ as we do” (RFM: I, 149). Most importantly, though, in neither the Lectures nor the Remarks does Wittgenstein say or even imply that the practice of the wood-sellers is per se unintelligible or impossible. Quite the contrary. In the Remarks he says that the wood-sellers “have a quite different system of payment from us” (RFM: I, 149), and in the Lectures he says, after considering to call the practice of the wood-sellers a kind of logical madness: “But there is nothing wrong with giving wood away. So what is wrong with this? We might say: ‘That is how they do it’” (LFM: XXI, 202).73 Wittgenstein seems to consider the practice of the wood-sellers a genuine alternative practice even though he also clearly voices doubts about our having a clear understanding of it. Since they most likely employ the terms “a little wood” and “a lot of wood” with a meaning substantially different from the meaning we attach to these terms—a meaning we cannot extract from their responses within the framework of wood trade alone—it follows that we cannot fully specify and therefore cannot completely understand their behavior. But this is not to say such a practice is impossible or unintelligible. Wittgenstein’s answer to the question whether such a practice is in the end really possible and intelligible seems to be that we can’t say. This answer may appear unsatisfying, disappointing even. But in my view, this seems to be precisely Wittgenstein’s point. Specifying and understanding (linguistic) behavior requires much more than we usually think because our (linguistic) behavior is connected to and interwoven with countless other aspects of our (linguistic) behavior. Just have a look at some of the questions Stroud raises about the wood-­ sellers, which casts doubt on the idea of the practice’s being literally intelligible: A man could buy as much wood as he could possibly lift, only to find, upon dropping it, that he had just lifted more wood than he could possibly

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lift. Or is there more wood, but the same weight? […] And do these people think of themselves as shrinking when they shift from standing on both feet to standing on one? […] And so on. Problems involved in understanding what it would be like to sell wood in this way can be multiplied indefinitely.74

Interestingly, Wittgenstein himself characterizes the structure of the thought experiment about the wood-sellers with a generality that also captures the structure of many other examples in which he explores possible cases of other-mindedness: We can now see why we should call those who have a different logic contradicting ours mad. The madness would be like this: (a) The people would do something which we’d call talking or writing. (b) There would be a close analogy between our talking and theirs, etc. (c) Then we would suddenly see an entire discrepancy between what we do and what they do—in such a way that the whole point of what they are doing seems to be lost, so that we would say ‘What the hell’s the point of doing this?’ (LFM: XXI, 203)

But, crucially, he immediately adds: But is there a point in everything we do? (LFM: XXI, 203)

All this textual evidence so far seems to suggest that the structural design of Wittgenstein’s examples of other-mindedness is indeed the “third way” besides convention idealism and mindedness idealism proposed by Stroud and Forster.75 Forster corroborates Stroud’s Wittgenstein interpretation after having thoroughly reviewed many other of Wittgenstein’s examples and concludes: In light of the copious and clear positive evidence for this commitment to the diversity thesis and for his intention to illustrate it by means of his examples, together with this alternative explanation of his initially puzzling refusal to imply that his examples convey literal understanding, one must instead conclude that his official position is exactly the one Stroud ascribes to him: an intention to persuade us by means of his examples that alternative grammars and concepts are possible (and therefore to combat

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Platonism) combined with a concession that his examples perforce fall short of making such alternatives literally intelligible us.76

Now, I want to focus on one particular aspect of Wittgenstein’s verdict of the wood-sellers because it sheds light on his conception of grammar and rules, and also points us a way that can help us overcome the dichotomy between realism and idealism. One of the main results Wittgenstein arrives at in considering the wood-sellers is that they most likely attach very different meanings to the terms “a lot of wood” and “a little wood.” However, this minimalist result contains more substance than one may think. Commentators on Wittgenstein’s examples of people playing different language-games in general, and on his rule-following considerations in particular, frequently make it look as if the crucial issue were about the possibility and/or intelligibility of following rules in different ways. Here I disagree not only with Dummett’s presentation of the problem but also with Stroud’s, both of whom seem to agree in this respect. According to Dummett, Wittgenstein raises the troubling possibility that even accepting certain axioms and inference rules doesn’t preclude that “at each step we are free to choose to accept or reject the proof.”77 Although Stroud, of course, doesn’t take Wittgenstein to be a proponent of radical conventionalism, he does concede that a “rule itself does not make ‘strange’ ways of following it impossible,”78 on the grounds that a rule does not contain within itself all future applications. In my view, though, Wittgenstein wants to make a stronger point than to make room for the possibility of following rules in substantially different ways. As we’ve seen in the last subsection, Wittgenstein conceives of rules and grammar as constitutive of language-games, that is, rules are not descriptions of but partially define language-games. They make for the possibility of true or false moves within a language-game but they are not themselves true or false. Since grammar consists of rules, grammar itself is also not a potential candidate for truth and falsity. One important consequence of this conception was the autonomy of grammar, meaning grammar cannot be justified with reference to facts simply because grammar is not descriptive. As Wittgenstein puts it:

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Grammar is not accountable to any reality. It is grammatical rules that determine meaning (constitute it) and so they themselves are not answerable to any meaning and to that extent are arbitrary. (PG: X, 133) As long as we remain in the province of the true-false games a change in the grammar can only lead us from one such game to another, and never from something true to something false. (PG: V, 68)

If we apply Wittgenstein’s conception of grammar and rules to the wood-­ sellers, I think this yields the following analysis. Recall that Wittgenstein says about the wood-sellers that they attach different meanings to “a little wood” and “a lot of wood.” Since they mean substantially different things by their words—although we cannot exactly specify what they mean— they also possess substantially different concepts, and that in turn entails that they also play a substantially different language-game.79 That is to say, it’s not so much, as Dummett, Stroud, and others frequently suggest, that the wood-sellers follow the same rules in substantially different ways, but rather that they  follow substantially different rules and thus  play a substantially different language-game. To say the wood-sellers play the same game as we do (selling wood) but in a different way is not the same as saying that they play different language-games. This way of spelling out Wittgenstein’s analysis of potential cases of other-mindedness has substantive advantages over alternative accounts. It allows us to acknowledge the diversity thesis, that is, the possibility of alternative practices (pace the Williams-Lear account) without sacrificing the notion of logical necessity (pace Dummett’s account). Convention idealism suggests that at each step we are free to choose to accept or reject the proof since we are free to accept or reject the rules of inference involved, whereas mindedness idealism says that these other possibilities (the possibility of adopting or even understanding rules of inference incompatible with ours) are merely an illusion—other-mindedness is simply incomprehensible. For both convention and mindedness idealism the notion of logical necessity evaporates entirely: for the former, logical necessity is undermined by the possibility of inferring, calculating, and so on, in different ways; for the latter, logical necessity turns out to be an illusion because what seems to be necessary consists in nothing but our inability to conceive of inferring, calculating, and so on, in different ways.

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Both parties, I believe, make the same mistake of misidentifying the proper conceptual place of logical necessity. Logical necessity is not a question of which concept (of inferring, calculating, etc.) is the right one, not a question of which rule (of inferring, calculating, etc.) is to be followed or which language-game is to be played.80 This concerns pragmatic justifications, and whether we can ultimately make sense of the answer given by the wood-sellers (“Yes, now it’s a lot of wood and costs more”) is an open question. Logical necessity, on the other hand, concerns the relation between the concepts or rules of a language-game and the moves made within it, that is, it concerns logical justifications. And here Wittgenstein seems to think that if we are clear about the rules we follow and the concepts we use, then it’s far from arbitrary which moves in the language-game are legitimate and which are not. That is why his conclusion about the wood-sellers is that they simply mean something different by “a lot of wood” and “a little wood” because they have a substantially different practice of selling wood; it’s not that they sell wood in the wrong way, that is, following the rules of calculations in a wrong way. So, if one means modus ponens by “→” or addition by “+,” then Wittgenstein wouldn’t dispute that Q follows from “P” and “If P, then Q,” and that “12” is the correct answer to “7 + 5.” Rather, he explores the possibility and intelligibility of practices attaching similar yet substantially different meanings to “→” and “+.” This seems to be borne out by the following passage: “But mathematical truth is independent of whether human beings know it or not!”—Certainly, the propositions “Human beings believe that twice two is four” and “Twice two is four” do not mean the same. The latter is a mathematical proposition; the other, if it makes sense at all, may perhaps mean: human beings have arrived at the mathematical proposition. The two propositions have entirely different uses.—But what would this mean: ‘Even though everybody believed that twice two was five it would still be four’?— For what would it be like for everybody to believe that?—Well, I could imagine, for instance, that people had a different calculus, or a technique which we should not call ‘calculating’. But would it be wrong? (PI: p. 226)

Again, Wittgenstein’s conclusion about a people for whom twice two was five is not that they calculate in the wrong way. Rather, they have a substantially different practice with numbers that we wouldn’t call

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“calculating.” As we could also put it, these people would attach quite a different meaning to the multiplication sign than we do (and they would presumably also have a different concept of “number”). That is exactly why Wittgenstein implies that they are not wrong. If one plays our multiplication game, uses our calculus, then it’s wrong to say “Twice two is five.” But since they employ a substantially different technique and attach substantially different meanings to their mathematical terms, we cannot simply state that they are wrong in saying “Twice two is five” because this statement would have a very different meaning from the one we usually associate with it. In sum, practices are not candidates for truth and falsity, only statements made within them are.81 The confusion of these fundamentally different levels is more often than not responsible for the widespread interpretation of Wittgenstein as a linguistic idealist or relativist, for whom truth is in a significant way dependent on our language-game. Anscombe, for example, proposes as a test for linguistic idealism to raise the following question: “Does this existence, or this truth, depend on human linguistic practice?”82 And Bloor defines linguistic idealism as the claim “that some truths or realities are created by our linguistic practices.”83 If we measure Wittgenstein’s views by that standard, then he is definitely not a linguistic idealist. As the passage quoted above already showed, Wittgenstein clearly distinguishes between the truth of a statement and people’s beliefs about it. Even more explicit is a passage right at the beginning of On Certainty, where he writes: From its seeming to me—or to everyone—to be so, it doesn’t follow that it is so. (OC: 2)84

For Wittgenstein, both realism and idealism “belong to metaphysics” because their advocates believe “they can say something specific about the essence of world” (PR: V, 55). Wittgenstein’s diagnosis of what generates misguided debates in metaphysics is exactly the confusion of the conceptual and factual levels—the level of rules, concepts, and grammar on the one hand, and the level of the truth and falsity of statements on the other. Debates between realists and idealists are just one instance of the general mistake in metaphysics to confuse the conceptual and factual levels:

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Philosophical Investigations: conceptual investigations. The essential thing about metaphysics: it obliterates the distinction between factual and conceptual investigations. (Z: 458)

This diagnosis for what goes wrong in debates between realism in idealism also appears in a prominent passage in the Investigations: For this is what disputes between Idealists, Solipsists and Realists look like. The one party attack the normal form of expression as if they were attacking a statement; the others defend it, as if they were stating facts recognized by every reasonable human being. (PI: 402)

Once again, we have to distinguish between the source of determination and the status of rules and concepts as well as the grammar they constitute. This harks back to our discussion of the rules of a symbolism and the determinations involved in constituting those very rules (Sect. 3.3). Once the Russellian descriptive model of logic is abandoned, it may appear as if the rules of logical syntax are not the necessary reflection of a mind-independent reality but rather the arbitrary projection of a contingent subjectivity. But we must not identify a rule’s being non-descriptive with its being non-objective. Objectivity and logical necessity are not primarily to be located in the source of determination of rules but in the relation between rules and what they constitute.85 And although Wittgenstein’s notion of grammar differs in some respects from the predecessor notion of logical syntax, this aspect of it remains constant. For example, sentences such as “Water is H2O” and “The bishop in chess moves only diagonally” would also express for Wittgenstein grammatical rules, sentences that are also not descriptions but constitute and regulate the “true-false games” within which descriptions are being made. Here the sources of determinations going into the constitution of the concepts involved in the respective rules are quite different, and they may be said to be rooted in empirical facts or human practices, respectively. However, the different sources of determination don’t affect and have to be distinguished from the status of these rules as non-descriptive. Let’s reconsider Wittgenstein’s famous pronouncement:

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Essence is expressed by grammar. (PI: 371)

Now it should be clear that essence is neither reflected nor imposed, but rather expressed in grammar. The fact that essence is expressed by grammar doesn’t mean that it’s created, nor does it mean that it merely represents an antecedent metaphysical structure. The “harmony between thought and reality is to be found in the grammar of the language” (PG: VIII, 112), but this is simply to emphasize the logical symmetry between grammar and the structure of the world. This doesn’t compromise the objectivity of the truth and falsity of statements made within language-­ games so long as we clearly distinguish between the conceptual and factual levels. Therefore, just as the rules of logical syntax the rules of grammar are best conceived of as a non-descriptive, metaphysically neutral expression of the structure of the world—neither mirror nor projection. Of course, particularly Wittgenstein’s rule-following considerations have generated a huge amount of literature, and in this section I could only sketch Wittgenstein’s general approach to rules and grammar as well as their connection to the dichotomy between realism and idealism. That is why I’ll examine in the next section the debate about the rule-following considerations in greater detail, which has also produced a realism-­ idealism divide in the literature, particularly represented by McDowell’s and Wright’s response to Kripke’s framing of the rule-following problem. In doing so, I’ll present a new solution to Kripke’s so-called skeptical challenge and how we can overcome the dichotomy between realism and idealism.

Notes 1. Conant (2002: 423–424). 2. B. Williams (1974). 3. B.  Williams (1974: 84–85). Cf. also Lear (1982: 385): “In both the Tractatus and the Philosophical Investigations we are supposed to glean some insight into the way we think and the limits of thought by moving around self-consciously and determining what makes more or less sense.” 4. Hutto (2003: 70).

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5. Hutto (2003: 48). Cf. M. McGinn (2006: 161), also a supporter of the elucidatory reading: “We now see that the task we are concerned with does not take us outside language; our task is one of clarifying, from inside language, how language signifies in the way it does.” 6. Cf. Sullivan (2013: 257–258). 7. Cf. A.W. Moore (2013: 240–241). 8. A.W. Moore (2013: 246). 9. Cf. B. Williams (1974: 83–84). 10. B. Williams (1974: 83). 11. B. Williams (1974: 84). Cf. also Lear (1982: 386) and Lear (1984: 233) for the same point. 12. Cf. B. Williams (1974: 84) and Lear (1982: 385). 13. B. Williams (1974: 85). 14. Dummett (1959: 329). 15. Dummett (1959: 336). 16. Cf. also (RFM: VI, 23): “The justification for the sentence 25 × 25 = 625 is, of course, that someone who has been trained in a certain way will obtain 625 when making the multiplication 25 × 25 under normal circumstances. But the arithmetical sentence doesn’t say that. It is an empirical sentence that has been hardened into a rule, so to speak. It determines that the rule has been followed only if this is the result of the multiplication.” 17. For an in-depth study about the precise sense in which linguistic conventions as such (what Wittgenstein calls “grammar”) are arbitrary and in which they are not cf. Forster (2004: ch. 2 and 3). 18. Just think of the example of the math teacher and the deviant pupil (cf. PI: 185–190). 19. I’ll elaborate in more detail on Wittgenstein’s notion of grammar and rules in the next subsection. 20. Cf. also (PI: 497): “The rules of grammar may be called ‘arbitrary’, if that is to mean that the aim of the grammar is nothing but that of language.” 21. Anscombe (1976: 192). 22. Anscombe (1976: 200). 23. Bloor (1996: 375). 24. Hacker (1986: 194). 25. Hacker (1986: 179). 26. Hacker (1986: 195). 27. Hacker (1986: 206). 28. Cf. Lear (1982: 401).

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29. Lear (1982: 385). 30. Cf. Lear (1982: 391–392). 31. Lear (1982: 385). 32. A.W. Moore (2013: 242). Cf. also Sullivan (2013). 33. Lear (1982: 392). 34. Lear (1982: 392). 35. Lear (1982: 386). Cf. also Lear (1984: 232). 36. Cf. Nagel (1986: 106–107) for a very similar characterization of Wittgenstein’s alleged idealism: “His view of how thought is possible clearly implies that any thoughts we can have of a mind-independent reality must remain within the boundaries set by our human form of life, and that we can’t appeal to a completely general idea of what there is to defend the existence of kinds of facts which are in principle beyond the possibility of human confirmation or agreement. We fall into nonsense, he thinks, if we try to take language too far from these conditions.” For more on the positions of Williams-Lear and Nagel cf. Cerbone (2011). 37. Cf. Forster (2004: 25). 38. Cf. Malcolm (1982), Forster (2004), and Mulhall (2008). 39. Dummett (2006: ch. 5) gives a particularly lucid presentation of his mature justificationist theory of meaning, which entails the rejection of the law of excluded middle. 40. Lear (1982: 401). 41. v. Wright (1963: 6). 42. Forster (2004: 7–8). Cf. also Glock (1996: 207): “But according to Wittgenstein necessary (grammatical) propositions determine rather than follow from the meaning of words.” Cf. also Marion (1998: 142) and Baker and Hacker (2009: 318) for a similar point. 43. Searle (1969: 34). 44. Searle (1969: 34). 45. Searle (1969: 35). 46. Cf. Glüer and Pagin (1998/1999: 215–217), who render Searle’s distinction in a notational variant as “Do θ!” and “Doing θ in C counts as doing φ” and explain that “while a prescription [i.e. a regulative rule] tells you what you ought to do or are allowed to do, a [constitutive] rule tells you what it is to φ.” 47. Cf. Searle (1969: 33): “The rules of football or chess, for example, do not merely regulate playing football or chess, but as it were they create the very possibility of playing such games. The activities of playing football

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or chess are constituted by acting in accordance with (at least a large subset of ) the appropriate rules.” Cf. also Glüer (2000: 465) and Travis (2006: 104) for similar points. 48. Cf. OC (65): “When language-games change, then there is a change in concepts, and with the concepts the meanings of words change.” 49. Cf. WL (76–77). Cavell (1976: 15) notes this “complementarity of rule and statement” and says that whether certain sentences “are statements or rules depends upon how they are taken: if they are taken to state facts and are supposed to be believed, they are statements; if they are taken as guides and supposed to be followed, they are rules.” Cf. also Thomasson (2007: 69): “So, similarly, even if (as I have argued) the forms of expression that occur in analytic statements are fundamentally used as illustrations of rules (in which case they are neither true nor false), they may also be used as descriptions, in which case the truth-conditions set by the rules of use are in force in establishing the truth-conditions for this (genuine) description.” Cf. also Marion (1998: 145). 50. Cf. OC (36): “‘A is a physical object’ is a piece of instruction which we give only to someone who doesn’t yet understand either what ‘A’ means, or what ‘physical object’ means. Thus it is an instruction about the use of words, and ‘physical object’ is a logical concept.” Cf. also Forster (2004: 8): “Just as the rules of a game are not assertions but instead more like commands or imperatives, similarly grammatical rules are not assertions but more like commands, commandments, or categorical imperatives.” 51. Hattiangadi (2007: 55). 52. I’m not a chess historian, but it’s clear that the rules of chess evolved significantly over time. At any rate, note that in our hypothetical case there wouldn’t have been a difference between bishops and rooks (provided that rooks were subject to the same rule they are today). It’s not as if those people would have had two “wrong” bishops and two rooks, but simply four rooks. 53. Cf. Forster (2004: 8). 54. This passage resurfaces verbatim at PI (p.  556). Cf. also WVC (184; emphasis added): “[W]hen we are talking about negation, for instance, the point is to give the rule ‘¬¬p = p’. I do not assert anything. I only say that the structure of the grammar of ‘¬’ is such that ‘p’ may be substituted for ‘¬¬p’. Were you not also using the word ‘not’ in that way? If that is admitted, then everything is settled. And this is how it is with grammar in general.” Cf. also PG (II, 15–16).

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55. Cf. Cavell (1976: 28): “You can push the little object called the Queen in many ways, as you can lift it or throw it across the room; not all of these will be moving the Queen.” Cf. also A.W. Moore (2003: 186), who considers “someone intending to play chess who moves his rook diagonally. We can say that such a person has made an illegal move. But we can also say that such a person has failed to make any move at all. An illegal move is not a special kind of move. It is as if he has poured coffee all over the board.” 56. Searle (1969: 41) seems to concede this, too: “Indeed, it is not easy to see how one could even violate the rule as to what constitutes checkmate in chess, or touchdown in football.” Cf. also Glüer and Pagin (1998/1999: 217–218) for a similar point. 57. As we’ve seen in Sect. 5.1, Wittgenstein is particularly explicit about this with respect to mathematics: “If it is not to be an empirical sentence that the rule [+ 1] leads from 4 to 5, then this, the result itself, must be taken as a criterion for someone’s having followed the rule. Therefore, the truth of the sentence that 4 + 1 equals 5 is, so to speak, overdetermined. It is overdetermined by the fact that the result of the operation has been declared a criterion for the operation’s having been executed” (RFM: VI, 16). Cf. also RFM (VII, 27): “In mathematics the result itself is a criterion for calculating correctly. Therefore, it is impossible to follow the rule correctly and generate different calculations.” 58. Thomasson (2015: 89). 59. I’ll come back to and elaborate on this topic in Sect. 6.3 in the context of my response to Kripke’s skeptical challenge. 60. Forster (2017: 271). Cf. also Screen (1984: 530–531), O’Neill (2001: 7), and Travis (2011: 201) for similar points. 61. Cf. Mulhall (2008: 396): “Wittgenstein’s thought is that grammatical structures do not stand in any kind of correspondence relation to reality, and so can neither correspond nor fail to correspond to the nature of things. In other words, they are not in the business of representing reality, but of providing means for the representation of reality; they articulate a field of meaning within which one can construct true or false descriptions of things, but they are not themselves descriptions of anything.” 62. Rawls (1955: 5). 63. Cf. Forster (2004: 46) who, after a battery of arguments, concludes: “In sum, it seems that none of the available strategies for justifying grammatical principles (over against alternatives) can work—not justification in terms of truth-in-virtue-of-meaning, nor justification by the facts, nor

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justification in terms of success in realizing purposes, nor justification by deduction from more fundamental grammatical principles.” 64. Cf. PI (654): “Our mistake is to look for an explanation where we ought to look at what happens as a ‘proto-phenomenon’. That is, where we ought to have said: this language-game is played.” 65. Cf. OC (604). 66. Lear (1982: 389). Cf. also B. Williams (1974: 90): “The point can be put also like this, that there is the gravest difficulty […] in both positing the independent existence of culturally distinct groups with different worldviews, and also holding that any access we have to them is inescapably and non-trivially conditioned by our own world-view. For the very question from which we started, of the existence and relative accessibility of different world-views, becomes itself a function of one world-view.” 67. Given that the Williams-Lear position and the resolute reading have a similar conception of the limits of language, it’s not much of a surprise that Williams-Lear’s assessment bears a striking resemblance to the austere conception of nonsense at the heart of the resolute reading. Cf. Sects. 3.3 and 4.1. 68. Stroud (1984: 255). Cf. also Stroud (1965), where he first developed this Wittgenstein interpretation. 69. Forster (2004: 107). 70. Forster (2004: 67). 71. Lear (1982: 389). 72. Cf. LC (128): “Like ethics, logic can also be called a normative science. How must I think in order to reach the goal, truth?” 73. Cf. also (LFM: XXI, 204): “Suppose I gave you a historical explanation of their behavior: (a) These people don’t live by selling wood, and so it does not matter much what they get for it. (b) A great king long ago told them to reckon the price of wood by measuring just two dimensions, keeping the height the same. (c) They have done so ever since, except that they later came not to worry about the height of the heaps. Then what is wrong? They do this. And they get along all right. What more do you want?” 74. Stroud (1965: 512). 75. For an account of the wood-sellers more sympathetic to Williams-­Lear’s mindedness idealism cf. Cerbone (2000). 76. Forster (2004: 167). 77. Dummett (1959: 330). 78. Stroud (1965: 514).

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79. Cf. OC (65): “When language-games change, then there is a change in concepts, and with the concepts the meanings of words change.” 80. Cf. again PG (X, 133): “There cannot be a question whether these or other rules are the correct ones for the use of ‘not’ (that is, whether they accord with its meaning.) For without these rules the word has as yet no meaning; and if we change the rules, it now has another meaning (or none), and in that case we may just as well change the word too.” 81. Cf. Glock (2015: 119–120): “A ‘way of speaking’ or form of expression cannot be at fault, at least not in the sense of saying something false. It is only statements made within a form of expression that can say something false. […] By this token, it is not just confused to think that a language-­ game, form of discourse, or conceptual scheme can be true of false; it is also confused to think that it can be more or less faithful to reality, in the sense of capturing more or less accurately those features that reality objectively possesses.” 82. Anscombe (1976: 193). 83. Bloor (1996: 356). 84. Cf. also RFM (VII, 40; transl. am.): “A language game: to bring something else; to bring the same. […] And does this mean e.g. that the definition of ‘same’ would be this: same is that which all or most human beings have agreed to consider the same?—Of course not.” 85. Cf. TLP (3.342): “Although there is something arbitrary in our notations, this much is not arbitrary—that when we have determined one thing arbitrarily, something else is necessarily the case. (This derives from the essence of notation).”

References Anscombe, G.E.M. 1976. The Question of Linguistic Idealism. Acta Philosophica Fennica 28: 188–215. Baker, G.P., and P.M.S.  Hacker. 2009. Wittgenstein: Rules, Grammar and Necessity. Vol. 2 of an Analytical Commentary on the Philosophical Investigations. 2nd ed. Oxford: Wiley-Blackwell. Bloor, D. 1996. The Question of Linguistic Idealism Revisited. In The Cambridge Companion to Wittgenstein, ed. H.  Sluga and D.G.  Stern, 354–382. Cambridge: Cambridge University Press. Cavell, S. 1976. Must We Mean What We Say? In Must We Mean What We Say? A Book of Essays, ed. S. Cavell, 1–43. Cambridge: Cambridge University Press.

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Cerbone, D.R. 2000. How To Do Things with Wood: Wittgenstein, Frege and the Problem of Illogical Thought. In The New Wittgenstein, ed. A. Crary and R. Read, 293–314. London: Routledge. ———. 2011. Wittgenstein and Idealism. In The Oxford Handbook of Wittgenstein, ed. O.  Kuusela and M.  McGinn, 311–332. Oxford: Oxford University Press. Conant, J. 2002. The Method of the Tractatus. In From Frege to Wittgenstein. Perspectives on Early Analytic Philosophy, ed. E.H. Reck, 374–462. Oxford: Oxford University Press. Dummett, M. 1959. Wittgenstein’s Philosophy of Mathematics. The Philosophical Review 68 (3): 324–348. ———. 2006. Thought and Reality. Oxford: Clarendon Press. Forster, M.N. 2004. Wittgenstein on the Arbitrariness of Grammar. Princeton: Princeton University Press. ———. 2017. The Autonomy of Grammar. In A Companion to Wittgenstein, ed. H.-J. Glock and J. Hyman, 269–277. Oxford: Wiley-Blackwell. Glock, H.-J. 1996. Necessity and Normativity. In The Cambridge Companion to Wittgenstein, ed. H. Sluga and D.G. Stern, 198–225. Cambridge: Cambridge University Press. ———. 2015. Wittgensteinian Anti-Anti Realism: One ‘Anti’ Too Many? Ethical Perspectives 22 (1): 99–129. Glüer, K. 2000. Bedeutung zwischen Norm und Naturgesetz. Deutsche Zeitschrift für Philosophie 48 (3): 449–468. Glüer, K., and P. Pagin. 1998/1999. Rules of Meaning and Practical Reasoning. Synthese 117 (2): 207–227. Hacker, P.M.S. 1986. Insight and Illusion. Themes in the Philosophy of Wittgenstein. Oxford: Clarendon Press. Hattiangadi, A. 2007. Oughts and Thoughts. Rule-Following and the Normativity of Content. Oxford: Clarendon Press. Hutto, D.D. 2003. Wittgenstein and the End of Philosophy. Neither Theory nor Therapy. Basingstoke: Palgrave Macmillan. Lear, J. 1982. Leaving the World Alone. The Journal of Philosophy 79 (7): 382–403. ———. 1984. The Disappearing ‘We’. Proceedings of the Aristotelian Society, Suppl. Vol. 58: 219–242. Malcolm, N. 1982. Wittgenstein and Idealism. In Idealism Past and Present, ed. G. Vesey, 249–268. Cambridge: Cambridge University Press. Marion, M. 1998. Wittgenstein, Finitism, and the Foundations of Mathematics. Oxford: Clarendon Press.

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McGinn, M. 2006. Elucidating the Tractatus. Wittgenstein’s Early Philosophy of Logic & Language. Oxford: Clarendon Press. Moore, A.W. 2003. Ineffability and Nonsense. Proceedings of the Aristotelian Society, Suppl. Vol. 77: 169–193. ———. 2013. Was the Author of the Tractatus a Transcendental Idealist? In Wittgenstein’s Tractatus. History & Interpretation, ed. P. Sullivan and M. Potter, 239–255. Oxford: Oxford University Press. Mulhall, S. 2008. ‘Hopelessly Strange’: Bernard Williams’ Portrait of Wittgenstein as a Transcendental Idealist. European Journal of Philosophy 17 (3): 386–404. Nagel, Th. 1986. The View from Nowhere. New York: Oxford University Press. O’Neill, M. 2001. Explaining ‘The Hardness of the Logical Must’: Wittgenstein on Grammar, Arbitrariness, and Logical Necessity. Philosophical Investigations 24 (1): 1–29. Rawls, J. 1955. Two Concepts of Rules. The Philosophical Review 64 (1): 3–32. Screen, D.P. 1984. Realism and Grammar. The Southern Journal of Philosophy 22 (4): 523–534. Searle, J.R. 1969. Speech Acts. An Essay in the Philosophy of Language. London: Cambridge University Press. Stroud, B. 1965. Wittgenstein and Logical Necessity. The Philosophical Review 74 (4): 504–518. ———. 1984. The Allure of Idealism. Proceedings of the Aristotelian Society, Suppl. Vol. 58: 243–258. Sullivan, P.M. 2013. Idealism in Wittgenstein: A Further Reply to Moore. In Wittgenstein’s Tractatus. History & Interpretation, ed. P. Sullivan and M. Potter, 256–270. Oxford: Oxford University Press. Thomasson, A.L. 2007. Ordinary Objects. New York: Oxford University Press. ———. 2015. Ontology Made Easy. New York: Oxford University Press. Travis, Ch. 2006. Thought’s Footing. A Theme in Wittgenstein’s Philosophical Investigations. Oxford: Clarendon Press. ———. 2011. Objectivity and the Parochial. New York: Oxford University Press. Von Wright, G.H. 1963. Norm and Action. A Logical Inquiry. London: Routledge & Kegan Paul. Williams, B. 1974. Wittgenstein and Idealism. In Understanding Wittgenstein, ed. G. Vesey, 76–94. London: Macmillan.

6 Case Study: The Rule-Following Considerations

In this section I provide an analysis of the rule-following problem and propose a solution. As a first step (Sect. 6.1), I reconstruct Kripke’s skeptical challenge to make clear the framework within which my analysis proceeds. The next step (Sect. 6.2) is then to outline two of the most important and influential responses to the challenge—McDowell’s and Wright’s—and to explore how and in what sense both of them remain within the confines of a version of the realism-idealism problematic. Against this backdrop, and drawing on Wittgenstein’s account of rules as constitutive developed in Sect. 5, I finally (Sect. 6.3) present my solution to the skeptical challenge and how we can thereby leave the realism-idealism problematic behind.

6.1 Kripke’s Skeptical Challenge Imagine Jones is asked to compute the sum of “57 + 68” and pretend she has never performed this specific arithmetical task before. Without hesitation, she adds the numbers “in her head,” double-checks the result, and responds with “125.” Jones is absolutely confident about the correctness of her answer, both in the “arithmetical sense”—that “125” is, in fact, the arithmetically correct result—and in (what Kripke calls) the © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 M. Bartmann, Wittgenstein’s Metametaphysics and the Realism-Idealism Debate, https://doi.org/10.1007/978-3-030-73335-3_6

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“metalinguistic sense”—that in using the expression “plus” (or the symbol “+”), as Jones “intended to use that word in the past” (WRPL: 8), she actually referred to the mathematical function addition. Enter a bizarre skeptic. The skeptic raises no doubts regarding the arithmetical sense of Jones’s response, that “125” is the correct result of “57 + 68.”1 But the skeptic does question the metalinguistic sense of Jones’s response, that Jones actually meant addition by “+.” Not only that, in addition to questioning her having meant addition by “+” the skeptic even suggests that by “+” Jones actually meant quaddition, a different arithmetical function symbolized by “⨁” and defined in the following way:



x  y  x  y, if x, y  57  5 otherwise  WRPL: 9 



Given the definition of the quaddition function together with the suggestion that by “+” Jones actually meant quaddition, the skeptic now claims her correct response should’ve been “5” and not “125”! Jones is stunned by this preposterous imputation and insists on having meant plus all along and not quus, a function she’s never even heard of. But the skeptic also persists and claims that, due to the influence of drugs (or whatever), Jones misinterpreted her own previous usage of “+” and always meant quus. Now, the skeptic’s suggestion is a “bizarre hypothesis” and obviously false, “but if it is false, there must be some fact about my past usage that can be cited to refute it” (WRPL: 9). Let’s call such a putative fact or set of facts meaning-determining facts.2 The skeptic generously grants Jones omniscience about herself and her past behavior and intentions regarding “+,” and the skeptical challenge consists in identifying the fact or set of facts (about Jones) determining that she meant plus rather than quus. Before I turn to a more detailed reconstruction of the skeptical challenge, two preliminary notes are in order to avoid misunderstanding. First, Kripke’s challenge is primarily constitutive or metaphysical in character, and not epistemological.3 Kripke is most explicit about this: [T]he problem may appear to be epistemological—how can anyone know which of these I meant [plus or quus]? Given, however, that everything in my mental history is compatible both with the conclusion that I meant

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plus and with the conclusion that I meant quus, it is clear that the sceptical challenge is not really an epistemological one. It purports to show that nothing in my mental history of past behavior—not even what an omniscient god would know—could establish whether I meant plus or quus. But then it appears to follow that there was no fact about me that constituted my having meant plus or quus. (WRPL: 21)

In general, and on a fairly basic and widespread reading of Kripke, then, the skeptical challenge consists in identifying the fact or facts corresponding to the claim of the challenged to have meant plus rather than quus by “+.” The challenge is not—assuming there to be a fact or facts—how knowledge of this (set of ) fact(s) is possible.4 The question is not how it’s possible to have epistemic access to an otherwise determinate (set of ) fact(s) constituting having meant plus or quus. Instead, the skeptic challenges the very existence of a (set of ) fact(s) determining having meant plus or quus. There are (at least) two reasons why the constitutive and epistemological aspects of the skeptical challenge have been conflated. First, there are many passages in which Kripke frames the problem in epistemological and/or justificational terms, which make it seem as if there might be facts about my having meant this or that, only that I’m somehow barred from accessing these facts and therefore lack the justification for having meant this rather than that.5 The passage cited above should make it clear that this is not the case.6 Second, and more importantly, while both the constitutive and epistemological aspects are, strictly speaking, separate issues, they are nevertheless inextricably linked to each other. Obviously, within the framework of the skeptical challenge, justification is said to consist in there being a fact as to what I’ve meant regardless of what kind of fact it is and regardless of whether I’m (ever) in the position to know it. Even if there were meaning-determining facts whose very nature would preclude our ever coming to know them, Kripke would have to deem the skeptical challenge answered and reduced to a “mere” epistemological problem. But Kripke’s skeptical conclusion is much more radical: there can be no justification as to what someone means by particular expressions, not because we don’t have access to meaning-determining facts of these expressions, but because there are no such facts to begin with. In short, “if there is no fact of the matter as to whether P there can be no plausible claim to know that P.”7

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The second preliminary note concerns Wittgenstein’s alleged attitude toward the skeptical challenge. Kripke takes Wittgenstein to accept the paradox.8 But many commentators have accused Kripke of having fundamentally misrepresented Wittgenstein’s treatment of the paradox. If correct, this would threaten to undermine Kripke’s skeptical challenge both exegetically and philosophically. The thrust of the objection, as McDowell put it, is that rather than accepting the devastating conclusion of the skeptic, the “right response to the paradox, Wittgenstein in effect tells us, is not to accept it but to correct the misunderstanding on which it depends.”9 However, it’s not easy to decide whether this type of objection is entirely accurate because there is a sense in which Wittgenstein accepts the skeptical paradox and a sense in which he doesn’t. Let me briefly elaborate. Regardless of how the paradox is to be treated, Wittgenstein doesn’t want to let it stand. This much is agreed upon by both parties, Kripke and his critics. According to Kripke, Wittgenstein clearly thinks the “sceptical conclusion is insane and intolerable” (WRPL: 60). Kripke also holds that the skeptical solution is capable of overcoming the paradox by rejecting the underlying misguided truth-conditional conception of meaning that generates it (more on that presently). But Kripke himself, appearances and many critics to the contrary, is not a skeptic.10 As Martin Kusch has pointed out: That is to say, rather than being a defense of blanket scepticism, WRPL tries to show that scepticism is unavoidable only given a meaning-determinist [i.e. truth-conditional] understanding of rules and meaning. The sceptical solution is sceptical in so far, and only in so far, as it preserves this negative point about meaning determinism. The sceptical solution is not sceptical about our ordinary talk of meaning in everyday life; in fact, it provides this talk with a new form of justification.11

From this more charitable perspective, Kripke can be interpreted as claiming that Wittgenstein accepts the paradox only as a necessary outcome of the traditional, truth-conditional conception of meaning. This negative result in turn forces us to supplant it with a conception of meaning based on assertability conditions that is not susceptible to the paradox. Ironically, then, McDowell’s own response turns out to be structurally identical to Kripke’s, and they only disagree on the source of the paradox. Both argue that the skeptical paradox rests on misguided assumptions

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concerning rules, meaning, and understanding, and that the paradox can be dispensed with once we have identified the error. Kripke opts for doing away with the truth-conditional conception of meaning (which is for Kripke the “misunderstanding on which it depends”), for McDowell the idea that grasping a rule always involves interpretations has to go. So even according to McDowell’s own account, Wittgenstein can be said to “accept” the skeptical paradox, namely insofar as it’s the necessary outcome of always conceiving of rule-following as mediated by interpretations. The dispute over whether Wittgenstein does or does not accept the skeptical paradox can be better understood if we distinguish the two different levels at which Wittgenstein is operating. He can be said to accept the paradox, insofar as it represents the inevitable result of certain presuppositions concerning meaning, rules, and understanding (whatever these presuppositions are supposed to be), and he can be said to reject the paradox, insofar as it leaves us with a distorted view of how our ordinary practice involving meaning, rules, and understanding actually functions (whatever the correct view, if any, is supposed to be). Be that as it may, charging Kripke with having failed to realize that Wittgenstein doesn’t accept the paradox seems to cut not much philosophical ice anyway. The important question regarding the source and form of the paradox as well as its proper treatment is still open even if the charge is legitimate. Kripke’s error, if he made one, must lie elsewhere. Thus, I’ll turn now to the specifics of the skeptical challenge. In essence, Kripke’s skeptical conclusion that there is “no fact as to what I meant, whether plus or quus” (WRPL: 38) leads to the devastating result that there “can be no such thing as meaning anything by any word” (WRPL: 55) and that, ultimately, “all language is meaningless” (WRPL: 71). In order to argue for this conclusion, Kripke targets a certain philosophical understanding of a class of sentences purporting to attribute meaning to other expressions or sentences. Roughly, these sentences comprise assertions as to what someone means by a particular expression or sentence. This class of sentences might usefully be called “meaning sentences,”12 and they usually, but not exclusively, exhibit the form (in particular with respect to the skeptical challenge) “X means Y by expression ‘Z.’”13 A paradigmatic example would be the familiar sentence “Jones means addition by ‘+,’” but meaning attributions can also take other forms. For example, since Kripke discusses at length Wittgenstein’s suggestion

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that meaning something by an expression amounts to or at least essentially involves (grasping and following) rules for that expression, Kripke also frequently paraphrases “Jones means addition by ‘+’” using formulations roughly equivalent to “Jones follows the rule for addition when employing ‘+,’” which also includes conditionals roughly equivalent to “If Jones intends to accord with her past meaning of ‘+’ (intends to follow the same rule for ‘+’ as before) she ought to answer ‘125.’”14 The challenge to cite a fact determining Jones’s having meant addition rather than quaddition by “+” is tantamount to the challenge to cite a fact determining Jones’s having followed the rule for addition rather than the rule for quaddition. As I’ve already indicated, Kripke is not a skeptic per se but rather employs the skeptical challenge to expose as misguided a particular conception of meaning forcing the transition from the challenge to the paradox. According to Kripke (or Kripke’s Wittgenstein), as long as “we remain in the grip of the natural presupposition that meaningful declarative sentences must purport to correspond to facts” we cannot but “conclude that sentences attributing meaning and intention are themselves meaningless” (WRPL: 78–79). What Kripke primarily (but not exclusively) attacks is nothing other than the truth-conditional conception of meaning central to semantic realism,, that is, roughly the familiar: thesis that a theory of meaning for a language can give a central role to the notion of conditions under which sentences are true, conceived as conditions that we are not, in general, capable of putting ourselves in a position to recognize whenever they obtain.15

Semantic realism and the truth-conditional conception of meaning may at first sight appear not to be the official target given that Kripke’s skeptical challenge concerns, first and foremost, the use of sub-sentential expressions such as “plus,” which don’t have truth conditions but correctness conditions (conditions under which an expression is correctly applied). But the connection is rather obvious. If an individual expression (such as “plus”) can be shown to be meaningless due to lack of facts of the matter as to what is meant by this expression then, of course, the meaning sentence involving the meaningless expression will itself be meaningless. If we make explicit that “truth-conditions of sentences are a

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function of the correctness conditions of the words in them, then it is obvious that the truth conditional picture of the meanings of sentences bears the brunt of the sceptical argument, albeit only indirectly.”16 In sum, Kripke’s skeptical conclusion that there is no fact of the matter as to what someone means by a particular expression is designed to show that the meanings of meaning sentences themselves—sentences attributing meaning to other expressions or sentences—cannot be conceived of in terms of truth conditions, and hence cannot be realistically construed. What makes Kripke’s skeptical conclusion particularly devastating is that its “blast radius” extends far beyond our realistic understanding of meaning sentences and also shatters our realistic understanding of declarative sentences in general. As Paul Boghossian has shown, it’s a “consequence of a non-factualism about meaning, that it entails a global non-­ factualism.”17 Non-factualism about meaning sentences entails non-­ factualism about all assertoric discourse. This means that no declarative sentence has truth conditions. If the skeptical challenge cannot be met (or somehow be rejected) so that its conclusion follows, then there’s nothing left of realism. With these distinctions and clarifications in place, I can now provide in the following my own generalized reconstruction of Kripke’s argument with which he purports to show that the determinate application of expressions in general (and not just “plus”) can have no basis in fact and is therefore unjustified or arbitrary. I’ll first present the reconstruction in compressed form and elaborate on it afterward: 1. A particular future application of an expression is justified only if there is a fact unambiguously determining my having meant a particular rule instantiated by the number of applications of that expression I made in the past. 2. A finite number of applications of any expression instantiates an infinite number of rules. 3. My past applications of any expression are finite. 4. My past applications of any expression instantiate an infinite number of rules. 5. There is no fact as to which one of an infinite number of rules instantiated by my past applications of an expression I actually meant.

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6. Any particular future application of an expression can be made compatible with my past applications of that expression by an infinite number of rules. 7. Any particular future application of any expression is arbitrary, an unjustified “leap in the dark” (WRPL: 55). Step (1) represents a version of semantic realism framed with respect to the use of expressions; (2) embodies, as we’ll see presently, a quasi-­ mathematical truism; (3) is simply a hardly deniable fact; (4) follows immediately from (2) and (3); (5) is the skeptical challenge; (6) follows from (4) and (5) if the skeptical challenge remains unanswered; and, finally, (7) is the skeptical conclusion that any particular application of any expression is completely arbitrary and therefore unjustified, which follows from (6). Of course, Kripke doesn’t present the paradox in this generalized form. As we’ve seen, he uses instead the arithmetical example “68 + 57” and questions the meaning of (or the rule followed in using) the “+”-symbol with respect to our past intentions regarding the application of the “+”-symbol to make his case. But the skeptical challenge is completely general and affects, if valid, any expression or symbol whatsoever.18 The arithmetical example is merely an instance of my general reconstruction of the paradox and can be formulated in the following abbreviated form: 1. I’m only justified to say “125” (rather than “5”) in response to “68  +  57” if there is a fact unambiguously determining my having meant plus by “+” (rather than quus). 2. There is no fact unambiguously determining my having meant plus by “+” (rather than quus). 3. I’m not justified to say “125” (rather than “5”) in response to “68 + 57.” Step (1) represents, again, a version of semantic realism framed with respect to the use of expressions, (2) is the skeptical challenge, and (3) is the skeptical conclusion that follows if the skeptical challenge remains unanswered. It’s crucial to understand why, exactly, any response to this simple arithmetical problem turns out to be arbitrary and hence unjustified. To see this, note that the skeptical challenge doesn’t argue that the

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addition function is somehow ill-defined, indeterminate, or vague. As noted, arithmetic (arithmetical facts) is never in dispute. Kripke doesn’t deny that “125” is the arithmetically correct answer. And he also doesn’t deny that I ought to answer “125” if I meant (followed the rule for) addition. The skeptical challenge in no way involves skepticism about arithmetic in particular, or doubts about the determinacy of rules, concepts, and meanings in general. “On the contrary,” Kripke writes: the word ‘plus’ denotes a function whose determination is completely precise—in this respect it does not resemble the vague notions expressed by ‘large’, ‘green’, and the like. The point is the skeptical problem, outlined above, that anything in my head leaves it undetermined what function ‘plus’ (as I use it) denotes (plus or quus), what ‘green’ denotes (green or grue), and so on. […] The skeptical problem indicates no vagueness in the concept of addition (in the way there is vagueness in the concept of greenness), or in the word ‘plus’, granting it its usual meaning (in the way the word ‘green’ is vague). (WRPL: 82)19

The rule for addition (and quaddition) is completely precise in that it specifies sums (and quums) for all pairs of integers, that is, the rule for addition (and quaddition) delivers definite results for an infinite number of computational tasks. If I meant (followed the rule for) addition, then the determinate result of “68 + 57” is (and I ought to answer) “125,” and if I meant (followed the rule for) quaddition, then the determinate result is (and I ought to answer) “5.” So, if the rules, concepts, and meanings in question are fully specified such that the addition function (and the quaddition function) yields perfectly determinate results for all pairs of integers what, then, is the problem? In my view, the epicenter of the skeptical argument is step (2) in my reconstruction presented above: 2. A finite number of applications of any expression instantiates an infinite number of rules. Its destructive impact stems from the fact that it’s virtually a tautology and hence almost unassailable. This becomes particularly clear if we

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consider the continuation of finite number sequences. Using Kripke’s own example, suppose we are asked to continue the series “2, 4, 6, 8, ….”20 You don’t have to be a mathematician in order to see that this number sequence (in fact, any finite number sequence) instantiates an infinite number of rules so that any continuation of the sequence can be made compatible with it according to some rule. Therefore, if asked to respond “with the unique appropriate next number, the proper response is that no such unique number exists, nor is there any unique (rule determined) infinite sequence that continues the given one” (WRPL: 18).21 And the same goes for applying expressions. The application of every expression in our vocabulary up to now is necessarily finite (3). Given step (2) of the argument, it immediately follows that the application of any expression so far instantiates an infinite number of rules. For example, Jones’s use of “green” so far may be compatible with both following the ordinary rule for the use of “green”— applying “green” only to green objects—and following a more peculiar rule—applying “green” only to green objects and also to red objects on the planet Alpha Centauri. Since Jones has never been to Alpha Centauri there is no discernible difference in her past applications of “green” that would reflect her following the ordinary rather than the peculiar rule. Now, in each case the ordinary as well as the peculiar rule for the use of “green” determines correctness conditions, which in turn determine for an infinite number of cases whether it’s correct to apply the expression or not (recall that the determinacy of rules, concepts, and meanings is not at issue). Hence what she ought to do when encountering an object depends on whether Jones follows the ordinary or the peculiar rule. Suppose Jones miraculously finds herself on the planet Alpha Centauri and sees a lot of red objects. If she hitherto followed the ordinary rule for “green” it would be incorrect (and she ought not) to call the red objects “green,” but if she hitherto followed the peculiar rule it would be correct (and she ought) to call the red objects “green” as well. And here the skeptic can simply point out that it’s always possible to interpret Jones’s use of “green” according to the peculiar rule (or any other rule compatible with Jones’s past use of “green,” for that matter).22 Since Jones’s past applications of the expression “green” instantiate an infinite number of rules, and since any future application of “green” Jones

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may make could be made compatible with her past applications of it by some rule, it follows that Jones could justify any arbitrary future application of “green” by citing a corresponding rule (in the same way the answer “5” to the task “68 + 57” could be justified by citing the quaddition rule). Obviously, if any future application of “green” could be justified as a correct application according to some rule, then there is no such thing as the correct application of “green.” If anything is correct, nothing is. The distinction between correct and incorrect application simply breaks down entirely. And so on for every expression. Warren Goldfarb has rightly noted that the paradox attacks the “constitution of correctness”23 and in its simplest form could be stated as: “Anything could be correct.”24 The fact that any finite sequence, whether number series or the application of expressions, instantiates an infinite number of rules, then, is a simple truth and the crucial lesson to be learned from Kripke’s paradox.25 What makes it so powerful is that it’s not restricted to past applications of an expression. It’s of no use to appeal to or include present and future applications, for they will still be finite and hence compatible with an infinite number of rules. The skeptical challenge is therefore not a problem of the transtemporality of the application of expressions, that is, “what it is to mean the same thing at different times,”26 as Colin McGinn holds. As Kusch rightly objects: “The problem of normativity is the relationship between acts of meaning and application, regardless of whether these two are distributed over different times or not.”27 It’s not as if, all of a sudden, I do or mean something different when I say “5” instead of “125” in response to “68 + 57” after having done computations where the results for sums and quums are identical (namely for all pairs of integers smaller than 57). If I meant quaddition by “+” in the past, then answering “5” is meaning the same as before (i.e. following the same rule as before) and cannot be distinguished from answering “125” with reference to my past applications of “+,” for in both cases my past applications instantiate addition as well as quaddition, and there is no telling, so the skeptic argues, which of these I actually meant. Of course, the skeptical conclusion is not the last word on the matter. There are roughly two kinds of approaches to answer the skeptic, which Kripke himself labels “straight” and “sceptical” solutions.28 On the one hand, a solution qualifies as straight if it accepts the skeptical challenge

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and tries to identify the appropriate “fact(s) of the matter” to avoid the skeptical conclusion. If a straight solution succeeds in specifying a type of fact that determines the meaning of expressions and sentences, the challenge will be met and the conclusion will be blocked. On the other hand, a solution qualifies as skeptical if it accepts the conclusion that there are no meaning-determining facts but rejects the challenge and the presuppositions that led to it.29 Most commentators seem to prefer a straight solution, that is, they attack step (5) of the argument: 5. There is no fact as to which one of an infinite number of rules instantiated by my past applications of an expression I actually meant. Many candidates for “facts of the matter” determining the meaning of a particular expression have been proposed, such as (communitarian) dispositions, (primitive) mental states, Platonist rules, and its cognates.30 Kripke, on the other hand, rejects step (1)—semantic realism—that he takes to be the faulty premise at the root of the paradox: 1. A particular future application of an expression is justified only if there is a fact unambiguously determining my having meant a particular rule instantiated by the number of applications of that expression I made in the past. For Kripke, the assumption that the justified application of an expression consists in there being facts about what I mean by a particular expression is misguided. Meaning sentences, sentences of the form “X means Y by sign ‘Z,’” don’t have (and need not have) truth conditions31: All that is needed to legitimize assertions that someone means something is that there be roughly specifiable circumstances under which they are legitimately assertible, and that the game of asserting them under such conditions has a role in our lives. No supposition that ‘facts correspond’ to those assertions is needed. (WRPL: 78)

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Kripke also attributes this skeptical solution to Wittgenstein. Its moral consists in giving up the traditional analysis of the meaning of expressions in terms of correctness conditions and the meaning of sentences in terms of truth conditions. Instead, the meaning of expressions should be analyzed in terms of warranted use—conditions under which expressions are legitimately used—and the meaning of sentences in terms of assertability conditions—conditions under which sentences are legitimately asserted. Shifting to assertability conditions enables the skeptical solution to incorporate the insight that there are no meaning-determining facts while preserving our ordinary practice of meaning attributions by showing that “it need not require the justification the sceptic has shown to be untenable” (WRPL: 66). It’s beyond the aim and scope of this section to assess the many straight solutions that have been developed in the literature, or even Kripke’s own skeptical solution. Regarding the latter, suffice it to say that it’s highly controversial whether Kripke’s strategy is successful.32 However, Kripke is right, it seems to me, to reject a crucial component contained in step (1) of the skeptic’s argument, that is, the idea that justification for applying expressions is essentially tied to facts about what I mean by a particular expression. This must be conceded or, at any rate, I’m going to concede this point: no justification for applying an expression in a particular way can be found in my past applications of that expression or among the intentions in my mental history regarding those applications. But that doesn’t mean there is no justification for applying expressions in general. Before we can address the skeptical challenge, though, we need to lay the ground first and consider the two most prominent responses to the paradox.

6.2 R  ealism or Idealism? McDowell vs. Wright In addition to the objection that Kripke wrongly takes Wittgenstein to accept the paradox, there is another objection also accusing him of having seriously misunderstood Wittgenstein’s argument. Kripke presents

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the paradox as emerging from the problematic link between my past and my present/future (intentions regarding) applications of a particular expression. As we’ve seen in the previous subsection, there are infinitely many ways to establish that link because there are infinitely many rules potentially mediating between my past and present/future applications of a particular expression. Since there are no facts as to which rule I meant, there are infinitely many different applications of a particular expression in the future compatible with my past applications of that expression. It follows that my future application of any expression is completely arbitrary, which is why I have no justification for a determinate future application of a particular expression rather than another. But that paradox, so the objection goes, is not at all Wittgenstein’s: “we just do not find Wittgenstein fretting over the question whether my present inclinations to apply a sign really conform with my past meaning.”33 Instead, critics object, the real paradox for Wittgenstein is how rules are capable of determining their applications in the face of the inherent possibility to interpret rules in many different ways.34 This objection seems to be borne out by the following rather clearly worded statement of the rule-following problem in the Remarks on the Foundations of Mathematics: “How can I follow a rule, when after all whatever I do can be interpreted as following it?” (RFM: VI, 38). The famous passage in the Investigations in which Wittgenstein presents the paradox (and Kripke claims he derived the paradox from this passage) just seems to be a more elaborate restatement of the problem how rules determine their application, and in this passage Wittgenstein also provides a diagnosis of what is responsible for the problem: This was our paradox: no course of action could be determined by a rule, because every course of action can be made out to accord with the rule. The answer was: if everything can be made out to accord with the rule, then it can also be made out to conflict with it. And so there would be neither accord nor conflict here. It can be seen that there is a misunderstanding here from the mere fact that in the course of our argument we give one interpretation after another; as if each one contended us at least for a moment, until we thought of yet another standing behind it. What this shews is that there is a way of grasp-

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ing a rule which is not an interpretation, but which is exhibited in what we call ‘obeying the rule’ and ‘going against it’ in actual cases. (PI: 201)

I agree with Kripke’s critics that Wittgenstein’s famous paradox is not so much concerned with intentions regarding the application of expressions but rather points to the disastrous consequence of understanding rule-­ following as always involving interpretations. But it also seems the objection leveled against Kripke is not on target. This is because what may be called the problem of multiple interpretability critics identify as Wittgenstein’s actual concern is an important, maybe even the central, aspect of Kripke’s skeptical challenge.35 After all, Kripke’s main point of his skeptical argument was this: whatever Jones may cite to justify what she meant by a particular expression (past usage, intentions, rules, etc.) in order to justify a certain future application of it, nothing could determine what Jones meant because whatever she cited could always be interpreted in different ways so that any future application of any expression could be made compatible with her past applications according to some interpretation.36 Kripke deliberately and expressly exploits “Wittgenstein’s well-­ known remarks about ‘a rule for interpreting a rule’” (WRPL: 17) by systematically employing the strategy of multiple interpretability to reject all candidates proposed to play the role of meaning-determining facts.37 Again, here it’s important to keep in mind that the determinacy of rules, concepts, and meanings themselves is not in dispute. On the contrary, at one point Kripke even generously grants Platonist rules (and Fregean senses, which for Kripke comes more or less to the same thing)— rules that are precisely defined and fully specified as to unambiguously determine their applications for an infinite number of cases—because Kripke thinks Platonist rules won’t help to meet the skeptical challenge. The reason for Kripke’s confidence is that, like any other kind of rule, Platonist rules must somehow be mentally represented if they are to guide our applications of them. And these mental representations, which act as intermediaries between rules and their applications, are finite entities open to different interpretations: But ultimately the sceptical problem cannot be evaded, and it arises precisely in the question how the existence in my mind of any mental entity

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or idea can constitute ‘grasping’ any particular sense rather than another. The idea in my mind is a finite object: can it not be interpreted as determining a quus function, rather than a plus function? […] Platonism is largely an unhelpful evasion of the problem of how our finite minds can give rules that are supposed to apply to an infinity of cases. Platonic objects may be self-interpreting, or rather, they may need no interpretation; but ultimately there must be some mental entity involved that raises the sceptical problem. (WRPL: 54)38

As soon as interpretations enter the picture, an infinite regress seems to become inescapable. If an interpretation is required to apply a rule (“a rule for interpreting a rule”) the problem of multiple interpretability simply recurs on the next level. The rule for interpreting the rule is itself as open to interpretation as the original rule. And so on ad  infinitum.39 Following Robert Brandom, we can call this regress the “regress-of-­ interpretations” or the “regress-of-rules.”40 McDowell’s Naturalized Platonism Now, the assumption that rule-­ following essentially involves interpretations is precisely what McDowell has vigorously objected to, and it reflects what he calls the “master thesis”: the thesis that whatever a person has in her mind, it is only by virtue of being interpreted in one of various possible ways that it can impose a sorting of extra-mental items into those that accord with it and those that do not.41

To be clear, McDowell credits Kripke with having forcefully expounded the regress-of-interpretations as an essential part of Wittgenstein’s rule-­ following considerations, namely as the inevitable outcome of the master thesis, which should therefore be abandoned.42 According to McDowell, however, Kripke has failed to grasp what Wittgenstein wants us to conclude from the rejection of the master thesis. Kripke, wrongly believing the master thesis to be a central presupposition of semantic realism, takes Wittgenstein’s argument therefore to be a reductio ad absurdum of semantic realism. As a result, we are forced to give up semantic realism and should adopt a version of non-factualism instead (the skeptical solution). For McDowell, on the other hand, semantic realism is not the target of

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Wittgenstein’s argument. Rather, the regress-of-interpretations is to reveal the master thesis as the source on which the skeptical paradox depends. As we’ll see later on, the rejection of the master thesis doesn’t entail for McDowell the rejection of semantic realism per se but only what is for him a fantastical version of it: Platonism. In sum, whereas Kripke takes Wittgenstein’s argument to be a reductio of semantic realism pushing us toward non-factualism about meaning, McDowell takes Wittgenstein’s argument instead to be a reductio of the master thesis, that is, the idea according to which rule-following necessarily involves interpretations in one way or other. Let’s take a closer look at McDowell’s position to see whether rule-following without interpretations can help survive semantic realism unscathed. McDowell’s main complaint is that Kripke completely neglects the second paragraph of PI (201), in which Wittgenstein, immediately after presenting the paradox, not only criticizes the idea that to follow a rule always involves interpretations but also sketches an alternative to it: It can be seen that there is a misunderstanding here from the mere fact that in the course of our argument we give one interpretation after another; as if each one contended us at least for a moment, until we thought of yet another standing behind it. What this shews is that there is a way of grasping a rule which is not an interpretation, but which is exhibited in what we call ‘obeying the rule’ and ‘going against it’ in actual cases. (PI: 201)

Now, according to McDowell, Wittgenstein’s often-neglected remark that “there is a way of grasping the rule which is not an interpretation” is supposed to draw our attention to a distinction between two different modes of following a rule. Let’s call them the interpretative mode and the non-interpretative mode of following a rule. As we’ve seen in the last section, rules essentially set standards of correctness by means of which possible courses of actions can be categorized into correct and incorrect applications of the rule. And both modes represent different ways of following a rule, that is, “acting in the light of a conception of correctness, acting on an understanding of something.”43 How do both modes differ? According to McDowell, the interpretative mode of grasping a rule is based on the presupposition that a rule considered in itself just “stands

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there like a sign-post”44 and doesn’t tell me on its own what I ought to do. Sign-posts—and expressions of rules in general—considered in themselves appear to be “normatively inert,” they are simply dead signs, marks on paper, indistinguishable from a “mere arrangement of matter.”45 It’s not until we impose an interpretation on a rule that it acquires normative powers, enabling it to sort “responses into those that are correct in the light of it and those that are not.”46 This is just another way of saying that rules “do not apply themselves”47 so that all training and teaching “cannot relieve me of the task of applying the rule.”48 For example, in order for an expression of a rule such as “→” to tell me which way to go I need to attach to it an interpretation such as “‘→’ means ‘Go to the right,’” grasping of which points me the way. This interpretation simultaneously establishes a standard of correctness, distinguishing between correct and incorrect applications of “→”; to follow it correctly is to go to the right, and incorrect otherwise. The trouble with this approach is, of course, that it’s possible to interpret “→” in many different ways by invoking (as Wittgenstein often does), for example, different cultural practices involving “→.” And this possibility immediately raises the question which interpretation of “→” is the correct one: A rule stands there like a sign-post.—Does the sign-post leave no doubt open about the way I have to go? Does it shew which direction I am to take when I have passed; whether along the road or the footpath or cross-­ country? But where is it said which way I am to follow it; whether in the direction of its finger or (e.g.) in the opposite one? (PI: 85)

One might object at this point that we could simply stipulate one interpretation of the rule as the correct one and disallow all the others while conceding their possibility (in principle). Multiple interpretability of rules doesn’t have to raise skeptical problems, one might think, as long as we agree on a particular interpretation. Alas, this is of no help. The interpretation (or rule) “‘→’ means ‘Go to the right’” purportedly providing us with the correctness conditions of “→” is clearly as open to interpretation as the original rule. We merely erected, so to speak, a second sign-­ post next to the first one, that is, all we did was giving a further rule for

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interpreting the original rule. Obviously, exactly the same problem we had with “→” now arises for “‘→’ means ‘Go to the right.’” Is there only one way of interpreting this instruction? And if not, what is the correct interpretation of it? We now owe an answer to the question as to how to interpret the rule for interpreting the original rule and the problem of how to decide which interpretation is the correct one poses itself once again. But then all we do is “give one interpretation after another” (PI: 201), and it seems clear that the infinite regress initiated by this argument cannot be countered by infinitely many (stipulated) interpretations: “Interpretation comes to an end” (RFM: VI, 38). Passages like the one about sign-posts (and there are numerous others)49 seem to undermine the very idea that rules are capable of determining their applications. Multiple interpretability of rules—always a possibility—will inevitably yield different correctness conditions, and hence different applications of the rule will count as correct or incorrect. The fact that it’s in principle open to us to apply rules in different ways via different interpretations threatens the idea of correctly following a rule since any application of it can be brought into accord with it under some interpretation. The distinction between correct and incorrect applications collapses again; anything goes. As we’ve seen in the previous subsection, the erosion of the distinction between correct and incorrect applications of a rule is precisely the skeptical conclusion drawn by Kripke. In the case of the sign-post, the skeptic would simply point out that all instances of Jones’s following “→” in the past can be interpreted in ways compatible with an infinite number of rules yielding an infinite number of ways to follow “→” in the future. Jones can follow it, for example, along the “road or the footpath or cross-­ country”; imagination is the only limit. Again, the skeptic can systematically exploit the multiple interpretability of each and every rule at each and every point, and the result is the regress-of-interpretations. As noted, McDowell takes the regress-of-interpretations to figure centrally in a reductio ad absurdum of the master thesis, the idea according to which rule-following necessarily involves interpretations. The argument can be summed up in the following three-step reductio50:

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1. Following a rule always requires an interpretation of it to endow the rule with correctness conditions that determine the correct application of the rule. 2. Any course of action can be counted as a correct application of the rule under some interpretation of it. 3. If any course of action can be counted as a correct application of the rule under some interpretation of it, then the contrast between correct and incorrect applications of a rule is obliterated. Anything goes. The fact that the interpretative mode of grasping and following a rule triggers the regress-of-interpretations that eventually annihilates the distinction between correct and incorrect applications of a rule prompts McDowell to abandon the “mistaken idea that grasping a rule is always an interpretation.”51 More specifically, his diagnosis of the problem runs as follows: We must not acquiesce in the idea that an expression of the rule, considered in itself, does not sort behaviour into performances that follow the rule and performances that do not. Once we start thinking like that, it can seem for a moment that an interpretation can bridge the gap—that adding an interpretation can yield something, the expression of the rule under an interpretation, that does effect the required normative sorting of behaviour. But only for a moment, until we realize that the same thought will be just as plausible about whatever we try to conceive as an expression of the interpretation. If we let the gap open at all, it will be unbridgeable.52

No matter how narrow we make the gap between rules and their applications by cutting down the number of interpretations (using, e.g., simplicity considerations and the like), there will always be enough space for skeptical maneuvers. The only way out of the problem is to close the gap altogether by dropping the idea of a mediating link between rules and their applications. This means discarding the interpretative mode of grasping a rule and making room for what I’ve called the non-­interpretative mode. According to McDowell, this in turn paves the way for the thought that a sign-post itself, and not only a sign-post under an interpretation, sets standards of correctness and “points the way, tells people which way to go.”53

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McDowell’s diagnosis of the source of the skeptical paradox promises to enable us to reject the choice with which Kripke presents us as a false dilemma. For Kripke, there are only two options on the table: semantic realism or non-factualism (the skeptical solution). Since semantic realism leads directly into paradox, non-factualism must be embraced as the only other available position. For McDowell, on the other hand, the real dilemma Wittgenstein wants to dissolve is the following. The first horn consists in the skeptical paradox fueled by the idea that rule-following is always dependent on interpretations. The second horn then represents a misguided overreaction to the skeptical paradox. Instead of abandoning the idea of interpretations as bridging rules and applications as a consequence of the regress-of-interpretations, we are tempted to resort to a seductive mythology. It’s the Platonist picture of rules as infinite rails we believe to be necessary if we are to stand a chance of blocking the regress. According to this picture, meaning is the last interpretation, something incapable of being interpreted and therefore the only candidate to stop the regress. McDowell takes Wittgenstein to debunk this myth in the Blue Book (a passage he frequently cites): “What one wants to say is: ‘Every sign is capable of interpretation; but the meaning mustn’t be capable of interpretation. It is the last interpretation’” (BB: 34). According to McDowell, to think of meaning as the last interpretation is to fall prey to a philosophical fantasy, a fantasy imagining rule-­following as being led by an “autonomous meaning,” a “super-rigid machinery” unambiguously determining the application of a rule in advance and independently of human practice.54 The common root of the dilemma wreaking philosophical havoc is the notion of interpretation, which can only issue in either paradox or mythology. But if we follow Wittgenstein’s advice and make room for the possibility of understanding a rule without the help of mediating interpretations, then another position comes into view: the “community-oriented conception of meaning that enables us to decline the choice.”55 When we encounter a sign-post, for example, our course of action is neither stymied by regress-inducing interpretations nor guided by Platonist rules. In the standard case, “I simply act as I have been trained to”56 without deliberation. Genuinely grasping and following a rule doesn’t consist in acting on an interpretation of it, as if we

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consciously picked out a possible understanding of the rule among others. Rather, we just act in the light of normative standards in a nonreflective manner, as McDowell reminds us with Wittgenstein’s famous remark: “When I obey a rule I do not choose. I obey the rule blindly” (PI: 219). Here McDowell is sensitive to the danger that his alternative position—the non-interpretative (blind) mode of following a rule—threatens to degenerate into brute dispositions to act in a certain way. How does non-interpretative rule-following differ from mere inclinations to act in one way rather than another? What distinguishes the non-interpretative rule-following model from, say, a stimulus-response model of rule-­ following? This would indeed result in a picture of rule-following not recognizable as specifically norm-guided behavior, and this is a picture McDowell is at pains to avoid. He is adamantly insisting on the normativity of meaning encapsulated in the idea: that to learn the meaning of a word is to acquire an understanding that obliges us subsequently—if we have occasion to deploy the concept in question—to judge and speak in certain determinate ways, on pain of failure to obey the dictates of the meaning we have grasped.57

The challenge, for McDowell, is to conceive of our behavior as essentially norm-guided without getting lost in the whirl of interpretations because this would lead us back into the familiar dilemma. As McDowell puts it, we must steer between “Scylla”—the idea that understanding a rule always involves interpretations, which informs both horns of the dilemma—and “Charybdis”—the idea that the “bedrock” of our language-­games is not constituted by irreducible normativity but rather consists in a level of raw dispositions governing our norm-free linguistic behavior. Accomplishing this difficult task requires: the idea of custom or practice. How can a performance both be nothing but a ‘blind’ reaction to a situation, not an attempt to act on an interpretation (avoiding Scylla); and be a case of going by a rule (avoiding Charybdis)? The answer is: by belonging to a custom […], practice […], or institution […].58

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McDowell also calls his intermediate position a “species of platonism”59 because although it relinquishes the idea of rule-following as being guided by a “super-rigid machinery,” it nevertheless retains the idea of rules, concepts, and meanings as imposing real constraints on the application of expressions. The recoil from Platonism has “nothing to do with rejection of the truth-conditional conception of meaning, properly understood.”60 McDowell de-mythologizes Platonism by tying its salient virtue—providing us with real, objective constraints on language use—to the notion of customs, practices, and institutions. This version of semantic realism, which McDowell also calls “naturalized platonism,”61 conceives of rule-­ following as non-reflectively acting within a social framework governed by objective constraints, but the “constraints imposed by our concepts do not have the Platonist autonomy with which they are credited in the picture of the super-rigid machinery.”62 At first sight, this seems to represent not only an appropriate and viable middle position but also a natural reading of Wittgenstein. It fits nicely Wittgenstein’s overall emphasis on (social) practices and institutions, matters revolving around learning and training, customs and traditions.63 Social activities appear to be the right place to locate non-reflective yet norm-sensitive behavior that is immune to the skeptical paradox.64 But although McDowell provides a clear diagnosis of the misconceptions underlying the skeptical paradox as well as helpful insights into how not to understand following a rule, he is, unfortunately, less forthcoming about the details of the cure for these philosophical ailments. A more comprehensive account of the precise status of his semi-autonomous, quasi-Platonist rules is wanting, and reference to and elaborations of shared customs, practices, and institutions remain somewhat vague. But for now I want to postpone to Sect. 6.3 the question whether McDowell’s account actually succeeds in steering between Scylla and Charybdis and go back instead to his primary motive for taking this middle course to begin with. After all, what would be wrong with acknowledging that language use consists in nothing other than communal propensities to apply expressions in a certain way and, by extension, assent to (or dissent from) certain sentences under the same circumstances? The problem, for McDowell, is that any conception that rejects

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the normativity of meaning also threatens what he calls “our familiar intuitive notion of objectivity,” namely: the idea of things being thus and so anyway, whether or not we choose to investigate the matter in question, and whatever the outcome of any such investigation. That idea requires the conception of how things could correctly be said to be anyway—whatever, if anything, we in fact go on to say about the matter; and this notion of correctness can only be the notion of how the pattern of application that we grasp, when we come to understand the concept in question, extends, independently of the actual outcome of any investigation, to the relevant case. So if the notion of investigation-­ independent patterns of application is to be discarded, then so is the idea that things are, at least sometimes, thus and so anyway, independently of our ratifying the judgment that that is how they are. It seems fair to describe this radical consequence as a kind of idealism.65

In essence, if the correct application of a particular expression is not rooted in objective matters of fact committing us to a determinate usage regardless of the opinions and judgments of the speech community (as McDowell’s naturalized Platonism holds), but rather depends on the speech community setting the standards of correctness for the application of expressions (and, by extension, for the assent to sentences), then this will inevitably introduce a substantive element of subjectivity into our practice of applying expressions.66 As McDowell points out, it wouldn’t be unjustified to call such a position “idealism.” And this brings us to the other prominent commentator on the rule-following considerations at whom this critique is directed: Wright. Wright’s Theory of Avowals Like Kripke, Wright concedes that the ever-­ present possibility of multiple interpretability poses a real philosophical problem for our understanding of rules, concepts, and meanings.67 Like McDowell, Wright sees the challenge of giving a proper account of rule-­ following in finding a viable middle position between two equally unsatisfying and extreme responses, namely Platonism (“Scylla”) and communitarism (“Charybdis”). Wright characterizes Platonism as the idea:

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that even (hypothetically) shared assessments are constitutively quite independent of the requirements they concern—that even in the far-fetched scenario where a whole speech community assents to a particular utterance, and where everybody is clear-headed, attentive, and generally competent, the communal impression of what ought to be said is one thing and what really ought to be said is something else.68

Communitarism, on the other hand, is the thesis that the requirements for assenting to (or dissenting from) particular sentences or utterances have to be: located within the propensities for assessment of the case possessed by others in my language community: that for my assent to the sentence in question to be—in the relevant context—in, or out, of line with the requirements imposed by its meaning is, in one way or another, for it to be in or out of line with others’ impressions of those requirements.69

Wright finds both positions problematic. As we’ve seen, for McDowell Platonism captures an important aspect of our intuitive notion of objectivity, the idea of “things being thus and so anyway” irrespective of our investigations into and our subsequent judgments about them. The “nature of things” is supposed to represent the source of independent and objective constraints on the application of expressions and the assent to sentences, whether we are capable of detecting those constraints or not. This implies a distinction between how things are and how they appear to us strong enough as to allow for the possibility that even an entire speech community may be in error about a particular matter. McDowell’s strategy was to keep this aspect of Platonism while purging it of its mythological elements. Although Wright shares with McDowell the assessment of Platonism as a “mythological picture,”70 he doesn’t seem willing to preserve any part of it, not even the notion of objectivity—as we’ll see, not this strong kind of objectivity, at any rate. In Wright’s view, the ontological price of Platonism is simply too high, and the epistemological burden it carries is simply too heavy.71 The non-factualism of communitarism—Kripke’s skeptical solution—is for Wright an equally unacceptable response because it faces the opposite

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danger. Whereas according to Platonism the correctness of assessment may be undetectable for an entire speech community and must admit of the possibility of global error, communitarism threatens to reduce correctness of assessment to “a kind of marching in step,”72 where what is correct or incorrect is not a standard to which the speech community as a whole is subject precisely because it’s constitutive of that standard. At the level of the speech community appearance and reality simply coincide such that whatever the (majority of the) speech community considers correct is correct. Applied to the rule-following considerations this amounts to the threat “that the requirements of a rule [i.e. its correctness conditions], in any particular case, are simply whatever we take them to be.”73 In sum, Wright roughly shares with McDowell the framework of the rule-following considerations, namely steering between Scylla and Charybdis. However, he draws different conclusions from the challenge they pose and, accordingly, develops a different response to them. While he agrees with Kripke’s and McDowell’s emphasis on social customs, practices, and institutions, Wright neither wants to preserve a Platonist conception of rules in any way, shape, or form (unlike McDowell with his naturalized Platonism) nor does accept that there are no facts of the matter as to what I mean (unlike Kripke with his assertability model of meaning). Wright’s alternative middle course, which I’ll outline presently, is based on a different interpretation of what Wittgenstein actually targets with his rule-following considerations. He sees Wittgenstein not as primarily making a wholesale attack on specific conceptions of our ordinary rule-governed behavior, for example, the factualist understanding of meaning sentences (Kripke) or the interpretative model of rule-­ following (McDowell), even though he concedes these conceptions may in some sense be aspects of Wittgenstein’s critique. Rather, Wright takes Wittgenstein, first and foremost, to undermine what he calls the objectivity of meaning: the notion that the meaning of a statement is a real constraint, to which we are bound, as it were, by contract, and to which verdicts about its truth-­ value may objectively conform, or fail to conform, quite independently of our considered opinion on the matter.74

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Again, not unlike McDowell, Wright wants to keep the intuitive notion of rules, concepts, and meanings as in some sense imposing constraints on the application of expressions and the assent to sentences, but claims that our social interactions involving rules, concepts, and meanings substantially contribute to shaping these constraints. Wright doesn’t want to give up the normativity of meaning altogether, but to sever its ties from the objectivity of meaning. Rules do, in a sense, determine their applications, but these determinations are not to be regarded as set in stone, as it were, settled once and for all and independent of the use we make of those rules in our everyday life. Wright puts his diagnosis of the rule-following considerations and the philosophical task it poses as follows: The rule-following considerations attack the idea that judgements about the requirements of a rule on a particular occasion have a ‘tracking’ epistemology, answer states of affairs constituted altogether independently of our inclination to make those judgments. How can judgements lack a substantial epistemology in this way, and yet still be objective—still have to answer to something distinct from our actual dispositions of judgment?75

How does Wright’s account manage to derive objective constraints from subjectively constituted requirements of rules (correctness conditions), and how does this account help provide an answer to the skeptic? Wright’s initial response to the skeptic is so simple he himself calls it “somewhat flat-footed.”76 However, he supports his simple response with a new and elaborate conception of avowals of intentions showing how the simple response can be satisfying and fully justified. Wright’s response to the skeptic here represents a species of straight solutions to the skeptical paradox, that is, he gives an answer to step (5) of my reconstruction of Kripke’s argument: 5. There is no fact as to which one of an infinite number of rules instantiated by my past applications of an expression I actually meant. Wright first complains that there is an “unacceptable reductionism”77 in Kripke’s argument because it allows from the outset only non-­intentional

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facts about one’s (past and present) mental life from which one is to infer what one previously meant. And, of course, it will be no problem for the skeptic to undermine any such inference because all non-­intentional facts one presents can be made compatible with skeptical scenarios in which the inference to what one meant is invalid. But why, so Wright, should we accept this restriction of possible answers to non-­ intentional facts? Kripke’s sceptic persuades his victim to search for recalled facts from which the character of his former understanding of [expression] E may be derived. And that is fair play only if knowledge of a present meaning has to be inferential; otherwise the sceptic is satisfactorily answered simply by recalling what one formerly meant.78

Wright’s response, then, straight and simple, is that “we may and usually do non-inferentially know of our present meanings and intentions, and may later non-inferentially recall them.”79 In other words, if asked by the skeptic “How do you know you meant plus and not quus by ‘+’?” the simple answer is “I just know I meant plus and not quus!” How is that possibly an answer to the skeptic? Isn’t my having meant plus rather than quus precisely what the skeptic casts doubt on? Of course, Wright is perfectly aware of the skeptic’s strategy to suggest, first, that the mental history of my previous intentions regarding the use of “+” is compatible with my having had both the intention to mean plus and the intention to mean quus and, second, that the present avowal of my past intention to have meant plus is simply wrong because I misinterpreted or misremembered my past intentions (due to the influence of drugs or whatever). Obviously, as long as we construe avowals of (past and present) intentions as knowledge claims about our (past and present) mental life, then the skeptic will again have no trouble coming up with scenarios in which these knowledge claims are false. And it’s at this stage where Wright introduces his new conception of avowals of intentions. Wright’s new account is informed by a broadly Wittgensteinian critique of a Cartesian construal of the first-person epistemology of mental states. Roughly, the Cartesian takes the undeniable epistemological asymmetry between knowing one’s own mental states and knowing the mental

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states of others as consisting in the fact that with respect to one’s own mental states one is “occupying a cognitively superior vantage point.”80 Accessing one’s own mental states is direct, immediate, and (more or less) infallible, whereas accessing the mental states of others is not. Each and every one of us has an epistemic advantage when it comes to our own mental states because in our own case we can use introspection to determine the truth-value of knowledge claims concerning our own mental states. But we cannot look into other people’s heads. Hence we are simply in an exceptional epistemological position with respect to knowledge claims of our own mental states, and that is the reason why first-person avowals of intentions enjoy authority. Now, Wright’s Wittgensteinian critique is that the Cartesian model of introspection gets the character of first-person avowals of intentions backward because it rests on a “grammatical misunderstanding”81: Self-ascriptions of a specific mode of understanding of some expression, like self-ascriptions of a large class of beliefs, intentions and sensations, are a kind of avowal. […] [I]t will suffice to recall that subjects are credited with a special authority for their avowals, that we think of knowledge which they thereby express as groundless and immediate.82

Avowals do enjoy authority, but this authority doesn’t derive from a cognitive advantage each of us has in describing one’s own mental states. Rather, it’s because such avowals are, strictly speaking, not descriptions at all.83 In other words, “subjects’ best opinions determine, rather than reflect, what it is true to say about their intentional states, with the consequence that the notion of detection or ‘inner tracking’, as it were, is inappropriate.”84 When it comes to avowals of one’s own intentional states, saying so makes it so, that is, avowals of intentions are not descriptions of mental states but more like performative speech acts bringing about the state of affairs they seemingly describe. According to Wright, when I find myself in cognitively ideal conditions (which he calls “C-conditions”), then the following conditional is a quasi a priori truth85:

C  Jones    Jones believes he intends to   Jones intends to  



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As we’ve seen, McDowell’s move against the skeptic consisted in reminding us of our ability to follow rules in a way that doesn’t involve interpretations. The equivalent move in Wright’s argument is pointing out that with respect to (avowals of ) what I mean by a certain expression (i.e. which rule I follow), all we need to answer the skeptic is to refer to first-­ person authority regarding avowals of intentions. Since the relation between avowals of intention and intentions themselves is constitutive or determinative, and not descriptive, saying to have meant plus rather than quus brings it about that I meant plus rather than quus. Wright’s point is that, barring interfering factors (self-deception, insincerity, etc.), believing to have a certain intention (rather than another) is constitutive of actually having it: Challenged to justify the claim that I formerly meant addition by ‘plus’, it will not be necessary to locate some meaning-constitutive fact in my former behaviour or mental life. A sufficient answer need only advert to my present opinion, that addition is what I formerly meant, and still mean, and to the a priori reasonableness of the supposition, failing evidence to the contrary, that this opinion is best.86

The constitutive relation between avowals of intentions and intentions themselves is here also reflected by our “positive-presumptive”87 attitude toward other people’s avowals of their intentions, which means that as long as there is no indication of interfering factors (self-deception, insincerity, etc.), we take others by their word and grant them authority over their avowals. But this, of course, is neither to claim infallibility for “knowing” our own intentions nor to take them to be logically independent of the speech community of which we are part. Avowals may be constitutive, but they are also defeasible: The proposal reinstates both a standard of correctness for my opinions about what I mean and the authority of those opinions—but in order for it to be so, I need to be considered as an at least potential object of interpretation, with my claims about my own meanings essentially defeasible in the light of the shape assumed by my actual practice.88

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As long as my verbal behavior—my application of particular expressions and my assent to and dissent from particular sentences and utterances— is consistent with my avowals of intentions regarding that behavior, I enjoy authority over my avowals. Verdicts concerning what I mean and meant in using particular expressions and in making particular judgments are then constitutive of what I mean and meant, and others are not only justified but even compelled to take my verdicts at face value and regard them as definitive. But as soon as my verbal behavior and my avowals of intention regarding that behavior begin to part company, or else I give other people reason to suspect that I fail to meet C-conditions, then others may legitimately call into question my authority over my avowals of intention. For example, if I were asked to compute “68 + 57” and were to answer “5” while simultaneously insisting on meaning (and having meant) plus by “+,” then the speech community in which I make this claim would be justified to question my authority. In short, according to Wright, rational agents may not be the measure of all things, but they are the (defeasible) measure of their own intentions. Given this rough outline of Wright’s theory of intentions and the anti-­ skeptical strategy it provides, we are now also in a position to address Wright’s broader question concerning the relation between a rule and its applications, namely “How can judgements [concerning the requirements of a rule] lack a substantial epistemology in this way, and yet still be objective?” The challenge was to conceive of the requirements of rules—their correctness conditions—in such a way as to avoid Platonism as well as communitarism. Platonism is undesirable because Platonist requirements may well be outside our cognitive reach and are in any case insensitive to human practices. Communitarism, on the other hand, runs the risk of identifying the requirements of a rule with whatever the speech community takes them to be. Now, against the backdrop of Wright’s theory of intentions it’s easy to understand his position concerning the relation between rules and their applications, simply because his treatment of judgments about intentions and his treatment of judgments about what a rule requires (i.e. what its correctness conditions are) is very similar. After having dismissed Platonism and communitarism as viable candidates he concludes:

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Abandoning Platonism need not involve abandoning the objectivity of rule-informed judgements. There remains the option of regarding such judgements as extension-determining, of seeing best opinion as constituting their truth.89

As we’ve seen, when a rational agent makes judgments under C-conditions concerning her intentions, these judgments have to be considered constitutive rather than reflective of her intentions. And it’s the same when it comes to judgments concerning what a rule requires in a particular case, that is, which applications of the rule are correct and which are not. But in contrast to individual avowals of intentions, the best judgment of the speech community as a whole (and not just the best judgment of one or more individuals) determines rather than reflects what the rule requires. It thereby sets standards of correctness and determines which applications of a rule are correct and which are not. The speech community is to the correctness conditions of rules as the individual is to the avowal of its intentions. As David Finkelstein has succinctly put it: The platonist thinks that a rule (or anyway, the meaning that lies behind the statement of a rule) autonomously calls for a course of action, and that when we set out to follow a rule, we intuit or perceive what it requires us to do. According to Wright’s Wittgenstein, this must be rejected: when we follow rules, we don’t perceive their requirements; we decide them.90

The upshot of Wright’s account (what he takes to be Wittgenstein’s central lesson) is to reverse the traditional picture of the determination relation between rules and their applications. The traditional picture has it that a rule, in a dubious Platonist fashion, somehow contains all of its possible applications, thereby determining the contrast between correct and incorrect regardless and independent of human discourse and practice. In this picture, rules are like rails laid out to infinity, and neither the individual nor the speech community has any say whatsoever in determining what counts as a correct application of it and what doesn’t. Even McDowell remains roughly within the confines of this top-down approach of the determination relation between rules and their applications, according to which our applications of expressions are subject to

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objective constraints, even though these constraints are not to be credited with Platonist autonomy. Unfortunately, McDowell’s semantic realism doesn’t flesh out what exactly the conception of semi-­autonomous, quasiPlatonist rules consists in. Wright, on the other hand, is much more explicit and goes even further in his rejection of the mythological understanding of rules than McDowell. He insists that the correct use of an expression is not something that is established in advance but is in a way “objectively indeterminate”91 and “has to be compatible with the capacity of ongoing use to determine meaning.”92 In contrast to McDowell, Wright defends a bottom-­up approach of the determination relation between rules and their applications, according to which the perpetual activity of the communitarian application of expressions and their best judgments about their usage constitute the standards of correctness for these very expressions. Rules in themselves don’t provide us with a standard of correctness, as McDowell would have it. Rather, it’s a “community of assent which supplies the essential background against which alone it makes sense to think of individuals’ responses as correct or incorrect.”93 To use an example from our previous discussions, the meaning of “→”—the rule associated with “→”—is not settled in advance but depends essentially on the applications we make of it, that is, it depends on our practices involving “→.” And it’s precisely the speech community that has the last word regarding the correct application of “→,” because “for the community itself there is no higher authority, so no standard to meet.”94 That is why “it is what competent speakers do […] which determines the correct use of expressions, rather than the other way about.”95 It’s clear that McDowell’s and Wright’s respective accounts are more nuanced than I’ve presented them so far. Nevertheless, my aim here is not to give an exhaustive assessment of their responses but rather to outline two very important positions representing opposite end points on the spectrum of possible answers to the rule-following considerations. I’ll present some criticism in the following subsection and use it as a foil against which I want to present my own account that enables us to reject the framework within which McDowell and Wright are operating.

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6.3 A  New Solution: Beyond Realism and Idealism Again Recall the basic form of the skeptical challenge and the basic two demands Kripke requires of every possible solution to meet: The sceptical argument, then, remains unanswered. There can be no such thing as meaning anything by any word. Each new application we make is a leap in the dark; any present intention could be interpreted so as to accord with anything we may choose to do. So there can be neither accord, nor conflict. This is what Wittgenstein said in §201. (WRPL: 55) An answer to the sceptic must satisfy two conditions. First, it must give an account of what fact it is (about my mental state) that constitutes my meaning plus, not quus. But further, there is a condition that any putative candidate for such a fact must satisfy. It must, in some sense, show how I am justified in giving the answer ‘125’ to ‘68 + 57.’ (WRPL: 11)

In this subsection, I’ll show that Kripke’s first demand—identifying the fact(s) as to what one means by a particular expression—contains a fundamental misunderstanding that allows us to dismiss it, and that Kripke’s second demand—showing how one is justified in giving a particular answer rather than another—can be met even if the first demand were a legitimate demand and couldn’t be met. That is, one can be justified in giving a particular answer rather than another even if there were no facts as to what one means by a particular expression. As we’ll see in the course of this subsection, the reason for this is that facts about what one means by particular expressions and being justified in using these particular expressions in one way rather than another are, contrary to what Kripke suggests, two categorically different and mutually independent things. In the following, I’ll first set the stage by briefly presenting some criticism of Wright and McDowell. Based on this critique, I’ll then develop a different account of how to understand Wittgenstein’s rule-following considerations against the backdrop of my account elaborated in Sect. 5. In doing so, I’ll show how this enables us to solve the skeptical challenge while avoiding the realist and idealist pitfalls of McDowell’s and Wright’s accounts, respectively.

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As we’ve seen, Wright and McDowell operate roughly within the same framework. Both are trying to steer between Scylla and Charybdis— Platonism and communitarism—in their own way. And both present their respective accounts as a straight solution to the skeptical challenge, that is, as a non-skeptical answer to step (5) of my reconstruction of the skeptical challenge: 5. There is no fact as to which one of an infinite number of rules instantiated by my past applications of an expression I actually meant. Wright’s strategy to address the skeptical challenge consisted in a simple response supported by a complex theory. The so-called flat-footed retort to the skeptic’s question, “How do you know you meant (followed the rule for) plus and not quus?” was simply to respond with “I just know I meant (followed the rule for) plus and not quus.” Wright’s elaborate antiCartesian theory of (avowals of ) intentions then tried to show how this simple answer is not only not question-begging but also the only adequate response to the skeptic. The key move against the skeptic here was to reject one of the central conditions an answer to the skeptical challenge must satisfy, namely to locate the fact(s) as to what one means by a particular expression in one’s own mental and/or behavioral history. As long as avowals of intentions are construed as descriptive self-­attributions, it’s impossible to answer the challenge because the skeptic will have no problem to cast doubt on these attributions. The simple reason is that descriptions are capable of being true or false, and there will always be imaginable skeptical scenarios in which the attributor is simply in error. With his new theory of avowals of intention Wright attacks the possibility of skeptical doubt right at its source. He points out that conceiving of the relation between avowals of intentions and intentions themselves in descriptive terms rests on a grammatical misunderstanding and instead urges that the relation be conceived of as constitutive. When placed in cognitively ideal conditions (Wright’s “C-conditions”) and absent any interfering factors, avowals of intentions determine rather than claim that one has a particular intention. As I put it in Sect. 6.2, when it comes to intentions, saying so makes it so, that is, sincerely expressing the possession of a particular intention is constitutive of possessing it, even

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though avowals of intentions are not indefeasible. In normal circumstances, when asked whether I meant (followed the rule for) plus or quus my mental and/or behavioral history need not be cited (nor would it even be appropriate to do so). All that is necessary is to respond to the skeptic that I meant (followed the rule for) plus, thereby bringing about the very fact the skeptic asked for. As Wright concludes: There are indeed facts about what I mean, contra Kripke’s sceptic, and they are constitutively constrained by what I take them to be; but the validity of these self-impressions is in turn constitutively constrained by their contribution to my ability to make sense of myself to others in my (speech-) community.96

There can be no question that Wright’s highly sophisticated account of intentions has its merits independently of the skeptical challenge. Here I don’t want to question the overall shape of Wright’s theory nor assess its internal consistency. Instead, I’d like to draw attention to a more basic and rather simple, yet very important point made by Kusch. He points out that, regardless of what one may think about the particulars of Wright’s theory, it’s hard to see how Wright’s response to the skeptic qualifies as a straight one.97 As we’ve seen in Sect. 6.2, Wright explicitly rejects the objectivity of meaning, a notion he also takes to be Wittgenstein’s primary target of the rule-following considerations: the notion that the meaning of a statement is a real constraint, to which we are bound, as it were, by contract, and to which verdicts about its truth-­ value may objectively conform, or fail to conform, quite independently of our considered opinion on the matter.98

Kusch comments: In rejecting the objectivity of meaning, Wright is rejecting the view that the meaning of an expression can determine in advance (causally as well as normatively) how this expression is to be used. The meaning sceptic can only applaud this move.99

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Indeed, sacrificing the objectivity of meaning puts Wright’s position close to the skeptic’s. However, haven’t we just seen that Wright is emphatically insisting, against the skeptic, that there are facts of the matter as to what one means? On closer inspection, though, this apparently substantive difference between Wright and the skeptic seems to evaporate as well. After all, the facts of the matter Wright invokes in order to counter the skeptic are of a rather peculiar kind because this type of fact is not independent of the respective speaker or thinker appealing to them. Rather, these facts are created rather than discovered by the respective speaker or thinker. What’s more, before the skeptic challenges one to cite a fact as to what one means, there are no such facts at all precisely because they are brought about by avowals of intentions made under cognitively ideal conditions. It’s not until Jones sincerely answers “I meant (followed the rule for) plus” that there is a fact of the matter as to what Jones meant. And it seems fair to be doubtful whether this elusive type of fact on which Wright is building his anti-skeptical response really constitutes a fully satisfying answer to the skeptical challenge. At any rate, even if we consider Wright’s response as a viable answer to the skeptic, it seems difficult to see how his solution is any different from Kripke’s. Here’s how Kripke presents the picture: Jones is entitled, subject to correction by others, provisionally to say, “I mean addition by ‘plus’,” whenever he has the feeling of confidence—“now I can go on!”—that he can give ‘correct’ responses in new cases; and he is entitled, again provisionally and subject to correction by others, to judge a new response to be ‘correct’ simply because it is the response he is inclined to give. (WRPL: 90)

Wrights account is strikingly similar to Kripke’s here. The two main ingredients of Kripke’s skeptical solution can also be identified in Wright’s solution. First, Jones enjoys first-person authority over his avowals of intentions in normal circumstances. According to Kripke, Jones is entitled to self-attributions when she has “the feeling of confidence,” and in the same way Jones is authoritative regarding her self-attributions when in C-conditions according to Wright. Second, Jones’s first-person authority is not absolute; she is “subject to correction by others.” According to

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Kripke, Jones entitlements are provisional, and in the same way the authority of first-person avowals is defeasible according to Wright. In sum, even if we consider Wright’s account as a viable strategy against the skeptic, there still remain serious doubts as to whether his response really qualifies as a straight rather than a skeptical solution. Let’s turn to McDowell. For McDowell, Wittgenstein’s primary target of the rule-following considerations is addressed in the second part of Wittgenstein’s famous paragraph: It can be seen that there is a misunderstanding here from the mere fact that in the course of our argument we give one interpretation after another; as if each one contended us at least for a moment, until we thought of yet another standing behind it. What this shews is that there is a way of grasping a rule which is not an interpretation, but which is exhibited in what we call ‘obeying the rule’ and ‘going against it’ in actual cases. (PI: 201)

McDowell extracts from this passage an assumption he takes to be responsible for generating the paradox, what he calls the master thesis. To recall, this is the thesis that whatever a person has in her mind, it is only by virtue of being interpreted in one of various possible ways that it can impose a sorting of extra-mental items into those that accord with it and those that do not.100

As elaborated on in Sect. 6.2, McDowell takes Wittgenstein’s solution as consisting in distinguishing between an interpretative and a non-­ interpretative mode of understanding a rule. McDowell’s main argument then seeks to establish that, according to Wittgenstein, rule-following is not always to be conceived of in terms of the former mode, thereby making room for the latter mode. On closer inspection, though, this thesis introduces a tension that is at odds with Wittgenstein’s account. On the one hand, McDowell’s repeated insistence on the idea that grasping a rule is not always an interpretation seems to imply that grasping a rule sometimes (if not in most cases) is an interpretation of a rule. To the best of my knowledge, McDowell nowhere expressly denies that the

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interpretative mode is a mode of following a rule or that rules can be interpreted in different ways. He just claims that it’s not the only mode of following a rule. On the other hand, McDowell appears eager to expose the very idea of interpretative rule-following as entirely bogus. Consider, for example, the following passage again: We must not acquiesce in the idea that an expression of the rule, considered in itself, does not sort behaviour into performances that follow the rule and performances that do not. Once we start thinking like that, it can seem for a moment that an interpretation can bridge the gap—that adding an interpretation can yield something, the expression of the rule under an interpretation, that does effect the required normative sorting of behaviour. But only for a moment, until we realize that the same thought will be just as plausible about whatever we try to conceive as an expression of the interpretation. If we let the gap open at all, it will be unbridgeable.101

Here McDowell seems to think not only that interpretations are incapable of bridging the gap between rules and their applications but also that nothing else can perform this task either. McDowell’s adamant opposition against interpretations leaves one wondering whether he would consider the interpretative mode of rule-following a viable option at all. Be that as it may, in my view Wittgenstein doesn’t wish to eliminate interpretations root and branch but to correct a false picture we may have of them. And this means that we have to rethink not only what it is to follow a rule but also the very conception of a rule itself. This reading is borne out by the fact that Wittgenstein gives a positive account of how interpretations are actually to be understood in the third paragraph of PI (201), which is barely discussed by McDowell: Hence there is an inclination to say: every action according to the rule is an interpretation. But we ought to restrict the term ‘interpretation’ to the substitution of one expression of the rule for another. (PI: 201)

Whatever the details of this passage (which I’ll address below), why would Wittgenstein give us here a positive account of the notion of interpretation if his concern had been all along to discredit this notion for good, as McDowell seems to suggest in some passages?

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In my view, Wittgenstein doesn’t only attack a misconception of the epistemological aspect of rule-following—how we know the correct application of a rule—but also a misconception of its constitutive aspect—how rules determine their applications. The reason why this is frequently overlooked is the same, I presume, why McDowell thinks Wittgenstein’s aim is merely to point out an alternative way of following a rule and thus primarily concerned with the epistemological aspect of it. The reason is the misleading translation of the phrase “daß es eine Auffassung einer Regel gibt, die nicht eine Deutung ist” as “that there is a way of grasping a rule which is not an interpretation.” The phrase “there is a way of grasping…” wrongly suggests that there are other, multiple, ways of grasping a rule by translating the phrase “Auffassung einer Regel” into the phrase “way of grasping.” This translation implies there may be different ways of grasping. In the original, however, there is not necessarily such an implication. Rather, what the passage says is that there is a conception of a rule (“Auffassung einer Regel”) that is not modeled on the conception of interpretations at all. This exegetical point might not be decisive on its own. But together with the fact that Wittgenstein only calls the non-­ interpretative mode a form of rule-following and the fact that he offers a new account of interpretations support this reading of PI (201). Ultimately, it seems to me, Wittgenstein’s point is not to say (as McDowell seems to suggest): rules are capable of being interpreted, all right, but in some or many cases we simply don’t do it and follow them blindly. In this case there would be no pressure at all to change our conception of interpretations. It would suffice to simply draw attention to the fact that we don’t have a need for them in particular circumstances. What, then, are interpretations? According to the standard picture, interpretations are some sort of intermediaries between rules and their applications. The regress argument showed this view—expressed in the interpretative mode of grasping a rule—to be highly problematic. McDowell’s conclusion was to make room for a way of grasping a rule— expressed in the non-interpretative mode—that doesn’t involve interpretations at all. But the trouble with this account is that even if the regress argument cannot be applied to the non-interpretative mode, this only solves the epistemological aspect of rule-following. So it may be true that when engaging rules non-interpretatively, we don’t choose (neither

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consciously nor subconsciously) a particular interpretation rather than another, which prevents the regress from arising. But this does nothing to solve the constitutive aspect of rule-following. For while we can counter the skeptic on the epistemological level with reference to our practice of following rules blindly, the question on the constitutive level, “What determines the correct application of the rule?”, remains unanswered. Why exactly? According to McDowell, the correct application of “→,” for example, is a matter of my having been initiated into a particular practice. Obviously, other practices involving “→” are possible; Martians might have a practice of following “→” in the opposite direction than we do, and further examples can easily be thought of. However, although the regress doesn’t arise on the epistemological level for individual rule-­ followers because they follow the rules blindly, we still run into a regress on the constitutive level because we can ask “What is the correct practice of following ‘→’?” The regress arises again because the problem is structurally identical to the one that led to the downfall of interpretations. All we did was replacing interpretations with practices. Interpretations were considered problematic because they occurred as intermediaries between rules and their application. But practices play exactly the same role, now functioning as communal intermediaries, so to speak, between rules and their applications. But this time we have no resources to block the regress. To see this more clearly, we need only insert “practice” for any instance of “interpretation” in McDowell’s three-step reductio I presented in Sect. 6.2 and change the wording accordingly in order to turn the argument against practices as well: 1. Following a rule always requires a practice to endow the rule with correctness conditions that determine the correct application of the rule. 2. Any course of action can be counted as a correct application of the rule according to some practice involving that rule. 3. If any course of action can be counted as a correct application of the rule according to some practice involving that rule, then the contrast between correct and incorrect applications of a rule is obliterated. Anything goes.

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The possibility of equally correct practices regarding a sign-post such as “→” may seem harmless. What’s the problem? Different people follow “→” differently, so what? The problem becomes more severe if we think of Kripke’s example with “+.” Do we really want to accept that there are as many equally correct plus-functions as there are (possible) practices involving “+” (quaddition, skaddition, etc.)? Even if there is a way to ward off this problematic result, at least our justification for responding “125” to “68 + 57” evaporates once more since one could just refer to the (possible) practice of quaddition to undermine “125” as the correct result. And this time the skeptical conclusion will not in the least be affected by pointing out the possibility of blind rule-following. This is because the epistemological distinction between the interpretative and non-interpretative modes of following a rule is simply irrelevant to the constitutive question which answer is the correct one; again, anything goes. Against the backdrop of the conception of rules I developed in Sect. 5, I can now provide an explanation of Wittgenstein’s remarks quoted above in the third paragraph of PI (201) that will prove essential in addressing the skeptical challenge. Recall that one astonishing consequence of the conclusion in Sect. 5.2—that constitutive rules are neither true nor false—was that, strictly speaking, there is no distinction between right and wrong applications. The reason was that it’s logically impossible to make a “wrong” application of a constitutive rule because a rule defines what an application is in the first place. An allegedly wrong application simply is not an application. That is why I proposed to replace the (contrastive) notion of correctness conditions with the (non-contrastive) notion of application conditions that allows one at best to distinguish between applications and non-applications regarding a particular rule, word, or concept. To see this in more detail, consider again the sign-post “→.” The problem was what determines the correct application of it, and what determines how I ought to follow it. As we’ve seen, neither the appeal to interpretations nor reference to practices involving “→” in which we follow the sign-post blindly provided us with a viable answer because both approaches led to an infinite regress. The non-interpretative mode of following a rule, while solving the problem on the epistemological level, left

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the constitutive question as to which application is the correct one unanswered. The reason was that it kept the possibility of interpreting a rule (at least in principle) in play and just excluded this possibility for certain circumstances (namely, when engaging rules non-­interpretatively) but not in general. This caused the regress argument to resurface on the level of practices. In my view, the cardinal mistake here is to think of interpretations as different versions of the same rule, as if there were different ways to follow the same rule. This is an illusion. It’s true, in encountering a sign-post such as “→,” there might be different responses to it, for example, going “along the road or the footpath or cross-country.” But what we actually do in the respective cases is not following the rule expressed by “→” or “Go to the right” in different ways. Rather, we follow different rules. Following “→” along the road or the footpath is not doing the same thing differently but simply doing different things. This is precisely what Wittgenstein means when he says “we ought to restrict the term ‘interpretation’ to the substitution of one expression of the rule for another.” In a certain sense, then, we don’t interpret rules at all. Rather, what constitutes different cases of rule-following is the substitution of one rule for another and that is what we should call an interpretation.102 The adequate characterization of a scenario in which Smith follows a sign-post along the road and Jones follows the same sign-post cross-­ country is neither to say they interpret the same rule differently nor to say they exhibit different blind responses to the same rule due to their having been initiated in different practices. It’s to say they follow different rules associated with the same sign, namely “→.” And that the same sign can be associated with different rules is no more mysterious than the fact that “bank” expresses or refers to (at least) two different things (riverbanks and financial institutions). Following “→” cross-country is not “wrongly” following it along the road, in the same way that using “bank” in the sense of “financial institution” is not using the word “bank” in the wrong kind of way; it simply is a different use of the same sign. The same goes for the diagonal rule for the bishop. Moving the bishop orthogonally is either not making a move at all or moving it according to a different rule, in which case the wooden piece has simply ceased to be the bishop—different rule, different chess piece. This harks back to a theme also prominent

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in the Tractatus. There Wittgenstein says that we “cannot give a sign the wrong sense” (TLP: 5.4732), and in a similar way we could say we cannot associate the wrong rules with a sign, for there: cannot be a question whether these or other rules are the correct ones for the use of ‘not’ (that is, whether they accord with its meaning.) For without these rules the word has as yet no meaning; and if we change the rules, it now has another meaning (or none), and in that case we may just as well change the word too. (PG: X, 133)103

What about (systematic) mistakes? Well, we simply call non-compliance with rules “wrong” applications or “mistakes” because the putative rule-­ follower is supposed to follow a particular rule (rather than another) and, for practical purposes and if we don’t philosophize, this is just fine. If Smith, for example, moves the bishop orthogonally we would call that a mistake, and if she repeats this mistake a few times we would say she either makes a systematic mistake or follows a different rule (e.g. confusing the bishop with the rook). However, from a logical point of view, any non-compliance with the rule is to be categorized as a non-application of it, and hence there is no such thing as a wrong application of a rule. Something either is or is not an application of a rule, and this is the whole of the matter. Here I’m fully aware of the phenomenon of vagueness and that, in many cases, the distinction between applications and non-­ applications will not be a sharp line but a gray area. However, this is irrelevant here for the simple reason that, as I’ve already emphasized repeatedly in Sect. 6.1, Kripke’s paradox is not about the determinacy of rules and concepts.104 We are now fully equipped with the conceptual resources to address the skeptical challenge and to answer the skeptic. Recall the distinction between pragmatic and logical justifications developed in Sect. 5.2, which roughly corresponds to the distinction between justifying a rule of a game and justifying a particular move falling under it. A pragmatic justification comprises reasons for preferring one rule to another that are not based on facts but on a diversity of pragmatic principles. Logical justifications, on the other hand, don’t concern the rules of a game but the moves that are

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made within it (the application of the rules). Whereas pragmatic justifications are highly context-sensitive and subject to dispute because they are not decisive, logical justifications are always available if a move is made in compliance with or according to a rule of the game regardless of whether one is capable of citing the rule in question. Logical justifications are therefore decisive simply because they concern the rules that are in force. Now, the skeptical challenge was that no matter what I do next (no matter how I will apply “+” in the future, continue a number series, use a certain word, etc.), my past usage of a particular sign will always be compatible with any kind of future usage of that sign according to some rule. This is correct, and I already conceded as much. The decisive point, though, is that all those rules are distinct, a fact the skeptic never challenges; quite the contrary. It’s not as if the addition and quaddition functions are indistinguishable from each other or that we don’t know what the addition function is. Rather, my (arithmetical) behavior is compatible with both (in fact, infinitely many) functions, which themselves are, by hypothesis, completely determinate. So the distinctness of each of the infinite rules compatible with my behavior is a prerequisite for the paradox to get off the ground. No matter what I do next can be construed, from a logical point of view, as an application of some rule even if I did not think of it. This is what the skeptic exploits. No matter what my response is to “68  +  57,” the skeptic can always construe it as falling under some bizarre “mathematical” rule, for example, quaddition, skaddition, and so on. The skeptic doesn’t claim there to be infinitely many ways of following one particular rule but that my behavior is compatible with infinitely many rules. And, of course, the challenge is that nothing in my mental history establishes which one: But ultimately the sceptical problem cannot be evaded, and it arises precisely in the question how the existence in my mind of any mental entity or idea can constitute ‘grasping’ any particular sense rather than another. The idea in my mind is a finite object: can it not be interpreted as determining a quus function, rather than a plus function? […] Platonism is largely an unhelpful evasion of the problem of how our finite minds can

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give rules that are supposed to apply to an infinity of cases. Platonic objects may be self-interpreting, or rather, they may need no interpretation; but ultimately there must be some mental entity involved that raises the sceptical problem. (WRPL: 54)

But we now see that my behavior with the “+”-sign (what I mean by that sign) is entirely irrelevant for my being justified in responding “125” to “68 + 57” because the only justification for it consists in the fact which rule is supposed to be in force (only a logical justification can be given) when tasked with this mathematical problem. This has nothing to do whatsoever with my mental behavior or my past usage of “+.” Maybe I did mean addition (or quaddition) by “+” in the past, maybe I did not. Who knows? It doesn’t matter. To be justified in responding “125” to “68 + 67” all I have to do and all I can do is referring to the rule that is supposed to be part of the calculation game we play. And there is a perfectly determinate fact about which rule is in force, that is, which rule is supposed to be part of the calculation game. And that is addition. The crucial point to realize here is, again, that there is no such thing as wrongly applying a rule. Responding anything other than “125” to “68 + 57” is, logically speaking, not a “wrong” result or an “incorrect” application of the addition function but simply not a result or application of the addition function at all: In mathematics the result itself is a criterion for calculating correctly. Therefore, it is impossible to follow the rule correctly and generate different calculations. (RFM: VII, 27)

Ironically, the skeptic’s most powerful argument—that any response I give to “68 + 57” can be brought into accord with an infinite number of rules—can now be turned against her. Suppose Smith gives “125” as the answer to “68  +  57.” Obviously, the skeptic will challenge her on the grounds that there is no fact in the world establishing her having meant addition rather than quaddition. While this is true, it’s also irrelevant. Who knows what Smith meant! I already conceded the simple truth that Smith’s arithmetical behavior with the “+”-sign is compatible with an

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infinite number of rules. But this truth doesn’t affect in any way Smith’s being justified in responding “125” because the justification for that doesn’t reside in her mental history but in the fact that addition is the rule in force, that is, part of the calculation game. The obvious question at this stage is this: “How do we know which rules are in force?” We seem to have run into Kripke’s initial skeptical challenge, namely that we cannot read off a practice or sign usage which rule the participants follow because the practice or sign usage is compatible with an infinite number of rules, a fact I even conceded from the outset. But the objection misfires because the stipulation of a rule, that is, a stipulation effected by the community leading to a particular rule’s being in force is itself not an assertion. Using Searlian terminology, the stipulation of a rule belongs to the category of Declarations and not Representatives.105 If, for example, the chess organization FIDE announces “The bishop obeys the diagonal rule,” then this is not an assertion that could be false. Rather, it determines which rule is supposed to be in force simply by fiat. The stipulation of a constitutive rule simply is identical with it’s being in force, provided the person or organization has been endowed with the authority for doing so. Of course, one can be wrong about which rule is in force, just as one can be wrong about which rule people actually follow. But again, this is “merely” an epistemological matter. The skeptical challenge is whether there are facts of the matter reference to which justifies my giving a particular response rather than another, and not whether knowledge of such facts is possible. Since the stipulation of a constitutive rule is tantamount to its being in force, stipulating a constitutive rule brings about the fact that the constitutive rule is in force to which the challenged may appeal if questioned. And the same goes for the addition rule. If the math community stipulated that addition is the rule in force, then it would thereby be the rule in force even if the entire math community consisted of quadders because stipulating it would be performing an illocutionary speech act of the type Declaration and not of the type Representative. That is why each member would be fully justified in responding “125” to “68 + 57” by referring to addition as the rule that is in force regardless of whether the member was an adder or a quadder.

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Thus, all Smith needs to say is that “125” is the result of adding “68” and “57”—an arithmetical fact not challenged by the skeptic—and that she was supposed to follow the addition function. If the skeptic tries to justify her deviating answer “5” by retorting, “Well, I thought ‘+’ denotes the quaddition function and all calculations ever carried out are compatible with it [let’s grant that], therefore I’m justified in responding with the quum” we can easily correct her. Of course, if the quaddition function was the rule in force you would be fully justified in responding with the quum; in fact, you would have to respond with the quum. But we can simply counter that, while giving the quum in the quaddition game would be justified (it would be, likewise, a logical justification), this is not the game we play! You were supposed to be adding and not quadding. That is, it’s simply false to respond with “5” to “68 + 57” and claim that this was a case of addition. It’s not, for the simple reason—granted by the skeptic—that it’s completely precise what the quum and what the sum is in each case. If the skeptic now asks why we should be playing the addition game rather than the quaddition game, the skeptic will illegitimately have changed the topic. She now demands a pragmatic (and not a logical) justification for the addition rule. However, that is an entirely different question. The skeptic’s misgivings vanish into thin air. The confusion rests—as I pointed out above—on conceiving of the quaddition function as some sort of bizarre, yet logically possible interpretation of the addition function. According to the skeptic’s own standards, this has turned out to be an illusion. For the quaddition function is simply a different arithmetical function. It’s not as if we first identify a rule and then interpret it in different ways such that we obtain two different arithmetical versions of the same rule. As long as we remain in the grip of that picture the skeptical paradox will be unsolvable. Rather, what we do when operating with the “+”-sign is identifying a particular rule rather than another. The same sign can be identified with different rules— which is precisely what Wittgenstein calls an interpretation—but the rules themselves are not interpreted at all (neither are they indeterminate or vague, as the skeptic concedes). But what in the world tells me with which rule I am supposed to identify a particular sign such as “→”? Enter the community.

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Recall that the problem was how I ought to follow a rule, what it is that tells me what to do next. Suppose Jones encounters the sign-post “→.” According to the standard picture, Jones is now confronted with infinitely many possibilities to interpret “→,” and there is no fact determining which interpretation is the correct one. Hence “→” cannot tell Jones which way to go. But according to the account of rule-following developed here, there is no such thing as interpreting a rule. Rather, what Jones does is associating a particular rule with the sign “→.” And as soon as she does that, then it’s settled which way she ought to go. It would be nonsensical for Jones to say “The sign-post ‘→’ points to the right but I have no idea what to do.” Associating (a set of ) application conditions with a particular sign is identifying a particular rule. Of course, if Jones is a little idiosyncratic or grew up in a speech community where the sign-­ post “→” expresses the rule “Go to the left,” then she would be fully justified in turning left upon encountering “→” according to that rule. But that is not the rule that is in force (in our speech community), and we can easily correct her by pointing it out. The misconception underlying this problem is to think of the speech community as dictating which applications of a rule are the correct ones. The applications of a rule are settled once their application conditions are, and that is where the speech community comes in. The speech community doesn’t determine which applications of a rule are correct (for there is no such thing); rather the community determines which rule we ought to follow. The difference between this and the standard picture is that in this case Jones identifies a different rule with “→,” which in turn means that “→” simply has different application conditions than it has in our speech community. But it makes no sense to say—logically speaking—that Jones, turning left, followed the rule usually associated with “→” incorrectly. She simply followed a different rule. In the same way, the word “bank” has one set of application conditions when it refers to financial institutions and a different set of application conditions when it refers to riverbanks. It follows that “bank” is simply capable of being associated with different sets of application conditions (hence with different rules). And this is nothing but a harmless lesson in the arbitrariness of signs.

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Here the skeptic might object in the following way. To use our previous example, suppose Jones is playing chess and moves the bishop, seemingly, according to the diagonal rule. Now the skeptic asks, “Well and good, but isn’t Jones’s behavior entirely compatible with her moving the bishop quiagonally, where ‘quiagonal’ means moving the bishop diagonally for the first 20 moves within a single game and orthogonally afterwards?” Of course it is. As long as Jones doesn’t make more than twenty moves per game with the bishop, we will never find out (hence we cannot rule out) whether she follows the diagonal or the quiagonal rule. Now, suppose Jones makes her first twenty-first move in a game and moves the bishop orthogonally. We are puzzled, but Jones explains, “What’s wrong, I’ve been doing the same thing the whole time” (namely following the quiagonal rule). And that is true, though this won’t help her to justify moving the bishop orthogonally. The only justification available to her is a logical one. For Jones to be justified, the quiagonal rule would have to be in force, that is, would have to be a rule of chess. And there is a perfectly determinate fact that this is not so because the chess community stipulated that the diagonal rule be in force and not the quiagonal rule. Again, even if the diagonal rule were vague or indeterminate, this doesn’t matter here because the skeptic already granted us completely precise and determinate rules. In short, pace the skeptic, Jones is not justified in moving the bishop orthogonally at the twenty-first move even if she meant to follow the quiagonal rule because it’s the chess community determining the diagonal rule (and not the quiagonal rule) as the one that is in force. The upshot of all this is that justified rule application (hence the meaning of signs and words) is logically independent of an individual’s meaning anything by her words. Smith would be justified in responding “125” to “68 + 57” even if she was a quadder (meant quaddition by “+”), for the only justification available is a logical one (although in that case she would probably not respond with “125” if she was a quadder). What about vagueness? Don’t chess rulebooks or math textbooks admit of different interpretations? Since vagueness is neither the target nor even part of Kripke’s skeptical challenge, I’ll be brief. Like Wittgenstein, I’m happy to allow that we cannot always straightforwardly tell whether something is or is not an application of a rule.106 But the reason for this is not that rules are somehow “objectively indeterminate”

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regarding new cases of application; rather it’s a question of modifying the application conditions of a rule in such a way so as to make something a case of the application of the rule. Again, this doesn’t mean we stretch, as it were, a rule so as to accommodate new applications. On the contrary, modifying its application conditions in any way, shape, or form is—logically speaking—tantamount to generating a new rule. The wording of the chess rulebook expressing the diagonal rule may allow our associating different rules with it other than that one. The important thing to note here, however, is that this is not an indeterminacy in the applications of the rule but an indeterminacy with respect to which rule ought to be in force. And here further clarifications suffice since the skeptic challenges neither which rule is in force (which rule people ought to follow) nor the determinacy of the rule itself. Indeterminacy is not a defect of rules but the simple fact that their application conditions are in principle open to modification and/or extension. The trap here is to think that the modified rule was the same rule as before; only that it now covered a different range of applications than before and to conclude that the rule was indeterminate regarding new cases, when in fact the modification generated a new rule. As before, different application conditions, different rule, hence different meaning. In general, any modification of application conditions produces a new rule, but since the rules are often very similar by sharing some (or many) application conditions we tend to treat them as different versions (“interpretations”) of the same rule for practical purposes. As we’ve seen, this is a mistake—in philosophy, not in ordinary life. The existence of facts about which rules are in force is the reason why there is objectivity of meaning. Of course, we could associate, or could have associated, different rules than we did with particular signs and sign-­ posts, words and wooden pieces; and the variety of games and languages we have involving them is proof that this is what happened and happens all the time. But when they are settled, then there are perfectly determinate facts about what signs and words mean. Sentences have objective meaning, idiosyncratic uses of quirky individuals such as Smith and Jones notwithstanding.

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Notes 1. Cf. WRPL (12–13). In fact, as we’ll see, throughout Kripke’s discussions neither arithmetic (arithmetical facts) in particular nor the determinacy of rules, concepts, and meanings in general is something the skeptic ever disputes. Cf. WRPL (54), where Kripke grants Platonism about rules but claims that the skeptical paradox arises even then. I’ll come back to this in the next subsection. Furthermore, with respect to word/concept application, I agree with Boghossian’s assessment that, pace C. McGinn and Searle, for the skeptical paradox to go through it doesn’t matter whether we operate on the level of words or concepts, which is why this distinction will only play a subordinate role in my analysis. Cf. Boghossian (1989: 509–511), C.  McGinn (1984: 144–146), and Searle (2002: 253). Whatever the treatment of the paradox, “[thought] content and [linguistic] meaning must stand or fall together” (Boghossian 1989: 510). Cf. also Hattiangadi (2007: 15) for a similar point. 2. I borrow this phrase from Kusch (2006: 4): “The expression ‘meaning determinism’ picks out one of the most central elements of the picture: the idea that what someone means by a sign determines both how he will use it (if he wishes to stick to his meaning), and how he should use it (if he wishes to speak correctly).” 3. Pace C. McGinn (1984: 149–150), who seems to see in Kripke’s skeptical challenge an epistemological problem. Commentators quickly revealed this to be a mistake, and by now there is overwhelming consensus about the constitutive character of the skeptical challenge. Cf. Boghossian (1989: 515), Ginsborg (2011: 228), Goldfarb (2012: 75), and M. McGinn (2013: 83). 4. Cf. Hattiangadi (2007: 20). 5. E.g. WRPL (21): “This, then, is the skeptical paradox. When I respond in one way rather than another to such a problem as ‘68 + 57’, I can have no justification for one response rather than another.” 6. There are other passages in which Kripke puts emphasis on the constitutive character of the skeptical challenge. For example, WRPL (38): “Recall that the sceptical problem was not merely epistemic. The sceptic argues that there is no fact as to what I meant, whether plus or quus.” 7. Miller (2006: 92).

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8. Cf. WRPL (68): “Like Hume, he [Wittgenstein] accepts his own sceptical argument and offers a ‘sceptical solution’ to overcome the appearance of paradox.” 9. McDowell (2002: 229). For similar objections cf. Baker and Hacker (1984: 19), Wright (2001: 186), and Goldfarb (2012: 79). As is well known, McDowell (2002: 229) proposes as solution the possibility of “grasping a rule which is not an interpretation.” There are other commentators who also see Wittgenstein’s answer to the paradox as consisting in attacking the notion that rules and their applications have to be mediated by interpretations, although there is no clear consensus on how exactly Wittgenstein intends to cut out the middleman. On this cf. Baker and Hacker (1984: 19–20), M. Williams (2002: 465), and Goldfarb (2012: 80). I’ll discuss McDowell’s response (together with Wright’s) in the next subsection. 10. At least Kripke’s official position is anti-skeptical. Cf. WRPL (69): “We do not wish to doubt or deny that when people speak of themselves and others as meaning something by their words, as following rules, they do so with perfect right. We do not even wish to deny the propriety of an ordinary use of the phrase ‘the fact that Jones meant addition by suchand-­such a symbol’, and indeed such expressions do have perfectly ordinary uses. We merely wish to deny the existence of the ‘superlative fact’ that philosophers misleadingly attach to such ordinary forms of words, not the propriety of the forms of words themselves.” 11. Kusch (2006: 240). 12. Kusch (2006: 2). 13. Cf. WRPL (69): “Jones meant addition by such-and-such a symbol.” 14. There are countless passages in which Kripke frames the skeptical challenge in terms of the problem of grasping and following rules. Cf. e.g. WRPL (7–8, 15–16, 18, 22, 27, 30, 37, 43–44, 46, and 54). Needless to say, that is why Kripke’s skeptical challenge and the rule-following considerations are inextricably linked. 15. McDowell (1998: 315). 16. Hattiangadi (2007: 13). 17. Boghossian (1989: 524). Wright has developed a particularly interesting argument, according to which global non-factualism (which he calls “projectivism”) is self-refuting by involving a contradiction (cf. Wright 2001: 105). For a critical reply cf. Boghossian (1989: 525).

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18. Cf. C. McGinn (1984: 141), Wright (2001: 99–100), and Hattiangadi (2007: 14). 19. Cf. also WRPL (12–13). 20. Cf. WRPL (18). 21. This is similar to what Brandom (1994: 28) calls the “gerrymandering argument,” an argument he attributes to Wittgenstein against what Brandom calls “regularism” (Brandom 1994: 27), a position that conceives of norms implicit in practice as mere regularities: “The problem is that any particular set of performances exhibits many regularities […]. There simply is no such thing as the pattern or regularity exhibited by a stretch of past behavior, which can be appealed to in judging some candidate bit of future behavior as regular or irregular” (Brandom 1994: 28). 22. Cf. Soames (1998: 212), who in a similar way sees Kripke’s argument as “based on an undeniable truism: What we mean by a word is not exhausted by the cases in which we, or those who have taught us the word, have actually used it.” 23. Goldfarb (2012: 75). 24. Goldfarb (2012: 79). 25. As Wright (2001: 98) succinctly puts the point with respect to behavior generally: “Finite behaviour cannot constrain its interpretation within uniqueness.” 26. C. McGinn (1984: 174). 27. Kusch (2006: 56). This objection goes back to Boghossian (1989: 513). Cf. Hattiangadi (2007: 19) for a similar point. 28. Cf. WRPL (66). 29. This binary classification is intended neither to exhaust the possible responses to Kripke’s paradox nor to cover the many variations of straight and skeptical solutions developed in the literature. It’s not always easy to assess whether a given solution belongs to one category or the other, or into none. For my present purposes, however, this rough classification will suffice. 30. Cf. McDowell (2002), Boghossian (1989), Katz (1990), Wright (2001), Pettit (2002), and Ginsborg (2011), to name only the most significant and influential approaches roughly specifiable as straight solutions. A notable exception is Kusch (2006), who undertakes a comprehensive defense of Kripke’s argument both as an interpretation of Wittgenstein and as an argument in its own right. Further accounts exploring new solutions have been developed by Panjvani (2008) and Yamada (2010).

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31. As I pointed out above, non-factualism concerning meaning sentences entails non-factualism concerning declarative sentences in general such that, if Kripke is correct, the truth-conditional conception of meaning must be given up for all assertions and not only for the subclass comprising meaning sentences. 32. Arguably, Baker and Hacker (1984) are the most prominent critics of Kripke’s skeptical solution. 33. C. McGinn (1984: 84). 34. For example, Baker and Hacker (1984: 27). 35. Cf. (WRPL: 55), where Kripke summarizes the skeptical argument with reference to the problem of multiple interpretability: “The sceptical argument, then, remains unanswered. There can be no such thing as meaning anything by any word. Each new application we make is a leap in the dark; any present intention could be interpreted so as to accord with anything we may choose to do. So there can be neither accord, nor conflict. This is what Wittgenstein said in §201.” 36. The following passage particularly strikes one as a faithful rendering of Wittgenstein’s paradox: “How can I justify my present application of such a rule, when a sceptic could easily interpret it so as to yield any of an indefinite number of other results? It seems that my application of it is an unjustified stab in the dark” (WRPL: 17). Cf. also Kusch (2006: 243): “To ask, as Kripke’s Wittgenstein does, how my past intentions regarding the use of ‘+’ relate to my current intentions is not to change the topic; it is to pick up on facets of the position of Wittgenstein’s patient. Indeed, it is to follow the patient’s suggestions on how to approach the question of how a rule determines its application.” 37. Cf. WRPL (9, 16, 19, 32, 52, 54, 55, and 107). Kripke’s treatment of reductive accounts of meaning (e.g. dispositionalism) forms an exception because all objections against them “boil down” (WRPL: 24) to the normativity of meaning. For an assessment of Kripke’s argument cf. Guardo (2014) and Ebbs (2017). 38. Kripke raises this problem for all finite (mental) states and objects, which is exactly why nothing in her mind is capable of determining what Jones means. Cf. WRPL (52) where Kripke asks rhetorically: “Can we conceive of a finite state which could not be interpreted in a quus-­like way?” 39. Cf. WRPL (17): “It is tempting to answer the sceptic by appealing from one rule to another more ‘basic’ rule. But the sceptical move can be

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repeated at the more ‘basic’ level also. Eventually the process must stop—‘justifications come to an end somewhere’—and I am left with a rule which is completely unreduced to any other.” 40. Brandom (1994: 26). As far as I can see, there is no substantial difference between both terms because in the standard case (for Brandom, Kripke, and McDowell, as we’ll see presently) an interpretation of a rule simply consists in another rule telling us how to follow the original rule. 41. McDowell (2002: 270). 42. Cf. McDowell (2002: 266). 43. McDowell (2009: 99). 44. McDowell (2009: 100) who is quoting here PI (85). 45. McDowell (2009: 100). 46. McDowell (2009: 100). Cf. also McDowell (2002: 264). 47. Brandom (1994: 20). 48. Baker and Hacker (1984: 12). 49. Cf. PI (139–141), for example, where Wittgenstein’s discusses the application of the expression “cube.” 50. Cf. McDowell (2002: 265) and McDowell (2009: 99–100). 51. McDowell (2002: 238). 52. McDowell (2009: 100–101). 53. McDowell (2009: 101). 54. McDowell (2002: 255). 55. McDowell (2002: 243). 56. McDowell (2002: 239). 57. McDowell (2002: 221). 58. McDowell (2002: 242). 59. McDowell (2002: 215). 60. McDowell (2002: 255). 61. McDowell (1994: 92). 62. McDowell (2002: 256). 63. E.g. PI (198, 202, 217, 219, and 241). 64. Cf. McDowell (2002: 277) and McDowell (2009: 94). 65. McDowell (2002: 222). 66. Cf. Ebbs (1997: 72–73). 67. Cf. Wright (2001: 11). 68. Wright (2007: 485). 69. Wright (2007: 485).

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70. Wright (2001: 189). 71. Cf. Wright (2007: 485). Cf. also McDowell (2002: 320): “Wright cannot stomach the idea that a mind can fully encompass something that contains within itself a determination of what counts as conformity with it, he cannot see anything for that idea to be but a form of platonism.” 72. Wright (2007: 485). 73. Wright (2007: 487). 74. Wright (1995: 5). Cf. also Wright (2001: 142), where he glosses the objectivity of meaning as “the idea that meanings can somehow be constituted, once and for all, either within a community or by a single subject, by finitely many events—explanations, uses, episodes in consciousness—so that thereafter there is only the objective question of fit between new uses of the relevant expression and the meanings thereby laid down.” 75. Wright (2001: 191). 76. Wright (2001: 177). 77. Wright (2001: 176). 78. Wright (2001: 111). 79. Wright (2001: 177). 80. Wright (2001: 86). 81. Wright (2001: 200). 82. Wright (2001: 122–123). 83. Cf. Wright (2001: 138): “It is, so to speak, such a subject’s right to declare what he intends, what he intended and what satisfies his intentions; and his possession of this right consists in the conferral upon such declarations, other things being equal, of a constitutive rather than descriptive role.” 84. Wright (2001: 200). 85. Wright (2001: 202). 86. Wright (2001: 206). 87. Wright (2001: 202). 88. Wright (2001: 87). 89. Wright (2001: 210). 90. Finkelstein (2000: 58). 91. Wright (2001: 50). 92. Wright (2001: 56). 93. Wright (2001: 39).

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94. Wright (2001: 40). 95. Wright (2001: 50–51). 96. Wright (2001: 87–88). 97. Cf. Kusch (2006: 217). For an assessment of Wright’s account cf. Boghossian (2012). 98. Wright (1995: 5). Cf. also Wright (2001: 142) for a similar gloss. 99. Kusch (2006: 217). 100. McDowell (2002: 270). 101. McDowell (2009: 100–101). 102. Admittedly, there is an ambiguity here regarding the terms “expression of the rule” and “rule.” Wittgenstein is not clear how the distinction between them is to be drawn, if any. For example, at PI (85) he calls a sign-post a rule, whereas at PI (198) he calls the (same) sign-post an expression of a rule. I’m not quite sure how Wittgenstein conceives of this difference. Regardless, it’s clear that, for all that has been said so far, an expression of the rule is not an interpretation of the rule. I will thus treat these terms interchangeably. After all, my arguments don’t depend on the verdict on this question. 103. This passage can also be found verbatim at PI (p. 556). 104. Even if we were to let vagueness into the picture my main point would remain unaffected, for admitting that a distinction is not a sharp one doesn’t cancel it out. Cf. PI (71): “Frege compares a concept to an area and says that an area with vague boundaries cannot be called an area at all. This presumably means that we cannot do anything with it.—But it is senseless to say: ‘Stand roughly here’?” 105. Cf. Searle (1976: 10–11). 106. Cf. again PI (71).

References Baker, G.P., and P.M.S. Hacker. 1984. Scepticism, Rules, and Language. Oxford: Blackwell. Boghossian, P.A. 1989. The Rule-Following Considerations. Mind 98 (392): 507–549. ———. 2012. Blind Rule-Following. In Mind, Meaning, and Knowledge. Themes from the Philosophy of Crispin Wright, ed. A. Coliva, 27–48. Oxford: Oxford University Press.

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Brandom, R.B. 1994. Making It Explicit. Reasoning, Representing, and Discursive Commitment. Cambridge, MA: Harvard University Press. Ebbs, G. 1997. Rule-Following and Realism. Cambridge, MA: Harvard University Press. ———. 2017. Rules and Rule-Following. In A Companion to Wittgenstein, ed. H.-J. Glock and J. Hyman, 390–406. Oxford: Wiley-Blackwell. Finkelstein, D.H. 2000. Wittgenstein on Rules and Platonism. In The New Wittgenstein, ed. A. Crary and R. Read, 53–73. London: Routledge. Ginsborg, H. 2011. Primitive Normativity and Skepticism about Rules. The Journal of Philosophy CVIII (5): 227–254. Goldfarb, W. 2012. Rule-Following Revisited. In Wittgenstein and the Philosophy of Mind, ed. J. Ellis and D. Guevara, 73–90. New York: Oxford University Press. Guardo, A. 2014. Semantic Dispositionalism and Non-Inferential Knowledge. Philosophia 42: 749–759. Hattiangadi, A. 2007. Oughts and Thoughts. Rule-Following and the Normativity of Content. Oxford: Clarendon Press. Katz, J.J. 1990. The Metaphysics of Meaning. Cambridge, MA: MIT Press. Kusch, M. 2006. A Sceptical Guide to Meaning and Rules. Defending Kripke’s Wittgenstein. Chesham: Acumen. McDowell, J. 1994. Mind and World. Cambridge, MA: Harvard University Press. ———. 1998. Meaning, Knowledge, and Reality. Cambridge, MA: Harvard University Press. ———. 2002. Mind, Value, and Reality. 2nd ed. Cambridge, MA: Harvard University Press. ———. 2009. The Engaged Intellect. Philosophical Essays. Cambridge, MA: Harvard University Press. McGinn, C. 1984. Wittgenstein on Meaning. An Interpretation and Evaluation. Oxford: Blackwell. McGinn, M. 2013. The Routledge Guidebook to Wittgenstein’s Philosophical Investigations. London: Routledge. Miller, A. 2006. Meaning Scepticism. In The Blackwell Guide to the Philosophy of Language, ed. M. Devitt and R. Hanley, 91–113. Malden, MA: Blackwell. Panjvani, C. 2008. Rule-Following, Explanation-Transcendence, and Private Language. Mind 117 (466): 303–328. Pettit, P. 2002. Rules, Reasons, and Norms. Selected Essays. Oxford: Clarendon Press. Searle, J.R. 1976. A Classification of Illocutionary Acts. Language in Society 5 (1): 1–23.

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———. 2002. Skepticism about Rules and Intentionality. In Consciousness and Language, ed. J.R. Searle, 251–264. Cambridge: Cambridge University Press. Soames, S. 1998. Skepticism about Meaning: Indeterminacy, Normativity, and the Rule-Following Paradox. Canadian Journal of Philosophy 23: 211–249. Williams, M. 2002. The Social Basis of Normativity in Wittgenstein and Brandom: Interpretation or Agreement. In Wittgenstein and the Future of Philosophy. A Reassessment after 50 Years. Proceedings of the 24th International Wittgenstein-Symposium, ed. R.  Haller and K.  Puhl, 457–470. Vienna: öbv & hpt. Wright, C. 1995. Realism, Meaning and Truth. 2nd ed. Oxford: Blackwell. ———. 2001. Rails to Infinity. Essays on Themes from Wittgenstein’s Philosophical Investigations. Cambridge, MA and London: Harvard University Press. ———. 2007. Rule-Following without Reasons: Wittgenstein’s Quietism and the Constitutive Question. Ratio XX: 481–502. Yamada, M. 2010. Rule Following: A Pedestrian Approach. Philosophy and Phenomenological Research LXXX (2): 283–311.

Index1

A

Aboutness, 6, 32, 33, 110–119, 123, 179, 183–185 by containment, 33, 118 by form, 118 by representation, 33, 118 Anscombe, Elizabeth, 13n5, 15n27, 15n36, 74n75, 108, 132n56, 133n76, 135n91, 136n103, 137n107, 137n114, 216, 217, 246, 249n21, 249n22, 254n82 Aristotle, 68n16 B

Baker, Gordon Park, 130n26, 250n42, 309n9, 311n32, 311n34, 312n48

Berkeley’s esse est percipi, 22 Bipolarity, see Contingency requirement Black, Max, 15n25, 15n26, 71n50, 130n34, 130n39, 139n138 Blackburn, Simon, 68n11 Bloor, David, 15n36, 217, 246, 249n23, 254n83 Boghossian, Paul, 263, 308n1, 308n3, 309n17, 310n27, 310n30, 314n97 Bounds of sense, see Limits of language Bradley, Francis Herbert, 27, 29 Bradley’s regress, 36, 38, 45, 63, 66, 97, 98

 Note: Page numbers followed by ‘n’ refer to notes.

1

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 M. Bartmann, Wittgenstein’s Metametaphysics and the Realism-Idealism Debate, https://doi.org/10.1007/978-3-030-73335-3

317

318 Index

Brandom, Robert, 57, 73n68, 85, 129n20, 272, 310n21, 312n40, 312n47 Bronzo, Silver, 14n8, 14n12, 137n110, 196n19, 196n22, 199n81, 199n83, 200n94 C

Campbell, Christopher, 93, 132n59, 132n60, 132n61 Candlish, Stewart, 14n15, 43, 68n11, 69n30, 70n34, 70n42, 70n43, 75n82, 133n81, 139n134 Carey, Rosalind, 44, 69n25, 69n30, 70n43 Carroll, Lewis, 85, 129n21 Carruthers, Peter, 96, 132n56, 133n75, 133n76, 133n79, 133n80 Cavell, Stanley, 251n49, 252n55 Cerbone, David, 250n36, 253n75 Cerezo, María, 69n30, 74n78, 75n86, 132n60, 133n80, 135n89, 138n121, 138n129, 139n134 Cheung, Leo, 15n20, 197n41 Child, William, 7, 15n23, 75n86, 136n101 Communitarism, see Rule-following, communitarist conception of Conant, James, see Tractarian nonsense, resolute reading of Connelly, James, 71n51, 74n81 Context principle, 122, 135n86, 167–179, 188, 191, 198n58 See also Semantic atomism and wholism

Contextualism ontological, 99, 108, 110, 182 semantic, 109, 182, 192 Contingency requirement, 52–55, 64, 65, 81–84, 88, 112, 117, 118, 180, 181, 187, 224 Conventionalism, 10, 213–219, 239, 243 See also Idealism, convention idealism Crary, Alice, 2, 13n4, 13n7, 14n9 D

Davidson, Donald, 135n96 Descriptive fallacy, 57, 82–84, 181, 182 Diamond, Cora, see Tractarian nonsense, resolute reading of Dilman, Ilham, 15n28, 139n137 Direction of fit, 122, 124, 149, 150 Direction problem, 37, 42, 64 Dispositions/dispositionalism, see Rule-following, dispositionalist conception of Dodd, Julian, 70n34, 70n43, 75n82 Dummett, Michael, 13n4, 74n75, 74n77, 74n78, 135n93, 213, 216, 219, 222, 223, 236, 237, 239, 243, 244, 249n14, 249n15, 250n39, 253n77 E

Ebbs, Gary, 12, 16n41, 16n43, 16n44, 311n37, 312n66 Engelmann, Mauro Luiz, 13n1 Erdmann, Benno, 239

 Index 

Expressions application conditions of, 229, 230, 298, 305, 307 correctness conditions of, 229, 262, 263, 266, 269, 274–276, 282, 283, 287, 288, 297, 298 saturated and unsaturated, 61, 100, 110, 182 F

Finkelstein, David, 288 Floyd, Juliet, 195n4 Forster, Michael Neil, 15n37, 15n38, 15n39, 224, 237, 238, 242, 249n17, 250n37, 250n38, 250n42, 251n50, 251n53, 252n60, 252n63, 253n69, 253n70, 253n76 Frascolla, Pasquale, 138n124, 139n131, 139n133 Frege, Gottlob, 32, 61, 80, 97, 100, 103, 112, 118, 167, 238, 239 G

Gabriel, Markus, 72n61 Gaskin, Richard, 14n15, 69n33, 70n43, 71n51, 74n79, 136n102 Geach, Peter, 70n39, 136n97 Ginsborg, Hannah, 308n3, 310n30 Glock, Hans-Johann, 13n1, 13n6, 15n37, 129n23, 130n29, 130n30, 136n103, 199n88, 199n89, 201n123, 201n124, 250n42, 254n81

319

Glüer, Kathrin, 250n46, 251n47, 252n56 Goldfarb, Warren, 72n61, 128n4, 267, 308n3, 309n9, 310n23, 310n24 Grammar, see Grammatical rules Grammatical rules, 10, 194, 214–219, 237, 241–244, 246–248 See also Rules Griffin, James, 95, 130n35, 132n56, 132n68, 133n76 Griffin, Nicholas, 27, 37, 50, 51, 69n26, 69n29, 69n30, 71n50, 71n52, 71n53, 71n55, 75n83 Guardo, Andrea, 311n37 H

Hacker, Peter, 13n4, 15n20, 15n22, 15n27, 15n31, 15n36, 130n26, 130n27, 130n31, 133n77, 138n129, 139n133, 139n134, 139n138, 149, 150, 156, 187, 195n5, 195n11, 196n13, 196n14, 196n15, 196n20, 196n31, 197n41, 197n42, 198n52, 198n54, 198n61, 199n69, 199n82, 199n84, 199n88, 199n90, 201n112, 201n124, 217, 249n24, 249n25, 249n26, 249n27, 250n42, 309n9, 311n32, 311n34, 312n48 Hanks, Peter, 65, 71n51, 72n57, 74n80, 74n81, 75n82, 75n85, 135n94, 136n100, 138n121

320 Index

Hattiangadi, Anandi, 251n51, 308n1, 308n4, 309n16, 310n18, 310n27 Hintikka, Jaakko, 13n4, 132n54, 133n77 Hintikka, Merrill, 13n4, 132n54, 133n77 Horwich, Paul, 14n9, 16n42 Hutchinson, Phil, 197n36, 197n50, 197n51 Hutto, Daniel, 15n18, 15n33, 88, 128n5, 130n33, 139n131, 150, 153–155, 157, 158, 195n10, 196n24, 196n27, 196n29, 196n30, 197n33, 197n35, 197n37, 197n38, 197n39, 197n45, 197n46, 197n51, 199n79, 199n80, 210, 248n4, 249n5 Hylton, Peter, 68n14, 68n17, 68n18, 69n30, 70n41, 70n46 I

Idealism convention idealism, 213–217, 236, 239 (see also Conventionalism) mindedness idealism, 217–222, 236 (see also Other-mindedness) Ishiguro, Hidé, 15n30, 92, 120–122, 132n57, 132n58, 136n103, 138n126, 139n138, 139n139, 139n144, 140n146, 149, 183, 185, 188, 194n1, 196n27, 208, 210, 213 Isomorphism, 7, 122, 123, 140n147, 157, 183

J

Johnston, Colin, 73n71, 91, 100, 131n43, 131n46, 132n60, 132n69, 133n80, 133n81, 135n87, 135n92 Justification of rules pragmatic and logical, 230–233 K

Kant, Immanuel, 29, 30, 35, 43, 68n16, 68n17, 68n22, 140n147, 149, 150, 195n5 Kenny, Anthony, 13n6, 15n27, 124, 125, 129n16, 131n43, 139n138, 140n152, 140n153 Kienzler, Wolfgang, 13n1 Kremer, Michael, 198n65, 200n105 Kusch, Martin, 260, 267, 292, 308n2, 309n11, 309n12, 310n27, 310n30, 311n36, 314n97, 314n99 L

Lampert, Timm, 75n86, 131n42, 131n45, 132n55, 133n80, 136n99, 137n114 Language-game, 9–11, 190, 209, 220, 221, 223, 233, 234, 238, 243–246, 248, 251n48, 253n64, 254n79, 254n81, 278 Law of excluded middle, 213, 222, 223, 250n39 Lear, Jonathan, see Idealism, mindedness idealism

 Index 

Limits of language, 4, 9, 11, 124, 151, 155, 185–190, 208–212, 220, 221 limits vs. limitations, 186–190, 208, 210, 212 Logical atomism, 7, 66, 99, 179, 180, 182, 187 Logical immanentism, 86, 182 Logical space, 81, 124, 128n11, 140n147, 168, 183, 184, 208 Logical syntax, 4, 14n11, 72n56, 151, 152, 157, 188, 193, 194, 196n16, 196n20, 201n124, 208–210, 224, 247, 248 violation of, 151, 156, 166–171, 188 Logocentric predicament, 81, 86, 87 M

Mácha, Jakub, 133n76, 135n85 Maddy, Penelope, 73n67 Malcolm, Norman, 13n2, 13n3, 15n29, 120–122, 137n117, 138n126, 139n138, 139n142, 149, 183, 185, 187, 195n6, 201n115, 208, 250n38 Marion, Mathieu, 137n118, 250n42, 251n49 McGinn, Colin, 267, 308n1, 308n3, 310n18, 310n26, 311n33 McGinn, Marie, 15n18, 15n33, 75n84, 75n86, 130n36, 153, 154, 156–158, 196n27, 196n28, 197n32, 197n34, 197n35, 197n40, 197n48, 197n49, 199n69, 249n5, 308n3

321

McGuinness, Brian, 74n74, 74n75, 89, 90, 100, 120–122, 127n2, 128n5, 130n36, 131n40, 132n60, 135n88, 137n116, 138n126, 139n138, 139n139, 140n144, 140n146, 149, 183, 185, 188, 194n1, 196n27, 197n32, 208, 210, 213 McManus, Denis, 15n24, 73n66, 139n137 Meaning assertion conditional conception of, 2, 260, 269, 282 normativity of, 12, 267, 278, 280, 283, 311n37 objectivity of, 282, 283, 288, 292, 293, 307, 313n74 truth conditional conception of, 2, 260–262, 311n31 (see also Semantic realism) Meaning determinism, 258, 259, 268, 269, 271 Meaning sentences, 261, 263, 282, 311n31 Meinong, Alexius, 39 Moore, Adrian William, 11, 16n40, 54, 73n64, 129n16, 186, 188, 195n7, 195n8, 195n11, 200n110, 208, 210–213, 220, 249n7, 249n8, 250n32, 252n55 Morris, Michael, 117, 138n131, 139n132, 140n148 Mulhall, Stephen, 196n23, 250n38, 252n61

322 Index

Nagel, Thomas, 9, 15n34, 15n35, 190, 201n114, 201n121, 209 See also Idealism, mindedness idealism

Preti, Consuelo, 67n7, 68n12, 68n15 Proops, Ian, 15n20, 15n21, 198n54, 198n66 Propositional variable, see Tractarian names

O

R

N

Ostrow, Matthew, 130n28, 130n37, 131n49, 136n104 Other-mindedness, 235–244 See also Idealism, mindedness idealism P

Palmer, Anthony, 131n40, 133n70, 135n83 Panjvani, Cyrus, 310n30 Pears, David, 13n2, 13n4, 71n50, 89, 90, 100, 120–122, 130n38, 138n126, 139n138, 139n140, 139n141, 139n142, 140n145, 140n146, 149, 183, 185, 187, 195n6, 201n115, 208 Pictorial form, 183 See also Picture theory of meaning Pictorial relationship, 183 See also Picture theory of meaning Picture theory of meaning, 103–127, 183 Plato, 14n15 Potter, Michael, 68n19, 71n51, 73n70, 74n75, 74n79, 75n86, 128n6, 129n11, 133n77, 136n98, 136n100

Ramsey, Frank Plumpton, 111, 134n81, 136n106, 137n114, 137n119 Rawls, John, 252n62 Read, Rupert, 2, 13n4, 13n7, 14n9, 14n12, 195n4, 197n36, 197n44, 197n50, 197n51 Reck, Erich, 135n86 Rhees, Rush, 13n5, 139n138, 194n1 Ricketts, Thomas, 75n86, 128n4, 128n8, 139n131 Rule-following communitarist conception of, 268, 280–282, 287, 289, 291 dispositionalist conception of, 12, 268, 278, 283, 311n37 naturalized Platonist conception of, 13, 279 Platonist conception of, 268, 272, 273, 279–282, 287, 291, 301, 308n1, 313n71 Rules multiple interpretability of, 271, 272, 274, 275, 280, 311n35 prescriptive (see Rules, regulative and constitutive) regulative and constitutive, 225 semantic (see Grammatical rules) See also Grammatical rules Ryle, Gilbert, 130n32

 Index  S

Searle, John, 225, 250n43, 250n44, 250n45, 250n46, 250n47, 252n56, 308n1, 314n105 Sellars, Wilfrid, 26, 67n9, 132n56, 133n76 Semantic atomism and wholism, 167–174, 188–194 See also Context principle Semantic realism, 262, 264, 268, 272, 273, 277, 279, 289 See also Meaning, truth conditional conception of Sheffer, Henry Maurice, 81, 128n7 Simons, Peter, 15n20, 74n78, 136n97 Skeptical challenge straight and skeptical solution of, 267 Sluga, Hans, 14n13, 132n64 Soames, Scott, 16n42, 310n22 Stenius, Erik, 130n36, 130n39, 133n77, 140n147, 188, 195n9 Stern, David, 5, 13n6, 14n13, 15n32, 130n36 Stevens, Graham, 69n30, 70n34, 70n39, 71n49, 71n51, 72n57, 73n65, 74n79 Stroud, Barry, 237, 238, 241–244, 253n68, 253n74, 253n78 Sullivan, Peter, 11, 16n40, 73n69, 130n35, 186, 187, 200n109, 201n111, 210, 249n6, 250n32 T

Tejedor, Chon, 128n11, 130n25, 135n88, 139n143, 140n150, 140n154

323

Thomasson, Amie, 229, 251n49, 252n58 Tractarian facts and complexes, 105, 115 conceived of as objects, 89, 105 and states of affairs, 90 Tractarian names incomplete, 107, 109, 110, 182 logical form of (see Tractarian names, occurrence space of ) occurrence space of, 108–127, 182, 183, 192 Tractarian nonsense austere reading of (see Tractarian nonsense, resolute reading of ) clash-theory of, 166, 167, 172, 174, 179, 188 elucidatory reading of, 154–158 ineffability reading of (see Tractarian nonsense, standard reading of ) misleading and illuminating, 150 resolute reading of, 158–179 standard reading of, 148–153 Tractarian objects formal conception of, 92, 103 incomplete, 100, 109, 182 logical form of (see Tractarian objects, occurrence space of ) nominalist interpretation of, 96 occurrence space of, 99–103, 115, 122, 123, 182, 183 Platonist interpretation of, 96 simplicity of, 93 substantial conception of, 92, 103 Tractarian pictures conceived of as facts, 118

324 Index

Tractarian propositions conceived of as facts, 112 conceived of as pictures, 112 Tractarian states of affairs and complexes, 136n99 and facts, 90 structure of, 101 Travis, Charles, 140n151, 251n47, 252n60 Truth correspondence theory of, 27, 28, 31, 41 identity theory of, 27, 31, 33, 39, 41 V

Vagueness, 72n60, 265, 300, 306, 314n104

Williams, Bernard, see Idealism, mindedness idealism Williams, Meredith, 199n69, 199n70, 309n9 Winch, Peter, 13n5, 132n60, 132n69, 139n138, 194n1 Wittgenstein’s objection to Russell’s theory of judgment internal reading of, 61–66 standard reading of, 50–51 Wittgenstein’s philosophical development resolute reading of, 3 standard/orthodox reading of, 2 Wright, George Henrik von, 223 Y

Yamada, Masahiro, 310n30 W

Weiss, Bernhard, 69n30, 70n34, 71n50, 72n57 White, Roger, 132n63, 137n113, 164, 197n41, 199n79 Wilke, Andrea, 140n151

Z

Zalabardo, José, 14n16, 69n30, 70n34, 70n43, 131n47, 132n60, 137n113